American Institute of Physics Handbook [3 ed.] 007001485X, 9780070014855

Table of contents :
Table of Fundamental Physical Constants
Title Page
Table of Contents
Contributors
Preface
Section 1 - MATHEMATICS BIBLIOGRAPHY; SI UNITS
1a. Mathematics Bibliography
1b. SI Units
Section 2 - MECHANICS
2a. Fundamental Concepts of Mechanies. Units and Conversion Factors
2b. Density of Solids
2c. Centers of Mass and Moments of Inertia
2d. Coefficients of Friction
2e. Elastic Constants, Hardness, Strength, Elastic Limits, and Diffusion Coefficients of Solids
2f. Viscosity of Solids
2g. Astronomical Data
2h. Geodetic Data
2i. Seismological and Related Data
2j. Oceanographic Data
2k. Meteorological Information
2l. Density and Compressibility of Liquids
2m. Viscosity of Liquids
2n. Tensile Strength and Surface Tension of Liquids
2o. Cavitation in Flowing Liquids
2p. Diffusion in Liquids
2q. Liquid Jets
2r. Viscosity of Gases
2s. Molecular Diffusion of Gases
2t. Compressible Flow of Gases
2u. Laminar and Turbulent Flow of Gases
2v. Shock Waves
Section 3 - ACOUSTICS
3a. Acoustical Definitions
3b. Standard Letter Symbols and Conversion Factors for Acoustical Quantities
3c. Propagation of Sound in Fluids
3d. Acoustic Properties of Gases
3e. Acoustic Properties of Liquids
3f. Acoustic Properties of Solids
3g. Properties of Transducer Materials
3h. Frequencies of Simple Vibrators. Musical Scales
3i. Radiation of Sound
3j. Architectural Acoustics
3k. Speech and Hearing
3l. Classical Dynamical Analogies
3m. Mobility Analogy
3n. Nonlinear Acoustics (Theoretical)
3o. Nonlinear Acoustics (Experimental)
3p. Selected References on Acoustics
Section 4 - HEAT
4a. Temperature Scales, Thermocouples, and Resistance Thermometers
4b. Thermodynamic Symbols, Definitions, and Equations
4c. Critical Constants
4d. Compressibility
4e. Heat Capacities
4f. Thermal Expansion
4g. Thermal Conductivity
4h. Thermodynamic Properties of Gases
4i. Pressure-Volume-Temperature Relationships of Gases; Virial Coefficients
4j. Temperatures, Pressures, and Heats of Transition, Fusion and Vaporization
4k. Vapor Pressure
41. Heats of Formation and Heats of Combustion
Section 5 - ELECTRICITY AND MAGNETISM
5a. Definitions, Units, Nomenclature, Symbols, Conversion Tables
5b. Formulas
5b-1. Capacitance Formulas in MKS Units
5b-2. Electrostatic-force Formulas
5b-3. Multipole Formulas
5b-4. Dielectric-boundary Formulas
5b-6. Dielectric Bodies in Electrostatic Fields
5b-7. Static-magnetic-field Formulas
5b-8. The Electromagnetic Field Equations
5b-9. Guided Waves
5b-10. Cavity Resonators.
5b-11. Radiation
5b-12. Scattering and Diffraction
5b-13. Waves in Plasma.
5b-14. Skin Effect
5c. Electrical Standards
5d. Properties of Dielectrics
5e. Electrical Conductions in Gases
5f. Magnetic Properties of Materials
5f-1. Types of Magnetism and Some Formulas
5f-2. Magnetic Properties of Elements
5f-3. Properties of Ferromagnetic Compounds
5f-4. Saturation and Curie Points of Magnetic Alloys
5f-5. Properties of Some Materials for Permanent Magnets
5f-6. Losses
5f-7. Antiferromagnetic Materials Studied by Neutron Dlffraction
5f-8. Gyromagnetic Ratios and Spectroscopic Splitting Factors
5f-9. Change of Curie Point and Neel Point with Pressure.
5f-10. Magnetic Anisotropy
5f-11. Magnetostriction
5f-12. Hall Constants of Ferromagnetic Elements and Alloys
5f-13. Faraday Effect.
5f-14. Susceptibility
5f-16. Very Low Temperature Data. Properties of Paramagnetic Salts.
5f-16. Susceptibility in High Magnetic Fields
5f-17. Demagnetizing and Form Factors
5g. Electrochemical Information
5h. Electric and Magnetic Fields in the Earth's Environment
5i. Lunar, Planetary, Solar, Stellar, and G-alactic Magnetic Fields
Section 6 - OPTICS
6a. Fundamental Definitions, Standards, and Photometric Units
6b. Refractive Index of Special Crystals and Certain Glasses
6c. Transmission and Absorption of Special Crystals and Certain Glasses
6d. Geometrical Optics and the Index of Refraction of Various Optical Glasses
6e. Index of Refraction for Visible Light of Various Solids, Gases, and Liquids
6f. Optical Characteristics of Various Uniaxial and Biaxial Crystals
6g. Optical Properties of Metals
6h. Reflection
6i. Glass, Polarizing, and Interference Filters
6j. Colorimetry
6k. Radiometry
6l. Wavelengths for Spectrographic Calibration
6m. Magneto-, Electro-, and Elasto-optic Constants
6n. Nonlinear Optical Coefficients
6o. Specific Rotation
6p. Radiation Detection
6q. Radio Astronomy
6r. Far Infrared
6s. Optical Masers
Section 7 - ATOMIC AND MOLECULAR PHYSICS
7a. The Periodic System
7b. The Electronic Structure of Atoms
7c. Energy-level Diagrams of Atoms
7d. Persistent Lines of the Elements
7e. Important Atomic Spectra
7f. X-Ray Wavelengths and Atomic Energy Levels
7g. Constants of Diatomic Molecules
7h. Constants of Polyatomic Molecules
7i. Atomic Transition Probabilities
Section 8 - NUCLEAR PHYSICS
8a. Nuclear Constants and Calibrations
8b. Properties of Nuclides
8c. Atomic Mass Formulas
8d. Passage of Charged Particles Through Matter
8e. Gamma Rays
8f. Neutrons
8g. Nuclear Fission
8h. Elementary Particles and Interactions
8i. Health Physics
8j. Particle Accelerators
Section 9 - SOLID-STATE PHYSICS
9a. Crystallographic Properties
9b. Structure, Melting Point, Density, and Energy Gap of Simple Inorganic Compounds
9c. Electronic Properties of Solids
9d. Properties of Metals
9e. Properties of Semiconductors
9f. Properties of Ionic Crystals
9g. Properties of Superconductors
9h. Color Centers and Dislocations
9i. Luminescence
9j. Work Function and Secondary Emission
Index

Citation preview

AMERICAN INSTITUTE OF PHYSICS HANDBOOK

OTHER McGRAW-HILL HANDBOOKS OF INTEREST

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American Institute of Physics Handbook Edition

Third

Section Editors BRUCE

H.

BILLINGS,

Ph.D.

Commissioner, Joint Commission on Rural Reconstruction Taipei, Taiwan

D. F.

BLEIL,

Ph.D.

K.

COOK,

Ph.D.

Special Assistant for Sound Programs, Office of Deputy Director The National Bureau of Standards

H. M.

CROSSWHITE,

R. FREDERIKSE,

R. BRUCE LINDSAY,

Associate Technical Director and Head, Research U.S. Naval Ordnance Laboratory RICHARD

H. P.

Ph.D.

Adjunct Professor of Spectroscopy, Physics Department The Johns Hopkins University

Ph.D.

Chief, Solid State Physics Section The National Bureau of Standards

Ph.D.

Professor of Physics, Emeritus, Brown 'University

J.

B. l\iARION,

Ph.D.

Professor of Physics, Department of Physics and Astronomy University of Maryland l\1ARK

W.

ZE~IANSKY,

Ph.D.

Professor of Physics The City College of the City University of N~w York

Coordinating Editor Dwight E. Gray, Ph.D. American Institute of Physics McGraw-Hill Book Company Dusseldorf New York St. Louis San Francisco Montreal Kuala Lumpur London Mexico Sydney Panama Rio de Janeiro Singapore

Johannesburg New Delhi Toronto

Library of Congress Cataloging in Publication Data American Institute of Physics. American Institute of Physics handbook. Includes bibliographies. 1. Physics-Handbooks, manuals etc. I. Gray, Dwight E., ed. II. Title. QC61.A5 1972 016.5301'5 72-3248 ISBN 07-001485-X

Copyright ® 1972, 1963, 1957 by McGraw-Hill, Inc. All Rights Reserved. Printed in the United States of America. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher.

tnolYb 4 5 6 7 8 9 10

EDPEDP

7832109

The editors for this book were Daniel N. Fischel, Harold B. Crawford, Don A. Douglas, and Winifred C. Eisler, and its production was supervised by George E. Oechsner. It was set in Modern 8A by The Maple Press Company.

It was printed and bound by The Kingsport Press,

me.

Contents

ix xiii

Contributors Preface

Section

l\IATHEIVIATICS BIBLIOGRAPHY; SI UNITS Mathematios bibliography.

1

SI units.

l\1ECHANICS . Editor, Dr, R. Bruce Lindsay, Brown University

2

Fundamental concepts of mechanics. Units and conversion factors. Density of solids. Centers of mass and moments of inertia. Coefficients of friction. Elastic constants, hardness, strength, elastic limits, and diffusion coefficients of solids. Viscosity of solids. Astronomical data. Geodetic data. Seismological and related data. Oceanographic data. Meteorological information. Density and compressibility of liquids. Viscosity of liquids. Tensile strength and surface tension of liquid. Cavitation in flowing liquids. Diffusion in Iiquids, Liquid jets. Viscosity of gases. Molecular diffusion of gases. Compressible flow of gases. Laminar and turbulent flow of gases. Shock waves. ACOUSTICS Editor, Dr. Richard K. Cook, The National Bureau of Standards Acoustical definitions. Standard letter symbols and conversion factors for acoustical quantities. Propagation of sound in fluids. Acoustic properties of gases. Acoustic properties of liquids. Acoustic properties of solids, Properties of transducer materials. v

3

VI

CONTENTS

Frequencies of simple vibrators. Musical scales. Radiation of sound. Architectural acoustics. Speech and hearing. Classical dynamical analogies. Mobility analogy. Nonlinear acoustics (theoretical). Nonlinear acoustics (experimental). Selected references on acoustics. HEAT 4 Editor, Dr. Mark W. Zemansky, The City College of the City University of New York Temperature scales, thermocouples, and resistance thermometers. Thermodynamic symbols, definitions, and equations. Critical constants. Compressibility. Heat capacities. Thermal expansion. Thermal conductivity. Thermodynamic properti es of gases. Pressure-volume-temperature relationships of gases. Virial coefficients. Temperatures, pressures, and heats of transition, fusion, and vaporization. Vapor pressure. Heats of formation and heats of combustion. ELECTRICITY AND MAGNETISl\1:. Editor, Dr. D. F. Bleil, U.S. Naval Ordnance Laboratory

5

Definitions, units, nomenclature, symbols, conversion tables. Formulas. Electrical standards. Properties of dielectrics. Electrical conductions in gases. Magnetic properties of materials. Electrochemical information. Electric and magnetic fields in the earth's environment. Lunar, planetary, solar, stellar, and galactic magnetic fields. OPTICS . Editor, Dr. Bruce H. Billings, Joint Commission on Rural Reconstruction, Taipei, Taiwan Fundamental definitions, standards, and photometrie units. Refractive index of special crystals and certain glasses. Transmission and absorption of special erystals and certain glasses. Geometrical optics and index of refraction of various optical glasses. Index of refraction for visible light of various solids, liquids, and gases. Optieal characteristics of various uniaxial and biaxial crystals. Optical properties of metals. Reflection. Glass, polarizing, and interference filters. Colorimetry. Radiometry. Wavelengths for spectrographic calibration. Magneto-, electro-, and photoelastic optical constants. Nonlinear optical coefficients. Specific rotation. Radiation detection. Radio astronomy. Far infrared. Optical masers.

6

CONTENTS

ATOMIC AND MOLECULAR PHYSICS Editor, Dr. H. M. Crossiohite, The Johns Hopkins University

Vll

7

The periodic system. The electronic structure of atoms. Energylevel diagrams of atoms. Persistent lines of the elements. Important atomic spectra. X-ray wavelengths and atomic energy levels. Constants of diatomic molecules. Constants of polyatomic molecules. Atomic transition probabilities. NUCLEAR PHYSICS. Editor, Dr. J. B. Marion, The University of Maryland

8

Nuclear constants and calibrations. Properties of nuclides. Atomic mass formulas. Passage of charged particles through matter. Gammarays. Neutrons. Nuclear fission. Elementary particles and interactions. Health physics. Particle accelerators. SOLID-STATE PHYSICS Editor, Dr. H. P. R. Frederikse, The National Bureau of Standards Crystallographic properties. Structure, melting point, density, and energy gap of simple inorganic compounds. Electronic properties of solids. Properties of metals. Properties of semiconductors. Properties of ionic crystals. Properties of superconductors. Color centers and dislocations. Luminescence. Work function and secondary emission. Index follows Section 9.

9

Contributors

J. R. Anderson, Ph.n., University of M aryland. Solid State Physics (gd) Gordon Atkinson, Ph.n., University of M aryland. Electricity and Magnetism (5g) Fred Ayres, Ph.n., Reed College. Mechanics (2n) H. W. Babcock, Ph.Di, Hale Observatories. Electricity and Magnetism (5i) Julius Babiskin, ph.n., U.S. Naval Research Laboratory. Solid State Physics (Dd) Stanley Ballard, Ph.n., University of Florida. Optics (6b, 6c) Philip Baumeister, Ph.D,, University of Rochester. Optics (6i) J. A. Bearden, Ph.n., The Johns HOllkins University. Atomic and Molecular Physics (7f) E. C. Beaty, Ph.n., The National Bureau of Standards, Boulder. Electricity and Magnetism (5e) L. 1. Beaubien, ph.n., U.S. Naval Research Laboratory. Mechanics (2e) Leo L. Beranek, Ph.n., Bolt Beranek and Newman Inc. Acoustics (3a, 3b, 3d, 3p) Robert T. Beyer, Ph.n., Brown University. Acoustics (30) Hans Bichsel, Ph.n., University of Washington. Nuclear Physics (8d) Bruce H. Billings, Ph.Di, Joint Commission on Rural Reconstruction, Taipei, Taiwan. Optics (6c, 6f, 6h, 61, 60) David T. Blackstock, Ph.Di, University of Texas. Acoustics (3n) E. Boldt, Ph.D., NASA-Goddard Space Flight Center. Electricity and Magnetism (5i) R. M. Bozorth, Ph.Di, U.S. Naval Ordnance Laboratory. Electricity and Magnetism (5f) Willem Brouwer, Ph.D,, Diffraetion Ltd. Ine. Optics (6d) James S. Browder, Ph.Di, University of Florida. Optics (6b, 6c) R. M. Burley, A.B., Baird-Atomic, Inc. Optics (6p) Constance Carter, M.S., Library of Congress. Mathematics Bibliography ; SI Units (la, lb)

Gregg E. Childs, Ph.D., The National Bureau of Standards, Boulder. Heat (4g) R. J. Collins, Ph.D., University of Minnesota. Optics (6s) W. R. Cook, Jr., M.A., Gould, Inc. Optics (6m) H. M. Crosswhite, Ph.Di, The Johns Hopkins University. Atomic and Molecular Physics (7a, 7b, 7c, 7d, 7e) Evan A. Davis, Ph.D,, Westinghouse Research Laboratory. Mechanics (2f) R. DjPippo, ph.n., Southeastern M assachusetts University. Mechanics (2r) E. S. Domalski, Ph.n., The National Bureau of Standards. Heat (4j) J. D. H. Donnay, Ph.D., The Johns Hopkins University. Solid State Physics (ga) Thomas B. DouglasyPh.Dv, The National Bureau of Standards. Heat (4e) J. F. Ebersole. Ph.D,, University of Floride, Optics (6b, 6c) Phillip Eisenberg, Ph.Dv, Hydronautics, Inc. Mechanics (20) Eugene Epstein, Ph.Di, Aerospace Corporation. Optics (6q) John Evans, Ph.D., Air Force Cambridge Research Laboratories. Optics (6i) Robley D. Evans, Ph.D., M assachusetts Institute of Technology. Nuclear Physics (8e)

ix

x

CONTRIBUTORS

H. P. R. Frederikse, Ph.D., The National Bureau of Standards. Solid State Physics (9b, 9c, ge) Eli Freedman, Ph.D., Ballistic Research Laboratories. Mechanics (2v) R. J. Friauf, Ph.D., University of Kansas. Solid State Physics (9f) Dudley Fuller, Ph.D., Columbia Unioersitu, Mechanics (2d) George T. Furakawa, Ph.D., The National Bureau of Standards. Heat (4e) John S. Gallagher, A.B., The National Bureau of Standards. Heat (4i) Murrey D. Goldberg, Ph.D., Brookhaven National Laboratory. Nuclear Physics (8f) David T. Goldman, Ph.D., The National Bureau of Standards. Nuclear Physics (8b) Edward F. Greene, Ph.D., Brown University. Mechanics (2v) Martin Greenspan, B.S., The National Bureau of Standards. Acoustics (3e) B. Gutenburg, Ph.D. (Deceased), California Institute of Technology. Mechanics (2i) George A. Haas, Ph.D., U.S. Naval Research Laboratory. Solid State Physics (9j) Lawrence Hadley, Ph.D., Colorado State University. Optics (6g) Thomas A. Hahn, B.S., The National Bureau of Standards. Heat (4f) William J. Hall, A.B., The National Bureau of Standards, Boulder. Heat (4a) Cyril M. Harris, Ph.D., Columbia University. Acoustics (3j) F. K. Harris, Ph.D., The National Bureau of Standards. Electricity and Magnetism (5c) Miles F. Harris, Ph.D., National Oceanic and Atmospheric Administration. Mechanics (2k) John A. Harvey, Ph.D., Oak Ridge National Laboratory. Nuclear Physics (8f) Georg Hass, Ph.D., U.S. Army Electronics Command. Optics (6g) J. P. Heppner, Ph.D., NASA-Goddard Space Flight Center. Electricity and Magnetism (5h, 5i) G. Herzberg, Ph.D., National Research Council of Canada. Atomic and Molecular Physics (7h) L. Herzberg, Ph.D. (Deceased), National Research Council of Canada. Atomic and Molecular Physics (7h) D. B. Herrmann, Ph.D., Bell Telephone Laboraiories, Inc. Electricity and Magnetism (5d) Joseph Hilsenrath, M.A., The National Bureau of Standards. Heat (4h) David L. Hogenboom, Ph.D., Lafayette College. Mechanics (2m) Robert Howard, Ph.D., Hale Observatories. Electricity and Magnetism (5i) K. P. Huber, Ph.D., National Research Council of Canada. Atomic and Molecular Physics (7g) R. P. Hudson, Ph.D., The National Bureau of Standards. Electricity and Magnetism (5f) Frederick V. Hunt, Ph.D., Harvard University. Acoustics (3c) Hans Jaffe, Ph.D., Gould, Inc. Optics (6m) T. L. Jobe, B.S., The National Bureau of Standards. Heat (4j) Joseph Kaspar, Ph.D., Aerospace Corporation. Optics (6k) R. Norris Keeler, Ph.D., Lawrence Radiation Laboratory. Heat (4d) George C. Kennedy, Ph.D., University of California. Heat (4d) Joseph Kestin, Ph.D., Brown University. Mechanics (2r) Richard K. Kirby, B.S., The National Bureau of Standards. Heat (4f) Max Klein, Ph.D., The National Bureau of Standards. Heat (4i) C. C. Klick, ph.n., U.S. Naval Research Laboratories. Solid State Physics (9h) Kar! R. Koch, Ph.D., National Oceanic & Atmospheric Administration. Mechanics (2h) R. Bruce Lindsay, Ph.D., Brown University. Mechanics (2a, 2b, 2c, 2g) Robert Lindsay, Ph.D., Trinity College. Mechanics (21) G. L. Link, Ph.D., Bell Telephone Loboratories, Ine. Electricity and Magnetism (5d)

CON'l'RIBUTORS

Xl

Ernest Loewenstein, Ph.D., Air Force Cambridge Research Laboratories. Optics (Gr) Lewis G. Longsworth, Ph.D., The Rockefeller University. Mechanics (2p) Walter Loveland, Ph.D., Oregon State University. Nuclear Physies (8g) David MacAdam, Ph.D., Eastman Kodak Company. Optics (6a, 6j) Nancy R. McClure, Eastman Kodak Company. Optics (6d) T. R. McGuire, Ph.D., IBM-Watson Research Center. Electricity and Magnetism (Si)

John E. McKinney, Ph.D., The National Bureau of Standards. Mechanics (21) J. B. Marion, Ph.D., University of M aryland. Nuclear Physics (8a) Robert S. Marvin, Ph.D., The National Bureau of Standards. Mechanics (2m) W. P. Mason, Ph.D., Columbia University. Acoustics (3f, 3g); Solid State Physics (9a) Frank Massa, M.S., Dynamics Corporation of America. Aeoustics (3i) W. J. Merz, Ph.D., RCA Laboratories. Solid State Physics (9f) B. M. Miles, Ph.D., The National Bureau of Standards. Atomic and Molecular Physics (7i) David Mintzner, Ph.D., Northwestern University. Mechanics (2a) Kar! Z. Morgan, Ph.D., Oak Ridge National Laboratory. Nuclear Physics (8i) Edwin B. Newman, Ph.D., Harvard University. Acoustics (3k) Wesley L. Nyborg, Ph.D./ University of Vermont. Meehanies (2n, 2q) Harry F. Olson, Ph.D., RCA Laboratories. Aeousties (31, 3m) Norman Pearlman, Ph.D., Purdue University. Heat (4e) Kar! B. Persson, Ph.D., The National Bureau of Standards, Boulder. Electrieityand Magnetism (Se) Harmon H. Plumb, Ph.D., The Noiional Bureau of Standards. Heat (4a) Robert L. Powell, Ph.D., The National Bureau of Standards, Boulder. Heat (4a, 4g) Martin P. Reiser, Ph.D., University of M aryland. Nuelear Physies (8j) B. W. Roberts, Ph.D., General Electric Research and Development Center. Solid State Physics (9g) R. C. Roberts, Ph.D., University of Maryland. lVIeehanics (2s, 2t, 2u) Arthur H. Rosenfeld, Ph.D., University of California. Nuclear Physies (8h) Bruee D. Rothroek, B.S., The National Bureau of Standards. Heat (4f) Hellmut H. Sehmid, Ph.D., National Oceanic & Atmospheric Administration. Meehanies (2h) R. H. Schumm, M.S., The National Bureau of Standards. Heat (4j) Arthur F. Seott, Ph.D., Reed College. Meehanics (2n) Philip A. Seeger, Ph.D., Los Alamos Scientific Laboratory. Nuclear Physies (8e) J. M. H. Levelt Sengers, Ph.D., The National Bureau of Standards. Heat (4i) J. C. Slater, Ph.D., University of Florida. Solid State Physies (Dc) Donald R. Smith, lVI.S., Air Force Cambridge Research Laboratories. Optics (6r) W. R. Smythe, Ph.D., California Institute of Technology. Eleetricity and Magnetism (5a, Sb) George A. Snow, Ph.D., University of Maryland. Nuclear Physies (8h) Irene A. Stegun, M.S., The National Bureau of Standards. Mathematies Bibliography; SI Units (La, lb) D. E. Stone, A.B., Vertex Corporation. Meehanics (2b, 2e) Daniel R. StulI, Ph.D., Dow Chemical Company. Heat (4k) Masahisa Sugiura, Ph.D., N ASA-Goddard Space Flight Center. Eleetrieity and Magnetism (5h, Si) James F. Swindells, A.B., The National Bureau of Standards. Heat (4a) Paul Tamarkin, Ph.D., RAND Corporation. Meehanies (2a) J. S. Thomsen, Ph.D., The Johns Hopkins Uniuersitu. Atomic and Molecular Physies (7f)

XlI

CONTRIBUTORS

H. M. Trent, Ph.D. (Deceased), U.S. Naval Research Laboratory. Mechanics (2b, 2e) James E. Turner, Ph.D., Oak Ridge National Laboratory. Nuclear Physics (Si) Allyn C. Vine, Ph.D., Woods Hole Oceanographic Institution. Mechanics (2j) D. D. Wagman, Ph.D., The National Bureau 0/ Standards. Heat (4j) David White, Ph.D,, University 0/ Pennsylvania. Heat (4c) J. E. White, Ph.D., Globe Universal Seien ces, Inc. Mechanics (2i) W. L. Wiese, Ph.D., The National Bureau 0/ Standards. Atomic and Molecular Physics (7i) Randolph C. Wilhoit, Ph.D., Texas A and M University. Heat (41) Ferd E. Williams, Ph.D., University 0/ Delaware. Solid State Physics (9i) E. A. Wood, Ph.D., Bell Telephone Laboratories. Solid State Physics (9a) Cavour Yeh, Ph.D., University 0/ California at Los Angeles. Electricity and Magnetism (5b) Kenneth F. Young, B.S., The National Bureau 0/ Standards. Solid State Physics (90 Robert W. Young, Ph.D., U.S. Naval Undersea Research and Deuelopmeni Center. Acoustics (3h) Mark W. Zemansky, Ph.D., The City College 0/ the City University 0/ New York. Heat (4b) Fritz Zernike, M.8., Perkin-Elmer Corporation. Optics (6n) Bruno J. Zwolinski, Ph.D., Tprr:rJ'l A and M University. Beat (41)

Preface

The American Institute 01 Physics Handbook has won wide acceptance among scientists and engineers. It is just such a degree of acceptance that has stimulated the issuance of this revised and updated third edition. This edition, like the previous two, continues the philosophy of supplying authoritative reference material-including tables of data, graphs, and bibliographies-selected and described with a minimum of narration by leaders in physical methods for research. Among the entirely new sections in this edition are those on nonlinear optics, calibration energies for alpha particles and gamma rays, nonlinear acoustics, atomic mass formulas, particle accelerator principles, atomic transition probabilities, electric and magnetic fields in the earth's environment, and far infrared. Examples of topics in which especially extensive revisions have been made are: optical masers, various optical constants, virial coefficients, heats of combustion and formation, and superconductors. A number of sections were completely rewritten; these include radioastronomy, radiometry, various crystal properties, molecular constants and phase transitions. The mathematics section now consists of a special treatment of SI units and a bibliography that has been revised to include references to new methods, algorithms, and computer programs. Publication of this Handbook was a mammoth undertaking that required the contributions and cooperation of many individuals and two organizations. Leading the individuals is Dr. Dwight E. Gray, who served as coordinating editor for this 1972 edition, as he also did for the 1957 and 1963 editions. Dr. Gray, who is a master of the pen and is weIl grounded in physics, was able to coordinate successfully the efforts of the eight section editors and the some 125 contributors. He did this work while also serving as the Washington Representative of the American Institute of Physics. Through his Washington office he was able xiii

XIV

PREFACE

to maintain contact with and coordinate the efforts of the many individuals concerned in the effort, as weIl as to handle the involvements of the sponsor-the American Institute of Physics-and the publisherthe McGraw-HiIl Book Company. Key McGraw-HiIl individuals for this project included Mrs. Winifred C. Eisler, who copy-edited the manuscript, and Mr. Don A. Douglas, the Editing Manager. To these individuals, editors and physicists alike, the scientific community is deeply indebted for their painstaking and conscientious contributions and acknowledges their efforts with thanks. As with any user-oriented publication, comments, suggestions, and criticisms are solicited on this edition of the Handbook. Only with such continuing contributions and cooperation can future Handbooks meet their responsibilities. H. WILLIAM KOCH, Director American Institute of Physics

AMERICAN INSTITUTE OF PHYSICS HANDBOOK

Section 1 MATHEMATICS BIBLIOGRAPHY; SI UNITS CONTENTS la. Mathematics Bibliography Ib. SI Units

"

1-2 1-8

The third edition of the AlP Handbook, like the second, presents a bibliography of mathematical references in lieu of an assortment of actual mathematical tables. Selection of such tables necessarily would have been arbitrary; they would have been bound to duplicate many tables already easily available to most physicists; and, most important, including them would have necessitated the omission of significant physics material. The basic pattern of the third-edition bibliography is described at the beginning of Sec. la. For reasons outlined in the first paragraph of Sec. Ib, it was believed neither practicable nor desirable to attempt excIusive use of the International System of Units in this edition of the Handbook. Section Ib outlines the background of SI Units, and presents a portion of a National Bureau of Standards bulletin on their interpretation.

1-1

la. Mathematics Bibliography IRENE A. STEGUN

The National Bureau 0/ Standards CONSTANCE CARTER Librari; 0/ Congress

In view of the appearance of large compendiums and the increasing use of eomputers with built-in functions or function subroutines in their compilers, many of the tables of elementary functions have been omitted from this bibliography. An effort has been made to include a dictionary; indexes of mathematical and statistical tables; compendiums of general tables, series, integrals, transforms, and differential equations; and references to numerical methods, new tables, and new disciplines. For algorithms covering a wide variety of subjects such as the evaluation of systems of linear equations, estimations of definite integrals, sorting of data, etc., reference should be made to the "Collected Algorithms from CACM" (Communications of the Association for Computing Machinery, Inc.). 1. Abramowitz, Milton, and Irene A. Stegun, eds.: "Handbook of Mathematieal Functions, with Formulas, Graphs, and Mathematieal Tables," Dover Publieations, Ine., New York, 1965, 1046 pages (Republieation of National Bureau of Standards, Applied mathematies series, 55. Government Printing Office, Washington. D.C., 1964): A eompendium eontaining most of the tables that have previously appeared in the United States, including the National Bureau of Standards Mathematieal Tables, Applied Mathematies, and Columbia University Press Series. Contains mathematieal properties, interreJations, and numerieal methods, as weil as an updated bibliography of textbooks and tables. 2. Arfken, George Brown: "Mathematieal Methods for Physicists," Aeademie Press, Ine., New York, 1968, 704 pages: Includes bibliographies. 3. Bierens de Haan, David : "Nouvelles Tables dTntögrales Definies" (New tables of definite integrals). Correeted 1867 edition, with an English translation of the introduetion by J. F. Ritt. Hafner Publishing Company, Inc., New York, 1965,716 pages: A special collection of so me 8,400 integrals. 4. British Association for the Advancement of Science: "Mathernatical Tables." Prepared under the auspi ces of the Royal Society, Carnbridge University Press, London, 1931-1958: Vol. 1: "Circular and Hyperbolic Functions," 3d ed, 1951. Vol, 2: "Emden Functions," 1932. New edition in preparation, Vol. 3: "Minimum Decompositions into Fiith Powers." 1933. Vol. 4: "Cycles of Reduced Ideals in Quadratic Fields," 1934. Val. 5: "Factor Table." 1935. Vol. 6: "Bessei Funetions," pt. I, 1958. Vol. 7: "The Probability Integral," 1939. Vol. 8: "Number-divisor Tables," 1940. Vol. 9: "T'able of Powers Giving Integral Powers of Iritegers," 1950. Vol. 10: "Bessel Functions," pt, 2, 1952. "Auxiliary Ta bles," nos, 1-2, 1946. Continued hy the Royal Soeiety mathematical tables.

1-2

MATHEMATICS BIBLIOGRAPHY

1-3

I. Burington, Richard S.: "Handbook of Mathematical Tables and Formulas," 4th ed.; McGraw-Hill Book Company, New York, 1965, 448 pages: A companion to the "Handbook of Probability and Statistics with Tables," by Richard S. Burington and Donald C. May , the 4th edition includes new sections on sets, relations, and functions; algebraic structures; Boolean algebra : numher systems; matrices; and statistics. A table of derivatives and a comprehensive table of integrals have been included. 6. Burington, Richard S., and Donald C. May: "Handbook of Probability and Statistics with Tables," 2d ed., McGraw-Hill Book Company, New York, 1970, 450 pages, 7. Byerly, William E.: "An Elementary Treatise on Fourier's Se ries, and Spherical, Cylindrical, and Ellipsoidal Harmonics, with Applicat.ions to Problems in Mathema'tical Physics," Dover Publications, Inc., New York, 1959, 287 pages. 8. By rd, Paul F., and Morris D. Friedman: "Handbook of Elliptie Integrals for Engineers and Physicists." (Die Grundlehren der mathematischen Wissenschaften, Band 67), Springer Verlag, Berlin, 1954,355 pages: A collection of over 3,000 Integrals and formulas using Legendre's and Jaeobi's notations. 9. Campbell, George A., and Ronald M. Foster: "Fourier Integrals for Pract.ical Applications," D. Van Nostrand Company, Inc., Princeton, N.J., 1948, 177 pages: A large number of the known closed-form evaluations of Fourier integrals are cornpiled and tabulated in compact form for convenient use. Tables give coefficient pairs, admittances, and transient solutions. 10. "C. R. C. Standard Mathematical Tables," 16th ed, edited by Samuel Selby, Chemical Rubber Co., Cleveland, 1968, 692 pages: An expanded, revised edition of a standard work. The seetions involving mensuration, trigonometry, analytio geometry, curves and graphs, and the algebra of sets have been completely rewritten, and sections to cover determinants and matrices have been added. An extension to the octal decimal conversion table to include hexadecimal and decimal conversion increases the usef'ulness of the volume. 11. David, F. N., M. G. Kendall, and D. E. Barton: "Symmetrie Function and Allied Tables," Carnbridge University Press, London, 1966, 278 pages: An elaborate set of 49 major tables accompanied by a detailed introduction of 63 pages, constituting a self-contained treatment of symmetrie functions and their applications in statistics. A definitive compilation. 12. Davis, Harold T.: "The Summation of Series," Principia Press of Trinity University , San Antonio, Tex., 1962, 140 pages: Special emphasis placed upon the case of finite limits. 13. Davis, Harold T., comp.: "Tables of the Higher Mathematical Functions," Principia Press, Bloomington, Ind., 1933-1935, 2 vols.: Vol. I: Various tables of the gamma and psi functions as well as seetions on classification and history of tables, interpolation and its uses, and interpolation tables. Vol. II: Tables of the polygamma functions (trigamma-hexagamma). the Bernoulli and Euler polynomials and numbers, gram polynomials, and polynomial approximation. 14. Davis, Philip J., and Philip Rabinowitz: "Numerical Integration," Blaisdell Publishing Company, Waltham, Mass., 1967, 230 pages: Includes bibliographiss. 15. Doetsch, Gustav: "Handbuch der Laplace-Transformation" (Handbook of Laplace transforms). Verlag Birkhäuser, Basel, 1950-1956, 3 vols. ("Lehrbücher und Monographien aus dom Gebiete der exakten Wissenschaften, Mathematische Reihe," vols. 14, 15, and 19): Contents: Vol. 1, "Theory of Laplace Transforms"; vols. 2-3, "Applications of Laplaee Transforms," including asymptotie expanaions, eonvergent expansions, ordinary and partial differential equations, integral equations, and whole exponential functions. 16. Dwight, H. B.: "Tables of Integrals and Other Mathematical Data," 4th ed., The Macmillan Company, New .York, 1961, 336 pages: Contains derivatives and Integrals, classified as algebraic, trigonornetric, inverse tr'igonometric, and exponential funetions; probability integrale: logarithmic, hyperbolic, inverse hyperbolic, elliptie, and Bessel funetions; surface zonal harmonies; definite integrals: and differential equations. Appendixes: A, Tables of Numerical Values: B, Bibliography, 17. Erdelyi, Arthur, and others: "Higher Transcendental Funetions" (Based, in part, on notes left by Harry Bateman and compiled by the staff of the Bateman Manuscript Proiect, California Institute of Teehnology), McGraw-Hill Book Company, New York, 1953-1955,3 vols.:

1-4

MATHEMATICS BIBLIOGRAPHY; SI UNITS

An account of the principal properties of such functions as garnma, hypergeometric, Legendre, Bessel, ellipt.ic, automorphic, and generating functions, with extensive lists of references at the end of each chapter. 18. Erdelyi, Arthur, and others: "Tahles of Integral Transforms" (Based, in part, on notes left by Harry Bateman and compiled by the staff of the Bateman Manuscript Project , California Institute of Technology) McGraw-Hill Book Company, New York, 1954, 2 vols: Intended as a cornpanion and sequel to "Higher Transcendental Funct.ions." Contains Fourier, Laplace, and Mellin transforms and their inversions, as well as Hankel transforms. Also included are garnma, Legendre, Bessel, and hypergeometric functions. The entries are arranged in tabular form. 19. Fettis, Henry E., and James C. Caslin: "Elliptic Functions for Cornplex Arguments," Aerospace Research Laboratories, Office of Aerospace Research, Wright-Patterson Air Force Base, Ohio, 1967, 404 pages, ARL 67-0001 (Available from Clearinghouse for Federal Scientific and Technical Information, Springfield, Va. 22151): These unique tables consist of 5D values of the Jacobian elliptio functions sn(w,k), en(w,k), and dn(w,k), where W = u + io, as functions of Jacobi's no me q, which equals exp ( - K' I K), where K and K' are the quarter-periods (the complete elliptic integrals of the first kind of modulus k and of complementary modulus k', respectivelv). The range of parameters in the table is: q = 0.005(0.005)0.480, ut K = 0(0.1) 1, and vi K' = 0(0.1) 1. 20. Fettis, Henry E., and James C. Caslin: "Ten-place Tables of the Jacobian Elliptic Functions," pt. 1, Aerospace Research Laboratories, Office of Aerospace Research, Wright-Patterson Air Force Base, Ohio, 1965,562 pages, ARL 65-180 (Available from Clearinghouse for Federal Scientific and Technicallnformation, Springfield, Va. 22151): This report contains IOD tables of the Jacobi elliptic functions am(u,k), sn(u,k), en(u,k), and dn(u,k), as weIl as the elliptio integral E(am(u),k), k 2 = 0(0.01)0.99, u = O(O.OI)K(k), and for k2 = 1, u = 0(0.01)3.69. 21. Fettis, Henry E., and James C. Caslin: "An Extended Table of Zeros of Cross Products of Bessel Functions," Aerospace Research Laboratories, Office of Aerospace Research, Wright-Patterson Air Force Base, Ohio, 1966, 126 pages, ARL 66-0023 (Available from Clearinghouse for Federal Scientific and Technical Information, Springfield, Va. 22151): This report presents IOD tables of the first five roots of the equations: (a) Jo(a) Yo(ka) - Yo(a)Jo(ka) = 0, (b) Jl(a) Y 1(ka) - Y 1(a)J 1(ka) = 0, (e) Jo(a) Y 1(ka) - Y o(a)Jl(ka) = O. 22. Fletcher, Alan, and others, eds.: "An Index of Mathernatical Tables," 2d ed., AddisonWesley Publishing Company, Inc., Reading, Mass., for Scientific Computing Service, Ltd., 1962, 2 vols.: The second edition is more than double the size of the 1946 edition, and includes, as a new feature, a list of errors found in published tables. Contains an index according to function, giving for each table the range, tabular interval, number of significant figures in the values, whether or not tables of proportional parts are given, wh at orders of differences are shown, etc. Also inc1udes an alphabetical list of references by author and publication year. Considered an important index to wel1-known tables of functions and to other less-known tables appearing in books and periodicals. 23. Forsythe, G. E., and P. C. Rosenbloom: "Numerical Analysis and Partial Differential Equations," John Wiley & Sons, Inc., New York, 1958, 204 pages. 24. Frazer, Robert A., W. J. Duncan, and A. R. Collar: "Elementary Matrices and Some Applications to Dynamics and Differential Equations," The Macmillan Company, New York, 1946,416 pages. 25. Great Britain, National Physical Laboratory: "Mathematical Tables," H. M. Stationery Office, London, 1956-Vol. 1: "The Use and Construction of Mathematical Tahles," by L. Fox, 1956. Vol. 2: "Tables of Everett Interpolation Coefficients," by L. Fox, 1956. Vol. 3: "Tables of Generalized Exponential Integrals," by G. F. Miller, 1960. Vol. 4: "Tables of Weber Parabolic Cylinder Functions and Other Functions for Large Arguments," by L. Fox, 1961. Vol. 5: "Chebyshev Series for Mathematical Functions," 1962. Vol. 6: "Tables for Bessel Functions of Moderate or Large Order," 1962. Vol 7: "Tahles of Jacobian Elliptie Functions Whose Arguments Are Rational Fractions of the Quarter Period, " 1964. . This series contains tables of mathematical functions wh ich rnay not co me within the range of the more fundamental tables. 26. Greenwood, Joseph A., and H. O. Hartley: 'Guide to Tables in Mathematical Ststistics." Princeton University Press, Princeton, N.J., 1962, 1014 pages.

MATltmMATICS BIBLIOG RAPHY

1-5

27. Gröbner, Welfgang. and N. Hofreiter. "Tntegraltafel (Integral table), pt, I, "Indefinite Integrals"; pt, Ir, "Definite Integrals," 2d improved ed., Springer Verlag, Vienna, 1965-1966, 2 vols., 166 and 204 pages: An extensive eolleetion of integrale incIuding abrief survey of methods of evaluation and transformation of integrals. 28. Hart, John F., and others: "Computer Approximations," John Wiley & Sons, Inc., New York, 1968,343 pages: Extensive in its range in aecuraey from a few digits up to 25D in the approximations; its wide selection of functions incIudes square root and eube root, exponential and hyperbolie, logarithm, trigonometrie and inverse trigonometrie funetions, gamma funetion and its logarithrn, error funetion, Bessel funetions, and eomplete eIIiptie integrals; and in the range of methods, the book describes and eompares them from the general methods of subroutine design to proeedures for the design of maximum effieieney prograrns for eommonly needed funetions. 29. Hartree, Douglas R.: "Numerieal Analysis," Oxford University Press, London, 1952, 287 pages: IncIudes interpolation and numerieal integration formulas, finite differenees, harmonic analysis, smoothing. 30. Harvard University Computation Laboratory: "Tables of the Bessel Functions of the First Kind," Harvard University Press, Carnbridge, Mass., 1947-1951, 12 vols.: Jn(x), 0 ~ x ~ 100, 18D for n = 1; IOD for n = 2 through 135. 31. Harvard University Computation Laboratory: "Tables of the Cumulative Binomial Probability Distribution," Harvard University Press, Carnbridge, Mass., 1955, 503 pages ("Annals of the Computation Laboratory of Harvard University," vol. 35). 32. Harvard University Computation Laboratory: "Tables of the Function arc sin z," Harvard University Press, Carnbridge, Mass., 1956,586 pages ("Annals of the Computation Laboratory of Harvard University," vol. 40). 33. Householder, Alston S.: "Prineiples of Numerieal Analysis," MeGraw-Hill Book Cornpany, New York, 1953, 274 pages, 34. Jahnke, Eugene, Fritz Emde, and Friedrieh Lösch: "Tables of Higher Funetions," 7th ed, B. G. Teubner, Stuttgart, 1966, 322pages: Text in German and English. Essentially a eorreeted version of the sixth edition, eontaining Bessel functions, circular and hyperbolic functions of a complex variable, cubie equations, miscellaneous conversion tables, Planck's radiation funetion, powers (2d to 15th), probability integral and related funetions, reciprocals and square roots of eornplex numbers, Riemann zeta function, theta functions, transcendental equations, vector addition, and sine, cosine, and logarithmic integral. 35. James, Glenn, and Robert C. James: "Mathematics Dictionary," 3d ed., D. Van Nostrand Company, Inc., Princeton, N.J., 1968, 448 pages: Correlated condensation of mathematical coneepts designed for time saving reference work. 36. Jolley, Leonard B. W.: "Summation of Series," Dover Publications, Inc., New York, 1961, 251 pages. 37. Kamke, Erich: "Differentialgleichungen, Lösungsmethoden und Lösungen (Differential equations, methods of solution, and solutions), 6th improved ed., Akademische Verlagsgesellschaft Geest & Portig, Leipzig, 1959, 666 pages ("Mathematik und ihre Anwendungen in Physik und Technik," Ser. A, vol, 18): A reference work containing general methods of solution and properfies of solution, boundary-, and characteristic-value problems, and a dictionary of some 1,600 equations in lexicographical order with solutions, teehniques for solving, and references. 38. Knuth, Donald E.: "The Art of Computer Prograrnming," Addison-Wesley Publishing Company, Inc., Reading, Mass., 1968-1969,2 vols. 39. Korn, Granino A., and Theresa M. Korn.: "Mathematical Handbook for Scientists and Engineers: Definitions, Theorems, and Formulas for Referenee and Review," 2d. enlarged and rev, ed., McGraw-HiII Book Company, New York, 1968, 1129 pages. 40. Lehmer, Derrick H.: "Guides to Tables in the Theory of Numbers," National Acaderny of Scienees-National Research Council, Washington, D.C., 1941, 177 pages (National Research Council Bulletin 105). 41. Lehmer, Derrick Norman: "Factor Table for the First Ten MiIIions Containing the Smallest Faetor of Every Number not Divisible by 2, 3, 5, or 7 between the Limits 0 and 10,017,000." Hafner Publishing Company, Inc., New York, 1956, 476 pages (Carnegie Institution of Washington Publ. 105): Introduction includes a list of errors in former tables by other authors. 42. Lehmer, Derrick Norman: "List of Prime Numbers from 1 to 10,006,721," Hafner Publishing Company, Inc., New York, 1956, 133 pages (Carnegie Institution of Washington Publ. 165):

1-6 43.

44.

45.

46.

47. 48. 49.

50.

51. 52. 53.

54.

55.

MATHEMATICS BI:BLIOGRAPHY; SI UNITS

The standerd list of primes. Arranged in such a way that it is easy to find the nth prime for a given n. Lieberman. Gerald J., and D. B. Owen: "Tables of the Hypergeometrie Probability Distribution," Stanford University Press. Stanford, Calif., 1961, 726 pages (Stanford studies in mathematics and statistics no. 3): In addition to the following tables of the hypergeometric probability distribution: N = 2, n = 1 through N = 100, n = 50; N = 1000, n = 500; k = n - I, n; n = N /2: N = 100, n = 50 through N = 2000, n = 1000, the theory, rationale, and specific applications of the hypergeometric probability are discussed. Luke, Yudell: "Integrals of Bessel Functions," McGraw-Hill Book Company, New York, 1962,424 pages: Designed to provide the research worker with basic information dealing with definite and indefinite integrals involving Bessel functions. Madelung, Erwin: "Die Mathematischen Hilfsmittel des Physikers" (Mathematical tools for the physiciat). 6th rev. ed., Springer Verlag, Berlin, 1957, 535 pages ("Die Grundlehren der Mathematischen Wissenschaften in Einzeldarstellungen," vol. IV): Comprehensive collection of formulas used in mathematical physics, Included are numbers, functions and operators, series, algebra, transformations, and statistics. Magnus, Wilhelm, Fritz Oberhettinger, and Raj Pal Soni: "Formulas and Theorems for the Special Functions of Mathematical Physics," 3d enlarged ed., Springer Verlag, Berlin, 1966, 508 pages ("Die Grundlehren der Mathematischen Wissenschaften in Einzeldarstellungen," Band 52): Survey of the properties of a number of special functions including the following: garnma, hypergeometric, Bessel, Legendre, theta, and ell ipt ic, as weIl as spherical harmonics, orthogonal polynomials, integral transforms and inversions, and coordinate transforms. Mangulis, V.: "Handbook of Series for Scientists and Engineers," Academic Press, Inc., New York, 1965, 134 pages. Margenau, Henry, and George M. Murphy: "The Mathematics of Physics and Chemistry, 2d ed., D. Van Nostrand Company, Ine., Princeton, N.J., 1956,2 vols. "Mathematics of Computation" (formerly: "Mathematical Tables and other Aids to Computation"), National Academy of Seiences National Research Council, quarterly, Washington, D.C.: Ajournal devoted to advances in numerical analysis, the application of computational methods, mathematical tables, high-speed calculators, and other aids to computation. Meyer zur Capellen, Walther: "Integraltafeln, Sammlung unbestimmter Integrale elementarer Funktionen" (Tables of integrals; Collection of indefinite integrals of elemetary functions), Springer Verlag, Berlin, 1950, 292 pages: Lists some 3,000 Integrals of algebraic and transeendental functions, as weIl as products of algebraie and transeendental functions. Tabulabion permits use for differentiation purposes. Morse, Philip M., and Herman Feshbach: "Methods of Theoretical Physics," McGrawHill Book Cornpany, New York, 1953, 2 vols, Oberhettinger, Fritz, "Tabellen zur Fourier Transformation" (Tables of Fourier transforms) , Springer Verlag, Berlin, 1957, 213 pages, Parke, Nathan Grier: "Guide to the Literature of Mathematics and Physics including Related Works on Engineering Science," 2d rev, ed., Dover Publications, I'nc., New York, 1958, 436 pages: A useful handbook comprising chapters on principles of reading and study, searching the literature, types of materials, library usage, etc.; includes an annotated bibliography of some 5,000 titles arranged by subject with author and subject indexes, Pearson, Karl: "Tables of the Incomplete Beta-function," 2d ed., with a new introduction by E. S. Pearson and N. L. Johnson, published for the Biometrika Trustees by the Cambridge University Press, Carnbridge, Mass., 1968, 505 pages: Gives l(u,p) with the argument u proceeding by increments of 0.1 from 0 up to that value of u which gives I(u,p) = 1.0000000 to the seventh decimal place, The argument p advanees from -1.0 by increments of 0.05, from 1.0 to 5.0 by increments of 0.1, and from 5.0 to 50.00 by intervals of 0.2. Two new tables give some additional values to the integral cornputed a number of years ago but not hitherto published, and a list of referenees has been added. Peirce, Benjamin 0.: "A Short Table of Integrals," 4th ed., rev. by Ronald M. Foster, Ginn and Company, Boston, 1956, 189 pages: Fourth revision of Peiree's tables consisting of indefinite integrale, definite Integrals, auxiliary Iormulas, and numerieal tables, including eommon algebraie expressions; funetions of angles in radians; differential equations; exponential functions; hyperbolic-Iunction formulas; elliptie integrals; natural logs; tables of logs of numbers, logs of sines, eosines, etc.: probability integral and trigonornetric Iormulas,

MATHEMATICS BIBLIOGRAPIty

1-7

56. Riordan, John: "An Introduction to Combinatorial Analysis," John Wiley & Bons, Ino., New York, 1958, 244 pages. 57. Roberts, G. E., and H. Kauiman: "Table of Laplace Transforms," W. B. Saunders Cornpany, Philadelphia, 1966, 367 pages: A comprehensive reference of Laplace transforms and their inverses which should prove useful to pure and applied mathematieians. The volume is in two partsthe first devoted to direct transforms and the seeond to inverse transforms. 58. Royal Society of London: "Royal Society Mathematical Tables," Carnbridge University Press, London, 1950--. Vol. 1: "Farey Series of Order 1025," 1950. Vol. 2: "Reetangular-polar Conversion Tables," 1956. Vol. 3: "Tables of Binomial Coefficients," 1954. Vol. 4: "Tables of Partitions," 1958. Vol. 5: "Representations of Primes by Quadratie Forms," 1960. Vol. 6: "Tables of the Riemann Zeta Funetion," 1960. Vol. 7: "Bessel Functions," pt, 3, "Zeros and Assoeiated Values," 1960. Vol. 8: "Tables of Natural and Common Logarithms to 110 Deeimals," 1964. Vol. 9: "Tables of Indices and Primitive Roots," 1968. Vol. 10: "Bessel Funetions," pt. 4, "Kelvin Funetions," 1964. Vol. 11: "Coulomb Wave Funetions," 1964. 59. Ryzhik, Iosif M., and I. S. Gradshteyn: "Table of Integrals, Series, and Products," translated from the 4th Russian ed., Aeademie Press Ine., New York, 1965, 1086 pages: An inclusive eompilation, the work is advertised as the most eomprehensive table of integrals ever published. New material on Mathieu, Struve, Lommel, as well as other special functions, has been added, 60. Slater, L. J.: "Confluent Hypergeometrie Funetions," Cambridge University Press, New York, 1960, 247 pages, 61. Smithsonian Institution: "Smithsonian Mathematieal Formulae and Tables of Elliptie Funetions," 3d reprinting, Washington. D.C., 1957, 314 pages. 62. Stroud, A. H., and D. Secrest: "Gaussian Quadrature Formulas," Prentiee Hall, Ine., Englewood Cliffs, N.J., 1966,374 pages: Valuable referenee book for use and applieation of Gaussian quadrature Iorrnulas. Text is divided into five parts. Fortran programs to cornpute the abseissas and weights for quadrature formulas based on classieal Jacobi, Laguerre, and Hermite polynomials are presented. Chapter 5 summarizes the tables of quadrature formulas found in the literature. 63. Todd, John, ed.: "Survey of Numerical Analysis," McGraw-Hill Book Cornpany, New York, 1962, 608 pages, 64. U.S. National Bureau of Standards: "Basic Theorems in Matrix Theory," Marvin Marcus, Government Printing Office, Washington, D.C., 1960, 27 pages (Applied mathematies series, 57). 65. - - : "Experimental Statistics," Mary Gibbons Natrella, Government Printing Office, Washington. D.C., 1963, 1 vol. (various pagings) (Handbook 91): A collection of statistieal procedures useful in the design, development, and testing of materials; the evaluation of equipment performance; and the conduet and interpretation of scientific experiments. 66. - - : "Guide to Tables of the Normal Probability Integral," Government Prinfing Office, Washington, D.C., 1952, 16 pages (Applied mathematics series, 21): A ready desk reference to the normal probability integral tabulated in standard statistical textbooks and other important sources, Provides a list of a vailable tables as well as the form of the function tabulated. 67. - - : "Matrix Representations of Groups," Morris Newman, Government Printing Office, Washington, D.C., 1968,79 pages (Applied mathematics series, 60). 68. - - : "Probability Tables for the Analysis of Extreme-value Data," Government Printing Office, Washington, D.C., 1953,32 pages (Applied mathematies series, 22): IntroductioiJ. outlines the theory and application of extreme values and deseribes nature, use, accuraey, and method of computation of tables. There are six tables for the asymptotie (cumulative) distribution of the largest value

Z I-l

o

r:J).

TABLE

2e-7.

ELASTIC AND STRENGTH CONSTANTS FOR SILVER, GOLD, PLATINUM, PALLADIUM ALLOYS (Continued)

Material

U.6 Au, 4.6 Ag, 43.4 Cu, Air cooled 5.0 Ni, 5.4 Zn 69 Au, 25 Ag, 6 Pt ....... Pt 99.99% .............. Pt + 5 Ir ............... Pt + 10 Ir .............. Pt + 25 Ir .............. Pt + 3.5 Rh ............. Pt + 5.0 Rh ............. Pt + 10.0 Rh ............. Pt + 20.0 Rh ............ Pt + 5 Ru .............. Pt + 10 Ru ............. Pt + 1 Ni ............... Pt + 2 Ni ............... Pt +5 Ni ............... 84 Pt, 10 Pd, 6 Ru ....... 96 Pt, 4 W .............. Pd (pure) ............... 60 Pd, 40 Ag ............ 60 Pd, 40 Cu ............ 95 Pd, 4 Ru, 1 Rh ........ • References are on p. 2-76.

E

Condition

Ann. Ann. Ann. Ann. Ann. Ann. Ann. Ann. Ann. Ann. Ann. ADJ1. Ann. Ann. Ann. Ann. Ann. and rolled Ann. Ann. Ann.

Tensile strength

u

............. ... .

0

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... . 14.7 X 1011 0.39 ... . ... . ... . . , .. ... . ... . ... . ... . ... . ... . ... . ... . ... .

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46.8 X 10 8 26.7 X 108 at 0.1 % offset 37.6 X 10 8 ........ . 12-13 X 10 8 ......... 27 X 10 8 ........ . 38 X 10 8 ........ . 86 X 108 . ........ 17 X 108 . ........ 21 X 10 8 ........ . 31 X 10 8 . ........ 48 X 10 8 ......... 41 X 108 . ........ 59 X 10 8 ........ . 21 X 108 ........ . 28 X 108 ........ . 45 X 10 8 55 X 108 48-52 X 108 ~15 X 10 8 35 X 108 52 X 108 38-41 X 10 8 ••

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Vhn 112 Vhn 38-40 90 130 240 60 70 90 120 130 190 Vhn 60-65 Vhn 80-90 Vhn 130-140 Vhn 150-170 Vhn 140-150 Vhn 37-39 Vhn 100

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

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TABLE

Alloys

2e-8.

ELASTIC AND STRENGTH CONSTANTS FOR ALUMINUM ALLOYS

E

Condition

G

"

Tensile strength

Yield strength

Elongation

Bhn

Shear strength

Ref.·

c ast alloys: AI, AI, AI, AI, AI, AI, AI, AI, AI, AI, AI, AI, AI, AI, AI,

12 Si. ••...................... 5 Si. ......................... 5 Si. ......................... 5 Si, 4 Cu ..................... 4 Cu, 3 Si. .................... 5 Si, 3 Cu ..................... 5 Si, 3 Cu ..................... 5 Si, 3 Cu ..................... 5.5 Si, 4.5 Cu .................. 7 Cu, 2 Si, 1.7 Zn .............. 7 Cu, 3.5 Si ......... .......... 10 Cu, 0.2 Mg ....... .......... ......... 10 Cu, 0.2 Mg ...... 12 Si, 2.5 Ni, 1.2 Mg, 0.8 Cu .... 12 Si, 1.5 Cu, 0.7 Mn, 0.7 Mg ...

AI, AI, AI, AI, .lil, AI, AI, AI, AI, AI,

4 Cu, 2 Ni, 1.5 Mg ............. 4.5 Cu .............. .......... 4.5 Cu, 2.5 Si .................. 3.8 Mg ....................... 8 Mg ......................... 10 Mg ........................ 6 Si, 3.5 Cu ................... 6 Si, 3.5 Cu ....... ............ 5 Si, 1.3 Cu, 0.5 Mg ............ 5 Si, 1.3 Cu, 0.5 Mg ............

AI, 7 Si, 0.3 Mg ................... AI, 7 Si, 0.3 Mg ................... AI, AI, AI, AI, AI, AI,

8 Si, 1.5 Cu, 0.3 Mg, 0.3 Mn .... 8 Si, 1.5 Cu, 0.3 Mg, 0.3 Mn .... 9.5 Si, 0.5 Mg .................. 8.5 Si, 3.5 Cu .................. 6.5 Sn, 1 Cu, 1 Ni. ............. 5.5 Zn, 0.6 Mg, 0.5 Cr, 0.2 Ti ...

Die cast Die cast Sand cast Die cast Sand cast Sand cast Sand cast, h-t, aged Perm. mold cast, h-t, aged Perm. mold cast, h-t, aged Sand cast Perm. mold cast Sand cast (ann.) H-t, artificially aged Perm. mold cast, art. aged Perm. mold cast (stress relieved) Ann. (sand cast) H-t, nat. aged H-t, nat. aged Perm. mold cast Die cast Sand cast, h-t, nat. aged H-t, art. aged As cast H-t, art. aged (sand cast) H-t, art. aged (perm. mold cast) H-t, art. aged (sand cast) H-t, art. aged (perm. mold cast) Sand cast (stress relieved) Perm. mold (strese relieved) Die cast Die cast (Perm. mold cast) art. aged Sand cast

7.10 7.10 7.10 7.10 7.10 7.10 7.10 7.10 7.10 7.10 7.10 7.10 7.10 7.10 7.10

X X X X X X X X X X X X X X X

1011 1011 1011 1011 1011 1011 1011 1011 1011 1011 1011 1011 1011 1011 1011

2.65 2.65 2.65 2.65 2.65 2.65 2.65 2.65 2.65 2.65 2.65 2.65 2.65 2.65 2.65

X X X X X X X X X X X X X X X

1011 1011 1011 1011 1011 1011 1011 1011 1011 1011 1011 1011 1011 1011 1011

0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33

25.5 20.7 13.1 27.6 14.5 18.6 24.1 28.9 19.3 16.5 20.7 18.6 27.6 24.8 24.8

X X X X X X X X X X X X X X X

10 8 10 8 10 8 10 8 10 8 10 8 10 8 10 8 10 8 10 8 10 8 10 8 10 8 10 8 10 8

12.4 9.65 6.20 15.2 9.65 9.65 13.8 15.2 11.0 10.3 16.5 13.8 20.7 19.3

X X X X X X X X X X X X X X

10 8 10 8 10 8 10 8 10 8 10 8 10 8 10 8 10 8 10 8 10 8 10 8 10 8 10 8

7.10 7.10 7.10 7.10 7.10 7.10 7.10 7.10 7.10 7.10

X X X X X X X X X X

1011 1011 1011 1011 1011 1011 1011 1011 1011 1011

2.65 2.65 2.65 2.65 2.65 2.65 2.65 2.65 2.65 2.65

X X X X X X X X X X

1011 1011 1011 1011 1011 1011 1011 1011 1011 1011

0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33

18.6 22.0 27.6 18.6 28.9 31.7 24.8 18.6 24.1 29.6

X X X X X X X X X X

10 8 10 8 10 8 10 8 10 8 10 8 10 8 10 8 10 8 10 8

12.4 11.0 15.2 11.0 15.8 17.2 16.5 12.4 17.2 18.6

X X X X X X X X X X

10 8 10 8 10 8 10 8 10 8 10 8 10 8 10 8 10 8 10 8

1O.0t 7.0t 7.0t 14.0t 2.0t 2.0t

16.5 X 10 8 18.6 X 10 8

7.10 X 1011 2.65 X 1011 0.33 22.7 X 10 8 7.10 X 1011 2.65 X 1011 0.33 27.6 X 10 8 7.10 7.10 7.10 7.10 7.10 7.10

X X X X X X

1011 1011 1011 1011 1011 1011

2.65 2.65 2.65 2.65 2.65 2.65

X X X X X X

1011 1011 1011 1()11 1011 1011

0.33 0.33 0.33 0.33 0.33 0.33

20.7 X 24.8 X 28.9 X 31.0 X 15.2X 24.1 X

10 8 14.5 X 10 8 10 8 10 8 15.8 X 10 8 10 8 17.2 X 10 8 10 8 6.89 X 10 8 10 8 17.2X10 8

1.8t 7.0t 6.0t 3.5t

2.5t 2.5t 4.0t 5.0t 2.0t

40'

9.65 X 10 8

55' RE65 RE80 RE85 70' 70' 80' 80' 115' 105' 100'

13.8 X 10 8

17.2 13.8 15.2 14.5 20.0 16.5

X X X X X X

10 8 10 8 10 8 10 8 10 8 10 8

70' 60' 75' 60'

14.5 16.5 20.7 15.2

X X X X

10 8 10 8 10 8 10 8

22.7 X 10 8

4.0t

75' 80' 70' 80' 90'

4.0t 5.0t

70' 90'

r.or

1.5t

RE76 RE88

1.8t 2.0t 12.0t 5.0t

45' 80'

1.5t LOt

i.or

0.5t 0.5t 0.5t

r.or 8.5t

2.5t

16.5 X 10 8 20.8 X 10 8 20.8 X 10 8 18.6 X 10 8

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

9.65 X 10 8 19.2 X 10 8

;, 1

WrougM alloys: Aluminum 99.996 AI. .............. Aluminum 99.996 AI. .............. Aluminum 99.0+ AI. ............... Aluminum 99.0+ AI ................ AI, 1.2 Mn ....................... AI, 1.2 Mn ....................... AI, 5.5 Cu, 0.5 Pb, 0.5 Bi. ......... AI, 5.5 Cu, 0.5 Pb, 0.5 Bi .......... AI, 4 Cu, 0.6 Mn, 0.6 Mg, 0.5 Pb, 0.5 Bi. ........................... '. AI, 4.4 Cu, 0.8 Si, 0.8 Mn, 0.4 Mg .. AI, 4.4 Cu, 0.8 Si, 0.8 Mn, 0.4 Mg .. AI, 4 Cu, 0.5 Mg, 0.5 Mn .......... AI, 4 Cu, 0.5 Mg, 0.5 Mn ........... AI, 4 Cu, 2 Ni, 0.5 Mg ............ AI, 4 Cu, 2 Ni, 1.5 Mg ............ AI, 4.5 Cu, 1.5 Mg, 0.6 Mn ........ AI, 4.5 Cu, 1.5 Mg, 0.6 Mn ...... ; . .AI, 4.5 Cu, 0.8 Mn, 0.8 Si. ......... AI, 12.5 Si, 1.0 Mg, 0.9 Cu, 0.9 Ni .. AI, 1.0 Si, 0.6 Mg, 0.25 Cr ......... AI, 2.5 Mg, 0.25 Cr .............. , AI, 2.5 Mg, 0.25 Cr ............... AI, 1.3 Mg, 0.7 Si, 0.25 Cr ......... AI, 1.3 Mg, 0.7 Si, 0.25 Cr ......... AI, 5.2 Mg, 0.1 Mn, 0.1 Cr ......... AI, 5.2 Mg, 0.1 Mn, 0.1 Cr ......... AI, 1.0 Mg, 0.6 Si, 0.25 Cu, 0.25 Cr. AI, 1.0 Mg, 0.6 Si, 0.25 Cu, 0.25 Cr. AI, 5.5 Zn, 2.5 Mg, 1.5 Cu, 0.3 Cr, 0.2 Mn ........................ AI, 5.5 Zn, 2.5 Mg, 1.5 Cu, 0.3 Cr, 0.2 Mn ........................ AI, 6.4 Zn, 2.5 Mg, 1.2 Cu ......... • References are on p. 2-76. t 34-in. round specimen. : )oS.in. round specimen.

Ann. Cold rolled 75 % Ann. Hard HII Ann. Hard HII H-t, then cold-worked H-t, then cold-worked, then art. aged

6.89 6.89 6.89 6.89 6.89 6.89 7.10 7.10

1011 1011 1011 1011 1011 1011 1011 1011

2.65 2.65 2.65 2.65 2.65 2.65 2.65 2.65

X X X X X X X X

1011 1011 1011 1011 1011 1011 1011 1011

0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33

4.74 11.2 8.96 16.6 11.0 20.0 36.5 39.3

10 8 10 8 10 8 10 8 10 8 10 8 10 8 10 8

1.22 10.6 3.45 14.5 4.14 17.2 32.4 30.3

X X X X X X X X

10 8 10 8 10 8 10 8 10 8 10 8 10 8 10 8

48.81 5.51 351 51 301 41 15t 14t

17' 27' 23' 44' 28' 55' 95' 100'

Quenched (h-t) Ann. H-t, art. aged Ann. H-t, nat. aged Forged, hot, aged Sand cast Ann. H-t, nat. aged H-t, art. aged H-t, art. aged H-t, art. aged Ann. Strain hardened (H) Ann. H-t, nat. aged Ann. Hard HI1 Ann. H-t, nat. aged

7.10 X 1011 7.31 X 1011 7.31 X 1011 7.17 X 1011 7.17 X 1011 7.10 X 1011 7.10 X 1011 7.31 X 1011 7.31 X 1011 7.17XlO 11 7.10 X 1011 7.03 X 1011 7.03 X 1011 7.03 X 1011 6.89 X 1011 6.89 X 1011 7.10 X 1011 7.10 X 1011 6.89 X 1011 6.89 X 1011

2.65 2.65 2.65 2.65 2.65 2.65 2.65 2.65 2.65 2.65 2.65 2.65 2.65 2.65 2.65 2.65 2.65 2.65 2.65 2.65

X X X X X X X X X X X X X X X X X X X X

1011 1011 1011 1011 1011 1011 1011 1011 1011 1011 1011 1011 1011 1011 10 1 J 1011 1011 1011 1011 1011

0.33 0.33 0.33 0.33 0.33 0.3& 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33

42.1 X 10 8 18.6 X 10 8 48.3 X 10 8 17.9XI08 42.7 X 10 8 43.4 X 10 8 19.3 X 10 8 18.6 X 10 8 46.9 X 108 39.3 X 10 8 38.6 X 10 8 32.4 X 10 8 20.0 X 10 8 28.3 X 10 8 11.0 X 10 8 22.8 X 10 8 29.0 X 10 8 40.0 X 10 8 12.4 X 10 8 24.1 X 10 8

24.1 9.65 41.4 6.89 27.6 32.4 16.6 7.58 31.7 24.1 31.7 27.6 9.65 24.8 4.83 13.8 13.8 33.1 5.52 14.5

X X X X X X X X X X X X X X X X X X X X

10 8 10 8 10 8 10 8 10 8 10 8 10 8 10 8 10 8 10 8 10 8 10 8 10 8 10 8 10 8 10 8 10 8 10 8 10 8 10 8

221 18t 13t 221

100' 45' 135' 45' 105' 115' 80' 42' 120'

Ann.

7.17 X 1011 2'.65 X 1011 0.33 22.8 X 10 8

10.3 X 10 8

171

H·t, art. aged Ann. (0.064 sheet)

7.17XJOll 2.65 X 1011 0.33 56.5 X 49.6 X 7.17 X 1011 2.69 X 1011 0.33 20.7 X 10 8 10.3 X 10 8

111 18

X X X X X X X X

X X X X X X X X

10 8

10 8

, lO-mm ball, 500-kg load. I Ma-in. sheet specimen. 11 H-atrain hardened to a prescribed hardness.

17t It 191 111 18t 8t 20t 251 71 35t 30t 35t

6.55 8.96 7.58 11.0 20.7 22.8

X X X X X X

10 8 10 8 10 8 10 8 10 8

12.4 29.0 12.4 26.2

X X X X

10 8 10 8 10 8 10 8

26' 65'

16.6 12.4 28.3 24.1 26.2 22.1 12.4 16.6 7.58 13.8

X X X X X X X X X X

10 8 10 8 10 8 10 8 10 8 10 8 10 8 10 8 10 8 10 8

30' 65'

8.62 X 10 8 16.5 X 10 8

110~

125' 100' 45' 85~

10 8

1t: 221 221

1 1 1 1 1 1 1 1

1 1 1 1 1 2 2

1 1 1 1 1 1 1 1 1 1 1 1

1 1

150' RE57RE62

1 1

TABLE

Alloy

2e-9.

ELASTIC AND STRENGTH CONSTANTS FOR COPPER ALLOYS

Condition

E

G

tT

1011 1011 1011

4.68 X to»

0.364

l{)11

...........

Tensile strength

Yield strength

Elongation

Reduetion in area

Bhn

Shear strength

Ref.-

--99.997 Cu, 0.0016 S....... " ......... 99.996 Cu, 0.002 S, 0.002 Fe .......... 99.950 Cu, 0.043 02, 0.002 Fe, 0.002 S 99.92 Cu, 0.04 02.................... 99.94 Cu, 0.02 P ..................... 95 Cu, 5 Zn......................... 95 Cu, 5 Zn......................... 90 Cu, 10 Zn........................ 90 Cu, 10 Zn........................ 85 Cu, 15 Zn ........................ 85 Cu, 15 Zn........................ 80 Cu, 20 Zn........................ 80 Cu, 20 Zn........................ 70 Cu, 30 Zn........................ 70 Cu, 30 Zn........................ 70 Cu, 30 Zn......•................. 65 Cu, 35 Zn........................ 65 Cu, 35 Zn........................ 60 Cu, 40 Zn........................ 89 Cu, 9.25 Zn, 1.75 Pb .............. 64.5 Cu, 35 Zn, 0.5 Pb ............... 67 Cu, 32.5 Zn, 0.5 Pb ............... 64.5 Cu, 34.5 Zn, 1.0 Pb .............. 62.5 Cu, 35.75 Zn, 1.75 Pb ............ 62.5 Cu, 35 Zn, 2.5 Pb ............... 61.5 Cu, 35.5 Zn, 3 Pb ............... 60 Cu, 39.5 Zn, 0.5 Pb ............... 60.5 Cu, 38.4 Zn, 1.1 Pb .............. 60 Cu, 38 Zn, 2 Pb .................. 57 Cu, 40 Zn, 3 Pb .................. 71 Cu, 28 Zn, 1 Bn................... 60 Cu, 39.25 Zn, 0.75 Bn.............

~2-in.

rod, cold drawn Ann., %-in. rod Ann., %-in. rod H.R. (0.040-in. flat) 0.040 in. flat spec. (G.S. 0.050 mm) Rolled strip 0.040 in. (G.S. 0.050 mm) Rolled strip 0.040 in. (spring) Flat, 0.040 in. (spring) Flat, 0.040 in. as H.R. Flat, 0.040 in. (G.B. 0.050 mm) Flat, 0.040 in. (spring temper) Flat, 0.040 in. (G.B. 0.050 mm) Flat, 0.040 in. (spring temper) Flat, 0.040 in. (G.B. 0.070 mm) Flat, 0.040 in. (spring temper) Flat, 0.040 in. (extra spring temper) Flat, 0.040 in., ann. Flat, 0.040 in. (spring temper) Flat, 0.040 in., ann. Rod, ann. Flat specimen, ann. Tubular specimen, ann. Rolled, flat spec., ann. Rolled, flat spee., ann. Rolled, flat spec., ann. Rod, ann. H.R. l-in. plate Light ann. 1.5-in. OD tubing Extruded l-in. rod Extruded I-in. section As H.R. (J-in. plate) As H.R. (Lin, plate)

12.77 X 11.2 X 10.9 X 11.7 X 11.7 X 11.7 X 11.7 X 11.7 X 11.7 X 11.7 X 11.7 X 11. 7 X 11.0 X 11.0 X 11.0 X 11.0 X 10.3 X 10.3 X 10.3 X 11.7 X 10.3 X 10.3 X 10.3 X 10.3 X 9.65 X 9.65 X 10.3 X 10.3 X 10.3 X 9.65 X 10.3 X 10.3 X

1011 1011 1011 1011 1011 1011 1011 1011 1011 1011 1011 1011 1011 1011 1011 1011 1011 1011 1011 1011 1011 1011 1011 1011 1011 1011 1011 1011

......... ........... .......... ........... 0.33

± 0.G1

.......... ........... .......... ........... .......... ........... .......... ...........

.......... .......... ........... .......... ...........

I

.......... ........... .......... .......... .......... .......... .......... .......... .......... ..........

........... ........... ........... ...........

........... ........... ........... ...........

.......... ........... .......... .......... .......... .......... .......... .......... .......... .......... ..........

........... ........... ...........

........... ........... ........... ........... ...........

........... .......... ........... .......... ...........

35.1 X lOS 21.3X108 21.7 X lOS 23.4 X 108 22.0 X lOS 23.4 X lOS 44.1 X lOS 49.6 X lOS 26.9 X 108 27.6 X 108 57.9 X lOS 30.3 X 108 62.7 X 108 31.7 X 108 64.8 X 108 68.2 X 108 33.8 X 108 62.7X108 37.2 X 108 25.5X1OS 33.8 X 108 32.4 X 105 33.8 X 108 33.8 X 108 33.8 X 108 33.8 X 108 37.2 X 108 37.2 X 108 35.8 X 108 41.3 X 108 33.1 X 108 37.9 X 108

34.0 3.44 3.79 6.89 6.89 6.89 40.0 42.7 9.65 8.27 43.4 9.65 44.8 9.65 44.8 44.8 11. 7 42.7 14.4 8.27 11.7 10.3 11. 7 11.7 11.7 12.4 13.8 13.8 13.8 13.8 12.4 17.2

X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X

lOSt 108t 108t lOSt lOSt lOSt lOSt 108t 108t lOSt 108t 108t lOSt 108t 108t 108t 108t 108t 108t 10Rt 108t 108t lOSt lOSt 108t lOSt 108 108 108 108 108t l08t

14 60 53 45 45 45 4 3 44 47 3 50 3 65 3 3 57 3 45 45 57 60 54 52 50 53 45 40 45 30 65 50

88 92 71

RB37

....

RF45 RF40 RF46 RB73 RB78 RF60 &59 RB86 RF61 RB91 RF58 RB91 RB93 RF68 RB90 RF80 RF55 RF68 RF64 RF68 RF68 RF68 RF68 RF80 RF80 RF78 RB65 RF70 RB55

.... . ...

.... .... .... . ... . ... . ...

.... .... .... .... .... .... .... 70

....

.... .... ....

....

.... .... .... ....

.... .... ....

.........

2 2

....... ......... ....... .........

2

15.8 X lOS 15.2 X 108

......... 27.6 28.9 21.4 21.4 31.7 22.0 33.1 22.0 33.1

X X X X X X X X X

lOS lOR

lOS lOS lOS 108 lOS 108 108

.......... 23.4 X 108 32.4 X lOS 27.6X108 16.5 X 108 23.4 X 108

......... 23.4 23.4 21.4 20.7 27.6

X X X X X

105 108 lOS 108 108

......... ......... .........

.........

27.6 X 108

\

1 1 1 1 1 1 1 1 1

1 1 1 1

1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1

60 Cu, 37.5 Zn, 1.75 Pb, 0.75 Sn ...... 58.5 Cu, 39 Zn, 1.4 Fe, 1 Sn, 0.1 Mn ... 95 Cu, 5 Sn......................... 92 Cu, 8 Sn......................... 92 Cu, 8 Sn......................... 90 Cu, 10 Sa ....•...•............... 90 Cu, 10 Sn........................ 98.75 Cu, 1.25 Sn .................... 98.75 Cu, 1.25 Sn .................... 70 ce, 30 Ni........................ 65 Cu, 18 Ni, 17 Zn.................. 55 Cu, 27 Zn, 18 Ni.................. 55 Cu, 27 Zn, 18 Ni. ................. Cu, 3 Si. ........................... Cu,3Si. ........................... Cu, 1.5 Si. .......................... 94.88 Cu, 5.02 AI, 0.04 Fe, 0.06 Zn.... 94.88 Cu, 5.02 AI, 0.04 Fe, 0.06 Zn .... 91.74 Cu, 8.10 AI, 0.04 Fe, 0.02 Ni, 0.10 Zn............................... 91.74 Cu, 8.10 AI, 0.04 Fe, 0.02 Ni, 0.10 Zn............................... 92.65 Cu, 7.35 AI.................... 92 Cu, 7 AI, 1 Ni ...........,....... 89.25 Cu, 9.25 AI, 0.6 Fe, 0.5 Ni ..... 87.45 Cu, 6.62 AI, 6.93 Ni. ........... 85.75 Cu, 10.75 AI, 3.50 Fe ........... 81.3 Cu, 10.7 AI, 4.0 Fe, 4.0 Ni ....... Cu, 2 Be, 0.25 Co (or 0.35 Ni) ........ 88 Cu, 6 Sn, 1.5 Pb, 4.5 Zn........... 87 Cu, 8 Sn, 1 Pb, 4 Zn.............. 85 Cu, 5 Sn, 9Pb, 1 Zn .............. 83 Cu, 7 Sn, 7 Ph, 3 Zn.............. 80 Cu, 10 Sn, 10 Pb ................. 78 Cu, 7 Sn, 15 Pb .................. 70 Cu, 5 Sn, 25 Ph .................. 85 Cu, 5 Sn, 5 Pb, 5 Zn....•......... 83 Cu, 4 Sn, 6 Pb, 7 Zn.............. 81 ce, 3 Sn, 7 Pb, 9 Zn .............. See page 1-76 for footnotes.

l-in. rod, soft ann.

L-in,rod, soft ann. Ann., flat spec. Ann., flat plate (0.040 in.) Spring temper plate (0.040 in.) Ann. flat plate (0.040 in.) Spring, flat plate (0.040 in.) Ann., flat plate (0.040 in.) Spring, flat plate (0.040 in.) H.R. I-in. plate. Ann., flat plate (0.040 in.) Ann., flat plate (0.040 in.) Spring, flat plate (0.040 in.) Flat plate (0.040 in.) (G.S. 0.070 mm) Flat plate (0.040 in.) spring l-in. rod (G.S. 0.035 mm) 0.041-in. sheet, ann. at 500°C 0.041-in. sheet, C.R., 44% reduction

10.3 X 1011 10.3 X 1011 u.o X 1011 11.0 X 1011 n.o X 1011 11.0 X 1011 11.0 X 1011 n.7 X 1011

n.z x ie15.2 12.4 12.4 12.4

X X X X

1011 1011 1011 1011

...........

...........

10.3 X 1011

........... ...........

.......... ........... .......... .......... .......... ..........

..........

.......... ..........

..........

..........

.......... ..........

.......... .......... .......... .......... .......... ..........

........... ........... ........... ........... ........... ........... ........... ........... ........... ........... ........... ........... ........... ...........

........... ........... . ..........

39.3 X loa 44.8 X loa 32.4 X loa 37.9,X lOs 77.2 X loa 45.5 X lOs 84.1 X 108 27.6 X lOs 51.7 X lOs 37.9 X lOs 40.0 X lOs 41.3 X lOs 79.2 X lOs 38.6 X lOS 7;j.8XI0s 27.6 X loa 41.5XlOs 68.9 X loa

20.7 X loaf 20.7Xloaf 13.1 X loa

...........

........... . .......... ........... 9.65 X lOs

........... 13.8 17.2 18.6 64.1 14.5 42.7 10.3 17.6 44.0

X X X X X X X X X

loa loa loa lOS 10sf loaf 10sf loaf loaf

40 33 64 70 3 68 4 48 4 45 40 40 2.5 63 4 50 65.8 8.0

.... ....

....

Ra55 124.8 X loa Ra65 28.9 X loa Ra26 ......... RF75 ......... Ra93 ......... Ra55 ........ RsI01 ......... RF60 ......... Ra 79 ......... Ra35 ......... Ra40 ......... ......... Ra55 Ra99 ......... Ra40 28.9 X 101 RB97 43.4 X lOS RF55 ......... RB48.5 ......... Ra93.5 .........

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

....

....

....

.... .... .... . ... .... ....

....

.... .... ....

.... ....

.

0.02Q-in. sheet, ann. at 400°C

........... .......... ...........

53.9 X 108 29.1 X lOSf

41.8

....

....... .........

0.02Q-in. sheet, C.R., 37 % reduction B.R. C.R., ann. Ann., rod B.R. Sand cast Forged, ann. at 845°C Solution treated, quenched Sand cast O.50S-in. section Sand cast mOOS-in. section Sand cast O.50S-in. section Sand east O.50S-in. section Sand east O.50S-in. section Sand east Sandcaat Sand east Sand east Sand cast

........... ...........

62.7 43.4 85.4 55.1

12.8 73 4.5 22 20 14 28.0 50 35 30 15 20 12 15 10 25 24 22

.... .... ....

.......

.......... .......... .......... ..........

........... ........... ....... .... .......... ........... .......... ~

11.2 11.7 8.96 9.65

X X X X

1011 1011 1011 1011

........... 9.99 X 7.58 X 7.23 X 6.89 X 9.30 X

1011 1011 1011 1()l1 1011

.......... ..........

...........

.......... .......... .......... .......... .......... ..........

..........

........... ..........

8.96 X 1011

..........

........... ........... ...........

X X X ............ X . .......... ts.: X ........... 6:r.0 X ........... 65.1 X ........... 49.6 X ........... 26.2 X ........... 2-LS X . .......... 20.7 X ........... 23.4 X ........... 22.0 X ........... 20.7 X ........... 14.5 X ........... 23.4 X ........... 22.0 X ........... 22.0 X

loa lOS lOS lOS lOS lOS lOS loa loa loa loa lOS loa lOS lOS lOS loa lOS

45.3 X loaf

........... ........... 27.6 71.2 25.5 41.4

X X X X

loaf lOS 10sf lOS

17.2X1oa~

11.0 X loaf 12.4X 10sf 10.3X1oaf 11.7 X loaf 11.7 X loaf 11.0 X loaf

........... 11.7 X 10sf 10.3 X 10sf 10.3 X 108f

....

.... .... .... ....

35

....

16 18 10.0 15 8 25 20 20

......... ......... ....... ......... 134f

. ....... 24U 17!i§ RB90 Ra60 66t 68t 60t 60t 65t 55t 48t 60t 55t 55t

.........

......... ......... ......... ......... ......... ......... ......... ......... ......... ......... ......... .........

.........

.........

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

TABLE

2e-9.

Alloy

ELASTIC AND STRENGTH CONs'rANTS FOR COPPER ALLOYS

Condition

G

u

.......... .......... .......... .......... ..........

........... ........... ........... ........... ...........

E

Tensile strength

(Continued) ReducElongation in tion area

Yield strength

--76 Cu. 3 Bn, 6 Pb, 15 Zn............. 71 Cu, 1 Sn, 3 Pb, 25 Zn............. 66 Cu, 1 Sn, 3 Pb, 30 Zn............. 60 Cu, 1 Sn, 1 Pb, 38 Zn............. 62 Cu, 26 Zn, 3 Fe, 5.5 AI, 3.5 Mn .... 58 Cu, 39.25 Zn, 1.25 Fe, 1.25 AI, 0.25

Sand cast Sand cast O.505-in. section Sand cast O.505-in. section Sand cast Sand cast

Mn.............................. Sand cast 59 Cu, 0.75 Sn, 0.75 Pb, 37 Zn, 1.25 Fe, 0.75 AI, 0.5 Mn ................... 66 Cu, 5 Sn, 1.5 Pb, 2 Zn, 25 Ni. ...... 64 Cu, 4 Sn, 4 Pb, 8 Zn, 20 Ni. ....... 57 Cu, 2 Sn, 9 Pb, 20 Zn, 12 Ni. ...... 60 Cu, 3 Sn, 5 Pb, 16 z», 16 Ni.. ..... 89 Cu, 1 Fe, 10 AI.. ................. 87.5 Cu, 3.5 Fe, 9 AI................. 86 Cu, 4 Fe, 10 AI................... 71t Cu, 5 Fe, 11 AI, 5 Ni. .............

• References are on p. 2-76. tAt 0.5% extension. t lo-mm ball, 500-kg load.

Sand cast Sand cast Sand cast Sand cast Sand cast Sand cast, cooledin sand Sand cast Sand cast, cooledin sand Sand cast

8.27)( 8.96 X 8.96 X 9.65 X 10.7 X

1011 1011 1011 1011 1011

10.3 X 1011

.......... ...........

10.3 X 1011

.......... ........... .......... ...........

........... ........... ........... ........... ........... 11.7 X io» 12.4 X io» 11. 7 X 1011

..........

.......... .......... .......... ..........

.......... .......... ~

Bhn

Shear strength

--- ---

Ref.·

--

10.3X108 t 8.27X108 t 8.96 X 108t 9.65 X 108 t 48.2 X lost

30 35 35 25 15

30 30 30 25 15

55t 48t 50t 65t 210§

. ........

......... ......... ......... .........

1 1 1 1 1

48.2 X lOS 19.3 X lost

30

30

125t

. ........

1

18 15 15 20 25 15 35 18 7

20 15 14 20 25 15 32 15 7

85t 130t 105t 60t 75t 140§ 120§ 155§ 195§

. ........ ......... ......... .........

1 1 1 1 1 1 1 1 1

22.0 24.1 23.4 27.6 79.2

X X X X X

108 108 108 108 108

44.8 X lOS 34.4 X lOB . .......... 27.6 X 108 ........... 23.4XI08 ........... 26.2 X 108 ........... 46.2X108 ........... 51. 7 X 108 ........... 51.7 X 108 ........... 65.5 X 108

At 0.01 % offset.

§ lo-mm ball, 3,OOO-kg load.

20.7 X 16.5 X 17.2 X 10.3 X 11. 7 X 22.0 X 18.6 X 24.1 X 31.0 X

lost 108 t 108 t 108 t 108 t

lost 108

t

108 t 108 t

.........

......... . ........ ......... . ........

TABLE 2e-10, ELASTIC AND STRENGTH CONSTANTS FOR VARIOUS SOLIDS

Material

Iridium ....... , . Osmium ........ Rhodium ....... Ruthenium ...... Antimony ....... Beryllium ....... Cadmium....... Calcium ........ Chromium...... Cobalt .......... Columbium ..... Columbium ..... Lithium ......... Manganese ...... Molybdenum .... Silicon .......... Sodium ......... Tantalum ....... Tantalum ....... Titanium ... ' ... Titanium ....... Tungsten ....... Zirconium .......

I

Condition

Ann. Ann. Ann. As cast

...............................................

E

52 X 1011 56 X 1011 0

••••••••••••

41 7.78 29 5.5 2-3

X 1011 X 1011 X 1011 X 10 l l t X 1011

G

..........

......... .

......... . .......... .. ............. ............... ..

Vacuum cast Chill cast f -in. section Cast slab As cast Cast Sheet, ann. O.OI-in. section Sheet, worked O.Ol-in. section ....................................................

. .................. ................. . .............. . .. . ...... .

Quenched Pressed + sintered (sheet) Chill cast 3.55 X 0.97 X 0.97 in. ........... . . ................. . Ann. O.OlO-in. sheet Worked O.OlO-in. sheet Ann. Hard, 60% reduction ............................... Hard drawn

............. 34 X 1011 11.26 X 1011 .... . ....... . ............ . ............. 11.6 X 1011 .... . ....... . 34 X 1011 9.99 X 1011

..................

21 X 1011

.......... .. . ................ ............... . ............ ............. . ........... .

Tensile strength

. ......... . .........

Yield strength at 0.2% offset

....... .

. ....... . ....... ....... .

50 X 108 ......... . 1.1 X 108 ......... . 12-15 X 108 .. ....... 7.1 X 108 .. ....... 5.5 X 108 3.8 X 108 .......... .. 23.7 X 108

34 X 108 69 X 108

. .........

......... . 50 X 10 8 ......... . 69 X 108 ......... . ......... . . ......... ......... . .......... 34 X 10 8 ......... . 76 X 108 .......... 54 X 108 .......... 76.82 X 108 13.5 X 1011 .. . ...... . .......... 84 X 10 8

......... .......... ......... .

..

..

. ...... . .......

24 X 10 8 . .... .. . . .... .. . . ....... . ....... . ....... 43 X 108 . .... . . . ...... 48 X 10 8

Elongation

Bhn

Ref.*

-Vhn 170 . .... Vhn 400 ..... .... . . .......... ..

.......

. ..... . .... 50 53-60 . .....

. ....... 30 1 . .... 40 ,.

....

..... .. ....

40 1 25.2 1.5 . .....

18~

1 1

1 1 I 1 I 1 I 1 1

Vhn 390 30-58 ..............

21-23 17 110-170 125

. .................. ............. Softer than pure lead Rc35 156 . .... . ..... 0.07t RE60 RE95 R G76 R G72 . .......... R B87.4

1

1

1 1 I 1 1 1 1 1 1 1

I .. References are on p. 2-76. t Sand cast. t 3.2-kg load, lO-mm ball. ~ Per cent in 4 in.

TABLE

2e-ll.

ELASTIC AND STRENGTH CONSTANTS FOR IRON AND STEEL ALLOYS

9C

Alloy

Condition

E

G

(1

Tensile strength

Yield strength

Elonga- Reduction in tion

Bhn

area

Shear strength

Ref.-

---

0.03 0.02 0.02 0.02 0.02 0.02 0.02 0.05 0.07 0.05 0.06 0.054 0.025 0.08 0.07 0.03 0.08 0.08 0.10 0.10 0.10 0.10 0.11 0.12 0.15 0.15 o.16 o.15 o.17 o.18 o.18 o.18 o.20

Iron: 2.50 C, 0.79 Si, 0.09 S, 0.04 P 3.52 C, 2.55 Si, 1.01 Mn, 0.215 P, 0.086 S 3.52 C, 2.55 Si, 1.01 Mn, 0.215 P, 0.086 S 1.15-2.30 C, 0.85-1.20 Si, 0.40 Mn, 0.020 P, 0.012 S 2.25-2.70 C, 0.80-1.10 Si Steel: 0.12 Mn, 0.005 Si, 0.45 Cu, 0.07 Mo 0.5 Cu 1.0 Cu r.s Cu 2.0Cu 2.5 Cu 3.0 Cu 0.39 Si, 0.25 Mn:0.014 P, 0.049 S 1.17 Si, 0.32 Mn, 0.013 P, 0.034 S 1.73 Si, 0.35 Mn, 0.014 P, 0.030 S 2.39 Si, 0.16 Mn, 0.010 P, 0.016 S 0.42 Mn, 0.025 Si, 0.031 AI, 0.265 Ti 0.30 Mn, 0.010.P, 0.023 S, 0.09 Ni, 0.09 Cu, 0.26 V 1.01 Cr, 0.41 Cu, 0.80 Si, 27 Mn, 0.145 P, 0.020 S 18.95 Cr, 7.69 Ni 13.47 Cr, 0.27 V, 0.04 P, 0.01 S 1.07 Cu, 0.54 Ni, 0.43 Mn, 0.16 Si, 0.104 P, 0.022 S 1.46 Si, 0.102 Mn 0.45 Mn, 3.71 Ni, 0.10 S 0.5 Cr, 0.3 Mo, 2.5 Ni 0.6 Cr, 0.3 Mo, 3.3 Ni 0.07 Si, 0.69 Mn, 0.092 P, 0.027 S, 0.16 Al, 1.09 Cu, 0.15 Mo, 0.63 Ni 0.6 Mn, 1.4 Cr, 0.17 Mo, 1.0 Ni 0.84 Mn, 0.12 S, 0.099 P, 0.01 Si 0.75 Mn, 0.30 Si, 1.75 Ni, 0.25 Mo 0.75 Mn, 0.30 Si, 3.50 Ni 0.4 Mn, 1.2 Cr, 0.25 Mo, 4.1 Ni 13.50 Cr, 0.11 Si 0.5 Mn, 0.25 Mo, 1.8 Ni 0.55 Mn, 0.25 Si 2.50 Cr, 0.55 Mn, 0.40 Si, 0.40 Mo, 0.20 V 0.92 Mn, 0.115 P, 0.12 S, 0.02 Si 16.17 Cr, 1.06 Mn, 0.30 Si

Cast

~s-io. cast, ann. bar 2-io. bar Malleable, cast, ann.

............................ H.R. at 540·C As normalized As normalized As normalized As normalized As normalized As normalized As rolled As rolled As rolled As rolled H.R., 5%-strained, aged Annealed

13.8 X 1011 12.1 X 1011 8.27 X 1011 17.2XI011

14

24.0 X 27 X 31 X 43 X 50 X 52 X 52 X 27.9 X 32.7 X 37.6 X 36.9 X 46.9 X 15.8 X

lost lOsi lOBi lOsi lOBi 108i 10ai 10si IOsi IOsi 10si 10si

35.8 46 41 36 31 27 26 29.5' 29.5~ 29.5 24.5' l1.9i 28.1

54.0 X lOS

41.3 X

108 11

4Q

..... .....

98.5 X 10s-' 56.8X 10~ 48.8 X lOS

............ 38:7 x' ioa....

21ft 16i 38

..... ..... ..... ..... .....

63.7 X lOS 60.4 X lOS 93.1 X lOS 122 X lOS 52.8XI0s

47.1 X 34.4 X 78.4 X 108 X 39.2 X

lOS" lOst 108t 108t 10at

16 37 13U IOU 45.8

60.8 X 52.4 X 44.8 X 44.8 X 120 X 75.8 X 66.8 X 25 X 82.7 X 45.5 X 61.2 X

lOst lOS

12.8" 18 20.0 20.0 15.8 21 21.2 32.0 15.0 15 10

............ ..... ..... ............ ..... ............ ..... ............

............ .....

............ . .... ............ ..... ............ .....

............ ..... ............ ..... ............ .....

............ ............ ..... 17.2 X 1011 18.2 X 1011 .8:54 'x'ioii 20.5 X 1011 7.92 X 1011

C.R. O.Q. {rom 1740·F, T at 840·F

22.4 X 108t

8.61 X 1011 0.17

............ .....

C.R. ~f1-in. bar H.R. 3%-in. bar H.R. %-in. bar

·C~t························

34.4 X 108

17.2 X 1011

............ ............ ............ ............ ............ ............ ............ ............ ............ ............ ............ ............

20.7 X 1011 8.20 X 1011

W.Q. {rom 900·C (carburized) 1 ~f1-in. diam C.R. bar Cast Cast O.Q. from 780 to 180· O.Q. from 1740·F, T at 1110·F P.(O.Q.)(carburized)

............ ........ ............ ........ 25.'8 x'ioat" ·22 ..·..

43.4 X 1011 8.61 X 1011 0.17

H.R. %-in. bar

W.Q. from 1830·F A.C. from 1550·F O.Q. from 820·C (earburized) O.Q. from 820·C (carburized) H.R. 4 hr at 540·C

32.8XI08 23.5 X 108 15.5 X lOs 39.3 X 108

............ ..... 5.10 X 1011 .....

20.9 X 1011

............ ............ ............ ............

.20:9')( ioii

............ ............ ............ 21.6 X 1011 ............ ............

............ ............ ............ ............ ............ ............ ............ ............ ............ ............ ............ ............ ............ ............

..... .....

108 lOs 108 lOS 108 lOs lOs lOs lOs lOS 108 lOS lOS

..... 85.8XI08

.....

57.4 X 108

..... 68.9XI0s ..... 68.9 X 108

..... ..... ...... ..... . .... ............ 20.5 X 1011 ............ ..... 22.6 X 1011

34.3 X 34 X 39 X 48 X 55 X 56 X 56 X 40.0 X 46.5 X 50.0 X 52.7 X 48.9 X 29.2 X

............ .....

135 X 90.9 X 83.8 X 45 X 96.5 X 67.6 X 130 X

lOS lOS 108 108 108 lOS 108

10~t

10~t

108t lOst lOS 108t lOst 108t lOS 108

266 30.7 X lOS .... 163 30.2 X lOs .... 164 25.1 X 108 .... .... 111-145 33.1 X 108 .... ........ 33.1 X lOs ........ ......... 65 ........ ......... 78 73 70 67 66 65 72 71.5 64 53.5 67.0

....

72

....

........ ........ ........ ........

. ........

......... ......... . ........ ......... "i«: ......... 130 ......... 140 ......... 181 ......... ........ ........... ........ ......... 156 ......... 302 175 145

2 2 2 2 2 12 1 1 1 1 1 1 1 1 1 1 13 1 2•

47:2 x'ios

2 2 2

72" . "'ias" ......... .... . ....... ......... .... ........ ......... .... ........ ......... . ........ 52" 'Vh~'205 ......... 35.0 200 ........ " 35.0 200 . ........ 50.0 . ........ ·· ..SS .. 63 ......... 52.1 ........ ..'iao" .......... 53.0 50.0 . ....... ......... 46 .... '''a5i'' .......... ........

2 4 5 5 6

26 69

......... .........

5 2 7 7 8 2 9 7 7 2 2

0.19 0.20 0.25 0.25 0.15 0.15 0.27 0.27 0.19 0.19 0.10 0.10 0.30 0.34 0.38 0.91 1.04 0.37 0.60 0.45 0.33 0.33 0.34 u.37 0.31 0.43 0.40 0.32 0.32 1.27 0.78

W.Q. from 1550°F 1.35 Mn, 0.10 S 0.45 Cr, 1.19 Mn, 0.67 Si, 0.033 P, 0.019 S Rolled Rolled, %-in. plate 0.45 Mn, 0.40 S, 0.03 Si, 0.012 P to 0.35 ·H:it·.······················· to 0.25; 0.3--{).6 Mn, 0.045 P, 0.05 S to 0.25; 0.3-0.6 Mn, 0.045 P, 0.05 S C.R. Wr., ann. at 1450°F, F.C. 0.72 Mn, 0.21 Si, 0.024 S, 0.014 P Wr. W.Q. from 1600°F, T at 0.72 Mn, 0.21 Si, 0.024 S, 0.014 P 1l00°F H.R. (trans. prop.) 0.85 Mn, 0.05 (max) S, 0.045 (max) P H.R. (long. prop.) 0.85 Mn, 0.05 (max) S, 0.045 (max) P H.R. (trans. prop.) 0.75 Mn, 0.20 S, 0.10 P H.R. (long. prop.) 0.75 Mn, 0.20 S, 0.10 P 0.70 Mn, 3.5 Ni Ann. 0.88 Mn, 0.35 Si, 0.035 S, 0.019 P [Rolled %-in. plate Wr., ann. at 1450°F; F.C. 0.65 Mn, 0.22 Si O.Q. from 1575°F, T at 940°F 0.38 Mn, 0.16 Si, 0.036 P 0.36 Mn, 0.16 Si, 0.018 S, O.oI5 P }-3 hr at 1550°F, O.Q. from 120°F, T }2 hr at 800°F 0.50 Cr, 1.14 Mn, 0.84 Si, 0.033 S, 0.021 P H.R. %-in. bar 0.56 Cr, 0.62 Mn, 0.26 Si O.Q. from 1470°F, T at 750°F Nat 1525°F 1.14 Cr, 0.69 Mn, 0.12 Si 0.78 Cr, 0.24 Mo, 0.54 Mn, 0.21 Si, 0.025 P, W., F.C. from 1450°F 0.029 S 0.78 Cr, 0.24 Mo, 0.54 Mn, 0.21 Si, 0.025 P, Wr., O.Q. from 1600°F, T at 0.029 S 1l00°F 0.46 Mn, 21.39 Cr, 10.95 Ni, 3.16 W, 1.39 A.C. from 1740°F Si 1.18 Cr, 0.16 V, 0.71 Mn, 0.33 Si, 0.037 S, F.C. from 1450°F 0.024 P 1.66 Mn, 0.25 Si, 0.024 S. 0.015 P Wr. F.C. from 1450°F 3.47 Ni. 0.64 Mn, 0.20 Si, 0.023 S. O.oI5 P F.C. from 1450°F 1.65 Ni, 0.99 Cr, 0.51 Mn, 0.20 Si. 0.D28S, Wr., F.C. from 1450°F 0.019 P 1.92 Ni, 0.86 Cr, 0.30 Mo, 0.60 Mn, 0.16 Si, Wr., F.C. from 1450°F 0.019 S, 0.014 P 2.42 Ni. 0.49 Cr, 0.38 Mo, 0.88 Mn, 0.23 Si, Cast ann. at 1575°F, 6-in. bar, 0.13 Cu, 0.04 S, 0.03 P Tat 1200°F 12.69 Mn, 0.12 Si W.Q. from 1830°F 0.10 Mn Ann. at 1472°F

• References are on p. 2-76. t At yield point. tAt 0.2 % offset. ~ %in 70mm. § % in Sin.

89.6 X 108t 60.8 X 108 0.276 59.0 X 108 37.4)( 108 1011 ............ 0.306 43.5 X 108 22.3 X 108 1011 78.5 X 1011 0.297 .......... ............ 1011 78.06 X 1011 0.313 .......... ............ 1011 78.20 X 1011 0.286 .......... ............ 1011 81.3 X 1011 0.316 46.4 X 108 25.8 X 108 1011 82.7 X 1011 0.310 62.8 X 108 37.9 X 108

20.4 20.3 20.53 20.12 18.9 20.4

X X X X X X

............ ............ ............ ............

............ ............ ............ ............ ............ . '2'0.'5'X'lOli ............ 19.8 X 1011 20.8 X 1011 20.5 X 1011

.....

42.6XI0 8

..... 44.1 X 108 ..... 43.1 X 108

..... 46.1 X 54.7 X 0.291 59.5 X 8.06 X io» 0.287 52.2 X 7.44 X io» ..... 155 X 7.44 X ro» ..... 163 X

lOS 108 108 108 108 108

.....

21 X 1011 ............ 86.1 X 108 21.1 X lOll 8.27 X io» ..... 164 X 108 21 X 1011 ............ ..... 83.4 X 108 19.7,X ro» 8.27 X ro» 0.288 52.8 X 108 19.8 X 1011 20.1 X io»

8.13 X lOll 0.272 86.8 X 108

............ .....

88.2 X 108

251 156 122

16 30 40

70"

46 42

64 70

36.0 43.5§§ 22.6§§ 37.5§§ 31.5 33 44 7 5

53.7 66.5 24.5 60.5 57.2 58 56

61. 7 X 108 29.3 X 108

23 2.5§ 12§ 48

58 2.0 50 66

255 469 250 170

60.2 X 108

2 2 2 2

62.4 X 108

28

60

229

78.5 X 108

2

25

35

269

.........

2

.20:9'x:ioii .82:0'X' ioii

22.5 25.0 24.7 27.5 39.3 28.6 241 99.2 99.2

X X X X X X X X X

55.6 X

108 108 108 108 108 108 10'18111 10 108 1081!

.... .......

30.9 X

10 8".

........ ........

44

.... .... ....

.... ....

....... . ...... ....... 153 191

....... ....... ....... ....... ....... 168 146 444

. ......

58."0 )("i08 ......... ......... ......... . ........

52.3 X 108

.........

. ........

. ........ .........

. ........ ......... . ........

55.0 X 108

. ........ ......... ......... . ........ . . . . . . . ..

4 2 2 2 10 10 2 2 1 1 1 1 1 2 2 2 2

w-.,

20.3 X lOll

8.13 X 1011 0.289 61.1 X 108

33.9 X 108

42

62

179

61.7 X 108

2

w-.

19.2 X 1011 21 X 1011 19.8 X 1011

8.27 X 1011 0.295 58.5 X 108 8.34 X io» 0.308 65.0 X 108 7.78 X lOll 0.299 61.9 X 108

29.8 X 108 36.5 X 108 30.2 X 10 8

42 33 40

54 45 54

169 187 170

58.1 X 108 60 X lOS 62.4 X 108

2 2 2

19.8 X 1011

7.92 X 1011 0.288 66.2 X 108

ro» ..... ............ ............ ..... ............ ............ ..... 20.2 X 1011 7.92 X

I! At 0.005 % permanent set. •• At 0.05 % permanent set. tt % in 1.5 in. if % in 3.94 in. ~~ % in 1.97 in.

34.2 X 108

37

58

202

66.0 X 108

2

81.3 X 108

67.5 X 108

10ttt

16

260

72.3 X 108

2

102 X 108 68.2 X 108

53.2 X 108 65.4 X 108

44 12

49 35

......... .........

1 1

§ § % in 0.75 in. At 0.001 % permanent set. • •• At 0.1 % offset. ttt % in 4/V area.

1111

....... .......

,TABLE

2e-12.

Alloy

ELASTIC AND STRENGTH CONSTANTS FOR LEAD AND LEAD ALLOYS

E

Condition

Yield strength at 0.5% offset

Tensile strength

IT

Elongation. % in 2 in.

Reduction in area

Bhn

Shear strength

Ref.·

--99.90 Ph .. ....................... 99.73 Ph ....................... 99.73 Ph ....................... 0.023-0.033 Ca. 0.02-0.1 Cu, 0.0020.02 Ag , .. . 1 ss. . ............... 4 Sh. 6 ss , ............... d Sh. . .............. 6 ss. ••

o

•

0

•••••••••

••••••••••••••

o'

•••••••••••••

..

................ 8 Sh .... . . ............... 9 Sb . .. ......... 4.5-5.5 Sn .. . ............. 20 Sn. . ............. 50 Sn. 4.50-5.50 Bn, 9.25-10.75 Sh ... 4.50 + 5.50 Sn, 14-16 Shoo .. 9.3-10.7 Sn, 14-16 Sh 0.75-1.25 Sn, 0.8-1.4 As, 14.5-17.5 Sh o.6-1.0 Sn, 1.5-3.0 As, 12.0-13.5 Sh

..

Rolled. aged Sand cast Chill cast Extruded Extruded and aged Rolled, 95% reduction Chill cast Extruded Cold rolled, 95 % reduction Rolled. 95% reduction Chill cast

.................... ................. ...

.................... Chill Chill Cast Chill Chill

• References are on p, 2-76. t M II-in. ball, 9.85-kg load for 30 see..

cast cast cast cast

•••

•••••

0

•

1.38 X 10 11

..........

..... ..... 1.38 X 1011

.......... · ......... · .........

....... .......

1. 77 X 10 8 0.95 X 10 8 1.1-1.3 X 10 8 0.55 X 10 8 0.40-0.45 1.4 X 10 8 . ..... ' "

.......

....... .......

....... .0

•••••

..........

.. . ···0

.......... .......... · ....... .......... . .........

. ...... ...... . . ...... . ...... . ...... ..... . ......

~

2.89 2.89 2.89 2.89 2.89

X 1011 X 1011 X 1011 X 1011 X 1011

"

....... ....... .......

...... . ........ . ........ . ........ . ........ . ........

2.1 2.1 2.77 4.71 2.27 2.82

X X X X X X

10 8 10 8 10 8 10 8 10 8 10 8

3.20 5.2 2.3 4.0 4.2 6.9 6.9 7.2 7.1 6.8

X X X X X X X X X X

10 8 . ........ 10 8 . ........ lOS 1.0 X 10 8 10 8 2.51 X 10 8 10 8 3.3 X 10 8 10 8 ......... 10 8 . ........ 10 8 . ........ 10 8 . ..... ' " 10 8 ." ......

'"

22 30 47

..... .

40 50 48.3 24 65 47

. ..... . .....

31.3 17 50 16 60 5 5 4 2 1.5

100 100

.... . ..... . ..... "

. ..... ..... . ..... . 80 50 70

. ... . ..... . ..... ...... . ..... "

RB75 3.2-4.5 4.2

. ........ 1.2 X 10 8 .........

...... . ........ 7 8.1 13.0 10.7

9.5t 15.4 8

. ........ . ........ . ........ . ........

. ........ . ........ . ........ . ........

U.3

. ........

14.5 19 20 22 20 22

4.04 X 10 8

.........

. ........ . ........ . ........ . ........

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

TABLE

2e-13.

ELASTIC AND STRENGTH CONSTANTS FOR MAGNESIUM ALLOYS

Yield strength at 0.2% offset

Elongation, % in 2 in.

Bhn

Shear strength

Rolf.·

4.48 X 1011 1.67 X 1011 0.35 4.48 X 1011 1.67 X 1011 0.35 16.5 X 10 1 9.65 X 10 1

2

65

13.1 X 10'

14

4.48 X 1011 1.67 X 1011 0.35 16.5 X 10 8 9.65 X 10 8

2

..

13.1 X 10 8

14

4.48 X 1011 1.67 X 1011 0.35 27.6 X 10 8 9.65 X 10 8

10

63

13.8 X 10·

14

9.65 X 10 8

6

50

12.4 X 10 8

14

4.48 X 1011 1.67 X 1011 0.35 20.0 X 10 1 9.65 X 10 8

5

..

13.1 X 10 8

14

4.48 X 1011 1.67 X 1011 0.35 27.6 X 10 8 9.65 X 10 8

12

55

13.1 X 10 8

14

4.48 X 1011 1.67 X 1011 0.35 16.5 X 10 8 9.65 X 10 8

2

52

.........

14

4.48 X 1011 1.67 X 1011 0.35 27.6 X 10 8 9.65 X 10 8

11

53

.........

14

13.1 X 10 8

4

66

.........

14

Die cast, as fabricated

4.48 X 1011 1.67 X 1011 0.35 22.7 X 10 1 15.2 X 10 8

3

60

13.8 X 10 1

14

Die cast, as fabricated

4.48 X 1011 1.67 X 1011 0.35 22.7 X 10 8

15.2 X 10 8

3

60

13.8 X 10 8

14

Sheet, ann.

4.48 X io»

1.67 X 1011 0.35 25.5 X 10 8

15.2 X 10 8

21

56

14.5 X 10'

14

Sheet, hard rolled

4.48 X 1011

1. 67 X 1011 0.35 28.9 X 10 8

22.0 X 10 8

16

73

15.8 X 10 1

14

Alloy

Condition

99.9+ Mg ............................ 8.3-9.7 AI, 0.10 Mn, 1.7-2.3 Zn, ::::;0.3 Si, ::::;0.05 Cu, ::::;0.01 Ni, 0.3 other 8.3-9.7 AI, 0.10 Mn, 1.7-2.3 Zn, ::::;0.3 Si, ::::;0.05 Cu, ::::;0.01 Ni, 0.3 other 8.3-9.7 AI, 0.10 Mn, 1.7-2.3 Zn, ::::;0.3 Si, ::::;0.05 Cu, ::::;0.01 Ni, 0.3 other 5.3-6.7 AI, ~0.15 Mn, 2.5-3.5 Zn, ::::;0.3 Si, ::::;0.05 Cu, ::::;0.01 Ni, 0.3 other 5.3-6.7 AI, ~0.15 Mn, 2.5-3.5 Zn, ::::;0.3 Si, ::::;0.05 Cu, ::::;0.01 Ni, 0.3 other 5.3-6.7 AI, ~0.15 Mn, 2.5-3.5 Zn, ::::;0.3 Si, ::::;0.05 Cu, ::::;0.01 Ni, 0.3 other 8.3-9.7 AI, ~0.13 Mn, 0.4-1.0 Zn, ::::;0.5 Si, ::::;0.10Cu, ::::;0.01 Ni, 0.3 other 8.3-9.7 AI, ~0.13 Mn, 0.4-1.0 Zn, ::::;0.5 Si, ::::;0.10 Cu, ::::;0.01 Ni, 0.3 other 8.3-9.7 AI, ~0.13 Mn, 0.4-1.0 Zn, ::::;0.5 Si, ::::;0.10 Cu, ::::;0.01 Ni, 0.3 other 8.3-9.7 AI, ~0.13 Mn, 0.4-1.0 Zn, ::::;0.5 Si, 0.10 Cu, ::::;0.01 Ni, 0.3 other.......... 8.3-9.7 AI, ~0.10 Mn, 0.4-1.0 Zn, ::::;0.5 Si, ::::;0.3 Cu, ::::;0.01 Ni, 0.3 other ......... 2.5-3.5 AI, ~0.20 Mn, 0.6-1.4 Zn, 0.080.30 Ca, ::::;0.3 Si, ::::;0.05 Cu, ::::;0.005 Fe, ::::;0.005 Ni, 0.3 other ................. 2.5-3.5 AI, ;::0.20 Mn, 0.Q-1.4 Zn, 0.080.30 Ca, ::::;0.3 Si, ::::;0.05 Cu, ::::;0.005 Fe, ::::;0.005 Ni, 0.3 other .................

........................ Sand and permanent cast molds, as fabricated Sand and permanent cast molds, cast and stabilized Sand and permanent cast, solution h-t Sand and permanent cast molds, as fabricated Sand and permanent cast molds, cast and stabilized Sand and permanent cast molds, solution h-t Sand and permanent cast molds, as fabricated Sand and permanent cast molds, solution h-t Sand and permanent cast, solution h-t, aged

E

G

tT

Tensile strength

4.48 X 1011 1.67 X 1011 0.35 20.0 X 10 8

4.48 X 1011 1.67 X 1011 0.35 27.6 X 10 8

TABLE

2e-13.

ELASTIC AND STRENGTH CONSTANTS FOR MAGNESIUM ALLOYS

(Continued) I

Alloy

Condition

E

\

2.5-3.5 AI, ~0.20 Mn, 0.6-1.4 Zn, 0.080.30 cs, ~0.3 Si, ~0.05 Cu, ~0.005 Fe, ~0.005 Ni, 0.3 other ................. ~1.20 Mn, 0.08-0.14 cs, ~0.3 Si, ~0.05 Cu, ~0.01 Ni, 0.3 other .............. ~1.20 Mn, 0.08-0.14 ce, ~0.3 Si, ~0.05 Cu, ~0.01 Ni, 0.3 other .............. ~1.20 Mn, 0.08-0.14 cs, ~0.3 Si, ~0.05 Cu, ~0.01 Ni, ~0.3 other ............ 5.8-7.2 AI, 0.15 Mn, 0.4-1.5 Zn, ~0.3 Si, ~0.05 Cu, ~0.OO5 Ni, ~0.005 Fe, +0.3 other 7.8-9.2 AI, ~0.15 Mn, 0.2-0.8 Zn, ~0.3 Si, ~0.05 Cu, ~0.005 Ni, ~0.005 Fe, 0.3 other 7.8-9.2 AI, ~0.15 Mn, 0.2-0.8 Zn, ~0.3 Si, ~0.05 Cu, ~0.OO5 Ni, ~0.005 Fe, 0.3 other ~0.06 Mn, 4.3-6.2 Zn, ~0.45 Zr, 0.3 other ~0.06 Mn

, 4.3-6.2 Zn,

~0.45

• References are on p.I-76.

G

IT

Tensile strength

Yield strength at 0.2% offset

Elongation, % in 2 in.

Bhn

Shear strength

Ref.·

..

14.5 X 10 8

14

12.4 X

10 8

14

11.7 X

10 8

14

"

Sheet, as fabricated'

4.48 X 1011 1.67 X 1011 0.35 25.5 X 10 8 15.2 X 10 8

21

Sheet, ann.

4.48 X 1011 1.67 X 1011 0.35 22.7 X

10 8 10 8

12.4 X

10 8

16

48

Sheet, hard rolled

4.48 X 1011 1.67 X 1011 0.35 25.5 X

19.3 X

10 8

7

56

Sheet, as fabricated Extruded bars, rods, or shapes, as fabricated

4.48 X 1011 1.67 X 1011 0.35 22.7 X ....... . . 4.48 X 1011 1.67 X 1011 0.35 30.3 X 10 8 20.7 X 10 8

"

..

. ........

14

60

13.1 X 10 8

14 14

Extruded bars, rods, or shapes, as fabricated

4.48 X 1011 1.67 X 1011 0.35 33.1 X 10 8 22.0 X 10 8

12

60

15.2 X 10 8

14

Extruded bars, rods, or shapes, aged

4.48 X 1011 1.67 X 1011 0.35 35.8 X 10 8 24.8 X 10 8

5

82

16.5 X 10 8

14

Extruded bars, rods, or shapes, as fabricated Zr, 0.3 other Extruded bars, rods, or shapes, aged

4.48 X 1011 1.67 X 1011 0.35 33.8 X 10 8 26.2 X 10 8

12

75

16.5 X 10 8

14

82

17.2X10 8

14

-,

10 8

4.48 X 1011 1.67 X 1011 0.35 35.1 X 10 8 28.9 X 10 8

10

TABLE

2e-14.

Alloy

ELASTIC AND STRENGTH CONSTANTS FOR NICKEL AND NICKEL ALLOYS

E

Condition

Yield strength at 0.2% offset

Tensile strength

C1

Elongation

Reduet.ion in area

Bhn

Shear strength

Ref.·

125

34-44 X 10 8

15

150

34-44 X

10 8

15

190 240

34-44 X 10 8 34-44 X 10 8

15 15

.......... ..........

15 15

--63-70 Ni, :::;2.5 Fe, :::;2.0 Mn, remainder Cu ................................. 63-70 Ni, :::;2.5 Fe, :::;2.0 Mn, remainder Cu ................................. 63-70 Ni, :::;2.5 Fe, :::;2.0 Mn, remainder Cu ................................. 63-70 Ni, :::;2.5 Fe, :::;2.0 Mn, remainder Cu 63-70 Ni, 2.0-4.0 AI, 0.25-1.0 Ti, remainder Cu ............................. 63-70 Ni, 2.0-4.0 AI, 0.25-1.0 Ti, remainder Cu 63-70 Ni, 2.0-4.0 AI, 0.25-1.0 Ti, remainder Cu ............................. 63-70 Ni, 2.0-4.0 AI, 0.25-1.0 Ti, remainder Cu ;:::99.0 Ni, :::;0.15 C, :::;0.35 Mn, :::;0.40 Fe ;:::99.0 Ni, ~0.15 C, :::;0.35 Mn, ~0.40 Fe ;:::99.0 Ni, ~0.15 C, ~0.35 Mn, :::;0040 Fe ;:::99.0 Ni, ~0.15 C, ~0.35 Mn, ~0.40 Fe

w-, w-,

ann. H.R.

Wr., cold drawn w-., C.R. (hard temper)

........... 17.9 X 1011

••

.0

0

51.7 X 10 8

24.1 X 10 8

••

10 8

10 8

35

. .... ...

68.9 X 75.8 X 10 8

10 8

55.1 X 68.9 X 10 8

25 5

. ....

•

........... ....

., .........

•

0

••

62.0 X

10 8

34.4 X

40

'"

'0 ' 0 '

H.R. H.R., age hardened

18 X 1011 0.32 18 X 10 11 ... .

68.9 X 10 8 103 X 10 8

31.0 X 10 8 75.8 X 10 8

40 25

.....

160 280

Cold drawn Cold drawn, age hardened Wr., ann. Wr., II.R. Wr., cold drawn Wr., cold rolled (hard temper) ;:::99.0 Ni, ~0.02 C .................... Ann. ;:::93.0 Ni, 4.00-4.75 AI, 0.25-1.0 Ti, :::;0.30 C .................................. H.R. ;:::93.0 Ni, 4.00-4.75 AI, 0.25-1.0 Ti, ~0.30 H.R., age hardened C ~93.0 Ni, 4.00-4.75 AI, 0.25-1.0 Ti, ~0.30 C .................................. Cold drawn ;:::93.0 Ni, 4.00-4.75 AI, 0.25-1.0 Ti, ~0.30 Cold drawn, age hardened C

18 X 10 11 . , .. 18 X 10 11

79.2 X 10 8 107 X 10 8

58.6 X 10 8 79.2 X 10 8

25 20

.....

210 290

21 X 1011 0.31

48.2 51. 7 65.4 72.3

10 8 10 8 10 8 10 8

40 40 25 5

.....

* References are on page 2-76.

•

0_.0

•••••••

........... .0

•••••••••

0

••

... . . , .. ... .

X X X X

10 8 10 8 10 8 10 8

13.8 17.2 48.2 65.4

X X X X

..... .....

.0

..

••••••••

"

...... 36 X 10 8

15 15

. ....

100 110 170 210

.......... . .........

15 15 15 15

. .... ••

'0'

•

••••••

0

••

21 X 10 11 0.31

41.3 X 10 8

10.3 X 10 8

50

.....

90

. .........

15

21 X 1011 0.31

72.3 X 10 8 117 X 10 8

34.4 X 10 8 89.6 X 10 8

35 15

.....

180 320

. ......... ..........

15 15

82.7 X 10 8 121 X 10 8

62.0 X 10 8 93.0 X 10 8

25 15

220 340

.......... . .........

15 15

........... . .. ,

........... ... .

...........

0"

•

•

••

..

'0

'"

'0'

••

TABLE

2e-14.

ELASTIC AND STRENGTH CONSTANTS FOR NICKEL AND NICKEL ALLOYS

Alloy

Ni, 14.0-17.0 Cr, 6.0-10.0 Fe, C ............................ 14.0-17.0 Cr, 6.0-10.0 Fe, ~72.0 Ni, ~0.15 C ............................ 14.0-17.0 Cr. 6.0-10.0 Fe, ~72.0 Ni, ~0.15 C ............... , ............ ~72.0 Ni, 14.0-17.0 Cr, 6.0-10.0 Fe, ~0.15 C 570.0 Ni, 14.0-16.0 Cr, 5.0-9.0 Fe, 2.252.75 Ti, 0.4-1.0 AI. 0.7-1.2 Cb (+Ta) .. ~70.0 Ni, 14.0-16.0 Cr, 5.0-9.0 Fe. 2.252.75 Ti, 0.4-1.0 AI, 0.7-1.2 Cb (+Ta) 63 Ni, 30 Cu, 4 Si, 2 Fe + .............. 'l7 Ni, 20 Mo, 20 Fe + ................. 62 Ni, 30 Mo, 5 Fe + .................. 58 Ni, 17 Mo, 15 Cr, 5 W, 5 Fe + ....... 85 Ni, 10 Si, 3 Cu + ................... 80 Ni. 14 Cr, 6 Fe + ................... 58 Ni, 22 Cr, 6 Cu, 6 Mo, 6 Fe .......... 80 Ni, 20 Cr + ........................

Condition

~72.0

~0.15

...References are on p, 1-76.

a

E

Tensile strength

Yield strength at 0.2% offset

58.6 X 10 8

(Continued)

Elongation

Reduction in area

Bhn

Shear strength

Ref....

24.1 X 10 8

45

.....

150

..0 .......

15

. .........

IS

Wr., ann.

...........

w-,

H.R.

........... .. ..

68.9 X 10 8

41.3 X 10 8

35

. .. 0.

180

Wr., cold drawn Wr., C.R. (hard temper)

......... ........... ....

79.2 X 10 8 93.0 X 10 8

62.0 X 10 8 75.8 X 10 8

20 5

. ..

200 260

..

79.2 X 10 8 124 X 10 8

34.4 X 10 8 82.7 X 10 8

50 25

.. ,-.

Ann. H.R., age hardened Sand cast Ann. Rolled, ann. Ann. plate Sand cast Ann. Sand cast Ann.

"

21 X 1011 21 X 1011 14.5 18.6 21.19 19.6 19.88 21 18.38 21

X X X X X X X X

1011 1011 1011 1011 1011 1011 1011 1011

•

0.0

0,

"

••

.... '0

"

o.

..

.... .... .... '0

••

.... .. ..

55-79 X 10 8 10 8 10 8 32.4-36 X 10 8 41-45 X 10 8 10 8 38-45 X 10 8 10 8 10 8 ............ ............ 19.3 X 10 8 41-50 X 10 8 65.4 X 10 8 ............

76-100 76-83 90-96 79-88 25-27.9

X X X X X

••••••••••

'0

1-4 40-48 40-45 25-50 0

•••••

·0

••••

4-9.5 25-35

..

..

"

'"

'"

200 360

'0 • • • • • • • • .0

••••••••

.0

••••••••

. ......... . ......... . .........

.....

. ....

275-350 200-215 210-235 160-210

. ....

. ....... . .......

. .........

8-11 55

160-210 RB85-90

. .........

••

"0

40-54 40-45

. .........

•

•••••••

0'

41.9 X 10 8 .0

••••••••

15 15

15 15 1 1 1 1 1 1 1 1

TABLE 2e-15. ELASTIC AND STRENGTH CONSTANTS FOR TIN AND TIN ALLOYS

Alloy

Condition

Pure tin ................ Pure tin ................ Pure tin ................ 99.8 Sn ] ............... 99.8 Sn ] ...............

Cast Chill cast O.I-in. sheet, ann. Cast Ann., 0.040-in. sheet Cast 0.040-in. sheet, aged at room temp. Cast Cast Chill cast Chill cast

95 Sn, 5 Sb ............. 95 Sn, 5 Ag............. 70 Sn, 30 Pb ............ 63 Sn, 37 Pb ............ 91 Sn, 4.5 Sb, 4.5 Cu .... 83.4 Sn, 8.3 Sb, 8.3 Cu ... '" References are on p. 2-76. t % in 4 in. tAt 0.3 % offset.

E

C1

Tensile strength

4.1-4.5 X 1011 . , .. 2.14 X ........................ ..... . 1.45 X .............. . ..... 1.65 X 4.13 X 1011 . .. 1.45 X 4.13 X 1011 0.33 1.52 X

................

Elongation

Bhn

Shear strength

Ref. *

. ..... . ......

2.00 X 108 . .......... . .........

............

55 69 96 54t 45

. ...... Vhn 7.2

0.896 X 10 8

1 1 1 1 1

............. . . 4.06 X 108 . ......... .............. . " . 3.17 X 108 2.48 X 10 8

38t 49

. ...... ...... .

4.13 X 108 . .........

1 1

............. ... . ............. . , .. 5.03 X 1011 .... ............. . . " .

.. . 32t

. .........

1 1 1 1

,

10 8 108 10 8 10 8 10 8

Yield strength at 0.2% offset

. ........... . ........... .

................

"

4.68 X 108 . .......... 5.17 X 10 8 . ......... 6.41 X 10 8 4.34 X 10 8 f . ........ 5.51 X 10 8 f

. .. . ..

5.3

12 14 17 27

...........

4.27 X 108 . ......... ..........

2-76 TABLE

MECHANICS

2e-16.

ELASTIC AND STRENGTH CONSTANTS FOR ZINC AND ZINC ALLOYS

Alloy

Condition

Tensile strength

3.5-4.3 AI, 0.03-0.08 Mg . . . . . . Die cast, ~-in. 28 X 10 8 section 3.5-4.3 AI, 0.75-1.25 Cu, 0.03--0.08 Die cast, ~-in. 33 X 10 8 Mg section 35.9 X"l08 3.5-4.5 AI, 2.5-3.5 Cu, 0.02--0.10 Die cast, ~-in. Mg section 4.5-5.0 AI, 0.2-0.3 Cu ........ Chill cast, ~19 X 10 8 in. section 5.25-5.75 AI. . . . . . . . . . . . . . . . . Chill cast, ~217 X 10 8 in. section ~0.10 Pb ................... H.R. strip 13.4-16 X 10 8 0.05-0.10 Pb, 0.05--0.08 Cd ...... H.R. strip 14-17 X 10 8 0.25-0.50 Pb, 0.25-0.45 Cd ...... H.R. strip 16-20 X 10 8 0.85-1.25 Cu ................. H.R. strip 16-22 X 10 8 0.85-1.25 Cu, 0.006-0.016 Mg ... H.R. strip 19-25 X 10 8

* References are

Elongation, % in 2 in.

Bhn

Shear strength

Ref.·

10

82

21 X 10 8

1

7

91

26 X 10 8

1

8

100

32 X 10 8

1

. ....

...

.......

1

1

...

.......

1

50-65 30-52 32-50 15-20 10-20

38 43 47 52 61

....... .......

1 1 1 1 1

•••• '0. ••••

0

••

.......

below.

References for Tables 2e-7 through 2e-16 1. "Metals Handbook," 1948 ed., American Society for Metals. 2. Nail. Bur. Standards (U.S.) Cire. C447, 1943. 3. Bain, E. C.: "Functions of the Alloying Elements in Steel," American Society for Metals, 1939. 4. Hoyt, S. L.: "Metals and Alloys Data Book" Reinhold Book Corporation, New York, 1943. 5. "Selection of Special Steels, Data Sheet," D.T.A. 72, Societe de Commentry, Paris, France, 1946. 6. Halley, J. W.: Pat. 2,402,135, 1946. 7. "Nickel Alloy Steel," 2d ed., The International Nickel ce., Inc., New York, 1949. 8. "Fox Alloy Steels," Samuel Fox and Co. Ltd., Sheffield, England, 1942. 9. "Case Hardening of Nickel Alloy Steels," International Nickel Co., New York, 1941. 10. Everett, F. L., and J. Miklowitz: J. Appl. Phys. 15 (1944). 11. Climax Molybdenum Company Laboratory Records. 12. "Sheet Iron, a Primer," Republic Steel Corp., 1934. 13. Comstock, G. F.: J. Am. Ceram, Soc. 29 (1946). 14. "Magnesium Alloys and Products," Dow Chemical Co., 1950. 15. "Nickel," The International Nickel Co., Inc., rev. 1951.

ELASTICITY, HARDNESS, AND STRENGTH OF SOLIDS

2-77

TABLE 2e-17. DIFFUSION COEFFICIENTS FOR METALS Metal

Test temp.

Ag into Ag .............................. Ag into Ag .............................. Ag into Ag .............................. Ag into Ag .................. , ........... Ag into Ag ............. " .......... " ... Ag into Ag ........ , ............. , ....... Al into Cu ............... , .. " " ... , .... Au into Au .............................. Au into Cu ...................... , ....... Be into Cu ........... " ......... , .... " . Bi into Ph ........ , ..................... Cd into Cu .................. , ........... Cd into Ag .............................. Cd into Ph .............................. Cl- into NaCI single crystals .............. Cl- into NaCI single crystals .............. Cl- into NaCI single crystals .............. Cl- into NaCl single crystals .............. Cl- into-NaCl single crystals .............. Cu into Cu .............................. Cu into Cu .............................. Cu into Cu .............................. Cu into Cu .............................. Cu into CuO ............. , .......... " .. Cu into CuO ............................ Cu into CuO ............................ Cu into Ag ........ " ., ... , .............. In into In ............................... In into In ......... , ..................... In into In ......... , ..................... In into In ............................... In into In ............................... In into In ......... , " ........... , ....... In into Ag .............................. Liq. Hg into liq. Hg ...................... Liq. Hg into liq. Hg ...................... Lig. Hg into liq. Hg ...................... Liq. Hg into liq. Hg ...................... Liq. Hg into liq. Hg ...................... Liq. Hg into liq. Hg ...................... Liq. Hg into liq. Hg .......... " .......... Mn into Cu ............................ Ni into Cu .............................. Ni into Ph .............................. Pd into Cu ..............................

Room 460°C 600°C 666°C 794°C 936°C Room Room Room Room Room Room Room Room 650°C 681°C 703°C 735°C 762°C Room 700°C 900°C 1000°C 800°C 900°C 1000°C Room 49.95°C 87.25°C 155.50°C 155.81°C 156.60°C 157.30°C Room 2.5°C 16.4°C 23.0°C 31.9°C 41.5°C 66.1°C 91.2°C Room Room Room Room

2

D (cm sec

)

0.895 8.0 X 10- 14 5.9 X 10- 12 2.45 X 10- 11 3.64 X 10- 10 4.61 X 10- 9 1. 75 X 10- 2 0.160 0.1 ± 0.06 2.32 X 10- 4 0.018 1.97 X 10- 9 7.3 X 10- 6 1.8 X 10- 3 7.25 X 10- 11 2.84 X 10- 10 6.76 X 10- 10 1.67 X 10- 9 2.52 X 10- 9 0.1-47 4.06 X 10- 12 3.58 X 10- 10 1.95 X 10- 9 0.19 X 10- 8 0.77 X 10- 8 3.2 X 10- 8 5.95 X 10- 6 7-8.5 X 10-13 1.4-1.5 X 10- 11 1.14 X 10- 9 1. 70 X 10- 7 6.52 X 10- 6 1.23 X 10- 6 4.85 X 10- 5 1.52 X 10- 6 1.68 X 10- 6 1. 79 X 10- 5 1.88 X 10- 6 1.98 X 10- 5 2.24 X 10- 5 2.57 X 10- 5 0.72 X 10- 5 6.5 X 10- 6 0.66 0.16 X 10- 5

Ref. 1 11 11 2 2 2 1 3 4 1 3 3 3 3 5 5 5 5 5

1 7 7 7 6 6 6 1 9 9 9 9 9 9 1 8 8 8 8 8 8 8 1

1 1 1

2-78

MECHANICS

TABLE 2e-17. DIFFUSION COEFFICIENTS FOR METALS (Continued) Test temp.

Metal Pt into Cu " Ph into Ph , Sh into Ag " Si into ferrite. . . . . . . . . . Si into Cu Sn into Ag Sn into Cu Sn into Ph Ti into In Ti into In. '" Ti into In Ti into In Ti into In Ti into In Ti into In Ti into Ph N. B. of H.

.

. Room . Room Room . . 1435 ± 5°C . Room . Room Room '" Room . . 49.27°0 74.19°C . . 101.55°C . 139.16°0 155.60°0 . . 155.91°0 . 157.80°0 . Room

The values quoted from ref. 1 are for Do in the equation D =

2

D (cm sec

)

1.02 X 10- 4 6.6 5.31 X 10- 6 1.1 X 10- 7 3.7 X 10- 2 7.82 X 10- 6 1.13 3.96 1.4 X 10- 12 9.2 X 10- 12 4.6-4.8 X 10- 11 2.8-3.2 X 10- 10 2.17 X 10- 9 1.87 X 10- 7 2.27 X 10- 6 0.025 Doe-BIRT.

1 1 1

10 1 1 1

1 9 9 9 9 9 9 9 1

Cf. ref. 1 for value.

References for Table 2e-17 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.

Ref.

Nowick, A. S.: J. Appl. Phys. 22, 1182 (1951). Slifkin, L., D. Lazarus, and T. Tomizuka: J. Appl. Phys. 23, 1032 (1952). Smithells, C. J.: "Metals Reference Book." Martin, A. B., and F. Asaro: Phys. Rev. 80, 123A (1950). Chemla, Marius: Compt. rend. 234, 2601 (1952). Moore, W. J., and Bernard Selikson: J. Chem, Phys. 19, 1539 (1951). Cohen, G., and G. C. Kuczynski: J. Appl. Phys. 21, 1339L (1950). Hoffman, R. E.: J. Chern. Phys. 20, 1567 (1951). Eckert, R. E., and H. G. Drickamer: J. Chern. Phys. 20, 13 (1951). Bradshaw, F. J., G. Hoyle, and K. Speight: Nature 171,488 (1953). Kuczynski, G. C.: J. Appl. Ph1Js. 21, 632 (1950).

ELASTICITY, HARDNESS, AND STRENGTH OF SOLIDS

2-79

7. Rockwell Hardness Number.) itA hardness value indicated on a direct-reading dial when a designated load is imposed on a metallic material in the Rockwell hardness testing machine using a steel ball or a diamond penetrator. The value must be qualified by reference to the load and penetrator used. Several scales are in common use: Rockwell A hardness is determined with a minor load of 10 kg and a major load of 60 kg using the diamond cone (brale): Rockwell B hardness is determined with a minor load of 10 kg and a major load of 100 kg using a T\-in. steel ball; Rockwell C hardness is determined with a minor load of 10 kg and a major load of 150 kg using the diamond cone"; Rockwell D hardness is determined with a minor load of 10 kg and a major load of 100 kg using a diamond cone indenter; Rockwell E hardness is determined with a minor load of 10 kg and a major load of 100 kg using a t-in. steel ball indenter; Rockwell F hardness is determined with a minor load of 10 kg and a major load of 60 kg using a T\-in. steel ball; Rockwell G hardness is determined with a minor load of 10 kg and a major load of 150 kg, using a fir-in. steel ball indenter. A second set of Rockwell hardness numbers are the Rockwell superficial hardness numbers. One of these is the Rockwell 15T hardness, which is determined with a minor load of 3 kg and a major load of 15 kg, using a frin. steel ball. Note: The methods of determining the hardness values can be found in Standard Methods of Test for Rockwell Hardness and Rockwell Superficial Hardness of Metallic Materials, ASTM EI8-42.

8. Brinell Hardness Number.' "A hard spherical indenter of diameter D mm is pressed into the metal surface under a load W kg and the mean chordal diameter of the resultant indentation measured (d mm). The Brinell hardness number (Bhn) is defined as Bhn =

W.. curved area of indentation 2W 'lrD(D - VD' - d')

and is expressed in kg/mm",' 9. Vickers Hardness Number.' itA pyramidal diamond indenter is pressed into the surface of a metal under a load of W kg and the mean diagonal of the resultant indentation measured (d rnm ). The Vickers hardness number (Vhn ), or Vickers diamond hardness (Vdh), is defined as W Vdh (or Vhn) = pyrami'd a1 area 0 f'III d en t anon . The indenter has an angle of 136 0 between opposite faces and 146 0 between opposite edges. From simple geometry, this means that the pyramidal area of the indentation is greater than the projected area of the indentation by the ratio 1:0.9272. Hence Vdh

0.9272W projected area of indentation = 1.8544W/d'

The value is expressed in kg/mm'." 10. Diffusion Coefficient. If the concentration (mass of solid per unit volume of solution) at one surface of a layer of liquid is d l , and at the other surface d., the thickness of the layer is h, the area under consideration is A, and the mass of a given substance which diffuses through the cross section A in time t is m, then the diffusion coe fficient is defined as

J. G. Henderson. "Metallurgical Dictionary." • D. Tabor, "The Hardness of Metals."

1

2-80

MECHANICS

2e-4. Effect of High Pressure on the Specific Volume of Solids. Tables 2e-18 to 2e-22 present data on the change of specific volume of certain solids as a result of the imposition of very high pressure. The general reference in this field is P. W. Bridgman, "The Physics of High Pressure," G. Bell & Sons, Ltd, London, 1949. Specific references are attached to each table. TABLE 2e-18. VOLUME OF SOLID HELIUM AT OOK* Pressure, kgjcm 2

Volume, ml /mole

Compressibility (ljv) (avjap).,.

52 91 141 207 305 475 718 1,105 1,715 2,240

19.0 18.0 17.0 16.0 15.0 14.0 13.0 12.0 11.0 10.5

184 X 10-6 135 100 73 52 37 25 16 12 10

• ,J. 8. Dugdale and F. E. Simon, Proe, Ro'U. Soc. (London) 218,291 (1953).

TABLE 2e-19. FRACTIONAL CHANGE OF VOLUME AT 25°C OF RELATIVELY INCOMPRESSIBLE METALS* Pressure, kgjcm 2

5,000 10,000 15,000 20,000 25,000 30,000

AVjVo

W

Pt

0.00155 0.00309 0.00475 0.00634 0.00797 0.00959

0.00176 0.00351 0.00526 0.00701 0.00877 0.01048

Fe 0.00289 0.00575 0.00856 0.01133 0.01407 0.01676

Cu

Ag

Au

AI

0.00353 0.00696 0.01039 0.01370 0.01695 0.02010

0.00473 0.00938 0.01385 0.01820 0.02236 0.02619

0.00281 0.00558 0.00831 0.01101 0.01367 0.01626

0.00668 0.01312 0.01932 0.02520 0.03090 0.03642

• P. W. Bridgman, Proe, Am. Acad. Arts Sci. 77. 187 (1949).

2-81

ELASTICITY, HARDNESS, AND STRENGTH OF SOLIDS TABLE

2e-20.

RELATIVE VOLUMES OF VARIOUS SOLIDS AT

Pressure, kg/cm 2

Lucite

Cellulose acetate

Bakelite

Hard rubber

Nylon

1 2,500 5,000 10,000 15,000 20,000 30,000 40,000

1.0000 0.9633 0.9329 0.8903 0.8613 0.8329 0.8051 0.7816

1.0000 0.9532 0.9216 0.8811 0.8514 0.8283 0.7935 0.7682

1.0000 0.9760 0.9562 0.9240 0.8978 0.8765 0.8436 0.8188

1.0000 0.9684 0.9390 0.8955 0.8655 0.8427 0.8083 0.7834

1.0000 0.9615 0.9345 0.8940 0.8652 0.8430 0.8100 0.7861

Pressure, kg /cm!

1 5.000 10,000 15,000 20,000 30,000 40,000

6-10

Calcite

Garnet

Iodoform

Urea nitrate

1.0000

1.0000

0.9866 tr. 0.9275 0.9113 0.8981

0.9929

1.0000 0.9451 0.9079 0.8806 0.8586 0.8241 0.7966

1.0000 0.9628 0.9358 0.9145 0.8966 0.8669 0.8431

..... .

......

......

0.9862 0.9800 0.9743

...P. W. Bridgman. Proe, Am. Acad. Arts Sci. 16,71 (1948).

25°C*

Teflon

1.0000 0.9473 0.9153 0.8547 0.8306 0.8125 0.7857 10.7661

Orthoclase

1.0000 0.9829 0.9667 0.9512 0.9366

Potassium Potassium phosphate alum

1.0000 0.9821 0.9665 0.9526 0.9401 0.9183 0.9004

1.0000 0.9718 0.9486 0.9296 0.9131 0.8843 0.8607

2-82

MECHANICS

TABLE 2e-21. RELaTIVE VOLUMES OF SOME OF THE MORE COMPRESSIBLE ELEMENTS, SALTS, AND OTHER SOLIDS AT 25°C* In Tables 2e-21 and 2e-22 the symbol tr denotes a phase transition Pressure, kg/em-

Li

Na

K

- -- -

I

10,000 20,000 30,000 40,000 50,000 60,000 70,000 80,000 90,000 100,000

* P.

1.000 0.928 0.874 0.833 0.801 0.773 0.748 0.727 0.707 0.689 0.672

1.000 0.889 0.816 0.770 0.737 0.708 0.683 0.661 0.641 0.623 0.606

1.000 0.814 0.723 0.668 0.628 0.595 0.568 0.546 0.528 0.513 0.500

Cs

Ca

Sr

Ba

C

~--

~--

---

---

--

1.000 0.925 0.878tr 0.828 0.791 0.761 0.734tr 0.702 0.683 0.665 0.648

1.000 0.914tr 0.841 tr 0.789 0.747 0.712tr 0.682 0.639 0.618 0.598 0.580

1.000

Rb --

1.000 0.802 0.708 0.652 0.612 0.578 0.551 0.528 0.507 0.489 0.473

1.000 0.761 0.656tr 0.571 0.521 tr 0.431 0.409 0.392 0.381 0.375 0.368

1.000 0.942 0.897 0.861 0.832 0.805 0.780 t r 0.748 0.732 0.716 0.702

0.940 0.929 0.919 0.911 0.P-03 0.896 0.890 0.885

W. Bridgman, Proc. Am. Acad. Arts Sci. 76, 55, 71 (1948); 74, 425 (1942).

TABLE 2e-22. RELATIVE VOLUMES OF SOLIDS AT 25°C* Pressure, kg/ernI

10,000 20,000 30,000 40,000 50,000 60,000 70,000 80,000 90,000 100,000

Mg

1

Sn

Pb

Bi

I

S

NaCl

NaI

- -- - --- - -- ---1.000 1.000 1.000 1.000 1.000 1.000 1.000 ..... 0.982 0.978 0.972 0.917 0.962 0.944 ..... 0.966 0.959 0.948tr 0.869 0.932 0.902 0.935 0.951 0.941 0.842 0.837 0.907 0.868 0.919 0.936 0.925 0.826tr 0.812 0.885 0.840 0.904 0.923 0.901 0.808 0.792 0.865 0.816 0.890 0.909 0.898 0.795tr 0.775 0.848 0.795 0.878 0.897 0.885 0.778 0.760 0.832 0.777 0.866 0.886 0.874 0.768 0.747 0.817 0.761 0.856 0.875 0.864 0.760tr 0.736 0.803 0.747 0.847 0.864 0.855 0.739 0.726 0.790 0.734

CsCI

CsI

---

----

1.000 0.952 0.914 0.882 0.856 0.834 0.816 0.801 0.788 0.777 0.767

1.000 0.935 0.887 0.849 0.818 0.792 0.770 0.751 0.734 0.719 0.706

I

1

kg/em!

NaNO a

PbS

PbTe

Quartz crystal

Quartz glass'

Pyrex glass

1 10,000 20,000 30,000 40,000 50,000 60,000 70,000 80,000 90,000 100,000

1.000 0.966 0.938 0.914 0.893 0.873 0.846t r 0.833 0.820 0.809 0.799

1.000 0.980 0.962t r 0.928 0.918 0.909 0.900 0.892 0.886 0.881 0.876

1.000 0.978 0.961 0.939 0.930t r 0.884 0.869 0.855 0.842 0.831 0.820

1.000 0.976 0.955 0.939 0.926 0.914 0.902 0.892 0.883 0.875 0.868

1.000 0.970 0.939 0.909 0.885 0.864 0.847 0.832 0.819 0.808 0.798

1.000 0.969 0.938 0.907 0.885 0.867 0.851 0.838 0.827 0.817 0.809

Pressure,

*P. W. Bridgman, Proc. Am. Acad. Arts Sci. 76, 55,71 (1948); 74,425 (1942).

2f. Viscosity of Solids EVAN A. DAVIS

Westinghouse Research Laboratory

Symbols

E t T u'

elastic modulus time absolute temperature elastic strain rate u" plastic strain rate 5 logarithmic decrement E' elastic strain E" plastic strain 17 viscosity (T stress 2f-1. Anelasticity. A perfectly elastic solid is truly an ideal material. Actual materials contain structural imperfections which prohibit them from behaving in a perfectly elastic manner. Even when the stresses are low enough to ensure that no perceptible permanent deformation takes place the total strain is made up of a purely elastic part that is directly proportional to the load and a time-dependent but fully recoverable part that will vary with the rate of loading and the duration of the load. The behavior associated with the E, time-dependent part of the strain has been called "anelasticity" by Zener,' who has endeavored to explain this behavior in terms of the atomic arrangement and the microstructure of the material. Anelastic behavior is observed in many ways, depending upon the manner in which the material is loaded. Its effect may be referred to as elastic hysteresis, internal friction, clastic aftereffect, specific damping capacity, or dynamic Ez and static moduli of elasticity. The fact that the term anelasticity has been limited to the region of no permanent deformation does not exclude the existence of such behavior at higher stresses. When a material deforms permanently, however, the anelastic effects are overshadowed by and engulfed in the plastic behavior. FIG. 2f-1. Mechanical In the realm of small deformations a metal or a plastic model for demonstratcan be represented qualitatively by the mechanical model of ing anelastic and creep springs and dashpots shown in Fig. 2f-1. For the anelastic behavior of solids. ! C. Zener, "Elasticity and Anelasticity of Metals," University of Chicago Press, Chicago, 1948.

2-83

2-84

MECHANICS

behavior at low stresses the viscosity '71 of the upper dashpot can be considered as infinite. The spring with the elastic modulus E 1 contributes the purely elastic strain. The time-dependent part of the strain comes from the parallel arrangement of spring E 2 and dashpot '72. This model will exhibit, though not in a quantitative manner, the various anelastic effects of solids. If the unit is elongated at a slow rate, dashpot '72 will have little effect in resisting the deformation of spring E 2 • The static or isothermal modulus of elasticity will be that of springs E 1 and E 2 connected in series. If the unit is elongated rapidly dashpot '72 will tend to act as a rigid mechanism. The dynamic or adiabatic modulus of elasticity will be that of spring E 1 acting alone. If the unit is put through a constant-rate loading and unloading cycle a hysteresis loop will be traced out in the stress-strain diagram. The area of the loop will be proportional to the amount of energy dissipated in dashpot '72. If the unit is loaded slowly and then unloaded rapidly the strain will not immediately return to zero. What appears to be a permanent strain or elastic aftereffect will be observed. The strain will return to zero when the stress trapped in the spring E 2 by dashpot '72 has been relaxed. If the mass is attached to the lower end of the unit and the entire mechanism is allowed to vibrate freely the amplitude of vibration will decrease with each cycle. The decrease in amplitude of vibration is due to the dissipation of energy in dashpot '72. If the springs are linear and elastic and the dashpot behaves in a perfectly viscous manner the ratio of the decrease in amplitude for any given cycle to the amplitude at the beginning of the cycle will be a constant. This constant is called the logarithmic decrement 0, and it is probably the most-used measure of the anelastic behavior of materials. The logarithmic decrement of actual materials is relatively high for dielectric materials and low for metals. Since this quantity depends upon imperfections in the atomic structure it will vary with such factors as heat-treatment, grain size, or the amount of cold working, and it will be impossible to assign a value to a specific material such as steel. The values listed by Kimball! and shown in Table 2f-l and those listed by Gemant> and shown in Table 2f-2 are to be considered as representative values which give the order of magnitude of the decrement or internal friction. The factors which affect the logarithmic decrement are discussed in detail by Zener and by Gemant. The decrement is influenced by such factors as frequency, temperature, amplitude, elastic modulus, grain size, annealing temperature, and aging time. In general there is not much change in decrement with frequency. Gemant and Jackson- found slight increases in the decrement of ebonite and glass over rather narrow frequency ranges (Fig. 2f-2). Gemant shows a slight increase in the decrement for paraffin wax and a slight decrease in the decrement for steel (Fig. 2f-3). An exception to this rule was found by Rinehart," who reported an appreciable increase in the decrement of Lucite at room temperature (Fig. 2f-4). Certain materials show steep peaks in the log decrement vs. log frequency curve. These peaks are associated with frequencies that correspond to the reciprocal of some characteristic time for the material. Such a curve, taken from Gemant and based on the work of Zener and Bennewitz and Rotger,> is shown in Fig. 2f-5. In this case the peak in the internal-friction curve is due to the diffusion of heat from parts heated by compression to parts cooled by tensile stresses. 1 A. L. Kimball, "Vibration Prevention in Engineering," John Wiley & Sons, Inc., New York, 1932. 2 A. Gemant, "Frictional Phenomena," Chemical Publishing Company, Inc., New York, 1950. 3 A. Gemant and W. Jackson, Phil. Mag. 23, 960 (1937). 4 J. S. Rinehart, J. Appl. Phys. 12, 811 (1941). 5 K. Bennewitz and H. R6tger, Z. tech. Phys. 19, 521 (1938).

2-85

VISCOSITY OF SOLIDS TABLE 2f~1. LOGARITHMIC DECREMENTS FOR VARIOUS MATERIALS*

Logarithmic Decrement ~ M aierial Phosphor bronze, cold rolled. . . . . . . . . . . . 0.37 X 10-3 Monel, cold rolled. . . . . . . . . . . . . . . . . . . . . 1.43 Nickel steel, 3}% swaged. . . . . . . . . . . . . . 2.3 Nickel, cold rolled. . . . . . . . . . . . . . . . . . . . . 3.2 Phosphor bronze, annealed. . . . . . . . . . . . . 3.2 Aluminum, cold rolled. . . . . . . . . . . . . . . . . 3.4 Brass, cold rolled. . . . . . . . . . . . . . . . . . . . . . 4. 8 Mild steel, cold rolled. . . . . . . . . . . . . . . . . . 4. 9 5.0 Copper, cold rolled. . . . . . . . . . . . . . . . . . . . Glass.... . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4 Molybdenum, swaged......... .. . . .. .. . 6.9 Swedish iron, annealed. . . . . . . . . . . . . . . . . 7. 9 Tungsten, swaged. . . . . . . . . . . . . . . . . . . .. 16.5 Zinc, swaged. . . . . . . . . . . . . . . . . . . . . . . . . . 20 Maple wood , , ... 22 Celluloid " 45 Tin, swaged. . . . . . . . . . . . . . . . . . . . . . . . .. 129 Rubber, 90% pure " 260

* A. L.

Kimball, "Vibration Prevention in Engineering," John Wiley & Sons, Inc., New- York, 1932.

TABLE

2f-2.

LOGARITHMIC DECREMENT OF VARIOUS MATERIALS·

Material ,

Steel Quartz Copper Lead glass Wood Polystyrene Ebonite Paraffin wax

Logarithmic Decrement ~ 0.6 X 10-3 2.6 3.2 4.2 27

,. ,. . ,. . . 48 . 85 . 150

* A. Gemant, "Frictional Phenomena," Chemical Publishing Company, Inc.,

New York, 1950.

The logarithmic decrement usually increases with increasing temperature. The viscous behavior changes more rapidly than the elastic properties with temperature, with the result that at higher temperatures more energy is dissipated in the dashpot. The decrement does not vary greatly with amplitude when the amplitudes are small. The decrement increases at higher amplitudes. This is evidence that the viscosity of materials is not of a pure viscous nature. The rate of strain increases more rapidly at the higher stresses than the linear viscous law would predict. Materials with high elastic moduli have lower decrements than those with low moduli. There is some evidence to show that the product of the elastic modulus and the decrement is nearly a constant value. The damping capacity of a structure depends upon the stress distribution in the structural members and the energy absorption characteristics of the material from which the members are made. This energy absorption may be brought about by

2-86

MECHANICS

plastic flow, thermoelastic effect, magnetoelastic effect, and atomic diffusion. The relative importance of these effects will depend upon the magnitude of the vibratory stresses.! 2£-2. Creep. When a material is subjected to the proper combination of high stress and temperature, it will deform permanently. A representative behavior will be produced by the model shown in Fig. 2f-1 if the viscosity of both dashpots 'II and '12 is finite. The continuing deformation of a material under a constant load is called

o

~200

Ebonite (Torstcncl}

E Q) t; 100

-

XIO'

Q)

o ~

-

0

Glass (Flexural) - LO

-0.5

0

0.5

1.0

2.5 3.0 3.5 Logarithm of Frequency

Logarithm of Frequency, Hz FIG. 2f-2. Logarithmic decrement vs. loga-

FIG. 2f-3. Logarithmic decrement vs, fre-

rithm of frequency for ebonite and glass. (Gemant and Jackson.i

quency at room temperature for steel and paraffin wax. (Gemant.)

40

50

60

Frequency, k Hz

70

10

Frequency, Hz

FIG. 2f-4. Logarithmic decrement vs, fre-

FIG. 2f-5. Logarithmic decrement vs, fre-

quency for Lucite at 26°C.

quency for German silver. (Measured points after Bennemitz and Rotger; theoretical curve after Zener.)

(Rinehart.)

"creep." It the model is loaded with a given load at t = 0, there will be an instantaneous elastic deflection .' of spring E I , dashpot '11 will deform at some constant rate u~', and dashpot '12 will deform at a decreasing rate.' The rate of strain in dashpot '12 1 This problem was discussed in detail during the early 1950s. See, for example, the following papers and their reference lists: B. J. Lazan, J. Appl. Meeh., Trans. ASME 75 (1953); A. W. Cochardt, J. Appl. Meeh., Trans. ASME 76 (1954). 2 A prime (') on a strain or strain rate indicates elastic deformation; a double prime (n) indicates plastic or permanent strain. The total strain, or strain rate, is the sum of the elastic and the plastic parts; i.e.,

e=e'+E"

or

2-87

VIS.cOSITY OF SOLIDS

decreases because the load is gradually transferred to spring E 2 as the deformation takes place, and this part of the deformation stops at a strain E~' when the spring E 2 carries the complete load. The creep curve for the model and for materials which are not stressed high enough to cause fracture will have the form shown in Fig. 2f-6 (the elastic strain E' is not shown). The plastic strain starts at a rapid rate but approaches the asymptotic value given by (2f-l) E" = E~' u~'t

+

The shape of the initial part of the creep curve or the manner in which the curve approaches the asymptote has been studied by Andrade! and by McVetty.! Andrade

t-Time

FIG. 2f-6. Typical creep curve.

found that the increase of strain during the first part of the test was proportional to the cube root of the time. (2f-2) i' = ptl

Me Vetty used an exponential relationship to describe the initial deformation. E"

= E~' (1 -

e- a t )

+ u~'t

(2f-3)

When creep tests are made to obtain design data for equipment having long service life, and most of the early creep tests were made under these conditions, the major part of the strain is accounted for by the u~'t term in Eq. (2f-l). The important relationship to be established, then, is that between the minimum creep rate u~' and the stress 0", and this is the only information reported by many investigations. If shorter service times are considered, the initial part of the creep curve becomes more important, and it becomes desirable to know the relationship between the plastic intercept E~' and the stress 0". Mc Vetty shows a plot of this relationship for the lower stress range where a power function or hyperbolic sine relationship would be suitable. or

E"

o

= B sinh !!-

(2f-4)

0"0

Such relationships indicate that, if the model of Fig. 2f-l is to represent actual materials, spring E 2 must be nonlinear. At higher stresses these relationships do not hold. 1 2

E. N. da C. Andrade, Proc. Roy. Soc. (London), ser. A, 84, 1 (1911); 90, 329 (1914). P. G. l\lcVetty, Mech. Eng. 56, 149 (March, 1934).

2-88

MECHANICS

TABLE 2£-3. CREEP RATES FOR VARIOUS MATERIALS* Temp Material and composition

Condition

Aluminum copper alloy, Cu 4.25, i diam rod, wrought, Mn 0.63, Mg 0.44, Fe 0.52, Si aged 0.25 Aluminum silicon alloy, Si 13.18, Wrought Ni 3.08, Cu 2.96, Mg 1.04, Fe 0.53 Fully annealed Electrocopper -f diam rod, cold Deoxidized copper drawn, annealed Copper nickel alloy, Ni 20.0, Zn -f diam rod, cold drawn, annealed at 5.08, Mn 0.69 1200°F Copper tin alloy, Sn 5.99, Zn 5.10, Cast Pb 2.33, Ni 0.23, Fe 0.06 Copper zinc alloy, Cu 96.43, Pb diam wire, drawn, fine-grained 0.05, Fe 0.01, Zn remainder

t

Carbon steel, C 0.15, Mn 0.46, Si 1 in. diam bar, wrought, annealed at 0.28 (basic open hearth) 1500°F, grain size 5-6 ASTM Carbon steel, C 0.15, Mn 0.50, Si 1 in. diam bar, wrought, annealed at 0.23 (basic electric furnace) 1550°F, grain size 4-5 ASTM Chromium steel, C 0.10, Cr 5.09, 1 in. diarn bar, wrought, annealed at Mo 0.55, Mn 0.45, Si 0.18 1550°F, grain size 4-5 ASTM Molybdenum steel, C 0.22, Mo Bar Ii sq. cast, 1.06, Mn 0.50, Si 0.13 (induc- annealed at 1650°F, tion furnace) grain size 7 Nickel steel, C 0.36, Ni 1.19, Mn 1 in. diam bar, hot 0.58, Cr 0.51, Mo 0.51, Si 0.22 rolled, normalized at (induction furnace) 1600°F, tempered 3 hr at 1250°F Grade 2 Lead Magnesium alloy, AI 3, Zn 1 Sand cast, j diam rods Nickel alloy, Cu 28.46, Fe 1.24, Wrought Mn 0.94, C 0.18, Si 0.10

I--~--I

Stress for 0.001 strain in 1,000 hr, psi

°C

of

150 250 350 205 315

302 482 662 400 600

22,000 5,700 1,500 8,800 950

205 205

400 400

6,700 20,500

315

600

27,800

260 315 149 205 260 427 538 648

500 600 300 400 500 800 1000 1200

10,000 3,000 50,000 3,500 700 17,200 3,300 540

427 482 538 593 648 482 538 593 648 427 482 538 454 538 593 648 43 150 427 482 538 593 648

800 900 1000 1100 1200 900 1000 1100 1200 800 900 1000 850 1000 1100 1200 110 302 800 900 1000 1100 1200

26,800 16,900 5,750 1,800 620 15,200 10,100 5,850 2,800 28,000 20,800 11 ,200 40,000 12,300 3,600 1,600 320 4,900t 30,000 23,000 3,700 1,300 450

• Mecbanical Properties of Metals and Alloys, NaIl. Bur. Standarde (U.S.) eire. CU7, 1943. t Stre.. for 0.005 strain in 1,000 hr,

2-89

VISCOSITY OF SOLIDS

TABLE 2f-3. CREEP RATES FOR VARIOUS MATERIALS (Continued) Temp Material and composition

Condition

Rolled, soft, tested parallel to rolling direction Rolled, soft, tested perpendicular to rolling direction

Zinc alloy, Cd 0.3, Pb 0.3

Zinc alloy, Cd 0.3, Pb 0.3

°C

OF

20 40 60 20 40 60

68 104 140 68 104 140

Stress for 0.001 strain in 1,000 hr, psi 10,100 8,000 6,300 15,400 12,100 8,000

As the stress is increased, a maximum value is reached above which the value of :: decreases with increasing stress. In the range of strain rates that can be tolerated in reasonable testing times the minimum creep rate u~ vs. stress (J" curve can be approximated by a straight line on either a double-log or a semilog plot. u~/

=

Dam

or

II

Uo

=

".

U1

(J" smh-

(2f-5)

(J"o

The hyperbolic sine relationship has been shown by Kauzmann I to have some theoretical foundation in terms of the "chemical rate theory." The power-function relationship has the advantage of being more workable from a mathematical point of view, but it suffers somewhat from the illogical conclusion that the viscosity of dashpot 711 should approach infinity as the stress approaches zero. Creep properties, like anelastic properties, vary with many factors, and compilation of creep data means very little unless heat-treatment, grain size, and amount of cold working are also specified. A few representative values of the stress required for a creep rate of 10- 6 per hour, taken from the 1943 compilation of the National Bureau of Standards," are given in Table 2f-3. 3 Materials held under constant load during long-time creep tests recover part of their plastic strain when the load is removed. According to the model of Fig. 2f-1 the recoverable strain should be equal to ~~. In actual practice, however, the recovery is usually much less than E~ and is generally less than the elastic strain of unloading. If after the first unloading and subsequent recovery the specimen is loaded and unloaded the new plastic intercept E~' and the recoverable strain are approximately equal. Both constants in either of the expressions of Eqs. (2f-5) vary with temperature. According to the chemical rate theory of Kauzmann and the various theories based on W. Kauzmann, Trans. AIME 143, 57-83 (1941). Mechanical Properties of Metals and Alloys, Natl. Bur. Standards (U.S.) Cire. C447, 1943. 3 Recent compilations of creep test data are published by the American Society for Testing and Materials in their Data Publication Series. 1

2

2-90

MECHANICS

diffusion phenomena the constants D and Ul should decrease with increasing temperature according to an exponential expression (2£-6)

This has been checked experimentally over reasonably wide temperature ranges. The constant 0"0, in the lower stress range, usually decreases slightly with increasing temperature. If the constant m changes with temperature caution must be observed in extrapolating toward regions where the curves for two different temperatures would cross.

2g. Astronomical Data R. BRUCE LINDSAY

Brown University

TABLE 2g-1. PLANETARY ORBITS· Mean distance Planet

Mercury ....... Venus.......... Earth .......... Mars .......... Jupiter ......... Saturn ......... Uranus ......... Neptune ....... Pluto ..........

to sun in terms

of earth's distancet

0.387,099 0.723,332 1.000,000 1. 523 ,691 5.202,803 9.538,843 19.181,951 30.057,779 39.438,71

Sidereal period, tropical

vearsf

0.24085 0.61521 1.00004 1.88089 11.86223 29.45772 84.01331 164.79345 247.686

I nel ination to the ecliptic Eccentricity in degrees

7.00399 3.39423 -

1.84991 1.30536 2.48991 0.77306 1. 77375 17.1699

0.205,627 0.006,793 0.016,726 0.093,368 0.048,435 0.055,682 0.047,209 0.008,575 0.250,236

• Taken from "Explanatory Supplement to the Astronomical Ephemeris and the American Ephemeris and Nautical Almanac" H. M. Stationery Office, London, 1961. t The mean distance from the earth to the sun is given as 1.00000003 astronomical units and is equal to 1.495 X 10' km. t See Sec. 2a-8 for definition of tropical year.

2-91

ASTRONOMICAL DATA TABLE

2g-2.

PHYSICAL DATA FOR THE PLANETS AND THE MOON*

Planet

Mass (Earth = 1)

Mean diameter (Earth = 1)

Mean density, g/cm 3

Mercury ...... Venus ......... Earth ......... Mars ......... Jupiter ........ Saturn ........ Uranus ........ Neptune ...... Pluto ......... Moon .........

0.056 0.817 1.000 0.108 318.0 95.2 14.6 17.3 0.9? 0.012

0.39 0.97 1.00 0.53 11.19 9.47 3.69 3.50 1:1 ? 0.27

5.13 4.97 5.52 3.94 1.33 0.69 1.46 2.27 4? 3.34

Surface Velocity Rotation gravity of escape, period, (Earth = 1) km/sec days

0.36 0.87 1.00 0.38 2.64 1.13 1.07 1.41 ? 0.16

4.3 10.4 11.3 5.1 61.0 36.7 22.4 25.6

Acceleration of gravity g 980.64 - 2.59 cos 2q, em/sec> where cP = latitude Precession of the equinoxes 50.2564 + 0.000,222(t - 1,900) seconds of arc per year where t = year in question Sun's radius 6.96 X 10 5 km Solar parallax 8.80 seconds of arc Sun's mean density 1.41 g/cm 3 Obliquity of the ecliptic 23°27'8.26" - 0.4684(t - 1,900) seconds where t is the year in question

* Taken from "Explanatory Supplement to the Astronomical Ephemeris and the American Ephemeris and Nautical Almanac, H. M. Stationery Office, London, 1961.

2h. Geodetic Data HELLMUT H. SCHMID AND KARL R. KOCH

National Oceanic & Atmospheric Administration

2h-l. Introduction. The fundamental task of geodesy is the formulation of a three-dimensional mathematical model to which can be related uniquely: 1. The geometry of the physical surface of the earth which is truly the "shape" of the earth, 2. The mathematical description of the gravitational field associated with the earth's mass, where the detailed description of the equipotential surface representing mean sea level-the geoid-is of special interest, and 3. the Universal Time and the astronomical Right Ascension-Declination System. Establishing the shape of the earth (1) requires the determination of three-dimensional coordinates for (ideally speaking) all points of the physical surface of the earth. Because of (2) it is convenient to establish the corresponding coordinate system in relation to the mass center of the earth. An expedient coordinate system is a geocentric equatorial cartesian (x,y,z) system, the origin of which coincides with the center of mass. In order to relate this system to both Universal Time and the astronomical reference system (3) it is necessary that the z axis coincide with the axis of rotation of the earth for a certain epoch, thus pointing toward a corresponding reference pole. The mean pole of the epoch 1900 to 1905, designated the Conventional International Origin (CIO), was adopted for this purpose by the International Association of Geodesy in 1968. The x axis points toward the meridian of Greenwich which is designated the null meridian for both the measurement of geographic longitude and Universal Time. 2h-2. Reference Ellipsoids. Mainly because of the uncertainty in the amounts of terrestial refraction (of. Sec. 2h-3), geodetic surveys are generally based on horizontal angle measurements and projected onto reference surfaces. Ellipsoids of revolution, also called reference ellipsoids (in the United States sometimes reference spheroids) are used for the reduction of surveys covering extended continental areas. Portions of spheres or planes are introduced for more restricted surveys. The method of triangulation for the purpose of surveying was introduced at the beginning of the seventeenth century. The horizontal angles in a triangle are measured with theodolites, and the size of the triangle-the scale of the triangulation-is determined by distance measurements. By connecting triangle to triangle, continents can be covered with triangulation nets. Chains of triangles along meridians and parallels were measured for determining the dimensions of the reference ellipsoids. Dimensions of reference ellipsoids are given in Table 2h-1. The Clarke 1866 ellipsoid was adopted by the United States for the North American Datum 1927, while Hayford's ellipsoid of 1910 was accepted as International Ellipsoid by the International Association of Geodesy in 1924. 2h-3. Different Geodetic Systems. The conceptual approach to the establishment of a triangulation system begins with the selection of a datum point-ideally located 2-92

2-93

GEODETIC DATA

near the center of the area under consideration. At this datum point the astronomical latitude, longitude, and azimuth of one side of a triangle, for which the datum point is a vertex, are determined. By setting these observed quantities equal to the corresponding ellipsoidal values, and with the additional assumption that the height above sea level is equal to the height above the reference ellipsoid, the surface of the ellipsoid provisionally becomes, neglecting the curvature of the plumb line, tangent to the geoid at this datum point. With the geodetic coordinates of one point thus fixed, the coordinates of other points in the triangulation net are then computed from the azimuths and lengths of the sides of the triangles. Only horizontal angles are used in a triangulation, i.e., the angles measured in the plane perpendicular to the direction of local gravity, because they can be determined much more accurately than the typically small vertical angles which are distorted by

TABLE 2h-1. DIMENSIONS OF THE REFERENCE ELLIPsom* (a = semimajor axis, f = (a - b)/a = flattening, b = semiminor axis)

Author

Year

a, meters

1/!

Bouguer, Maupertuis........... Delambre ..................... Walbeck ...................... Airy .......................... Bessel ........................ Clarke ........................ Hayford ...................... Krassowski ................... lAD adoptedt ................. Anderlef ......................

1738 1800 1819 1830 1841 1866 1910 1938 1964 1967

6,397,300 6,375,653 6,376,896 6,376,542 6,377,397 6,378,206 6,378,388 6,378,245 6,378,160 6,378,144

216.8 334.0 302.8 299.3 299.15 295.0 297.0 298.3 298.25 298.23

* W. A. Heiskanen and F. A. Vening Meinesz, "The Earth and Its Gravity Field," p. 230, McGrawHill Book Company, New York, 1958. t Cf. Sec. 2h-7. t Cf. Sec. 2h-5. refraction of the light path. As a consequence the triangulation computations must be based on a two-dimensional solution on the surface of a suitable reference ellipsoid. Once the observations have been made on points of the physical surface of the earth, the necessity arises to reduce these observations to the chosen reference ellipsoid. This reduction requires the deflection of the vertical (the small angle between the ellipsoid normal and the direction of gravity) and the height of the triangulation station above the ellipsoid. Some of these reduction corrections, being of small magnitude, were neglected in older triangulations but are at present considered significant in meeting modern accuracy requirements. The deflection at a triangulation station is obtained by observing astronomical latitude and longitude and comparing these data with the corresponding geodetic coordinates computed on the ellipsoid. Integrating the deflections along the path between two points and adding the difference in mean sea level elevations gives the difference in height above the reference ellipsoid between these two points. This approach is known as the method of astrogeodetic deflections.' Since the deflections of the vertical are needed in the reduction of the observations to the ellipsoid, it is necessary that the geodetic coordinates-latitude and longitude1 W. A. Heiskanen and H. Moritz: "Physical Geodesy," W. H. Freeman and Co., San Francisco, 1967.

2-94

MECHANICS

be available, which can be computed only after the necessary reductions on the observations are made. Therefore an iterative procedure becomes necessary, an approach which is typical for the solution of many classical geodetic problems. In the course of such iterative steps, certain a priori assumptions are progressively modified. For example the condition of tangency of geoid and ellipsoid at the datum point may be relaxed and, at least in principle, the parameters of the originally chosen reference ellipsoid can be improved. However, despite the application of complex theoretical reduction methods, classical geodetic triangulation systems cannot establish ties between continents. Consequently triangulation systems on different continents have only partially related coordinate systems on, usually, different reference ellipsoids. Approximately a hundred different datums have been established in various parts of the earth, approximately eight of them being designated as major datums. One of these is the North American Datum (NAD 1927). The quantities needed for reducing observations in triangulation nets can also be computed as functions of gravity anomalies. Furthermore, the gravimetric method (cf, Sec. 2h-6) also provides, at least in principle, a means for establishing a worldwide geodetic system by determining absolute geoidal undulations and deflections of the vertical with respect to a mass-centered reference ellipsoid.' Because of lack of sufficient observations over the oceans the usefulness of this method is impaired, particularly when considering modern accuracy requirements. With the use of man-made satellites in geodesy the limitations of classical geodetic methods can be surmounted. In a strictly geometric method satellites serve as highly elevated target points for a three-dimensional triangulation of ground-based observation stations (cf. Sec. 2h-4). A dynamic interpretation of the observed satellite orbits leads to a simultaneous solution for the mass-center-referenced station coordinates, parameters of the orbital model, and certain gravitational parameters. Theoretical limitations arise from the necessary assumption that the effect of higherorder terms in the gravitational field is negligibly small. Practical difficulties result from the large number of unknowns solved for simultaneously, including, in addition to the geodetic parameters, nongravitational parameters for instance, for the air drag. The ultimate geodetic solution can therefore be expected when, in the foreseeable future, both the geometrically and dynamically obtained solutions are combined in a statistically significant result. 2h-4. Satellite Triangulation. The main objective of geometric satellite geodesy is the establishment of three-dimensional positions of a selected number of points on the physical surface of the earth. The significance of geometric satellite geodesy rests on the fact that, for the first time, such a spatial triangulation can be established on a worldwide basis with a minimum of a priori hypothesis; specifically without reference to either the direction or magnitude of the force of gravity. By simultaneously interpolating the satellite position, as seen from at least two observing stations, into the star background, the spatial directions are not only determined directly in terms of the astronomical system (cf. Sec. 2h-1) but are also interpolated in a physical sense into the astronomical refraction effect, thus providing {t method essentially free of bias errors. This method-sometimes referred to as stellar triangulation 2 • 3 - i s presently being applied in establishing a worldwide reference frame including some 40 stations, and, among other applications, in providing a precise spatial triangulation framework inthe area of the North American Datum. Positional accuracy of one part per million Ibid. Y. Vaisala, An Astronomical Method of Triangulation, Helskinki, Sitzber. Finn. Akad. Wiss.1947. 3 H. Schmid, Precision and Accuracy Considerations for the Execution of Geometric Satellite Triangulation, Proc. 2d Intern. Symp. on Use of Artificial Satellites for Geodesy II, Athens, Greece (1965). 1

2

2-95

GEODETIC DATA

is obtained for the worldwide triangulation net, and accuracies of ± 2 m are obtained for continental densification nets, where distances between stations are typically on the order of 1,000 to 1,500 km. In common with all strictly geometric methods, satellite triangulation-executed as stellar triangulation or as a kind of three-dimensional trilateration, based on opticalelectronic ranging-can only provide positions relative to an arbitrarily chosen origin. To obtain positions relative to the center of mass requires recourse either to potential theory, in the case of the gravimetric method, or to celestial mechanics in the dynamic method of satellite geodesy (cf. Sec. 2h-5). 2h-6. Dynamical Methods in Satellite Geodesy. The equations of motion of an artificial earth satellite are given by

r=F where r is the position vector of the satellite in the geocentric equatorial coordinate system and F the force vector. F is a combination of individual terms

where FE is the earth's gravitational effect, FSM is the sun's and the moon's gravitational effects, F D is the atmospheric drag effect, and F R is the effect, due to solar radiation pressure. Generally for earth satellites the terms FSM, F D , and FR are small in comparison to FE and can be computed from solar and lunar ephemerides and from models for the air drag and the radiation pressure. The force term FE is obtained as

FE = grad V where V is the potential of gravitation of the earth, usually given by an expansion into spherical harmonics

GM [ V = -r- 1

~ +~

*' (a) ~

~

1_.

_

Plm(sm q;)(Clm cos ms.

.] + 8_ 1m sm mA)

l=2m=O

G is the gravitational constant; M is the mass of the earth, r, q;, Aare polar coordinates in the geocentric equatorial coordinate system; a is the equatorial radius of the earth; tiM and 8 1m are normalized harmonic coefficients of degree I and order m; P,m(sin q;) is the associated Legendre functions, usually normalized in such a manner that -1

471"

t: 0

mA}]2 COS

!7r/2 [ Plm(sin {COS q;). -7r/2 sin ms:

q; dq; dA =

1

If the harmonic coefficients in the expression for V are known, orbits of earth satellites can be computed by numerical integration of the equations of motion or by perturbation theories, provided the initial position and velocity of the satellite are given. If, on the other hand, satellite orbits are observed by means of photographic cameras or electronic tracking devices, the initial positions and velocities of satellites and the harmonic coefficients in the expression for V can be deterrnined.t-! Because of the restricted number and accuracy of the observations, only the harmonic coefficients of 1 I. I. Mueller, "Introduction to Satellite Geodesy," Frederick Ungar Publishing Co., New York, 1964. 2 W. M. Kaula, "Theory of Satellite Geodesy," Blaisdell Publishing Co., a division of Ginn and Company, Waltham, Mass., 1966.

2-96

MECHANICS

low degrees are computed. To diminish the correlation between the coefficients, satellite orbits with different orbital parameters are used in the solution. At the present time the most complete set of harmonic coefficients is published by the Smithsonian Institution and given in Table 2h-2. More complete sets exist, but are unpublished. TABLE 2h-2. HARMONIC COEFFIcmNTs IN THE EARTH'S GRAVITATIONAL POTENTIAL* l

m

c « 10

6

S

X 10 6

l

---

m

ex

10 6

S

X 10 6

---

2 2

0 2

-484.1735 2.379

0 -1.351

3 3 3 3

0 1 2 3

0.9623 1.936 0.734 0.561

0 0.266 -0.538 1.620

4 4 4 4 4

0 1 2 3 4

0.5497 -0.572 0.330 0.851 -0.053

0 -0.469 0.661 -0.190 0.230

5 5 5 5 5 5

0 1 2 "3 4 5

0.0633 -0.079 0.631 -0.520 -0.265 0.156

0 -0.103 -0.232 0.007 0.064 -0.592

6 6 6 6 6 6 6

0 1 2 3 4 5 6

-0.1792 -0.047 0.069 -0.054 -0.044 -0.313 -0.040

0 -0.027 -0.366 0.031 -0.518 -0.458 -0.155

7 7 7 7 7 7 7 7

0 1 2 3 4 5 6 7

0.0860 0.197 0.364 0.250 -0.152 0.076 -0.209 0.055

0 0.156 0.163 0.018 -0.102 0.054 0.063 0.096

8 8 8 8

0 1 2 3

0.0655 -0.075 0.026 -0.037

0 0.065 0.039 0.004

* Smithsonian

8 8 8 8 8

4 5 6 7 8

-0.212 -0.053 -0.017 -0.0087 -0.248

-0.012 0.118 0.318 0.031 0.102

9 9 9

0 1 2

0.0122 0.117 -0.0040

0 0.012 0.035

10 10 10 10 10

00 01 02 03 04

0.0118 0.105 -0.105 -0.065 -0.074

0 -0.126 -0.042 0.030 -0.111

11

11

00 01

-0.0630 -0.053

0 0.015

12 12 12 12

00 01 02 12

0.0714 -0.163 -0.103 -0.031

0 -0.071 -0.0051 0.0008

13 13 13

00 12 13

0.0219 -0.059 -0.059

0 0.050 0.077

14 14 14 14 14

00 01 11 12 14

-0.0332 -0.015 0.0002 0.094 -0.014

0 0.0053 -0.0001 -0.028 -0.003

15 15 15 15

09 12 13 14

-0.0009 -0.0619 -0.058 0.0043

-0.0018 0.0578 -0.046 -0.0211

Astrophys. Observatory Spec. Rept. 200, p, 2, Cambridge, Mass., 1966.

Satellite observations are not only a function of the initial position and velocity of the satellite, and the harmonic coefficients in the expansion of the earth's potential, but also a function of the coordinates of the tracking stations. Hence, together with the harmonic coefficients, these coordinates can be determined in the geocentric equatorial coordinate system used to formulate the equation of motion of the satellite.

2-97

GEODETIC DATA

With the coordinates of the tracking stations the dimensions of the reference ellipsoid and datum shifts are obtained. These shifts are needed to transform the coordinates of the various datums to the geocentric equatorial system. With the value GM = 398,601 km 3/sec 2 as determined by lunar probes, it was found! that a

= 6,378,144 m

Ilf = 298.23

and

and the datum shifts are given in Table 2h-3. 2h-6. Physical Geodesy. Another method for determining the earth's gravity potential is given by the solution of the geodetic boundary-value problem. The earth's potential W, consisting of the potential V of gravitation and the potential of TABLE 2h-3. DATUM SHlFTS* Rectangular coordinate shifts Datum ~x

meters

-23 -81 -147 52

North American 1927 ....... European ........ " ........ Tokyo ..................... Old Hawaiian ..............

* Anderle et

I

~y

~z

meters

meters

159 -99 530 -262

185 -118 676 -183

al., op. cit., p. 13.

the centrifugal force, is separated into the potential V of a given reference ellipsoid, whose surface is an equipotential surface, and the disturbing potential T:

W=V+T T can be regarded as a harmonic function if the reference ellipsoid closely approximates the geoid and if the rotational axes of the ellipsoid and the earth and their angular velocities are identical. The unknown potential T is connected with the gravity anomalies ~g, measured at the surface of the earth, by the boundary condition, which is given here with the relative error of the flattening of the earth: ~g = -

aT 2T aH - Ii

2

- Ii

(V o - W o)

H is the height (i.e., the normal height), R the mean radius of the earth, U 0 the potential at the surface of the ellipsoid, and W o the potential of the earth at mean sea level. If the mass of the reference ellipsoid equals the earth's mass,

V0

-

Wo

= - ~

JJ~g

cos cP d cP dX

1 R. J. Anderle, and S. J. Smith, "NWL-8 Geodetic Parameters Based on Doppler Satellite Observations," p. 7, U.S. Naval Weapons Laboratory, Dahlgren, Va., 1967.

2-98

MECHANICS

The gravity anomalies t:.g are computed by subtracting the gravity of the reference ellipsoid at height H above the ellipsoid from the gravity measured at the earth's surface at height H above sea level. Usually gravity anomalies are referred to the International Ellipsoid whose gravity at its surface is defined by the International Gravity Formula adopted in 1930 by the International Association of Geodesy: l'

= 978.0490(1

+ 0.00;'5,2884 sin!

B - 0.000,0059 sin" 2B)

cmysec"

is called the normal gravity, and B is the ellipsoidal latitude. Table 2h-4 shows the normal gravity from the equator to the pole. The value l' H at height H above the ellipsoid is computed approximately by l'

l' El

=

l' -

with H in km

0.3086H cm zsec!

The units of gravity anomalies are usually milligals, abbreviated mgal = 10- 3 crrr/sect. The easiest way to obtain the disturbing potential T is by expressing T as the potential of a simple layer distributed over the surface of the earth. If T in the boundary condition is replaced by this expression, an integral equation is obtained, with the density of the surface layer as sought function and the gravity anomalies as absolute values. This integral equation has been derived by Molodenskii! who solved it by successive approximations. The first approximation To of T is the wellknown formula of Stokes, 2 To with

=~

ff

t:.g

S(~) = sin (~/2)

S(~)

cos

- 6 sin

e/>

de/> dA

~+1

- '5 cos

~

- 3 cos

~ In

(sin ~

+ sin2~)

This formula holds if the mass of the earth equals the mass of the reference ellipsoid and if both centers of mass coincide. ~ is the spherical distance between the fixed point where To is computed and the variable point at the surface of the sphere with radius R on which the anomalies t:.g are assumed to be given. Hence, by means of gravity anomalies the earth's gravitational potential can be computed. The value of T /l'H1 where T is the value of the disturbing potential at the earth's surface, approximately equals the geoid undulation, i.e., the distance between the surface of the reference ellipsoid and the equipotential surface W 0 = const at mean sea level, the geoid (cf. Sec. 2h-1). The deflection of the vertcal is found by differentiating the disturbing potential T in the horizontal direction. The horizontal derivative of Stokes' formula is known as Vening Meinesz' formula. Thus, by means of gravity anomalies we are able to compute geoid undulations and deflections of the vertical with respect to an ellipsoid whose mass is identical with the mass of the earth and whose center coincides with the mass center of the earth. By knowing the undulations and the deflections of the vertical for the different datums of the world, all datums can be shifted into one common system. To determine the earth's potential from the solution of the geodetic boundary-value problem requires that the earth's surface be covered with grav.ty measurements. At present, huge parts of the earth, especially the oceans, are without gravity anomalies. Hence, the gravity measurements have to be combined with the results of satellite observations to improve the knowledge about the earth's gravity field. Either given gravity anomalies are expanded into spherical harmonics and compared 11\1. S. Molodenskii, V. F. Eremeev, and :;\1. 1. Yurkina, "Methods for Study of the External Gravitational Field and Figure of the Earth," Israel Program for Scientific Translations, Jerusalem, 1962. 2 M. Hotine, "Mathematical Geodesy," ESSA Monograph 2, Government Printing Office, October, 1969.

2-99

GEODETIC DATA

TABLE 2h-4. NORMAL GRAVITY FROM THE EQUATOR TO THE POLE: COMPUTED FROM THE INTERNATIONAL GRAVITY FORMULA ["y = 978.0490(1 + 0.0052884 sin! B - 0.0000059 sin! 2B) cmysee". Unit 1 milligal] B,

deg

Gravity

B, Difference deg

Gravity

B, Difference deg

Gravity

Difference 77.55 75.89 74.14 72.28 70.35 68.33 66.22 64.03 61.76 59.42

978,049.00 978,050.57 978,055.27 978,063.10 978,074.06 978,088.12 978,105.26 978,125.48 978,148.74 978,175.02

1.57 4.70 7.83 10.96 14.06 17.14 20.22 23.26 26.28

31 32 33 34 35 36 3.7 38 39 40

979,416.53 979,496.80 979,578.46 979,661.40 979,745.54 979,830.77 979,916.98 980,004.08 980,091.94 980,180.48

78.78 80.27 81.66 82.94 84.14 85.23 86.21 87.10 87.86 88.54

61 62 63 64 65 66 67 68 69 70

982,001.46 982,077.35 982,151.49 982,223.77 982,294.12 982,362.45 982,428.67 982,492.70 982,554.46 982,613.88

12 13 14 15 16 17 18 19

978,204.29 978,236.50 978,271.63 978,309.63 978,350.44 978,394.04 978,440.35 978,489.33 978,540.92 978,595.05

29.27 32.21 35.13 38.00 40.81 43.60 46.31 48.98 51.59 54.13

41 42 43 44 45 46 47 48 49 50

980,269.57 980,359.12 980,449.01 980,539.14 980,629.39 980,719.65 980,809.82 980,899.78 980,989.42 981,078.64

88.09 89.55 89.89 90.13 90.25 90.26 90.17 89.96 89.64 89.22

71 72 73 74 75 76 77 78 79 80

982,670.89 57.01 982,725.41 . 54.52 982,777.37 51.96 982,826.72 49.35 982,873.39 46.67 982,917.33 43.94 .982,958 .47 41.14 982,996.77 38.30 983,032.19 35.42 983,064.67 32.48

20 21 22 23 24 25 26 27 28 29 30

978,651.66 978,710.68 978,772.05 978,835.68 978,901.49 978,969.42 979,039.38 979,111. 28 979,185.03 979,260.55 979,337.75

56.61 59.02 61.37 63.63 65.81 67.93 69.96 71.90 73.75 75.52 77.20

51 52 53 54 55 56 57 58 59 60

981,167.33 981,255.37 981,342.67 98f,429.10 981,514.58 981,598.99 981,682.23 981,764.19 981,844.79 981,923.91

88.69 88.04 87.30 86.43 85.48 84.41 83.24 81.96 80.60 79.12

81 82 83 84 85 86 87 88 89 90

983,094.19 983,120.69 983,144.16 983,164.55 983,181.85 983,196.03 983,207.08 983,214.99 983,219.73 983,221.31

0 1 2

3 4 5 6 7 8 9 10 11

29.52 26.50 23.47 20.39 17.30 14.18 11.05 7.91 4.74 1.58

I

with the harmonic coefficients found by satellite observations, or gravity anomalies are computed, using the harmonic coefficients obtained from satellites, and compared with given gravity anomalies, in order to compute corrected harmonic coefficients. The gecid map of Fig. 2h-l and the gravity anomalies for 5° by 5° surface elements of Tables 2h-5 and 2h-6 were obtained by such a combination. Combination methods, using instead of the expansion into spherical harmonics the solution of the geodetic boundary-value problem to express the earth's potential, are under investigation.I-! 1 K. Arnold, An Attempt to Determine the Unknown Parts of the Earth's Gravity Field by Successive Satellite Passages, Bull. Geod. no. 87, p. 97, Paris, 1968. 2 Koch, K. R.: Alternate Representation of the Earth's Gravitational Field for Satellite Geodesy, Boll. Geofieica teorica ed applicata 10 (40) (1968).

TABLE

2h-5. 5° BY 5° DATA

MEAN GRAVITY ANOMALmS FROM A COMBINA'rION OF SATELLITE AND GRAVIMETRIC

REFERRED TO THE

INTrmNATIONAL GRAVITY

FORMULA:

EASTElRN HEMrsPHF~Rf;~*

(Units milligals) 600

300

e

19 21 10

55 24

7 14 25 17 67 25

5 18 -3 11 9 23 20 22 23 23 20 -14

Il:)

I f-'

o

o

-1 -28 -25 3 8 -1

8 5 4 8 25 11

13 7 10 7 16 8

3 -2 -3 15 14 13 21 18 16 7 12 8 I 6 I~ 21 33 10

1200

1500

3 .5 2 2 3 .5 .5 5 5 5 4 .5 .5 .5 5 2 8 4 7 5 3 0 -2 -4 -5 -6 -5 -4 15 15 16 16 15 14 11 .~ 3 4 9 -8 S 6 2 -12 -4-14 -4 4 2 -0 0 -2 I 7 6 8 5 3 -4 -10 -6 -2 -2 -2 -1 -5 8 11 12 H 3 -5 -5 -10 -11 -9 -7 -6 -7 -9 -6 3 17 29

3 13 39 20 12 9

3 15 36 20 22 4

2 8 32 17 I\J

3 1 10 -4 -G 8 8 22 8 16 26 31 18 16 16 17 38 57 46 8 22 -5 -9 21 15 2 -1 -35 -15 18

12 14 .5 1 32 38

2 -1 -1 -30 -3.5 -21 -20 -8 16 13 3 4 11 18 17 20 13 3 5 -13 -21 -2 -3 -27 -19 -15 -0 -0 -3 8 10 13 8 11 \) 1 8 1 -5 10 -6 -6 -5 -9 -9 -15 -22 -18 -1 0 10 1 -8 -28 -24 -11 -8 -0 -25 -26 -23 -10 -8 -3 4 4 43 -11 2 31 2.3 -5 -14 -25 -20 14 14 -10 -16 -1 18 -37 -15 -6-11 6 5 52 39 39 16 -17 -26 -3 9 11 20 16 21 22 -45 25

3 3 2 2 11 22 7 20 20 27 18 12 8 32 1\\ 8 -2 -15

-7 -24 -26 20 13 -2 12 10 -15 1 4 31 16 7 11 4 -20 1 -11 -10 -14 -1 7 14

900

3 11 19 9 7 0

ic

3 16 28 17 7 14

-7 -1 2 4 7 -2 -12 -3 -3 13 19 -19 -3 -4 4 5 29 -11 7 4 9 10 6 -5 -14 3 3 3 13 -0 -20 3 -3 -1 -34 -26

3 16 11

4 3 5

-24 5 14 -24 17 -18 -9 3 -12 -6-11 -1.5 -51 -7 -11 -28 -19 -21

-3 -3 -2 -20 -28 -34

1 4 -20 -31 -45 -42

-31 6 -22 -21 -20 -47

-17 -27 -38 7 -4 22 -29 -22 -12 -16 -23 -30 -42 -8 -12 -6 -3 -2 0-31 -22 1 -6 -15 -10 -9 9 -12 -10 1 -22 -21 2 -10 -14 -15 -4 -8 -7 -2 -0 -4 -0 7 -8 12 9 -4 -13 4 16 -14 5-10 -.5 4 13 -;> 11 25 35 19 8 17 -7 1 3 23 8 26 17 1 12 13 31 3 -4 -16

-49 -30 -25 -12

8 -5 -10 -6 -6 -14

-49 -4 1 -8 -8 -50

11 9 18 18 23 21

17 14 8 16 20 19

2 14 16 29

15 20 23 213 28 21

32 13 10 35 32 33

7 -2 3 -7 Hl 17 30 21 30 20 33 23

3 8 12 16 19 17 14 13 5 6 -6 -8 -10 -12 -12 -10 -5 35 1.5 29 50 58 62 60 54 45 37 33 32 34 7 15 14 11 3 -1 -4 -.5 -,1 -2 -4 -6 -6 -.5 -3 0 5 10 16 22 -8 5 5 5 5 5 6 6 6 6

11 38 34 2 28 6

8 37 32 6 32 6

2 -1 28 15 25 16 9 12 27 22 6 6

1 10

,5 14 9 15 34 5

12 13 9 11 22 9

30 12 15 11 24 13

18 13 17 9 20 15

13 21 19 16 21 17

2 7 19 23 25 1\1

5 2 1.5 21 24 20

HI

18

11

14 36 5

- 58 -6-14 -5 -7 -21 -17 -14 -11 1 -11 -8 -16 -10 7 -uo -4 -5 -1 16 -30 3 7 -1 3 -16 9 14 18 19

-50 -iii -14 -28 -11 -13 -\\ 2 -11 -34 -25 -25 -4 -G -5 -3 3 -1 -4 -9

9 3 20 21 23 21

14 10 11 8 14 7

-6 -8 -30 -32 -23 -36

6

23 11 37 31 '1

-1 2 5 -34 -iS4 -11

1 3 13 15 16 27

1 13 41 32 31 28

6 .'5 21 13 12 23 21 17 27 23 4 -8

17 16 5 7 17 27

.5

.5

.5

0 22 10 13 31

3 24 10 10 25

6 25 10 8 21

18 9 15 33

.5 8 25 9 11 22

.5 5 11 14 24 -2 10 12 18 23 25 26

5 14 6 16 24 22

1.5 9 13 25 30 25 14 5 2 22 6 13 32 35 18 11 15 18 8 6 16 4 10 6 10 6 3 1 30 -1 -5 2 6 -3 9 11 35 19 17 -·3 5 -16 -8 4 -6 45 -25 3 -7 -9 -19 -13 -16 0

10 -15 19 11 15 -7 -5 s 7 1 3 -4 -3 1 9 -2 -0 3 -0 -0 -4 4 -6 -2 -22 -4 -11 2 2 15 48 8 12 2 3 19 52 3 15 10 3 9

22 32 29 28 4 11 25 16 17 -3 12 18 11 -2 -18 -12 15 26 2 - 9 -14 -7 8 9 28 20 17 -10 -14 -4 11 9 21 6 5 27 -28 -17 2 12 -6 -16 -14 0 12 -18 -32 4 -12 -24 -9 -0 4 10

-1 -25 -27 -32 -31 -3 -4.5 5 -6 -12 -24 -42 -l.~ -12 -22 1.5 11 -0 -4 -6 -10 -12 -12 18 17 12 4 -4 -9 -11 -11 4 3 -2 11 11 13 3 9 13 12 13 11 7 s 4 6

-~

12 4 7 3 13 20

.5

-'"

-25 -Iii 4 1 -25 -14 1 8 (J -9 -10 -14 -3 4 -0 -1 (J -1 5 9 4 s 4 1

4 -1 -4 -4 -1 -3 -6 6 5 6 9 -2 28 26 25 21 23 20 19 19 4 -52 -11 7 14 11 10 -37 6 5 7 17 -45 1 11 4 0 -4 -35 -37 7 -25 -27 -19 -16 18 14 11 8 8 1 -10 7 1 5 6 9 10 -9 -11

-900 * R. H. Rapp, Comparison of Two Methods ror the Combination of Satellite and Gravimetric Data, Ohio State Univ.Dept.Geod. Sci. Rept. 113, p. 26, 1968.

33 13 2 -20 15 11 11 53 24 10 2 20

22 21 23 8 5 6

-R -14 -10

8

-8 -11 -10-10 -5-11 -2 -11 -2 -20 -6 0 -5 -1 4 2

8 21 8 3

9 -7 9 10 20 -25 -1 i 9 12 10 37 4 21 17 19 36 23 22 21 11 21 18 11

22 16 9 25 14 17 22 9 27 14 2 22 ~l • 0 3 27 8 -8 -6 -11 -3 ;l -8 -4 7 -2 10 6 2 7 -0 3 0 -2 13 1 -4 -12 -11) -16 2 1 -6 4 -2 -5 0 6 2 -3 -7 -12 -16 8 3 -16 -17 -23 -24 3 -35 -29 21 -36 -9 -13 -0 -21 3 7 6 8 -8 0 11 6 -7 -4

-3 -18 -7 -13 -16 20

TABLE

2h-6. 5°

BY

5°

MEAN GRAVITY ANOMALIES FROM A COMBINATION OF SATELLITE AND GRAVIMETRIC

DATA REFJ -9 -11 -8 -2 3 1 -3 -14 -15 -9 -13 -12 -6 -6 -5 -13 -18 -7 -37 -11 2 7 0 -8 -5

-13 -.'>

...... o

6 10

9 -7 -.'> -5 -2.'> -12

1 -0 -36 3 -8 15 -6 22 -21 -8 -15 -20 -25 -18 -19 -18 -11 -3

10 -7 -2 -3 -14

-s

10 -8 -14 -2 -10 -6

-7 -12 -14 -5 -5 -2

-21 -16 -29 -8 -4 -2

-.'> -8 -0 -2 -6 -7 7 12 10 -1 -6 6 3 14 -2 -1 5 9 13 6 t: 0 .'> 4 -2 4 3 -3 -2 -0

-8 -1 -3 8 -8 -6

-6 -7 -13 -3 -6 -4

-5 -5 -3 -.'> -1 -6

9 8 11 36 -8 -3 -·1 1 -2 22 -7 21

2 0 26 3 2 -7 9 -16 21 -12 1 -8

2700

2400

-26 -19 -23 10 -12 -7

-2 -18 -19 -18 -18 20

-6 -17 -24 -22 -1.3 20

-7 -15 -28 -28 -19 20

-900 * Rapp, Of'. cii., p. 27.

-6 -14 -31 -12

-4 -15 -32 -15 -14 -12 -11 20

-6 -16 -20 -8 -10 21

-7 -16 -24 -22 -7 20

-6 -13 -16 -16 -5 20

8 13 16 12 2 2 2 2 4 13 2 3 2 24 26 28 16 16 27 34 6 37 38 39 38 37 29 34 34 32 211 13 10 39 33 15 -14 -11 -15 8 17 0 -3 1 4 22 20 24 3 12 -5 -2 2 1 2 9 4 1 2 4 -17 11 46 23 5 0 -3 -7 -10 -5 -7 -7 -2 -4 -17 -27 39 26

o -11 -4 1 3 -33 -22 -5 11 -2 -2 11 2 3 -9 7 3 -10 -15 -9 -6 17 0-22 20 11 27 6 11 19 3 11 17 33 3 22 18 22 11 11 -8 -.'> -10 -11 -6 -3 -5 -2 -7 27 13 4 14 24 10 10 -15 -20 0 17 6 -16 -15 -10 -8 -7 -3 1 -0 6 5 22 -1 -6 -3 2 -0 II -6 -31 -18 -2 -9 -7 -2 12 -10 7 -0 -1

-15 -21 -15 -22 -14 -7

-19 -11 -10 2 -1 -3

2 26 -4 -12 17 -4 -5 1 23 -3 -4 0 -12 -1 0 -6 -2 -3

2 7 5

4 1 6

12 23 -27 -28 22 -2 -5 -58 4 15 -7 -20 18 22 -11 --28 12 17 34 12 9 5 31 24

-24 -27 -49 -36 18 23

-18 -28 -23 -28 -16 -27 -18 -liO -8 -17 11 -1

-19 -13 -26 -29 -22 -4

11 3 -16 -34 -37 -11

21 12 18 19 12 Ii 24 -4 -17 -13 -29 -19

24 22 39 22 23 19

7 7 3 8 8 9

3

8 5

5 8 5 6

E

s

6 5 5

6 8 9 5 1(' 9

4 -2 10 9 12 14 9 12 13 7 11 8

9 4

0 3 1 5

5

s

7 0 29 6

2 13 11 28 6 7

-2 9 11 12 1 2 8 0 4 6 7 9 6 -10 -8 -7 -6 -3 2 -1 1 3 8 -2 5 17 -8 -1 4 7 8 10 11 -6 27 20 12 15 40 -5 13 5 1 -9 -18 -11 -12 13 16 11 15 22 -19 -2 -22 -2 -23 -1 17 17 13 7 -9 -6 -4 20 20 -6 20 20 20 20 20 -23 -9 19 18 18

10 lC 7 5 2 9

1 34 22 27 36 28

0 -1 30 24 19 48 23 22 34 31 20 49

2.'> 30 13 23 3.'> 23

30 27 16 20 15 11 2.'> 14 36 16 16 -5

-1-10 -11 -13 -20 -9 -14 -17 -8 4 -7 4

-1 -4 -6 -8 -5 2 -5 2 4 -9 -6 -5 -15 -7 9 3 11 24 19 -7 -4 -5 -1 -3 -4 1 -5 -9 -6 13 1 2 -7 -10 -36 -34 3 -7 -3 2 -4 1 2 -2 2 0 5 -11 2 0 -8 26 18 13 4 -fl -ll 2 1 -0 -3 -6 -20 -.'> 44 21 -8 -I -3 2 -7 7 -2 -5 10 -11 4 -2 8 -12 21 -12 -2 4R -8 -7 -18 -7 -ll -16 3 0 -4 1 -5 -2 -4 -1 6-10 13 -4 21 27 16 10 1 8 -4 5 8 -2 -21 -23

-20 4 8 11 4 -2 -3 -6 -3 -3 -1 -.5 -3 -2 4 II 9 7 7 7 -1 -2 -2 -1 -2 -1 9 9 7 8 10 8 6 a 4 0 -.'> -1 3 ;1 3 -0 0 7 8 4 1 6 2 1 1 -1 -7 -8 -6 -4 -6 -3 2 6 3 5 8 3 4-12 -10 -10 -IC -7 -2 1 -1 -1 3 8 10 11 -1 -18 -13 -18 -19 -9

9 21 33 10 3 4

3300

3000

-1 -19 -10 -13 -11 -8

1 16 40 24 37 31

0 16 31 24 28 40

1 13 15 8 19 42

10 14 23 23 33 24 5 -5 -5 13 3 14 -2 11 30 14 -4 43

21 17 13 24 19 52

-10 -7 8 -I.'> -8 -1 -4 14 2 -12 -10 15 1 3 5 2 -4 6

1 12 17 23 47 49

24 4 14 21 16 0

10 -'> -7 -11 -3 11 5 6 29 18 7 19

-6 -8 -4 -7 -10 -4 -13 -12 -5 -9 -12 -4 -10 -6 -4 -13 -5 -1

(l 10 2 0 -4 -4 -0 4 5 0 6 7

1 -2 -4 -7 -9 -2

15 11 -0 16 -9 -1 11 0 0 6 9 16 4- -5 -3 -5 -3 -4 1 3 4 3 3 -1 -2 -3 8 6 -4 -3 14 -1 -.5 -4 2 9 0 -2 -2 0 9 10 14 6 -1 15 15 16 16 12 2 0 1 8 10 18 20 16 13 I.'>

4 0 5 3 8 8 12 11 18 23 16 15

16 9 5 9 28 13

3 14 25 30 25 16 12 15 18 17 14 12 10 6 1 1 -3 -6 -8 -7 -6 4 -3 -1 31 21 30 Ii 2 6 14 2.5 38 40 32 21 9 -1 -6 -6 -4 -1 0-14 -13 2 4 7 9 11 13 14 13 -10 8 3 2 0 -2 18 -10 -22 -9 -14 7 7 7 6 5 4 7 -25 9 8 -22 6 -14 -19 13 -2i 11 10 13 7

2-102

MECHANICS

2h-7. Geodetic Reference System: 1967. In 1967 the General Assembly of the International Union of Geodesy and Geophysics recommended replacing the International Ellipsoid and the International Gravity Formula with the Geodetic Reference System 1967 defined by' a = 6378160m GM = 398 603 km t/sec! J~ = 10827 X 10- 7 with J 2 = - V5 C20. This set of parameters is identical with the parameters adopted by the International Astronomical Union in 1964 as part of a system of new

FIG. 2h-1. Geoid obtained by combining satellite and gravimetric data. ,Units: meters. (W. Kohnlein, Smithsonian Astrophysical Observatory Special Report 264, p. 57, 1967.)

astronomical constants. The values for a, GM, and J 2 , together with the value for the earth's rotational velocity, define an equipotential ellipsoid of revolution completely, so that the shape of the ellipsoid and its external gravity field are determined by the four constants. Only preliminary numerical values for the shape of the ellipsoid and the gravity formula of the Geodetic Reference System 1967 have been published until now.' ,3 Bull. Geod, no. 86, p. 367, Paris. 1967. A. H. Cook, The Polar Flattening and Gravity Formula in the Geodetic Reference System 1967, Geophys. J. 15. p. 431, Oxford, 1968. 3 H. Moritz, "The Geodetic Reference System 1967," Allaem, Vermes8., p. 2, Karlsruhe, 1968. I

2

2i. Seismological and Related Data B. GUTENBERG 1

California Institute of Technology J. E. WHITE

Globe Universal Sciences, Inc.

2i-1.

List of Symbols

V v P S k

velocity of longitudinal wave P velocity of transverse wave S symbol denoting longitudinal wave symbol denoting transverse wave bulk modulus or volume elasticity J.l rigidity or shear modulus p density T Poisson's ratio A ratio V Iv t temperature in degrees centigrade, time p pressure in bars h depth in the earth T period of seismic disturbance G symbol denoting surface shear waves R, symbol denoting Rayleigh waves Ll epicentral distance SH symbol denoting component of S wave in horizontal plane SV symbol denoting component of S wave in vertical plane i actual angle of incidence at a discontinuity apparent angle of incidence at a discontinuity u ratio of horizontal ground displacement to incident amplitude 2i-2. Fundamental Equations for Elastic Constants and Wave Velocities. In purely elastic, isotropic, homogeneous media the velocity V of longitudinal waves P, v of transverse waves S, the bulk modulus k, the rigidity J.L, the density p, and Poisson's ratio a are connected by the following equations:

V2 = k

+ tJ.L

v2

A=~

iA2 - 1 a

= A2 - 1

k = p(V 2 1

= I!. p

P

-

tv

2)

Deceased.

2-103

J.L

v = v2p

(2i-l) (2i-2) (2i-3)

2-104

MECHANICS

2i-3. Elastic Constants and Wave Velocities in Rocks (Laboratory Experiments). In rocks the elastic constants and the wave velocities usually increase with increasing pressure p (Tables 2i-2 and 2i-3) and decrease with increasing temperature t and with porosity. Phase changes affect all elastic quantities. Many sedimentary rocks show significant anisotropy, with an axis of symmetry. Table 2i-4 gives an example of velocity differences for vertical and horizontal travel' and for shear polarization. TABLE 2i-1. CORRESPONDING VALUES OF POISSON'S RATIO H,o, M s is found from ground amplitudes b (in microns) of surface waves with periods of 20 sec in shallow earthquakes. The magnitude M is based on amplitudes a of P, PP, and S waves in shocks (focal depth h) recorded at the epicentral distance Ll:

Ll

+ F(Ll) M = log a - log T + f(Ll,h) M = M s - 0.37 (M s - 6.7 4) (approximately)

(2i-12)

M s = log b

For F(Ll) and f(Ll,h) , see Table 2i-12; small station corrections are to be added. The amplitudes b of surface waves of length L decrease with increasing focal depth h

TABLE 2i-12. VALUES OF f(Ll,h) IN EQ. (2i-12) FOR VERTICAL COMPONENTS Z OF P AND PP, HORIZONTAL COMPONENT SH OF S, AND F(Ll) FOR HORIZONTAL COMPONF;NT OF l\IAXIMUM (MAX) (h = focal depth; Ll = epicentral distance, deg*) h = 25 km

h = 300 km

r

h = 600 km

Ll

PZ

PPZ

SH

20 30 50 80 100 160

6.0 6.6 6.7 6.7 7.4

.. .

.. .

PPZ

SH

PZ

--- --- ------ ---

5.8 6.3 6.6 6.7 7.4

6.7 6.7 6.9 7.2 6.9

PZ

Max

---

4.0 4.3 4.6 5.0 5.1 5.4

. ..

6.1 6.3 6.1 6.6 7.2

.. .

.. . 6.4 6.6 6.9 6.8 6.6

5.8 6.1 6.7 6.4 6.7

6.4 6.4 6.3 6.2 7.2

., .

.,

.

PPZ

SH

---

--~

... 6.3 6.5 6.8 7.0 6.7

5.9 6.0 6.4 6.5 6.7

* B. Gutenberg, Amplitudes of Surface Waves and Magnitudes of Shallow Earthquakes, Bull. Seis, Soc. Am. 35, 3-12 (1945); Magnitude Determination for Deep-focus Earthquakes, Bull. Seis, Soc. Am. 35, 117~130 (1945). B. Gutenberg and C. F. Richter, Magnitude and Energy of Earthquakes. Ann. Geofis. Rome, 9, 1-15 (1956).

TABLE 2i-13. INTENSITY I AT THE EPICENTER, CORRESPONDING l\IAXIMUM ACCELERATION a, CM/SEC2, MEAN RADIUS r p OF AREA OF PERCEPTIBILITY, KM, FOR A GIVEN MAGNITUDE M IN AVERAGE SHOCKS IN SOUTHERN CALIFORNIA (h = 16 ± KM) (Values for I, a, r are based on empirical equationsj)

M

2.2

3

4

I

6

5

--- ---

I a

rp

1.5 1 0

2.8 3 25

4.5 10 55

6.2 36 110

7

8

81. 2

9.5 460 390

11.2 1,670 740

12.0 3,160 1,000

--7.8 130 200

t B. Gutenberg and C. F. Richter, Earthquake Magnitude, Intensity, Energy, and Acceleration, Bull. Seis, Soc. Am. 32, 163-191 (1942). corresponding to a factor e- q h I L , where q (about 2) depends on crustal structure. The average relationship of intensity to magnitude in California earthquakes is given in Table 2i-13. The energy E corresponding to the magnitude M found from body waves is given to a first approximation I by log E = 12.24 1

+ 1.44M

M. Bath, Earthquake Seismology, Earth-Sci. Revs. 1, 69-86 (1966).

(2i-13)

2-115

SEISMOLOGICAL AND RELATED DATA

2i-l1. Seismicity of the Earth.

Earthquakes are divided into shallow shocks > 300, maximum 720 ± km). Most shocks occur in narrow belts (Table 2i-14).1 Deep and intermediate shocks are limited to the circumpacific belt and the trans-Asiatic (Alpide) belt. For the magnitude of the largest observed shock and the relative frequency of earthquakes in various depth intervals, see Table 2i-15, which also shows examples of regional differences. 2i-12. Energy E of Earthquakes. Most calculations of E depend on Eq. (2i-13). This empirical formula is based on many observations, but is subject to adjustment. (h ::; 60 km), intermediate (60 < h ::; 300), and deep (h

TABLE 2i-14. NUMBER OF SHALLOW, INTERMEDIATJ:c

u

G:i

:c

50 40 30 20 10 5

i

105

I

106

600

500

'" ~~

!;;: w

~ w

:?i

~~ ~'"

~

DISSOCIATION AND RECOMBINATION REACTIONS

AURORAL FORMS

~\It

, =++

1\\1

lIIIlIU\\\\

~

~

I I

1 \

N2+h.-N+N

400

.

l

I c,

>-3 t':l 0 !=O 0

r-

'" 51

>'6300 OFO

-1

300

w

w '" :c

200

Q

0

Q

.....

o

~

t"' E REGION

100

.....

Z

'Xi

--L

0 !=O

CLOUDS

METEORS CAUSE EXCITATION AND IONIZATION

50 40 30

MAXIMUM IONIZATION BY COSMIC RAYS

ZO

10 5

TROPOSPHERE

0

1200

FIG. 2k-2. Structure of the upper atmosphere.

~

M

>'5577 OFO

DRAPERIES

~o;;;:;~ENT

LEVELS OFAIRGLOW EMISSION

II

I

>.< 1250(?) A

\\\\\\ARCS

N

I

104

8 ~~

z

~,

103

0

'"

200

I

102

10\

600

(Prepared in collaboration with W. W. Kellogg and A. Kochanski.)

~ ~

>-3 ..... 0

Z

2-140

MECHANICS

tooo

\ \

\MAXIMUM OF SUNSPOT \ CYCLE

\

"-

~~'::P'b~ ~LE

\ '\

\

-, '\.

~-

\ f.-JF

V~Fl

0

103

105

10"

10'

ELECTRON CONCENTRATION, ELECTRONS Icm 3 (a)

1,000

\ \M:~~~~TUI" \ CYCLE

M~'II:Sl(.~T'\

~ ~ 500

CYCLE

\

\

l-

S e:t c::::: 010 2

jr-*-..:'k--:>.k----4----:?k-';....;B--l'~

Tu

~ 102I---t--t--+---'''k----''k-~__*''---~

:;

~ 10 I 1--+_+----1----:

'-JO

10-

1

t-:3r''---t--t--+---+ ~

10-2 /--+- +--+-

D AT HEIGHT DIAGRAM:

-

1-10 KM FOR ORDINARY TURBULENCE 1-10 KM FOR CUMULUS CONVECTION 1-10 KM FOR CUMULONIMBUS CONVECTION

0 0 0

B 0

z IS DENOTED BY CHARACTERISTIC AREAS ON THE DIFFUSION 0-1 KM

25-35 KM 45 -80 KM

10-25 ,35-45 AND BO-IOO KM

00

xl

HORIZONTAL GROSS -AUSTAUSCH OF THE GENERAL CIRCULATION

FIG. 2k-8. Diffusion diagram.

TABLE

2k-7.

(From Lettau.)

AVERAGE WATER CONTENT OF TYPICAL CLOUDS

Cloud type ...............

Cumulus congestus

Cirrus"

Water content, g m- 3 ••••. 0.01-0.05

4

Fair-weather cumulus 1

Stratus

Strate-

0.3

cumulus 0.2

*

Cirrus clouds consist mainly of column-shaped ice crystals. In cirrostratus, single. more or less completely built columns (twin crystals) of about 100 microns in lengtb and 25 microns in diameter predominate. In dense cirrus and cirrocumulus clouds the columns are incompletely built and occur in clusters. Tbe length of tbe individual crystals in such clusters is approximately 100 to 300 microns and tbe diameter 30 to 100 microns.

TABLE

2k-8.

HEAT BUDGET OF THE ATMOSPHERE·

Absorbed

Units

Lost

Units

Solar radiation ...................

13

Latent heat ...................... Infrared radiation from earth's surface ..........................

23

Infrared radiation to earth's surface ........................... Infrared radiation to space ........

106 47

120

Eddy transfer to ground ..........

3

• After Byers [51.

2-146

MECHANICS

time and space scale. Figure 2k-8 (see Lettau [21]) gives the magnitude of the coefficient of eddy diffusion D as a function of the characteristics of the eddies, as well as the variation of the coefficient of molecular diffusion d with height. In Fig. 2k-8 , each point of the A, \ plane determines a diffusion coefficient (em! seo"). In molecular diffusion, A '" free path and \ '" mean molecular speed; d = A\ is fixed by the density and temperature of the atmosphere; consequently, the height variation of d is marked by a curve. In eddy diffusion, A '" mixing length and \ '" mixing velocity, owing to the variability of these elements, D = AI and its variation with height are denoted by characteristic areas when the possible variability of D is narrowed by the consideration of limiting values of eddy accelerations (\2/ A) and time terms (Vr). Another approach to the problem of turbulent diffusion [Pasquill (27)J has been used to deal with the small-scale dispersion of contaminants in the lower atmosphere. The normal (gaussian) distribution function provides a solution of the form x(x,Y,z,l) = Q(Z".,,-y)-!

-r2

exp - 22 G'y

to the Fickian diffusion equation. In this generalized formula (Gifford [14]), X is the concentration in the cloud or plume of material (which may be invisible), Q is the source strength at an instantaneous point source, and G'y 2 is the variance of the dis-

~

/

~~/ ~

/- ~ ~~

-:'l /; >F

V

/ A

~ ~ ~V :/: ~ 0

/ /

UNSTABLE ~ // // v.\B -- EXTREMELY MODERATELY UNSTABl

~~ ~ 10'V/ 4xI00 ~ 2

C0EF-

2

SLIGHTLY UNSTABLE NEUTRAL SLIGHTLY STABLE MOOERATLEY STABLE

10 2

5 103 2

5

104 2

5

G'y.

/

t V

/c

105

(From Gifford.)

/V

V ./

10---:::V

/0 .>:-;/ \ ....... V

t// h

///

1022

5

./'

»: / ' ......--....-

---

A - EXTREMELY UNSTABLE B - MODERATELYU'lSTABLE C - SLIGHTLY UNSTABLE -NEUTRAL E - SLIGHTLY STABLE F - MODERATELY STABLE

o

/'

DISTANCE FROM SOURCE, METERS

FIG. 2k-9. Graph of

/

'~ / /

10

-:

I

/

10' 2

5

10" 2

5 1

DISTANCE FROM SOURCE, meters

FIG. 2k-l0. Graph of

G'z.

(From Gifford.)

tribution of material in the plume. Since x is assumed equal to ut, where ii. is the unfiuctuating wind velocity component and t is the travel time of the cloud, r 2 = [(x - ii,t)2 + y 2 + Z2]. (Initially it is assumed that the diffusion is isotropic, i.e., G'x = G'y = G'z.) In practice, the assumption is made that the diffusion takes place independently in the three coordinate directions, so that with the graphs of G'y and G'z shown in Figs. 2k-9 and 2k-IO it is possible [14J to compute the concentration under different conditions of atmospheric stability represented by the curves A, B, etc. References 1. Ackerman W. C.: Trans. Am. Geophys. Union. 48, (2) 427-563 (June, 1967). 2. Bates, D. R., P. A. Sheppard, and R. C. Sutcliffe: Proc, Roy. Soc. (London), ser. A, 288,478-588 (1965). 3. Blackadar, A. K., ed.: M eteorol. Monographs. 3, (12-20) 283 pp. + iv, American Meteorological Society, Boston (July, 1957). 4. Bolin, Bert, ed.: "The Atmosphere and the Sea in Motion, The Rossby Memorial Volume," 509 pp., Rockefeller Institute Press in association with Oxford University Press, New York, 1959.

METEOROLOGICAL INFORMATION

2-147

5. Byers, H. R.: The Atmosphere up to 30 Kilometers, pp. 299-370 in "The Earth as a Planet," G. P. Kuiper, ed., Chicago University Press, Chicago, 1954. 6. Committee on Space Research, International Council of Scientific Unions, CI RA 1965 (Cospar International Reference Atmosphere, 1965), North-Holland Publishing Company, Amsterdam, 1965. 7. Environmental Data Service, ESSA: Climatological Data, National Summary (issued, monthly, with an annual summary), Government Printing Office, Washington, D.C., 1950- . 8. Environmental Data Service, ESSA: "Climatic Atlas of the United States," Government Printing Office, Washington, D.C., 1968. 9. Environmental Data Service, ESSA: "World Weather Records" (monthly values and decadal means of pressure, temperature, and precipitation), Government Printing Office, Washington, D.C., 1968. 10. Environmental Jata Service, ESSA: Selective Guide to Published Climatic Data Sources, Rey to Meteorological Records Documentation No. 4.11, Government Printing Office, Washington, D.C., (1969). 11. Fritz, S.: Heating and Ventilating 46, 69-74 (1940). 12. Fritz, S.: J. Meteorol. 11(4), 291-300 (August, 1954). 13. Fritz, S., and T. H. MacDonald: Heating and Ventilating 46, 61-64 (1949). 14. Gifford, F. A., Jr.: An Outline of Theories of Diffusion in the Lower Layers of the Atmosphere, pp. 65-116, in ".vleteorology and Atomic Energy, 1968," D. H. Slade, ed., J. S. Atomic Energy Co-n mission, Oak Ridge, Tenn., July 1968. 15. Glasstone, S.: "Source book on the Space Sciences," 937 pp. + xviii, D. Van Nostrand Co., Inc., Princeton, N.J., 1965. 16. Glueckauf, E.: "The Composition of Atmospheric Air," pp. 3-10, T. F. Malone, ed., American Meteorological Society, Boston, 1951. 17. Greathouse, G. A., and C. J. Wessel, eds.: Deterioration of Materials: Causes and Preventative Techniques, Chap. I in "Climate and Deterioration," Reinhold Book Corporation, N ew York, 1954. 18. Johnson, F. S., ed.: "Satellite Environment Handbook," 2d ed., 193 pp. + xiv, Stanford University Press, Stanford, Calif., 1965. 19. Keeling, C. D.: Tellu8 XII(2), 200-203 (1960). 20. Landsberg, H. E., and J. van Miegham, eds.: "Advances in Geophysics," vols, 1-12, Academic Press, Inc., New York, 1954-1967. 21. Lettau, H.: Diffusion in the Upper Atmosphere, pp. 320-333 in "Compendium of Meteorology," T. F. Malone, ed., American Meteorological Society, Boston, 1951. 22. Letestu, S., ed.: "International Meteorological Tables," WMO-No. 188 TP. 94, Secretariat of the World Meteorological Organization, Geneva, Switzerland, 1966. 23. List, R. J., ed.: "Smithsonian Meteorological Tables," 6th ed., 527 pp. + xi, Smithsonian Institution, Washington, D.C., 1951. 24. Malone, T. F., ed.: "Compendium of Meteorology," 1334 pp. + viii, American Meteorological Society, Boston, 1951. 25. Mintz, Y.: Bull. Am. Meteorol. Soc. 35(5), 208-214 (May, 1954). 26. Oort, A. H.: Monthly Weather Rev. 92(11), 1964,483-493 (November, 1964). 27. Pasquill, F.: "Atmospheric Diffusion," D. Van Nostrand Company, Ltd., London, 1962. 28. Ratcliffe, J. A., ed.: "Physics of the Upper Atmosphere," Academic Press, Inc., New York, 1960. 29. Reed, R. J.: Quart. J. Roy. Meteorol. Soc. 90, 441-466 (1964). 30. Rigby, M., ed.: "Meteorological and Geoastrophysical Abstracts," American Meteorological Society, Boston, 1950-. 31. Thompson, P. D.: "Numerical Weather Analysis and Prediction," The Macmillan Company, New York, 170 pp. + xiv, 1961. 32. U.S. Air Force, Geophysics Research Directorate: "Handbook of Geophysics," rev. ed., The Macmillan Company, New York, 1960. 33. U.S. Environmental Science Services Administration, U.S. National Aeronautics and Space Administration, U.S. Air Force: "U.S. Standard Atmosphere Supplements, 1966," 289 pp. + xx, Government Printing Office, Washington, D.C., 1967. 34. U.S. National Aeronautics and Space Administration, U.S. Air Force, U.S. Weather Bureau: "U.S. Standard Atmosphere, 1962," Government Printing Office, Washington, D.C., 1962. 35. U.S. Navy: "Marine Climatic Atlas of the World," vol. VIII, Government Printing Office, Washington, D.C., 1968. 36. van Zandt, T. E., and R. W. Knecht: The Structure and Physics of the Upper Atmosphere, pp. 166-225 in "Space Physics," D. P. LeG alley and A. Rosen, eds., John Wiley & Sons, Lnc., New York, 1964. 37. World Data Center A, Reports, National Academy of Sciences, Washington, D.C.• 1964-.

21. Density and Compressibility of Liquids! JOHN E. McKINNEY

National Bureau of Standards ROBERT LINDSA Y

Trinity College

Symbols

B* B' B" cs

c C» d~i

K

K* K' K" P S T

t v vo lXp

f3 f3s f3r P Po

complex compressibility Re B* 1m B* adiabatic velocity of sound velocity of sound specific heat at constant pressure specific gravity (t l is temperature of liquid; t2 is temperature of standard) instantaneous bulk modulus complex bulk modulus Re K* 1m K* pressure entropy absolute temperature Celsius temperature specific volume specific volume in reference state isobaric coefficient of volume expansivity instantaneous compressibility adiabatic compressibility isothermal compressibility density density at reference state

21-1. Density of Liquids. Introduction. The density of a homogeneous liquid is defined as the mass per unit volume. The specific volume is the reciprocal of the density. Density can be expressed in either an absolute or a relative scale. The SI (Systeme International) absolute units are kilograms per cubic meter, and the cgs absolute units are grams per cubic centimeter. Before 1964 the liter was defined as the volume required to contain one kilogram of water at 3.98°C and 760 mm Hg pressure, equal to 1.000028 cubic decimeters. In 1964 2 the liter was redefined to be exactly equal to the cubic decimeter. This difference of 28 parts per million may be Contribution of the National Bureau of Standards. not subject to copyright. s Proc. 12th General Conj. Weights and Measures. Paris, p. 21, Oct. 6-13, 1964.

1

2-148

DENSITY AND COMPRESSIBILITY OF LIQUIDS

2-149

significant in measurements of high accuracy. Accordingly, in order to avoid misunderstanding, it has been recommended that for volume measurements of high accuracy the units be expressed in cubic meters or their submultiples, in lieu of liters or their submultiples. The following tables which express densities in grams per milliliter have not been corrected. In cases where accurate data are required, the original source should be consulted to determine the correct units. Table 21-1 gives the conversion factors for the density units most commonly used. TABLE

Units

21-1.

kg/m 3 (SI)

CONVERSION FACTORS FOR DENSITY UNITS*

g/cm 3 (cgs)

g/ml (old)

Ib/ft 3

lb/Ins

10- 3 1.000028 X 10- 3 6.24280 X 10- 2 3.61273 X 1 kg/m 3 (SI). 1 1 1.000028 62.4280 3.61273 X 1 g/cm 3 (cgs) 10 3 1 3.61263 X 0.999972 62.4262 1 g/ml (old). 9.99972 X 10 2 2 2 1.60185 X 10- 1.60189 X 101 16.0185 5.78704 X 1 Ib/fV ...... 4 3 27.6807 1 lb/In! ..... 2.76799 X 10 27.6799 1.72800 X 10 1

10- 6 10- 2 10- 2 10- 4

* Conversions to SI units taken from ASTM Metric Practice Guide, U.S. Department of Commerce, Natl. Bur. Standards Handbook lOll, 38 (Mar. 10, 1967). For expressing densities on a relative scale the specific gravity is used. The specific gravity gives the ratio of the density of a liquid at a particular temperature to the density of a standard liquid (usually pure water) at a standard temperature. The conventional symbol for absolute density is p or d. The former will be used in this set of tables. The conventional symbol for specific gravity is where t 1 is the temperature of the liquid and t 2 is the temperature of the standard. 21-2. Methods of Measurement. The pycnometer method is most commonly used when precise density measurements on a particular liquid are desired at fixed temperature. 1 A pycnometer is a vessel made of glass with a low coefficient of expansion whose volume can be determined very precisely in terms of its capacity for a standard liquid. Most pycnometers have a capacity of about 30 ml. The general procedure consists in filling the pycnometer with the unknown liquid, thermostatting the system at the desired temperature, determining the volume of the pycnometer occupied by the liquid, and then weighing the pycnometer. For accurate work air buoyancy corrections should be applied. For determining densities of the same sample over a range of temperatures, the dilatometer method is sometimes used. In one variation of this method a secondary standard liquid such as mercury is placed in contact with the liquid sample. As the temperature is raised, the secondary liquid is displaced out of the dilatometer. The weight of the displaced secondary liquid is a measure of the change in volume of the unknown liquid. Another variation of this method involves the observation of the change in level of the unknown liquid in a narrow calibrated capillary attached to the main flask. (The measurements of densities of liquefied gases at or near their boiling points are more complicated, since a closed system may have to be used and significant corrections must be made for the density of the vapor in equilibrium with the Iiquid.s) Where less accuracy is required, hydrostatic weighing methods" and hydrometers are expedient. Hydrostatic weigh-

d::

A. Johnson, J. Research Natl. Bur. Standards 69C, 1 (1965). W. H. Keeson, "Helium," pp. 206ff., American Elsevier Publishing Company, Inc., New York, 1942; E. R. Grilly, E. F. Hammel, and S. G. Sydoriak, Phys. Rev. 75, 1103 (1949); E. R. Grilly, J. Am. Chern. Soc. 73, 5307 (1951). 3 H. A. Bowman and R. M. Schoonover, J. Research Natl. Bur. Standards 71C, 179 (1967). (Although this reference is strictly applicable to solids, many of the procedures described here are also applicable to liquids.) 1

2

2-150

MECHANICS

ing involves obtaining the apparent weight of solids (weights) of known mass and density submerged in the liquid from an analytical (or Westphal) balance on a thin wire or thread. A hydrometer is simply a calibrated float which reads the density directly. The performance of the last two methods is impaired by surface tension. Modifications which avoid this are the flotation and the elastic helix methods. The flotation method involves the adjustment of a submerged weight to the same average density as the density of the unknown liquid. At this point the weight will neither sink nor float. Alternatively, a balance is sometimes obtained by appropriately adjusting the temperature of the liquid. The method is tedious, but high accuracy can be obtained. In one version 1 a known electric current producing a magnetic field is adjusted until an iron weight suspended in the field and submerged in the liquid is stationary. With the elastic helix a weight is suspended in the unknown liquid from a completely submerged coil often made of quartz. The density of the liquid is related to the length of the helix. The falling-drop method has been used recently on molten metals" and for the isotopic analysis of water. 3 This method involves measuring the transit time, usually at terminal velocity, of a drop of liquid sample falling within an immiscible liquid or gas. In another version 4 the volume of a falling drop of molten metal is determined by measuring the dimensions of its profile from a photograph. The radiation method," for which the gamma radiation from an irradiated isotope is claimed to be proportional to its density, has been used successfully on liquids at high temperatures. References" are recommended for more detailed and general discussion on most of the methods mentioned above. 21-3. Reliability. The reliability of the density measurements tabulated is variable. This compilation does not pretend to evaluate for extreme accuracy. Such factors as uncertainty in the temperature scale, possible impurities of the samples, and in some cases even changes in atomic weights must be taken into consideration when applying a critical analysis. The data are given as reported in the original literature or in other standard works and are to be interpreted in the spirit of being representative values. Reference to the original literature is recommended in cases of doubt. 21-4. Selected Reference Works with Density Data "International Critical Tables," McGraw-Hill Book Company, New York, 1928. Landolt-Bornstein: "Zahlenwerte und Funktionen aus Physik, Chemie, Astronomie, Geophysik, Technik," 6th ed., Springer Verlag, Berlin, 1950--. Timmermans, J.: "Physico-chemical Constants of Pure Organic Compounds," American Elsevier Publishing Company, Inc., New York, vol. 1, 1950; vol. 2, supplement, 1965. Timmermans, J.: "The Physico-chemical Constants of Binary Systems in Concentrated Solutions," 4 vols., Interscience Publishers, Inc., New York, 1959-1960. Mellor, J. W.: "Comprehensive Treatise of Inorganic and Theoretical Chemistry," Longmans, Green & Co., Ltd., London, 16 vols., 1921-1937; supplements, 1956-1967. Simons, J. H., ed.: "Fluorine Chemistry," Academic Press, Tnc., New York, 1950. Lyon, R. N., ed.: "Liquid Metals Handbook," U.S. Atomic Energy Commission and Bureau of Ships, Chap. 2, 1952; Sodium-NaK Supplement, 1955. F. J. Millero, Jr., Rev. Sci. Lnstr. 38, 1441 (1967). 217. V. Naidich and V. N. Erernenko, Fiz. Metal. i Metalloved. (USSR) 11,883 (1961); English translation in Phys. Metals Metallo(}. 11(6), 62 (1961). 3 M. Pascalau, L. Blaga, and L. Blaga, J. Sci. Lnstr. 43, 310 (1966). 4A. E. El-Mehairy and R. G. Ward, Trans. Met. Soc. AIME 227,1226 (1963). 5 I. G. Dillon, P. A. Nelson, and B. S. Swanson, J. Chern. Phys. 44,4229 (1966); Rev. Sci. Lnstr, 37, 614 (1966). 6 P. Hidnert and E. L. Peffer, Nail. Bur. Standards Circ. 487 (Mar. 15, 1950); N. Bauer, Chap. 6 in "Physical Methods of Organic Chemistry," vol. I, A. Weissberger, ed., Interscience Publishers, Inc., New York, 1949; J. Reilly and W. N. Rae, "Physico-chemical Methods," vol. I, pp. 609-628, D. Van Nostrand Company, Inc., Princeton, N.J., 1953. 1

DENSITY AND COMPRESSIBILITY OF LIQUIDS

2-151

Stewart, R. B., and V. J. Johnson, eds.: "Compendium of the Properties of Materials at Low Temperature" (Phase I), Wright Air Force Development Division Technical Report, 1961. Morey, G. W.: "The Properties of Glass," Reinhold Book Corporation, New York, 1954. Janz, G. J.: "Molten Salts Handbook," Academic Press, Inc., New York, 1967. Janz, G. J., F. W. Dampier, G. R. Lakshminarayanan, P. K. Lorenz, and R. P. T. Tomkins: Molten Salts: vol I, Electrical Conductance, Density, and Viscosity Data, Natl. Bur. Standards Ref. Data Ser. 15, October, 1968. The following contain tabulated sheets published periodically: Zwolinski, B. J.: "Selected Values of Properties of Hydrocarbons and Related Compounds,"! Thermodynamics Research Center, Texas A&M University, College Station, Texas, 1966--. Zwolinski, B. J.: "Selected Values of Properties of Chemical Compounds," Thermodynamics Research Center, Texas A&M University, College Station, Texas, 1966--. Zwolinski, B. J.: "Selected Data on Thermodynamics and Spectroscopy," Thermodynamics Research Center, Texas A&M University College Station, Texas, 1969--.

21-6. Density of Water. A rather complete analysis of all the investigations of the physical properties of water is given by N. Ernest Dorsey.! He points out that the data from which the density tables are made up do not take into consideration the isotope effect. Because of this there may be uncertainties of the order of 8 parts in 10 7 introduced when the densities of samples from various sources are considered. The removal of deuterium from an average sample of distilled water increases the density by about 17 parts per million. There is also some reason to believe that the polymerization is a factor in the variability of the physical properties of water. Values of the density of water as a function of temperature are presented in Table 21-2. American Petroleum Institute Project 44. N. Ernest Dorsey, "Properties of Ordinary Water Substance," Reinhold Book Corporation, New York, 1948. 1

2

2-152 TABLE

MECHANICS

21-2.

H 20 AT (p = g/rnl*; t = °C)

DENSITY OF PURE AIR-FREE

ATMOSPHERIC PRESSURE

Range G-40°ct

t

t 15 16 17 18 19 20 21 22 23 24 25

0 1 2 3 4 0.0 0.9991286 0.9989721 0.9988041 0.9986248 0.9984346 0.9982336 0.9980221 0.9978003 0.9975684 0.9973266 0.9970751

p t p t p 0.9998676 0.9999919 5 10 0.9997281 0.9999265 6 0.9999683 0.9996336 11 0.9999678 0.9999297 12 7 0.9995261 0.9999922 8 0.9998765 13 0.9994059 9 0.9998092 1.0000 14 0.9992732 I 0.1 -0.2- -0.3- -0.4- -0.5- -0.6- -0.7- -0.81134 0982 0828 0674 0518 0360 0202 0043 9558 9394 9229 9062 8895 8726 8557 8386 7867 7691 7515 7337 7158 6979 6798 6616 6063 5877 5689 5501 5311 5120 4928 4735 4150 3953 3754 3555 3355 3153 2950 2747 2130 1922 1713 1503 1292 1080 0867 0653 0004 9786 9567 9346 9125 8903 8679 8455 7776 7547 7318 7088 6856 6624 6390 6156 5447 5208 4969 4729 4487 4245 4002 3758 3019 2771 2522 2272 2021 1769 1516 1262 0494 0237 9978 9718 9458 9196 8934 8671

t

p

t

p

t

p

26 27 28 29 30

0.9968141 0.9965437 0.9962642 0.9959757 0.9956783

31 32 33 34 35

0.9953722 0.9950575 0.9947344 0.9944030 0.9940635

36 37 38 39 40

0.9937159 0.9933604 0.9929970 0.9926260 0.9922473

Range 40-100°Ct

t

p

t

p

t

p

40 45 50 55 60

0.99224 0.99024 0.98807 0.98573 0.98324

65 70 75 80 85

0.98059 0.97781 0.97489 0.97183 0.96865

90 95 100

0.96534 0.96192 0.95838

Range 100-370°C§ t

p

t

p

t

p

100 110 120 130 140 150 160 170 180

0.95841 0.95099 0.94317 0.93494 0.92629 0.91721 0.90771 0.89776 0.88733

190 200 210 220 230 240 250 260 270

0.87639 0.8i3492 0.85290 0.84031 0.82712 0.81330 0.79881 0.78368 0.76769

280 290 300 310 320 330 340 350 360

0.75063 0.73237 0.71266 0.69118 0.66747 0.64095 0.61071 0.57497 0.52872

See page 2-153 for footnotes.

0.9 9882 8214 6433 4541 2542 0438 8230 5921 3512 1007 8406

DENSITY AND COMPRESSIBILITY OF LIQUIDS TABLE

21-2.

DENSITY OF PURl~ AIR-FRl. Max. temperature: 425°C Substance: Liquid naphthalene Reference: R. B. Owens, J. Chern, Phys. 44, 3918 (1966). Pressure range: 450 to 9,000 atm Temperature range: 300 to 500°C Substances: (molten nitrates') Lithium nitrate Sodium nitrate Potassium nitrate Rubidium nitrate Silver nitrate I For general reference on molten salts, see: G. J. Janz, "Molten Salts Handbook," Academic Press, Inc., New York, 1967.

DENSITY AND COMPRESSIBILITY OF LIQUIDS

2-183

Reference: J. W. M. Boelhouer, Physica 34, 484 (1967). Pressure range: 1 to 1,400 atm Temperature range: - 20° to 200°C Substances: (alkanes") Heptane Hexane Octane Nonane Hexadecane

21-12. Compressibility of Liquids.

The instantaneous compressibility is defined by {j =

_

~ dv v dp

(21-8)

and its reciprocal, the instantaneous bulk modulus, is accordingly defined by K = -v dp

(21-9)

dv

In some definitions v preceding the derivatives in the above is replaced by Vo, the value of v at one atmosphere. Bridgman" uses this form which he calls the compressibility proper. As with the specific volume (Sec. 21-6) the compressibility depends upon the temperature and pressure history of the sample. The simplest and most familiar thermodynamic paths are the isothermal and adiabatic (which are reversible when not influenced by viscosity) for which the instantaneous isothermal compressibility is

(jT =

_

!

v

(av) ap

T

(21-10)

and the instantaneous adiabatic compressibility is

(js = where S is the entropy," to be related by

_

! v

(av) ap s

(21-11)

From reversible thermodynamics! the above may be shown {jT -

{js

Ta

2

p =pCp

(21-12)

where T is the absolute temperature, a p is the isobaric thermal expansivity, and C» is the isobaric heat capacity. Isothermal compressibilities may be derived from equilibrium PVT isobars. Adiabatic compressibilities are usually obtained directly from acoustic propagation using the relation (21-13) where Cs is the adiabatic phase velocity, and po is the density in the absence of the acoustic field. In order to apply Eq. (21-13), measurements must be made at frequency well removed from the dispersion region of the phase velocity. The values of {jT in Tables 21-26 through 21-30 were obtained by first determining mean values of {jT from equilibrium PVT data using 1,000 kgjcm 2 intervals and then interpolating from the smoothed curve on a {jT versus pressure curve. 1

Adiabatic compressibilities taken from sound velocity data.

P. W. Bridgman, "The Physics of High Pressure," p, 169, G. Bell & Sons, Ltd.• London. 1949. 3 In reversible systems there is no distinction between the adiabatic and isentropic path. 4 See. for example. M. W. Zemansky, "Heat and Thermodynamics," p. 260. McGrawHill Book Company, New York, 1957. 2

2-184

MECHANICS

TABLE 21-26. ISOTHERMAL COMPRESSIBILITY OF WATER (Calculated from PVT data of Table 21-13; all values in units of 10-12 ems/dyne: reliability ±5%) Pressure, kg/ern!

O°C

20°C

60°C

100°C

--- --- --- --I

45 41 36 30 25 21 18

46 43 37 30 25 22 19 ., . .. . ., .

250 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000 10,000 11 ,000

47 42 35 29 25 21 19 16 15 14 13 12 11

. .. ... . .. ., . ...

.. . .. . .. .

"

.

51 46 36 30 25 22 19 17 15 14 13 12 12

For adiabatic and isothermal values obtained from velocity of sound data, see R. Vedam and G. Holton, J. Aco'Ust. Soc. Am. (3, 108 (1968).

TABLE 21-27. ISOTHERMAL COMPRESSIBILITY OF 99.9% D 20 (Calculated from PVT data of Table 21-14; all values in units of 10-12 ems/dyne: reliability ±5%) Pressure, kg/em!

O°C

20°C

100°C

--- --- --I

1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000 10,000 11,000

54 41 32 26 21 18

... ...

...

.. . .. . .. .

47 37 30 25 21 18 16 15 14

... ...

...

48 36 30 26 22 19 17 15 14 13 12 11

2-185

DENSITY AND COMPRESSIBILITY OF LIQUIDS TABLE

21-28.

ISOTHERMAL COMPRESSIBILITIES OF CERTAIN ORGANIC LIQUIDS

({3T in

units of 10- 12 cm 2jdyne; reliability ±5%)

Substance

Pressure, kgjcm 2

t(OC)

{3T

Ref.

-----

20 20 20 20 20 20 20 20 20 20 25 20 20 20 20 20 20 20 20 20 20 20 20 20

1 1 5,000 1 1 1 5,000 1 1

Acetic acid ................ Acetone ............ , ...... Aniline ................... Benzene .................. Carbon disulfide ........... Carbon tetrachloride ....... Chlorobenzene ............. Chloroform ................ Cyclohexane ............... Ether .....................

1.. 1 1 5,000 1 1 5,000 1 1 5,000 1 1 5,000 1 1

Ethyl acetate .............. Ethyl alcohol .............. Ethylene chloride .......... Glycerin ... , .............. Heptane .................. Methyl alcohol. ........... Nitrobenzene .............. Toluene ...................

91 126 21 45 95 93 21 106 74 101 110 187 22 113 111 22 80 21 12 144 123 21 49 91

1 2 3 1 2 2 3 2 1 2 1 2 3 1 2 3 1 3 3 2 2 3 1 2

References for Table 21-28 1. Data from "International Critical Tables," McGraw-Hill Book Company, New York. 2. Data from "Tables annuelles de constantes et donnees numeriques," vol. 9, GauthierVillars, Paris, and McGraw-Hill Book Company, New York, 1929. 3. Calculated from PVT data in this section. TABLE

21-29.

ISOTHERMAL COMPRESSIBILITY OF SULFURIC AND NITRIC ACIDS*

Mean compressibility cofficient

-

106 (VI - V2) am t -1 --

{3T=-

VI

P2 - PI

t,OC

Substance

PI, P2, atm

~T

1, 161 1, 32

,,-,33 "-'35

---

Sulfuric acid ............ Nitric acid ..............

12.6 0

* L. Decombe and J. Decombe, p. 35 in "International Critical Tables," vol. 3, McGraw-Hill Book Company, New York, 1928. 21-13. Complex Compressibility.

If a liquid is subjected to a sinusoidally time-

2-186

MECHANICS

dependent excitation, the oscillating pressure may not be in phase with the corresponding oscillating volume. If the amplitude of the pressure is sufficiently small to obtain linear response, the amplitude and phase relationships bet-ween pressure and dilatation may be given by a complex (frequency-dependent) compressibility,

B*

=

B' - iB"

(21-14)

where B' is the ratio of the amplitude of the component of negative dilatation in phase with the pressure to pressure, and B" is the corresponding ratio of negative

TABLE 21-30. ISOTHERMAL COMPRESSIBILITY {3T AND ADIABATIC COMPRESSIBILITY {3s OF MERCURY* (Units of bars") Pressure, kbars 1 2 3 4 5 6 7 8 9 10 11 12 13

{3T

X 106

3.881 3.751 3.632 3.522 3.419 3.324 3.235 3.15 3.07 3.00 2.93 2.87 2.80

{3s

t = 52.9°C

t = 40.5°C

t = 21.9°C X 10 6

{3T

3.395 3.289 3.192 3.102 3.018 2.941 2.868 2.799 2.735 2.674 2.616 2.562 2.510

X 10 6

{3s

3.963 3.827 3.702 3.587 3.481 3.383 3.290 3.20 3.12 3.05 2.98 2.91 2.84

X 10 6

3.444 3.334 3.234 3.141 3.055 2.975 2.900 2.829 2.763 2.701 2.641 2.585 2.532

{3T

X 106

4.018 3.878 3.749 3.632 3.523 3.422 3.327 3.24 3.16 3.08 3.01 2.94 2.87

{3s

X 106

3.477 3.365 3.262 3.167 3.080 2.998 2.921 2.850 2.782 2.719 2.6.59 2.602 2.548

Adiabatic values were obtained from acoustic propagation, using Eq, (21-13). These were converted to isothermal values, using Eq. (21-12). For isothermal values over a wider temperature range, see: L. B. Smith and F. G. Keyes. Proc. Am. Acad. Arts Sci. 69, 313 (1934). * L. A. Davis and R. B. Gordon. J. Chern. Phys. 46, 2650 (1967).

dilatation lagging the pressure by 11"/2. is the complex bulk modulus,

K*

The reciprocal of the complex compressibility

=

K'

+ iK"

(21-15)

All the components must be nonnegative quantities in both the above definitions. The complex functions are usually used to study viscoelastic response.' Accordingly, it is necessary to separate the contributions from viscosity and heat of compression. The mest convenient manner to obtain this resolution is by a selection of frequencies or boundary conditions to achieve (essentially) either adiabatic or isothermal conditions over a cycle. However, in obtaining extensive data over a wide 1 See, for example: J. D. Ferry, "Viscoelastic Properties of Polymers," John Wiley & Sons, Inc., New York, 1961.

VISCOSITY OF LIQUIDS

2-187

range of frequencies, achieving the above conditions is not always possible, and resolution may be extremely difficult. Complex compressibility data may be obtained by acoustic propagation (using both bulk and shear waves) by means of the relations given by Herzfeld and Litovitz.! These relations reduce to Eq. (21-13) at the low-frequency limit. Except for the molten metals, the conditions are approximately adiabatic for most liquids below 10 MHz. Marvin and McKinney 2 review other, more novel methods used in polymer and glass-forming liquids to obtain complex compressibilities and time-dependent response functions which are equivalent. Table 21-30 gives the compressibilities for mercury obtained from velocity of sound data at frequencies well below the dispersion region. The adiabatic compressibilities were obtained using Eq. (21-13). These were converted to isothermal values by means of Eq. (21-12).

2m. Viscosity of LiquidsROBERT S. MARVIN

National Bureau of Standards DAVID L.

HOGENBOOM

Lafayette College

2m-I. Units and Symbols TJ

J1

T

viscosity Dimensions: ML-IT-l cgs unit: poise = dyne-s cm- 2 = g crn " S-1 81 unit (no coined name) = kg m:" S-1 = 10 poise (viscosity of water ~ 10- 2 poise = 10- 3 81 unit) kinematic viscosity = viscosity/density Dimensions: L2T-l cgs unit: stokes = cm 2 S-1 81 unit: (no coined name) = m 2 S-1 = 10 4 stokes (kinematic viscosity of water ~ 10- 2 stokes = 10- 6 81 unit) Kelvin temperature Celsius temperature

2m-2. Introduction. Definition of Viscosity. Viscosity is a material property involved in the relationships between the internal forces in a moving fluid and the kinematical quantities describing its motion. A more specific definition must be based on certain assumptions about the material which are normally expressed in terms of a constitutive equation-in effect, a nonequilibrium equation of state relating 1 K. F. Herzfeld and T. A. Litovitz, "Absorption and Dispersion of Ultrasonic Waves," p. 450, Academic Press, Inc., New York, 1959. 2 R. S, Marvin and J. E. McKinney, chap. 9 in "Physical Acoustics," vol. 2B, W. P. Mason, ed., Academic Press, Lnc., New York, 1965. 3 Contribution of the National Bureau of Standards, not subject to copyright.

2-188

MECHANICS

stress (which reduces to the static pressure when the fluid is in static equilibrium), temperature, density, the rate of deformation, and perhaps other state properties which vanish at equilibrium.' The Navier-Stokes equation includes the familiar Newtonian hypothesis about the resistance to flow in fluids. This can be formulated in terms of a constitutive equation involving two material parameters, a bulk and a shear viscosity, analogous to the bulk and shear moduli of classical elasticity theory. These viscosities are assumed to be functions of density and temperature, but not of kinematical quantities. The unmodified term viscosity implies shear viscosity. We cannot, strictly speaking, be sure that any real liquid obeys this linear constitutive equation under all conditions, since in some types of flow the influence of various complicating factors such as inertial and viscous heating effects precludes an unambiguous evaluation of material properties. But, at least in the types of flow normally studied, the behavior of most low-molecular-weight homogeneous liquids is described by the Navier-Stokes equation. Such liquids are commonly termed Newtonian. Many other liquids show marked deviations from such behavior, and their properties must be described by a more complicated constitutive equation. In such liquids the stress associated with a steady flow is not proportional to the velocity gradient and, indeed, will not even be oriented in the same direction. Nonetheless, it is frequently possible to define a viscosity for such liquids as the ratio of stress to rate of strain measured in simple steady shear flow which has persisted for a sufficiently long period of time. The viscosity so defined is, of course, a function of the rate of shear. Even in a non-Newtonian fluid the stress associated with a flow whose amplitude is sufficiently small or velocity sufficiently slow will be (at least within the precision of ordinary measurements) proportional to the magnitude of the velocity gradient, but time effects (or frequency effects) may be observed. We term the idealization which represents this type of behavior a linear viscoelastic material, and consider this one special case of a non-Newtonian material. One method of expressing the properties of a linear viscoelastic material is in terms of a (complex) dynamic viscosity (and dynamic bulk viscosity) defined as a ratio of stress to rate of strain for a strain varying sinusoidally in time.! Values of dynamic viscosity (or other equivalent linear viscoelastic properties) are reviewed by Ferry" for a number of polymeric systems. Acoustic measurements of both shear and volume viscosity, and results for a number of different types of liquids, are discussed by Litovitz and Davis." Many measurements of viscosity as a function of rate of shear, and attempts to relate this function to other rheological and/or structural properties, have been reported. The general, though not universal, pattern shows it decreasing monotonically with rate of shear, with (established or at least suggested) limiting values at both high and low rates. Changes in temperature, concentration, and molecular weight cause pronounced and often complex changes. Though some generalizations are suggested by recent work, nothing that permits a simple and concise tabulation of such behavior is yet established. 2m-S. Accuracy and Precision of Measurement. The remainder of this section will deal only with the shear viscosity (or simply viscosity) of Newtonian liquids. W. E. Langlois, "Slow Viscous Flow," The Macmillan Company, New York, 1964. At one time the term dynamic viscosity was used for the shear viscosity of a Newtonian liquid (to distinguish it from kinematic viscosity, the viscosity divided by density). Though still occasionally used in this sense, dynamic viscosity now generally denotes the frequency-dependent quantity defined above. 3 J. D. Ferry, "Viscoelastic Properties of Polymers," 2d ed. John Wiley & Sons, Inc., N.Y., 1970. 4 T. A. Litovitz and C. M. Davis, in "Physical Acoustics," W. P. Mason, ed., vol. 2A, Academic Press, Inc., N.Y., 1965. 1

2

VISCOSITY OF LIQUIDS

2-189

Most measurements have been made in relative instruments which require calibration with a liquid of known viscosity, generally (either directly or indirectly) water at 20°C and one atmosphere. Normal variations in atmospheric pressure and in the exact composition of distilled water do not influence its viscosity appreciably. Significantly different values have been used as the basis for such calibrations during the past 40 years. Dorsey, in compiling viscosities for the International Critical Tables, adopted the value of 0.01009 poise, based on his evaluation of measurements available at that time. Bingham and Jackson,' evaluating the same measurements, selected a value of 0.01005 poise which was rather generally accepted for a number of years. The value currently used throughout most of the world is 0.01002 poise (corresponding to 1J/p = 0.01004 stokes) due to Swindells, Coe, and Godfrey.! All these values are based on measurements in capillary viscometers with a precision of 0.1 per cent or better. The differences appear due to various systematic errors, some associated with end effects which cannot be calculated exactly. Experiments just completed at the National Bureau of Standards suggest that we should assign an uncertainty of ± 0.2 per cent to the value 0.01002, this representing an unexplained disagreement between two absolute measurements, each with a precision of 0.1 per cent. One involved flow through a pipe; the other oscillations of a liquid contained within a sphere. Ordinary low-molecular-weight liquids have viscosities no greater than a few centipoises at room temperature and one atmosphere. Measurements relative to water can be reproduced to ±0.1 per cent in this low-viscosity range. Comparative measurements of viscosities up to several hundred poises can be made with nearly this precision, and are often used in specifications for liquids whose exact composition is unknown. A determination of the viscosity of such liquids relative to water, however, requires additional measurements which increase the uncertainty to about ± 0.5 per cent. Above about 10 3 poises, problems of measurement andtemperature control normally limit the reproducibility of viscosity measurements to a figure greater than one per cent. 2m-4. Relationship to Structure, Temperature, and Pressure. Our understanding of the liquid state has advanced considerably during the past decade, but we cannot yet calculate transport properties from equilibrium properties, except for a few nearly spherical molecules, and even then with an accuracy significantly less than the accuracy of measurement. 3-5 Viscosities of the inert gases in both liquid and gaseous states can be represented rather successfully in terms of an empirical correlation involving reduced viscosities, temperature, and pressure (actual values divided by values at the critical point)." For more complex liquids, other correlations, whose form is suggested by theory but involving some empirical quantities, have been developed to express the influence of temperature, pressure, the variations between similar compounds, and the viscosities of mixtures.?"! 1 E. C. Bingham and R. F. Jackson, Standard Substances for the Calibration of Viscorneters, Bull. Bur. Standards 14, 59 (1918-1919); Scientific Paper 298. 2 J. F. Swindells, J. R. Coe, Jr., and T. B. Godfrey, J. Research Natl. Bur. Standards 48, 1 (1952); RP 2279. 3 S. G. Brush, Chern. Rev. 63, 513 (1963). 4 S. A. Rice, J. P. Boone, and H. T. Davis, in "Simple Dense Fluids," H. L. Frisch and Z. W. Salsburg, eds., Academic Press, Inc., New York, 1968. "P. Gray, in "Physics of Simple Liquids," H. N. V. Temperley, J. S. Rowlinson, and G. S. Rushbrooke, eds., North-Holland Publishing Company, Amsterdam, 1968. 6 H. Shimotake and G. Thodos, A.I.Ch.E. Journal 4, 3,257 (September, 1958). 7 A. Bondi, in "Rheology: Theory and Applications," vol. 4, F. R. Eirich, ed., Academic Press, Inc., New York, 1967. 8 A. Bondi, "Physical Properties of Molecular Crystals, Liquids, and Glasses," John Wiley & Sons, Ine., New York, 1968. 9 R. C. Reid and T. K. Sherwood, "The Properties of Gases and Liquids," 2d ed., MeGraw-Hill Book Company, New York, 1966.

2-190

MECHANICS

In the higher-temperature portion of the normal liquid range, the prediction of the reaction-rate theory that viscosity is proportional to exp (liT) is reasonably accurate. In the lower-temperature range, particularly for glass-forming liquids, it is more nearly proportional to exp [l/(T + A)]. This latter proportionality can be predicted from the free-volume theory of Cohen and Turnbull,' the significant structure theory of Eyring and coworkers," or the configurational entropy theory of Adam and Gibbs." For most liquids no single expression of either type holds over the whole liquid range. 4 Attempts to represent the influence of pressure by anything other than a strictly empirical expression have been relatively unsuccessful. The reaction-rate and freevolume theories mentioned above can represent such data, but only by adjusting the parameters involved so that their original meaning becomes questionable. 2m-5. Values of Viscosity. The various general tabulations or handbooks ("International Critical Tables," Landeldt-Bornstein, "Smithsonian Physical Tables," "Handbook of Chemistry and Physics," etc.) generally contain extensive data on the viscosity of liquids. Most of these tabulations were prepared by individuals well qualified to select the best available values, or were reproduced from earlier tabulations prepared by such individuals. The measurements on which most of them are based are equivalent to those commonly used today, but they may not be consistent with present measurements simply because of the different values for the viscosity of water to which relative measurements have been referred from time to time. Some extensive tabulations may not even be internally consistent because of this factor, and in some cases the basis used is not stated. For most liquids, however, particularly those with viscosities of less than one poise, impurities in the samples measured are likely to introduce greater uncertainties than systematic errors in measurement. For many organic liquids viscosity is at least as sensitive a measure of purity as most of the methods normally employed. We may reasonably assign an uncertainty of ± 0.2 per cent to the values given here for water, this representing a limitation due to possible systematic errors in measurement. Critical evaluations of the measurements on most other liquids have not been made. Where such evaluations have been attempted, the uncertainty estimates are rarely less than one percent. This point is stressed because values of viscosity are often reported and tabulated to 0.1 per cent-a reasonable precision or reproducibility of measurement, but seldom a realistic uncertainty in the values. There is no general tabulation of viscosity values based on a current critical assessment of the purity of the material and the adequacy and reliability of the measurements. Nor is there likely to be such a tabulation produced by any single group. Both the magnitude of the problem and the special background required for a critical evaluation of the data for any given class of compounds suggest that such tabulations will probably be made by different individuals or groups for each class of compounds or materials. 2m-G. Selected Values at One Atmosphere. We emphasize here a few cases in which at least a start has been made toward a critical evaluation of the available data. Because of limited space we reproduce only a few values, and give references to more complete tabulations. W utero The viscosity of water has been studied extensively, and careful relative measurements by various investigators agree to within about 0.1 per cent. No particular problem arises because of impurities, and any variation due to the quantity M. H. Cohen and D. Turnbull, J. Chem. Phys. 31, 5, 1164 (1959). T. S. Ree, T. Ree, and H. Eyring, J. Phys. Chem. 68(11), 3262 (1964). 3 G. Adam and J. H. Gibbs, J. Chem. Phys. ~3(1), 139 (1965). 4 A. Bondi, in "Rheology: Theory and Applications," op, cit. 1

2

2-191

VISCOSITY OF LIQUIDS TABLE

2m-I.

VISCOSITY OF LIQUID WATER AT ATMOSPHERIC PRESSURE

T'em perature.Pt) Viscosity, cp 5 1. 518* 20 1.002t 40 0.6527t 60 O. 4665t

Temperature, °C 75 100 125 150

Viscosity, cp 0.3784t O. 2820t 0.2:219t 0.1815t

... R. C. Hardy and R. L. Cottington, J. Research Natl. Bur. Standards 42, 573 (1949) (adjusted to 1.002 cp at 20°) t A. Korosi and B. M. Fabuss, Anal. Chem, 40, 157 (1968).

of dissolved gas appears to be less than the ± 0.2 per cent uncertainty that we must assign owing to present limitations in absolute measurements.! Both sets of measurements were carried out in relative capillary instruments. They agree to within 0.1 per cent where the temperature ranges overlap (20 to 125°C). Pressures up to those required to maintain the liquid state above 100° did not have any significant effect on measurements below 100°. The measured values are given with an error of less than 0.1 per cent up to 75° and a maximum of 0.16 per cent to 150° by I '720 A(t - 20) + B(t - 20)2 OglO~ = C +t with A = 1.37023 B = 0.000836 C = 109

'720 7]1

t

is viscosity at 20°C is viscosity at tOC is temperature in "C

Simple Liquids. "Simple" liquids refers here to those whose molecules are essentially spherical, which current statistical mechanical theories attempt to describe. They include the noble gases, the homonuclear diatomic molecules, and some polyatomic but nearly spherically symmetrical molecules. References 1. Johnson, V. J. ed.: "A Compendium of the Properties of Materials at Low Temperatures" (Phase I), part I, "Properties of Fluids," Wright Air Force Development Division Technical Report, 60-56, July, 1960 (available from Clearinghouse for Federal Scientific and Technical Information, Springfield, Va.). Includes tables and graphs of selected values of the viscosity of liquid (and gaseous) : Helium, hydrogen, neon, argon Nitrogen, oxygen, carbon monoxide, fluorine, methane 2. Rice, S. A., J. P. Boone, and H. T. Davis: "Simple Dense Fluids," H. L. Frisch and Z. W. Salsburg, eds., Academic Press, Inc., New York, 1968. Includes a literature survey to November, 1966, of theoretical and experimental results on transport properties of simple fluids. 3. Gray, P.: "Physics of Simple Liquids," H. N. V. Ternperley, J. S. Rowlinson, and G. S. Rushbrooke, eds., North-Holland Publishing Company, Amsterdam, 1968. Discusses measurements on liquid argon. 4. Shimotake, H. and G. Thodos, A.I.Ch.E. Journal 4(3), 257 (September, 1958). Includes an often-reproduced Reduced State Viscosity Chart for the Inert Gases.

Organic Compounds. An evaluation of measurements on organic compounds requires that careful attention be given to the adequacy of the methods of purification, particularly for the higher members of a homologous series (from about C, or C I O on in most cases). Most existing tabulations make no statement about the criteria applied to the measurements selected. Two which do are the American Petroleum Institute Research Project 44 "Tables of Selected Values of Properties of Hydrocar1

J. Kestin and J. H. Whitelaw, Phys. of Fluids 9(5), 1032 (May, 1966).

2-192

MECHANICS

bons and Related Compounds,"! and Timmermans' "Physico-chemical Constants of Pure Organic Compounds."! In both cases the compilers considered both the purity of the compounds measured and the techniques of measurement in selecting values they considered reliable. Timmermans presents the original data considered reliable; the API compilers present "average" values calculated from an empirical viscositytemperature equation fitted to the selected data for each compound. Timmermans includes all organic compounds for which he found measurements which met his criteria in the literature to the end of 1964 (vol. 2; vol. 1 covers literature to 1950). The API tabulations aim at a more limited class of materials. The coverage of their present tables is shown in our Table 2m-2; additional issues on viscosity are planned for about 1971. The estimated uncertainty in the API Tables is indicated in a general way as varying between ±3 in the last figure listed to 10 times this amount (except where values are tabulated to 10- 4 cp, in which case they estimate the uncertainty as between 1 and 3 X 10- 3 cp). Though not stated specifically, these estimates presumably represent a lack of agreement bi-tween various measurements deemed equally reliable. These estimates are consistent with Timmermans' statement that few measurements of viscosity are reliable to better than one per cent. Timmermans' listing of separate measurements considered reliable permits some evaluation of uncertainty on the part of the reader, though generally the temperatures of the original measurements are not exactly the same, and so no direct and simple comparison of the values that he lists is possible. A tabulation of the viscosities of over 300 organic compounds up to C Sh including many ring and many sulfur-containing compounds, is given in a report." of the work carried out at The Pennsylvania State University over a period of several years. The estimated accuracy of these measurements is ± 0.5 per cent.! The primary emphasis of this project was on the preparation and purification of the compounds used." Measurements of the viscosity of normal paraffins from C 6 to C 64 have been reported by Doolittle and Peterson. 6 Glycerol-Water Solutions. Glycerol has been the subject of a number of studies. Unfortunately, it is difficult to obtain (and maintain) this compound free of water, and most measurements have been made on samples which apparently were not pure. Table 2m-3 shows the unusual sensitivity of the viscosity of this liquid to small amounts of water as a contaminant. Note that even the relative values (viscosities at various temperatures divided by the viscosity at a reference temperature) change significantly with composition. Molten Salts. The first output of the National Standard Reference Data System to include critical evaluations of viscosity data is a recent publication by Janz, 1 American Petroleum Institute Research Project 44, "Selected Values of Physical and Thermodynamic Properties of Hydrocarbons and Related Compounds," Carnegie Institute of Technology, Pittsburgh, Pa. (Present address: Thermodynamics Research Center, Texas A&M University, College Station, Tex.) 2 J. Timmermans, "Physico-chemical Constants of Pure Organic Compounds," American Elsevier Publishing Company, Inc., New York, vol. 1, 1950; vol. 2, supplement, 1965; J. Timmermans, "The Physico-chemical Constants of Binary Systems in Concentrated Solutions," vols, 1 and 2, "Two Organic Compounds," 1959; vol , 3, "Systems with Metallic Compounds," 1960; vol. 4, "All Other Systems," 1960; Interscience Publishers, Inc., New York. 3 "Properties of Hydrocarbons of High Molecular Weight Synthesized by Research Project 42 of the American Petroleum Institute," American Petroleum Institute, New York, 1967. 4 Private communication, Professor J. A. Dixon, Director, API Research Project 42, 1955-1967. 5 R. W. Schiessler and F. C. Whitmore, Ind. En(J. Chem. 47(8), 1660 (August, 1955). 6 A. K. Doolittle and R. H. Peterson, J. Am. Chem Soc. 73, 2145 (1951).

TABLE

2m-2.

VISCOSITIES OF HYDROCARBON LIQUIDS*

Viscosity in centipoiset (multiply by 10-1 for 8I Units) Compound

Formula

lmax,oC

tmin,OC tmin

I

0

n-Paraffins (CnH2n+2), CI through C20. Table -185 0.225: CH4 ....... Methane ............................. -130 0.278 3.62: n-Pentane ............................ CSHl~ -55 2.11 0.7104 n-Octane ............................. CaHlS -10 2.901: 2.271 n-Dodecane .......................... Cl2H 26 3.474 20 n-Hexadecane ......................... ClsHa4 ...... 35 4.685: n-Eicosane ........................... C2oH42 .0

••••

20

I

I

25

I

30

I

100

I

t max

20c (Part I), 1955

. ......

..... .

. .....

0.234 0.5450 1.503

0.224 0.5136 1.374 3.086

0.215 0.4850 1.261 2.758

3.474~

. ......

..... .

. .....

Normal Alkyl Cyclopentanes (C nH 2n), C6 through C21. Table 22c (Part 1), -25 0.78 0.553 0.438 0.415 Cyclopentane ......................... CSHIO C 6H12 -25 0.93 0.505 0.477 Methylcyclopentane ................... 0.648 -20 8.60 3.55 3.19 n-Decylcylopentane ................... 5.52 C 15Hao It-Hexadecylcyclopentane ............... 20 8.41 C 21H42 9.60: ...... 9.60:

1955 0.393 0.451 2.86 7.38

Normal Alkyl Cyclohexanes (CnH2n), C6 through C22. Table 23c (Part 1), 5 0.895 C 6H l2 1.296: ...... 0.977 Cyclohexane .......................... -25 1.55 0.732 0.990 0.683 Methylcyclohexane .................... C7Hl4 -5 5.24 9.23 4.59 n-Decylcyclohexane ................... 10.n CI6H32 8.73 35 n-Hexadecylcyclohexane ............... ...... ..... . C22H44

1955 0.824 0.639 4.04

Normal Monoolefins (l-Alkenes), (C nH2n), C2 through C20. Table 24c (Part -170 0.70: ....... Ethene ............................... C 2H4 ..... . . ..... -55 0.69 0.26 C 6Hl2 0.33 0.25 1-Hexene............................. 0 1.95 1.30 1.20~ 1-Dodecene........................... 1.95 C12H24 30 ...... . ........ .. ....... 1-Eicosene............................ C2oH 4o 4.76:

1), 1955

0

••••••

. .....

. ..... 0.24 1.114 4.76:

0.115§ 0.206 0.2109 0.2070 0.202 0.20

-160 35 125 215 285 340

0.322§ 0.286§ 0.85 1.58

50 75 110 110

0.30 1.12 2.03

0.410 0.30 0.97 1.69

80 100 110 110

. ..... ...... 0.475 1.35

0.15§ 0.19§ 0.41 1.10

-100 65 115 115

. ..... ••••

0.

0.2547 0.5168 0.8992 1.406

...... ...... 0.96 1.83

. .....

TABLE

2m-2.

VISCOSITIES OF HYDROCARBON LIQUIDS*

(Continued)

Viscosity in centipoise'] (multiply by 10-1 for SI Units) Compound

Formula

tmin,OC

tmax,OC

tmin

I

0

I

Normal Alkyl Benzenes (C6+nH6+2n), C6 through C 2 2. Benzene .............................. C6H6 5 0.8235t ...... -25 Methylbenzene (Toluene) .............. C7H8 1.17 0.771 -20 n-Decylbenzene ....................... C 16H 26 6.70 16.0t n-Hexadecylbenzene .......... " ....... C 22H38 25 ..... . 8.96t

Ethy lbenzene .........•.....••........ 1 1,2-Dlmethylbenzene (o-Xylene) ....."... n-Propylbenzene ......................

20

I

I

30

Table 21c (Part 1), 1955 0.6468 0.6010 0.5604 0.5848 0.5500 0.5187 3.01 3.36 3.79 ....... 8.96t 7.74

Alkyl Benzenes (C6+n H6+2n) , C6 through Cg. Table 5c, -25 0.892 1.35 0.6763 CSH10 -5 1.211 1.105 0.807 CSHlO CgH 12 -25 0.8545 1.90 1.178 I

* A sampling of values given in American Petroleum Institute Research Project 44,

25

1955 0.6354 0.754 0.7962

I

0.5985 0.706 0.7444

I

tmax

100 I

. ..... 0.268 0.974 1.817

0.307 0.344 0.359

.

0.301§ 0.248 0.56 0.92

85 110 150 150

0.230§ 0.244§ 0.25

140 145 150

I

"Tables of Selected Values of Properties of Hydrocarbons and Related Compounds op. cit. The original tables contain values of viscosity tabulated every 5° from tmin through tmal

Q. I

pI)

~

I>

D

2.0

Appearance af Co"i1orlOft Inc..pl,on CX-21

t:

.,

3.0

I

-7.0

Temperc1u,r·90· :;)I ()'.,Of>O

i=

cr

5.0

o

6.0

7.0

8.0

9.0

10.0

11.0

12.0

13.0

PRESSURE DIFFERENTIAL IN INCHES OF MERCURY I

!

I

!

!

I

40

45

50

55

60

65

VELOCITY IN CONSTRICTION IN FEET PER SECOND

FIG. 20-1. Cavitation inception in fresh water of varying air content.

a U

'jlC

..... .... 3 0

::'4.0

i

.

0 0

o

~ r13tJ :~o "'ego .... 0 0 tP

i

-

--~

CD 0

o'

o Appearance o CQ'tito1ion Inception 0

" o

00

"

0

a

0

o ~ 8C

0 00

a

ort>

0

0

a

o

d'oJp

rV-""c 10

~

o

0 ~

...

0

o

0.

0

a 0

0

a

{

n

J

a 0

0 0

Steady S'ot.

0

o~

Bubbles

a

0

6 0

'l.

0 0

'6 ~"I.O

5.0

0

1

,

~ 1.0

~

~o

o

~

t

.. 1\

0 0

J

0

C all, 0

0

12.0

i

(After Crump.)

,..... .2.

..D 0

-

-

I E 1

U

00

6 P

8 0

6.0

s.o

7.0

9.0

10.0

11.0

12.0

13.0

14.0

15.0

16.0

17.0

Pressure Differential dH in inches of Mercury

40

45

!

I

,

,

50

55

60

65

Velocity in Constriction in t,.t per leeond

70

FIG. 20-2. Critical pressure for inception of cavitation in sea water.

(After Crump.)

2-216

MECHANICS

It may be expected that a relation exists between the dissolved and entrained gas content, at least in an undisturbed liquid. Some evidence for this assumption exists in the measurements of Strasberg! on tap water with ultrasonically induced cavitation. Since, according to the analysis of Noltingk and Neppiras.! the time duration of the pressure for times of the order of milliseconds has very little influence on the inception pressure, and since this is also of the order of the time duration in hydraulic applica8

U)

UJ

ffi6 :J:

a-

R:. -

o::=;

!.;{

W 0::

Po =ATMOSPHERIC T =20-24°C

•• • •

-5~

01.....

•

U)

-7

I

~ •

~4

0

U)

UJ 0::

a. o

0:: UJ

:I:

-..'"

z

§ "" ;'52

l}; o ::=; !.;{ W

1. The term hypersonic is often used to describe flows where

M >5. Dynamic Similarity. If the same gas flows around two geometrically similar bodies, it might be expected that under the right conditions the streamline pattern would be similar. This is true if the Mach numbers of the two flows are equal. It then follows that all other dimensionless coefficients such as drag coefficient, lift coefficient, pressure coefficient, etc., are also equal. In determining the Mach number in a flow it is necessary to know not only the flow velocity but the sound velocity as well. For a perfect gas the sound velocity is proportional to the square root of the temperature; i.e., a =

V'YRT

Table 2t-1 is based on this relationship. 2t-3. Basic Idea of One- dimensional Flow. In many cases, as in a pipe of slowly varying cross section, it is possible to make the assumption of constant flow properties across any cross section perpendicular to the pipe axis. Although strictly speaking there are no one-dimensional flows, because of viscous effects on the boundaries, it is still possible to get much valuable information of a practical nature from the assumptions. TABLE

2t-1.

VARIATION OF VELOCITY OF SOUND WITH TEMPERATURE

T, oK

a, fps

a, m/sec

805 832 857 882 907 930 953 975 997 1,019 1,040 1,060 1,081 1,100 1,120 1,139 1,158 1,176 1,195 1,213 1,230

246 254 261 269 276 283 290 297 304 311 317 323 329 335 341 347 353 359 364 370 375

---150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350

Basic Equations.

On the assumption of isentropic flow the equations of motion are

au + u au = _! ap at ap

at

oX pax 1 a + A ax (puA) = 0

(momentum)

(2t-5)

(continuity)

(2t-6)

2-256

MECHANICS

where A is the cross-sectional area. For unsteady one-dimensional flow in general and in particular for an excellent treatment of flow in pipes of constant area see ref. 3. The above equations also cover the case of cylindrical and spherically symmetric flow; i.e., 1 aA 1 (for cylindrical flow)

if ax = 1 aA

if ax

=

x 2 x

(for spherically symmetric flow)

In the important case of steady flow the equations can be integrated to give

E + ! u 2 = const 2 puA = m = const

(2t-7)

_1'_

'Y-lp

(2t-8)

where m is the mass flow. By taking logarithmic derivatives and remembering the definition of the Mach number M, the continuity equation may be written

du (1 _ M2) u

+ dA A

= 0

(2t-9)

Thus, if du ~ 0 and M = I, we see that dA = O. In other words, the Mach number becomes equal to unity only in a section of the pipe where the area is a minimum. This fact is of prime importance in the design of supersonic wind tunnels. The dependence of the various flow variables on the Mach number for steady onedimensional isentropic flow is given in Table 2t-2. 2t-4. Two-dimensional and Axially Symmetric Flow. Many important types of flow belong to the class of two-dimensional or axially symmetric flows. These include flows past wedges, cones, bodies of revolution, etc. The important distinctions to be made are those between subsonic and supersonic flow. Purely subsonic flow is qualitatively quite similar to incompressible flow, while supersonic flow exhibits many startlingly different properties. Among these are the appearance of shock waves (see Sec. 2v) and the existence of wavefronts. A general discussion of the above topics can be found in refs. 2, 3, and 6. The greater bulk of the literature on two-dimensional and axially symmetric flow is concerned with steady flow. The unsteady cases are usually extremely difficult to solve. Velocity Potential and Stream Function. In cases of irrotational or steady flow it is convenient to introduce the velocity potential or the stream function. This reduces the number of equations to one. The velocity potential exists whenever there is a state of steady or unsteady irrotational flow; i.e., the velocity components satisfy the equations

Then the velocity components u, V, w can be expressed as the components of the gradient of the velocity potential cPo Thus

u = acP

ax

V

= acP

w

ay

acP

(2t-1O)

= az

For steady isentropic flow the equations of motion reduce to the single equation for cP, cPzz

(1 - ~2) + cPvv (1 - cP;2) + cPu (1 - ~z2) - 2cPv zcP~~cP -

2cPzz

- 2cP zv cPzcPv a2 where

a2

=

1'-1

- 2 - (qmax 2

-

cPz 2

-

cPi - epz2)

cP~~z =

0

(2t-ll)

2-257

COMPRESSIBLE FLOW OF GASES TABLE

2t-2.

DEPENDENCE OF FLOW VARIABLES ON MACH NUMBER FOR ONE-DIMENSIONAL ISENTROPIC

Fr.ow "

A/A·

pu,2/2po

Pu,/poao

p/po

T/To

a/ao

00

5.822 2.9635 2.0351 1.5901

0.00000 0.00695 0.02723 0.05919 0.10031

0.00000 0.09940 0.19528 0.28437 0.36393

1.00000 0.99502 0.98028 0.95638 0.92427

1.00000 0.99800 0.99206 0.98232 0.96899

1.00000 0.99900 0.00602 0.99112 0.98437

0.48795 0.57950 0.66803 0.75324 0.83491

1.3398 1.1882 1.0944 1.0382 1.0089

0.14753 0.19757 0.24728 0.29390 0.33524

0.43192 0.48704 0.52880 0.55739 0.57362

0.88517 0.84045 0.79161 0.73999 0.68704

0.95238 0.93284 0.91075 0.88652 0.86059

0.97590 0.96583 0.95433 0.94155 0.92768

0.52828 0.46835 0.41238 0.36091 0.31424

0.91287 0.98703 1.0574 1.1239 1.1866

1.00000 1.0079 1.0304 1.0663 1.1149

0.36980 0.39670 0.41568 0.42696 0.43114

0.57870 0.57415 0.56161 0.54272 0.51905

0.63394 0.58170 0.53114 0.48290 0.43742

0.~3333

0.80515 0.77640 0.74738 0.71839

0.91287 0.89730 0.88113 0.86451 0.84758

1.5 1.6 1.7 1.8 1.9

0.27240 0.23527 0.20259 0.17404 0.14924

1.2457 1.3012 1.3533 1.4023 1.4479

1.1762 1.2502 1.3376 1.4390 1.5553

0.42903 0.42161 0.40985 0.39476 0.37713

0.49203 0.46288 0.43264 0.40216 0.37210

0.39484 0.35573 0.31969 0.28684 0.25699

0.68966 0.66138 0.63371 0.60680 0.58072

0.83045 0.81325 0.79606 0.77904 0.76205

2.0 2.1 2.2 2.3 2.4

0.12780 0.10935 0.09352 0.07997 0.06840

1.4907 1.5308 1.5682 1.6033 1.6360

1.6875 1.8369 2.0050 2.1931 2.4031

0.35785 0.33757 0.31685 0.29614 0.27579

0.34294 0.31504 0.28863 0.26387 0.24082

0.23005 0.20580 0.18405 0.16458 0.14719

0.55556 0.53135 0.50813 0.48591 0.46468

0.74535 0.72894 0.71283 0.69707 0.68168

2.5 2.6 2.7 2.8 2.9

0.05853 0.05012 0.04295 0.03685 0.03165

1.6667 1.6953 1.7222 1.7473 1.7708

2.6367 2.8960 3.1830 3.5001 3.8498

0.25606 0.23715 0.21917 0.20222 0.18633

0.21948 0.19983 0.18181 0.16534 0.15032

0.13169 0.11788 0.10557 0.09463 0.08489

0.44444 0.42517 0.40683 0.38941 0.37286

0.66667 0.65205 0.63784 0.62403 0.61062

3.0 3.1 3.2 3.3 3.4

0.02722 0.02345 0.02023 0.01748 0.01512

1.7928 1.8135 1.8329 1.8511 1.8682

4.2346 4.6573 5.1210 5.6287 6.184

0.17151 0.15774 0.14499 0.13322 0.12239

0.13666 0.12426 0.11301 0.10281 0.09359

0.07623 0.06852 0.06165 0.05554 0.05009

0.35714 0.34223 0.32808 0.31466 0.30193

0.59761 0.58501 0.57279 0.56095 0.54948

3.5 3.6 3.7 3.8 3.9

0.01311 0.01138 0.00990 0.00863 0.00753

1.8843 1.8995 1.9137 1.9272 1.9398

6.790 7.450 8.169 8.951 9.799

0.11243 0.10328 0.09490 0.08722 6.08019

0.08523 0.07768 0.07084 0.06466 0.05906

0.04523 0.04089 0.03702 0.03355 0.03044

0.28986 0.27840 0.26752 0.25720 0.24740

0.53838 0.52763 0.51723 0.50715 0.49740

4.0 4.1 4.2 4.3 4.4

0.00659 0.00577 0.00506 0.00445 0.00392

1.9518 1.9631 1.9738 1.9839 1.9934

10.72 11.71 12.79 13.95 15.21

0.07379 0.06788 0.06250 0.05759 0.05309

0.05399 0.04940 0.04524 0.04147 0.03805

0.02766 0.02516 0.02292 0.02090 0.01909

0.23810 0.22925 0.22084 0.21286 0.20525

0.48795 0.47880 0.46994 0.46136 0.45305

4.5 4.6 4.7 4.8 4.9

0.00346 0.00305 0.00270 0.00239 0.00213

2.0025 2.0111 2.0192 2.0269 2.0343

16.56 18.02 19.58 21.26 23.07

0.04898 0.04521 0.04177 0.03862 0.03572

0.03494 0.03212 0.02955 0.02722 0.02509

0.01745 0.01597 0.01464 0.01343 0.01233

0.19802 0.19113 0.18457 0.17832 0.17235

0.44499 0.43719 0.42962 0.42228 0.41516

5.0

0.00189

2.0412

25.00

0.03308

0.02315

0.01134

0.16667

0.40825

M

p/po

0.0 0.1 0.2 0.3 0.4

1.00000 0.99303 0.97250 0.93947 0.89561

0.00000 0.09990 0.19920 0.29734 0.39375

0.5 0.6 0.7 0.8 0.9

0.84302 0.78400 0.72093 0.65602 0.59126

1.0 1.1 1.2 1.3 1.4

u/ao

* A more complete table may be

found in refs. 4, 5, and 7.

2-258

MECHANICS

and qrnax is the velocity with which the gas flows into a vacuum. Other forms of this equation in different numbers of dimensions and for unsteady flow can be found in ref. 2. - - TRANSONIC THEORY

0.6

0.4

10.0·

0.2

7.50

Cp

4.50 1.2

M_

1.4

1.6

(a!

..i

~'iit.-T

2 WEDGE SEMI-ANGLE

D

o

X=

4

tC-l [(r+1)M!{t/c)]~

3

4.50 7.50 10.00

o 0

o X (IJ! FIG. 2t-1. Comparison of the extended transonic similarity law with experiment. (a) Plotted in conventional coordinates. (b) Plotted in transonic similarity coordinates. (After J. R. Spreiter, N ACA; taken from ref. 6.)

In compressible flow a stream function if; exists only for steady two-dimensional or axially symmetric flow. The introduction of the function if; causes the continuity equation to be satisfied identically. In two dimensions

u =

1

pif;.

v

=

-

1

p

if;x

(2t-12)

If cylindrical coordinates (z, r, 0) are used and the flow is independent of 0, then the function if; may be defined by

u

=

1

Pi'if;,

v

(2t-13)

COMPRESSIBLE FLOW OF GASES

2-259

Note that u and v are now the velocity components in the x and r directions and r = y2 + Z2. Further details are given in ref. 2. Equations of Small-perturbation Theory. For many slender or flat two- and threedimensional bodies it may be assumed that the flow is disturbed very little from uniform flow. Thus if the free-stream velocity U is parallel to the x coordinate and M.., is the free-stream Mach number, the velocity components can be written in the form

V

u = U

+ cPx

v

=

cPy

(2t-14)

w = cPt

Here cP is called the disturbance potential. When Eqs. (2t-14) are put into Eq. (2t-ll) and all nonlinear terms are neglected, the equation

+ cPyy + cPu

(1 - M ..,2)cPxx

(2t-15)

= 0

is obtained. This equation holds for subsonic and moderate supersonic flows. If M.., is very close to 1, Eq. (2t-I.5) is no longer valid and must be replaced by the equation ~1 2) (1 _ 1'.., cPxx

+

cPyy

+

_ Af..,2(,,(

cPu -

U

+ 1)

cPXcPXT

(2t-16)

Similarity Rules. In many flows where the velocity perturbations are small, it is possible to show that the pressure, lift, drag, etc., depend on the various flow parameters in a simple manner. For example, in two-dimensional flow the pressure coefficient

is related to M.., and the thickness ratio

T

by the formula

This holds for subsonic, transonic, and supersonic flow. For hypersonic flow the similarity parameter is K = Af..,T. Van Dyke in ref. 8 showed that the parameter K' = M..,2 - 1 T could be used as a unified similarity parameter. More information may be found in ref. 9. The well-known Prandtl-Glauert rule can be found as a special case of the above formula. Further details can be found in ref. 6. The power of similarity rules is shown in Fig. 2t-1, where data and theory for flow past different wedges can be directly compared if plotted in terms of the similarity parameter x-

V

References 1. Lieprnann, H. W., and A. E. Puckett: "Introduction to Aerodynamics of a Compressible Fluid," John Wiley & Sons, Inc., New York, 1947. 2. Ferri, A.: "Elements of Aerodynamics of Supersonic Flows," The Macmillan Company, New York, 1949. 3. Courant, R., and K. O. Friedrichs: "Supersonic Flow and Shock Waves," Interscience Publishers, Lnc., New York, 1948. 4. Emmons, H. W.: "Gas Dynamics Tables for Air," Dover Publications, Inc., New York, 1947. 5. Aeronautical Research Council: "Compressible Airflow Tables," Oxford University Press, New York, 1952. 6. Liepmann, H. W., and A. Roshko: "Elements of Gasdynamics," John Wiley & Sons, Jnc., New York, 1957. 7. Ames Research Staff: Equations, Tables and Charts for Compressible Flow, N ACA Rept. 1135, 1953. 8. Van Dyke, M. D.: A Study of Small Disturbance Theory, NACA Rept. 1194, 1954. 9. Hayes, W. D., and R. F. Probstein, "Hypersonic Flow Theory," 2d ed. Academic Press, Inc.• New York, 1966.

2u. Laminar and Turbulent Flow of Gases R. C. ROBERTS

University of Maryland-Baltimore County

Symbols

CD Cj

Cp

d E G

Gr g

KN k L

Pr p Q

R r

r/k St T

Te Tw Too t u, v, w u X, Y,Z x, y, z

o (J

Il-

"p Tw

drag coefficient skin-friction coefficient specific heat at constant pressure pipe diameter internal energy per unit mass mass rate of flow per unit cross-sectional area of pipe Grashof number acceleration of gravity Nusselt number coefficient of heat conductivity, surface roughness reference length (for Reynolds number) Prandtl number pressure external-heat-production rate per unit mass gas constant, Reynolds number pipe radius surface-roughness factor Stanton number absolute temperature adiabatic wall temperature wall temperature free-stream temperature time velocity components of fluid flow free-stream velocity rectangular components of external body force rectangular coordinates boundary-layer thickness momentum thickness coefficient of viscosity kinematic viscosity density wall shear stress per unit area

2u-1. Equations of Motion. The study of the motion of any real gas or fluid must of necessity take into consideration the effects of viscosity. The transfer of momentum due to viscosity and the transformation of kinetic energy into heat must be considered in formulating the equations of motion. The following equations govern

2-260

LAMINAR AND TURBULENT FLOW OF GASES

2-261

the motion of a viscous, compressible, heat-conducting gas. The viscosity and heat conductivity are assumed to be functions of the temperature only. Momentum Equations. In rectangular coordinates, the momentum equations can be written as

p

p

(~~ + u :~ + v :~ + w ~~) (~ av + v ay av + w~) at + u ax az

+ a~ [: ~ :~ - ~ ~ (:: + ~~)] +~ av)] + ~ ay [~ (~ ay + ax az [ ~ caw ax + au) az ] _ ap ax y + ~ [ (av + ~) ] p ax ~ ax ay

= pX

=

+ [~ ~ p caw + u aw + v aw + w aw) = at ax ay az

!y

:: - ~ ~ (:~ + aa:) ] + ~ [~ (~ + ~~)] - :: p

Z

+~ au)] ax [ ~ caw ax + az

+ ay a [ (aw + av)] + ~ [~ aw _ p. ay az az 3 ~ az where

~

~

(au + av) ] _ ap ax ay az

3 p.

(2u-l)

is the coefficient of viscosity and the other terms are as defined in Sec. 2t. The equation of continuity is

Continuity Equation.

ap

at

+ ax ~ (pu) + ~ (pv) + ~- (pw) ay az

=

0

(2u-2)

Energy Equation. By using the first law of thermodynamics and by considering that heat conduction may take place in the gas, the following energy equation may be written p

(aE + u aE + v aE + w aE) + (au. + av + aw) at ax ay az p ax ay az =

-o + Ix (k ~~) +!y (k ~~)

+

:z (k ~~) +

_ ~~ ~ (au + av + aW)2 + (au + aV)2 + 3 ax ay az ~ ay ax

~

2p.

[(:~r + (~)2 + (~~)2]

(au + aW)2 + (av + aW)2 az ax ~ az ay

(2u-3)

where k = heat-conductivity coefficient E = internal energy per unit mass Q = external-heat-production rate per unit mass T = absolute temperature The coefficients p. and k may be functions of the temperature T. Equation of State. For a perfect gas the equation of state is p = pRT

(2u-4)

Stream Function. For a steady flow in two dimensions or for axially symmetric flow a stream function may be defined as in Sec. 2t. It has great utility in boundarylayer work (see ref. 3). 2u-2. Definitions of Basic Parameters. The basic dimensionless parameters of a viscous, compressible, heat-conducting gas are usually considered to be the Mach number, the Reynolds number, the Prandtl number, and the Grashof number (see ref. 2). The Mach number has been defined in Sec. 2t. The other three parameters may be defined as follows:

2-262

MECHANICS

Reynolds Number. In a flow with reference velocity u and reference length L, the Reynolds number R is defined as R = uL

(2u-5)

11

where 11 = p.lp is the kinematic viscosity. Two viscous flows may not be dynamically similar unless their respective Reynolds numbers are the same. Prandtl Number. The Prandtl number is defined as (2u-6) where Cp is the specific heat at constant pressure. The Prandtl number depends only on the material properties of the gas. The Prandtl number is primarily a function of the temperature only. For small temperature changes it is often assumed to be constant (see ref. 2). The variation of P, with temperature is shown in Tables 2u-l and 2u-2 for air and for molecular hydrogen H 2 • Grashof Number. The Grashof number may be defined as G _ r

;L3

-

g (T l 112

To)

-

(2u-7)

To

where g is the acceleration of gravity and T 1 and T 2 are two reference temperatures. The Grashof number is important in the study of flows with free convection, e.g., the flow of gas above a heated plate. 2u-3. Exact Solutions. Because of the extreme complexity of the equations of motion, few exact solutions have been found. Nearly all of these are limited to the mcompressible steady flow case, with zero heat transfer through the walls bounding the flow. Since gases often behave as if they were nearly 'incompressible, these solutions may have practical importance. Pipe Flow. The exact incompressible solution for two-dimensional or axially symmetric steady flow through a pipe of constant cross section is characterized by a parabolic velocity distribution. In the two-dimensional case the complete solution is given by 1 ap z(h - z) 2p. ax w = 0

u = -

v

=

-

ap = const

ax

ap

ay

=

ap

az

(2u-8)

=

0

where the boundaries are at z = 0 and z = h. In the case of flow through a circular pipe, the theoretical solution has been shown to coincide almost exactly with experiment for laminar flow. Other Exact Solutume. There are a number of other exact solutions for the incompressible case such as steady flow between concentric cylinders and flow through tubes of noncircular cross section. These can be found by consulting refs. 1 and 3. Hamel (ref. 5) has found a number of nontrivial exact solutions. 2u-4. Boundary Layers, When the Reynolds number of the flow is large, most of the viscous effects take place in the immediate vicinity of the boundaries. The outer flow may then be considered determined by the inviscid flow equations while in the boundary layer certain simplifications of the equation of motion may be made. For the case of two-dimensional flow past flat or slowly curving surfaces the pressure may be assumed to be completely determined by the outer flow.

LAMINAR AND TURBULENT FLOW OF GASES

2-263

If the viscous effects are confined to a thin region next to a boundary, it then turns out that most of the viscous terms in Eqs. (2u-1) and (2u-3) can be neglected. The simplified equations are much easier to treat than the full equations. TABLE

2u-1.

PRANDTL NUMBER

P,

FOR

T, oK

Pr

T, oK

Pr

100 120 140 160 180

0.770 0.766 0.761 0.754 0.746

560 580 600 620 640

0.680 0.680 0.680 0.681 0.682

200 220 240 260 280

0.739 0.732 0.725 0.719 0.713

660 680 700 720 740

0.682 0.683 0.684 0.685 0.686

300 320 340 360 380

0.708 0.703 0.699 0.695 0.691

760 780 800 820 .840

0.687 0.689 0.690 0.692

400 420 440 460 480

0.689 0.686 0.684 0.683 0.681

860 880 900 920 940

0.003 0.695 0.696 0.697 0.698

500 520 540

0.680 0.680 0.680

960 980 1000

0.700 0:701 0.702

AIR

0.6~8

Basic Equations. For two-dimensional steady flow as outlined above, the momentum, continuity, and energy equations are, respectively,

p (u au + v au) = ~ (Po au) _ ap ax ay ay ay ax 0= ap ay a a - (pu) + - (pv) = 0 ax ay !!!!.) = .i. p ( u aE ax + v aE) ay + P (au ax + ay ay (k aT) ay + Po (au)2 ay

(2u-9)

For a perfect gas the equation of state is P = pRT. In the above equations x may be considered as the distance along the boundary while y is the distance perpendicular to the boundary. The velocity components u and v are interpreted in like manner. The equations then hold also for a slowly curving boundary.

2-264

MECHANICS

Blasius Flow. For incompressible steady flow past a flat plate with no pressure gradient, the equations of motion are au au a!u u--+v-=vax ay ayz

+ (}v

au ax

with the boundary conditions u TABLE

2u-2.

ay

=v =0

(2u-lO)

=0

= 0 and

at y

u

= UI = const

at y

PRANDTL NUMBER FOR MOLECULAR HYDROGEN H 2

T, oK

P,

T, OK

P,

60 80

0.713 '0.711

440 460

0.684 0.681

100 120 140 160 180

0.712 0.715 0.718 0.719 0.720

480 500 520 540 560

0.678 0.675 0.671 0.669 0.667

200 220 240 260 280

0.719 0.717 0.715 0.712 0.709

580 600 620 640 660

0.665 0.664 0.663 0.663 0.662

300 320 340 360 380

0.706 0.703 0.699 0.696 0.693

680 700 720 740 760

0.661 0.661 0.661 0.660 0.660

400 420

0.690 0.687

780 800

0.660 0.660

=

00

*

*

The values in Tables 2u-l and 2u-2 are taken from the National Bureau of Standards, "NACA Tables of Thermal Properties of Gases" (cf. ref. 6).

and at x = O. UI is the free-stream velocity. of the change of variable '1

(U1)! Y

= -21 -vx

v = ~ (u~v)l (71f'

1

U

Blasius solved this problem by means

= iud'

- f)

(2u-ll)

This reduces the problem to the ordinary differential equation and boundary conditions 3 2 d f +f d f = 0 d71 3 d71 2

f

=

f'

=

0 at

'1 =

0

and

f'

=

2 at

71 =

00

(2u-12)

2u-6. Turbulent Flow. For small values of the Reynolds number most flows are characterized by a certain uniformity of velocity distribution and smoothness of the

2-265

LAMINAR AND TURBULENT FLOW OF GASES

streamline pattern. This type of flow is called laminar. As the Reynolds number is increased, the flow will remain laminar until a certain critical value of R is reached. At this time swirling or eddying motions begin to appear in the flow. These smallscale eddying motions move with the main flow but also possess an apparent random nature in the way they appear and decay. Such flows are called turbulent. Turbulent flows also exhibit other striking features. The velocity distribution has a different behavior from that of laminar flow. The viscous drag and heat transfer

24 I

I

I

II

I II

I

I

I

- - 'Ie; = 4.04+3.94 LOG

22

0

D

4

x

20

+

_1_

~

I

1 em 2 em 3 em 5 em 10 em

PIPE PIPE PrPE PIPE PIPE

Ie

;

16

I

~~

I

.vc,

R•

DATA DATA DATA DATA DATA

[p

101 ...

""

r+. .J
f/ + u· f"

(3c-63)

The significance of this result can be made more apparent by using the continuity equation again, this time in the form (E/p)[ap/ae + V· (pu)] = o. Adding this "zero" to the left-hand side of (3c-63), after first using (3c-3) to express the material derivative in terms of fixed spatial coordinates, allows the continuity of acoustic energy to be expressed by

m + V. (pu)

p D(E/p)

=

p a(E/p)

m

+ pU· V ~ +

V· (pu)

p

+ [~p ap + ~p V • (PU)] at aE

at =

-V· (pu

+ Eu)

- Pot! - V· q + u- ftl + 4>,

(3c-64)

The acoustic energy-flux vector can be identified as pu = J, inasmuch as this term represents the instantaneous rate at which one portion of the medium does mechanical work on a contiguous portion in the process of forwarding the sound energy. The time average of the sound-energy flux through unit area normal to u is defined as the sound intensity, (J) == I. Ordinarily it is only the time average of each term of (3c-64) that is of interest, but the equation itself holds at every instant and asserts that growth of the total energy density of a volume element is accounted for by the influx of acoustic and thermal energy across the boundaries of the element, by the energy dissipated in viscous losses, and by the work done by the equilibrium pressure on the

PROPAGATION OF SOUND IN FLUIDS

3-55

volume element during condensation. The latter component is represented by (-Po~) and by a corresponding linear term contained implicitly in E [cf. (3c-Hn]. It is omitted in most textbook descriptions of acoustic energy density, the neglect being justified if at all on the grounds that the stored energy varies linearly with the dilatation and hence will have a vanishing net value when averaged over an integral number of periods or wavelengths, or over the entire region occupied by the sound field. Care must be taken to ensure that it does indeed vanish rigorously on the average inasmuch as the peak values of this component of energy storage are larger than the acoustic energy in the ratio Po/po Acoustic Radiation Pressure. The appearance of the product Eu as an additive term in the first right-hand member of (3c-64) is notable and represents the net energy density carried across the boundary of a volume element by convection, the net flow being measured by the divergence of the particle velocity. 1 No approximations have been made in deducing (3c-64), which holds, therefore, within the scope of validity of the basic assumptions. It is significant to remark the fact that E is directly additive to p when the divergence term is written as V • (p + E)u, thereby identifying the additive term as a radiation pressure whose magnitude at every instant is just equal to the total energy density, E = }pu' u + pe. This interpretation can be fortified by revising (3c-64) by expanding V· (Eu) = E(V· u) + u· vE. The last term can be used to restore the material time derivative of E and the other can be merged with the linear term in Po, yielding a revised power equation in the form DE = Dt

-v·

(pu) - (Po

+ E)~

-

v· q + q,,, + u· f"

(3c-65)

The role of E as an additive or radiation pressure is thus retained in (3c-65) where its time-independent part is now exhibited appropriately as a slight change in the equilibrium pressure. When seeking to evaluate the net mechanical force due to radiation pressure on a material obstacle or screen exposed to a sound field, care must be taken to specify the boundary conditions and to account for all the reaction forces involved, including the steady-state interaction of the obstacle with the medium as well as the dynamic interaction of the obstacle with the sound field itself. Thus, for example, if a long tube is "filled" with a progressive plane wave, the walls of the tube, which interact only with the medium, would experience only the mean increment of the equilibrium pressure [cf. (3c-53)], and this would disappear if the walls were permeable to the medium, but not to the sound wave (e.g., with capillary holes). On the other hand, if a sound-absorbing screen were freely suspended athwart the wavefronts, it would experience just the pressure E shown by (3c-64) to be additive to p; but if the screen were to form an impermeable termination of the tube it would experience both components of pressure, including changes due to the enhancement of (E) by the reflected wave.' Be-D. Sound Absorption and Dispersion. The basic manifestation of the absorption or attenuation of sound is the conversion of organized systematic motions of the particles of the medium into the uncoordinated random motions of thermal agitation. Schock, Acustica 3, 181-184 (1953). Suggested references: On fundamentals, see L. Brillouin, "Les Tenseurs en mecanique et en elasticitll," Dover Publications, New York, 1946. On influence of oblique incidence and of obstacle's reflection coefficient, see F. E. Borgnis, On the Forces upon Plane Obstacles Produced by Acoustic Radiation, J. Madras Inst: Technol, 1 (2), 171-210 (November, 1953), and (3), 1-33 (September, 1954); also condensed in Revs. Modern Phys., 15, 653-664 (1953). For review, critical bibliography, and sophisticated analysis of general topic, see E. J. Post, J. Acoust. Soc. Am. 15,55-60 (1953); Phys. Rev. 118, 1113-1118 (1960). 1

2

3-56

ACOUSTICS

Various agencies of conversion can be identified as viscosity, heat conduction, or as Borne other mechanism that gives rise to a delay in the establishment of thermodynamic equilibrium; but all are mechanisms of interaction that lead to the same result, viz. that the energy of mass motion imparted intermittently to the medium by the sound source becomes increasingly disordered and "unavailable." Describing this in terms of the irreversible production of entropy leads to the definition of dissipation functions and paves the way for formulating an acoustic energy balance. Equation of Continuity for Acoustic Energy, This may take the form of a statement that the mean net influx of sound energy across the boundaries of a volume element situated in a sound field must just balance the average time rate at which this energy is degraded, or made unavailable, throughout the volume element by irreversible increase of entropy; thus, by extension of (3c-20),

-f

A

J, da, =

(

JV

DEd iss dV =

Dt

(

JV

T DS ir r dV = Dt

J( V

(4),,

+ 4>'1) dV

(3c-66)

where the sound energy flux vector is J, = PUt, and E d iss is the degraded component of internal energy associated with the irreversible entropy Sire. The differential form of (3c-66) can be obtained in the usual way by using the divergence theorem to convert the surface integral to a volume integral. Then, after introducing the explicit forms of the dissipation functions, (3c-24a) and (3c-24b), the acoustic energy continuity relation becomes

-VoJ

=

(3c-67a) where it is understood that only the time-independent parts of each side of (3c-67a) are to be retained. The algebraic complexity of dealing with (3c-67a) is considerably abated by considering only plane waves, for which case the running subscripts each reduce to unity and can be dropped. The plane-wave form of the 'acoustic-energy relation then becomes, after introducing P as an implicit variable in VT,

_ a(pu) ax

= !.. (DT)2 (a p)2

T DP

ax

+

7]

'0

(aU)2 ax

(3c-67b)

in which 7]1) has been written for 7]' + 27] [cf. (3c-1O)]. The thermal dissipation term can then be maneuvered into more suggestive form by further manipulation involving the equation of state T = T(P,p) and various thermodynamic identities including the useful relation that holds for all fluids, T(j2 C2 = Cp('Y - 1). This leads, still without approximation, and with the time average explicitly indicated, to

(_ a(pu» ax

= (7]1)

(aU)2) + (...!.- [(pc2/ K T) - 21]2 (a p)2) ax pCp ("I - 1)pc ax

(3c-68)

It can now be observed that p, u, and their derivatives must be known throughout the sound field in order to evaluate the sound energy flux and the dissipation functions that make up (3c-67a) or its reduced form (3c-68). On the other hand, if these field variables are known explicitly, the effects of dissipation will already be in evidence without recourse to (3c-68). Such a continuity equation for acoustic energy is therefore redundant, as might have been expected inasmuch as the conservation of energy has already been incorporated in the basic equations (3c-5), (3c-15), and (3c-23). Nevertheless, (3c-68) retains some logical utility as an auxiliary relation, even though it no longer needs to be relied on for the pursuit of absorption measures, at least for plane waves.

3-57

PROPAGATION OF SOUND IN FLUIDS

Exact Solution of the First-order Equations. An exact solution of the complete first-order equations (3c-26a), (3c-26b), (3c-26c) for the plane-wave case and a definitive discussion of its implications have been given recently by Truesdell. 1 The specific problem considered is that of forced plane damped waves in a viscous, conducting fluid medium. It is assumed that each of the first-order incremental state and field variables can be described by the real parts of (3c-69) and of similar equations for PI, PI, 91. It is assumed that (Ul):r:_O = ul0e i c.l& is the simple-harmonic velocity imparted to the medium by the vibrating surface of a source located at z = 0, but the other amplitude coefficients may be complex in order to embody the phase angles by which these variables lead or lag UI. The exponent expressing time dependence is written +jwt, as required in order to preserve both the conventional form R + jX for complex impedances and the positive sign for inductive or mass reactance. The attenuation constant a and the phase constant k == w/c, or k« == w/co, are the real and imaginary parts of the complex propagation constant x == a + jk; and Co == (oP /op).l is the reference value of sound speed. When the assumed solutions (3c-69) are systematically introduced in (3c-26a), (3c-26b), and (3c-26c), three algebraic equations in PI, UI, 91 are obtained, as follows:

+ jk)Ul + jk)2]UI

-jwPI

po{a

[jwpo - 7]'O(a -

l'

i"o

1 (a

- (a

+ jk)UI + [jw

-

+ jk) [C~2 (PI + (jopolh)] po~"

(a

+ jk)2 + q] «.

= 0 =

0

(3c-70)

= 0

If these equations are indeed to admit solutions of the assumed form (3c-69), the determinant of the coefficients of Ul, PI, and 8 1 must vanish. The characteristic or secular equation formed in this way (Kirchhoff, for perfect gases, 1868; extended to any fluid with arbitrary equation of state by P. Langevin 2) turns out to be a biquadratic in the dimensionless complex propagation variable (a + jk)/k o. Writing this out in full, however, will be facilitated by first considering the question of how best to specify the properties of the medium. Dimensional Analysis and Absorption Measure. Examination of (3c-70) reveals that, in addition to (a + jk) /k o and the three independent variables, there are 10 parameters that pertain to the behavior of the medium at the angular frequency t», One of these could be eliminated, in principle at least, by using the relation T{j2 C2 = (1' - 1)C p , leaving 9 that are independent: Cp , C", TI, 7]', K, po, co, q, and w. Then, since each of these can be expressed in terms of 4 basic dimensional units (e.g., mass, length, time, and temperature), it follows from the pi theorem of dimensional analysis! that just 5 independent dimensionless ratios can be formed out of combinations of these 9 parameters. This leads to a functional expression of the absorption measure in the symbolic form a

+jk= t/t ko

(Cp,~, 7]Cp,~,~) C" TI K poco 2 W

(3c-71)

The first two ratios have already been incorporated in l' and the viscosity number == 2 + TI'/7]; the third is the Prandtl number (p == 7]Cp / K, and the fourth and fifth can be identified as Stokes numbers 8 == W7]/pOC{)2 and 8' == w/q. The present purpose

'l)

I C. A. Truesdell, Precise Theory of the Absorption and Dispersion of Forced Plane Infinitesimal Waves According to the Navier-Stokes Equations, J. Rational Mechanics and Analysis 2, 643-741 (October, 1953). 2 Reported by Biquard, Ann. phys. (11) 6, 195-304 (1936). a E. Buckingham, PhY8. Rev. ,. 345 (1914) j Phil. Mag. (6) '2, 696 (1921).

3-58

ACOUSTICS

is served somewhat better by substituting for the third and fourth ratios their products with the dimensionless viscosity number, thus defining a frequency number X and thermoviscous number Y through X

==

'US = w17'U

(3c-72)

PoCo"

The frequency parameter X also provides a natural criterion for designating frequencies as "low," "medium," or "high" according to whether X is much less than, comparable with, or much greater than unity. It may also be noted that, for nearly perfect gases, poco" == 'YPo, from which it follows that X ga s == (W/P o)(17"lJ!'Y). Hence variation of pressure may be used to extend in effect the accessible range of frequency in measurements on gases, and the ratio w/P o is a proper parameter in terms of which to report such results. Solutions of the Characteristic Equation. If the dimensionless ratios discussed above are now introduced in the expanded determinant of the coefficients of (3c-70), the resulting Kirchhoff-Langevin secular equation can be written as k)" [1 +iX(1 + 'YY) + "'IX"'IS'- i ] (1- s'i) + (a +i k ik + (a t )4XY(j o

"'IX) = 0

(3c-73)

The standard "quadratic formula" can be used at once to solve (3c-73) for the reciprocal square of the propagation constant,

-2 (1 - ~ )

(a ~ ik)" = 1 + ~ + i [ X(1 + 'YY) - 'Y~'] ± [(1 + ~)2 - [X(l - 'YY) - 'Y~'

r

+ 2} {X[l -

(2 - ,,)YJ

+ X2 ~?Y 1

- [1

+ ;;/S')]}

T

(3c-74a)

Skillful abbreviation might allow this complete solution to be carried somewhat further but no algebraic magic can lighten very much the burden of depicting the behavior of a and k as a function of four independent parameters-and it might have been five but for the welcome fact that 'U does not appear except as embodied in X and Y. Moreover, each parameter that does appear in (3c-74a) occurs in one or more product combinations, and hence it can not be assumed in general that the effects of viscosity and heat exchange will be linearly additive. The common practice of assessing these one at a time and then superimposing the results must therefore be considered unreliable unless justified explicitly and quantitatively. Nevertheless, something must give, and it is customary to abandon first the radiant-heat exchange, at least temporarily, by letting S' become infinite in (3c-74a). With this simplification, and with some new abbreviations, (3c-74a) becomes -2

(a ~ ik)" E

= 1 + iX(l + 'YY) ± {I - X"(1 - 'YY)2 + i2X[l == G + [H = 1 + iX(1 + 'YY) ± (E + iF)i == 1 - X"(1 - 'YY)" F == 2X[l - (2 - 'Y)Y]

- (2 - 'Y)Ylli

(3c-74b)

This equation has two pairs of non coincident complex roots, but only the one of each pair that has a nonnegative real part corresponding to real attenuation is to be retained. These two physical solutions comprise the two branches of a complex square root; one branch pertains to typical compressional sound waves identified as type I, the other to so-called thermal waves identified as type II. It is an unwarranted oversimplification, however, to describe these simply as "pressure" waves and "thermal" waves

3-59

PROPAGATION OF SOUND IN FLUIDS

inasmuch as all the state and condition variables-pressure, density, velocity, temperature, heat flux, etc.-are simultaneously entrained and propagated by each wave type, and waves of both types are always excited simultaneously by any source. On the other hand, the absorption and dispersion measures for waves of type I and type II will, in general, be quite different and will vary differently with the frequency parameter X and with the thermoviscous parameters l' and Y that characterize the fluid. For example, type II waves are so rapidly attenuated in ordinary fluids at accessible frequencies that they cannot be observed, whereas in strongly conducting liquids such as mercury (and perhaps in liquid helium II) the absorption for type II waves becomes less than for type I waves when the frequency is high enough for X to exceed l It should be noticed, parenthetically, that if the basic first-order equations (3c-70) had not been restricted to plane waves, the last term of (3c-26b) would not have dropped out. Instead, there would have turned up eventually in (3c-70) a pair of terms in the first-order vector velocity potential Al [see (3c-55)] on the basis of which it would have been predicted that still another type of allowed wave motion can exist in viscous fluids-a transverse viscous wave that is propagated by virtue of the transverse shear reactions due to viscosity. 1 Viscothermal Absorption and Dispersion Measures. The problem of branch determination arising in the solution of (3c-74b) has been discussed thoroughly by Truesdell.! One view of it can be expressed by writing the formal solution in the explicit form a

k 2G

A

H

271" + (G2 + H2)! + G = 1 ± f(h) ( +Ei) 2H =

(C)2

C;;

=

X(1

2(G2

=

+ 1'Y)

+ H2)

+ (G2 + H2)i + G ± (sgn F)g(h)( +Ei)

(3c-75a)

(upper signs yield type I waves, lower signs type II waves) h

F

==-E

+ Vi [+(1 + h 2)i + 1]

f(h)

==

g(h)

== + v'2 [+(1 +

h 2)! -

1]

+ cosh j(sinh+ sinh j(sinh-

1

h)

1

h)

(3c-75b)

where the plus signs associated with roots denoted by fractional exponents indicate that the principal or positive root is to be used. The solution (3c-75a) can now be attacked frontally, either by means of power-series expansions for large or small values of X or by resorting to brute-force numerical computation for intermediate frequencies. The several square-root operations on complex quantities required by the latter procedure are often facilitated by using the f and g functions defined by (3c-75b), for which the principal values have been tabulated." The clue to a basis for classifying fluids according to their viscothermal behavior is afforded by noting that the algebraic sign of F appears in (3c-75a) in such a way as to interchange the wave types when F changes sign, and that this occurs when (2 - 1') Y passes through unity. On this basis, one may categorize fluids as strong conductors if Y is greater than (2 - 1')-1. The contrary alternative can be further subdivided usefully! into weak conductors for which Y is less than 1'-1, and moderate conductors for which Y has intermediate values. Most liquids (including the liquefied noble gases) qualify as weak conductors, most gases as moderate conductors. On the other hand, the fact that mercury, the molten metals, and liquid helium II rank as strong 1 Rayleigh, "Theory of Sound," vol. II, §§347; Mason, Trans. ASME 69,359-367 (1947); Epstein and Carhart, J. Acoust. Soc. Am. 25, 553-565 [557J (1953). 2 C. A. Truesdell, Precise Theory of the Absorption and Dispersion of Forced Plane Infinitesimal Waves According to the N avier-Stokes Equations, J. Rational Mechanics and Analysis 2, 643-741 (October, 1953). aG. W. Pierce, Proc. Am. Acad. Arts Sci. 57, 175-191 (1922).

3-60

ACOUSTICS

conductors emphasizes the value of including a wide range of parameter values in any general survey of thermoviscous behavior. For weak or moderate conductors, the absorption and dispersion measures for type I waves at moderately low frequencies can be expressed with any desired precision by means of power-series expansions in the frequency number X:

2= ( .£) Co

1

+ ~4 X2f3 + 1O(')' -

I)Y -

(')' -

{I + (')' -

I)Y -

~ X2[5 + 35('}'

~ == ::

=

~X

+ (')' ~ == 2~

=

~X

{I

+ (')' -

I)Y -

1)(7 - 3'}')y2]

1)(5'}'2 -

~ X2[1 +

+ 0(X4)

+ (')' - 1)(35'}' - 63)Y2 30'}' + 33)Y3)} + O(X6) (3c-76) - I)Y

11('}' - I)Y - (')' - 1)(23 - 11'}')Y2

+ (')' -

1)('}'2 -

1O'}'

+ 13)ya]} + O(X6)

Note that a/k == aA/27r == A/27r, where A is the amplitude attenuation per wavelength, and that a/k o is similarly related to the attenuation per reference wavelength Ao. The series (3c-76) can be used with confidence for almost any values of '}' and Y so long as the frequency is low enough to keep X < 0.1, and for a somewhat wider range of X when certain restrictions on '}' and Yare satisfied." On the other hand, for frequencies high enough to make X-2 « 1, the absorption and dispersion are given, within O(X-2), by (c/co)! 2X

= ~ == k

=

-.:! 27r

= A o2X = 27r 2

l-Y

1 - (1 _ ')'Y)X

(.!!)2 2X ko (3c-77)

It can be inferred at once from (3c-77) that, for sufficiently high frequencies, dispersion is always anomalous (i.e., speed increases with frequency) regardless of '}' and Y; that a/k = A/27r approaches the limit 1, and that afk« and A o recede to zero as the actual wavelength decreases with respect to the reference wavelength Ao. It also follows, from comparison of this result with (3c-76 a), that as frequency increases, a = A/A = Ao/Ao will always have at least one maximum that is characteristic of viscothermal resonance. The frequency at which this resonance occurs lies in the range X = 1 to 1.7, but the peak is relatively broad and fiat and often cannot be located experimentally with high precision. It can also be deduced from (3c-77) that the asymptotic speed of sound at very high frequencies will always be determined by viscosity alone, without regard for the form of the equation of state; thus, 2W71'O 2 (c

) x -+ oo

= -p

(3c-78a)

Under the same limiting conditions, the asymptotic speed of type II, or "thermal," waves is similarly determined by thermal conductivity alone, according to

2WK (C'2) X-+oo = poe p

(3c-78b)

The steady increase of c' with wi predicted by (3c-78b) has sometimes been cited as a basis for denying that second sound in helium II, which displays small dispersion and low attenuation.! can be a type II thermal wave of the sort predicted by viscothermal Truesdell, J. Rational Mechanics and Analysis 2, 643-741 (October, 1953). Peshkof, J. Phys. (U.S.S.R.) 8, 381 (1944); 10, 389-398 (1946); Lane, Fairbank, and Fairbank, Phys. Rev. 71, 600-605 (1947). 1

2

3-61

PROPAGATION OF SOUND IN FLUIDS

theory. This conclusion is probably correct but the argument is faulty inasmuch as the vanishing viscosity of the superfluid would make it more appropriate to use as a type criterion the behavior predicted for the limiting condition X - O. Thus, if the Kirchhoff-Langevin secular equation (3c-73) is reduced by letting X - 0 while XY is held fixed, and if XY is then allowed to increase indefinitely as required by the superconductivity of helium II, what is left of (3c-73) does have a pair of roots for which the attenuation vanishes and the speed is nondispersive, viz., a = A o = 0 and C = coh·!. This result looks, at first sight, like just an isothermal velocity for type I waves, as might be expected to prevail if uniform temperature were enforced by infinite conductivity. On the other hand, the wave types would be expected to interchange, according to (3c-75a), as Y becomes very large; and one has also to deal with the standing conclusion that any viscosity however small will eventually take over control of dispersion when X departs sufficiently from zero. These remarks are intended to emphasize primarily the fact that the problem of branch determination, or type identification, under such extreme circumstances needs probably to be attacked by considering the relative rates at which the various limiting conditions are approached. Other considerations need also to be taken into account, of course, in dealing with the two-fluid-mixture theory of liquid helium; but it seems clear that further inquiry is warranted concerning the relevance of classical viscothermal concepts now that a more exact theory of these effects is available. The Kirchhoff approximation for weak or moderate conductors at low frequencies can be obtained directly from (3c-76) by neglecting terms in X2 or higher. The dispersion is thereby predicted to be negligible, so that C == co; and the II Kirchhoff " attenuation a s: is given by as: =

=

~2 ko[X

+ ('Y - 1)XY] = !2 koS ('0 + 'Y

o

~

0.40

Q.

0.35

a:::

-

"

I

~ 1'00....

\

, V / .....

.......

I I

i-

~ .... - / ,.VoI

..,/ o

100

200

I

POLYCRYSTAL

"

/'

lL

...

~.'''' 1' .......

/

~

,

ELASTIC CON1STA,T

~~

Q:

IL.

;J

\

...o

f..--- SINGLE CRYSTAL-

~SINGLE

CRYSTAL

300

TEMPERATURE IN

400

500

"c

FIG. 3f-2. Elastic constants and Q for single-crystal and polycrystal aluminum.

(After Ke.)

3f-7. Acoustic Losses in Ferromagnetic and Ferroelectric Materials. Stresses in ferromagnetic and ferroelectric materials can cause motion of domain walls or rota tion of domain directions. These occur in such a manner that domains are strengthened in directions parallel, antiparallel, or perpendicular to the direction of the stress. The Mason, op. cit., p. 422. L. G. Merkulov, Soviet Phys.-Tech. Phys. (English Translation) 1, 59-69 (1950). 3 See Emmanuel P. Papadakis, "Physical Acoustics," vol, IVB, chap. 15, Academic Press, Inc., New York, 1968. 1

2

ACOUSTIC PROPERTIES OF SOLIDS

3-111

increased polarization in the direction of the stress produces increased strains which are the same sign in both parallel and antiparallel domains since magnetostriction and electrostriction are square-law effects and hence the elastic stiffnesses of demagnetized materials are less than those of completely magnetized materials. For polarizations directed along cube axes, the difference in elastic constants for the saturated and depolarized states, i.e., the t:.E effect, is!

s»

9p.X.!E.

(3f-23)

ED = 2HlI'P.·

where p. is the initial permeability or dielectric constant, X. the saturated change in length along a polycrystalline rod, E. and ED the saturated and demagnetized elasticstiffness constant, and P, the saturated magnetic or electric polarization. When the polarization lies along a cube diagonal-as in nickel-X. is replaced by jX 1ll[5CH/ (Cll - Cl2 + 3CH)J where Xlll is the saturated increase in length along the [111J direction and 5CH/(Cll - Cl2 + 3CH) is a ratio of elastic constants. The motion of walls or the rotation of domains in metallic ferromagnetic materials generates eddy currents and hence causes an acoustic loss. It has been shown that the permeability follows a relaxation equation 1 - if/fo p. = p.o 1 + P/ f 0 2

where [« ~ 4R/25Po oLc · , R is the resistivity, L, is the domain diameter, and jt For a distribution of domain sizes

(3f-24) 0=

-1.

m

~

p. = Poo

V, 1 - if/It

L 11 1 + P/lt t

(3f-25)

i=l

where V, is the volume occupied by domains of size L. and V is the total volume. Inserting in Eq. (3f-23) the t:.E/E D and Q are given by

1. = Q

9X.2E. [~(V,/VHf/f,)] 201lP.· L 1 + (f/fiP

(3f-26)

Figure 3f-3 shows measurements of the t:.E effect and the decrement a = 7r /Q plotted over a frequency range, for a poly crystalline nickel rod. Another effect causing losses in ferromagnetic and ferroelectric materials is the microhysteresis effect. In this effect the domain walls or domain rotations lag behind the applied stress and produce a hysteresis loop. Hence the initial susceptibility has a hysteresis component which is a function of the amount of stress. Average values of the parameters can be written in the form p. = Poo[1 - jf(A)J

(3f-27)

where f(A) is a function of the amplitude. Inserting this value of Po in Eq. (3f-23), the value of the microhysteresis loss is given. This type of loss is present in ferroelectric materials and is the principal cause of the low mechanical Q. 3f-8. Other Types of Losses. In addition to these recognized types of losses, other types exist which appear to be associated with the motion of dislocations. Figure 3f-4 shows the Q of a number of materials measured- in a frequency range from 103 to 1 R. M. Bozorth, "Ferromagnetism," p, 691, D. Van Nostrand Company, Inc., Princeton, N.J., 1951. I R. L. Wegel and H. Walter, Physics 6, 141 (1953).

3-112

ACOUSTICS

IDS Hz for small strains. Except for nickel and iron rods, whose decrease in Q with increase in frequency is accounted for by microeddy-current effects, the materials have a Q nearly independent of frequency. When a single or polyerystal sample is strained, an internal friction peak develops, as shown by Fig. 3f-5, whose peak temperature depends on the frequency. This peak, known as the Bordoni peak after its discoverer,' is believed to be due to the motion of dislocation segments from one minimum energy position in the crystal to adjacent ones under the combined action of thermal and mechanical applied stresses. This action takes place over the Peierl barrier which determines the forces returning the dislocations to their minimum energy positions. In fact, the Bordoni peak measurements provide the most reliable estimates of the Peierl barrier values. At high frequencies and for pure materials, the internal friction is determined by the damping of dislocation 100ps2 by loss of energy to phonons and electrons. 1.0 5 00 Q

2

BOZORTH.MASON AND MCSKI~N ~~It- _ _

Z

.;: 0 Ul

0.1

....w

AH, gauss -em FIG. 3f-l0. Relative attenuation in pure single-crystal copper as a function of the product of the wavelength times the magnetic field for several orientations of magnetic field and wave direction. (After Morse.)

superconducting field H c 2• Above H c 2 the material is in the normal state, and the attenuation rises rapidly with the field. MagnetoacQu8tics and Fermi Surface Determinations. In the presence of a magnetic field, the attenuation in metals in the normal state shows variations which are cyclic when plotted as a function of 'AH, where H is the magnetic field. Figure 3f-l0 shows

ACOUSTIC PROPERTIES OF SOLIDS

3-117

measurements in a very pure copper single crystal at 4.2 K. These cyclic variations can be related to the shape of the Fermi surface, which is a constant-energy surface that bounds the occupied states of electrons in momentum space. The electrical effects in a metal are primarily determined by the electrons whose energy is near the Fermi surface, since these are the only ones free to move. For free electrons, such surfaces are spherical with a radius determined by the Fermi energy. The effect of the periodic crystal potential in the band-theory approximation is to distort the Fermi surface from a spherical surface. Electrons of the same energy (which all lie on the Fermi surface) will then have different momenta. Figure 3f-ll shows the probable Fermi surfaces for monovalent copper, gold, and silver, and their relation to the Brillouin zone. If an electron's orbit in momentum space carries it

FIG. 3f-lI. Fermi surfaces for copper, gold, and silver, and their relation to the Brillouin zone. (After Pippard.)

to the Brillouin zone face, the electron will be refracted to the opposite Brillouin zone face. In momentum space, this has the effect of repeating the zone over and over in an extended zone scheme. The effect of a magnetic field is to localize the electrons that can move onto a plane perpendicular to the magnetic field in momentum space. It can be shown that the periodicity of the attenuation-AH curves can be related to the linear dimension of the Fermi surface perpendicular to the magnetic field and perpendicular in momentum space to the direction of wave propagation in real space. The various measurements of Fig. 3f-IO give details of the Fermi surface for different directions in momentum space. Several other types of oscillations in the attenuation occur.' These are the de Haas-van Alphen oscillations of the attenuation, the giant quantum oscillations, acoustic cyclotron resonance, and open orbit resonances. 1 See B. W. Roberts, "Physical Acoustics," vol. IVB, chap. 10, Academic Press, Inc. New York, 1968.

3g. Properties of Transducer Materials W. P. MASON

Columbia University

To determine the acoustic properties of gases, liquids, and solids and to utilize them in acoustic systems, it is necessary to generate the appropriate waves by means of transducer materials which convert electrical energy into mechanical energy and vice versa. For liquids and solids, the most common types of materials are piezoelectric crystals, ferroelectric materials of the barium titanate type, and magnetostrictive materials. 3g-1. Piezoelectric Crystals. The static relations for a piezoelectric quartz crystal producing a single longitudinal mode are for rationalized mks units (3g-1)

where 8 2 and T 2 are the longitudinal strain and stress, respectively, S,.E the elastic compliance along the length measured at constant electric field, d 2 1 the piezoelectric constant relating the strain with the applied field E z , D z the electric displacement, and 'IT the dielectric constant measured at constant stress. Equations of this type suffice to determine the static and low-frequency behavior of piezoelectric crystals. Using the first equation, one finds that the increase in length for no external stress and the external force for no increase in length are, respectively, VI ill = d u -

(3g-2)

t

where V is the applied pottlntial, I, w, and t are the length, width, and thickness of the crystal.and F is the force which is considered positive for an extensional stress. From the second equation one finds that the open-circuit voltage and the short-circuited charge for a given applied force are, respectively,

Q

=

(I

t- D'; dl dw

Jo Jo

=

ri

d 21 T

(3g-3)

Another important criterion for transducer use is the electromechanical-coupling factor k whose square is defined as the ratio of the energy stored in mechanical form to the total input electrical energy. Using Eqs. (3g-I), this can be shown to be (3g-4)

It is readily shown that the clamped dielectric constant

,s,

obtained by setting

8 2 = 0, and the constant-displacement elastic compliance SD, obtained by setting D« = 0, are related to the constant-stress dielectric constant .T and the constant-field elastic compliance

S22 E

by the equations (3g-5)

PROPERTIES OF TRANSDUCER MATERIALS

3-119

Equivalent circuits in which the properties of the crystal are expressed in terms of equivalent electrical elements are often useful (see Sec. 31). An equivalent circuit for a piezoelectric crystal for static conditions is shown by Fig. 3g-1A. In this network the compliance C1 = 8 u E l/ wt represents the compliance of the crystal with the electrodes short-circuited, the capacitance Co is the capacitance of the clamped crystal, i.e., Co = lWEI S [t, while the transformer shown is a perfect transformer, i.e., a transformer having no loss between zero frequency and the highest frequency for which the piezoelectric effect is operative, having a turns ratio of Ip to 1 where (3g-6) The fact that this equivalent circuit presents the same information as Eq. (3g-1) is readily verified by substitution and integration over the area of the crystal. d IEJ sl ~a-~' Ca.!L· C a~ [' I tw • 0 t IU

A

B

HoI' l~o~o1 C 2 Ct .• M... a C.. a wi

.f!!:!! 2 '.

M..•

:2

C•• JL Plwt wI

Plwt

FIG. 3g-1. Equivalent circuit for a piezoelectric crystal for clamped and free conditions.

As an example of the use of such a network, one can calculate from it the efficiency of transformation of mechanical to electrical energy, or vice versa, under various conditions. Suppose that we clamp one end of the crystal and apply a force through the sending-end mechanical resistance Ry and receive the power generated into an electrical resistance RE. Solving the network equations and obtaining the conditions for maximum power output, it is readily shown that the maximum power is obtained if

R« = _ _--=1==

",c1 V1=7C'2

where", = 2r times the frequency f.

(3g-7)

With these values the power in the termination

ito!,

(31-8)

3-120

ACOUSTICS

The available power that can be obtained from a source having an open-circuit force F with an internal impedance R M is maximum when q>2R E = RM. This power is then (3g-9) and hence the power-conversion efficiency is (3g-1O) Hence, unless the coupling is high, the efficiency of conversion by static means is low. This efficiency can be improved by resonating the capacitance Co by an electric coil L« at the frequency of operation and can be further improved by mechanically resonating the static compliance of the crystal. The simplest way to analyze these circuits for their optimum conditions is to observe that, if the perfect transformer is moved to the end of the circuit, both equivalent sections are half sections of wellknown filters. Equation (3g-11) gives the element values of the first filter resonated by an electrical coil, while Eq. (3g-14) gives the element values for the section tuned on both ends. 1 C~ = 822 E 21W) 2 wt 822 E

l(d

ESlw Co = - - -

fl

£0

=

, - ----'-------

21r!2(f2 - ft)Zo 21r(h 2 - ft2)ZO 2)ZO 2 2), i.e., the actual mechanical resistance, we find

Hence, if there is no dissipation in the elements of the crystal, perfect power conversion can be obtained but only over a bandwidth of

h - ft h

= 1 -

vI1"=k2

(3g-13)

We consider next a wider bandpass filter having the element values

t: _

pit (822E)2 = Zo W d 21 21r(f2 - !1) 1 (!2 - !l)ZO ESlw £0 = Co = t 21r(h - ft)Zo 21r!d2 1-

(3g-14)

Solving for the bandwidth and the impedances

(3g-15) This filter section can efficiently transform mechanical into electrical energy and vice versa with a loss determined only by the dissipation in the elements of the crystal.

3-121

PROPERTIES OF TRANSDUCER MATERIALS

'I'he simplest method for mechanically resonating the crystal is to use it near its natural mechanical resonance. An exact equivalent circuit for a vibrating crystal is shown by Fig. 3g-1B. Near the first resonant frequency, the equivalent circuit for a clamped quarter-wave crystal is shown by Fig. 3g-1C while the equivalent circuit for a half-wave crystal is shown by Fig. 3g-1D. When the half-wave crystal resonated by a shunt coil is applied to converting electrical into mechanical energy, the same formulas given in Eqs, (3g-14) and (3g-15) are applicable except that k 2j(1 - k 2 ) is replaced by (8/1r2)[k2/ (1 - k 2)]. By using the complete representation of Fig. 3g-1B the effect can be calculated by using various backing plates on the radiation from the front surface. The general form of Eq. (3g-1) holds for any single mode whether it is longitudinal or transverse as long as the appropriate constants are used. For longitudinal thickness modes when the radiating surface is a number of wavelengths in diameter, 822 E is replaced by I/cn E and d 21 by e2I!cnE, the appropriate thickness piezoelectric constant. For a thickness shear mode, the appropriate shear stiffness (C4~ Clili, or C66)

B

A

"

'2

FREQUENCY

C

"

,2

FREQUENCY

FIG. 3g-2. Use of equivalent circuit in determining the optimum conditions for energy transmission.

replaces 11822 and the appropriate shear piezoelectric constant replaces d 21 • Table 3g-1 lists the constants in mks units for a number of standard crystal cuts. 3g-2. Electrostrictive and Magnetostrictive Materials. Other types of materials that have been used in transducers are ferroelectric crystals and ceramics of the barium titanate type and ferromagnetic crystals, polycrystals, and sintered materials of the ferrite type. All these materials have changes in lengths proportional to squares and even powers of the polarization and to obtain a linear response they have to be polarized. These polarized materials have relations between stresses, strains, electric and magnetic fields, and electric displacement and magnetic flux similar to those for a piezoelectric crystal shown by Eq. (3g-l) and hence these materials can be said to have "equivalent" constants which depend not only on the material but also on the degree of poling and in some cases on aging effects. The dielectric and permeability constants are those associated with the polarized medium as are also the elastic constants. To obtain these equivalent piezoelectric and piezomagnetic constants, one can start with the more fundamental potential equations which have the same form for either electrostrictive or magnetostrictive materials. For polycrystalline or sintered materials, these potential equations can be written in the form

3g-1.

TABLE

Crystal and cut

Quartz X cut, length Y

Elastic constant, lO- n m'J/ newton

Mode

L.L.

X cut

T:L.

Ycut

T.S.

Rochelle salt, 45-deg X cut L.L.

8u

B

= 1.27

1

-g = 1.16

Cll

-

1

css E

= 2.57

PROPF.RTIF..S OF PIEZOELECTRIC CRYSTALS IN MKS UNITS

Piezoelectric constant d, 10-11 coulomb/ newton d 21 = 2.25 en -2.04 cnB = e2S

css E

8~f = 6.7

du

2

= +4.4 = 435

Open-circuit ElectroDielectric voltage capacitivity mechanical g = diE, coupling E, 10-11 volt- meters/ k farad/m newton

Force factor dis, newtons/ voltmeter

I

Density, 10' kg/m a

4.06

0.099

0.055

0.177

2.65

4.06

0.093

0.050

0.175

2.65

4.06

0.137

0.108

0.171

2.65

0.78

0.098

6.5

1.77

0.288

0.29

0.287

1.77

444.0

45-deg Y cut

L.L.

s~f = 9.89

d~5 =

-28.4

ADP, 45-deg Z cut

L.L.

sf: =

5..3

d~s

24.6

13.8

0.29

0.178

0.465

1.804

KDP, 45-deg Z cut

L.L.

sf: =

4.85

d~s = 10.7

19.6

0.12

0.058

0.22

2.31

EDT, Y cut, length X DKT, 45-deg Z cut L.R., Y cut

L.L. L.L. T.L.

SllE

L.R., hydrostatic

= 3.88

sf: =

d n = 11.3 d;l = -12.2

7.4 5.8

0.215 0.245

0.152 0.21

0.29 0.287

1.538 1.988

cuE

CuE

~ = 15

9.15

0.35

0.165

0.75

2.06

0.3

3.1

4.25 __1_ = 2

H.

Tourmaline, Z cut

T.L.

Tourmaline, hydrostatic

H.

=

9.85

d u + dn + du

1

~ Cn

= 0.61

~ cuE

=

= 13

9.15

-1.84

6.65

=

6.65

d l l +d u

-2.16

0.143 0.092

0.0275 0.0325

I

Abbreviations: L.L. = length longitudinal; T.L. ... thickness longitudinal; T.S ... thickness shear; ADP ... ammonium dihydrogen phosphate; KDP ... potassium dihydroaen phosphate; EDT ... ethylene diamme tartrate; L.R.... lithium sulfate monohydrate.

3-123

PROPERTIES OF TRANSDUCER MA'rERIALS

G

+

+

+ +

+

+

+

+ +

2s 12 D(T 1T 2

-j.[SllD(T 12 T 22 T a2) T1T a T 2T s) - S12 D)(T 42 To! T 62)] - {Qll(D 12T1 +"D 22T2 Da"T a) + Q12[T1(D 22 D a2) T 2(D 12 D a2) T a(D 12 D 22)] + 2(Qll - Q12)(T 4D2Da ToD1D a T 6D 1D 2) I -iJ111 T ( D 12 D 22 D a2) + K llT(D 14 D 24 D a4) K 12T(D 12D22 D 12D a2 D 22Da2) + K 11lT(D 16 D 26 D a6 ) K 112T[D 14(D 22 D 32) D 24(D 12 D a2) + D S4(D 12 D 22)] K 123T D 12D 22Da2 (3g-16)t

+ 2(SllD

+

+ + +

+ +

+

+ + +

+

+ +

+

+

+

+

+ +

+

+

+

where T 1, T 2 , T a are the three extensional stresses, T 4 , Tr., T 6 the three shearing stresses, D 1, D 2 , D« the three components of the electrical displacement for ferroelectric materials or the three components of the magnetic flux B for ferromagnetic materials, the s constants are the compliance constants for an isotropic material measured at constant electric or magnetic displacement, the Q's are the electrostrictive or magnetostrictive constants, J111 T the inverse of the initial dielectric constant or permeability measured at constant stress, and the KT'S are constants determining the total energy stored for higher polarizations. The static equations can be obtained by differentiation of G according to the relations

S,

=

-

sa

-

aT,

Em

= -

eo

(3g-17)

aD m

Since linear equations are obtained only if a permanent polarization Po is introduced, we assume that (3g-18) D, = Po + D a* where D a* is a small variable component superposed on PI). Also, D 1 and D 2 are small so that their squares and higher powers can be neglected compared with Po. Introducing these into (3g-16) and differentiating, we have 8 1 = SllDT l + s12D(T 2 + T 1) + Q12(P 02 + 2P oD a*) S2 = SllDT 2 + s12D(T l + T a) + Q12(P 0 2 + 2P oD 3*) s, = SllDT a + S12 D(T 1 + T 2) + Qll(P 02 + 2P oD a*) 8 4 = 2(SllD - S12 D)T 4 + 2(Qll - Q12)P OD 2 SO = 2(SllD - S12 D)T o + 2(Q11 - Q12)P OD 1 8 6 = 2(SllD - S12 D)T 6 E 1 = -2(Qll - Q12)P oTo + D 1 (J1 11 T + 2K 12TP02 + 2K 112TP 04) E 2 = -2(Qll - Q12)P oT 4 + D 2( J1 l1T + 2K 12TP02 + 2K112TP 04) E« = -2Q11P oT a - 2Q12P O(T 1 + T 2) + D 3 *(J1 11 T + 12K 11TP02

(3g-19)

+ 30K

1l1TP

04)

It is obvious that the variable components of Eq. (3g-19) follow the same rule as for a piezoelectric crystal. There are three longitudinal modes and a shearing mode. The length longitudinal mode has the following constants:

L.L. mode

E _ D[ Sl1 - Sl1 1

4Q122P02]

+ J133 T(P o)Sl1D

d 31

_ -

2Q12P o

J1aa T(P o)

1 E3a T (P o) - - - J1aa(Po)

(3g-20)

where J1aa T (P o) = (J111 T + 12K 11TPo2 + 30K 111TP04) is the dielectric impermeability of the ceramic when it has a permanent polarization Po L.T. bar

SHE

= Sl1D [ 1

4Q112P02 ]

+ J1aa T(P o)Sll D

2QllP O d aa = J133 T(P O) E33 T (P Q)

1 J1aa T (P o)

(3g-21)

t If higher-order terms than those considered here are used, second-order electrostrictive and magnetostrictive terms and the change in elastic constants with polarization can be taken care of. For example, see W. P. Mason, Phys. Rev. 82 (5),715-723 (June 1, 1951).

3-124

ACOUSTICS

These formulas hold for a bar which is long in the direction of vibration compared with the cross-sectional dimensions. When a plate is used which is a number of wavelengths across, the sidewise motions 8 1 and 8 2 are zero and the constants are

L.T. plate

1

(3g-22)

cuE

where d '33 = 2P o (

D

2812 D ------v--+

Qll -

811

812

1

') QI2)f33(PO

and

The thickness shear mode has the fundamental constants 2(su E

-

1900

8u E);

d u; EIlT(P o),

E

lBoo~ Z

1700 1600

o 0'~273 -200

-100

0

100

200

3Oh500

TEMPERATURE, C FIG. 3t-3. Temperature variation of kp , permittivity, and bar frequency constant for prestabilized PZT-4.

PROPERTIES OF 'l'RANSDUCER MATERIALS

3-125

i.e., the dielectric constant perpendicular to the poling direction, where 2( 8 u 1l'

-

8u

E)

=

EIIT(P o)

2(8u

=

D

-

8n

D)

4(Qu - Qn)'Po• -r. -'-==-fJ-u""'T"""(P;':o"")-=1

({JUT

+ 2K n TP o• + 2K

ll2 TP o' )

(3g-23)

Two other modes have been used in electrostrictive and magnetostrictive materials, 20

200

900

:z ....

~ 15

600

>

':'

~ 10 ;;; co

400 ~

...

;;;

5

o

200

o-273 -200

-100

0

100 200

0

300

TEMPERATURE,C 'FIG. 3g-4. Temperature variation of gil, dill and mechanical Q for prestabilized PZT-4.

3000

20 0 . 6 , - - - - - - - - - - - - .

2500

18

0.5

2000 ~

16

0.4

1500 ~

14",,"'0.3

N

e

¥

1000

-iof l2

500

10

o

8

O='-==-~:-'-'":_'_~~...L-L-L...l-L...J

-200 -160 -120 -80 -40

0

40

80

120

TfMPERATURE,C FIG..3g-5. Temperature variation of k p , permittivity K, and Young's modulus (1/811 E) for

BaTIO, cerarmc,

TABLE 3g-2. PROPERTIES OF FERROELECTRIC CERAMICS AT 25°C

Material

Piezoelectric Piezoelectric Young's Dielectric constant d a1, constant d aa, capacitivity modulus, 10- 11 10- 11 1011 newEaa T, 10- 11 coulomb/ coulomb/ farad/m tons/rn! newton newton

I Commercial Ba'I'iO, ceramics ............. 97% BaTiO a, 3% CaTIO a ................ 96% BaTiO a, 4% PbTiO a ................ 90% BaTiO a, 4% PbTiO a, 6% CaTiO a .... 84% BaTiO a, 8% PbTiO a, 8% CaTiO a .... 80% BaTiO a, 12% PbTiO a, 8% CaTiO a ... PZT #4*.......................... " ... PZT #5*............................... PZT #6*............................... NbO a (K 50%; Na 50%)t ................ Pb(NbO a) 2t ...............•............

* Data from Clevite Brush Company. t L. Egerton, ~.

J. Am. Ceram, Soc. 42,438 (1959). G. Goodman, J. Am. Ceram, Soc. 36, 368 (1953).

1.18 1.22 1.14 1.24 1.31 1.28 0.815 0.675 0.865 1.02 0.29

I

-5.6 -5.3 -3.8 -4.0 -2.7 -2.0 -9.7 -14.0 -7.8 -3.2 -3.3

16 13.5 10.5 11.5 8.0 6.0 23.5 32.0 19.1 8.0 9.0

1,250 1,230 880 710 530 400 875 1,200 860 235 240

Electromechanical coupling factors

k 31

i.;

0.17 0.17 0.14 0.167 0.124 0.113 0.28 0.32 0.25 0.226 0.115

0.45 0.43 0.39 0.48 0.4 0.34 0.63 0.70 0.60 0.52 0.31

Open -circuit Force voltage factor daaYoE, g = daalEaa T , volt-meters/ newtons/ newton volt-meter

0.0106 0.0111 0.012 0.016 0.015 0.015 0.0268 0.0266 0.022 0.034 0.037

13.5 11.0 9.2 9.3 6.1 4.7 19.2 21.6 16.5 8.15 2.0

PROPERTIES OF TRANSDUCER MATERIALS

3-127

the radial mode and the torsional mode. The first is driven by polarizing the disk perpendicular to the major surface and involves the same fundamental constants as the length longitudinal mode of Eq. (3g-20). It has been shown 1 that the effective coupling and the resonant frequency of such disks are given by the equations k2

=

_2_ 1 - (f'

4Q11

2

P o2 f T(P o) suE

(3g-24)

where (f' is Poisson's ratio, which is approximately 0.3 for barium titanate ceramics. The torsional mode is generated in electrostrictive and magnetostrictive materials when the alternating displacement is at right angles to the polarization. This is easily accomplished for a magnetostrictive material by polarizing a cylinder radially by one set of windings and driving the cylinder by a set of windings coaxial with the cylinder. In an electrostrictive material, a torsional vibration can be obtained by inducing a permanent polarization in different directions on two sides of the cylinder and driving the cylinder by a set of two electrodes with the two gaps between them coming in the region of greatest permanent polarization. The fundamental elastic constant is the shear constant (suE = SuE) while the fundamental piezoelectric constant is the shear piezoelectric constant d u or the similar magnetostrictive constants. Table 3g-2 gives some typical constants for a number of barium titanate compositions with lead and calcium titanate additions. A number of new ceramics, particularly lead zirconate titanate (trade name PZT), sodium potassium niobate, and lead metaniobate, have recently appeared. These have higher Curie temperatures than barium titanate combinations but lower values of electrical and mechanical Q's. The stored electrical polarization in lead zirconate titanate (nearly 30 microcoulombs/ em 2) is higher than in any other ceramic and such materials are especially useful for producing a high current when depolarized by a mechanical shock (E.E.T. transducers). Figures 3g-3, 4, and 5 show how the fundamental constants vary with temperature over a wide temperature range for the most used ceramic PZT-4, and for the original BaTiO a ceramic. Table 3g-3 gives some typical constants for a number of magnetostrictive materials. 3g-3. Equivalent Circuits for Magnetostrictive Transducers. The energy equation (3g-16) is the same for magnetostrictive and electrostrictive materials, provided the electric field and displacement are replaced by the magnetic field H and the magnetic flux density B. Hence the equivalent circuit of Fig. 3g-1 also applies to a magnetostrictive material, provided we replace E and i by

h l

Hi dl = U, the magnetomotive

force, and BS = 4>, where S is the cross-sectional area, ~ the total flux through the magnetostrictive transducer, and 4> the time rate of change of this flux. Hence all the fundamental quantities and coupling factors can be expressed in terms of the analogous quantities as shown by Table 3g-3. These hold for materials having a closed magnetic circuit such as a ring or a rod with closing magnetic circuit having a reluctance small compared with that for the rod. If this is not true, demagnetizing factors and additional reluctance values have to be taken account of and the value of ~ is the average value determined by all these factors. In a transducer, however, it is not U and 4> that we deal with, but rather the input voltage and current. These quantities are related by equations of the type

E

=

Nd~ dt

U

= Ni

(3g-25)

where N is the number of turns and the voltage, current, flux, and magnetomotive forces are directed as shown by Fig. 3g-6. These are the equations of a gyrator, shown 1 W. P. Mason, "Piezoelectric Crystals and Their Application to Ultrasonics," chap. XII, D. Van Nostrand Company, Ino., Princeton, N.J., 1950.

3g-3. MAGNETOSTRICTIVE PROPERTIES OF METALS AND FERRITES Data from C. M. Van der Burgt, Phillips Research Repts. 8, 91-132, 1953

TABLE

du X 10 9 du X 10 9 webers/newton webers/newton

Material

99.9 nickel ..................... 50 Co; 0.5 Cr; 49.5 Fe ........... 35 Co; 0.5 Cr; 64.5 Fe ........... NiO (15 %); ZnO (35 %); Fe20a (50%) ....................... NiO (18%); ZnO (32%); Fe202 (50%) ....................... NiO (25 %); ZnO (25 %); Fe201 (50%) ....................... NiO (32 %); ZnO (18 %); Fe201 (50%) ....................... NiO (40 %); ZnO (10 %); Fe201 (50%) ....................... NiO (50%); Fe201 (50%) ........

-5.3 12.3 13.4

...... ...... ......

Rev. per. long. ,.T(Po)

X 10 henrys/m 4

Rev. per shear

yoH =

-.!.-8

X 10- 11

8

,.T(Po)

ku

X 10 henrys/m 4

newtona/mr

%.84 8.3 19.2

2.0 2.2 2.1

0.14 0.20 0.14

...... ...... ......

.... .... ....

..... ...... ....

0.05 0.09 0.047

8.9 8.2 8.1

-11.1

-28.5

1.8

0.034

139

0.68

0.063

0.003

5.06

-16.0

-39.5

77.5

1.62

0.073

74

0.62

0.115

0.0165

4.9

-9.8

-20.3

22.0

1.53

0.082

20

0.59

0.110

0.022

4.85

-8.7

-15.8

13.4

1.5

0.093

13.2

0.5'8

0.105

0.0282

4.85

-5.9 -4.4

-13.0

5.5 2.8

1.37 0.93

0.112 0.08

0.54 0.36

0.13 0.09

0.0315 0.0344

4.76 4.20

......

190

Shear stiff- Torsional Energy stored Density, ness GB coupling Hdu 2/ ,.T) X 1012 kg/ma X 10- 11 l X lO- a kT joules-m/newton 2 newton/m

5.35 2.4

Data from R. M. Bozorth, E. A. Nesbit, and H. J. Williams Flux density B, webera/rna

Long. rev. per ,.T(Po) X 10 1 henrys/m

Young's modulus YoA X 10- 11 newtons/m 2.

Longitudinal coupling ku

dll X 10 9 webers/newton

Energy stored HdI3 2/ ,. T) X 1012 [oulee-m/newtoe!

0.4 0.5 0.55

0.98 0.515 0.317

2.1

0.232 0.208 0.177

-5.0 -3.26 -2.18

0.127 0.103 0.075

8.9

45 % N i, 55 % Fe, i.e., 45 % Permalloy ..............

0.722 0.965 1.2 1.4

8.94 7.36 4.45 1.97

1.6

0.154 0.179 0.178 0.15

11.5 12.2 9,4 5.3

0.074 0.101 0.099 0.071

8.17

2V Permindur, 2%V, 50% Co. 4i% Fe ..... " " " , .

1.5 1.6 1.8 2,0

3.54 2,61 2.23 1.14

2.3

0,238 0,222 0.202 0.18

0.123 0.108 0,089 0.07

8.3

Material

99.9 % nickel, ...................................

'" '"

... ... ... ,

..

... ...

9,35 7.5 6.3 4.0

Density, kg/ma X 10-1

PROPERTIES OF TRANSDUCER MATERIALS

by the symbol of Fig. 3g-6, which does not satisfy the reciprocity relationship. call ZM the magnetic impedance defined by

U

ZM = d4>/dt

3-129 If we

(3g-26)

it is evident that the electrical impedance at the terminals of the transducer is equal to

E N2 ZE =-;- = ~

(3g-27)

ZM

Hence the effect of the gyrator coupling is to invert all the elements of the equivalent

J'SI

Co= 5

;

.r:::-H

sV P10

.CH

=V~

-r

d33YoHS

; ., = P FIG. 3g-6. Equivalent circuit of a magnetostrictive rod. Zo=

;

II"

circuit. Hence one should determine the element values of Fig. 3g-6 for the appropriate terminating conditions and then invert the values in accordance with Eq. (3g-27) to determine the elements of a magnetostrictive transducer. The values given in Fig. 3~-6 are for a longitudinally vibrating rod where S is the cross-sectional area and I the length. P.s is the average value of the permeability in the equations for the reluctance R R = _l_

p'sS

where

P.s

is for the constant stress condition.

(3g-28)

3h. Frequencies of Simple Vibrators.

Musical Scales

ROBERT W. YOUNG

U.S. Naval Undersea Research and Development Center

3h-l. Strings.

The fundamental frequency of vibration of an ideal string is (3h-l)

where 10 is the frequency, I is the free length, F is the force (tension) stretching the string, and m is the mass per unit length. Values of m for steel and gut strings are given in Table 3h-1. In addition to the vibration in a single loop which gives rise to the fundamental frequency, the ideal string may vibrate in harmonics whose frequencies are

Ira = nlo

(3h-2)

where n is the integer denoting the particular mode of vibration. The length of each vibration loop is lin. These successive lengths and the corresponding periods of vibration (i.e., the reciprocals of the frequencies) constitute a harmonic series according to the strict mathematical definition; nowadays, however, the frequencies themselves are usually said to make up a harmonic series. The frequencies of actual strings depart somewhat from the frequencies computed from the simple formula because actual strings are stiff, they may be partially clamped at the ends, they are not infinitely thin, the tension increases with amplitude of vibration, the mass per unit length is not exactly uniform, there is internal damping and damping due to the surrounding air and supports, and the supports are not infinitely rigid. In the formulas which follow damping has been neglected. For an actual string set (3h-3) I = nlo{l + G) where the factor (I + G) is a measure of the departure (i.e., the inharmonicity) from the ideal harmonic values. Table 3h-2 lists values of G for various small perturbations. The approximations are valid only when G is small. For musical purposes it is often convenient to give the inharmonicity in cents (hundredths of an equally tempered semitone) by setting 1

+ G = 28 / 1, 200 = e8 / 1, 7 31

(3h-4)

where 6 is the inharmonicity. To a usually acceptable approximation, 6 = 1,731G. If the stiff string listed in Table 3h-2 is of steel music wire, Yip = 25.5 X 106 2/sec 2, Y being Young's modulus and p the density. m The tension is very nearly F = l2 p/ 021r d 2• Thus for steel wire, and by virtue of the stiffness formula, the inharmonicity in cents is 6 = 3.4 X 1013d 2n 2 /102l 4, provided that the diameter and length are in centimeters.

3-130

FREQUENCIES OF SIMPLE VIBRATORS. TABLE

Diam

3h-1.

MUSICAL SCALES

3-131

MASS PER UNIT LENGTH OF STEEL AND GUT STRINGS*

Steel, g/m

Gut, g/m

Diam

Steel, glm

Gut,

Diam

Steel, Gut, g zrn glm mm in. -- - - - -- - -- - - - -- ---- - - -- -

mm

in.

mm

in.

g zrn

0.20 0.22 0.24 0.26 0.28

0.0079 0.0087 0.0094 0.0102 0.0110

0.25 0.30 0.35 0.42 0.48

0.04 0.05 0.06 0.07 0.09

1.00 1.02 1.04 1.06 1.08

0.0394 0.0402 0.0409 0.0417 0.0425

6.15 6.40 6.65 6.91 7.17

1.10 1.14 1.19 1.24 1.28

1.80 1.82 1.84 1.86 1.88

0.0709 0.0717 0.0724 0.0732 0.0740

19.9 20.4 20.8 21.3 21.7

3.56 3.64 3.72 3.80 388

0.30 0.32 0.34 0.36 0.38

0.0118 0.0126 0.0134 0.0142 0.0150

0.55 0.63 0.71 0.80 0.89

0.10 0.11 0.13 0.14 0.16

1.10 1.12 1.14 1.16 1.18

0.0433 0.0441 0.0449 0.0457 0.0465

7.44 7.71 7.99 8.27 8.56

1.33 1.38 1.43 1.48 1.53

1.90 1. 92 1.94 1.96 1.98

0.0748 0.0756 0.0764 0.0772 0.0780

22.2 22.7 23.1 23.6 24.1

3.97 4.05 4.14 4.22 4.31

0.40 0.42 0.44 0.46 0.48

0.0157 0.0165 0.0173 0.0181 0.0189

0.98 1.08 1.19 1.30 1.42

0.18 0.19 0.21 0.23 0.25

1.20 1.22 1.24 1.26 1.28

0.0472 0.0480 0.0488 0.0496 0.0504

8.86 9.15 9.46 9.76 10.1

1.58 1.64 1.69 1. 75 1.80

2.00 2.02 2.04 2.06 2.08

0.0787 0.0795 0.0803 0.0811 0.0819

24.6 25.1 25.6 26.1 26.6

4.40 4.49 4.58 4.67 4.76

0.50 0.52 0.54 0.56 0.58

0.0197 0.0205 0.0213 0.0220 0.0228

1.54 1.66 1. 79 1.93 2.07

0.27 0.30 0.32 0.34 0.37

1.30 1.32 1.34 1.36 1.38

0.0512 0.0520 0.0528 0.0535 0.0543

10.4 10.7 11.1 11.4 11.7

1.86 1.92 1.97 2.03 2.09

2.10 2.12 2.14 2.16 2.18

0.0827 0.0835 0.0843 0.0850 0.0858

27.1 27.6 28.2 28.7 29.2

4.85 4.94 5.04 5.13 5.23

0.60 0.62 0.64 0.66 0.68

0.0236 0.0244 0.0252 0.0260 0.0268

2.21 2.36 2.52 2.68 2.84

0.40 0.42 0.45 0.48 0.51

1.40 1.42 1.44 1.46 1.48

0.0551 0.0559 0.0567 0.0575 0.0583

12.1 12.4 12.8 13.1 13.5

2.16 2.22 2.28 2.34 2.41

2.20 2.22 2.24 2.26 2.28

0.0866 0.0874 0.0882 0.0890 0.0898

29.8 30.3 30.9 31.4 32.0

5.32 5.42 5.52 5.62 5.72

0.70 0.72 0.74 0.76 0.78

0.0276 0.0283 0.0291 0.0299 0.0307

3.01 3.19 3.37 3.55 3.74

0.54 0.57 0.60 0.64 0.67

1.50 1.52 1.54 1.56 1.58

0.0591 0.0598 0.0606 0.0614 0.0622

13.8 14.2 14.6 15.0 15.4

2.47 2.54 2.61 2.68 2.74

2.30 2.32 2.34 2.36 2.38

0.0906 0.0913 0.0921 0.0929 0.0937

32.5 33.1 33.7 34.3 34.8

5.82 5.92 6.02 6.12 6.23

0.80 0.82 0.84 0.86 0.88

0.0315 0.0323 0.0331 0.0339 0.0346

3.94 4.14 4.34 4.55 4.76

0.70 1.60 0.74 1.62 0.78 1.64 0.81 1.66 0.85 1.68

0.0630 0.0638 0.0646 0.0654 0.0661

15.7 16.1 16.5 16.9 17.4

2.81 2.89 2.96 3.03 3.10

2.40 2.42 2.44 2.46 2.48

0.0945 0.0953 0.0961 0.0968 0.0976

35.4 36.0 36.6 37.2 37.8

6.33 6.44 6.55 6.65 6.76

0.90 0.92 0.94 0.96 0.98

0.0354 0.0362 0.0370 0.0378 0.0386

4.98 5.20 5.43 5.67 5.91

0.89 0.93 0.97 1.01 1.06

0.0669 0.0677 0.0685 0.0693 0.0701

17.8 18.2 18.6 19.0 19.5

3.18 3.25 3.33 3.41 3.48

2.50 2.52 2.54 2.56 2.58

0.0984 0.0992 0.1000 0.1008 0.1016

38.4 39.1 39.7 40.3 40.9

6.87 6.98 7.09 7.21 7.32

1. 70 1. 72 1. 74 1. 76 1. 78

* This table is based on a density of steel of 7.83 g/cm l • Density of gut is assumed to be 1.4 g/cm l • about one-sixth that of steel. This is only approximate, since the density of gut varies from sample to sample, and increases markedly with humidity. Brass wire has a density of 8.7 g/cm 3, about 1.1 times that of steel.

3-132

ACOUSTICS

3h-2. Air Columns and Rods. The air within a simple tube of constant cross section, open at both ends or closed at both ends, vibrates freely at a frequency near

f = nc

(3h-5)

2l

where n is an integer (mode of vibration number), c is the speed of sound in the contained air, and l is the length of the tube. (See Sec. 3d for speed of sound in air and its dependence on temperature.) The diameter of the tube must be relatively small;

TABLE

3h-2.

PERTURBATION IN FREQUENCY OF A STRING

Cause Stiffness

Y is Young's modulus, d is the diameter of

n 211" 3d 4 Y

128l 2F 4ml

Yielding support

Variable density

Explanation

G

-

1 -

l

l

h 0

. lI"nx (l(x) sm 2 dx

l

the string The support consists of a mass M on a spring of transverse force constant K. Multiply by 2 if there are two such supports The mass per unit length is m = moll + (l(x)] where ma is the mean value over the string and x is the distance from one end of the string; the function (l(x) must be small in comparison with unity

plane sound waves propagated longitudinally are assumed. The same formula applies to thin rods vibrating longitudinally and suitably supported (say, at distances l/2n from the ends) so that the vibration is not inhibited. (See Sec. 3f for speed of sound in solids.) An open organ pipe is an example of a doubly open tube of constant cross section. To calculate its frequency adequately it must be recognized, however, that the air beyond the physical ends of the tube partakes of the vibration and adds inertia to the vibrating system. (This does not mean, however, that there is a velocity antinode beyond the end of the tube.) The necessary corrections to the simple formula are usually introduced as empirical "end corrections" to be added to the geometrical length i thus nc (3h-6)

f =

2(l

+ Xl + X2)

where Xl = O.3d is the correction for the unimpeded end (d being the inside diameter of the pipe) and X2 = lAd is the correction for the mouth of the pipe. These are rough approximations; the literature on the end correction is extensive. I The air inside a cylindrical tube that is closed at one end and open at the other vibrates at frequency nc (3h-7)

f =

4(l

+ x)

where x = O.3d if the open end is unimpeded. In the case of the "closed" organ pipe (meaning closed at one end only), for the mouth X = lAd. IE. G. Richardson ed, "The Technical Aspects of Sound," vol. I, pp. 493-496, 578, Elsevier Publishing Company, Amsterdam, 1953; Harold Levine, J. Acoust. Soc. Am. 26, 200-211 (1954).

FREQUENCIES OF SIMPLE VIBRATORS.

3-133

MUSICAL SCALES

The speed of sound c (and thus the frequency of vibration) in a gas contained within a tube is reduced somewhat from its value Co in free space, as a consequence of friction and loss of heat to the wall of the tube. If the frequency of vibration f and the tube diameter d are such that df! > 211!, II being the kinematic viscosity of the gas, the speed of sound (longitudinal phase velocity) within the tube is'

where 'Y is the ratio of specific heats, and P r the Prandtl number for the gas. For air at 20°C, and when df! > 0.8 with d in em and f in hertz, with slight approximation the Helmholtz-Kirchhoff correction for the speed of sound is C

= Co ( 1

-

0.33) df!

Correspondingly the interval by which the frequency of vibration is lowered owing to friction and heat conduction is 5721df! cents. As df! becomes less than 211! a transition I occurs to an even more marked reduction in the speed of sound propagation in the tube. The air in a conical tube is resonant in some cases at the same frequencies as a doubly open cylindrical tube of the same length, but there is the important difference that the contained sound waves are spherical rather than plane. Table 3h-3 gives equations! to be solved for each combination of end conditions; k = 27rfIc. "Closedopen," for example, means that the smaller end of the truncated cone is closed while the larger end is open; rl is the slant distance from the extrapolated apex of the cone to the smaller end and r2 is the slant distance to the larger end. The slant length of the resonator is thus r2 - rl. When rl = 0, the length is r2 and the cone is complete to the apex. Formulas for computing frequency when the cone is complete are shown at the right of Table 3h-3. As in the case of cylindrical tubes, the length should be TABLE 3h-3. FREQUENCIES OF CONICAL RESONATORS Ends

Equation

For rl = 0

Closed-cloaed tan k(r2 - rt) = -krt

Open-closed

tan k(r2 - rr) = kr z

Open-open

= kr2 t. =~ 2n

tan kr z

Closed-open

J=

tan kr2 = kr« nc

2(n - rr)

J

=

nc 2r2

slightly modified by end corrections. As the angle of the cone increases the correction decreases and may even become negative. 3 3h-3. Volume Resonators. The Helmholtz resonator consists of a nearly closed cavity of volume V with an opening of acoustical conductance C. If the opening is 1 A. H. Benade, J. Acoust. Soc. Am. 44, 616-623 (1968). Multiplication by the correction term is erroneously shown there in eq. (13c), instead of division. 2 Eric J. Irons, Phil. Mao. 9,346-360 (1930). 3 A. E. Bate and E. T. Wilson, Phil. Mao. 26, 152-757 (1938).

3-134

ACOUSTICS

If the opening is

in a thin wall the conductance is simply d, the diameter of the hole. through a short neck of length l, approximately 1rd 2

C = 4(l

+ 0.8d)

(3h-8)

The natural frequency of the resonator is (3h-9) the speed of sound in the opening being c. The equation is valid for wavelengths large in comparison with the dimensions of the resonator. The ocarina may be recognized as an instrument of the resonator type because the position of an open hole of given size is immaterial; when the holes are all equal, they can be opened in any order to give the same scale. The total conductance for use in the formula given above is the sum of the conductance of individual holes, provided that they are separated far enough that there is no interaction.

TABLE

3h-4.

FREQUENCIES OF TRANSVERSE VIBRATION OF BARS

Frequency

Ratio

Ends Mode- 1

2

3

4

2

-----0.5597K ~Y l2 p

Clamped-free

/1=---

Free-free, or clamped-clamped

/1 = 3.561K ~ l2

p

_31_ 4

4,960

6,124

5.404 8.933 1,75512,921

I 3,791

6.267 17.548 34.387 3,177 2.756

-

Cents

3h-4. Bars. A long thin bar clamped and/or free at the end(s) can vibrate transversely at the fundamental frequencies listed in Table 3h-4 under mode 1. The length of the bar is l, Y is Young's modulus, p is the density, and K is the radius of gyration about the neutral axis of the cross section. For a round bar K = d/4, where d is the diameter. For a flat bar of thickness t (in the plane of vibration) K = t/"\/ii the width is immaterial. The frequency of a bar clamped at both ends is the same as that of a bar free at both ends. The frequency of a higher mode of vibration can be found by multiplying the fundamental frequency by the ratio indicated in Table 3h-4; the intervals in cents corresponding to these ratios are given at the extreme right of the table. These are the classic' values for thin bars; the frequencies of actual bars are lowered slightly as a consequence of rotatory inertia, lateral inertia, and shear.! For example, for a steel bar whose length is 40 times the thickness, the frequencies of the first four modes of vibration are expected to be 0.997,0.992,0.984-, and 0.974 times the corresponding "thin" values (i.e., lowered 5, 14, 28, and 46 cents, respectively). I Lord Rayleigh, "Theory of Scund," vol. I, p, 280, Macmillan & Co., Ltd., London, 1894. The interval erroneously given as 2.4359 octaves has been corrected here to 2.4340 octaves = 2,921 cents. 2 William T. Thomson, J. Acoust. Soc. Am. 11, 1\-)9-204 (1939). There is an error: m == {j/[l {j2(kIL)2]t, not m =. {j/[l {j2(kIL)2]t.

+

+

FREQUENCIES OF SIMPLE VIBRATORS. TABI.E

3h-5.

Note

S

Co Do Eo Fo

ao Ao Bo C1 D1

E1 F1 01

A1 B1

C2 D2

E2 F2 G2 A2 B2

f

271"f

Note

S

-- 36 16.352 102.74 Ca 37 17.324 102.74 18.354 115.32 Da 38 39 19.445 122.18 20.602 129.44 E a 40 21.827 137.14 Fa 41

f

A = 440 271"f

HERTZ

6 7 8 9 10 11

23.125 145.30 24.500 153.93 25.957 163.09 27.500 172.59 29.135 183.06 30.868 193.95

12 13 14 15 16 17

32.703 205.48 34.648 217.70 36.708 230.64 38.891 244.36 41.203 258.89 43.654 274.28

18 19 20 21 22 23

46.249 290.59 48.999 307.87 51.913 326.18 55.000 345.58 58.270 366.12 61.735 387.90

24 25 26 27 28 29

65.406 410.96 69.296 435.40 73.416 461.29 77.782 488.72 82.407 517.78 87.307 548.57

30 31 32 33 34 35

92.499 581.19 97.999 615.74 103.83 652.36 110.00 691.15 116.54 732.25 123.47 775.79

Ga

Aa Ba C.

D. E. F.

G. A. B. C6 D6 E5 F5

G5 A5 B5

S

Note

-

--- - -

0 1 2 3 4 5

3-135

FREQUENCIES OF THE EQUALLY TEMPERED SCALE, BASED ON THE INTERNATIONAL STANDARD

---

MUSICAL SCALES

f

271"f

---

6,575.4 6,966.4 7,380.6 7,819.5 8,284.4 8,777 .1

130.81 821.92 C6 138.59 870.79 146.83 922.58 D 6 155.56 977.43 E6 164.81 1,035.6 174.61 1,097.1 F6

72 1,046.5 73 1,108.7 74 1,174.7 75 1,244.5 76 1,318.5 77 1,396.9

42 43 44 45 46 47

185.00 1,162.4 196.00 1,231.5 207.65 1,304.7 220.00 1,382.3 233.08 1,464.5 246.94 1,551.6

78 1,480.0 9,299.0 79 1,568.0 9,851.9 80 1,661.2 10,438 81 1,760.0 11,058 82 1,864.7 11,716 83 1,975.5 12,413

48 49 50 51 52 53

261.63 1,643.8 277.18 1,741.6 293.66 1,845.2 311.13 1,954.9 329.63 2,071.1 349.23 2,194.3

54 55 56 57 58 59

369.99 2,324.7 392.00 2,463.0 415.30 2,609.4 440.00 2,764.6 466.16 2,929.0 493.88 3,103.2

60 61 62 63 64 65

523.25 3,287.7 554.37 3,483.2 587.33 3,690.3 622.25 3,909.7 659.26 4,142.2 698.46 4,388.5

66 67 68 69 70 71

739.99 4,649.5 783.99 4,926.0 830.61 5,218.9 880.00 5,529.2 932.33 5,858.0 987.77 6,206.3

G6

A6 B6 C7 D7 E7 F7

G7 A7 B7

84 2,093.0 13,151 85 2,217.5 13,933 86 2,349.3 14,761 87 2,489.0 15,639 88 2,637.0 16,569 89 2,793.8 17,554 90 2,960.0 18,598 91 3,136.0 19,704 92 3,322.4 20.875 93 3,520.0 22,117 94 3,729.3 23,432 95 3,951.1 24,825

Cs

96 4,186.0 26,301 97 4,434.9 27,865 Ds 98 4,698.6 29,522 99 4,978.0 31,278 Es 100 5,274.0 33,138 F s 101 5,587.7 35,108 102 5,919.9 37,196

Gs 103 6,271.9 39,408 As Bs

104 6,644.9 41,751 105 7,040.0 44,234 106 7,458.6 46,864 107 7,902.1 49,651

Numerous subscript notations have been employed to distinguish the notes of one octave frem those of another. The particular scheme used here assigns to Co a frequency which corresponds roughly to the lowest audible pitch. S is the number of semitones counted from this C..

3-136

ACOUSTICS

The simple tuning fork may be recognized as an example of dual clamped-free bars. The frequency of a tuning fork made of ordinary steel can be computed approximately from f = 80,OOOt Hz (3h-1O) [2

provided that the thickness t and length l of the prongs are given in centimeters. It is evident from Table 3h-4 that the different modes of vibration of a uniform bar are inharmonic, However, the cross section of the bar in the modern xylophone or marimba is often given an empirical lengthwise "undulation" such that the second

TABLE

3h-6.

INTERVALS IN CENTS CORRESPONDING TO CERTAIN FREQUENCY RATIOS

Name of interval

Unison Minor second or semitone Semitone , Minor tone or lesser whole tone Major second or whole tone Major tone or greater whole tone Minor third Minor third Maj or third M a] or third Perfect fourth Perfect fourth Augmented fourth Augmented fourth Diminished fifth. . . . . . . . Diminished fifth Perfect fifth Perfect fifth Minor sixth Minor sixth Ma] or sixth Major sixth Harmonic minor seventh Grave minor seventh Minor seventh Minot seventh Major seventh Major seventh , Octave "

Frequency ratio

. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1:1 1.059463:1 16: 15 10:9 1.122462:1 9:8 1.189207:1 6:5 5:4 1. 259921: 1 4:3 1.334840:1 45:32 1. 414214: 1 1. 414214: 1 64:45 1.498307:1 3:2 1. 587401: 1 8:5 5:3 1. 681793: 1 7:4 16:9 1. 781797: 1 9:5 15:8 1.887749: 1 2: 1

Cents

o 100 111. 731 182.404 200 203.910 300 315.641 386.314 ,OO

498.045 500 590.224 600 600 60S).777 700 701.955 800 813.687 884.359 900 968.826 996.091 1,000 1,017.597 1,088.269 1,100 1,200.000

mode of vibration of the free-free bar is changed in frequency to 3 or 4 times the fundamental frequency. 1 The frequencies of the higher modes of vibration are also modified by variation in cross section for special purposes such as the simulation of the sound of a bell.! 3h-6. Membranes. The membrane often assumed for vibration calculations is flexible, thin, and of uniform mass per unit area a, The membrane is stretched by a tension T, this being the force per unit length anywhere in the membrane. The See U.S. Pats. 1,838,502 (1931) and 1,632,751 (1927). See U.S. Pats. 2,273,333 (1942), 2,516,725 (1950), 2,536,800 (1951), and 2,606,474 (1952). 1

2

FREQUENCIES OF SIMPLE VIBRATOHS.

MUSICAL SCALES

3-137

characteristic frequencies of transverse vibration for such a rectangular membrane clamped at its edges are given by

f=-2c where

c=

[(m)2 -a + (n)2]! -b

C3h-H)

~~

C3h-12)

is the speed of propagation of transverse wave motion, a and b are the lengths of the sides, and m and n are integers. Note the similarity of Eq. C3h-H) to Eq. C3h.,.I). TABLE

Cents

Ratio

3h-7. Cents

RATIOS FOR INTERVALS TO

100

CENTS

Ratio

Cents

Ratio

Cents

Ratio

--

-0 1 2 3 4

1.000000 1.000578 1.001158 1.001734 1.002313

25 26 27 28 29

1. 014545 1. 015132 1.015718 1.016305 1. 016892

50 51 52 53 54

1.029302 1.029896 1,030492 1. 031087 1. 031683

75 76 77 78 79

1.044274 1.044877 1.045481 1.046085 1.046689

5 6 7 8 9

1.002892 1.003472 1.004052 1.004632 1.005212

30 31 32 33 34

1. 017480 1. 018068 1. 018656 1. 019244 1.019833

55 56 57 58 59

1.032079 1.032876 1.033473 1.034070 1.034667

80 81 82 83 84

1.047294 1.047899 1.048505 1. 049111 1.049717

10 11 12 13 14

1.005793 1.006374 1.006956 1. 007537 1.008120

35 36 37 38 39

1.020423 1.021012 1.021602 1.022192 1.022783

60 61 62 63 64

1.035265 1.035863 1.036462 1. 037060 1.037660

85 86 87 89

1.050323 1.050930 1.051537 1.052145 1.052753

15 16 17 18 19

1.008702 1.009285 1.009868 1. 010451 1.011035

40 41 42 43 44

1.023374 1.023965 1.024557 1. 025149 1.025741

65 66 67 68 69

1.038259 1.038859 1.039459 1.040060 1. 040661

90 91 92 93 94

1. 053361 1.053970 1.054579 1.055188 1.055798

20 21 22 23 24

1.011619 1.012204 1. 012789 1.013374 1.013959

45 4'3 47 48 49

1.026334 1.026927 1.027520 1. 028114 1.028708

70 71 72 73 74

1.041262 1.041864 1.042466 1.043068 1.043671

95 96 97 98 99

88

1.056408 1. 057018

1.057629 1.058240 1.058851

The characteristic frequencies of a circular membrane clamped at its boundary are given by

f =

c 2a

e.;

where a is the radius of the membrane. For n = 1, 2, and 3, f30n = 0.766, 1.757, and 2.755, these numbers being the first three roots divided by 7f of the Bessel function of zero order set equal to zero. Similarly, f3Im = 1.220, 2.233, and 3.238 are from the Bessel function of first order and f32n = 1.635, 2.679, and 3.699 are from the Bessel function of second order. The number of diametral nodes is m; the number of circular nodes is n, including the node at the boundary. The modes of vibration are not in general harmonics; the lowest characteristic frequencies are in the proper-

3-138

ACOUSTICS

tions 1.000: 1.593: 2.135. For a circular membrane constrained to certain radial (not diametral) nodes, harmonics are, however, possible. The tambourine is a musical instrument that consists of a free membrane nearly of the kind discussed above. In most drums, however, the membrane closes a cavity; in the case of the kettledrum (and some kinds of capacitor microphones) this cavity is relatively rigid and airtight. If the speed of transverse waves in the membrane is significantly less than the speed of sound in the contained air, the cavity has little effect on those modes of vibration with diametral nodes. The frequencies of other modes of vibration are increased! by the stiffness of the contained air. 3h-6. Musical Scales. By international agreement the standard tuning frequency for musical performance is the A of 440 Hz. The frequencies of the equally tempered scale based on this frequency appear in Table 3h-5. Middle C thus has a frequency of 261.6 Hz. The C of 256 Hz, frequently used in the past for demonstrations in physics, has never been adopted for practical musical performance. For many calculations with musical intervals it is convenient to deal with logarithmic units that can be added instead of the ratios which must be multiplied. The octave is equal to 1,200 logarithmic cents, and the equally tempered semitone is 100 cents. The interval in cents corresponding to any two frequencies it and /2 is 1,200 log2(fdit) = 3,986 IOglo(fdfl). Table 3h-6 lists certain common intervals in cents and the corresponding ratios; the frequency ratios for intervals up to 100 cents are given in Table 3h-7. 1 Philip M. Morse, "Vibration and Sound," 2d ed., p. 193, McGraw-Hill Book Company, New York, 1948.

3i. Radiation of Sound FRANK MASSA

Massa Division, Dynamics Corporation of America

3i-1. Introduction. Radiation of sound may take place in a number of ways, but basically, all sound generators cause an alternating pressure to be set up in the fluid medium within which the sound energy is established. The sound energy that is set up in a medium depends not only on the physical characteristics of the medium and the oscillatory volume displacement of the fluid set up by the vibrating source but also upon the size and shape of the generator. The acoustic power generated by any vibrating source can be expressed by watts

(3i-l)

where U = rate of volume displacement of fluid, cc/sec R A = acoustic radiation resistance seen by source, acoustic ohms If the rate of volume displacement is taken in peak co/sec, Eq, (3i-1) will yield peak watts of power. If the volume displacement is taken in rms cc/sec, the power will be given in rms watts. Of the many possible methods for generating sound, two types of generators will effectively serve to typify most of them. These basic generators are (1) pulsating sphere and (2) vibrating piston. Each type of generator has its own acoustic impedance characteristic which depends on the dimensions of the source and on the frequency of vibration. 3i-2. Acoustic Impedance. Pulsating Sphere. The specific acoustic impedance of a pulsating sphere is given by pc

Z

where

= 1

.

pC/(-lrD/X)

+ [1/('Il'"D/X)]2 + J 1 + [1/('Il'"D/X)]2

p

= density of the medium, g/cc

c

= velocity of sound in

(3i-2)

the medium, em/sec

X

= diameter of the sphere, em = clf

f

=

D

acoustic ohrns /cm!

frequency, Hz

Dlx becomes very large, the specific acoustic impedance becomes a pure resistance equal to pc and the reactance term vanishes. At low frequencies, where D IX is small, the specific acoustic impedance becomes It can be seen from inspection that at high frequencies, where

z

'Il'" D ) = pc ( T

2

•

'Il'"D

+JPcT

acoustic ohms /cm!

(3i-3)

A. plot of the specific acoustic resistance and reactance of a pulsating sphere as a function of D IX is shown in Fig. 3i-1. To obtain the total acoustic radiation resistance 3-139

3-140

ACOUSTICS

RA of the sphere, it is necessary to divide the specific acoustic resistance by the total surface area of the sphere in ems. The value of RA thus determined, when substituted in Eq. (3i-1), will give the actual acoustic watts being generated by the spherical source. Vibrating Piston. The specific acoustic impedance of a circular piston set in an infinite rigid baffle and radiating sound from one of its surfaces is given by

_ [1 _Jl(21rD/X)] +. K (21rD / X) 1rD/X JpC 2(1rD/X)2 1

acoustic ohms /cm!

z - pC

(3i-4)

where D is the diameter of the piston in centimeters, J 1 and Klare Bessel functions, and the remaining symbols are defined under Eq. (3i-2). 2 ~

""""" . / In ~~

71/

v7 1//

,,,\, ,

.1

~

/

~~ ~

I

If'

~.

IJ

V

/R I

......

.... r... I'lo.

r-.

t-o.I'

tl'l , 1\

',-

~!\ ~~\ I

I

",

.

,

IT

I

II J

//

V/

tr

'/

J

1/

.0 I I ~

"" "

D[

IU~ ~

j

II

'""'"

T

I

/

/

" IiII

II J II

I

II

II

I

/

,/

V

/1

.001 . .01

.1

10

RATIO 0/), FIG. 3i-1. Speeific acoustic resistance R and reactance X of a pulsating sphere (dashed curves) and a vibrating piston set in an infinite baffle (solid curves). To obtain magnitude of R or X multiply ordinates by pc of the medium.

At high frequencies, where D/X is large, Eq. (3i-4) reduces to a pure resistance equal to pc, At low frequencies, where D /X is small, the specific acoustic impedance for a piston set in an infinite baffle with one side radiating becomes _ pC(1rD/X)2 2

z-

+.

8D )pC l i

acoustic ohms/em I

(3i-5)

3-141

RADIATION OF SOUND

A plot of the specific acoustic resistance and reactance for a vibrating piston mounted in an infinite baffle is shown in Fig. 3i-1. To obtain the total acoustic radiation resistance of the piston, it is necessary to divide the specific resistance by the piston area in em". The value of RA so determined, when substituted in Eq. (3i-l), will give the actual acoustic watts being generated by a piston. Summary of Radiation Impedance Characteristics. In Table 3i-1 are shown the magnitudes of the acoustic radiation resistance and reactance for a sphere and piston for both low-frequency (D Ix small) and high-frequency (D Ix large) operation. TABLE 3i-1. TABULATED VALUES OF THE TOTAL ACOUSTIC RADIATION RESISTANCE AND REACTANCE OF A SPHERE AND PISTON IN ACOUSTIC OHMS

DIX« 1

RA

DIX» 1

XA

RA

XA

-1r oc 4X2 1r

Pulsating sphere ............................ Vibrating piston (in infinite baffle) ............ p = density of the medium, g/em 2 e = velocity of sound in the medium, emlsee

>.. so wavelength of sound in the medium, em >.. .. ell

I D A

pc

2X2

pc

pc

pc

1rDX

A

8

pC

31rDX

A

0 0

= frequency of the sound vibration. Hz = =

diameter of sphere or piston, em surface area of sphere or piston, em'

3i-3. Directional Radiation of Sound. Whenever sound energy is generated from a source whose dimensions are small compared with the wavelength of the vibration in the medium, the intensity will be uniform in all angular directions and the generator is generally defined as a point source. When the dimensions of the vibrating surface are large compared with the wavelength, phase interferences will be experienced at different points in space due to the differences in time arrival of the vibrations originating from different portions of the surface, which results in a nonuniform directional radiation pattern. Practical use is made of this phenomenon when it is desired to produce special directional patterns by arranging the geometry and size of the vibrating surfaces of a sound generator to create the desired characteristic. In many instances, a transmitter is designed so that the sound is radiated in a relatively sharp beam so that the energy is concentrated only within a specific desired angular region. When such a directional structure is employed as a receiver, the transducer will be more capable of picking up weak signals from a specified direction than would be the case from a non directional transducer. The reason for this im provement is the reduced sensitivity of the directional receiver to random background noises that will be present in all directions from the source. The number of decibels by which the signal-to-noise ratio is improved by a directional receiver over a nondirectional receiver is known as the directivity index (directional gain) of the transducer. It will be defined more fully later. The following will show the directional radiation characteristics of several common structures. Uniform Line Source. If a uniform long line is vibrating at uniform amplitude, the radiated sound intensity will be a maximum in a plane which is the perpendicular bisector of the line. At angles removed from the perpendicular bisector of the line, the intensity will fall off to a series of nulls and secondary maxima of diminishing amplitudes as the angle of incidence to the axis of the line deviates from the normal bisector of the line. For a line of length L vibrating uniformly over its entire length

3-142

ACOUSTICS

at a frequency corresponding to a wavelength of sound X in the medium, the ratio of the sound pressure pe produced at an angle 0 removed from the normal axis of maximum response to the sound pressure po on the normal axis is given by po po

= sin

OJ

[en"L/X) sin (7rL/X) sin 0

(3i-6)

If L is large compared with X, the response as a function of 0 will go through a series of nulls and secondary maxima of successively diminishing amplitudes" 200 A

~

100

I~ C

r\. I"

"

en

,""

&£J &£J

,,~

a: (,!) C

&£J .J

(,!)

et 2 et

~~ "~ ~i' ~i'

"

~

Z

~

'''"~

&£J

10

~" I..........

"-"-

l&J CD

'""'"'

~

'",~"" "~"~

.J

:! ~

~

I .5

10

1'\

~~r\ ~~r\ 100

RATIO D/~ OR L/~ FIG. 3i-2. Total beam angle for a piston, ring, and line source as a function of size of source to wavelength of sound being radiated. A, thin ring of diameter D. B, uniform line oi length L. C, piston of diameter D. (Curves A and C from Massa, .. Acoustic Design Charts," The Blakiston Division, McGraw-Hill Book Company, Inc., New York, 1942.)

Circular Piston in Infinite Baffle. The directional radiation pattern from a large circular piston vibrating at constant amplitude and phase and set into an infinite rigid baffle may be obtained from the expression pe

po

= 2Jd(7rD/X) sin OJ (7rD/X) sin 0

(3i-7)

where pe = sound pressure at an angle 0 from the normal axis of the piston po = sound pressure on normal axis of piston D = diameter of piston X = wavelength of sound J 1 = Bessel function of order 1 From this equation, it can be seen that, as D /x increases, the beam width becomes smaller and the sound pressure goes through a series of nulls and secondary maxima as 0 progressively departs from the normal axis to the piston. Thin Circular Ring. The directional radiation pattern from a large narrow circular ring of diameter D vibrating at constant amplitude and fitted into an infinite plane

3-143

RADIATION OF SOUND

baffle may be obtained from the expression pe po

r, (1rD sin e) A

=

(3i-8)

where J 0 = Bessel function of order zero and all other symbols are defined under Eq. (3i-7). Beam Width for Line, Piston, and Ring. From Eqs. (3i-6), (3i-7), and (3i-8), the total beam width has been computed for the radiation from each of the three types of sound generators. The total beam width is here defined as the angle 2e at which the pressure pe is reduced 10 dB in magnitude from the maximum on axis reponse po. By setting pe/po equal to -10 dB or 0.316 in magnitude in these equations, the three curves plotted in Fig. 3i-2 were computed.

o

.,. /

10

m

/~

o

)1

~

x

w

o z > t:: > i=

20

/

V

30

u

II

W 0::

o

/~

40

50

V I

V 10

100

200

TOTAL SEA M ANGLE IN DEGREES

FIG. 3i-3. Directivity index of a piston or ring as a function of total beam angle where beam angle is defined as the included angle of the main beam between the lO-decibel-down points in the directional response. (Computed from Massa, "Acoustic Design Charts," The

Blakiston Division, McGraw-Hill Book Company, Inc., New York, 1942.)

3i-4. Directivity Index. It has already been mentioned that a directional transducer has an advantage over a nondirectional structure whenever it is desired to send or receive signals from a particular localized direction only. The fact that the directional transducer is less sensitive to sounds coming from random undesired directions makes it possible for it to detect weaker signals than would be possible with a nondirectional unit. The measure of this improvement in decibels corresponds to the directivity index of the transducer, which is 10 times the logarithm (to the base 10) of the ratio of intensity of the response along the axis of maximum sensitivity to the average intensity of the response over the entire spherical region surrounding the transducer. See Sec. 3a for a more detailed definition. The directivity index of a transducer is expressed in decibels, and a plot of the directivity index as a function of beam width for a piston or ring is shown in Fig. 3i-3.

3j. Architectural Acoustics CYRIL M. HARRIS

Columbia University

3j-1. Sound-absorptive Materials. When sound waves strike a surface, the energy may be divided into three portions: the incident, reflected, and absorbed energy. Suppose plane waves are incident on a surface of infinite extent. For this case, the absorption coefficient a of the surface may be defined as

a=

Is I

l

p •

ds

(3j-l)

IA· ds

where I p is the time average of the intensity vector of the sound field at the absorptive surface, ds is the vector surface element-the positive direction being into the material from the incident side, and I A is the time average of the intensity vector which would exist at the surface element if the surface were removed. The absorption coefficient defined above is a function of angle of incidence and frequency. For acoustical designing in architecture, it is convenient to employ an absorption coefficient a (at a given sound frequency) which represents an average over all angles of incidence. But a depends also on the area of the absorbent surface; the larger the area of a sound absorber on a wall, floor, or ceiling of a room, the smaller is its sound absorption coefficient. The data for a presented in this section are for measurements made on areas of about 72 sq ft, but we assume these are valid for all areas. A surface of S ft 2 is said to have an absorption of as sabins. Thus the sabin (sometimes called a square-foot unit of absorption) is the absorption equivalent of I ft 2 of material having an absorption coefficient of unity. A quantity which describes the acoustical properties of a material that is more fundamental than absorption coefficient is its acoustic impedance, defined as, the complex ratio of sound pressure to the corresponding particle velocity at the surface of the material. Because of the complexities involved in the solutions to problems of roam acoustics by boundary-value theory in terms of boundary impedances, the simpler concept of absorption coefficient is usually employed in calculating the acoustical properties of rooms, as indicated in the following section. Most manufactured acoustical materials depend largely on their porosity for their acoustic absorption, the sound waves being converted into heat as they are propagated into the interstices of the material and also by vibration of the small fibers of the material. Another important mechanism of absorption is panel vibration; when sound waves force a panel into motion, the resulting flexural vibration converts a fraction of the incident sound energy into heat. The average value of absorption coefficient of a material varies with frequency. Tables usually list the values of a at 125, 250, 500, 1,000, 2,000, and 4,000 Hz, or at 3-144

ARCHITECTURAL ACOUSTICS

3.,...145

128, 256, 512, 1,024, 2,048, and 4,096 Hz, which for practical purposes are identical. In comparing materials which are used for noise-reduction purposes in offices, banks, corridors, etc., it is sometimes useful to employ a single figure called the noisereduction coefficient (abbreviated NRC) of ~ 1.00...--------------., the material which is the average of the f5 .90 NRC absorption coefficients at 250, 500, 1,000, §.eo ---- .70 and 2,000 Hz, to the nearest multiple of 70 0.05. 8 .60 Figures 3j-1 through 3j-3 give the ab~ .50 i= .40 sorption coefficient vs. frequency for sev~ .30 eral types of acoustical material.' The ab~.ro sorption-frequency characteristics of regu or n Volume velocity

(Gram) (centiI meter)! Radians per dyne CR per centimeter Ergs per second PR .-

Symbol

Unit

Acoustic impedance Acoustic resistance Acoustic reactance Inertance Acoustic capacitance Power

Symbol

Unit Dynes per square centimeter Cubic centimeters Cubic centimeters per second Acoustic ohms Acoustic ohms

p

X

,

Xor U

I

Z.. . R.. .

Acoustic ohms X .... Grams per M (centimeter) 4 (Centimeter) 5 C.. . per dyne Ergs per second p ....

3m. Mobility Analogy HARRY F. OLSON

RCA Laboratories

The analogies that have been presented and considered in Sec. 31have been formal ones owing to the similarity of the differential equations of electrical, mechanical and acoustical vibrating systems.. For this reason these analogies have been termed the classical impedance analogies; they are, however, not the only ones possible of development for useful applications. For example, mechanical impedance has been defined by some authors-in addition to the ratio of force to velocity as developed in Sec. 31as the ratio of pressure to velocity, the ratio of force to displacement, and the ratio of pressure to displacement. During the past three decades the developments in the field of analogies have been reported in publications' by many investigators. In this connection a useful analogy, developed by Firestone and designated by him as the "mobility analogy," has been employed on a wide scale to solve problems in mechanical vibrating systems. In the mobility analogy mechanical mobility is defined as the complex ratio of velocity to force. Although the mobility analogy can be applied and used with all types of vibrating systems, its most direct and useful application is in the field of mechanical vibrating systems. Therefore, in order to make the subject of analogies complete in this handbook, it seems logical to include the mobility analogy. Accordingly, it is the purpose of this chapter to develop the mobility analogy, particularly as applied to mechanical rectilineal systems.t 3m-I. Mechanical Rectilineal Mobility. Mechanical rectilineal mobility is the inverse of mechanical rectilineal impedance. Mechanical rectilineal mobility ZI, in mechanical mhos, is defined as the complex ratio of linear velocity to linear force as follows: Zl

where v

= velocity,

V

=-

1M

(3m-I)

em/sec

1M = force, dynes It will be evident that a mechanical element in the mechanical mobility sense is analogous to the electric element if velocity difference across the mechanical element is analogous to the voltage difference across the electric element and if the force through the mechanical element is analogous to the electric current through the electric element. See the end of Section 3 for a list of references. The considerations in this section will be confined to mechanical rectilineal systems. The mobility analogy is equally applicable to mechanical rotational systems. In this connection mechanical reetilineal and mechanical rotational systems are not sufficiently different to warrant a separate treatment for the mechanical rotational system, particularly in view of the fact that fundamental aspects of the two systems have been considered from the classical impedance analogy viewpoint in this book. 1

2

3-176

MOBILITY ANALOGY

Mechanical rectilineal mobility may be written as follows:

ZI,

in mechanical mhos, is a complex quantity and

ZI = TI

where

TI

3-177

+ jXI

(3m-2)

= responsivity, mechanical mhos

= excitability, mechanical mhos Sm-2. Responsivity (Mobility Resistance). In the mechanical rectilineal mobility system mechanical rectilineal responsivity (mobility resistance) TI, in mechanical mhos, is defined as v 1 Tl = =(3m-3) XI

1M

where v 1M TM

TM

= velocity, em/sec = force, dynes = mechanical impedance, mechanical ohms

Sm-S. Mass (Mobility Capacitance). In the mechanical rectilineal mobility system the mass (mobility capacitance) mr, in grams, is analogous to electric capacitance CEo The mechanical rectilineal excitability XI of a mass (mobility capacitance), in mechanical mhos, is defined as (3m-4) where

c.l

= 2rl

I = frequency, hertz Equation (3m-4) shows that the mass (mobility capacitance) mr in the mechanical rectilineal mobility system is analogous to electric capacitance CE in the electric system. Mass (mobility capacitance) m, in the mechanical rectilineal mobility system may also be defined as follows: (3m-5) (3m-6) In the electric system electric capacitance C E may be defined as follows: .

2

de = C E di

(3m-7)

where i = electric current, abamp CE = electric capacitance, abfarads e = electromotive force, abvolts t = time, sec

e=l..-fidt CE

(3m-8)

where i = current in abamperes. It will be seen that Eqs. (3m-5) and (3m-6) in the mechanical rectilineal mobility system are analogous to Eqs. (3m-7) and (3m-8) in the electric system. Sm-4. Compliance (Mobility Inertia). In the mechanical rectilineal mobility system the compliance (mobility inertia) CI, in centimeters per dyne, is analogous to electric inductance L. The mechanical rectilineal excitability XI of a compliance (mobility inertia), in mechanical mhos, is defined as (3m-9) XI = CAJCI where CAJ = 2rl I = frequency, Hz Equation (Brn-D) shows that compliance (mobility inertia) CI, in centimeters per dyne, is analogous to inductance.

3-178

ACOUSTICS

Compliance (mobility inertia) Ct in the mechanical rectilineal mobility system may also be defined as V =

diM

Cr dI

(3m-lO)

In the electric system inductance may be defined as

e=L':I:i dt

(3m-H)

where L = inductance in abhenrys. It will be seen that Eq. (3m-lO) in the mechanical rectilineal mobility system is analogous to Eq. (3m-H) in the electric system. 3m-5. Representation of Electrical and Mechanical Rectilineal Mobility Elements. Electric elements have been defined in Sec. 31. Elements in the mechanical rectilineal mobility system have been described in this section. rM

,,,,",,,,;

m

D MECHANICAL ELEMENTS

mI

--HMOBILITY ELEMENTS

ELECTRICAL ELEMENTS

FIG. 3m-I. Graphical representation of the three basic elements in mechanical rectilineal, mobility, and electric systems. r M = mechanical rectilineal rt = responsivity r E = electrical resistance resistance CM = compliance Ct = mobility inertia L = inductance m = mass mr = mobility capacitance CE = electric capacitance (After Olson, "Solutions of Engineering Problems by Dynamical Analoaies," D. Van Nostrand c«, Princeton, N.J., 1966.)

Figure 3m-l illustrates schematically the mechanical elements and the analogous elements in the electric and mechanical rectilineal mobility systems. Mechanical rectilineal resistance r u in the mechanical rectilineal system is represented as sliding or viscous friction. Mechanical rectilineal responsivity (mobility resistance) rr in the mechanical rectilineal mobility system is the reciprocal of mechanical rectilineal resistance ru and is analogous to electrical resistance r sCompliance CM in the mechanical rectilineal system is represented as a spring. Compliance (mobility inertia) Ct in the mechanical rectilineal mobility system is analogous to inductance L in the electric system. Mass m in the mechanical rectilineal system is represented as a mass or weight. Mass (mobility capacitance) mi in the mechanical rectilineal mobility system is analogous to electric capacitance Cs in the electric system.

3-179

MOBILITY ANALOGY

The electrical and the mechanical rectilineal quantities in the mobility system are shown in Table 3m-I. The units and the analogous elements and symbols also are shown in Table 3m-I. 3m-G. Mechanical Vibrating System Consisting of a Mass, Compliance, and Mechanical Resistance. The vibrating system 1 of one degree of freedom consisting of a mass, compliance, and mechanical resistance has been considered from the standpoint of the classical mechanical impedance analogy in Sec. 31. It is the purpose of this section to consider the same mechanical vibrating system from the standpoint of the mechanical mobility analogy.! TABLE 3m-I. CORRESPONDENCE BETWEEN ELECTRICAL AND MECHANICAL QUANTITIES IN THE MOBILITY SYSTEM Electrical

Mechanical rectilineal mobility

Syrnbol

Unit

Syrnbol

Volts X 10-8

e

Velocity

Centimeters per second

Charge or quantity

Coulombs X 10-\

q

Impulse or momentum

Gram-centimeter per second

Current

Amperes X 10- 1

i

Force

Dynes

Electrical irnpedance

Ohms X 10 9

ZE

Mechanical mobility

Mechanical mhos

%1

Electrical resistance

Ohms X 10 9

TE

Responsivi ty

Mechanical mhos

rt

Electrical reactance

Ohms X 10 9

XE

Excitability

Mechanical mhos

XI

Inductance

Henrys X 10 9

L

Compliance or mobility inertia

Centimeters per dyne

CI

Electrical capacitance

Farads X 10 9

CE

Mass or mobility Grams capacitance

Joules per second

PE

Power

Quantity

Electromotive force

Power

Quantity

Unit

Ergs per second

x or

v

Q

1M

ml

PI

The mechanical system consisting of a mass, compliance, and mechanical resistance is shown in Fig. 3m-2A. The mechanical vibrating system may be rearranged to form the equivalent as shown in Fig. 3m-2B. From the mechanical vibrating system of Fig. 3m-2B it is a relatively simple matter to develop the mobility analogy of Fig.3m-2C. 1 The preceding paragraphs have been concerned with fundamental considerations. Therefore, the modifier rectilineal has been employed for the sake of accuracy. Since the remainder of this section will be concerned with applications of the mechanical rectilineal mobility, the modifier rectilineal will be dropped. 2 In view of the fact that this section is concerned with mechanical systems, the modifier mechanical in relation to the mechanical mobility analogy is also superfluous and need not be used.

3-180 A

ACOUSTICS f

CM

~££~ . '~rM WWWW " MECHANICAL SYSTEM

c

D

v

e

MECHANICAL SYSTEM

MOBILITY ELECTRIC NETWORK NETWORK FIG. 3m-2. A mechanical vibrating system consisting of a mass, compliance, and mechanical resistance. A. Mechanical system. B. Mechanical system equivalent to the mechanical system of A. C. Mobility network of the mechanical system. D. Electric network analog of the mobility system. (After Olson, "Solution of Engineering Problems by Dynamical Analoaiee,' D. Van Nostrand Company, Princeton, N.J., 1966.)

The sum of the forces through the three branches of the mobility network! of Fig. 3m-2C is (3rn-12) 1M = IMl + 1M2 + 1M' where

1M] =!!..

(3m-13)

rs

dv

1M2 = mr (Ii 1M3 = ..!Cr

(3m-H)

J

(3m-15)

v dt

From the sum of Eqs. (3m-13) to (3m-15) the differential equation of the mobility network of Fig. 3m-2C is dv + -v + -1 1M = mrv dt dt ri Ct

J

The sum of the electric currents of the electric network of Fig. 3m-2D is

where

i = il + i2 . e ~1 = rE .

'l2

=

i. =

+ i.

(3m-17) (3m-18)

C de

Edt

(3m-19)

J

(3m-20)

~

edt

1 In establishing analogies between electric and mechanical systems the elements in the electric network have been labeled r s. L, and CEo However, in using analogies in actual practice, the convent.ional procedure is to label the elements in the analogous elect.ric network as r u, m, and CM for the classical mechanical rectilineal system and as TI, Cr, and mr for the mobility mechanical rectilineal system. This procedure will he followed in this section in labeling the elements of the analogous electric network. It is literally accurate to label the network with the caption "Analogous electric network of the mechanical rectilineal system" (or, of the mohility mechanical rect.ilineal system). For the sake of brevity, these networks will be labeled "mechanical network" and "mohility network." Where there is only one path, "circuit" will be used instead of "network."

3~181

MOBILITY ANALOGY

From the sum of Eqs. (3m-IS) to (3m-20) the differential equation of the electric network of Fig. 3m-2D is . de e 1 (3m-2I) Z=CE-+-+edt dt rs L

f

Comparing the variables and coefficients of the mobility and electric networks in the differential equations (3m-16) and (3m-21) establishes the analogous variables and quantities in the two systems as given in Table 3m-I. The classical mechanical impedance analogy of the mechanical system of Fig. 3m-2 has been considered in Sec. 31 and will not be repeated here. B

A

r""

e

c

SCHEMATIC VIEW OF THE ELECTRIC AND MECHANICAL SYSTEMS

MECHANICAL SYSTEM

LjVI~

rII

-,

ELECTRIC AND MOBILITY NETWORKS

D

l

e

ELECTRIC NETWORK FIG. Bm-S, Cross-sectional view, the mechanical system, the electric and mobility networks, and the electric network of a direct radiator dynamic loudspeaker. In the electric and mechanical networks: e, the electromotive force of the electric generator. rEG, the electrical resistance of the electric generator. L, the inductance of the voice coil. REI, the electrical resistance of the voice coil. ml, the mass of the cone. CM, and T MI, the compliance and mechanical resistance of the suspension. 1n2 and rM2, the mass and mechanical resistance of the air load. mt, the mobility capacitance of the cone. C/ and rn, the mobility inertia and responsivity of the suspension. m12 and r n, the mobility capacitance and responsivity of the air load. B, the flux density in the air gap. l, the length of the voice coil conductor. a, the radius of the cone. p, the density of air. (After Olson, "Solutions

of Enoineerino Problems by Dynamical Analooies," D. Van Nostrand Company, Princeton, N.J., 1966.)

3-182

ACOUSTICS

3m-7. Direct Radiator Loudspeaker. The direct radiator dynamic loudspeaker shown in Fig. 3m-3 is almost universally used for radio, phonograph, television, and other small-scale sound reproduction. The electric and mechanical systems of the complete loudspeaker are shown in Fig. 3m-3A. The mechanical vibrating system consisting of the voice coil, cone, suspension, and air load is presented in Fig. 3m-3B. The mass ml of the cone and voice coil, and the compliance CM and mechanical resistance of the suspension system, can be obtained from measurements of the vibrating system. The mechanical system of the air load-namely, the mechanical resistance TM2 and mass m2 of the air load upon the front of the cone-is depicted in Fig. 3m-4A and A

rM

MECHANICAL SYSTEM

0

c:J

c:J

MECHANICAL SYSTEM

B

t'M

rM

~J

,m

MECHANICAL NETWORK

MOBILITY CIRCUIT _1_ 8 pa2

C

tpa

~1

2

MECHANICAL MOBILITY NETWORK CIRCUIT FIG. 3m-4. Air load upon a loudspeaker cone. A. Mechanical system: m, the mass of the air load. r u, the mechanical resistance of the air load. B. Mechanical network of the air load upon a loudspeaker cone. C. Mechanical network of the air load upon a loudspeaker cone: a, the radius of the cone. p, the density of air. c, the velocity of sound. D. Mechanical system same as A. E. Mobility circuit of the air load upon a loudspeaker cone: mI, the mobility capacitance of the air load. TI, the responsivity of the air load. F; Mobility circuit of the air load upon a loudspeaker cone: a, the radius of the cone. p, the density of air. c, the velocity of sound. (After Olson, "Solution of En()ineerin(} Problems by Dynamical Analogies." D. Van Nostrand Company, Princeton, N.J., 1966.)

3m-4D. The mechanical network of the air load upon the front of the cone is shown in Fig. 3m-4B. The constants of the mechanical resistance and mass of the air load upon the front of the cone are shown in the mechanical network of Fig. 3m-4C. The mobility circuit of the air load upon the front of the cone appears in Fig. 3m-4E. The constants of the responsivity and compliance are given in the mobility circuit of Fig. 3m-4F. The electric and mobility networks with the ideal transformer connecting the electric and mobility sections are shown in Fig. 3m-3. In Fig. 3m-3D the ideal transformer has been eliminated, and the entire vibrating system reduced to an electric network. The electrical impedance due to the mechanical system is given by Eq. (31-26) as follows: ZEM

= (Bl)2 ZM

(3m-22)

NONLINEAR ACOUSTICS (THEORETICAL)

where

ZEM ZM

= electrical impedance due

3-183

to the mechanical system, abohms

= mechanical impedance of the mechanical system, mechanical ohms

B = flux density in the air gap, gauss l = length of the voice coil conductor, em Since l/zM = ZI, Eq. (3m-22) may be written as ZEM

(3m-23)

= (Bl)2ZI

where ZI = mobility in mechanical mhos. By means of Eq. (3m-23) it is possible to convert the combined electric and mobility networks to the electric network, as shown in Fig. 3m-3. The process employing the mobility analysis of this section may be compared with the classical impedance analysis of Sec. 31. References 1. Olson. H. F.: "Dynamical Analogies" 2d ed., D. Van Nostrand Company, Inc., Princeton, N.J., 1958. 2. Olson, H. F.: "Solution of Engineering Problems by Dynamical Analogies," Van Nostrand Reinhold Co .. New York, N.Y., 1968.

3n. Nonlinear Acoustics (Theoretical) DAVID T. BLACKSTOCK

University of Texas

Until the early 1950s most of what was known about sound waves of finite amplitude was confined to propagation, and to a lesser extent reflection, of plane waves in lossless gases. Since that time a great deal has been learned about propagation in other media, about nonplanar propagation (still chiefly in one dimension), about the effect of losses, and about standing waves. Inroads have been made on problems of refraction. Diffraction is still relatively untouched. In this section the exact equations of motion for thermoviscous fluids will first be stated. Various retreats from the full generality of these equations will then be discussed. No attempt will be made to cover streaming and radiation pressure. See Sees. 3c-7 and 3c-8 for a discussion of those topics.

GENERAL EQUATIONS FOR FLUIDS The basic conservation equations will be stated briefly for viscous fluids with heat flow. Other compressible media, such as solids and relaxing fluids, are discussed later in the section. 3n-L Conservation of Mass, Momentum, and Energy. In Eulerian (spatial) coordinates the continuity and momentum equations are respectively

Dp Dt p

DUi

Dt

+

aUi p aXi

=

0

a (' + ap ax. = ax. dkkl'Jij + 1]

l

J

(3n-l) 21]

d ) ij

(3n-2)

3-184

ACOUSTICS

An entropy equation is stated here in place of the usual energy equation: P

T DS = C [ D'J _ " - 1 DpJ = Dt v P Dt (3, Dt

1/;(1/)

_

aQ, ax,

(3n-3)

Here P is the density, Ui is the ith (cartesian) component of particle velocity, P is pressure, 5ij is the Kronecker delta, dij = t(audaxj + aui/aXi) is the rate-of-deformation tensor, 'TI and 'TI' are the shear and dilatational coefficients of viscosity, Cvand Cp are the specific heats at constant volume and pressure, 'J is absolute temperature, S is entropy per unit mass, " = C p/C7; is the ratio of specific heats, (3, = -p-1(ap/a'J)p is the coefficient of thermal expansion, 1/;(1/) = 2'T1dijdji + 'TI'dk,."dii is the viscous energy dissipation function, and Qi is the ith component of the total heat flux. The material derivative D( )/Dt stands for a( )/at + Uia( )/aXi. If the flow of heat is due to conduction, (3n-4) where K is the coefficient of thermal conduction. For heat radiation the relation between q and 'J is generally quite complicated; see, for example, Vincenti and Baldwin (ref. 1). The model used by Stokes (ref. 2) amounts to Newton's law of cooling and may be expressed by (3n-5) where 'Jo is the ambient temperature, and q is the radiation coefficient. Although too simple to describe radiant heat transfer in a fluid adequately, this equation is worth considering because of (1) its analytical simplicity and (2) its application as a convenient model for relaxation processes. 3n-2. Equation of State. To the conservation equations must be added an equation of state. Perfect Gas. The gas law for a perfect gas is p

= Rp'J

(3n-6)

where R is the gas constant. An approximate form of this equation will now be derived. For a perfect gas the small-signal sound speed Co is given by co2 = "R'J o = "Po/po, where Po and Po are the ambient values of p and p, Let 'J = (3,0(1 + 0), p = p» + poc0 2p , and p = po(1 + 8), where (3'0 is the ambient value of (3, (for perfect gases (3'030 = 1). Assume that 0, P, and 8 are small quantities of first order. Expansion of Eq. (3n-6) to second order yields (3n-7) First-order relations are now defined to be those that hold in linear, lossless acoustic theory; examples are PI = -po\" u and p - Po = c02(p - po). At this point we assert that any factor in a second-order term in Eq. (3n-7) may be replaced by its first-order equivalent. The justification is that any more precise substitution would result in the appearance of third- or higher-order terms, and such terms have already been excluded from Eq. (3n-7). Thus in the last second-order term in Eq. (3n-7) P may be replaced by 8 to give (3n-8) correct to second order.

This is a useful approximate form of the perfect gas law.

NONLINEAR ACOUSTICS (THEORETICAL)

3-185

One of the most fruitful special cases to consider is the isentropic perfect gas. When a perfect gas is inviscid and there is no heat flow, Eq. (3n-3) can be used to reduce the gas law, Eq. (3n-6), to

(p)"( p;

p

po =

(3n-9)

The square of the sound speed, which by definition is, &

(aap p

==

)

(3n-10)

s

becomes cJ)

P) = -'YP = Co2 ( -po P

("(-1)11

(3n-ll)

An expanded form of Eq. (3n-9) is as follows:

p

= s + i('Y

-

1)S2

+

(3n-12)

Other Fluids. For liquids and for gases that are not perfect, one can start with a general equation of state 3 = 3(p,p). Recognizing that (a'Jjap)p = 'Y(pc 2{3e)- I, one obtains the exact expression ()t

= ~e:

+ S)-1 ["I (~)2 r, -

(1

(3n-13)

StJ

In order to obtain an approximation analogous to Eq. (3n-8), it is first necessary to set down a general isentropic equation of state,

(s + 2A ~

p - p« = Poc02

S2

+ 3A .!!.- S3 + ...)

(3n-14)

where the coefficients BjA, CIA, etc., are to be determined experimentally (see Sec. 30). With the help of this expression and some elementary. thermodynamic relations, one invokes the approximation procedure described following Eq. (3n-7) and reduces Eq. (3n-13) to (ref. 3)

() = 'YP - s - (h -

1)S2

(3n-15)

- ("I - 1)2(4{3eo'J)- t

(3n-16)

correct to second order, where h

= 1 + ;~ + H'Y -

~)

1) (1 -

If Eqs. (3n-14) and (311-12) are compared, it will be seen that BjA replaces the quantity "I - 1 in describing second-order nonlinearity of the p - p relation. For a perfect gas, therefore, replace BIA by "I - 1 and {3dJ by 'Jo- 1 in Eq. (3n-16). The quantity h then reduces to "I, and Eq. (3n-7) is recovered.

PROPAGATION IN LOSSLESS FLUIDS For isentropic flow (taken here to mean that the entropy of every particle is the same and remains so) Eqs. (3n-l) and (3n-2) reduce to

+ paUl =0 ax, pDu, + i3p = 0 Dp

Dt

ax,

Dt

and the equation of state may be expressed simply by p = pep). dynamic quantity X

==

l

pc d l

-,

po P

p

(3n-17a)

(3n-17b) If the new thermo-

(3n-18)

3-186

ACOUSTICS

is introduced, Eqs. (3n-17) take the following symmetric form:

+ COUi

Dx Dt

= 0

(3n-19a)

OXi

DUi

+ CoX = oX,

Dt

0

(3n-19b)

Very little has been done in the way of solving these general equations. 3n-3. Plane Waves in Lossless Fluids. For one-dimensional flow in the x direction Eqs. (3n-19) become (3n-20a) Xt + uX x + cU x = 0 (3n-20b) Ut + uU x + cXx = 0 where subscripts x and t now denote partial differentiation, and U represents the particle velocity in the x direction. Hyperbolic equations of this form have been studied in great detail (ref. 4). Their solutions are of two general types: (1) those representing simple waves (waves propagating in one direction only), and (2) those representing compound waves (waves propagating in both directions). Simple Waves. Simple-wave flow is characterized by the existence of a unique relationship between the particle velocity and the local thermodynamic state of the fluid. For simple waves traveling into a medium at rest, this relationship is (ref. 5) X

= ±U

(3n-21)

where the (+) sign holds for outgoing waves (waves traveling in the direction of increasing x), and the (-) sign for incoming waves (waves traveling in the direction of decreasing x). Hereinafter when multiple signs are used, the upper sign pertains to outgoing waves. Equations (3n-20) now reduce to the single equation Ut

+ (u ± c)u

x

=0

(3n-22)

which becomes autonomous once the equation of state is specified, since Eqs. (3n-18) and (3n-21) imply a relationship C = c(u). Note that the linearized version of Eq. (3n-22), u, ± CoU x = 0, possesses the familiar traveling-wave solution u = f(x =+= cot) of linear acoustics. The most important nonlinear effect in simple-wave flow can be readily identified directly from Eq. (3n-22). Combine that equation with the differential expression du = U x dx + Ut dt to obtain

) (dX dt

u=const

=

_

Ut Ux

=

U

+ -

C

(3n-23)

This relation states that the propagation speed of a given point on the waveform (the point being identified by the value of U there) is U ± c. In linear theory the propagation speed of all points is the same, namely, ± co. The ramifications of the variable propagation speed are discussed in Sec. 3n-4. Compound Waves. When waves traveling in both directions are present, there is no fixed relationship between U and X. A propagation speed can still be defined, however. New dependent variables r and ~, called "Riemann invariants," may be defined by (3n-24) 2~ = X - U 2r = X + U If Eqs. (3n-20) are first added and then subtracted, the results are respectively

r, ~,

+ (u + c)r = 0 + (u - c)~x = 0 x

(3n-25a) (3n-25b)

3-187

NONLINEAR ACOUSTICS (THEORETICAL)

Thus, as first found by Riemann (ref. 6),

(~)

r=const

(dx) dt

"_const

=

U

(3n-26a)

+C

=u -

(3n-26b)

C

Despite its apparent simplicity, this result is much more complicated to apply than Eq. (3n-23). 3n-4. Plane, Simple Waves in Lossless Gases. For perfect gases the isentropic equation of state is given by Eq. (3n-9). For this case X = 2(c - cO)/("y - I), and the simple-wave relation Eq. (3n-21) becomes C

where {j = -!("y + 1).

=

Co

±

({j -

(3n-27)

l)u

Combination of this equation with Eq. (3n-ll) leads to

P - Po = po

U]2'Y/('Y-1 ) }

{ [

1 ± ({j - 1) "Cr;

(3n-28)

- 1

which can be used to obtain the characteristic impedance for finite-amplitude waves. For weak waves, i.e., ufc« « 1, this expression reduces to the traditional one, (3n-29)

P - Po = ±pocou

The nonlinear differential equation for simple waves, Eq. (3n-22), becomes Ut

+ ({ju

± co)ux = 0

(3n-30)

If we restrict ourselves momentarily to outgoing waves, the propagation speed is

) = {ju + Co (-dX dt u=const

(3n-31a)

which shows quite clearly that the peaks of the wave travel fastest, the troughs slowest. Equivalently, as the wave travels from one point to another, the peaks suffer the least delay, the troughs the most. This latter view is illustrated in Fig. 3n-l, u

u

u

u

t'

(a)X=O (b) X>O (c) X =X (d) X >X FIG. 3n-I. Progressive distortion of a finite-amplitude wave. Symbols are: u = particle velocity, x = spatial coordinate, t = time, t' = t - x/co (delay time), x = point at which a shock begins to form.

which shows the time waveform of an outgoing disturbance at various distances from the source. The progressive distortion is quite striking, leading eventually to the curious waveform shown in Fig. 3n-ld. The interpretation of Fig. 3n-ld will be discussed presently. Why physically does the exact propagation speed differ from Co, the accepted value in linear theory? Two effects are at work: one kinematic, the other thermodynamic.

3-188

ACOUSTICS

The sound wave travels with speed c with respect to the fluid particles. But these particles are themselves in motion, moving with velocity u. To a fixed observer, therefore, the net speed is u + c. This is the kinematic effect and is frequently referred to as convection (the fluid particles convect the wave along as a result of their own motion). The thermodynamic effect is the deviation from constancy of the sound speed c. Where the acoustic pressure is positive, the gas is a little hotter. Consequently c is greater. Conversely, in the wave troughs, where the gas is expanded and therefore colder, c is less. The variation of c from point to point along the wave can be traced to nonlinearity of the pressure-density relation. As Eq. (3n-l0) shows, c would be constant if p were linearly related to p; This would be true, for example, for an isothermal gas. For an incoming wave the propagation speed is

(-ddtX)

u_con.t

= fJu -

Co

(3n-31b)

Similar arguments apply in this case. A difference is that the troughs of the particle velocity wave travel fastest (in a backward direction), the peaks slowest. Because pressure and particle velocity are out of phase in an incoming wave, however, it is still true that the peaks of the pressure wave proceed most rapidly and the troughs least so. General Solutions. Three forms of the general solution of Eq. (3n-30) are now given. First is what might be called the "Poisson solution" (ref. 7)

= I[x

u

-

({3u

±

co)t]

(3n-32)

which is implied by Eq. (3n-31); I is an arbitrary function. This result is most easily interpreted as the solution of an initial-value problem for which the spatial dependence of the particle velocity is prescribed everywhere at t = 0, i.e., u(x,O) = I(x). The problem is somewhat artificial, however, because the progressive wave motion must already exist at t = O. Of more practical interest are boundary-value problems involving a source; then simple waves arise quite naturally. If the time history of the particle velocity is known at a particular place, say u(O,t) = get), the solution is

u

=g

(t - __X_) ± {3u

Co

(3n-33)

This equation has been used to construct the waveforms in Fig. 3n-1. To make such constructions, it is convenient to use the following "inverted" form of the solution:

t' =

g-l(U) -

~ ~ ± {3u Co

Co

(3n-34)

where t' = t =+= x/co is the delay (for outgoing waves) or advance (for incoming waves) time appropriate for zeros of the waveform, and «: (u) is the inverse function corresponding to g, i.e., g-l[g(U)] = u. The solution of the classic piston problem, in which a piston at rest begins at time t = 0 to move smoothly with a given displacement X (t) in a lossless tube, is more complicated because of the moving boundary condition u[X(t),t] = X'(t)H(t)

(3n-35)

where H(t) is the unit step function. The solution of this problem may be given in parametric form as follows (refs. 5, 8): u

where

=

q, =

X)

+= X (q,)H ( t----c;x - X(q,) t fJX'(q,) ± Co

(3n-36a) (3n-36b)

NONLINEAR ACOUSTICS (THEORETICAL)

3-189

The parameter tP represents the time at which a given signal (i.e., given value of u) left the piston. It is generally quite difficult to convert any of the three general solutions into an explicit analytical expression u(x,t). One can, however, always obtain a sketch of the waveform through use of the inversion procedure indicated by Eq. (3n-34). Shock Formation. A more far-reaching limitation, both mathematically and physically, is that these solutions contain the seeds of their own destruction. Except for a wave of pure expansion, the dependence of the propagation speed on u will cause steepening of the waveform. Steepening eventually leads to multivalued shapes like that shown in Fig. 3n-Id. But these must be rejected because pressure disturbances in nature cannot be multivalued, either in time or in space. In fact, once any section of the waveform attains a vertical tangent, as in Fig. 3n-Ic, results cannot in general be continued further (ref. 9). Physically, what happens is that a shock wave begins to form. For reasons discussed in detail in Sec. 3n-8, this formally marks the end of validity of lossless, simple-wave theory. For mathematical analyses of shock formation see, for example, refs. 4 and 8. Fubini Solution. A problem of special interest in acoustics is the propagation of a finite-amplitude wave that is sinusoidal at its point of origin. Suppose that the wave is produced by sinusoidal vibration of a piston in a lossless tube. Let the piston displacement be given by X (t) = (uo/w) (1 - cos wt) where Uo is the velocity amplitude of the piston, and w is the angular frequency. The solution is given by applying Eqs. (3n-36). For the outgoing wave we have

~ = sin Uo

(t - 3:)

wtPH

(3n-37a)

~

where wtP

= wt -

kx - E(I - cos web) . 1 (3E sin wtP

(3n-37b)

+

Here k = w/co is the wave number, and E = uo/co is the velocity amplitude expressed as a Mach number. An explicit solution is now sought by writing u as a Fourier series,

~ Uo

= 2;An cos n(wt

- kx)

+ 2;Bn sin n(wt

- kx)

(3n-38)

Although the exact expressions for all the coefficients An and B n have not been obtained, an approximate computation is available. First expand Eq. (3n-37b), writing (T for {3Ekx, and t' for t - x/co, and rearrange as follows: wtP - wt' = (T sin wtP If (T

»

E (i.e., (jkx

»

+ E(I

- cos web - (3o sin! q,) '+ 0(E2)

1), and E « I, this equation reduces to

web = wt'

+ (T sin wtP

(3n-39)

Under this approximation the Fourier coefficients An vanish, and the B n can be evaluated in terms of Bessel functions. The final result is (ref. 8)

~ = ~ " no ~Jn(n(T) Uo

sin n(wt - kx)

(3n-40)

n=l

which is generally referred to as the Fubini solution (ref. 10). The acoustic pressure signal is found by substituting the value of u given by Eq. (3n-40) in the linear impedance elation, Eq. (3n-29). Use of a more accurate

3-190

ACOUSTICS

expansion of Eq. (3n-28) for this purpose would not. be consistent with the approximations that led to Eq. (3n-39). The shock formation distance for this problem can be deduced by inspection of Eqs. (3n-39) [or, alternatively, the exact expression Eqs. (3n-37b)] and (3n-37a). The relationship of u to t' is one-to-one only if a < 1. For a ;:::: 1 the waveform curve u(t') is multivalued. Hence a shock starts to form at (f = 1, i.e., at (3n-41) where the overbar signifies shock formation. The physical interpretation of a is therefore that it is a spatial variable scaled in terms of the shock formation distance. The Fubini solution is not valid beyond the point a = 1. 3n-6. An Approximate Theory of Lossless Simple Waves. The approximations leading to the Fubini solution can be used to obtain a general approximate theory of traveling waves of finite amplitude. The mathematical restrictions required are (f

E

where the definitions of

(f

and

E

»

(3n-42a) (3n-42b)

E

«1

are generalized to (f

~EX

=-

E

Xc

Uo

=Co

(3n-43)

Here Xc is a characteristic distance defined so that significant distortion (for example, shock formation) takes place over the range 0 < a < 1, and Uo is the maximum particle velocity that occurs in the flow. The physical implications of these restrictions are as follows: 1. The finite displacement of the source can be neglected. In other words, the exact boundary condition given by Eq. (3n-35) can be replaced by (3n-44)

u(O,t) = X'(t)H(t)

Any error thus committed is made small by inequality (3n-42a). 2. The linear impedance relation, Eq. (3n-29), can be used to obtain the acoustic pressure, once the particle velocity waveform is known. 3. The nonlinear effect that must be taken into account is the non constancy of the propagation speed. But this effect is approximated by writing Eqs. (3n-31) as follows: ±co (3n-45) dt U_CODst = 1 + {ju / Co

(dX)

.

Retention of nonconstancy of the propagation speed as the only important nonlinear effect gives recognition to the fact that this effect is the only cumulative one. It is the cause of the progressive distortion that engulfs the wave. We neglect the other nonlinear effects because they are noncumulative, or local. The distortion they cause does not grow with distance. The formal theory based on these ideas will now be developed. An approximate differential equation may be derived by applying the method used earlier to convert Eq. (3n-7) to (3n-8). For simple waves the appropriate first-order relation is U x = +CO-lUt. When this is substituted in the nonlinear term in Eq. (3n-30), the result is COU",

± Ut

-

~co -lUUt

=0

(3n-46)

This differential equation could also have been deduced from Eq. (3n-45). Next let x and t' = t + x/co be new independent variables. Equation (3n-46) reduces to (3n-47) co 2U x - {Juu" ... 0

NONLINEAR ACOUSTICS (THEORETICAL)

3-191

For the boundary condition

ulx where it is assumed that get)

=

=0

= g(t)H (t) = get')
= t'

+ (3co- 2xg(cf»

(3n-49b)

When the excitation is sinusoidal, i.e. get) = Uo sin wt, the Fubini solution follows exactly. It is also worth noting that within the limits of the approximate theory the difference between Lagrangian and Eulerian coordinates is negligible. As a general rule, the approximate theory is useful when E < 0.1 (ref. 8). 3n-6. Plane, Simple Waves in Liquids and Solids. Liquids. For lossless fluids whose isentropic equation of state is not given by Eq. (3n-9), we may proceed by using Eq. (3n-14). The propagation speed is (ref. 8) (3n-50) where U = ufc« and Cl = B/2A, C2 = C/2A + B/4A - (B/2A)2, etc. Thus, in the exact solution of the piston problem [Eqs. (3n-36)], the parameter cf> is given by

x - X(cf»

cf>

=

t - u

± co(l

(3n-51)

+ c.U + C2U2 . . .)

where U is to be interpreted as co-1xe(cf». Solids. The mathematical formalism for plane, longitudinal elastic waves in solids, either crystalline or isotropic, is very similar to that for liquids and gases (refs. 11-13). The wave equation is given in Lagrangian coordinates as ~tt

= co2G (~a) ~aa

Gaa ) = 1 + (~:) ~a + (~:) ~aa

where

(3n-52) •••

(3n-53)

Here a represents the rest position of a particle; ~ is partical displacement; and M 2, M a, M 4, etc., are quantities involving the second-, third-, fourth-, and higher-order elastic coefficients (ref. 12). The quantity co 2G plays the same role that (pc/ PO)2 does for fluids (ref. 14). By the Lagrangian equation of continuity, pol P = 1 + ~a; thus replace Eq. (3n-18) by A

fo ~a [G(~a')]! d~a'

=

-Co

=

-CO[~a -

-!ma~a2

+ (t -

(3n-54) -!m4)ma2~aa

••. J

(3n-55)

where ma = -M a/M2, m4 = 1 - M4/M2ma2, etc. Riemann invariants are defined as before by Eq. (3n-24). Note that u = ~e in Lagrangian coordinates. Simple-wave fields are again specified by Eq. (3n-21), which when combined with Eq. (3n-5) leads to (3n-56) ~a = =+ U + -!m aU2 =+ -!m4ma2ua • The propagation speed for simple waves is

(ddta)

_ ±coGI

u-const-

(3n-57)

The factor u, which appears in Eq. (3n-23), is absent here because the coordinate system is Lagrangian. Equation (3n-57) expanded in series form is (3n-58)

3-192

ACOUSTICS

Therefore, the solution of the piston problem, given u(O,t) (jJ

=

t += 1

±

=

alco

imaU

+ ima2(1

- 2m4) U2

Xt(t), is (3n-59)

where U is to be interpreted, as in Eq. (3n-51), as co-1Xt«(jJ). More complete versions of some of the series expansions given above can be found in ref. 12. Approximate Theory. The approximate theory of simple waves described in Sec. 3n-5 is very easily generalized to apply to liquids and solids. For liquids I' - 1 is replaced by BIA, as mentioned after Eq. (3n-16). For solids I' + 1 is replaced by -MaiM 2 (see ref. 12 for other useful associations). Therefore, let (j = i(I'. {3 =

+ 1)

B 1 + 2A

-t«,

{3=-

2M 2

for gases

(3n-60a)

for liquids

(3n-60b)

for solids

(3n-60c)

and all results stated in Sec. 3n-5 become applicable for a very wide range of continuous media. For many liquids and solids the first "nonlinearity coefficient" (B I A for liquids, M 31M 2 for solids) is known, but higher-order ones are not. In such cases it is difficult to justify using anything more precise than the approximate theory. But see ref. 12 for a discussion related to this point. 3n-7. Nonplanar Simple Waves. In this section one-dimensional nonplanar waves are considered, namely, spherical and cylindrical waves, and waves in horns. The general theory is not very highly developed. One fundamental difficulty is that simple waves of arbitrary waveform do not generally exist for nonplanar waves (ref. 15). Consider, for example, the wave motion generated by a pulsating sphere in an infinite medium. Most of the wave field consists of outgoing radiation, but there is also some backscatter (ref. 15). In the far field, however, simple waves do occur as an approximation. This is the case treated here. The results represent an extension of the approximate theory developed in Sees. 3n-5 and 3n-6. Spherical and Cylindrical Waves. For large values of the radial coordinate r (actually large kr, where k is an appropriate wave number of the disturbance), the following approximate equation for simple waves in a fluid can be obtained (ref. 16): (3n-61) where t' = t :+ (r - ro)lco, ro is a reference distance, and {3 is given by Eq. (3n-60a) or (3n-60b). This equation may also apply to longitudinal waves in an isotropic solid, but so far no derivation has been given. The dependent variable w equals (rlro)iu and (rlro)u for cylindrical and spherical waves, respectively. The independent variable z is given for the two cases by Cylindrical: Spherical:

= 2(yr - yT;;) z = ro In.!:.. ro

z

y~

(3 [\-tj:,2o)

(3n-ti2b)

Note that z > 0 for diverging waves (r > ro), but z < 0 for converging waves (r < ro). Equation (3n-61) is solved by recognizing that it has the same form as the planewave equation (3n-47). For the boundary condition take u(ru,t) = get), which may represent either the motion of a source at ro or the measured time signal of a wave as it passes by the point roo Since z = 0 and t' = t when r = rOt the condition on w is w(O,t')

= get')

(an-63)

NONLINEAR ACOUSTICS (THEORETICAL)

3-193

Therefore, for the two kinds of waves the solution is Cylindrical:

Spherical:

U

= (

rr o)! gee/»~

e/>

= t'

+

U

=~ gee/»~ r

e/> =

t'

(3n-64a)

vf;;( vr - vf;;)g(e/»

2{3co-2

(3n-64b) (3n-65a)

+ (3co-

2ro

In !.... gee/»~ ro

(3n-65b)

Some applications of these results are given in refs. 16 to 18. It has been shown (ref. 19) that Eq. (3n-65b) corresponds to a second-order approximation of results obtained using the Kirkwood-Bethe hypothesis (ref. 20). Many special solutions for spherical and cylindrical waves have also been found. Most are of the similarity type. The most famous is Taylor's solution for the compression wave generated by a sphere that expands at a constant rate (refs. 21, 22). Waves in Horns. For waves traveling in ducts whose cross-sectional area A = A (z) does not vary rapidly, the waves may be assumed to be quasi-plane. It is assumed that the effect of variations in the cross section can be accounted for simply by correcting the continuity equation as follows: D(Ap)

Dt

+pAu z

=0

(3n-66)

The one-dimensional formalism is thereby retained. By the same methods used for spherical and cylindrical waves it is possible to derive an equation exactly like Eq. (3n-61). However, wand z are now defined as (3n-67a) (3n-67b)

where Xo is a reference distance, A o = A(xo), and t' = t ± (z - xo)/co. The sign of z identifies the wave as outgoing (x > xo) or incoming (z < xo). Note that a conical horn (A cc x 2) gives results identical with those for spherical waves, and a parabolic horn (A cc x) gives results identical with those for cylindrical waves. The general solution for a boundary condition of the form given by Eq. (3n-63) is (ref. 23)

(1J! u = gee/»~

w

=

e/>

= t'

+

(3co-2

zg(e/»

(3n-68a) (3n-68b)

For reference the value of the stretched coordinate z for an exponential horn (A cc e21z ) is z = i-l(l - e-1(z-zo» (3n-69a) and for a catenoidal horn (A

cc

cosh 2 ix) is (3n-69b)

All the results previously obtained for plane waves (approximate theory) may now be applied to nonplanar one-dimensional waves simply by replacing u and x by w and e, as given by Eqs. (3n-67). For example, for sinusoidal excitation at x = Xo the shock formation distance is found by putting z = ± ({3fk)-l and then making use of Eq. (3n-67b).

3-194

ACOUSTICS

Parametric Array. An application of particular interest is the so-called parametric, end-fired array, conceived by Westervelt (ref. 53). A source such as a baffled piston emits radiation consisting of two high-frequency carrier waves into an open medium. The carriers, whose frequencies are W1 and W2, interact nonlinearly to produce a difference-frequency wave (frequency Wd = W2 - (1). Also produced, of course, but not of interest here, are the harmonics of the two carriers as well as the sum-frequency and other intermodulation components (ref. 54). In Westervelt's original treatment the two carrier waves were assumed to be collinear beams of collimated plane waves. More recently, Muir (ref. 55) has taken the directivity and spherical spreading of the carriers into account. In any case, however, the interaction to produce the differencefrequency wave amounts to setting into operation a line of virtual sources of frequency Wd, all phased so as to constitute an end-fired array. The result is that the differencefrequency wave has a very high directivity. In other words, a low-frequency beam is produced that is much more highly directive than would have been the case had the source emitted the difference-frequency signal directly. Typically, too, there are no minor lobes. Absorption by the medium may be relied upon to filter out the two carrier waves and the sum-frequency component, eventually leaving the differencefrequency wave as the most prominent signal. Experiments have confirmed the remarkable properties of the parametric array (refs. 5.5, 56), and many further studies of it have been done (ref. 57). WEAK-SHOCK THEORY 3n-B. General Discussion. The appearance of shocks in a flow poses a serious challenge to the theory of simple waves as developed thus far. In the first place, the waveform gradient at a shock is so high that the dissipation terms in Eqs. (3n-2) and (3n-3), heretofore deemed negligible, are in fact very large. A second problem is that since the shock is (at least approximately) a discontinuity in the medium, it can cause partial reflection of signals that catch up with it. The presence of reflected waves invalidates the simple-wave assumption. Strictly speaking, therefore, the flow cannot be simple wave, once shocks form (ref. 9). The situation is not quite so bad as it seems, however, provided we restrict ourselves to relatively weak waves, i.e., uo/co < 0.1, approximately. Under this condition the signals that are reflected from a shock in the waveform are so feeble as to be negligible. The simple-wave model may therefore be retained as a good approximation. Next, triple-valued waveforms of the kind shown in Fig. 3n-1 must be avoided. This requires that provision be made for dissipation. There are two approaches. First, one can take explicit account of the dissipation terms. This leads to Burgers' equation, or variations thereof; the method is described in See. 3n-12. Alternatively, one can postulate mathematical discontinuities-shocks-at places where the waveform would otherwise be triple valued. The Rankine-Hugoniot relations are invoked to relate conditions on either side of each shock. In this way dissipation is accounted for indirectly. A tacit assumption, it will be noted, is that all the dissipation takes place at the shocks. The mathematical method is more fully appreciated if the physical aspects of the process are first understood. The history of a typical waveform is depicted in Fig. 3n-2 (taken from ref. 27). Figure 3n-2a shows the initial waveform. Numbered dots indicate initial phase points (values of cJ» on the wave. In the beginning, distortion takes place as described in Sec. 3n-4 (Fig. 3n-2b and c). After the shock is born (Fig. 3n-2c), it travels supersonically. In consequence of Eq. (3n-72), however, phase points just behind, such as number 5, travel faster. As they catch up with the shock, it grows because the top of the discontinuity is always determined by the amplitude of the phase point that just caught up with it. (Conversely, the bottom of the discontinuity always coincides with the phase point just overtaken by

3-195

NONLINEAR ACOUSTICS (l'HEORETICAL)

the shock.) The top reaches a maximum when phase point 5 catches up. Mter that, the top decays (Fig. 3n-2e). In Fig. 3n-2f the decay has progressed to the extent that all phase points of the original waveform between 4 and 6 have disappeared. Eventually all that remains (Fig. 3n-2g) is the shock and a linear section connecting it with the zero, phase point 7. This is the asymptotic shape toward which many waveforms or waveform sections tend (ref. 26). 3n-9. Mathematical Formulation of Weak-shock Theory. For the continuous sections of the waveform the most general solution from the approximate theory of simple waves is adopted, namely, Eqs. (3n-68), where wand z are given by Eqs. (3n-67). Plane, cylindrical, and spherical waves, which are not really "quasi-plane," are nevertheless included formally within the framework of this solution by taking A = I, z, and x 2, respectively. u

u

u

u

i!+t' ~ ~ ~f 4

I

4

6

3

t'

7

l

t

7

3

7

2

2

(0) X-O u

6

3

(c) X =

(b) XX

u

~t' ~ I

X

-+ Jr t

i

x

V-I

dp.

I t will arrive

(3n-7I)

where v is the shock's propagation speed. The Rankine-Hugoniot relations can be combined to give v in terms of U a and Ub, the particle velocities just ahead of and just behind the shock, respectively. An approximation of the required relation is (3n-72) or, to the same order, (3n-73) Substitution of this value in Eq. (3n-71) leads to (3n-74) where overbars continue to indicate values at the instant of shock formation, and primes denote retarded (or advanced) time. In terms of the generalized dependent and independent variables wand z, Eq. (3n-74) becomes (3n-75)

3-196

ACOUSTICS

An equivalent relation is (3n-76) Once the particle velocity u has been determined, the linear impedance relation, Eq. (3n-29), is used to find the pressure signal (ref. 23). This completes the formal solution, except for some interpretation. The waveform in the continuous sections between shocks is prescribed by Eqs. (3n-68). For each shock tee path and amplitude are determined by Eq. (3n-75) or Eq. (3n-76) together with Eqs. (3n-68), which are to be evaluated just ahead of the shock (u = U o, q, = q,a, tt = t:) and just behind it (u = uc, q, = rt>b, tt =t:). In principle, Eqs. (3n-68) can be combined to eliminate the parameter rt> as follows: (3n-77) Hence just ahead of the shock (3n-78a) and just behind (3n-78b) Equations (3n-78a), (3n-78b), and (3n-75) or (3n-76) are to be solved simultaneously for W a , Wb, and (

w

~luo

I--=:::::J ·~ T

z -3/b FIG. 3n-3.

N wave.

3n-lO. Applications of Weak-shock Theory. N Wave. Perhaps the most famous application is to the wave shaped like the letter N. The sonic boom is a cylindrical N wave in the far field. For the present consider outgoing waves only. Refer to Fig. 3n-3 for notation. At t = 0, U = -uotlT o for - To < t < To. Thus g(rt» = -uort>ITo, and Eq. (3n-68b) yields q, = t'/(1 + bz), where b = ~uolco2To. The solution is given by Eq. (3n-68a) as

t'

Uo

w=---To 1 bz

+

-T

< t' < T

To determine T, make use of Eq. (3n-76) for the head shock: that is,

dt: __

-

dz

Integration gives

.1..bt'

i~co -2W b = _ 2_ 8 -

1

-t:

c:

T

= T o(1

+ bz

+ bz)!

The amplitude of the wave is therefore given by Ub

=

(AAo)l (1 + bz)l Uo

NONLINEAR ACOUSTICS (THEORETICAL)

3-197

Next consider incoming waves. The major difference in the results is that z i8 replaced by -z. But z itself also changes sign [see the discussion following Eqs. (3n-67)]. The following formulas cover both incoming and outgoing waves:

_

Uo

t'

-T

+ blzl To T o(l + blzl)!

W

= + 1

T

=

IUb I = ( AA o) !

< t' < T

(3n-80)

Uo

(1

(3n-79)

(3n-81)

+ biz!)!

The growth of a converging wave (A < A 0) and the diminution of a diverging wave (A > A o) are not comparable because the factor (1 + blz!)-! acts to diminish both types of waves. Both waves spread at the same rate, however. From Eq. (3n-81) one obtains the classical results that outgoing plane, cylindrical, and spherical waves decay at great distances as x- i, r-l, and r-l(ln r)-!, respectively. Sawtooth Wave. Assume that the wave shown in Fig. 3n-3a is repetitive. The magnitude of the jump at the shock is now 2uo to begin with. Because of the symmetry, we have Ua = -Ub, which means that, by Eq. (3n-72), the shocks all travel at sonic speed. Unlike the N wave, therefore, the sawtooth does not stretch out as it travels. The decay is more rapid however. Proceeding as before, we find the wave amplitude to be given by (3n-82) where k is the fundamental wave number of the wave. See ref. 28 for a discussion of power loss and related topics for sawtooth waves in an exponential horn. Originally Sinusoidal Wave. It will be recalled that a sinusoidally vibrating piston gives rise to periodic waves whose mathematical description, for outgoing waves, is given by Eq. (3n-40), the Fubini solution. Weak-shock theory makes it possible to obtain a solution of this problem for distances beyond the point of shock formation. It turns out that after forming at x = x = ({3Ek)-I, the shocks reach a maximum amplitude at x = 7rx/2 and thereafter decay. For distance greater than 3x the wave is effectively a sawtooth of amplitude 7rUo

Ub = 1

+

(3n-83)

CT

where (see Sec. 3n-4) CT = {3Ekx = x/x. This problem is treated in full in ref. 27, as is the similar one of an isolated sine-wave cycle. To generalize Eq. (3n-83) to other one-dimensional outgoing waves it is merely necessary to replace Ub by Wb and CT by {3Ekz. 3n-11. Limitations of Weak-shock Theory. The primary advantage of weak-shock theory over the method based on Burgers' equation (see below) is that results are obtained quickly and easily. Details of the actual profile of the wave in the neighborhood of each shock are suppressed simply by approximating the shock as a mathematical discontinuity. The method's strength is also its weakness, however. At great distances the shocks may become so weak that they become dispersed and are no longer approximate discontinuities. As a test we may compare the shock rise time (ref. 29) T with a characteristic period or time duration T of the wave. Thus consider the ratio T

125

120

T = COlUblT = COIWblT

( A)! Ao

(3n-84)

where 0 is proportional to the viscosity and heat conduction coefficients of the fluid [see Eq. (3n-86)]. For an N wave IWbjT is a constant (= 'UoT o) so that TIT is simply

3-198

ACOUSTICS

proportional to (AI4. o)t . Therefore, if the N wave is plane, TIT is constant, which means that the validity of the weak-shock computation does not change with distance. The wave simply spreads out as rapidly as the shock. For all other outgoing N waves, however, the shock disperses more rapidly, and eventually T "-' T, beyond which point weak-shock theory should not be trusted. Let f m ax designate the distance at which TIT = 1. For spherical N waves we obtain, (3n-85a)

The comparable result for cylindrical N waves is froa~ = ({3uuCOTO)2 fo 128

(3n-85b)

For an outgoing sawtooth wave TIT is proportional to (1 + (3EklzIHAIA o)! , which means that weak-shock theory is always limited, even when the wave is plane. Even for converging waves T may approach T in certain instances (refs. 17, 18). Care must therefore be exercized in using asymptotic formulas based on Eq. (3n-82). Calculations of f m ax for sawtooth waves based on taking T = T are in agreement with estimates obtained by other methods (ref. 27). The importance of the limitation on weak-shock theory varies a great deal in practice. For sonic booms the limitation is apparently not significant. Typically at ground level T is of the order of milliseconds, whereas T is measured in tenths of a second. For long-range propagation of pulses from underwater explosions (ref. 30), however, the limitation can be crucial. In conclusion we remark that "weak-shock theory" is in some respects a misnomer. The theory is valid for weak shocks but not, in general, for very weak ones.

BURGERS' EQUATION AND OTHER MODELS We now consider explicitly the effects that viscosity, heat conduction, and relaxation have on the propagation of finite-amplitude waves. The full-fledged equations-(3n-I), (3n-2), (3n-3), and (3n-6) or other equation of state-must be dealt with. Successful attacks on these equations have been mainly directed at specific problems, such as the profile of a steady shock wave (ref. 29). General exact results analogous to those for lossless waves are not known. The only general approach presently available, that based on Burgers' equation, is limited to relatively weak waves. For our purposes, however, this method is a fitting companion for weak-shock theory and its predecessor, the approximate theory of lossless simple waves. 3n-12. Thermoviscous Fluids. Burgers' Equation. Plane Waves. By employing an approximation procedure similar to that used to change Eq. (3n-7) into (3n-8), Lighthill (ref. 29) reduced the equations of motion for outgoing plane waves in a thermoviscous perfect gas to Burgers' equation,

u,

+ {3uu x '

=

oUx'x'

(3n-86a)

Here x' = x - cot, 0 = -!p['D + ('Y - I)/Pr), P = T/lpo is the kinematic viscosity, 'D = ("I' + 2"1)/"1 is the viscosity number, and Pr = T/CpIK is the Prandtl number. The equation applies as well to fluids of the arbitrary equation of state (refs. 31, 32); simply let {3 be given by Eq. (3n-60b). In certain cases it applies also to solids (ref. 33). Equation (3n-86a) is convenient for initial-value problems because the moving coordinate x' reduces to x' = x at t = O. For boundary-value problems a more convenient, yet equally valid, form is (refs. 31, 3, 34) (3n-86b)

3-199

NONLINEAR ACOUSTICS (THEORETICAL)

where t' = t +: »[c«. [To make Eq. (3n-86a) apply to incoming as well as outgoing waves, redefine x' as z +: cot.] Burgers' equation has a known exact solution. The introduction of the logarithmic potential r by

u

=

± ~ (In r)t

=

(jcQ

+ ~ rt' - (jco

(3n-87)

r

causes Eq. (3n-86b) to be reduced to

± co3rz

-

Ort't' = 0

(3n-88)

which is a diffusion equation with the usual roles of space and "time" reversed. To avoid confusion we drop the multiple-sign notation at this point and focus attention on outgoing waves. It is clear that an incoming wave can be considered simply by replacing 0 with - o. The solution of Eq. (3n-88) [with the (+) sign] is

"f. 1_

00

r =

(3n-89)

ro(X) exp [-K(X - t')!] dX

00

where K = co3 / 4 ox . The quantity roCt') = r(O,t') represents the transformed boundary condition. If the original boundary condition is given by Eq. (3n-48), then, by Eq. (3n-87), so(t')

= exp

[f_

t' 00

(jco ] U y(p.) dp.

(3n-90)

Normally one takes Yet) = 0 for t < 0, in which case So = 1 for t' < 0, and the integral's lower limit is zero. The solution of Burgers' equation has been applied to a number of specific problems (refs. 29, 32). The only solution reviewed here is the one for which the piston motion is sinusoidal (refs. 31, 34, 35): u(O,t) = uo sin wtH(t). Equation (3n-90) gives so = exp [ir(l cos wt')] for t' > 0 (ro = 1 otherwise), where (3n-9l) and a};. = a/k is the dimensionless small-signal attenuation coefficient (a};. = wo/c0 2). The dimensionless parameter I' characterizes the importance of nonlinear effects relative to dissipation. The value r = 1 roughly marks the dividing line between the importance and unimportance of nonlinearity in a periodic wave (ref. 36). When the value of ro is substituted in Eq. (3n-89), the potential can be separated into transient and steady-state parts. The steady-state part, to which we restrict ourselves, may be expressed as an infinite series,

s

00

s=

Io(ir)

+2

L (-l)nIn(ir)e-n'az cos

(3n-92)

nwt'

n=l

where In is the Bessel function of imaginary argument. The most interesting case is that of strong waves, i.e., I' »1. In this circumstance S reduces to a theta function, and the logarithmic differentiation required by Eq. (3n-87) is easy to carry out. The result is (ref. 35) 2 \'

u uo =

sin nwt'

r ~ sinh n(l + u)/r

(3n-93)

If a is not which is Fay's solution (ref. 37) with Fay's constant ao taken to be rlarge, the hyperbolic sine function may be approximated by its argument, giving 1•

u =

~ ~n-l sin 1

+a

nwt'

(3n-94)

3-200

ACOUSTICS

which represents a sawtooth wave of amplitude 1rU

o

Ub=--

1

+0'

This is exactly the same result found by means of weak-shock theory; see Eq. (3n-83). For strong waves at great distances, i.e., 0' » r » 1, the waveform is found, either by the Fay solution or directly by Eqs. (3n-92) and (3n-87), to be (3n-95) The simple exponential decay is expected because the wave has now become quite weak. What is remarkable is the absence of the original amplitude factor Uo. The wave amplitude at great distances is independent of the source strength. In other words saturation is reached. This result is obviously of great importance. Saturation has been observed experimentally (refs. 15, 55, 58). Note from Eq. (3n-83) that the asymptotic amplitude given by weak-shock theory is (ref. 26) (3n-96) but this result is accurate only in the sawtooth region, which is defined roughly by < x < a-I (ref. 35). Nonplanar Waves. For other one-dimensional waves the analog of Eq. (3n-86b) is

3x

(3n-97) (again, for incoming waves replace 0 by -0). It is necessary to make the far-field assumption in deriving this equation. The transformations that have proved so helpful in previous cases, namely, Eqs. (3n-67), lead to (311-98) which is similar to Burgers' equation, but has one variable coefficient. No exact solutions are known. For periodic spherical and cylindrical waves, solutions of Eq. (3n-98) have been obtained that are valid in the shock-free region (z < z) and in the sawtooth region (refs. 17, 18). These solutions correspond, respectively, to the Fubini solution for spherical and cylindrical waves and to the related weak-shock solutions (ref. 27). The latter are improved upon, however, because the detailed configuration of the waveform in the vicinity of the shocks is obtained. The behavior of the shock thickness is strongly dependent upon whether the wave is a diverging or a converging one. This can be seen from the form of Eq. (3n-98). A diverging wave (A > A o) is equivalent to a plane wave in a medium in which the dissipation increases with distance. Conversely, for a converging wave (A < A o) the dissipation seems to decrease with distance (refs. 17, 18). 3n-13. Equations for Other Forms of Dissipation. If dissipation is due to an agency other than the thermoviscous effects discussed in the last section, it may still be possible to derive an approximate unidirectio~al-waveequation similar to Burgers'. Relaxing Fluids. An elementary example of a relaxing fluid is one that radiates heat in accordance with Eq. (3n-5)(ref. 38). For simplicity take the fluid to be a perfect gas, and let it be inviscid and thermally nonconducting. At very low frequencies infinitesimal waves travel at the isothermal speed of sound, given by bo2 = Pol Po. At very high frequencies the speed is the adiabatic value, given by boo2 =

3-201

NONLINEAR ACOUSTICS (THEORETICAL)

'YPol Po (the notation b", is used here in place of frequency). The dispersion m, defined by

Co

to emphasize the role played by

(3n-99) is equal to 'Y - 1 for the radiating gas. If the dispersion is very small, i.e., m « 1 (which in this case implies 'Y == 1), the following approximate equation for plane waves can be derived:

(q + a~}' -

b,-,

(~;q +P. ~}u: = ± ;,:, ui«

(3n-l00)

where t' = t += »[b«. It is seen that the radiation coefficient q [see Eq. (3n-5)] is the reciprocal of a relaxation time. Subscripts a and i used with f3 indicate adiabatic and isothermal values, respectively; that is, f3a = ('Y 1)/2 and {3i = (1 1)/2 = 1. The two values are essentially the same, since it has been assumed that 'Y == 1. At either very low frequencies (wq-l « 1) or very high frequencies (wq-l » 1) the lefthand side of the equation takes on the same form as Eq. (3n-47). If the equation is linearized, a dispersion relation can be found that gives the expected behavior for a relaxation process (the actual formulas for the attenuation and phase velocity agree with the exact ones for a radiating gas only for m « 1). Polyakova, Soluyan, and Khokhlov considered a relaxation process directly and obtained a pair of equations that can be merged to form a single equation exactly like Eq. (3n-l00) except that {3i and {3a are equal (ref. 39). Some solutions (refs. 39,40) have been found. One represents a steady shock wave. The shock profile is singlevalued for very weak shocks. But when the shock is strong enough that its propagation speed [see Eq. (3n-72)] exceeds b; the solution breaks down (a triple-valued waveform is predicted). This illustrates an important fact about the role of relaxation in nonlinear propagation: Relaxation absorption can stand off weak nonlinear effects, but not strong ones. In frequency terms, relaxation offers high attenuation to a broad mid-range of frequencies. If the wave is quite weak, the distortion components are easily absorbed because their frequencies fall in the range of high attenuation. But if the wave is strong, many more very high frequency components are produced, and these are not attenuated efficiently by the relaxation process. To keep the waveform from becoming triple valued, it is necessary to include a viscosity term in the approximate wave equation. In ref. 40 the problem of an originally sinusoidal wave is treated. Quantitative approximate solutions are obtained for cases in which the source frequency is either very low or very high, and a qualitative discussion is given for source frequencies in between. Marsh, Mellen, and Konrad (ref. 30) postulated a "Burgers-like" equation for spherical waves. It is similar to Eq. (3n-100) but is corrected to take account of spherical divergence. A viscosity term is added, and {3i and {3a are the same. At either very low or very high frequencies the equation takes on the form of Eq. (3n-98) (for spherical waves (A/A o)! = r/ro = ez l r o], and some initial attempts at solving this equation were described. Boundary-layer Effects. Consider the propagation of a plane wave in a thermoviscous fluid contained in a tube. The wave can never be truly plane because the phase fronts curve a great deal as they pass through the viscous and thermal boundary layers at the wall of the tube. If the boundary-layer thicknesses are small compared with the tube radius, however, the curvature of the phase fronts is restricted to very narrow regions, and the wave may be considered quasi-plane. The boundary layers still affect the wave, causing an attenuation that is proportional to V~ and a comparable dispersion. If the frequency is low, the attenuation from this source is much

+

+

3-202

ACOUSTICS

more important than that due to thermoviscous effects in the mainstream (central core of the fluid), and so it makes sense to find a Burgers-like equation for this case. A one-dimensional model of time-harmonic wave propagation in ducts with boundary-layer effects treated as a body force has been given by Lamb (ref. 41). Chester (ref. 42) has generalized this model and applied it to compound flow in a closed tube. His method can be used to obtain the following equation for simple-wave flow: U", -

~UUt' = 2

=+=

1

+ (1' -1)/vPr (!:)! I" coD / 2

co

7r

Jo

ut,(x,t' -

J.L) dJ.L_

VJ.L

(3n-l01)

where D is the hydraulic diameter of the duct (four times the cross-sectional area divided by the circumference). No solutions are presently available. But the equation does have proper limiting forms. If the effect of the boundary layers (right-hand side) is neglected, the result is Eq. (3n-47). If the nonlinear term is dropped, the time-harmonic solution can be found, and this solution yields the correct attenuation and dispersion. Because of the relative weakness of boundary-layer attenuation (the dimensionless attenuation a~ varies as 1/ ~), the higher spectral components generated as a manifestation of steepening of the waveform are not efficiently absorbed. Thus discontinuous solutions, modified somewhat by the attenuation and dispersion, are to be expected.

REFLECTION, STANDING WAVES, AND REFRACTION 3n-14. Reflection and Standing Waves. For plane interacting waves in lossless fluids we return to Eqs. (3n-24) to (3n-26). For perfect gases the Riemann invariants are given by t=_c_+~ l' -

1

2

~=_c_+~ l' -

1

2

(3n-l02a) (3n-l02b)

Equations (3n-26) tell us that the quantity r is forwarded unchanged with speed + c = !('Y + l)t - i(3 - 'Y)~. Similarly, the speed for the invariant ~ is U C = !(3 - 'Y)r - i( l' + 1)~. The roles of independent and dependent variables can be reversed to give the following differential equation for the flow:

U

tr~

+ N(r + ~)-l(tr + t~) = 0

(3n-103)

where N = !('Y + 1)/(1' - 1). For monatomic and diatomic gases N = 2 and N = 3, respectively. An exact solution of this equation in terms of arbitrary functions f(r) and g(~) is known, but it is usually difficult to determine f and g from the initial conditions (ref. 4). Reflection. Certain valuable information about reflection can be obtained without solving for the entire flow field. Consider the problem of reflection from a rigid wall. For the moment we need not be specific about the equation of state. Let the incident wave be an outgoing simple wave. The Riemann invariant r for a particular signal in this wave is, by Eqs. (3n-21) and (3n-24), 2r = Ai + Ui = 2Ai But r can also be evaluated at the wall during the interaction of the incident and reflected waves: i.e., 2r = Awall + Uwall = Awall Elimination of r between these two expressions gives

NONLINEAR ACOUSTICS (THEORETICAL)

3-203

This is an exact statement of the law of reflection for continuous finite-amplitude waves at a rigid wall: The quantity A doubles, not the acoustic pressure. To see what happens to the pressure, we must specify an equation of state. Take the case of a perfect gas, for which A = 2(c - co)/("1 - l)(thus C - Co doubles at a rigid wall). Using Eq. (3n-11), we obtain P) ( -Po

where

J.1.

= 2"1/("1 -

1).

=

[(Pi) 2 - 1I/l -1 ]/l

Now define a. wall amplification factor

=

(:t

(3n-105)

Po

wall

pwall -

a by

Po

Pi - Po

Substitution from Eq. (3n-105) gives

a=

r2 (pi/po) 1I/l

- 1)/l - 1 Pi/Po - 1

(3n-106)

An analogous result in terms of the source that generated the incident simple wave is given in ref. 43; Eq. (3n-106) was first obtained by Pfriem (ref. 44). For weak waves (Pi - po «Po) a = 2, in agreement with linear theory. The limiting value for very strong waves is a = 2/l (= 2 7 for air), a quite startling result. It is only of passing interest, however, because a wave this strong would already have deformed into a shock by the time it reached the wall [for shocks the expression for a is entirely different; the limiting value for strong shocks is a = 2 + ("I + 1)/("1 - 1) = 8 for air (ref. 4)]. In fact, the deviation from pressure doubling is small even for fairly strong waves. For an originally sinusoidal wave of sound pressure level 174 dB, the maximum deviation is about 6 percent (ref. 43). For a pressure release surface the law of reflection for finite-amplitude waves is the same as for infinitesimal waves. To see this, evaluate r as before, first in the incident wave (2t = Ai + Ui = 2Ui) and then at the pressure-release surface (2t = Aeurface + Uaurface = Usurface, since A = 0 when P = po, P = po). The result is Usurface

= 2Ui

that is, the particle velocity doubles at the surface. The reflection has an interesting effect on the wave, however. Consider a finite wave train so that after interaction the reflected signal is a simple wave. To a good approximation, the acoustic pressure wave suffers phase inversion as a result of the reflection. A wave that distorts as it travels toward the surface therefore tends to "undistort" after reflection. This effect has been observed experimentally (ref. 45). Reflection from and transmission through other types of surfaces, such as gaseous interfaces, are considered in ref. 43. Oblique reflection of continuous waves from a plane surface has not been solved in any general way; see ref. 46 for a perturbation treatment. Standing Waves. First consider finite-amplitude wave motion in a tube closed at one end and containing a vibrating piston in the other end. This problem is one of the few in which much experimental evidence is available (refs. 47,48,50). At resonance, if the piston amplitude is sufficiently high, shocks occur traveling to and fro between the piston and the closed end. Slightly off resonance, again for high enough amplitude, the waveform exhibits cusps. Below resonance the cusps occur at the troughs of the waveform, above resonance at the peaks. It would seem that such rich phenomena would have stimulated intensive theoretical treatments of the problem. In fact, the theoretical problem has proved a difficult nut to crack. The Riemann solution [of Eq. (3n-103») is of no avail because of the presence of shocks. There is no well-developed weak-shock theory for compound waves as there is for simple

3-204

ACOUSTICS

waves. For weak waves perturbation treatments have been used (ref. 48). For strong waves one approach has been to assume the existence of shocks at the outset. The Rankine-Hugoniot relations are used to provide boundary conditions for the continuous-wave flow in between shocks (refs. 47,49). A more fundamental approach has been taken by Chester (ref. 42). His treatment is of general interest because of the way the effect of the boundary layer is assimilated in the one-dimensional model [see Eq. (3n-101) for an adaptation to simple waves]. An "inviscid solution" is first obtained; it contains discontinuities at and near resonance, and cusps at one point on either side of resonance. General agreement with experimental observation is thus good (ref. 50). Improved solutions are then considered in which thermoviscous effects, first in the mainstream and then in the boundary layers, are taken into account. 3n-16. Refraction. Treatments of oblique reflection and refraction at interfaces have mainly been confined to shock waves in which the flow behind the shock is basically steady. Slow, continuous refraction, such as that caused by gradual changes in the medium or by gradual variations along the phase fronts of the wave, has been treated, however (refs. 26, 51, 52). The basis of the method is ordinary ray acoustics. The propagation speed along each ray tube and the cross-sectional area of the tube are modified to take account of nonlinear effects. The approach is similar to that given in Sec. 3n-7 except that the cross-sectional area of the horn varies in a manner that depends on the wave motion. Acknowledgment. Support for the preparation of this review came from the Aeromeohanics Division, Air Force Office of Scientific Research. References 1. Vincenti, W. G .. and B. S. Baldwin, Jr.: J. Fluid M echo 12, 449-477 (1962). 2. Stokes, G. G.: Phil. Ma(J., ser. 4,1,305-317 (1851). 3. Blackstock, D. T.: Approximate Equations Governing Finite-amplitude Sound in T'hermoviscous Fluids, Suppl. Tech. Rept. AFOSR-5223 (AD 415442), May, 1963. 4. Courant, R., and K. O. Friedrichs: "Supersonic Flow and Shock Waves" Interscience Ppblishers, Inc., New York, 1948. 5. Earnshaw, S.: Trans. Roy. Soc. (London) 150,133-148 (1860). 6. Riemann, B.: Abhandl. Gee. W iss. U(jttin(Jen, M ath.-Physik. Kl. 8, 43 (1860), or .'Gesammelte Mathematische Werke," 2d ed., pp. 156-175, H. Weber, ed., Dover Publicat.ions, Ino., New York, 1953. 7. Poisson, s. D.: J. Ecole Polytech. (Paris) 7, 364-370 (1808). However, Poisson's sol'ution is for the special case of a constant-temperature gas, which in our notation correspcnds to {j = 1. 8. Blackstock, D. T.: J. Acoust. Soc. Am. 34,9-30 (1962). 9. Stokes, G. G.: Phil. Mao., ser. 3, 33, 349-356 (1848). 10. Fubini, E.: Alta Frequenea 4, 530-581 (1935). Fubini was the first to render the Fourier coefficients in terms of Bessel functions. He used Lagrangian coordinates, not Eulerian as in the derivation here, and attempted to calculate some of the higherorder terms. The mathematical similarity of this problem to Kepler's problem in astronomy is -discussed in ref. 8. 11. Gol'dberg, Z. A.: Akust. Zh. 6, 307-310 (1960); English translation: Soviet Phys.4coust. 6,306-310 (1961). 12. Thurston, R. N .. and M. J. Shapiro: J. Acoust. Soc. Am. 41, 1112-1125 (1967). 13. Breazeale, M. A., and Joseph Ford: J. Appl. Phys. 36, 3486-3490 (1965). 14. Qompare Eq. (3n-51) with Eq. (I), p. 481 in H. Lamb, "Hydrodynamics" 6th ed., Dover Publications. Inc., New York, 1945. 15. Laird, D. T., E. Ackerman, J. B. Randels, and H. L. Oestreicher: Spherical Waves of Finite Amplitude, W ADC Tech. Rept. 57-463 (AD 130 949), July, 1957. 16. Blackstock, D. T.: J. Acoust. Soc. Am. 36, 217-219 (1964). 17. Naugol'nykh, K. A., S. 1. Soluyan, and R. V. Khokhlov: Vestn. Mosk. Univ. Fiz. 4stron. 4, 65-71 (1962)(in Russian). 18. Naugol'nykh, K. A., S. 1. Soluyan, and R. V. Khokhlov: Akust, Zh. 9, 54-60 (1963); English translation: Soviet Phys.-Acoust. 9, 42-46 (1963). 19. Akulichev, V. A., Yu. Ya. Boguslavskii, A. 1. Ioffe, and K. A. Naugolnykh: Akust. Zh. 13, 321-328 (19672; English translation: Soviet Phlls.-Acoust. 13, 281-285 (1968)

NONLINEAR ACOUSTICS (THEORETICAL)

3-205

20. Cole, R. H.: "Underwater Explosions," Dover Publications, Inc., New York, 1965. 21. Taylor, G. I.: Proc. Roy. Soc. (London), ser. A, 186,273-292 (1946). 22. Naugol'nykh, K. A.: Akust. Zh. 11, 351-358 (1965) English translation: Soviet Phys.Acoust. 11, 296-301 (1966). 23. This solution has been derived by G. B. Whitham, J. Fluid Mech. 1, 290-318, (1956), on a somewhat different basis. 24. Landau, L. D.: J. Phys. U.S.S.R. 9,496-500 (1945). 25. Friedrichs, K. 0.: Commun. Pure Appl. Math. 1, 211-245 (1948). 26. Whitham, G. B.: Commun. Pure Appl. Math. 6, 301-348 (1952). 27. Blackstock, D. T.: J. Acoust. Soc. Am. 39, 1019-1026 (1966). 28. Rudnick, I.: J. Acoust. Soc. Am. 30,339-342 (1958). 29. Lighthill, M. J.: In "Surveys in Mechanics," pp. 250-351, edited by G. K. Batchelor and R. M. Davies, eds., Cambridge University Press, Cambridge, England, 1956. 30. See, for example, H. W. Marsh, R. H. Mellen, and W. L. Konrad, J. Acoust. Soc. Am. 38,326-338 (1965). 31. Mendousse, J. S.: J. Acoust. Soc. Am. 26, 51-54 (1953). 32. Hayes, W. D.: "Fundamentals of Gas Dynamics," chap. D, H. W. Emmons, ed., Princeton University Press, Princeton, N.J., 1958. 33. Pospelov, L. A.: Akusi, Zh. 11, 359-362 (1965); English translation: Soviet Phys.Acoust. 11, 302-304 (1966). 34. Soluyan, S. 1., and R. V. Khokhlov: Vestn. Mosk. Univ. Fiz. Astron. 3, 52-61 (1961) (in Russian). 35. Blackstock, D. T.: J. Acoust. Soc. Am. 36, 534-542 (1964). 36. Gol'dberg, Z. A.: Akusi, Zh. 2, 325-328 (1956); 3, 322-328 (1957); English translation: Soviet Phys.-Acoust. 2, 346-350 (1956); 3, 340-347 (1957). 37. Fay, R. D.: J. Acou.~t. Soc. Am. 3, 222-241 (1931). Fay was concerned with a viscous gas. 38. Truesdell, C. A.: J. Math. Mech. 2, 643-741 (1953). 39. Polykova, A. L., S. 1. Soluyan, and R. V. Khokhlov: Akust. Zh. 8, 107-112 (1962); English translation: Soviet Phys.-Acoust. 8, 78-82 (1962). 40. Soluyan, S. 1., and R. V. Khokhlov: Akust, Zh. 8, 220-227 (1962); English translation Soviet PhYs.-Acoust. 8, 170-175 (1962). 41. Ref. 14, art. 360b. 42. Chester, W.: J. Fluid Mech. lS, 44-64 (1964). 43. Blackstock, D. T.: Propagation and Reflection of Plane Sound Waves of Finite Amplitude in Gases, Harvard Univ. Acoust. Res. Lab. Tech. Mem. 43 (AD 242 729), June, 1960. 44. Pfriem, H.: Forsch. Gebeite I naenieurio. B12, 244-256 (1941). 45. See, for example, R. H. Mellen and D. G. Browning: J. Acoust. Soc. Am. 44, 646-647 (1968). 46. Shao-sung, F.: Akust, Zh. 6,491-493 (1960): English translation: Soviet Phys.-Acoust. 6,488-490 (1961). 47. Saenger, R. A' and G. E. Hudson: J. Acoust. Soc. Am. 32, 961-970 (1960). 48. Coppens, A. B., and J. V. Sanders: J. Acoust. Soc. Am. 43, 516-529 (1968). 49. Betchov, R.: Phys. Fluidsl, 205~212 (1958). 50. Cruikshank, D. B. :An Experimental Investigation of Finite-amplitude Oscillations in a Closed Tube at Resonance, Univ. Rochester Acoust. Phys. Lab. Tech. Rept. AFOSR 69-1869 (AD 693 635), July 31, 1969. 51. Whitham, G. B.: J. Fluid Mech. 2, 145-171 (1957). 52. Friedman, M. P., E. J. Itane, and A.Sigalla: AIAA Journal 1, 1327-1335 (1963). 53. Westervelt, P. J.: J. Acoust. Soc. Am. 35, 535-537 (1963). 54. Thuras, A. L., R. T. Jenkins, and H. T. O'Neil: J. Acoust. Soc. Am. 6,173-180 (1935). 55. Muir, T. G.: "An analysis of the parametric acoustic array for spherical wave fields," Ph.D. dissertation, University of Texas at Austin, Texas (1971). 56. Bellin, J. L. S. and R. T. Beyer: J. Acottst. Soc. Am. 34, 1051-1054 (1962). 57. See, for example, Berktay, H. 0.: J. Sound Vib. 5, 155-163 (1967). 68. Lester, W. W.: J. Acoust. Soc. Am. 40,847-851 (1966). j

30. Nonlinear Acoustics (Experimental) ROBERT T. BEYER

Brown University

30-1. Fluids. In the experimental study of nonlinear acoustics, three types of quantities have been measured. These are the effective sound absorption for waves of finite amplitude, the growth of harmonic content, and the nonlinear variation terms in the isentropic expansion of the pressure in the medium in terms of the density changes. Since the comparison of the first two of these properties with theory depends on the third, it is most effective to consider first the nonlinearity of the equation of state. This isentropic equation of state can be expanded in a Taylor series in the condensation s = (p - po) / po: p - Po

B

C

= As + 2i S2 + 31 8 8 + ' , .

(30-1)

Here P» and Po are the equilibrium values of the pressure and the density. Also, A = poco 2 • By application of thermodynamics (ref. 1) the ratio B/A can be written

B A

= 2poco

(ac) ap T

+ 2cCnT{j (8C) aT p

(30-2)

p

In this equation, {j is the coefficient of thermal expansion, c p the specific heat at constant pressure, and the derivatives are evaluated under condition of sound waves of infinitesimal amplitude. B/A is sometimes known as the parameter of nonlinearity, Evaluation of C/ A is more involved. It can be shown that (ref. 2)

Q = ~ (Ij._) 2 A 2 A

+ 2p0 2Co3(a2c) ~2

•

(30-3)

At a hydrostatic pressure of one atmosphere, the second term on the right is generally quite small compared with the first, although it is likely to become appreciable at higher hydrostatic pressures (ref. 3). For an ideal gas, we can expand the adiabatic equation of state p

=

po

(~) 'Y =

Po [ 1

+ 1'8 + 1'(1' 2~ 1) 8 2 + ' . ,]

(30-4)

where l' is the ratio of specific heats. By comparing coefficients in Eqs. (30-1) and (30-4) we find

B = 1'(1' - I)po whence

for an ideal gas

(30-5)

The ratio B / A has now been measured for a considerable number of liquids at atmospheric pressure and, in some instances, over a modest temperature range. A number 3-206

3-207

NONLINEAR ACOUSTICS (EXPERIMENTAL)

of these experimental values are given in Table 30-1. The error in these measurements is generally of the order of 2 to 3 percent, except for the liquid metals, where the larger uncertainties are listed in the table. The few samples of temperature dependence of B I A shown indicate that B I A can increase or decrease with temperature, depending on the material, but that the temperature variation is usually quite slight. TABLE 30-1. VALUES OF B I A FOR VARIOUS LIQUIDS Liquid

T, °C

Reference

Liquid

9.2

2

Sulfur ..................

121

9.5

6

Water (distilled) .........

0 10 20 30 40 50 60 80

4.1 4.6 5.0 5.2 5.5 5.55 5.6 5.7

3 1 1 3 3 3 3 3

Water (sea, 33 % salinity).

0 10 20 30

4.9 5.1 5.2 5.4

2 2 2 2

Liquid Metals Bismuth ................ 66 Bi (wt %), 34 In

318 125

7.1 6.1

8 8

15 5

48 Bi 52 In 34 Bi 76 In 17 Bi 83 In Indium ................. Mercury ................ Potassium ............... Sodium ................. Tin ....................

125 125 125 160 30 100 110 240

5.1 5.1 4.9 4.55 2.9 2.9 2.7 4.4

8 8 8 8 8 7 8 8

5 5 5 5 3 15 2 11

BfA

T, °C

--20 20

9.6

2

Ethyl ........

20

10.5

2

n-Propyl .....

20

10.7

2

n-Butyl. .....

20

10.7

2

Benzene .......

30 40 50 60 70

2 2 2 2 2

Benzyl alcohol .. Chlorobenzene ..

30 30

10.2 9.3

2 2

Cyclohexane ....

30 40 50 60 70 30 30 30 30 30 30 30

10.1 10.1 10.1 9.85 9.75 10.3 9.7 9.8 10.0 9.9 9.7 8.2

2 2 2 2 2 2 5 5 4 4 2 5

Diethylamine ... Ethylene glycol. Ethyl formate .. Heptane ....... Hexane ........ Methyl acetate. Methyl iodide ..

Reference

Estimated error, %

-- --

Acetone ....... Alcohol Methyl. .....

9.0 9.2 9.3 9.45 9.5

BfA

The dependence of B I A on hydrostatic pressure is shown in Table 30-2 for several liquids. Table 30-3 gives the few known values of the third-order ratio, CIA, all under the approximation

The general form of the acoustic wave equation for a fluid satisfying Eq. (30-1) (with neglect of the S3 and higher terms) is, in Lagrangian coordinates, a2~

at 2

co2

=

(1

a2~

+ a~;ax)2+BIA ax 2

(30-6)

where t is the particle displacement, and Co is the speed of sound for infinitesimal t. In approximate solutions of this equation [such as Eqs. (3n-40) and (3n-92)], the ratio B I A always appears in the form

fJ = 1

B + 2A

(30-7)

3-208

ACOUSTICS

Hence distortions of the wave form of an initial sinusoid can be used to determine the ratio BIA. Finally, the effective absorption coefficient for a finite-amplitude wave can be written for a nonrelaxing medium as

~o + 3w -4exc 2

-exeff = 1

(

2

ex

1

B ) + -2A

e- 2a 2: ( 1 - e- 2a 2: ) 2

+ h'Igh er-order terms

(30-8)

where ex is the absorption coefficient for infinitesimal displacement amplitude ~o. The ratio B I A could therefore be obtained from this equation, although with reduced accuracy. TABLE 30-2. VALUES

OF

BIA AT VARIOUS PRESSURES Pressure p, kg/cm 2

-c

Temperature T,

1

250

500

1,000

2,000

4,000

8,000

4.08 5.49 5.74

4.90 5.59 5.79

5.58 5.69 5.84

6.35 5.84 5.86

6.78 6.00 5.82

6.60 6.06 5.64

5.79 5.50

.....

8.9

8.0

7.3

6.4

5.7

....

...... ..

........

7.84

7.37

7.01

Water [3]

0 40 80 I-Propyl alcohol [9]

30

10.4

Mercury [9]

40.5

8.33

..

TABLE 30-3. VALUES Pressure at 300 e

OF

CIA

j(BIA)2

2po2coa(a2clap2)r at 30 0 e

CIA

40.7 55.5 57.5 52.7

-8.7 -16.9 -25.0 -26.7

32.0 38.6 32.5 26.0

162 49

-87 -24

75 25

Water [3]

1 atm 2,000 kg/cm 2

4,000 kg/cm 2 8,000 kg/cm 2 I-Propyl alcohol [9] 1 kg/cm 2

8,000 kg/cm 2

30-2. Solids. Equation (3n-60c) indicates that the coefficient {3 = 1 + B 12A for liquids must be replaced by {3 = -M a/2M 2 for solids, where M 2 and M.« are elasticconstant combinations that appear in the partial differential equation for purely longitudinal waves in solids (ref. 10), 2u

a iJi2 =

1

a2u (

~ ax2

M2

. ) + M aa ax u + higher-order terms

(30-9)

where u is the displacement velocity. The constants M 2 and M a are often written in terms of other so-called second- and third-order elastic coefficients K 2 and Kv: M«

= K, + 2K 2

The coefficients K 2 and K« are in turn related to the more familiar second- and thirdorder elastic constants Cc, and Ciik. The connections for the [100], [lID], and [111]

3-209

NONLINEAR ACOUSTICS (EXPERIMENTAL)

directions are shown in Table 30-4. More detailed relations of this sort are given in ref. 12. By measurement of the distortion of an initially sinusoidal longitudinal wave through a solid, it is therefore possible to determine the third-order elastic constants. A number of these constants have been determined. Their values are given in Table 30-5 (ref. 13). TABLE

30-4. K 2

AND

K,

[100], [110],

FOR THE

AND

K

Direction

[100]

CII CII + C12 + 2Cu

[110]

CIII C111

CII + 2C12 + 4Cu 3

30-5.

DIRECTIONS

[11]

3

+ 3Cm + 12C166

4 Clll + 6C J1 2 + 12C l 44 + 24C166 + 2C123 + 16Cm 9

2

[111]

TABLE

[111]

MEASURED THIRD-ORDER ELASTIC CONSTANTS OF SOME CUBIC CRYSTALS AT ROOM TEMPERATURE

[13]

(x 10 12 dynes Zom") Crystal

Ge Si GaAs GaAs InSb Cu Cu Ge Ge MgO NaCI KCI NaCI KCI BaF2 Approx. accuracy, %

CIII

ClI2

C123

C144

C166

-7.10 -8,25 -6.22 -6,72 -3.14 -15.0 -12.71 -7.32 -7.16 -48.9 -8.3 -7.1 -8.80 -7.01 -5.84

-3.89 -4.51 -3.87 -4,02 -2.10 -8,5 -8,14 -2.90 -4.03 -0.95

-0.18 -0,64 +0.57 -0.04 -0.48 -2.5 -0.50 -2.2 -0.18 -0.69

-0.23 +0,12 +0.02 -0.70 +0.09 -1.35 -0,03 -0.08 -0,53 +1.13

-2,92 -3.10 -2.69 -3.20 -1.18 -6.45 -7.80 -3.03 -3.15 -6,6

-0,57 -0.224 -2.99

0.284 0.133 -2.06

0.257 0.127 -1.21

-0.611 -0.245 -0.889

±10

±50

±50

±3

±5

C456

-0.53 . -0.64 -0.39 -0.69 +0.002 -0.16 -0.95 -0.41 -0.47 +1.47 0,271 0.118 0.271

Ref.

14 14 15 16 17 18 19 20 21 21 22 22 23 23 24

±15

References 1. Beyer, R. T.: J. Acoust. Soc. Am. 32, 719-721 (1960). 2. Coppens, A. B., R. T. Beyer, M. B. Seiden, J. Donohue, F. Guepin, R. D. Hodson and C. Townsend: J. Acoust. Soc. Am. 38,797-804 (1963). 3. Hagelberg, M. P., G. Holton, and S. Kao: J. Acoust. Soc. Am. 41, 564-567 (1967). 4. Maki, W. C.: M.A.T. thesis, Brown University, Providence, R.I., June, 1966. 5. Freeman, R. A.: M.A.T. thesis, Brown University, Providence, R.I., June, 1966. 6. Dunn, F. W.: M.A.T. thesis, Brown University, Providence, R.I., June, 1967. 7. Sander, C. F.: M.A.T. thesis, Brown University, Providence, R.I., June, 1969. 8. Coppens, A. B., R. T. Beyer, and J. Ballou: J. Acoust. Soc. Am. 41, 1443-1448 (1967). 9. Hagelberg, M. P.: J. Aco1lst. Soc. Am. 47, 158-162 (1970). 10. Thurston, R. N., and M. J. Shapiro: J. Acoust. Soc. Am. 41, 1112-1125 (1967). 11. Breazeale, M. A., and Joseph Ford: J. Appl. Phys. 36,3486, 3490 (1965).

3-210

ACOUSTICS

12. Thurston, R. N., ann K. Brugger: Phys. Rev. 133A, 1604-1610 (1964); erratum, ibid. 135 (AB7) , 3 (1964). 13. Beyer, R. T., and S. V. Letcher: "Physical Ultrasonics," p. 255, Academic Press, Inc., New York, 1969. 14. McSkimin, H. J., and P. Andreatch, Jr.: J. Appl. Phys. 35, 3312 (1964). 15. McSkimin, H. J., and P. Andreatch, Jr.: J. Appl. Phys. 38, 2610 (1967). 16. Drabble, J. R., and A. J. Brammer: Solid State Commun. 4,467 (1966). 17. Drabble, J. R., and A. J. Brammer: Proc, Phys. Soc. (London) 91,959 (1967). 18. Salama, K., and G. A. Alers: Phys. Rev. 161, 673 (1967). 19. Hiki, Y., and A. V. Granato: Phys. Rev. 144, 411 (1966). 20. Bateman, T., W. P. Mason, and H. J. McSkimin: J. Appl. Phys. 32, 928 (1961). 21. Bogardus, E. H.: J. Appl. Phys. 36, 2504 (1965). 22. Stanford, A. L., Jr., and S. P. Zehner: Phys. Rev. 153, 1025 (1967). 23. Chang, Z. P.: Phys. Rev. 140A, 1788 (1965). 24. Gerlich, D.: Phys. Rev. 168, 947 (1068).

3p. Selected References on Acoustics LEO L. BERANEK

Bolt Beranek and Newman Inc.

Acoustical Materials Association: Sound Absorption Coefficients of Architectural Acoustical Materials, Acoust. Materials Assoc. Bull. XXIX, New York, 1969. Adam, N.: "Akustik," Verlag Paul Haupt, Bern, 1958. Albers, V. M.: "Underwater Acoustics Handbook," 2d ed. Pennsylvania State University Press, University Park, Pa., 1965. Albers, V. M.: "Underwater Acoustics," vols. 1 and 2, Plenum Publishing Corporation, New York, 1963, 1967. ASHRAE: "Guide and Data Book: Systems and Equipment," chap. 31, Sound and Vibration Control, 1967. Babikov, O. 1.: "Ultrasonics and Its Industrial Applications," translated from Russian, Consultants Bureau, Plenum Publishing Corporation, New York, 1960. Bartholomew, W. T.: "Acoustics of Music," Prentice-Hall, Inc., Englewood Cliffs, N.J., 1946. Beranek, L. L.: "Acoustics," McGraw-Hill Book Company, New York, 1954. Beranek, L. L.: "Acoustic Measurements," John Wiley & Sons, Inc., New York, 1960. Beranek, L. L.: "Noise Reduction," McGraw-Hill Book Company, New York, 1960. Beranek, L. L.: "Music, Acoustics and Architecture," John Wiley & Sons, Inc., New York, 1962. Beranek, L. L.: "Noise and Vibration Control," McGraw-Hill Book Company, New York, 1971. Bergmann, L.: "Der Ultraschall und seine Anwendung in Wissenschaft und Technik," 6th ed., S. Hirzel Verlag KG, Stuttgart, 1954. Brekhovskikh, L. M.: "Waves in Layered Media," Academic Press, Inc., New York, 1960. Burris-Meyer, H., and L. S. Goodfriend: "Acoustics for the Architect," Reinhold Publishing Corporation, New York, 1957. Canac, F., ed.: "Acoustique musicale," Editions du Centre National de la Recherche Scientifique, Paris, 1959. Carlin, B.: "Ultrasonics," 2d edt McGraw-Hill Book Company, New York, 1960. Chalupnik, J. D.: "Transportation Noises," University of Washington Press, Seattle, Washington, 1970. Crede, C. E.: "Shock and Vibration Concepts in Engineering Design," Prentice-Hall, Inc., Englewood Cliffs, N.J., 1965.

SELECTED REFERENCES ON ACOUSTICS

3-211

Crede, C. E.: "Vibration and Shock Isolation," John Wiley & Sons, Inc., New York, 1951. Cremer, L.: "Die wissenschaftlichen Grundlagen der Raumakustik," vol. I, S. Hirzel Verlag KG, Stuttgart, 1949. Cremer, L.: "Die wissenschaftlichen Grundlagen der Raumakustik," vol. II, S. Hirzel Verlag KG, Stuttgart, 1961. Cremer, L.: "Die wissenschaftlichen Grundlagen der Raumakustik," vol. III, S. Hirzel Verlag KG, Stuttgart, 1950. Cremer, L., and M. Heckl: "K6rperschall," Springer-Verlag OHG, Berlin, 1967. Culver, C. A.: "Musical Acoustics," 4th ed., McGraw-Hill Book Company, New York, 1956. Davis, H. and S. R. Silverman, eds.: "Hearing and Deafness," rev. ed., Holt, Rinehart and Winston, Inc., New York, 1960. Eckart, C., ed.: "Principles and Applications of Underwater Acoustics." U.S. Government Printing Office, Washington, D.C., 1968. Fant, G.: "On the Acoustics of Speech," 3 vols, Mouton & Co., The Hague, 1960. Fletcher, H.: "Speech and Hearing in Communication," D. Van Nostrand Company, Inc., Princeton, N.J., 1953. Fliigge, S., ed.: "Handbuch der Physik," vol. XI/I, Akustik I; vol. XI/2, Akustik II, Springer-Verlag OHG, Berlin, 1961, 1962. Frayne, J. G., and H. Wolfe: "Sound Recording," John Wiley & Sons, Inc., New York, 1949. Frederick, J. R.: "Ultrasonic Engineering," John Wiley & Sons, Inc., New York, 1965. Furrer, W.: "Room and Building Acoustics and Noise Abatement," (Butterworths) Plenum Publishing Corporation, New York, 1964. Hansen, H. M., and P. F. Chenea: "Mechanics of Vibrations," John Wiley & Sons, Inc., New York, 1952. Harris, C. M., ed.: "Handbook of Noise Control," McGraw-Hill Book Company, New York, 1957. Harris, C. M., and E. Crede: "Shock and Vibration Handbook," 3 vols, McGraw-Hill Book Company, New York, 1961. Helmholtz, H. L. F.: "On the Sensations of Tone as a Physiological Basis for the Theory of Music," translated from 3d German ed. by A. J. Ellis, Longmans, Green & Co., Ltd., London, 1875; 5th rev. ed., 1930. Herzfeld, K. F., and T. A. Litovitz: "Absorption and Dispersion of Ultrasonic Waves," Academic Press, Inc., New York, 1959. Hirsch, I. J.: "The Measurement of Hearing," McGraw-Hill Book Company, New York, 1952. Hueter, T. F., and R. H. Bolt: "Sonics," John Wiley & Sons, Inc., New York, 1955. Hunt, F. V.: "Electroacoustics," Harvard University Press, Cambridge, Mass., and John Wiley & Sons, Inc., New York, 1954. Hunter, J. L.: "Acoustics," Prentice-Hall, Inc., Englewood Cliffs, N.J., 1957. Kacherovich, A. N., and E. E. Khomootov: "Acoustics and Architecture of Cinema Theaters," State Publishing House "Art," Moscow, 1961. Keast, D. N.: "Measurements in Mechanical Dynamics," McGraw-Hill Book Company, New York, 1967. Kikuchi, Y.: "Ultrasonic Transducers," Corona Publishing Company, Tokyo, 1969. Kinsler, L. E., and A. R. Frey: "Fundamentals of Acoustics," 2d ed., John Wiley & Sons, Inc., New York, 1962; 5th printing, 1967. Knudsen, V., and C. Harris: "Acoustical Designing in Architecture," John Wiley & Sons, Inc., New York, 1950. Krasil'nikov, V. A.: "Sound and Ultrasound Waves." 3d rev. ed., translated from the Russian by N. Kaner and M. Segal, Israel Program for Scientific Translations Ltd., Jerusalem, 1963. Kryter, K. D.: The Effects of Noise on Man, J. Speech Hearing Disorders, Mono(Jraph Suppl. 1, September, 1950. Kryter, K. D.: "The Effects of Noise on Man," Academic Press, New York, 1970. Kurtze, G.: "Physics and Techniques of Noise Control," (in German) Verlag G. Braun, Karlsruhe, Germany, 1964. Lamb, H.: "The Dynamical Theory of Sound," 2d ed., N.Y., Dover Publications, Inc., New York, 1960. Lamb, H.: "Hydrodynamics," 6th ed., Dover Publications, Inc., New York, 1945. Lindsay, R. B.: "Mechanical Radiation," McGraw-Hill Book Company, New York, 1960. Lyon, R. H.: "Random Noise and Vibration in Space Vehicles," U.S. Government Printing Office, Washington, D.C., 1967. Malecki, I.: "Physical Foundations of Technical Acoustics," Pergamon Press, New York, 1968.

3-212

ACOUSTICS

Mason, W. P.: "Electro-mechanical Transducers and Wave Filters," 2d ed., D. Van Nostrand Company, Inc., Princeton, N.J., 1948. Mason, W. P.: "Piezoelectric Crystals and Their Application to Ultrasonics," D. Van Nostrand Company, Inc., Princeton, N.J., 1950. Mason, W. P.: "Physical Acoustics," 7 vols., Academic Press, Inc., New York, 1964-1971. Mason, W. P.: "Physical Acoustics and the Properties of Solids," D. Van Nostrand Company, Inc., Princeton, N.J., 1958. Miller, G. A.: "Language and Communication," McGraw-Hill Book Company, New York, 1951. Morse, P. M.: "Vibration and Sound," 2d ed., McGraw-Hill Book Company, New York, 1948. Morse, P. M., and K. U. Ingard: "Theoretical Acoustics," McGraw-Hill Book Company, New York, 1968. Ol'shevskii, V. V.: "Characteristics of Sea Reverberations," translated from Russian, Consultants Bureau, Plenum Publishing Corporation, New York, 1967. Olson, H. F.: "Acoustical Engineering," 3d ed., D. Van Nostrand Company, Inc., Princeton, N.J., 1957. Olson, H. F.: "Solution of Energy Problems by Dynamical Analogies," D. Van Nostrand Company, Inc., Princeton, N.J., 1958. Olson, H. F.: "Musical Engineering," McGraw-Hill Book Company, New York, 1952. Parkin, P. H., and H. R. Humphreys: "Acoustics, Noise and Buildings," Faber & Faber, Ltd., London, 1958. Parkin, P. H., H. J. Purkis, and W. E. Scholes: "Field Measurements of Sound Insulation Between Dwellings," Her Majesty's Stationery Office, London, 1960. Peterson, A. P. G., and E. E. Gross, Jr.: "Handbook of Noise Measurement," 6th ed., General Radio Company, West Concord, Mass., 1967. Pierce, J. R., and E. E. David Jr.: "Man's World of Sound," Doubleday & Company Inc., Garden City, N.Y., 1958. Purkis, H. J.: "Building Physics: Acoustics," Pergamon Press, New York, 1966. Lord Rayleigh: "The Theory of Sound," 2d ed., vols. 1 and 2, Dover Publications, Inc., New York, 1945. Rettinger, M.: "Acoustics: Room Design and Noise Control," Chemical Publishing Company, Inc., New York, 1968. Reichardt, W.: "Foundations of Technical Acoustics" (in German), Portig K. G., Leipzig, 1968. Richardson, E. G.: "Technical Aspects of Sound," 3 vols., American Elsevier Publishing Company, Inc., New York, 1962. Rschevkin, S. N.: "A Course of Lectures on the Theory of Sound," translated from the Russian by O. M. Blunn, edited by P. E. Doak, Pergamon Press, New York, 1963. Schaafs, W.: "Landolt-Bornstein New Series, Group II," "Atomic and Molecular Physics," vol. 5, "Molecular Acoustics," Springer-Verlag New York Inc., New York, 1967. Skudrzyk, E.: "Die Grundlagen der Akustik," Springer-Verlag HG, Vienna, 1954. Skudrzyk, E.: "Simple and Complex Vibrating Systems," Pennsylvania State University Press, University Park, Pa., 1968. Stephens, R. W. B., and A. E. Bate: "Acoustics and Vibrational Physics," St. Martin's Press, Inc., New York, 1966. Stevens, S. S., J. G. C. Loring, and D. Cohen: "Bibliography on Hearing," Harvard University Press, Cambridge, Mass., 1955. Stevens, S. S., ed.: "Handbook of Experimental Psychology," John Wiley & Sons, Inc. New York, 1951. Swenson, G. W., Jr.: "Principles of Modern Acoustics," D. Van Nostrand Company, Inc., Princeton, N.J., 1953. Tolstoy, 1. and P. S. Clay: "Ocean Acoustics," McGraw-Hill Book Company, New York, 1966. Trapp, W. J., and D. M. Forney, Jr., eds.: "Acoustical Fatigue in Aerospace Structures," Syracuse University Press, Syracuse, New York, 1965. Tucker, D. G., and B. Z. Gazey: "Applied Underwater Acoustics," Pergamon Press, N ew York, 1966. Urick, R. J.: "Principles of Underwater Sound for Engineers," McGraw-Hill Book Company , New York, 19'67. Wever, E. G., and M. Lawrence: "Physiological Acoustics," Princeton University Press, Princeton, N.J., 1954. Wiethaup, H.: "Noise Abatement in Western Germany" (in German), Carl Heymann! Verlag KG, Cologne, 1961. Wood, A.: "Acoustics," Dover Publications, Inc., New York, 1966. Zwikker, C., and C. W. Kosten: "Sound Absorbing Materials," American Elsevier Publishing Company, Inc., New York, 1949.

Section 4

HEAT MARK W. ZEMANSKY, Editor The City College of the City University of New York

CONTENTS 4a. 4b. 4c. 4d. 4e. 4f. 4g. 4h. 4i. 4j. 4k. 41.

Temperature Scales, Thermocouples, and Resistance Thermometers. . . . .. Thermodynamic Symbols, Definitions, and Equations. . . . . . . . . . . . . . . . .. Critical Constants Compressibility............................................... . . . .. Heat Capacities Thermal Expansion Thermal Conductivity Thermodynamic Properties of Gases Pressure-Volume-Temperature Relationships of Gases. Virial Coefficients Temperatures, Pressures, and Heats of Transition, Fusion, and Vaporization Vapor Pressure Heats of Formation and Heats of Combustion

4-1

4-2 4-22 4-33 4-38 4-105 4-119 4-142 4-162 4-204 4-222 4-261 4-316

4a. Temperature Scales, Thermocouples, and Resistance Thermometers 1 H. H. PLUMB, R. L. POWELL, W. J. HALL, AND J. F. SWINDELLS

The National Bureau of Standards

The Comite International des Poids et Mesures (CIPM) in October, 1968, agreed to adopt the International Practical Temperature Scale of 19682 (IPTS-68) in accordance with the decision of the 13th General Conference of Weights and Measures, Resolution 8, of October, 1967. IPTS-68 has replaced IPTS-48 (amended edition of 1960). It was formulated in such a way that temperature measured on it closely approximates the thermodynamic temperature, and extends the range of definition down to 13.81 kelvins. (The previous scale, IPTS-48, terminated at -183°C.) The basic temperature is the thermodynamic temperature, symbol T, the unit of which is the kelvin, symbol K. The kelvin is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water." The Celsius temperature, symbol t, is defined by t = T - To where To = 273.15 K (the ice point). The unit employed to express a Celsius temperature is the degree Celsius, symbol "C, which is equal to the kelvin. A difference of temperature is expressed in kelvins; it may also be expressed in degrees Celsius. The International Practical Temperature Scale of 1968 distinguishes between the International Practical Kelvin Temperature with the symbol T 68 and the International Practical Celsius Temperature with the symbol t 6 8. The relation between T 68 and t G8 is t 68

= T 68

-

273.15 K

The units of T 68 and t 68 are the kelvin, symbol K, and degree Celsius, symbol "C, as in the case of the thermodynamic temperature T and the Celsius temperature t. The IPTS-68 is based on the assigned values of the temperatures of a number of reproducible equilibrium states (defining fixed points) and on standard instruments calibrated at those temperatures. Interpolation between the fixed-point temperatures is provided by formulas used to establish the relation between indications of the standard instruments and values of the International Practical Temperature. The defining fixed points are given in Table 4a-1. 1 Acknowledgment is made of the previous contributions to this section in the second edition of the Handbook by H. F. Stimson, J. F. Swindells, and R. E. Wilson. Data on optical pyrometry and thermal radiation are given in Sec. 6. 2 The text in French of this scale is published in Compt. rend. 13eme con], yen. poids mesures, 1967-1968, Annexe 2, and Cornite Consultatif de 'I'hermometrie, 8 e session, 1967. Annexe 18. The English text is published in Metroloqia 5(2),35 (1969). 3 13th General Conference of Weights and Measures, 1967, Resolutions 3 and 4.

4-2

4-3

TEMPERATURE SCALES, THERMOCOUPLES TABLE

4a-1.

DEFINING FIXED POINTS OF THE IPTS-68*

Assigned value of International Practical Temperature

Equilibrium state

T6iJK

Equilibrium between the solid, liquid, and vapor phases of equilibrium hydrogen (triple point of equilibrium hydrogen) Equilibrium between the liquid and vapor phases of equilibrium hydrogen at a pressure of 33330.6 N /m 2 (25/76 standard atmosphere) Equilibrium between the liquid and vapor phases of equilibrium hydrogen (boiling point of equilibrium hydrogen) Equilibrium between the liquid and vapor phases of neon (boiling point of neon) Equilibrium between the solid, liquid, and vapor phases of oxygen (triple point of oxygen) Equilibrium between the liquid and vapor phases of oxygen (boiling point of oxygen) Equilibrium between the solid, liquid, and vapor phases of water (triple point of water)t Equilibrium between the liquid and vapor phases of water (boiling point of water)tt Equilibrium between the solid and liquid phases of zinc (freezing point of zinc) Equilibrium between the solid and liquid phases of silver (freezing point of silver) Equilibrium between the solid and liquid phases of gold (freezing point of gold)

t6 °C

13.81

-259.34

17.042

-256.108

20.28

-252.87

27.402

-246.048

54.361

-218.789

90.188

-182.962

273.16

0.01

373.15

100

692.73

419.58

1235.08

961.93

1337.58

1064.43

*

Except for the triple points and one equilibrium hydrogen point (17.042 K) the assigned values of temperature are for equilibrium states at a pressure po = 1 standard atmosphere (101325 N/m 2) . In the realization of the fixed points small departures from the assigned temperatures will occur as a result of the differing immersion depths of thermometers or the failure to realize the required pressure exactly. If due allowance is made for these small temperature differences, they will not affect the accuracy of realization of the Scale. t The water used should have the isotopic composition of ocean water. t The equilibrium state between the solid and liquid phases of tin (freezing point of tin) has the assigned value of tes = 231.9681 °C and may be used as an alternative to the boiling point of water.

In the range 13.81 to 273.15 K, the interpolating instrument is a platinum thermometer and T 68 is defined by the relation (4a-l) where WeT 68) is the resistance ratio of the platinum thermometer as defined by

R(273.15 K)

and WCCT-68(T68) is the resistance ratio as given by the reference function in Table 4a-2. The deviations .1.W(T 68) at the temperatures of the defining fixed points are the differences between the measured values of W(T 68) and the corresponding values of W CCT-68(T68).

4-4:

HEAT

TABLE 4a-2. THE REFERENCE FUNCTION WCCT-68(T68) FOR PLATINUM RESISTANCE THERMOMETERS FOR THE RANGE FROM 13.81 TO 273.15 K* 20

T 68

=

2: Ai[ln WCCT_68(T68)]i} K

{A o +

i=l

,

A,

i

0.27315 X 10 3 0.250846 209 678 803 3 0.135099 869 964 999 7 0.5278567590085172 0.276768 548854 1052 0.391 053 205 376 683 7 0.655 613 230 578 069 3 0.808 035868 559 866 7 0.705242 1182340520 0.4478475896389657 0.2125256535560578

0 1 2 3 4 5 6 7 8 9 10

X X X X X X X X X X

Ai

11 12 13 14 15 16 17 18 19 20

10 3 10 3 10 2 10 2 10 2 10 2 10 2 10 2 10 2 10 2

0.7679763581708458 0.213 6894593828500 o.459 843 348 928 069 3 0.763 614 629 231 648 0 0.969 328 620 373 121 3 0.923 069 154 007 007 5 0.638 116590 952 653 8 0.3022932378746192 0.877 551391303 760 2 0.117702613125477 4

X 10 X 10 X X X X X X X

10- 1 10- 2 10- 3 10- 4 10- 6 10- 7 10- 8

* The reference function WCCT-6S(T6S) is continuous at T6B = 273.15 K in its first and second derivatives with the function W(t6S) given by Eqs. (4a-6) and (4a-7) for a = 3.9259668 X 1O-3(OC)-1 and o = 1.496334°C. A tabulation of this reference function, sufficiently detailed to allow interpolation to an accuracy of 0.0001 K. is available from the Bureau International des Poids et Mesures, 92-SE)vres. France.

The following interpolation formulas are used to determine a W(T 6S) at intermediate temperatures: 13.81 to 20.28 K: 20.28 to 54.361 K: 54.361 to 90.188 K: 90.188 to 273.15 K:

+ B T 6s + C 6S + D 6S3 + B 68 + C T 68 + D T 683 + B 3T 68 + C aT 683 A 4t 68 + C4t683(t68 - 100°0)

.1W(T 68) = Al .1W(T 68) = A 2 .1W(T 6S) = A 3

.lW(T 68) =

I

1T

2

IT

2T

2

2

2

(4a-2)1 (4a-3) 2 (4a-4) 3 (4a-5) 4

In the range 0°0 (273.15 K) to 630.74°0, t 68 is defined by

(t 10000 - 1 t (419.t~800 - 1) (630. ; 400 - 1) °0 t' ) (t' ~1 [Wet') - 1] + 0 ( 10000 10000 - 1 ) f

t 68 = t

f

where t is defined as

t'

=

f

t + 0.045 10000

f

)

(4a-6)

(4a-7)

1 Constants for Eq. (4a-2) are determined by the three measured deviations-at the triple point of equilibrium hydrogen, the temperature of 17.042 K. and the boiling point of equilibrium hydrogen-and by the derivative of the deviation function at the boiling point of equilibrium hydrogen as derived from Eq. (4a-3). 2 Constants for Eq. (4a-3) are determined by the three measured deviations-at the boiling point of equilibrium hydrogen, the boiling point of neon. and the triple point of oxygen-and by the derivative of the deviation function at the triple point of oxygen as derived from Eq. (4a-4). 3 Constants for Eq. (4a-4) are determined by the two measured deviations-at the triple point and the boiling point of oxygen and by the derivative of the deviation function at the boiling point of oxygen as derived from Eq. (4a-5). 4 Constants for Eq. (4a-5) are determined by the two measured deviations at the boiling point of oxygen and the boiling point of water.

TEMPERATURE SCALES, THERMOCOUPLES

4-5

The resistance ratio W(t') = R(t')/R(O°C) and the constants R(O°C), a and 0 are determined by measurement of three resistances-at the triple point of water, the boiling point of water (or the freezing point of tin), and the freezing point of zinc. Equation (4a-7) is equivalent to W(t')

when

A

= a

(1 + lO~OC)

1

+ At' + Bt'2

and

B

=

(4a-8)

-10- 4 ao(OC)-2

From 630.74 to 1064.43°C, t ss is defined by (4a-9) where E(t ss) is the electromotive force of a standard thermocouple of rhodiumplatinum alloy and platinum, when one junction is at the temperature t 6 8 = O°C and the other junction is at temperature t 6 8 • The constants a, b, and c are calculated from the values of E at 630.74 ± 0.2°C, as determined by a platinum resistance thermometer, and at the freezing points of silver and gold. Above 1337.58 K (1064.43°C) the temperature T 6 8 is defined by exp [cdXT 6 8(Au)] - 1 exp [c2/XT 68 ] - 1

(4a-10)

where L>.(T 6S ) and L>.(T 68(Au» are the spectral concentrations at temperature T S8 and at the freezing point of gold, T 68(Au) of the radiance of a black body at the wavelength! X; C2 = 0.014388 meter kelvin. Table 4a-3 (p. 4-6) lists the approximate differences between the IPTS-68 and IPTS-48 and should prove to be a utility for many references to this section. To avoid creating conflicting statements, the preceding description of IPTS-68 has for the most part been taken from the English language version of the International Practical Temperature Scale of 1958 as it appeared in M etrologia. For a more complete description of the IPTS-68 and pertinent supplementary information the reader should refer fOthe defining text.> In Tables 4a-4, 4a-5, and 4a-6 which follow, values have been adjusted to agree with IPTS-68. 1 Since T 6s(Au) is close to the thermodynamic temperature of the freezing point of gold, and C2 is close to the second radiation constant of the Planck equation, it is not necessary to specify the value of the wavelength to be employed in the measurements [see M etroloqia 3, 28 (1967)]. 2 M etrologia 5 (2), 35 (1969).

t

~

TABLE

4a-3.

ApPROXIMATE DIFFERENCES

(t 88

-

t (8 ) , OF

-10

-20

0.013 0.006

0.003 0.012

IN KELVINS, BETWEEN THE VALUES OF TEMPERATURE GIVEN BY THE

1968

AND THE IPTS OF

IPTS

1948

-30

-40

-50

-60

-0.006 0.018

-0.013 0.024

-0.013 0.029

-0.005 0.032

40

50

60

70

80

90

100

-0.010 0.016 0.058 0.077 0.074 0.094 0.23 0.50 0.78 1.07 1.36

-0.010 0.020 0.061 0.077 0.074 0.100 0.25 0.53 0.81 1.10 1.39

-0.010 0.025 0.064 0.077 0.074 0.108 0.28 0.56 0.84 1.12 1.42

-0.008 0.029 0.067 0.077 0.075 0.116 0.31 0.58 0.87 1.15 1.44

-0.006 0.034 0.069 0.077 0.076 0.126 0.34 0.61 0.89 1.18

-0.003 0.038 0.071 0.076 0.077 0.137 0.36 0.64 0.92 1.21

0.000 0.043 0.073 0.076 0.079 0.150 0.39 0.67 0.95 1.24

300

400

500

600

700

800

900

1000

1.8 4.0 6.9

2.0 4.2 7.2

2.2 4.5 7.5

2.4 4.8 7.9

2.6 5.0 8.2

2.8 5.3 8.6

3.0 5.6 9.0

3.2 5.9 9.3

t&s°C

0

-100 0

0.022 0.000

t68°C

0

10

20

30

0 100 200 300 400 500 600 700 800 900 1000

0.000 0.000 0.043 0.073 0.076 0.079 0.150 0.39 0.67 0.95 1.24

-0.004 0.004 0.047 0.074 0.075 0.082 0.165 0.42 0.70 0.98 1.27

-0.007 0.007 0.051 0.075 0.075 0.085 0.182 0.45 0.72 1. 01 1.30

-0.009 0.012 0.054 0.076 0.075 0.089 0.200 0.47 0.75 1.04 1.33

t68°C

0

100

200

1000 2000 3000

3.2 5.9

1.5 3.5 6.2

1.7 3.7 6.5

-70

-80

-90

-100

0.007 0.034

0.012 0.033

0.029

0.022

~

t:r.l

> J-3

4-7

TEMPERATURE SCALES, THERMOCOUPLES TABLE

4a-4.

THERMAL EMF OF CHEMICAL ELEMENTS RELATIVE TO

Sodium, mV

Temp., °C

Lithium, mV

-200 -100 0 +100 200 300

-1.12 -1.00 0 +1.82

..... .

..... .

....... . ....... . ....... .

Temp., °C

Magnesium, mV

Zinc, mV

-200 -100 0 +100 200 300 400 500 600

+0.37 -0.09 0 +0.44 +1.10

..... . ..... . ...... ..... .

....... .

Temp. °C

Carbon, mV

Silicon, mV

-200 -100 0 +}OO 200 300 400 500 600 700 800 900 1000 1100

...... ......

+63.13 +37.17 0 -41.56 -80.57 -110.07 ........ .

0 +0.70 1.54 2.55 3.72 5.15 6.79 8.82 10.98 13.55 16.46 19.46

+1.00 +0.29 0

-0.07 -0.33 0 +0.76 1.89 3.42 5.29 ••••

0

•••

....... . ....... . ........

I

Potassium, mV

Rubidium, mV

Cesium, mV

+1.61 +0.78 0

+1.09 +0.46 0

+0.22 -0.13 0

. ..... . ..... . .....

...... ...... . .....

Mercury, mV

Indium, mV

...... . ••

0

••

0

•

....... Cadmium, mV

-0.04 -0.31 0 +0.90 2.35 4.24

...... . ...... . ...... . Germanium, mV

-46.00 -26.62 0 +33.9 72.4 91.8 82.3 63.5 43.9 27.9

• '0 ••• ••

0

•••

0 -0.60 -1.33

. ..... ..... . ..... . . .....

PLATINUM*

Calcium, mV

0 -0.51 -1.13 -1.85

. ..... ......

0 +0.69

0 +0.58 1.30 2.16

0

•

...... . .....

0

•••••

. .....

. ..... . .....

Tin, mV

Lead, mV

Antimony, mV

+0.26 -0.12 0 +0.42 1.07

+0.24 -0.13 0 +0.44 1.09 1. 91

...... ..... .

. ..... ..... .

......

...... ...... ......

0 +1.14 2.46

Thallium, AlumimV num, mV

...... .... " ••••

Cerium, mV

. ..... . ..... 0 +4.89 10.14 15.44 20.53 25.10 28.87

+0.45 +0.06 0 +0.42 1.06 1.88 2.84 3.93 5.15

Bismuth, mV

+12.39 +7.54 0 -7.34 -13.57

4-8 TABLE

HEAT 4a-4.

THERMAL EMF OF CHEMICAL ELEMENTS RELATIVE TO PLATINUM·

(Continued)

Temp., °C

Copper, mV

Silver, mV

Gold, mV

Cobalt, mV

Nickel, mV

-200 -100 0 +100 200 300 400 500 600 700 800 900 1000 1100 1200

-0.19 -0.37 0 +0.76 1.83 3.15 4.68 6.41 8.34 10.47 12.81 15.37 18.16

-0.21 -0.39 0 +0.74 1.77 3.05 4.57 6.36 8.41 10.73 13.33 16.16

-0.21 -0.39 0 +0.78 1.84 3.14 4.63 6.29 8.12 10.11 12.26 14.58 17.05

....... .......

+2.28 +1.22 0 -1.48 -3.10 -4.59 -5.45 -6.16 -7.04 -8.10 -9.33 -10.67 -12.11 -13.60

..... .

..... .

...... ...... . .....

Temp., °C

Iridium, mV

Rhodium, mV

Palladium, mV

-200 -100 0 +100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500

-0.25 -0.35 0 +0.65 1.49 2.47 3.55 4.78 6.10 7.55 9.10 10.77 12.57 14.45 16.45 18.45 20.47 22.51

-0.20 -0.34 0 +0.70 1. 61 2.68 3.91 5.28 6.77 8.39 10.14 12.01 14.02 16.15 18.39 20.69 22.99 25.36

+0.81 +0.48 0 -0.57 -1.23 -1.99 -2.82 -3.84 -5.03 -6.40 -7.96 -9.69 -11. 61 -13.67 -15.86 -18.11 -20.40 -22.75

,I

......

0 -1.33 -3.08 -5.10 -7.24 -9.35 -11.28 -12.87 -13.99 -14.49 -14.21 -13.01 -10.70

Molybdenum, mV

Tungsten, mV

Tantalum, mV

+0.43 -0.15 0 +1.12 2.62 4.48 6.70 9.30 12.26 15.58 19.25 23.30 27.73 32.53 37.72

+0.21 -0.10 0 +0.33 0.93 1. 79 2.91 4.30 5.95 7.86 10.02 12.45 15.15 18.13 21.37

. .....

••

0

•••

••

0

•••

0 +1.45 3.19 5.23 7.57 10.20 13.13 16.33 19.83 23.63 27.74 32.15 36.86

..... .

..... .

......

Thorium, mV

0 -0.13 -0.26 -0.40 -0.50 -0.53 -0.45 -0.21 +0.22 +0.86 +1.72 +2.78 +4.03 +5.41

• A positive sign means that in a simple thermoelectric circuit the resultant emf given is in such a direction as to produce a current from the element to the platinum at the reference junction'CO°C). The values below O°C, in most cases, have not been determined on the same samples as the values above O°C. Based upon the original table in American Institute of Physics, "Temperature, Its Measurement and Control in Science and Industry," pp. 1309-1310, Reinhold Book Corporation, New York, 1941. Values of the emf have been adjusted to correspond to temperatures expressed on the International Practical Temperature Scale of 1968.

4-9

TEMPERATURE SCALES, THERMOCOUPLES TABLE

4a-5.

THERMAL EMF OF IMPORTANT THERMOCOUPLE MATERIALS RELATIVE TO PLATINUM*

Temp., °C

Chromel P, mV

Alumel, mV

Copper, mV

Iron, mV

Constantan, mV

-200 -100 0 +100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400

-3.36 -2.20 0 +2.81 5.96 9.32 12.75 16.21 19.61 22.94 26.20 29.37 32.47 35.52 38.48 41.38 44.04

+2.39 +1.29 0 -1.29 -2.17 -2.89 -3.64 -4.43 -5.28 -6.18 -7.07 -7.94 -8.78 -9.57 -10.33 -11.06

-0.19 -0.37 0 +0.76 1.83 3.15 4.68 6.41 8.34 10.47 12.81 15.37 18.16

-2.92 -1.84 0 +1.89 3.54 4.85 5.88 6.79 7.80 9.11 10.84 12.82 14.28

+5.35 +2.98 0 -3.51 -7.45 -11.71 -16.19 -20.79 -25.46 -30.15 -34.81 -39.39 -43.85

-11.77

*

American Institute of Physics, "Temperature, Its Measurement and Control in Science and Industry," p. 1308, Reinhold Book Corporation, New York, 1941. Values of the emf have been adjusted to correspond to temperatures expressed on the International Practical Temperature Scale of 1968.

TABLE

4a·6.

THERMAL EMF OF SOME ALLOYS RELATIVE TO PLATINUM*

mium, mV

Copperberyllium, mV

Yellow brass, mV

Phosphor bronze, mV

0 -0.17 -0.32 -0.44 -0.55 -0.63 -0.66

0 +0.67 1.62 2.81 4.19 ...... ......

0 +0.60 1.49 2.58 3.85 5.30 6.96

0 +0.55 1.34 2.34 3.50 4.81 6.30

Man-

Gold-

Temp., °C

ganin,

ehro-

mV

0 +100 200 300 400 500 600

0 +0.61 1.55 2.77 4.25 5.95 7.84

Solder 50 So50 Pb, mV

Solder 96.5 Sn3.5 Ag, mV

0 +0.46

0 +0.45

4-10

HEAT

TABLE

4a-6.

THERMAL EMF OF SOME ALLOYS RELATIVE TO PLATINUM*

(Continued)

Temp., °C

0 +100 200 300 400 600 600 700 800 900 (000

18-8 stainless steel, mV

0 +0.44 1.04 1.76 2.60 3.66 4.67 6.92 7.35 8.96

Spring steel, mV

80 Ni20 Cr, mV

60 Ni24 Fe16 Cr, mV

0 +1.32 2.63 3.81 4.84 6.80 6.86

0 +1.14 2.62 4.34 6.25 8.31 10.53 12.89 15.41 18.07 20.87

0 +0.85 2.01 3.41 5.00 6.76 8.68 10.76 13.03 15.47 18.06

......

...... .0

......

•

••••

•••

0

•

Copper coin (95 Cu4 Sn1 Zn), mV

0 +0.60 1.48 2.60 3.91 5.44 7.14

Nickel coin (75 Cu25 Ni), mV

Silver coin

(90 Ag10 Cu), mV

0 +0.80 1.90 3.25 4.81 6.69 8.64

°

-2.76 -6.01 -9.71 -13.78 -18.10 -22.59

• American Institute of Physics, "Temperature, Its Measurement and Control in Science and Industry, p. 1310, R.einhold Book Corporation, New York, 1941. Values of the emf have been adjusted to correspond to temperatures expressed on the International Practical Temperature Scale of 1968.

Thermocouple Reference Tables. Tables 4a-7 through 4a-12 contain abbreviated data on the thermoelectric voltages of six thermocouple combinations, two noblemetal types Sand R and four base-metal types E, J, K, and T. The full tables, functional representations, approximations, and material descriptions appear in NBS Monograph 125, "Thermocouple Reference Tables Based on the IPTS-68" by R. L. Powell, W. J. Hall, C. H. Hyink, L. L. Sparks, G. W. Burns, and H. H. Plumb, U.S. Government Printing Office, Washington, D.C., 1972. 4a-7. TYPE S. PLATINUM-10% RHODIUM vs. PLATINUM THERMOCOUPLES (Emf, absolute millivolts; temp., °C (IPTS-68); reference junctions at O°C]

TABLE

°C

°

10

20

30

40

50

60

70

80

90

100

------ - - - - - - --- - - - - - - --- - ----

0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700

0.000 0.055 0.113 0.173 0.235 0.299 0.365 0.432 0.502 0.573 0.645 0.645 0.719 0.795 0.872 0.950 1.029 1.109 1.190 1.273 1.356 1.440 1.440 1.525 1.611 1.698 1.785 1.873 1.962 2.051 2.141 2.232 2.323 2.3~3 2.414 2.506 2.599 2.692 2.786 2.880 2.974 3.069 3.164 3.260 3.260 3.356 3.452 3.549 3.645 3.743 3.840 3.938 4.036 4.135 4.234 4.234 4.333 4.432 4.532 4.632 4.732 4.832 4.933 5.034 5.136 5.237 5.237 5.339 5.442 5.544 5.648 5.751 5.855 5.960 6.064 6.169 6.274 6.274 6.380 6.486 6.592 6.699 6.805 6.913 7.020 7.128 7.236 7.345 7.345 7.454 7.563 7.672 7.782 7.892 8.003 8.114 8.225 8.336 8.448 8.448 8.560 8.673 8.786 8.899 9.012 9.126 9.240 9.355 9.470 9.585 9.585 9.700 9.816 9.932 10.048 10.165 10.282 10.400 10.517 10.635 10.754 10.754 10.872 10.991 11.110 11.229 11. 348 11.467 11.587 11.707 11.827 11.947 11.947 l2.067 12.188 12.308 12.429 12.550 12.671 12.792 12.913 13.034 13.155 13.155 13.276 13.397 13.519 13.640 13.761 13.883 14.004 14.125 14.247 14.368 14.368 14.489 14.610,14.731 14.852 14.973 15.094 15.215 15.336 15.456 15.576 15.576 15.697 15.817 15.937 16.057 16.176 16.296 16.415 16.534 16.653 16.771 16.771 16.890 17.008 17.125 17.243 17.360 17.477 17.594 17.711 17.826 17.942 17.942 18.056 18.170 18.282 18.394 18.504 18.612

4-11

TEMPERATURE SCALES, THERMOCOUPLES

TABLE 4a-8. TYPE R. PLATINUM-13% RHODIUM VS. PLATINUM THERMOCOUPLES [Emf, absolute millivolts; temp., °C (IPTS-68); reference junctions at DOC] 0

°C

20

10

30

40

--- --- - - - - - - - 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700

50

60

70

80

90

100

- - - - - - - - --- - -

0.00 0.054 0.111 0.171 0.232 0.296 0.363 0.431 0.501 0.573 0.647 0.647 0.723 0.800 0.879 0.959 1.041 1.124 1.208 1.294 1.380 1.468 1.468 1.557 1.647 1.738 1.830 1.923 2.017 2.111 2.207 2.303 2.400 2.400 2.498 2.596 2.695 2.795 2.896 2.997 3.099 3.201 3.304 3.407 3.407 3.511 3.616 3.721 3.826 3.933 4.039 4.146 4.254 4.362 4.471 4.471 4.580 4.689 4.799 4.910 5.021 5.132 5.244 5.356 5.469 5.582 5.582 5.696 5.810 5.925 6.040 6.155 6.272 6.388 6.505 6.623 6.741 6.741 6.860 6.979 7.098 7.218 7.339 7.460 7.582 7.703 7.826 7.949 7.949 8.072 8.196 8.320 8.445 8.570 8.696 8.822 8.949 9.076 9.203 9.203 9.331 9.460 9.589 9.718 9.848 9.978 10 .109 10.240 10.371 10.503 10.503 10.636 10.768 10.902 11. 035 11.170 11.304 11.439 11.574 11. 710 11.846 11.846 11.983 12.119 12.257 12.394 12.532 12.669 12.808 12.946 13.085 13.224 13.224 13.363 13.502 13.642 13.782 13.922 14.062 14.202 14.343 14.483 14.624 14.624 14.765 14.906 15.047 15.188 15.329 15.470 15.611 15.752 15.893 16.035 16.035 16.176 16.317 14.458 16.599 16.741 16.882 17.022 17.163 17.304 17 .445 17.445 17.585 17.726 17.866 18.006 18.146 18.286 18.425 18.564 18.703 18.842 18.842 18.981 19.119 19.257 19.395 19.533 19.670 19.807 19.944 20.080 20.215 20.215 20.350 20.483 20.616 20.748 20.878 21.006

TABLE 4a-9. TYPE E. CHROMEL VS. CONSTANTAN THERMOCOUPLES (Emf, absolute millivolts; temp., °C (IPTS-68); reference junctions at DOC] °C

0

10

20

30

40

50

60

70

80

90

100

-9.797 -7.631 -3.306 3.683 10.501 17.942 25.754 33.767 41.853 49.911 57.873 65.700 73.350

-9.835 -7.963 -3.811 4.329 11.222 18.710 26.549 34.574 42.662 50.713 58.663 66.473 74.104

-8.273 -4.301 4.983 11.949 19.481 27.345 35.382 43.470 51.513 59.451 67.245 74.857

-8.561 -4.777 5.646 12.681 20.256 28.143 36.190 44.278 52.312 60.237 68.015 75.608

-8.824 -5.237 6.317 13.419 21.033 28.943 36.999 45.085 53.110 61.022 68.783 76.358

- - - - - - - - - - - - - - - -I- - - - - - - - - - - - -200 -8.824 -9.063 -9.274 -9.455 -9.604 -9.719 -100 -5.237 -5.680 -6.167 -6.516 -6.907 -7.279 (-)0 0.00 -0.581 -1.151 -1. 709 -2.2M -2.787 0.00 (+)0 0.591 1.192 1.801 2.419 3.047 100 6.317 6.996 7.683 8.377 9.078 9.787 13.419 14.161 14.909 15.661 16.417 17.178 200 300 21.033 21.814 22.597 23.383 24.171 24.961 400 28.943 29.744 30.546 31.350 32.155 32.960 500 36.999 37.808 38.617 39.426 40.236 41. 045 600 45.085 45.891 46.697 47.502 48.306 49.109 700153.110 53.907 45.703 55.498 56.291 57.083 800 61. 022 61.806 62.588 63.368 64.147 64.924 900 68.783 69.549 70.313 71.075 71.835 72.593 1000 76.358

4-12

HEAT

TABLE 4a-lO. TYPE J. IRON VS. CONSTANTAN THERMOCOUPLES [Emf, absolute millivolts; temp., °C (IPTS-68); reference functions at O°C]

°C

0

10

20

30

40

------

~I~

70

-200 -7.890 -8.096 -100 -4.632 -5.036 -5.426 -5.801 -6.159 -6.499 -6.821 -7.122 (-)0 0.00 -0.501 -0.995 -1.481 -1.960 -2.431 -2.892 -3.344 (+)0 0.00 0.507 1.019 1.536 2.058 2.585 3.115 3.649 6.907 7.457 8.008 8.560 9.113 5.268 5.812 6.359 100 200 10.777 11.332 11.887 12.442 12.998 13.553 14.108 14.663 300 16.325 16.879 17.432 17.984 18.537 19.089 19.640 20.192 400 21. 846 22.397 22.949 23.501 24.054 24.607 25.161 25.716 500 27.388 27.949 28.511 29.075 29.642 30.210 30.782 31.356 600 33.096 33.683 34.273 34.867 35.464 36.066 36.671 37.280 700 39.130 39.754 40.382 41.013 41.647 42.283 42.922

80

90

100

-7.402 -3.785 4.186 9.667 15.217 20.743 26.272 31. 933 37.893

-'-7.659 -4.215 4.725 10.222 15.771 21.295 26.829 32.513 38.510

-7.890 -4.632 5.268 10.777 16.325 21.&46 27.388 33.096 39.130

TABLE 4a-11. TYPE K; CHROMEL VS. ALUMEL TH.It-3

TABLE

4d-1. VIVo

OF ELEMENTS

(Continued)

kilobars

Te at 25°C [12]

Te at -78.5°C [10, 13]

Th [2]

Ti [2,13]

Tl [12]

Tm [17]

U [2]

0 5 10 15 20 25 30 35

1.000 0.975 0.955 0.930 0.918 0.902 0.888 0.876

1.000 0.976 0.958 0.942 0.928 0.915 0.903 0.892

1.000 0.990 0.981 0.972 0.963 0.955 0.947 0.940

1.000 0.994 0.989 0.985 0.980 0.977 0.973 0.968

1.000 0.987 0.975 0.965 0.955 0.946 0.937 0.929

1.000 0.987 0.975 0.965 0.955 0.946 0.937 0.928

1.000 0.995 0.990 0.985 0.981 0.976 0.973 0.969

1.000 0.998 0.996 0.994 0.993 0.992 0.991

40

0.865

0.882

0.932

0.965

0.911

0.921

m

0

45 50 55 60 65

0.791 0.785 0.779 0.774 0.770

0.873 0.869

0.926 0.920 0.916 0.911 0.907

0.962 0.958 0.955 0.953 0.950

0.903 0.895 0.887 0.880 0.872

.....

0.903 0.900 0.896 0.894 0.890 0.888 0.885

0.947 0.945 0.944 0.942 0.940 0.938 0.936

0.865 0.859 0.852 0.846 0.840 0.834 0.829

P,

Y [16]

Yb [17]

Zn [12]

Zr [2]

........

1.000 0.986 0.973 0.961 0.950 0.940 0.930 0.921

1.000 0.962 0.928 0.889 0.874 0.852 0.832 0.814

1.000 0.992 0.988 0.978 0.967 0.960 0.952 0.944

1.000 0.994 0.987 0.982 0.975 0.970 0.965 0.959

o

0.966

......

0.913

0.797

0.937

0.954

l;:d

0.963 0.960 0.957 0.955 0.952

. ....

..·1 .

•

••

0

•

•

••

0

•

. .... . ....

•

••

0

•

•

••

0

•

0

••••

•• _0'

0

••••

..00

•

0.930 0.923 0.917 0.910 0.904

0.950 0.945 0.940 0.935 0.931

•

••

•

•

0.897 0.891 0.886 0.881 0.876 0.872 0.867

0.927 0.924 0.920 0.917 0.915 0.912 0.909

U

[13]

p

n

70 75 80 85 90 95 100

0.760 0.754 0.748 0.744 0.740 0.735 0.730

•••

0

•

..... .....

..... .... . ••

I

••

.... . ...... .. ....... ...... ..

••

I

••

..... ••

I

••

. .... ..

'"

..... ••

I

••

..... ....... ••

e.l

..

......

0.950 0.948 0.945 0.944 0.943 0.942 0.941

..

'"

. .... .....

. .... . .... ..

'"

•

...

0

..

. .......

•

••

_0'

.,

I

0

. .......

0

...

••

0

..

•

••

••

0

0

•

..... . .... . ......

. .....

..

..... .. .. ......

..... . ..... ..

......

o

~ '"d

t?:J

00 00 H

to

H

~

H

8

t- 1-':3

TABLE

0

HgSe at 25°C [2,10] 1.000

HgSe at -78.5°C [10] 1.000

5

0.991

0.991

h

j

10

0.888

0.890

i

i

15

0.872

P,

kilo bars

4d-2. V /V o

OF INORGANIC COMPOUNDS·

(Continued)

HgTe [2]

HIOa [21]

KAI(S04h·12H20 [5]

1.000

1.000

1.000

KBr 2O at 25°C [9] 1.000 1.000

KBr at -78.5°C [10] 1.000

KCI at 25°C [9] 1.000

KCI at -78.5°C [10] 1.000

0.948

0.978

0.970

0.923

0.917

0.959

0.947

0.900

0.970

0.973

0.974

0.976

0.896

0.943

0.929

0.880

0.944

0.948

0.951

0.955

0.923

0.926 n 0.804

0.932

l

m

0.933

0.856

0.800

0.915

0.918

KB~08' 4H

[5] k

20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100

0.862 0.852 0.843 0.834 0.827 0.820 0.813 0.808 0.803 0.798 0.794 0.790 0.786 0.784 0.782 0.779 0.777

0.872 0.861 0.851 0.842 0.834 0.828 0.822 0.817

.....

.... . . .... .... . ...... .. ...... .. .....

0

...... ...... ......

..

.. .. ..

0.881 0.868 0.808 0.800 0.792 0.785 0.778 0.771 0.761 0.758 0.751 0.745 0.739 0.732 0.726 0.720 0.714

• For references, see p, 4-96. Volume at 6.9 = 0.987 and at 7.1 = 0.891. ; Volume at 10.7 = 0.8. i Volume at 7.1 = 0.9. k Transition at 3.5; volumes 0.979 and 0.934. I Transition at 19.9; volumes 0.865 and 0.859. m Transition at 18.0; volumes 0.912 ad 0.807• .. Transition in this region. o Transition at 19.7; volumes 0.915 and 0.803. .. Transition in this region.

0.927 0.915 0.903 ...... •••

0.

•••

0.

•••

0.

.... . . .... . ....

.... . ...... . .. .....

....

..

...... .. ....... .. ......

0.912 0.897 0.883 0.870 0.858 ..... ..... . .... •••

0.

..• 0. •••

0

•

•••

0

..

0.844 0.832 0.821 0.811 . .... •

••

0.

. .... . .... . .... . .... ..

......

..

...

........ ........

..

........

..

. ..... ......

..

...

..

......

0

..

...... ...... 0

..

0.785 0.770 0.757 0.745 0.739 0.724 0.715 0.707 0.699 0.693 0.686 0.681 0.675 0.671 0.667 0.663

0.790 0.778 0.767 0.757 0.750 0.742 •

••

0

•

. .... . .... ...

0

...

..

......

..

...

..

......

0

..

. ...... .. ...... . ......

0

p

0.787 0.775 0.764 0.754 0.745 0.737 0.729 0.722 0.715 0.708 0.702 0.697 0.691 0.687 0.682 0.678

0.793 0.782 0.773 0.765 0.758 p.750

o

o

~ "tI ~ t;j

(fl (fl ~

t:rl ~

~ ~

8

~

h

!

~

TABLE

4d-2. VIVo

OF INORGANIC COMPOUNDS*

t

(Continued)

Cll

o

KCI03 [6]

KCI04 [6]

KCN [5]

KI at 25°C [9]

KI at -78.5°C [10]

KI03 [6]

KI04 [6]

KNaC4H406 [21]

KN03 [9]

KP03 [21]

LiCI04 [6]

0

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

5

0.973

0.978

0.970

0.965

0.967

0.984

0.990

0.975

1.000 u 0.877

0.983

0.980

0.935 0.907

0.937 0.912 t 0.805 0.789 0.774 0.760 0.746 0.733 0.722

0.970 0.958

0.981 0.972

0.953 0.935

0.861 0.845

0.967 0.954

0.964 0.948

0.947 0.938

0.964 0.955 0.948 0.940

0.919 0.905 0.894

0.830 0.817 0.803 0.791 0.780 0.770 0.761 0.752 0.745 0.737 0.730 0.724 0.719 0.714 0.710 0.705 0.700

0.941 0.930 0.920

0.918 0.907

P,

kilobars

q

*

10 15

0.944 0.927

0.959 0.942

0.945 0.921 r

8

20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100

0.912 0.898 .... .

0.926

0.807 0.795 0.783 0.775 0.768 . ....

0.802 0.785 0.770 0.756 0.743 0.730 0.718 0.708 0.698 0.690 0.682 0.676 0.670 0.665 0.660 0.655 0.650

.....

..... ..... ..... ..... ... .. .... . .... . .... . .... . .... . .... . ..... .....

..... ••

•

00

••

0

•

•

. .... . .... . .... . .... 0

••••

..... . .... •

••

0.

.....

..... . .... •••

0.

. ....

. .... . .... ......

. .... •••

0

•

•••

0

•

. .... . ....

.....

. .... ••

0

••

For references, see p. 4-96. Transition at 7.5; volumes 0.961 and 0.906. • Transition at 19.9; volumes 0.899 and 0.811. • Transition at 17.8; volumes 0.895 and 0.810. , Transition in this region. .. Transition at 3.6; volumes 0.977 and 0.887. " Transition at 16.1; volumes 0.944 and 0.928. Q

.... . . .... .... . . ....

.... . . .... . .... . .... .... . .... .

. .... •

••

0

•

. ....

. .... . .. 0.

. .... . .... . .... . ....

. ....

•••

0.

•••

0.

. .... •

••

0

•

. ....

v

. .... ••

•

0

••

••

0.

. ....

. .... . ....

•

••

.

....

0.

.....

. .... •

••

0.

. ....

. ....

. .... . ....

. ....

. .... . ....

. .... . .... ••

•

••

0

•

0

••

•

••

0.

..00.

. ....

. ....

•

••

0

•

~

t?::l

>8

4d-2. V /V o

TABLE

OF INORGANIC COMPOUNDS*

(Continued)

LiNaCr207 [21J

MgS04 [5J

NaBr at 25°C [9]

NaBr at -78.5°C [10]

NaBr03 [6J

NaCl at 25°C [9J

NaCl at -78.5°C [IOJ

NaClO3 [5J

NaClO4 [6]

NaI at 25°C [9J

NaI at -78.5°C [IOJ

NaI03 [6J

0 5

1.000 0.982

1.000 0.975

1.000 0.978

1.000 0.980

1.000 0.983

1.000 0.980

1.000 0.982

1.000 0.981

1.000 0.979

1.000 0.970

1.000 0.970

1.000 0.983

10 15 20

0.965 0.951 0.038

0.953 0.937 0.969

0.959 0.940 0.923

0.967 0.954 0.942

0.962 0.947 0.932

0.966 0.950 0.935

0.964 0.949 0.936

0.961 0.946 0.933

0.944 0.922 0.902

0.944 0.922 0.903

0.968 0.955 0.943

25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100

0.925 0.917

0.954 0.915 0.900 x 0.856 0.845 0.834 0.824 . .......

0.954 0.940 0.927 0.916 0.905 0.895 0.886 0.877 0.870 0.862 0.855 0.848 0.842 0.836 0.830 0.825

0.957 0.944 0.932 0.922 0.912 0.905

0.931

0.919 0.907 0.895 0.884 0.874 0.864 0.855 0.846 0.838 0.830 0.822 0.815 0.808 0.801 0.794 0.788

0.922 0.911 0.900 0.890 0.881 0.873

0.923 0.913 0.902 0.894

0.921

0.883 0.866 0.851 0.837 0.825 0.813 0.802 0.792 0.783 0.774 0.766 0.758 0.751 0.745 0.739 0.733

0.885 0.870 0.857 0.844 0.834 0.825

0.932

P, kilobars

w

........ .. "

...

........ ...... ....... ........ ....

e

.....

...

0

..

..

......

...... .. ...... .. ...... .. ...... ..

........ ........ ........

.."

.......

..

.."

... ...

. ..... ........

........

. .....

........

..

..

.......

...... .. ...... .. ...... .. ...... .. ........ .. ...... ..

.... ..

.." ..

...

......

...

.....

.......... .. ...... .. ....... .. ........ .. ........ .. ...... .. ........ .. ........ .. ...... .. ........ .. ........ .. ........ ........ .. .. ........ ..

........

..

......

..

..

eo

..

.. ...... ..

...

0

..

...... .. .. ...... ...... .. ..

........

..

......

..

........

...... .. .. ...... ...... .. ...... .. ...... .. .. ...... .. ...... .. ...... .. ...... .. ........ .. ........ .. ......

...... .. ...... .. ...... .. ...... .. ...... ..

..

......

.. ........

........ .. ........ .. ...... .. ...... ..

..

..

..

.......

..

...... ......

..

eo

..

o

o a:: ~

~ t';j

tn tn

tij

H

~

H

t-3 1--~

TABLE

P,

kilobars

0

4d-2. V /V o

OF INORGANIC COMPOUNDS*

NH4P04 [5]

NiS04 [21]

PbI 2 [5]

NH 2SOaH [21]

NH 4CI04 [6J

1.000

1.000

1.000

1.000

1.000

(Continued)

NH4I NH4H 2P0 4 at 25°C [21J [9J 1.000

1.000

NH4I at -78.5°C [10J

NH4IOa [6]

PbS at 25°C [2J

PbS at -78.5°C [10]

1.000

1.000

1.000

1.000 0.989 0.980 0.971 0.962 dd 0.933 0.925 0.918 0.913 0.909 0.905

cc

bb

5 10 15 20

0.981 0.965 0.951 0.939

0.983 0.967 0.953 0.940

0.897 0.878 0.863 0.850

0.979 0.963 0.948 0.935

0.971 0.948 0.927 0.910

0.982 0.966 0.952 0.940

0.832 0.807 0.781 0.767

0.967 0.941 0.920 0.901

0.986 0.973 0.961 0.950

0.983 0.969 0.956 0.945

25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100

0.877 0.867 0.857 0.848

0.886 0.861 .... .

0.838 0.827 0.818

0.923 0.913

0.895 ..... .

0.929 0.919

0.754 0.740 0.728 0.716 0.705 0.695 0.686 0.678 0.670 0.662 0.655 0.648 0.642 0.635 0.628 0.622

0.885 0.870 0.858 0.846 0.837 0.828

0.940

. .......

........

0.935 0.928 0.921 0.915 0.909 0.903 0.899 0.896 0.892 0.890 0.887 0.885 0.882 0.880 0.878 0.876

... 0.

.... . .... ......

.

........

......

0

•

.... . ••

0

••

..

.......

..

..

•

••

0

..

..

•

...

0

..

...... .. .......

•••

.... .

..

•

••

0

•

. ....

.... .

. ....

.... .

.... . . .... ..

........

. ....

.... .

.... . .......

.......

.. ..

..

...

..

......

..

...

0

•

.......

..

....

..

....... ..

. ......

......

..

..

...

0

..

.......

.... . .... .

.. ... ..... ..

•••

.......

..

.... . .... . .... .

....

00

..

....

0

..

.....

0

..

.....

0

..

0

0

..

..

.......

..

.....

..

..

...

0

..

..

......

......

..

..

...

0

..

..

.......

.....

..

....

00

..

..

......

...... ..

..

. ....

.... .

. ....

....

0

...

.... .

.. ...

0

...... .. ...

0

..

..

..

.......

...... .. ........ ...... ..

.......

..

....

00

..

....

00

..

......

..

.... .

..... •••

0

•

..... •••

0

•

.....

.........

..

......

..........

......

..

0·0

......

..

. ....... ..

..

....... .......

......

....... .....

0

..

.......

....... .....

0

..

..

.......

. ....

.....

........

('1

o

~

'"d ;t1 t;j

r:J2 r:J2

63 H

~

H

1-3

~

* For references,

see p, 4-96. Transition at 5.0; volumes 0.963 and 0.924. ee Transition at 0.5; volumes 0.997 ± and 0.856. dd Volume at 24.2 = 0.958 and at 22.3 = 0.937. bb

t

ce

TABLE

4d-2. V /V o

OF INORGANIC COMPOUNDS*

t

(Continued)

Con ~

P, kilobars

0

PbSe at 25°C [2J

PbSe at -78.5°C [10J

PbTe at 25°C [2J

PbTe at -78.5°C [10J

PCh [23J

1.000

1.000

1.000

1.000

1.000

5 10 15 20 25 30 35 40

0.983 0.967 0.955 0.945 0.937 0.930 0.925 0.922

45 50 55 60 65 70 75 80 85 90 95 100

0.892 0.886 0.881 0.875 0.870 0.865 0.861 0.856 0.852 0.848 0.843 0.840

ee

* For references,

0.986 0.974 0.962 0.951 0.941 0.931 0.924 0.916 if 0.900 0.892

.... . .... . ..... .... . .·.0 .

.... . .....

..... .....

.... .

0.984 0.970 0.960 0.950 0.943 0.937 0.933 0.930

see p. 4-96.

uu Transition at 44.1; volumes 0.925 and 0.892.

Transition at 4.5; volumes 0.967 and 0.834. Transition in this region. ii Transition at 4.9; volumes 0.970 and 0.830. I:k Transition in this region. ii

0.833 0.774

..... ..... .....

.... .

.....

RbBr at -78.5°C [10]

1.000 hh 0.830 0.811 0.794 0.777 0.762 0.748 0.735 0.722

1.000

Rb 2C 4H 40 6 [21]

RbCl at 25°C [9]

RbCl at -78.5°C [10]

RbCI0 4 [6]

1.000

1.000

1.000

1.000

jj

kk

0.830 0.811 0.795 0.780 0.765 0.752 0.740 0.728

0.831 0.812 0.796 0.782 0.770 0.758 0.748 0.740

0.717 0.706 0.696 0.687 0.678 0.670 0.663 0.657 0.650 0.645 0.640 0.635

0.733 0.726

ii

0.830 0.812 0.796 0.782 0.768 0.756 0.745 0.736

0.979 0.960 0.944 0.935 0.916 0.904

0.728 0.720

. .... . .... . ....

..... . ....

O(J

0.943 0.933 0.925 0.916 0.909 0.902 0.895 0.890 0.884 0.879 0.873 0.868

ee Transition at 44.1; volumes 0.917 and 0.893. II Volume at 42.45 = 0.916 and at 42.49 = 0.906. 1111

0.985 0.973 0.962 0.952 0.944 0.936 0.929 0.923

RbBr at 25°C [9]

0.917 0.913

..... ..... .... . ..... .... .

.... . •

,

_0'

.... .

. .... ......

..... ..... .... .

.... .

.... . .... . . ....

..... .... . .... . .... . .... .

0.711 0.701 0.692 0.683 0.675 0.668 0.661 0.655 0.650 0.645 0.639 0.634

. .... .... . ....

.

. .• 0.

. ....

. .... . .... . ....

. ....

. .... . .... . .... . .... . ....

..00

•

..... . .... •

••

0

•

. ....

0.975 0.954 0.934 0.917 0.901

::r: t.:rJ > 1-:3

TABLE

P, kilobars

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100

4d-2. V /V o

RbI at 25°C [9]

RbI at -78.5°C [10]

RbI04 [6]

RbNOa [9]

1.000

1.000

1.000

II

mm

0.832 0.807 0.783 0.762 0.743 0.725 0.710 0.695 0.683 0.672 0.661 0.651 0.643 0.635 0.628 0.621 0.615 0.609 0.605 0.600

0.834 0.811 0.790 0.774 0.759 0.745 0.735 0.724 0.715 0.706

0.978 0.959 0.943 0.930 0.918 0.907 ....... .

..... •••

0

•

.... . .... . .... . •••

0

•

.... . ..... .... . •••

0

•

.... . •••

0

•

.... . . .... . .... .,

eo

•••

.0

0

•

•

•••

. .... .....

. .... •••

0

•

. .....

OF INORGANIC COMPOUNDS*

(Continued)

Sr(CH02)2 [21]

SrS at 25°C [10]

SrS at -78.5°C [10]

SrSe at 25°C

1.000

1.000

1.000

0.978 0.956 0.937 0.920 0.904 0.889 0.875 0.863 0.851 0.841 0.832 0.823 0.815 0.808 0.802 0.796 0.792 0.787 0.783 0.780

0.983 0.966 0.953 0.941 0.931 0.921 .....

0.984 0.969 0.957 0.948 0.940 0.934 0.928 0.924 0.920 0.917

.....

.....

.....

[10]

SrSe at -78.5°C [10]

SrTe at 25°C [10]

SrTe at -78.5°C [10]

1.000

1.000

1.000

1.000

1.000

0.985 0.973 0.963 0.955 0.949 0.944 0.940 0.937 0.934 0.932

0.988 0.978 0.969 0.961 0.953 0.946 0.939 0.933 0.928 0.923

0.988 0.979 0.970 0.962 0.954 0.947 0.941 0.935 0.930 0.925

0.985 0.972 0.960 0.949 0.940 0.931 0.923 0.916 0.908 0.902

0.987 0.976 0.965 0.955 0.946 0.937 0.929 0.922 0.915 0.909

o

o

a::

'"d

~ t:z:j Ul tn

5; r-

I-l I-l

t-3 ~

'" For references, see p. 4-96. Transition at 4.0; volumes 0.965 and 0.839. "'''' Transition in this region.

II

tc.n

t

~

4d-2. V /V o

TABLE

P,

kilobars

*

OF INORGANIC COMPOUNDS*

TlBr TICI TICI TIl TIl TlBr at 25°C at -78.5°C at 25°C at -78.5°C at 25°C at -78.5°C [10] [9] [IOJ [IOJ [9J [9J

O':l

(Continued)

I

ZnS ZnS ZnTe ZnSe ZnSe ZnTe TINOa at 25°C at -78.5°C at 25°C at -78.5°C at 25°C at -78.5°C [9J [2J [IOJ [2J [IOJ [2J [IOJ

0 5 10 15 20 25 30 35

1.000 0.978 0.957 0.939 0.922 0.906 0.892 0.878

1.000 0.980 0.960 0.942 0.925 0.911 0.899 0.888

1.000 0.978 0.959 0.942 0.927 0.912 0.899 0.881

1.000 0.980 0.962 0.946 0.933 0.920 0.909 0.899

1.000 0.973 0.950 0.928 0.910 0.892 0.875 0.860

1.000 0.973 0.950 0.930 0.912 0.897 0.884 0.871

1.000 0.980 0.962 0.945 0.930 0.917 0.903 0.891

1.000 0.993 0.987 0.982 0.977 0.972 0.967 0.963

1.000 0.993 0.987 0.980 0.975 0.970 0.964 0.959

1.000 0.988 0.977 0.968 0.960 0.953 0.949 0.947 nn

00

pp

qq

40 45 50 55 60 65 70 75 80 85 90 95 100

0.867 0.857 0.847 0.837 0.829 0.821 0.813 0.805 0.798 0.792 0.786 0.780 0.774

0.880 0.872 0.866

0.875 0.864 0.854 0.844 0.835 0.827 0.820 0.813 0.807 0.801 0.795 0.790 0.785

0.890 0.882 0.875

0.847 0.833 0.822 0.810 0.800 0.790 0.781 0.773 0.766 0.760 0.753 0.746 0.740

0.860 0.850 0.841

0.880 0.870 0.861 0.853 0.846 0.840 0.834 0.828 0.823 0.818 0.814 0.809 0.805

0.958 0.955 0.951 0.948 0.945 0.942 0.938 0.936 0.933 0.930 0.928 0.926 0.924

0.954 0.949 0.945

0.938 0.933 0.928 0.924 0.920 0.915 0.910 0.905 0.901 0.897 0.893 0.890 0.886

0.940 0.937 0.935

0.932 0.925 0.920 0.914 0.908 0.902 0.897 0.892 0.886 0.881 0.875 0.870 0.866

0.922 0.916 0.910

..... •••

0.

.....

..... .... . .....

..... ..... ••

00

•

.....

. .... . ....

. .... . .... •••

0

•

. .... . .... . .... . ....

. ....

For references, see p. 4-96. "" Small transition at 37.2 . .. Volume at 37.7 = 0.946 and at 35.6 = 0.944. pp Small transition here. 'l'l Transition at 35.3: volumes 0.933 and 0.928.

.... . ··.0 . ··.0 .

.... . ••

0

••

.... .

.... . •• 0 . '

.... . •••

0

•

. .... .. '... ..00.

. .... . ....

. .... ••

0

••

..... . .... . ....

1.000 0.990 0.979 0.970 0.963 0.957 0.951 0.948

. ....

. .... . .... . .... . .... . .... . .... . .... . .... . ....

1.000 0.987 0.975 0.965 0.957 0.950 0.944 0.940

1.000 0.988 0.978 0.968 0.959 0.950 0.943 0.935

=: t%j ;>

8

TABLE

4d-3. V

H 20,

OF

IN CM 3/G

[291

Temperature, °C

P, kilobars 0

10

20

30

40

50

70

60

80

90

100

200

300

400

500

600

700

800

900

1000

- - - - - - - - - - - - - - - - - - -- -- --- --- --- --- --- --- --- --- --0 1 2 3 4 5 6 7 8 9 10 15 20 25 30 40 50 100 150 200 250

1.00013 1.00027 1.00177 1.00434 1.00781 1.01208 1.01706 1.02271 1.02900 1.0359 0.9564 0.9589 0.9616 0.9649 0.9687 0.9729 0.9774 0.9824 0.9878 0.9937 0.925 0.928 0.932 0.936 0.940 0.944 0.948 0.953 0.958 0.963 0.900 0.904 0.907 0.911 0.915 0.919 0.924 0.928 0.933 0.938 0.879 0.883 0.887 0.890 0.894 0.898 0.902 0.906 0.911 0.916 0.862 0.865 0.869 0.872 0.876 0.8S0 0.884 0.888 0.893 0.897 0.847 0.849 0.853 9.857 0.861 0.865 0.869 0.873 0.877 0.881 ....... 0.835 0.839 0.843 0.847 0.851 0.855 0.859 0.862 0.866 ....... ....... 0.826 0.830 0.834 0.838 0.842 0.846 0.849 0.853 ....... ....... ....... 0.819 0.823 0.827 0.831 0.835 0.838 0.842 ....... ....... ....... 0.809 0.813 0.817 0.821 0.825 0.829 0.833 ....... ....... ....... . ...... ....... ....... 0.780 0.784 0.787 0.791 ....... ...... ...... . ..... . ..... ...... ...... ..... 0.757 0.760

... .... ....... ....... .. ..... ....... ....... ....... .. . .... -

_

-

....... ....... ....... ....... . ...... ....... ....... ....... _

....... ....... ....... ....... ....... ....... ....... .......

....... . ...... ....... ....... ....... ....... . ...... .......

....... ....... ....... ....... ....... ....... ....... ....... ....... . ...... . ...... ....... ....... .......

....... ....... ....... . ......

* Probably supercooled with respect to

....... ....... ....... . ...... ....... .......

3565.7 4491. 1.0434 2171.0 3102.6 4028. 2638.6 0.9999 1.442 1.892 2.670 3.547 1.0811 1.2131 1.435 1.980 0.968 1.032 1.260 1. 666 1.127 0.943 0.921 0.902 0.944 1.065 1.139 ........ ........ 0.995 0.885 0.870 0.857 0.846 . ........ ......... . ........ . ........ ........ ........ 0.978 . ....... ........ 0.837 0.872 0.937 0.907 0.900 . ....... ........ 0.794 0.821 0.846 0.873 0.848 . ....... . ....... 0.762 0.783 0.806 0.826 0.814 ........ ........ 0.794 ....... . ...... . ..... ...... 0.754 0.774 0.732 0.751 0.770 0.789 ........ ........ . ...... ...... ...... ...... 0.749 . ....... ........ 0.713 0.731 ....... . ...... ...... ...... 0.700 0.715 . ....... ........ ....... ....... ...... . ..... ......... 0.681* 0.698 0.599 . ....... . ....... ....... ....... ...... . ..... ......... 0.575* 0.587 0.531* . ....... ........ . ...... . ...... . ..... ...... ......... 0.514* 0.523* ....... ....... ...... . ..... ......... 0.478* 0.483* 0.489* ........ ........ ....... ....... ...... . ..... ......... 0.454* 0.459* 0.463*

.

.

4951. 4.40~

2.348

5413. 5875. 5.163 5.863 2.722 3.097

(J

o

~ ~

........ ........

1.616

:;:0 t.:rJ [J2 [J2

J-l

........ ........ . ....... . ....... ........ ........ ........ ........ ........ ........ ........ ........ . ....... ........ . ....... ........ ........ ........ . ....... ........ . ....... ........

1.189 1.040 0.959 0.914 0.886 0.839 0.799 0.658 0.573 0.519 0.484

b:1 J-l t"4 J-l >-3 ~

ice.

t

.....:J

TABL]8

TABLE

P, kilobars

Ameripol 0-7700

Buna S 8774

Butyl Butyl Dugum tread prene

Goodrich D-402

Goodrich D-420

Goodrich D-453

4d-5. VIVo Goodrich D-453

OF RUBBERS

Hard Hard rubber rubber (new, (old, 2-3 25 yrs) yrs)

[6]

Hevea gum

Hevea tread

Hood 844 A

Roroseal 89023

Neoprene 832

Rubber A

Rubber B

Rubber C

[30J

- - --- - -- - - -- - --- --- --- --- --- --- --- --- ------ --- --- --- --0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40

1.000 0.965 0.941 0.922 0.908 0.894 0.884 0.873 0.864 0.855 0.847 0.840 0.833 ..... ..... ..... ..... ..... ..... ..... .....

1.000 0.952 0.925 0.906 0.890 0.876 0.865 0.854 0.844 0.840 0.827 0.818 0.811 ..... .....

..... ..... ..... ..... .....

......

1.000 0.937 0.912 0.895 0.880 0.868 0.857 0.847 0.838 0.830 0.822 0.815 0.809 ..... ..... ..... ..... ..... ..... ..... .....

1.000 0.956 0.929 0.910 0.895 0.882 0.872 0.863 0.856 0.849 0.843 0.839 0.934 ..... . .... ..... .....

..... . .... ..... .....

1.000 0.973 0.952 0.936 0.922 0.910 0.899 0.890 0.882 0.874 0.867 0.861 0.855 .....

1.000 0.956 0.930 0.911 0.894 0.885 0.868 0.857 0.848 0.839 0.831 0.924 0.817

.....

..... . ....

..... . .... ..... ..... ..... . ....

..... . .... ..... ..... ..... . ....

1.000 0.956 0.932 0.914 0.899 0.887 0.875 0.865 0.856 0.847 0.840 0.932 0.825 . .... . .... . .... . .... . .... . .... . .... . ....

1.000 0.872 0.950 0.933 0.918 0.906 0.895 0.885 0.877 0.869 0.862 0.856 0.850 . .... ..... . ....

. .... ..... . .... . .... . ....

1.000 0.857 0.931 0.910 0.893 0.879 0.867 0.855 0.846 0.837 0.829 0.822 0.815 . .... . .... . ....

. .... . .... . .... . .... . ....

1.000 0.968 0.944 0.925 0.909 0.895 0.883 0.871 0.860 0.851 0.842 0.834 0.826 0.819 0.812 0.806 0.800 0.795 0.790 0.886 0.882

1.000 0.966 0.943 0.924 0.907 0.893 0.880 0.868 0.858 0.849 0.840 0.832 0.824 0.816 0.810 0.803 0.797 0.792 0.787 0.782 0.778

1.000 0.945 0.914 0.892 0.873 0.857 0.845 0.833 0.822 0.813 0.805 0.797 0.790

1.000 0.945 0.921 0.903 0.888 0.875 0.863 0.853 0.843 0.835 0.826 0.819 0.812

1.000 0.953 0.929 0.910 0.894 0.881 0.870 0.860 0.850 0.841 0.833 0.825 0.818

1.000 0.948 0.913 0.891 0.873 0.859 0.847 0.936 0.826 0.817 0.810 0.803 0.796

1.000 0.950 0.923 0.903 0.886 0.872 0.859 0.848 0.837 0.827 0.818 0.810 0.802

1.000 0.983 0.955 0.931 0.912 0.898 0.874

1.000 0.977 0.941 0.918 0.900 0.887 0.874

1.000 0.974 0.937 0.910 0.892 0.877 0.855

o

o

~

"'d

~

l":l

Ul Ul

;; t-;

et-;

1-3 ~

Notes: A. Hard rubber from panel made by the Goodrich Company. It is a rubber-sulfur compound containing no inorganic fillers. The total sulfur amounts to 27.4 %, of which 0.21 % is free sulfur. Density equals 1.149 at 27°C. B. A rubber-sulfur compound containing 90 % smoked rubber and 10 % sulfur, and vulcanized 105 min at 300°F. Density = 0.990 at 25°C. C. 90.75 % pale crepe rubber, 5 % zinc oxide, 4 % sulfur, 0.25 % tetramethylthiuram disulfide. It was vulcanized 30 min at 260°F. Density = 0.990 at 27°C.

t

~

~

4-62

HEAT TABLE

P, kilobars

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100

Basalt glass

[31] 1.000 0.988 0.978 0.968 0.959 0.951 0.942 0.934 0.927 0.921 0.915 ..... ..... .....

..... ..... ..... I

••••

..... ..... .....

4d-6. VIVo

OF GLASSES

[2]

Borax glass

Quartz glass

Pyrex glass

Glass A

Glass C

Glass D

1.000 0.965 0.936 0.913 0.894 0.877 0.864 0.851 0.840 0.830 0.821 0.812 0.803 0.791 0.788 0.781 0.775 0.769 0.863 0.757 0.752

1.000 0.982 0.963 0.946 0.932 0.918 0.905 0.893 0.882 0.872 0.862 0.853 0.844 0.836 0.829 0.822 0.816 0.810 0.805 0.800 0.797

1.000 0.981 0.963 0.947 0.931 0.917 0.905 0.894 0.883 0.874 0."865 0.857 0.849 0.842

1.000 0.984 0.969 0.956 0.944 0.933 0.923 0.913 0.903 0.895 0.887 0.879 0.872 0.865 0.S59 0.853 0.847 0.841 0.836 0.830 0.825

1.000 0.988 0.975 0.964 0.954 0.945 0.935 0.927 0.918 0.910 0.902 0.894 0.887 0.880 0.873 0.867 0.862 0.856 0.861 0.846 0.841

1.000 0.983 0.967 0.953 0.940 0.930 0.921 0.912 0.904 0.897 0.890 0.883 0.876 0.870 0.865 0.859 0.853 0.847 0.842 0.837 0.833

0.~35

0.829 0.824 0.'S19 0.815 0.811 0.807

Notes: A. A potash-lead silicate of very high lead content.

C. A soda-potash-lime silicate. D. A soda-zinc borosilicate.

TABLE

P, kilobars

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40

4d-7. VIVo

OF DIMETHYLSILOXANE POLYMERS

[24]

Dimer

Trimer

Tetramer

Pentamer

Hexamer

Heptamer

Octamer

1.000 0.857 a 0.760 0.738 0.720 0.707 0.695 0.685 0.676 0.668 0.660 0.653 0.647 0.641 0.635 0.630 0.625 0.620 0.616 0.612 0.607

1.000 0.863

1.000 0.869

1.000 0.871

1.000 0.877

1.000 0.876

1.000 0.880

0.809 0.789 0.740 0.722 0.708 0.695 0.685 0.675 0.666 0.658 0.651 0.644 0.638 0.633 0.628 0.623 0.618 0.614 0.610

0.816 0.797 0.758 0.740 0.725 0.712 0.701 0.692 0.683 0.676 0.669 0.663 0.657 0.652 0.647 0.643 0.639 0.635 0.632

0.818 0.800 0.763 0.745 0.730 0.71"7

0.824 0.806 0.765 0.748 0.734 0.722 0.712 0.702 0.693 0.686 0.679 0.673 0.667 0.662 0.657 0.652 0.648 0.645 0.641

0.823 0.805 0.762 0.747 0.734 0.723 0.712 0.704 0.695 0.689 0.682 0.675 0.670 0.664 0.660 0.655 0.651 0.647 0.643

0.828 0.810 0.764 0.750 0.736 0.725 0.715 0.706 0.698 0.691 0.685 0.678 0.673 0.668 0.663 0.659 0.655 0.652 0.648

" Freezes at 3.7 j volumes 0.805 and 0.768.

O.iOn 0.697 0.6S8 0.680 0.673 0.667 0.661 0.656 0.651 0.647 0.642 0.638 0.635

4-63

COMPRESSIBILITY TABLE

4d-8. V /V o

P, kilobars

5000.65

5001.00

0 2

1.000 0.854 a 0.756 0.734 0.717 0.703 0.691 0.681 0.671 0.663 0.655 0.649 0.643 0.637 0.632 0.628 0.624 0.619 0.615 0.611 0.607

OF "DOW-CORNING FLUIDS"*

5002.00

50012.8

200100

200350

[241

2001,000

200 12,500

550112

------ --- --- --- --- --- ---

4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40

1.000 0.866

1.000 0.873

1.000 0.887

1.000 0.880

1.000 0.880

1.000 0.888

1.000 0.885

1.000 0.918

0.811 0.777 0.754 0.736 0.722 0.710 0.699 0.690 0.682 0.675 0.668 0.663 0.657 0.652 0.647 0.643 0.639 0.636 0.632

0.813 0.780 0.757 0.739 0.725 0.712 0.701 0.691 0.682 0.675 0.668 0.663 0.657 0.652 0.646 0.642 0.637 0.633 0.629

0.831 0.800 0.780 0.764 0.750 0.738 0.727 0.717 0.709 0.701 0.694 0.687 0.682 0.676 0.672 0.667 0.663 0.659 0.656

0.833 0.803 0.781 0.764 0.750 0.738 0.728 0.719 0.712 0.705 0.698 0.692 0.686 0.681 0.676 0.671 0.667 0.663 0.659

0.837 0.809 0.787 0.769 0.754 0.740 0.728 0.717 0.709 0.698 0.690 0.682 0.676 0.669 0.664 0.658 0.654 0.650 0.646

0.836 0.806 0.785 0.768 0.754 0.743 0.733 0.724 0.716 0.709 0.702 0.696 0.690 0.685 0.680 0.675 0.671 0.667 0.664

0.834 0.807 0.786 0.771 0.757 0.745 0.740 0.726 0.717 0.710 0.703 0.697 0.690 0.685 0.680 0.676 0.671 0.667 0.663

0.875 0.852 0.835 0.82) 0.807 0.795 0.785 0.776 0.767 0.759 0.752 0.745 0.739 0.733 0.727 0.722 0.718 0.714 0.710

* 500 and 200 series are primarily dimethylsiloxane polymers of varying viscosities. portion of the methyl groups replaced by phenyl groups. a Freezes at 3.9; volumes 0.796 and 0.760. TABLI':

4d-9. V /V o

OF OIL AND KF.:ROSENE

Fluorocarbons [24] P,

kilobars

Kerosene [32]

0 5 10

1.000 0.898 0.856

15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100

0.825 0.800 0.776 0.763

P,

kilobars Light

Oil

0 2 4

1.000 0.848 0.792

1.000 0.918 0.879

6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40

0.743 0.725 0.711 0.700 0.690 0.682 0.675 0.669 0.664 0.658 0.655 0.650 0.647 0.643 0.641 0.638 0.636 0.634

a

o

Freezes at 4.3; volumes 0.786 and 0.761.

550 series has a

r

~

~

TABLE

4d-10. V /V o

OF ALLOYS AND INTERMETALLIC COMPOUNDS*

Ag-Au alloys'] [14] Pressure, kilobars

0 2 4 6 8 10 12 14 16 18

20 22 24 26 28 30

AgzAl [13]

1.000 0.997 0.995 0.993 0.991 0.989 0.987 0.986 0.984 0.982 0.980 0.979 0.977 0.976 0.974 0.972

* For references see p. 4-96. tAt 30°.

Ag-Mn system [37]

75 Ag 25 Au

50 Ag 50 Au

25 Ag 75 Au

1.000 0.998 0.997 0.995 0.994 0.993 0.992

1.000 0.998 0.997 0.9Q6 o 995 0.994 0.993

1.000 0.998 0.997 0.996 0.994 0.993 0.992

..... ..... .....

. .... . ....

..

". "

.... . .... . •••

0

•

.... . •

0

•••

.... . ... " " "

••

0

"

.... .

•••

0.

..... .....

"

•

••

0

•

. .... •

••

0

••••

. "".

"

"

...

"

"

"

....

0.

.... ....

Ag 98.70 Cd 1.30 [13]

Ag 91.40 In 8.60 [37]

Ag 96.92 Mg 3.08 [37]

100 Ag

96.15 Ag 3.85 Mn

85.41 Ag 14.59 Mn

1.000 0.997 0.995 0.993 0.992 0.990 0.988 0.987 0.985 0.983 0.981 0.980 0.978 0.977 0.975 0.974

1.000 0.997 0.995 0.993 0.991 0.990 0.988 0.986 0.985 0.983 0.981 0.980 0.978 0.976 0.975 0.973

1.000 0.998 0.996 0.994 0.992 0.990 0.988 0.987 0.985 0.983 0.982 0.980 0.978 0.977 0.975 0.973

1.000 0.998 0.996 0.994 0.992 0.990 0.988 0.987 0.985 0.983 0.982 0.980 0.'978 0.976 0.975 0.973

1.000 0.998 0.996 0.994 0.992 0.990 0.988 0.986 0.984 0.982 0.980 0.978 0.977 0.975 0.973 0.971

1.000 0.998 0.996 0.993 0.991 0.989 0.987 0.985 0.983 0.981 0.979 0.977 0.975 0.973 0.972 0.970

P::: tr:l

>

"'3

TABLE

4d-lO. V /V o

OF ALLOYS AND INTERMETALLIC COMPOUNDS*

Ag-Pt system [37J

Ag-Pd system [33J Pressure, kilobars 100 Ag

79.0 Ag 21.0 Pd

48.9 Ag 51.1 Pd

29.5 Ag 70.5 Pd

0 2 4 6 8 10 12 14

1.000 0.998 0.996 0.994 0.992 0.990 0.988 0.987

1.000 0.998 0.996 0.995 0.993 0.991 0.989 0.988

1.000 0.999 0.997 0.996 0.994 0.993 0.991 0.990

1.000 0.999 0.997 0.996 0.994 0.993 0.992 0.991

16 18 20 22 24

0.985 0.933 0.982 0.980 0.978

9.986 0.985 0.983 0.982 0.981

0.988 0.987 0.986 0.984 0.983

26 28 30

0.976 0.975 0.973

0.979 0.978 0.977

0.982 0.981 0.980

(Continued)

100 Pd

100 Ag

1.000 0.998 0.996 0.994 0.992 0.990 0.988 0.987

0.990 0.988 0.987 0.986 0.985

1.000 0.998 0.997 0.996 0.995 0.994 0.993 0.992 a 0.991 0.990 0.989 0.988 0.987

0.984 0.983 0.982

0.986 0.985 0.985

92.75 Ag 7.25 Pt 1.000 0.998 0.996 0.994 0.Y92

AI-Mg system [33J AgZn [13J

Ag 5 Zn s [13J

Ag 96.44 Zn 3.56 [13J

100 Al

85.7 Al 14.3 Mg

0.988 0.987

1.000 0.998 0.996 0.993 0.991 0.989 0.987 0.985

1.000 0.998 0.996 0.993 0.992 0.989 0.987 0.985

1.000 0.998 0.996 0.994 0.992 0.991 0.989 0.987

1.000 0.1;197 0.994 0.991 0.989 0.986 0.984 0.982

1.000 0.997 0.993 0.990 0.987 0.984 0.981 0.978

0.985 0.983 0.982 0.980 0.978

0.985 0.983 0.982 0.980 0.978

0.983 0.981 0.980 0.978 0.976

0.983 0.981 0.979 0.977 0.975

0.985 0.983 0.982 0.980 0.979

0.979 0.977 0.974 0.972 0.970

0.975 0.973 0.970 0.967 0.965

0.976 0.975 0.973

0.977 0.975 0.974

0.975 0.973 0.972

0.973 0.972 0.970

0.976 0.975 0.973

0.967 0.965 0.963

0.963 0.961 0.958

0.9\J0

o

o

~

~

~

t-~

TABLE

I

4d-lO. V jVo

Ca-Mg system [36]

Pressure, kilobars 100 Ca

61.9 Ca 38.1 Mg

28.6 Ca 71.4 Mg

0 2 4 6 8 10 12 14 16 18 20 22 24

1.000 0.987 0.974 0.962 0.952 0.941 0.931 0.922 0.913 0.904 0.896 0.888 0.881

1.000 0.989 0.980 0.971 0.963 0.955 0.947 0.940 0.933 0.926 0.920 0.914 0.908

1.000 0.990 0.982 0.974 0.968 0.961 0.955 0.948 0.942 0.937 0.932 0.926 0.921

26 28

0.873 0.867

0.902 0.897

0.917 0.912

30 32 34 36 38 40

0.860 0.853 0.848 0.842 0.836 0.830

* For references see

0.892 0.887 0.882 0.877 0.873 0.869

0.907 0.903 0.899 0.895 0.891 0.888

OF ALLOYS AND INTERMETALLIC COMPOUNDS*

0.05C Carboloy 0.09 Mn 0.01 Si 999t 36.0 Ni [13] 63.88 Fe 100 Mg [37]

100 Fe

95.69 Fe 4.31 C

0.941

1.000 0.997 0.995 0.993 0.992 0.990 0.988 0.986 0.984 0.993 0.981 0.98Q 0.978

1.000 0.998 0.997 0.996 0.995 0.993 0.992 0.991 0.990 0.989 0.988 0.987 0.986

1.000 0.998 0.997 0.996 0.995 0.993 0.992 0.991 0.990 0.989 0.988 0.987 0.986

0.936 0.932

0.993 0.993

0.976 0.975

0.985 0.984

0.985 0.984

0.928

0.992

0.974

0.983

0.983

........

......

....

......

.. " ... .. ... ..... .... ...

.....

0.g45

.....

o.

...... ..

..

..

..

....

..

..

...

6

....

........

........

....

... .....

..

..

.....

..

..

o.

......

....

......

1.000 0.995 0.991 0.987 0.983 0.979 0.975 0.972 0.968 0.965 0.962 0.959 0.956

...

.....

....

....

75.10 Cd 100.00 Cd 24.90 Bi

........ ........ ........ ......... ........

...... .. ...... .. ., ..... ..

Cd-Bi system [35]

Carbon steel [37]

1.000 0.999 0.998 0.998 0.997 0.997 0.996 0.996 0.995 0.995 0.995 0.994 0.994

1.000 0.994 0.988 0.983 0.977 0.972 0.968 0.963 0.958 0.953 0.949

(Continued)

..

..

.. ... o.

1.000 0.994 0.990 0.985 0.980 0.976 0.972 0.968 0.964 0.960 0.956 0.952 0.949 m 0.928 0.925

50.05 Cd 49.95 Bi 1.000 0.994 0.989 0.983 0.978 0.974 0.970 0.965 0.961 0.957 0.953 0.949 0.946

24.40 Cd 100.00 Bi 75.58 Bi 1.000 0.994 0.988 0.983 0.978 0.973 0.968 0.964 0.959 0.955 0.950 0.946 0.942

0

q

c

0.910 0.902

0.899 0.897

0.902 0.899

n

p

r

0.905 0.902 0.899 0.897 0.895 0.892

0.884 0.880 0.877 0.874 0.872 0.870

0.863 0.860 0.857 0.854 0.852 0.850

p, 4-96. WC with 3 % Co binder. Transition in this region. m Volumes at 24.5 = 0.948 and 0.931. .. Volumes at 28.4 = 0.925 and 0.910. 0 Volumes at 24.5 ... 0.945 and 0.915. " Volumes at 28.4 = 0.901 and 0.888. q Volumes at 24.5 =- 0.941 and 0.901. r Volumes at 28.4 = 0.897 and 0.868.

t

c

1.000 0.993 0.987 0.981 0.976 0.970 0.965 0.961 0.956 0.952 0.948 0.944 0.940

o

o

~ ~

~

tr:1

w

w

ttl

H

r-

H

8

~

0.896 0.893 0.890 0.887 0.885 0.882

t

~ ~

to TABLE

4d-lO. VIVo

OF ALLOYS AND INTERMETALLIC COMPOUNDS*

Cd-Pb system [36] Pressure, kilobars

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40

(Continued)

Cd-Sn system [36]

Cd-Zn system [36]

100 Cd

50 Cd 50 Pd

100 Pd

100 Cd

75 Cd 25 Sn

50 Cd 50 Sn

25 Cd 75 Sn

100 Sn

100 Cd

1.000 0.995 0.990 0.987 0.983 0.979 0.976 0.973 0.969 0.965 0.962 0.959 0.956 0.952 0.950 0.947 0.944 0.942 0.939 0.937 0.935

1.000 0.994 0.991 0.987 0.983 0.979 0.975 0.971 0.967 0.963 0.960 0.957 0.953 0.949 0.946 0.943 0.940 0.937 0.934 0.931 0.929

1.000 0.994 0.990 0.986 0.982 0..977 0.973 0.969 0.966 0.962 0.958 0.955 0.951 0.948 0.944 0.941 0.938 0.935 0.932 0.929 0.926

1.000 0.995 0.990 0.987 0.983 0.979 0.976 0.973 0.969 0.965 0.962 0.959 0.956 0.952 0.950 0.947 0.944 0.942 0.939 0.937 0.935

1.000 0.995 0.991 0.987 0.983 0.979 0.976 0.972

1.000 0.996 0.992 0.988 0.984 0.980 0.977 0.973 0.970 0.966 0.963 0.960 0.957 0.953 0.951 0.948 0.945 0.942 0.940 0.937 0.934

1.000 0.996 0.992 0.988 0.984 0.981 0.977 0.974 0.911 0.968 0.965 0.961 0.958 0.956 0.953 0.950 0.948 0.945 0.942 0.940 0.938

1.000 0.996 0.922 0.988 0.984 0.981 0.977 0.974 0.971 0.967 0.964 0.961 0.958 0.956 0.953 0.950 0.948 0.945 0.943 0.940 0.938

1.000 0.995 0.990 0.987 0.983 0.979 0.976 0.973 0.969 0.965 0.962 0.959 0.956 0.952 0.950 0.947 0.944 0.942 0.939 0.937 0.935

* For references see

p,

4-96.

0.969

0.965 0.962 0.958 1).955 0.952 0.949 0.946 0.943 0.941 0.939 0.937 0.934

50 Cd 50 Zn 1.000 0.995 0.992 0.988 0.985 0.981 0.978 0.974 0.9 i71

0.968 0.965 0.962 0.959 0.956 0.953 0.950 0.947 0.945 0.942 0.940 0.938

100 Zn

1.000 0.996 0.993 0.990 0.987 0.984 0.981 0.977 0.975 0.972 0.969 0.966 0.964 0.961 0.958 0.956 0.954 0.951 0.949 0.947 0.945

~

t;r.j

>

t-3

TABLE

4d-IO. VIVo

Cu-Ag system [33]

Co-Fe system [33] Pressure, kilobars

OF ALLOYS AND INTERMETALLIC COMPOUNDS*

(Continued)

Cu-Au system [33]

Cu-AI system [33]

100 Co

59.06 Co 40.94 Fe

100 Fe

100 Cu

96.0 Cu 4.0 Ag

100 Cu

90.02 Cu 9.90 Al

100 Cu

93 Cu 7 Au

85 Cu 15 Au

75 Cu 25 Au

0 2 4 6 8

1.000 0.998 0.997 0.996 0.995

1.000 0.998 0.997 0.996 0.995

1.000 0.998 0.997 0.996 0.995

1.000 0.998 0.997 0.995 0.994

1.000 0.998 0.996 0.995 0.993

1.000 0.998 0.997 0.995 0.994

1.000 0.998 0.997 0.995 0.994

1.000 0.998 0.997 0.995 0.994

1.000 0.998 0.996 0.995 0.993

1.000 0.998 0.997 0.995 0.994

1.000 0.998 0.997 0.995 0.994

10 12 14 16 18

0.994 0.993 0.992 0.991 0.990

0.994 0.993 0.992 0.991 0.990

0.993 0.992 0.991 0.990 0.989

0.992 0.990 0.989 0.987 0.986

0.992 0.990 0.988 0.987 0.986

0.992 0.990 0.989 0.987 0.986

0.993 0.991 0.990 0.988 0.987

0.992 0.990 0.989 0.987 0.986

0.992 0.991 0.990 0.988 0.987

0.993 0.992 0.990 0.989 0.988

0.993 0.991 0.990 0.989 0.987

20 22 24

0.989 0.988 0.987

0.989 0.987 0.986

0.988 0.987 0.986

0.984 0.983 0.982

0.984 0.983 0.982

0,984 0.983 0.982

0.985 0.984 0.983

0.984 0.983 0.982

0.985 0.984 0,982

0.987 0.985 0.984

0.986 0.985 0.984

26 28 30

0.986 0.985 0.984

0.985 0.984 0.983

0.985 0.984 0.983

0.980 0.979 0.978

0.980 0.979 0.978

0.980 0.979 0.978

0.980 0.979 0.978

0.980 0.979 0.978

0.981 0.980 0.979

0.983 0.982 0.980

0.983 0.981 0.980

b

b

c

o

o

~ '"d :;:0 t'j W W ~

tt1

~

tot 8

~

~

* For references see b

c

p, 4-96. Slight discontinuity here. Transition in this region.

t

-1

.....

1; ~

TABLE

4d-10. VIVo

I Pressure, kilobars

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

C U3 Au [13]

1.000 0.999 0.997 0.996 0.995 0.993 0.992 0.990 0.989 0.988 0.986 0.985 0.984 0.983 0.982 0.980

'" For references see p. 4-96.

OF ALLOYS AND INTERMETALLIC COMPOUNDS'"

Cu-Cr system [37]

Cu-Ga system [33]

(Continued)

Cu-Ge system [33]

Cu-Mn system [37]

CU5Cd g R.T. [13]

100 Cu

99.818 Cu 0.182 Cr

100 Cu

95.85 Cu 4.15 Ga

100 Cu

98.29 Cu 1.71 Ge

100 Cu

95.40 Cu 4.60 Mn

90.86 Cu 9.14 Mn

1.000 0.997 0.995 0.992 0.990 0.988 0:985 0.983 0.981 0.978 0.975 0.973 0.971 0.969 0.966 0.964

1.000 0.998 0.997 0.995 0.994 0.992 0.990 0.989 0.987 0.986 0.984 0.983 0.982 0.980 0.979 0.978

1.000 0.998 0.997 0;995 0.994 0.992 0.990 0.989 0.987 0.986 0.984 0.983 0.982 0.980 0.979 0.978

1.000 0:998 0.997 0.995 0.994 0.992 0.990 0.989 0.987 0.986 0.984 0.983 0.982 0.980 0.979 0.978

1.000 0.998 0.997 0.995 0.994 0.992 0.991 0.989 0.988 0.987 0.985 0.984 0.982 0.981 0.980 0.978

1.000 0.998 0.997 0.995 0.994 0.992 0.990 0.989 0.987 0.986 0.984 0.983 0.982 0.980 0.979 0.978

1.000 0.998 0.997 0.995 0.993 0.992 0.990 0.989 0.988 0.986 0.985 0.984 0.982 0.981 0.980 0.979

1.000 0.998 0.997 0.995 0.994 0.992 0.990 0.989 0.987 0.986 0.984 0.983 0.982 0.980 0.979 0.978

1.000 0.998 0.997 0.995 0.994 0:992 0.991 0.989 0.988 0.987 0.985 0.984 0.982 0.981 0.980 0.978

1.000 0.998 0.996 0.995 0.993 0.992 0.990 0.989 0.987 0.986 0.984 0.983 0.981 0.980 0.978 0.977

~

trJ

> 8

TABLE

4d-IO. VIVo

OF ALLOYS AND INTERMETALLIC COMPOUNDS*

Cu-Ni system [33] Pressure, kilo bars

Cu-Pd system [37]

100 Cu

60 Cu 40 Ni

50 Cu 50 Ni

40 Cu 60 Ni

100 Ni

0 2 4 6 8 10

1.000 0.998 0.997 0.995 0.994 0.992

1.000 0.998 0.996 0.995 0.993 0.992

1.000 0.998 0.997 0.996 0.995 0.993

1.000 0.999 0.998 0.996 0.995 0.994

1.000 0.999 0.998 0.997 0.996 0.995

12 14 16 18 20 22 24

0.990 0.989 0.987 0.986 0.984 0.983 0.982

0.991 0.989 0.988 0.987 0.986 0.985 0.984

0.992 0.991 0.990 0.988 0.987 0.986 0.985

0.993 0.991 0.990 0.989 0.988 0.987 0.986

26 28 30

0.980 0.979 0.978

0.983 0.982 0.981

0.984 0.982 0.981

0.985 0.983 0.982

(Continued)

Cu-Pt system [37]

Cu-Si system [33] C U31S n g [13]

100 Cu

98.662 Cu 1.338 Pt

100 Cu

89.86 Cu 10.14 Si

1.000 0.998 0.996 0.995 0.994 0.993

1.000 0.998 0.997 0.995 0.994 0.992

1.000 0.998 0.996 0.995 0.993 0.992

1.000 0.998 0.997 0.995 0.994 0.992

1.000 0.998 0.996 0.995 0.994 0.992

1.000 0.998 0.996 0.994 0.992 0.991

0.990 0.989 0.987 0.986 0.984 0.983 0.982

0.991 0.990 0.988 0.987 0.986 0.984 0.983

0.990 0.989 0.987 0.986 0.984 0.983 0.982

0.991 0.990 0.989 0.987 0.986 0.985 0.984

0.990 0.989 0.987 0.986 0.984 0.983 0.982

0.991 0.990 0.988 0.987 0.986 0.985 0.983

0.989 0.987 0.985 0.984 0.983 0.981 0.980

0.980 0.979 0.978

0.982 0.980 0.979

0.980 0.979 0.978

0.982 0.981 0.980

0.980 0.979 0.978

0.982 0.981 0.980

0.978 0.976 0.974

100 Cu

95.91 Cu 4.09 Pd

1.000 0.998 0.997 0.995 0.994 0.992

0.993 0.992 0.991 0.990 0.988 0.987 0.986 0.985 0.985 0.984

C1

o

e::

"'d

~

t?'.J

U1 U1 I-;

b:l

8

I-;

~

I-;

1-3 ~

b

* For references see 6 I

p. 4-96. Slight discontinuity here. Cusp at 10.1.

t

""-l CIo:l

t

""-l

~

TABLE

4d-1O. V /V{)

OF ALLOYS AND INTERMETALLIC COMPOUNDS*

Cu-Zn system [33)

Fe-Ni alloys [37]

Pressure. kilobars

CuZn [13]

CU5Z n g {13]

100 Cu

90 Cu 10 Zn

80 eu 20 Zn

52.7 eu 47.3 Zn

6

1.000 0.998 0.997 0.,995

1.000 0.998 0.996 0.995

1.000 0.998 0.996 O.£l94

1.000 0.997 0.995 0.Jl93

1.000 0.998 0.996 0.994

1.000 0.998 0.996 0.994

8 10

0.994 0.992

0.993 0.992

0.992 0.991

0.992 0.990

0.992 0.990

0.991 0.990

0 2 4

(Continued) Fe-Si system [33)

85.58 Fe 14.42 Ni

76.16 Fe 23.84 Ni

63.0 Fe 37.0 Ni

100 Fe

94.25 Fe 5.75 Si

1.000 0.998 0.997 0.996 t 0.994 0.993

1.000 0.999 0.997 0.996

1.000 0.998 0.996 0.994

1.000 0.998 0.997 0.996

1.000 0.999 0.997 0.996

0.994 0.993

0.993 0.991

0.995 0.994

0.995 0.994

0.993 0.992 0.990 0.989 0.988 0.987 0.986 0.985 0.984 0.983

0.993 0.992 0:991 0.900 0.989 0.988 0.987 0.986 0.985 0.984

u

12 14 16 18 20 22 24 26 28 30

0.990 0.989 0.987 0.986 0.984 0.983 0.982 0.980 0.979 0.978

* For references see p. 4-96. Cusp at 6.8; volume 0.996. • Cusp at 11.0: volume 0.991.

I

0.990 0.989 0.988 0.986 0.985 0.983 0.982 0.981 0.980 0.978

0.989 0.988 0.986 0.985 0.983 0.982 0.980 0.979 0.978 0.976

0.988 0.986 0.985 0.983 0.982 0.980 0.978 0.977 0.976 0.975

0.989 0.987 0.985 0.984 0.982 0.981 0.979 0.977 0.976 0.974

0.988 0.986 0.984 0.982 0.980 0.978 0.976 0.975 0.973 0.972

0.992 0.990 0.989 0.988 0.987 0.986 0.985 0.984 0.983 0.982

0.992 0.991 0.990 0.988 0.987 0.986 0.985 0.984 0.983 0.982

0.990 0.988 0.986 0.985 0.983 0.982 0.980 0.978 0.977 0.975

~

tzj

> ~

TABLE

4d-lO. V /V o

OF ALLOYS AND INTERMETALLIC COMPOUNDS*

(Continued)

Li-Mg system (36)

In-Ph system (36)

Martensite [13]

Pressure, kilobars

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40

100 In

75 In 25 Ph

50 In 50 Ph

25 In 75 Ph

1.000 0.995 0.990 0.985 0.981 0.976 0.972 0.968 0.963 0.959 0.955 0.952 0.948 0.944 0.940 0.937 0.933 0.930 0.927 0.923 0.921

1.000 0.995 0.990 0.985 0.980 0.975 0.971 0.966 0.962 0.958 0.954 0.950 0.947 0.943 0.939 0.936 0.933 0.930 0.927 0.923 0.921

1.000 0.995 0.990 0.985 0.980 0.975 0.971 0.967 0.963 0.959 0.955 0.952 0.948 0.945 0.941 0.938 0.934 0.931 0.928 0.925 0.922

1.000 0.99'5 0.990 0.985 0.981 0.977 0.972 0.968 0.965 0.961 0.957 0.954 0.950 0.947 0.943 0.940 0.937 0.934 0.931 0.928 0.925

* For references see

100 Ph

100 Li

80 Li 20 Mg

1.000 0.995

1.000 0.982 0.967 0.954 0.940 0.927 0.915 0.904 0.892 0.882 0.872 0.862 0.853 0.845 0.835 0.828 0.820 0.813 0.807 0.800 0.794

1.000 0.987 0.975 0.963 0.952 0.941 0.931 0.921 0.911 0.902 0.893 0.885 0.877 0.869 0.862 0.855 0.848 0.841 0.835 0.830 0.825

0 ..\!I90

0.986 0.982 0.\J78

0.\:)74 0.970 0.966 0.962 0.958 0.954 0.951 0.947 0.944 0.941 0.937 0.935 0.932 0.929 0.927

60 Li 40 Mg

40 Li 60 Mg

20 Li 80 Mg

1.000 0.990 0.980 0.970 0.96J. 0.953 0.944 0.936 0.928 0.920 0.914 0.906 0.900 0.894 0.888 0.882 0.877 0.872 0.866 0.861 0.856

1.000 0.992 0.984 0.977 0.969 0.962 0.955 0.948 0.942 0.935 0.929 0.924 0.918 0.913 0.908 0.903 0.899 0.895 0.890 0.887 0.884

1.000 0.993 0.98-5 0.978 0.971 0.965 0.959 0.953 0.947 0.941 0.935 0.930 0.925 0.920 0.915 0.910 0.906 0.902 0.898 0.894 0.890

100 Mg

1.000 0.994 0.988 0.983 0.977 0.973 0.968 0.963 0.958 0.953 0.949 0.944 0.940 0.936 0.932 0.929

1.000 0.998 0.997 0.996 0.995 0.994 0.992 0.991 0.990 0.989 0.987 0.986 0.985 0.984 0.983 0.982

c

o

~ '"d

~ t."'.J

tn

tn

63 H

t'"

H

~

~

p, 4-96.

r

-.:r c.n

t

--.:t 0:>

TABLE

4d-10. V jV o

Ni-Mn system [33J Pressure, kilobars

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40

OF ALLOYS AND INTERMETALLIC COMPOUNDS*

Ni-Si system [33]

35% Ni 65% Fe [13]

100 Ni

71.0 Ni 29.0 Mn

100 Ni

1.000 0.998 0.996 0.994 0.992 0.990 0.988 0.986 0.985 0.983 0.982 0.981 0.979 0.978 0.977 0.975

1.000 0.999 0.998 0.997 0.996 0.995 0.994 0.992 0.991 0.990 0.989 0.988 0.987 0.986 0.985 0.984

1.000 0.998 0 ..997 0.995 0.994 0.993 0.991 0.990 0.989 0.987 0.986 0.985 0.983 0.982 0.981 0.979

1.000 0.999 0.998 0.·997 0.996 0.995 0.994 0.992 0.991 0.990 0.989 0·.988 0. >-3

TABLE

4d-ll. VIVo

OF ORGANIC COMPOUNDS*

(Continued)

Cyana-

n-

kilobars

mide [5]

Decane [24]

Dextrin [6]

Dextrose [6]

Diethylene glycol [27]

Diphenyl [24]

Diphenyl amine [28]

decane [24]

Ethyl ether [23]

Ethyl bromide [23]

Ethyl chloride [23]

Ethyl iodide [23]

0

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

Pressure,

n-Do-

k

2

0.985

0.892

0.980

0.990

0.949

0.964

0.964

0.800

0.859

0.910

0.849

0.877

0.964 0.948 0.935 0.9.23 0.912 0.903 0.895 0.886 0.879 0.872 0.866 0.860

0.980 0.972 0.964 0.956 0.949 0.942 0.935 0.928 0.922 0.916 0.911

0.915

0.938 0.920 0.914 0.890 0.878

0.790 0.761 0.734 0.714 0.695

0.830 0.789 0.766 0.746 0.731

0.793 0.761 0.735 0.715 0.695

0.835 0.805 0.779 0.758 0.740

.....

0.783 0.770 0.758 0.747 0.737 0.727 0.719

••

G.711

.... .

. ....

0.939 0.920 0.905 0.891 0.880 0.869 0.860 0.850 0.842 0.834 0.827 0.820 0.813 0.808 0.802 0.797 0.792 0.788 0.784

j

4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40

0.971 0.959 0.947 0.938 0.928 0.920 0.911 0.904 0.897 0.890 0.882 0.876 0.870 0.865 0.859 0.853 0.848 0.843 0.838

0.766 0.756 0.741 0.728 0.717 0.707 0.699 0.690 0.684 0.677 0.672 0.666 0.662 0.657 0.652 0.649 0.645 0.642 0.638

* For references see p. 4-96. ; Freezes.at 3.0; volumes, 0.863 and 0.789. A: Freeses at 1.65; volumes 0.916 and 0.813.

.... . .... . ••

0

••

0

•

..... ..... ..... •••

0

•

.... . .... .

.... . .... .

.... .

.... . .... . . ....

..... .... .

. ....

.... . . ....

.0'0.

. ....

.... .

. ....

.....

•••

..

••

0

•

.... .

•

,

0"

. .... . ....

..... to

•

..... ••

00

•

..... ..... . .... ..... ..... ..... ••

00

•

..... . ....

0.703 0.696 0.690 0.684 0.628 0.623 0.618 0 ..615 0.611 0.607 0.604

o o

~ '"d

::0

t'j

if! if!

I-l

to

t"i

I-l

1-:3 ~

I

--l

TABLE

4d-ll. V /V o

OF ORGANIC COMPOUNDS*

t

(Continued)

00

Pressure, kilobars

0

Eugenol [27]

Fluoranthene [24]

Fluorene [16]

Glycerin [27]

Guanidine sulfate [5]

1.000

1.000

1.000

1.000

1.000

1.000

Ethylene Ethylene glycol bromide [27] [5]

1.000 l

tane [24]

1.000

1.000

1.000

1.000

1.000

0.865 0.816

0.918 0.876

0.914 0.865

0.916 0.873

0.912 0.867

0.799 0.755 0.734

0.846

.....

0.842

2 4

0.829 0.804

0.948 0.915

0.989 0.978

0.971 0.950

0.975 0.952

0.964 0.935

6 8 10

0.782 0.765 0.751

....

.

0.967 6.957 0.947

0.931 0.915 0.901

0.933 0.917 0.902

0.912 0.893 0.877

0.818 0.810 0.803 n

0

12 14 16 18 20 22 24 26 28 30 32 34 36 38 40

0.740 0.727 0.717 0.708 0.700 0.693 0.687 0.682 0.677 0.672 0.668 0.666 0.663 0.661 0.660

0.938 0.Q30 0.923 0.916

0.890 0.879 0.869 0.860 0.852 0.844 0.837 0.830 0.824 0.818 0.813 0.808 0.805 0.801 0.798

0.890 0.879 0.868 0.859 0.850 0.842 0.835 0.829 0.824 0.819 0.815 0.812 0.810 0.809 0.808

0.863

0.792 0.786 0.780 0.775 0.770 0.766 0.762 0.757 0.754 0.750 0.747 0.744 0.741 0.738 0.735

0.675 0.665 0.655 0.646 0.638 0.630 0.623 0.616 0.610 0.604 0.591 0.594 0.590 0.586 0.583

* For references see p.

.....

..... •••

0

•

.... . •••

0

•

.... . .... . .... .

.... . .... . .... . .... . .... . .... . .... . .... . .... .

•••

0

•

a

o

•

••

m

O.QlO

0.904 0.898 0.893 0.887 0.883 0.878 0.873 0.870 0.866 0.862

4-96. Freezes at 0.5; volumes 0.967 and 0.870. m Three transitions below 4.9. " Transition at 10.3; volumes 0.803 and 0.797. '0 Freezes at 11.2; volumes 0.722 and 0.680. I

n-Hep-

3-Methyl- 2-Methyl2-Methyl3-Methylhephephepheptanol tanol-5 tanol-1 tanol-3 [25] [25] [25] [25]

..... •••

0

•

..... ..... ..... .....

.....

..... ..... ..... .....

..... .....

I

.....

=

t':J

:>

1-3

TABLE

Pressure, kilobars

n-Hexane

[26]

Cyclohexane

[24]

Methyleyclohexane

[24]

4d-ll. VIVo

n-Hexadecane

[24]

OF ORGANIC COMPOUNDS*

Hexamethylenetetramine

n-Hexyl alcohol

(Continued)

Iodoform

Isoprene

Levulose

[26]

[5]

[27]

[6]

1.000

1.000

1.000

1.000

0.977 0.955 0.937 0.922 0.908 0.896 0.885 0.875 0.865 0.857 0.848 0.841 0.833 0.827 0.820 0.815 0.809 0.804 0.799 0.794

Ethyl dldibenzyl Limonene malonate

Melamine

[24]

[27]

[5]

1.000

1.000

1.000

1.000

0.860 0.819 0.789

0.990 0.981 0.972

0.896 0.853 0.826

0.929 . ....

0.983 0.969 0.953

0.764 0.743 0.725 . ....

0.963 0.955 0.947 0.940 0.934 0.927 0.920 0.915 0.909

0.806 0.790 0.775 0.763 0.752 0.742 0.733 0.725 0.717 0.711 0.705 0.700 0.695 0.691 0.687 0.683 0.679

. ....

[5]

- -

0

1.000

1.000

1.000

2 4 6

0.876 0.823 0.790

0.862 0.825 0.799

1.000 r

p

0.886 0.840 0.810

0.828 0.803 0.783

0.980 0.962 0.947

0.918

0.786 0.767 0.751 0.737 0.725 0.715 0.706 0.698 0.690 0.684 0.677 0.672 0.666 0.660 0.655 0.650 0.646

0.768 0.755 0.744 0.735 0.725 0.717 0.710 0.703 0.697 0.692 0.698 0.682 0.678 0.674 0.670 0.666 0.663

0.935 0.925 0.915 0.906 0.898 0.890 0.883 0.876 0.870 0.863 0.857 0.851 0.845 0.840 0.836 0.831 0.827

.... .

q

8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40

•••

0

•

.... . ..... •••

0

•

.....

..... ..... ..... ..... ..... .....

.....

..... ••

00.

· ....

· .... · ....

0.747 0.729 0.715 0.704 0.694 0.685 0.678 0.672 0.665 0.660 0.655 u.650 0.645 0.641 0.637 0.633 0.630

..... •••

0

•

. .... . ....

.... . .... .

. .. ... .... . .... . .... . .... . .... . .... . .... . .... . ....

.... . .... .

. .... ..00

•

. .... . .... . .... . .... .... . •

••

0.

. .... . .... . .... . .... . ....

•

0

•••

. .... •••

o

•

.... . .... . •

0

•••

.... . .....

.

.....

•••

0

•

..... . .... . ....

. .... . .... •

••

0

•

. .... ••

0

••

. .... . ....

. ....

. .... •

••

0

•

. .... ."

eo

•

0.947 0.938 0.929 0.921 0.914 0.907 0.900 0.894 0.888 0.882 0.877 0.872 0.867 0.864 0.860 0.856 0.852

o

o

~ "tl ~

t':l

tn

in

ttl

H

e-

H

8

~

* For references see

p. 4-96. Freezes at 0.3; volumes 0.967 and 0.926. (Volume liquid = 0.977 at 0.2.) Q Transition at 7.4; volumes 0.784 and 0.757. .. Freezes at 0.4; volumes 0.970 and 0.861. II

t

00 CO

4d-ll. V IVa

TABLE

Pressure .' kilobars

o 2

I

M

Menthol [6J

1.000 0.966

I

. esitylene [24]

1.000 0.909

. T rrphenyl-

Ime[;~ine 1.000 0.974

Methyl. amme hydrochloride

OF ORGANIC COMPOUNDS*

M h I 1 et y. ene chloride [24]

[5] 1.000 0.982

1.000 0.910

IM orp h I

t'wre 1.000 0.985

4

0.941

0.825

0.952

6 8

0.921 0.905 0.888 0.875

0.802 0.784 0.764 0.756

0.935 0.919 0.906 0.893

14 16 18 20 22

24

0.861 0.849 0.837 0.826 0.816 0.806

1.000 0.970

I

R M th I ,..e y naphtha-

1[~~J

1.000 0.965

0.967 t 0.900 0.890 0.880 0.871

0.745 0.735 0.725 0.717 0.710 0.702

0.883 0.872 0.862 0.854 0.845 0.838

0.862 0.853 0.845 0.838· 0.830 0.823

0.697 0.691 0.685 0.680 0.676 0.672 0.668 0.665

0.832 0.825 0.819 0.814 0.809 0.804 0.800 0.796

0.801 0.795 0.788 0.782 0.775 0.769 0.763 0.758

0.860

0.971

0.946

0.937

II

[24] 1.000 0.926

I

s 0 etacosane [24]

n-

I 1. 000

1.000 0.883

1 . 000 0.893

0.828

0.835

0.930

0.803

0.912 0.896 0.883 0.872

0.955

* For references see p, 4-96. • Freezes at 3.4; volumes 0.871 and 0.837. .. Transition at 24.8; volumes 0.821 and 0.805. '" Freezes at 2.99; volumes 0.902 and 0.840.

0.819 0.787 0.762 0.744 v 0.690 0.678 0.669 0.660 0.652 0.645

0.959 0.949 0.939 0.930

0.928 0.912 0.899 0.887

0.915 0.896 0.881 0.868

0.813 0.800 0.788 0.777

0.750 0.725 0.707 0.695

0.922 0.914 0.907 0.900 0.893 0.886

0.877 0.867 0.858 0.849 0.841 0.833

0.856 0.845 0.835 0.826 0.818 0.810

0.768 0.760 0.751 0.744 0.737 0.731

0.683 0.674 0.665 0.658 0.650 0.645

0.861 0.851 0'.842 0.834 0.826 0.818

0.639 0.633 0.628 0.623 0.619 0.615 0.612 0.609

0.880 0.874 0.869 0.864 0.858 0.854 0.849 0.845

0.826 0.820 0.813 0.807 0.802 0.797 0.792 0.787

0.803 0.797 0.790 0.785 0.779 0.774 0.770 0.765

0.725 0.720 0.715 0.710 0.706 0.702 0.798 0.795

0.639 0.634 0.630 0.625 0.621 0.618 0.615 0.611

0.813 0.806 0.800 0.795 0.789 0.784 0.779 0.775

Transition at 5.4; volumes 0.956 and 0.904. Freezes at 12.2; volumes 0.741 and 0.701. '" Freezes at 5.4; volumes 0.741 and 0.701. I

v

0.829

x

u.

26 28 30 32 34 36 38 40

I

hTetrad I y ron-Octane sonaphthaoctane Iene [24J [27J

w

s

10 12

I

I' I N h h 0 me hydrogen ap t alene [24J

t

(Continued)

~

t::J

>1-3

TABLE

Pressure, kilobars

n-Octadecane [24]

Octanol-3 [25]

Octylene

[24]

4d-ll. V /V o Methyl oleate [27]

(Continued)

OF ORGANIC COMPOUNDS*

Oxalic acid anhydrous [5]

n-Pentane [26]

Isopentane [26]

2-Methyl- 3-Methylpentane pentane [26] [26]

Phenylenediamine [5] ort.ho-

meta-

para-

--- ---

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40

1.000 0.966 0.935 0.913 0.895 0.880 0.868 0.857 0.846 0.837 0.828 0.820 0.813 0.806 0.800 0.794 0.787 0.782 0.776 0.772 0.767

* For references see

1.000 0.916 0.871

..... .,

0

••

..... ..

'"

..... .....

..... ••

0

••

..... ..... ..... •••

0

•

..... .....

..... ..... ..... .....

1.000 0.905 0.845 0.805 0.778 0.757 0.742 0.728 0.715 0.705 0.695 0.686 0.678 0.670 0.663 0.657 0.650 0.644 0.638 0.633 0.628

1.000 0.932 •••

0

•

. .... . .... •

••

0

•

..... •

••

0

•

•

••

0

•

••

0

••

. ....

. .... . ....

. .... •

••

0

•

. .... . ....

. ....

.

.... . .... . ....

1.000 0.985 0.971 0.958 0.947 0.937 0.928 0.920 0.912 0.905 0.898 0.892 0.885 0.880 0.874 0.868 0.863 0.858 0.853 0.849 0.845

1.000 0.852 0.802 0.765 0.738 0.717 •

••

0

•

.... . ••

.

0

••

....

.... .

. .... •••

••

•

0

••

0

•

••

0

•

.... .

. ....

1.000 0.857 0.802 0.765 •

••

•

•

....

.

....

.

. ....

•

•

••

•••

•

••

0

1.000 0.863 0.816 0.784

0

0.

0

•

••

0

•

•••

0

•

•

••

0

•

•

••

0

•

•

••

0

•

. ....

. ....

. ....

. ....

. .... .... . •

••

0

•

.... . ••

0

••

.... . . ....

. ....

. .... . ....

. .... . ....

•

••

0

•

.·.0 .

···0 .

1.000 0.867 0.R13

0.780 0.755 0.736

. ....

. .... ..00 . •

••

0

•

..00

•

•

0

•

..00

••

•

..00

•

. ....

. ....

•

••

0

•

••

•••

0

•

•

. .... . .... •••

0

•

. ....

_0

••

0

•

•

.·.0 . ..00

•

•

••

•

.

....

0

1.000 0.977 0.959 0.944 0.930 0.918 0.907 0.897 0.888 0.879 0.871 0.864 0.856 0.850 0.844 0.838 0.833 0.828 0.823 0.819 0.816

1.000 0.978 0.960 0.945 0.932 0.920 0.910 0.900 0.890 0.882 0.874 0.867 0.860 0.854 0.848 0.843 0.838 0.834 0.830 0.826 0.822

1.000 0.977 0.959 0.944 0.930 0.918 0.907 0.897 0.888 0.880 0.873 0.865 0.858 0.852 0;847 0.841 0.836 0.832 0.828 0.824 0.821

o

o

~

"t1

~ t;j

tn

rf1

;-..t

to

;-..t

t"f

;-..t

'"3

to
8

TABLE

Pressure, kilobars

Triacetin [27]

Tricaproin

[26]

4d-ll. V /V o

Triethanolamine [25]

Trimethylene glycol [27]

0 2 4

1.000 0.937 0.900

1.000 0.929 0.885

1.000 0.952 .....

1.000 0.943 0.905

6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40

.....

0.855 0.832

.... .

. ....

•••

0.

••

0

••

•

.....

. ....

.... . .... .

••

0

•

..... ..... ••

00

•

..... ..... •••

0

•

.....

..... ..... ..... .....

..... .....

(Continued)

I Tricresyl thiophosphate [5]

Sodium xylene sulfonate [5] Urea [5]

ort.ho-

para-

1.000 0.973 0.951

1.000 0.970 0.947

1.000 0.982 0.968

0.933 0.919 0.906 0.895 0.885 0.875 0.866 0.858 0.850 0.843 0.837 0.830 0.824 0.818 0.813 0.808 0.803 0.799

0.927 0.911 0.897 0.885 0.873 0.862 0.852 0.843 0.835 0.827 0.820 0.813 0.807 0.802 0.797 0.792 0.788 0.784

0.890 0.878 0.867 0.856 0.847 0.838 0.830 0.823 0.815 0.809 0.803 0.797 0.792 0.787 0.782 0.777 0.773 0.769

or tho-

meta-

para-

1.000 0.982 0.966

1.000 0.979 0.961

1.000 0.986 0.972

0.951 0.938 0.927 0.916 0.906 0.897 0.889 0.881 0.874 0.867 0.862 0.855 0.850 0.845 0.839 0.835 0.831 0.827

0.946 0.933 0.921 0.910 0.900 0.892 0.883 0.871 0.869 0.862 0.857 0.851 0.845 0.841 0.837 0.832 0.829 0.825

0.960 0.959 0.949 0.930 0.922 0.913 0.907 0.900 0.894 0.888 0.882 0.877 0.872 0.868 0.864 0.860 0.856 0.852

(J()

..... •••

OF ORGANIC COMPOUNDS*

••

0

0

•

••

•••

0

•

. ....

•••

0

•

••

••

••

0

••

•••

0.

•

0.

••

. .... . ....

. .... . .... •

••

0

•

•

••

0

•

•••

0

•

. .... •

••

0

•

0

. ....

. .... .·.0 . . .... •••

0

•

. ....

.... . . ....

. .... . ..... . ....

•

.

. ....

...

0

•

.... . . ....

. ....

.... . . .... •

••

0.

•

••

0

•

....

. ....

. .... . .... . .... . .... . .... .'

0

••

o

o

~ 100

~ t'=:1 U2 U2

""'t:d"

""'t'"" ""'""3-" ~

* For references see 00

p, 4-96. Transition at 5.4; volumes 0.959 and 0.895.

t

~

01'

4-96

HEAT

References for Tables 4d-l to 4d-11 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34 35. 36. 37. 38.

Bridgman, P. W.: Proc. Am. A cad. Arts Sci. 59, 173-211 (1924). Bridgman, P. W.: Proc, Am. Acad. Arts Sci. 76, 55-70 (1948). Bridgman, P. W.: Proc. Natl. Acad. Sci. U.S. 21, 109-113 (1935). Swenson, C. A.: Phys. Rev. 99, 423-430 (1955). Bridgman, P. W.: Proc. Am. Acad. Arts Sci. 76, 71-87 (1948). Bridgman, P. W.: Proc. Am. A cad. Arts Sci. 76,9-24 (1945). Bridgman, P. W.: Proc, Am. A cad. Arts Sci. 70, 1-32 (1935). Bridgman, P. W.: Proc. Am. Acad. Arts. Sci. 62,207-226 (1927). Bridgman, P. W.: Proc. Am. A cad. Arts Sci. 76, 1-7 (1945). Bridgman, P. W.: Proc. Am. A cad. Arts Sci. 74,21-51 (1940). Bridgman, P. W.: Proc, Am. Acad. Arts Sci. 58, 165-242 (1923). Bridgman, P. W.: Phys. Rev. 60, 351-354 (1941). Bridgman, P. W.: Proc. Am. A cad. Arts Sci. 77, 189-234 (1949). Bridgman, P. W.: Proc, Am. A cad. Arts Sci. 68,95-123 (1933). Bridgman, P. W.: Proc. Am. A cad. Arts Sci. 60, 385-421 (1925). Bridgman, P. W.: Proc. Am. A cad. Arts Sci. 84, 112-129 (1955). Bridgman, P. W.: Proc. Am. A cad. Arts Sci. 83, 3-21 (1954). Bridgman, P. W.: Proc. Am. Acad. Arts Sci. 44, 255-279 (1909). Bridgman, P. W.: Proc. Am. Acad. Arts Sci. 47, 347-438 (1911). Bridgman, P. W.: J. Appl. Phys. 30, 214-217 (1959). Bridgman, P. W.: Proc. Am. A cad. Arts Sci. 76,89-99 (1948). Bridgman, P. W.: Proc. Am. A cad. Arts Sci. 67,345-375 (1932). Bridgman, P. W.: Proc. Am. A cad. Arts Sci. 49,3-114 (1913). Bridgman, P. W.: Proc. Am. A cad. Arts Sci. 77, 129-146 (1949). Bridgman, P. W.: Proc. Am. Acad. Arts Sci. 68, 1-25«1933). Bridgman, P. W.: Proc. Am. Acad. Arts Sci. 66, 185-233 (1931). Bridgman, P. W.: Proc. Am. A cad. Arts Sci. 67, 1-27 (1932). Bridgman, P. W.: Proc. Am. Acad. Arts Sci. 64, 51-73 (1929). Kennedy, George C., and William T. Holser: "Handbook of Physical Constants," G.S. .4.. Mem. 97, 373-383, 1966. Adams, L. H., and R. E. Gibson: J. Wash. A cad. Sci. 20, 213 (1930). Bridgman, P. W.: Am. J. Sci. 237,7-19 (1939). Bridgman, P. W.: Proc, Am. A cad. Arts Sci. 48, 309-362 (1912). Bridgman, P. W.: Proc. Am. A cad. Arts Sci. 84, 131-177 (1957). Bridgman, P. W.: Proc. Am. A cad. Arts Sci. 84,43-109 (1955). Bridgman, P. W.: Proc. Am. Acad. Arts Sci. 82, 101-156 (1953). Bridgman, P. W.: Proc. Am. A cad. Arts Sci. 83, 151-190 (1954). Bridgman, P. W.: Proc. Am. Acad. Arts Sci. 84, 179-216 (1957). Bridgman, P. W.: Proc. Am. A cad. Arts Sci. 84, 1-42 (1955).

4d-2. High-pressure Compressibilities;' The high-pressure 25°C isotherms presented here were calculated from dynamic equation-of-state measurements made at Lawrence Radiation Laboratory, Livermore; Los Alamos Scientific Laboratory; Ballistics Research Laboratory; and in the Soviet Union. The shock-wave data were chosen on the basis of completeness, accuracy, and absence of effects which would tend to introduce large errors into the calculations. The isotherms were all calculated from experimental data compiled in the Compendium of Shock Wave Data [1]. In dynamic high-pressure experiments, a high-pressure shock wave is passed through the material under investigation. The one-dimensional mass and momentum conservation relationships [7] (4d-l) (4d-2)

and

were used to calculate the pressure and specific volume behind the shock front from the experientally determined shock-wave velocity U 8 and the bulk material velocity (particle velocity) behind the shock front Up. Hugoniot curves were obtained from 1

Work performed under the amp ices of the U. S. Atomic Energy Commission..

4-97

COMPRESSIBILITY

a large number of experiments in which the shock strengths were varied. A Hugoniot is defined as the locus of all points that can be reached by shocking a material from a given initial state. The conversion of the Hugoniot to the 25°C isotherm is done by means of the Gruneisen equation of state P = P(V,E) in the form PH(V) - P = 'Y(V) EH(V) - E

V

(4d-3)

where the subscript H refers to conditions on the Hugoniot, and E H is calculated from the conservation relationship EH(V) = Eo

+ [PH(V) + Po] -V -o -2 V-

(4d-4)

'Y(V) is the Gruneisen gamma and is assumed to be a function of V only.

Since the

°K

isotherm and isentrope coincide,

(V P dV

E OK = -

(4d-5)

lv,

and Po K(V) can be calculated as soon as 'Yen is known. Several models have been proposed for relating 'Y(V) to the curvature of the 0 K isotherm. Some of them are contained in the formula t - 2 V (d 2jdV2)(PV2tl3) 0 K (4d-6) 'Y(V) - -3- -"2 (djdV)(PV2t/3) When t = 0, a formula derived by Slater [2] is given; t = 1 yields a formula proposed by Dugdale and MacDonald [3] and rederived by Rice [4] et al.; and t = 2 gives a relationship derived by Zubarev and Vashchenko [5]. Rice et al. have shown that the Dugdale-MacDonald form gives results that are in agreement with thermodynamic data on metals. The Dugdale-MacDonald form was used to calculate the isotherms given here. Once the 0 K curve and 'Y(V) are calculated, the 25°C isotherm is obtained by adding to the 0 K isotherm the correction obtained from the Gruneisen equation:

~P(V)

=

'Y(V) E z5°c(V) - Eo K(V)

V (25°C

=

'Y(V)

~ 'Y(V)

io K

Cv(V)

dT

y-

(4d-7)

Eo

V

Hugoniot measurements cannot be used indiscriminately for generating hydrostatic isotherms for comparison with static high-pressure work. Careful evaluations of the assumptions and possible sources of error should be made. First, it is important to note that the Gruneisen equation as it is normally derived is baeed on a model of the crystalline solid state, and its application to a Hugoniot is consistent with this derivation only if the material remains in the same solid phase all along the Hugoniot; i.e., if no phase transitions are encountered on the Hugoniot. The Gruneisen gamma is assumed to be a function of volume only, and this is a good approximation for temperatures at and above the Debye temperature. In addition, the presence of effects of finite yield strength can cause the measured Hugoniot to be offset above the hydro-

4-98

HEAT

static Hugoniot; i.e., the longitudinal stress measured in a shock-wave experiment is not identical with the hydrostatic pressure. The materials for which isotherms were calculated have a relatively low yield strength so that corrections for finite yield strength are low and can be neglected, with the exception of A1 20 3 • For this material, corrections were applied, and so the Hugoniot data used as inputs were essentially hydrostatic. The temperatures involved are of the order of magnitude or well above the Debye temperatures of the materials. Therefore, the assumption that the Gruneisen gamma is a function of volume only is valid, at least in the solid phase as presented in Table 4d-12. The only part of these calculations that merits serious scrutiny is the use of the model in the situation where melting occurs along the Hugoniot, as it does with the alkali metals at shock pressures less than 100 kilobars. For most materials, the Hugoniot is characterized by a linear relationship between shock and particle velocity. This behavior is characteristic of materials that do not experience a phase transition along the Hugoniot (except for liquids at very low pressures) and is true of almost all metals. Extrapolation of shock velocity versus particle velocity to zero pressure (Up = 0), yields a value of U. within .5 per cent of that calculated from the ordinary elastic constants for the solid metals at 1 atm. This indicates: either (1) that the change in volume and enthalpy on melting is negligible at high pressures, or (2) that the effect of the change in volume cancels the effect of the change in enthalpy in determining the Hugoniot. At high pressures, experimental evidence indicates that both alternatives are true to some extent. A careful comparison of the Bridgman [6] data and the Hugoniot data reveals no systematic differences that can be attributed to melting on the Hugoniot. Thus, the error in assuming that the isotherm derived from the experimental Hugoniot represents the solid is certainly no worse than ±.5 per cent and probably far less. _ Although the values of Gruneisen gamma calculated by the three models mentioned previously differ successively from one another by one-third at zero pressure, the correction to the Hugoniot at low pressures is small, and the uncertainty in gamma does not affect the calculated 0 K curve. At high pressure, the correction is important, but here gamma is reasonably well known. In fact, the values of the three gammas differ by less than 10 per cent in the high-pressure range. Thus, the 0 K curve is probably calculated to ±.5 per cent in pressure in the range of interest. The experimental measurements are probably precise to ±2 per cent. Consideration of the errors mentioned previously leads to the conclusion that the calculated 2.5°C isotherms are probably accurate to ±.5 per cent in pressure, and certainly better than ± 10 per cent. References for Sec. 4d-2

1. van Thiel, M.: Compendium of Shock Wave Data, Univ. Calij., Lawrence Radiation Lab. (Livermore) Rept. UCRL-50108, 1966. 2. Slater, J. C.: "Introduction to Chemical Physics." chaps. 13 and 14, McGraw-Hill Book Company, New York, 1939. 3. Dugdale, J. S., and D. MacDonald: Phys. Rev. 89, 832 (1953). 4. Rice, M. H., et al.: Solid State Phys. 6, 1 (1958). 5. Zubarev, V. N., and V. Ya. Vashchenko: Fiz.Tverd. Tela 5, 886 (1963); Soviet Phys.Solid State 5, 653 (1963). 6. Bridgman, P. W.: Phys. Rev. 46, 930 (1934). Other documents include: 7. Duvall, G. E. and G. R. Fowles: "High Pressure Chemistry and Physics," R. S. Bradley, ed., vol. 2, p. 209, Academic Press Inc., London, 1963. 8. AI'tshuler, L. V.: Uspekhi Fiz. Nauk 85, 197 (1965) [English transl.: Societ Phys.U8p. 8, 52 (1965)]. 9. Skidmore, I. C.: Appl. Mater. Research 4,131 (1965). 10. Hamann, S. D.: "Advances in High Pressure Research," R. S. Bradley, ed., vol I, p. 85, Academic Press, Inc., London, 1966.

4-99

COMPRESSIBILITY TABLE 4d~12. RELATIVE VOLUMES OF SOLIDS AT

P, kilobars

Be

Li

Mg

Na

--- ---

Ti

Ca

V

--- .--- --- ---

. ....

. ....

0.992 0.988 0.984 0.980

0.931 0.878 0.837 0.803 0.775

0.973 0.961 0.949 0.938

0.987 0.981 0.976 0.970

0.878 0.802 0.747 0.704 0.669

0.975 0.953 0.932 0.912 0.894

0.990 0.985 0.981 0.976

0.994 0.991 0.988 0.985

0.819 0.800 0.783 0.766 0.751

0.976 0.973 0.969 0.965 0.962

0.750 0.728 0.708 0.691 0.675

0.928 0.918 0.909 0.900 0.891

0.964 0.959 0.954 0.949 0.944

0.640 0.615 0.593 0.574 0.557

0.877 0.861 0.846 0.832 0.819

0.971 0.967 0.963 0.958 0.954

0.982 0.979 0.976 0.973 0.971

60 70 80 90 100

0.725 0.701 0.680 0.661 0.644

0.955 0.948 0.942 0.935 0.929

0.647 0.622 0.601 0.583 0.566

0.875 0.860 0.847 0.834 0.822

0.935 0.926 0.918 0.910 0.902

0.527 0.502 0.480 0.461 0.445

0.794 0.771 0.750 0.731 0.713

0.946 0.938 0.931 0.924 0.917

0.965 0.960 0.955 0.950 0.945

120 140 160 180 200

0.614 0.588 0.566 0.546 0.528

0.918 0.906 0.896 0.886 0.876

0.537 0.513 0.492 0.474 0.458

0.800 0.780 0.762 0.746 0.731

0.888 0.875 0.862 0.851 0.840

0.417 0.393

0.680 0.652 0.626 0.604 0.583

0.903 0.891 0.879 0.867 0.857

0.935 0.926 0.917 0.909 0.901

220 240 260 280 300

....

. .... .

0.867 0.858 0.850 0.841 0.834

.... . ..... .... .

0.717 0.705 0.693 0.681 0.671

0.830 0.820 0.811 0.802 0.794

.....

.....

0.564 0.547 0.530 0.516 0.502

0.846 0.837 0.827 0.818 0.810

0.893 0.886 0.879 0.872 0.865

0.826 0.819 0.812 0.805 0.798

.... .

0.661 0.652 0.643 0.634 0.626

0.786 0.778 0.771 0.764 0.757

..... ..... . ....

0.489 0.476 0.465

0.802 0.794 0.786 0.779 0.772

0.859 0.853 0.846 0.841 0.835

0.619 0.612 0.605 0.598 0.591

0.751 0.744 0.738 0.732 0.726

'" .. ., ... '" .,

0.765 0.758 0.752 0.746 0.740

0.829 0.824 0.819 0.813 0.808

0.576 . ....

0.713 0.700 0.688 0.677 0.667

0.725 0.712 0.700 0.688 0.677

0.796 0.785 0.774 0.764 0.755

0.666 0.657 0.647 0.638 0.630

0.746 0.737 0.729 0.721 0.713

5 10 15 20 25

0.958 0.922 0.891 0.864 0.841

30 35 40 45 50

320 340 360 380 400 420 440 460 480 500 550 600 650 700 750 800 850 900 950 1,000 1,200 1,400 1,600 1,800 2,000

.... .

.... . .... . ••

0

••

'0' .,

.... . .... . .. ... •••

0

•••

0.

•

.... . .... . ..... .... . .....

.....

K

Al

--- ---

25°C

0.792 0.786 0.780 0.774 0.768

.... .

0.755 0.742 0.730 0.719 0.708

.... .

0.698

.... .

.... .

.... . .... .

••

0

••

••

0

••

•

0

•••

.....

.... . .... . .... . . ... ... .. ,

.... . ... .. •••

•

0

... ..

.... . ... o.

.....

.... . .... . . ....

••

..0 .. 0

••••

00

•••

. ....

.... .

0.657

. ....

0

••

00

00

•••

000

••

00.

•••

0.

0000

•

••

00.

•

0000

•

0.'

0.0

••

0

0

••

0.0

•

0

0

•••

0

•••

0

0

..... ... .. ••••

0

••••

0

.000.

••

00.

..... ..... 00

••

0

•••

•••

. ....

.....

0

••

••

0

.... .

. .... . ....

.... .

..00.

00.0.

•

•••

0.000

.....

••••

o

0

•

.0.00

000.

..... ..... ..... • • • 0.'

..... .....

..... .....

..... ..... ..... ..... ..... ••

0

••

..... .....

..... ••

0

••

..... . .... 0

••

0.

. .... 0

•••

..0

,

••

. .... 0

••

00

. .... .0

••

0

. .... . ....

•

•••

0

•

•••

0

..... •

•••

0

. ....

.....

. .... . .... . .... . .... •

••

00

o'

0.'

••

0"

.0

•••

0

••••

..000

.....

0.599 0.573 0.550 0.530 0.512

I

4d-12.

RELATIVE VOLUMES OF SOLIDS AT

Cr

Co

TABLE

P,

kilobars

Ni

Cu

Zn

25°C (Continued)

Zr

Rb

Nb

Mo

--- --- --- --- --- --- --- ---

. ....

. .... . ....

0.993 0.990 0.988

0.992 0.990 0.987

09900 0.986 0.983

0.985 0.983 0.980 0.978 0.976

0.985 0.983 0.981 0.978 0.976

0.985 0.982 0.980 0.978 0.975

60 70 80 90 100

0.967 0.967 0.963 0.958 0.954

0.972 0.967 0.963 0.959 0.955

120 140 160 180 200

0.947 0.939 0.932 0.925 0.918

0.947 0.940 0.932 0.925 0.919

..... .

.....

'0' ••

0

5 10 15 20 25

0.992 0.990 0.987

30 35 40 45 50

••••

. .... 0.970 0.964

0.838 0.750 0.691 9.646 0.611

0.995 0.990 0.985 0.980 0.975

0.994 0.991 0.989 0.986

0.996 0.994 0.993 0.991

0.980 0.977 0.974 0.971 0.968

0.957 0.951 0.945 0.939 0.934

0.582 0.557 0.536 0.517 0.501

0.970 0.965 0.961 0.956 0.952

0.983 0.980 0.978 0.975 0.972

0.989 0.987 0.986 0.984 0.982

0.971 0.966 0.962 0.958 0.954

0.962 0.956 0.951 0.945 0.940

0.924 0.914 0.905 0.896 0.888

0.472 0.449 0.429 0.411 0.396

0.943 0.935 0.927 0.919 0.911

0.957 0.962 0.958 0.953 0.948

0.979 0.975 0.972 0.969 0.966

0.946 0.938 0.931 0.924 0.917

0.930 0.921 0.912 0.904 0.896

0.873 0.859 0.847 0.835 0.825

0.370 0.349 .....

0.897 0.883 0.870 0.857 0.846

0.939 0.931 0.922 0.915 0.907

0.960 0.954 0.948 0.942 0.937

.....

0.834 0.824 0.813 0.803 0.794

0.900 0.893 0.886 0.879 0.873

0.931 0.926 0.921 0.916 0.911

..... .....

0.785 0.776 0.767 0.759 0.751

0.866 0.866 0.855 0.849 0.845

0.906 0.902 0.897 0.893 0.889

0.744 0.736 0.729 0.722 0.715

0.838 0.833 0.823 0.823 0.818

0.884 0.880 0.876 0.872 0.868

0.699 0.684 0.670 0.657 0.644

0.806 0.795 0.785 0.775 0.766

0.859 0.850 0.841 0.833 0.825

0.632 0.621 0.611 0.600 0.591

0.757 0.748 0.740 0.732 0.725

0.818 0.811 0.804 0.797 0.790

•

••

0

•

..,

.0

.....

220 240 260 280 300

0.912 0.906 0.900 0.894 0.889

0.912 0.906 0.900 0.894 0.888

0.911 0.904 0.898 0.893 0.887

0.889 0.881 0.874 0.868 0.861

0.815 0.805 0.797 0.788 0.781

320 340 360 380 400

0.883 0.878 0.873 0.868 0.864

0.883 0.877 0.872 0.867 0.862

0.881 0.876 0.871 0.866 0.861

0.855 0.849 0.843 0.838 0.832

0.773 0.766 0.760 0.753 0.747

420 440 460 480 500

0.859 0.854 0.850 0.846 0.842

0.857 0.853 0.848 0.844 0.839

0.857 0.852 0.848 0.843 0.839

0.827 0.822 0.817 0.812 0.808

0.741 0.736 0.730 0.725 0.720

550 600 650 700 750

0.832 0.822 0.813 0.805 0.797

0.829 0.819 0.810 0.801 0.792

0.829 0.820 0.811 0.802 0.794

0.797 0.786 0.777 0.768 0.759

0.708 0.698 0.688 0.679 0.670

800 850 900 950 1,000

0.789 0.782 0.775 0.769 0.762

0.784 0.777 0.769 0.762 0.755

0.786 0.779 0.772 0.765 0.758

0.751 0.743 0.736 0.729 0.722

0.662 0.654 0.647 0.640 0.634

1,200 1,400 1,600 1,800 2,000

0.739 .....

0.730

0.735

0.697 0.677 0.658 0.642 0.627

0.611 0.592 0.576 0.561 0.548

0.596 0.571 0.550 0.532 0.516

0.521

2,500 3,000 3,500 4,000 4,500

....

..

....... ..

,

...

....

..

...... .. ..

,

...

"'0 ••

.......

0

••••

..

....

,

. ..... . ..... .., ..

. ...... . .... 0

.......

0

......

.... . 0

.....

0

•••

..

.......

0

.....

. ..... 0

0

,

,

.......

. .....

. ...

,

4-100

.0.0.

..

'"

.....

..... '0

•••

••

0

••

•• '0' '0

•••

..... •••

0

•

..... .... , , .... •••

0

•

'0 • • • ••

0'0

.... , .....

.....

..... .... ..... .0

•••

.....

..... . .... . .... , ..... ..

••

f"

0

..

,-

........

. ......

. .....

......

..

0.556 0.527 0"

••

0"" • •

....... 0

......

......

.....

..,

'0

. ..... 0

........

. ......

. ...... .......

. ..... ..

......

0.766 0.745 0.726 0.709 0.693 0.659 0.631 0.606

TABLE

P, kilobars

4d-12. Pd

RELATIVE VOLUMES OF SOLIDS AT

Ag

25°C (Continued)

Cd

In

Sn

Ta

Pt

Au

10 15 20 25 30

.... .

.... .

.....

0.993 0.990 0.988 0.985

0.987 0.982 0.978 0.974

0.973 0.965 0.957 0.950

0.977 0.966 0.957 0.947 0.938

0.979 0.969 0.960 0.951 0.943

0.995 0.993 0.990 0.988 0.985

0.995 0.993 0.991 0.990

0.992 0.990 0.987 0.985

35 40 45 50 60

0.983 0.981 0.978 0.976 0.972

0.970 0.966 0.963 0.959 0.952

0.943 0.936 0.930 0.924 0.912

0.930 0.922 0.915 0.907 0.894

0.935 0.928 0.920 0.914 0.901

0.983 0.981 0.978 0.976 0.972

0.988 0.986 0.985 0.983 0.980

0.982 0.980 0.977 0.975 0.970

70 80 90 100 120

0.968 0.963 0.959 0.955 0.948

0.945 0.939 0.932 0.926 0.915

0.901 0.891 0.882 0.873 0.857

0.882 0.870 0.859 0.840 0.831

0.889 0.878 0.868 0.858 0.841

0.967 0.963 0.959 0.955 0.947

0.977 0.974 0.971 0.968 0.962

0.966 0.962 0.957 0.953 0.945

140 160 180 200 220

0.941 0.934 0.927 0.921 0.914

0.905 0.895 0.886 0.877 0.869

0.843 0.829 0.817 0.806 0.796

0.814 0.800 0.786 0.774 0.762

0.825 0.811 0.798 0.786 0.775

0.939 0.932 0.924 0.917 0.911

0.956 0.951 0.946 0.941 0.936

0.938 0.930 0.923 0.917 0.910

240 260 280 300 320

0.908 0.903 0.897 0.892 0.887

0.861 0.854 0.847 0.840 0.834

0.786 0.777 0.768 0.760 0.753

0.752 0.742 0.732 0.724 0.715

0.764 0.755 0.746 0.737 0.729

0.904 0.898 0.892 0.886 0.880

0.931 0.927 0.922 0.918 0.913

0.904 0.898 0.893 0.887 0.882

340 360 380 400 420

0.882 0.877 0.872 0.867 0.863

0.828 0.822 0.816 0. 1811 0.806

0.746 0.739 0.732 0.726 0.720

0.708 0.700 0.693 0.687 0.680

0.722 0.715 0.708 0.701 0.695

0.875 0.869 0.864 0.859 0.854

0.909 0.905 0.901 0.898 0.894

0.877 0.871 0.867 0.862 0.857

440 460 480 500 550

0.859 0.854 0.850 0.846 0.837

0.800 0.796 0.791 0.786 0.775

0.715 0.709 0.704 0.699 0.687

0.674 0.668 0.663 0.657 0.645

0.689 0.684 0.678 0.673 0.661

0.849 0.844 0.839 0.835 0.823

0.890 0.886 0.883 0.880 0.871

0.853 0.846 0.844 0.840 0.830

600 650 700 750 800

0.828 0.819 0.811 0.803 0.796

0.765 0.756 0.747 0.739 0.731

0.676 0.666 0.657 0.648 0.640

0.633 0.623 0.613 0.604 0.595

0.649

0.813 0.803 0.794 0.785 0.776

0.863 0.856 0.849 0.842 0.835

0.821 0.812 0.804 0.796 0.789

850 900 950 1,000 1,200

0.789 0.782 0.776 0.770 0.747

0.724 0.717 0.710 0.704 0.681

0.633 0.626 0.619 0.613

0.587 0.580

.....

0.768 0.760 0.752 0.745 0.718

0.829 0.823 0.817 0.811 0.791

0.781 0.775 0.768 0.762 0.739

1,400 1,600 1,800 2,000

0.728 0.711

0.662 0.645 0.630 0.617

0.694 0.674 0.655

0.773 0.756 0.742 0.728

0.719 0.702 0.686

.....

.....

... ..

.....

..... .....

..... ••

0

••

..... 0.0

••

.... .

. .... . ....

..... .....

. .... . ....

. .... . ... .

..

. .... .....

••

'" ••

0

••

0"

4-101

0

••••

. ....

•

••

0

•

4-102

HEAT TABLE

P,

kilobars

4d-12.

Tl

RELATIVE VOLUMES OF SOLIDS AT

Pb

Th

LiF

25°C (Continued)

Liel

LiBr

LiI

NaF

--5 10 15 20 25

.... .

.....

. ....

. ....

. ....

0.974 0.963 0.952 0.942

0.979 0.969 0.960 0.952

0.982 0.973 0.965 0.957

0.978 0.971 0.964

0.972 0.959 0.947 0.935

." .. 0.960 0.942 0.926 0.912

0.985 0.971 0.958 0.945 0.933

0.980 0.970 0.961 0.953

30 35 40 45 50

0.933 0.924 0.915 0.908 0.900

0.943 0.936 0.928 0.921 0.914

0.950 0.942 0.935 0.929 0.922

0.958 0.952 0.946 0.940 0.934

0.925 0.914 0.905 0.896 0.887

0.898 0.886 0.874 0.863 0.853

0.921 0.910 0.899 0.888 0.878

0.944 0.936 0.929 0.921 0.914

60 70 80 90 100

0.886 0.873 0.861 0.850 0.840

0.901 0.890 0.878 0.868 0.858

0.910 0.898 0.887 0.877 0.867

0.924 0.914 0.904 0.895 0.887

0.870 0.855 0.841 0.828 0.816

0.834 0.817 0.801 0.787 0.773

0.859 0.842 0.825 0.809 0.795

0.900 0.888 0.876 0.865 0.854

120 140 160 180 200

0.822 0.805 0.790 0.777 0.765

0.841 0.825 0.810 0.797 0.785

0.848 0.832 0.816 0.802 0.789

0.871 0.857 0.843 0.831 0.820

0.794 0.774 0.756 0.740 0.725

0.750 0.729 0.711 0.694 0.679

0.767 0.743 0.720 0.699 0.680

0.834 0.816

220 240 260 280 300

0.753 0.743 0.733 0.724 0.715

0.773 0.763 0.753 0.744 0.735

0.777 0.765 0.754 0.744 0.734

0.809 0.799 0.789 0.780 0.772

0.712

0.666 0.653

0.662 0.646 0.631 0.616

320 340 360 380 400

0.707 0.700

0.727 0.719 0.712 0.705 0.698

0.725 0.716 0.708 0.700 0.693

0.764 0,756 0.749 0.742 0.735

420 440 460 480 500

.....

0.692 0.686 0.680 0.674 0.669

0.685 0.678 0.672 0.665 0.659

0.729 0.722 0.716 0.711 0.705

550 600 650 700 750

.....

0.656 0.645 0.634 0.624 0.615

0.644 0.631 0.619 0.607 0.596

0.692 0.680 0.669 0.659 0.649

800 850 900 950 1,000

.... . .... . .... .

.....

0.586 0.577 0.568 0.560 0.552

0.640

••

0

••

.....

..... •. , o. .0

•••

.0 ...

.. , .. .....

..... ..... • '0 ••

..... .....

.....

..... . .... . ....

.....

'"

..

.10

••

.....

. .... .0

•••

4-103

COMPRESSIBILITY TABLE

P,

kilobars

4d-12.

NaCl

RELATIVE VOLUMES OF SOLIDS AT

25°C (Continued)

NaBr

NaI

KF

KI

RbF

RbCl

RbBr

5 10 15 20 25

.... .

... ..

0.963 0.946 0.932 0.918

0.958 0.939 0.923 0.907

0.976 0.955 0.936 0.918 0.902

... .. 0.936 0.910 0.888 0.869

0.954 0.916 0.886 0.859 0.837

0.944 0.921 0.901 0.883

0.886 0.849 0.820 0.796

0.946 0.903 0.870 0.842 0.818

30 35 40 45 50

0.905 0.894 0.883 0.873 0.863

0.893 0.880 0.868 0.856 0.846

0.887 0.873 0.860 0.848 0.836

0.852 0.837 0.823 0.811 0.800

0.816 0.798 0.782 0.767 0.753

0.867 0.852 0.838 0.826 0.814

0.775 0.757 0.741 0.727 0.713

0.797 0.779 0.762 0.748 0.734

60 70 80 90 100

0.845 0.829 0.815 0.802 0.789

0.826 0.808 0.792 0.777 0.763

0.815 0.796 0.778 0.762 0.748

0.779 0.761 0.746 0.731 0.719

0.729 0.707 0.689 0.672 0.657

0.793 0.774 0.757 0.741 0.728

0.690 0.671 0.654 0.639 0.625

0.710 0.689 0.671 0.655 0.640

120 140 160 180 200

0.767 0.748 0.731 0.715 0.701

0.738 0.717 0.698 0.680 0.665

0.721 0.698 0.678 0.659 0.643

0.696 0.677 0.660 0.646 0.633

0.630 0.608 0.588 0.571 .....

0.703 0.681 0.663 0.646 0.631

0.602

0.615 0.594 0.575

220 240

..... .....

0.651 0.638

0.627 0.613

0.621 0.610

. ....

. ....

0.618 0.605

... ..

0

••••

..... .....

4-104

HEAT

4d-12.

TABLE

P, kilobars

RELATIVE VOLUMES OF SOLIDS AT

25°0 (Continued)

RbI

CsCl

CsBr

CSI

H 2O

MgO

A120a

Brass

5 10 15 20 25

0.954 0.917 0.886 0.860 0.838

..... 0.952 0.932 0.914 0.898

0.979 0.959 0.941 0.925 0.910

0.966 0.937 0.913 0.892 0.873

.....

· .. -.

0.737 0.707

... ,. 0.990 0.987 0.984

0.996 0.994 0.992 0.990

0.984 0.980

30 35 40 45 50

0.817 0.799 0.783 0.768 0.754

0.884 0.870 0.858 0.846 0.836

0.896 0.883 0.871 0.859 0.848

0.855 0.840 0.826 0.813 0.801

0.684 0.664 0.647 0.632 0.618

0.981 0.978 0.975 0.973 0.970

0.988 0.987 0.985 0.983 0.981

0.976 0.973 0.969 0.965 0.962

60 70 80 90 100

0.730 0.709 0.690 0.673 0.658

0.816 0.799 0.783 0.768 0.755

0.828 0.810 0.794 0.778 0.764

0.779 0.760 0.743 0.727 0.713

0.595

0.964 0.959 0.954 0.949 0.944

0.977 0.974 0.970 0.967 0.964

0.955 0.949 0.942 0.936 0.931

120 140 160 180 200

0.631 0.609 0.589 0.572 .... .

0.732 0.712 0.694 0.678 0.664

0.739 0.717 0.697 0.680 0.663

0.935 0.927 0.919 0.911 0.904

0.957 0.951 0.945 0.939 0.933

0.919 0.909 0.899 0.890 0.881

0.651

0.649 0.635 0.623 0.611 0.600

0.897 0.890 0.884 0.878 0.872

0.927 0.922 0.916 0.911 0.906

0.873 0.865 0.857 0.850 0.843

0.867 0.861 0.856 0.851 0.846

0.901 0.896 0.892 0.887 0.883

0.836 0.830 0.823 0.817 0.812

0.841 0.837 0.832 0.828 0.824

0.878 0.874 0.870 0.866 0.862

0.806 0.800 0.795 0.790 0.785

0.814 0.805 0.796 0.788 0.780

0.852 0.843 0.834 0.825 0.817

0.774 0.763 0.752 0.743 0.734

0.772 0.765 0.759

0.725 0.717

220 240 260 280 300

.... . .... .

320 340 360 380 400

... .. ... .. . , ... '" .. . , ...

. ....

420 440 460 480 500

.....

.... .

I"

0

..... .....

.....

550 600 650 700 750

..... ..... ... .. ... .. . ....

.... . . ....

•••

0

•

... .. •

0

•••

••

., ...

. , ...

0"

0

••

••••

.,

...

.... . 0

••••

0

••••

0

••••

0

••••

••••

.... . 0

••••

....

••••

,

••••

•••

0

•

•

,

•

0

•

0

••••

••

1,200

... ..

. ....

.... .

••

•

••

0.

••

.....

..... .... . .... . .... .

.... .

.... .

0

0

0.505

.,. o. . ....

••

••

... ..

0

.... .

.. , ..

.... . .... .

0.547 0.540 0.533 0.526 0.520

.... . .... .

'"

..... .....

..... .... .

800 850 900 950 1,000

..

•••

0.590 0.581 0.572 0.563 0.555

0

0.'

II

.... . .... .

.... .

.... . .... . .. , .. .... .

••

0

••

. ....

..... '"

•

I

I.

•••

•••

II

..... •

I

•••

..... . .... '"

..

0"

••

.....

..... ..... . .... ••••

0

.....

..... .... ..

'"

. .... 0

••••

. .... .

....

'"

'0

'"

'0

.....

... , . .....

.. , ..

.....

... .... .

.....

••••

0

••••

•

•

'.'

..

'.'

..

.... .

.....

0.809 0.802 0.795 0.788 0.781

.....

. ....

.....

0.757

.0

•••

..... 0'

'

"

0

••

0

••

..... ... ..

.....

4e. Heat Capacities GEORGE T. FURUKAWA AND THOMAS B. DOUGLAS

The National Bureau of Standards NORMAN PEARLMAN

Purdue University

In both Tables 4e-l and 4e-2, temperatures are given in kelvins (K);' The formula weights accompanying the symbols of the elements are based on the International Atomic Weights of 1961 (C12 = 12.0000). The heat capacity is given in calories per kelvin per gram-formula-weight (I cal = 4.1840 joules). Except for separate listings for allotropic modifications of a few elements, the heat capacity is given only for the physical state in which the element is stable at one atmosphere pressure and at the temperature in question. (For condensed gases of Table 4e-l, the values are given for the saturation pressures.) This state of the element (crystalline, liquid, or gaseous) is indicated in parentheses by the appropriate letters, except that when two or more crystalline forms of an element are known, these are distinguished as «, (3, 1', etc. In Table 4e-l the values given are for the crystalline phase unless indicated otherwise; changes in phase are identified. The asterisks (*) indicate that the values given are in the region of sharp transitions or "heat effects," and the parentheses enclose values that were obtained by extrapolation or interpolation over a broad temperature range. These values may contain large errors. No attempt was made to resolve the discrepancies in the existing data for the few elements where Tables 4e-l and 4e-2 disagree at the temperature 298.15 K. In the preparation of Table 4e-l, the results of an unpublished critical analysis of elemental substances being conducted as a part of the National Standard Reference Data System have largely been used. Wherever data more recent than the above analysis were known to have been published, they were examined for any major changes. When the authors tabulated smoothed values at even temperatures, their values were freely used with minor adjustments whenever needed. The following compilations were also used in the preparation of the table: K. K. Kelley, Contributions to the Data on Theoretical Metallurgy: XIV, Entropies of the Elements and Inorganic Compounds, U.S. Bur. Mines Bull. 592,1961; and R. Hultgren, R. L. Orr, P. D. Anderson, and K. K. Kelley, "Selected Values of Thermodynamic Properties of Metals and Alloys," John Wiley & Sons, Inc., New York, 1963. In Table 4e-2, the values cover, in general, only the temperature range of experimental measurements (or of statistical-thermodynamic calculation in the case of the 1 The name of the unit of thermodynamic temperature was changed from degree Kelvin (symbol: OK) to kelvin (symbol: K); and kelvin is now defined as the fraction 1/273.16 of the thermodynamic temperature of the triple point of water [NBS Tech. News Bull. 52, 10 (1968)]. The temperatures and temperature intervals used in the experimental measurements of heat capacity are taken to be consistent with the above definition within the accuracy of the values of heat capacity given in Table 4e-l and 4e-2,

~105

TABLE

4e-1.

MOLAR HEAT CAPACITY AT CONSTANT PRESSURE OF ELEMENTAL SUBSTANCES AT

Low

TEMPERATURES, CAL/MOLE •

K

As revised December, 1967 Element

10

15

I-'"

o 20

25

30

50

70

100

--Aluminum Al 26.9815 ..................... Antimony Sb 121.75 ................ " .... Argon A 39.948 .......................... Arsenic As 74.9216 ....................... Barium Ba 137.34 ........................ Beryllium Be 9.0122 ...................... Bismuth Bi 208.980 ...................... Boron (crystalline) B 10.811 ............... Boron (amorphous) B 10.811 .............. Bromine Brs 159.818 ..................... Cadmium Cd 112.40...................... Calcium Ca 40.08 ............ " .......... Carbon (graphite) C 12.01115 ............. Carbon (diamond) C 12.01115............. Cerium Ce 140.12 ........................ Cesium Cs 132.905 ....................... Chlorine Ch 70.906 ........... " .......... Chromium Cr 51.996 ..................... Cobalt Co 58.9332 ....................... Copper Cu 63.54 ......................... Dysprosium Dy 162.50 ................... Erbium Er 167.26 ........................ Europium Eu 151.96 ..................... Fluorine Fz 37.9968 ...................... Gadolinium Gd 157.25 .................... Gallium Ga 69.72 ........................ Germanium Ge 72.59 ..................... Gold Au 196.967 ......................... Hafnium Hf 178.49 ....................... Helium He 4.0026 ........................ Holmium Ho 164.930 ..................... n-Hydrogen Hz 2.01594 ................... n-Deuterium D z 4.02820 .................. Indium In 114.82 ........................ Iodine 12 253.8088 ........................ Iridium Ir 192.2 ......................... Iron Fe 55.847 ........................... Krypton Kr 83.80 ........................ Lanthanum La 138.91 .................... Lead Pb 207.19 .... " ............ , ....... Lithium Li 6.939 ......................... Lutetium Lu 174.97 ...................... Magnesium Mg 24.312 .................... Manganese (a) Mn 54.9380................

0.0098 0.026 0.10 0.36 0.90 1.89 (0.03) 0.12 0.44 1.11 0.0006 0.002 0.51 1.21 ........ ........ . . . . . . . . ........ (0.55) 1.72 0.22 0.69 0.05 0.15 0.004 0.01 0.0001 0.0002 1.05* 1.14* 2.64 3.91 (0.30) 0.89 (0.006) 0.014 0.014 0.037 0.013 0.044 (0.18) 0.60 (0.47) 1.60 0.93 2.08 . . . . . . . . 1.75 0.18 fL46 0.058 0.25 0.014 0.077 0.103 0.352 0.04 0.16 4.97(g) 4.97 0.64 1.57* 0.47(c) 3.32(1)

t

0.054 0.11 0.20 0.91 1.85 3.12 0.74 1.17 1.59 3.09 4.10 4.92 2.82 3.70 4.39 5.93 6.96(c) 4.97(g) 0.27 0.50 0.78 1.90 2.88 3.98 1.90 . ........ ......... ......... ........ ........ 0.003 0.006 0.009 0.04 0.12 0.43 1.80 2.32 2.86 4.29 4.99 5.52 0.006 0.009 0.006 0.02 0.08 0.26 0.02 0.01 0.01 0.04 0.12 0.33 3.04 4.30 5.36 7.97 9.23 10.42 1.23 1. 79 2.30 3.80 4.64 5.28 0.35 0.62 0.97 2.60 3.64 4.66 0.02 0.03 0.04 0.12 0.23 0.40 0.0003 0.0007 0.001 0.005 0.016 0.059 1.76 2.46 3.08 3.10 5.83 6.46 4.67 5.08 5.36 5.80 5.97 6.16 1.85 2.89 3.99 6.99 8.68 10.10 0.026 0.054 0.095 0.45 1.20 2.39 0.071 0.14 0.24 0.98 2.05 3.3t 0.110 0.230 0.405 1.47 2.60 3.82 1.34 2.20 3.04 5.52 6.97* 8.32* 5.02* 3.73 4.60 6.78* 7.35* 5.87 2.38 3.31 3.10 .6:03(~1)' ii :79(~z)' i3:S6(1) . '6:96(g)' 4.61 1.06 1.77 2.44 4.64 5.40 6.91 0.54 0.84 1.19 2.45 3.47 4.43 0.22 0.41 0.63 1.48 2.27 3.30 0.762 1.25 1. 76 3.41 4.38 5.12 0.41 0.77 1.20 2.90 4.00 4.92 4.97 4.97 4.97 4.97 4.97 4.97 2.29* 2.98 3.67 5.86 7.41 9.39 4.55 6.22 10.10(1) 4.98(g) 5.06 5.39 < -------.--------- 99.8 % para ---------------> 0.54(c) I 1.64(c) I 5.49(1) 1 . . . . . . . . . 1 5.06(g) 5.95 6.89 7.19 < ---------·--97.8 % ortho----> 0.43 1.01 1.67 2.36 2.94 4.41 5.08 5.58 0.96 2.45 3.87 5.14 6.16 8.57 9.96 10.96 (0.014) 0.038 0.094 0.22 0.43 1. 75 2.98 4.15 0.017 0.034 0.061 0.11 0.18 0.73 1.61 2.88 1.46 2.90 3.67 4.43 5.01 6.01 6.57 7.55(c) 0.26 0.80 1.48 2.20 2.81 4.41 5.12 5.64 0.66 1.68 2.58 3.37 3.94 5.12 5.57 5.85 0.015 0.043 0.095 0.17 0.28 0.97 1.86 3.19* (0.12) 0.40 0.88 1.46 2.02 3.79 4.72 5.40 0.010 0.034 0.086 0.18 0.33 1.36 2.51 3.77 0.04 0.068 0.12 0.19 0.33 1.16 2.24 3.52*

150

200

250

298.15

Ci:l

--- --- --- --4.43 5.55 4.97 4.94 ........ 1.36 5.85 0.77 0.86 11.75 5.74 5.49 0.77 0.24 6.71* 6.41* 12.20(c) 3.94 4.65 4.90 10.88* 6.21 6.99 7.81 5.26 4.44 5.64 5.55 4.97 6.34 6.07 7.03

5.16 5.82 4.97 5.43 ........ 2.41 5.99 1.45 1.55 12.85 5.94 5.91 1. 18 0.56 (6.90) 6.59* 15.95(1) 4.81 5.33 5.41 6.96 6.46

.7:iO'" 8.64 5.69 5.0:3 5.84 5.83 4.97 6.33 6.52 6.98

5.56 5.82 5.95 6.03 4.97 4.97 5.75 5.89 ........ (6.30) 3.30 3.93 6.11 6.19 2.11 2.65 2.22 2.86 14. 16(c) 18.08(1) 6.08 6.22 (6.12) (6.30) 1.63 2.04 0.99 1.46 ........ (6.44) 6.94 7.67* 15.95(1) 8. 11 (g) 5.30 5 ..56 5.75 5.95 5.68 5.84 6.73 6.73 6.59 ' 6.72 (6.48) .7:28'" 7.49 9.95* 8.86* 5.95 6.24 5.37 5.59 5.97 6.08 6.01 6.15 4.97 4.97 6.42 6.49 6.77 6.89 6.98

6.98

5.99 6.17 6.31 6.38 11.86 12.32 12.73 13.01 5.17 5.58 5.87 (6.12) 4.33 5.13 5.63 5.99 4.97(g) 4.97 4.97 4.97 6.04 ........ ........ (6.65) 6.04 6.17 6.27 6.36 4.48* 5.15 5.60 5.91 5.91 6.16 6.31 6.42 4.90 5.43 5.75 5.95 4.79 5.51 5.97 6.29

:I1 t.".:1

>

>-3

Mercury Hg 200.59 ....................... Molybdenum Mo 95.94 ................... Neodymium Nd 144.24 ................... Neon Ne 20.183 .......................... Neptunium Np (237) ..................... Nickel Ni 58.71 .......................... Niobium (columbium) Nb(Cb) 92.906 ...... Nitrogen N 2 28.0134 ...................... Osmium Os 190.2 ........................ Oxygen 0231.9988 ....................... Palladium Pd 106.4 ...................... Phosphorus (red) P 30.9738 ............... Phosphorus (white) P 30.9738 ............. Platinum Pt HJ5.09 ....................... Plutonium Pu (239) ...................... Polonium Po (210) ....................... Potassium K 39.102 ...................... Praseodymium Pr 140.907 ............. , ... Rhenium Re 186.2 ....................... Rhodium Rh 102.905 ..................... Rubidium Rb 85.47 ...................... Ruthenium Ru 101.07 .................... Samarium Sm 150.35 ..................... Scandium Sc 44.956 .................. , ... Selenium Se 78.96 ..•..................... Silicon Si 28.086 ................. " ...... Silver Ag 107.870 ........................ Sodium Na 22.9898 ....................... Strontium Sr 87;62 ....................... Sulfur (monoclinic) S 32.064 ............... Sulfur (rhombic) S 32.064 ................. Tantalum Ta 180.948..................... Technetium Tc (99) ...................... Tellurium Te 127.60 ...................... TerbiumTb 158.924 ...................... Thallium '1'1 204.37 ....................... Thorium Th 232.038 ...................... Thulium 'I'm 168.934 ..................... Tin (gray) Sn 118.69 .... " " " " " . " .... Tin (white) 118.69 .............. '" ...... Titanium Ti 47.90 ........................ Tungsten W 183;80 ....................... Uranium U 238.03 ....................... Vanadium V .50.942 ...................... Xenon Xe 131.30 ........................ Ytterbium Yb 173.04 ............ '" ...... Yttrium Y 88.905 ........................ Zinc Zn 65.37 ............................ Zirconium Zr 91.22 .......................

1.12 0.010 1.26 1.2.'5

1.85 0.024 1.79 2.85

2.52 0.050 2.45* 4.37(c)

3.04 0.099 2.85 8.44(1)

0.024 0.050 (1.06)

0.043 0.12 2.87

0.077 0.24 4.50

0.14 0.42 6.50

(0.60) 0.050

1.59 0.12

3.27(Cl) 0.24

'0:06" .

0.17

0.36

0.65

1.51 2.02

2.34 3.18

3.08 4.36 0.32 0.14 4.49 0.084 2.40 (0.29) 1.17 0.057 0.733 1.44

........ ........ ......... .........

........ ........ ......... .........

........ ........ .........

5.30(C2) 0.41

.........

........ ........ ......... ......... ........ ........ ......... ......... 0.66 0.99

........ ........ 0.15 0.016 1. 73 (0.010) 0.63* (0.038) (0.18) 0.0018 0.044 0.14 0.17 (0.10) (0.10) 0.050

(0:2ii' . (0.12) (0.81) 0.16 0.47 (0.16) 0.22 0.015 0.011 0.084 0.028 1.94 0.35 (0.055) 0.039 0.03

0.033 2.95 0.022 1.35* (0.087) 0.4.'5 0.0073 0.160 0.42 0.57 (0.31) 0.31 0.15

0.067 3.83 0.042 1.77 (0.17) 0.83 0.0023 0.394 0.88 1.14 (0.61) 0.61 0.34

0.62 0.47 1.59 0.52 1.32 0.50 0.64 0.036 0.032 0.31 0.052 3.24 1.05 0.19 0.17 0.10

1.09 1.07 2.40 1.11 2.54 0.89 1.11 0.079 0.077 0.73 0.087 4.00 1.89 0.45 0.42 0.25

......... (0.86) 0.86 0.62 1.57 1.85 3.18 1.80 3.93* 1.24 1.65 0.15 0.17 1.31 0.13 4.73 2.70 0.70 0.77 0.45

3.53 0.18 3.39

......... 0.23 0.65 8.26(Cl)

4.76 0.90 5.16

5.36 1.92 (5.9!!)

0.96 1.88 9.92(C2)

1.97 3.02 13.4(1)

.......... ........

6.19 5.80 3.21 4.52 (6.36) (6.77) 4.97(g) 4.97 3.28 4.17 6.96(g)

6.52(c) 5.15

6.78(1) 5.50

6.69 5.68

4.97

4.97

4.97

5.37 5.52 6.96

5.83 5.77 6.96

........ ........ (6.57)

........ . ....... ........ (7.0) 4.62 5.10 6.96

6.23 5.90 6.96 (S.90) 11.0(ca) 12.7(1) 6.96(g) 6.96 6.96 6.96 6.98 7.02 0.67 1.96 3.10 4.26 5.79 6.06 6.21 5.30 ......... ......... . . . . . . . . ........ ........ ........ ........ 4.98 5.63 .i:03"·· 2.56 4.65 6.05 3.68 5.47 5.83 6.19 ......... ......... ........ 4.56* 6.34* 7.06* 7.65* 5.50* ......... ......... ........ ........ . . . . . . . . . ....... . ....... (6.30) 3.70 5.01 5.52 6.44 6.22 5.89 6.70 7.06 5.07 6.18* (6.51) (6.56) (6.59) 6.22 6.42 6.30* 0.54 1. 89 3.08 4.31 6.14 5.33 5.80 6.08 0.26 1.20 2.32 4.82 .5.97 3.61 5.41 5.75 4.90 5.60 5.88 6.10 6.34 6.56 6.85 7.39 0.17 0.89 1.92 3.23 4.52 5.17 5.54 5.80 3.11 5.39 7.01 6.47 9.08* 6.28 6.74 7.06 (0.47) 1.54 2.70 3.92 5.59 6.12 5.05 5.89 1.51 2.62 3.42 4.34 5.18 5.58 5.80 6.07 0.12 0.53 1.02 1.74 4.36 2.86 3.74 4.78 1.14 2.79 3.90 4.80 5.47 5.77 5.95 6.06 2.00 3.70 4.65 5.36 6.20 6.45 6.74 5.91 . ........ ........... . ....... . ....... ........ ........ . . . . . . . . (6.30) (1.08) 1.77 2.36 4.06 4.80 5.64 3.10 5.29 1.08 1.77 2.35 3.06 3.96 4.64 5.42 5.08 1.00 2.60 3.7.'5 4.74 5.45 5.76 5.94 6.05 (5.80) '3:55" .. 4.47 2.00 5.09 5.69 5.91 6.07 6.15 2.64 5.10 6.46 7.56 7.55 8.90 11.20 6.91 3.80 5.01 5.60 5.48 6.06 6.15 6.23 6.29 2.40 4.05 4.88 5.48 5.97 6.22 6.39 6.53 5.27* 9.12* 5.84* 6.04* 6.20* 6.34* 6.39 6.46 1.58 2.69 3.70 4.67 5.44 5.81 6.02 6.16 2.20 3.68 4.53 5.35 5.85 6.20 6.30 6.08 1.13 0.27 2.17 a.43 4.68 5.32 5.72 5.97 0.32 2.57 1.39 3.83 4.90 5.37 5.66 5.81 1.93 3.75 4.59 5.32 5.87 6.17 6.40 6.61 0.23 0.89 1.83 3.07 4.41 5.16 5.64 5.97 5.19 8.04(c) 4.97(g) 4.97 5.99 6.32 6.7.'5 4.97 3.34 4.78 .5.36 5.74 6.14 6.25 6.00 6.39 1.26 2.91 6.20 4.02 5.64 6.00 6.34 4.95 1.16 2.65 4.61 3.67 5.43 5.74 5.94 6.07 0.75 2.18 3.37 4.49 5.74 5.30 6.08 5.97

::r: t?'J >1-3 o

>""d o>H

1-3 t?'J

H

tn

t ...... o

~

TABLE

4e-2.

MOLAR HEAT CAPACITY AT CONSTANT PRESSURE OF THE CHEMICAL ELEMENTS AT HIGHER THAN ROOM TEMPERATURE, CAL/MOLE .

t

K

~

o

As revised December, 1967 Element

298.15

400

500

600

Aluminum Al 26.9815 ................ Antimony Sb 121.75 ................. Argon Ar 39.948 .................... Arsenic As 74.9216 ................ , . Beryllium Be 9.0122 ................. Bismuth Bi 208.980 ................. Boron (crystalline) B 10.811 .......... Boron (amorphous) B 10.811 ......... Bromine Br2 159.818 ........... '" .. Cadmium Cd 112.40................. Calcium Ca 40.08 ................... Carbon (graphite) C 12.01115 ........ Carbon (diamond) C 12.0115 ......... Cerium Ce140.12 ................... Chlorine Cb 70.906 .................. Chromium Cr 51.996 ................ Cobalt Co 58.9332 .................. Copper Cu 63.54 ..•................. Erbium Er 167.26 ................... Europium Eu 151.96 ................ Fluorine F2 37.9968 ........... , '" .. Germanium Ge 72.59 ................ Gold Au 196.967 .................... Hafnium Hf 178.49 .................. Helium He 4.0026 ................... Holmium Ho 164.930 ................ n-Hydrogen H2 2.01594 .............. n-Deuterium D2 4.02820 ........... , . Indium In 114.82 ................... Iodine 12253.8088 ................... Iridium Ir 192.2 .................... Iron Fe 55.847 ...................... Krypton Kr 83.80 ................... Lanthanum La 138.91. .............. Lead Pb 207.19 ................... , . Lithium Li 6.939 .................... Lutetium Lu 174.97 ................. Magnesium Mg 24.312 ..... " ........

5.8l(c) 6.03(c) 4. 968(g)

6.16 6.22 4.968 6.15 4.73 6.45 3.72 3.78 8. 78(g) 6.49 6.62 2.85 2.45 6.76 8.44 6.02 6.34 6.08 6.79 6.68 7.90 5.85 6.17 6.34 4.968 6.65 6.975 6.989 6,93(e) 19.28(1) 6.14 6.54 4.968 6.81 6.56 6.62(c) 6.42 6.24

6.45 6.38 4.968 6.32 5.20 6.69(c) 4.49 4.40 8.86 6.78(c) 7.03 3.50 3.24 7.10 8.62 6.41 6.74 6.25 6.87

6.72 6.56 4.968 6.50 5.54 7.6(1) 4.99 4.88 8.91 7.10(1) 7.45 4.04 3.85 7.46 8.74 6.73 7.09 6.39 6.97 7.24 8.43 6.03 6.40 6.70 4.968 6.76 7.008 7.078 6.99 8.98 6.41 7.66 4.968 7.13 7.02(c) 7.06 6.50 6.80

5.89(a)

3.93(c) 6.20(c) 2.65(c) 2.86(c) 18.09(1) 6.20(c) 6.26(a)

2.04(c) 1.46(c) 6.44(P)

8. 11 (g) 5.58(c) 5.93(a)

5.84(e) 6.71(e) 6.48(c) 7.49(g) 5.58(c) 6.06(c) 6.15(a)

4.968(g) 6.49(a)

6.892(g) 6.978(g) 6.39(c) 13.01(c) 6.00(c) 5.97(a)

4.968(g) 6.65(P)

6.32(c) 5.78(e) 6.40(c) 5095(c)

*

8.21 5.95 6.29 6.52 4.968 6.74 6.993 7.018 7.03(1) 8.95(g) 6.27 7.10 4.968 6.97 6.79 7.20(1) 6.46 6.52

700

800

4.44 4.31 7.84 8.82 7.00

7.37(c) 7.15(c) 4.968 7.02(a) 6.06 7.6(1) 5.56 5.57 8.97 7.10 7. 86(fj) 4.74 4.66 8.25 8.88 7.22

7.42(a)

7.75(P)

6.52 7.11 7.52 8.59 6.10 6.51 6.88 4.968 6.80 7.035 7.171 6.96 9.00 6.55 8.27 4.968 7.29 7.25(1) 6.93 6.61 7.08

6.62 7.27 7.88 8.71(g) 6.19 6.65 7.06 4.968 6.95 7.078 7.288 6.93(1) 9.02(g) 6.69 9.07 4.968

7.00 6.88 4.968 6.74 5.82 7.6 5.32 5.26 8.94 7.10 7.87(a)

00

1000

7.59(1) 7.50(1) 4.968 6.54(c) 5.95 6.05 9.01(g) 7.10(1) 9.32(P)

5.15 5.16 9.14(P) 8~"96

7.66 8.84 6.82 7.67 9.09(e)

1200

7.59(1) 7.50(1) 4.968

1500

4.968

4.968

4.968

......... ......... ......... .......... 6.26 6.39 4.968(g) 7-.4(1) 5.43 5.60(c) 9.35(1) 9.01(g) 8.48 10.33 7.00(e) 8.18 9.11(1)

6.67 6.75

7.12(c) 7.07(c)

4.968

4.968 5.008(g) 5.86

......... 5.67

4.968 5.219 5.97

3000

4.971(g) 4. 968(g) 5.020(g)

4.969(g) 5.796(g) 6.06(c)

.........

......... .........

7.358(g)

......... .........

6.01O(g)

5. 10 (g)

5.61

6.74(g)

4.968

4.968

4.968(g)

6.60(1) 7.0(1)

6.86(e) 7.13(c)

6.96 4.968

7.24 8.13(')') 4.968

7.65(c) 8.73(')') 4.968

7.03 6.89 7.24 7.8(1)

6.88(1) 6.87(1) 7.85 7.8(1)

.........

7.79(a)

4.968 8.58 7.401 7.824

= >tr:l

9.68(e) 9.50(8) 7.5(1) 9. 14(e)

6.50 6.89 7.43 4.968 7.61 7.215 7.557

4.968 1O.69(a) 7.706 8.164

8. 162(g) 8.568(g)

......... ......... ......... ......... 13.01(a)

2500

......... ......... . ........

7.45(P)

7.17 6.92 6.79 7.36(c)

2000

9.09(c) 4.968(g)

4.968

......... 4.969

5.709(g) 5. 509 (g)

4.968

4.968(g)

6.951(g) 7.925(g) 4.977

5.022(g)

8

Manganese Mn 54.9380 .............. Mercury Hg 200.59 .................. Molybdenum Mo 95.94 .............. Neodymium Nd 144.24 ............. Neon Ne 20.183 ................. , ... Nickel Ni 58.71 ..................... Niobium (columbium) Nb(Cb) 92.906 .. Nitrogen Nt 28.0134 ............... , . Osmium Os 190.2 ................... Oxygen Os 31.9988 .................. Ozone 0.47.9982 ................. , . Palladium Pd 106.4 ................. Phosphorus (red, triclinic) P 30.9738 .. Phosphorus (white) P 30.9738 ........ Platinum Pt 195.09 .................. Plutonium Pu[239] .................. Potaesium K 39.102 ................. Radon Rn [222] ..................... Rhenium Re 186.2 .................. Rhodium Rh 102.905 ................ Ruthenium Ru 101.07 ............... Samarium Sm 150.35 ................ Scandium Be 44.956 ................. Selenium (metallic) Se 78.96 •......... Silicon Si 28.086 .................... Silver Ag 107.870................... Sodium Na 22.9898 .................. Sulfur S 32.064 ..................... Tantalum Ta 180.948................ Tellurium Te 127.60 ................. Thallium TI 204.37 .................. Thorium Th 232.038 ................. Thulium Tm 168.934 ................ Tin (white) Sn 118.69 ............... Titanium Ti 47.90 ................... Tungsten (wolfram) W 183.85 ........ Uranium U 238.03 .................. Vanadium V 50.942 ................. Xenon Xe 130.30 ................... Ytterbium Yb 173.04 ................ Yttrium Y 8.905 .................... Zinc Zn 65.37 ....................... Zirconium Zr 91.22 ..................

6.28(c) 6.69(1) 5.73(c)

7.21 6.76 6.54 6.48 6.25 6.05 6.55(a) 7.24 6.88 4. 968(g) 4.968 4.968 6.23(c) 6.80 7.37 5.88(c) 6.18 6.09 6.96(g) 7.07 6.99 5.90(c) 5.99 6.09 7.02(g) 7.20 7.43 9.38(g) 10.46 11.30 6.21(c) 6.49 6.35 5.07(c) 5.54 5.85 5.70(fJ) 6.29(1) 6.29(1) 6. 18(c) 6.31 6.44 7. 64(a) 8.03(fJ) 8.53(')') 0.70(c) 7.53(1) 7.34 4.968(g) 4.968 4.968 6.16(c) 6.22 6.32 5.97(c) 6.21 6.45 5.75(c) 5.82 5.91 7.06(a) 7.93 8.94 6.IO(a) 6.29 6.41 6.06(c) 6.65(c) 8.40(1) 4.78(c) 5.30 5.61 6.07(c) 6.18 6.30 6.72(c) 7.53(1) 7.30 5.40(rh) 7.73(1) 9.08 6.06(c) 6.22 6.30 6.14(c) 7.21 6.68 6.29(a) 7.03(a) 6.57 6.53(a) 7.15 6.85 6.46(c) 6.51 6.49 6.45(c) 7.32(c) 6.89 5.98(a) 6.31 6.53 5.81(c) 5.96 6.06 6.61(a) 7.10 7.65 5.95(c) 6.27 6.44 4.968(g) 4.968 4.968 6.39(a) 7.41 6.60 6.34(a) 6.49 6.65 6.07(c) 6.31 6.55 6.06(a) 6.54 6.78

7.63 6.48(1) 6.38 7.66 4.968 8.31 6.28 7.20 6.18 7.67 11.92 6.62 6.16 6.57

8. 35(a) 8.01 4.968(g) 4.968 6.48 6.55 8.14 8.71 4.968 4.968 7.37 7.44 6.38 6.48 7.51 7.35 6.27 6.63 8.06 7.88 12.70 12.37 6.76 6.90 6.50(c)

9.01(fJ)

9.21(fJ)

4.968 6.70 10.03(a) 4.968 7.88 6.68 7.82 6.54 8.34 13.15 7.17

4.968 6.93 10.65(')') 4.968 8.34 6.88(c) 8.06 6.72 8.53 13.43 7.44

10.99(0) 4.968 7.47

......... 4.968 8.63

5.039(g) 5. 252 (g) 4.968 4.968(g) 1O.46(c)

4.968 8.65(c)

4.968 10.30(1)

4.968

4.968(g)

8.33 7.00(c) 8.74 13.68(g) 7.86(c)

8.60

8.76

8.86(g)

4.968

4.968(g)

7.34 6.82 6.70 7.08 7.72 9.00(0) 8.40(e) 7.11 7.26(1) 7.20 7.13 4.968 4.968 4.968 >.968 4.968 4.968 6.43 6.566.69 7.22(c) 6.95 6.69 6.93 7.17 7.65(c) 6.04 6-42 6.23 6.75 7.11 7.24(c) 9.75 10.19 10.52 10. 82(a) 1l.22(fJ) ......... 7,46 6.57 6.75 6.96 9.14(a) 8.06 8.40(1) 5.82 6.13 5.99 6.49 6.66(c) 6.35 6.42 6.72 6.56 7.15 7.62(c) ......... 7.12 7.00 6.92 6.92(1) 7.80(1) 8.20 6.33 6.45 6.39 6.57 6.69 6.87 8.26(c) 7.73 9.00(1) 9.00(\) 7.2(1) ......... ......... ......... ......... ......... 7.45 7.76 8.06 8.67 9.28(a) 6.59 6.76 7.08 7.52 8.43(c) 7.89 6.87(1) 6.85 6.85(1) ......... ......... ......... 7.01 6.77 7.25 7.73(a) 7. 85 ({I) 7·1O(fJ) 6.16 6.27 6.37 6.59 7.14 6.80 8.31 9.08 9.99(a) 10. 26(fJ) 9.15(')') 11.45(1) 6.57 6.70 6.85 7.27 7.85 8.69(c) 4.968 4.968 4.968 4.968 4.968 4.968 7.13 7.25 7.37 7.64(a) 8.79(1) 4.97(g) 7.00 6.82 7.18 7.53 8.43(a) 7.90 6.79(c) 7.5(1) 7.5 7.5(1) 4.968(g) 4.968 7.01 7.23 7.45 7.90(a) 7.50(fJ) 7. 50 ({I)

9.03(g)

8.37(c)

9.00(0)

4.968

l:I1 t?:l

~

1-3

.........

6.06(g)

6.08(g)

o

~

"j

~

.........

4.968(g) 4.969(g)

o....

1-3

.... t?:l

U2

7.17

7.46(c)

5.420(g)

5.830

6. 173(g)

5.20(g)

5.32(g) 6.266(g)

7.71

8.30

9.80(c)

4.968 4.97

4.968 5.01

4.968(g) 5.16(g)

4.968

4.968

4.969(g)

.........

. ........

t

1-4

o

CO

4-110

HEAT

gases). With the exception of B (amorphous), C (diamond), Se, Te, and the gases H 2, D 2, Eu, Sm, Tm, and Yb, the tabulated values are based on (1) R. Hultgren, R. L. Orr, P. D. Anderson, and K. K. Kelley, "Selected Values of Thermodynamic Properties of Metals and Alloys," John Wiley & Sons, Inc., New York, 1963 (and later looseleaf supplements); (2) JANAF Thermochemical Tables, Clearinghouse, U.S. Department of Commerce, Springfield, Va. (PE Rept. 168370, 1965; PE Rept. 168370-1, 1966) (and later looseleaf supplements); and (3) J. Hilsenrath, C. G. Messina, and W. H. Evans, Ideal Gas Thermodynamic Functions for 73 Atoms and Their First and Second Ions to 10,000 K, Air Force Weapons Lab. Rept. TDR-64-44, Kirtland Air Force Base, N.Mex., 1964. TABLE 4e-3. HEAT CAPACITY OF WATER (Osborne, Stimson, and Ginnings, National Bureau of Standards) Temp,oC

J g·K

0 5 10 15 20 25 30 35 40 45 50

4.2177 4.2022 4.1922 4.1858 4.1819 4.1796 4.1785 4.1782 4.1786 4.1795 4.1807

Temp.,oC

50 55 60 6.5 70 75 80 85

gO 95 100

J g·K

--

4.1807 4.1824 4.1844 4.1868 4.1896 4.1928 4.1964 4.2005 4.2051 4.2103 4.2160

As a first approximation in explaining the temperature dependence of the heat capacity of solids, Einstein made the assumption that all oscillators in the lattice vibrated with the same frequency Vo. If h is Planck's constant and k is Boltzmann's constant, let

BE

i-;

BE T

=T

X =-

and denote the zero-point energy per mole by U o. Then the Einstein theory of specific heat yields for the molar energy U at the temperature T x ' tei ) U - U 0 (E msem ~=ex-1

where R is the universal gas constant. volume is given by C v = dU jdT, or

(4e-1)

The Einstein molar heat capacity at constant

. . Cv (Emstem) 3R

x 2e x (ex _ 1)2

=

(4e-2)

The molar entropy S is equal to f(Cv/T) dT, whence

(Einstein).~ = _x_ - In (1 - e- x ) 3R

eX -

1

(4e-3)

Numerical values of the quantities in Eqs. (4e,..1), (4e-2), and (4e-3) are given in Tables 4e-4, 4e-5 and 4e-6, taken from "Contributions to the Thermodynamic Functions by a Planck-Einstein Oscillator in One Degree of Freedom," prepared by Herrick L. Johnston, Lydia Savedoff, and Jack Belzer, of the Cryogenic Laboratory of the

4-111

HEAT CAPACITIES TABLE

E>E T

0.0

0.1

0.2

4e-4.

0.3

U - U« 3iIT 0.4

(EINSTEIN)

0.5

0.6

0.7

0.8

0.9

----- - - - - - - - ---- --- ------ - 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

1.00000 0.95083 0.90333 0.85749 0.81330 0.77075 0.72982 0.58198 0.54886 0.51722 0.48702 0.45824 0.43083 0.40475 0.31304 0.29304 0.27414 0.25629 0.23945 0.22356 0.20861 0.15719 0.14624 0.13598 0.12638 0.11739 0.10898 0.10113 0.07463 0.06909 0.06394 0.05915 0.05469 0.05055 0.04671 0.03392 0.03128 0.02885 0.02658 0.02450 0.02257 0.02079 0.01491 0.01371 0.01261 0.01159 0.01065 0.00979 0.00899 0.00639 0.00586 0.00538 0.00494 0.00453 0.00415 0.00381 0.00269 0.00246 0.00225 0.00206 0.00189 0.00173 0.00158 0.00111 0.00102 0.00093 0.00085 0.00078 0.00071 0.00065 0.00045 0.00042 0.00038 0.00035 0.00032 0.00029 0.00026 0.00018 0.00017 0.00015 O.OOON 0.00013 0.00012 0.00011 0.00007 0.00007 0.00006 0.00006 0.OD005 0.00005 0.00004 0.00003 0.00003 0.00002 0.00002 0.00002 0.00002 0.00002 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001

TABLE

eE

-

T

0.0

0.1

0.2

0.3

Cv 4e-5. 3R 0.4

0.69050 0.65277 0.37998 0.35646 0.19453 0.18129 0.09380 0.08695 0.04314 0.03983 0.01914 0.01761 0.00826 0.00758 0.00349 0.00320 0.00145 0.00133 0.00059 0.00054 0.00024 0.00022 0.00010 0.00009 0.00004 0.00004 0.00002 0.00001 0.00001 0.00001

0.61661 0.33416 0.16886 0.08057 0.03676 0.01621 0.00696 0.00293 0.00121 0.00050 0.00020 0.00008 0.00003 0.00001 0.00001

(EINSTEIN)

0.5

0.6

0.7

0.8

0.9

-- - - - - - - - - - - - - - - - - - - - - - - - - - - 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

1.00000 0.99917 0.99667 0.99253 0.98677 0.92067 0.90499 0.88817 0.87031 0.85151 0.72406 0.70127 0.67827 0.65515 0.63200 0.49627 0.47473 0.45363 0.43301 0.41289 0.30409 0.28806 0.27264 0.25783 0.24363 0.17074 0.16053 0.15083 0.14162 0.13290 0.08968 0.08383 0.07833 0.07315 0.06828 0.04476 0.04166 0.03876 0.03605 0.03351 0.02148 0.01993 0.01848 0.01713 0.01587 0.01000 0.00925 000855 0.00791 0.00731 0.00454 000419 000387 0.00357 0.00329 0.00202 0.00186 0.00172 0.00158 0.00145 0.00088 0.00081 0.00075 0.00069 0.00063 0.00038 0.00035 0.00032 0,0003° 0.00016 0.00015 0.00014 0.00013 0.00012

0.97942 0.97053 0.96015 0.94833 0.93515 0.83185 0.81143 0.79035 0.76869 0.74657 0.60889 0.58589 0.56307 0.54049 0.51820 0.39331 0.37429 0.35584 0.33799 0.32073 0.23004 0.21704 0.20462 0.19277 0.18149 0.12464 0.11683 0.10944 0.10247 0.09588 0.06371 0.05942 0.05539 0.05162 0.04808 0.03115 0.02894 0.02687 0.02495 0.02316 0.01471 0.01362 0.01261 0.01168 0.01081 0.00676 0.00624 0.00577 0.00533 0.00492 0.00304 0.00280 0.00258 0.00238 0.00219 0.00134 0.00123 0.00114 0.00104 0.00096 0.00058 0.00054 0.00049 0.00045 0.00042 0.00025 0.00023 0.00021 0.00019 0.00018 0.00011 0.000100.00009 0.00008 0.00008

1°.00027

Ohio State University, under contract between the Office of Naval Research and the Ohio State University Research Foundation, 194.9. Debye assumed that the oscillators occupying the lattice points in a crystalline solid vibrated with a continuous spectrum of frequencies from zero to a maximum value Vm. Defining the "Debye temperature" E>D and y by the equations

hVm

E>D=T

4--112

HEAT TABLE

S 4e-6. 3R

(EINSTEIN)

I

E>E T

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

--- - - - - -- - - -- - - - - - - - - 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

co 3.30300 2.61110 2.20772 1.92293 1.70350 1.52569 1.37684 1.24939 1.13845 1.04066 0.95363 0.87560 0.80521 0.74139 0.68331 0.63027 0.58171 0.53714 0.49617 0.45845 0.42367 0.39158 0.36194 0.33455 0.30921 0.28579 0.26410 0.24403 0.22546 0.20826 0.19234 0.17760 0.16396 0.15133 0.13964 0.12884 0.11883 0.10958 0.10102 0.09312 0.08580 0.07905 0.07281 0.06704 0.06172 0.05681 0.&3228 0.04809 0.04423 0.04068 0.03740 0.03438 0.03159 0.02903 0.02666 0.02450 0.02249 0.02064 0.01896 0.01739 0.01596 0.01464 0.01343 0.01232 0.01130 0.01035 0.00949 0.00869 0.00797 0.00730 0.00669 0.00613 0.00562 0.00514 0.00470 0.00431 0.00394 0.00361 0.00330 0.00303 0.00276 0.00252 0.00231 0.00211 0.00193 0.00176 0.00162 0.00148 0.00135 0.00123 0.00113 0.00103 0.00094 0.00086 0.00078 0.00072 0.00065 0.00060 0.00055 0.00050 0.00046 0.00042 0.00038 0.00035 0.00032 0.00028 0.00026 0.00024 0.00022 0.00020 0.00019 0.00016 0.00015 0.00014 0.00013 0.00012 0.00011 0.00010 0.00009 0.00008 0.00008 0.00007 0.00006 0.00005 0.00005 0.00004 0.00004 0.00004 0.00003 0.00003 0.00003 0.00002 0.00002 0.00002 0.00002 0.00002 0.00002 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001 O.OOOCI 0.00001 0.00001

4e-7.

TABLE

E>D T

0.0

0.1

0.2

0.3

---

U - U«

~ (DEBYE)

0.4

0.5

I

0.6

0.7

0.8

0.9

-- - - - - -- - - -- -

0 1.000000 .963000 .926999 .891995 .857985 .824963 .792923 .761858 .781759 .702615 1 .674416 .647148 .620798 .595351 .570793 .547107 .524275 .502280 .481103 .460726 2 .441128 .422291 .404194 .386816 .370137 .354136 .338793 .324086 .309995 .296500 3 .283580 .271215 .259385 .248070 .237252 .226911 .217029 .207589 .198571 .189959 4 .181737 .173888 .166396 .159246 .152424 ~145914 .139704 .133780 .128129 .122739 5 .117597 .112694 .108016 .103555 .099300 .095241 .091369 .087675 .084152 .080789 6 .077581 .074520 .071598 .068809 .066146 .063604 .061177 .058858 .056644 .054528 7 .052506 .050573 .048726 .046960 .045271 .043655 .042109 .040630 .039214 .037858 8 .036560 .035317 .034126 .032984 .031890 .030840 .029834 .028869 .027942 .027053 9 .026200 .025380 .024593 .023837 .023110 .022411 .021739 .021092 .020470 .019872 10 .019296 .018741 .018207 .017692 .017196 .016718 .016257 .015812 .015384 .014970 11 .014570 .014185 .013813 .013453 .013106 .012770 .012445 .012131 .011828 .011534 12 .011250 .010975 .010709 .010452 .010202 .009960 .009726 .009499 .009279 .009066 13 .008859 .008658 .008463 .008275 .008091 .007913 .007740 .007572 .007409 .007251 14 .007097 .006947 .006801 .006660 .006522 .006388 .006258 .006132 .006008 .005888

- - - - - - - - - - - - - -- -

E>D T

_. 10 20 30 40

0

1

2

3

4

5

6

7

8

9

- -- - - - - - - - - - - -- .019296 .014570 .011250 .008859 .002435 .002104 .001830 .001601 .000722 .000654 .000595 000542 .000304 .000283 .000263 .000245

.007097 .001409 000496 .000229

.005771 .004756 .003965 .003340 .002840 .001247 .001108 .000990 .000887 .000799 .000454 .000418 .000385 .000355 .000328 .000214 .000200 .000188 .000176 .000166

4-113

HEAT CAPACITIES

-aD T

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 -

0.0

0.1

Cv 4e-8. 3R

0.3

0.4

(DEBYE)

0.5

0.6

0.7

0.8

0.9

- - - - - - - - - - - ---- - 1.000000 .999500 .998003 .915514 .992046 .987611 .982229 .975922 .968717 .960643 .951732 .942020 .931545 .920346 .908467 .895950 .882842 .869186 .855031 .840422 .825408 .810034 .794347 .778392 .762213 .745853 .729355 .712759 .696103 .679424 .662758 .646137 .629593 .6VH54 .596848 .5807UO .564732 .548966 .533421 .518113 .503059 .488272 .473763 .459543 .445620 .432002 .418693 .405700 .393024 .380669 .368635 .356922 .345529 .334456 .323698 .3132,~5 .303121 .293293 .283767 .274536 .265597 .256943 .248568 .240466 .232631 .225056 .217735 .210662 .203828 .197229 .190856 .184704 .178766 .173035 .167505 .162169 .157021 .152055 .147264 .142644 .138187 .133889 .129744 .125746 .121890 .118172 .114585 .111126 .107790 .104572 .101467 .098472 .095583 .092795 .090J 05 .087509 .085004 082585 .080251 .077997 .075821 .073719 .071690 .069729 .067835 .066005 .064236 .062526 .060874 .059276 .057731 .056237 .054791 .053393 .052039 .050730 .049462 .048235 .047046 .045895 .044780 .043700 .042653 .041639 .040655 .039702 .038777 .037880 .037010 .036166 .035347 .034552 .033781 .033031 .032304 .031597 .030910 .030243 .029595 .028964 .028352 .027756 .027177 .026613 .026065 .025532 .025013 .024508 .024016 .023537 - - - - --- - - --- - - --- ---

8D T

0

1

10 20 30 40

.075821 .009741 .002886 .001218

.057731 .008414 .002616 .001131

-

0.2

TABLE

2

4

3

6

5

7

8

9

--- --- - - --- --- --- -----.044780 .007318 .002378 .001052

.035347 .006405 .002168 .000980

.028352 .005637 .001983 .000915

.023071 .004987 .001818 .000855

.019018 .004434 .001670 .000801

.015859 .003959 .001538 .000751

.013361 .003550 .001420 .000705

.011361 .003195 .001314 .000662

the values of molar energy, molar heat capacity at constant volume and molar entropy were found to be U - U; 3 (Y Z3 dz (4e-4) (Debye) ;w:r- = D(y) = 1J2}o ez - 1 Cv

(Debye) 3R

= 4D(y) -

S (Debye) 3R

= - D(y) -

4

3

3y

1

(4e-5)

In (1 - e- Y )

(4e-6)

ell -

Values of the quantities in Eqs. (4e-4), (4e-5) and (4e-6) are given in Tables 4e-7, 4e-8 and 4e-9, prepared by John E. Kilpatrick and Robert H. Sherman, of the Los Alamos Scientific Laboratory, under contract with the U.S. Atomic Energy Commission, 1964. To calculate U - U 0 in joules/mole, and Cv and S in joules/mole kelvin, take as the value of R R = 8.3143 joules/mole kelvin To convert to calories, it must be kept in mind that there are three different calories: The 15-degree calorie = 4.1858 joules The International steam table calorie = 4.1868 joules The thermochemical calorie = 4.1840 joules

4-114

HEAT TABLE

8D

-

T

0.0

0.1

0.2

0.3

S 4e-9. 3R

0.4

(DEBYE)

0.5

0.6

0.7

0.8

0.9

-- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

CIO

1.357896 0.733585 0.429176 0.260801 0.163557 0.105924 0.070920 0.049083 0.035057 0.025773 0.019444 0.015007 0.011814 0.009463

3.636168 1.267635 0.693684 0.407715 0.248562 0.156373 0.101605 0.068257 0.047393 0.033952 0.025029 0.018928 0.014639 0.011546 0.009263

2.943771 1.186113 0.656362 0.387463 0.236970 0.149554 0.097495 0.065715 0.045775 0.032892 0.024313 0.018431 0.014284 0.011286 0.009069

2.539553 1.111987 0.621403 0.368341 0.225990 0.143077 0.093583 0.063289 0.044227 0.031873 0.023623 0.017950 0.013940 0.011034 0.008881

2.253613 1.044212 0.588616 0.350279 0.215585 0.136926 0.089858 0.060972 0.042744 0.030895 0.022959 0.017485 0.013607 0.010790 0.008697

2.032703 0.981958 0.557832 0.333211 0.205724 0.131083 0.086310 0.058760 0.041324 0.029956 0.022318 0.017037 0.013284 0.010552 0.008519

1.853102 0.924550 0.528900 0.317077 0.196375 0.125530 0.082930 0.056646 0.039963 0.029053 0.021701 0.016603 0.012972 0.010321 0.008345

1.702152 0.871435 0.501685 0.301819 0.187510 0.120252 0.079709 0.054626 0.038658 0.028184 0.021106 0.016184 0.012669 0.010097 0.008176

1.572296 0.822152 0.476064 0.287386 0.179103 0.115234 0.076639 0.052695 0.037407 0.027349 0.020532 0.015778 0.012375 0.009880 0.008011

1.458656 0.776313 0.451928 0.273728 0.171126 0.110462 0.073712 0.050849 0.036208 0.026546 0.019978 0.015386 0.012090 0.009669 0.007851

-- --- --- --- --- --- --- --- --- - - - --8D

-

T

-

0

--10 20 30 40

0.025773 0.003247 0.000962 0.000406

1

2

3

5

4

6

7

8

9

--- --- --- --- --- ---

---

--- ---

0.019444 0.002805 0.000872 O.OOO::J77

0.005287 0.001320 0.000513 0.000250

0.004454 0.001183 0.000473 0.000235

0.015007 0.002439 0.000793 0.000351

0.011814 0.002135 0.000723 0.000327

0.009463 0.001879 0.000661 0.000305

0.007695 0.001662 0.000606 0.000285

0.006341 0.001478 0.000557 0.000267

0.003787 0.001065 0.000438 0.000221

At values of the temperature less than 8D/IOO, the Debye theory can be relied upon to give correctly the contribution to the heat capacity attributable to lattice vibrations. In some cases it holds well at temperatures up to 8D/50. At these low temperatures the Debye expression for Cv reduces to (4e-7) or

C v = 124 8

~ (~)3 8D

. mole· K

(4e-8)

For metals there is a contribution to the heat capacity due to the free electrons equal to "IT, where "I is known as the electronic constant. The total heat capacity of a metal is therefore (4e-9) The most reliable values of 8D and "I are obtained from heat-capacity measurements in the liquid helium region. It is customary in such work to plot C v /T against T2. On such a plot a nonmetal gives a straight line through the origin, whereas a metal gives a straight line with a positive intercept. Values of 8 n and "I are given in Table 4e-10. They were obtained in almost all cases by calorimetric measurements in the liquid helium range or lower. Values of 8p are given in kelvins, and those of "I in millijoules per mole kelvin squared.

4-115

HEAT CAPACITIES TABLE

4e-IO.

VALUES OF

en AND

/"

IN THE :a}D,Qo and k are known, {j can be calculated. Table 4f-5lists values for E>n, Qo, and k for 19 elements. Values of E>D E from expansion measurements are in reasonable agreement with room-temperature values of E>D from heatcapacity measurements. A consequence of Gruneiaen's theory of the solid state is the approximate proportionality of Qo with the melting temperature T ",. Values of T m are listed in the last column of Table 4f-5.

4g. Thermal Conductivity ROBERT L. POWELL AND GREGG E. CHILDS

Cryogenics Division, NBS Institute for Basic Standards

Symbols and Units

A Cp

e, J L l

cross-sectional area, meters! specific heat at constant pressure, joules/kilogram· kelvin specific heat at constant volume, joules/kilogram· kelvin heat current density, watta/meter> Lorenz ratio == 'A/u T, volts-/kelvin! mean free path, meters

THERMAL CONDUCTIVITY M

Q R

T t

v x a

X J1. p (T

4-143

molecular weight, kilograms/mole heat current, watts gas constant per mole, 8.3143 joule/kelvin· mole temperature, kelvins time, seconds velocity, meters/second space coordinate, meters thermal diffusivity, meters-/second thermal conductivity, watts/meter· kelvin dynamic viscosity, Newton· second/meter", (= 10 poise) density, kilograms /meter! electrical conductivity, l/ohm . meter

4g-1. General Definitions and Units. The thermal conductivity is a nonequilibrium property usually determined in a steady-state experiment utilizing the Fourier law for linear heat flow in a homogeneous, isotropic substance:

Q=

-XA dT dx

where Q is the thermal energy current, A is the cross-sectional area, dT/dx is the temperature gradient, and X is the thermal conductivity coefficient. Commonly used units and their conversion factors are given in Table 4g-1. For nonisotropic bodies such as some dielectric crystals the basic differential equation is modified to J

=

-X grad T

where J is the vector thermal current density, and X is a symmetric tensor of second order. Heat-conduction equations and their solutions for nonhomogeneous and nonlinear systems are discussed at length by McAdams [38], Schneider [62], and Carslaw and Jaeger (10). In general, the total heat transport is affected by radiation, convection, and conduction mechanisms and may depend on temperature, pressure, density, material, and temperature gradient, etc. However, the coefficient A, as defined by the above equations, refers only to heat transport by conduction mechanisms. It is usually assumed that the thermal conductivity is not a function of the temperature gradient, but is a function of the temperature, composition, purity, perfection, and other similar intensive parameters of the system. It is also assumed that the conductivity is not size- or shape-dependent, though this is not always true. Size and shape effects become significant whenever the size of the conductor is comparable to the mean free path for motion of the particles (or quasi-particles) that transport the thermal energy. These effects have been observed for conduction by molecules in rarefied gases and for conduction by phonons (quantized normal modes of lattice vibration) in small, highpurity dielectric crystals at low temperatures. Representative values for the temperature dependence of several substances are given in Fig. 4g-1. They are typical curves for a high-purity metal (copper), highpurity crystalline dielectric (sapphire), nonferrous alloy (aluminum alloy), ferrous alloy (stainless steel), disordered dielectric (glass), fluid (helium), and water. The Thermophysical Properties Research Center at Purdue University has published a large compilation of thermal conductivity data and graphs over large temperature ranges for many solids and fluids [72]. A general survey of the experimental and theoretical aspects of thermal conductivity is given in the book edited by Tye [73]. Proceedings of the annual conferences on thermal conductivity [71) are usually available from the sponsoring agency; sometimes they are formally published.

4-144

HEAT

,-IJ'YY r-, CJr

~

/ \ 1\

v 5

1\\

~

If

f---~

I J

2

~ Irr .... J ~

~

.....

5

s

~

2

8

5

z~ 10'

...J


~

TAnL}~

4h-7.

T, K

1 atm

4 atm

100 200 300 400 500

20.049 22.497 23.917 24.929 25.723

21.091 22.524 23.539 24.335

I

ENTROPY OF AIR,

SIR

TABLE

7 atm

10 atm

40 atm

70 atm

100 atm

20.513 21.958 22.976 23.773

20.139 21.594 22.616 23.414

18.551 20.138 21.194 22.006

17.767 19.513 20.602 21.428

17.184 19.095 20.214 21.056

22.104 22.685 23.196 23.655 24.071

21.736 22.320 22.833 23.293 23.709

24.454 24.809 25.138 25.448 25.741

24.093 24.448 24.777 25.087 25.380

--- --- ------ --- ---------

900 1000

26.383 26.954 27.460 27.915 28.330

24.995 25.567 26.073 26.528 26.944

24.434 25.006 25.512 25.968 26.384

24.077 24.649 25.155 25.610 26.025

22.677 23.253 23.762 24.219 24.634

1100 1200 1300 1400 1500

28.713 29.068 29.399 29.711 30.005

27.327 27.682 28.013 28.324 28.618

26.767 27.122 27.453 27.764 28.058

26.408 26.763 27.093 27.404 27.698

25.018 25.373 25.702 26.013 26.306

600 700 800

1600 1700 1800 1900 2000

30.284 30.549 30.804 31.048 31.284

28.897 29.162 29.416 29.660 29.896

28.337 28.602 28.856 29.100 29.335

27.977 28.242 28.496 28.740 28.974

26.585 26.850 27.104 27.348 27.582

26.020 26.287 26.542 26.785 27.019

25.659 25.926 26.181 26.424 26.658

2100 2200 2300 2400 2500

31.514 31.740 31.964 32.191 32.423

30.124 30.346 30.563 30.778 30.992

29.563 29.784 29.999 30.212 30.422

29.201 29.421 29.636 29.847 30.055

27.808 28.027 28.240 28.447 28.650

27.245 27.463 27.676 27.883 28.084

26.884 27.102 27 .3~4 27.520 27.721

2600 2700 2800

32.663 32.917 33.188 33.481 33.799

31.208 31.428 31.654 31.889 32.136

30.632 30.844 31.059 31.279 31.507

30.263 30.471 30.6$1 30.895 31.114

28.849 29.046 29.242 29.438 29.634

28.281 28.476 28.669 28.861 29.052

27.918 28.111 28.302 28.491 28.678

2900

3000

4h-8.

COMPRESSIBILITY FACTOR FOR ARGON,

Z

=

PVIRT

1 atm

4atm

7 atm

10 atm

40 atm

70 atm

100 atm

100 200 300 400 500

0.9782 0.99706 0.99937 0.99998 1.00018

0.98818 0.99750 0.99991 1.00072

0.97923 0.99565 0.99986 1.00127

0.97023 0.99382 0.99982 1.00183

0.8778 0.9773 1.0002 1.0079

0.7838 0.9643 1.0022 1.0147

0.6917 0.9553 1.0057 1.0224

600 700 800 900 1000

1.00025 1.00027 1.00028 1.00027 1.00026

1.00101 1.00111 1.00111 1.00109 1.00104

1.00178 1.00194 1.00195 1.00191 1.00183

1.00255 1.00278 1.00279 1.00273 1.00261

1.0105 1.0113 1.0113 1.0110 1.0105

1.0190 1.0201 1.0199 1.0194 1.0185

1.0279 1.0292 1.0288 1.0279 1.0265

1100 1200 1300 1400 1500

1.00025 1.00024 1.00023 1.00021 1.00020

1.00100 1.00095 1.00090 1.00085 1.00081

1.00174 1.00166 1.00158 1.00149 1.00142

1.00249 1.00237 1.00225 1.00213 1.00203

1.0100 1.0095 1.0090 1.0085 1.0081

1.0176 1.0167 1.0158 1.0149 1.0142

1.0252 1.0239 1.0226 1.0213 1.0203

1600 1700 1800 1900 2000

1.00019 1.00018 1.00018 1.00017 1.00016

1.00077 1.00073 1.00070 1.000u7 1 ;00064

1.00135 1.00128 1.00123 1.00117 1.00111

1.00193 1.00183 1.00175 1.00167 1.00159

1.0077 1.0073 1.0070 1.0067 1.0064

1.0135 1.0128 1.0123 1.0117 1.0111

1,0193 1.0183 1.0175 1.0167 1.0159

2100 2200 2300 2400 2500

1.00015 1.00015 1.00014 1.00014 1.00013

1.00061 1.00058 1.00066 1.00054. 1.00052

1.00107 1.00102 1.00098 1.00095 1.00091

1.00153 1.00146 1.00140 1.00135 1.00130

1.0061 1.0058 1.0056 1.0054 1.0052

1.0107 1.0102 1.0098 1.0095 1.0091

1.0153 1.0146 1.0140 1.0135 1.0130

UJ

2600 2700 2800 2900 3000

1.00013 1.00012 1.'po012 1.00011 1.00011

1.00050 1.00048 1.00046 1.00045 1.00043

1.00088 1.00084 1.00081 1.00078 1.00076

1.00125 1.00120 1.00116 1.00112 1.00108

1.0050 1.0048 1.0046 1.0045 1.0043

1.0088 1.0084 1.0081 1.0078 1.0076

1.0125 1.0120 1.0116 1.0112 1.0108

UJ

T, K

- - -- - - - - - - - - - - - - - - - - - - - 8

~

t::l

~

a::

o

t::' ~

Z

> a::

H

n "'d

~

o

"'d

t::l

~

8 H

t::l

oI:I:j o > t::l

UJ

t ~ """"' -...:J

TABLE

4h-9.

RELATIVE DENSITY OF ARGON,

--- ----_. 10 atm

40 atm

pjpo

TABLE

1 atm

100 200 300 400 500

2.79 1.3685 0.91023 0.68226 0.54570

5.5232 3.6477 2.7292 2.1816

9.754 6.3954 4.7764 3.8157

14.064 9.1531 6.8237 5A480

62.18 37.23 27.28 21.66

121.9 66.03 47.65 37.65

197.3 95.22 67.84 53.38

600 700 800 900 1000

0.45471 0.38975 0.34103 0.30314 0.27283

1.8175 1.5577 1.3630 1.2116 1.0905

3.1781 2.7237 2.3832 2.1185 1.9068

4.5367 3.8877 3.4017 3.0239 2.7219

18.00 15A2 13.49 12.00 10.80

31.25 26.75 23.41 20.82 18.76

44.25 37.88 33.16 29.50 26.59

1100 1200 1300 1400 1500

0.24803 0.22736 0.20987 0.19489 0.18189

0.99136 0.90879 0.83893 0.77904 0.72714

1.7336 1.5893 1.4671 1.3625 1.2717

2.4747 2.2688 2.0945 1.9451 1.8156

9.825 9.011 8.322 7.731 7.219

17.07 15:66 14.47 13.44 12.56

24.20 22.21 20.53 19.09 17.83

1600 1700 1800 1900 2000

0.17053 0.16050 0.15158 0.14361 0.13643

0.68172 1.1923 0.64164 1.1223 0.60601 1.0600 0.57414 1.0042 0.54544 0.95408

1.7023 1.6023 1.5134 1.4339 1.3623

6.770 6.375 6.022 5.707 5.423

11.78 11.09 10.48 9.938 9.447

16.73 15.76 14.90 14.13 13.43

2100 2200 2300 2400 2500

0.12993 0.12403 0.11863 0.11369 0.10914

0.51949 0.49589 0.47434 0.45458 OA3641

0.90868 0.86742 0.82974 0.79520 0.76342

1.2975 1.2386 1.1848 1.1355 1.0902

5.167 4.933 4.720 4.524 4.344

9.000 8.595 8.225 7.885 7.572

12.80 12.23 11.70 11.22 10.78

2600 2700 2800 2900 3000

0.10495 0.10106 0.097452 0.094092 0.090956

OA1963 0.40410 0.38967 0.37624 0.36371

0.73408 0.70692 0.68169 0.65820 0.63628

1.0483 1.0095 0.9735 0.93997 0.90868

4.178 4.024 3.881 3.747 3.623

7.283 7.016 6.768 6.536 6.320

10.37 9.987 9.635 9.306 8.999

7 atm

SPECIFIC HEAT OF ARGON,

t

CpjR

~

~

I

T, K

4atm

4h-1O.

70 atm

100 atm

- - - - - - - - - - - - - - - - - - - - - ---

T, K

--100 200 300 400 500

10 atm 1 atm 4atm 7 atm 40 atm --- --- --------2.6077 2.5154 2.5626 2.663 2.612 3.31 2.5057 2.5230 2.5404 2.5581 2.74 2.5294 2.5029 2.5118 2.5206 2.61 2.5018 2.5071 2.5124 2.5176 2.570

70 atm

100 atm

00

-----4.2 2.93 2.70 2.621

5.2 3.12 2.79 2.670

600 700 800 900 1000

2 5012 2.5008 2.5006 2.5005 2.5004

2.5047 2.5033 2.5025 2.5020 2.5015

2.5082 2.5058 2.5043 2.5033 2.5026

2.5117 2.5082 2.5062 2.5047 2.5037

2.546 2.532 2.524 2.519 2.515

2.579 2.555 2.541 2.531 2.525

2.611 2.578 2.558 2.544 2.1136

1100 1200 1300 1400 1500

2.5003 2.5002 2.;0>002 2.5002 2.5001

2.5012 2.5010 .2.5008 2.5007 2.5006

2.5021 2.5017 2.5014 2.5012 2.5010

2.5030 2.5024 2.5020 2.5017 2.5014

2.512 2.510 2.508 2.507 2.506

2.520 2.516 2.514 2.512 2.510

2.528 2.523 2.519 2.516 2.513

1600 1700 1800 1900 2000

2.5001 2.5001 2.5001 2.5001 2.5001

2.5005 2.5004 2.5004 2.5003 2.5003

2.5009 2.5007 2.5006 2.5006 2.5005

2.5012 2.5011 2.5009 2.5008 2.5007

2.505 2.504 2.504 2.503 2.503

2 509 2.507 2.506 2.506 2.505

2.511 2.511 2.509 2.508 2.507

2100 2200 2300 2400 2500

2.5001 2.5001 2.5000 2.5000 2.5000

2.5002 2.5002 2.5002 2.5002 2.5002

2.5004 2.5004 2.5003 2.5003 2.5003

2.5006 2.5005 2.5005 2.5004 2.5004

2.502 2.502 2.502 2.502 2.502

2.504 2.504 2.503 2.503 2.503

2.506 2.505 2.505 2.504 2.504

2600 2700 2800 2900 3000

2.5000 2.5000 2.5000 2.5000 2.5000

2.5001 2.5001 2.5001 2.5001 2.5001

2.5002 2.5002 2.5002 2.5002 2.5002

2.5003 2.5003 2.5003 2.5003 2.5002

2.501 2.501 2.501 2.501 2.501

2.502 2.502 2.502 2.502 2.502

2.503 2.503 2.503 2.503 2.502

:r1 t"'.J

> 8

TABLE

T, K

4h-ll.

1 atm

ENTHALPY OF ARGON,

4atm

7 atm

10 atm

(H - EoO)jRT o

40atm

70 atm

100 atm

---- - -- - - - - -- - - - - - - - - - - 100 200

300 400

500

0.8935 1.8236 2.7422 3.6590 4.5750

1.8029 2.7319 3.6532 4.5718

1. 7819 2.7217 3.6476 4.5686

1.7606 2.7114 3.6418 4.5654

1.53 2.610 3.586 4.535

TABLE

T, K

1 atm

4h-12.

4atm

ENTROPY OF ARGON,

7 atm

10 atm

40 atm

SjR 70 atm

100 atm

------ --------- --- ------

500

15.8425 17.6069 18.6245 19.3449 19.9032

16.2012 17.2308 17.9548 18.5146

15.6218 16.6637 17.3913 17.9527

15.245 16.2995 17.0308 17.5937

13.64 14.8389 15.6067 16.1850

12.83 14.2067 15.0118 15.6037

12.2 13.781 14.618 15.2261

600 700 800 900 1000

20,3593 20.7449 21.0787 21.3733 21.6368

18.9715 19.3575 19.6917 19.9864 20.2500

18.4104 18.7969 19.1313 19.4263 19.6900

18.0522 18.4391 18.7739 19.0690 19.3328

16.6513 17.0426 17.3802 17.6772 17.9423

16.0776 16.4732 16.8134 17.1122 17.3785

15.7072 16.1070 16.4498 16.7503 17.0179

100 200 300

1.3 2.512 3.533 4.506

2.42 3.48 4.48

400

700 800 900 1000

5.4907 6.4063 7.3218 8.2372 9.1525

5.4891 6.4057 7.3220 8.2380 9.1538

5.4874 6.4052 7.3222 8.2388 9.1551

5.4859 6.4047 7.3226 8.2396 9.1564

5.471 6.400 7.326 8.249 9.170

5.457 6.397 7.330 8.258 9.184

5.445 6.395 7.335 8.268 9.198

1100 1200 1300 1400 1500

10.0679 10.9832 11.8985 12.8138 13.7291

10.0696 10.9852 11.9007 12.8162 13.7316

10.0712 10.9871 11.9029 12.8186 13.7342

10.0729 10.9891 11.9051 12.8210 13.7367

10.090 11.009 11.927 12.845 13.763

10.107 11.029 11.950 12.869 13.788

10.125 11.049 11.972 12.894 13.815

1100 1200 1300 1400 1500

21. 8751 22.0926 22.2927 22.4780 22.6505

20.4884 20.7060 20.9062 21.0916 21.2640

19.9285 20.1462 20.3464 20.5318 20.7043

19.5715 19.7892 19.9895 20.1749 20.3474

18.1819 18.4003 18.6010 18.7869 18.9597

17.6190 17.8381 18.0394 18.2256 18.3988

17.2592 17.4789 17.6807 17.8673 18.0408

1600 1700 1800 1900 2000

14.6443 15.5595 16.4749 17.3901 18.3053

14.6470 15.5624 16.4778 17.3931 18.3085

14.6497 15.5652 16.4808 17.3962 18.3116

14.6524 15.5680 16.4837 17.3992 18.3147

14.680 15.597 16.513 17.430 18.346

14.707 15.625 16.543 17.460 18.377

14.735 15.654 16.572 17.491 18.409

1600 1700 1800 1900 2000

22.8119 22.9635 23.1064 23.2415 23.3698

21.4254 21.5771 21.7200 21.8551 21.9834

20.8657 21.0174 21.1603 21.2955 21.4238

20.5089 20.6606 20.8035 20.9387 21.0670

19.1214 19.2733 19.4165 19.5518 19.6802

18.5607 18.7128 18.8561 18.9915 19.1201

18.2029 18.3552 18.4987 18.6343 18.7630

2100 2200 2300 2400 2500

19.2206 20.1358 21.0510 21.9662 22.8815

19.2238 20.1390 21.0543 21.9696 22.8849

19.2269 20.1423 21.0576 21.9729 22.8884

19.2301 20.1456 21.0609 21.9763 22.8918

19.262 20.178 21.094 22.010 22.926

19.294 20.211 21.127 22.044 22.960

19.326 20.243 21.160 22.077 22.994

2100 2200 2300 2400 2500

23.4917 23.6080 23.7192 23.8256 23.9276

22.1053 22.2217 22.3329 22.4393 22.5413

21.5457 21.6620 21.7732 21.8797 21. 9817

21.1890 21. 3053 21.4165 21.5229 21.6249

19.8022 19.9187 20.0299 20.1364 20.2385

19.2422 19.3587 19.4701 19.5766 19.6787

18.8851 19.0017 19.1131 19.2197 19.3218

2600 2700 2800 2900 3000

23.7967 24.7120 25.6272 26.5424 27.4576

23.8002 24.7154 25.6307 26.5459 27.4612

23.8036 24.7189 25.6342 26.5495 27.4647

23.8071 24.7224 25.6377 26.5530 27.4683

23.842 24.757 25.673 26.589 27.504

23.876 24.792 25.708 26.624 27.540

23.911 24.827 25.743 26.659 27.575

2600 2700 2800 2900 3000

24.0257 24.1200 24.2109 24.2987 24.3834

22.6394 22.7337 22.8246 22.9124 22.9971

22.0798 22.1741 22.2650 22.3528 22.4375

21. 7231 21.8174 21.9083 21. 9961 22.0808

20.3366 20.4310 20.5219 20.6098 20.6945

19.7769 19.8713 19.9623 20.0501 20.1349

19.4201 19.5145 19.6055 19.6934 19.7782

600

""3

::t: t:rj

~

s::

o

tl

~

Z

>

s::

H

o ~

~

o

~

trJ

~

""3

H

t:rj (j).

o

~

o > (j). trJ

tn

t

f--'

c»

sc

TABLE

4h-13.

t

COMPRESSIBILITY FACTOR FOR HYDROm;N,

Z

=

PV/RT

TABLE

4 atm 7 atm 10 atm 40atm 70 atm 100 atm l'atm --- --- --- ------ --- --- --0.8853 0.9845 0.9362 0.8317 40 0.8757 0.8700 0.9955 0.9822 0.9691 0.95640.9395 60 0.9682 0.9908 0.9872 0.9782 0.9986 0.9946 1.0174 80 0.9987 1.0029 1.0222 0.9992 0.9983 1.0560 100 0.9998 1.0176 1.0405 1.0003 1.0012 1.0021 1.0030 1.0726 120 T, K

4h-14.

Ih~LATIVE DENSITY OF HYDROGEN,

4atm 7 atm --- --------54.029 6.9408 29.195 40 18.552 32.905 4.5761 60 3.4214 13.740 24.138 80 10.942 19.158 2.7338 100 9.0999 15.910 2.2771 120 T, K

1 atm

lOatm

40atm

70 atm

p/po

--- --- --- --82.160 47.632 34.609 27.379 22.709

208.08 141.15 109.01 89.532

366.53 244.49 187.17 153.23

484.88 335.82 258.83 212.36

220

1.0020 1.0024 1.0028 1.0028 1.0028

1.0036 1.0043 1.0048 1.0048 1.0048

1.0052 1.0062 1.0067 1.0068 1.0067

1.0243 1.0271 1.0283 1.0283 1.0276

1.0488 1.0516 1.0523 1.0513 1.0497

1.0786 1.0798 1.0785 1.0760 1.0730

140 160 180 200 220

1.9514 1.7073 1.5174 1.3657 1.2415

7.7937 6.8167 6.0569 5.4512 4.9557

13.617 11.907 10.578 9.5206 8.6551

19.422 16.978 15.084 13.574 12.341

76.240 66.528 59.067 53.160 48.361

130.30 113.71 101.01 90.995 82.849

181 ;01 158.21 140.80 127.01 115.79

240 260 280 300 320

1.0007 1.0006 1.0006 1.0006 1.0006

1.0027 1.0024 1.0024 1.0024 1.0024

1.0047 1.0044 1.0042 1.0042 1.0041

1.0066 1.0064 1.0061 1.0059 1.0057

1.0269 1.0259 1.0247 1.0238 1.0229

1.0480 1.0459 1.0439 1.0420 1.0402

1.0698 1.0667 1.0636 1.0607 1.0579

240 260 280 300 320

1.1381 1.0506 0.97559 0.91055 0.85364

4.5431 4.1949 3.8953 3.6356 3.4084

7.9347 7.3265 6.8045 6.3509 5.9546

11.314 10.446 9.7026 9.0575 8.4931

44.361 40.988 38.105 35.596 33.401

76.068 70.358 65.457 61.204 57.479

106.46 98.553 91.780 85.896 80:740

340 360 380 400 420

1.0005 1.0005 1.0005 1.0005 1.0005

1.0021 1.0020 1.0020 1.0020 1.0019

1.0037 1.0036 1.0035 1.0034 1.0033

1.0054 1.0052 1.0050 1.0048 1.0046

1.0217 1.0209 1.0201 1.0193 1.0185

1.0384 1.0367 1.0353 1.0339 1.0325

1.0553 1.0529 1.0507 1.0486 1.0466

340 360 380 400 420

0.80351 0.75887 0.71893 0.68298 0.65046

3.2088 3.0309 2.8714 2.7278 2.5982

5.6065 5.2956 5.0174 4.7670 4.5404

7.9959 7.5532 7.1571 6.8006 6.4780

31.473 29.748 28.204 26.815 25.558

54.192 51.265 48.632 46.286 44.120

76.178 72.110 68.458 65.165 62.181

440

1.0004 1.0004 1.0004 1.0004 1.0004

1.0017 1.0016 1.0016 1.0016 1.0016

1.0030 1.0029 1.0028 1.0028 1.0028

1.0045 1.0043 1.0041 1.0040 1.0039

1.0180 1.0172 1.0165 1.0160 1.0155

1.0314 1.0301 1.0289 1.0280 1.0271

1.0448 1.0431 1.0415 1.0400 1.0385

440 460 480

0.62095 0.59396 0.56921 0.54644 0.52542

2.4806 2.3729 2.2741 2.1831 2.0991

4.3353 4.1473 3.9749 3.8159 3.6691

6.1842 5.9165 5.6711 5.4448 5.2359

24.408 23.365 22.407 21.522 20.704

42.160 40.377 38.740 37.223 35.823

59.457 56.964 54.675 52.563 50.615

1.0004 1.0004 1.0003 1.0003

1.0016 1.0015 1.0013 1.0012

1.0026 1.0026 1.0024 1.0023

1.0037 1.0036 1.0035 1.0034

1.0148 1.0144 1.0140 1.0136

1.0260 1.0252 1.0244 1.0237

1.0372 1.0360 1.0348 1.0337

540 560 580

0.50596 0.48789 0.47112 0.45541

2.0214 1.9494 1.8826 1.8200

3.5339 3.4077 3.2908 3.1815

5.0430 4.8634 4.6961 4.5400

19.951 19.246 18.590 17.977

34.533 33.326 32.202 31.150

48.801 47.113 45.541 44.070

200

460 480

500 520 540 560 580 600

500

520

600

o

100 atm

1.0005 1.0006 1.0007 1.0007 1.0007

140 160 180

.......

--l

0::

t::J

:»

1-3

4-171

THERMODYNAMIC PROPERTIES OF GASES

I

I

I

I

·ENTROPY.Btu/lb OR .6 7

.5

4 I

I

I

1

I

1

I

~~)I I I PRESSURE P, otm

.1

j

1

1

I

l'

yg

I~

II f--'I

f--;.

275

~

II

v E

f\

IJ:~

~; -

r-

I\h

,r\

I

I

I,

9 I

I

I

I

I

I

Ii

I

1-

I

-

I

I

-

330

I

II

N OCII V I

I I

U"I\ "

r

'r

'j

I

-

I I

I I

I I

il

I I

-

III

-

,- 400

i- IJ.,I I

"

,

'Ii

~} I}I I~I'

~/, YSlj

VIi 'jtt--

v

J:jJII ~

150

r'i/jV/irJ 1/'1Vlllrl

If~'/

-

I I

rYi"\ l.oI r1

~

.,,~

Ir'--,... IN II I I 4 I I .t IV I I I r ... ~ I'

'f / / /;. \1 U'\

1-

I~-Iti

-

290

-

!

-

~

I

111

II

I

I

I

\;

1-

f

II

_

-

I

I

-

'I

11 I /I II

§J. '11'1. } !!? Jj ,I "Ii \.f \\r\-. ~ 'I If} fIJo A A";> \U,\\: ,\' II V, t I.J I ~ __ ~A'J rjj Il. "' ]I 'f:\il\"l I~r 0\""'\ I '(\1 /1'4

_!/;fJ.

'300

~~

Hf+ s S.Ii

'\ ~

\. V\I

II

Nil

8 :/

Y

H '\ tT Y ) 11.-,/ .\

11// 'I. 'J..

~

I - 450

III I

0

175

-

s _

I

11\ 'I Trt-~ Va I d'i I1I1 III 8 if:\ A ~ I f"- II v J V II .I~ II I ~ 'f\II II I -- H1\ \ IIi ~ 1\ II II~ I /I I I ~II II rJ II 1;- . § p i I N- I I . r 'IJI ~ Q ') A I I II J VljlJ I'I~ II 1/ II II 1/

225

I

I

i~

V ~ l:t

f-I~~

I

J

,/~I

1\

I

1111

fI

V

·10 I

1\

~

\I

1

r

\

I

~

I

I

1\

1\ \ \

f II

8 I

t

1\

d

Iff

IV

1

If

1\

r

I

I

I ~

'~ l/l.~tn"J lD d/"N 1\ I

I-- _DENSITY P., t/em l TEMPERATURE,K I-- -ENTHALPY H, J/t 1--1-- ENTROPY S, J/tK._f--

250

I

I

I

I:

/

I

270

J I II I

I

- 250

I

/ I

260

~\I~r

\\ %'\1 'iJ T ~ ! / I / I I / I ~.: 01 ,~ .~!~ r\ '\ , \ IU" I ~~ ~'AL 1 Ie ~~ Z :r Y;, \. :'.o~ \~rt" ~ / r-, 'I i/ll ~ ~ li' ~ ~ ~ ..~';" ~ "~ /V\ n r \~~/~ l\' _~~ I II r-. .-J. ! II I /25O fi 200 ~;~ .... 00 rZ' 'VI,/ '\~~"\ \.f\t~l\~i\ f-o I I I IJ ! Ij II ~ '/Iv V' \ ~/ e- Ii" ~ ~ ~~ ~ ~ I / II II V I 1 j II 100 !\-' Vtt % % ~ -1\, ,z\P,f'\ \r-.\ ,~/M / II IJ / / I '~W t---

125

t -

*

85

U

0-

ii¥ --t~'rrI~ I~

~

0

W

fl

J-- e- \

\ l\-I~ r~\' ~

1\ ~~ ~r\.ITt'II-J.

,,\ ~ ~~WJU ~

II "

I

I

J1

1//

[I

III

lo~J,. 'iii

rJ

I

1'-_

~

ENTROPY, J/g.K

(From NSRDS-NBS 27 entitled Thermodynamic Properties of Argon from the Triple Point to 300 K at Pressures to 1,000 Atmospheres, authored by A. L. Gosman, R. D. McCarthy, and J. G. Hurt, U.S. Government Printing Office, Washington, D.C.) FIG. 4h-1. Temperature-entropy diagram for argon.

4-172

HEAT TABLE

4h-15. lotm

Cp/R

O.Olotm

O.lotm

lotm

100tm

l000tm

1.0175 1.2042 1.3981 1.6020 1.8163

1.0172 1.2040 1.3980 1.6020 1.8163

1.0142 1.2021 1.3968 1.6012 1.8158

0.9833 1.1837 1.3852 1.5936 1.8108

0.7818 1.0577 1.3059 1.5449 1.7825

160 180

240

2.0398 2.2710 2.5085 2.7509 2.9973

2.0398 2.2710 2.5085 2.7509 2.9973

2.0394 2.2708 2.\!O84 2:7ii1O 2.9975

2.0365 2.2595 2.5083 2.7519 2.9993

2.0234 2.2690 2.5178 2.7692 3.0236

260 280 300 320 340

3.2467 3.4983 3.7517 4.0063 4.2617

3.2467 3.4984 3.7517 4.0063 4.2617

3.2470 3.4986 3.7521 4.0067 4.2622

3.2495 3.5017 3.7556 4.0106 4.2664

3.2792 3.5363 3.71141 ".0525 4.3114

3.532 3.536 3.5311 3.539 3.539

360 380 400 420 440

4.5178 '.77'3 5.0312 5.2883 5.5455

4.5178 4.7744 5.0312 5.2883 5.5456

4.5183 4.7748 5.0317 5.2889 5.5461

'.5229 4.7797 5.0368 5.2941 5.5516

'.5705 4.8296 5.0887 5.3478 5.6067

3.516 3.518 3.519 3.520 3.521

3.539 3.538 3.538 3.537 3.536

460

500 520 540

5.8029 6.0604 6.3180 6.5757 6.8335

5.8030 6.0605 6.3181 6.5768 6.8336

5.8035 6.0610 6.3187 6.5764 6.8342

5.8091 6.0669 6.3246 6.5824

8.84040

5.8659 6.12'9 6.3839 6.6427 6.9015

3.523 3.524 3.526 3.527 3.529

3.536 3.536 3.536 3.536 3.536

560 580 600

7.0915 7.3495 7.6077

7.0915 7.3496 7.6078

7.0921 7.3602 7.6084

7.0984 7.3565 7.6147

7.1606 7.4194 7.6784

20 40 60 80 100

2.500 2.501 2.519 2.591 2.714

2.564 2.544 2.605 2.722

3.463 2.780 2.723 2.790

3.957 3.564 3.295

120 140 160 180

2.857 2.993 3.108 3.204 3.280

2.862 2.996 3.111 3.206 3.282

2.905 3.026 3.135 3.226 3.296

3.242 3.264 3.326 3.377 3.413

300

3.340 3.387 3.424 3.450 3.469

3.341 3.388 3.425 3.451 3.470

3.355 3.399 3.433 3.458 3.476

3.454 3.486 3.504 3.516 3.526

320 340 360 380 400

3.483 3.494 3.601 3.507 3.510

3.484 3.495 3.602 3.508 3.511

3.489 3.499 3.506 3.510 3.514

420

3.513 3.515 3.516 3.518 3.519

3.514 3.516 3.517 3.518 3.519 3.521 3.522 3.524 3.525 3.527

280

440

460

.so 500 li20 540 560 580 600

TABLE

3.521 3.522 3.524 3.525 3.527

4h-17.

ENTROPY OF

HYDROGEN,

ENTHALPY OF

(H - EoO)/RT o

50 80 100 120 140

l000tm

Ootm

220 240 260

4h-16.

HYDROGEN, K

100tm

T, K

- - -- - - - - - - - - ---

200

TABLE

SPECIFIC

HEAT OF HYDROm:N,

- -- - - - - -- - - - - -- - -

200 220

.so

TABLE

SIR

4h-18.

COMPRESSIBILITY FACTOR

FOR NITROGEN,

Z = PV/RT

70atm 100 otm 100tm 4O.atm ~I~-4-atm- -70tm - - --- - - - - - - ---

T, K

O.Olotm

O.lotm

lotm

100tm jlooatm

80 100 120 140

16.287 16.878 17.386 17.836

13.984 14.575 15.083 15.533

11.676 12.269 12.778 13.229

9.324 9.937 10.456 10.913

6.642 7.400 7.996 8.496

100 200 300 400 500

0.981 0.99788 0.99982 1.00028 1.000401

0.909 0.99150 0.99930 1.00113 1.00164

0.783 0.98514 0.99882 1.00201 1.00289

1.00414

160 180 200 220 240

18.244 18.616 18.958 19.273 19.566

15.941 16.313 16.655 16.970 17.263

13.637 14.009 14.352 14.667 14.960

11.324 11.699 12.043 12.359 12.653

8.935 9.331 9.688 10.015 10.317

600 700 800 900 1000

1.00044 1.00043 1.00041 1.00038 1.00036

1.0017. 1.00171 1.00163 1.00154 1.00144-

1.00306 1.00301 1.00286 1.00269 1.00252

1.00439 1.06430 1.0M09 1.00384 1.00360

260 280 300 320 340

19.838 20.003 20.331 20.556 20.768

17.535 17.790 18.029 18.254 18.455

15.232 15.487 15.726 15.951 16.162

12.926 13·.182 13.421 13.646 13.858

10.596 10.857 11.100 11.328 11.542

1100 1200 1300 1400 1500

1.0003. 1:00032 1.00030 1.00028 1.00026

1.00135 1.00126 1.00119 1.00112 1.00105

1.00236 1.00221 1.00208 1.00195 1.00184

860 380 400 420 440

20.967 21.157 21.337 21.508 21.671

18.665 18.854 19.034 19.206 19.369

16.362 16.552 16.731 16.903 17.066

14.058 14.248 14.428 14.600 14.763

11.744 11.936 12.117 12.290 12.454

1600 1700 1800 1900

1.00025 1.00024 1.00022 1.00021 1.00020

1.00100 1.0000. 1.00089 1.00085 1.00081

460

520 640

21.828 21.977 22.121 22.260 22.392

19.525 19.675 19.818 19.957 20.090

17.223 17.372 17.515 17.655 17.787

14.919 15.069 15.213 15.352 16.484

12.612 12.762 12.906 13.046 13.179

2100 2200 2300 2400 2500

1.00019 1.00018 1.00018 1.00017 1.00016

560 580 600

22.520 22.644 22.764

20.218 20.341 20.461

17.915 18.038 18.158

15.612 15.736 15.856

13.308 13.431 13.552

2600 2700 2800 2900 3000

1.00016 1.00015 1.00015 1.00014 1.0001.

----------- ---60- -15.554 5.557 8.535 13.251 10.938

480 500

2000

1.01726

0.8705 0.9984 1.0248 1.0313

0.844 1.0054 1.0383 1.0461

1.01795 1.01744 1.0165 1.0155 1.0145

1.0320 1.0300 1.0292 1.0273 1.0255

1.6465 1.6446 1.6420 1.0391 1.0365

1.00337 1.00316 1.00297 1.00279 1.00263

1.0135 1.0127 1.0119 1.0112 1.0105

1.0223 1.0200 1.0196 1.0ll15

1.0319 1.0299 1.0280 1.112M

1.00174 1.00165 1.00156 1.00148 1.00141

1.00249 1.00235 1.00223 1.00212 1.00202

1.0100 1.0094 1.0089 1.0085 1.0081

1.0175 1.01115 1,01116 1.01408 1.0141

1.0250 1.0236 1.0223 1.0212 1.0202

1.00077 1.00074 1.00070 1.00068 1.00065

1.00135 1.00129 1.00123 1.00118 1.00113

1.00193 1.00184 1.00176 1.00169 1.00162

1.0077 1.007. 1.0070 1.0068 1.0065

1.0135 1.0129 1.0123 1.0118 1.0113

1.0193 1.0184 1.0176 1.0169 1.0162

1.00062 1.00060 1.00058 1.00056 1.00054

1.00100 1.00105 1.00102 1.00007 1.00005

1.00156 1.00150 1.00145 1.00139 1.00135

1.0062 1.0060 1.0058 1.0056 1.0054

1.0100 1.0105 1.0102 1.0097 1.0095

1.0156 1.0150 1.0145 1.0139 1.0135

0.9788 0.99838

0.9185 0.9962

1.00290 1.01292

L0238 1.0341

4--173

THERMODYNAMIC PROPERTIES OF GASES PRESSURE, atm

~~~g~ 2Q

I

130

...L 480

/

V+ v-I-D

HYDROGEN

110

L

I

I

1/ /

/ / I

W

~ 80

70

.~

/

I

380

-

-, .360

I

.1-

420

J 400

;/

J

90

460 440

I

/ct ltI 'r-I- 11 ILl / J. Lf I{[Iff I{J ~tt / 77 ~~ li ~ 1/

100

II 340 320 300

D'~V-L J / 1~280 £;K>< Y. hl ~ rJ7 2 PX'K>D hZ I/J V ~ ~ 11 '> V) N r..LV· 59.297 1. 995( -2) 8 43.076 2 .118(-1) 35.540 2.207 26.894 2.402(1) 17.333 2.860(2) 12.550 3.973(3)

T = 39,811 K

...... ..........

2. 8770( -2) 0.2946 3.0614 3.2057(1) 3.5337(2) 4.30041(3)

p/po

o

25,119 K

..... . ...... .

log T = 4.8 -5 -4 -3 -2

P,atm

2.5019 18.6759 1. 5319( -2) 2.0914 11.5787 1. 7622(-1) 2.0087 10.1592 1.8313 1.9877 9.9100 1. 8499(1) 1.8570 8.9608 1.9925(2)

log T = 4.6 -5 -4 -3 -2

=

o

Air

IE*/RTI

T

ttv

AIRt

T

..

..

...........

27.3687 20.3529 17.7458 12.2432 8.1263 5.9211

,

..............

::r:

63,096 K

=

....... .. 4.8626 4.3333 3.9217 3.3899 2.8576 2.1272

..

............

...................

39.9829 31.2774 25.0767 18.7528 13.4707 8.8848

2. 9080( -2) 0.3003 3.1009 3.2762(1) 3.5531(2) 4.35934(3)

..

1.11(-6) 1. 242( -5) 1.402( -4) 1. 643( -3) 1. 970( -2) 0.26574 4.335

11.0061 10 . 054 9.134 8.085 7.076 5.763 4.307

98.885 81 . 138 66.335 50.930 39.187 26.897 17.953

2.822( -3) 2.884( -2) 0.2958 3.070 3.221(1) 3.538(2) 4.31288(3)

* Air is taken to be 0.78847 N 2 0.211530 2 • t The symbols z* and £* refer to the compressibility factor and energy, respectively, of the gas mixture in the ideal gas approximation, with dissociation and ionization effects included, but without intermolecular and ionic force corrections.

4h-31.

TABLE

log

THERMODYNAMIC PROPERTIES OF HIGHLY IONIZED NITROGEN, OXYGEN, AND

Oxygen

Nitrogen

c, p/po

I

Z*

I E*/RT I P,atm

p/po

....

........... ........

2.002( -5) 2. 023( -4) 2.166( -3) 2. 530( -2) 0.31486 4.5067

.. ...........

........... 5.9941 39.9015 4.3932( -2) 1. 775( -5) 1. 985( -4) 5.9442 39.2902 0.4402 2.264( -3) 5.6159 35.2938 4.4532 2.653( -2) 4.9529 27.6217 4.5876(1) 0.3312 4.1760 20.2730 4.8137(2) 4.7320 3.2189 13.8801 5.3108(3) ..

............

..

....

,

....

p/po

9.62( -7) 6.6336 54.5680 4. 3108( -2) 9.75(-6) 1.007( -4) 6.0370 44.7463 0.4387 1.093( -3) 5.4160 35.7412 4.4891 1. 2774( -2) 4.7695 27.5515 4.6323(1) 4.0197 19.9701 4.8739(2) 0.1591 3.1133 13.6880 5.3934(3) 2.2736

I

Z*

I E*/RT I

P,atm

..

..............

....

••••

0

........

12.400 88.347 4.367( -3) 12.259 86.008 4.376( -2) 11. 928 80.888 0.4398 11.147 70.777 4.461 9.828 55.214 4.596(1) 8.286 40.418 4.826(2) 6.393 27.679 5.328(3)

8

::t1

trJ ~

s:::

o

t;j ~

Z

~

s::: H

o

T = 158,490 K

'"d ~

2 .OOO( -5) 2.000( -4) 2 .003( -3) 2.025( -2) 0.2194 2.8280

5.9999 5.9994 5.9937 5.9392 5.5589 4.5360

28.5422 28.5379 28.4949 28.0852 25.2956 18.8699

6.9627( -2) 0.6962 6.9641 6.9784(1) 7.0764(2) 7.4431(3)

1. 667( -5) 1. 669( -4) 1. 692( -3) 1. 835( -2) 0.2175 2.8802

6.9990 6.9902 6.9085 6.4490 5.5974 4.4719

log T = 5.4 -5 -4 -3 -2 -1 0 +1

P,atm

T = 100,000 K

..........

log T = 5.2 -5 -4 -3 -2 -1 0 +1

Air

I E*/RT I

Z*

I

log T = 5.0 -5 -4 -3 -2 -1 0 +1

AIR (Continued)

....

.............

1. 998( -5) 2.000( -4) 2.000( -3) 2. 002( -2) 0.2022 2.1844

............

6.0038 6.0003 5.9995 5.9945 5.9465 5.5780

..

............

21.4332 21.3407 21.3298 21.3127 21.1549 19.9145

6. 769( -2) 0.6770 6.7823 6.8664(1) 7.0637(2) 7.4734(3)

9 .595( -6) 9.599( -5) 9.6395( -4) 9.9069( -3) 0.1095 1.4194

12.422 12.418 12.374 12.094 11.134 9.045

62.862 62.814 62.367 59.617 51.714 38.120

.........

1.1031( -1) 1.1036 1.1034(1) 1.1035(2) 1.1057(3) 1.12054(4)

7.0000 6.9998 6.9981 6.9814 6.8305 6.0354

..

...........

..

30.5070 30.5059 30.4954 30.3921 29.4678 24.9055

..

6.92( -2) 0.692 6.92 6.95(1 ) 7.074(2) 7.449(3)

'"d

trJ

~

8 H trJ

U2

o

1"'.1 4.)

T = 251,190 K

.... ............. .... ...........

1. 667( -5) 1. 667( -4) 1. 667( -3) 1. 672( -2) 0.1715 1.9859

42.1981 42.1008 41.2041 36.2326 27.9500 19.7684

o

~

............... 9.5( -7)

0.1073 1.0731 1.0728(1) 1.0734(2) 1.0772(3) 1.10221(4)

9.59( -6) 9. 594( -5) 9. 596( -4) 9. 609( -3) 9. 740( -2) 1.070

12.481 12.429 12.423 12.421 12.407 12.267 11.350

48.109 46.705 46.559 46.537 46.467 45.827 41. 941

U2

1.090( -2) trJ U2 0.110 1.097 1.097(1) 1.097(2) 1.099(3) 1.1170(4)

~

o

~

4h-31.

TABLE

THERMODYNAMIC PROPERTIES OF HIGHLY IONIZED NITROGEN, OXYGEN, AND

Nitrogen log C.

I

p/po

-5 -4 -3 -2 -1

o +1

Z*

1. 553( -5) 7.4409 1. 673( -4) 6.9782 1. 822( -3) 6.4876 1. 967( -2) 6.0831 5 9883 10.20046 12.0749 15.8194

Oxygen

I E*/RT I

43.5716 34.2161 25.3735 18.2776 16.9174 16.5657

P,atm

0.1684 1. 7016 1.7227(1) 1.7437(2) 1. 7496(3) 1.7599(4)

I

I E*/RT I

log T = 5.6

T

= 398,110 K

-3 - 2 -1

o +1

= 5.8

.J

::: ··ll:2~i~5)180000 29:24i3 -3 Il.429( -4) 18.0000 - 2' j I . 429( - 3) I 7.9996 -1 i 1.4:!86( -2)17.9961 o i 0.1436 ! 7.9618 +1 ! 1.498 7.6748 I

29.2410 29.2388 29.2170 29.0039 27.2651

1.277( -4) 1.371( -3) 1. 485( - 2) 0.1621 1.7010

log T = 6.0 ........... .. ........

0.4184 4.184 4.1839(1) 4.1820(3) 4.1856(3) 4.2090(4)

p/po

I

Z*

t-.:l

I E*/RT I

P.atm

T = 630,960 K

~.: 9995 39:3i90 0: 2640" ... 1.253( -5)18.9802150.7353

1. 430( -4) ! 7.9953 39.2610 2.6410 1. 438( - 3) I 7. 95471 38. 7050 2. 6423(1 ) 1. 499( -2) 17.6706 34.8243 2.6560(2) 0.1657 17.0362126.4910 2.6932(3) 1.88!~__ 6.2987 18.860712.7459(4)

P,atm

1. 591( -5) 7.2854 29.2764 1. 689( -1) 7 .80( -6) 14.816 81.096 0.168t 1. 656( -4) 7.0382 23.9473 1.6987 8.346( -5) 13.982 64.088 1.701 1.666(-3) 7.0037 23.2082 1. 7006(1) 8.934( -4) 13.194 49.831 1.718( 1) 1. 667( -2) 6.9973 23.1256 1.7001(2) 9.476( -3) 12.553 38.606 1. 734( 2) 0.1675 6.9700 23.0593 1.70157(3) 9.623(-2) 12.392136.433 1. 739( 3) 1. 7409 16.744222.54491.7112(4) ,0.9970 112.300 35.661L!·750( (4)

. ......... :

'1

tt-.:l

o

Air

Z*

p/po

log T

=~ Ii: 429( .~ 5)

AIR (Continued)

1. 250( -5) 1.250( -4) 1. 250( -3) 1.254( -2) 0.1288 1.4231

......

1 .......

8.8308148.1188 8.2929 38.7624 7. 7337129.6449 7.1689 21.2538 6.8787 18.6828

T

. ....... 0.2599 2 . 6049 2 . 6264 2.6530(2) 2.6844(3) 2.7028(4)

'16. 9( - 7) 16 . 422 6.94( -6) 16.414 ! 6. 972( - 5) 16. 344 ! 7 . 116( - 4) 16. 052 1 7 . 48 1( -3) 15.368 1°.08245 /14.128 0.9225 12.843

83 .60912. 62( -2) 83.468 0.2631 82.269 2.633 77.434 2.639(1) 67.457 2.655(2) 50.766 2.691(3) 37.646 2.7367(4)

= 1,000,000 K

..... . ...... . 9.0000 8.9997 8.9971 8.9719 8.7657 8.0268

37.2123 37.2095 37.1809 36.9010 34.6534 27.3929

.. ......... 6. 93( -7)

0.41186 4.1186 4.1186(1) 4.1186(2) 4.133(3) 4.1819(4)

6. 933( -6) 6. 933( -5) 6. 934( -4) 6. 942( -3) 0.07011 0.74082

16.423 61.855 16.423 61.855 16.423 61.853 16.421 61.838 16.405 61.685 16·.264 60.398 15.498 54.584

4.17(-2) 0.417 4.17 4.17(1) 4.17(2) 4.175(3) 4.2033(4)

::I:: t"=J

>

>-3

4h-31.

TABLE

THERMODYNAMIC PROPERTIES OF HIGHLY IONIZED NITROGEN, OXYGEN, AND

Nitrogen log

Oxygen

c, p/po

I

Z*

AIR (Cordinued)

I E*/RT I

P,atm

I

p/po

log T

=

6.2

Air

I E*/~T I

Z*

P,atm

p/po

I

Z*

I E*/RT I

P,atm

8 :::c1

t::l

~

T = 1,584,900 K

~

o

i:'

-5 -4 -3 -2 -1 0 +1

~

1.429( -5) 1. 429( -4) 1. 429( -3) 1. 429( -2) 0.1431 1.4510

22.8785 22.8785 22.8784 22.8777 22.8705 22.8025

8.0000 8.0000 7.9999 7.9988 7.9881 7.8916

0.6631 6.631 6.631(1) 6.630(2) 6.6326(3) 6.6440(4)

1. 250( -5) 1. 250( -4) 1. 250( -3) 1. 250( -2) 0.1252 1.2717

9.0000 9.0000 8.9999 8.9985 8.9851 8.8631

log T = 6.4

T

28.4617 28.4616 28.4614 28.4587 28.4318 28.1745

0.65276 6.5276 6.5276(1) 6.5265(2) 6.527(3) 6.5402(4)

6. 993( -6) 6.933( -5) 6.934( -4) 6. 935( -3) 6.945( -2) 0.7045

16.423 16.423 16.423 16.420 16.398 16.194

48.119 48.119 48.119 48.116 48.094 47.878

0.661 6.61 6.61(1) 6.61(2) 6.609(3) 6.6200(4)

Z

>-

~ H

o ~

~

o

~

t':j ~

8

= 2,511,900 K

H

t':j [f.J

-5 -4 -3 -2 -1 0 +1

o

I 1. 429( -5) 1. 429( -4) 1. 429( -3) 1. 429( -2) 0.14306 1.4477

8.0000 8.0000 7.9999 7.9990 7.9899 7.9074

18.8639 1.0.51 18.8639 1.0.51(1) 18.8038 1 .0.31(2) 18.8637 1.0.31(3) 18.8618 1.0511(4) 18 .8-l50 11.0527(5)

1. 250( -5) 1.250( -4) 1. 250( -3) 1.250( -2) 0.12516 1.2651

9.0000 9.0000 8.9999 8.9989 8.9896 8.9043

22.9401 22.9402 22.9401 22.9399 22.9372 22.9124

1.035 1.0346(1) 1. 0346(2) 1.0345(3) 1.0338(4) 1.0359(5)

"':l

6. 933( -5) 6.933( -4) 6.934( -3) 6. 943( -2) 0.7024

16.423 16.423 16.421 16.403 16.237

39.452 39.452 39.452 39.448 39.411

1.047(1) 1.047(2) 1.047(3) 1. 0474(4) 1.0490(5)

~

>-

tn t':j

tn

I

~

o

~

4-204

HEAT

at uniform logarithmic intervals to 2.5 million kelvins. The tables taken from Hilsenrath, Green, and Beckett [4] represent the properties of atoms in equilibrium with their ions. The formulation in terms of electron concentration permits a solution of the equations for equilibrium properties in closed form and allows the computation of properties of a mixture directly frem the equilibrium properties of the constituent gases. In these tables the asterisk refers to properties of the gas mixture in the ideal-gas approximation (with dissociation and ionization effects included but without intermolecular and ionic force corrections). References 1. Hilsenrath, J., et al.: Tables of Thermal Properties of Gases, NBS Cire. 564, 1955.

Reprinted in 1960 by Pergamon Press under the title "Tables of Thermodynamic and Transport Properties of Air, Argon, Carbon Dioxide, Carbon Monoxide, Hydrogen, Nitrogen, Oxygen, and Steam." 2. Hilsenrath, J. and M. Klein: "Tables of Thermodynamic Properties of Air in Chemical Equilibrium including Second Virial Corrections from 1,500oK to 15,OOooK," Arnold Eng. Develop. Center Rept, AEDC-TR-65-58, March, 1965. Available under the designation AD 612301 from the Clearinghouse for Federal Scientific and Technical Information, U.S. Department of Commerce, Springfield, Virginia 22151 (price $3.00). 3. Hilsenrath, J., C. G. Messina, M. Klein, and R. C. Thompson: Thermodynamic and Shock Wave Properties of Argon and Nitrogen in Chemical Equilibrium with Virial and Ionic Corrections, vols, I, II, and.III. Air Force W.eapons Lab. Rept. AFWL-TR68-60, Kirtland Air Force Base, New Mexico, May, 1969. 4. Hilsenrath, J., M. S. Green, and C. W. Beckett: Internal Energy of Highly Ionized Gases, Proe. IXth Intern. Astronaut. Conqr. (Amsterdam), 1958, pp. 120-136, SpringerVerlag OHG Vienna, 1959.

4i. Pressure-Volume-Temperature Relationships of Gases; Virial Coefficients! J. M. H. LEVELT SENGERS, MAX KLEIN, AND JOHN S. GALLAGHER

The National Bureau of Standards

4i-1. Definition. Vidal coefficients are the coefficients in the expansion of the compressibility factor PV of a gas in powers of the density I/V, PV

=

Bv + Cv + 11 VI + ... )

(4i-l)

+ BpP + CpP2 + ...)

(4i-2)

RT ( 1

or in powers of the pressure P, PV = RT(1

The density expansion is the more fundamental of the two. It can be proved that such an expansion exists for gases at moderate densities, and its consecutive coefficients can be related to interactions between pairs, triplets, etc., of molecules [1]. The pressure expansion is often more practical, the pressure being more readily meal Supported in part by the Air Force Systems Command, Arnold Engineering Development Center, Tullahoma Tenn., on Delivery Order no. (40-600) 66-938.

VIRIAL COEFFICIENTS

4-205

sured than the volume, but it usually converges more slowly, and its coefficients are not as simply related to molecular interaction. In what follows, the emphasis will be on the expansion (4i-l). 4i-2. Units. The units of the virials depend on the units of volume (4i-l) or pressure (4i-2) chosen. We will express the volume in cm 3/mol and give the virials in the corresponding units. However, a practical unit of volume frequently used is the amagat unit; the volume in amagat units is the ratio of the actual volume of a gas over the normal volume, i.e., that which it would occupy at DoC and 1 atm (1.013250 bars). The normal volume for a mole of a real gas differs slightly from the normal volume V o = 22,413.6 cm 3/mol of a perfect gas, owing to deviations from ideality at DoC and 1 atm. The virial expansion used in conjunction with amagat units of volume is PVA = AA + B A + CA + ... (4i-3) VA V~ In Table 4i-l, the virials B», C p; AA, B A, C A are expressed in terms of Bv, C v. TABLE

4i-1.

RELATIONS BETWEEN VOLUME AND PRESSURE VIRIAL COEFFICIENTS

Gas constant

Ideal-gas normal volume per mole

R = 8.3143 J K-l mol- l Vo = 22,413.6"cm 3 mol- 1 (= 82.056cm 3 at K - l m o l - 1) (Both on unified scale) Amacai virials (4i-3) Pressure virials (4i-2)

v, Ao AA BA CA

Bp = Bv/RT Cp = (Cv - B~)/(RT)2

= Vo/Ao

= 1 - BA (O°C) - CA (O°C) = AoT /273.15

= BVAA/Vn = CVAA/V~

4i-3. Theoretical Interest.

Of great interest is the fundamental relationship of If the molecular field is represented by a function ¢(r) where r specifies the relative coordinates of two molecules, then

Bv, Cv, . . . to the molecular interaction. Bv(T)

=!i2 joroo

(l - e-.prrJlkT) dr

(4i-4)

The virial Bv(T) is uniquely determined through Eq. (4i-4) if the molecular interaction ¢(r) is known but the reverse is not true. Higher virials can be likewise related to interactions between triplets, etc., of interacting molecules. These expressions for the higher virials are less useful in practice, not only because the higher virials are poorly known experimentally, but also because the influence of potential function nonadditivity [1] on these virials is poorly known theoretically. We have used the relationship (4i-4) between second virial and potential function for smoothing the experimental B(T) values; for obtaining derivatives dBjdT, d 2B/dT2; and where reasonable, for extrapolating the B(T) tables beyond the temperature range where experimental data are available. 4i-4. Practical Importance. The virials B» and Cv represent the initial deviations of the equation of state from ideality as a gas is compressed [Eqs. (4i-l and 4i-2)]. Functions of these virials serve to estimate the initial density dependence of thermodynamic properties. Thus, the internal energy U i = U (V, T) - U ( 00, T) is given by

U. l

=

-RT (,£dB v V dT

+ .I: dCv + ...) 2V2 dT

Similar expressions are valid for other thermodynamic functions [2].

4-206

HEAT 4i-2.

TABLE

TABLE

4i-3.

THE SECOND VIRIAL COEFFICIENT OF HELIUM

T, K

B, cm v mol

T, K

B, ems/mol

9.00 10.00 11.00 12.00 13.00 14.00 15.00 16.00 17.00 18.00

-26.0 -21.7 -18.1 -15.2 -12.7 -10.5 -8.7 -7.1 -5.6 -4.3

35.00 40.00 45.00 50.00 60.00 80.00 100.00 120.00 160.00 200.00

5.4 6.6 7.5 8.2 9.2 10.6 11.4 11.8 12.3 12.3

19.00 20.00 22·00 22.64 24.00 26.00 28.00 30.00

-3.2 -2.2 -0.5 0.0 0.9 2.0 3.0 3.8

273 .15 373.15 400.00 600.00 800.00 1000.00 1200.00 1400.00

12.0 11.3 11.1 10.4 9.8 9.3 8.8 8.4

THE SECOND VIRIAL COEFFICIENT

OF

NEON

TEMPERATURE DERIVATIVES

B, cm- /rnol

T dB/dT, cm 3/mol

T2 d 2B/dT2, cm 3/mol

80.00 90.00 100.00 110.00 120.00 122.11 130.00 140.00 160.00 200.00

-11.8 -7.8 -4.8 -2.3 -0.4 0.0 1.2 2.6 4.8 7.6

37 31 27 24 21 21 19 18 15 11

-87 -73 -63 -55 -49 -48 -44 -40 -34 -26

240.00 273.15 280.00 320.00 360.00 373.15 400.00 500.00 600.00 700.00

9.4 10.4 10.6 11.5 12.1 12.3 12.6 13.3 13.8 14.0

9 7 7 6 5 5 4 3 2 1

-20 -17 -17 -14 -12 -12 -11 -8 -6 -5

800.00 900.00 1000.00

14.2 14.3 14.3

1 1 0

-4 -3 -3

T, K

AND

ITS

4-207

VIRIAL COEFFICIENTS

4i·G. Determination; Errors. Virial coefficients, in the majority of cases, are not directly measured but are obtained by analysis of PVT data of gases. The most common practice is a least-squares fit of the PV values along isotherms with either density or pressure as an independent variable. Using this procedure, the precision of the vi rials can then be obtained from linear least-squares estimates of their standard deviations. For a single experimental set in the very best cases, it may be better TABLE

4i-4.

THE SECOND VIRIAL COEFFICIENT OF ARGON

AND ITS TEMPERATURE DERIVATIVES

T, K

B, TdB/dT, T 2d 2B/dT2, cm t/rnol cm r/rnol cm r/mol

80.00 82.00 84.00 86.00 88.00 90.00 92.00 94.00 96.00 98.00

-288.0 -274.2

T, K

B, T d8/dT, T 2d 2B/dT2, orn r/rnol cm 3/mol cm 3/mol

-249.7 -238.7 -228.6 -219.1 -210.3 -202.0 -194.3

577 544 514 488 463 441 420 401 384 367

-1,954 -1,820 -1,700 -1,592 -1,495 -1,408 -1,328 -1,256 -1,190 -1,129

172.00 176.00 180.00 190.00 200.00 210.00 220.00 230.00 240.00 250.00

-66.9 -63.8 -60.9 -54.4 -48.7 -43.7 -39.2 -35.2 -31.5 -28.2

135 130 126 116 107 100 93 88 83 78

-345 -331 -318 -290 -266 -245 -228 -212 -198 -186

100.00 102.00 104.00 106.00 108.00 110.00 112.00 114.00 116.00 118.00

-187.0 -180.2 -173.8 -167.7 -161.9 -156.5 -151.3 -146.4 -141. 7 -137.3

352 338 325 313 302 292 282 272 264 255

-1,074 -1,023 -976 -932 -892 -855 -820 -788 -757 -729

260.00 273.15 280.00 300.00 320.00 340.00 360.00 373.15 380.00 400.00

-25.3 -21.7 -20.1 -15.7 -11.9 -8.7 -5.8 -4.2 -3.4 -1.1

74 69 67 61 56 51 48 46 44 42

-176 -163 -157 -142 -130 -119 -110 -105 -102 -96

120.00 124.00 128.00 132.00 136.00 140.00 144.00 148.00 152.00 156.00

-133.1 -125.2 -118.0 -111.4 -105.4 -99.8 -94.6 -89.8 -85.3 -81.1

247 233 220 209 198 188 180 172 164 157

-702 -654 -612 -573 -539 -509 -481 -456 -433 -413

411.52 450.00 500.00 550.00 600.00 700.00 800.00 900.00 1000.00 1100.00

0.0 3.4 6.9 9.7 11.9 15.4 17.8 19.7 21.1 22.2

40 36 31 28 25 20 17 14 12 11

-92 -82

160.00 164.00 168.00

-77.2 -73.5 -70.1

151 145 140

-394 -376 -360

1300.00* 1500.00

23.8 24.8

8 7

-21 -18

~261.4

-71 -63 -57 -47 -40 -34 -30 -27

------------- ----------- ------------ - --------- - -----

• Data below the dashed line in this and succeeding tables are extrapolations.

than 0.1 cm 3Jmol for Band 50 cm 6Jmol2 for C. However, virial data from different experiments usually differ by much more than their combined precision because of the presence of systematic errors. The main sources of systematic errors are: 1. Experimental: (a) errors in the value of RT because of temperature errors or the use of scales other than the thermodynamic scale, (b) systematic errors in the volume because of calibration problems, and (c) difficulties with extrapolation to zero density, especially with data obtained by the Burnett method [3].

4-208

HEAT

2. Cutoff problems: A finite polynomial has to be used rather than the theoretically correct infinite series [Eqs. (4i-l) and (4i-2)], but errors arise if the powers omitted would have contributed in the density range studied. To minimize systematic errors, if there is evidence that any existed, we have refitted the experimental data when available. The data refitted are indicated by asterisks in the literature reference for the tables. Wherever feasible, we reduced temperatures

TABLE 4i-5. THE SECOND VIRIAL COEFFICIENT OF KRYPTON AND ITS TEMPERATURE DERIVATIVES T, K

B, cm r/mol

TdB/dT, T2 d 2B/dT2, cm r/mol cm v/mcl

T, K

B, TdB/dT, T2 d 2B/dT2, cm r/mol cm r/mol cmv/rnol

----------------- ------- -------- ----

106.00 108.00 110.00 112.00 114.00 116.00 118.00 120.00 122.00 124.00

-394.3 -379.6 -365.8 -352.8 -340.5 -329.0 -318.1 -307.8 -298.0 -288.8

807 771 737 706 677 650 625 601 579 559

---------------

-2,813 -2,659 -2,518 -2,389 -2,270 - 2,160 -2,059 -1,965 -1,878 -1,797

215.00 220.00 230.00 240.00 250.00 260.00 270.00 273.15 280.00 290.00

-102.4 -97.9 -89.8 -82.4 -75.9 -69.9 -64.5 -62.9 -59.6 -55.1

198 191 178 166 156 147 139 136 132 125

-521 -499 -459 -425 -396 -369 -346 -340 -326 -308

126.00 128.00 130.00 132.00 134.00 136.00 138.00 140.00 144.00 148.00

-280.0 -271.6 -263.7 -256.1 -248.9 -242.0 -235.4 -229.1 -217.3 -206.4

539 521 504 488 473 458 444 432 408 386

-1,722 -1,651 -1,586 -1,524 -1,467 -1,413 -1,362 -1,314 -1,226 -1,148

300.00 310.00 320.00 340.00 360.00 373.15 380.00 400.00 420.00 440.00

-51.0 -47.2 -43.7 -37.4 -31.9 -28.7 -27.1 -22.9 -19.1 -15.8

119 113 108 100 92 87 85 80 75 70

-291 -276 -263 -239 -219 -207 -202 -187 -175 -163

152.00 156.00 160.00 164.00 168.00 172.00 176.00 180.00 186.00 192.00

-196.4 -187.1 -178.5 -170.5 -163.1 -156.1 -149.5 -143.4 -134.9 -127.1

366 348 332 317 303 290 279 268 253 239

-1,078 -1,015 -959 -907 -860 -817 -778 -742 -693 -650

460.00 500.00 550.00 575.00 600.00 650.00 700.00 800.00 900.00 1000.00

-12.7 -7.5 -2.2 0.0 2.0 5.6 8.5 13.2 16.7 19.5

66 59 52 49 47 42 38 32 28 24

-153 -137 -120 -113 -107 -96

198.00 205.00 210.00

-119.9 -112.2 -107.2

227 214 206

-611 -570 -545

1100.00 1300.00 1500.00

21.6 24.8 27.0

21 17 14

-50 -40 -34

-88 -74 -64 -56

-------------- ----------- ----- ------- ---------------

to the thermodynamic scale, using the known relation between this scale and the IPTS [4]. If a laboratory maintained its own gas scale, this scale was used. In a few cases, notably He at low temperatures, where one of the purposes of the experiment was gas thermometry, we had to leave the intercept free. Regarding the cutoff criterion [5], we chose the maximum density range in which the (k + l)th virial does not contribute beyond experimental error, and fitted this range with a polynomial of degree k - 1. Depending on the amount of low-density data availal.lo, we took k = 3 or 4. In order to do this, an estimate of the size of the (k + l rth

4-209

VIRIAL COEFFICIENTS

virial was necessary. In cases where it could not be obtained from the data, we used the theoretical value as calculated for the Lennard-Jones six-twelve potential. This procedure was justified since only order-of-magnitude estimates were needed. After second and third virials had been obtained from each set of experimental data for a given substance, and after obviously wrong results had been eliminated, a smoothing or averaging procedure was established. Use was made of the fundamental relation (4i-4) between the second virial coefficient and the intermolecular potential. 4i-6. Potential Functions-Determination, Use. Equation (4i-4) applies to substances for which quantum effects are negligible. For such substances, Eq. (4i-4) is TABLE

4i-6.

THE SECOND VIRIAL COEFFICIENT OF XENON

AND ITS TEMPERATURE DERIVATIVES

T,

K

B, T dB/dT, T 2d 2B/dT2, cm-/mol cm 3/mol cm t/mcl

220.00 225.00 230.00 235.00 240.00 245.00 250.00 255.00 260.00 265.00

-230.7 -221.2 -212.4 -204.0 -196.2 -188.7 -181. 7 -175.1 -168.8 -162.8

429 411 395 380 366 353 341 329 319 308

270.00 273.15 280.00 290.00 300.00 310.00 320.00 330.00 340.00 350.00 360.00 370.00 373.15

-157.2 -153.7 -146.6 -137.0 -128.3 -120.2 -112.8 -106.0 -99.7 -93.8 -88.4 -83.3 -81.7

299 293 281 266 252 239 227 217 207 198 190 182 180

----------- ------------ -------------

-1,225 -1,166 -1,111 -1,061 -1,015 -972 -933 -896 -861 -829 -799 -781 -745 -697 -654 -616 -582 -551 -523 -497 -474 -452 -446

- - - --- -- - - - - - --

T,

K 380.00 390.00 400.00 420.00 440.00 460.00 480.00 500.00 525.00 550.00

B, TdB/dT, T2 d 2B/dT2, ems/mol cm 3/mol cm-/rnol

-78.5 -74.0 -69.8 -62.2 -55.4 -49.2 -43.7 -38.8 -33.1 -28.1

175 169 163 152 142 133 126 119 111 104

-433 -415 -398 -368 -342 -319 -299 -282 -262 -245

575.00 -23.6 98 -230 600.00 -19.6 93 -216 650.00 -12.5 84 -193 700.00 -6.6 76 -175 768.03 0.0 67 -154 800.00 2.7 64 -146 900.00 9.6 55 -125 - ------------ -----------_. -----------_. --------------1000.00 15.0 48 -110 1100.00 42 19.3 -97 1200.00 22.8 38 -87 1300.00 1400.00 1500.00

25.6 28.0 30.1

34 31 28

-79 -72 -66

exact. Quantum effects become important for only the lightest gases [6], e.g., helium, hydrogen, etc. These latter are generally referred to as quantum gases. For such gases, Eq. (4i-4) can represent only a first approximation whose quality goes down with decreasing molecular weight. In either case, i.e., whether Eq. (4i-4) is exact or an approximation, the use of it requires a knowledge of the intermolecular potential function q,(r). In principle, such functions can be .obtained by direct quantum-mechanical calculation. In practice, this procedure is not feasible even for the simplest system. This has required, in effect, the partial reversal of the process. Thus, instead of using Eq. (4i-4) with a known function q,(r) to predict B(T), one uses (4i-4), in part, to produce information on q,(r) and, in part, to predict B(T). This is done by assuming a form for q,(r) (often referred to as a potential model), based on whatever fundamental knowledge is available, inserting a number of parameters in this form [for example, E and a of (4i-5)], and varying the values of these

4-210

HEAT

parameters to obtain the best agreement between the B(T) values calculated from Eq. (4i-4) and those determined from the analysis of PVT data described above, The predictive power of (4i-4) remains essentially intact, provided the number of experimental points used is far in excess of the number of parameters sought. Frequently used in this way to describe the intermolecular potential of simple nonpolar substances is the Lennard Jones twelve-six potential, a member of the more general class of spherically symmetric m - 6 potentials: _ me cfJ(r) - m - 6 TABLE

4i-7.

(m) 6/(m-6) [(u)m 6 r -

(u) r 6]

(4i-5)

THE SECOND VIRIAL COEFFICIENT OF NITROGEN AND ITS TEMPERATURE DERIVATIVES

TdB/dT, T2 d 2B/dT2, cm-/rnol cm Vmol

B, TdB/dT, T 2d 2B/dT2, orn-/mol cm r/mol cm Vrnol

T, K

B, crn Vmol

100.00 102.00 104.00 106.00 108.00

-160.0 -154.1 -148.5 -143.2 -138.2

304 293 283 273 264

-874 -837 -802 -769 -739

210.00 220.00 230.00 240.00 260.00

-31.1 -26.9 -23.2 -19.7 -13.8

94 88 82 78 70

-224 -209 -195 -183

110.00 112.00 116.00 120.00 124.00

-133.4 -128.7 -120.4 -112.7 -105.7

256 248 230 220 208

-711 -684 -637 -594 -557

273.15 280.00 300.00 320.00 327.22

-10.5 -8.9 -4.7 -1.2 0.0

65 63 58 53 52

-152 -147 -134 -122 -119

128.00 132.00 136.00 140.00 144.00

-99.3 -93.4 -87.9 -82.8 -78.1

197 188 179 171 163

-524 -494 -467 -442 -420

340.00 360.00 373.15 380.00 400.00

1.9 4.6 6.2 7.0 9.1

49 46 44 43 40

-113 -105 -100

148.00 152.00 156.00 160.00 166.00

-73.7 -69.7 -65.8 -62.3 -57.3

156 150 144 139 131

-400 -381 -364 -349 -327

450.00 500.00 550.00 600.00 700.00

13.5 16.8 19.5 21.7 25.0

34 30 26 24 19

-78 -68 -61 -54 -45

172.00

-52.7 -48.6 -44.7 -41.2 -35.9

125 118 113 108 100

-308 -291 -276 -262 -242

----------- ------------

178.00 184.00 190.00 200.00

._----------- ---------------

T, K

~163

~97

-91

800.00 27.3 16 -38 29.1 900.00 14 -33 ------------------------- -----------12 -29 1000.00 30.4 1200.00 32.3 9 -23 1400.00 33.5 -19 7

------------

where E and sr are parameters to be determined for each substance. This expression, with proper choice of m, adequately describes the second virial coefficient of simple nonpolar substances. It should be noted that once a "best" set of parameters has been decided upon, a potential function exists which can serve as a representation for the "actual" potential function appropriate to the gas of interest. The use of such potential functions need not be restricted to Eq. (4i-4). They can also be employed in various statistical mechanical theories for calculating macroscopic thermodynamic quantities from molecular properties. In short, these potential functions have their own importance.

4-211

VI RIAL COEFFICIENTS

Various methods, of which the use of Eq. (4i-4) is only one example, by means of which potential parameters are determined from experimental data have recently been subjected to close scrutiny [7]. In that study it was determined that all reasonable three-parameter potential models should produce essentially the same set of second virial coefficients. Because of this it was reasonable to fix on one particular model, and we chose Eq. (4i-5) for that purpose. A second result of the study of methods for determining potential parameters was the discovery of a reduced temperature range, for each property, over which that property cannot be used to distinguish between TABLE

4i-8.

THE SECOND VIRIAL COEFFICIENT OF OXYGEN

AND ITS TEMPERATURE DERIVATIVES

TdB/dT, T2 d 2B/dT2, cm t/mol ern r/mol

B, TdB/dT, T 2d 2B/dT2, cm s/rnol cm 3/mol cm r/rnol

T,

B,

K

cm 3/mol

100.00 102.00 104.00 106.00 108.00

-197.5 -190.1 -183.1 -176.5 -170.3

383 367 352 339 326

-1,201 -1,141 -1,087 -1,036 -989

210.00 220.00 230.00 240.00 250.00

-44.8 -40.1 -35.9 -32.1 -28.7

104 97 91 86 81

-259 -240 -223 -208 -195

110.00 112.00 114.00 116.00 120.00

-164.4 -158.9 -153.6 -148.6 -139.3

314 303 293 283 265

-946 -906 -868 -833 -770

260.00 273.15 280.00 300.00 320.00

-25.6 -22.0 -20.2 -15.7 -11.8

77 72 69 63 58

-184 -171 -164 -148 -135

124.00 128.00 132.00 136.00 140.00

-130.9 -123.2 -116.2 -109.7 -103.8

249 235 222 210 200

-715 -667 -624 -585 -551

190 182 170 159 150

-520 -492 -454 -422 -393

405.88 450.00 500.00 550.00 600.00

0.0 4.1 7.7 10.6 12.9

42 37 32 29 25

-97 -85 -74 -65 -58

142 134 127 121 112

-368 -346 -326 -308 -281

700.00 800.00 1000.00 1200.00 1400.00

16.5 19.1 22.4 24.5 25.9

21 18 13 10 8

-48 -41 -31 -25 -20

144.00 -98.3 -93.2 148.00 -----------154.00 -86.2 160.00 -79.9 166.00 -74.2 172.00 178.00 184.00 190.00 200.00

-69.1 -64.3 -60.0 -56.0 -50.0

------------ ---------------

T,

K

340.00 -8.4 53 360.00 -5.5 49 373.15 -3.7 47 . - ----------- ------------- ------------2.9 380.00 46 400.00 -0.6 43

-124 -114 -109 --------------. -106

-99

potential functions. For the second virial coefficient, this range is given approximately by 0.6 < T /TBoyle < 3.0. We have included a table (Table 4i-17) of experimental Boyle temperatures to facilitate the conversion of these numbers into experimental temperatures for the various gases studied. The second result mentioned states, in effect, that one should not use Eq. (4i-4) with a potential function determined by data entirely contained in the insensitive range to predict B(T) outside that range; nor should one use the resulting potential function in other theories. On the other hand, potential functions determined with data entirely outside the insensitive range can be used in an extrapolation to predict B(T) values within that range. 4i-7. Construction of the Tables. Using linear and nonlinear [8] least-squares techniques, calculated second virial coefficients based on the function (4i-5) were

4-212

HEAT

fitted to the experimental second virial coefficient data for eight substances. Each value of m was taken to define a separate potential, with E and (T in (4i-5) the adjustable parameters for the fit. The value of m was varied until the standard deviation of the fit was a minimum. The "best" m - 6 potential was used to generate a table of B, T dB/dT and T2 d 2B/dT2 values at various temperatures. Furthermore, it was used for extrapolation beyond the range of experimental data. Such extrapolations are indicated in each case by a dashed line across the tables.

TABLE

4i-9.

THE SECOND VIRIAL COEFFICIENT OF DRY CO 2-FREE AIR AND ITS TEMPERATURE DERIVATIVES

T, K

B, cm t/rnol

100.00 102.00 104.00 106.00 108.00 110.00 112.00 114.00 116.00 118.00

-167.3 -161.2 -155.3 -149.8 -144.6 -139.6 -134.9 -130.4 -126.0 -122.0

120.00 124.00 128.00 132.00 136.00 140.00 144.00 148.00 152.00 156.00

-118.2 -110.9 -104.3 -98.1 -92.5 -87.3 -82.5 -78.0 -73.8 -69.9

160.00 166.00 172.00 178.00 184.00 190.00 200.00

----------~-

-66.2 -61.1 -56.5 -52.2 -48.3 -44.7 -39.3

TdB/dT, T2 d 2B/dT2, ems/mol em 3/mol

318 307 295 285 275 266 258 249 242 235

-935 -893 -854 -818 -785 -754 -725 -698 -673 -649

T, K

210.00 220.00 230.00 240.00 250.00 260.00 273.15 280.00 300.00 320.00

B, em 3/mol

-34.5 -30.2 -26.4 -22.9 -19.8 -16.9 -13.5 -11.9 -7.7 -4.1

T dB/dT, T2 d 2B/dT2, cm t/mol ems/mol

95 89 84 79 75 71 66 64 58 54

-230 -214 -200 -187 -176 -166 -155 -150 -136 -124

228 340.00 50 -627 -1.0 -114 215 346.81 0.0 48 -586 -111 204 360.00 46 -550 1.7 -106 193 -517 373.15 3.4 44 -101 184 380.00 43 -488 4.2 -98 -------- ----- ._-------------400.00 40 -92 6.3 176 -462 450.00 10.7 35 -79 168 -438 ------------ ------------ ------------ --------- - -- - -161 500.00 14.1 30 -416 -69 154 550.00 -396 16.8 27 -61 24 148 600.00 -378 19.0 -55 142 134 127 121 115 110 102

-361 -339 -319 -301 -284 -270 -248

650.00 700.00 800.00 900.00 1000.00 1200.00 1400.00

20.8 22.3 24.7 26.4 27.8 29.7 30.9

21 19 16 14 12 9 7

-50 -45 -38 -33 -29 -23 -19

Equation (4i-4) and the procedures described above were used for the quantum gases He, H 2 , and D 2 as well. In these cases, however, the methods were used only to facilitate smoothing and interpolation of vi rial data. For H 20, D 20, and CO 2 a potential of the form (4i-5) was found to be inadequate. These substances were therefore treated as were the quantum gases; that is, the methods outlined were used only for smoothing and interpolation. The tables prepared for these six substances consist only of smoothed experimental B (T) values, with no extrapolations attempted. Tables of T dB/dT and T2 d 2B/dT2 are not given, nor are potential parameters used in the smoothing process reported since they are without clear meaning. Since the B(T) tables for these six substances are so closely tied to the experimental values, minor departures from smoothness in the tables may be detected.

4-213

VIRIAL COEFFICIENTS

Third virials, in all cases, were obtained by graphical interpolation of the (refitted) experimental values for C. They are summarized in Table 4i-16. Table 4i-17 contains values for the Boyle temperature and the inversion temperature. In those cases where the form (4i-5) for the intermolecular potential applies, the potential parameters and the value of m are summarized in Table 4i-18. We note that the optimum value of m is much closer to 18 than to the popular value of 12. 4i-8. Accuracy of the Tables. From a computational point of view, in all cases, the temperature spacing is sufficiently fine to allow for an interpolation to be made

TABLE

4i-l0.

THE SECOND VIRIAL COEFFICIENT OF HYDROGEN

T, K

B,

T, K

ems/mol

24.00 25.00 26.00 27.00 28.00

-112.8 -106.2 -100.3 -94.8 -89.6

74.00 78.00 82.00 86.00 90.00

-12.9 -10.9 -8.9 -7.2 -5.7

29.00 30.00 31.00 32.00 33.00

-85.0 -80.7 -76.7 -73.0 -69.5

100.00 110.00 110.04 120.00 130.00

-2.5 -0.0 0.0 2.0 3.7

34.00 35.00 36.00 38.00 40.00

-66.2 -63.2 -60.2 -55.0 -50.3

140.00 150.00 160.00 170.00 180.00

5.1 6.4 7.6 8.6 9.5

42.00 44.00 46.00 48.00 50.00

-46.2 -42.5 -39.2 -36.2 -33.4

190.00 200.00 250.00 273.15 300.00

10.2 10.8 13.0 13.7 14.4

54.00 58.00 62.00 66.00 70.00

-28.6 -24.5 -21.0 -17.9 -15.2

350.00 373.15 400.00 420.00

15.3 15.6 15.9 16.1

B,

ems/mol

using a quadratic formula without the introduction of errors. Furthermore, linear interpolation can be used without introducing an error of more than 0.3 em t/mol in B(T) owing to the neglect of quadratic terms. It should be noted that where B, T dB/dT, and T2 d 2B/dT2 are available, a Taylor series expansion can be used for in terpolation. It is much harder to assess the absolute accuracy of the tables in any general way. Where data from many sources are available for one substance, as is the case for most of the noble gases and for nitrogen, one usually finds discrepancies up to 1.5 ems/mol in B and up to 30 percent in C between data from different laboratories. Discrepancies in B may become much larger at temperatures below critical. The main source

4-214

HEAT TABLE

TABLE

4i-12.

4i-ll.

THE SECOND VIRIAL COEFFICIENT OF DEUTERIUM

T, K

B, cms /mol

T, K

B, cmj /mol

84.00 88.00 92.00 96.00 100.00

-10.4 -8.7 -7.0 -5.6 -4.2

200.00 220.00 240.00 260.00 273.15

10.2 11.3 12.2 12.8 13.1

110.00 115.00 120.00 130.00 140.00

-1.3 0.0 1.0 3.0 4.6

280.00 300.00 320.00 340.00 360.00

13.2 13.5 14.0 14.4 14.7

150.00 160.00 170.00 180.00 190.00

6.0 7.1 8.1 8.9 9.5

373.15 380.00 400.00 420.00

14.9 15.0 15.2 15.5

THE SECOND VIRIAL COEFFICIENT OF WATER VAPOR

T,K

B, om r/mol

T,K

B, em 3/mol

432.00 434.00 436.00 438.00 440.00

-311.2 -304.5 -298.1 -291.9 -285.5

500.00 505.00 510.00 515.00 520.00

-176.2 -170.4 -165.0 -160.0 -155.3

442.00 444.00 446.00 448.00 450.00

-279.7 -273.9 -268.5 -263.2 -258.2

530.00 540.00 550.00 560.00 570.00

-146.7 -139.1 -132.0 -125.3 -119.0

452.00 454.00 456.00 458.00 460.00

-253.4 -248.9 -244.7 -240.5 -236.5

580.00 590.00 600.00 610.00 620.00

-113.1 -107.6 -102.5 -97.6 93.0

462.00 464.00 466.00 468.00 470.00

-232.6 -228.9 -225.4 -222.1 -218.5

630.00 640.00 650.00 660.00 670.00

-88.6 -84.4 -80.4 -76.6 -72.9

475.00 480.00 485.00 490.00 495.00

-210.2 -202.5 -195.4 -188.6 -182.2

680.00 690.00 700.00 710.00 720.00

-69.4 -66.1 -62.9 -59.9 -57.0

(H 20)

4-215

VIRIAL COEFFICIENTS

of oxygen data (L. A. Weber) is particularly precise, "'0.1 cm in B, and agrees with the others within combined precision. For hydrogen and deuterium, problems with the temperature scale between 100 and 274 K may cause errors in B as large as 0.5 cm 3/mol. For H 20 and D 20 , there is only one source for which the precision ranges from several cm s/mol at the lower temperatures to 0.2 cm 3/mol at the higher ones. For CO 2 , discrepancies of several cm 3/mol in B exist between data of different sources, and for CH 4, of 0.7 cm 3/mol in B and of 10 percent in C. 3/mol

TABLE

4i-13.

THE SECOND VIRIAL COEFFICIENT OF HEAVY WATER VAPOR

T,K

B, em r/mol

T,K

B, cm 3/mol

432.00 434.00 436.00 438.00 440.00

-314.5 -307.8 - 301.3 -295.0 -288.6

500.00 505.00 510.00 515.00 520.00

-177 .6 -171.8 -166.3 -161.1 -156.4

442.00 444.00 446.00 448.00 450.00·

-282.6 -276.9 -271.3 -265.9 -260.8

530.00 540.00 550.00 560.00 570.00

-147.7 -140.0 -132.8 -126.1 -119.6

452.00 454.00 456.00 458.00 460.00

-255.9 -251.4 -247.0 -242.8 -238.8

580.00 590.00 600.00 610.00 620.00

-113.6 -108.1 -103.0 -98.0 -93.3

462.00 464.00 466.00 468.00 470.00

-234.8 -231.1 -227.6 -224.2 -220.5

630.00 640.00 650.00 660.00 670.00

-88.8 -84.6 -80.6 -76.7 -73.1

475.00 480.00 485.00 490.00 495.00

-212.2 -204.4 -197.2 -190.3 -183.8

680.00 690.00 700.00 710.00 720.00

-69.5 -66.2 -63.0 -59.9 -57.0

(D 20)

4i-9. Use of the Tables. The averaged virials presented here can be used for calculations of precise PV products at low pressures. However, in the process of separately averaging and rounding the second and third virials, correlations in their experimental errors have been obliterated; thus, they cannot be used to represent the PVT data from which they were derived within experimental precision over the entire density range. If precise PVT values are needed at higher densities, it is usually preferable to interpolate in the original data. The tables of virials and their temperature derivatives can be used to calculate the initial density dependence of other thermodynamic properties [2].

4-216 TABLE

HEAT 4i-14.

THE SECOND VI RIAL COEFFICIENT OF CARBON DIOXIDE (C0 2)

T,K

B, cm 3/mol

T,K

B, cm t/mcl

250.00 255.00 260.00 265.00 270.00 273.15 275.00 280.00 290.00

-181.8 -174.1 -166.8 -160.0 -153.5 -149.7 -147.4 -141. 7 -136;2 -131.1

420.00 430.00 440.00 450.00 460.00 480.00 500.00 520.00 540.00 560.00

-52.6 -49.1 -45.9 -42.8 -40.0 -34.7 -30.0 -25.8 -21.9 -18.4

295.00 300.00 310.00 320.00 330.00 340.00 350.00 360.00 370.00 373.15

-126.2 -121.5 -112.8 -104.8 -97.5 -90.8 -84.7 -19.0 -73.8 -72.2

580.00 600.00 620.00 640.00 660.00 680.00 700.00 714.81 750.00 800.00

-15.3 -12.4 -9.8 -7.4 -5.1 -3.1 -1.3 0.0 2.7 6.0

380.00 390.00 400.00 410.00

-68.9 -64.4 -60.2 -56.3

850.00 900.00 950.00 1000.00

8.8 11.1 13.0 14.6

285~OO

4-217

VI RIAL COEFFICIENTS TABLE

4i-15.

THE SECOND VIRIAL COEFFICIENT OF METHANE AND ITS TEMPERATURE DERIVATIVES

T dB/dT, T2 d 2B/dT2, cm t/rnol cm 3/mol

B, T dB/dT, T2 d 2B/dT2, cm r/rnol om r/mol cm r/mol

T,K

B, cm 3/mol

110.00 112.00 114.00 116.00 118.00 120.00 122.00 124.00 126.00 128.00

-334.0 -322.2 -311.0 -300.5 -290.5 -281.1 -272.2 -263.7 -255.6 -248.0

671 643 618 594 571 550 531 512 495 479

-2,244 -2,132 -2,029 -1,934 -1,846 -1,764 -1,688 -1,617 -1,551 -1,490

210.00 220.00 230.00 240.00 250.00 260.00 270.00 273.15 280.00 290.00

-95.3 -86.6 -78.9 -72.0 -65.8 -60.2 -55.2 -53.6 -50.5 -46.3

193 179 167 157 147 139 131 129 124 118

-505 -463 -428 -397 -369 -346 -324 -318 -306 -289

130.00 132.00 134.00 136.00 140.00 144.00 148.00 152.00 156.00 160.00

-240.7 -233.7 -277 .0 -220.7 -208.8 -197.9 -187.8 -178.5 -169.9 -161.9

464 449 435 422 398 377 357 340 323 309

-1,432 -1,378 -1,327 -1,280 -1,193 -1,115 -1,046 -984 -928 -877

300.00 320.00 340.00 360.00 373.15 380.00 400.00 450.00 500.00 509.66

-42.3 -35.4 -29.4 -24.2 -21.2 -19.7 -15.7 -7.4 -1.1 0.0

113 103 94 87 83 81 76 65 56 55

-273 -247 -225 -207 -196 -191 -177 -150 -130 -126

164.00 168.00 172.00 176.00 180.00 184.00 188.00 192.00 196.00 200.00

-154.5 -147.5 -141.0 -134.9 -129.2 -123.8 -118.7 -113.9 -109.4 -105.1

295 282 271 260 250 241 232 224 216 209

-831 -789 -751 -716 -683 -653 -626 -600 -576 -554

550.00 600.00 650.00 700.00 800.00 900.00 1000.00 1100.00 1300.00 1500.00

4.0 8.1 11.5 14.3 18.8 22.1 24.7 26.8 29.8 31.9

T,K

-- --- -------

50 45 40 37 31 26 23 20 16 13

------------

-114 -102 -92 -83 -70 -61 -53 -47 -39 -32

- - -- ---- - - - ----

4-218

HEAT

TABLE

4i-16.

THE THIRD VIRIAL COEFFICIENTS OF VARIOUS SUBSTANCES

(C in units of l02 cm 6/ mo12)

He Ne Ar Kr Xe N2 O2 Air H 2 D 2 H 2O D 20 CO2 CH4 - -- - - - - -- - - - - - - --- -- ---- -- -T,K

.. . ... ... .. . .. . .. .

· .. . .. ... · .. ... · .. .. . .. ,

.. .

· .. ... · .. · .. · ., .. . . .. ...

.. . . .. ... .. . ... ... .. .

7

...

.. . .. . .. . .,. .. . · .. ...

· .. · .. · ..

25 30 35 40 45 50 55 60 70 80

2.7 2.5 2.4

4 4 4

90 100 110 120 130 140 150 160 180 200

2.3 2.2 2.1 2.0 1.9 1.8 1.7 1.6 1.5 1.3

4 4 3 3 3 3 3 3 3 3

9 12 16 20 23 25 23 22 20 18

220 240 260 273 280 300 320 340 360 380

1.2 1.1 1.1 1.1 1.0 1.0 1.0 0.9 0.8 0.8

3 3 3 3 3 2 2 2 2 2

16 15 13 12 12 11 11 10 9 9

33 30 28 27 26 24 23 21 20 19

... ...

400 420 440 460 480 500 525 550 575 600

0.7 0.7

2

9

18 18 17 16 16 15 15 14 14 13

34 32 30 28 26 24 22 20 18

650 700

.. . .. . .,. ... ... ... .. . ... ...

.. .

.. . .. .

... 9 ... 8 8 · .. ... 8 7 · .. 7 · .. 7 · .. ... 7 .. . 7 .. . .. . .. . .. .

· .. · ..

. . .. ... . .. ·.. . .. · .. .. . · .. ., . · .. . .. ., . · .. . .. . . ... .. . . .. ·.. . .. . .. · .. . .. .. . · .. . .. ... ... .. . . .. . .. 28 .,

.. . .. . ... · ..

... · .. .. . .. . ... ·.. · .. ... · .. .. . ... . .. ., . 26 23 ... 21 20

.. . ... ... .. . .. . ... ... .. . .. . . .. ...

13 12

.. . ·.. . .. ... . .. . ..

...

62 59 54 50 46 41 36

,

19

17

17 16 15 15 15 14 14 14 13 13

15 13 12 11 11 10

13 12 12 12 12 12

... . .. .. .

.. . .. .

6.4 6.1 5'.9 5.7 5.5 5.4 26 5.3 24 5.2 21 5.0 19 4.8

6 5 5 5 5 5 5 5 5

4.6 4.5 4.4 4.2 4.1 3.9 3.6 3.4 3.2 3.0

5 5 5 5 5 5 5 5 5 4

2.9

4 .... . 3 .... .

18 17 16 15 15 15 14 14

.. . .. . .. . .. .

.. . · .. .. . .. .

14.0 16.0 14.3 12.1 10.7 9.6 8.9 8.4 7.4 6.9

.. . .. . .. . .. . .. . .. . .. . .. . ... .. . · .. .. . · .. .. . .. . · ..

. ...

.... . ....... .... . ..... . ..... . .... ...... . .... ..... .... . . .... .....

.......

.0

•••

.0

•••

.0

•••

. ... .. . . .... . .... . ... .. . . ... .. . .0 ... .... . .0

. ... ·..

•••

•

0

•••

-100 -150

57 56 52 49 45 42 38

29 28 26 24 22 21 19

36 32

18 17 16 16 15 15 14 14 14 13

. .. ... ... . .. ...

. ... . .. - 53 - 64 . ... . .. - 17 - 20 ...

... . · .. + . .... · .. ·.. .. . · .. .. . .. . · .. ..0 . . .. · .. . .. · .. · .. .... I ...

2 9

0 8

12 10

12 12

. .. . ..

4-219

VIRIAL COEFFICIENTS TABLE

4i-17.

THE BOYLE TEMPERATURE AND THE INVERSION TEMPERATURE OF VARIOUS SUBSTANCES

Bovle temperature, K

Substance

Helium Neon Argon Krypton Xenon Nitrogen .. , Oxygen Air Hydrogen Deuterium Carbon dioxide Methane

TABLE

4i-18.

. . " . . . , .. . . . . . .

I temperature, Inversion K

22.64 122.11 411.52 575.00 768.03 327.22 405.88 346.81 110.04 115.30 714.81 509.66

231.42 779.91 1089.72 1455.79 620.63 764.43 658.79

967.81

POTENTIAL PARAMETERS FOR Tm~

m - 6

POTl'~NTIAL

OF SELECTED SUBSTANCES

Substance

m

Elk, K

2~N bo ( = -3cm

Neon ........... Argon .......... Krypton ........ Xenon .......... Nitrogen ........ Oxygen ......... Air ............. ~ethane........

18 18 18 18 21 21 21 21

47.74 160.87 224.78 300.29 139.41 172.93 147.76 217.14

0'3

)

,

3/mol

22.83 43.74 53.78 73.32 54.41 44.49 50.95 57.96

References 1. Hirschfelder, J. 0., C. F. Curtiss, and R. B. Bird: "Molecular Theory of Gases and Liquids," chap. 3, John Wiley & Sons, Inc., New York. 2. Appendix 3B of ref. 1. 3. Burnett, E. S.: J. Appl. Mech., Trans. ASME 58, A136 (1936). Hoover, A. E., F. B. Canfield, R. Kobayashi, and Th. W. Leland, Jr.: J. Chem, Eng. Data 9, 568 (1964). 4. Thomas, H. Preston, and C. G. M. Kirby: Metroloqia 4, 30 (1968). 5. Senger's, J. M. H. Levelt: ASME Proc, 4th Symp. Thermophys. Properties, p. 37, 1968.

6. de Boer, J.: Rept. Proar. Phys. 12,305 (1948). 7. Klein, Max, and H. J. M. Hanley: NBS Tech. Note 360; Trans. Faraday Soc. 64,2927 (1968). 8. Marquardt, D. W.: J. Soc. Ind. Appl. Math. 11,431 (1963). References for Table 4i-2 to 4i-15 Experimental PVT data from sources marked by an asterisk were fitted.

Table 4i-2 : Helium 1. Holborn, L., and H. Schultze: Ann. Physik 47, 1089 (1915). *2. Holborn, r., and J. Otto: Z. Physik 30, 320 (1924).

4-220 3. 4. 5. 6. 7. 8. 9. *10. 11. 12. 13. 14. 15.

HEAT

Michels, A., and H. Wouters: Physica 8, 923 (1941). Kistemaker, J., and W. H. Keesom: Physica 12,227 (1946). Schneider, W. G., and J. A. H. Duffie: J. Chem. Phys. 17, 751 (1949). Yntema, J. L., and W. G. Schneider: J. Chem. Phys. 18, 641 (1950). Keller, W. E.: Phys. Rev. 97,1 (1955). Silberberg, J. J., K. A. Kobe, and J. J. McKetta: J. Chem, Eng. Data 4, 314 (1959). Stroud, L., J. E. Miller, and L. W. Brandt: J. Chem. Eng. Data 5, 51 (1960). White, D., Th. Rubin, P. Carnky, and H. L. Johnston: J. Phys. Chem. 64, 1607 (1960). Canfield, F. B., T. W. Leland, and R. Kobayashi: Advances in Cryog. Eng. 8, 146 (1963}. Witonski, R. J., and J. G. Miller: J. Am. Chem, Soc. 85, 282 (1963). Hoover, A. E., F. B. Canfield, R. Kobayashi, and Th. W. Leland, Jr.: J. Chem. Eng. Data 9, 568 (1964). Boyd, M. E., S. Y. Larsen, and H. Plumb: J. Research NBS 72A, 155 (1968). Cataland, G., and H. Plumb: To be published.

Table 4i-3: Neon *1. *2. 3. *4.

Holborn, L., and J. Otto: Z. Physik 33, 1 (1925). Holborn, L., and J. Otto: Z. Physik 38, 359 (1926). Nicholson, G. A., and W. G. Schneider: Can. J. Chem. 33, 589 (1955). Michels, A., T. Wassenaar, and P. Louwerse: Physica 26, 539 (1960).

Table 4i-4: Argon Holborn, L., and H. Schultze: Ann. Physik 47, 1089 (1915). Holborn, L., and J. Otto: Z. Physik 23,77 (1924). Holborn, L., and J. Otto: Z. Physik 30, 320 (1924). Tanner, C. C., and I. Masson: Proc. Roy. Soc. (London), ser. A, 123, 268 (1930). Michels, A., H. Wijker, and H. Wijker: Physica 15, 627 (1949). Whalley, E., Y. Lupien, and W. G. Schneider: Can. J. Chem. 31,722 (1953). Michels, A., J. M. H. Levelt and W. de Graaff: Physica 24,659 (1958). Lecocq, A., and J. Rech: CNRS 50, 55 (1960). Crain, R. W., and R. E. Sonntag: Advances in Cruoq. Eno. 11, 379 (1965). Weir, R. D., I. Wynn Jones, J. S. Rowlinson, and G. Saville: Trans. Faraday Soc. 63, 1320 (1967). 11. Byrne, M. A., M. R. Jones, andL. A. K. Staveley: Trans. Faraday Soc. 64, 1747 (1968).

*1. *2. *3. 4. *5. 6. *7. 8. *9. 10.

Table 4i-5: Krypton Beattie, J. A., J. S. Brierley, and R. J. Barriault: J. Chem. PhY8. 20, 1613 (1952). Whalley, E., and W. G. Schneider: Trans. ASME, 76, 1001 (1954). Fender, B. E. F., and G. D. Halsey: J. Chem. PhY8. 36, 1881 (1962). Thomaes, G., and R. Van Steenwinkel: Nature 13,160 (1962). Trappeniers, N. J., T. Wassenaar, and G. J. Wolkers: Physica 32, 1503 (1966). Weir, R. D., I. Wynn Jones, J. S. Rowlinson, and G. Saville: Trane. Faraday Soc. 63. 1320 (1967). 7. Byrne, M. A., M. R. Jones, andL. A. K. Staveley: Tran8. Faraday Soc. 64,1741 (1968).

*1. 2. 3. 4. *5. 6.

Table 4i-6: Xenon *1. Beattie, J. M., R. J. Barriault, and J. S. Brierley: J. Chem. PhY8. 19, 1219 (1951). *2. Michels, A., T. Wassenaar, and P. Louwerse: Phueica 20, 99 (1954). 3. Whalley, E., Y. Lupien, and W. G. Schneider: Can. J. Chem. 33. 633 (1955).

Table 4i-7: Nitrogen Holborn, L., and J. Otto: Z. PhY8ik 10, 367 (1922); 23, 77 (1924); 30,320 (1924). Michels, A., H. Wouters, and J. de Boer: Phueica 1. 587 (1934). Saurel, J., and J. Rech: CNRS 42, 21 (1958). Canfield, F. B., T. W. Leland, and R. Kobayashi: Advances in Cryog. Eng. 8. 146 (1963) . 5. Witonsky, R. J., and J. G. Miller: J. Am. Chem. Soc. 85. 282 (1963). *6. Crain, R. W., and R. E. Sonntag: Advance8 in Cruoq. Eng. 11, 379 (1965). *1. *2. 3. 4.

Table 4i-8: Oxygen *1. Holborn, L., and J. Otto: Z. Physik 10, 367 (1922). *2. Michels, A., H. W. Schamp, and W. de Graaff: Phaeica 20. 1141 (1954).

VIRIAL COEFFICIENTS *3. Weber, L. A.: NBS Rept. 9710, 1968. refitting his data for our purpose.)

4-221

(We acknowledge the help of Dr. Weber in

Table 4i-9: Air *1. Holborn, L., and H. Schultze: Ann. Physik 47, 1089 (1915). *2. Michels, A., T. Wassenaar and W. Van Seventer: Appl. Sci. Research A4, 52 (1953). *3. Michels, A., T. Wassenaar, J. M. H. Levelt, and W. de Graaff: Appl. Sci. Research A4, 381 (1954).

Table 4i-l0: Hydrogen *1. Michels, A., W. de Graaff, T. Wassenaar, J. M. H. Levelt, and P. Louwerse: Physica 25, 25 (1959). 2. Goodwin, R. D., D. E. Diller, H. M. Roder, and L. A. Weber: J. Research NBS 68A 121 (1964).

Table 4i-ll: Deuterium *1. Michels, A., W. de Graaff, T. Wassenaar, J. M. H. Levelt, and P. Louwerse: Physica 25, 25 (1959). 2. Knaap, H. F. P., M. Knoester, C. M. Knobler, and J. J. M. Beenakker: Physica 28, 21 (1962).

Table 4i-12: Water Vapor (H 20) 1. Kell, G. S., G. E. McLaurin, and E. Whalley: J. Chem. Phys. 48, 3805 (1968).

Table 4i-13: Heavy Water Vapor (D!O) 1. Kell, G. S., G. E. McLaurin, and E. Whalley: J. Chem. Phys. 49,2839 (1968).

Table 4i-14: Carbon Dwxide (CO!) 1. 2. 3. 4. 5. 6.

Michels, A., and C. Michels: Proc. Roy. Soc. (London), ser. A, 153, 201 (1935). MacCormack, K. E., and W. G. Schneider: J. Chem. Phys. 18, 1269 (1950). Kendall, B. J., and B. H. Sage: Petroleum 14, 184 (1951). Pfefferle, W. C., J. A. Goff, and J. G. Miller: J. Chem. Phys. 23, 509 (i955). Dadson, R. S., E. J. Evans, and J. H. King: Proc. Phys. Soc. 92, 1115 (1967). Vukalovich, M. P., and V. V. Altunin: "Thermophysical Properties of Carbon Dioxide," United Kingdom Atomic Energy Authority Translation, Collet's Publishers, London and W ellingborough, England, 1968.

Table 4i-15: Methane 1. Michels, A., and G. W. Nederbragt: Physica 3, 569 (1936). 2. Schamp, H. W., E. A. Mason, A. C. B. Richardson, and A. Altman: Phys. Fluids 1, 329 (1958). 3. Douslin, D. R.: Proqr. Intern. Research Thermodyn. Transport Properties, p. 135, ASME, Princeton University, 1962. 4. Byrne, M. A., M. R.·Jones, and L. A. K. Staveley: Trans. Faraday Soc. 64; 1747 lI968).

4j. Temperatures, Pressures, and Heats of Transition, Fusion and Vaporization D. D. WAGMAN, T. L. JOBE, E. S. DO:\fALSKI, AND R.

H. SCHUMM

The National Bureau of Standards

Table 4j-l summarizes the data on the temperatures, pressures, and heats for the processes of transition, fusion, and vaporization for a selected list of substances. The table comprises data on stoichiometric inorganic compounds and a small number of organic compounds containing one carbon atom. We have included all the chemical elements for which data are available. We have also included data for halides, oxides, and some nitrates, sulfates, sulfides, and other miscellaneous salts. In some cases, thermodynamic data for vaporization have not been given because of vapor dissociation or decomposition. Noncongruent melting data have also not been included.

Symbols in Table 4j-l c crystal liq liquid g gas tr transition fus fusion vap vaporization sub sublimation equil. equilibrium mixture of molecular species gas in the standard state (ideal gas at 1 atm) g, std. orthorh. orthorhombic monocI. monoclinic Units in Table 4j-l The units of energy in Table 4j-l are the kilojoule (kJ) and the kilocalorie (kcal), connected by the relation 1 kcal = 4.1840 kJ The unit of mass is the mole (mol) based on the mass in grams corresponding to the formula as written in the column headed "Substance." The atomic weights are taken from A. E. Cameron and E. Wichers, J. Am. Chern. Soc, 84, 4175 (1962). The equilibrium saturation pressure is given in mm Hg (1 mm Hg = 133.322 N 1m 2 ) . When needed, exponents of the base 10 are indicated in parentheses. For example, 2.66 (E-9) means 2.66 X 10- 9 • The equilibrium temperature is given in kelvins (K) on the International Temperature Scale (1948).

Sources of the Data The data on transition properties of inorganic substances were summarized in NBS Circ. 500 (see ref. 320). Selected references to data published since ]9.50 are indicated in Table 4j-2, in which the numbers following the chemical formulas refer to the bibliography. We have also made considerable use of such reviews as those by Hultgren et al. [164) and Glushko [129).

4-222

4-223

TRANSITION, FUSION AND VAPORIZATION TABLE

4j-1.

TEMPERATURES, PRESSURES, AND HEATS

State Substance

Initial

Ac .••....... Ag .......... AgBr ........

P

T

mm Hg

K

t>H

Procesa Final

fUB vap

C

liq

liq

g

Ius vap

c liq

g

fU8 vap

c Iiq

liq liq g

............ 760

............ 760

............ 760

............ ............

1234 2436

2.70 59.90

11.30 250.63

697 1778

2.32 44.0

9.707 184.1

3.04 45.5

190.~

1.45 2.25 34.4

6.067 9.41 143.9

AgCN .......

fus

c

Iiq

fus vap

c liq

liq

AgF .........

fU8 vap

c liq

Iiq g

............

708

AgI ..•......

tr fUB vap

c, fl c,a

c, a liq g

............ ............

423 831 1777

liq

760

760

kJ/mol

1323 3473

AgCI ........

g

kcal/mol

619 728.6 1818

12.12

tr fU8

c

C

............

C

liq

............

432.5 483

0.57 2.89

2.38 12.09

AgsS .........

tr

c, fl

c, a

............

450

1.0

4.18

AgSSOL .....

tr fUB

C C

c liq

............ ............

703 933

1.9 4

7.95 16.7

c liq

............

406 1163

liq g

2.66(E - 9) 760

933.2 2793

2.58 70.13

10.79 293.43

4.38 4.38 760

371.1 371.1 528

5.4 18.4 11.6

22.6 76.98 48.53

465.6 465.6

27.1

AgNO •....•..

Ag!Se ........ AI ........... AhBr~ ........

tr fus fus vap fU8 eub vap

C C C

liq C

liq

C

g

liq

g

flU! sub

c

Iiq

C

g

AIF •.........

tr

C

C

All •.........

Ius

C

liq

AhO•........

fus

C

liq

AbCle .......

0.11

1,690 1,690

............

728

2323 978

0.26

1268

2.9

AIPOL ......

tr

C

C

............ ............ ............

Am ..........

fUB

C

liq

1.4(E - 3)

Ar ...........

fUB vap

Q

liq

Iiq

g

516.8 760

As ...........

sub

C

g, equil.

AsCla ........

fUB

C

Iiq

vap

Iiq

g

fU8 vnp vap

C

Iiq liq

liq g g

AsF •••.......

1.68

760

............ 760

............ 142.6 760

0.135

7.029

113.4 0.5648

461.4

83.81 87.29

0.284 1.555

1.098 12.1 1.188 6.506

885 257 404.5

2.44 8.20

10.21 34.31

267.21 292.50 331

2.486 8.566 8.00

10.401 35.840 33.472

4-224

HEAT TABLE

4j-1.

TEMPERATURES, PRESSURES, AND HEATS

State Substance

Final

Ius Yap yap

c liq liq

liq g

g

Ius Yap

c liq

liq

tr

Ius yap Yap

C, III c, II c, I liq liq

c, II c, I liq

Ius yap

c liq

Ius sub fus Yap

c, octahed. c, octahed. c, monoel. liq

fus yap

c liq

liq

fus yap

c liq

liq

fus yap

c liq

liq

Ius yap

c liq

liq

fus yap

c

liq

Iiq

g

BF3 .........

fus Yap Yap

c liq liq

liq g g

B1H G • • • • • • • •

fus yap

c

liq

liq

g

tr

fus Yap

c c liq

c liq

fus yap

c liq

liq

tr

c, a c, fJ c, fJ

c, fJ liq

fus yap yap

c liq liq

liq

tr tr

AsFaO ....... AsHa ........

tr

AsIa ......... As~O~ ........

Au .......... B ........... BBr•........ B(CHa)a ..... BCIa .........

BIHg ........

B20•......... Ba ..........

EaCO' ....... BaCb ........

T

mm Hg

K

kcal/mol

192.9 192.9 220.6

2.71

11.34

4.96

20.75

g

5.0

20.92

g g

Iiq g

liq g

Iiq g

g

g

g

g

g

149 149 760 ............ 760

204.9 248

............ ............ 22.38 22.38 760

32 105.55 156.23 156.23 210.68

0.024 0.131 0.286 3.998

kJ/mol

0.100 0.5481 1.197 16.728

1.1 760

413.6 643.7

5.21 13.45

21.80 56.28

28 28 67 760

551 551 587 734

11.9 26.1 8.8 13.40

49.79 109.2 36.8 56.06

2.955 80.88

335.03

2.15(E - 5) 760

1336 3081

............ 760

2340 4075

5

20.9

227.3 363.1

7.72

32.30

46.5 46.5

199.92 199.92

0.777 5.52

3.250 23.09

............ 760

165.16 285.7

1.627 5.727

6.807 23.962

144.79 144.79 173.2

1.10 4.48 4.16

4.602 18.74 17.40

108.30 180.57

1.069 3.412

4..473 14.276

136.7 226.34 296

0.45 1.466 7.259

1. 88 6.134 30.372

0.686 760

61 61 760 ............

760 ............ ............ 190.2 ............ 0.020

723 1500

5.85 94

24.48 393

58. (E - 6) 0.0107 1.1(E - 3)

648 1002 900

40.5

169.5

g g

............ 0.0037 760

1130 1200 2120

7.63 67.1

31.92 280.7

c, orthorh. c, hexag,

c, hexag. c, cubic

............ ............

1079 1241

4.5 0.7

18.8 2.9

tr

c

fus yap

c

c liq

17.2 16.3

g

1193 1233 2450

4.10 3.90

liq

............ ............ 760

fus sub BaBn .......

t:.H

P

Process Initial

AsFI ........

(Continued)

g

g

4-225

TRANSITION, FUSION AND VAPORIZATION TABLE

4j-1.

TEMPERATURES, PRESSURES, AND HEATS

State Substance

BaI2 .........

T

mmHg

K

t.H

Process Initial

BaF, ........

P

(Continued)

Final

liq

fus sub

c c

g

fus yap

c

liq

liq

g

kcal /mol

kJ/mol

1.58(E - 4) 1.58(E - 4)

1617 1617

6.8 86

28.5 360

1. 18(E - 4) 0.016

984 1200

6.34 53.6

26.53 224.3

9.9

41.4

Ba(NOI)z ....

fus

c

liq

............

865

BaO .........

fus sub

c c

liq

............

2190 1700

BaTiOa ......

tr tr tr tr fus

c c c c, cubic c

c c c c. tetrag.

liq

............

tr fus yap

c. a c. fJ

c, fJ

............

liq

liq

g

0.037 760

tr fus sub yap

c, fJ c, a c, fJ

c. a

liq

g

fus sub

c c

g

tr fus

c c

c

liq

BeSO, .......

tr tr

c, a c. fJ

Bi ...........

fus yap

c c

liq

liq

g

fus yap

c

liq

liq

g

BiF•........ ,

fus

c

liq

............

1033

Bi20 •........

tr fus

c, monocl. c, cubic

c, cubic

liq

............ ............

1003 1100

Bi2S3........

fus

c

liq

............

1036

Br1. .........

fus yap

c

liq

liq

g

45.83 760

265.90 332.35

2.527 7.06

10.573 29.45

fus yap

c

liq

............

liq

g. equil.

281.92 398.90

2.875 9.65

12.029 40.376

fus yap

c

liq g

212.6 314.44

6.96

29.12

sub sub

c, graphite C, graphite

171.291

716.682

Be ...........

BeCh ........

BeF2 ........ BeO .........

BiBr•........

BiCla ........

BrF.......... BrF6 ......... C ...........

-_.

tr fus yap

g

0.0030

............ ............ ............

201.6 285 390 1548 1970

103

431

0.012 0.024 0.050

0.050 0.100 0.209

1527 1560 2745

0.611 2.92 69.89

2.556 12.21 292.41

7.6(E - 4) 760

676 688 504 754

1.32 2.07 33.0 28.9

5.523 8.661 138.1 120.9

1.3(E - 3) 9.8(E - 3)

825 880

1.13 52.9

4.728 221.3

............ ............

2323 2820

1.25

5.23

c, fJ c, "Y

............ ............

861 912

1.2 0.5

5.02 2.1

c

liq

............

liq

g. equil.

liq

liq g

liq

c

g. std. g. equil,

. ...........

............ ............

760

............ 2.59 987

............ 760

760

............ 760 760 760

544.52 1837

2.70

11.30

431 492.0 741

0.74 5.10 17.26

3.10 21.34 72.22

506 713

5.64 17.0

23.60 71.13

7.31 3.99

30.58 16.69

298.15 4100

19.0

79.50

4-226

HEAT TABLE

4j-1.

TEMPERATURES, PRESSURES, AND HEATS

Process Final

Initial

CBn ........

CCI4 .........

CF4 .........

CH4 .........

CHaBr .......

CHaC!.. ..... CHaF........ CH.I ........ CH.OH ......

CHtCh ......

tr fus vap

c, II c, I

c, I

liq

g

tr fus vap

e, II c, I

c. I

liq

liq

liq

g

tr fus vap

c, II c, I

liq

liq

II:

tr fus vap

c, II c, I

c, I

c. I

liq

87.7 760

1.41 0.94 10.4

5.90 3.93 43.5

225.5 250.28 349.9

1.09 0.59 7.17

4.56 2.47 30.00

76.23 89.57 145.14

0.35 0.167 3.01

1.46 0.699 12.59

20.44 90.68 111.66

0.0181 0.225 1.955 0.113 1.429 5.715

0.473 5.98 23.911

0.0757 0.941 8.18

liq

g

760

173.80 179.49 276.71

fus vap

C

liq

liq

g

65.66 760

175.43 248.93

1.537 5.14

6.431 21.50

c

liq

............

liq

g

131.4 195.0

4.06

16.99

206.70 315.65

6.73

28.16

157.6 175.4 337.8 298.15

0.17 0.755 8.43 9.08

0.71 3.159 35.27 37.99

176 312.94

1.1 6.69

4.60 27.99

221.46

5.0

20.92

278.75 279.25 340.7

3.00 2.87 10.2

12.55 12.01

154.9 253.9

5.7

23.8

281.2 422.7

2.65 8.7

11.09 36.4

fus vap

liq

fus vap

C

liq

liq

g

tr fus vap vap

e, III c, I

liq

liq liq

e, I g

g, std.

fus vap

c

liq

liq

g g

c, II c, I

liq liq

CHtO (formaldehyde)

fus vap

COBra .......

760

............

320.1 365.7 460

kJ/mol

g

liq

COt .........

760

............ ............ ............ ............ ............

kcal/mol

c, I

vap

CO ..........

............ ............

K

liq

fus fus vap

CHFa ...•....

Hg

c, II c, I

CHtFt .......

CHCla .......

mrn

tr fus vap

CHtIt .......

CHBra .......

tlH

T

P

State Substance

(Continued)

fus vap

liq

g

C

liq

liq

g

c

liq

liq

g

............

............

760

............ 760

............ ............ 760 760

............

............ 760

............ ............ 15

............ 760

............ 760

............

fus vap

C

liq

liq

g

760

209.7 334.4

2.27 7.10

9.50 29.71

fus vap

C

liq

liq

g

0.456 760

117.97 190.97

0.970 3.994

4.058 16.711

e, II c, I

c, I

............

liq

115.3 760

61.57 68.10 81.66

0.151 0.200 1.444

0.632 0.837 6.042

760

194.640 217.0

6.031 1.99

25.234 8.33

760

333

7.2

30.1

tr fus vap

liq

g

sub fus

c c

g

vap

liq

g

liq

............

4-227

TRANSITION, FUSION AND VAPORIZATION TABLE

TEMPERATURES, PRESSURES, AND Hr~ATs

4j-1.

State Substance

(Continued)

P

T

DoH

mm Hg

K

kcal/mol

kJ/mol

............ ............ ............

139.19 142.09 145.37 280.66

1. 131 1.336 1.371 5.832

4.732 5.590 5.736 24.401

161. 89 188.58

1.603 4.368

6.707 18.276

Process Initial

Final

fus ius ius yap

c, III c, II c, I tiq

ius yap

c tic}

g

ius yap

c !iq

g

760

161. 2 319.37

1.05 6.390

4.39 26.736

ius yap

c tic}

tiq

0.8 760

134.31 222.87

1.130 4.423

4.728 18.506

tr ius yap

c, a c, fJ tiq

c, (J liq

CaBzOI ......

ius

Ca2B206 ..... Ca Bra .......

COCb .......

COF2 ........ CS2 .......... COS ......... Ca ..........

!iq !iq tiq

760

g

tiq

............ 760

............

!iq

g

............

g

6.0(E - 5) 760

720 1112 1757

0.22 2.04 36.72

0.920 8.54 153.64

c

tiq

... , ........

1435

17.67

73.93

tr ius

c, a c, (J

c, {J !iq

............ ............

804 1585

1.10 24.09

4.60 100.79

ius yap yap

c tiq tiq

tiq

............

g g

0.079 760

1014 1250 2088

6.90 56.6

28.87 236.8

CaCz ........

tr ius

e, tetrag. c, cubic

c, cubic !iq

............ ............

720 2430

1.33

CaCOa .......

tr

c, aragon.

c, calcite

. ...........

753

0.05

0.21

CaCh ........

ius yap

c tiq

!iq g

7.3(E-3)

1055 1195

6.78 62.1

28.37 259.8

CaF2 ........

tr ius sub

c, a

C,

............

C,

fJ c, fJ

liq

1424 1691 1625

1.14 7.1 92.0

4.77 29.7 384.9

ius sub

C

!iq

.... ........

C

g

2.6(E - 7)

2887 1675

tr ius

c, a

C,

c, {J

liq

............ ............

1486 1738

5.0 6.7

20.9 28.0

tr ius

C

C

............

C

!iq

............

1398 1817

13.4

56.1

tr tr tr Ius

C,

C, a' C, a' c, a !iq

............ ............ ............ ............

970 1120 1710 2403

0.44 3.44 3.39

1.84 14.39 14.18

CaTiOa ......

tr ius

C, II c, I

e, I !iq

............ ............

1530 2188

0.55

2.30

Cd ..........

ius yap

C

!iq

tiq

g

0.109 760

594.18 1040

1.48 23.79

6.19 99.54

841.2 921

7.97 27.5

33.35 115.1

7.22 31.7

30.21 132.6

CaO ......... CaSOI ....... CaSiO a....... CazSiOl. .....

CdBrs ....... CdCh ........

fus yap tr ins yap

fJ

C, 'Y

c, a' C,

a

fJ

g

fJ

............ 0.08 0.029

C

tiq

!iq

g

12.8 53.2

C

C

............

C

!iq g

!iq

2.04 17.5

73:i 842

950

12 125

5.565

50 523

4-228

HEAT TABLE

4j-1. TEMPERATURES, PRESSURES, AND HEATS (Continued) State

Substance

Initial

Final

Ius sub yap

c c liq

fus Yap

c liq

tr tr tr

c, a

fus

yap

c, ~ liq

fus sub

c c

liq

Ce20•........

fU8

CI2..........

fus Yap

fus yap

c liq

liq

CIF•..•......

tr fU8 yap

c c liq

c liq g

CIO, .........

Ius Yap

c liq

liq

Co ..........

tr fus yap

c, a c, fJ liq

c, fJ liq

CoCh ........

fus yap

C

liq

liq

g

C

liq

C

g

CdF, ........

CdI, ......... Ce .....•.....

CeO, ........

CIF ..•......

CoF, ........

P

T

mm Hg

K

t1H

Process

fus sub

liq

kcal/mol

kJ/mol

............ 1322

g g

0.024 760

1185 2021

64.5 52.3

269.9 218.8

liq

0.52 760

661.2 1013

4.95 26.4

20.71 110.46

............ 760

125 350 999 1071 3699

0.715 1.305 99

2.992 5.460 414

g

1.2(E - 3) 1.2(E - 3)

2670 2670

88

368

c

liq

............. 2415

C

liq

liq

g

o, fJ o, 'Y

g

c, fJ c, 'Y c, ~ liq g

g

g

g

CoO .........

fU8

C

liq

Cr ...•.......

fus yap

C

liq

liq

g

............ ............ ............

10.1 760

172.12 239.05

1.531 4.878

6.406 20.410

119 172.9

5.34

22.34

760

190.50 196.84 284.90

0.36 1.819 6.580

1.51 7.611 27.531

20.8 760

214 282.8

6.2

25.9

............ 760

............ ............

............ 700 ............ 1768 760 ............ 760

3.01 3.01

3201

0.108 3.87 90.0

0.452 16.19 376.6

1000 1323

7.4 27.2

30.9 113.8

1400 1400

10.72 68.1

44.85 284.9

4.047 82.3

16.93 344.3

890

56.6

236.8

420

15.7

............ 2078 3.25 760

2130 2945

CrBr•..•.....

sub

C

g

Cr(CO)e. ....

Bub

C

g

CrF•.•.•.....

tr tr sub

C

C

C

C

............ ............

c

g

2.7(E - 3)

CnO•........

tr fus

c c

c liq

............ 305 ............ 2548

0.10

0.418

Cs ........•..

fus yap

c liq

liq

1.4(E - 6) 760

0.52

2.18

fus Bub yap

C

liq

c liq

g

5.64 46.6 36.0

23.60 195.0 150.6

CsBr ........

g, equil,

g

0.076 724

0.20 5.9(E - 3) 760

45.6 69.8 1000

301.8 955 909 800 1576

57.8

65.69

241.8

4-229

TRANSITION, FUSION AND VAPORIZATION TABLE

4j-1.

TEMPERATURES, PRESSURES, AND HEATS

State Substance

P

T

mm Hg

K

(Continued) AH

Process Initial

Final

kcal/mol

kJ/mol

g

............ 101.1 760

743 918 1573

0.90 4.82 35.4

3.76 20.16 148.1

g liq g

0.008 ............ 760

800 976 1524

46.4 5.19 34.3

194.1 21.71 143.5

c Iiq

liq g g

0.260 0.260 760

899 899 1524

5.90 45.5 34.3

24.68 190.37 143.5

tr fUB

c, hexag. c, cubic

c, cubic liq

............ ............

424.7 678

0.89 3.37

3.72 14.10

CBOH .......

tr fus

c, a c,fJ

c, fJ liq

............ ............

488 619

1. 76 1.6

CB2S0 •.......

tr fUB

c c

c liq

............ ............

1005 1286

9.6

40.17

fUB yap

C

liq

liq

g

4.49(E - 4) 760

1356.5 2839

3.14 71.77

13.14 300.29

tr tr fUB Bub

c, 'Y c, fJ c, a c, a

fJ c, a liq g

............ ............ 0.276 0.276

658 743 756 756

29

121

fUB Bub

C

liq

C

g

............ 2.54(E - 4)

703 550

35.4

148.1

CUF2 ........

fUB Bub

C

liq g

7.9(E - 6) 8.85(E - 3)

1058 960

59.5

248.9

(Cu Ij s .......

tr tr fUB

c,

............

c, fJ c, a

c, fJ c, a liq

............ ............

644 682 871

tr fUB

c c

c liq

............

329

tr tr

c, III c, II

c, II C, I

............

............

376 ........

tr fUB yap

fJ

liq

fUB yap

liq

fUB yap

liq

CsCl .........

tr fus yap

c, II c, I liq

c, I liq

CsF .........

Bub fUB yap

c c liq

CBI ..........

fUB Bub yap

C

CBNO a.......

Cu .......... (CuBr)a ......

(CUCl)a ......

CU20 ........ CU2S........

Dy ..........

Er ........... ErCl: ........ ErFa ......... Eu .......... EuCl a........

C

'Y

C,

............ 1515

4.2 2.1

5.1 2.3

7.363 6.69

17.57 8.79

21.3 9.62

15.35

64.224

0.92 0.20

3.85 0.837

C,

a

C,

C,

fJ

liq g

............ 0.591 760

1657 1682 2835

0.955 2.64 55.0

3.996 11.06 230.1

liq g

0.317 760

1795 3136

4.76 62.47

19.92 261. 37

1049 1250

7.8 53.6

32.6 224.3

C

C

liq g

............ 2.07

tr fUB

C

C

............ 1369

C

liq

............

1413

fUB yap

C

liq

Jiq g

0.72 760

1090 1870

2.20 34.30

9.21 143.49

fUB yap

Jiq

Iiq g

............ 1.0

891 1140

31

130

C

4-230

HEAT TABLE

4j-1.

TEMPERATURES, PRESSURES, AND HEATS

Process Final

Initial

mm Hg

t::.H

T

P

State Substance

(Continued)

I

K

kcal/mol

kJjmol

0.174 0.122 1.562

0.728 0.5104 6.535

1373 2510

EU20a .......

tr Ius

c c

c liq

............ ............

F2...........

tr

c c liq

c liq g

............ 1.66 760

C

liq

liq

g

............ 760

yap

c. a c. {J c. 'Y c. li liq

c. {J c, 'Y c. s liq g

............ ............ ............ 0.026 760

tUB

C

liq

yap

liq

g

Fe(CO)G .....

fus yap

c liq

liq

FeCh ........

fus yap

c liq

liq g

8.84 760

(FeClah ......

sub

c c liq liq

g

yap yap

126 547 610 760

FeF2 .........

tr fus sub

c c c

g

............ 6.0 2.1(E - 3)

72.4

302.9

FeF, .........

Bub

c

g

9.6(E - 3)

880

52.7

220.5

FeI2 .........

tUB

c liq liq

liq

yap yap

5.8 5.8 760

867 867 1208

13.3 35.6

55.65 148.9

g

Feo.g470......

tr fus

c c

c liq

............ ............

189 1650

0.06 7.5

Fe20J ........

tr tr

c. III c, II

c. II c. I

............ ............

960 1050

0.16 0.0

Fe.Of ........

tr fUB

c. II C, I

c. I liq

............ ............

880 1867

FeS .........

tr tr

c. III c. II c. I

c. II c, I liq

............ ............ ............

411 598 1468

fUB yap

C

liq g

............ 760

302.9 2520

fus Bub yap

c c liq

liq

10.4 10.4 760

350.9 350.9 474.4

5.2 17.4 10.5

21.8 72.80 43.93

fUB vap

c liq

17.2 760

485 619

3.1 16.5

13.0 69.04

fus

yap F20 ......... Fe ...........

tUB yap tr tr tr tUB

FeBrs ...... , .

tUB

tUB

Ga .......... (GaClah. ....

Gal, .........

liq

g

liq g

g c liq

~

g g

liq g

21 102 ............ 760

45.55 53.54 85.02 49.4 128.1

2.41

10.08

1033 1184 1665 1809 3135

0.0 0.215 0.200 3.30 83.55

0.0 0.8996 0.837 13.81 349.56

962 1073

31.6

132.2

252.88 378

8.7

36.4

950 1299

10.28 30.2

43.011 126.4

550 577 583 592

30.6 18.3 12.3 12.1

128.0 76.57 51.46 50.63

78.35 1373 1060

0.0 33

0.25 31.4 0.669 0.0 0.0 138

0.57 0.12 7.73

2.38 0.502 32.34

1.335 61.46

5.585 257.16

4-231

TRANSITION, FUSION AND VAPORIZATION TABLE

4j-1.

TEMPERATURES, PRESSURES, AND HEATS

State Substance

P

T

mmHg

K

AH

Process Final

Initial

............

liq

c, {J liq g

c

liq

fUB vap

c liq

liq g

GdF3 ........

tr fUB

c c

GdsO, .......

tr fus

Ge ..........

fU8 vap fU8 vap

C

liq

liq

g

fUB Bub vap

c c liq

liq

sub fUB

c c

tr tr fU8 vap

c, III c, II c, I liq

sub fUB

c c

GeOs ........

tr fUB

HI ..........

kJjmol

3.912 10.04 359.4

............ 1058

8.7

36.4

............ 0.37

875 1183

9.6 44.0

40.2 184.1

c liq

............ ............

1280 1301

c, monoc!. c

c, cubic liq

............ ............

1473 2595

C

liq

............ 1210.4

liq

g

8.83 79.1

36.94 330.9

c, a e, fJ

GdBr' .......

fUB

GdCl s ..•..•.

.............

760

760

1533 1585 3539

kcal z'mol

0.935 2.40 85.9

tr fUB vap

Gd ..........

(Continued)

3107

............ 760

299.3 462

9.4

39.3

0.59 0.59 760

221.6 221.6 356.4

1.8 10.9 7.2

7.53 45.61 30.12

236.6 258.1

7.8

32.6

............ ............ ............ 760

73.2 76.6 107.25 184.79

0.050 0.086 0.200 3.361

0.209 0.360 0.8367 14.062

liq

0.22 ............

380 417

c, II c, I

c, I liq

............ ............

1306 1389

fUB vap vap

c liq liq

liq

54.0 54.0 760

tr tr fus vap

c, III c, rhombic c, cubic liq

c, rhombic c, cubic liq

tr fUB vap

c, II e, I liq

c, I liq

Hel ...•.....

tr fU8 vap

c, rhomb, e, cubic liq

c, cubic liq

HF ..........

fU8 vap

c liq

liq

tr tr fUB vap

c, III c, II c, I liq

c, II c, I liq

GeBrL ...... GeCl», .•.....

GeFL ....... GeH •........

Gel•.........

HBr .........

HCN ........

HI ..........

g g g

liq c. II c, I liq g g

g g

g

g

g

g, equil,

g

760 3032

13.957 13.957 20.38

19.5 5.05 3.59 0.028 0.219 0.219

81.6 21.13 15.02 0.117 0.9163 0.9163

............ ............ 285 760

89.8 116.9 186.24 206.38

0.575 4.210

2.406 17.615

170.42 140.4 760

0.004 259.91 298.85

2.009 6.027

8.4057 25.217

............ 103.4 760

98.36 158.91 188.07

0.284 0.476 3.860

1.188 1.992 16.150

4.03 760

189.79 292.67

0.939 1.790

............ ............ 371 760

70.1 125.7 222.31 237.75

0.686 4.724

3.929 7.4894

2.870 19.765

4-232

HEAT TABLE

4j-1.

TEMPERA,TURES, PRESSURES, AND HEATS

State Substance

t:.H

P

T

mm Hg

K

kcal/mol

k.l /mol

............

231.55 293.1

2.503 9.42

10.473 39.41

4.58 4.58 23.75 760 760

273.16 273.16 298.15 298.15 373.15

1.436 10.767 10.514 10.520 9.717

6.0082 45.0491 43.9906 44.0157 40.656

............

103.50 187.61 187.61 212.80

0.365 0.568 4.67 4.463

1.527 2.377 19.54 18.673

Process Initial

Final

fus yap

c liq

liq g

H,O .........

fus yap yap yap yap

c liq liq liq liq

liq g g g, std. g

H,S .........

tr fus yap yap

c, II c, I liq liq

c. I liq g g

HNO •.......

(Continued)

48

174 174 760

H'SOL ......

fus

c

liq

............

283.5

2.560

10.711

H,Se ........

tr fus yap yap

c, II c, I liq liq

c, I liq g g

............

205.4 205.4 760

82.3 207.46 207.46 231.8

0.309 0.601 5.48 4.76

1.293 2.514 22.93 19.91

H,Te ........

fus yap

c liq

liq g

70 760

222 270.9

1.0 5.6

4.18 23.4

H.PO~.......

fus

c

liq

315.5

3.07

12.84

IH'H ........

fus yap

c Iiq

liq g

93 760

IH!HO .......

yap yap

liq liq

g g

22.0 760

298.15 374.0

10.65

44.56

!H20 ........

fus yap yap

c liq Iiq

liq g g

5.01 5.01 760

276.96 276.96 374.58

1.508 11.105 9.933

6.309 46.463 41.559

He ..........

Ius tr yap

c liq, II liq, I

liq liq, I g

22.5(E + 3) 37.8 760

Hf ...........

tr fus yap

c, a c, fJ liq

c, fJ liq g

............

sub fus

C

g Iiq

83.3 15,270

fus sub yap

C

sub sub

C

g

C

g

c, a

c, fJ c, 'Y g

............

Hf Br s, .......

HfeIL .......

HfFL ....... Hf!.. ........

tr tr sub

C

C

liq

c,fJ c, 'Y

liq g g

............

1.1(E - 3) 760

2.2(E - 4) 2.2(E - 4) 2.2(E - 4) 54.1 760

760

HfO, ........

fus

C

Iiq

............

Hg ..........

fus yap

C

............

liq

liq g

fus yap

liq

liq g

.... , ....... 760

HgBrz .......

C

760

16.62 22.14

1.764 2.172 4.214

0.038 0.257

0.159 1.075

0.002

0.0084

0.020

0.084

2013 2500 4876

1.61 5.75 137

6.736 24.06 573.2

531 693

23.5

98.40

705 705 705

23.8 14.1

99.58 58.99

1112 1240

56.9

238.1

697 745 667

14.4 5.4 28.2

60.25 22.6 118.0

3026 234.29 629.73

0.548 14.172

2.292 59.296

511.2 592

4.28 14.08

17.91 58.91

4-233

TRANSITION, FUSION AND VAPORIZATION TABLE

4j-1.

TEMPERATURES, PRESSURES, AND HEATS

State Substance

T

Final

mmHg

K

kcal/rnol

kJ/mol

............ ............

428 553.2 575.0

0.077 4.55 14.08

0.322 HL04 58.91

178

575 918

16

66.9

0.20 8.8 8.8 760

404.6 530 530 627

0.65 19.95 4.53 14.26

2.72 83.47 18.95 59.664

659

1.0

4.18

1701 1743 2968

1.12 2.91 57.6

4.686 12.17 241.0

993 1143

7.0 62.7

29.3 262.3

1416 1416 1416

105.0 85.1

439.32 356.1

2640

tr fus yap

c c

c

liq

g

su.b fus

c c

g

tr Bub fUB yap

c, red c, yellow c, yellow

liq

g

HgS .........

tr

c, red

c, black

Ho ..........

tr Ius yap

C, a

c, fJ

c,fJ

liq

liq

g

fUB yap

c

liq

liq

g

fus sub yap

e

liq

c

g

liq

g

1.57(E.- 3) 1.57(E - 3) 1.57(E - 3)

fUB

c

liq

............

Bub fus yap

c c

g

liq

liq

g

fUlJ 8Ub

o

liq

c

g

fUB yap

c

liq

liq

IF1 ..........

tr sub

In ...........

fus yap

HgFI ........ HgII .........

HoCIa ........ HoFI ........

HOIOI ....... II ...........

ICi. ......... IF, .•........

InBrl ........ InCl .........

AH

P

Process Initial

HgCh .......

(Continued)

liq

liq e, yellow g

liq

760

............

............ ............ ............ 760

............ 0.25

0.31 92.0 760

298.15 386.75 458.39

14.93 3.71 9.99

62.467 15.52 41.80

32.62 32.62

300.53 300.53

2.76 12.62

11.55 52.80

g

10.45 760

282.58 374

9.04

37.82

c c

c

............

7.46

31.21

c

liq

g

liq

g

fU8 sub

c c

liq

tr fus yap yap

e, II c, I liq

liq

g

760

............ 760

153 277 429.76 2343

392 9.9(E - 4)

709 460

c, I

............

liq

0.038 6.63 760

393 498 656 926

g

g

............

0.78 55.4

231.8

33.5

140.2

21.2

88.70

fUB sub

c

liq

c

g

6.3(E - 4}.

859 510

37.0

fus

c

liq

yap

liq

g

0.26 0.26

480 480

19.2

80.33

InIOI ........

fUB

c

liq

............

2183

Ir ........ " .

fus yap

c

liq

liq

g

............ ............

2716 4662

6.3146.3

2.64 612.3

c c

o

liq

g

InCh ........ InII .........

IrFa .........

tr fUB yap

liq

61. 7 531.3 531.3

273.5 316.9 316.9

1. 70 0.1 7.65

154.8

7.11 2.. 93 32.01

4-234

HEAT TABLE

4j-1.

TEMPERATURES, PRESSURES, AND HEATS

State Substance

P

T

mm Hg

K

Final

............

fUB yap

c

Iiq

Iiq

g

fUB yap

c

Iiq

liq

g, equil,

KCN ........

tr fUB

c, II c, I

c, I Iiq

............ ............

KCl .........

fUB yap

c

Iiq

Iiq

g, equil,

0.40 760

fUB yap

c Iiq

liq g

............

fUB yap

c

Iiq

Iiq

g, equil,

KNO a.......

tr fus

c, II c, I

e, I liq

............ ............

KOH ........

tr fUB yap

c, II c, I Iiq

c, I Iiq

............ ............

g

K2S04. ......

tr fus

c, II c, I

c, I Iiq

Kr ..........

fus yap

C

Iiq

liq

g

549 760

Bub

C

g

29

KBr .........

KF .......... KI ..........

KrFs ........

760

KrF•........

sub

C

g

tr tr fUB yap

c, a

C,

c,

(J c, 'Y

C. 'Y

Iiq

liq

g

LaCIa ........ LaF •.........

Bub fUB Bub fUB

C

g

C

liq

C

g

c

liq

760

1657

0.562 19.18 6.1 30.8

kJ/mol

2.351 80.23 25.5 128.9 1.26 14.6

1044 1700

6.282 28.7

26.284 120.1

1130 1775

6.75

28.24

760 0.36 760

954 1617

............ ............

168.3 908

kcaI/mol

0.30 3.5

401.1 610

5.7 26.9 1.22 2.413

23.8 112.5 5.104 10.096

522 677 1600

1.52 1.8 30.8

6.360 7.53 128.9

856 1342

1.94 8.76

8.12 36.65

115.78 119.93

0.392 2.162

273

9.9

41.42

1.640 9.046

341

8.3

34.73

550 1134 1193 3730

0.087 0.746 1.481 98.9

0.364 3.121 6.196 413.7

0.0032 0.0102

1026 1061

70.7 13.0

295.8 54.39

0.0010 0.0072

1067 1131

72.3 13.0

302.5 54.39

8.9(E - 3) 1.46

1495 1763

99.4

415.9

9.0(E - 3) 9.0(E - 3)

1034 1034

69.9

292.5

760 {J

336.4 1031

............ 1007

760

La ..........

LaBra ........

t:.H

Process Initial

K ...........

(Continued)

............ ............ ............ 760

Bub Ius

C

g

C

liq

fus Bub

C

liq

C

g

LasOa ..•.....

fus

C

Iiq

............

2490

Li ...........

tr fUB yap

c, II C, I liq

c, I liq

............ ............

77 453.69 1597

0.717 35.40

3.000 148.13

fUB yap

C

liq

liq

g, equil,

823 1555

4.22 27.0

17.65 113.0

fUB yap

C

Iiq

19.83

g

883 1656

4.74

liq

fUB yap

C

liq

27.087

g, equil,

1121 1966

6.474

liq

LaI •.........

LiBr .••...... LiCl. ........ LiF ..••......

g

760

............ 760

............ 760

............ 760

4-235

TRANSITION, FUSION AND VAPORIZATION TABLE

4j-1.

TEMPERATURES, PRESSURES, AND HEATS

State

Substance

T

mm Hg

K

tJ.H

Process Initial

LiI ..........

P

(Continued)

Final

fUB yap

liq

liq g, equil.

C

............

760

kcal/mol

kJjmol

742 1415

3.50 26.4

14.64 110.4

LiNOa .......

fUB

c

liq

............

525

6.1

25.5

LiOH ........

fUB

c

liq

............

744.3

5.01

20.96

Li tS04 .......

tr fUB

e, II c, I

c, I liq

............ ............

859 1132

6.5 1.8

27.2 7.53

Lu ..........

fUB yap

c liq

liq g

0.011 760

1936 3668

4.46 85.06

18.65 355.89

fUB yap

C

liq

............

liq

g

1165 915

57.2

239.3

tr Bub fUB

c c c

c g liq

............

1200 1368 1455

96.1

402.1

............

LU20a ........

fUB

c

liq

............

2740

Mg ..........

fUB yap

c liq

liq g

3.10 760

922 1363

2.140 30.45

8.954 127.40

Mg'Brs .......

Bub fUB

c c

liq

842 984

50.3 8.3

210.5 34.7

fUB Bub yap

c c liq

liq g

0.120 0.120 30.7

987 987 1310

10.30 57.7 43.08

43.095 241.4 180.25

MgFt ........

fUB yap

c liq

liq g

0.077 0.077

1525 1525

13.90 72.6

58.158 303.8

MgI2 ........

Bub

c

g

757

45.0

188.3

MgaN2 .......

tr tr

c, III c, II

c, II c, I

............

LuCia ........ Lu Fs ........

MgCb .......

g

g

0.89 1.1(E - 3)

0.017 ............

0.015

............

823 10.61

MgO ........

fUB

C

liq

............ 3125

MgSO•.......

tr fUB

c, II c, I

c, I liq

............ 1283 ............ 1400

Mn ...•......

tr tr tr fUB yap

c, a c, fl c, 'Y e, Ii liq

c, fl c, 'Y c, Ii liq g

............ 980 ............ 1360 1.03 760

1410 1517 2335

MnBn .......

fUB

c

liq

............

971

MnCh .......

fUB yap yap

C

liq

liq liq

g g

0.24 0.24 760

fUB Bub

C

liq

c

g

............

911 2088

MnF2 ........

............

0.031 0.031

0.22 0.26

0.920 1.09

18.5

77.40

3.5

14.6

0.532 0.507 0.449 2.88 54.0

2.226 2.121 1.879 12.05 225.9

923 923 1511

8.97 40.0

37.53 167.4

1203 1203

72.0

301.2

Mnh ........

fUB

C

liq

MnO ........

fUB

C

liq

............

MnIO •.......

tr fUB

c, II c, I

c, I liq

............ 1445 ............ 1840

4.97

20.79

4-236

HEAT TABLE

4j-1.

TEMPERATURES, PRESSURES, AND HEATS

State Substance

P

T

mm Hg

K

(Continued) !:J.H

Process Initial

Final

kcal/mol

kJ/mol

fus yap

c

liq

liq

g

Mo(CO)e. ....

sub

c

g

Mo Fs ........

fus yap

c

liq

liq

g

MoF 6 • • • • • • • •

tr Ius yap

c, II c, I

c, I

liq

MoOa ........

fus

c

N2 ..........

tr fus yap yap

c, II c, I

e, I

liq

liq liq

g g

............ 93.9 93.9 760

35.61 63.15 63.15 77.35

0.055 0.172 1.446 1.335

0.230 0.719 6.050 5.586

fus yap yap

c

liq

liq liq

g g

45.37 45.37 760

195.40 195.40 239.73

1.351 6.061 5.581

5.652 25.359 23.351

fus yap

c

liq

liq

g

............ 764

274.69 386.7

3.025 9.70

12.656 40.58

tr fus

c, II c, I

c, I

............ ............

411.0 815

0.77

3.22

tr tr fus

c, III c, II c, I

............ ............ 2.62(E 4)

243 457.7 793

0.27 1.0

1.13 4.18

NH.F .......

tr

c, II

e, I

............

289.1

0.81

3.39

NH.I ........

tr fus

c, II c, I

c, I

............

0.70

2.93

liq

............

260 824

tr tr tr tr fus

c, c, e, e, c,

c, c, c, o,

256.2 305.4 357.4 398.4 442.8

0.111 0.410 0.32 1.01 1.3

0.464 1.715 1.34 4.23 5.44

fus yap yap

C

liq

liq liq

g g

164.4 164.4 760

109.50 109.50 121.4

0.550 3.43 3.293

2.301 14.35 13.778

fus yap yap

C

liq

liq liq

g g

659 659 760

182.1 182.1 184.6

1.56 3.97 3.958

6.527 16.61 16.560

fus yap

C

liq

liq

g

760

370.98 1156

0.622 23.43

2.601 98.01

0.4 760

1020 1665

6.25

26.15

0.15 0.70 4 37

0.628 2.93 17 155

6.73

28.16

Mo..........

NHa .........

N 2H4. ....... NH.Br....... NH.Cl. ......

NH.NOa.....

NO ..........

N 2O.........

Na .......... NaBr ........ NaCN .......

NaCl ........

fus yap tr tr fus yap fus yap

V IV III II I

0.031 760

2890 4880

6.65 141.6

27.82 592.45

375

16.3

68.20

2.67 760

340.1 486.7

11.9

49.79

g

............ 408.5 760

263.50 290.76 307.2

liq

1. 76(E - 2)

48

liq

liq c, II c, I

liq

IV III II I

liq

C

liq

liq

g, equil.

c, III c, II c, I

c, II c, I

liq

liq

g

C

liq

liq

g, equil,

+

............ ............ ............

............ ............

............

............ ............ ............ 760

1074

172.1 288.5 836 1770

............ 1074 760

1730

1.953 1.034 6.75 11.69

8.171 4.326 28.242 48.911

4-237

TRANSITION, FUSION AND VAPORIZATION TABLE

4j-1.

TEMPERATURES, PRESSURES, AND HEATS

State Substance

Nal ...•..... Na2Mo04 .... NaNO •...... NaOH ....... Na2S04 ......

Na2TiO•..... Nb .......... NbCla .......

NbF•........ Nb02........

liq g, equil,

fU8 vap

liq

e. equil,

tr fU8

e, II c, I

liq

tr fU8

c, II c, I

c, I

tr fU8

c, II c, I

c, I

tr tr fU8

c, V c, III c, I

c, III e, I

tr fU8

C, C,

fU8 yap

C

liq

liq

g

760

fU8 sub yap

C

liq

C

liq

g g

260 260 760

fU8 yap

C

liq

liq

g

lig

C

II I

fU8

C

Nd ..........

tr fU8 yap

C, a

NdIs ........

Nd20 •....... Ne ..........

Ni ...........

fU8 sub fU8 sub

C, a

fJ

C, 'Y

c, I

liq liq

liq c, I

liq

c, fJ c, 'Y

Hg

............

c

Nb20•.......

NdF•........

mrn

liq

C,

NdCla .......

Final

fU8 yap

tr tr fU8

NdBrl .......

T

fj.H

Process Initial

NaF ..•......

P

(Continued)

760

............ 760

............ ............ ............ ............ ............ ............ ............ ............ ............ ............ ............

............

2.44 58.0

............ ............

K

kJ/mol

1269 1977

7.92

3&.14

933 1577

5.64

23.60

713 960

14.6 3.6

549 579.5

0.94 3.696

566.0 592.3

1.520 1.52

450 515 1157

0.74 1. 79 5.70

61.09 15.1 3.93 15.464 6.3597 6.360 3.10 7.489 23.85

560 1303

0.4 16.8

1.7 70.29

2740 5017

6.30 163

26.36 682.0

478.9 478.9 520.5

8.09 21. 3 12.6

33.85 89.12 52.72

350.7 423

2.92 12.9

12.217 53.97

5.0(E - 4)

1090 1200 1900

0.72 0.0' 21

3.01 0.0 87.9

liq

............

1780

24.69

103.30

c, fJ

............

1128 1289 3341

0.72 1.71 65.2

3.01 7.15 272.8

1.06(E - 4) 1.06(E - 4)

955 955

10.8 67.6

45.19 282.8

2.2(E - 3) 2.2(E - 3)

1032 1032

12.0 69.1

50.21 289.1

1460 1647

85.7

358.6

3.4 66.3 9.7

14.2 277.4 40.6

liq

c, fJ

liq

liq

g

C

liq

C

g

C

liq

C

g

............ 760

8ub fU8

C

g

C

liq

tr sub fU8

C

C

C C

liq

4.5(E - 3) 0.063

847 978 1060

tr fU8

C,a

c,fJ liq

............ ............

1395 2485

c, IJ

kcal/mol

g

fU8 yap yap

C

liq

liq liq

g g

fU8 yap

C

liq

liq

g

0.012 0.35

............

324 324 760 3.1(E - 3) 760

24.544 24.544 27.15 1726 3187

0.14

0.586

0.08 0.431 0.429

0.33 1.803 1.795

4.176 88.5

17 .472 370.3

4-238

HEAT TABLE

4j-1.

TEMPERATURES, PRESSURES, AND HEATS

P

T

mmHg

K

State Substance

t:..H

Process Initial

NiBrt ........

(Continued)

sub sub CU8

c c c

Final

g

0.044 760

g

liq

••

ee

••••••••

823 1193 1236

kcal /rnol

52.5

kJ/mol

219.7

CU8

c

liq

yap

liq

g

46.6 760

NiCls ........

eub sub

g g

0.045 760

CU8

c c c

liq

NiFt .........

sub

c

g

Nilt .........

sub

c c

liq

............

c. III c. II C, I

c. II c. I

............ ............

c, III c, II c. I

c, II c, I

fus CU8

C

liq

yap yap

liq liq

g g

tr tr CU8

c, III C, II c, I

liq

yap yap

liq liq

g g

CU8

c

liq

yap

liq

g

CU8

C

liq

............

sub

C

g

6.2(E - 6)

CU8

c

liq

yap yap

liq liq

g g

0.566 15.1 760

343.1 400 499.0

15.69

65.647

81.3 463.6 463.6 760

272.7 306.5 306.5 320.6

2.0 1.6 8.40 6.70

8.37 6.69 35.15 28.03

305.6 332.3 354.0

1.62 8.74

6.778 36.57

195.35 317.30 317.30 530

0.500 0.628 13.32 12.48

2.092 2.628 55.731 52.216

232.7 446.4

9.33

39.04

183 348.3

7.17

30.00

Ni(COk ....

CU8

NiO .........

tr tr CU8

Np ..........

NpF•........

Ot .••........

0 •........... Os ....•...... OsF•.•••.....

OaF•.........

OsOF•.......

tr tr

PCla .........

liq

c, II c, I

18.47

1080

77.3

323.4

0.43

750 1070

36.5

152.7

525 565 2263

0.0 0.0

0.0 0.0

533 850 910

2

4.4

327.92 327.92 328.33

4.189 7.133

87

............ ............ ............ 748.6 748.6 760

............ ............ 1.14 1.14 760 0.86 760

ty

c

c

C

liq

c

liq

g g

c, II c. I

c. I

............

liq

liq

g

175.6 394.6

tr fus yap yap

c. IV C, III

c, III

liq liq

g g

CU8

C

liq

yap

liq

g

CU8

C

liq

yap

liq

g

tr

liq

............ ............ ............ 760

............ 760

............ 760

23.85 43.77 54.363 54.363 90.180 80.65 161.3 3323 2550

53.0

13.832 29.3

2.5(E - 3)

............

CU8

yap

PBr. .........

liq

3.306 7.0

850 1243 1303

sub yap

CU8

P •...........

g

253.86 315.4

0.022 0.178 0.106 1.828 1.630 0.5 3.58 187.4

221.7 77.28

17.527 29.844 0.0920 0.745 0.4435 7.648 6.820 2.1 14.98 784.1

4-239

TRANSITION, FUSION AND VAPORIZATION TABLE

4j-1.

TEMPERATURES, PRESSURES, AND HEATS

State Substance

PF•..•......

PF•.........

PH•.........

P.06.........

P.OIO........

Pb .......... PbBrs .......

Pb(CH.) •.... PbCh ........

PbF.........

PbO .••••....

mmHg

K

............

437.7 432

l:1H

Final

kcal /mol

kJ/mol

ius Bub

c c

liq

tr tr iUB vap

c, III c, II c, I liq

c, II c, I liq

iUB vap vap

c liq liq

liq

tr tr tr ius vap

c, IV c, III c, II c, I liq

c, III c, II c, I liq g

iUB vap vap

c liq liq

g

ius Bub iUB Bub

e, c, c, c,

liq g

ius vap

c liq

liq

tr iUB vap

c, II c, I liq

c, I liq g

.............

iUB vap

c liq

liq g

............

tr iUB vap

c, a c,fJ liq

c, fJ liq g

............ ............

tr iUB

c, rhomb. c, cubic liq

c, cubic liq g

............ ............

tr iUB Bub

c, II c, I c, I

c, I liq g

.............

tr iUB vap

c, red c liq

c, yellow liq g, equil.

............ 0.35 760

762 1158 1813

0.394 6.57

1.648 27.49

-vap

PbI•..•......

T

Process Initial

PCh .........

p

(Continued)

g, equil,

hexag. hexag, rhomb. rhomb.

g

g

g

liq g

liq g

g

760

............

6.1 18.1

25.5 75.73

9.80 760

83.7 110.6 121. 8 171.8

0.060 0.55 0.224 3.48

0.251 2.30 0.9372 14.56

427 427 760

179.4 179.4 188.7

2.7 4.2 4.1

11.3 17.6 17.2

27.2 760

30.31 49.46 88.15 139.40 185.43

0.0196 0.186 0.115 0.270 3.486

0.08200 0.7782 0.4812 1.130 14.585

1.7 1.7 760

297.1 297.1 448.5

3.36 11.14 10.38

693 693 844 844

5.0 13.9 16.1 36.4

20.9 58.16 67.36 152.3

600.45 2023

1.147 42.5

4.7990 177.8

617 643.1 1166

5.0 30.2

20.9 126.4

............

............ ............ ............

3690 3690 570 570

............ 760 0.011 760 760

760

760 0.23 0.23

242.92 383.2

14.06 46.610 43.430

2.58 7.87

10.79 32.93

695 773 1227

5.25 30.4

21.97 127.2

723 1099 1566

3.0 38.4

12.6 160.7

645 685 685

3.9 36.8

16.3 154.0

PbS .........

iUB

c

liq

............

1382

4.2

17.6

PbSO•.......

tr iUB

c, II c, I

c, I liq

............ ............

1139 1360

4.06 9.6

16.99 40.2

Pd ..•.•..•..

Ius vap

c liq

liq g

0.031 760

1825 3237

4.20 85.4

17.56 357.3

iUB

C

liq

............

953

PdClt .......

5

21

4-240

HEAT TABLE

4j-1.

TEMPERATURES, PRESSURES, AND HEATS

State Substance

Pr ...........

PrBr•........ PrCI•........

PrF•......... PrI•......... Pt ........... PtFe .........

Pu ..........

PuBr•....... PuCI......... PuF•........ PUFf ........ PuFe ........ Ra .......... Rb .......... RbBr ........ RbCl. ....... RbF .........

T

mm Hg

K

AH

Process Final

Initial

Po ..........

p

(Continued)

tr fus yap

c, II c, I liq

c, I liq

tr fus yap

c, a

c, (J liq

c, {J liq

fus sub

c c

liq

fus sub yap

c c liq

liq

fus sub

c c

fus sub

g

g

............ ............ 760

............ ............ 760

kcaI/mol

kJ/mol

327 527 1235

3.0

12.5

1068 1204 3785

0.76 1.65 70.9

3.18 6.904 296.6

............ ............

966 966

11.3 68.1

47.28 284.9

3.5(E - 3) 3.5(E - 3) 23

1059 1059 1523

12.1 70.3 54.7

50.62 294.1 228.9

liq g

............ 1.3(E - 3)

1668 1400

82.3

344.3

c

liq

c

g

............ ............

1011 1011

12.7 66.5

53.14 278.2

fus yap

c

liq

............

liq

g

2043 4097

4.7 121.8

19.7 509.6

tr fus yap

c,orthorh. c, cubic liq

g

tr tr tr tr tr fus yap

c, VI c, V c, IV c, III c, II c, I liq

c, V c, IV C, III c, II e, I liq

fus yap

c liq

liq

fus yap

c

liq

liq

g

fus sub

c

liq

c

g

g

g g

c, cubic liq

g g

760

............

2.14 1.08 7.06

8.954 4.519 29.54

395 480 588 730 753 913 3503

0.80 0.14 0.13 0.02 0.44 0.68 82.1

3.35 0.586 0.544 0.084 1.84 2.85 343.7

2.1(E - 3) 2.1(E - 3)

954 954

11.6 57.3

48.53 239.7

1.9(E - 3) 1.9(E - 3)

1033 1033

13.3 58.6

~45.2

93 •.0

389.1

45.9

192.0

............ 760

............ ............ ............

............ ............ ............ 760

276.15 334.45 342.29

0.72 1698 2.33(E - 3) 1400 4.3(E - 4) 8.2(E - 3)

1123 1310

sub fus

c

g

c

liq

fus yap

c

liq

liq

g

fus

c

liq

............

973

............

533.0 760

55.65

4.456 7.03

18.644 29.41

312 967

0.54

2.26

324.74 335.31

fus yap

o liq

liq

fus yap

c liq

liq g

760

965 1625

5.57 37.1

23.30 155.2

fus yap

c

liq

liq

g

0.27 760

995 1654

5.67 36.9

23.72 154.4

fus sub

c c

liq

0.6 0.6

1068 1068

5.5 52.3

23.0 2i8.8

g, equil,

g

760

............

4-241

TRANSITION, FUSION AND VAPORIZATION TABLE

4j-1.

TEMPERATURES, PRESSURES, AND HEATS

State Substance

Final

liq

mm Hg

K

AH

5.27 46.7 35.9

c, III c, II c, I

............ ............ ............

0.90

3.77

liq

............

437 501 564 589

0.88 1.10

3.68 4.602

............ ............

518 656

1. 70

7.113

0.024 760

3453 5960

tr tr

tr fus

c, c, c, c,

RbOH .......

tr fus

c, II c, r

c, Iiq

Re ..........

fus yap

c Iiq

liq

g g

IV III II I

kJ/mol

920 920 1578

c c

liq

kcal/mol

0.4 0.4 760

fus sub yap

RbNO •......

T

Process Initial

ltbI. ........

P

(Continued)

r

g

7.9 171

22.05 195.4 150.2

33.1 715.5

(ReBrl)a .....

Bub

c

g

............

550

47.6

199.2

(Reell)I ......

Bub

c

g

............

550

49

205

ReF•........

fus yap yap

c

liq

liq liq

g g

0.37 5.61 760

321.1 367 494

13.9

c, II c, r

liq

153.1 426.5 760

271.2 291.8 306.9

2.09 1.10 6.8

8.745 4.602 28.5

163 321.4 321.4

1.80 7.35

7.531 30.75

ReFe ........

ReF7 ........

Re207 ........

Rh .......... Rn .......... Ru .......... RuFI ........

RuFe ........

RuO•........

S...•........

SF•...•......

c,

r

tr fUB vap

liq

g

tr fus vap

c, II c, r

liq

liq

g

fus sub vap

C

liq

C

liq

g g

fus vap

C

liq

liq

g

fus vap

C

liq

liq

g

ius Yap

C

liq

liq

g

fUB vap vap

C

liq

liq liq

g g

tr Bub iUB

e, II c, r c, r

g

liq

ius vap

C

liq

liq

g

e, monoc!. c, monocl,

c, I

c,

............ 311.6 311.6

72 72 760 ............ 760

502 760

r

tr tr fus vap

c, rhomb, c, rhomb, c, monocl.

liq

liq

g, equil,

fus vap

c

liq

liq

g

573.5 573.5 634

58.16

14.7 32 16.8

61.50 134 70.29

2233 4000

5.15 118

21.55 493.7

202 211

0.69 4.0

2.89 16.7

............ 760

2700 4390

6.2 141

5.71 5.71 760

379 379 500

10.4 15.6

43.51 65.27

9.1

38.1

............

275.6 281 327

10.6 10.6

298.5 298.5

2.6 10.6

10.9 44.35

3.8(E - 3) ............ 760

368.46 374.15 388.33 717.75

0.096 0.0 0.411 2.2

0.54 41. 7

152.1 192

6.3

............ 40

............

25.9 589.9

0.402 0.0 1.711 9.20 26.4

4-242

HEAT TABLE

T} ...... . ....... 34.8 34.2 o 95.8 34.5 ~ . - ..... ....... ...... . ...... . ....... ...... . 165.3 35.3 ...... . 318.7 37.9 ~ ...... . t?:i 118.0 130.2 141. 7 157.2 77.7 '(JJ '(JJ 17.5.0 187.8 198.0 218.3 83.6 q

194.0 101.6 48.1 17.8 169.9 100.7 55.8 84.6 - 78.4 -103.2 + 8.0 121.4 ...... . ...... .

.0

•••••

'" '"

~

t?:i

~

~ ~

TABLE

4k-3.

1

VAPOR PRESSURE OF ORGANIC COMPOUNDS-PRESSURES LESS THAN

t

ATMOSPHERE

'-l

o

Temp.. oC Formula

CCIF, ......... CCI2F2 ........ CChO ......... CCbF ......... CCI.. ......... CHCIF2 ....... CHChF ....... CHCb ......... CHN .......... CH20 ......... CH202 ......... CH,Br ........ CHICl. ........ CHIF ......... CH,!. ......... CHIN02 ....... CH4 ........... CH40 ......... CH4S ......... CHiN ......... CO ........... CS2 ........... C2CIF, ........ C2ChF 4........ CzChF 3 •••••••• CzHz .......... C2H2Ch ....... C2H2Ch ....... C,H4.......... CzH4Brz ....... C ZH 4Ch .......

Name

Chlorotrifluoromethane Dichlorodifluoromethane Carbonyl chloride Trichlorofluoromethane Carbontetrachloride Chlorodifluoromethane Dichlorofluoromethane Trichloromethane Hydrocyanic acid Formaldehyde Formic acid Methyl bromide Methyl chloride Methyl fluoride Methyl iodide Nitromethane Methane Methanol Methanethiol Methylamine Carbon monoxide Carbon disulfide J-Chloro-Lz.z-trifluoroethylene 1,2- Dichloro-l,I,2 ,2-tetrafluoroethane 1,1,2-Trichloro-l,2,2-trifluoroethane Acetylene cis-l,2-Dichloroethylene trans-l,2-Dichloroethylene Ethylene 1,2- Dibromoethane 1,1- Dichloroethane

M.P. Imm

5mm

10 mm

20mm

40 mm

60 mm

100 mm

200 mm

400 mm

760 mm

-149.5 -118.5 - 92.9 - 84.3 - 50.0. -122.8 - 91.3 - 58.0 - 70.8.

-139.2 -104.6 - 77.0 - 67.6 - 30.0. -110.2 - 75.5 - 39.1 - 55.6.

- 29.0 -205.9. - 44.0 - 90.7 - 95.8. -222. O. - 73.8

5.0. - 80.6 - 99.5. -137.0 - 55.0 - 7.9 -199.0. - 25.3 - 75.3 - 81.3 -217.2. - 54.3

-121.9 - 81.6 - 50.3 - 39.0 4.3 + - 88.6 - 48.8 - 7.1 - 31.3. - 70.6 24.0 - 54.2 - 76.0 -119.1 - 24.2 27.5 -187.7. 5.0 + - 49.2 - 56.9 -210.0. - 22.5

-117.3 - 76.1 - 44.0 - 32.3 12.3 - 83.4 - 42.6 + 0.5 - 25. S. - 65.0 32.4 - 48.0 - 70.4 -115.0 - 16.9 35.5 -185.1. 12.1 - 43.1 - 51.3 -208.1. - 15.3

-111.7 - 68.6 - 35.6 - 23.0 23.0 - 76.4 - 33.9 10.4 - 18.8. - 57.3 43.8 - 39.4 - 63.0 -109.0 7.0 46.6 -181.4 21.2 - 34.8 - 43.7 -205.7. 5.1

-102.5 - 57.0 - 22.3 - 9.1 38.3 - 65.8 - 20.9 25.9 5.9 + - 46.0 61.4 - 26.5 - 51.2 - 99.9 8.0 + 63.5 -175.5 34.8 - 22.1 - 32.4 -201.3 + 10.4

92.7 43.9 7.6 6.8 + 57.8 - 53.6 - 6.2 42.7 + 9.8 - 33.0 80.3 - 11.9 - 38.0 - 89.5 25.3 82.0 -168.8 49.9 7.9 - 19.7 -196.3 28.0

-

-

-128.5 - 90.1 - 60.3 - 49.7 - 8.2 - 96.5 - 58.6 - 19.0 - 40.3. - 79.6 10.3 - 64.0 - 84.8 -125.9 - 35.6 14.1 -191.8. 6.0 - 58.8 - 65.9 -212.8. - 34.3

-

-

-134.1 - 97.8 - 69.3 - 59.0 - 19.60 -103.7 - 67.5 - 29.7 - 48.2. - 88.0 + 2.1. - 72.8 - 92.4 -131. 6 - 45.8 2.8 + -195.5. - 16.2 - 67.5 - 73.8 -215.0. - 44.7

81.2 29.8 8.3 + 23.7 76.7 - 40.8 8.9 + 61.3 25.8 - 19.5 100.6 3.6 + - 24.0 - 78.2 42.4 101.2 -161. 5 64.7 6.8 + - 6.3 -191. 3 46.5

-116.0

-102.5

-

95.9

-

88.2

-

79.7

-

74.1

-

66.7

-

55.0

-

41.7

-

27.9

-

-

-

72.3

-

63.5

-

53.7

-

47.5

-

39.1

-

26.3

-

12.0

+

3.5

·

20.0. 96.3.

·

-147.3

·

95.4

- 68.0. -142.9. - 58.4 - 65.4. -168.3 - 27.0. - 60.7

.

80.0

- 49.4. -133.0. - 39.2 - 47.2 -158.3 4.7. + - 41.9

- 40.3. -128.2. - 29.9 - 38.0 -153.2 18.6 - 32.3

-

- 30.0 -122.8. - 19.4 - 28.0 -147.6 32.7 - 21.9

- 18.5 -116.7. - 7.9 - 17.0 -141.3 48.0 - 10.2

- 11.2 -112.8. - 0.5 - 10.0 -137.3 57.9 - 2.9

-

-

-

1.7 -107.9. 9.5 + - 0.2 -131.8 70.4 + 7.2

+

13.5 -100.3. 24.6 + 14.3 -123.4 89.8 22.4

-

-

30.2 92.0. 41.0 30.8 -113.9 110.1 39.8

-

47.6 84.0. 59.0 47.8 -103.7 131.5 57.4 -

-104 - 22.6 -160 -135 - 63.5 - 14 - 92 8.2 - 93 - 97.7 - 64.4 - 29 -182.5 - 97.8 -121 - 93.5 -205.0 -110.8 -157.5 -

94

- 35 - 81.5 - 80.5 - 50.0 -169 10 - 96.7

~

t.'=j

>

~

C2H4Ch ....... C 2H402 ........ C 2H402 ........ C2H 5Br ........ C2H5Cl. ....... C2H 5F ......... C2Hs .......... C 2HsO ........ C2HsO ........ C2HsS ......... C2HsS ......... C2H7N ........ C2H7N ........ C 2N2.......... C aH4 .......... C aH4 .......... C aH 5N a09 .... , CaHs .......... CaHsO ........ C aHS02 ........ C aHS02 ........ C aHS02 ........ CaHs .......... CaHsO ........ CaHsO ........ CaHsO ........ CaHsOa ........ CaHgN ........ C aH 9N ........ C4H2 .......... C4Hs .......... C 4Hs .......... C4Hs .......... C4Hs .......... CIHs .......... C4HsO, ........ C4Hs04 ........ C4Hs02 ........ C4Hs02 ........ C4Hs02 ........ C4Hs02 ........

1,2-Dichloroethane Acetic acid Methyl formate Ethyl bromide Ethyl chloride Ethyl fluoride Ethane Ethanol Dimethyl ether Dimethyl sulfide Ethanethiol Ethylamine Dimethylamine Cyanogen Propadiene Propyne Nitroglycerine Propylene Acetone Propionic acid Methyl acetate Ethyl formate Propane I-Propanol 2-Propanol Ethyl methyl ether Glycerol Propylamine Trimethylamine 1,3-Butadiyne 1,2-Butadiene l,3-Butadiene Cyclobutene 1-Butyne 2-Butyne Acetic anhydride Dimethyl oxalate Butyric acid Isobutyric acid Ethyl acetate Methyl propionate

- 44.5. - 17.2. - 74.2 - 74.3 - 89.8 -117.0 -159.5 - 31.3 -115.7 - 75-.6 - 76.7 - 82.3. - 87.7 - 95.8. -120.6 -111.0. 127 -131.9 - 59.4 4.6 - 57.2 - 60.5 -128.9 - 15.0 - 26.1 - 91.0 125.5 - 64.4 - 97.1 - 82.5. - 89.0 -102.8 - 99.1 - 92.5 - 73.0. 1.7 20.0 25.5 14.7 - 43.4 - 42.0

-

24.0 6.3. 57.0 - 56.4 - 73.9 -103.8 -148.5 - 12.0 -101.1 - 58.0 - 59.1 - 66.4 - 72.2 - 83.2. -108.0 - 97.5 167 -120.7 - 40.5 28.0 - 38.6 - 42.2 -115.4 5.0 - 7.0 - 75.6 153.8 - 46.3 - 81.7 - 68.0. - 72.7 - 87.6 - 83.4 - 76.7 - 57.9. 24.8 44.0 49.8 39.3 - 23.5 - 21.5

+ -

+

-

13.6 17.5 - 48.6 - 47.5 - 65.8 - 97.7 -142.9 - 2.3 - 93.3 - 49.2 - 50.2 - 58.3 - 64.6 - 76.8. -101.0 - 90.5 188 -112.1 - 31.1 39.7 - 29.3 - 33.0 -108.5 14.7 2.4 - 67.8 167.2 - 37.2 - 73.8 - 61.2. - 64.2 - 79.7 - 75.4 - 68.7 - 50.5. 36.0 56.0 61.5 51.2 - 13.5 - 11.8

+

-

2.4 29.9 - 39.2 - 37.8 - 56.8 - 90.0 -136.7 8.0 - 85.2 - 39.4 - 40.7 - 48.6 - 56.0 - 70.1. - 93.4 - 82.9 210 -104.7 - 20.8 52.0 - 19.1 - 22.7 -100.9 25.3 12.7 - 59.1 182.2 - 27.1 - 65.0 - 53.8. - 54.9 - 71.0 - 66.6 - 59.9 - 42.5. 48.3 69.4 74.0 ti4.0 3.0 - 1.0

+

-

+

10.0 43.0 - 28.7 - 26.7 - 47.0 - 81.8 -129.8 19.0 - 76.2 - 28.4 - 29.8 - 39.8 - 46.7 - 62.7. - 85.2 - 74.3 235 - 96.5 - 9.4 65.8 - 7.9 - 11.5 - 92.4 36.4 23.8 - 49.4 198.0 - 16.0 - 55.2 - 45.9. - 44.3 - 61.3 - 56.4 - 50.0 - 33.9. 62.1 83.6 88.0 77.8 9.1 11..0

+ +

18.1 51. 7 - 21.9 - 19.5 - 40.6 - 76.4 -125.4 26.0 - 70.4 - 21.4 - 22.4 - 33.4 - 40.7 - 57.9. - 78.8 - 68.8 251d - 91.3 2.0 74.1 0.5 - 4.3 - 87.0 43.5 30.5 - 43.3 208.0 - 9.0 - 48.8 - 41.0. - 37.5 - 55.1 - 50.0 - 43.4 - 27.8 70.8 92.8 96.5 86.3 16.6 18.7

-

29.4 63.0 - 12.9 - 10.0 - 32.0 - 69.3 -119.3 34.9 - 62.7 - 12.0 - 13.0 - 25.1 - 32.6 - 51.8. - 72.5 - 61.3 e

-

+ + + -

+ -

84.1 7.7 85.8 9.4 5.4 79.6 52.8 39.5 34.8 220.1 0.5 40.3 34.0 28.3 46.8 41.2 34.9 18.8 82.2 104.8 108.0 98.0 27.0 29.0

45.7 80.0 0.8 4.5 - 18.6 - 58.0 -110.2 48.4 - 50.9 2.6 1.5 - 12.3 - 20.4 - 42.6. - &1.3 - 49.8

+ +

+ +

••••••

-

-

-

eo

73.3 22.7 102.5 24.0 20.0 68.4 66.8 53.0 22.0 240.0 15.0 27.0 20.9 14.2 33.9 27.8 21.6 5.0 100.0 123.3 125.5 115.8 42.0 44.2

64.0 99.0 16.0 21.0 - 3.9 - 45.5 - 99.7 63.5 - 37.8 18.7 17.7 2.0 - 7.1 - 33.0 - 48.5 - 37.2 ........ - 60.9 39.5 122.0 40.0 37.1 - 55.6 82.0 67.8 7.8 263.0 31.5 - 12.5 - 6.1 1.8 - 19.3 - ]2.2 - 6.9 10.6 119.8

+

-

+

+

res.a

144.5 134.5 59.3 61.8

82.4 118.1 32.0 38.4 12.3 - 32.0 - 88.6 78.4 - 23.7 36.0 35.0 16.6 7.4 - 21.0 - 35.0 - 23.3 ........ - 47.7 56.5 141.1 57.8 54.3 - 42.1 97.8 82.5 7.5 290.0 48.5 2.9 9.7 18.5 - 4.5 2.4 8.7 27.2 139.6 163.3 163.5 154.5 77.1 79.8

+

+

+

+ +

+ +

-

35.3 16.7 - 99.8 -117.8 -139 -183.2 -112 -138.5 - 83.2 -121 - 80.6 - 96 - 34.4 -136 -102.7 11 -185 - 94.6 - 22 - 98.7 - 79 -187.1 -127 - 85.8 17.9 - 83 -117.1 - 34.9

~

>

"'d

o

~

"'d ~ t"j

W W

q

~ t"j

-108.9 -130 - 32.5 -73

-

4.7 47 82.4 87.5

~

~

I-"

TABLE

4k-::L

YAPOR PRESSURE OF ORGANIC COMPOUNDS-PRESSURES LESS THAN

t

1 ATMOSPHERI~ (Continued)

tv '1 tv

Temp.,oC Formula

Name

M.P. 1 mm

C4Hs02 ........ C4HIO......... C4HIO......... C 4H IUO ........ C4HIOO ........ C.HIOO ....... C 4H IOO ........ C.H100 ........ C.H10S ........ C.HllN ........ C.HI2Si ........ CsH IO02....... C SH\OO2 ....... CSHIO02 ....... C SHIO02....... CSHI002 ....... CsH 12 ......... CSH12......... CsH12 ......... CsH120 ........ CsHsBr ........ CsHsCl. ....... CsHsF ........ CsHsI ......... CsHs .......... CsHsO ........ CSH7N ........ CsH 12 ......... CsH 14 • • • • • • • . . CSHI4 ......... C7Hs .......... C7HlS ......... CSHIO......... CSHlS ......... C 12H26 .........

Propyl formate Butane 2-Methylpropane Butyl alcohol sec-Butyl alcohol Isobutyl alcohol tert-Butyl alcohol Diethyl ether Diethyl sulfide Diethylamine Tetramethylsilane Ethyl propionate Propyl acetate Methyl butyrate Methyl isobutyrate Isobutyl formate Pentane 2-Methylbutane 2,2- Dimethylpropane Ethyl propyl ether Bromobenzene Chlorobenzene Fluorobenzene Iodobenzene Benzene Phenol Aniline Cyclohcxane Hexane 2.3-Dimethylbutane Toluene Heptane Ethylbenzene Octane Dodecane

- 43.0 -101.5 -109.2 1.2 - 12.2 9.0 - 20.4. - 74.3 - 39.6

.

- 83.8 - 28.0 - 26.7 - 26.8 - 34.1 - 32.7 - 76.6 - 82.9 -102.0. - 64.3 2.9 - 13.0 - 43.4. 24.1 - 36.7. 40.1. 34.8 - 45.3. - 53.9 - 63.6 - 26.7 - 34.0 - 9.8 - 14.0 47.8

+

5 mm

-

+ + + -

-

-

-

-

+ +

22.7 85.7 94.1 20.0 7.2 11.0 3.0. 56.9 18.6

.

66.7 7.2 5.4 5.5 13.0 11.4 62.5 65.8 85.4, 45.0 27.8 10.6 22.8 50.6 19.6. 62.5 57.9 25.4 s 34.5 44.5 4.4 12.7 13.9 8.3 75.8

10 mm

-

+ -

+ + + -

-

+ -

12.6 77.8 86.4 30.2 16.9 21. 7 5.5. 48.1 8.0 33.0 58.0 3.4 5.0 5.0 2.9 0.8 50.1 .57.0 76.7. 35.0 40.0 22.2 12.4 64.0 11.5. 13.8 69.4 15.9. 25.0 34.9 6.4 2.1 25.9 19.2 90.0

20 mm

-

-

+ -

+ + -

-

-

-

+

1.7 68.9 77.9 41.5 27.3 32.4 14.3. 38.5 3.5 22.6 48.3 14.3 16.0 16.7 8.4 11.0 40.2 47.3 67.2. 21.0 53.8 35.3 1.2 78.3 2.6. 86.0 82.0 5.0s 14.1 24.1 18.4 9.5 38.6 31.5 104.6

40 mm

+ -

-

-

+ + + -

10.8 59.1 68.4 53.4 33.1 44.1 24.5. 27.7 16.1 11.3 37.4 27.2 28.8 29.6 21.0 24.1 29.2 36.5 56.1. 12.0 68.6 49.7 11.5 94.4 7.6 100.1 96.7 6.7 2.3 12.4 31.8 22.3 52.8 45.1 121. 7

60 mm

-

-

-

-

+ -

18.8 52.8 62.4 60.3 45.2 51. 7 31.0 21.8 24.2 4.0 30.3 3fi.1 37.0 37.4 28.9 32.4 22.2 29.6 49.0. 4.0 78.1 58.3 19.6 105.0 15.4 108.4 106.0 14.7 5.4 4.9 40.3 30.6 61.8 53.8 132.1

100mm

-

-

+ -

-

+

+

29.5 44.2 54.1 70.1 54.1 61.5 39.8 11.5 35.0 6 ..0 20.9 45.2 47.8 48.0 39.6 43.4 12.6 20.2 39.1. 6.8 90.8 70.7 30.4 118.3 26.1 121.4 119.9 25.5 15.8 5.4 51.9 41.8 74.1 65.7 146.2

200 mm

45.3 31.2 41.5 84.3 67.9 75.9 52.7 2.2 51.3 21.0 - 6.5 61.7 64.0 64.3 55.7 60.0 1.9 - 5.9 - 23.7. 23.3 110.1 89.4 47.2 139.8 42.2 139.0 140.1 42.0 31.6 21.1 69.5 58.7 92.7 83.6 167.2

-

+

+

400 mm

62.6 16.3 27.1 100.8 83.9 91.4 68.0 17.9 69.7 38.0 10.0 79.8 82.0 83.1 13.6 79.0 - 18.5 10.5 - 7.1 41.6 132.3 110.0 65.7 163.9 60.6 160.0 161.9 60.8 49.6 39.0 89.5 78.0 113.8 104.0 191.0

-

+

+

760 mm

-

81.3 0.5 11. 7 117.5 99.5 108.0 82.9 34.6 88.0 55.5 27.0 99.1 101.8 102.3 92.6 98.2 36.1 27.8 9.5 61. 7 156.2 132.2 84.7 188.6 80.1 181.9 184.4 80.7 68.7 58.0 110.6 98.4 136.2 125.6 216.2

+

- 92.9 -135 -145 - 79.9 -114.7 -108 25.3 -116.3 - 99.5 - 38.9 -102.1 - 72.6 - 92.5 - 84.7 - 95.3 -129.7 -159.7 - 16.6 -

30.7 45.2 42.1 28.5 5.5 40.6 - 6.2 6.6 - 95.3 -128.2 - 95.0 - 90.6 - 94.9 - 56.8 - 9.6

+ +

~

tr1

>

1-3

VAPOR PRESSURE

4-273

Tables 4k-5 to 4k-14, Vapor Pressures of Special Gases, listing values of the vapor pressures of He4, Hes, normal and equilibrium H 2 , Ne, N 2, and O 2 , were taken from Thermometry at Low Temperature, a master's essay at the University of Pittsburgh, 1965, by Edward R. Simco. This booklet is also entitled Research Report 4 and was supported in part by the National Science Foundation. Table 4k-15, Vapor Pressures of the Chemical Elements, lists values of the vapor pressure, temperature, and heat associated with the phase transitions for the chemical elements. The numbers represent temperature in degrees Celsius at which the vapor pressure is the value appearing at the top of the column. A circled dot between columns indicates a change of phase. The six columns on the right side list the following information:

t::.H V298 heat of vaporization at 25°C, or atmospheric boiling temperature if the value contains an asterisk (*), cal/mol Tm melting temperature t::.H m heat of melting, cal/mol Tt transition temperature su, heat of transition, cal/mol Trans designates solid-state transition

Equilibrium vapor pressures are listed for substances with polymorphic vapor or condensed forms (As, Sb, Bi, P, Po, S, Se, Te). The basic sources should be consulted for vapor pressures of the various polymorphic forms. The sources for this table are: (1) Ralph Hultgren, Raymond L. Orr, Philip D. Anderson, and Kenneth K. Kelley, "Selected Values of Thermodynamic Properties of Metals and Alloys," John Wiley & Sons, Inc., New York, 1963 (updated by privately distributed supplements); (2) Daniel R. Stull and Gerard C. Sinke, "Thermodynamic Properties of the Elements," Advances in Chern. Ser. No. 18: (3) Richard E. Honig, "Vapor Pressure Data for the Solid and Liquid Elements," RCA Rev. 23(4),567-586 (1962); (4) Richard E. Honig and H. O. Hook, "Vapor Pressure Data for Some Common Gases," RCA Rev. 21(3), 360-368 (1960). Table 4k-16, Vapor Pressure of Ice, has been taken from the NBS Circ. 564, Tables of Thermal Properties of Gases, by J. Hilsenrath, C. W. Beckett, W. S. Benedict, L. Fano, H. J. Hoge, J. F. Masi, R. L. Nuttall, Y. S. Touloukian, and H. W. Woolley, U.S. Government Printing Office, Washington, D.C., 1955. The values were smoothed, and adjusted to agree with the ice-point value adopted in Table 4k-17. Table 4k-17, Vapor Pressure of Liquid Water below lOO°C,and Table 4k-18, Vapor Pressure of Liquid Water above lOO°C, have been taken from the recent work of M. R. Gibson and E. A. Bruges, J. M echo Eng. s«, 9(1), 24-35 (February, 1967). Table 4k-19, Vapor Pressure of Mercury, is taken from the compilation of J. Johnston, F. Fenwick, and H. G. Leopold, "International Critical Tables," vol. III, McGraw-Hill Book Company, New York, 1928. Table 4k-20, Vapor Pressure of Carbon Dioxide, is from C. H. Meyers and M. S. Van Dusen, J. Research NBS, 10, 409 (1933). Table 4k-21, Vapor Pressure of Ethyl Alcohol, and Table 4k-22, Vapor Pressure of Methyl Alcohol, are reprinted by permission from the "Smithsonian Physical Tables," 9th ed. Smithsonian Institution, Washington, D.C., 1954. Table 4k-23, Constants in the Equation for the Rate of Evaporation of Metals, is taken by permission from pages 752-754 of "Scientific Foundations of Vacuum Technique," by S. Dushman, John Wiley & Sons, Inc.• New York. 1949.

TABLE

Formula

4k-4.

VAPOR PRESSURE OF ORGANIC COMPOUNDS-PRESSURES GREAT1!:R THAN

~

ATMOSPHERE

--.:r ~

Temp.,oC

Name

1 atm CCIF a.... Chlorotrifluoromethane - 81.2 CCbF 2... Dichlorodifluoromethane - 29.8 CCI 20 .... Carbonyl chloride 8.3 CClaF .... Trichlorofluoromethane 23.7 CCI•..... Carbon-tetrachloride 76.7 CHCIF 2.. Chlorodifluoromethane - 40.8 CHCbF .. Dichlorofluoromethane 8.9 CHCl a.... Trichloromethane 61.3 CHN ..... Hydrocyanic acid 25.8 CHaBr ... Methyl bromide 3.6 CHaCI .... Methyl chloride - 24.0 CHaF .... Methyl fluoride - 78.2 . 42.4 CHaI. .... Methyl iodide CH •...... Methane -161. 5 CH.O .... Methanol 64.7 CH.8 ..... Methanethiol 6.8 CHiN .. ,. Methylamine - 6.3 CO ...... Carbon monoxide -191.3 08 2...... Carbon disulfide 46.5 02CIF a... 1-Chloro-1,2,2-trifluoroethylene - 27.9 02CI2F•... 1,2-Dichloro-1,1,2,23.5 tetrafluoroethane 02Cl aFa... 1,1,2-Trichloro-1,2,247.6 trifluoroethane

1

2 atm - 66.7 - 12.2 27.3 44.1 102.0 - 24.7 28.4 83.9 45.5 23.3, 6.4 - 64.5 65.5 -152.3 84.0 26.1 10.1 -183.5 69.1 - 11.1 22.8

-

+

70.0

Tc Pc 5 atm 10 atm 20 atm 30 atm 40atm 50 atm 60 atm ----- --- --- 42.7 - 18.5 34.8 52.8 12.0 53 40.3 42.4 74.0 95.6 ....... ...... . ...... . 111.5 39.6 16.1 57.2 85.0 119.0 141.8 159.8 174.0 ....... 181.7 56.0 77.3 108.2 146.7 172.0 194.0 ....... ...... . 198.0 43.2 141.7 178.0 222.0 251.2 276.0 ....... ...... . 283.1 45.0 0.3 24.0 52.0 70.3 85.3 ....... ...... . 96 48.7 59.0 87.0 121.2 144.0 162.6 177.5 ....... 178.5 51.0 120.0 152.3 191.8 216.5 237.5 254.0 ....... 260 54.9 75.5 103.5 134.2 154.0 170.2 183.5 ....... 183.5 50.0 54.8 84.0 121.7 147.5 170.2 190.0 ....... 194 51.6 ~ 47.3 77.3 97.5 113.8 126.0 137.5 143.8 65.8 t;j 22.0 > - 42.0 - 21.0 2.6 15.5 26.5 36.0 43.5 44.9 62.0 8 101.8 138.0 176.5 206.0 228.5 248.0 ....... 255 54.6 -138.3 -124.8 -108.5 - 96.3 - 86.3 ....... ...... . - 82.1 45.8 112.5 138.0 167.8 186.5 203.5 214.0 224.0 240.0 78.7 55.9 83.4 117.5 140.0 157.7 172.0 185.0 If)6.8 71.4 36.0 87.8 106.3 121.8 133.7 144.6 156.9 73.6 59.5 -170.7 -161.0 -149.7 -141.9 ....... ...... . ...... . -138.7 34.6 104.8 136.3 175.5 201.5 222.8 240.0 256.0 273.0 72.9 40.0 71.1 91.9 ....... ...... . ...... . 107.0 39.0 15.5 54.0 82.3 117.5 140.9 ....... ...... . ...... . 145.7 32.3

+

+

--~

+

+

+

+

105.5

138.0

177.7

205.0 ....... ...... . ...... .

214.1 33.7

C 2H 2 ••••• C 2H2Cl 2 •• C 2H2Cl 2 •• C 2H •..... C 2H.B r 2 •• C 2H.CI 2 •• C 2H.CI 2 •• C 2H.0 2 ••• C 2H 40 2 ••• C 2H sBr ... C 2H sCI ... C 2H sF .... C 2H 6 ••••• C!H 60 .... C 2H 60 .... C2H 6S .... C2H 6S .... C2H 7 N ... C 2 Ih N ... C2 N 2 ••••• CaH•..... CaH•..... C aH6 ••••• C aH 60 .... CaH 60 2 •••

Acetylene cis-l,2-Dichloroethylene trans-I, 2,Dichloroethylene Ethylene 1,2-Dibromoethane 1,1-Dichloroethane 1,2-Dichloroethane Acetic acid Methyl formate Ethyl bromide Ethyl chloride Ethyl fluoride Ethane Ethanol Dimethyl ether Ethanethiol Dimethyl sulfide Ethylamine Dimethylamine Cyanogen Propadiene Propyne Propylene Acetone Propionic acid

- 84.0. 59.0 47.8 -103.7 131.5 57.3 83.7 118.1 32.0 38.4 12.3 - 32.0 - 88.6 78.4 - 23.7 35.0 36.0 16.6 7.4 - 21.0 - 35.0 - 23.3 - 47.7 56.5 141.1

- 71.6 82.1 69.8 - 90.8 157.7 80.2 108.1 143.5 51.9 60.2 32.5 - 16.7 - 75.0 97.5 - 6.4 56.6 57.8 35.7 25.0 - 4.4 - 18.4 7.1 - 31.4 78.6 160.0

- 50.2 - 32.7 - 10.0 + 4.8 119.3 152.3 194.0 221.5 104.0 135.7 174.0 199.8 - 71.1 - 52.8 - 29.1 - 14.2 200.0 237.0 269.0 286.0 117.3 150.3 192.7 220.0 147.8 183.5 226.5 254.0 180.3 214.0 252.0 276.5 83.5 112.0 147.2 169.7 95.0 126.8 164.3 188.0 64.0 92.6 127.3 149.5 + 7.7 30.2 57.5 75.7 - 52.8 - 32.0 6.4 + 10.0 126.0 151.8 183.0 203.0 + 20.8 45.5 75.7 96.0 90.7 121.9 159.5 184.3 92.3 124.5 163.8 188.5 65.3 91.8 124.0 146.0 53.9 80.0 111. 7 132.2 + 21.4 44.6 72.6 91.6 + 8.0 33.2 64.5 85.5 + 19.5 43.8 74.0 94.0 4.8 + 19.8 49.5 70.0 113.0 144.5 181.0 20.1.0 186.0 203.5 220.0 228.0

16.8 244.5 220.0 1.5 295.0 243.0 272.0 297.0 188.5 206.5 167.0 90.0 23.6 218.0 112.1 204.7 209.0 163.0 149.8 106.5 108.5 111.5 85.0 214.5 233.0

26.8 34.8 260.0 236.5 ............ .. + 8.9 .............. 300.0 304..5 261..5 ............ .. 285.0 ............ .. 312..5 ............ .. 213.0 .............. 220.0 229.5 180.5 ............ .. •

oo

..........

.............. ............ .............. ............

.. '"

230.0 242.0 125.2 .............. 220.0 ............ .. 224.5 ............ .. 176.0 ............ .. 162.6 ............ .. 118.2 .............. 118.0 ............ 125.0 .............. .............. ............ ..

.............. ..........

..

238.0 .............

36.0 62. 271.0 57. 243.3 54. 9.6 50. 309.8 70. 261.5 50. 288.4 53. 321.6 57 . < 214.0 59. > "t1 230.8 61. o ~ 187.2 52 . "t1 102.2 49. ~ t;rj 32.3 48. rJl 243.5 63. to q 126.9 52. ~ 225.5 54 . t;rj 229.9 54. 183.2 55. 164.5 52. 4 126.6 58. 2 120.7 51. 8 128 52. 8 91.4 45. 4 235.0 47. o 239.5 53.

o

t

tv -:J C1

TABLE

Formula C aHlI02 .•• C aHlI02 ••• CaHs..... CaHsO.... CaHsO.... CaHsO.... CaHgN... C.H lI ..... C.HlIOa... C.H lI04 ••• C.H S0 2 .•• C.H S0 2 .•• C.H S0 2 ••• C.H S0 2 ••• C.H S0 2 ••• C.H 10.... C.H 10.... C.H100 ... C.H 100 ... C.H 100 ... C.H 100; .. C.H100 ... C 4H 10S ... C.HuN ... C.H 12Si. ..

4k-4.

VAPOR PRESSURE OF ORGANIC COMPOUNDS-PRESSURES GREATER THAN

(Continued)

ATMOSPHERE

1 atm 57.8 54.3 - 42.1 97.8 82.5 7.5 48.5 - 4.5 139.6 163.3 163.5 154.5 77.1 79.8 81.3 - 0.5 - 11. 7 117.5 99.5 108.0 82.9 34.6 88.0 55.5 27.0

2 atm 79.5 76.0 - 25.6 117.0 101.3 26.5 69.8 + 15.3 162.0 189.6 188.3 179.8 100.6 103.0 104.3 + 18.8 + 7.5 139.8 118.2 127.3 102.0 56.0 112.0 77.8 48.0

~

~ ~

Temp.,oC

Name Methyl acetate Ethyl formate Propane I-Propanol 2-Propanol Ethyl methyl ether Propylamine 1,3-Butadiene Acetic anhydride Dimethyl oxalate Butyric acid Isobutyric acid Ethyl acetate Methyl propionate Propyl formate Butane 2-Methylpropane Butyl alcohol sec-Butyl alcohol Isobutyl alcohol tert-Butyl alcohol Diethyl ether Diethyl sulfide Diethylamine Tetramethylsilane

1

Tc Pc 10 atm 20 atm 30 atm 40 atm 50 atm 60 atm --- --- --- --- ---- --113.1 144.2 181.0 205.0 225.0 .. ........... ...... . 233.7 46.3 110.5 142.2 180.0 205.0 225.0 . ...... ...... . 235.3 46.8 + 1.4 26.9 58.1 78.7 94.8 ....... ...... . 96.8 42.0 149.0 177.0 210.8 232.3 250.0 . .......... ............ .. 263.7 49.9 130.2 155.7 186.0 205.0 220.2 232.0 .............. 235 53 84.0 108.0 141.4 160.0 .. ............ ............ .. 164.7 43.4 56.4 102.8 133.4 170.0 194~3 214.5 .............. ............ . 223.8 46.8 76.0 114.0 139.8 158.0 ............. ............ . 161.8 42.6 47.0 194.0 221.5 253.0 272.8 288.5 .............. ........... .. 296 46 ::r: 9.5 l?!.J 228.7 ............ .. ............ .............. ............ .. ............ .. ............ .. 260 225.0 257.0 295.0 319.0 338.0 352.0 .............. 355 52.0 > 1-3 217.0 250.0 289.0 315.0 336.0 .. ............ ............ .. 336 40.0 136.6 169.7 209.5 235.0 ............ .. .............. .. ............ 250.1 37.9 139.8 172.6 212.5 239.0 ............ .. .. ............ ............ .. 257.4 39.3 142.0 176.4 217.5 245.0 ............. ............ .. .......... .. 264.8 39.5 79.5 116.0 140.6 ............ .. .............. .......... .. 152.8 36.0 50.0 66.8 99.5 120.5 ........... .. .............. ............ .. 134.0 37.0 39.0 172.5 203.0 237.0 259.0 277.0 .. ............ ............ .. 287 48.4 147.5 172.0 204.0 230.0 251.0 ............. ........... . 265 48 265 48 156.2 182.0 212.5 232.0 251.0 .............. ............ 130.0 '154.2 184.2 207.0 222.5 .............. ........... .. 235 49 90.0 122.0 159.0 183.3 .............. ........... .. .......... . 193.8 35.5 153.8 190.2 234.0 263.0 .. ............ ............ .. ............ .. 283.8 39.1 113.0 145.3 184.5 210.0 ............ .. .............. .. ......... 223.3 36.6 82.0 113.0 152.0 178.0 ....... . .. . . . . . . 185 33 5 atm

--~

..

..

~

~

~

~

~

C SH I00 2.. C SH I00 2.. C SH I00 2.. C SH I00 2.. C SH I00 2.. C SH I2.... C SH I2.... C SH 12 • • • • C SH I20 ... C 6HsBr ... C 6HsCl. .. C 6H sF .... C 6HsI. ... C 6H6..... C 6H60 .... C 6H7N ... C 6HI2.... C 6H1 2 0 2.. C 6H 14 • • • • C 6H14 • • • • C 7H s ..... C 7H 16.... CSHIO.... CSHIS.... C 12H26....

Ethyl propionate Propyl acetate Isobutyl formate Methyl butyrate Methyl isobutyrate Pentane 2-Methylbutane 2,2-Dimethylpropane Ethyl propyl ether Hromobenzene Chlorobenzene Fluorobenzene Iodobenzene Benzene Phenol Aniline Cyclohexane

Ethyl isobutyrate Hexane 2,3-Dimethylbutane Toluene Heptane Ethylbenzene Octane Dodecane

99.1 101.8 98.2 102.3 92.6 36.1 27.8 + 9.5 61.7 156.2 132.2 84.7 188.6 80.1 181.9 184.4 80.7 110.1 68.7 58.0 110.6 98.4 136.2 125.6 216.2

123.8 126.8 121.8 127.5 116.7 58.0 48.8 29.5 85.3 186.2 160.2 109.9 220.0 103.8 208.0 212.8 106.0 135.5 93.0 82.0 136.5 124.8 163.5 152.7 249.2

162.7 165.7 157.8 166.7 155.2 92.4 82.8 61.1 123.1 232.5 20,5.0 148.,5 270.0 142.5 248.2 2.54.8 146.4 174.2 I:H.7 120.3 178.0 16,5.7 207.5 196.2 300.0

197.8 200.5 192.4 203.0 190.2 124.7 114.5 90.7 156.2 274.5 245.3 184.4 315.7 178.8 283.8 292.7 184.0 210.0 166.6 1.5,5.7 21.5.8 202.8 246.3 235.8 345.8

240.0 242.8 234.0 244.5 232.0 164.3 154.0 127.6 197.2 327.0 292.8 227.6 371.5 221.5 328.7 342.0 228.4 2.53.0 209.4 198.7 262.5 247.;) 294 ..5 181.4

264.5 .......... .. 269.0 .............. 261.0 .......... 272.0 .............. 259 ..5 .............. 191.3 .............. 180.3 ............ .. 152.5 ........ " .. " 223.0 ............ .. 359.8 387.5 324.4 349.8 257.0 279.3 406.0 437.2 249.5 272.3 358.0 382.1 375.,5 400.0 257.5 ............ 280.0 .......... .... " ........ ............

225.5 292.8

............

326.5

............

............

..

............ ............

..

.............. ............

..

..

.............. .. .. " ........ ............ ... " .. " .... .............. ............ ..

............ ............ .. ............

290.3 400.0 422.4

418.7 ..............

........

...........

..

..

.............. ..........

..

..

..

............ ............

..

.............. ............ .............. ............

..

............ ............

..

..

.. ..

10

....

............ ..........

..

............ .......... .. " .... "" .... .............. .. " .......... .......... .. . ....... "

............ .............. "

..

319.0

.............. ..........

.......... " " ..... .......... .. .......... .. .......... .. .......... .. .......... .. ............ .. ........... .. ............ ..

............

"

• .1

.......... ...... . ""

272.8 33. 2 276.2 33. 2 278.0 38. o 281.2 34. 2 267.5 33. 9 197.2 33. o 187.8 32. 8 1.59.0 33. o 227.4 32. 1 397 44. 6 359.2 44. 6 286.5 44. 7 448 44. 7 290 ..5 .50. 1 ~ 419 60. a 4 426 52. 279.9 39. 8 280.0 30. o 234.8 29. 6 227.4 30. 7 320.6 41. 6 266.8 26. 9 346.4 :38.1 296.2 24. 7 385 17. 5

-< > "'d 0 ~

"'d

~

l".:l

~ 0

~

l".:l

~

~ ~

4-278

HEAT

The 1958 He 4 temperature scale is defined by the equation!

In P =

. 10 -

Lo RT

5

+ 2 1n T

where

1'0

and

E

==

1 (T - RT 10 Sz dT

== In

(21rm)J

PV 2BN In NRT - V-

1

(P

+ RT 10

V z dP

+

E

~, 3 CN2

- 2 V2

L, is heat of vaporization of liquid He 4 at 0 K, S, and V z are the molar entropy and volume of liquid He 4, m is the mass of a He 4 atom, and Band Care virial coefficients of He 4 • The scale has been approved by the International Committee on Weights and Measures and is used for temperature measurements between the boiling point of helium (4.2150 K) and about 1.0 K and can be used up to the critical point of helium (T = 5.1994 K, P = 1,718 mm Hg). It is in agreement with the thermodynamic scale to within ± 2 millikelvins. The vapor-pressure-temperature relation for He 3 is based on the equation

In P, =

2.4~174

+ 4.80386

+ 0.198608T2 - 0.0502237T3 + 0.00505486T4 + 2.24846 In T 0.2 :5 T

- 0.286001T

:5 3.324 K

which defines the T 6 2 He! temperature scale. The T 62 He 3 temperature scale is the result of the work done by Sydoriak, Roberts, and Sherman 2 at the Los Alamos Scientific Laboratory. Table 4k-7, which gives the temperature as a function of vapor pressure for He 3, is taken from the work of R. H. Sherman, S. G. Sydoriak, and T. R. Roberts," Temperature measurements using the vapor pressure of liquid hydrogen are complicated by the phenomenon of ortho-para conversion. For ortho-hydrogen the proton spins are parallel while for para-hydrogen the spins are antiparallel. Due to the different energies of the two states, the equilibrium composition varies from 75% ortho-H, and 25% para-H, at room temperature to 99.79% para-H; and 0.21 % ortho-H, at 20.4 K.4 However in the absence of a catalyst the rate of conversion from the ortho to the para form is very slow; thus it is possible to liquefy hydrogen and preserve for many hours the equilibrium composition at room temperature," Hydrogen having the composition 75 % ortho-H, and 25 % para-H, is generally called normal hydrogen and hydrogen having the composition 99.79% para-H; and 0.21 % ortho-H, equilibrium hydrogen. The vapor-pressure-temperature relation for equilibrium hydrogen (99.79% para-H; and 0.21 % ortho-Hs) is based on an equation proposed by Durieux," log P (mm)

= 4.635384 - 44.~674

+ 0.021669T

- 0.000021T2

1 F. G. Briokwedde, H. Van Dijk, M. Durieux, J. R. Clement, and J. K. Logan. J. Research NBS 64.A, 1 (1960). 2 S. G. Sydoriak, T. R. Roberts, and R. H. Sherman, J. Research NBS 68A, 559 (1964). 3 R. H. Sherman, S. G. Sydoriak, and T. R. Roberts, Los Alamos Rept. LAMS 2701, pp. 17-21, 1962; J. Research NBS 68A, 579 (1964). 4 G. K. White, "Experimental Techniques in Low Temperature Physics," p. 41, Oxford University Press, London, 1959. b R. P. Hudson, in "Experimental Cryophysics," p, 224, F. E. Hoare, L. C. Jackson, and N. Kurti, eds., Butterworth & Company (Publishers), Ltd., London, 1961. 6 M. Durieux, Thesis, p, 95, Leiden, 1960.

4-279

VAPOR PRESSURE TABLE

4k-5.

VAPOR PRESSURE OF HELIUM

Vapor pressure of 4He. Unit 10- 3 mm Hg at T

0.00

0.01

0.02

0.03

0.04

ooe,

0.05

(J

4 (1958

SCALE)

= 980.665 cm/sec!

0.06

0.07

0.08

0.09

-- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 0.5

.016342 .28121 2.2787 11.445 41.581

.022745 .031287 .042561 .057292 .44877 .56118 .69729 .35649 2.7212 3.2494 3.8549 4.5543 13.187 15.147 17.348 19.811 46.656 52.234 58.355 65.059

.076356 .86116 5.3591 22.561 72.386

.10081 1.0574 6.2820 25.624 80.382

.13190 1.2911 7.3365 29.027 89.093

.22021 .17112 1.5682 1.8949 8.5376 9.9013 32.800 36.974 98.567 108.853

1.0 120.000 292.169 625.025 1208.51 2155.35

132.070 316.923 670.411 1284.81 2274.99

145.116 343.341 718.386 1364.83 2399.73

159.198 371.512 769.057 1448.73 2529.72

174.375 401. 514 822.527 1536.61 2665.09

190.711 433.437 878.916 1628.62 2805.99

208.274 467.365 938.330 1724.91 2952.60

227.132 503.396 1000.87 1825.58 3105.04

247.350 541.617 1066.67 1930.79 3263.48

269.006 582.129 1135.85 2040.67 3428.07

1.5 3598.97 5689.88 8590.22 12466.1 17478.2

3776.32 5940.76 8931.18 12913.7 18047.7

3960.32 6199.90 9282.06 13372.8 18630.1

4151. 07 6467.42 9643.02 13843.6 19225.5

4348.79 6743.57 10014.3 14326.1 19834.1

4553.58 7028.47 10395.9 14820.7 20455.9

4765.68 7322.31 10788.2 15327.3 21091.1

4985.18 7625.21 11191.2 15846.3 21739.7

5212.26 7937.40 11605.1 16377.7 22402.0

5447.11 8259.02 12030.1 16921.7 23077.9

2.0 23767.4 31428.1 40465.6 51012.3 63304.3

24470.9 32271.1 41446.6 52160.2 64635.2

25188.1 33128.0 42443.5 53325.8 65985.4

25919.2 33998.6 43456.5 54509.2 67354.8

26664.2 34882.8 44485.7 55710.5 68743.5

27423.3 35780.3 45531.3 56930.0 70152.0

28196.3 36690.9 46593.5 58167.8 71580.2

28983.2 37614.3 47672.5 59423.8 73028.1

29784 ..2 38550.2 48768.6 60698.8 74496.0

30599.1 39500.3 49881.8 61992.0 75984.2

2.5 77493.1 79022.2 80572.2 82142.9 83734.6 85347.2 86981.2 88636.7 90313.8 92012.6 93733.4 95476.0 97240.8 99028.2 100838 102669 104525 106403 108304 110228 126465 128603 130765 114145 116139 118156 120198 122263 124353 112175 151349 153763 132952 135164 137401 139663 141949 144260 146597 148961 156204 161164 158671 163684 166230 168802 171402 174028 176682 179364 3.0

182073 210711 242266 276880 314697

184810 213732 245587 280516 318659

187574 216783 248939 284183 322654

190366 219864 252322 287883 326684

193187 222975 255736 291615 330747

196037 226115 259182 295380 334845

198914 229285 262658 299178 338976

201820 232484 266166 303008 343141

204755 235714 269706 306871 347341

207719 238974 273278 310768 351575

3.5

355844 400471 448702 500688 556574

360147 405130 453729 506098 562383

364485 409825 458794 511547 568234

368860 414556 463897 517036 574126

373269 419324 469038 522564 580059

377714 424128 474218 528132 586034

382194 428968 479435 533739 592051

386710 433846 484691 539387 598110

391262 438760 489985 545075 604210

395849 443713 495317 550805 610352

4.0

616537 680740 749328 822411 900258

622764 687399 756431 829978 908313

629033 694103 763579 837592 916418

635345 700851 770772 845255 924573

641700 707643 718010 932778

648099 714479 785294 860725 941033

654541 721360 792623 868533 949338

661026 728285 799999 876390 957693

667554 735255 807422 884296 966099

674125 742269 814893 892252 974556

983066 1071029 1164339 1263212 1367870

991628 1080114 1173972 1273414 1378662

1000239 1089254 1183662 1283673 1389516

1008905 1098449 1193407 1293991 1400429

1017621 1107699 1203209 1304367 1411404

1026390 1117002 1213066 1314802 1422438

1035213 1126359 1222981 1325297 1433533

1044087 1135772 1232955 1335850 1444690

1053014 1145239 1242983 1346462 1455911

1061995 1154761 1253069 1357136 1467191

4.5

852~66

5.0 1478535 1489940 1501409 1512940 1524535 1536192 1547912 1559698 1571546 1583458 1595437 1607481 1619589 1631761 1644000 1656305 1668673 1681108 1693612 1706180 1718817 1731521 1744290

4-280

HEAT

TABLE

4k-6. 1958

FUNCTION OF

P

IN MILLIMETERS MERCURY AT GRAVITY,

p

2

1

0

K

HE 4 VAPOR-PRESSURE-TEMPERATURE SCAI.E, TIN

980.665

5

--- --- ---

AS A

AND STANDARD

CM/SEC 2

4

3

O°C

7

6

8

9

--- --- --- --- ---

0.01 0.7907 0.02 0.8407 0.03 0.8727

657972 388445 278754

61 8033 358480 268780

578090 358515 258805

538143 338548 258830

508193 328580 248854

478240 328612 248878

458285 308642 238901

438328 298671 228923

408368 288699 228945

39 28 22

0.04 0.8967 0.05 0.9161 0.06 0.9325

218988 189179 159340

219009 179196 159355

209029 179213 159370

209049 179230 159385

199068 16 9246 149399

209088 17 9263 14 9413

189106 17 9279 14 9427

199125 159294 14 9441

189143 169310 149455

18 15 13

0.07 0.9468 0.08 0.9595 0.09 0.9710

149482 129607 11 9721

139495 129619 11 9732

139508 12 9631 109742

13 9521 129643 11 9753

139534 11 9654 109763

129546 11 9665 11 9774

139559 129677 10 9784

129571 11 9688 10 9794

12 9583 11 9699 109804

12 11 10

0.10 0.9814

109824

109834

109844

109854

99863

109873

10 9883

99892

99901

10

0.11 0.9911 0.12 1.0000 0.13 1.0083

99920 90009 80091

99929 80017 80099

99938 90026 80107

99947 80034 80115

99956 80042 80123

99965 90051 80131

99974 80059 80139

99983 80067 70146

89991 80075 80154

9 8 8

0.14 1.0162 0.15 1. 0236 0.16 1.0305

70169 70243 70312

80177 70250 70319

70184 70257 70326

80192 70264 60332

70199 70271 70339

70206 70278 70346

80214 70285 60352

70221 70292 70359

70228 70299 60365

8 6 7

0.17 1.0372 0.18 1. 0435 0.19 1.0496

60378 60441 60502

70385 70448 60508

60391 60454 50513

70398 60460 60519

60404 60466 60525

60410 60472 60531

70417 60478 60537

60423 60484 50542

60429 60490 60548

6 6 6

0.2 0.3

1. 0554 1.1032

550609 411073

540663 39 1112

520715 38 1150

490764 38 1188

490813 36 1224

460859 36 1260

450904 35 1295

440948 34 1329

430991 33 1362

41 33

0.4 0.5 0.6

1.1395 1. 1691 1.1942

32 1427 27 1718 241966

32 1459 26 1744 231989

311490 26 1770 222011

301520 261796 232034

30 1550 251821 222056

291579 25 1846 222078

29 1608 251871 212099

28 1636 24 1895 21 2120

27 1663 24 1919 21 2141

28 23 21

0.7 0.8 0.9

1. 2162 1. 2359 1. 2536

21 2183 182377 172553

202203 182395 172570

202223 192414 162586

202243 182432 172603

202263 172449 16 2619

202283 182467 162635

192302 182485 16 2651

192321 172502 162667

192340 172519 162683

19 17 16

1.0

1.2699

152714

162730

152745

152760

152775

152790

152805

152820

142834

15

1.1 1.2 1.3

1.2849 1.2989 1.3119

142863 133002 13 3132

152878 133015 133145

142892 143029 12 3157

14 2906 133042 123169

142920 13 3055 13 3182

14 2934 133068 123194

14 2948 133081 123206

132961 133094 123218

14 2975 133107 123230

14 12 12

1.4 1.5 1.6

1.3242 1.3359 1.3469

123254 11 3370 11 3480

123266 11 3381 11 3491

123278 123393 10 3501

123290 11 3404 11 3512

11 3301 11 3415 11 3523

123313 11 3426 10 3533

12 3325 11 3437 11 3544

11 3336 11 3448 103554

123348 11 3459 10 3564

11 10 11

1.7 1.8 1.9

1.3575 1.3675 1.3771

10 3585 103685 93780

10 3595 10 3695 10 3790

10 3605 93704 93799

103615 103714 10 3809

10 3625 10 3724 93818

10 3635 93733 93827

10 3645 103743 93836

103655 93752 93845

10 3665 10 3762 93854

10 9 9

2 3

1. 3863 1.4632

893952 654697

864038 634760

82 4120 634823

804200 60 4883

774877 60 4943

754352 585001

734425 565057

714496 565113

694565 555108

67 53

4 5 6

1.5221 1.5707 1.6123

535274 44 5751 396162

515325 44 5795 386200

515376 435838 386238

495425 425880 376275

495474 425922 376312

485522 41 5963 366348

475569 416004 366384

475616 406044 366420

465662 406084 356455

45 39 35

7 8 9

1.6490 1.6820 1.7120

356525 316851 28 7148

346559 31 6882 297177

346593 316913 287205

336626 306943 287233

336659 306973 287261

336692 307003 277288

326724 297033 287316

32 6756 297062 277343

326788 29 7091 277370

32 29 26

10

1.7396

277423

267449

26 7475

267501

267527

257552

267578

257603

257628

25

257727 237962 21 8184

247751 237985 228206

247775 238008 21 8227

247799 228030 228249

247823 238053 218270

237846 22 8075 218291

247870 228097 218312

23 22 21

11 12 13

1.7653 1.7893 1.8119

257678 23 7916 22 8141

247702 237939 228163

14 15 16

1.8333 1.8536 1.8729

208353 198555 198748

218374 208575 19 8767

218395 208595 188785

208415 198614 198804

208345 208634 198823

218456 198653 188841

208476 198672 198860

208496 198691 188878

208516 198710 188896

20 19 18

17 18 19

1. 8914 1. 9092 1.9262

188932 179109 179279

188950 179126 17 9296

188968 189144 169312

188986 179161 179329

189004 179178 169345

18 9022 179195 17 9362

179039 17 9212 16 9378

189057 179229 169394

17 9074 179246 17 9411

18 16 16

20

1.9427

169443

16 9459

169475

169491

169507

16 9523

16 9539

159554

169570

16

4-281

VAPOR PRESSURE TABLE

HE 4 VAPOR-PRESSURE-TEMPERATURE SCALE, TIN

4k-6. 1958

FUNCTION OF

p

1

0

K

AS A

IN MILLIMETERS MERCURY AT O°C AND STANDARD GRAVITY, 980.665 CM/SEC 2 (Contin'l)&1J

P

2

3

4

5

--- --- --- ---

6

7

8

9

--- --- --- ---

21 22 23

1. 9586 1.9740 1.9889

16 9602 15 9755 149903

159617 159770 15 9918

24 25 26

2.0033 2.0174 2.0311

150048 140188 130324

140062 14 0202 14 0338

14 0076 130215 130351

140090 140229 140365

140104 140243 130378

140118 140257 130391

14 0132 130270 140405

140146 140284 130418

140160 130297 130431

14 14 13

27 28 29

2.0444 2.0575 2.0702

140458 130588 130715

130471 120600 120727

130484 130613 130740

130497 130626 120752

130510 130639 130765

130523 130652 120777

130536 120664 130790

130549 130677 120802

130562 130690 120814

13 12 13

15 9632 15 9785 149932

169648 159800 159947

159663 159815 14 9961

169679 159830 15 9976

159694 14 9844 14 9990

159709 15 9859 150005

159724 159874 140019

16 15 14

30

2.0827

120839

120851

120863

130876

120888

120900

120912

120924

120936

13

31 32 33

2.0949 2.1068 2.1185

12 0961 121080 12 11117

120973 12 1092 11 1208

1120985 11 1103 12 1220

120997 12 1115 11 1231

12 1009 12 1127 12 1243

12 1021 12 1139 11 1254

11 1032 11 1150 12 1266

12 1044 12 1162 11 1277

121056 12 1174 12 1289

12 11 11

34 35 36

2.1300 2.1413 2.1524

12 1312 11 1424 11 1535

11 1323 12 1436 11 1546

11 1334 11 1447 11 1557

12 1346 11 1458 11 1568

11 1357 11 1469 11 1579

11 1368 11 1480 11 1590

11 1379 11 1491 11 1601

12 1391 11 1502 11 1612

111482 11 1513 11 1623

11 11 11

37 38 39

2.1634 2.1741 2.1848

10 1644 11 1752 10 1858

11 1655 11 1763 11 1869

11 1666 10 1773 111880

11 1677 11 1784 10 1890

11 1688 11 1795 10 1900

10 1698 101805 10 1910

11 1709 11 1816 11 1921

11 1720 10 1826 10 1931

11 1731 11 1837 11 1942

10 11 10

40

:. The following interpolation equation has been derived for oxygen by a least-squares fit of the vapor-pressure data of Hoge! log P (mm)

= 8.01602 - 415;909 - 0.0058382T

the equation being valid for the region from the triple point (54.363 K) to 90.827 K. Table 4k-14 gives the temperature in kelvins for integral values of vapor pressure P, in millimeters of mercury at O°C and standard gravity, 980.665 cm/sec 2• 1

H. J. Hoge, J. Reeearch. NBS 44,326 (1950).

4-294

HEAT

TABLE

4k-13.

LIQUID NITROGEN TEMPERATURES IN

OF VAPOR PRESSURE

K

FOR INTEGRAL VALUES

P,

IN MILLIMETERS OF MERCURY AT STANDARD GRAVITY, 980.665 CM/SEC 2

p

0

1

2

3

4

5

6

7

ooe

AND

8

9

- --- - -- -- - -- - -- - -- -- -90 100 110 120 130 140 150

63.162 63.220 63.277 63.333 63.389 63.445 63.500 63.555 63.609 63.663 63.717 63.770 63.822 63.875 63.926 63.978 64.029 64.080 64.130 64.180 64.230 64.279 64.328 64.376 64.425 64.473 64.520 64.568 64.615 64.661 64.708 64.754 64.799 64.845 64.890 64.935 64.980 65.024 65.068 65.112 65.156 65.199 65.242 65.285 65.327 65.370 65.412 65.453 65.495 65.536 65.578 65.618 65.659 65.700 65.740 65.780 65.820 65.859 65.899 65.938 65.977 66.015 66.054 66.092 66.131 66.169

160 170 180 190 200

66.206 66.244 66.281 66.319 66.356 66.393 66.429 66.466 66.502 66.538 66.574 66.610 66.646 66.681 66.717 66.752 66.787 66.822 66.856 66.891 66.925 66.960 66.994 67.028 67.061 67.095 67.129 67.162 67.195 67.228 67.261 67.294 67.327 67.359 67.392 67.424 67.456 67.488 67.520 67.552 67.583 67.615 67.646 67.677 67.709 67.740 67.771 67.801 67.832 67.862

210 220 230 240 250

67.893 67.923 67.953 67.984 68.013 68.043 68.073 68.103 68.191 68.220 68.249 68.278 68.307 68.336 68.365 68.393 68.479 68.507 68.535 68.563 68.591 68.619 68.647 68.674 68.757 68.784 68.811 68.838 68.865 68.892 68.919 68.946 69.025 69.052 69.078 69.104 69.131 69.157 69.183 69.209

68.132 68.422 68.702 68.972 69.235

68.162 68.450 68.729 68.999 69.260

260 270 280 290 300

69.286 69.312 69.337 69.363 69.388 69.413 69.439 69.464 69.489 69.539 69.564 69.588 69.613 69.638 69.662 69.687 69.711 69.736 69.784 69.808 69.833 69.857 69.881 69.904 69.928 69.952 69.976 70.023 70.047 70.070 70.093 70.117 70.140 70.163 70.186 70.209 70.255 70.278 70.301 70.324 70.347 70.369 70.392 70.414 70.437

69.514 69.760 69.999 70.232 70.459

310 320 330 340 350

70.482 70.504 70.526 70.549 70.571 70.593 70.615 70.637 70.659 70.681 70.702 70.724 70.746 70.768 70.789 70.811 70.832 70.854 70.875 70.897 70.918 70.939 70.960 70.981 71.003 71.024 71.045 71.066 71.086 71.107 71.128 71.149 71.170 71.190 71.211 71.232 71. 252 71.273 71. 293 71. 313 71.334 71.354 71.374 71.394 71.415 71.435 71.455 71 .475 71.495 71.515

360 370 380 390 400

71.535 71.555 71.574 71.594 71.614 71.634 71.653 71.673 71. 692 71.731 71. 751 71.770 71.790 71.809 71.828 71. 847 71.867 71.886 71.924 71. 943 71.962 71.981 72.000 72.019 72.038 72.057 72.075 72.113 72.131 72.150 72.169 72.187 72.206 72.224 72.243 72.261 72.298 72.316 72.334 72.353 72.371 72.389 72.407 72.425 72.443

410 420 430 440 450

72.479 72.497 72.515 72.533 72.551 72.569 72.586 72.604 72.657 72.675 72.692 72.710 72.728 72.745 72.762 72.780 72.832 72.849 72.867 72.884 72.901 72.918 72.935 72.952 73.004 73.021 73.038 73.055 73.071 73.088 73.105 73.122 73.172 73.189 73.206 73.222 73.239 73.256 73.272 73.289

460 470 480 490 600

73.338 73.354 73.371 73.387 73.501 73.517 73.533 73.549 73.661 73.677 73.693 73.709 73.819 73.835 73.850 73.866 73.975 73.990 74.005 74.021

510 520 530 540 550

74.127 74.143 74.158 74.173 74.188 74.203 74.218 74.233 74.248 74.263 74.278 74.293 74.308 74.323 74.338 74.353 74.367 74.382 74.397 74.412 74.427 74.441 74.456 74.471 74.485 74.500 74.515 74.529 74.544 74.558 74.573 74.587 74.602 74.616 74.631 74.645 74.660 74.674 74.688 74.703 74.817 74.831 74.845 74.717 74.731 74.746 74.760 74.774 74.788

73.404 73.420 73.566 73.582 73.725 73.741 73.882 73.897 74.036 74.051

71. 712 71. 905 72.094 72.279 72.461

72.622 72.640 72.797 72.815 72.970 72.987 73.139 73.156 73.305 73.322

73.436 73.452 73.469 73.485 73.598 73.614 73.630 73.646 73.756 73.772 73.788 73.804 73.913 73.928 73.944 73.959 74.067 74.082 74.097 74.112

174.803

4-295

VAPOR PRESSURE TABLE

4k-13.

LIQUID NITROGEN TEMPERATURES IN

OF VAPOR PRESSURE

P,

STANDARD GRAVITY,

p

0

1

2

K

FOR INTEGRAL VALUES

IN MILLIMETERS OF MERCURY AT

3

980.665 4

CM/SEC 2

5

ooe

AND

(Continued)

6

I

7

8

9

- -- -- - -- - - - -- - - -- - - - - 560 570 580 590 600

74.859 74.873 74.888 74.902 74.916 74.930 74.944 74.958 74.972 74.986 75.000 75.014 75.027 75.041 75.055 75.069 75.083 75.097 75.111 75.124 75.138 75.152 75.165 75.179 75.193 75.207 75.220 75.234 75.247 75.261 75.275 75.288 75.302 75.315 75.329 75.342 75.356 75.369 75.383 75.396 75.409 75.423 75.436 75.450 75.463 75.476 75.490 75.503 75.516 75.529

610 620 630 640 650

75.543 75.556 75.569 75.582 75.595 75.609 75.622 75.635 75.648 75.661 75.674 75.687 75.700 75.713 75.726 75.739 75.752 75.765 75.778 75.791 75.804 75.817 75.830 75.843 75.855 75.868 75.881 75.894 75.907 75.919 75.932 75.945 75.958 75.970 75.983 75.996 76.008 76.021 76.034 76.046 76.059 76.071 76.084 76.097 76.109 76.122 76.134 76.147 76.159 76.172

660 670 680 690 700

76.184 76.197 76.209 76.221 76.234 76.246 76.259 76.271 76.283 76.296 76.308 76.320 76.333 76.345 76.357 76.369 76.382 76.394 76.406 76.418 76.430 76.443 76.455 76.467 76.479 76.491 76.503 76.515 76.527 76.539 76.551 76.564 76.576 76.588 76.600 76.612 76.623 76.635 76.647 76.659 76.671 76.683 76.695 76.707 76.719 76.731 76.742 76.754 76.766 76.778

710 720 730 740 750 760

76.790 76.801 76.813 76.825 76.837 76.848 76.860 76.872 76.883 76.895 76.907 76.918 76.930 76.942 76.953 76.965 76.977 76.988 77 .000 77 .011 77.023 77.034 77.046 77.067 77 .069 77.080 77.092 77.103 77.115 77.126 77.137 77 .149 77 .160 77 .172 77.183 77 .194 77.206 77.217 77.228 77.240 77.251 77 .262 77.274 77.285 77.296 77.307 77.319 77.330 77.341 77.352 77.363 77 .375 77.386 77.397 77 .408 77.419 77.430 77.441 77.453 77.464

4-296

HEAT

TABLE

4k-14.

LIQUID OXYGEN TEMPERATURES IN

OF VAPOR PRESSURE

K

FOR INTEGRAL VALUES

P,

IN MILLIMETERS OF MERCURY AT STANDARD GRAVITY, 980.665 CM/SEC 2

p

0

1

2

3

4

5

6

7

oDe 8

AND

9

- - - - - - - - - -- -- - - -- - - - - 0 10 20 30 40 50

53.980 56.278 57.719 58.790 59.650 60.373 60.998 61.551 62.048 62.499 62.913 63.297 73.654 63.989 64.303 64.601 64.883 65.151 65.407 65.652 65.887 66.112 66.329 66.539 66.741 66.936 67.125 67.308 67.486 67.659 67.827 67.991 68.150 68.305 68.457 68.605 68.749 68.891 69.029 69.164 69.297 69.427 69.554 69.679 69.802 69.922 70.040 70.156 70.270 70.383 70.493 70.601 70.708 70.813 70.917 71. 019 71.120 71. 219 71.316

60 70 80 90 100

71.413 71. 508 71.601 71.694 71.785 71.875 71.964 72.052 72.139 72.225 72.309 72.393 72.476 72.558 72.639 72.719 72.798 72.876 72.953 73.030 73.106 73.181 73.255 73.329 73.402 73.474 73.545 73.616 73.686 73.756 73.824 73.893 73.960 74.027 74.094 74.159 74.225 74.289 74.354 74.417 74.480 74.543 74.605 74.667 74.728 74.788 74.849 74.908 74.968 75.026

110 120 130 140 150

75.085 75.646 76.170 76.663 77 .127

160 170 180 190 200

77.568 77.611 77.653 77.695 77.738 77.780 77.821 77 .986 78.027 78.068 78.108 78.148 78.188 78.228 78.386 78.425 78.463 78.502 78.540 78.579 78.617 78.768 78.805 78.842 78.879 78.916 78.953 78.989 79.134 79.169 79.205 79.241 79.276 79.311 79.346

210 220 230 240 250

79.485 79.520 79.554 79.588 79.622 79.656 79.690 79.724 79.757 79.791 79.824 79.857 79.890 79.923 79.956 79.989 80.021 80.054 80.086 80.118 80.150 80.182 80.214 80.246 80.278 80.309 80.341 80.372 80.403 80.435 80.466 80.497 80.527 80.558 80.589 80.619 80.650 80.680 80.710 80.741 80.771 80.801 80.831 80.860 80.890 80.920 80.949 80.979 81.008 81.037

260 270 280 290 300

81.066 81.095 81.124 81.153 81.182 81.211 81. 239 81.268 81. 296 81.324 81.353 81.381 81.409 81.437 81.465 81.493 81.521 81.548 81.576 81.604 81.631 81.658 81. 686 81.713 81.740 81.767 81.794 81.821 81. 848 81.875 81. 902 81.928 81.955 81. 981 82.008 82.034 82.060 82.087 82.113 82.139 82.165 82.191 82.217 82.242 82.268 82.294 82.319 82.345 82.370 82.396

310 320 330 340 350

82.421 82.446 82.472 82.497 82.522 82.671 82.696 82.720 82.745 82.769 82.915 82.939 82.963 82.987 83.011 83.153 83.177 83.200 83.223 83.247 83.386 83.409 83.432 83.454 83.477

360 370 380 390 400

83.613 83.636 83.658 83.680 83.703 83.725 83.747 83.769 83.792 83.814 83.836 83.858 83 .880 83. 902 83.923 83.945 83.967 83.989 84.010 84.032 84.054 84.075 84.097 84.118 84.139 84.161 84.182 84.203 84.225 84.246 84.267 84.288 84.309 84.330 84.351 84.372 84.393 84.414 84.435 84.455 84.476 84.497 84.518 84.538 84.559 84.579 84.600 84.620 84.641 84.661

75.143 75.200 75.257 75.314 75.370 75.426 75.482 75.537 75.591 75.700 75.753 75.807 75.860 75.912 75.964 76.016 76.068 76.119 76.221 76.271 76.321 76.371 76.420 76.469 76.518 76.566 76.615 76.710 76.758 76.805 76.852 76.898 76.945 76.991 77 .036 77.082 77 .172 77.217 77.262 77.306 77.350 77.394 77.438 77.481 77.525 77.863 77.904 77.945 78.268 78.307 78.347 78.655 78.693 78.730 79.025 79.062 79.098 79.381 79.416 79.451

82.547 82.572 82.597 82.622 82.646 82.794 82.818 82.842 82.867 82.891 83.035 83.058 83.082 83.106 83.129 83.270 83.293 83.316 83.340 83.363 83.500 83.523 83.545 83.568 83.591

4--297

VAPOR PRESSURE TABLE

4k-14.

LIQUID OXYGEN TEMPERATURES IN

OF VAPOR PRJ (300)-ll1> F 10 5F 9- 110- 11Z* 9- 11O-11L* 3- 11O-1OB 3-110- sB (300)-IE* 3- 11O-4E* 3 X 10 1°H 1211"10 7H

l 10 2l

(411")-lm'* (411")-110 1Om'* 1O-1m* 10 3m* (411")-IM'* (411")-110 4M'* 1O-1M*

lO-IM*

l

i

lOtl (l211")-110-1Om' (1211")-lm' 3 X 109m 3 X 10 1lm (l211")-110-1OM' (1211")-11O- SM' 3 X 10 9M 3 X 10 7M

A formula given in cgs emu, cgs esu, or Gaussian (starred) units, in which the capacitivity or permeability, if relevant, appears explicitly, may be expressed in (a) un rationalized cgs practical units or (b) rationalized mks units by replacing eaeh symbol with its value in the emu, esu, or .tarred column. respectively, Each line may be read as an equation relating the .ize of the unit. involved. In preci.e work. replace 3 by 2.9979 and 9 by 8.9874. o

6-11

DEFINITIONS, UNITS, NOMENCLATURE, SYMBOLS TABLE

5a-4.

REDUCTION OF FORMULA TO RATIONALIZED MKS UNITS

(a) Practical cgs (b) mks

Quantity ~agnetomotance.........

Mass .................... Permeability ............. Polarization, electric ...... Pole strength ............ Potential, electric ......... Potential, vector .......... Power ................... Reactance ............... Reluctance ............... Resistance ............... Resistivity, area .......... Resistivity, volume .......

g: gilbert g: amp-turn m gram m kilogram 1'0 gauss/oersted 1'0 henry /m P coulomb/em! P coulomb /m! m maxwell m weber V volt (a) A gauss-em (b) A weber /m (a) P erg/sec (b) P watt X ohm (a) CR. gilbert/max (b) CR. amp-turn/weber Rohm e ohm (a) p ohm-em (b) p ohm-m (a) (b) (a) (b) (a) (b) (a) (b) (a) (b)

(Continued)

Emu

Esu

g:* 41r1O- 1g:* m 10 3m 1'0* (471'")-110 71'0* lO-lp 1O-5P (47r)-l m * (47r )-1108m* 108 V A* 10sA*

3 X 1010g: 121r X 100g: m 10 3m 9- 110-2°1'0 (3611")-110- 131'0 3 X io-r3 X 105P* (12w)-lJO- IOm (1200r)-tm (300)-IV* 3-lJO- IOA 3- 11O-4A

P 107P lO'X CR.*

P 107P

471'"10-°(R* 100R 10 0u lOop

10 11p

9- 11O-11X * 9 X 10 2OCR. 3671'" X 1011 1,

= alb +

(bll

-

a 2 )l J- l

=

= 2k- l[K(k)

- E(k)]

(1 - k'2)l

the following recurrence formula may be used to find both P" and Qn (2n

+ 1)Pn+

1 -

4na- 1bP"

+ (2n

- 1)P n- 1 = 0

A capacitance table is given in Australian J. Phys. [7, 350 (1954)]. Torus formed by rotation of a circle of diameter d about a tangent line

L 00

C

=

81rEd

[J 1 (k nd) ]- 1 So.o(knd)

~

0.970 X lO- l Od

n=-1

where So,o(k"d) is a Lommel function and J o(knd)

=

O.

For additional intersecting sphere-capacitance formulas, see Snow, J. Research Natl. Bur. Standards 4:3, 377-407 (1949). 1

6-14

ELECTRICITY AND MAGNETISM

Aichi's formula for a nearly spherical surface

C ~ 3.139 X 10- 1181 where 8 is surface area. Cube of side a. Close lower limit C

= a(cos u + k

Figure of rotation, z C

~

~

0.7283 X 1O-10a cos 2u),

1.11278 X 1O-

Flat circular annulus, with edges at C

:::s

4510 X lO-l1b [cos- 1 ~ . b

10a(1

+ (1

= a(sin u

- k sin 2u), 0

p

= b. a < b

- ~)! tanh-l~] (1 b2 b

Error varies from about ±O.OOIC at b = 1.1a to zero at b C

:::s

17.48 X lO-12(a

c, a' > b' > c',

> a'

and a

Small sphere of radius a midway between planes a distance 2c apart C

~

1 1.1128 X 10- 10 ( Ii

c )-1

- 1 In 2

Sphere of radius b on axis of infinite cylinder of radius a C

= b[1.11285

where r = b f a,

- 0.9277r - 0.114r 2

-

0.1955r 3

+ 1.8858r(1

The error is less than 1 part in 4,000 for 0

-

r)-0.U63]

a c = - --e·..• p iJep °L

or

(5b-92) (5b-93)

where U« or V n are solutions of Laplace's equation in two dimensions; explicitly

u; or

n

V =

{:~n}

in';

lnp } U o or V 0 = { constant 1

(5b-94)

e

{con~ant}

(5b-95)

C. Yeh, and K. F. Casey, IEEE Trans. Microwave Theory and Tech. MTT-13, 297

(1965).

5-48

ELECTRICITY AND MAGNETISM

TM Waves i

= V X (ez J {e±i'YzJ = (k 2 - A2)i

H J {e±i'YzJ (k 2 - A2)i

(5b-IOO) (5b-IOl)

where Z p(Ap) have been defined earlier. 3. Spherical Coordinates. In the spherical coordinates r, 8, cP the three distinct types of basic spherical wave functions, characterized by the relationship between the field vectors and the radial r direction (the direction of propagation), are: TEM Waves E, = H, = 0 e±ikr

Ee = - - . r sin 0

Hcf>

= ± ~Ee JJ.

(5b-102)

TM Waves H = V X (err

=

X (ezcf:»

E

(Um(l),(2)(~)}

= WE -i V

X V X (ezcf:»

(V m(I),'2)(.,,)} {e±i'YzJ

(5b-ll1) (5b-112)

where U and V satisfy Weber's equation of the confluent hypergeometric type,"

[:;2 + (q2~2 +

U(~) =

0

(5b-113)

~ + (q27]2 - m)] V(77) = 0 [ 077

(5b-114)

m) ]

2

q2

=k

2 -

1'2

TE Wave E 'l!

= V X (ez'l!) H =~V X V X 'lWJ1. = {Um(l)·(2)(~)J {V".(l),(2)(7])J (e±i'YzJ

(e z'1')

(5b-115) (5b-116)

Polarization of Waves. Consider a plane wave in free space propagating in the z direction and having the following components:

E = ezEle+ikz-iwl

B

=

+ eyE2eikz-iWt + eyE l vi J1.oEo eikz-iwt

-e zE2 vi J1.0Eo eikz-iWt

(5b-117) (5b-118)

with k = w~. Note that (Er,B y ) and (Ey,B z) are linearly independent fields, and E l and E 2 are complex constants. LINEARLY POLARIZED WAVE. E 1 and E 2, have the same phase. In this case E at any point in space oscillates along a directional line which makes a constant angle q, with the x axis, this angle being given by q, = tan- l(E 2/E1) . CIRCULARLY POLARIZED WAVE. E 1 and E 2 have the same magnitude but their phases differ by 90°. Hence

E

= Re (ez ± iey)Eleikz-iWt = E1[ez cos (wt - kz) ± e y sin

(wt -

kz)]

Hence E at any point in space does not oscillate. Its magnitude is constant, but its direction rotates at the angular velocity t», When E 2 = -iE 1, the wave is said to be 1 J. Meixner and F. W. Schafke, "Mathieu-funktionen und Spharoid-funkt.ionen," Springer-Verlag OHG, Berlin, 1954. 2 In terms of the rectangular coordinates x, y, the parabolic coordinates ~, 1] are defined by the following relations: x = !(~2 - 77 2) , Y = ~'TJ (- 00 < ~ < 00, 0 ~ 7] < oe). 3S. O. Rice, Bell S1l8tem Tech. J. 33,417 (1954).

5-50

ELECTRICITY AND MAGNETISM

right-handed circularly polarized. handed circularly polarized.

When E 2

= iE 1,

the wave is said to be left-

E 1 and E 2 have arbitrary relative amplitudes At any point in space the tip of E describes a locus which is an ellipse.

ELLIPTICALLY POLARIZED WAVE.

and phases. References

1. Stratton, J. A.: "Electromagnetic Theory," McGraw-Hill Book Company, New York,

1941. 2. Smythe, W. R.: "Static and Dynamic Electricity," 3d ed., McGraw-Hill Book Company, New York, 1968. 3. Elliott, R. S.: "Electromagnetics," McGraw-Hill Book Company, New York, 1966. 4. Papas, C. H.: "Theory of Electromagnetic Wave Propagation," McGraw-Hill Book Company, New York, 1965. 5. Van Bladel, J.: "Electromagnetic Fields," McGraw-Hill Book Company, New York, 1964. 6. Panofsky, W. K. H., and M. Phillips: "Classical Electricity and Magnetism," 2d ed., Addison-Wesley Publishing Company, Inc., Reading, Mass., 1962. 7. Kraichman, M. B., "Handbook of Electromagnetic Propagation in Conducting Media," NA VMAT P-2302, 1970, U.S. Government Printing Office, Washington, D.C. 20402.

6b-9. Guided Waves. In this section some basic properties of guided waves are given. These properties are found from the solutions that satisfy the source-free Maxwell's equations and the appropriate boundary conditions. When the guided waves propagate along a straight-line path, one may assume that every component of the electromagnetic wave may be represented in the form (5b-119) in which z is chosen as the propagation direction and u, v are generalized orthogonal coordinates in a transverse plane.! 'Y is the propagation constant. Under this assumption, the transverse field components in homogeneous isotropic medium (E,J.I.) are (5b-120) (5b-121) (5b-122) (5b-123) and the longitudinal field components satisfy the following equation:

Only discrete values of r 2 will satisfy the boundary conditions. These allowed r 2 values are called eigenvalues; and corresponding to these eigenvalues are the eigenfunctions. The orthogonality properties of the field components can therefore be found according to the well-known orthogonality properties of the eigenfunction. It will be recalled from Sec. 5b-8 (Basic Wave Types) that T"Af modes refer to waves having Hz = 0, TE modes having E, = 0, HE modes having all field components ~ 0, and TEM modes having E, = 0 and Hz = O. Propagation Characteristics. Propagation characteristics of guided waves refer to the behavior of the propagation constant 'Y as a function of frequency. In general, 1 J. A. Stratton, "Electromagnetic Theory," chap. 1, McGraw-Hill Book Company, New York, 1941.

5-51

FORMULAS

l' may be complex: l' = ia + {J, where a is the attenuation constant and {J is a phase constant. Several commonly used terms to describe guided waves are defined as follows:

Cutoff frequency, Cutoff wavelength,

k=w~

Guide wavelength, w

= :y

(5b-125)

Phase velocity,

Vp

Group velocity,

dw v(/ = d'Y =

l' WEJl •

1 1 - (r /k)(dr /dk)

The above considerations are applicable for TE, TM, or HE waves only. For TEM modes, we have l' = k, Ie = 0, Vp = w/k, and Ao = 2'Tr/k with k = w vi;;. Bounded Waveguides. Only T M waves and T E waves are physically possible in a cylindrical region bounded by a simply connected conducting region. However, in a coaxial region with perfectly conducting walls, a TEM as well as TM and TE waves can be present. The propagation parameters for cylindrical waveguides bounded by good (but not perfectly) conducting walls are summarized as follows: FOR PROPAGATING MODES,

I > t. a=O l'

= (J = k

vp

= {j =

w

[ 1 -

(j)

2

J

1

(5b-126)

----;====::::::==:===~

vi JlE(l

-

(fe/IF)

1 v(/=JlEVp

FOR NONPROPAGATING MODES (THE EVANESCENT WAVES),

{J=O l'

= 'la. = 'l'k [ (Ie) T 2-

1

I < Ie

]!

(5b-127)

ATTENUATION DUE TO IMPERFECTLY CONDUCTING WALLS

nepers /m

(5b-128) (5b-129) (5b-130) (5b-131) (5b-132) (5b-133) (5b-134)

5-52

ELECTRICITY AND MAGNETISM

where IHtl2 is the square of the total transverse magnetic field, alan is the normal derivative at the boundary conducting wall, aHzlal is the derivative of Hz tangent to curve L along the cross-sectional bounding wall, A is the cross-sectional area of the guide, R. = ('Trfp.lu c )! is the surface resistance, and Uc is the conductivity of the boundary conductor. ATTENUATION DUE TO IMPERFECT DIELECTRIC

!!i. WEr

«

1

(5b-135)

where E = Er(1 - udliwEr), Ud is the conductivity of the dielectric in the guide, and Er is the real part of the dielectric constant E. ad is in nepers /meter. The above approximate expressions for the attenuation constant are not valid for frequencies very close to the cutoff frequencies and for very high frequencies. It has also been assumed that the field configurations are not affected by the presence of small wall and dielectric losses. Field components and propagation parameters for waves guided in rectangular and circular tubes are summarized in Table 5b-1. Table 5b-2 provides the field configurations for several lower-order modes in rectangular and circular waveguides. In a bounded waveguide, an arbitrary field E or H within the waveguide may be expanded in terms of the mode functions as follows: E

I =I =

ApETM + BpETE

P

H

BpHTE

+ ApHTM

p

Le., the mode functions for

T E and T M waves are a complete set. For details concerning bounded waveguides of other simple shapes (such as elliptical, parabolic, triangular, etc.), the reader is referred to the literature. 1 For waveguides of arbitrary cross-sectional shape for which solutions in terms of known and tabulated eigenfunctions are not available, one must resort to numerical means! or to approximations based on variational techniques. 3 Numerically speaking, the problem reduces to finding the eigenvalue r which satisfies the Helmholz equation (V 2 + r 2)F = 0 and the boundary condition F = 0 on C for TM waves and aFIan = 0 on C for TE waves by the use of a computer. The well-known difference method has been used successfully for this type of problem.! The variational method offers a way to obtain a rather accurate value for the eigenvalue I' which is related to the propagation constant l' by the relation l' = VW 2P.E - r 2, from the knowledge of an approximate field configuration (i.e., a trial function). Specifically, for a TM modes, if a trial function u(x,y) vanishes on the boundary and satisfies the conditions

fA uEz(O) dx dy where Ez(O), E z(1) ,

= 0, fA «s;» dx •••

dy

= 0,

. . . , fA

«s»:» dx

dy

=0

(5b-136)

,E/n-l) are the eigenfunctions for the equation

1 F. E. Borgnis and C. H. Papas, Electromagnetic Waveguides and Resonators. "Handbuch der Physik," vol. 16, Springer-Verlag OHG, Berlin, 1958. 2 R. F. Harrington, Field Computation by Moment Methods, the Macmillan Company, New York, 1968. 3 F. E. Borgnis and C. H. Papas, "Randwertproblems der Mikrowellenphysik," SpringerVerlag OHO, Berlin, 1955.

5b-1.

TABLE

Field components TM",n modes . (m'll" x ) E. = Eo SIn

a

H

-iWE

., = 4,..2/e2

.

SIn

(n,.. b y)

(fe)",n

=

2

~;; [ (~Y +

TE waves-

Field components Rectangular waveguides TE",n modes

(iY]l

aE •

7iY

4,..2/e2

ax

i1'

aE.

H. = H 0 cos

E., =

H,,=~_aE. E., = 4,..2/e2

FORMULAS FOR RECTANGULAR AND CIRCULAR WAVEGUIDES

TMwaves I Propagation parameters

(Xg)",n

1/ 1.5

Right: inductive iris.

5-68

ELECTRICITY AND MAGNETISM

References 1. Marcuvitz, N., (ed.): "Waveguide Handbook," vol. 10 of MIT Rad. Lab. Ser., McGraw-

Hill Book Company, New York, 1951. 2. Collin, R. E.: "Foundations for Microwave Engineering," McGraw-Hill Book Company, New York, 1966. 3. Ghose, R. N.: "Microwave Circuit Theory and Analysis," McGraw-Hill Book Company, New York, 1963. 4. Ramo, S., J. R. Whinnery, and T. Van Duzer: "Fields and Waves in Communication Electronics," John Wiley & Sons, Ine., New York, 1965.

6b-l0. Cavity Resonators. Resonant cavities are used at high frequencies in place of lumped-circuit elements, primarily because they eliminate radiation and in general possess very low losses. Only eigenvalue solutions exist in a lossless cavity resonator completely enclosed by perfectly conducting walls. For a cavity filled with a homogeneous, isotropic dielectric, the pth eigenvector E p satisfies (V 2

+k

p

2)E

p

n X Ep

=0 =0

(everywhere within the cavity) (on the enclosing wall)

(5b-206)

where k p = C&lp ~ (p = 1, 2, 3,. .) are the eigenvalues. C&lp is the resonant frequency for the pth mode. The Qp of a resonator for the pth mode is defined as follows:

Q _ p

-

total time-average energy stored time-average power dissipated

C&lp

AC&l

(5b-207) (5b-208)

C&lp

where AC&l is the bandwidth of the resonance curve. Hence Qp is a measure of the amount of power dissipated for the pth mode. For an enclosed cavity with slightly lossy walls,

2lvHp.

Qp =_-=-c-

s, 1. H ':fA p

H: dV _

(5b-209)

. H* dA p

where H p is the magnetic field of the pth mode of the cavity without losses, and o. is the skin depth of the walls. A is the total surface enclosing the cavity region. For a cavity composed of a uniform transmission line (which may support the TE, TM, TEM, or HE mode) with short-circuiting perfectly conducting ends, the Qp of this cavity is related to the attenuation constant O:p of the transmission line by the relation 1 (5b-210)

v:

where V~ha.e, r ou p and ')'p are respectively the phase velocity C&lp/')'p, the group velocity and the phase constant of the pth mode. If the end plates possess a very small loss, then the total QT of this cavity is

OC&lp/o')'p,

1 QT =

1 Qend plates

+ -:::--__ Qtrans. line

where Qend plates is calculated according to Eq. (5b-209) and according to Eq. (5b-21O). 1

C. Yeh, Proc, IRE 50, 2145 (1962).

Qtrans.line

can be calculated

5-69

FORMULAS

Simple Resonators. The mode functions for a cylindrical waveguide of simple cross section closed at both ends by short-circuiting plates are! (with d = length of the cavity) : For T M mnl modes

E Zm nl =

H Zm nl = 0

E

= -

tmnl

H

with (V t2 frequency

=

tmnl

+ r m n(TM)2)cf>mn

cos

Amncf>mn

l7rZ

d

(5b-211) (5b-212)

l7r d

A mn

•

rmn(TM) Vtcf>mn SIn

. A mn ( 1,Wf rmn(TM) ez

= 0 and

cf>mn

=

X

mnl

(5b-213)

d

)

cos

d17rZ

0 on the cylindrical wall.

1- [ r mn (TM) 2 =_ /-

W TM

Vtcf>mn

17rz

(5b-214) The resonant

+ (17r)2]! -d

V J.Lf

For TE m nl modes

E Zm nl = 0 H zmnl

=

. 17rZ SIn

d

-iwJ.L

E t m nl = H t m nl

(5b-215)

B mn '¥ mn

rmn(TE) Bmn(e z

17r

=d

(5b-216)

X V

1 rmn(TE) Bmn(vt'¥mn)

+

with (V t2 r m n(TE)2)'¥mn = 0 and resonant frequency

a'¥mn/an

cos

17rZ

d

l7rz

d

(5b-217) (5b-218)

= 0 along the cylindrical wall.

The

+ (17r)2]! -d

=1- [ r mn (TE)2 _ /-

TE wmnl

.

sm

t'¥mn)

V J.Lf

For a rectangular resonator with cross sections a X b we have

. m7rX

with

rmn(TM)

n7rY

cf>mn

= sm------a-cos b

'¥mn

=

=

(5b-219)

m7rX . n7rY cos ------a- sm

rmn(TE)

=

b [ (:7r) 2+ (;:r) 2T

(5b-220) (5b-22l)

For a circular cylindrical resonator of radius a, we have

mn

=

J

m

(r m n(TM)r)

C?S mA.

SIn

~

(5b-222) (5b-223)

where

rmn(TM)

and

rmn(TE)

satisfy the following equations: Jm(rmn(TM)a)

=0

J~(rmn(TE)a) = 0

(5b-224) (5b-225)

1 Solutions are also available for resonators of more complex shapes, such as the ellipsoidhyperbolid resonators [W. W. Hansen and R. D. Richtmeyer, J. Appl. Phys. 10, 189 (1930)] and the reentrant cavities [D. C. Stinson, Trans. IRE MTT-3, 18 (1955)].

5-70

ELECTRICITY AND MAGNETISM

Solutions are also available for spherical cavity of radius a: E~~l

=V

TE H mnl

= - -i

H~~

= V X ['lfmnlrerJ

wp.

TM Umnl = -i

V

(5b-226)

X (cf>mnrer)

V X V X [cf>mnlrerJ

X

(5b-227) (5b-228)

X ['lfmnlrerJ

V

(5b-229)

WE

cf>mnl = jm(k~f)r)Pml (cos 8)~f~ lq, 'lfmnl = jm(k"/2). By matching the polynomial A(O,e/» in Eq. (5b-285) to a Chebyshev polynomial, one may obtain an array of a given number of elements which gives the lowest side lobes for a prescribed antenna gain, or highest gain for a prescribed side-lobe level.

°

6--80

ELECTRICITY AND MAGNETISM

UNEQUALLY SPACED LINEAR ARRAYS. Although Eq. (5b-284) for unequally spaced array is considerably more difficult to handle than Eq. (5b-285) for equally spaced array, with the use of a computer numerical results can be obtained in a straightforward manner. An unequally spaced array is generally more "broadband" than an equally spaced array. Radio-astronomical Antennas. Consideration must be given to the case where the incident wave from cosmic sources is partially polarized and polychrornat.ic.! Assuming that the radio-astronomical antenna is conjugate-matched to the load, the power absorbed by the load is

-

r.; = ~ ~~ A (O,f/»

~

Tr(pradprad*) . «EincEinc* »

(5b-287)

where A( O,e/» is the effective area of the receiving antenna, i.e., A( O,f/» (>'2/47r)G( O,f/» , G(O,f/» is the gain function of antenna in transmission. prad is the field polarization vector, . (5b-288) where Erad is the electric vector of the far-zone field radiated by the antenna in transmission.

(EincEinc*) is the transpose of (EincEinc) and, (W) means

(W)

=

.

fT

1

lim 21' r-.»

-T

W dt

(5b-289)

For example, if the incident polychromatic wave is narrow-band and has the form (5b-290) where E(J(t) and E",(t) are slowly varying functions of time, and CrJ is a mean frequency, then the time-average power absorbed by the conjugate-matched load is Paba

= ~ (1 -

m)A(O,f/»(Sinc(O,f/»)

+ mA(O,cj»(Sinc(o,cj») cos" ~

(5b-291)

with cos "Y

= cos 2x' cos (Sinc(O,f/>))

2x cos (21/;' - 21/;) sin 2x' sin 2x

=!

J.:. «E(JE;) 2~J.L

+ (E",E:»

(5b-292) (5b-293)

'Y is the angle between the point (21/;, - 2x) describing the polarization ellipse of the incident wave and the point (21/;',2x') describing the polarization ellipse of the radiated wave, and m is the degree of polarization which is the ratio of the power density of the polarized part to the total power density. 2 A way to measure the degree of coherence I"YI of an incoming polychromatic signal by the use of a correlation interferometer which requires no phase-preserving link has been suggested by Brown and Twiss. 3 The correlation interferometer (which consists of two identical antennas) measures the correlation coefficient I"Y I which is defined as

I"YI

where

=

{

u 2( M

([M I2 - (M I2)][M22 - (M 22)1)}! u(M I2)u(M 22)

1 2)

u 2( M 22) M 12

= «M 1 2 = =

-

(11-1 1 2»

2)

«M 22 - (M 22»)2) V1V: M 22 = V 2V:

(5b-294) (5b-295) (5b-296) (5b-297)

H. C. Ko, Proc. IRE 49, 1446 (1961). 2 M. Born and E. Wolf, "Principles of Optics," 2d ed., Pergamon Press, New York, 1964. 3 R. H. Brown and R. Q. Twiss, Phil. Ma(). 45, 663 (1954). 1

5-81

FORMULAS

V1(t)Vi(t) is the power output of one antenna operating singly and Vz(t)V:(t) is the power output of the other antenna operating singly. The correlation interferometer of Brown and Twiss is an interferometer that measures b-(M 12,M z2)I, while the conventional interferometer measures 1'( VI, V 2). Hence, no phase-preserving link is necessary in the measurement of 1'Y(MI2,M z2) I, the antennas can be separated greatly, and thus high resolving powers can be realized. If the source of the polychromatic signal is a rectangular distribution of width 2w, t.' e correlation coefficient II'I is related to the width by the equation

II'I = Isi~l~w I

(5b-298)

where l is the separation of the interferometer, k = wlc, and w is a mean frequency. Lorentz Reciprocity Theorem. Let (Ea,H a) be the fields generated by sources (Ja,Jma), and (Eb,H b) be the fields generated by sources (Jb,Jmb), operating at the same frequency. Then, Lorentz reciprocity theorem states that [

J all space

(Ea'

Js - a, . Jmb)

dV =

[ (E b J all space

•

J, - a, . Jma) dV

(5b-299)

With regard to antennas, the above theorem means that the receiving pattern of any antenna constructed of linear isotropic matter is identical to its transmitting pattern. In general, reciprocity does not hold for an anisotropic medium. However, for the special case of an anisotropic plasma or ferrite, the concept of reciprocity can be generalized. This is based on the fact that the dielectric tensor of a magnetically biased plasma or the permeability tensor of a ferrite is symmetrical under a reversal of the biasing magnetostatic field: i.e., e(B o) = e( -B o) or !leBo) = Il( -B o) where the tilde indicates the transpose dyadic. The reciprocity theorem then becomes [

JaIl space

(E b( -B o) • Ja - H b( -B o) • Jma) dV =

[ (Ea(B o) • Jb Jail space

Ha(B o) • Jmb) dV

(5b-300)

Elementary Relations Con-cerning Antennas. Consider a transmitting antenna and a receiving antenna separated by a large distance r, The power absorbed by the receiving antenna is

(5b-301)

where P is the total power transmitted by the transmitting antenna, Gt and Gr are the respective gain functions of the two antennas for the direction of transmission, and A is the wavelength of the radiated wave. Now if an antenna is used for transmission as well as reception, such as for radar application, the power absorbed by the receiver from the scattered wave is UA2Gt 2

P r = P (41r)3r4

(5b-302)

where r is the distance from the antenna to the scatterer, and a is the scattering cross section of the scatterer. The scattering cross section is defined as the actual cross section of a sphere that in the same position as the scatterer would scatter back to the receiver the same amount of energy as is returned by the scatterer. Radiation from Charged Particles. Radiation results when a charged particle accelerates or decelerates (Bremsstrahlung), when a charged particle moves along a curved path at a constant velocity (cyclotron radiation), when a charged particle moves at 8.

5-82

ELECTRICITY AND MAGNETISM

constant velocity which is faster than the phase velocity of light in the medium (Cerenkov radiation), when a charged particle moves at a uniform velocity along an uneven surface (Smith-Purcell radiation), or when a charged particle moves through two media with different electrical properties (transition radiationj.! POINT CHARGE IN ARBITRARY MOTION IN FREE SPACE. The fields are:

E

= .s.: 41rEOS 3{r" (I

- ~) c2

+ C-!2 [r X (r.. X it)1}

B=l.rXE

(5b-304)

rc

with

S

r ..

(5b-303)

r·u

(5b-305)

=r--

c

=r

ru

C-

-

(5b-306)

dr

• u

u = -dt' -

du

(5b-307)

= dt'

where r is the retarded radius vector which is the radius vector from the retarded position of the particle to the field point, u and it are respectively the velocity vector and the acceleration vector of the particle at the retarded position, t' is the time of emission, and c is the velocity of light in vacuum. q is the charge of the particle. The second term in Eq. (5b-303) represents the radiated field. EO is the free-space permittivity. The directional rate of radiation is 2

_dUd _ q r I X(r" X u·)j 2 dn dt' n - 161r 2EOS 5C3 r

(5b-308)

and the total rate of radiation is dU q2 - dt' = 67rEoc3

litl2

-

(1 -

lu X it!2/C2

-dU /dt' is also the rate of energy loss by the particle. listed ill the following:

ul!it

(5b-309)

U 2/C 2)3

Two useful special cases are

(Linear Motion) 2

dU litl ( q2 ) dt' dn = C3 161r 2Eo (1 dU _ q2/it!2 di! - 67rEoc3(1 - U 2/C 2)3

-

-

sin 28

dn

(u/c) cos 8)5

(5b-310) (5b-31l)

where 8 is the angle between u and r.

it

.L u (Circular Motion) _ dU dn

=

dt' dU

- dt'

=

q

2

q2 1 itl2 (I 161r2EoC3

1it/

2

U

2/C 2)

cos 2 a + (u/c - sin a cos q,)2 dn [I - (u/c) sin a cos q,j5

1

611"EoC3 (1 - U2/C2)2

(5b-312) (5b-313)

where sin a = cos 8/cos q" 8 is the angle between u and r, q, = wot', lui = awo, and lui = awo2. The charge is assumed to be moving in a circle of radius a with a constant angular velocity woo CERENKOV RADIATION. Cerenkov radiation occurs when a charged particle is moving in a material medium at a uniform speed u which is faster than the phase velocity of light in the medium. If n is the index of refraction of the medium, 1

J. V. Jelley, "Cerenkov Radiation," Pergamon Press, New York, 1958.

5-83

FORMULAS

Cerenkov radiation occurs (when nu > c, n > 1) at a cone angle of () = cos"! (c/nu) with respect to the direction of motion. The field components are singular in that direction. c is the speed of light in vacuum. Energy radiated per unit length of path per frequency interval (dU /dt) dw is (5b-314) and the total radiation rate is (5b-315) where the integration is carried out over ranges of w where c 2/n2u 2 < l. TRANSITION RADIATION. A burst of radiation occurs when a charged particle, moving at constant speed u, passes through the boundary between two media having different optical properties. Unlike Cerenkov radiation, this transition radiation will occur at any velocity of the particle, though its intensity increases with the energy. Assuming that a charged particle enters normally into a half space of refractive index n from vacuum, the energy radiated per frequency interval per unit solid angle u for u «c is 2- 1 q2u2 U dO. dw = 4--a3 sin 2 (J cos! (J V. do. dw (5b-316) 7( C EO n 2 cos () + n 2 - sm 2 ()

(n

)2

where () is the angle between the outward unit normal from the dielectric half space and the line connecting the observation point with the point that the charge particle enters into the dielectric half space. If the half space is a perfect conductor, we have u2 = 4--a3 sin" e dO. dw C EO q2

U dO. dw

u« c

(5b-317)

7(

The total energy spectral density per unit frequency interval for the perfectly conducting half-space case is q2u2 (5b-3l8) u« C Udw=-3 2 3 dw 7( C EO SMITH-PURCELL RADIATION. Radiation occurs when a charged particle moves at a uniform velocity u along an uneven surface. Assuming that the uneven surface is a sinusoidal diffraction grating of period d and amplitude a, and the medium above the grating is vacuum, the power radiated per unit solid angle (for u « c) is

P dO. = 2q 2a 27( 2u 4 Ifl - (ulc) cos ()J2 - [l - (ulc)2] sin 2 EOc 3d4 [1 - (ulc) cos (J]6

()

cos 2 O

t=~ 2-rra2

ka-« ee

2

67 4

1

-rr -

2

(ka)4[1

+ ~ ~(ka)2 + 0.3979

1 1 . y; (ka)! sin

(k2 a -

(ka)4

+ ... J

(5b-409)

-rr)

4

+ (k~)2 [~ + 2-rr sin 2 (2ka -~) ] 1

(5b-41O)

A typical transmission coefficient of a circular aperture is given in Fig. 5b-16. Holography. Holography may be described as a method for recording and reconstructing the amplitude and phase information of a propagating field in a given plane. 2 Strictly speaking, rigorous electromagnetic theory of diffraction and polarization is required for an exact treatment of optical holography. Since the electromagnetic field under consideration is almost completely linearly polarized (i.e., only a small fraction of the energy is in the cross-polarization component of the field) and the wavelength of the field is much smaller than the smallest characteristic length of the scattering objects, a scalar physical optics description of the field is therefore adequate. THE RECORDING PROCESS. The magnitude and the phase of a scattered wavefront can be recorded photographically by superposing a coherent reference wave on the field striking the photographic plate. One of the techniques for carrying out this H. Levine and J. Schwinger, Commune. Pure Appl. Math. 3, 355 (1950). D. Gabor, Proc. Roy. Soc. (London), ser. A, 197, 454 (1949); ser. B, 64, 449 (1951); E. N. Leith and J. Upatnieks, J. Opt. Soc. Am. 62, 1123 (1962); G. W. Stroke, "An Introduction 10 Coherent Optics and Holography," Academic Press, Inc., New York, 1966, 1

2

5-97

FORMULAS

superposition is illustrated in Fig. 5b-17 wherein a plane wave illuminates a region containing the scattering object and a triangular prism. The scattering object diffracts the incident radiation to generate a field with magnitude A(x) and phase cP(x) ~t the recording photographic plate, while the prism turns the incident plane wave through a small angle (J to give a field with a uniform magnitude A o and a linear phase variation oz where a = 271" sin (J/A ~ 271"(J /A with 8 small

A = wavelength.

The total field at the recording plate is (5b-411 )

t

I J--f--"o,~r-_~!>:-

and the intensity to which the emulsion is sensitive is lex) =

IUtotad2

= A 02

+ A2(X) + 2A oA(x) cos [ax + cP(x)]

(5b-412)

o

5

10

ka

Note that the intensity recorded by the photographic plate contains information concerning not only A(x), the FIG. 5b-16. Transmission amplitude of the scattered wave, but also cP(x), the phase coefficient of a circular aperture of radius a. of the scattered wave. [From C. Huaruj, R. D. THE RECONSTRUCTION PROCESS. Let us first consider Kodis, and H. Levine, J. the transmission characteristics of the recording photo- Appl. Phys. 26, 151 (1955).] graphic plate. The transmittance T(x) of the resultant photographic plate, provided that the linear range of the Hurter-Driffield curve is used, is T(x)

I""V

[1(x)]-'Y/ 2 I""V

+

+

= {A 02 A2(X) 2A oA(x) cos [ax 2A 02 - 1'A 2(X) - 1'A oA(x)e i cl> (x l + i a x -

+ cP(X)]}-'Y I2 1'A oA(x)e- i cl> (x l - i a x

(5b-413)

where l' is the slope of the Hurter-Driffield curve. It has been assumed that the intensity of the reference wave is much greater than that of the radiation scattered

rPR~SM

t\" - "8-

INCIDENT PLANE

WAVE

~

L1

r

DEFLECTED PLANE WAVE

~.~

J-.L

~~RIN: LeAHERING fJ~ I

\

)

OBJECT WAVE RECORDING PHOTOGRAPHIC PLATE

FIG. 5b-17. Schematic arrangement to illustrate recording of hologram.

by the object, so that the approximation made in dropping the higher-orders terms of the binomial expansion is justified. Note that neither the sign nor the exact magnitude of l' is of any consequence in the recording process; i.e., making a contact print of the photograph (hologram), which is equivalent to changing the sign of 1', serves only to shift the phase of the nonconstant portion of the transmittance an inconsequential 180°, whereas changing slightly the magnitude of l' serves only to enhance or to suppress the magnitude of this same portion of the transmittance.

5-98

ELECTRICITY AND MAGNETISM

To reconstruct the original wavefront it is only necessary to illuminate the hologram with a plane incident wave, as shown in Fig. 5b-18. As the plane wave passes through the photographic plate, it is multiplied by the transmittance T(x), thereby producing four distinct components of radiation corresponding to four terms of Eq. (5b-413). The first term, being a constant, attenuates the parallel beam uniformly, but otherwise does not alter it. The second term also attenuates the beam, but not uniformly, so that the plane wave suffers some diffraction as it passes through the hologram. Recall that a common triangular prism shifts the phase of an incident ray by an amount proportional to its thickness at the point of incidence, a positive phase shift deflecting the ray upward and a negative one deflecting it downward. In the case of the third term in Eq. (5b-413), it represents an upward deflected beam multiplied by the scattered wave A(x)eic/>(x); hence it is a reconstruction of the scattered wavefront. The fourth term represents a downward beam multiplied by the complex conjugate of the scattered wave. Hence, a copy of the scattered wavefront is con-

RECONSTRUCTED WAVEFRONT

t

HOLOGRA

INCIDE';-PLANE WAVE

-

:"=:===:=::;~-U-N-:P:E::R:::TU::::R""'B-E.e:D'""--}~~~~~r~~ED BEAM

~() ~

BEAM

IMAGE OF SCATTERING OBJECT

FIG. 5b-18. The reconstruction process-image formation from a hologram for the case of plane-wave ill umination.

structed except that it travels backward in time. Consequently, a three-dimensional image of the scattering object is constructed. Magnification. Magnification or demagnification of the image may be accomplished if one uses an incident wave with wavelength X for making the hologram and uses an incident wave with wavelength }..' in the reconstruction of the image. The formula for linear magnification }"f is }"f

= ~ rL }.. q

(5b-414)

where q is the distance of the original object from the hologram, and q' is the distance of the hologram from the final image plane. Resolution. The ultimate resolution of the conventional Fresnel-transform projection wavefront-reconstruction technique described above is approximately onehalf that of the recording media. However, higher resolutions may be obtained by the use of Fourier-transform holography. References 1. Van Bladel, J.: "Electromagnetic Fields," McGraw-Hill Book Company, New York,

1964. 2. Born, M., and E. Wolf: "Principles of Optics," 2d ed., Pergamon Press, New York. 1964. 3. Jones, D. S.: "The Theory of Electromagnetism," Pergamon Press, New York, 1964.

5-99

FORMULAS

4. King, R. W. P., and T. T. Wu: "The Scattering and Diffraction of Waves," Harvard University Press, Cambridge, Mass., 1959. 5. HonI, H., A. W. Maue, and K. WestpfahI: Theory of Diffraction, "Handbuch der Physik," vol. 25, Springer-Verlag ORG, Berlin, 1961. 6. Some recent references on scattering and diffraction are given in the August, 1965, issue of Proc. IEEE on Radar Reflectivity.

6b-13. Waves in Plasma. Three basic features characterize plasmas and distinguish them from ordinary solids, liquids, or gases. The first feature is that at least some or all of the particles in a plasma are charged although the plasma as a whole is electrically neutral. The second feature is that Debye shielding effect must be present in plasmas. The third feature is that the product WT must be large in order that plasma effects may be important. (w = frequency of the wave in plasma, T = the average time an electron travels between collisions with neutral molecules, or lattice ions, or impurities, etc.) Basic Equations. The basic equations governing the waves in plasmas are the Boltzmann equation and Maxwell's equations:

+ v • afa + a • afa = (af a)

afa at

ar

av

aB

v X E = - iii v XH =J V· D V'B Pc

=

=

at

(5b-415) c

D = foE (5b-416)

aD

+ iii

B

= .uoH

Pe

=0

I fff 'l«

a

J = Iqa

JJJ

fa dvz dvy dvz (5b-417)

vfadvzdvydvz

where fa(x, v,i) is the distribution function for particles of type a, and a is the acceleration due to external forces, which for an electromagnetic field would be the Lorentz accleration a = (qa/maHE v X B). (afa/at)e is the time rate of change due to collisions. E, H, B, D are the electromagnetic field vectors. Pe and J are respectively the charged density and the vector current density. qa and m a are respectively the charge and mass for particles of type a. V and r are the velocity and position vectors. When collisions are neglected, we may set (afa/at)e = 0 in Eq. (5b-415). This equation is called the collisionless Boltzmann equation or the Boltzmann-Vlasov equation. HYDRODYNAMIC-CONTINUUM MODEL. Taking the appropriate moments of Eq. (5b-415) and making the assumption that (I) the mass density Pa for each species is unchanged, (2) the Lorentz force per unit mass for each species is (a)a = (qa/ma) (E + u, X B), (3) viscous effects are negligible, i.e., the pressure is a scalar quantity, and (4) the flow-velocity difference among the various gas species is small and each gas has a maxwellian velocity distribution, one obtains the following equations for the hydrodynamic-continuum model:

+

apa

7ft + V

aaUta

• PaUa

+ Ua' VUa

=0

(5b-418)

(mass conservation)

= qa (E ma

+ Ua

X B) - VPa - \' Jla(ua,8 - U,8) Pa

L

fJ

(momentum conservation)

(energy conservation)

(5b-419) (5b-420)

5-100 with Pa = mana, Pc =

ELECTRICITY AND MAGNETISM

L

J =

qana, and

a

L

qanaua.

The subscript a refers to particles

a

of type a. Pa, m a, n a, Pc, J, U a , and Pa are respectively the mass density, mass, number density, charge density, current density, average velocity vector, and scalar pressure. Ua is the adiabatic or the isothermal sound speed, depending on the problem at hand. V a (1 is the collision frequency for momentum transfer for particles of type a with those of type (3. Equations (5b-418) to (5b-420), together with Maxwell's equations (5b-416) provide a complete set of equations for the hydrodynamic model. LINEARIZED MAGNETOHYDRODYNAMIC (MHD) MODEL. A set of linearized mhd equations may be obtained if we replace the above set of individual-species equations (5b-418) to (5b-420) by a set of equations for the gas as a whole:

ap at Po

+ poV' U = 0 au

at = J x n, -

(5b-421) Vp

Vp = U 8 2V p

J = O"o(E

+U

X B o)

(5b-422) (5b-423) (5b-424)

where B o is the applied magnetostatic field, 0"0 is the conductivity of the gas, U8 is the isothermal or adiabatic sound speed for the gas, Po is the equilibrium mass density of the gas. P, U, p, E, and B are all infinitesimal disturbances. A simplified Ohm's law [Eq. (5b-424) has been assumed. Equations (5b-421) to (5b-424), together with Maxwell's equations (5b-416)-with the assumption that the displacement vector term aD/ at is negligible-provide a complete set of equations for the linearized mhd model. MAGNETOIONIC MODEL (COLD PLASMA MODEL). If we further assumed that the thermovelocity of electrons or ions is zero, (i.e., the term VPa/Pa in Eq. (5b-419) is zero, and the inertial term U a • VU a is omitted, then (5b-425) (5b-426)

Equations (5b-425) and (5b-426), together with Maxwell's equations (5b-416), provide a complete set of equations for the cold plasma model. Waves in Cold Plasmas. The linearized equations I (with harmonic time dependence e- i wt ) for waves in cold (electron) 2 plasmas are

v

X B

V X E

I:

=

[

= - iWJ.l.ol: • E = iwB

'" i~y

-iE",y EVY

0

n

(5b-427) (5b-428) (5b-429)

1 The linearization procedures are justified if the phase velocities of the waves under consideration are much greater than the average electron velocity. 2 In an electron plasma, only the motion of electrons is important. The ions and the neutrons are assumed to be stationary. For very-low frequency waves the motion of ions may be important. In that case the components of the dielectric tensor must be modified. See E. Astrom, Arkiv Fysik. 2, 443 (1950).

5-101

FORMULAS Ezz

=

EO

Wp2(W + iv) } { 1 - W[(W + iV)2 _ We2]

Ezy

=

EO

[W(W

Ez;

=

EO

+ iv + ::;~~ + iv

- weJ

[1 - w(ww~ iv)]

with Wp = (nee2/meEo)! and We = - (e/me)B o. Wp, We, and v are respectively the plasma frequency for electrons, and the gyro frequency and collision frequency of electrons with all other heavy particles. B, = Boe z is the applied static magnetic field. E and B are the complex amplitudes of the electromagnetic fields. vph For a plane wave propagating in the n direction, the electric vector has the form E = Eoeik ·r

(5b-430)

where Eo is a constant vector, r is the position vector, k = nw/vph is the vector wave number, and Vph is the phase velocity of the wave. The dispersion relation for the phase velocity, called the Appleton-Hartree equation, is obtained by substituting Eq. (5b-430) into Eqs. (5b-427) and (5b-428):

lWei

W0 1

We ../

I

W

CAl

oz

W~+W~

\:: w0 1

We

IWe

I

W02

./ we 2+w/

(5b-431) (5b-432) U=l+i~ W

1

c =---

FIG. 5b-19. Phase velocity vs,

frequency for waves traveling in an arbitrary direction relative to BOt the applied magnetic field. in an electron plasma. The above results are obtained according to the cold plasma model. lWei = eBo/m.,

vi JloEo WOl

We

=

(e 2no/meEo)!

= [-lwei

+

(we2 + 4we 2) 1]/2,

where I' is the angle between the direction of wo: =WOl + lWei. no = number density propagation and the direction of the static of electrons. me = mass of electrons. magnetic field e z • n is in the yz plane. A and c = velocity of light in vacuum. sketch of the phase velocity vs. frequency for waves traveling in an arbitrary direction relative to B o is given in Fig. 5b-19. A great deal of work on wave propagation in plasma filled guide! and on the scattering of waves by a plasma column! has also been carried out. Alfven Wave. Alfven wave exists in a plasma at very low frequencies when the plasma can be adequately represented by the linearized mhd model. Assuming that p, U, p, E, and B in Eqs. (5b-416) and (5b-421) to (5b-424) are all proportional to exp i(kx -wt) 0"0 = 00; and the applied static magnetic field B, lies in the xy plane and makes an angle I' with the positive x axis; one may obtain the following set of equations: (5b-433) Ux(W 2 - k 2V a 2 sin 2 I' - k 2U 2) + u llk 2V a2 sin I' cos I' = 0 (5b-434) u xk 2V a2 sin I' cos I' + u ll(w 2 - k 2V a2 cos! 1') = 0 (5b-435) u.(w 2 - k 2V a2 cos" 1') = 0 1 2

See, for example, A. W. 'I'rivelpieee and R. W. Gould. J. Appl. Phus. 30, 1784 (l95g) See, for example, C. Yeh and W. V. T. Rusch, J. Appl. Phys. 36, 2302 (1965).

5-102

ELECTRICITY AND MAGNETISM

where Va = Bo/(p.opo)! is called the Alfven velocity. According to Eq. (5b-435), we see that a wave linearly polarized in the z direction (the direction perpendicular to both k and Bs) can exist if Vph

= ~k = Va cos

(5b-436)

l'

This wave is called the pure Alfven wave. Solving of Eqs. (5b-433) and (4b-434) gives the phase velocity of mhd waves containing components u'" and U/I:

,, ,, \

"-

...

_-

--I.c.p - - - r.c.p

(a 1 TRANSVERSE WAVES

~-.......

_-...L...._.....,.,';"'--~-;-----_w

FIG. 5b-20. Phase velocity vs. frequency for waves in a fully ionized plasma according to the hydrodynamic-continuum model. Waves are assumed to be propagating in the direction of Bo, the applied magnetic field. IWee! = eBo/me, Wei = eBo/mi, We = (e2no/meEo)1 Wi = (me/m,)!we and Up = 'YK(T. T,) /m, (the plasma sound speed). Va is the Alfven velocity. U. = -yKT./m., U; = -yKTdmi' -y is the ratio of specific heats at constant pressure and constant volume, and K is the Boltzmann's constant. T., T" m., mi are respectively the electron temperature, the ion temperature, the electron mass, and the ion mass. The above curves are valid only if T. » 1\ and the phase velocity of the wave is not close to the thermovelocity of ions or electrons.

f = fo(v)

+ ft(v)eikz-iwt

Iftl «fo (5b-438) (5b-439)

+

where fo is the equilibrium distribution function for electrons, and substituting Eqs. (5b-438) and (5b-439) into Eqs. (5b-415) and (5b-416), one has wp2 [ n ok 2

J

(iJjo/iJv",) d3v - 1] E = 0 (5b-440) v'" - w/k

where no is the equilibrium electron density. Setting the quantity in the square brackets to zero gives the dispersion equation for the longitudinal electron waves. The solution of this dispersion equation has been obtained for the case when fo is the maxwellian velocity distribution for a stationary plasma; i.e., fo = noe-v2/a2/7rJa3 1 The description of the propagation characteristics of waves according to the hydrodynamic-continuum model is not valid when the phase velocity of a particular mode of interest is close to the thermovelocity of ions or electrons. In that case, Boltzmann'! equations must be used. See B. D. Fried and R. W. Gould, Pbu«. Fluids 4, 139 (1961).

5-103

FORMULAS

with a 2

= 2KT /m.,

K is the Boltzmann's constant, and T is the temperature: k2

=

r-

k o?

(1 - 2C foC e

zL c 2

dz

+ i7r!Ce-

C2 )

(5b-441)

where C = w/ka, and k o? = 2wp 2/a 2 is the Debye wave number. The integral in the above equation is called the dispersion function and has been tabulated.! The last term, which is imaginary, is known as the Landau damping term. When w/k --+ 00, Eq. (5b-441) may be written as

3KTk = w 2 + --+. m. 2

w2

(5b-442)

p

Hence the longitudinal waves will decay in a collisionless electron plasma. The Landau damping characteristics are also present for transverse waves. 2 Motion of a Charged Particle in Electromagnetic Fields. The motion of a charged particle in electromagnetic fields is governed by the following equation:

dv

m dt = q(E

+v

(5b-443)

X B)

where m, q, v, E, and B are respectively the mass of the particle, the charge, the velocity, the applied electric field, and the applied magnetic field. Some important behaviors of a charged particle in such an applied field are listed below: IN CONSTANT AND UNIFORM

E

AND

B

FIELDS

1. The particle rotates about the B direction at a gyrofrequency (we) = /qB/m) and with a radius IVo/wel, where Vo is the initial velocity of the particle in a plane normal to the B direction. meg X B)/qB2, where 2. The particle possesses a drift velocity, v » = E X B/B2 g is the uniform gravitational field. 3. There is a constant acceleration in the B direction unless q and E are perpendicular to B. (In the last case the particle drifts in the B direction with its initial velocity.) IN A NONUNIFORM B FIELD. The particle possesses a drift velocity,

+

v»

V.l.B =- (1- V.l.2 + V/l2) et: WeB 2

where V.l.B is the gradient of the scalar B in the plane perpendicular to B, V.l. and VII are respectively the initial velocities perpendicular and parallel to the magnetic field B, and en is a unit vector in the direction B X VB. ADIABATIC INVARIANCE OF y. When the applied magnetic field changes slowly with space or time, dy. = 0 dt

where y. is the magnetic moment for the changed particle and y. = -w.l.B/B2 with W.l. = imV.l.2, which is the kinetic energy of the motion perpendicular to B. ENERGY CONSERVATION IN A STATIONARY FIELD

d

dt (i mv2 + q is the potential energy per unit charge. The above equation indicates that the sum of kinetic and potential energies stays constant in a stationary field with E = -V4>. References 1. Stix, T. H.: "The Theory of Plasma Waves," McGraw-Hill Book Company, New York,

1962. 2. Allis, W. P., S. J. Buchsbaum, and A. Bers: "Waves in Anisotropic Plasmas," The MIT Press, Cambridge, Mass., 1963. 3. Spitzer, L., Jr.: "Physics of Fully Ionized Gases," 2d ed., Interscience Publishers, a division of John Wiley & Sons, Inc., New York, 1962. 4. Heald, M. A., and C. B. Wharton: "Plasma Diagnostics with Microwaves," John Wiley & Sons, Inc., New York, 1964. 5. Huddlestone, R. H., and S. L. Leonard: "Plasma Diagnostics," Academic Press, Ino., New York, 1965. 6. Tanenbaum, B. S.: "Plasma Physics," McGraw-Hill Book Company, New York, 1967.

6b-14. Skin Effect. At high frequencies currents in a conductor tend to concentrate on the surface and decay approximately exponentially into the conductor. The concentration increases as frequency, conductivity, or permeability increases. The result is an increased resistance and decreased internal inductance at frequencies for which the effect is significant. The basic equations governing the skin-effect phenomena are the Maxwell's equations applied to good conductors. A good conductor is defined by the following characteristics: the free-charge term is zero, i.e., p = 0; conduction current is given by Ohm's law, J = e-E, where u is the conductivity; displacement current is negligible in comparison with conduction current, WE «u. Under this assumption, Maxwell's equations are: v X E = iWJ.LH V·n = 0 (5b-444) V X H = uE V'B = 0 with B = J.LH, D = EE, and J = uE. A time dependence of e-'WI has been assumed for all field components and suppressed. Combining these equations and assuming that E, J.L, a are independent of the position vector (i.e., a homogeneous medium), one has (5b-445) where P may be E, or H, or J; and 7 2 = -iwJ.Lu = -2i/0 2• 0 = (2/wJ.Lu)! is called the skin depth; it is a measure of the decaying characteristics of fields within a conductor. The surface resistivity R. is defined as R. = 1/uo = (wJ.L/2u)!. Data for 0 and R. as functions of frequency are given for several common materials in Table 5b-5. The boundary conditions at the surface between a good dielectric and a good conductor are n : J = 0 and J = uE o, where n is normal to the surface, and Eo is the applied field at the surface. The boundary conditions at the surface between two good conductors are the continuity of tangential electric and magnetic fields. The internal impedance Zi of a good conductor is defined as the ratio of the electric field at the surface to total cutrent. The time-averaged power dissipated as Joules heat within the volume V is i fulE[2 dv. Formulas jor Several Simple Conductors. PLANE SEMI-INFINITE CONDUCTOR. The plane conductor extends from z = 0 to x = 00, and Eo is an applied field in the z direction at x = o. J, = uEoe-xloeixlo (5b-446) (5b-447) Zi = R, - iwL i = (l - i)R.

5-105

FORMULAS

TABLE 5b-5. SKIN-EFFECT QUANTITIES FOR CONDUCTORS

Relative" Reaistivity" permeability (ohm-mj l Os at 0.002 weber /ms

Metal

Aluminum .............. Brass (65.8 Cu, 34.2 Zn). Brass (90.9 Cu, 9.1 Zn) .. Graphite ........... " .. Chromium .............. Copper......... Gold................... Lead ................... Magneffiu~............. Mercury ............... Nickel. ................ Phosphor bronze ........ Platinum ..... ............. Silver.................. Tin .................... Tungsten ............... Zinc ................... Magnetic iron ........... Permalloy (78.5 Ni, 21.5 Fe) .................. Supermalloy (5 Mo, 79 Ni, 16 Fe) ............ Mumetal (75 Ni, 2 Cr, 5 Ou, 18 Fe) ............ I

• • .• •

•

•

•

2.828 6.29t 3.65t 1,000 2.6t 1.724 2.22t 22 4.6 95.8t 7.8 7.75t 9.83t 1.629 11.5 5.51 5.38t 10

1 1 1 1 1 1 1 1 1 1 100 1 1 1 1 1 1 200

16

8,000 105

60 62

20,000

o=

oy';

depth of penetration, m,J1 = frequency, Hz 0.085 0.126 0.096 1.592 0.081 0.066 0.075 0.236 0.108 0.493 0.014 0.140 0.158 0.064 0.171 0.118 0.117 0.011

107R./V~

R. = surface resistivity, ohms/m! 3.33 4.99 3.79 62.81 3.21 2.61 2.96 9.32 4.26 19.43 55.71 5.54 6.22 2.55 6.73 4.67 4.60 90.9

0.0022

727

0.0012

4,880

0.0029

2,140

• Values from Pender and McIlwain, .. Electrical Engineers' Handbook," 4th ed., John Wiley & Sons, Ine., New York, 1950. t Values at o-c, others at 20°C.

SOLID ROUND WIRE. For a solid round conductor of radius a with applied axial electric field Eo at the surface, we have Jo(itr/o)

J%

= -s, Jo(ila/o)

Zi

=

. R, - 'UlJLi

(5b-448) -R. Jo(ila/o)

= V2a7l' J~(ila/o)

(5b-449)

where Jo(i1a/o) is a Bessel function of order zero with complex argument. 1 For a/o « 1, (5b-450) for

a/a »

I, (5b-451)

1 S. Ramo, J. R. Whinnery, and T. Van Duzer, "Fields and Waves in Communication Electronics," chap. 5, John Wiley & Sons, Inc., New York, 1965: S. J. Haefner, Proc. IRE IS,434 (1937); H. A. Wheeler, ibid. 43,805 (1955).

5~106

ELECTRICITY AND MAGNETISM

Formulas are also available for tabular conductors and rectangular conductors as well as coated conductors.' An example of skin depth and high-frequency resistance of copper is given in Fig. 5b-21.

>-

0.1- 1.0

0.00 I 0.1

0:: W :I: Q.

~ffi

wQ.

'~

o~

~~'\ vI--'

zo < .......

CH3 lj>CH2CH 3 lj>'lj>

@@

'" represents a. benzene ring minus one hydrogen.

0.20 0.243

10,60 0, 90

........ ..

......................

0.18 ...........

75, 155 ..

..............

t'4

t;I:j

a

~ ~ ~

a

~

~ ~

>

Z

t:::1

~

o> Z

t;I:j ~ ~

5.5 -95 ..

..........

70 80.2

80.1 nO.8 146 254 217.9

U2

~

TABLE

Type/Name

5d-4.

ORGANIC COMPOUNDS (SMALL MOLECULES) (Continued)

t,OC

Formula

Ea

Eoo

n0 2

t; Hz

10 2a

Range

... .

. ...

. ......

1. 77

0.264

5,55

Melting point

Boiling point

-97.8

64.6

-117.3

78.5

-17.4

197.2

---Alcohols Methanol ..................... (wood alcohol) ..............

CHaOH ..........................

Ethanol ...................... (grain alcohol) ...............

CHa·CH 2OH ..........................

Glycol ....................... (ethylene glycol) ............ I-Propanol ...................

CH 2OH·CH 2OH

2-Propanol ................... (isopropyl alcohol) ........... l,2-Propanediol. .............. l,3-Propanediol. .............. Glycerol ...................... l-Butanol .................... 2-Butanol .................... 1-Pentanol. ................... 1-Hexanol .................... 1-Heptanol ................... 1-0ctanol. ....................

•••••••••••••••••••••••••

1-Decanol ....................

0

CHa·CH 2·CH 2OH CHa'CHOH'CHa •••••••••••••••••••

0

••••••

CH a·CHOH·CH 2OH CH 2OH·CH2·CH20H CH 2OH·CHOH·CH20H CHa(CH2) 2CH 2OH CHaCH 2CHOH·CHa CH a(CH2)aCH20H CH3(CH2)nCH 2OH (n = 4) ................ .......... (n = 5) •••••••••••••••••••••••

(n

1-Nonanol. ...................

0 20 40 0 20 40 20 40 0 20 0 20 20 20 25 25 20 20 120 2 120 2 120 2 120 2 120

0

••

= 6)

.......................... (n = 7) .......................... (n = 8)

•

0

••

37.98 33.64 29.73 28.39 25.07 22.14 38.7 34.9 25.0 20.8 24.4 19.0 32.0 35.0 42.5 17.1 15.8 15.3 12.9 3.2 11.7 3.10 10.35 3.05 9.05 3.05 7.75 3.10

6.1 5.7 5.2 4.4 5 4.2 6 4.18 2.65 3.45 6.0 2.65 6.7 3.2 ... . ... .

1.87X10 9 3.00 X 10 9 4.6 X 10 9 6.17X10 8 1.11 X 10 9 1.8X10 9 1.5X10 9 3.0 X 10 9 1. 56 X 10 8 3.7 5 X 10 8 1.3 X 10 8 5.45 X 10 8

... .

......... .

2.95 3.5 3.8 3.3 2.34 3.10 2.35 3.05 2.35 3.05 .... 3.10 2.40

3.3a X 10 3.1 6 X 10 8 2.1 4 X 10 8 1. 52 X 10 8 7.5 X 10 9 1.10 X 10 8 7.0 X 10 9 9.1 X 10 7 5.75 X 10 9 8.0 X 10 7 3.5 X 10 9 9.6X10 7 3.0 X 10 9

......... . ......... .

8

... .

... .

.......

1.85

0.270

-5,70

2.05

0.224

20, 100

... . .... ... .

. ...

.......

1.90

. ...

2.08 2.18 1.95 1.95 1. 99 '''

..

0.293

"tI

t-3 H tr.l

82.3

o

UJ

20, 90

.......

-89

0.310 0.27 0.23 0.208 0.300

20,70 20, 20, 0,100

...... ......

40 , 20

... .

.......

0.23 0.35

15,35 15,35

~

97.2

. ...

1_

tr.l

-127

....... -89.2 -89 -78.5 -51.6

I"'.l

189 214(d)

240 117.7 99.5 138 157.2

2.00

... .

"tI

~

o

I;j H

tr.l to" tr.l

(J

t-3 ~

H

(J

UJ

. ...

.......

-34.6

176

0.410

20,60

-16.3

195

2.03 ..0.

2.03

. ...

. ...

0

••••••

-5

213

o

••••••

-6

231

2.05

. ...

. ...

2.07 01

I

(d) = decomposes

I--' ~

·COOH 0

58.5 6.15 20. 7 3.30 2.97 2.71 2.40

16 20 19 10 20 10

25 .....

•

••••

0

••

••

0

•••

0

••

.......... . ••••••

0

•••

•

.......... . - O. 23(a) ••••

0

••••••

•••••••• 0.' ••

•••

0

•••••••

.......... . ........... .......... . 00

••••••••

•

10,70 . .........

. ........... . ......... .

249

qr-CO-Ij>

=0

~

>

20 25 19 25 25

8.5 7.16 7.72 6.02 6.02

0,20

5(a) •••••

0

••

0

••

.......... . 2.2(a) 1.5(a)

......... .. -

........... 25. 40 25

-99.0 -79.4 -92.9 -98.7 -83.6

31.8 54.2 80.9 57.8 77.2

~

c> Z

tr.l J-3

I-t

[f1

~ . . . O.

0

•••••••

21 20

21.1 17.8

25 25 50

20.70 17.39 11.4

. .......... ••

0.0

••••••

........... .0'

0

•••••••

...........

. ..........

0.205

-60.40 25

-92 -123.5 -26

-21 21 179.5

-95 19.7 48.5

56.5 202.3 306

II

R·CO·R,-CCRa·CO·CHa qr-CO-CH a

J-3

t::i

II

RCHO,-C-H H·CHO CHa'CRO Ij>·CHO 0

o

I-t

Z

II

R·COOR', -C-OH'COOCHa H·COOCH2CHa H·COO(CH2)2CH a CRaCOOCHa CHaCOOCR 2CH a 0

tr.l t'4 tr.l

4(a)

....... ....

...........

CH=CH Quinone........................ 1 Ethers ...... . . . . . . . . . . . . . . • . . . . . Methyl ether ................... Ethyl ether..................... Propyl ether .................... Vinyl ether..................... Phenyl ether..................... N itro(Jen Derivatives Ethylamine .........•........... Aniline .........................

O=C

/

-,

-,

/

CHaCH 2·NH 2 cp·NH2 CH HC

Pyridine ....................... 1

~

/

II

N Ethane Derivatives Chloride ....................... Bromide ....................... Iodide ......................... Hydroxide (ethanol) ............. (acid) (acetic acid) .............. Amine ......................... Nitrite (nitroethane ............. Nitrate ........................ Zinc ................ .............. Thiol (ethanethiol) .............. Thiocyanate .................... Benzene Derivatives Fluorobenzene .................. Chlorobenzene .................. Bromobenzene ..................

c=o

CH=CH R-O-R' CHa'O'CHa CHaCH 2·O·CH 2CHa CHaCH 2CH2·O·CH 2CH 2CHa CH 2=CH'O'CH=CH2 cfr-O- cp

23

I

2.66

25 20 26 20 30

5.02 4.335 3.3a 3.94 3.65

10 20

6.94 7.07

I ..........• I ........... I

2.38(a) 2.0(a) ............. ..................

0.7(a) .............

25, 100 20 ..

............

. ................. 30,50

..

-20, 10 . ...........

115.7

-138.5 -116.3 -95.2 ..

28

-23.6 34.6 142 39 259

-80.6 -6.2

16.6 184.4

..........

..

"d

~

0

"d

t.: TN is

x=

N g2{J2J(J + 1) 3k(T + 8)

C

= T +8

where 8 = CTN, and c = 1 for the simple model.! The susceptibility below the Neel temperature for this simple model consists of two parts, the susceptibility parallel (XII) and perpendiculare {x.d to the antiferromagnetic axis. xII decreases and becomes W. Heisenberg, Z. Physik 49,619 (1928). J. H. Van Vleck, J. Chern. Phys. 9,85 (1941). 3 For other models see J. Samuel Smart, Phys. Rev. 86,968 (1952) i see also ref. 3.

1 2

5-142 zero as T

ELECTRICITY AND MAGNETISM -+

0; thus the susceptibility at absolute zero for a polycrystalline solid is

Ferrimagnetism (Molecular Field). Ferrimagnetic substances are those in which the magnetic ions can be divided into nonequivalent sublattices which become spontaneously magnetized in an antiparallel arrangement below some temperature Tn. A ferrite, i.e., NiFe 20 4, is used as an example. It is a spinel structure having a c1osepacked cubic oxygen lattice in which there are 8 tetrahedral and 16 octahedral sites occupied by magnetic ions. The sites are labeled A and B, respectively. Neel.! using the molecular field theory, gave the effective fields at the A and B sites as HA HB

+ "YAAM A

= =

Ho Ho -

"YABM A

-

"YABMB

+ "YBBMB

2z i AJ;j

where

= NiY 2{3 2

"Yij

is the number of nearest neighbors on the j sublattice to an atom on the i sublattice, is the exchange coupling between the electrons of those atoms, and N', is the total number of magnetic ions on the j sublattice. For T > r., Zij

g]ij

C

x=---

T - 8'

T - Te T - Te'

where

C= Te = T~ = 8'

For T

=

< T e,

Ng2{32J(J 3k

+ 1)

NA

X=N

+ IJ."YBB + V (AI'AA + IJ."YBB - V(A"YAA XIJ.C("YAA + "YBB + 2"YAB)

NB

Jl.=N

iC[X"YAA

-

IJ."YBB)2

tC[A"YAA

-

IJ."YBB)2

+ 4AIJ.AB J + 4AIJ.AB 2 2

]

where

where BJ(x) is the Brillouin function. Gyromagnetic Ratio. The magnetic moment of an amperian current loop is proportional to its angular momentum, g'e . V = 2mc J = "Y'j

or summed over an entire body, M = "Y'J

where J is the total angular momentum corresponding to the magnetic moment M. 2mc

Both 1" and g' = - - 1" are called the "gyromagnetic ratio." They are more properly e called the "magnetomechanical ratio." A change in either J or M produces a corresponding change in the other. BARNETT 2 EFFECT. Change of magnetization by rotation. EINSTEIN-DE HAAS 3 EFFECT. Change of rotation by magnetization. L. Neel, Ann. PhY8. 3, 137 (1948). S. J. Barnett, Rev8. Modern Phys. 7, 129 (1935). 3 A. Einstein and W. J. de Haas, Verhandl, deui, physik. Ge8. 17, 152 (1915). 1

2

MAGNETIC PROPERTIES OF MATERIALS

5-143

Measurements of many ferromagnetic materials by these methods yield values of g' ~ 2, indicating that for them the electron spin is the predominant source of magnetism. For a free ion g' = g (spectroscopic splitting factor), but in a crystalline field both g' and g may depart considerably from 2. When the orbital admixtures are not necessarily small, the relation 1

g'

= -gg-p

departs from the Kittel-Van Vleck relation for which p = 1. For substances where p ¢ 1 see Smart [3] and Smit [.5]. Spin Resonance. A substance with a magnetic moment in a static magnetic field H will absorb energy from an oscillating magnetic field of small intensity at right angles to the static field. The peak of the absorption curve occurs at the angular frequency

where

w

= 27rgj,lH = 'YrH

'Yr

=

h ge 2mc

where j,l is the appropriate unit for the magnetic moment, and g is the spectroscopic splitting factor. PROTONS. j,l is the nuclear magneton j,lP = eh/47rM pc, and g = 5.58.

~

=

p(kHz)

=

~

= 4.26H

(oersteds)

FREE ELECTRONS

~

\' (M Hz)

and g = 2 = 2.80H (oersteds)

PARAMAGNETIC SALTS. 2 The equation of motion, treating the body as a whole, may be obtained? by the use of M = 'YrJ, and the torque dJ/dt = M X H,

dM (it = 'Yr(M X H) where the components of Hare Hz

=

Hz

2H 1 cos wt

= static field

The amplitude of the oscillatory field is small compared with that of the static field, and the resonance frequency is FERROMAGNETIC RESONANCE. Kittel" has shown that the above equations hold for ferromagnetic resonance if all demagnetizing effects are included. For example, the resonance frequency becomes w = 'Y(BH)1

for a specimen in the form of a thin disk with the static field parallel to the disk. ANTIFERROMAGNETIC RESONANCE. Above the Curie temperature, paramagnetic resonance is found. Below the Curie temperature, the effective field b becomes He«

=

[HA(2HE

+ HA)]!

where H A is the effective anistropy field of one sublattice, and HE is the exchange field. 1 M. Blume, S. Geschwind, and Y. Yafet, Generalized Kittel-Van Vleck Relation between g and o', Validity for Negative g-Factors, Phys. Rev. 181,478 (1969). 2 For metals, see F. J. Dyson, Phys. Rev. 98, 349 (1955). a F. Bloch, Phys. Rev. 70, 460 (1946). 4 C. Kittel, Phys. Rev. 71, 270 (1947); 73, 155 (1948). Kittel, Phys. Rev. 82, 565 (1951).

be.

5-144

ELECTRICITY AND MAGNETISM

FERRIMAGNETIC RESONANCE. The individual sublattices must be considered in the resonance equation. An effective splitting factor! for the combined sublattices is given by e IMI 12;M1'! geff 2mc = 1ST = 1.2;(Md"Y,)! where Mi is the magnetization of the individual sublattice, and "Yi = gi(e/2mc) describes its magnetomechanical ratio. References 1. Van Vleck, J. H.: "The Theory of Electric and Magnetic Susceptibilities," Oxford University Press, New York, 1932. 2. Kittel, C.: "Introduction to Solid State Physics," 3d ed., John Wiley & Sons, Ine., New York, 1967. 3. Smart, J. S.: "Effective Field Theories of Magnetism," W. B. Saunders Company, Philadelphia, 1966. 4. Bozorth, Richard M.: "Ferromagnetism," D. Van Nostrand Company, Inc., Princeton, N.J., 1951. 5. Smit, J., and H. P. J. Wijn: "Ferrites," John Wiley & Sons, Ine., New York, 1959.

6f-2.

Magnetic Properties of Elements TABLE 5f-l.

Element

fT.(20°C)

SATURATION MAGNETIZATION AND CURIE POINTS OF FERROMAGNETIC ELEMENTS *

M.(20°C)

fTo(O K)

nB

Te' K

8, K

TN, K

J.l.eff

Ref.

--- --- --- --- - Fe ....... Co ...... Ni ....... Gd ...... Tb ...... Dy ...... Ho ...... Er ....... Tm ...... Cr ...... Mn ......

*

(1,

Tc

and 0"0 M.

218.0 161.8 54.39

......

..... ••

0

••

.....

.....

..... . ..... . .... .. = =

1,714 1,422 484

t . .... •

••

0

•

. ....

. .... .... .... . ~

0

••

0

•

221.7 162.5 58.57 250 330 350 345 300 230

...... . . ......

2.216 1. 72 0.616 7 9 10 10 9 7

. .... 0

••••

1043 1404 631 293 222 85 20 20 25

1100 1415 650 302 238 159 87 40 '"

.

.... . ..... .... . .....

... ... ... . .. 229 179 131 84 56 475 100

3.20 3.15 1. 61

1,3 2 3

~

saturation moments per gram saturation moment per em'

nB = number of Bohr magnetons per atom and 8 = ferromagnetic and paramagnetic Curie points TN = Neel temperature pelf = effective Bohr magneton number in the paramagnetic state

t Values of M« (M, at 0 K) are 2,000 (Gd) to 3,000 (Ho) for the ferromagnetic rare earths, zero at 20°C; nB is nearly the theoretical value of (JJ (Table 5f-3) with an uncertain additional value of a few tenths of a unit. t Values of pelf of the trivalent rare earths are nearly the theoretical ones given in Table 5f-3, except for 8m and Eu [4] and Yb. References for Table 5f-1 1. Vogt, E.: "Landolt-Bornstein Tabellen," vol. II, part 9, p. 16, Springer-Verlag OHG, Berlin, 1962. 2. Myers, H. P., and W. Sucksmith: Proc, Roy. Soc. (London), serf A, 207, 427 (1951). 3. Danan, H., A. Herr, and A. J. P. Meyer: J. Appl. Phys. 39,669 (1968); Crangle, J., and G. M. Goodman, Bull. Am. Phys. Soc. II, 15,269 (1970). 4. Van Vleck, J. H.: "Theory of Electric and Magnetic Susceptibilities," Clarendon Press, Oxford, 1932.

6f-3. Properties of Ferromagnetic Compounds. Tables 5f-4 and 5f-5 show respectively properties of binary compounds of iron group elements and of rare earth elements; Tables 5f-6 to 5f-8 list properties of pure spinel ferrites, of spinel ferrites containing ZnFe 204, and of other ferrites; Table 5f-9 applies to garnet ferrites and Table 5f-IO to known weak ferromagnets of various compositions and structures. I

R. K. Wangsness, Phys. Rev. 93,68 (1954).

6-145

MAGNETIC PROPERTIES OF MATERIALS TABLE

5f-2.

U./UO,

RELATIVE SATURATION MAGNETIZATION

AS DEPENDENT ON TEMPERATURE RELATIVE TO THE CURIE POINT

T /Te

0./00

T

observed

Molecular field theory

T;; Co, Ni J = !

Fe

I

1

J

-- -- - - --- -- -1 0 0.1 0.996 0.99 0.2 0.3 0.97/> 0.4 0.95 0.45 0.5 0.93 0.55 0.6 0.90 0.65 0.7 0.85 0.75 0.8 0.77 0.85 0.70 0.9 0.61 0.95 0.40 0 1

1 1 0.996 1.000 0.99 1.000 0.98 0.997 0.96 0.986 0.974 0.94 0.958 0.936 0.90 0.907 0.872 0.83 0.829 0.776 0.73 0.710 0.66 0.630 0.56 0.525 0.40 0.379 0 0

2

!

3

-- --

1 1 1 1 1.000 1.000 1.000 1.000 0.999 0.998 0.997 0.994 0.993 0.987 0.980 0.974 0.973 0.960 0.949 0.938 0.957 0.941 0.927 0.915 0.937 0.918 0.901 0.889 0.911 0.889 0.872 0.858 0.879 0.856 0.838 0.824 0.841 0.817 0.798 0.784 0.796 0.771 0.753 0.739 0.742 0.717 0.699 0.686 0.678 0.654 0.636 0.624 0.599 0.576 0.56] 0.549 0.498 0.479 0.465 0.454 0.359 0.344 0.334 0.327 0 0 0 0

7

2

4

l

6

J!

8

00

-- -- -- -- -- -- -- -1 1 1.000 1.000 0.992 0.989 0.967 0.962 0.929 0.922 0.905 0.897 0.878 0.870 0.848 0.839 0.813 0.804 0.773 0.764 0.728 0.719 0.675 0.667 0.6]4 0.606 0.540 0.533 0.448 0.442 0.322 0.317 0 0

1 0.999 0.986 0.957 0.915 0.890 0.862 0.831 0.796 0.757 0.712 0.660 0.600 0.528 0.438 0.314 0

1 1 1 1 0.999 0.998 0.996 0.995 0.984 0.977 0.971 0.969 0.952 0.941 0.933 0.931 0.910 0.897 0.888 0.885 0.884 0.871 0.862 0.860 0.856 0.843 0.834 0.831 0.825 0.812 0.803 0.800 0.790 0.777 0.768 0.766 0.751 0.738 0.729 0.727 0.706 0.694 0.686 0.684 0.655 0.643 0.635 0.633 0.595 0.584 0.577 0.575 0.523 0.514 0.507 0.506 0.434 0.426 0.420 0.419 0.311 0.305 0.302 0.301 0 0 0 0

1 0.965 0.928 0.887 0.841 0.816 0.789 0.759 0.726 0.689 0.647 0.600 0.545 0.479 0.397 0.285 0

I

Theoretical values as calculated by S. Smart, "Effective Field Theories of Magnetism," pp. 139-154, W. B. Saunders Company, Philadelphia, 1966; M. I. Darby, Brit. J. Appl. Phys. 18, 1415 (1967); and private communication for J > ~.

TABLE

5f-3.

SOMF..l ATOMIC CONSTANTS, AND PROPERTIES, OF RARE-EARTH ELEMENTS*

S

Elements

0 0 0.5 1 1.5 2 2.5 3 3.5 3 2.5 2 1.5 1 0.5 Yh .... Lu ....... 0 (Y) ......

La ....... Ce ....... Pr ....... Nd ....... Pm ....... Sm ....... Eu ....... Gd ....... Th ....... Dy ....... Ro ....... Er ....... Tm ......

'''1

:

* S,

d,

m.p.,

b.p.,

6.77 6.78 7.00

795 935 1024

7.54 5.26 7.89 8.27 8.54 8.80 9.05 9.33 6.98 9.84

1072 826 1312 1356 1407 1461 1497 1545 824 1652

2900 3020 3180 2700 1600 1430 2700 2500 2300 2300 2600 2100 1500 1900

G em (J/cm 3 °C jJ.eff aJ DC - --- --- - - - - --- --{i 4.48 1509 0 0 0 0 .. 0 0 0 6.19 920 4200 0 0 0 0 ....

L

J

(J

3 5 6 6 5 3 0 3 5 6 6 5 3 0

2.5 4 4.5 4 2.5 0 3.5 6 7.5 8 7.5 6 3.5 0

6/7 4/5 8/11 3/5 2/7

....

2 3/2 4/3 5/4 6/5 7/6 8/7 0

15/7 16/5 36/11 12/5 5/7 0 7 9 10 10 9 7 4

....

2.535 5/28 0.804 3.578 1.600 4/5 3.618 81/44 1.636 2.683 16/5 0.900t 0.845 125/28 0.089t 0 0 °t 7.879 7.937 63/4 9.721 21/2 11.818 10.646 85/12 14.171 10.607 9/2 14.069 9.581 51/20 11.481 9.149 7.561 7/6 4.536 9/28 2.573 0 0 0

... ,

..

I

L, and J = quantum numbers of trivalent rare-earth ions and usually apply to the elements {} = Lande factor gJ = theoretical saturation in Bohr magnetons per atom p.elf = effective paramagnetic moment per atom G = (0 - 1)2J(J + I), DeGennes factor C« = Curie constant per mole (see Sec. 5f-1) d = density t Cm, the theoretical Curie constant for trivalent atoms, is usually observed in the metals and compounds except for 8m and Eu and Yh.

5-146

ELECTRICITY AND MAGNETISM TABLE

5f-4.

MAGNETIC MOMENT AND CURIE TEMPERATURE OF SOME BINARY COMPOUNDS

Compound

AU4Mn .......... AU4V........... CoB ............ C02B ........... C03B ........... CoPt ........... COS2............

Structure (type)

bc tetr. (Ni4Mo) hc tetr. (Ni4Mo) orthorhombic (FeB) tetragonal (Cual-) orthorhombic (Fe3C) tetragonal (AuCu) fcc pyrite (FeS2)

CrBe12 .......... tetragonal (MoBel2) Cr.Brs ........... hexagonal (Bil 3) CrGe2 ........... CrI3............ h~~~g~~~t"(Bii3) ........ Cr02 ............ tetragonal (Ti02) Crl.2Phs ........ fcc (Cu3Au) CrSL19.......... hexagonal (NiAs) CrTe ........... hexagonal (NiAs) Cr3Te4 .......... monoclinic FeAI ............ cubic (CsCI) Fe3Al ........... bcc (CsCl superlattice) FeB ............ Fe2B ............ FeBe5 ........... Fe3C ............ Fe3Cr........... Fe3Ge ........... FeP ............. FeIP............

orthorhombic (FeB) tetragonal CuA12 fcc (MgCU2) orthorhombic (Fe3C) cubic (Cu3Au) hexagonal (NhSn) orthorhombic (MnP) hexagonal (Fe2P)

Fe3P ............ tetragonal (NbP) FePd3 ........... fcc (Cu3Au) FePt ............ tetragonal (AuCu) FeRh ........... cubic (CsCl)

Te, K

363 55 477 429 747 813 122 130 50 37 98 68 378 386 >77 TN = 160 Te = 305 239-334 TN = 80 Te = 329 623 773

598 1043 75 483 993 365 215 266 278 716 540 743 TN Tc

= 330 = 675

Fe3Si ........... cubic (Cu2MnAI)

808

Fe3Sn ........... hexagonal (NhSn) MnAs ........... hexagonal (NiAs)

743 up 318 down 306 578 143 157 633 470 28 320 583 400 75 136 33 7.5 18

nB per magnetic atom

4.15 0.92 0.28 0.76 1.11 0.17 0.84 0.96 """"0.2 3.0 """"0.1 3.1 2.07 Cr Pt

= =

Refs.

1 2,3 4 5 5 6 7-9 10

11.12 13; 14 15 16

2.56 -0.47 0.11

18

2.45 2.3

19-21 22

,...,.,,1.0 FeI = 1.46 Fell = 2.14 1.12 1. 91 """"0.1 2.01 """"1.3 1.90 0.36 0.77 1.32 1.84 Fe = 2.7 Pd = 0.5 """"0.2 Fe = 3.0 Rh = 0.9 FeI = 1.15 Fell = 2.15 1.9 3.4 1.92 0.19 0.25 3.52 """"0.02 0.38 2.5 """"0.1 Mn = 3.60 Pt = 0.17 3.53 0.4 1.23 2.2 """"1.0 """"0.1 0.06 0.16 0.06/Sc """"0.2

17

23 23,24 25 26 27 26,28 29 48 30 30,31 30,32 17,33 34 35,36 37,38 39 40,41 42 43,44 45,46 47 48 49 50 51 52,53 54

55 56,57 58,59 60 61 62 63,64 65-68

MAGNETIC PROPERTIES OF MATERIALS

5-147

References for Table 5f-4. 1. Meyer, A. J. P.: Compt. rend. 242, 2315 (1965); 244,2028 (1957); J. phys. radium 20, 430 (1959). 2. Creveling, L., H. L. Luo, and G. S. Knapp: Phys. Rev. Letters 18, 851 (1967). 3. Cohen, R. L., R. C. Sherwood, and J. H. Wernick: Phys. Letters 26A, 462 (1968). 4. Lundquist, N., H. P. Myers, and R. Westin: Phil. Ma(}. 7, 1197 (1962). 5. Fruchart, R.: Compt. rend. 256, 3304 (1963). 6. Velge, W. A., and K. J. DeVos: Z. anqeui, Phys. 21, 115 (1966). 7. Morris, B., V. Johnson, and A. Wold: J. Phys. Chem. Solids 28, 1565 (1967). 8. Miyakara, S., and T. Teranishi: J. Appl. Phys. 39,896 (1968). 9. Adachi, K., K. Sato, and M. Takeda: J. Appl. Phys. 39, 900 (1968). 10. Wolcott, N. M., and R. L. Falge: Bull. Am. Phys. Soc. 13,572 (1968). 11. Tsubokawa, 1.: J. Phys. Soc. Japan 15,1664 (1960). 12. Dillon, J. F.: J. Phys. Soc. Japan 19, 1662 (1964). 13. Margolin, S. D., and 1. G. Fakidov: Phys. Metals Metallo(}. 9(6), 22 (1960). 14. Davidenko, N. 1., and 1. G. Fakidov: Phys. Metals Metallo(}. 24(1), 194 (1967). 15. Dillon, J. F., and C. E. Olsen: J. Appl. Phys. 36, 1259 (1965). 16. Swoboda, T. J., A. P. Cox, J. N. Ingraham, A. L. Oppegard, and M. S. Sadler: J. Appl. Phys. 32,3745 (1961). 17. Pickart, S. J., and R. Nathans: J. Appl. Phys. 33, 1336 (1962). 18. Dwight, K., N. Menyuk, D. B. Rogers, and A. Wold: J. Appl. Phys. 33, 1341 (1962). 19. Lotgering, F. K., and E. W. Gorter: J. Phys. Chem, Solids 3, 238 (1957). 20. Aduchi, K.: J. Phys. Soc. Japan 16, 2187 (1961). 21. Bertaut, E. F., G. Roult, R. Aleonard, R. Pauthenet, M. Chevreton, and R. Jansen: Journal de Physique 25,582 (1964). 22. Chevreton, M., and E. F. Bertaut: Compt. rend. 255, 1275 (1962). 23. Dekhtyar, Phys. Metals Metallo(}. 23(1), 36 (1967). 24. Nathans, R., M. T. Pigott, and C. G. Shull: J. Phys. Chern, Solids 6, 38 (1958). 25. Lundquist, N., H. P. Myers and R. Westin: Phil. Ma(}. 7, 1187 (1962). 26. Bozorth, R. M.: "Ferromagnetism" D. Van Nostrand Company, Inc., Princeton, N.J., 1951. 27. Herr, A., and A. J. P. Meyer: Compt. rend. 265, 1165 (1967). 28. Jannin, C., P. Lecocq, and A. Michel: Compt. rend. 257, 1906 (1963). 29. Dekhtj ar, M. V.: SovietPhys.-Solid State 5,2297 (1963). 30. Meyer, A. J. P., and M. C. Cadeville: J. Phys. Soc. Japan 17B, 223 (1962). 31. DeVos, K. J., W. A. Velge, M. G. Van der Steeg, and H. Zijlstra: J. Appl. Phys. 33, 1320 (1962) . 32. Gambino, R. J., T. R. McGuire, and Y. Nakamura: J. Appl. Phys. 38, 1253 (1967). 33. Cable, J. W., E. O. Wollan, and W. C. Koehler: Phys. Rev. 138, A755 (1965). 34. Velge, W. A., and K. J. DeVos: Z. anaeio. Phys. 21, 115 (1966). 35. Kouvel, J. S., and C. C. Hartelius: J. Appl. Phys. 33, 1343 (1962). 36. Shirane, G., C. W. Chen, P. A. Flinn, and R. Nathans: J. Appl. Phys. 34, 1044 (1963). 37. Nakamura, Y.: J. Phys. Soc. Japan 18, 797 (1963). (Ref. to A. Paoletti.) 38. Lecocq, P., and A. Michel: Compt. rend. 258, 1817, (1964). 39. Janniri, C., P. Lecocq, and A. Michel: Compt. rend. 257, 1906 (1963). 40. Guillaud, C.: J. phys. radium 12, 223 (1951). 41. Goodenough, J. B. and J. A. Kafalas: Phys. Rev. 157, 389 (1967). 42. Lundquist, N., H. P. Myers, and R. Westin: Phil. Ma(}. 7, 1197 (1962). 43. Cadeville, M. C.: J. Phys. Chern; Solids 27, 667 (1966). 44. Anderson, L., B. Bellby, and H. P. Myers: Solid State Commun. 4, 77 (1966). 45. Guillaud, C.: J. phys. radium 12, 223 (1951). 46. Adachi, K.: J. Phys. Soc. Japan 16, 2187 (1961). 47. Tsuboya, 1., and M. Sugihara: J. Phys. Soc. Japan 18, 143 (1963). 48. Lecocq, Y., P. Lecocq, and A. Michel: Compt. rend. 256, 4913 (1963). 49. Castelliz, L.: Z. Metallk, 46, 198 (1955). 50. Aoyagi, K., and M. Sugihara: J. Phys. Soc. Japan 17, 1072 (1962). 51. Pickart, S. J., and R. Nathans: J. Appl. Phys. 33, 1336 (1962). 52. Guillaud, C.: J. phys. radium 12, 223 (1951); 489 (1951). 53. Ido, H., T. Kameko, and K. Kamigaki: J. Phys. Soc. Japan 22,1418 (1967). 54. Williams, H. J., J. H. Wernick, R. C. Sherwood, and G. K. Wertheim: J. Appl. Phys. 37, 1256 (1966). 55. Yasukochi, K., K. Kanematsu, and T. Ohoyama: J. Phys. Soc. Japan 16, 429 (1961); 1123 (1961). 56. Cherry, L. V., and W. E. Wallace: J. Appl. Phys. 32,340 (1961). 57. Nassau, K., L. V. Cherry, and W. E. Wallace: J. Phys. Chem. Solids 16, 123 (1960).

5-148 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68.

ELECTRICITY AND MAGNETISM

Tezuka, S., S. Sakai, and Y. Nakagawa: J. Phys. Soc. Japan 15, 931 (1960). Nakagawa, Y., S. Sakai, and T. Hori: J. Phys. Soc. Japan 17, Suppl. B.l, 168 (1962). deBoer, F. R., J. Biesterbos, and C. J. Schinkel: Phys. Letters 24A, 355 (1967). Watanabe, M., and S. Miyahara: J. Phys. Soc. Japan 23,451 (1967). Paccard, D., and R. Pauthenet: Compt. rend. 264B, 1056 (1967). Matthias, B. T., A. M. Clogston, H. J. Williams, E. Corenzwit, and R. C. Sherwood: Phys. Rev. Letters 7,7 (1961). Gardner, W. E., T. F. Smith, B. W. Howlett, C. W. Chu, and A. Sweedler: Phys. Rev. 166, 577 (1968). Matthias, B. T., and R. M. Bozorth: Phys. Rev. 169, 604 (1958). Pickart, S. J., H. A. Alperin, G. Shirane, and R. Nathans: Phys. Rev. Letters 12, 444 (1964). Ogawa, S., and N. Sakamoto: J. Phys. Soc. Japan 22, 1214 (1967). Foner, S.,' E. J. McNiff, and V. Sadagopan: Phys. Rev. Letters 19, 1233 (1967); E. P. Wohlfarth: Phys. Letters 20,253 (1966).

5-149

MAGNETIC PROPERTIES OF MATERIALS TABLE

5f-5.

To,

CURIE POINTS OF FERROMAGNETIC BINARY COMPOUNDS

OF RARE-EARTH ELEMENTS

R

IN KELVIN*

Part 1

R=

Ce

R6Mn23 ........... RFe2 ............. RFea ............. RsFe2a............ R2Fe17 ............

Pr

Nd Sm Gd

Tb Dy

Ho

Er Tm

Lu

.. .

429? ... '" 659 574 524 651 491 475 485 471 91 287 327 395 460 409 362 319 293 248 235 245

48 106 209 413 238 154 90 38 3~ .. . RC02 ............. ... RCoa ............. 78 349 395 ... 612 506 450 418 401 370 . .. R2C07............ 151 574 609 713 762 693 647 644 644 ... .. . RCo5............. 737 912 910 1020 1008 980 966 1000 986 1020 ... R2C017 ............ 1083 1171 1150 1190 1209 1180 1152 1173 1186 1182 ... 20 35 45 73 50 48 31 10 4 .. . RNi. ............. ... 20 22 77 46 32 23 14 14 .. . 8 RNb ............. ... 20 27 85 116 98 69 66 62 43 . .. RNi a............. ... 87 ... 118 101 81 70 67 ·.. ... R2Nh ............ 48 85 9 25 36 27 15 10 13 7 ... RNis ............. ... '" R 2Ni17 ........... RAh ............. R 5Si4, ............ RRu2 ............. RRh 2............. ROs 2............. RIr2 ............. RPt2 .............

Y

Refs.

- - -- -- - - - - - - - - - - - - - - - --.. . .. . .. . 439 469 ... 443 434 415 . .. .. . 486 1,2 221 .. . ... 675 793 695 640 603 587 613 610 . .. 3 .. . ... . .. 651 728 648 600 567 550 539 529 . .. 3

... . .. 641 8 33 63 122 ... ... . .. ... ... 39 29 ... 2 8 7 ... ... 28 22 36 ... 15 12 '"

6

'"

4

3~1

623 615 604 611 602 603 176 119 51 27 20 5 336 225 140 76 25 " . 85 .. . .. . ... 8 ·" 73 39 28 17 7 ·" 67 34 15 9 3 · .. 89 44 23 12 4 1 37 16 14 9 3 '"

3 3

. ..

4 301 5 459 3, 23 977 6, 23 1167 7, 23 . .. 8 . .. 8 .. . 9 58 10 . .. n,8

... ... . .. .. . ... . .. . "

'"

621 '"

... . .. . .. . .. ... ...

24 12 13 14 15 14 14 15

Part 2 Compound

To

Ref.

Compound

To

Ref.

Compound

To

Ref.

--RMn2 ........ PrFe7 ........ NdFe7 ....... 'I'ms Ni , ...... EuB ......... PrSb......... CeGe2........ PrGe2 ........ NdGe2 ....... TbZn ........ GdCd ........ TbHg ........

... 283 327 12 8

11 5 19 4 160 262 80

11, 16 17 17 17a 18 19 19 19 19 20 21 20

TbGa ...... 155 Gd5Pd 2..... 335 TbsPd2 ..... 30 Dy5Pd 2..... 25 Ho 5Pd 2..... 10 Gd 2AgIn .... 122 NdH2. ..... 10 EuH 2....... 25 NdN ....... 35 GdN ....... 69 TbN ....... 42

20 22 22 22 22 21 27 25 28,29 30 29,31

29,31 DyN ....... 17 29 HoN ....... 13 29 ErN ........ 16 32 DyP ....... 5 31,32 HoP ........ 5 2 33 Dy.As ....... 34 EuO ........ 69 34 EuS ........ 17 EuSe ....... 7 34,35,36 26 EuI 2....... 5 37 DyaAh ..... 76

* Data for compounds with nonmetallic elements compiled by F. Holtzberg and S. Methfessel, IBM Watson Research Center.

6-150

ELECTRICITY AND MAGNETISM

References for Table 6f-5 (R and metallic elements) 1. DeSavage, B. F., R. M. Bozorth, F. E. Wang, and E. R. Callen: J. Appl. Phys. 36,992 (1965) . 2. Kirchmayer, H. R: IEEE Trans. MAG-2, 493 (1966). 3. Salmans, L. R, K. Strnat, and G. 1. Hoffer: Technical report, Air Force Materials Lab., Wright-Patterson Air Force Base, Ohio 45433 (1968). 4. Farrell, J., W. E. Wallace: Tnorq. Chem. 5, 105 (1966). 5. Lemaire, R, R. Pauthenet, J. Schweizer, and 1. S. Silvera: J. Phys. Chem. Solids 28, 2471 (1967). 6. Lemaire, R.: Cobalt 32, 132 (1966). 7. Lemaire, R.: Cobalt 33,201 (1966). 8. Abrahams, S. C., R. C. Bernstein, J. H. Sherwood, J. H. Wernick, and H. J. Williams: J. Phys. Chem. Solids 25, 1069 (1964). 9. Laforest, J., R. Lemaire, D. Paccard, and R. Pauthenet: Compt. rend. (B)264, 676 (1967). 10. Lemaire, R, D. Paceard and R Pauthenet: Compt. rend. (B)265, 1280 (1967). 11. Nesbitt, E. A., H. J. Williams, J. H. Wernick, and R. C. Sherwood: J. Appl. Phys. 33, 1674 (1962). 12. Williams, H. J., J. H. Wernick, E. A. Nesbitt, and R C. Sherwood: J. Phys. Soc. Japan 17(1),91 (1962). 13. Holtzberg, F., R. J. Gambino, and T. R. McGuire: J. Phys. Chem. Solids28, 2283 (1967). 14. Bozorth, R. M., B. T. Matthias, H. Suhl, E. Corenzwit, and D. D. Davis: Phys. Rev. 115, 1595 (1959). 15. Crangle, J., and J. W. Ross: Proe. Intern. Coni. Maonetism, Nottinoham, p. 240, The Institute of Physics and the Physical Society, London, 1964. 16. Felcher, G. P., L. M. Corliss, and J. M. Hastings: J. Appl. Phys. 36, 1001 (1965). 17. Strnat. K., G. Hoffer, and A. E. Ray: IEEE Trans, MAG-i, 489 (1966). 17a. Feron, J.-L., R. Lemaire, D. Paccard, and R. Pauthenet: Compt. rend. (B) 267, 371 (1968). 18. Matthias, B. T., T. H. Geballe, K. Andres, E. Corenzwit, G. W. Hull, and J. P. Maita: Science 159, 530 (1968). 19. Matthias, B. T., E. Corenzwit, and W. H. Zachariasen, Phys. Rev. 112,89 (1958). 20. Cable, J. W., W. C. Koehler, and E. O. Wollan: Phys. Rev. 136,240 (1964). 21. Sekizawa, K., and K. Yasukochi: J. Phys. Soc. Japan 21,684 (1966). 22. Berkowitz, A. E., F. Holtzberg, and S. Methfessel: J. Appl. Phys. 35, 1030 (1964). 23. Buschow, K. H. J., J. F. Fast, and A. S. VanderGoot: Phys. Status Solid 29, 719 (1968). 24. Carfagna, P. D., and W. E. Wallace: J. Appl. Phys. 39,5259 (1968). 25. Zanowick, R L., and W. E. Wallace: Phys. Rev. 126,537 (1962). 26. McGuire, T. R., and M. W. Shafer: J. Appl. Phue. 35,984 (1964). 27. Henry, W. E.: Phys. Rev. 98, 226 (1955). 28. Schumacher, D. P., and W. E. Wallace: Tnorq. Chem, 5, 1563 (1966). 29. Busch, G., P. Junod, F. Levy, A. Menth, and O. Vogt: Phys. Letters 14,264 (1965). 30. Schumacher, D. P., and W. E. Wallace: J. Appl. Phys. 36, 984 (1965). 31. Child, H. R, M. H. Wilkinson, J. W. Cable, W. C. Koehler, and E. O. Wollan: Phys. Rev. 131,922 (1963). 32. Busch, G., P. Schwob, O. VOgt, and F. Hulliger: Phys. Letters 11, 100 (1964). 33. Busch, G., O. Vogt, and F. Hulliger: Phys. Letters 15, 301 (1965). 34. McGuire, T. R,and M. W. Shafer: J. Appl. Phu«. 35,984 (1964). 35. McGuire, T. R, F. Holtzberg, and R. Joenk: J. Phys. Chem. Solids 29, 410, (1967). 36. Busch, G., P. Junod, R G. Morris, and J. Muheim: Helv. Phys. Acta 37, 637 (1964). 37. Barbara, B., C. Bede, J.-L. Feron, R. Lemaire, D. Paccard, and R. Pauthenet: Compt. rend. (B) 267, 244 (1968).

6-151

MAGNETIC PROPERTIES OF MATERIALS TABLE

5f-6.

SATURATION MAGNETIZATION AND CURIE POINTS OF SOME SIMPLE FERRITE SPINELS a

Ferrite

X-ray density"

MnFe204. .......... FeaO' .............. CoFe20' ............ NiFe20, ............ CuFe204 ............ MgFe20' ........... CdFe20L ........... ZnFe204/ ........... Lie. sFe2,50, ..........

5.00 5.24 5.29 5.38 5.35 4.55 . ... 5.33 4.75

41rM s at room temperature

4,900" 6,000b 5,300b

3,230"

1,700b,e

1,450",0 0 0 3 , 240-3 , 900",d

te,OC

295-330",d 585 b 520 b 580-600 c ,d 455 b

320, 440",d,e 60 590-680",d

Prepared by F. G. Brockman, Philips Laboratories, Briarcliff Manor, N.Y. J. Smit and H. P. J. Wijn, "Ferri tes," John Wiley & Sons, Inc., New York, 1959. Wilhelm H. von Aulock, ed., "Handbook of Microwave Ferrite Materials." Academic Press, Inc., New York, 1965. tJ Range of values indicates extremes of reported values from various workers. • Depends on heat treatment. I ZnFe20, magnetic when quenched, otherwise nonmagnetic; to for rapid quench. a b e

TABLE

5f-7.

BOHR MAGNETON NUMBERS OF SOME FERRITE SPINELS

AND OF CORRESPONDING SOLID SOLUTIONS WITH ZnFe 2 0 ,a

Mol % ZnFe20' ............ MnFe204 b.... . . . . . . . . . . . ,.

FeFe20l, ................. CoFe20,b .................

NiFe20'b .................. MgFe20,b ................. (Lio, sFeo. 5)Fe 2O," .......... CuFe20," ............... , .

20

40

---

---

4.5 4.2 3.7 2.4

5.6 5.2 5.0 3.8

6.7 5.7 6.1 5.1

7.0 5.8 6.3 5.3

6.3 5.4 5.2 5.1

1.8d

3.3d

4.2 d

4.4 d

4.2 d

2.6

2.8

4.4

4.0

1.8

0

r.s-

...

...

50

4.7 d

Prepared by F. G. Brockman, Philips Laboratories, Briarcliff Manor, N.Y. by interpolation of data in references. b C. Guillaud et al., from summary of E. W. Gorter. c E. W. Gorter, Philips Research Repts, 9, 295, 321, 403 (1954). tJ Depends on heat treatment. b > c; b is the symmetry axis. t The crystallographic axes are labeled such that a < b < c. § Weak ferromagnetism is observed below 81.5 K. , Here !l = Y, La, and the rare earths. The data refer to the ordering of the Fe sublattioes: the moment is temperature dependent because of spin reorientation and rare-earth ordering at various lower temperatures. ** The z axis is the threefold symmetry axis, and z is a twofold axis; (J is the polar angle. tt There is a transition to an uncanted state at 260 K. t:I: More than two sublattices are probably required for a descriptive model.

MAGNETIC PROPERTIES OF MATERIALS

5-155

References for Table of-l0. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32.

Sugawara, F., S. Iida, Y. Syono, and S. Akimoto: J. Phys. Soc. Japan 20, 1553 (1968). Joenk, R. J., and R. M. Bozorth: J. Appl. Phys. 36, 1167 (1965). Burgiel, J. C., V. Jaccarino, and A. L. Schalow: Phys. Rev. 122,429 (1961). Meijer, H. C., and J. van den Handel: Physica 30, 1633 (1964). Shane, J. R., D. H. Lyons, and M. Kestigan: J. Appl. Phys. 38, 1280 (1967). Pickart, S. J., H. A. Alperin, and R. Nathans: J. phys. radium 20, 565 (1964). Yudin, V. M., and A. B. Sherman: Phys. Status Solidi 20, 759 (1967). Gurevich, A. G., E. 1. Golovenchits, and V. A. Sanina: J. Appl. Phys. 39, 1023 (1968). Ogawa, S.: J. Phys. Soc. Japan 15,2361 (1960). Heeger, A. J., O. Beckman, and A. M. Portis: Phys. Rev. 123, 1652 (1961). White, R. L.: J. Appl. Phys. 40, 1061 (1969); this is a review paper and contains an extensive list of references; for CeFeOa see M. Robbins, G. K. Wertheim, A. Menth, and R. C. Sherwood: J. Phys. Chem. Solids 30, 1823 (1969). Turov, E. A., and V. E. Naish: Phys. Metals Metallo(J. 9(1), 7 (1960); V. E. Naish and E. A. Turov: ibid, 11(2), 1 and 11(3), ~ (1961). Dzialoshinski, 1. E.: Soviet Phys.-JETP 6, 1120 (1958). Moriya, T.: Phys. Rev. 117, 635 (1960). Joenk, R. J., and R. M. Bozorth: Proc. Intern. Coni. Ma(Jnetism, Nottin(Jham, p. 493, The Institute of Physics and the Physical Society, London 1964, p, 493. Rao, R. P., R. C. Sherwood, and N. Bartlett: J. Chem. Phys. 40, 3728 (1968). Wollan, E. 0., H. R. Child, W. C. Koehler, and M. K. Wilkinson: Phys. Rev. 112, 1132 (1958). Bozorth, R. M., and V. Kramer: J. phys. radium 20, 393 (1959). Hansen, W. N., and M. Griffel: J. Chern, Phys. 30, 913 (1959). Shane, J. R., and M. Kestigan: J. Appl. Phys. 39, 1027 (1968). Dzialoshinski, 1. E.: Soviet Phys.-JETP 5, 1259 (1957); J. Phys. Chem. Solid8 4, 241 (1958). Moriya, T.: Phys. Rev. Letters 4, 228 (1960); Phys. Rev. 120, 91 (1960). Tasaki, A., and S. Iida: J. Phys. Soc. Japan 18, 1148 (1963). Flanders, P. J., and W. J. Schuele: Phil. Ma(J. 9,485 (1964). Borovik-Romanov, A. S., and M. P. Orlova: Soviet Phys.-JETP 4, 531 (1957). Borovik-Romanov, A. S.: Soviet Phys.-JETP 9, 539 (1959). Borovik-Rornanov, A. S., and V. 1. Ozhogin: Soviet Phys.-JETP 12, 18 (1961). Kaczer, J.: Soviet Phys.-JETP 16, 1443 (1963). Bizette, H., and B. Tsai: Compt. rend. 241, 546 (1955). Alikhanov, R. A.: J. Phys. Soc. Japan 17, suppl, BIll, 58 (1962). Hambourger, P. D., and J. A. Marcus: Phys. Rev. 158,438 (1967). Cracknell, A. P.: PhY8. Leuere 27A, 426 (1968).

6-156 cI)

ELECTRICITY AND MAGNETISM

3.0r---.---r--.--..,.----r--,----,--_---_ • Fe-V

Z

o ~

+ Fe-Cr

~

o Fe-Nl • Fe-co c Nl- Co

~ 2.5t---t----t---+--+~=+--~-_._jI_-~

-c ~

a: 2.0 t---t----t---+---:::;""+--..p,..----.~-_._jl_-.....j J:

o

NL- Cu.

• Nl-Zn

ID ~

A

1.5t---t---t-~-hf---+--+---IJ+_3:t1.______l'_-_I

v NL-V

o

NL-Cr

~

z

b Nl-Mn

o

~ 1.0 I----+--~~-_+_.-_+--_+_J~_+--::O--4...31t1_'t'-~

• co-er

~

o Co-Mn x PURE

METALS

su 0.5 o

~

Mn 25

Fe

Co

NL

26

27

28

ELECTRONS PER ATOM FIG. 5f-1. Saturation magnetization of intra-iron-group alloys as dependent on electron concentration. Data by Peschard (1925), Weiss, Forrer and Birch (1929), Forrer (1930), Sadron (1932), Fallot (1936, 1938), Farcas (1937), Marian (1937), and Guillaud (1944). [R. M. Bozorth, Phys. Rev., 79,887 (1950).]

!

450

J~AN~ANElE

400 3~0

~ ,~~

250

.,§ ~

1!:lO

o a.

'" 100

ii: ~

Co)

GOLD

r--~~OIU

I I I

~;;~,

Ir~

~~

I

Xif

~

~"

~

4,000

SAMARIUM COBALT, SmCoS \. ...... (18.5xI06 ) :\. ...........

2,000 f----+---+-~..,c.:;___iI-----t----h,ilC_--t-c-:"7"9-~.-=--t--r-----1

-7,000

-1,000

-6,000 -5,000 -4,000 -3,000 FIELD STRENGTH, H,IN ~RSTEDS

o

FIG. 5f-12. Demagnetization curves and maximum energy products, (BH)m, of several types

(Prepared by H. H. Helms and E. Adams, U.S. Naval

of permanent-magnet materials. Ordnance Laboratory.)

This is valid only at low frequencies, when eddy-current shielding is negligible. Hysteresis losses at low inductions are described by the Raleigh relation Wh = 411'" dJ,L H3 3 dH

per cycle, H being the maximum field strength during the cycle and dJ,L/dH the slope of the J,L vs. H curve (near J,Lo). At high inductions, e.g., B = 100 to saturation, the relation often used to calculate hysteresis loss per cycle at maximum induction B is Wh 71

=

7l B 1. 6

being an empirical constant varying from 1 to 10 6• TABLE

5f-14.

MATERIAL CONSTANTS FOR LOSSES AT Low INDUCTIONS

(a is hysteresis constant, c the "lag" constant, and e the eddy-current constant)

Material

Size

J,Lo

a X 10 6

c X 10 6

e X log

Carbonyl iron .......... Mo Permalloy .......... Mo Permalloy .......... Mo Permalloy .......... Mn Zn ferrite .......... Ni Zn ferrite ...........

5p. O.OOl-in. sheet 120 mesh 400 mesh

13 13,000 125 14 1,500 200

5 2 1.6

60 O. 30 140 4.8*

1 10 19 7 0.3 0.2

•

..

..

..

4

•

~

..

..

..

..

...................

..

..

11

1.6 7

........

e

...

* < 1 Me/sec, higher values at higher frequencies. J'

6f-7. Antiferromagnetic Materials Studied by Neutron Dlffraction.! Introduction. Since Table 5g-22 in the second edition of the Handbook was compiled, any magnetic structural distinction between ferro- (and ferri-) magnetic and antiferromagnetic materials has become increasingly arbitrary in view of the existence of many complex noncollinear or modulated structures with ferromagnetic components, which in some 1

Compiled by D. E. Cox, Brookhaven National Laboratory, Upton, N.Y.

MAGNETIC PROPERTIES OF MATERIALS

5-167

cases transform at some intermediate temperature to yet another structure. In general, such materials have been included in the table, and the only ones which have been systematically excluded are collinear ferromagnetic and ferrimagnetic materials. Even a few of the latter have been listed, however, if it is felt that the structural features are closely related ,to a basic antiferromagnetic arrangement. Although the table was initially compiled in considerable detail with a format very similar to that of its predecessor, space limitations competing with an almost tenfold increase in the literature have necessitated the present highly abbreviated and concise form (Table 5f-15). A more detailed compilation is available on request from the author (Brookhaven National Laboratory Report No. 13822). For similar reasons, it has also not been possible to provide any structural details of a number of very interesting complex arrangements, in either the table or the accompanying figures. This is also true for solid solutions, where it is clearly impracticable to attempt to list all the relevant data. Reference to the original article is strongly urged in these cases. Format and Abbreviationsfor Table 5f-15. COLUMN 1: MATERIAL. Materials have as far as possible been listed within structurally similar groups with the magnetic atoms in alphabetical order. There are, however, a number of departures from the latter scheme, for example, where compounds contain more than one such atom. COLUMN 2: CRYSTAL CLASS AND NEEL TEMPERATURE. The crystal classes have been abbreviated as follows: C(cubic), T(tetragonal), H(hexagonal), R (rhombohedral) , O(orthorhombic), and M(monoclinic). The magnetic structures of all rhombohedral systems have been described in terms of the hexagonal unit cell. The crystal class is usually that cited in the neutron diffraction determination above the initial ordering temperature. The actual structure is sometimes known to be distorted from that assumed, and where there is a distortion associated with the (or one of the) magnetic transition(s), this has been denoted by *. A distortion apparently unconnected with any magnetic transition has been denoted by **. The Neel temperatures where listed are those cited in the neutron diffraction references, and are not necessarily determined by diffraction techniques. A second (or third) figure in parentheses indicates the temperature of a second (or third) transition, and t implies that the temperature in question corresponds to a Curie point (i.e., the appearance of a spontaneous moment). A typical entry might be C: 64, which means a cubic lattice with a Neel point of 64 K. COLUMN 3: MAGNETIC STRUCTURE. Most of the abbreviations used here can be found by reference to the figures and captions at the end. The description f. (or a.i.) sheets implies a structure with ferromagnetic (or antiferromagnetic) sheets which are coupled antiparallel to adjacent sheets. The symbol tt denotes that the structure described occurs over part of the composition range in solid solutions, and the symbol # (also used in column 4) denotes the presence of two magnetic phases. The use of braces indicates that the magnetic structure in question involves components from more than one type of mode and is therefore noncollinear. Changes in magnetic structure or additional magnetic ordering are entered opposite the appropriate transition temperature listed in parentheses in column 2. It is to be noted that the magnetic unit cell is in many cases some multiple of the chemical cell; in order to save space this is not explicitly stated in the table but is very often obvious by reference to the appropriate figure. COLUMN 4: MOMENT AND DIRECTION. A typical entry in this column lists first the magnetic moment in boldface type, followed by its direction. For example, the entry 1.7: 1. [1001; 36°, [010] means a moment of 1.7#loB directed perpendicular to [1001 and 36° from [0101. Where there are multiple entries of this sort, each moment and direction is that appropriate to the entry listed in column 3 on the same horizontal line. The moments which have been tabulated are for the most part those determined at the lowest temperature studied, which is 4.2 K in the majority of cases.

5f-15.

TABLE

N aCl and related structures, (see also Fig. 5f-13) CoO CrN FeO LiFe02 MnO (Mn,Co) 0 a-MnS Mno.33Cro.67S (Mn,Cr) S MnSe Mno.9Lio. 1Se (Mn,Li) Se NiO CeAs CeSb ErP ErSb

~

Crystal class and Neel temperature, K

Material

1

C*: 291 C*: 273 C*: 198 C

C*: 120 C

C

C: 240 C C

, C*: 71

Magnetic* structure

C*: 530 C: 8 C: 16 C: 3.1 C: 3.7

EuSe

C: 5.8 C: 7.8 C C C

C C 5.5t C 9 C 12

C 9 C 14

00

Moment (in IJ.B) and direction

f2 (Fig. 5f-13) f2 or complex f4A f2 f2 f2 f2 f2 f1

3.8: 11.5°, [001] 3.5: 27.4°, [001] 2.4: [110] 3.3: [111] 2.5-4.5: .i[111] 5: .1[111]

f2 f3

.1[111] 4.6: 45°, [001]

f2 f1 complex f2 f2 f2 { sinusoidal f2 f2 f2 f2 f2 complex f2 f2 f2 f2

1.8: .i[111] 0.7: [001]

5: .i[111] 4.1: .1 [001]

C

EuTe GdBi GdS GdSb GdSe HoP HoSb TbAs...................•...... TbP ..................•........ TbSb ........•.....••....•.....

cr.....

ANTI FERROMAGNETIC MATERIALS STUDIED BY NEUTRON DIFFRACTION

5.7: .i[111] 7.0: .i[111] .1[111]? .1[111] .1[111]

8.8 9.3 7.7 6.2 8.2

.1[001] [100] [111] [111] [111]

References

290, 343, 363 247, 248 125 343, 345, 363 138 343, 362, 363 42 123, 363 96 96 363 318 318 15, 16, 344, 346, 363 341 341 112 112 323 410 266 266 266 266 112 112 112 112 112

trJ

t"

trJ

o 8

~

I-l

oI-l 8

to


Z

t:1

r::::

o> Z

trJ

8

I-l [fl

r::::

UAs••••••••................... C: 123, 128 (>4.2) UN ...............•........... C: 53 UP ............................ C: 125 UPo.USO.05 ..... , ............... C: 122 (27) U(P,S) ...................•.... C USb ........................... C: 243 Perovskite and related 8tructure8 (see also Fig. 5f-14)

1.9, 2.1: [001] 2.2: [001] 0.8: [OOIJ 1.7, 1.9: [OOIJ 1.7: [OOIJ 1.9: [OOIJ . ........................ >2.6,2.2

260, 388, 412

f2 (Fig. 5f-13b) G

'.7: [1001 7.2: [OIOJ 6-.9: [100J '.6: [010J 2.0: 23°, [HI]

81, 195

Ba2CoWOe..................... C: 17 KCoF•........................ C: 135

{~ {~

TbCoO•....................... 0: 3.&1

{~(TJ»

DyCrOa ....................... 0: 146 (2.16) ErCrOa ......................... 0: 133 (16.8) HoCrOa ....................... 0: 140

G(Cr) complexf Dy) G(Cr) C(Er) G(Cr)

6.': [100J '.6: [OIOJ 2.8: [0011 9.6: J.£OOI] 2.9 =- varies 6.2: [0011 2.9: varies 3.': l1001 7.0: [0101 4.3: 1..[0011 2.6, 2.8: 1..[0011 2.6: 1..[OIOJ; 63°, [100J 2.6: varies 1.3: [001 1.9 2.6 varies 0.6 [0011 2.9 [0011

DyAlO•..•...................•. 0: 3.48 TbAlO•.......•.....•.......... 0:4.0

(""12) KCrF•......................... LaCrO."'.•..................... LuCrOa ....•................... NdCrOa .•••...................

T

0: 282 0: H2 0: 224 (""10) PbCrOa ........•............... C: 240 PrCrOa ........................ 0: 239 (>4.2) TbCrOa ........................ 0: 158 (4)

(3.05) TmCrO•....................... 1 0: 124 (>4)

* The use

fl flA fl fl fl fl and flA#

... . . . . . . . . . . . . . . . .

f1

{~(Ho) A G G G(Cr) C(Nd) G G(Cr) F(Pr) G(Cr)

148 149,367 255 246 260,312 ~

>

0

82, 267

,.,

143 353 267 70,77 70.. 74 62,70

Z

t;j

....o

1-3 '"d

~

0

'"d

t;j ~

1-3

.... t;j

f7J

0 353 70,216,296 70 70, 74 349 70

I:rj

~

>

1-3 t;j ~

.... > tot

f7J

70,76,267

{ ~(Tb) complex (Tb) G(Cr) F(Tm)

18.6 1..[001] 2.6 varies 0.8 [0011

70 1

en r

~

~

of fl and f2 are explained in Fig. 5f-13; G, A, F, and C in Fig. 5f-14.

~

TABLE

5f-15.

ANTIFERROMAGNETIC MATERIALS STUDIED BY NEUTRON DIFFRACTION

(Continued)

en I

~

Material

Z

...............................

.........

321 321 340 340 321 79 143 353 159 265 267,272

..........

3.2-3.4(tetr.): [110] 2.9-2.1(oct.): ±58-39°, [110]

190 336 127, 157, 187

t."'J 8 H

Q

"tl

l:O

0 "tl t."'J

l:O 8 H t."'J tn 0 "".1 ~

> 8 t."'J

335 339 184 330, 331 332 264 183 85 88

l:O

H

>

to" o:

01

I

I--'

'"'1 I--'

TABLE

5f-I5.

ANTIFERROMAGNETIC MATERIALS STUDIED BY NEUTRON DIFFRACTION

(Continued)

CI

I

I--l

Material

'-1

Crystal class and Nilel temperature, K

CrMn20....................... T: 65t (>4.2)

ferrimagnetic (Fig. 5f-15b)

FeMn20•...................... T: 393t (55) NiMn 20 •.•.................... C: 116-164t (70) (various degrees of inversion) ... GeNbO•....................... C: 15 a-Mn 2TiO •..................... T: 62

ferrimagnetic complex ferrimagnetic complex complex complex

CoV 20 •........................ C MgV 20 •....................... C: 45 MnV 20 •................•...... T: 56t (52)

complex? complex ferrimagnetic (Fig. 5f-15a)

NiAs and related etructure« CrAs.......................... Cr(Mn,As) ..................... Cr2:f'eSe •....................... Cr2NiS•........................ Cr 2TiS •........................ CrS ................•.......... Cr2Sa .......................... Cr2Sa ................... '" .... CraS •.......................... CriSe .......................... CrSb .......................... Cr(Sb,Te) ...................... (Cr,Mn)Sb ..................... CrSe .......................... CraSe•.........................

o (Pnma) : 300

spiral

0 M M M M: 460 H: 125 R: 122 M: 280 H: 303t (168) H: 705,723 H H H: 300 M: 80

(Fig. 5f-16b) (Fig. 5f-16b) (Fig. 5f-16b) complex spiral complex (Fig. 5f-16b) ferrimagnetic spiral (Fig. 5f-16a) cantedtt cantedtt triangular (Fig. 5f-16b)

..

......................

~

Moment (in IJ.B) and direction

Magnetic* structure

..

......

oo

References

....................

89

4.1(tetr.): [110] 1.7(oct.): ±23°, [110]

..............................

90

!:I:j

86, 87

o

67 80

1-4

4.3(tetr.), 3.1(oct.)

..............................

3.9(tetr.), 1.3(oct.) 2.2: 1.[111] 4.9(Mnr), 4.8 (MnIl and Mnm): 1. [010] •

••••

~

.. . . . . . . . . . . . . . . . . . "oo • • • • • •

156 327 156, 326. 329, 337

4.4-4.5(Mn): [001] 1.2(V): ±ca.500, [001]

..........................

oo.·

...

oo.

'". . . . . . . . . . . . . . . . . . . . .

oo

2.6(Cr),3.4(Fe): 55°, [IOI] 2.l)(Cr), 1.,3(Ni) : 45°, [IOI]

............................

3.4 2.1: 1.[001] 2.4: 61°, [001] 2.3: 29°, [101] ..

•••••

oo

.....................

1.6-3.0: 1. [001] 2.7,2.8: [001]

.......................... . ...........................

..

2.9: mainly 1.[001] (1OI); 30°, [010]

~

o1-4 ~

oo . . . . . . . . . . . . . . . . . . . . .

1.1: [001]

..

~

!:I:j

400 400 111 24 253 380 250 78 25,65 249 376,384 139, 385 139, 315, 384 126 65

~

> Z e

a:: c> z

!:I:j ~

1-4

Ul

a::

CrTe .......................... 1 H: 330t (150) CraTe4 ........................

1

M: 329t (80)

FeS ........................... Fel_"'S ......................... FeaSe4 ......................... Fe 7Ses ......................... MnP ..........................

H*: 600 ...........

......

M M: 483, 460t O(Pnma): 291 t (50) MnTe ......................... H: 320, 323 NiS ........................... H: 263 Rutile and related structures CoF2 .......................... T: 50 CrCI 2.......................... 0: 20 CrF 2.......................... M: 53 Cr 2Te06 ....................... T: 105 Cr2W06 ....................... T: 69 FeF2 .......................... T: 90 FeOF ......................... T: 315 Fe2Te06 ....................... T: 219 Mno.5Cro.502 ................... T: 390t MnF 2 • • • • • • • • • • • • • • • • • • • • • • • • • T: 75 Mn02 ......................... T: 84 NiF2 .......................... T: 83 VF 2........................... V 2W06 ........................ Olivine and related structures (see also Fig. 5(-18) CaCoSi04. ..................... C02Si04. .......................

T:7 T O(Pbnm): 16 O(Pbnm): 49

LiCoP04 ....................... O(Pbnm): 23 Cr2Be04 ....................... O(Pbnm): 28

ferromagnetic { ferromagnetic a.f. (101) sheets ferromagnetic { ferromagnetic Fig. 5f-16b) (Fig. 5f-16a) (Fig. 5f-16a) (Fig. 5f-16a) (Fig. 5f-16a) ferromagnetic spiral (Fig. 5f-16a) (Fig. 5f-16a) (Fig.5f-17a) complex (Fig.5f-17a) G (Fig. 5f-17b) A (Fig. 5f-17b) (Fig. 5f-17a) (Fig.5f-17a) G (Fig. 5f-17b) {(Fi g.5f-17a) ferromagnetic (Fig.5f-17a) spiral (Fig. 5f-17a) (Fig. 5f-17a) spiral A(Fig. 5f-17b) complex C(COI) C(Con) A spiral

I........................

1385

......................... 165 4: varies . ........................ 2.2(Fel), 1.4(Fen): [110] 3.6(Fel), 4.5(Fen): varies ••••••••••••

0

•••••••••••••

1.3, 1.6: .1.[001] 4.6: .1.[001] 1.7: [001]

18,22 22, 365, 377, 378, 380 23 19, 208 l63,166

~

154, 244, 370 379,380

I-t

Z

t.;j

3.0: [001] """"'3 : along long Cr-CI ........,3: along long Cr-F 2.5: .1.[001] 2.1: .1.[001] 4.6: [001 4.8: [001 4.2, 4.7: [001] 0.5: .1.[001 0.4: .1.[001] 5.0: [001] .1.[001] 5.0: 10°, [001]; .1.[001 .1.[001] .1.[001] ...........................

161 98 98 242, 280 242, 278, 280 161 109 242, 279 395

......................... [001] 3.3: [001] [001] 1.6(Crr), 2.8(Crn): .1.[010]

305 307

~.3;

>~

161, 295 160, 422 161 8 256 242

351 146

8

Q

"d ~

0

"d

t.;j ~

8

I-t

t.;j

U2

0

~

~

>-

8

t.;j ~ I-t

>t'l

U2

01 J I--'

-l CI.:i

TABLE

5f-15.

ANTIFERROMAGNETIC MATERIALS STUDIED BY NEUTRON DIFFRACTION

(Continued)

en I ...... -..:(

Material

Magnetic* structure

Moment (in JlB) and direction

References

O(Pbnm): 23 O(Pbnm): 34

{g(Mnr) C(Mnu) A complex

[001] [001] [001] [100] [010] 3.2: [001] 2.1: [100] 1.1: [010] 3.9: [001] 3.8: [001] [100] 6.2: [010] [010] [010] [010] [100] 3.6: [010] 3.6: [001] 4.7: [010] [100] 1..[001]

351 302

T: T: T: T: T: T: T:

(Fig. (Fig. (Fig. (Fig. (Fig. (Fig. (Fig.

1.6: 1.6: 1.9: 2.2: 2.7: 1.0: 0.9:

309 259 50 287 286 387 259

Fe2SiO•........•......••....... O(Pbnm): 65 (23) 65 LiFePO•...•.•••....••......... o (Pbnm) : 50 CaMnSiO•....•...••••.•....... O(Pbnm): 9 LiMnPO •..••...•..••••........ O(Pbnm): 35 Mn2SiO•..••.•......••......... O(Pbnm): 50 (13)

LiNiPO•....................... Ni2SiO •...................•.... PbFCl and related structures UAs 2.......................... UBh .......................... UOS .......................... UOSe ......................... UOTe ......................... UP2 ........................... USb2 .......................... Corundum and related structures CoTiOa ........................

H:o-

Crystal class and Neel temperature, K

283 183 55 90 160 203 206

R: 38

C(Fer) C(Feu)

1~(FerJ 1~(Fel) C(Feu) A G A C(Mnr) C(Mnu) {g(Mn r)

5f-19b) 5f-19a) 5f-19c) 5f-19c) 5f-19a) 5f-19b) 5f-19b)

(Fig. 5f-20c)

[001] [001] [001] [001] [001] [001] [001]

1..[001]

350 t:':l ~

t:':l

141

o..,;; ~ ~

o

~

352 108 303 350

1-3 ~

>-

Z

tl

a:::

141

o>-

Z

t:':l

1-3 ~

300

w. a:::

Nb2CO.O g............•........ '1 H 30 Cr20a .............•........... R 318 a-Fe20a ...... . . . • • . • . . . . . . . . . . . R 948

f. [001] chains (Fig. 5f-20a) (Fig. 5f-20b)

a-(Fe,Cr) 20a 1 R a-(Fe,Rh) 20a ..............•....

spiraltt

a-(Fe, V)

"'-'3: [001] 2.8: [001] "'-'5: varies

203 • • • • • • • • • • • • • • • • • • • .

. . . . .

FeTiOa a-FezOa-FeTiO a MnTiOa Nb 2Mn40g NiTiOa Cr V04 type structures (see also Fig. 5f-21)

R: 68 R R: 41 H: 125 R

'FeS04 MnS04 NiS04 NiSe04 CUS04 type structures (see also Fig. 5f-21) I9-CoS04

4.6: [001] "'-'5: [001] 2.3: .1[001]

354

a::: ~

o zt"j 8

"

{g

. 0: 22 . 0: 50

spiral A

'1 0: 21

C spiral C A

0 0: 37 0

1

0: 12

CoSeO•........................ IO CuS04. MnSe04 Calcite type structures CoCOa FeCOa MnCOa NiCOa

"'-'4.0: [001]

1-1

a-CoSO •....................... 0: 15.5 I9-CrP04 CrV04

(Fig. 5f-20c) ferrimagnetic tt a.f. (001) sheets f. [001] chains (Fig. 5f-20c)

58 91, 131 122, 135, 147, 284, 297, 320, 342, 363 137 235 235 355 357 354 58

0: 35 0: 20 , R R R R

20.4 20 32 25

2.9: [010] 1.4: [001] 2.5: .1[001] 2.1: 27°, [100]; 64°, [010]; 81°, [001] 4.1: [010] 4.8 2.1: [010] .1[001]

o

1'44. 168

o

1411 [68

8 1-1 t'::l

'"

t'::l ~

168 171

!g !g

2.3, 2.7: [100] 161,93 1.5, 1.9: [010] 1.7, 1.9: [001] ................. " ...... 1171

A A

0.8: [100] 5.0: [100]

114, 271 171

46°, [001] 5.0: [001] .1[001] 63°, [001]

9 7,317 7, 95, 316 110

(Fig. (Fig. (Fig. (Fig.

'"

~

145 168

Ul

oI'%j a::: ~

8 t'::l

~ 1-1

~

t'"

5f-22) 5f-22) 5f-22) 5f-22)

Ul

en 1

-l

c.n

TABLE

5f..15.

ANTIFERROMAGNETIC MATERIALS STUDIED BY NEUTRON DIFFRACTION

(Continued)

9' ~

Material

Garnet type structures DyaAls012 ...................... EraGas012...................... HoaAl s012 ...................... Nd aGas012 ..................... Tb3AI s012...................... Y M nOa type structures (see also Fig. 5£-23) ErMn03 ....................... HoMn03 ....................... LuMn03 ....................... ScMnOa ....................... TmMnOa ...................... YMn03 ........................ VFa and related structures CoF 3.......................... CrF 3.......................... FeF 3.......................... MnF3 ......................... MoF3 ......................... Miscellaneous anhydrous halides CoBr2 ......................... CoCh ....................... ,. CoCs3Cls .................... ,. CrCla .......................... FeBr2 ......................... FeCh.......................... FeCla .......................... K2IrCI6 ........................ Cs2MnCI4 ......................

Crystal class and Neel temperature, K

C: C: C: C: C:

2.49, 2.54 0.79 0.95 0.52 1.35

Magnetic* structure

a.f. [100] chains a.f. [100] chains a.f. [100] chains f. [100] chains a.f. [100] chains

"-l O:l

Moment (in }.I.B) and direction

9.0, 9.5: (100) 5.9: (100) 5.8: (100) 3.6: (100) 5.7:(100)

References

188, 195 180 181 179 181

trJ

~

trJ

o 8

~ H

221 221 221 221 221

oH

62, 64, 69, 221

a:: ~ o

H: 80

triangular

3.5(Mn): -l [001]; 70° (100) 3.5(Mn): (100) 3.7(Mn): 1..[001]; 55°, (100) '""-'4.0: .1.[001]; '""-'24°, (100) '""-'3.8(Mn): 1..[001]; '""-'45°, (100) 3.5: (100)

R: 460 R: 80 R: 394 M: 43 R: 185

(Fig. 5£-22) (Fig. 5£-22) (Fig. 5£-22) f. (101) sheets (Fig. 5f-22)

4.4: [001] 3.0: 1..[001] '""-'5.0: .1.[001] 4.0: (101) '""-'3: .1.[001]

416 416 416 416 407

H: 19 R: 25 T: 0.52 H: 17

(Fig. 5£-24a) (Fig. 5£-24b) f. (101) sheets (Fig. 5£-24b, with vacancies) (Fig. 5£-24a) (Fig. 5£-24b) spiral £3A (Fig. 5f-13c) (Fig. 5f-24c)

2.8: 3.0: 3.2: 2.7:

405 405 182 99

H: H: H: H: H:

79 76 91 '""-'120 '""-'86

H 11 R 24 R 15 C 3.05 T

triangular triangular triangular triangular triangular

1..[001] 1..[001] [001] 1..[001]

4.4: [OOIJ 4.5: [001] 4.3: -l [140J [OOIJ [OOlJ

405 192, 405 102 197, 275 262

8

~

~

Z

t:;

Z

trJ

8 H

U1

a::

CsMnFa ....................... K 2MnF4 ....................... MnBr2 ........................ MnI 2.......................... K2NiF4 ........................ RbNiFa ........................ K2ReBr8......•................ K2ReCI6....................... a-RuCla ....................... Mi8cellaneou8oxide8 CoalhOs ....................... COU04 ........................ ~-CaCr204 ..................... CrU04.........................

H: 64T H: 2.16 H: 3.4 T: 97 H C**: 15.3 C**: 11.9, 12.4 H:c""30

f. (001) sheets (Fig. 5f-24c) complex spiral (Fig. 5f-24c) complex f1 (Fig. 5f-13a) f1 (Fig. 5f-13a)

0: 30 0: 12 0 0

complex f. (111) sheets complex A(Cr) (Fig. 5f-25) A(U) f (101) sheets complex

CuO .......................... M: 230 Er20a ......................... C: 3.36 Bao. 4Sr U Zn2Fe 12 0

22 • • • • • • • • • • • • •

BaCoFe11021 ................... BaScl. SFeIO. 201g................. CaFe204 ....................... Ca(Fe,Cr) 204................... Ca2Fe205......................

H: 400t (380) H H 0: 200, 285 (120-170,140) 0 0: 720, 730

...................

ferrimagnetic spiral spiral spiral a.f. chains fI

...................

complex

FeSb204 ....................... T

{g

FeTh05 ....................... FeW04 ........................ LiFe02 ........................ ~-NaFe02...................... FeU04 .........................

a.f. [100] chains f. (100) sheets complex f. (101) sheets C(Fe)

0 M: 66 T: ""315 0: 723 0: 55

{~

(42t) G~hOa ..... '" .... " .... " .... '1 C: ""1.6 BIMn205. . . . . . . . . . . . . . . . . . . . . .. 0: 52

.........................

.1..[OOl]? 2.6,2.7: .1..[001] ""0.2

............ ............ ,

4.2(Co): .1.. [010]

.........................

2.4: [010] 0.3: [010]

.........................

6.1(ErI): (111) 6.4(Ern): (100)

......................... .1..[001] .......................... .........................

4.1-4.4: [001]

. ........................ 4.5, 4.9: [001] 3.5: .1..[001]

321 263 217, 415 101 83,325,328 322 275 275, 374 164 301,304 59 133 38 92 71, 282 314, 371, 372

(Fe) (Fig. 5f-25)

........................ , 4.4: .1..[010]; 29°, [100] 4.6: [001] 4.2: [001] [01OJ 2: [100] 4: [001] 0.4: [100]

~

>

0

Z

t::.l 8

~

a

"d !;O

0

"d

t::.l

!;O

419 6 13, 72, 133, 399

8~ t::.l

r.Jl

0 133 131, 170, 383 175

(F;g. 5f-21)

C(U) unsolved complex

I

.1..[001] 4.6: [001] [010] 4.6: .1..[307] [001]

~

~

>

8 t::.l

!;O

273 390 138 63 40, 41

i"[ooij ................... Ig5

~

> r-

tn

en I

~

'-l

-.)

TABLE

5f-I5.

ANTIFERROMAGNETIC MATERIALS STUDIED BY NEUTRON DIFFRACTION

(Continued)

01

I

I--"

Material

CaMn 204...................... MnaB 206 ...................... a-Mn 20a ....................... MnU04 ........................ MnW04........................ NiaB 20 6....................... CaV 204 ........................ U0 2....... '" .... , ............ Yb20a .........................

Miscellaneous chalcoqenides AgCrSe2 ....................... NaCrSe2 ....................... CuFeS2 ........................ FeNbaS6....................... FeS2 .......................... I3-MnS ........................ tl-MnS ........................ MnS2 .......................... MnSe2 ......................... MnTe2 ........................ Miscellaneous hydrates CoCh·2D 20 .................... CoCh·6H 20 ....................

Crystal class and Neel temperature, K

0: 225 0 C: 90 0: ("'-'50)12 M: 16 0: 49 0 C: 30.8, 30.6 C: 2.25 R: 50 R:40

-l

Magnetic* structure

complex spiral? unsolved f. (100) sheets complex complex complex f1 (Fig. 5f-13a) complex

......................... ••••••••••••••••••••••

1.1: [010J 1.8: .1..[001] 1.1 (Ybr): (111) 1.9(Ybn): (110)

M: 17.5 M: 2.25

f. [OOlJ chains a.f. (001) planes

2.8: [OlOJ [OOlJ "'-'1 : [100J "'-'0.1: [OOlJ 0.8: "-'[OOIJ "-'1: .1.. [OI0J; 49°, [001]; 158°, [100J 4.6: "'-'.1..[100J; 10°, (101) .1.. [OlOJ 10°, [100J

CuCh·2D 20 .................... 0: 4.3

{~(Fig. 5f-21)

CuF2·2H 20 ..................... M: 10.9 LiCuCla·2H20 ....••............ M: 4.4

(Fig. 5f-17a) a.f. [100] chains

Fe3(P04h4H 20 ................. M: 15t Fe 2S04·H20 ..•................. M NiCh·6H 20 .................... M

complex f. (100) sheets f. (101) sheets

••

........................ ,

C C C

H

0

4.9: [OlOJ [lOIJ

2.7: 2.3: 3.9: 3.7:

C C

References

3.6: [100J

(Fig. 5f-24b) (Fig. 5f-24b) f. (001) sheets complex f2 (Fig. 5f-13b) f3A complex f3A (Fig. 5f-13c) complex f1 (Fig. 5f-13a)

T H

00

Moment (in J.LB) and direction

0

••

0

•••••••••••••••

.1..[OOlJ .1.. (011) [OOlJ [OOlJ .1..[OOlJ

t:1

et."'.1

o

8

~

l-I

(') l-I

8

~

.1..[111J .1..[111J [OOlJ [OOlJ

•••••

6: 6: 6: 6: 6:

12 304 110 39 151 304 189 169, 191, 413 282

,

252 252 153 251 84 123 123 185 130, 185 185 140, 142 213 360, 373, 392 1 3 4 261 214

>

Z

t:l ~

>

Q

Z

t:rj

8

l-I

[fl

~

CaC 2 and related ztructuree AICr2 .......................... T: 598 MnAu2 ........................ CeC 2.......................... DyC2 .......................... HOC2.......................... NdC2 .......................... PrC2.......................... TbAu2.........................

363 33 59 26 29 15 55 (42.5) TbAg 2......................... T: 35 TbC2 .......................... T: 66 (40) a-K02 ......................... T**: 7.1 CsCl and related structures (see also Fig. 5f-14) DyAg ......................... C: 51 FeRh............ '" ........... C: 678t (338) Fe-Rh ......................... ..... ..... ...... AuMn ......................... C*: 515 (403) Au-Mn ........................ ................... Au2MnAl ...................... C: 147t (ordered) ....... " ............. (65) AU2(Mn,Al) 2................... ........... ... ....... MnHg......................... C*: 460 ~-MnZn

T: T: T: T: T: T: T:

....................... C

Pd2MnAl ...................... (disordered) Pd2MnIn ...................... (disordered) Pd2MnIn ...................... (ordered) TbAg ......................... Tb(Ag,In) ..................... Tb(Ag,Pd) ..................... TbCu .........................

f. (001) sheets in sequence ( + spiral (Fig.5f-17a) sinusoidal spiral (Fig. 5f-17a) (Fig. 5f-17a) sinusoidal f. (100) sheets f. (100) sheets spiral

0.9: 65°, [001]

29

3.0: 1. [001] 1.7: [001] 11.8: [001] 6.9: 1. [100] 3.0: [001] 1.1: [001] [001] 9.0: [001] 9.0: [001] 6.1: 1. [1001

193, 194 30 33 30 30 30 31 32 30,32

f. (001) sheets

"-'1(02-); .1[001]

375

C F G

9.8: [001]

26 359

- - +)

,,"

3.3

••

0

••••••••••••••••

A A 0

..

........................

.................................

1.[001] 4.1: [100] and [001]# ....................

F spiral

..................... G

{~

0

.................................

...................................

60, 233, 285, 359 44,46

..

.................................

46 49 49 291, 310, 311 196, 192

G

C

G

4.3

401

C: 142

f2 (Fig. 5f-13b)

4.3: 1.[111]

401

C: 100 C C C: 115

C

"'9.0: [001)

1 104

"

C

402

~.[~~~~ ................... ~g;

"-'8.9: [001]

l-3

I-i

(1

"'d ;0

0 "'d t;j

;0

l-3

I-i

t;j

0 ""'J

a:: >l-3 t;j

;0

C: 240

........................ .......................

Z

t;j

tn

4.4: 1.[001] 3.7, 3.9: varies 1.7 2.9 4.4

a::

o>-

104

I-i

>e-

U2

C1

I

f--l.

"

('.C

TABLE

5f-15.

ANTIFERROMAGNETIC MATERIALS STUDIED BY NEUTRON DIFFRACTION

(Continued)

en I

I--'-

Material

CuA u-I and related structures CrPt . MnNi . Mn-Ni . MnPd . Mn2Pd3 . MnllPd21 . Mn:..Pd . MnPt . Mn-Pt . CU3Au and related structures Pt3Fe . Pt-Fe . Pt3_z(Fe,Mn) 1+20' ••.•••.••.••.•• (Pt,Pd)3Fe . MnaPt .

Mn-Pt ...•..................... M n3(Pt,Rh) . (Mn,Fe)aPt . Mn3Rh . Pd 3Mn . o--Zns Mn . CU2Sb and related structures Cr2As . Fe2As . FeMnAs . Mn2As . Mn2Sb . Mn2Sbo. 7Aso.3 .

Crystal class and Neel temperature, K

C T: T T: T: T T .T: T

•••••••••••

813 643,653

(Fig. 5f-26) (Fig. 5f-26) (Fig. 5f-26)

973,970

(Fig. 5f-26)

•••••••••••

•••••••

C: 170

393 353 573 550t (308-388)

Moment (in J1.B) and direction

0

•••

••••

t

••

o

0

•••

0

•••••••

0

•••••••

0

••••••••

0

•••••••••••

0

•••••••

•••

••

•

complex triangular

................... .................... •••••

0

~

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

••

. ... ·· ... ·.0 .....•.•..•.. 4.3: varies

••••••

00.0

o

4.4: .1[001] 4.1, 4.3: J.. (001) 4.0: .1..[001]

•••••••

•••••

References

2.2: .1.. [001] 3.8, 4.0: .1 [001]

C(Fig. 5f-14) 0

.... ...... ...... C C: 475 (365) 523 (388) C C C C: 855 T: 170 C*: 150 T: T: T T: T: T

*

Magnetic structure

(Fig. 5f -26) (Fig. 5f-26)

1073

•••••••••••

00

•••••••••••••

...................

0

••••

00

••••••••••••••••••

3.4: [001] J..[001] 0

••••

•

••••••••••

0

••••••••

0

0

••••••••••

••••••

0

••••••

[001] 3.0: (112) 0

••••••••••••••••••••••••

319 205,313 313, 368, 369 212, 238, 313 176, 215, 239 212 212, 313 20, 313 20, 21, 313

o

tr:J

~

tr:J

(1

1-3

P:l ~

(1

~

1-3 ~

47,209,236 47 48 210, 232 241, 416

> Z

366

Z

t:;1

~

> ~

tr:J

0

.....

0

•••••••••••••••••••

. ........................

. ........................

triangular complex A (Fig. 2)

3.5: (112) 4.0(Mn), 0.2(Pd): J..[001] 2.5: .1..[001]

complex (Fig. 5f-27c) (Fig. 5f-27a) (Fig. 5f-27a) (Fig. 5f-27b) (Fig. 5f-27b) (Fig. 5f-27a)

1.I(Crl), 1.2(Crll): .1..[001] 1.0(FeI), 1.5(Fell): .1 [001] 0.2(Fe), 3.6(Mn): .1[001] 3.7(Mnl), 3.5(Mnll): J..[001] 2.1(Mnf), 3.9(Mnu): varies [001] 2.3(Mnl), 2.8(Mnll): .1.. [001]

241 241 240, 241 229, 241 103 292 397 207 421 34 17,404 34

1-3 ~

w

~

MnuCrO.lSb

1T

Mn1,97Cro.oaSb

1T

(135) (115) Mnl,vCrO,lSbuo!nO.Ob

1T

(Mn,Cr) 2Sb Rare-earth metals and alloys (see also Fig. 5f-28) Ce Dy

IT

Er

Eu Ro Nd

Pr Tb Tm

ErAI RoAI TbAI. TbMn2

. H: 12.5

. H: 179 (90t) . H: 80 (52) (20t) . C: 91 . H: 130 ("-'40) (,,-,20t) . H: 19 (7.5) . H: 25 . H: 226, 229 (216,221 t) . H: 56 (40) . 0: 10 . 0: 26t . 0: 72 . C: 40

TbNh

.

Dy-X (X = Er,Y) Er-X

.

(X = RO,Sc,Th,Y) Gd-X (X = Sc,Y)

~:

t .4.6. ...........

[001] 1120 1.4(MnI), 2.8(Mnu): [001] varies 35 ..L[OOl] 1.8(MnI), 3.7(Mnu): ..L[OOl] I 119 [001] ..L[OOl] 35

complex spiral ferromagnetic sinusoidal complex spiral spiral spiral distorted spiral distorted spiral sinusoidal (N dr) sinusoidal (Nd2) sinusoidal spiral ferromagnetic sinusoidal antiphase complex complex complex spiral

0.6: [001] 9.5..L[001]

408 409

o>

7.6: [001] 9.0

100, 106

t:z:l 1-3

I ~~ ................

. .

(Fig. 5f-27b) (Fig. 5f-27a) (Fig. 5f-27b) complex (Fig. 5f-27a) (Fig. 5f-27b) (Fig. 5f-27a)

: : : : : : : : : : : : : : :: :

0

~

~

298 1 222,

225, 393

~

o

~

t:z:l 1281

..........................

..L[OOl] [001] 7.0: [001] 7: ..L[001] 8.4: 1.[001] 8.8: 1.[001] 5.0-8.0(Tb), 1.1-2.5 (Mn) : ..L[OOl] 7.2(Tb): [l11J? ..L[111]? .................

Z

o

5.9: ..L[100] ..L[OOl] ..L[OOl] 9.5 2.3: [1010] 1.8: 30°, [1010] ••

~

0

............

S~~~~l~~' . . . . . . . . . . .. I :::::::::::::::::::::::::

105 152, 220, 393 219 55 54

56 129

~ ~

t:z:l

[J).

o

~

~

>

1-3 t:z:l ~ ~

> e-

[J).

162 113 113, 116, 117, 224, 274, 361 118

Y' I--l

00 I--l

TABLE

Sf-IS.

ANTIFERROMAGNETIC MATERIALS STUDIED BY NEUTRON DIFFRACTION

01

(Continued)

I .......

00

Crystal class and Neel temperature, K

Material

Ho-X (X = Sc,Tb,Th,Y) Nd-Th Pr-Th Tb-X (X = La,Lu,Sc,Th,Y) Tm-Y Transition metals and miscellaneous alloys and intermetallic compounds Cr

t-..:l

Magnetic* structure

Moment (in fJ.B) and direction

References

.

113, 116, 117, 224, 258

. . .

116 116 113, 114, 116, 117,220,226

.

113

tr:l

tot

tr:l

(")

1-3

~

10-0;

o

10-0;

.

Crl_"'Co"' , (z ~ 0.053) Crl_"'Fe"' (x ~ 0.047) Crl_"'Mn"' (x ~ 0.48) Cro. 995_",Mn", V 0.005. • • • • • • • • • • • • .• (x ~ 0.025) Crl_"'Ni"' (x ~ 0.01) Crl_"'Re"' (x ~ 0.008) Crl_"'V"' (x ~ 0.02) Crl_:l:X (X = V,Mn,Nb,Mo,Tc,Ru,Rh, Ta,W,Re) CrAu•........................ '1 "Y-CU:l:Mnl_"' , (0.05 ~ 0.31)

c.

1-3

311.5 (115)

.L(100)

27, 45, 53, 94, 97, 124, 172, 174, 186, 276, 356, 364, 394, 403, 406 158

C

sinusoidal sinusoidal (Fig. 5f-17a) tt

C

(Fig. 5f-17a) tt

28, 199

C

(Fig.5f-17a)tt

5~

C

(Fig. 5f-17aHt

228

0.6: (100)

277

(Fig. 5f-17a) tt

178, 227, 277

C C T: ""'400 C*

223

(Fig. 5f-17a) in a number of cases for x > ca. 0.01

f1 (Fig. 5f-13a)

[001]

386 43, 269

Z t;; ~

17~

158

C C

173,

~

>

178, 204, 243, 277

> o Z

tr:l 1-3 10-0; [fJ.

~

-y-Fe ....•.•............. , " FeGe Fer. 77Ge

C: 8 H: 410 H: 500t

FeGe2.....•..........••....... T: 270, 315 (Fe,Mn) 6Gea. . . . . . . . . . . . . . . . . .. FeaMn. . . . . . . . . . . . . . . . . . . . . . .. Feo. 69 M n o.al . . . . . . . . . . . . . . . . . . .. -y-Fe-Mn .... (Fe,Ni)aMn. . . . . . . . . . . . . . . . . . .. FeSn ......•................... FeSn2. . . . . . • • . . . . . . . . . . . . . . . .. a-Mn j ••••••••••••••••••

H C: 425 C: 435

C (Fig. 5f-2l)

0.7: 19°, [OOlJ 1.7: [001] 1.3(FeI), 1.1 (FeII) : .i [001] .i[OOlJ .i [001] .i[001]

pyramidal pyramidal

1.7: (Ill) 1.5: (111)

{g (Fig. 5f-21)

C C

H: 373 T: 384 C: 95 MnsGe , . . . . . . . . . . . . . . . . . . . . . .. H: 360 Mna(Pt,Rh). . . . . . . . . . . . . . . . . . .. C* (disordered) Mn5Sia H: 68 MnaSn. . . . . . . . . . . . . . . . . . . . . . .. H: 420 '"'-'(270) (Mn,Fe)aSn " H MnSnl. . . . . . . . . . . . . . . . . . . . . . .. T: '"'-'325 ("-'74)

Other compounds a-FeOOH

f1 (Fig. 5f-13a) (Fig. 5f-29) complex

,

O(Pbnm): 362, 403 Ho.D, C: 8 MnzN 0: 301 MnOOH. . . . . . . . . . . . . . . . . . . . . .. 0: "-'40 Mn2P H: 103 a-02. . . . . . . . . . . . . . . . . . . . . . . . .. M(C2/m): 24 TbD 2 • • • • • • • • • • • • • • • • • • • • • • • • • • C: 40 "There is also a small sinusoidal component in the region 74

(Fig. 5f-29) C (Fig. 5f-21) complex triangular f1 (Fig. 5f-13a)

1.5: .i[001] 1.6 0.1-1.8 2: varies [001]

sinusoidal triangular spiral

0.4(MnI), 1.2(Mnn): .i[001] 2.5: .iarbitrary [hkO]

f. (110) sheets" f. (110) sheets in sequence

2.3: [110] 2.3: [110]

f. (001) sheets unsolved complex spiral sinusoidal f. (100) sheets f. (100) sheets sinusoidal

5: [001]

K.

68,234,289 36, 381 230 391 200,201 230 418 202, 306 203, 2M>, 308, 364 229 237 254

229

~

o>Z

trJ 8

1-4

o

~

~

o

'i:l

l'1 ~

81-4

l'1

Ul

++ - -

< T < 90

2 5, 398 206 165

231 128, 134

o

a::"'" >-

1.6: [001]; 15°, [100] "-'O(MnI), 0.8(MnlI): .i (100) .i (001) [010] 7.9: [001]

167, 382 136 268 150 420 51, 121 11 136

8

l'1

~

> ~

tn

Ot

I

J--l

00

~

5-184

ELECTRICITY AND MAGNETISM

00

(0)

(b)

00

(c)

(d)

00

(e)

FIG. 5f-13. Ordering in f.c.c, structures: (a) type l(fl), (b) type 2(f2), (c) type 3A (f3A), (d) type 1A(flA), (e) type 4(f4).

• 0

A B

51,5S 52,56 53,57 54,58

6 Co ("'2o c)

F C

+ +

A G

+ +

+ +

+ +

+ +

5

FIG. 5f-14. Ordering in orthorhombic perovskite (ABOa) type structures. cubic cell (ac) is shown in heavy outline.

The ideal simple

5-185

MAGNETIC PROPERTIES OF MATERIALS

(b)

(0)

FIG. 5f-15. Ordering in spinel-type structures: (a) tetrahedral (A) nearest parallel, (b) schematic Yefet-Kittel canting of octahedral (B) moments.

n~ighbors anti-

Co

00

(a)

(b)

FIG. 5f-16. (a) CrSb and (b) CraS4 type magnetic structures. (all,ell) is shown in heavy outline in the latter cafe.

The ideal hexagonal cell

e

A B

SI

S2

0

Co

S3 $4

C

+ + + + + +

A

+

G

+

F

+

+

°0 (0)

FIG. 5f-17. (a) b.c. tetragonal antiferromagnetic MnF 2 type structure; (b) ordering in trirutile (A2B0 6) type structures. B is a nonmagnetic ion. The rutile cell is shown in heavy outline.

5-186

ELECTRICITY AND MAGNETISM bo

05 Co

T3 I I

0

G8

~------~4------~ 87

I I

0.0

Sl,S5 S2'S,

F C A G

06

I

X"

e x .. 0.5

1

+ + + +

+ +

salsa S4'S,

+

+

+ +

FIG. 5f-18. Ordering in olivine (Mg 2Si04) type structures projected on (IOO)-Pbnm orientation. Atoms 5 to 8 have been placed in idealized positions.

Co

00

00

(b)

(0)

(e)

FIG. 5f-19. (a) UBh, (b) UAs2, and (c) UOS type magnetic structures.

o

4_

o-

o

n

o

Co

n (

o

c)

(

•

C)

e

A

Ti

4,

o () (

u

n o

n (

4 C)

n

o

Co

°0

(d)

FIG. 5f-20. (a) Cr20a, (b) Fe20a, and (c) FeTiOa type magnetic structures projected on (110). (d) cation positions in corundum and related structures.

5-187

MAGNETIC PROPERTIES OF MATERIALS

---=--":> ~.:-. 3. Bozorth, R. M.: Phys. Rev. 96, 311 (1954). 4. Doring, W., and G. Simon: Ann. Physik 5, 373 (1960). See also: E. R. Callen and H. B. Callen: Phys. Rev. 139, A455 (1965); and W. J. Carr, Secondary Effects in Ferromagnetism, "Handbook der Physik," vol. 18/2, Springer-Verlag OHG, Berlin, 1966. 5. Callen, H. n., and N. Goldberg: J. Appl. Phys. 36, 976 (1965). 6. Bozorth, R. M., and T. Wakiyama: J. Phys. Soc. Japan 17, 1669 (1962). 7. Clark, A. E., B. F. DeSavage, N. Tsuya, and S. Kawakami: J. Appl. Phys. 37, 1324 (1966).

+

+

5-210

ELECTRICITY AND MAGNETISM

5f-21.

TABLE

MAGNETOSTRICTION CONSTANTS OF SOME CUBIC METALS

A100 X 10 6

A11l X 10 6 Reference

Metal 17K

,.....,293K

4K

17K

,.....,293K

.

... .

... .

....

. .. ... .

-30

-30

... .

20 24 -51 -54 25 7 40 92 26 28 43 33 39 51 52 18 15 13 12

-21 -22 -23 -23 -3 2 -14 -6 -14 -12 -10 -10 -8 -6 -3 -16 -13 -15 -14

4K

--Fe ..

........ ...... .........

'"

23

Ni .......................... Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe

,

+ 3.9 wt. % Si ............ 16 + 5.6 wt. % Si. ........... -8 + 4.6 wt. % Al. ........... 32 + 8.6 wt. % Al. ........... ... . + 5.32 wt. % Ge ........... .... + 6.07 wt. % V ........... "0

+ 14.4 wt. + 5.72 wt.

+ 7.24 wt. wt. + 14.7 19.9 wt. + 1.39 wt. + + 2.09 wt. + +

% V ...........

% Mo .......... Mo .......... Cr ........... Cr ........... Ti ........... Ti ........... Sn ........... Sn ...........

% % % % % 2.47 wt. % 3.76 wt. %

•

23 -57 16 -7 34 85 22 "0

•

... .

. ... ... .

••

0.

"0

••

0

••

0.

•

.. ... . . ' .. " .. "

••

0.

•

... . ... . . ' .. ••

0

••

0.

•

... .

. ... ....

-2 2 -20

. ... . ...

. ...

-28 -2 2 -19 -8 -20

••

0.

"0

••

0

'.0 •

"0

••

•

•

0.

... .

... . ... . .... ... . ... .

•

•. 0.

.... ••

0

•

••

0

•

.... . ... '.0

•

. ...

1 2 3 4 2 2 2 2 2 5 5 5 5 5 5 5 5 5 5

References for Table 5f-21 1. Carr, W. J., Jr., and R. Smoluchowski: Phys. Rev. 83, 1236 (1951). 2. Gersdorf, R., J. H. M. Stoelinga, and G. W. Rathenau: J. Phys. Soc. Japan 17, suppl. B-1, 342 (1962). 3. Bozorth, R. M., and R. W. Hamming: Phys. Rev. 89,865 (1953). 4. Corner, W. D., and F. Hutchinson: Proc. Phys. Soc. (London) 72, 1049 (1958). 5. Hall, R. C.: J. Appl. Phys. 31, 1037 (1960). TABLE

5f-22.

ROOM-TEMPERATURE MAGNETOSTRICTION

OF SOME MAGNETIC COMPOUNDS

Compound

Fea04. ....... Coo.sFe2.20 •.. NiFe204. .... Nio.aFe2.204.. MnFe204 .... YaFes012 .... DyaFe6012 ... HoaFes012 ...

Al00 X 10 6 Am X 10 6 Ref. -20 -590 -46 -36 -35 -1 -14 -6

80 120 -22 -4 -1 -3 -8 -4

1 2 3 2 2 4,6 5,6 5,6

Compound

EraFes012 .... EuaFes012 ... GdaFe,,012 ... TbaFe,,012 ... TmaFes012 ... YbaFe.012 ... CoO (10 kOe, 77 K) .....

>"100 X 10 6 Am X 10 6 Ref. 1 21 0 -3 1 1 9

-5 2 -3 12

-5 -5

..

5,6 6 6 6 6 6 7

References for Table 5f-22 Bickford, L. R., J. Pappis, and J. L. Stull: Phys. Rev. 99, 1210 (1955). Bozorth, R. M., E. F. Tilden, and A. J. Williams: Phys. Rev. 99, 1788 (1955). Smith, A. B., and R. V. Jones: J. Appl. Phys. 37, 1001 (1966). Clark, A. E., B. F. DeSavage, W. Coleman, E. R. Callen, and H. B. Callen: J. Appl. Phys. 34, 1296 (1963). 6. Clark, A. E., B. F. DeSavage, N. Tsuya, and S. Kawakami: J. Appl. Phys. 37, 1324 (1966). 6. Iida, S.: J. Phys. Soc. Japan 22, 1201 (1967). 7. Nakamichi, J., and M. Yamamoto: J. Phys. Soc. Japan, 17, suppl. B-1, 214 (1962). 1. 2. 3. 4.

5-211

MAGNETIC PROPERTIES OF MATERIALS TABLE

5f-23.

MAGNETOSTRICTION OF SOME HEXAGONAL CRYSTALS

T, K

Crystal

)..,'Y

X 10 6

)..,e

X 10 6

)..,la

)..,2 a

X 10 6

X 10 6

Ref.

-CO.......... · . MnBi. ........ Gd ........... Gd ........... Tb. Tb. Dy .... ....... Dy .. ......... Ho ........ , · . Ho. ·. Er .......... · . Er .......... · . 0

••••

00

·0

••••

•••

0.0

0

•••

••

••

'" H = 10 kOe

RT RT 0 200 0 150 0 200 0 150 0 150

50 -45* 105 14 8,500 4,700* 9,000 24* 2,300 3* -5,100t -1*

-233

70 37* 143 42 -2,600t

..... . . 34 4 15,000t

. ...... . .

.0.0

•

......... . . .... 0

0

•

•••

0

.·0 ..

•

......... . . .... •••

,

0"

..0 .......

5,500t 10* •••

•••

-110 -50* -105 -110 9,OOOt

.0.0

••

•

.. .

••

0

"

..0 .. ..0 ..

. . .... "

•

•••••

·0

. .. . .. ..

..0 .......

.. .. .

.. .. . .... . ••••

•••

•••

... .. . ....

0.

0.0.

•••

0.

1 2 3,4 3,4 5,6 5 7,8 7,8 9 9 10 10

t Extrapolated from paramagnetic region.

References for Table 5f-23 1. Bozorth, R. M.: Phys. Rev. 96, 311 (1954). 2. Williams, H. J., R. C. Sherwood, and D. L. Boothby: J. Appl. Phys. 28, 445 (1957). 3. Bozorth, R. M.: J. Phys. Soc. Japan 17,1669 (1962). 4. Alstad, J., and S. Legvold: J. Appl. Phys. 35, 1752 (1964). 5. Rhyne, J. J., and S. Legvold: Phys. Rev. 138, A507 (1965). 6. DeSavage, B. F., and A. E. Clark: Fifth Rare Earth Research Conference, Ames, Iowa, 1965. 7. Clark, A. E., B. F. DeSavage, and R. M. Bozorth: Phys. Rev. 138, A216 (1965). 8. Rhyne, J. J.: Ph.D. Thesis, Iowa State University, 1965. 9. Rhyne, J. J., S. Legvold, and E. T. Rodine: Phys. Rev. 154, 266 (1967). 10. Rhyne, J. J., and S. Legvold: Phys. Rev. 140, A2143 (1965).

·40 r----...-----r---"""T'"--~---.,;__--_r_--..,

20 1------,f--+-----+--+-~..,...._-.,::"Q:.____-+_--_+-----1 ~

~

s

Ot----+--r---t---+----+--....-.....,..""t---+-----1

ii:

et; -20

t----+-----i----+-----t----f-+----4d::---"~

I&J

z (l)

CI

~ ·40t--~-t-

QUENCHED ----i----+-----+---1ll...---I SLOWLY COOLED (ORDERED)

-60 '-...,...-'"""-----'-----''-_ _....L-_ _.....L. 30 40 50 60 70 80 NICKEL (0) !i'IG.

5f-34a. See legend OD page 5-212.

I----:~"...

90

6-212

ELECTRICITY AND MAGNETISM 200x166r--~~~:-:-:'::":"":":"=:-"""'!"':'"=-=-:::==......., - 0 WATER QUENCHED; DISORDERED 20°C/HR;ORDERED

---x

-< o

1501---+--_t_--+--t-~C"f=:::::=~

:z o

«

~ 100.---+---+--~fF_-+--_t_~__1 :z i=

o u

0: ..... g

50t----+-----,...=t--,..---f-

(/)

I.&J

:z

C)

«

::iii:

-500

10 20 30 40 50 60 WEIGHT PERCENT COBALT IN IRON (bl

140 10-6 ~

120

V+'

100

/

80

~'OOI

/

/

o -20

-40

V

~/

I

/

'/

i/to---. V 10

20

~m

30

-----40

~

50

6OWt-%70

Co(c)

FIG. 5f-34. Saturation magnetostriction constants of iron-nickel. iron-cobalt, and nickel.

cobalt alloys. (a) Iron-nickel, from R. M. Bozorth and J. G. Walker: PhY8. Rev. 89, 624 (1953). (b) Iron-cobalt from R. C. Hall: J. Appl. PhY8. Suppl. 31, 1578 (1960). (c) Nickel-cobalt; X taken from M. Yamamoto and T. Nakamichi: J. PhY8. Soc. (Japan) 13,228 (1958); 0, 6 from R. C. Hall: J. Appl. PhY8. 30,816 (1959). (Figure taken from "Secondary Effect8 in Ferromaqnetiem," W. J. Carr, "Handbuch del' PhY8ik," Vol. XVIII, 12 Springer-Verlao, OHG, Berlin, 1966.

+,

5-213

MAGNETIC PROPERTIES OF MATERIALS 40

_

3 -Hc·le........

10 6 30

Cf)

UJ

J

::>

....J

455

~

0 UJ

20

!;i

~

t:'fj ~ ~

> er:tl

cr t-:) ~

"1

5-218

ELECTRICITY AND MAGNETISM TABLE

5f-30.

HALL CONSTANTS OF SINGLE CRYSTALS

B in basal plane Element

Ref.

T,K

u,

X 1011, m 3/coul

Gd .........

19ft

Dy .........

20

Tb .........

21

Fe .......... Co .......... Ni ..........

22 2, 23 23

240 200 150 100 50 148 119 78 39 162 119 79 40 4 to 300 4 to 300 4 to 300

52.3 8.7 -30.1 -40.0 -34.7

-

29.8 -3.5 -11.7 -15.8 -10 to 1 10 5

R. X 1011, m 3/coul

-872 -367 -161 -167 -29 117 210 130 22 163 200 82.2 5.7 -1 to 50 -10 to 10 50

B along c axis*

s,

X 1011, m 3/coul

-27.2 -9.4 8.5 25.0 38.9

R. X 1011, m t/coul

-4,080 -3,200 -1,900 -890 -170

* Applies only to rare-earth elements.

t See also Volkenshtein [26]. t This reference contains data for this alloy for temperature(s) additional to those given here. References for Tables 5f-26 through 5f-30 1. Soffer, S.: Thesis, Carnegie Institute of Technology, 1964; see also S. Soffer, J. A. Dreesen, and E. M. Pugh: Phys. Rev. 140, A 668 (1965). 2. Dubois, J.: Thesis, Institute de Physique Experimentale de I'Universite de Lausanne; see also J. Dubois and D. Rivier: To be published. 3. Huguenin, R.: Thesis, Institute de Physique Experimentale de I'Urriversite de Lausanne, 1964; see also R. Huguenin, and D. Rivier: Helv. Phys. Acta 38,900 (1965). 4. Ehrlich, A. C., and D. Rivier: J. Phys. Chern. Solids 29, 1293 (1968). 5. Smit, J., and J. Volger: Phys. Rev. 92, 1576 (1953). 6. Jellinghaus, W., and M. P. de Andres: Ann. Physik 5, 187 (1960). 7. Foner, S .• and E. M. Pugh: Phys. Rev. 91, 20 (1953). 8. Cohen. P.: Thesis, Carnegie Institute of Technology, 1955; A. 1. Schindler: Thesis, Carnegie Institute of Technology, 1950; see also A. 1. Schindler and E. M. Pugh: Phys. Rev. 89, 295 (1953); and E. M. Pugh: Phys. Rev. 97, 647 (1955). 9. Dreesen, J. A., and E. M. Pugh: Phys. Rev. 120, 1218 (1960). 10. Smit, J., and J. Volger: Private communication. 11. Dreesen, J. A.: Phys. Rev. 125, 1215 (1962). 12. Sanford, E. R., A. C. Ehrlich, and E. M. Pugh: Phys. Rev. 123, 1947 (1961). 13. Ehrlich, A. C., J. A. Dreesen, and E. M. Pugh: Phys. Rev. 133, A 407 (1964). 14. Lavine. J. M.: Phys. Rev. 123, 1273 (1961). 15. Beitel, F. P., and E. M. Pugh: Phys. Rev. 112, 1516 (1958). 16. Carter, G. C., and E. M. Pugh: Phys. Rev. 152, 498 (1966). 17. Volkenshtein, N. V., and G. V. Fedorov: Soviet Phys.-JETP 11, 48 (1960). 18. Kooi, C.: Phys. Rev. 95, 843 (1954). 19. Lee, R. S.: Private communication; see also R. S. Lee and S. Legvold: Phys. Rev. 162, 431 (1967). 20. Rhyne, J. J.: Phys. Rev. 172,523 (1968). 21. Rhyne, J. J.: J. Appl. Phys. 40, 1001 (1969). 22. Dheer, P. N.: Phys. Rev. 156,637 (1967). 23. Volkenshtein, N. V., G. V. Fedorov, and V. P. Shivokovskii: Phys. Metals Metallo(}. 11, 151 (1961). 24. Okamoto, T., H. Tange, A. Nishomuva, and E. Tatsumoto: J. Phys. Soc. Japan 17, 717 (1962). 25. Volkenshtein, N. V., and G. V. Fedorov: Phus. Metals Metalloy. 9, 21 (1960). 26. Volkenshtein, N. V., I. K. Grigovova, and G. V. Fedorova: Soviet Physics-JETP 23, 1003 (1966).

MAGNETIC PROPERTIES OF MATERIALS

5-219

24 r--.....,...--~----r"--~----,.---.------.----r-----,

a C;::~~~:i:n:o:o=oD"~-1---~'{i]Jrn=:;5O=a::=80 290 ..... 480 70 ..... 300

~3,870

.........

.. '13',060' 4,700 8,660 13,100 10,860 9,050 5,235 3,520 10,200 9,780 12,400 7,700 7,330 6,860 4,450 6,700 1,610 10,500 10,600 5,320 6,320 1,340 ... '1',340' 1,570 · . 43',200' ·~45·,OOO·

· . 38',600' 28,700 36,500 26,600 5,550 23,800 25,800 13,200 12,060 13,900 4,100 9,460 11 ,500 12,400 11,930 13,100 12,100 14,900 14,000 14,560 ......... ......... 24,700 ......... .. 24',500' 28,700 · . 23',400' ......... .. 27',500'

90-500 500 50 ..... 300 >300 50-300 >8 >300 >155 95-300 77-350 . ":>'100" >225 210-690 >65 >100 >560 >11 >19 >20

. i55~670' 300 76 540"

3,450 4,370 3,700

21

285'':''; 700 4,450 ",,4,900

65

198 2,240 525 3,060 6,700 ""8,600 625 5,750

c 7.81 8.11 7.8 1.934 13.7 13.7 ]3.8 13.6 4.05 0.383

" }·.86" 1.47 4.26 3.93 4.17 1.91 2.54 ""4.10 3.01 4.21 4.90 3.40 1.80 4.60 4.58 4.34 4.36 1.861 1. 76 1. 75 1.53 1. 70 1.82 1.50 1.37 1.34 1.31 1.01 1.24 1.69 1.60 1.62 1.64 12 10.8 11.86 4.87 6.64 7 .2 7 .2 7 .2 6.33 1.35 1.21 1.35 1.15 1.36 1.36 1.30 1.47 1. 31 1.45 1.06 0.24 1.32 2.43 2.92 0.21 1.67

(Continued)

fJ,K

-0.4 -2 -279.6 12 -14 -8

-7 22

-7 -350 -750

-2

-40 3 -380 -10 82 8 -4 -680 -188 -480 20 -23 "" -260oK -22 -219 -57.4 -56 10 32 -42 -44 28 71 -97

o

21 -11 -29.4 4

-71

-44 35 5 -16 148

······0· . .. ':-"ii:i -62 -35 25 -29 -147 5 -122 -108 -101 -290 -185 -170 -140 -68 -42 -20 +10

• Compiled by E, E. Anderson and A. Stelmach, Clarkson College of Technology.

7.90 8.06 7 .9 3.92 10.5 10.5 10.5 10.43 5.7 1. 75 3.18 3.84 3.43 5.84 5.61 5.78 3.91 4.51 5.98 4.91 5.80 6.26 5.21 3.78 5.5 6.05 5.88 3.87 3.75 3.74 3.50 3.69 3.81 3.47 3.32 3.27 3.24 2.86 3.15 3.69 3.57 3.60 3.62 9.82 9.28 9.74 6.25 ""7.6 7.28 7.56 ""7.6 ",,7.6 7 .11 3.29 3.12 3.29 3.03 3.30 3.31 3.30 3.45 3.25 3.40 2.92 1.39 3.25 4.40 4.83 1.3 3.66

5-228

ELECTRICITY AND MAGNETISM

References for Table 5f-34 1. Benoit, R.: Compt. rend. 231, 1216 (1950). 2. Lotgering, F. K.: Philips Research Repts. 11, 190, 337 (1956). 3. Johnson, A. F., and H. Grayson-Smith: Can. J. Research 28A, 229 (1950). 4. Elliott, N.: J. Chem. Phys. 22, 1924 (1954). 5. Stickler, J. J., S. Kern, A. Wold, and G. S. Heller: Phys. Rev. 164,765 (1967). 6. Hansen, W. N., and M. Griffel: J. Chem. Phys. 30,913 (1959). 7. Munson, R. A., W. DeSorbo, and J. S. Kouvel: J. Chem. Phys. 47, 1769 (1967). 8. Yaguchi, K.: J. Phys. Soc. Japan 21, 1226 (1966). 9. Davidson, D., and L. A. Welo: J. Phys. Chem. 32, 1191 (1928), 10. Iandelli, A.: R. C. Accad. Naz. Lincei (Italy) 30, 201 (1961). 11. Thoburn, W. C., S. Legvold, and F. H. Spedding: Phys. Rev. 110, 1298 (1968). 12. Yaguchi, K.: J. Phys. Soc. Japan 22,673 (1967). 13. Meisenheimer, R. G., and J. D. Swalen: Phys. Rev. 123, 831 (1961). 14. Klemm, W., and E. Krose: Z. anoro. Chem. 253, 226 (1947). 15. Kouvel, J. S., C. C. Hartelius, and L. M. Osika, J. Appl. Phys. 34, 1095 (1963). 16. Sanchez, A. E.: Rev. acado cienc. exaci., fie. y nat. Madrid 34, 202 (1940). 17. Kizhaev, S. A., A. G. Tutov, and V. A. Bokov: Fiz. Tverd. Tela 7, 2868 (1965). 18. Busch, G., A. Menth, O. Vogt, and F. Hulliger: Phys. Letters 19, 622 (1966). 19. Perakis, N., and F. Kern: Phys. Kondens. Materie 4, 247 (1965). 20. Dawson, J. K.: J. Chem, Soc. 1951, 429. 21. Elliott, N.: Phys. Rev. 76, 431 (1949). 22. Schilt, A. A.: J. Am. Chem. Soc. 85,904 (1963). 23. Watanabe, T.: J. Phys. Soc. Japan 16,1131 (1961). 24. Bizette, H., C. Terrier and B. Tsai: J. Phys. Radium 20, 421 (1959). 25. Singer, J. R.: Phys. Rev. 104, 929 (1956). 26. Benoit, R.: J. Chim. Phys. 52, 119 (1955). 27. Boravik-Romanov, A. S., V. R. Karasik, and N. M. Kreines: Zh. Eksp. i Tear. Fiz. 31, 18 (1956). 28. Cable, J. W., M. K. Wilkinson, and E. O. Wollan: Phys. Rev. 118, 950 (1960). 29. Wilkinson, M. K., J. W. Cable, E. O. Wollan, and W. C. Koehler: Phys. Rev. 113,497 (1959). 30. Frazer, B. C. and P. J. Brown: Phys. Rev. 125, 1283 (1962). 31. Guha, B. C.: Proc. Roy. Soc. (London) A206, 353 (1951). 32. Ishakawa, Y., and S. Akimoto: J. Phys. Soc. Japan 13,1298 (1958). 33. Trapp, C., and J. W. Stout: Phys. Rev. Letters 10, 157 (1963). 34. Escoffier, P., and J. Gauthier: Compt. rend. 252, 271 (1961). 35. Blasse, G., and J. F. Fast: Philips Res. Repts. 18, 393 (1963). 36. Farrell, J., and W. E. Wallace: [nary. Chern, 5, 105 (1966).

for axial symmetry. Here, D, A, and B are constants and I is the nuclear spin. D is determined by the crystalline electric field, and A and B by the hyperfine coupling. gil and g.l are the spectroscopic splitting factors for the z direction (parallel to the crystal-field symmetry axis) and in the xy plane, respectively. Terms representing the nuclear electric quadrupole interaction (for I > .}) and the direct coupling of the nuclear magnetic moment with the external field ha;e been omitted from Eq. (Sf-I). The parameters in the spin Hamiltonian are determined by electron paramagnetic resonance (epr) spectroscopy, and the correctness of the assumed crystal field symmetry can be checked by studying the angular dependence of the resonance pattern. Frequently the line width due to magnetic dipole interaction is comparable with the fine structure and hyperfine structure (hfs) separations. Then the established practice is to dilute the subject salt with an isomorphous diamagnetic salt. In most cases the electric field acting on the ion remains unaltered, but there are instances of drastic modifications occurring. If all the ions in the crystal have the same symmetry axis, the susceptibility will be given by the formulas [1]. _ N

XII -

_ N Xl. -

2

2

gil JJ.B 2

fl.i JJ.B

8(8 + 1) [1 D(28 - 1) (28 3kT 15kT

2

8 (8 + 1) [1 3kT

+ D(28

- 1)(28 30kT

+ 3)]

+ 3)]

(5f-2)

5-229

MAGNETIC PROPERTIES OF MATERIALS

J

er l +AN) MnS+

COZ+

---,...l!.L

212

,!!L~==

I

13 x 4

I

SIX 7x4 Ir--~:=:::: DOUBLETS ~~ SPLIT BY \ 115 '" 200 CM-1 \ 112 \ , - - FIVE '31(4 21(6 -_FREE 10N'-:: FREE 10N~/ SINGLETS CUBIC 2 x6 -, ~;l 2 CUBIC 2 gll(!)2[1

+ exp

(o/T)J

Adiabatic demagnetization studies have been carried out down to 0.02 K by Johnson and Meyer [84]; T; = 0.05 3 K at SIR = 0.48. Meyer and Smith [86] have measured the specific heat between 0.6 and 20 K. They find that 0 = 6.7 K and also observe an excess specific heat in the region of the maximum of the Schottky anomaly. This has been explained by Becker and Clover [87] in terms of an anomalous phonon spectrum arising from the spin-phonon interaction, taking account of the substantial broadening of the lowest energy levels. 15. Neodymium Magnesium Nitrate. 2Nd(N0 3)a·3Mg(N0 3h·24H 20; gram-ionic weight, 768.99; density, ; Nd 3 +; 4f3; 4/;. The 4/; ground state is split by a crystalline electric field of C 3v symmetry [66] into five Kramers doublets. At liquid-helium temperatures only the lowest of these is populated. This is a mixture of states with J z = ±i, ±i, ±t- gil = 0.45; gl.. = 2.72 [87J. The low-temperature thermal and magnetic behavior is modified by nuclear hyperfine coupling. Nd 143 (12.20 percent) and Nd 14s (8.30 percent) both have I = i, resulting in a contribution to the entropy of 0.205R In 8 or 0.426R. The hfs parameters in the spin Hamiltonian are: B 143 = 0.0312, B 145 = 0.0194, A 143 rv 0.005, A U 6 rvO.003 cm". Adiabatic demagnetization experiments down to 0.06 K have been made by Cooke, Meyer, and Wolf [31,34]. Deviations from Curie's law begin at 0.1 K, owing to the influence of the hfs. b = 8.74 X 10- 4 K2. Calculated values are: b, = 3.0 X lO- s, b14 3 = 6.53 X 10- 4, b145 = 1.70 X 10- 4 K2. Spin-lattice relaxation in the liquid-helium region has been investigated by Hudson and Mangum [88] and down to 0.3 K, in lanthanum-diluted crystals, by Jeffries et al. [89]. The Zeeman effect in the

MAGNETIC PROPERTIES OF MATERIALS

5-237

optical spectrum has been studied in detail by Dieke and Heroux [90]. Their values for gil and Yl. for the ground state (0.420 and 2.629, respectively) are in reasonably good agreement with the epr data. They obtain 3.38 and zero for the Y values of the J = ± ~ level, which is found to lie at 33.13 cm- I • 16. Neodymium Ethylsulfate. Nd(C 2H6S0 4)a·9H20; gram-ionic weight, 681.80; density, 1.872; Nd3+; 4f3; 4[;. The 4[ ground state lies about 1,800 cm- I below the next higher level. In a crystal field of C,1l symmetry it is split into five doublets and only the lowest is effectively occupied at 20 K and below. This is a mixture of the basic J. states I ±i) and I ± j) [79c]. The first excited doublet, I +j), lies at 150 cm- I (see below). There is one ion in the unit cell. Detailed paramagnetic resonance investigations have been made by Bleaney, Scovil, and Trenam [91], who find discrepancies between the strong field and weak field results. The Hamiltonian of Eq. (5f-I) cannot be fitted to the latter. A possible explanation is that given by Stevens to account for the similar but much larger effects in gadolinium ethyl sulfate; viz., here one is not dealing with a static crystalline electric field, but the equilibrium positions of the surrounding dipoles may depend upon the state of the magnetic ion. gil = 3.535; gl. = 2.072. The hfs parameters in the spin Hamiltonian are: A w = 0.0380, A 146 = 0.0236, B w = 0.0199, B 146 = 0.0124 cm"". (See also Erickson [92]). Optical transitions and the Zeeman effect have been studied by Dieke and Heroux [90], who obtain gil = 3.50 and Yl. = 2.06 for the lowest doublet. The next doublet lies at 149.64 cm", Low-temperature studies, between 0.015 and 2 K, were made by Meyer [93] (b = 1.13 X 10- 3 K2), and in the liquid-helium region by Roberts, Sartain, and Borie [94] (b = 1.09 X 10- 3) . The theoretical value for b. is 0.176 X 10- 3- K2, and from the epr data one calculates bw = 6.073 X 10- 3, b U 6 = 2.348 X 10- 3 K2; these together lead to a theoretical value of 1.11 X 10- 3 K2 for b. T r ::::: 0.016 K at SIR r v 0.45. The theory of dipole-dipole interaction in anisotropic crystals and of the added effect on x of the hfs developed by Daniels [82] has been applied to this salt by Meyer. The effect is much larger for the "parallel" direction (2t percent correction at 0.5 K) than for the "perpendicular" direction (2 percent correction at 0.2 K). Blok, Shirley, and Stone [95] have determined the susceptibility temperature scale down to 0.01 K, using both gamma-ray heating and nuclear orientation methods. Their values of T agree with those of Meyer [93] down to 0.025 K. The specific heat between 1.5 and 20 K has been measured by Meyer and Smith [86]. The lattice contribution CI showed the same features here as in several rare-earth ethyl sulfates; viz., Cz/T3 fell rapidly between 1.5 and 3 K, then rose again, and passed through a broad maximum at 8 to 9 K, falling slowly with further increase of temperature. 17. Gadolinium Sulfate. Gd2(S04)a·8H20; gram-ionic weight, 373.42; density, 3.010; Gd 3 ; 4J7; 8S . The free ion having an 8S ground state, the effect of the crystalline electric field is small and the splittings produced are only of the order of 1 cm"". Hebb and Purcell [96] showed that the eightfold degenerate ground level is split by a cubic field into two doublets and a quadruplet, and specific-heat data have always been interpreted on this basis. Epr studies at room temperature by Bogle and Heine [97] on a 200: 1 samarium-diluted crystal showed, however, that there are four doublets lying at 0, 0.20, 0.48, and 0.82 cm- I , respectively. There are two magnetically inequivalent ions in the unit cell, the crystal b axis being the twofold axis. g = 1.99 and is isotropic. The spin Hamiltonian can be written most conveniently 6

en

TABLE 5f-35. PROPERTIES OF PARAMAGNETIC SALTS

Paramagnetic salt

1. Titanium cesium alum

2. 3. 4. 5. 6. 7. 8. 9. 10. 11.

TiCs(SO.)2·12H 2O Chromic potassium alum CrK(SO.)2·12H tO Chromic methylammonium alum Cr(CH 3NH3 ) (SO.h·12H 2O Vanadous ammonium sulfate V(NH.MSO.)2·6H 2O Ferric ammonium alum Fe(NH.) (SO.)2·12H 2O Ferric methylammonium alum Fe(CH 3NH 3)(SO.)2·12H 2O Manganous ammonium sulfate Mn (NH.)2 (SO.h·6H 2O Cobaltous ammonium sulfate Co(NH.MSO.)2·6H tO Cobaltous fluosilicate CoSiF 6·6H 20 Nickel fluosilicate NiSiF 6·6H 2O Cupric potassium sulfate CuK 2(SO.)2·6H 2O

12. Cupric sulfate CuSO.·5H 2O

Gramionic weight M, g

Roomtemp. density p, g/cm 3

589

2.019

g values

gil

gJ. 499

~

~

00

1.83

Curie const.

= 1.25 = 1.14 1.98

492

1.645

1.976

387

.........

1.95

D, cm- 1

Spec. heat const b, Kt

0.130 a

............

3.9 X 10-1

1.84

0.135 0.075b

1.8 X 10-1

0.087

1.9 X 1O-1c:

G, emu/g-ion

1.83 1. 78

0.15 s

5.6 X

d

1.71

2.003

4.39

0.016/

496

1.659

2.003

4.39

0.188"

391 395

1.83 1.902

4.38 2.95'

0.027/

309

2.113

2.00 = 6.45 gJ. = 3.05 gil = 5.82 g1. = 3.44

= 3.18

................ A:

309 442

2.134 2.22

250

2.281

g., gil g.

2.29 = 2.14 = 2.040 = 2.36

......................

Gil

1O-~

'"1. 3 X 10-1

1

................ i

Gil = 0.480 C.r. = 0.407 q

-0.12" ..................

::0 .... (1

.... ~

~

>

Z

t::1 ~

0.45

o>

3.2 X 104.2 X 10-3

1

(18.5 X 10-3 ) '

CJ.=1.11 1.31 m 0.4451'

~

tr.1

(1 ~

482

gil

tr.1

1.3 X 10-2 5.7 X 10-4

Z

tr.1 ....>-3 ta ~

13. Cerous magnesium nitrate Ce2Mg3(NOa) 12· 24 H 2O 14. Cerous ethylsulfate Ce(C 2HsSO.)3·9H 2O 15. Neodymium magmesium nitrate Md 2Mg 3(N03)12·24H2O 16. Neodymium ethyl sulfate Nd(C 2H sSO.k9H 2O 17. Gadolinium sulfate Gd 2(SO.k8H2O "txll

+h

r

765

2.10

gil

ss 678

1.839

~ >

gil =

as. = 769

2

682

1.872

gil g1. gil g1.

= = = =

0.026 1.840 3.80 0.22" 0.45 2.72 3.535 2.072

CII C1. CII C 1. CII C1.

= = = = = =

1.35 0.0045 0.019 0.694 1.170 0.402

.................

6 X 10- 6

..................

1.12 X 10- 3

..................

8.74 X 10- 4•

..................

11.1 X 1O- 4t

a::

:> Q

Z

373

3.010

1. 99

Two types of ion below 160 K. c 1.7 X 10- 2 using epr data. tJ E = 0.04, em-I. e b./R, Stark contribution (calculated from epr data). I a = -0.0128 cm- I ; splitting sensitive to temperature and dilution. Q a = 0.010 cm- I ; splitting little affected by dilution. 10 E = 0.005, a = 0.0008, A = 0.0093 cm- I ; D and E sensitive to temperature and dilution. • Along K I axis. i A = 0.0245, B = 0.002 cm- I • Tetragonal axes 68 deg apart. k A = 0.0184, B = 0.0047 em-I. I Conflicting experimental data. m Weiss 8,..., -0.07 K. .. D varies with temperature and dilution. o Rhombic symmetry; z axes 84 deg apart. P For powder. Weiss 8 ~ 0.035 K. q Tetragonal axes ~o deg apart. Weiss 8,..., -0.6 K. r Second doublet at 4.6 cm- I with gil = 1.0, g.L = 2.2; order of levels inverted in diluted salt. • Mostly due to hfs. I Mostly due to hfs, " E = 0.013, F = 0.004 cm ", Spectrum observed at room temperature. • All experiments give one or the other of these two figures. b

C1. = 0.317

7.80

I

0.0633 11

0.32 or 0.37"

~

8 t-;

o

'"d

~

o

'"d ~

~

t-;

~

17l

o

~

a::

:> 8

~

l;O 1-1

:> e-

17l

!

~ ~

5-240

ELECTRICITY AND MAGNETISM

where the P "m are operators [26,79c] which have the same transformation properties as the corresponding spherical harmonics Y"m, and B"m are coefficients determined by fitting to the observed spectrum. The findings are: b 2 0 = 3B 2° = 0.0633, b 2 2 = 3B 2 2 = 0.038, b4 0 = 60B 4 0 = -0.0013 cmr". The Stark specific-heat term be is calculated to be 0.195 K2 from the expression 21 (b 20 ) 2 + 7(b 2 2 ) 2 + 77(b 4 0 ) 2, in kelvins, while b, = 0.10 K2; adding, one finds that b = 0.30 K2. The last figure is notably smaller than that which is obtained from relaxation experiments [98] between 77 and 290 K. These give bRIG = 3.9 X 10~ Oe 2, and taking GIR = 9.38 X 10- 8 K 20 e - 2, b = 0.37 K2. There are discrepancies among different measured values at low temperatures, viz., 0.32 from relaxation experiments [99-101], 0.37 from adiabatic demagnetization [102J and calorimetry [103J. The T-2 dependence of the specific heat breaks down below 3 K, owing to the large value of D (= b 20), and relaxation-type determinations involve rather large corrections for saturation effects owing to the large Curie constant. Giauque and MacDougall [104J used this substance for their pioneering magnetic cooling experiments in 1933. Because of its large specific heat it is most useful as a cooling substance in the 0.1 to 1 K range (compare ferric methylammonium alum). Van Dijk [105] has measured the departures from the Curie Law down to 0.22 K. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. '31. 32. 33. 34.

Bleaney, B.: Phys. Rev. 78,214 (1950). Van Vleck, J. H.: J. Chern. Phys. 5,320 (1937). Daniels, J. M.: Proc. Phys. Soc. (London), ser. A, 66,673 (1953). Bleaney, B., G. S. Bogle, A. H. Cooke, H. J. Duffus, N. C. M. O'Brien, and K. W. H. Stevens: Proc. Phys. Soc. (London). ser. A, 68, 57 (1955). van den Handel, J.: Thesis, Leiden University, 1940. Benzie, R. J., and A. H. Cooke: Proc. Roy. Soc. (London), ser A, 209, 269 (1951). Kurti, N., P. Laine, and F. Simon: Com-pi, rend. 204, 675 (1937). Bleaney, B.: Proc, Roy. Soc. (London), ser. A, 204, 203 (1950). Vilches, O. E., and J. C. Wheatley: Phys. Rev. 148, 509 (1966). Bleaney, B., and K. D. Bowers: Proc. Phys. Soc. (London), ser. A, 64, 1135 (1951). de Klerk, D.: Thesis, Leiden University, 1948. Daniels, J. M., and N. Kurti: Proc. Roy. Soc. (London), ser. A, 221, 243 (1954). Ambler, E., and R. P. Hudson: Phys. Rev. 95, 1143 (1954). Beun, J. A., A. R. Miedema, and M. J. Steenland: Physica 23, 1 (1957). Kapadnis, D. G.: Physica 22, 159 (1956). de Klerk, D., M. J. Steenland, and C. J. Gorter: Physica 15, 649 (1949). Durieux, M., H. van Dijk, H. ter Harmsel, and C. van Rijn: "Temperature: Its Measurement and Control in Science and Industry," vol. 3, part 1, p. 313, Reinhold Publishing Corporation, New York, 1962. de Klerk, D., and R. P. Hudson: Phys. Rev. 91, 278 (1953). Gardner, W. K, and N. Kurti: Proc. Roy. Soc. (London), ser. A, 223, 542 (1954). Hudson, R. P., and C. K. McLane: Phys. Rev. 95, 932 (1954). Ambler, E., and R. P. Hudson: J. Chern. Phys. 27, 378 (1957). Baker, J. M.: Proc. Phys. Soc. (London), ser. B, 69,633 (1956). Hutchison, C. A., and L. S. Singer: Phys. Rev. 89,256 (1953). Kikuchi, C., H. M. Sirvetz, and V. W. Cohen: Phys. Rev. 92, 109 (1953). Bleaney, B., D. J. E. Ingram, and H. K D. Scovil: Proc. Phys. Soc. (London), ser. A, 64, 601 (1951). Bowers, K. D., and J. Owen: Repts. Proqr. Phys. 18, 304 (1955). Benzie, R. J., and A. H. Cooke: Proc. Phys. Soc. (London), ser, A, 63, 213 (1950). Meijer, P. H. E.: Physica 17,899 (1951). Ubbink, J., J. A. Poulis, and C. J. Gorter: Physica 17, 213 (1951). Kimura, 1., and N. Uryu: J. Phys. Soc. Japan 23, 1204 (1967). Cooke, A. H., H. Meyer, and W. P. Wolf: Proc. Roy. Soc. (London), ser, A. 233, 536 (1956). Cooke, A. H.: Proc. Phys. Soc. (London), ser. A, 62, 269 (1949). Steenland, M. J., D. de Klerk, M. L. Potters, and C. J. Gorter:Physica 17,149 (1951). Cooke, A. H .• H. Meyer, and W. P. Wolf: Proc. Roy. Soc. (London), ser. A, 237, 395 (1956),

MAGNETIC PROPERTIES OF MATERIALS

5-241

35. Benzie, R. J., A. H. Cooke, and S. Whitley: Proe. Roy. Soc. (London), ser. A, 232, 277 (1955). 36. van der Marel, L. G., J. van den Broek, and C. J. Gorter: Physica 23, 361 (1957). 37. Bleaney, B., and R. S. Trenam: Proc. Roy. Soc. (London), ser, A, 223, 1 (1954). 38. Cooke, A. H., H. Meyer, and W. P. Wolf: Proc. Roy. Soc. (London), ser. A, 237,404 (1956). 39. Croft, A. J., and R. H. B. Exell: Proc. Roy. Soc. (London), ser, A, 262, 110 (1961). 40. Bleaney, B., and D. J ..E. Ingram: Proc. Roy. Soc. (London), ser. A, 205,336 (1951). 41. Abragam, A., and M. H. L. Pryce: Proc. Roy. Soc. (London), ser. A, 206, 173 (1951). 42. Bijl, D.: Physica 16, 269 (1950). 43. Steenland, M. J., L. C. van der Marel, D. de Klerk, and C. J. Gorter: Physica 15, 906 (1949). 44. Dabbs, J. W. T., and L. D. Roberts: Phys. Rev. 95, 970 (1954). 45. Miedema, A. R., J. van den Broek, H. Postma, and W. J. Huiskarnp: Physica 25,1177 (1959). 46. Bleaney, B., K. D. Bowers, and D. J. E. Ingram: Proc. Roy. Soc. (London), ser. A, 228, 147 (1955). 47. Bleaney, B., and D. J. E. Ingram: Proc. Roy. Soc. (London), ser. A, 208, 143 (1951). 48. Malaker, S. F.: Phys. Rev. 84, 133 (1951). 49. van den Broek, J., L. C. van der Marel, and C. J. Gorter: Physica 25, 371 (1959). 50. Garrett, C. G. B.: Proc. Roy. Soc. (London), ser. A, 206, 242 (1951). 51. Penrose, R. P., and K. W. H. Stevens: Proc. Phys. Soc. (London), ser. A, 63,29 (1950). 52. Griffiths, J. H. E., and J. Owen: Proc. Roy. Soc. (London), ser. A, 213,459 (1952). 53. Hill, J. S., H. Meyer, and J. H. Milner: Cryogenics 2, 170 (1962). 54. Svare, I., and G. Seidel: Phys. Rev. 134, A172 (1964). 55. Giauque, W. F., E. W. Hornung, G. E. Brodale, and R. A. Fisher: J. Chem. Phys. 46, 1804 (1967); 47, 2685 (1967). 56. Bleaney, B., R. P. Penrose, and B. I. Plumpton: Proc. Roy. Soc. (London), ser, A, 198, 406 (1949). 57. Steenland, M. J., D. de Klerk, J. A. Beun, and C. J. Gorter: Physica 17. 161 (1951). 58. Bagguley, D. M. S., and J. H. E. Griffiths: Proc. Roy. Soc. (London), ser, A, 201, 366 (1950). 59. Krishnan, K. S., and A. Mookherji: Phys. Rev. 54, 533, 841 (1938). 60. Benzie, R. J., and A. H. Cooke: Proc. Phys. Soc. (London), ser. A, 64, 124 (1951). 61. Polder, D.: Physica 9,709 (1942). 62. Giauque, W. F., R. A. Fisher, E. W. Hornung, and G. E. Brodale: J. Chem. Phys. 48, 3728, 3906 (1968). 63. Geballe, T. H., and W. F. Giauque: J. Am. Chem, Soc. 74, 3513 (1952). 64. Miedema, A. R., H. van Kempen. T. Haseda, and W. J. Huiskamp: Physica 28, 119 (1962). 65. Wittekoek, S., N. J. Poulis, and A. R. Miedema: Physica 30, 1051 (1964). 66. Judd, B. R.: Proc. Roy. Soc. (London), ser. A, 232,458 (1955). 67. Estle, T. L., H. R. Hart, Jr., and J. C. Wheatley: Phys. Rev. 112, 1576 (1958). 68. Williamson, S. J., H. C. Praddaude, R. F. O'Brien, and S. Foner, Phys. Rev. 181, 642 (1969). 69. Thornley, J. H. M.: Phys. Rev. 132, 1492 (1963). 70. Finn, C. B. P., R. Orbach, and W. P. Wolf: Proe. Phys. Soc. (London), ser, A. 77, 261 (1961). 71. Hudson, R. P., and W. R. Hosler: Phys. Rev. 122, 1417 (1961). 72. Leask, M. J. M., R. Orbach, M. J. D. Powell, and W. P. Wolf: Proc. Roy. Soc. (London), ser. A, 272,371 (1963). 73. Daniels, J. M., and F. N. H. Robinson: Phil. Mag. 44(7), 630 (1953). 74. Bailey, C. A.: Phil. Mag. 4, 833 (1959); Proc, Phys. Soc. (London), ser. A, 83, 369 (1964). 75. Frankel, R. B., D. A. Shirley, and N. J. Stone: Phys. Rev. 140, A1020 (1965); 143, 334 (1966). 76. Hudson, R. P., and R. S. Kaeser: Physics 3, 95 (1967). 77. Peverley, J. R., and P. H. E. Meijer: Phys. Status Solidi 23, 353 (1967). 78. Wheatley, J. C.: Ann. Acad. Sci. Fennicae, ser, A, VI-210, 15 (1966). 79. Elliott, R. J., and K. W. H. Stevens: Proc. Roy. Soc. (London), ser. A, (a) 215, 437 (1952); (b) 218, 553 (1953); (c) 219, 387 (1953). 80. Bogle, G. S., A. H. Cooke, and S. Whitley: Proc. Phys. Soc. (London), ser. A, 64,931 (1951). 81. Cooke, A. H., S. Whitley, and W. P. Wolf: Proc. Phys. Soc. (London), ser, B, 68,415 (1955).

5-242 82. 83. 84. 85. 86. 87. 88. 89. 90. 91. 92. 93. 94. 95. 96. 97. 98. 99. 100. 101. 102. 103. 104. 105.

ELECTRICITY AND MAGNETISM

Daniels, J. M.: Proe. Phys. Soc. (London), ser. A, 66, 673 (1953). Finkelstein, R., and A. Mencher : J. Chem. Phys. 21, 472 (1953). Johnson, C. E., and H. Meyer: Proc. Roy. Soc. (London), ser. A, 253, 199 (1959). Baker, J. M.: Phys. Rev. 136, A1633 (1964). Meyer, H., and P. L. Smith: Phys. Chem. Solids 9, 285 (1959). Cooke, A. H., and H. J. Duffus: Proc, Roy. Soc. (London), ser. A, 229,407 (1955). Hudson, R. P., and B. W. Mangum: "Magnetic and Electric Resonance and Relaxation," p. 135, North-Holland Publishing Company, Amsterdam, 1963. Scott, P. L., and C. D. Jeffries: Phys. Rev. 127, 32 (1962); R. H. Ruby, H. Benoit, and C. D. Jeffries: ibid. 51. Dieke, G. H., and L. Heroux: Phys. Rev. 103, 1227 (1956). Bleaney, B., H. E. D. Scovil, and R. S. Trenam: Proc. Roy. Soc. (London), ser. A, 223, 15 (1954). Erickson, L. E.: Phys. Rev. 143, 295 (1966). Meyer, H.: Phil. Mao. 2(8),521 (1957). Roberts, L. D., C. C. Sartain, and B. Borie: Ret's. Modern Phys. 25, 170 (1953). Blok, J., D. A. Shirley, and N. J. Stone: Phys. ReD. 143,78 (1966). Hebb, M. H., and E. M. Purcell: J. Chem. Phys. 5,338 (1937). Bogle, G. S., and V. Heine: Proc. Phys. Soc. (London), ser. A, 67,734 (1954). Broer, L. J. F., and C. J. Gorter: Physica 10, 621 (1943). Bijl, D.: Physica 16, 269 (1950). Benzie, R. J., and A. H. Cooke: Proc. Phys. Soc. (London), ser. A, 63,201, 213 (1950). deVries, A. J., D. A. Curtis, J. W. M. Livius, A. J. van Duyneveldt, and C. J. Gorter: Physica 36, 91 (1967). Giauque, W. F., and D. P. MacDougall: J. Am. Chem. Soc. 57, 1175 (1935). van Dijk, H., and W. V. Auer: Physica 9, 785 (1942). Giauque, W. F., and D. P. MacDougall: Phys. Rev. 43, 768 (1933). van Dijk, H.: Physica 9, 720 (1942).

6f-16. Susceptibility in High Magnetic Pields.! The magnetic behavior of materials in high magnetic fields (H ~ 25 kOe) can yield useful information whether the material is paramagnetic (P), ferromagnetic (F), ferrimagnetic (Fr), antiferromagnetic (A), weakly ferromagnetic (WF), i.e., canted antiferromagnetism, or some combination of these. In Table 5f-36, an abbreviated notation is used to give a capsule view of the type of behavior encountered. For usual paramagnetics, a comparison with a Brillouin curve reflecting the energylevel structure and the paramagnetic saturation moment (PS) are of interest. Special cases occur with ions whose ground state is nonmagnetic and whose magnetization is induced rather than aligned. Closely related behavior also occurs as a residual highfield susceptibility (XHF) of the Van Vleck type (Xvv ) after saturation by alignment. Other phenomena embraced by residual XHF are electron band susceptibility (band), magnetic sublattice rotation or a less well organized aligning process against antiferromagnetic interactions, magnetization rotation in monocrystals against large anisotropies (K), approach to ferro- or ferrimagnetic saturation (FS) in polycrystalline samples, and puzzling jumps in x vs. H above the antiferromagnetic N eel point (dx/dH; T > TN). A large number of substances undergo first-order transitions as a function of temperature at H = 0 between two different ordered magnetic states below the paramagnetic region, e.g., A-F, A-F i , A-WF, etc. A related case is the first-order change from paramagnetic (P) to an ordered state. In all these instances a high field can induce a transition from the less magnetic state to the more magnetic one, as manifested by the externally measurable total magnetic moment. The critical fields for these transitions are distinctly temperature-dependent; i.e., Hc(T - T t ), where T', is the transition temperature in vanishingly small field. These transitions lend themselves to thermodynamic analysis using the Clausius-Clapeyron equation. One should also note the spiral or helical antiferromagnetic or ferromagnetic-like states (A/l,F/l) and their field-induced variants such as fan (Fan) or other intermediate states 1

Prepared by 1. S, Jacobs, General Electric Research and Development Laboratories.

5-243

MAGNETIC PROPERTIES OF MATERIALS TABLE

5f-36.

MAGNETIZATION BEHAVIOR IN HIGH FIELDS

Behavior

Substance

. A -+ F. -+ P . A -+ F.I -+ F,II -+ P . A -+ F: -+ P Co'Cl s . SF~ P, dx/dH CoCh·2HtO . A -+ F. -+ P CoF t . A-+ WF p-Co(OH)2 . SF ~ P, dx/dH p-CoSO•.................. A-+ WF Co~Y . K CoVO •.... . . . . . . . . . . . . . . . A-+P Cr . dx/dH CnBeO•.................. Ah ~ Fan (?) CnCuO •.................. XIIF CnFeO •.................. XHF CrK(SO.k12HtO . PS CrtMnO •................. XHF CeBi CeSb CoBrt·2HtO

Cr NaSe

. A -+ SF -+ P A -+ SF Ah -+ P

CnOa . CrtZnSe•.................. Cuo.sCdD.2Fe tO •............ CuC!t·2HtO . . Cu(NO a)t·2.5H tO Dy . Dy,Ah . Dy Au . Dy'Cu, . Dy Erj . DySb . Er . ErSb . EuTe

.

Fe . Feo.8'Alo. 1 7. . • . • . . . . . . . . . . . FeBra . FeCOa . FeCla . FeCh-2HaO . FeGe . FeK a(CN)8 . FeNH.(SO,)·12HtO . Feo.~Nio.~Bra . FeO . a-FetOa . FeRh . Fe7Ss . GdAIO •................... GdAB . GdCua ..••................ Gd.Fe~012.. , . GdP . Gda(SO.),·8H20 . Ho , . HoAI . HoSb . MnAB . MnAua . MnCO •................... MnCh . MnCh·4HtO . MnuCrO.ISb . MnF 2 • • • • • • • • • • • • • • • • • • • • Mnl.uFeo.8IAB

Mn.GaC Mn.Ge2

XIIF

A -+ SF -+ P, dx/dH

A-+P

K A(?) -+ F, He(T - Tt) A-+P Ah -+ P Ah -+ X -+ F A -+ F, -+ P Fh -+ X -+ F A -+ P, dx/dH SF -+ P, dx/dH XHF, Band XHF, Band A-+P;xvv A-+P AII . .1 -+ P, XHF A-+Fi-+P A -+ SF PS PS A-+X-+P dx/dH, T TN AII-+ SF A.1 -+ WF A -+ F, He(T - Tt) K A -+ SF -+ P, dx/dH SF-+ P Ah -+ X -+ P

.

TN

SF -+ P, dx/dH SF-+ P; PS Fi, He(T - Tt) SF F, He(T - Tt) F, He(T -Tt) WF, He(T - Tt)

He, kOe, or Xv, emu/cc

T,K

11, 43 7, 22, 38 H II [100] 13.7,29.8 H I b H 1. c 34 31.6, 46.0 H II b 130 H 1. c 35 H 1. c 12.5 H II c K = 5.7 X 10 7 erg/cc 55 !:J.x/x < 0, "" 300 kOe 30, H II b; 48, H II c 1.3 X 10-4 3.9 X 10- 4 3.0"'B/Cr 3+ 3.6 X 10- 4 20, 138 H 1. c 59 H II c 64 7 X 10-', > 110 kOe 7,150 35 H II b K = 4.9 X 10 8 erg/cc 21, r, = 20 0 22 ",,20 22,45 H II a 22, 40 H II [100] 20, 140 H 1. c 25 75 3.2 X 10- 5 , 4.3 X 1O-~ 3.0 X 10-. 31.5 H II c ""150 Hllc 10.6, 100 39,46 H II a 67 1.0"'B/Fe3+ 5.0"'B/Fe 3+ 35,60 H 1. c H > 90,150 68 H II c 130, 162 H 1. c 270,230; r, = 330 0 K "" 10 7 erg/cc 11,34 H II b 165 50, 100 1 X 10-', H > 70 kOe 90 7.0"'B/Gd 3+ 106 H II c 7.1 ± 0.21-'B/Ho 17,23 H II [100] 29(p = 0), 110(p = 1 kb) ""47 !:J.x/x "" 0.14, 150 kOe 9, 32 7.5,20.6 H II c' ""100, Tt = 305 0 93 H II c 64, Tt = 283 0 150, Tt = 150 0 190, = 160 0

1.3 1.5 4.2 4.2 4.2 4.2 4.2 4.2 300 4.2 295 4.2 4.2 4.2 1.3 4.2

r,

~4

4.2 4.2 300 1 1.2 4.2 4.2 4.2 4.2 4.2 1.5 4.2 1.5 2.1 4.2 4.2 2

4.2 4.2 4.0 4.2 1.3 1.3 4.2 150-400 77 120,77 77 1.2-300 1

1.6 4.2 300 1.6 1.3 40 4.2 1.6 307, 329 4.2 300 1.3 0.26; 1.3 265 4.2 301 100 77

Ref. 1 2

3 4

3, 5 6, 7 8 9

10 11 12 13 14 14 15 14 16, 17 18 19 20 21 22 23 23a 24 25 26 27 26 27 4, 28 29-31 32 33 34, 6 35,36 37 38 39 15,39 40 41 42-44 45,46 47,48 49 50,51 52 53,25 54 28 15 55,23 56 57 58 59,60 61 62 63,64 65 66,67 68 69 70,65

5-244

ELECTRICITY AND MAGNETISM

TABLE

5f-36.

MAGNETIZATION BEHAVIOR IN HIGH FIELDS

Substance

Behavior

MnKaF4 .................. A~ SF Mnl_~LaOI ....... """" . XHF MnLiP04 ................. A~ SF MnO ..................... XHF MI10 2 •••••••••••••••••••. dx/dH. T> TN < MnI04. ................... XHF MnRb2F4 ................. A~ SF MnS04 ................... Ah ~ SF ~ P, dx/dH ax/an, T > TN MI1S04·H20 ............... A ~ SF ~P, dx/dH dx/dH. T > TN MnSna ................... A~ WF, He(T- Tt) Ni ....................... XHF. Band NiaAl ..................... XHF. Band NiIGa .................... XHF. Band Ni(OH)2 .................. A~P Pd ....................... XHF. Band R aGaaOI2................. PS [R = Gd.Er,Yb]ScIIn '" .... XHF. Band Tb ....................... K TbaAh .................... Fh(?) ~ F. He(T - Tt) TbAs ..................... A~P Tbeua .................... Ah~ P Tm ...................... Fi~F TmSb .................... Induced KHF YbaFeaOla ................ XHF ZrZna .................... XHF, Band

He, kOe, or Xv, emuycc

55 H II c 8X 10- 4, 0 y ~ 0.05 40 Hila dx/dH > O. Z e ~

c> zt:rj 1-3 1-1

C1J

t(

m

CUS04

MgS0 4

ZnS04

CdS0 4

U0 2S0 4

AlCia

0.1 0.2 0.5 1.0 2.0 4.0

(0.150) 0.104 0.062 0.043

(0.150) 0.108 0.068 0.049 0.042

(0.150) 0.104 0.063 0.043 0.035

(0.150) 0.102 0.061 0.041 0.032 ...... .

(0.150) 0.102 0.0611 0.0439 0.0367 0.0433

0.337 0.305 0.331 0.539

....... ...... .

. ......

. ......

LaCla

--0.314 0.274 0.266 0.342 . .... 0.825

. ....

. ....

EuCla

0.318 0.282 0.276 0.371 0.995

..... I

KaFe(CN)s K 4Fe(CN)s

0.268 0.212 0.155 0.128

. ....

.....

0.139 0.100 0.062

..... . .... . ....

Al 2(S04)a

Th(NOa).

0.0350 0.0225 0.0143 0.0175

0.279 0.225 0.189 0.207 0.326 0.647

. ..... . .....

5-259

ELECTROCHEMICAL INFORMATION

TABLE 5g-6. MEAN-ACTIVITY COEFFICIENTS 'Y± OF HCl IN AQUEOUS SOLUTION (m in mole kg-I) m

0°

10°

20°

25°

40°

50 0

60°

0.0001 0.0002 0.0005

0.9890 0.9848 0.9756

0.9890 0.9846 0.9756

0.9892 0.9844 0.9759

0.9891 0.9842 0.9752

0.9885 0.9833 0.9741

0.9879 0.9831 0.9738

0.9879 0.9831 0.9734

0.001 0.002 0.005

0.9668 0.9541 0.9303

0.9666 0.9544 0.9300

0.9661 0.9527 0.9294

0.9656 0.9521 0.9285

0.9643 0.9505 0.9265

0.9639 0.9500 0.9250

0.9632 0.9491 0.9235

0.01 0.02 0.05

0.9065 0.8774 0.8346

0.9055 0.8773 0.8338

0.9052 0.8768 0.8317

0.9048 0.8755 0.8304

0.9016 0.8715 0.8246

0.9000 0.8690 0.8211

0.8987 0.8666 0.8168

0.1 0.2 0.5

0.8027 0.7756 0.7761

0.8016 0.7740 0.7694

0.7985 0.7694 0.7616

0.7964 0.7667 0.7571

0.7891 0.7569 0.7432

0.7850 0.7508 0.7344

0.7813 0.7437 0.7237

1.0 2.0 4.0

0.8419 1.078 2.006

0.8295 1.053 1.911

0.8162 1.024 1.812

0.8090 1.009 1.762

0.7865 0.9602

0.7697 0.9327

0.7541 0.9072

in the reverse direction to fit plan B. It should also be noted that his equations are written for integral values of N but not necessarily for N = l. The Use of Table 5g-3. To calculate Eo of any cell, e.g., (5g-7)

Tl, TICl(aq), AgCl(s), Ag write the half-cell reaction and Eo for the right-hand electrode 8

+ AgCl---+ Ag + Cl"

Eo

=

0.2223 volt

Subtract both the half-cell reaction of Eo of the left-hand electrode

- [8 to give Tl

+ Tl " ---+ Tl]

-Eo = - (0.3363 volt)

+ AgCI---+ Ag + TICI(aq)

Eo

0.5568 volt

=

(5g-8)

or the completely equivalent form TI

+ AgCl---+ Ag + TI+ + Cl-

Eo

=

0.5568 volt

Since Eo is positive, t1Go is negative for the reaction. Equation (5g-8) is therefore the equation for the reaction actually taking place in the cell when all activities are unity. If the cell had been written Ag, AgCl, TICI(aq), TI the indicated reaction would have been (5g-9) Eo = - 0.5586 volt Ag + TIC1(aq) ---+ TI + AgCl The conclusions about the actual reaction and the absolute values of Eo and t1Go are unchanged.

TABLE

5g-7.

DISSOCIATION CONSTANTS OF WATER AND OF ELECTROLYTES IN AQUEOUS SOLUTIONS

(Constants* are on the molality scale.

Italics indicate maximum values)

Ct

~

Q)

o Material

°C

0°

5°

10°

15°

Water ................ K X IOU

0.1139

0.1846

0.2920

0.4505

Formic acid ........... K A X 104

1.638

1.691

1.728

1.749

Acetic acid ............ K A X 106

1.657

1.700

1.729

1.745

1.274

1.305

1.326

1.336

1.563

1.574

1.576

1.569

Chloroacetic acid ....... K A X 103

1.528

· · . · 0 ..

1.488

..........

Lactic acid ............ KA X 10

4

1.287

............

..

Glycolic acid ........... KA X 10 4

1.334

....... .

..... .

Propionic acid ......... K A X 106 n-Butyric acid ......... KA X 106

- - ------ - -

..........

..

..

..........

......

Sulfuric acid ........... K 2A X 10

.......

1. 80

..

7

Carbonic acid .......... KIA X 10 K 2A X 1011

2.64 2.36

3.04 2.77

3.44 3.24

Phosphoric acid ........ KIA X 103 K 2A X 108

8.97 4.85

5.24

5.57

5.89

Nitric acid ............ KA

..........

. .....

. .......

. .....

. ......

2

........

1.36 3.81 3.71

Glycine ............... KA X 10 K B X 106

....... ........

. ......

3.94 4.68

5.12

Alanine ............... KA X 10 KB X 106

........ .......

. ......

. .....

. ....... . .......

3

3

..

.......

25°

20°

30° 35° 40° 45° 50° --------- --- --0.6809 1.008 1.469 2.089 2.919 4.018 5.474 - - -- - - ---- - - - - - 1.765 1.772 1.768 1. 747 1.716 1.685 1.650 -----------------1.751,. 1. 750 1.728 1.703 1.670 1.633 1. 753 --------------1.338 1.336 1.326 1.310 1.280 1.257 1.229 --------------1.542 1.515 1.484 1.439 1.395 1.347 1.302 --------------.......... 1.379 .. ........ .. ........ 1.230 --------------.. .......... 1.371,. ....... .. .. ........ . ..... . ..... 1.270 ---- -----------------. ...... 1.1,.75 ..... . . ..... . ..... .. ...... 1.415 --------- -----.. ......... 1.01 . ...... 0.56 ...... . 0.75 --- ------------ -----5.19 4.16 4.45 4.71 4.90 5.04 5.13 6.73 4.20 5.62 6.03 6.38 4.69 5.13 -----------------..... 5.50 7.52 6.55 6.34 6.58 6.59 6.12 6.46 6.53 --- --------- -----. ..... 21 --------------4.47 4.81 4.31 4.59 7.43 7.87 6.04 6.52 6.98 5.57 - - - - - - - - - - - - --4.74 4.76 4.57 4.66 4.71 4.47 8.61 9.60 6.90 7.47 8.08 9.10 ..

• Letter subscripts on K indicate dissociation as acid or base, respectively; number subscripts indicate first or second dissociation.

l.%j

~

o 8

l:O

I-(

o.... 8

~

>Z

t:I

a:::

>o zt;j

8

U2

a:::

5-261

ELECTROCHEMICAL INFORMATION TABLE

5g-8.

RATE CONSTANTS FOR PROTON TRANSFER REACTIONS IN H 20 AT

2.j°

kj

Reaction: A

+ B~ C + D kb

H+ - OH-~ H 20 D+ OD-~ D 20 H+ + 80(-- ~ H80(-

1.4 X 1011

+

H++~~HF

8.4 X 10 10 1 X 1011 1.0 X 1011

H+ + H8-~H28 H+ + HCOs- ~ H2CO S H+ + HCOO-~ HCOOH H+ + CHsCOO- ~ CHsCOOH OH- + NH4+ ~ NH s·H 20 OH- + C6H50H ~ H 20 + C6H50OH- + HCN ~ H 20 + CNOH- + HP04-- ~ H 20 + P04 a-

7.5X10 1 0 4.7 X 10 1 0 5 X 10 1 0 4.5 X 10 10 3.4 X 10 1 0 1.4 X 10 1 0 3.7Xl09 2 X 10 9

TABLE

5g-9.

RELATIVE

ApPARENT MOLAL HEAT CONTENT

MOLAL HEAT CONTENT

£2

2.5 2.5 1 7 4.3

X 10- 5 X 10- 6 X 10 9 X 10 7 X lOa X 10 6 X 10& X 10 5 X 10 5 X 10 6 X 10 4 X 10 7

8

8.6 7.8

6 1.3

5.2 2

tpL

AND PARTIAL

OF SOLUTES IN DILUTE

AQUEOUS SOLUTIONS AT

25°0

(cal mole':")

m NaCI

tpL

£2 NaIO a

KCI

f{'L

£2 f{'L

£2 KCIO.

f{'L

£2 Li2S O ( C8 2SO.

SrCh

f{'L

£2 f{'L

£2 f{'L

£2 SrBr 2

f{'L

£2 Ba(NOah

f{'L

£2

0.0001

0.0004

0.0016

0.0064 0.0100

4.5 6.5

8.5 12.5

17.0 24.0

33 46

4.0 5.8

7.5 11.0

14.0 19.8

4.5 6.5

8.5 12.5

4.3 6.2

8.0 11.3

0.0400

0.0900

40 57

67 92

83 104

21 24

21 20

0 -41

16.0 24.0

31 46

38 55

65 82

13.0 16.6

16 13

14 4

-28 -86

77 91

24 35

47 69

91 135

177 260

218 317

377 508

488 620

20 29

39 57

71

102

121 161

139 176

161 152

137 87

23 34

46 66

86 125

161 232

195 277

332 443

420 528

23 33

44 64

82 119

152 216

182 254

293 383

366 452

19 27

36 51

59 75

72 68

66 37

-46 -195

-223 -528

5-262

ELECTRICITY AND MAGNETISM

TABLE 5g-10. STANDARD ENTROPIES OF MONATOMIC IONS IN AQUEOUS SOLUTIONS AT 25°C (Referred" to H 2-+ 2H+ + 29; tJ.S o = 0; cal mole'< deg- 1)

• Ion Cs" TI+ Rb+ K+ Ag" Na+ Li+ Pb++ Ba++ Hg++ Sn++ Sr++

So

Ion

So

Ion

So

Ca++ Cd""

-13.2 -14.6 -20 -23.6 -25.45 -27.1 -28.2 -36 -39 -43 -62 -70.1

Cr3+ Al3+ Ga3+ UH Pu H 1Br-

-73.5 -74.9 -83 -78 -87 26.14 19.25

,...

31.8 30.4 29.7 24.5 17.67 14.4 3.4 5.1 3.0 -5.4 -5.9 -9.4

Mn"" Cu++ Zn++ Fe++ Mg++ U3+ Pu3+ Gd3+ In 3+ Fe 3+

CIF-

13.17 -2.3

S-

-6.4

• This is not equivalent to the setting of So of H+ equal to zero; cf. Klotz (1950).

TABLE 5g-11. STANDARD ENTROPIES OF POLYATOMIC IONS IN AQUEOUS SOLUTIONS AT 25°C (Referred." to H 2-+ 2H+ + 28; tJ.S o = 0; cal mole ? deg ") Ion

So

OHCIOHC0 2CI0 2N0 2NO aCI0 3BrOa10aCIO.MnO.HCO aHSO aSH-

-2.5 10.0 21.9 24.1 29.9 35.0 39.0 38.5 28.0 43.2 45.4 22.7 26 14.9

Ion HSO.H 2AsO.H 2PO.HN 2O.Be02CO aSOaSO.SeO.N 202C 2O.Cr 207HPO.HAsO.-

Ion

SO

PO.3ASO.3HF 2BF.SiF 6CuCI 2AuCI.PdCI.PtCI.PtCI 6 I aAg(CNhNi(CN).FeCI++

-52 -34.6 0.5 40 -12 49.2 61 36 42 52.6 41.5 49 33 -22

So 30.3 28 21.3 34 -27 -12.7 -7 4.1 5.7 6.6 10.6 51.1 -8.6 0.9

• This is not equivalent to the setting of So of H+ equal to zero: cf. Klotz (1950).

Effect of Concentration. For the case where the reactants are not at unit activity, the Nernst equation is used: E

For the example above (N

=

=

Eo - RT log 'Ira ,Vi NF '

(5g-1O)

1, 25°C) this reduces to

E = 0.5586 - 0.059 log

aAgaTICI aTlaAgCl

(5g-11)

ELECTROCHEMICAL INFORMATION

6-263

The activities of pure solids and liquids are conventionally taken as unity so that aAg

and

E

=

aAgCl

=

aTl

= 1

= 0.5586 - 0.05915 log aTlCl

In many cases the activities of the dissolved species (e.g., TICI above) are approximated by their molar concentrations. References 1. Bates, R. G.: "Electrometric pH Determinations," John Wiley & Sons. Inc., New York, 1954. 2. Bierrum, J., G. Schwarzenbach, and L. G. Sillen: "Stability Constants of Metal-Ion Complexes with Solubility Products of Inorganic Substances," 2d ed., Chemical Society, London, 1964. 3. Caldin, E. F.: "Fast Reactions in Solution," Blackwell Scientific Publications, Ltd., Oxford, 1964. 4. Christiansen. J. A.: J. Am. Chem. Soc. 82,5517 (1960). 5. Conway, B. E.: "Electrochemical Data," Elsevier Publishing Company, Amsterdam, 1952. 6. Daniels, F., and R. A. Alberty: "Physical Chemistry," 2d ed., John Wiley & Sons, Inc., New York, 1961. 7. Harned, H. S.: in Electrochemical Constants, Natl. Bur. Standards (U.S.) Circ. 524, 1953. 8. Harned, H. S., and B. B. Owen: "The Physical Chemistry of Electrolytic Solutions," 3d ed., Reinhold Publishing Corporation, New York. 1958. 9. Hood, G. C., O. Redlich, and C. A. Reilly: J. Chern. Phys. 22, 2067 (1954). 10. "International Critical Tables of the Numerical Data of Physics, Chemistry and Technology," McGraw-Hill Book Company, New York, 1926-1933. 11. Klotz, r. M.: "Chemical Thermodynamics," revised ed., W. A. Benjamin, Inc., New York, 1964. 12. Kolthoff, r. M., and J. J. Lingane: "Polarography," 2d ed., Interscience Publishers, Inc., New York, 1952. 13. Kortum, G.: "Treatise on Electrochemistry," Elsevier Publishing Company, Amsterdam, 1965. 14. Kortum, G., and J. O'M. Bockris: "Textbook of Electrochemistry," vol. II, Elsevier Publishing Company, Amsterdam, 1951. 15. Landolt-Bornstein: "Physikalische-Chemische Tabellen," 5th ed., Springer-Verlag OHG, Berlin, 1927-1935; 6th ed., 195Q-? 16. Latimer, W. M.: "The Oxidation States of the Elements and Their Potentials in Aqueous Solution," 2d ed., Prentice-Hall, Inc., Englewood Cliffs, N.J., 1952. 17. Parsons, R.: "Handbook of Electrochemical Constants," Butterworth Scientific Publishers, London, 1955. 18. Powell, R. F., and W. M. Latimer: J. Chern. Phys., 19, 1139 (1951). 19. Redlich. 0.: Chem, Revs., 39,333 (1946). 20. Robinson, R. A., and R. H. Stokes: Trans. Faraday Soc., 45, 612 (1949). 21. Robinson, R. A., and R. H. Stokes: "Electrolyte Solutions," 2d ed., Butterworth Scientific Publications, London, 1959. 22. Rossini, F. D., D. D. Wagman, W. H. Evans, S. Levine, and r. Jaffe: Selected Values of Chemical Thermodynamic Properties, Natl. Bur. Standards (U.S.) Circ. 500, 1952. 23. Scudder, H.: "The Electrical Conductivity and Ionization Constants of Organic Compounds," D. Van Nostrand Company, Inc., Princeton, N.J., 1914. 24. Stuehr, J., and E. Yeager: Chap. 6 in "Physical Acoustics," vol. IIA, Academic Press, Ine., New York, 1965. 25. van Stackelberg, M.: "Polarographische Arbeitsmethoden," Walter De Gruyter & Co., Berlin, 1950.

5h. Electric and Magnetic Fields in the Earth's Environment M. SUGIURA AND J. P. HEPPNER

NASA-Goddard Space Flight Center

EARTH'S MAIN MAGNETIC FIELD 6h-1. Sources of the Magnetic Field at the Earth's Surface. The largest contribution to the magnetic field observed on the surface of the earth comes from its main field. The main field is considered to be produced in the earth's fluid core where the magnetic field and the convective motion of thermal origin are coupled to constitute a self-maintaining dynamo. The main field (Sees. 5h-4 and 5h-5) at the earth's surface is distorted to varying degrees by the earth's crustal anomalies (Sec. 5h-7) and by the magnetic fields from sources external to the solid earth. The latter include those from ionospheric currents (Sees. 5h-8 to 5h-1O), effects of plasmas in the magnetosphere (Sees. 5h-1l and 5h-21), and the distortion of the magnetospheric magnetic field by the solar wind (Sees. 5h-12 and 5h-20). 6h-2. Units Conventionally Used in Geomagnetism [IJ. Except in dealing with magnetic material, the magnetic permeability is unity in cgs units, and thus the distinction between magnetic induction B and magnetic field intensity H can be dispensed with without confusion. Hence, although the cgs unit for H is oersted, the unit for B, namely gauss (r), is conventionally used for both Band H. For weak magnetic fields and for describing time variations of the field, the unit gamma (y) is used, where 1 'Y = 10- 5 I'. Declination and inclination are expressed in angular measure, normally in degrees and minutes. 6h-3. Component Nomenclature [1,2J. The magnetic field vector is described by three orthogonal components, by the magnitude and two angles specifying the direction, or by a mixture of these. The standard nomenclature in geomagnetism is as follows: X, Y, and Z three components measured positively northward, eastward, and vertically downward, respectively B (or F) the magnitude of the field vector, (also called total force or intensity) F = (X2 + Y2 + Z2)! H the magnitude of the horizontal intensity, H = (X2 + Y2)! D declination: the angular deviation of the horizontal projection of the field vector from geographic north, taken positive when eastward, D = tan-ICY IX) I inclination, or dip angle: the inclination of the field vector from the horizontal plane, taken positive when downward, I = tan- l (Z I H) 6h-4. Dipole Description of the Main Field [1-3J. The main field is described, to a first approximation, by the field of a magnetic dipole placed at the earth's center (i.e., a centered dipole) with the following equations and parameters [4J: H Z

M

= H 0 (~) 3 sin e

= 2H 0 (~) 3 cos e = H oa 3

6-264

MAGNETIC FIELDS IN THE EARTH'S ENVIRONMENT

5-265

where M = 8.0052 X 1025 gauss em 3, the dipole moment H 0 = 0.30953 gauss, the field intensity at the magnetic equator (1 = 0°, e = 90°) for r = a a = 6371.2 km, the reference radius for a spherical earth r = radial distance, km, from the earth's center e = geomagnetic colatitude, from the geomagnetic coordinate system, below Geomagnetic coordinates (8 and A, respectively, for geomagnetic colatitude and east longitude) are given in terms of geographic coordinates «() and A, respectively, for geographic colatitude and east longitude) by cos e sin A

= cos (J cos ()o + sin () sin (Jo cos = sin () sin (A - AO) Isin e

(A - AO)

where [4] ()o = 11.44°, the geographic colatitude of the north geomagnetic pole (also called the north dipole pole); Ao = 290.24°, the geographic east longitude of the north geomagnetic pole The errors in describing the magnetic field at the earth's surface by means of the above centered dipole are as great as 10 percent in some regions. For a somewhat more accurate dipole description some use has been made of an eccentric dipole [5] representation in which a dipole is located at a position displaced from the earth's center. This is equivalent to adding the potential terms for g2 1, h 2 1, g2 2, and h 2 2 from the spherical harmonic description (Sec. 5h-5) to the potential term H 0 cos () for the centered dipole. As indicated by the (alr)n+t dependence of the potential in the spherical harmonic description (Sec. 5h-5), the errors in describing the main field by means of a dipole decrease rapidly with increasing distance r from the earth. The study of phenomena related to the interaction between the geomagnetic field and the solar wind (Sees. 5h-10 to 5h-12), including many of the indirect effects of this interaction, is often facilitated by use of the parameter geomagnetic local time in place of either local mean or standard time. This is a consequence of the magnetic field being symmetrical, to a first approximation, about the magnetic axis rather than the geographic axis. Geomagnetic Local Time [1,2] is defined analogous to the conventional local time system by replacing the geographic axis with the geomagnetic axis and defining geomagnetic noon for a location P as being the time when the sub solar point lies on the geomagnetic meridian of P. Geomagnetic Local Time for any location P is thus given in angular measure by 180° + A p - As, where A p and As are the geomagnetic longitudes of the location P and the sub solar point, respectively. An additional coordinate parameter which has been effective in organizing the data on geomagnetic phenomena related to particle motions in space is the invariant latitude, '1' = cos -1 IlL!. Here, L is the shell parameter defined in Sec. 5h-22 that gives the distance in the geomagnetic equatorial plane (in units of earth radii R e) to a field line having its intercept at the earth's surface at the invariant latitude '1'. Although L, and thus '1', is usually computed from a spherical harmonic field description (Sec. 5h-5), it is noted here because invariant latitude is frequently used in place of the dipole geomagnetic latitude. 6h-6. Spherical Harmonic Description of the Main Field [1,2,5]. The main field can be described, outside its source region, by a scalar magnetic potential V satisfying Laplace's equation v 2V = O. B = - vV then defines the vector magnetic field. Expressed in a spherical harmonic series,

V

""

n

n=l

m=O

~L (a;:)n+lL ~ =a

P n"" (cos () (gn"" cos mA

+ hn"" sin

mA)

5-266

ELECTRICITY AND MAGNETISM

where e = geographic colatitude (see Sec. 5h-4 for other coordinate symbols). P n m (cos e) = associated Legendre function of degree n and order m. The normalization introduced by Schmidt is most frequently used. gn m, h n m = constants called the Gauss coefficients. The vector components of the magnetic field (Sec. 5h-3) are given by X y

1 aV

= rao 1

= - rsin

Z =

aV

()~

av ar

X and Z above are applicable to a spherical earth; for accurate evaluations of X and Z on the surface of the actual earth, its oblateness should be taken into account. TABLE 5h-1. GAUSS COEFFICIENTS FOR THE INTERNATIONAL GEOMAGNETIC REFERENCE FIELD [4] FOR EpOCH 1965.0· (Units: gammas) n

m

(Jn

m

hn m

n

m

(Jn

m

-- -I

1 2 2 2 3 ~

3

3 4 4 4 4 4 5 5 5 5 5 5 6 6

0 1 0 1 2 0 1 2 3 0 1 2 3 4 0 1 2 3 4 5 0 1

hn m ---

-30,339 -2,123 -1,654 2,994 1,567 1.297 -2,036 1,289 843 958 805 492 -392 256 -223 357 246 -26 -161 -51 47 60

0 5,758 0 -2,006 130 0 -403 242 -176 0 149 -280 8 -265 0 16 125 -123 -107 77 0 -14

6 6 6 6 6 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8

2 3 4 5 6 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 8

4 -229 3 -4 -112 71 -54 0 12 -25 -9 13 -2 10 9 -3 -12 -4 7 -5 12 6

106 68 -32 -10 -13 0 -57 -27 -8 9 23 -19 -17 0 3 -13 5 -17 4 22 -3 -16

I

• Courtesy of J. C. Cain and S. J. Cain.

Table 5h-1 gives the Gauss coefficients for the International Geomagnetic Reference Field [4] for epoch 1965.0. Table 5h-2 gives a second set of coefficients determined directly from measurements by the OGO-2 and OGO-4 satellites [6] taken between October, 1965, and December, 1967, but referenced through use of secular change terms (Sec. 5h-6) to the same date, t = 0 at time 1965.0. Comparison of different sets of coefficients gives an indication of the accuracy of spherical harmonic descriptions of the main field. The relatively uniform latitude and longitude distribution of data from the polar orbiting OGO satellites selected for magnetically quiet periods (K p = 0, Sec. 5h-13) provides a data set suitable for examining differ-

MAGNETIC FIELDS IN THE EARTH'S ENVIRONMENT TABLE

5h-2.

GAUSS COEFFICIENTS BASED ON THE DATA

[6]

OGO-2 AND 4 1965.0*

5-267

SATELLITE

AND REFERENCED TO EpOCH

(Units: gammas) n

m

(}"m

h"m

n

m

(}"m

h"m

0 1 0 1 2 0 1 2 3 0 1 2 3 4 0 1 2 3 4

- 30,338 -2,114 -1,661 2,994 1,597 1,298 -2,041 1,295 856 956 807 480 -387 260 -221 360 250 -33 -152 -61 46 60 8 -229 -3 4 -100 71 -53 3 14 -31 -3 12 3

0 5,768 0 -2,013 103 0 -403 237 -169 0 153 -269 16 -274 0 17 128 -127 -100 99 0 -11 104 70 -31 -12 0 0 -62 -27 -6 7 19 -24 -26 0 9 -13

8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10

3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 11

-11 -2 5 -6 12 10 10 8 2 -12 14 0 0 2 4 0 -3 -2 2 -5 -2 7 6 0 0 2 0 2 -1 -2 4 -1 1 -1 1 2 -1 4 3

5 -18 6 20

-I 1 2 2 2 3 3 3 3 4 4 4 4 4 5

5 5 5 5 5 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 8 8 8

5 0 1 2 3 4 5 6 0 1 2 3 4 5 6 7 0 1 2

10

5 -4

10

10 11 11 11 11 11 11 11 11 11 11 11 11

-3 -22 0 -22 15 4 -2

-3 10 13 1 4 0 2 1 2 6 -4 1 -2 4 3

-10 0 1

3 -1

-3 0 -1 -2 -1 -4 -1 3

• Courtesy of J. C. Cain and S. J. Cain.

ences between calculated and measured values-particularly because the data, at altitudes > 400 km, is not significantly affected by the crustal anomalies described in Sec. 5h-7. Using the OGO set of coefficients, the root-mean-square values of the residuals in scalar B for the difference (measured minus computed) for OGO-2 and OGO-4 data are 7 and 9 'Y, respectively. The corresponding rms residuals, using the coefficients adopted for the International Geophysical Reference Field, are 39 and 57 'Y, respectively. Figure 5h-1 illustrates the form of the main magnetic field at the earth's surface in terms of the total scalar intensity B. The lack of dipole symmetry and the possible am biguity of using the term magnetic pole without further definition are evident features. The preferred terminology is to use the term dip pole when referring to the

5-268

ELECTRICITY AND MAGNETISM

location where I = 0° and the term geomagnetic pole, or dipole pole (Sec. 5h-4), when referring to the surface intercepts of the axis of the centered dipole determined from the coefficients gI O, gIl and hI 1. It is further evident that pole positions do not correspond to locations of maximum field intensity. 6h-6. Secular Variations of the Main Field [1,2,7-9]. The main magnetic field as observed at the earth's surface varies noticeably on a time scale of several or more years. These changes are called the secular variations. The secular variations can be represented by maps with contours of equal rate of change for various quantities.

180° 160° 1400 120° 100° 90° 80°

80°

60°

40°

20°

0°

20°

40°

60°

80°

100° 120° 140° 160° 180° 1965.01GRF 90°

_ _"""'=_ 80°

t:;:=;:::~~....-......I---":-'--':""""""'L....L-!.-~==::::=:;:==:=:;:::::;::===~--"---'---""""""''''''''''''''''....-......I--==::::~::::::;:;:::L:::::d 90°

9°180° 160° 140° 120°

1000 80° 60° 40° ODIP POLES

20°

0°

20° 40° 60° 80° 100° 0DIPOLE POLES

120° 140° 160° 180°

FIG. 5h-1. The earth's main magnetic field (Sec. 5h-5): the distribution of the magnitude B

on the earth's surface as calculated from the 1965.0 International Geomagnetic Reference Field (Table 5h-l); B measured in gauss. (Courtesy of S. J. Cain.)

Such contours for the total force B are referred to as tsopors; an example of an isopor chart for the epoch of 1965 is shown in Fig. 5h-2. The secular variation is also expressed by regarding the Gauss coefficients (Sec. 5h-5) as being time-dependent [10]. The coefficients gnm and h;» are then replaced, respectively, by gn + gnmt and h nm + hnmt, where t IS time measured in years from a specific epoch date. The coefficients gnm and hnm are given in Table 5h-3 for epoch 1965.0 for the International Geomagnetic Reference Field. The nondipole part of the main field as expressed by the spherical harmonics for different epochs appears to indicate the presence of two types of gross features: (1) regions over which the pattern of deviations from a dipole field has remained relatively constant through the history of accurate measurements, and (2) regions over which the pattern of deviations appears to be drifting westward at rates of 0.2 to 0.3 deg /year. The analyses also suggest a poleward shifting of the dipole field as indicated by a change

MAGNETIC FIELDS IN THE EARTH'S ENVIRONMENT

5-269

of 24 'Y/year in the term dY20/dt (Table 5h-3) of the harmonic analysis which is the largest change observed in any single coefficient. There are also indications that the dipole moment (Sec. 5h-4) has decreased at a relatively uniform rate from about 8.55 X 102 6 gauss em! in 1835 [5] to 8.005 X 10 26 in 1965. 6h-7. Crustal Anomalies [8,11,12]. The main magnetic field is locally distorted at the earth's surface by differences in the degree of magnetization of various rock formations. This magnetization is primarily dependent on the magnetite, Fe a0 4, content and exists to the depth at which the Curie temperature (575°C for magnetite) is reached. Over many regions of the earth this depth is estimated to be about 20 km, 60·

80·

100· 120·

140" 160" 180·

1965.0 IGRF

90·

FIG. 5h-2. The secular variations (Sec. 5h-6) in the magnitude B of the main magnetic field: calculated from the secular variation terms in the 1965.0 International Geomagnetic Reference Field (Table 5h-3); units are gammas. (Courtesy of S. J. Cain.)

but variations in estimates range from 10 to 30 km. The magnetization is of two types: induced (proportional to the rock susceptibility and the main field B), and permanent (the remnant magnetization from a geologically earlier state of magnetization). Extensive mapping of magnetic anomalies has been carried out over many regions of the earth's surface to aid in inferring the subsurface geology. The distribution, intensity, and number of anomalies as a function of their dimensions are highly variable for different regions. However, considering dimensions > 1 km, statistics indicate: (1) that the number of anomalies sharply decreases between anomaly dimensions of 25 and 50 km, (2) that between anomaly dimensions of 50 and 300 km the number of anomalies gradually decreases with increasing dimensions, and (3) that the comparatively small number of anomalies that have a-maximum dimension >300 km usually appear in a lineation pattern that marks a major geologic boundary resulting from large-scale tectonic activity. On a similar scale (resolution about 1 km), anomaly intensities are statistically indicated by noting that contour

5-270

ELECTRICITY AND MAGNETISM

TABLE 5h-3. SECULAR VARIATION TERMS FOR EpOCH 1965.0 IN TlfE SPlfERICAL HARMONIC EXPRESSION: BASED ON THE INTERNATIONAL GEOMAGNETIC REFERENCE FIELD [41* (Units: gammas/year) n

m

On

kn m

m

-I

1 2 2 2

3 3 3 3 4 4 4 4 4 5

5 5 5 5 5 6 6

* Courtesy of J.

n

m

'm On

hn m

2 3 4 5 6 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 8

1.1 1.9 -0.4 -0.4 -0.2 -0.5 -0.3 -0.7 -0.5 0.3 -0.0 -0.2 -0.6 0.1 0.4 0.6 0.0 -0.0 -0.1 0.3 -0.3 -0.5

-0.4 2.0 -1.1 0.1 0.9 0.0 -1.1 0.3 0.4 0.2 0.4 0.2 0.3 0.0 0.1 -0.2 -0.3 -0.2 -0.3 -0.4 -0.3 -0.3

-0 1 0 1 2 0 1 2 3 0 1 2 3 4 0 1 2 3 4 5 0 1

15.3 8.7 -24.4 0.3 -1.6 0.2 -10.8 0.7 -3.8 -0.7 0.2 -3.0 -0.1 -2.1 1.9 1.1 2.9 0.6 0.0 1.3 -0.1 -0.3

0.0 -2.3 0.0 -11.8 -16.7 0.0 4.2 0.7 -7.7 0.0 -0.1 1.6 2.9 -4.2 0.0 2.3 1.7 -2.4 0.8 -0.3 0.0 -0.9

6 6 6 6 6 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8

C. Cain and S. J. Cain.

maps are often prepared in units of 100 "Y. Anomalies involving changes of several thousand gammas over horizontal distances of several tens of kilometers are considered to be strong anomalies.

SURFACE GEOMAGNETIC VARIATIONS OF SPACE ORIGIN 6h-8. Solar Daily Variation on Quiet Days [1-31. The regular magnetic variation observed on an average magnetically quiet day is called the Sq variation. The source of Sq is a system of electric currents in the E region of the ionosphere (Sec. 5h-15). Systematic winds produced mainly by the solar heating of the atmosphere generate the current through a dynamo action which is effective between roughly 95 and 130 km where the electric conductivity is high. The relevant conductivity elements are given in Sec. 5h-18. Examples of magnetograms on a typical quiet day are shown in Fig. 5h-3 for observatories at low and middle latitudes and near the dip equator. An illustrative picture of the Sq current system is shown in Fig. 5h-4. Within about 200 km of the dip equator, I = 0° (Sec. 5h-3), the Sq range in H is very large, as indicated by the Huancayo, Peru, magnetogram in Fig. 5h-3. The concentrated ionospheric current along the dip equator on the day side of the earth which produces this large change in H is referred to as the equatorial electrojet. It results from an enhanced effective conductivity (Cowling conductivity, Sec. 5h-18) in the east-west direction in a narrow belt at the dip equator. Typical ranges in the magnitude of Sq at the earth's surface are roughly 50 to 250 "Y at the dip equator and 30 to 60 "Y at magnetic latitudes 10 to 60°. Both the form and magnitude of Sq can vary considerably from one day to the next and also with season and solar activity.

5-271

MAGNETIC FIELDS IN THE EARTH'S ENVIRONMENT

6h-9. Lunar Geomagnetic Variation [1,2]. The tidal oscillation of the atmosphere due to the gravitational force of the moon generates an electric current in the ionosphere which gives rise to the lunar geomagnetic variation, conventionally denoted by L. Amplitudes of L are about one-tenth of those of Sq, and are not generally recognizable in the magnetograms by the eye. An exception to this is L near the dip equator, where its amplitude is enhanced over the corresponding amplitudes at higher latitudes by a rate greater than that for the similar enhancement in Sq (Sec. 5h-8). The current system for L varies greatly with lunar phase and season. (Note. The use of L for lunar variations is not related to the L shell parameter described in Sec. 5h-22.) _

~ Z FREDERICKSBURG, VIRGINIA (Mag. Lot. =49.6°N)

~'[:~ ~JULY 13.1957

L __,- L

o

~

~>Oo[

I

L_

l _

-L_ L~I __

NOON

J.

-.1_-'-----1

6

m= ~

~

I

J

I

12

OH~T

J~--1---.L--l--.J

18

24

HONOlUlU'HA~

OZ

H JULY /3. 1957

=========t==--NOON pHUT

L _~ __ -.L--'-----I_L_~L..-l--'-

>--;r

I

o

__

L_

-------

1----'-'--'-------'---'----'I~ __ l_L_-l

6 12 HUANCAYO, PERU (Mag. Lal.=0.6°S)

18

24

~------------+----------H-----JULY 13.1957 I

I

I

L-----L.-...l--l- I

02468

OHUT

NOON ,

,

,

I

,

t

I , I I I --,--I-----'-'-----'-'-----'-------'-----'-----'-----'-----'-----'------l

10 12 14 16 LOCAL MEAN TIME

18

20

22

24

FIG. 5h-3. Typical magnetograms on a quiet day, showing the solar daily variation Sq (Sec. 5h-8). H is the horizontal component, D the declination, and Z the vertical component. The H trace for Huancayo shows the effect of the equatorial electrojet.

6h-l0. High-latitude Magnetic Disturbances [2,3,13,14]. At high latitudes the magnetic field is disturbed more frequently and more severely than at middle and low latitudes. Disturbances are statistically greatest along oval-shaped belts encircling the dipole poles in each hemisphere roughly at e (or 90° - '1J) = 15 to 20° near noon, 17 to 23° near the twilight meridians, and 19 to 26° near midnight [15-17]. (Note. e is used in this section as geomagnetic colatitude for each hemisphere.) As the ionospheric electric currents causing the magnetic disturbances in these belts are associated with the occurrence of aurora, they are usually referred to as the auroral belts or auroral ovals [18]. Within these belts maximum disturbance intensities are most commonly encountered at e = 20 to 25° in the nighttime geomagnetic local time range (Sec. 5h-4) 20 h to 04 h • The frequency of occurrence of aurora is also a maximum in these nighttime strips, and this statistic has led to the designation

5-272

ELECTRICITY AND MAGNETISM

of the strips centered near e = 23° as the auroral zones. The colatitudes e indicated above decrease by several degrees during times of weak activity and increase during times of intense activity and magnetic storms. During intense storms values of e as great as 35° are not uncommon in the midnight sector. Figure 5h-5 is an idealized representation of the distribution of ionospheric electric currents for a disturbance of moderate intensity (Note. Because current may also flow along magnetic field lines to magnetospheric regions, currents are not drawn as being continuous within the ionosphere.) Several major features to note are: (1) The most intense current flows westward in the auroral belt toward the 22 h to 23 h region from the morning sector. This concentration of current is often called the ROTATIONAL AXIS

EQUATOR IAL+---==-J" ELECTROJET

FIG. 5h-4. Illustration of the ionospheric current system for the solar daily variation Sq (Sec. 5h-8); the stronger current vortex represents the average condition in northern summer.

auroral elecirojet. (2) A weaker auroral electrojet current flows eastward toward the 22 h to 23h region from the evening sector. (3) A comparatively uniform current flows across the polar cap (the region poleward from minimum e for the auroral belt) from the late evening sector to the late morning sector. (4) Much weaker currents spread outward to the middle-latitude regions. Although shown only for one hemisphere, the same distribution occurs simultaneously in the other hemisphere, indicating that the magnetic field lines connecting the two auroral belts are also lines of electrical equipotentials in the electric field system (Sec. 5h-28) driving the electrojet currents. Sounding rocket measurements have shown that the auroral electrojets are primarily Hall currents (Sec. 5h-18) driven by horizontal electric fields (Sec. 5h-28) in the region of the ionosphere where energetic electrons precipitate from the magnetosphere and increase the ionization and hence the conductivity. Enhancements of these disturbances typically last one to several hours and are often repeated at intervals of several hours. Disturbances of this type are sometimes

MAGNETIC FIELDS IN THE EARTH'S ENVIRONMENT

5-273

referred to as magnetic bays (a term originating from the resemblance of the H trace on magnetograms during such events to the coastline of a bay on a map). Directly beneath the auroral electrojets, variations are largest in the H component and usually lie within the range 100 to 1,000 'Y, but may on occasions reach values greater than 2,000 'Y. Large bay disturbances often occur during magnetic storms (Sec. 5h-11). The magnetic activity indices K p and AE (Sec. 5h-13) are essentially measures of the severity of magnetic disturbances in the auroral belt. 6h-11. Magnetic Storms [l,2,19J. Worldwide magnetic disturbances lasting one to several days are called magnetic storms. Magnetic storms often, but not always, begin with a sudden, worldwide increase in the magnetic field. This sudden field increase, called a sudden commencement and denoted by SC, is due to a compression of

+

SUN

h 12

Oh FIG. 5h-5. Illustration of ionospheric currents for a high-latitude disturbance. circles represent geomagnetic latitude (90 0 - 8) circles.

Concentric

the magnetosphere by a sudden increase in the pressure on the magnetosphere boundary exerted by the solar wind; magnetic variations of this type are discussed in Sec. 5h-12. Examples of magnetograms taken during a magnetic storm are shown in Fig.5h-6. Typically, one-half to a few hours after an SC the magnetic field begins to decrease all over the globe, and after reaching a minimum in several hours recovers slowly toward the prestorm level. The field decrease, often called a Dsi decrease (Sec. 5h-13) is due to a creation of a plasma belt at a distance of 2.5 to 6 earth radii [20]. The plasma belt exerts magnetic stress such that the magnetic field in the magnetosphere is inflated, resulting in a field decrease inside the plasma belt and an increase outside it [21]. In the developing phase of a magnetic storm the plasma belt grows most rapidly in the late afternoon sector of the magnetosphere, and consequently the field decrease observed on the earth is also larger in this sector than in other sectors. The magnetic stress of the plasma belt mainly comes from its protons in the energy range 10 to 100 kev. During magnetic storms high-latitude disturbances of the type discussed in Sec. 5h-l0 occur in greater intensity than under normal conditions (e.g., see College, Alaska, in Fig. 5h-6). Field variations produced by an auroral electrojet may reach 3,000

5-274

ELECTRICITY AND MAGNETISM COLLEGE, ALASKA (Mag. Lot.- 64.7'N)

LOCAL

LOCAL

MDNGHT

tmN

20'

~ I

'h"

'4'

I

'a"

~

12

20

16

BI

Z~OlULU,

~

0-------------

~I

HNNAII (M~_2_I.O_'N_)",--,,

_

H

, 20

,

20 0 4 8 .HUANCAYO, PERU (Mag. Lot. -0.6'S)

12

0-------------Z- - - - - - - - "

16

--------LOCAL tmN

20'

,

1

!

(,

Nov. 27, 1959

I

,

1

,

!

8 UNIVERSAL TIME

I

I

12

!

t

!

I

!

16 20 Nov. 28,/959

FIG. 5h-6. Magnetograms taken during a magnetic storm (Sec. 5h-ll) : examples from highlatitude (top) and low-latitude (middle and bottom) stations. "Y during

an exceptionally large storm.

In such a storm the Dst decrease may exceed

400 "Y.

The frequency of occurrence and the average intensity of magnetic storms are statistically correlated with solar activity. However, individual magnetic storms can by no means be traced to active regions on the sun, and conversely solar flares do not always produce magnetic storms on the earth. During the International Geophysical Year, July, 1957, to December, 1958, representing a period of maximum solar activity, magnetic storms with Dst decreases exceeding 40 "Y occurred at a rate of 55 storms per year, and the average Dst decrease was 110 "Y, with a maximum of

MAGNETIC FIELDS IN THE EARTH'S ENVIRONMENT

5-275

434 'Y observed on September 13, 1957, which was still the largest (as of November 1, 1968) since 1957. In 1964 a year of solar activity minimum, there were only 15 magnetic storms (as defined above), and the average Dst decrease of these storms was 61 'Y, with a maximum of 109 'Y [22,23]. 5h-12. Magnetic Variations Caused by Compressions and Expansions of the Magnetosphere. Compression or expansion of the magnetosphere responding to an increase or decrease of the solar wind pressure on its boundary surface produces a class of magnetic variations of considerable interest, in spite of their generally small magnitudes. Sudden commencements (8C) of magnetic storms (Sec. 5h-ll) and sudden impulses belong to this class. A sudden impulse, often denoted by 81, is a sudden increase or decrease in the magnetic field observed simultaneously over the world [2]. The theoretical magnetic field change li.B at the ground is related to changes in the proton density n and the velocity v of the solar wind approximately by the formula [24] li.B

= 0.03li.(n!v}

where li.B is in 'Y, n in protona/cm-, and v in km/sec. For sudden commencements li.B ranges from several to 100 'Y, whereas li.B for sudden impulses is normally less than 20 'Y. The effect of an abrupt compression of the magnetosphere boundary is transmitted inward hydromagnetically [25]. Presence of continuous time variations in Dsi (Sec. 5h-13) with appreciable amplitudes suggests that occurrences of more gradual, as compared with sudden, compression or expansion of the magnetosphere are not infrequent, but their significance has not as yet been explored. 6h-13. Magnetic Indices [1,26,27]. Planetary 3-hourly Index Kp. The Kp index expresses the intensity of geomagnetic activity mainly at high latitudes (Sec. 5h-10) for each 3-hr interval of the Greenwich day, in a scale of thirds in the order: 00

0+

1-

10

1+

2-

20

2+ . . . 8 -

80

8+

9-

90

which may be condensed to a scale of integers from 0 to 9. Kp is based on magnetic records from 12 selected observatories lying between 47.7 and 62.5° dipole latitude with the average of 56°. The Kp index is published regularly by the International Association of Geomagnetism and Aeronomy in the No. 12 series of its Bulletin. Indices ap, Ap, Ci, Cp, etc., are also found in the same publication. Three-hourly Equivalent Planetary Amplitudes, ap. The conversion from Kp to ap is made according to the following table: Kp ap

=

00

=

0 Kp = 5-

ap = 39

0+

1-

10

1+

2-

2

3 5+ 56

4

5

6-

60 80

6 6+ 94

50 48

67

20 7

3-

30 12 15 7- 70 7+ 8111 132 154 179 2+

9

3+ 418 22 80 8+ 207 236

40 27 9300

4+ 32 90 400

At a standard station the average range of the most disturbed of the three magnetic components is 2 ap ('Y); for instance, if Kp = 6+, the range is 188 'Y. The scale for ap is linear, while that for Kp is quasi-logarithmic. Daily Equivalent Planetary Amplitude, Ap. The average of the eight values of ap for each day is the daily equivalent planetary amplitude Ap. Hence Ap is also expressed in units of 2 'Y for a standard station. Daily International Character Figure Ci, and Daily Planetary Character Figure Cp, The daily international character figure Ci is the average of the daily character figure C for all collaborating observatories; Ci varies from 0.0 to 2.0. Ci is available for every day since 1884.

5-276

ELECTRICITY AND MAGNETISM

A more recently introduced substitute index Cp is derived from the daily sum of ap according to the following scheme.

ap sum up to: Cp

=

22 0.0

34 0.1

44 0.2

55 0.3

66 0.4

78 0.5

90 0.6

104 0.7

120 0.8

139 0.9

164 1.0

190 1.1

228 1.2

ap sum up to: Cp

=

273 1.3

320 379 453 561 729 1119 1.4 1.5 1.6 1.7 1.8 1.9

1399 2.0

1699 2.1

1999 2399 2.2 2.3

3199 2.4

3200 2.5

Though values of Ci and Cp are found to be nearly the same, Cp is more reliable and should be used in preference to Ci. Auroral Electrojet Index AE [28}. The AE index is designed to be a measure of global auroral electrojet activity with higher time resolution than Kp. The index is normally given at 2.5-min intervals, but hourly averages are also used. AE represents the instantaneous range of disturbance of the horizontal component H from a set of observatories that are relatively uniformly distributed in longitude between magnetic colatitudes e of 30 and 19°. AE = AH (maximum) '+ IAH (minimum)', where AH (maximum) is taken from the observatory showing the maximum positive deviation of H, and IAH (minimum) I is taken from the observatory showing the largest negative value in H. Dst Index [22}. The component of disturbance magnetic field that is axially symmetric with respect to the geomagnetic dipole axis is called Dst. The Dst index, computed at hourly or 2.5-min intervals, is useful for studies of magnetic storm phenomena (Sec. 5h-11). Dsi = lin (AH 1 + AH 2 + ... + AHn ) represents the average deviation of the horizontal component from quiet-day values for a set of n observatories that are relatively uniformly distributed in longitude and located at low ( 100 km in length. Density contrasts between adjacent filaments can involve changes by factors of 2, but contrasts of the order of 1 to 10 percent are much more common. When observed from the ground using radio sounding techniques, these irregularities give the normal F region the appearance of being spread upward. The term spread F has been commonly used to describe this appearance of the F region. Spread F is also observed frequently over the magnetic dip equator but appears to be more confined to F -region altitudes. 6h-18. Electric Conductivity in the Ionosphere [2,40,411. Because of the low collision frequencies and of the presence of the strong magnetic field, the conductivity in the ionosphere above 70 km height is highly anisotropic for low-frequency electromagnetic waves and for d-e electric fields. Writing the current density j as j =

where B E

:B

0"0

Ell

=

magnetic induction electric field intensity

=

B/IBI

=

+

0"1

Ej,

+ eB X 0"2

E)

Ell = (E . B)'B = electric field intensity parallel to B Ej, = E - Ell = electric field intensity perpendicular to B The conductivity elements 0"0,0"1, and 0"2 are called the direct (or longitudinal), Pedersen, and Hall conductivities, respectively. For electromagnetic waves of frequency w, conductivities 0"0, 0"1, and 0"2 are respectively given, in mks units, by

where n e me.i We.i

= = =

=

electron density in electron-ion pairs /m 3 electronic charge in coulombs electron, or ion, mass in kilograms eB/me.i = cyclotron (or gyro) frequency in radians/sec

5-280

ELECTRICITY AND MAGNETISM

The d-e conductivity is obtained by setting '" = O. In the case when the electric field is perpendicular to the magnetic field, the energy loss per unit volume due to joule heating can be expressed as j • j/0'3 (= j . E), where

The effective conductivity 0'3 is called the Cowling conductivity. If the electric field is parallel to the magnetic field, the energy loss is j . i/O'o as in the absence of the magnetic field. The Cowling conductivity plays an important role in the dynamo

10-4

10-3

ero (MHO/M) 10-2

KJI

10-5

10- 4

10'

360

320

280

200

160

120

AT DIP EQUATOR 2800 E LONGITUDE

VIICT2

(MHO/M)

FIG.5h-8. Typical conductivity profile (Sec. 5h-18) ; the upper scale for 0'0, the direct conductivity, and the lower scale for 0'1 and 0'2, the Pedersen and Hall conductivities, respectively.

region of the ionosphere. For instance, over the dip equator, where the magnetic field is horizontal, the effective conductivity for a horizontal electric field directed perpendicular to the magnetic field becomes 0'3 when the vertical Hall current is inhibited by polarization of the medium. The value of 0'3 is larger over the dip equator, and this is the reason for the existence of the equatorial electrojet mentioned in Sec. 5h-8. The conductivities are latitude-dependent through the magnetic field, and also vary with the electron density distribution and hence with local time, latitude, season, and solar activity. The following rules generally hold: (1) The direct conductivity 0'0 is much larger than 0'1 and 0'2 throughout the ionosphere above about 70 km height; at this height 0'0 and 0'1 are approximately equal, indicating that the conductivity is nearly isotropic. (2) In the 90- to 130-km region, where the Sq (and L) current flows (Sec. 5h-8), 0"2 is larger than 0'1' (3) Above this region 0'1 becomes greater

MAGNETIC FIELDS IN THE EARTH'S ENVIRONMENT

6-281

than 0'"2. Figure 5h-8 shows a typical conductivity profile for noon over the dip equator. 6h-19. Refractive Index in the Ionosphere [42]. For a plane electromagnetic wave propagating in a homogeneous magneto-ionic medium permeated by a uniform magnetic field, the complex refractive index n in the Appleton-Hartree approximation is given (in the standard notations and mks units) by

where

"'0· WH

"'L

"'T

=

= = =

X = YL =

YT=

Ne 2/ EOm ~oHo!el/m (~oHoe/m)

(~oHoe/m) "'0

cos 0 sin 0

2/",2

wd", WT/'"

p/",

Z

=

W

= angular frequency of the wave

electric permittivity of free space magnetic permittivity of free space e = electron charge, numerically negative m = electron mass H« = magnitude of the ambient magnetic field H o N = number density of electrons o = angle between H o and the direction of propagation of the plane wave P = frequency of collision of electrons with heavy particles The upper and lower signs in the above equation correspond to the ordinary and the extraordinary wave, respectively. For ionospheric propagation there are two useful approximations: the quasi-longitudinal (QL) and the quasi-transverse (QT) approximations. EO

=

~o =

2..!..1-

For QL:

n..

X 1 - iZ ± J Y L I

where the upper and lower signs are for the ordinary and the extraordinary wave, respectively.

1-

For QT:

1 - iZ

+ (1 -

X

X -

~'Z)

coV 0

for the ordinary wave, and X

n2 9 1

Y T 2/ (1 - X - iZ)

- iZ -

for the extraordinary wave. These approximations are valid if the following conditions are satisfied: y

1

,4

'4YL 2

y T4

«

4Y } » 1

1(1 - X - iZPI

for QL

1(1 - X - iZ)2J

for QT

The existence of the two modes, the ordinary and the extraordinary, is due to the presence of the magnetic field. In the absence of the latter the refractive index n would be given, ignoring the collision effects and the ion motions, by n2

= 1

Ne -

2

EOm",2

6-282

ELECTRICITY AND MAGNETISM

A plane wave of angular frequency CAl propagating vertically upward in a medium with electron density N varying with height will be reflected back at the height at which N reaches a value that makes n vanish; this value of N is given by

N

=

1.24 X 1O- 8j2

in terms of the wave frequency f (= CAl/2w-) in hertz. Given N, the angular frequency CAlO (= yNe2 / EOm) is called the electron plasma frequency. If there is a peak in the electron density, say N m, the plasma frequency is also a maximum, say CAlm, at the same height. Then radio waves with angular frequency CAl less than CAlm will all be reflected from varying heights, and those with CAl greater than CAlm will penetrate through the medium. The frequency fm (= w m/ 27r ) is called the critical or penetration frequency of the medium. The electron collisions with heavy particles result in an absorption of the wave energy and a modification of the refractive index. In the ionosphere the latter modification is generally slight, and reflection still occurs near the level where the plasma frequency is equal to the wave frequency. The presence of the geomagnetic field introduces another complication, namely, that an incident wave is split into two waves, ordinary and extraordinary, with different polarizations, which propagate in general independently. The penetration frequencies for these two waves are different. For the ordinary wave this frequency is, under normal conditions, the maximum plasma frequency mentioned above. MAGNETOSPHERE 6h-20. The Magnetic Field Configuration [2,43,44]. The earth's magnetic field is confined to a bounded region of space by the solar wind plasma (Sec. 5h-21) ; this region is called the magnetosphere, and its outer boundary, the magnetopause. Its inner boundary is not well-defined, but may be regarded as the altitude above which the convection of the plasma and the motion of the energetic charged particles are predominantly controlled by the geomagnetic field. If this altitude is taken to be that at which the cyclotron frequency of the main constituent ions becomes comparable with their collision frequency, this is about 150 km height or near the base of the ionospheric F region. The magnetopause along the sun-earth line is at about 10R.OR. = earth's radius = 6371.2 km, Fig. 5h-9), and flares out toward its flanks to about 14R. in the meridian plane through 6 and 18 hr local time [45,46]. Beyond about 20R. behind the earth the magnetopause is nearly a cylindrical surface of radius 15 to 20R., enclosing the magnetosphere tail [46]. The surface current on the magnetopause (which is a consequence of the solar wind particles being reflected away from the magnetopause) increases the magnetic field inside it; the effect of the current is such that the magnetic field intensity just inside the magnetopause is made approximately twice as large as it would be if there were no confinement of the field. Roughly speaking, the surface current flows from the morning to the evening side on the sunlit part of the magnetopause and closes its circuit by flowing around two foci, one in each hemisphere, so as to form two vortices around them. The magnetic field immediately inside the magnetopause is everywhere parallel to the magnetopause except directly behind the foci, where the magnetic field just inside is normal to the magnetopause. These two singular points are called the null pionts. The current on the nearly cylindrical part of the magnetopause enclosing the magnetosphere tail flows from the evening toward the morning side both on the northern and southern halves; how the current closes is not as yet understood, though there have been models in which the current returns to the evening side along the equatorial plane where the magnetic field is weak. The general picture depicted above is necessarily highly idealized and serves merely as a guide

MAGNETIC FIELDS IN THE EARTH'S ENVIRONMENT

5-283

toward a better understanding of the real magnetopause, which must have a much more complex structure. The magnetic field configuration in the magnetosphere is schematically shown in Fig. 5h-l0. Let the polar angle of the points at which the two magnetic field lines through the null points intersect the earth's surface be denoted by 81, assuming, for simplicity, a symmetry with respect to the dipole equator. Then, 81 is near 15° (i.e., near, but not necessarily always identified with, the poleward boundary of the auroral electrojet belt near noon, as shown in Fig. 5h-5) [47]. In the (geomagnetic) noon meridian half plane containing the null points, the field lines intersecting the

,,\Ol't-\lst

~ :. :. ~.:"~_;\":'" ;'_:"._~: '!"_

...;mc,g:·f::I'l·\;\',:\·.'.•:. .•: .·,:.•.

':':i":/>\»~--' .c .

"/

'.' : '. /I

" '. '. \" i

>

HIGH

.:.:,':',':

Il REGION:·· ..

()

I ----'Ir---,....:-.,....-..----l

: .'. : : \ PlASMASPHERE }

./::.. :.... :.::>:---'--/

. - • • '"- ... t.. ... : .

EQUATORIAL

CROSS

-I.

~' ~

,

e

..

••

SECTION

FIG. 5h-9. Illustrations of the magnetosphere (Sees, 5h-20 and 5h-21): equatorial cross section; dots represent presence of plasmas; the sun is to the left.

earth's surface at polar angles greater than 81 are dipolar in their gross character, though they are deformed by the compression from the front. The field lines intersecting the earth's surface at polar angles less than 81 are drawn back over the pole toward the tail. In the midnight meridian half plane all field lines extend toward the tail, but there is a somewhat analogous polar angle, say 82, where the field lines leaving the earth at angles greater than 82 maintain some characteristics of a dipolar field at large distances. This angle, 82, is frequently near 19° and corresponds roughly to the poleward boundary of the auroral electrojet belt near midnight, as shown in Fig. 5h-5. The magnetic lines leaving the earth at polar angles less than 82 extend to great distances in the geomagnetic tail (Fig. 5h-1O) where they become nearly parallel to the direction of the solar wind flow outside the magnetosphere. The magnetospheric tail

6-284

ELECTRICITY AND MAGNETISM

®

®

RADIATION BELTS QUASI-TRAPPED RADIATION

NOON-MIDNIGHT CROSS SECTION FIG. 5h-IO. Illustrations of the magnetosphere (Sees. 5h-20 and 5h-21): noon-midnight meridianal cross section; dots represent presence of plasmas; the sun is to the left, and the tail extends to the right.

extends to at least 80R e [48] and may still exist at 1,000R e in a less well-defined form [49,50]. In the midnight meridian a third polar angle, 8 3 , can be designated corresponding to the lowest latitude of the east-west auroral electrojet, shown schematically in Fig. 5h-5. The radiation belts (region A of Fig. 5h-lO) lie on magnetic shells emanating from the earth at 8 > 8 3 • The magnetic field in the radiation-belt region is represented fairly accurately by the spherical harmonic description given in Sec. 5h-5. A transitory region (region B of Fig. 5h-lO) where trapping of energetic (e.g., >40 kev) particles is highly variable usually bounds the outermcst magnetic shell of

MAGNETIC FIELDS IN THE EARTH'S ENVIRONMENT

5-285

the radiation belts. Within the shells of this transitory region the spherical harmonic and dipole descriptions of the field become less accurate, and large deviations commonly occur. It has not been clearly established whether nightside field lines in region B (Fig. 5h.;.10) emanate from the earth at 8 > 83 or 8 < 8 3; 83 field lines could lie within region B or at the boundary between regions A and B. The uncertainty is greatly influenced by the fact that 83 (as noted in Sec. 5h-10) varies greatly with the level of activity. Close to the nightside equatorial plane beyond region B (Fig. 5h-10), in what can be called the near-tail region, the magnetic field maintains a shelllike structure, but is highly deformed by internal plasma pressures that inflate and stretch the field shells toward the antisolar direction. These shells emanate from the earth at 6 2 S 8 < 8 3 , For accurate mathematical description of the field in the outer magnetosphere expressions for the distortions created by the solar wind compression and the stresses exerted by plasmas within the magnetosphere and magnetospheric tail need to be added to the spherical harmonic description (Sec. 5h-5). However, as of 1970, expressions which adequately represent these effects analytically throughout the magnetosphere had not been derived. The time variability is one of the principal problems that is illustrated by considering some of the effects observed during storms, below, but present to some degree at all times: (1) a high solar wind pressure compresses the magnetosphere inward (Sec. 5h-12) such that 8 1 is increased and more magnetic flux is pushed back into the tail; (2) an enhanced plasma belt is created deep in the magnetosphere and exerts stresses that inflate the magnetosphere (Sec. 5h-11); (3) -complex changes in the plasma behavior in the near-tail region locally disturb the field [,51J; and (4) at the times of magnetic bays (Sec. ,5h-10), or substorms, the plasma stress is partially released and the near-tail field suddenly relaxes, or collapses, toward a more dipolar configuration [45J. 6h-21. Charged Particle Content. Plasmas [20,52,,53]. The presence of plasmas in the magnetosphere and their influences on the magnetic field have been mentioned in Sec. 5h-20. High fluxes of plasma are observed in the plasma sheet that lies approximately on the equatorial plane separating the earthward magnetic field in the northern half of the tail from the oppositely directed field in the southern half (Fig. 5h-1O). The thickness of the sheet is 4 to 6R. at the distance from the earth of about 17R•. The electrons in the plasma sheet have a broad, quasi-thermal energy spectrum peaked anywhere between a few hundred and a few thousand electron volts with a non-Maxwellian high-energy tail. In the midnight sector the plasma sheet reaches, under quiet conditions, distances of about lOR. from the earth and comes closer when disturbed. The sheet extends to the flanks and toward the front side, enveloping the magnetosphere, as shown in Figs. 5h-9 and 10. The inner boundary of the plasma sheet is well-defined on the evening to the afternoon side, but appears to be more diffuse on the morning side; however, detailed plasma behaviors on the dayside of the magnetosphere are as yet not known. On the nightside the plasma and the magnetic field show shell-like structures often with distinct discontinuities between neighboring shells. Whenever the ratio {3 of the plasma kinetic energy density (inmv2) to the magnetic field energy density (B2 /871') exceeds unity, the magnetic field is disturbed by the diamagnetic effect of the plasma, and the dipolar characteristics of the field are appreciably modified or completely lost. An example of the latter is seen in the outer skirts of the magnetosphere near the dawn and dusk meridians and near the geomagnetic equator where the magnetic field gradient is almost zero from about lOR. to the magnetopause. From ground-based observations of whistlers (Sec. 5h-33) and direct satellite measurements, it has been found that sudden decreases in electron densities occur near the magnetic equatorial plane at distances from the earth's center that vary with local time and disturbance from 3.5 to 7R ; The region of higher electron densities, about

5-286

ELECTRICITY AND MAGNETISM

10 cm- is called the plasmasphere, as shown in Fig. 5h-9. The outer boundary of the plasmasphere is referred to as the plasmapause, and its position moves toward the earth during periods of high magnetic activity [.54]. The plasmas inside the plasmasphere are of much lower energy than those in the plasma sheet, and unlike the latter, the plasma within the plasmapause is not known to play any major role in causing magnetic disturbances except that their presence makes the conductivity along the magnetic field lines very large. Energetic Particles [19,55,56]. The magnetosphere is populated with charged particles of a wide range of energies. These particles are distinguished from such transients as galactic and solar cosmic rays by their being "trapped" in the geomagnetic field for varying lengths of time. Hence their motion in the geomagnetic field is of fundamental importance; basic properties of their motion are discussed in Sec. 5h-22. Energies of the plasmas discussed above partially overlap with the low-energy part of particles described here, and the division of the charged-particle content of the magnetosphere into plasmas and energetic particles becomes arbitrary in some cases. Grouping of the particle populations is not definitively settled and is subject to future revisions. However, roughly speaking, the energetic particles in the magnetosphere can be divided into two groups: trapped and quasi-trapped particles. The definition of "being trapped" is by no means unambiguous; if a particle drifts around the earth repeatedly, it is considered to be trapped; see Sec..5h-22 for particle drifts. The region of trapped particles is from L r-....> 1.2 to 6; see Sec. 5h-22 for the definition of L. This population includes the so-called inner and outer radiation zones or belts that were discovered by the early probes. The inner zone contains protons of energies, E > 30 Mev, with fluxes of about 10 4 cm ? sec-I, and peak intensities near L r-....> 1.5; these particles are relatively stable with a time constant of the order of 1 year. The outer zone with electrons of E > 1..5 Mev is at L r-....> 3 to 4, and its flux is highly variable, particularly during magnetic storms. The time constant for these electrons is roughly hours to weeks. These early observations of penetrating radiation with heavily shielded Geiger tubes led to the concept of the inner- and outer-zone structure with a "slot" near L r-....> 2 where the count rate was a minimum [57]. However, later observations of particles in wider energy ranges have revealed that the structure described above was, to some extent, due to instrumental factors, and that different group of particles have grossly different spatial distributions and time variations, some with double peaks and a minimum near L r-....> 2, and others without such a structure. Nevertheless the terms "inner and outer zones" are used to refer to the regions approximately L < 2 and L > 2, respectively, without implying that the two regions are separated by a sharply defined boundary. Protons in the energy range 0.1 Mev < E < 5 Mev occupy the outer zone from L r-....> 2 to 6 and are found to be relatively stable with small fluctuations on time scales of days; this population of protons has high fluxes with a peak of the order of 108 cm" sec" near L r-....> 3.5 and carries most of the energy content of the trapped particles. Low-energy protons of E from a few kev to about 50 kev occupy a broad region from 3 to lOR., and their fluxes vary greatly during magnetic storms. These low-energy protons are mainly responsible for the inflation of the magnetosphere and the Dst decrease on the earth's surface during magnetic storms, described in Sec. 5h-11. The contribution to the storm effects from electrons in the energy range from a few hundred ev to 50 kev is likely to be appreciable, but probably only about one-fourth of that from the protons [20]. Electrons with higher energies (e.g., E 2:; 300 kev) occupy the outer zone, and their fluxes suddenly increase at the time of magnetic storms and decay to an equilibrium level with a time constant of days to weeks [58,59]. The sources of the trapped particles are not as yet well understood. The radioactive decay of albedo neutrons produced by nuclear collisions of galactic (and solar) cosmic-ray protons with oxygen and nitrogen nuclei in the atmosphere has been proposed to be the main source for the high-energy protons 2

3

MAGNETIC FIELDS IN THE EARTH'S ENVIRONMENT

5-287

in the inner zone. For the outer-zone protons, several processes involving an inward diffusion and acceleration have been propcsed; but there are no definitive proofs as to how efficient these mechanisms are. One suggestion is that the diffusion is caused by violation of the third adiabatic invariant (Sec. 5h-22), due to such magnetic perturbations as sudden impulses (Sec. 5h-12), and that conservation of the first and second invariants (Sec. 5h-22) leads to energization of the particles as they diffuse inward. A similar process resulting from fluctuations in the electric field of the magnetospheric convection system (Sec. 5h-23) has also been considered. The series of high-altitude nuclear explosions of 1958 (i.e., the Argus experiment) was designed to test the possibility of trapping energetic particles by the geomagnetic field [60J. Electrons mainly from the (3 decay of the fission fragments were injected into a thin shell near L ,-..,., 2, and were found to be stable in position during their lifetme of a few weeks. The Starfish explcsion of July 9, 1962 [61Jcreated a more intense and extensive artificial radiation belt; initially, a maximum flux (,-..,.,10 9 electrons em"? sec") was near L ,-..,., 1.3 with large fluxes extending to beyond L ,-..,., 4. For L < 1.5 the electron decay was slow, with lifetimes of the order of years, and was in agreement with the theoretical expectation for decay from Coulomb scattering of the electrons in the atmosphere. Beyond L ,-..,., 1.7 the decay was considerably faster, with lifetimes of months to a week; the rapid decay was thought to be due to resonant interaction of electrons with electromagnetic waves such as whistlers (Sec. 5h-33) or due to processes related to magnetic disturbances. Interactions between particles and electromagnetic waves of various frequencies from VLF to ELF or ULF (Sees. 5h-29 to 5h-33) constitute an important subject concerning the particle behaviors in the magnetosphere [62], but direct observational evidence for these interactions is in most cases still lacking. The quasi-trapped particles occupy regions between the trapping region and the magnetopause on the front to the flanks of the magnetosphere, and the near-earth tail region on the nightside. These particles mainly consist of low-energy protons and electrons with E :S 50 kev. Their fluxes are highly variable with geomagnetic activity; this population and its extension into the near-tail plasma sheet is probably the reservoir for the particles precipitating into the atmosphere during high-latitude disturbances. A major supply of particles for the trapping region may also come from the quasi-trapping region. Occasional high fluxes of particles have been observed in different regions; for instance, sudden flux increases of electrons with E ~ 40 kev and with omnidirectional fluxes up to about 10 7 electrons cm- 2 sec- 1 observed in the tail [63J (often referred to as electron "islands") and "spikes" of directional electron fluxes up to 10 9 electrons cm- 2 sec ? sterad"! encountered at low altitudes ('-""'1,000 km) [64J are examples of intensified particle activity in the quasi-trapping region. 6h-22. Energetic Particle Motion [2,56,65,66J. There are three fundamental characteristics in the motion of a charged particle in a dipole-type magnetic field such as the earth's field: (1) gyration about a line of force, (2) oscillation between mirror points along lines of force, and (3) longitudinal drift around the center of the dipole. Corresponding to these three periodicities there are three adiabatic invariants that are conserved. For the gyrating motion the first, or magnetic moment, invariant J..l is given by

where P J..

=

mo

=

B =

the component of the (relativistic) momentum perpendicular to the magnetic field vector B the particle rest mass

IBI

6-288

ELECTRICITY AND MAGNETISM

The motion of a charged particle can be investigated with high accuracies by an approximation in which the center of the gyrating motion, referred to as the guiding center, is followed. For the oscillatory motion of the guiding center between mirror points, the second, or longitudinal, invariant is conserved. This invariant, J, is defined by J = § P/I ds where PII is the guiding-center momentum parallel to the line of force, and the integral is taken over a complete oscillation. For J to be conserved, the drift velocity perpendicular to the lines of force along which the guiding center oscillates must be small compared with its velocity along the line of force. The guiding center drifts from a line of force to an adjacent line of force such that J is constant, and thus the lines of force, along which the guiding center moves, form a surface on which J is constant. If this surface is closed, namely, if the guidingcenter returns to a line of force which it previously traversed, there is a third periodicity. For this precessional motion of the guiding center, the third, or flux, invariant is conserved. The invariant is the magnetic flux , enclosed by the closed surface just described. Obviously, if the magnetic field is static, this invariant is trivial, but it remains constant even when the field varies in time, provided that the time of precession is small compared with the time scale for the field variations. Thus the third invariant is the first to be violated when the time scale of field fluctuations becomes short; the next is the second invariant J; and the first invariant J.l. is violated only by very rapid field variations with periods less than the particle's gyroperiod. From the constancy of J.l., the relation between the magnetic field strength Band the pitch angle a (= the angle between the velocity vector and the line of force about which the particle gyrates) is

Si~ a

=

constant

In particular, if B = B m at the mirror point (where a the equator ao is given by (Bo)~ SIn ao = B

=

7r

12), the pitch angle at

.

m

where B« is B at the equator. If J.l. is constant, and if there is no electric field,

J

= 2P

t: ( A

B)! ds

1 - B

m

where P is the linear momentum, and the integral is taken over a half oscillation from one mirror point A to its conjugate point A '. The quantity I defined by I

=L 2P

is a function of the mirror point A and the magnetic field configuration, and is independent of the particle properties. I can be considered as a function of position only, if the mirror point A is taken to be coincident with the point for which I is being evaluated. For a dipole field of moment M the quantity L d3BIM can be expressed as a function, say F, with an argument PBIM,

MAGNETIC FIELDS IN THE EARTH'S ENVIRONMENT

5-289

where Ls is the distance from the dipole to the equatorial crossing of the line of force that passes the point at which I is being evaluated. For the earth's magnetic field the magnetic shell parameter [67], L, is defined by the formula

where the functional form of F is taken to be identical with the corresponding function for the dipole field, but B and I are now computed using the spherical harmonic expression as given in Sec. 5h-5; M is the earth's magnetic dipole moment. L is usually measured in units of earth radii. Data for the trapped particles are normally organized in the (B,L) coordinate system. Because of the distortions of the geomagnetic field by the solar wind (Sec. 5h-20) and the charged particles inside the magnetosphere (Sec. 5h-21), the B, L coordinates as computed from the spherical harmonic expression for the surface field are usually accurate only to L '" 5. Beyond this distance the B, L coordinates computed in this way become gradually meaningless with increasing distance. At present there is no adequate analytical expression for the distorted magnetosphere field. So far the motion of a charged particle has been considered in the presence of a magnetic field B. In the presence of an electric field E in addition to B, the particle drifts in a direction transverse to B with a velocity v, given in a guiding-center approximation by B vB R v, = E X B2 + E.i B X qB3 + 2EliB X qB2R2 where E.i and Ell are kinetic energy perpendicular and parallel to B, respectively; q is the charge; R is the vector radius of curvature of the field line about which the particle gyrates: R = IRI, and in the absence of currents, l/R = V.iB/B. The three terms are often referred to as the E X B drift, the gradient drift, and the curvature drift, respectively. The longitudinal drift mentioned earlier corresponds to the combined effects of the gradient and curvature drifts in the geomagnetic field. 5h-23. Plasma Convection [2,68]. If a plasma in a magnetic field is taken to be a perfect conductor, Ohm's law is expressed by

E+vXB=O where E and B are the electric and magnetic field intensities, respectively, and v is the bulk velocity of the plasma. Under these conditions the magnetic field is referred to as a frozen-in field [66,69,70), and magnetic field lines can be identified by the plasma. E + v X B = 0 is also referred to as the hydromagnetic approximation, and as an approximation it has been useful in explaining the generation of electric fields in the magnetosphere and the consequences of these electric fields in causing electric currents in the ionosphere and electric field drifts (Sec. 5h-22) (proportional to E X B/B2) of energetic particles (i.e., particles of higher energy in populations of lower-energy density than the plasma particles moving in bulk with velocity v). In the frozen-in state, motions of plasma and magnetic field lines leave the magnetic field configuration unchanged and are said to interchange the lines of force. This has led to the concept that there may be a continuous convection of plasma in the magnetosphere. The geomagnetic field lines are also tightly "frozen" into the earth because of its high conductivity; however, the presence of a nonconducting neutral atmosphere between the earth and the ionosphere decouples the two frozen-in regions and makes magnetospheric interchange motions [71] possible. If the magnetic field configuration is unchanged, aBjat = 0, and consequently curl E = curl (-v X B) = O.

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This implies that magnetic lines of force and the streamlines of the flow are equipotentials of the electric field. Also, because magnetospheric magnetic fields are not uniform, interchange motions are accompanied by changes in plasma density and by adiabatic heating and cooling of the plasma during compressions and expansions. The gross pattern of convection in the magnetosphere and magnetospheric tail has been largely inferred from the distribution of currents associated with the auroral electrojets (Sec. 5h-l0), using two assumptions: (1) that the Hall conductivity 0"2 is much greater than the Pedersen conductivity 0"1 in the lower ionosphere (Sec..Sh-18), and (2) that the magnetic field lines in and above the lower ionosphere are lines of infinite conductivity and thus equipotential lines [47,72-74]. The electric field E = - y X B perpendicular to the electric current in the direction - Y (i.e., opposite v as a consequence of the electron motion in the region 100 to 130 km where the ion's transverse motion is inhibited by collisions) then maps directly into the magnetosphere from hemisphere to hemisphere. In the magnetospheric equatorial plane this produces a flow pattern in which plasma adjacent to the magnetopause on the nightside and near the twilight meridians flows, in general, away from the sun, and plasma in the central regions of the near-earth tail flows toward the sun. This picture is frequently interpreted as indicating that viscous interaction between the solar wind and magnetosphere pushes the outermost magnetospheric field and plasma roughly parallel to the direction of the solar wind flow. The flow from the tail toward the earth and sun is then regarded as the return flow. There are substantial reasons for believing that some such convection pattern exists associated with the auroral electrojects. In detail, however, the hydromagnetic approximation cannot strictly hold in that the ionospheric Pedersen conductivity is not negligible and tends to short-circuit the convective electric field. Deviations from the hydromagnetic approximation involving electrical loading in the ionosphere may, in fact, be responsible for many of the dynamical changes (e.g., the collapse of the near-tail magnetic field with the onset of a magnetic bay (Sec. 5h-20) can be viewed as being caused by an ionospheric release of the plasma pressure in the distant magnetosphere). Other effects, in addition to Pedersen current short circuiting, can cause a breakdown of the hydromagnetic approximation. Lack of sufficient plasma density to justify the infinite conductivity assumption is one possibility that could be important along the polar cap field lines extending deep into the magnetospheric tail. The hydromagnetic approximation also loses validity in regions where the electron and ion pressures are large; in these cases the expression becomes E + v X B = (ne)-1 grad p, where n, e, and p are the number density, charge, and pressure. Thus, in association with field shell discontinuities (Sec. 5h-20) in the near-tail and other large irregularities, significant deviations from the approximation are expected. Many outstanding problems in magnetospheric dynamics are closely related to determining the degree of applicability of the hydromagnetic approximation. Inasmuch as the problems relate to having information on electric fields in space, additional discussion is given in Sec. 5h-28. INTERPLANETARY MEDIUM

6h-24. The Solar Winds [43,44,75,76]. One of the basic dynamical properties of the solar corona is its continuous expansion outward. The resulting plasma flow is referred to as the solar wind. The solar wind velocity varies with activity on the sun, and ranges from 300 to about 850 km sec-I. The azimuthal direction of the average flow of the ions is 2 or 3 deg east of the sun after aberration due to the earth's orbital motion is corrected for, but the deviations in the arrival angle from the above average can be as large as 15 deg. Deviations of the flow direction from the solar ecliptic plane by as much as 5 deg have also been observed. Statistically the daily mean

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solar wind velocity v is related to the daily sum of three-hourly geomagnetic activity index x, (Sec. 5h-13) by a formula [77] v km sec- l

= 8.44~Kp

+ 330

However, on a finer time scale geomagnetic activity is not related to the solar wind velocity in any simple manner. The solar wind gas is mainly composed of electrons and protons. It also contains alpha particles in considerably variable quantity, from less than 1 to nearly 20 percent, with an average of 3 to 6 percent. A typical ion density in the solar wind is 1 to 10 protons ern-a, but low values of less than 0.1 proton ern-a and a maximum exceeding 80 protons ern-a have been observed. A transverse "temperature" (for the direction normal to the bulk velocity) has been determined from the angular distribution of the ion velocities. The proton temperature so defined varies from 10 4 to 10 6 K. The temperature determined for the direction parallel to the bulk velocity appears to be greater than the transverse temperature by a factor typically about 5 [78J. Data on the electron temperature in the solar wind are scarce, but a characteristic temperature of 8 X 10 5 K has been reported for low-energy electrons in the energy range between 33 and 1,000 ev; however, the electron temperature is likely to change appreciably with solar activity, as does the bulk velocity of the ions [79]. 6h-25. Interplanetary Magnetic Field [43,44,75,80]. Solar magnetic fields that extend beyond the solar corona are swept outward into interplanetary space by the solar wind (Sec. 5h-24). Thus, interplanetary space is permeated by magnetic fields of solar origin to distances that are thought to be of the order 100 AU (l AU = mean sun-earth distance, 1.496· 1013 ern). The intensity of the interplanetary magnetic field near the earth's orbit is usually within the range 2 to 10 1', with an average near 5 I' [81], but values as high as 25 I' are occasionally encountered. Although highly variable in direction, the statistical average direction in the ecliptic plane is closely approximated, considering only the rotation of the sun and the solar wind velocity. Thus, taking a as the angle between a radial line from the sun and the magnetic field in the ecliptic plane: a = tan-l(wr Iv) = tan ? (428/v) at 1 AU where r = distance from the sun, w = angular velocity of the sun's rotation, and v = solar wind velocity in km sec", In the ecliptic plane the magnetic field pattern sometimes indicates a sector structure with the field direction alternately pointing toward or away from the sun (on an average at angle a) in neighboring sectors. This pattern then corotates with the sun at its rotational period of approximately 27 days [81]. Although the magnetic field is clearly dominated by the solar wind, in that its energy density is only of the order of 1 percent of the kinetic energy density of the solar wind, it significantly modulates the flux of solar cosmic rays whose energy density is considerably less than that of the field. The flux of solar cosmic rays is thus anisotropic and roughly follows the filamentary magnetic flux tubes that constitute the prominent fine structure of the field [82]. In addition to this fine structure, hydromagnetic discontinuities are caused by the transient and nonuniform emission of solar wind plasma from the sun. These discontinuities develop into shock waves or form stationary contact surfaces, in the frame of reference of the plasma [83]. Effects of interplanetary discontinuities on the magnetosphere are discussed in Sec. 5h-26. 6h-26. Solar Wind-Magnetosphere Interaction [2,44]. The Alfven speed VA (Sec. 5h-29) in the solar wind is typically 60 km sec- l (with density n = 3 protons ern-a, and B = 5 1'); and hence the solar wind is hydromagnetically supersonic with a representative Alfven Mach number, M A( = viVA), of 7. Because of the variability in nand B, M A may be as low as 1.5 or may exceed 10. A standing bow shock is created on the upstream side of the magnetosphere boundary (Sec. 5h-20), analogous to that

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ELECTRICITY AND MAGNETISM

of an object placed in a supersonic flow of fluid. Whereas in the latter case sound waves communicate the presence of the object upstream to divert the flow around it, magnetoacoustic waves, which have a group velocity of the order of the Alfven speed, convey the message upstream in the solar wind to the shock. Since the mean free path in the interplanetary medium is of the order of 1 AU, the magnetosphere bow shock is a collision-free shock. In the subsolar region the flow is subsonic behind the shock with ion velocities considerably randomized. As the gas flows toward the flanks of the magnetosphere, the flow becomes more ordered, and beyond a sonic line the velocity is again supersonic. The flow pattern appears to be in agreement with theoretical results obtained using continuum models for the solar wind. According to gasdynamical calculations, the distance D from the earth's center to the magnetosphere boundary along the sun-earth line is approximately given by [84]

where a H0

=

earth's radius

=

6.3712 X 108 em

p

= dipole field intensity on earth's surface at the equator = 0.30953 gauss = solar wind density

v

=

solar wind velocity an adjustable constant which depends on the ratio of the specific heats, 'Y( = Cp/C v ) For large Mach numbers K approaches 0.844 for 'Y = 2 and 0.881 for 'Y = t. For a Newtonian gas model K is 2 if the particle reflection at the boundary is assumed to be specular or "elastic," or unity if this is assumed to be "inelastic." For large Mach numbers the standoff distance A at the nose of the magnetosphere can be expressed approximately by [84] A 1.1[h - l)MA 2 + 2] K

=

15

('Y

+ 1)MA 2

These theoretical results roughly agree with observations [45]. Representative observational values of D and A are 10 and 3 earth radii, respectively. As a result of the solar wind-magnetosphere interaction, the earth's magnetic field is drawn out to large distances forming a magnetosphere tail (Sec. 5h-20). ELECTRIC FIELDS 6h-27. Atmospheric Electricity [85,86]. Electrical phenomena between the earth's surface and an altitude of 30 km (roughly the peak altitude for airplane and balloon observations) are usually referred to as being atmospheric. At altitudes > 80 km, measurements of "electric fields in space" (Sec. 5h-28) have only recently been initiated. Between 30 and 80 km, measurements are essentially nonexistent, and theory is at most only an extrapolation from the lower "atmospheric" regions. Within the atmospheric region the ionizing agents are primarily cosmic rays and radiation from radioactive material in the earth and dust (both natural and from bomb debris). The vertical atmospheric electric field under clear weather conditions decreases rapidly with altitude from roughly 100 to 200 volts meter"! at the surface to 10 to 30 volts meter-I at an altitude of 6 km. Above roughly 10 km the potential gradient is often too weak to measure reliably, but appears typically to decrease to about 5 and 1 volts meter:", at 10 and 20 km, respectively. The conductivity (which depends primarily on ion mobilities) increases over these altitudes and ranges roughly from 1 to 10 to 30 X 10- 14 ohm"! meter"! at 0, 6, and 10 km, respectively. Field intensity and conductivity values, such as those above, are subject to many

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variations, even under clear weather conditions. Both seasonal and diurnal variations are generally recognized. Secular changes are also reported, which appear to be related to artificial factors such as changes in air pollution and periods of bomb testing. The fair weather electric field is negative upward such that positive ions move toward the earth. This fair weather electric current is, in general, considered to be a return current in that the principal generators for air-earth currents lie in regions where the atmosphere is disturbed by thunderstorms and precipitation. Models of the electrical structure of thunderstorms have been constructed for particular cases , but there is little agreement on the generality of such models when ligh tning and precipitation are included. Electric fields of several thousand volts per meter are commonly associated with disturbed conditions. The total potential drop associated with lightning reaches values of several million volts. 5h-28. Electric Fields in Space [14119]. Direct space measurements of the electric field E have only recently become feasible by measuring differences in floating potential between identical probes, symmetrically oriented relative to the spacecraft motion and the sun, and separated by long base lines for each axis of measurement [87]. The measurements have been successfully conducted in the ionosphere between 80 and 300 km at middle latitudes and in the auroral belt. Measurements have also been attempted in traverses through the magnetosphere and into the interplanetary medium, but these, to date, have involved errors, due to insufficient base line relative to plasma sheath phenomenal that prohibit accurate d-e values. Limits on the electric field and valid a-c electric field measurements (Sees. 5h-32 and 5h-33) have, however, come from these early efforts. Electric fields have also been indirectly measured by observing the motion of artificially created barium ion clouds above the region (approximately below 180 km) where collisions affect the cloud motion. The motion v in the known magnetic field B gives the electric field E frem E + v X B = 0 (Sec. 5h-23) [88]. The principal source of electric fields in the outer magnetosphere and high-latitude ionosphere appears to be the convection of plasma (Sec. 5h-23) driven indirectly by interaction between the solar wind and the earth's magnetic field. Both direct probe measurements [89] of E and motion measurements of v for artificial Ba+ clouds [90] have demonstrated that auroral electrojet currents are mainly Hall currents (in the direction -vas shown by the simultaneous magnetic disturbance field of the current) in that the quantities v and E have both been found to be at right angles to Bin a number of cases I including examples of both eastward and westward electrojet flow (Fig. 5h-5). These measurements essentially show that the hydromagnetic approximation (Sec. 5h-23) E + v X B = 0 gives a reasonable picture of the convection dynamics in the auroral belt (Sec. 5h-1O) region. The lack of a v component along B and one example [89] of a constant value for E between roughly 90 and 130 km when a probe trajectory fell along a magnetic field line during that section of a rocket flight provide additional support for treating the magnetic field lines as equipotentials. However, while verifying the proper vector relationships for E + v X B = 0 the measurements have shown that the electric field is highly variable in magnitude and can drop to extremely low values in narrow shells where the ionospheric conductivity is exceptionally high. These narrow shells contain discrete auroral forms. Over most of the belt within which aurora is occurring E is found to be > 0.01 volt meter ? with values between 0.02 and 0.05 volt meter"? being fairly common [89190]. Values as high as 0.13 volt meter"! have been observed I and as the total time of sampling has been small, it is highly probable that greater intensities are not uncommon. In contrast, directly on shells of discrete auroral forms E has been observed to drop below 0.005 volt meterr", which suggests that the E field is partially short-circuited in local strips of exceptionally high ionospheric conductivity. Observations that visual auroral structures show identical details when observed simultaneously at

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ELECTRICITY AND MAGNETISM

conjugate points in the northern and southern auroral belts [91] and that the magnetic disturbances are correlated in detail [92] illustrate that the potential distribution maps from hemisphere to hemisphere along magnetic field lines. Corresponding field intensities in the equatorial plane of the magnetosphere, taking into account the magnetic field geometry and its distortion in the near-tail region, are roughly 20 to 100 times less than in the ionosphere along the same magnetic shells. Over the polar cap (Sec. 5h-l0) there have not been definitive electric field measurements. If the polar-cap ionospheric currents are Hall currents, it can be estimated that the electric field has properties similar to those observed in the auroral belt. It is also not known whether or not magnetic field lines emanating from the polar cap can be treated as electrical equipotential lines in that plasma densities at large distances along these shells outside the equatorial plasma sheet in the tail have been below measurement thresholds. In middle- and low-latitude regions E and v measurements in and above the ionosphere have given values in the range 10- 4 to 2 X 10- 3 volt meter:", which in most cases is close to the magnitude of possible errors in measurement [88-90]. Measurements have not been made during periods of large disturbances, or storms, when one might expect the high-latitude convection system to penetrate more deeply into the magnetosphere. E magnitudes of the order 10- 3 volt meter"! can be expected from the Sq (Sec. 5h-8) dynamo (i.e., winds) in the ionospheric E region [93]. In addition to the convection process, a variety of mechanisms have been proposed for generating electrostatic fields relevant to specific problems in the ionosphere and magnetosphere [74,94,95]. Other than those cases where the indirect evidence is convincing (e.g., the polarization field required for the equatorial electrojet, Sec. 5h-8), their existence and/or importance is unproved. Electrostatic electric fields also play an essential role in a number of theoretical treatments of the magnetopause boundary and the bow shock (Sec. 5h-26). In the case of the bow shock, fields as strong as 5 volts meter"? have been postulated as existing in a thin region at the shock front [96]. However, the limited measurements available indicate that the fields are more of the order -v X B, where v is the plasma bulk velocity as in the hydromagnetic approximation (Sec. 5h-23) [89]. Similarly, in the interplanetary medium, E, as indicated in the spacecraft frame of reference, is compatible with -v X B for the solar wind velocity v (Note. This field does not exist in the frame of reference of the solar wind which is moving with velocity v.) For typical ranges of solar wind-interplanetary magnetic field parameters, the range of E (in spacecraft coordinates) is roughly 10- 3 to 10- 2 volt meter"? [89]. Relative to accelerating charged particles that enter the earth's (magnetospheric) frame of reference from inertial space, an additional electric field exists which is caused by charge separation induced by the rotation of the ionosphere with the earth [72,73]. The potential of this corotational field in the ionosphere is V = 90 sin! e in kilovolts, where e is the colatitude. As the corotational field is zero in the earth's reference frame, it does not create currents.

WAVE PHENOMENA 6h-29. Magnetohydrodynamic Waves [66,69,97]. Alfven Waves. In a perfectly conducting fluid permeated by a uniform magnetic field B o, Alfven waves propagate in the direction of B o with the Alfven velocity V A given by

Eo VA =--= V41rp where B« = !B o! (in emu, i.e., in gauss) and p = density (in cgs units, i.e., gem-a). The magnetic perturbation b and the fluid velocity v are both transverse to B o; and b2j 81r = ipv 2 ; i.e., an equipartition of energy holds.

MAGNETIC FIELDS IN THE EARTH'S ENVIRONMENT

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M aqneioacoustic Waves. In a perfectly conducting, compressible fluid permeated by a uniform magnetic field B o, magnetohydrodynamic waves propagate with a phase velocity V that satisfies

where V A = Alfven velocity (= B o/ V47rp) Co = sound velocity (= V 'YP/ p; 'Y = ratio of specific heats, p = pressure, and p = density) 8 = angle between Bo and direction of propagation When 8 = 0, the roots of the above equation are ± Co and ± V A, corresponding to a pure acoustic wave and a pure Alfven wave propagation along B o• When 8 = 7r/2, there is only one mode propagating with phase velocity, V = ± (C 0 2 + V A 2 )! ; in this wave the fluid velocity v is perpendicular to B o, and the magnetic perturbation b is parallel to Bo• The latter velocity is called the magnetoacoustic velocity. Between 8 = 0 and 7r/2 the two modes are coupled. 6h-30. Plasma Waves [98,99]. General. For a two-component (electron-ion) cold plasma in a uniform magnetic field B« the dispersion equation is given by

An 4

-

Bn 2

+C

=

0

where n = refractive index (= /k/c/w; k = angular wave number, c = velocity of light) A = S sin 2 8 + P cos! 8 B = RL sin! 8 + PS (1 + cos! 8) C =PRL S = i(R + L) D = i(R - L) R = 1 - aw 2/[(w + ni)(W - n.)] L = 1 - aw 2/[(w - ni)(W + n.)] P = 1- a a = (II.2 +II;2)/w 2 II.2 = 47rn.e2 /m. II;2 = 41rn;Z 2e2/mi n. = e Bo/mec = electron cyclotron frequency ni = Z e BO/mic = ion cyclotron frequency W = angular frequency of the wave B« = /Bol e(or Ze) = magnitude of electron (or ion) charge in esu units ms., = electron or ion mass in grams n•.; = electron or ion number density, cm- 3 8 = angle between the propagation direction (i.e., that of k) and B o The dispersion equation is quadratic in n 2, and hence there are in general two modes. In particular, for 8 = 0: n 2 = R (with right-handed circular polarization), and n 2 = L (with left-handed circular polarization); and for 8 = 1r/2: n 2 = RL/S (the extraordinary mode), and n 2 = P (the ordinary mode). Polarization, left- or righthanded, is defined, for positive w, with respect to the direction of the ambient magnetic field B o• Resonances occur when n 2 = ± 00, and cutoffs, when n 2 = O. Resonances: (1) 8 = 0: the electron cyclotron resonance at w = n. (R -+ ± 00); and the ion cyclotron resonance at w = ni (L -+ ± 00). (2) () = 1r /2: the lower hybrid resonance at WLH, where WLH approximately satisfies

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ELECTRICITY AND MAGNETISM

and the upper hybrid resonance at

where

WUH,

WUH

approximately satisfies

Numerous modes of plasma waves have been investigated extensively, but only those that are frequently encountered in the geophysical environment are mentioned below. All these modes are defined in a homogeneous plasma. The plasma in the magnetosphere cannot necessarily be regarded as being homogeneous, and drift waves may play an important role in inducing instabilities, but these and other instabilities are not discussed here since they are not as yet adequately understood under geophysical conditions. M agnetohydrodynamic Waves (w «ni)

n2 = 1 n cos! 8 = 1 2

+ 'Y + 'Y

where

'Y

for the fast mode (compressional wave) for the slow mode (Alfven wave) c2

(5h-l) (5h-2)

= 411"(ni mi + nom.) B o2 411"pc 2 B o2

~ --

P

= plasma density

the characteristic velocity c/ vi 1 + 'Y is called the Alfven velocity. When 'Y » I, this reduces to B o/ vf4;P, which is VA given in Sec. 5h-29. The slow mode disappears at w = ni. The fast mode exists at frequencies above n, and continues on to the whistler mode. The phase velocity of the fast mode is isotropic. Ion Cyclotron Waves (w S ni). The slow wave in Eq. (5h-2) has a characteristic dispersion relation just below the ion cyclotron frequency. In the neighborhood of w = n" n 2 for the two modes are approximately for the fast mode

(5h-3)

for the slow mode

(5h-4)

The ion cyclotron resonance appears in the slow mode; for this mode the dispersion relation can be rewritten as w2

(1 + kll 2 + kll

~ ni 2

IIi

2 2 C

2C 2

IIi

2 )-1

+ k 1.C2

where kll and k 1. denote the components of k parallel and perpendicular to B o, respectively. Waves in this mode are called ion cyclotron waves. The "Whistler" Mode (ni < w < no)' The branch that is an extension of the fast mode in Eq. (5h-l) is called the whistler mode. The term "whistler mode" originates from the circumstance that whistlers (Sec. 5h-33) propagate in this mode; however, the use of this term is not limited to the propagation of natural whistlers. The refractive index for this mode is approximately given by n2

= 1

aw w - no cos 8

provided that 0. sin' 8 «4w 2(1 -

and that

ap

cos! 8

(quasi-longitudinal propagation)

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where a = II e 2/ w 2 in the present approximation. For 8 = 0 the wave has a righthanded, circular polarization, and exhibits a resonance at w = ne , i.e., the electron cyclotron frequency; the wave becomes evanescent above ne• Ion Acoustic and Electrostatic Ion Cyclotron Waves. In a plasma with finite electron and ion temperatures 'I', and T i , respectively, ion acoustic waves propagate in the direction parallel to B o with a dispersion relation

if f3e (== 81rn eKT e/ B o2) is small and if T', « Te, where K is the Boltzmann constant. If To is comparable to T e, the ion thermal velocity becomes comparable to the wave phase velocity, and the wave will be strongly Landau-damped. For 8 ~ 0, and for frequencies above no but close to it, the electrostatic ion cyclotron wave can propagate, under certain conditions, with a dispersion relation

where k.l is the component of k perpendicular to Bs, Electrostatic Plasma Waves. In the absence of a magnetic field, a plasma resonates electrostatically with the frequency lIe (~ -vi 41rn ee 2/m e, ignoring the ion motion). This frequency is called the Langmuir or plasma frequency. The reflection of radio waves from the ionosphere is due to this resonance (Sec. 5h-19). 5h-31. Geomagnetic Pulsations [100-102]. Rapid geomagnetic fluctuations with periods approximately from 0.2 sec to 10 min (or roughly 5 to 0.001 Hz in frequency) are generally referred to as pulsations or micropulsations. Fluctuations (or signals) in the frequency range 3,000 to 3 Hz are often grouped under ELF (extra low frequency) waves and those with frequencies 300 km in the late morning hours along L shells (Sec. 5h-22), corresponding to invariant latitudes of 55 to 65° [106,89]. The percentage of time of occurrence as a function of signal intensity decreases markedly for E between 60 and 180 p'v meter'"! (rrns) at an altitude of 700 km [89]. Similarly, for samples distributed between 240 and 2,700 km altitude, occurrences decrease markedly for B between 2 and 6 milligammas (rms) [106]. Although occurrence is most frequent near 60° invariant latitude in the late morning, the total region of frequent occurrence (e.g., > 10 percent of the time) extends throughout the dayside hours 6h to 18h local time and invariant latitudes 50 to 70°. Although the ELF hiss signal is relatively steady in the sense that rapid changes in intensity are absent, it is frequently accompanied by a second signal, called ELF chorus. The chorus signals consist of a long series of wave packets, each having a duration of the order of one second, and the characteristic that the frequency rises with time within each packet. The time-space distribution of ELF hiss and chorus observed from satellites, and the fact that their occurrence at the earth's surface is less common and more erratic, suggest that these signals are repeatedly reflected from hemisphere to hemisphere from ionospheric levels. There is evidence that this reflection occurs roughly at the altitude where the signal frequency equals the proton gyrofrequency (but is presumably affected by the presence of heavier ions), and that the effective gyrofrequency also acts as a low-frequency cutoff [107]. Some signal apparently reaches the earth's surface through mode-coupling mechanisms. ELF signals of a more transient nature than the ELF hiss, noted above, are encountered in the auroral-belt and polar-cap regions. These are frequently associated with irregularities (Sec. 5h-17) in electron density and electric fields when observed by satellites [89]. Although most ELF emissions propagating in the whistler mode are believed to be generated in the magnetosphere, it has been suggested that a strong sigr al near 700 Hz in the auroral zone might be caused by proton cyclotron radiation in the ionosphere [108]. Part of the energy of the ELF (and VLF) emission from a lightning impulse propagates upward into the ionosphere and sometimes triggers a proton whistler [109]. In a frequency-time display, such as in a sonogram, a proton whistler has a dispersion characteristic of slowly rising frequency that asymtotically approaches the proton cyclotron frequency at the point of observation by a satellite. The frequency at which this proton whistler originates in the frequency-time display is an extension of the trace that corresponds to the "electron whistler," to be discussed in Sec. 5h-33. Proton whistlers are thought to be ion cyclotron waves (Sec. 5h-30). 6h-33. Whistlers and VLF Emissions [100,104]. Whistlers are electromagnetic signals in audio frequencies originating from lightning strokes. They are called whistlers because of their whistling sound when converted into audio signals. Whistlers typically have a descending tone from above 10 to 1 kHz; however, the upper limit can be as high as 30 kHz or even higher, and the lowest may extend to the ELF or even ULF range. The duration of a whistler is about one second, but some whistlers last only for a fraction of a second and others for two or three seconds. Whistlers propagate in the whistler mode (Sec. 5h-30), which is roughly a guided mode along the magnetic field lines. Only a slight electron density gradient is required to make tubes of magnetic force act like ducts for whistler propagation. Ducted whistlers often propagate back and forth between the two hemispheres repeatedly. The

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group velocity, with which wave energy propagates, has a maximum at a frequency of say, ft, and decreases for frequencies above and below ft. Therefore, in a frequencytime display (e.g., in a sonogram) a signal trace for a whistler that traveled a long distance shows the earliest arrival at ft and a gradual delay in arrival time as f departs from ft above and below. A whistler exhibiting such a dispersion characteristic is called a nose whistler, and the frequency ft of the minimum delay, the nose frequency. In a homogeneous medium fl is ifH, where f H is the electron cyclotron frequency (= Qe/21T-). The group delay time, say t, for a whistler that has traversed a one-hop path from one hemisphere to the other can be approximately expressed by

for f well below the nose frequency; the constant D, called the dispersion constant or simply the dispersion, is given approximately by

where c is the velocity of light, and [» the electron plasma frequency (= II e/21r). Apart from a constant, the integrand reduces to (ne/B)! where n e is the electron density, and B the magnetic field intensity. Thus various models for the electron density in the magnetosphere can be tested by comparing the observed D with the calculated values. Studies of electron densities in the magnetosphere by means of whistlers have shown that there is a "knee" in the electron density profile at several earth radii and that the electron density drops substantially beyond this distance (Sec. 5h-21). Whistlers have been detected by satellites at various altitudes in the magnetosphere, and their behaviors are now being investigated in detail. In addition to whistlers, there are other types of emissions in the VLF range; these are called VLF emissions. Several types of these emissions are observed in close association with whistlers, suggesting that they are triggered by the latter. VLF emissions may last steadily for minutes, or even hours, or may occur in bursts; converted to sound waves, they may produce a hissing sound or show a musical tone. (A division of hiss into ELF and VLF groups is entirely artificial.) VLF emissions are most frequently observed at middle and high latitudes, and indicate similarity in occurrence and form at magnetically conjugate areas in the northern and southern hemispheres. Such mechanisms as electron cyclotron radiation and Cerenkov radiation have been suggested for the origin of VLF emissions. The possibility of these VLF waves having significant interaction with energetic particles in the radiation belt has been extensively investigated [56,62]. References 1. Chapman, S., and J. Bartels: "Geomagnetism," Clarendon Press, Oxford, 1940, 1951, 1962 (corrected). 2. Matsushita, S., and W. H. Campbell, eds.: "Physics of Geomagnetic Phenomena," Academic Press, Inc., New York, 1967. 3. Vestine, E. H., L. LaPorte, 1. Lange, and W. E. Scott: The Geomagnetic Field, Its Description and Analysis, Carnegie Lnst. Wash. Publ, 580, 1947. 4. Adopted at the International Association of Geomagnetism and Aeronomy Symposium on Description of the Earth's Magnetic Field, Washington, D.C., Oct. 22-25, 1968. 5. Vestine, E. H.: Chap. II-2, p. 181, in ref. 2. 6. Cain, J. C.: Personal communication December, 1968. 7. Vestine, E. H., L. Laporte, C. Cooper, 1. Lange, W. C. Hendrix: Description of the Earth's Main Magnetic Field and Its Secular Change, Carnegie Insi, Wash. Publ. 578, 1947. 8. Symposium on Magnetism of the Earth's Interior: J. Geomaq. Geoei., 17 (3-4) (1965). 9. Cain, J. C., and S. J. Hendricks: The Geomagnetic Secular Variation 1900-1965, NASA Tech. Note TN-D-4527, 1968.

MAGNETIC FIELDS IN THE EARTH'S ENVIRONMENT

5-301

10. Cain, J. C., S. J. Hendricks, R. A. Langel, and W. V. Hudson: J. Geomaq. Geoel. 19,335 (1967). 11. Beloussov, V. V., P. J. Hart, B. C. Heezen, H. Kuno, V. A. Magnitsky, T. Nagata, A. R. Ritsema, and G. P. Woollard, eds.: The Earth's Crust and Upper Mantle, Am. Geophys. Union Geophys. Monooraph 13, Washington, D.C., 1969; in particular, chap. 5. 12. Serson, P. H., and W. L. W. Hannaford: J. Geophys. Research 62, 1 (1957). 13. MeCormac, B. M., ed.: Aurora and Airglow, Proc. NATO Study t-«; 1966, Reinhold Book Corporation, New York, 1967. 14. McCormac, B. M., ed.: Aurora and Airglow, Proc. NATO Study Lnst., 1968, Reinhold Book Corp., New York, 1969. 15. Harang, L.: Terrest. Magnetism and Atmospheric Elec., 51, 353 (1946). 16. Fukushima, N.: J. Fac. Sci. Univ., Tokyo, 8,293 (1953). 17. Heppner, J. P.: Ref. 13, p. 75. 18. Akasofu, S.-I.: Space Sci. Rev. 4,498 (1965). 19. McCormac, B. M., ed.: Earth's Particles and Fields, Proc. NATA Advanced Study Tnst., 1967, Reinhold Book Corporation, New York, 1968. 20. Frank, L. A., Ref. 19, p. 67. 21. Hoffman, R. A., and L. J. Cahill, Jr.: J. Geophys. Research 73, 6711 (1968). 22. Sugiura, M.: Ann. IGY 35,9, Pergamon Press, New York, 1964. 23. Sugiura, M., and S. J. Hendricks: NASA Tech. Note, NASA TN D-5748, 1970. 24. Mean, G. D.: J. Geophys. Research 69, 1181 (1964). 25. Sugiura, M.: J. Geopliu«. Research 70, 4151 (1965). 26. Bartels, J.: Ann. IGY 4,227, Pergamon Press, New York, 1957. 27. Lincoln, J. V.: Chap. 1-3, p, 67, in ref. 2. 28. Davis, T. N., and M. Sugiura: J. Geophys. Research 71, 785 (1966). 29. Rikitake, T.: "Electromagnetism and the Earth's Interior," Elsevier Publishing Company, Amsterdam, 1966. 30. Price, A. T.: Chap. II-3, p. 235, in ref. 2. 31. Madden, T. R .. and C. M. Swift, Jr.: In ref. 11. 32. Ratcliffe, J. A., ed.: "Physics of the Upper Atmosphere," Academic Press, Inc., New York, 1960. 33. Rishbeth, H.: Rev. Geophys. 6, 33 (1968). 34. Donahue, T. M.: Science, 159,489 (1968). 35. Cohen, R.: Chap. III-4, p. 561, in ref. 2. 36. Herman, J. R.: Rev. Geophys. 4, 255 (1966). 37. Symposium on Upper Atmospheric Winds, Waves, and Ionospheric Drifts, IAGA Assembly, 1967; J. Atmospheric and Terrer1t. Phys. 30(5), (1968). 38. Smith, E. K., and S. Matsushita, eds.: "Ionospheric Sporadic E," Pergamon Press, Oxford, 1962. 39. Smith, E. K., Jr.: Chap. III-5, p. 615, in ref. 2. 40. Baker, W. G., and D. F. Martyn: Phil. Trans. Roy. Soc. London, Ser. A, 246, 281 (1953). 41. Chapman, S.: Nuovo Cimento 4 (suppl.), 1385 (1956). 42. Ratcliffe, J. A.: "The Magneto-ionic Theory and its Applications to the Ionosphere," Cambridge University Press, London, 1959. 43. Hess, W. N., and G. D. Mead, eds.: "Introduction to Space Science," 2d ed., Gordon and Breach, Science Publishers, Iric., New York, 1968. 44. King, J. W., and W. S. Newman, eds.: "Solar-Terrestrial Physics," Academic Press, Inc., New York, 1967. 45. Heppner, J. P., M. Sugiura, T. L. Skillman, B. G. Ledley, and M. Campbell: J. Geophys. Research 72, 5417 (1967). 46. Ness, N. F.: Ref. 44, p. 57. 47. Heppner, J. P.: In ref. 14. 48. Ness, N. F., K. W. Behannon, S. C. Cantarano, and C. S. Scearce: J. Geophys. Research 72, 927 (1967). 49. Ness, N. F., C. S. Scearce, and S. C. Cantarano: J. Geophys. Research 72, 3769 (1967). 50. Wolfe, J. H., R. W. Silva, D. D. McKibbin, and R. H. Mason: J. Geophys. Research 72, 4577 (1967). 51. Sugiura, M., T. L. Skillman, B. G. Ledley, and J. P. Heppner: Presented at International Symposium on the Physics of the Magnetosphere, Washington, D.C., September, 1968. Sugiura, M.: In "The World Magnetic Survey 1957-1969," IAGA Bulletin No. 28. 52. Bame, S. J.: Ref. 19, p, 373. 53. Vasyliunas, V. M.: J. Geophys. Research 73, 2839 (1968). 54. Carpenter. D. L.: J. Geophys. Research 71, 693 (1966).

5-302

ELECTRICITY AND MAGNETISM

55. McCormac, B. M., ed.: Radiation Trapped in the Earth's Magnetic Field, Proc. Advanced Study Lnst., Bergen, 1965, D. Reidel Publishing Co., Dordrecht, Holland, 1966. 56. Hess, W. N.: "The Radiation Belt and Magnetosphere," Blaisdell Publishing Company, a division of Ginn and Company, Waltham, Mass., 1968. 57. Van Allen, J. A., and 1.. A. Frank: Nature 183, 430 (1959), 58. Brown, W. L., L. J. Cahill, L. R. Davis, C. E. McIlwain, and C. S. Roberts: J. Geophys. Research 73, 153 (1968). 59. Williams, D. J., J. F. Arens, and 1.. J. Lanzerotti: J. Geophys. Research 73, 5673 (1968). 60. Symposium on Scientific Effects of Artificially Introduced Radiations at High Altitudes, J. Geophys. Research 64(8), 865 (1959). 61. Collected Papers on the Artificial Radiation Belt from the July 9, 1962, Nuclear Detonation, W. N. Hess, ed., J. Geophys Research 68(3), 605 (1963). 62. Kennel, C. F., and H. E. Petschek: J. Geophys. Research 71, 1 (1966). 63. Anderson, K. A.: J. Geophys. Research 70, 4741 (1965); P. Serlemitsos: ibid. 71, 61 (1966); A. Konradi: ibid. 2317; E. W. Hones, Jr., S. Singer, and C. S. R. Rao: ibid. 73, 7339 (1968). 64. McDiarmid, 1. B., and J. R. Burrows: J. Geophys. Research 70, 3031 (1965). 65. Northrop, T. G.: "The Adiabatic Motion of Charged Particles," Interscience Publishers, a division of John Wiley & Sons, Inc., New York, 1963. 66. Alfven, H., and C.-G. Falthamrnar: "Cosmical Electrodynamics," Clarendon Press, Oxford, 1963. 67. McIlwain, C. E.: Ref. 55, p. 45. 68. Hines, C. 0.: Space Sci. Rev. 3, 342 (1964). 69. Cowling, T. G.: "Magnetohydrodynamics," Interscience Publishers, Inc., New York, 1957. 70. Dungey, J. W.: "Cosmic Electrodynamics," Cambridge University Press, London, 1958. 71. Gold, T.: J. Geophys. Research 64, 1219 (1959). 72. Axford, W. 1., and C. O. Hines: Can. J. Phys. 39, 1433 (1961). 73. Taylor, H. E., and E. H. Hones: J. Geophys. Research 70, 3605 (1965). 74. Obayshi, T., and A. Nishida: Space Sci. Rev. 8,3 (1968). 75. Parker, E. N.: "Interplanetary Dynamical Processes," Interscience Publishers, a division of John Wiley & Sons, Inc., New York, 1963. 76. Axford, W. 1.: Space Sci. Rev., 8, 331 (1968). 77. Snyder, C. W., M. Neugebauer, and U. R. Rao: J. Geophys. Research 68, 6361 (1963). 78. Hundhausen, A. J., J. R. Asbridge. S. J. Bame, H. E. Gilbert, and 1. B. Strong: J. Geophys. Research 72, 87 (1967). 79. Frank, L. A.: (abstract) Trans. Am. Geophys. Union 49,262 (1968). 80. Wilcox, J. M.: Space Sci. Rev. 8, 258 (1968). 81. Ness, N. F., C. S. Scearce, J. B. Seek, and J. M. Wilcox: "Space Research," vol. VI, p. 581, R. L. Smith-Rose, ed., Spartan Books, Washington, D.C., 1966. 82. McCracken, K. G., and N. F. Ness: J. Geophys. Research 71, 3315 (1966). 83. Colburn, D. S., and C. P. Sonett: Space Sci. Rev. 5, 439 (1966). 84. Spreiter, J. R., A. L. Summers, and A. Y. Alksne: Planet. Space Sci. 14, 223 (1966). 85. Coroniti, S. C., ed.: Problems of Atmospheric and Space Electricity, Proc, 3d Intern. Con], Atmospheric and Space Elec., 1963, Elsevier Publishing Company, Amsterdam, 1965. 86. Smith, L. G., ed.: Recent Advances in Atmospheric Electricity, Proc. 2d Con], Atmospheric Elec., Pergamon Press, New York, 1958. 87. Fahleson, U.: Space Sci. Rev. 7,238 (1967). 88. Haerendel, G., R. Liist, and E. Rieger: Planet. Space Sci. 15, 1 (1967). 89. Aggson, T. L., J. P. Heppner, N. C. Maynard, and D. S. Evans: Personal Communications; presentations at International Symposium on the Physics of the Magnetosphere, September, 1968. 90. Wescott, E. M., J. Stolarik, and J. P. Heppner: Trans. Am. Geophys. Union 49, 155 (1968). 91. Davis. T. N.: In ref. 14. 92. Wescott, E. M., and K. B. Mather: J. Geophys. Research 70, 29 (1965). 93. Maeda, H.: J. Geomaq. Geoelec, 7, 121 (1955). 94. Kern, J. W.: In ref. 2. 95. Chamberlain, J. W.: "Physics of the Aurora and Airglow," Academic Press, Inc., New York, 1961. 96. Tidman, D. A.: J. Geophys. Research 72, 1799 (1967). 97. Ferraro, V. C. A., and C. Plumpton: "An Introduction to Magneto-fluid Mechanics," Oxford University Press, London, 1961.

MAGNETIC FIELDS IN THE EARTH'S ENVIRONMENT

6-303

98. Stix, T. H.: "The Theory of Plasma Waves," McGraw-Hill Book Company, New York, 1962. 99. Akhiezer, A. I., I. A. Akhiezer, R. V. Polovin, A. G. Sitenko, and K. N. Stepanov: "Collective Oscillations in a Plasma," tr. H. S. H. Massey, tr. ed. R. J. Tayler, The MIT Press, Cambridge, Mass., 1967. 100. Bleil, D. F., ed.: "Natural Electromagnetic Phenomena below 30 kc/s," Plenum Press, Plenum Publishing Corporation, New York, 1964. 101. Campbell, W. H.: Ref. 2, p. 822. 102. Troitskaya, V. A.: Ref. 44, p. 213. 103. Madden, T., and W. Thompson: Re1). Geophys. 3, 211 (1965). 104. Helliwell, R. A.: "Whistlers and Related Ionospheric Phenomena," Stanford University Press, Stanford, Calif., 1965. 105. Gurn~tt, D. A.: Ref. 19, p. 349. 106. Taylor, W. W. L., and D. A. Gurnett: J. Geophys. Research 73, 5615 (1968). 107. Gurnett, D. A., and T. B. Burns: Unit'. Iowa Preprint 68-28, Department of Physics and Astronomy, 1968. 108. Egeland, A., G. Gustafsson, S. Olsen, J. Aarons, and W. Barron: J. Geophys. Research 70, 1079 (1965). 109. Gurnett. D. A., S. D. Shawhan, N. M. Brice, and R. L. Smith: J. Geophys. Research 70, 1665 (1965).

5i. Lunar, Planetary, Solar, Stellar, and G-alactic Magnetic Fields M. SUGIURA,l J. P. HEPPNER,! AND E. BOLDT 2

NASA-Goddard Space Flight Center H. W. BABCOCK 3 AND ROBERT HOWARD 4

H ale Observatories Carnegie Institution of Washington California Institute of Technology

LUNAR AND PLANETARY MAGNETIC FIELDS 6i-1. Moon. 5 , 6 According to the measurements made aboard the satellite Explorer 35, there appeared to be no magnetic field attributable to the moon at the distance of 800 km from the lunar surface. On the basis of the Explorer 35 observations the magnetic moment of the moon, even if the moon is magnetized, must be less than 4 X 10 20 cgs units, which is less than 10- 5 times the earth's magnetic moment. The conductivity of the moon seems to be sufficiently low to allow the interplanetary Lunar and planetary fields. Galactic fields. 3 Stellar fields. 4 Solar fields. 5 N. F. Ness, K. W. Behannon, C. S. Scearce, and S. C. Cantarano, J. Geophys. Research 72, 5769 (1967). 6 C. P. Sonett, D. S. Colburn, and R. G. Currie, J. Geophys. Research 72, 5503 (1967). J

2

5-304

ELECTRICITY AND MAGNETISM

magnetic field to be convected through it without noticeable change; the upper limit to the effective average conductivity has been estimated to be 10- 6 mho meter", 6i-2. Venus. I Mariner V detected a bow shock around Venus; the bow shock appeared to be similar to, but much smaller in dimension than, that of the earth (Sec.5h-20). The creation of the bow shock has been attributed to the presence of a dense ionosphere which prevents rapid penetration of the solar wind magnetic field and plasma into the atmosphere. The standoff distance of the bow shock at the time of the Mariner V traversal appeared to be about 4,000 km (or about 0.7 Venus radii) from the surface of the plane. No planetary magnetic field was detected at this distance. The upper limit to the magnetic dipole moment of Venus was estimated to be about 10- 3 times that of the earth. The observation that trapped charged particles (electrons with E; > 45 kev and protons with E p > 320 key) were absent in the vicinity of Venus is in agreement with the above estimate.

SOLAR FIELD 6i-3. General Magnetic Field of the Sun. Magnetic fields on the solar surface are measured by means of the Zeeman effect in solar spectrum lines. Since 1952 measurements of magnetic fields outside sunspots have been made with the solar magnetograph. 2 Tables 5i-1 and 5i-2 summarize data on magnetic fields in polar regions. TABLE 5i-1. THE POLAR MAGNETIC FIELDS OF THE SUN: 1912-1954 Investigator

Field intensity at North Polea

Hale, Langer" .......... -4 gauss Nicholson, Ellerman, +3 ± 1. 7 and Hickox" -2.0 ± 2.8 d von Khi ber ••.••.•.•.• eo>-

8H

(j

~

o>-

Z

tr.1 8H

o

"=i

H

tr.1 ~

t:J

lfL

en

eb o

'1

01

I

~

o

00

TABLE

No.

Star or HD

R.A.*

Dec.*

5i-3.

m"

MAGNETIC STAR DATA (AS OF

Sp,

wt

No. of obs.f

1958) (Continued)

Ht extremes§

Per. II

Remarks#

-71. .... 72 .....

187474 188041

73 ..... 74 ..... 75 ..... 76 .....

190073 191742 192678 192913 77 ..... 73 Dra 78 ..... Jf Equ 79 ..... 8 1 Mic 80 ..... AG Peg 81. .... VV Cep 82 ..... 215038 83 ..... 216533 84 ..... K Psc 85 ..... ~ Sel 86 ..... , Phe 87 ..... 108 Aqr 88 ..... 224801 89 ..... 4778

* Position for

19h48 ID27" 19 50 42

-40°01' - 3 15

5.4 5.6

AOp A5p

0.1+ 0.11

5/5 75/84

-1870 - 230

20 00 20 08 20 12 20 14 20 32 21 07 21 17 21 48 21 55 22 38 22 50 23 24 23 30 23 32 23 48 23 58 047

+ 536 +4224 +5330 +2737 +7447 + 956 -41 01 +1223 +6323 +7524 +5833 + 558 -3806 -4254 -19 11 +4458 +4444

7.9 7.8 7.1 6.7 5.2 4.8 4.9 7.6 5-6 8.0 7.9 4.9 4.5 4.8 5.3 6.2 6.1

Aep A7p A4p AOp A2p A7p

0.2+ 0.12 0.2: 0.2: 0.13 0.09 0.6-

1/12 2/5 0/1 4/10 9/14 21/31 1/3 14/30 5/17 0/2 5/6 0/17 1/3 0/2 0/12 2/22 0/4

+ 120 - 510

31 04 18 23 11 55 34 37 14 18 36 22 18 23 46 10 30

1950. Index of line width, w. t Number of plates measured/number of plates taken.

t

A.2P B+M M+B AOp A2p A2p B9p A2p AOp AOp AOp

••

0

•••

••

0.0

0.8: 0.15 0.8v 0.3: 0.4: 0.8: 0.8:

i-I

•

- 670 - 700 + 180 - 650 -1000 - 360 -3000: - 650

-

+1700 +1470 - 175 +2000: + 380 + 200: + 880 + 500 + 850 0 + + 660 + + +2300 +

2350 226

..... ..... ..... ..... ••

0

••

••

0

••

••

0

••

Eu, Si, Ti, Fe, (Mn, AI) Gd, Eu, Sr; secular changes; variable amplitude Ca Sr, (Si, Eu) Cr Si, X 4201 Ti, Eu, Sr; sp, variations periodic? Eu, Mg, Sr, (Si) Eu, Sr, Cr; diverse profiles

..0 ..

Sp, binary

.....

Si, X 4201 Sr, Cr, Eu, (Si) Sr, Ca, Eu, Cr Mn, Si; Y has neg. polarity Sr, Cr; pee. profiles Sr, Ca, Eu, Si, X 4201; pee. Eu, Si, Sr, X 4201 Eu, My, Sr, Cr

••

0

...

··0· • · . 0 •• ••

0

••

••

0

••

••

0

••

.....

§ H. = effective field intensity in gauss; crossover effect indicated by x, 1\ Period in days, or irregular. {I Elements showing abnormal line intensity, italicized if variable.

t:z:j

r-

t:z:j (1

~

~

'""" (1

'~ """ ~

>Z t:::1

a:::

o>Z

t:z:j

~

'""" a:::

tn

GALACTIC MAGNETIC FIELDS

5-309

ESSA Research Laboratory monthly series, IER-FB Solar Geophysical Data (Superintendent of Documents, Government Printing Office, Washington, D.C.). STELLAR MAGNETIC FIELDS 6i-6. Spectral Observations. Many stars have strong magnetic fields that can be detected and measured by means of the Zeeman effect. This method requires that the spectrum lines be relatively sharp, i.e., not much broadened by stellar rotation, and that the magnetic field be largely coherent as to polarity over the visible hemisphere of the star. The presence of numerous lines of the metals and of the rare-earth elements, showing predictable Zeeman splitting and polarization in a magnetic field, facilitates measurement. Instrumentation includes a rather large telescope for lightgathering power, a differential optical analyzer for polarization, and spectrographic equipment of high dispersion and high resolution. Most of the results to date have been obtained with the 100-, 120-, and 200-in. telescopes and coude spectrographs of the Mount Wilson, Lick, and Palomar Observatories, respectively. Results have been limited to stars brighter than 8.5 magnitude (photographic). Brighter stars can be observed at higher dispersion (4.5 A/mm) and with better precision. Except in a very few instances (e.g., HD215441), the components of Zeeman patterns are not individually resolved, but the use of a differential analyzer for righthand and left-hand circular polarization permits measurement of the displacement of the centroid of the blended Zeeman pattern when the two modes of polarization are compared. Results are expressed in terms of the effective field He. This is the uniform longitudinal magnetic field in gauss that would produce the measured displacement. It has been shown that a uniformly magnetized spherical star, with limbdarkening, viewed pole-on, would have a field strength at the pole equal to 3.3 H eBy convention, the polarity is taken to be positive when the field vector points toward the observer. Stars showing strong magnetic fields are mostly of spectral type late B, A, and early F.l.2 The most outstanding are the stars previously classified as the peculiar stars and spectrum variables of type A, practically all of which show fields in the range of several hundred to a few thousand gauss. All stellar fields adequately tested are found to be variable; many of the variations are periodic. Among the spectrum variables, the magnetic variations, roughly sinusoidal, are synchronous with periodic variations in the intensity of lines of various groups of elements such as the rare earths, chromium, and strontium. These variations are generally attributed to axial rotation of a star carrying an asymmetric distribution of magnetic areas. The periods of variation are characteristically a few days, but range up to 226 days for HD188041 and 2,350 days for HD187474. Preston! has tabulated the periodic magnetic variables as identified in 1967. Of these, 15 show reversals of magnetic polarity; only 3-HD188041, 78 Virginis, and HD215441-show always the same polarity. The strongest magnetic field yet measured in nature is that of the AOp star HD215441; for this the field at maximum has been measured at 35,700 gauss. Table 5i-3 summarizes data for 89 magnetic stars as of 1958,1 except that recently determined periods have been added for several stars from the work of Preston, Renson, Steinitz, and Wehlau. Table 5i-4 provides data for 38 additional magnetic stars discovered between 1958 and 1966. Much of the observational and interpretive work on the subject is reviewed by various authors in the Proceedings of the American Astronomical Society-National 1 2

8

H. W. Babcock, Astrophys. J. 128,228 (1958). H. W. Babcock, Astrophys.J. Supp. 3 (30), (1958). G. W. Preston, Astrophys. J. 160. 547 (1967).

5-310

ELECTRICITY AND MAGNETISM

TABLE 5i-4. MAGNETIC STAR DATA (FOR STARS DISCOVERED 1958-1966) Star or HD

R.A.*

Dec.*

2837 5797 9393 12288 16778 17775 18078 24712 50729 51106 E Pup} 55719 59435 89069

Oh29m59 8 058 6 1 30 53 2 o 14 2 40 51 2 50 48 2 53 34 3 53 23 6 52 19 6 53 52

+43°29' +60 14 +43 41 +6923 +5940 +61 43 +56 1 -12 13 - 451 - 1 30

9.1 8.8 8.5 8.0 7.7 8.8 8.0 5.9 9.1 7.7

7 10 56

-4026

5.4

7 27 42 10 17 42

-910 +7859

7.9 8.1

94660 115606 133652 141988 143939 162950 170973 171782 177984 179259 183806 186343 190145 190068 189932 355163 192687 +29°4202 200311

10 53 13 16 15 4 15 47 16 2 17 50 1830 1834 19 4 19 8 19 30 19 41 19 58 20 0 20 1 20 10 20 13 2049 20 59

-42 2 +13 13 -3046 +6228 -3920 +27 12 + 338 + 5 15 + 737 +44 30 -45 18 +22 12 +6722 +15 15 -3354 +1352 +q 43 +2939 +4354

6.3 8.3 6.0 8.3 7.0 7.8 6.3 7.9 9.1 8.9 5.9 8.2 7.4 8.0 6.9 8.7 8.6 8.8 7.9

201174 204411

21 4 56 21 25 26

+45 6 +4840

8.5 5.3

212385 215441 220147 221568

2222 16 2242 42 23 19 3 23 30 55

-3920 +55 22 +62 11 +5741

6.9 8.6 7.6 8.0

m.

Sp

w

No. of obs.

He extremes

--

12 4 7: 53 3 57 7 31 45 36 27 17 48 52 3 44 47 3 47

AO AOp AOp AOp B9p(?) AOp A2p A5, FO A5p A3p

2

A2 A5p (AOp) A3p AO A2 AOp A2p B9p A3 AOp AOp A2p A5p AOp A2p A2p AOp FOp AOp A2 AOp (AOp) B9p AOp (A3p) FO? A2p AOp B9p AOp

1/1 3/S 4/4 4/5 3/6 1/1 3/3 3/4 1/1 1/3

o±

148 -1960 ± 272 -1345 ± 95 +21 ± 153 +700 ± 90 +575 ± 60 -540 ± 88

+890 ± 190 +1215 ± 150

1/1

""'0.1 ""'0.3 ""0.5 ""'0.5

""'0.5 0.4 ""'0.3

+700 ± 127 +1420 ± 120 +2790 ± 170 -195 ± 109 +1620 ± 141 +1290 ± 111 +1075 ± 115 + 1000 ± 125

2/2 6/6

-430 ± 88 -440 ± 114

+848 ± 103 +445 ± 112

7/12 2/4 1/4 4/5 2/3 1/1 8/8 11/16 1/1 2/3 1/3 1/1 1/2 4/4 1/4 1/1 1/2 4/4

-1960 ± 87 -810 ± 139 -2080 ± 320 -810 ± 122 +690 ± 236 -565 ± 87 -1140±71 -1380 ± 130 -785 ± 110 -540 ± 77 -720 ± 271 -430 ± 60 -580 ± 77 +990 ± 192

-1020 ± 108 -60 ± 143

7/13

-1900 ± 159

+760 ± 139

27/32

-1825 ± 143

+1765 ± 177

-515 ± 41

+665 ± 70

-1260 ± 319 +4100 ± 370 -835 ± 151 -225 ± 172

+35, 700 +735 ± 138 +470 ± 69

5/6 1/2 28/37 4/5 6/8

-1520 ± 90

+1235 ± 129 +730 ± 260 +755 ± 52 +1190 ± 181 +40 ± 118

+1780 ± 183 +525 ± 86 +790 ± 228 + 1120 ± 264 + 1500 ± 134

* Position for 1960.

Aeronautics and Space Administration Symposium held at Greenbelt, Maryland, in 1965. 1 The book is replete with references.

GALACTIC MAGNETIC FIELD 6i-6. Summary. Some of the gross features of the galactic magnetic field have been inferred from information related to ccsmic rays (d. Ginzburg and Syrovatskii, 1964). A comparison of the observed cosmic-ray electron spectrum with the nonthermal radio spectrum arising from galactic synchrotron radiation indicates (Okuda and Tanaka, 1968) that the magnetic field is 10 to 20 microgauss near the galactic center, 5 to 10 microgauss near the solar system, and ~2.5 microgauss for the halo. Dynamical considerations (Parker, 1968) of the cosmic-ray pressure, due mainly to energetic protons, suggest that the average field of the disk is about 5 microgauss. 1 "The Magnetic and Related Stars," Robert C. Cameron, ed., Mono Book Corporation, Baltimore. 1967.

GALACTIC MAGNETIC FIELDS

5-311

Polarization measurements (cf. van de Hulst, 1967) of galactic nonthermal radio emission indicate that the coherence scale of the magnetic field of the disk is about 102 light years. The Faraday rotation measure for the polarization of distant discrete radio sources varies quite smoothly with galactic coordinates (Morris and Berge, 1964; Gardner and Davies, 1966) and corresponds to a field whose lines of force run parallel to the galactic plane in the direction [II ~ 70° for bII > 0, while below the plane (b II < 0) the direction of the field is opposite. These directions are in general agreement with the studies of the polarization of starlight by magnetically aligned interstellar grains (Smith, 1956; Behr 1959) and with the direction of the local Orion spiral arm (Sharpless, 1965). A search (Verschuur, 1968) for the Zeeman splitting of the 21-cm-absorption line by the atomic hydrogen of this local arm yields a limit to this HI-associated field as 0.6 ± 0.9 microgauss. A relatively strong magnetic field of 20 microgauss in the Perseus spiral arm, in the direction of Cassiopeia A, was clearly detected by the Zeeman effect in the course of the same observations. This measurement of a strong HI-associated magnetic field suggests that the search for detectable Zeeman effects in other absorption or emission spectra throughout the galactic disk should yield much new information. References Behr, A.: Nachr. Akad. Wiss. Gottinoen Math.-physik. Kl. I1a 185 (1959). Gardner, F. F .. and R. D. Davies: Australian J. Phys. 19, 129, 441 (1966). Ginzburg, V. L., and S. 1. Syrovatskii: "Origin of Cosmic Rays," Pergamon Press, New York, 1964. Morris, D., and G. L. Berge: Astrophys. J. 139, 1388 (1964). Okuda, H., and Y. Tanaka: Can. J. Phys. 46, S642 (1968). Parker, E. N.: "Stars and Stellar Systems," vol. 7., "Nebulae and Interstellar Matter," B. Middlehurst and L. Aller, eds., University of Chicago Press, Chicago, 1968. Sharpless, S.: "Stars and Stellar Systems," vol. 5, "Galactic Structure," A. Blaauw and M. Schmidt, eds., University of Chicago Press, Chicago, 1965. Smith, E. van P.: Astrophys. J. 124,43 (1956). van de Hulst, H. C.: "Annual Review of Astronomy and Astrophysics," vol. 5, L. Goldberg, ed., Annual Reviews, Inc., Palo Alto, 1967. Verschuur, G. L.: Phys. Rev. Letters 21,775 (1968).

Section 6

OPTICS BRUCE H. BILLINGS, Editor

Joint Commission on Rural Reconstruction, Taipei, Taiwan.

CONTENTS 6a. 6b. 6c. 6d. 6e. 6f. 6g. 6h. 6i. 6j. 6k. 61. 6m. 6n. 60. 6p. 6q. 6r. 6s.

Fundamental Definitions, Standards, and Photometric Units Refractive Index of Special Crystals and Certain Glasses. . . . . . . . . . . . . .. Transmission and Absorption of Special Crystals and Certain Glasses. . .. Geometrical Optics and Index of Refraction of Various Optical Glasses .. Index of Refraction for Visible Light of Various Solids, Liquids, and Gases Optical Characteristics of Various Uniaxial and Biaxial Crystals Optical Properties of Metals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Reflection Glass, Polarizing, and Interference Filters Colorimetry Radiometry Wavelengths for Spectrographic Calibration Magneto-, Electro-, and Photoelastic Optical Constants. . . . . . . . . . . . . . .. Nonlinear Optical Coefficients. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Specific Rotation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Radiation Detection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. , , Radio Astronomy Far Infrared Optical Masers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . • . . . . . . . ..

8-1

6-2 6-12 6-58 6-95 6-104 6-111 6-118 6-161 6-170 6-182 6-198 6-222 6-230 6-242 6-248 6-252 6-271 6.277 6-313

6a. Fundamental Definitions, Standards, and Photometric Units

6a-1. Fundamental Definitions Absorptance. The ratio of the radiant flux lost by absorption to the incident radiant flux. If 1 0 represents the incident flux, I r the reflected flux, I, the transmitted flux, the absorptance is given by the expression

Absorption, Bouger's Law. If 1 0 is the incident flux, I the flux passing through a thickness z of a material whose absorption coefficient is a,

where it is implied that I and 1 0 are measured within the material. The extinction coefficient k is given by the relation k = aX/41r, where A is the wavelength in vacuo and a is the absorption coefficient. The mass absorption is given by k/d, where d is the density. The transmittance is given by 1/10 • Absorption Spectrum. The spectrum obtained by the examination of light from a source that gives a continuous spectrum, after this light has passed through an absorbing medium. The absorption spectrum will be marked by dark lines or bands; in the case of gases these will be the reverse of many of the features of the emission spectrum. When the absorbing medium is in the solid or liquid state, the spectrum of the transmitted light shows broad, dark regions which are not resolvable into lines and usually have no sharp or distinct edges. Achromatic. A term applied to a lens, signifying that its focal length is the same for two quite different wavelengths. Angular Aperture. The arc sine of the ratio of radius to focal length of a lens. Apochromat. A term applied to a photographic or microscopic objective indicating that its focal length is the same for three quite different wavelengths. Astigmatism. An error characteristic of the formation of images oblique to the axis of axially symmetric optical systems. When astigmatism is present, the sharpest image of a radial line will be formed at a distance from the lens different from the sharpest image of a tangential line. Balmer Series of Spectral Lines. The wavelengths of a series of lines in the spectrum of hydrogen given in nanometers by the equation A

N2

= 364.6 N2 _ 4

where N is an integer having values greater than 2. Beer's Law (1852). If two solutions of the same salt are made in the same solvent, one of which is, say, twice the concentration of the other, the absorptance of a given 6-2

DEFINITIONS, STANDARDS, AND PHOTOMETRIC UNITS

6-3

thickness of the first solution should be equal to that of twice the thickness of the second. Blackbody. An almost completely enclosed cavity in a material of constant temperature. A small hole in the cavity completely absorbs all wavelengths of incident radiant energy. Brewster's Law (1811). The tangent of the polarizing angle for a nonabsorbing substance is equal to the index of refraction. The polarizing angle is that angle of incidence for which the completely polarized reflected ray is at right angles to the refracted ray. If n is the index of refraction, and (J the polarizing angle, n = tan (J. Candela. Symbol cd. International unit of luminous intensity. It is -10 of the intensity of one square centimeter of a blackbody at the temperature of solidification of platinum (2045 K). Chemiluminescence. Emission of light during a chemical reaction. Christiansen Effect. When a clean, finely powdered, homogeneous substance such as glass or quartz is immersed in a liquid of the same index of refraction, nearly complete transparency can be obtained, but only for substantially monochromatic light. If white light is incident, the transmitted color corresponds to the particular wavelength band for which the two substances, solid and liquid, have very nearly equal indices of refraction. Because of differences of dispersion, the indices of refraction will sufficiently match for only a narrow band of the spectrum. Chromatic Aberration. Because of the differences in the indices of refraction for different wavelengths, light of various wavelengths from the same source cannot be sharply focused at the same distance by any lens. The differences of focus are called chromatic aberration. Coma. An aberration characteristic of the formation of images oblique to the axis of axially symmetric optical systems. The image of a point consists of a family of eccentric circles all tangent to two intersecting, nearly straight lines in the focal plane. Conjugate Foci. Rays close to the axis, divergent from a point source on the axis of an axially symmetric optical system, converge on another point on the axis. The point of convergence and the position of the source are interchangeable and are called conjugate foci. Diffraction. Deviation of light from the paths and foci prescribed by rectilinear propagation (geometrical optics) consequent on the wave nature of light. Thus, even with a very small, distant source, some light, in the form of bright and dark bands, is found within a geometrical shadow because of the diffraction of the light at the edge of the object forming the shadow. Diffraction Grating. An array of fine, parallel, equally spaced reflecting or transmitting lines which mutually enhance the effects of diffraction at the edges of each so as to concentrate the diffracted light very close to a few directions characteristic of the spacing of the lines and the wavelength of the diffracted light. If i is the angle of incidence, d the angle of diffraction, s the center-to-center distance between successive rulings, n the order of the spectrum, the wavelength is

x = n~ (sin i

+ sin d)

Dispersion. In any spectrum-forming device, the difference of position along the spectrum per unit of wavelength difference, e.g., 1 millimeter per nanometer. Dispersion Equations. It is convenient and sometimes necessary to obtain equations relating refractive index to wavelength so that one can interpolate or perhaps even extrapolate with considerable accuracy and also obtain the most accurate values for dnldX. The equation due to Hartmann is n = no + (C I>" - >"0)' That due to Cauchy is n = A + (BI>..2) + (CI>..4), and a more complicated one derived by

6-4 Sellmeier is n 2

OPTICS

= 1 + (A oA2/ A2

-

Ao 2) .

An extension of the Sellmeier equation that m

. .IS n 2 = 1 . is useful for covering more than one a b sorption region

+~ \'

X2AiX _

2

xl

i=O

Finally, the Helmholtz expression, which includes an additional term B;j(A 2 - A;2) is useful within absorption regions as well. Usually, some of the terms of the summation are replaced by a constant. In practice, one of the above expressions is often used, and then a more accurate fit is found by an appropriate curve-fitting technique such as the method of least squares. A formula developed by Herzberger, which in some respects resembles Helmholtz's, is employed in Sec. 6d-2 to generalize the data in a condensed glass table. Dispersive Power. If nl and n2 are the indices of refraction of a substance for wavelengths Al and A2, and n is the mean index, or that for sodium light, the dispersive power of that substance for the specified wavelengths is n2 - nl

w=--n-l

This is also called Mean Dispersion, See also Reciprocal Dispersion. Doppler Effect (Light). Change of wavelength of the light observed which arises from any change of relative velocity of the observer with respect to the source of light. Emissive Power. See Radiation Formula, Planck's. Emissivity. Ratio of flux radiated by a hot substance to the flux radiated by a blackbody at the same temperature. Emissivity is usually a function of wavelength. Extinction Coefficient. See Absorption. Faraday Effect. Rotation of the plane of polarization produced when linearly polarized light is passed through certain substances in a magnetic field, the light traveling in a direction parallel to the magnetic field. For a given substance, the rotation is proportional to the thickness traversed by the light and to the magnetic field strength. Fermat's Principle of Least Time. The path followed by a ray between two points is that along which light can be propagated in less time than for any neighboring path. Fraunhofer's Lines. When sunlight is examined through a spectroscope, an enormous number of dark lines parallel to the length of the slit are seen against a bright continuous spectrum. The dark lines are Fraunhofer's lines. They are caused by resonance absorption by all the elements in the layers of vapors by which the sun is surrounded. The continuous spectrum from which those resonant frequencies are absorbed is produced by the extremely hot, highly compressed substances in the body of the sun proper. Many of the reversed or dark lines have the same wavelengths as bright lines found in the emission spectrum of the absorbing elements. Huygens' Theory of Light. Light is a continuous, cyclical disturbance propagated through space with constant velocity, frequency, and wavelength in any homogeneous transparent substance. Every point (subjected to that disturbance) acts as the center of a new disturbance having the same frequency, velocity, and wavelength radiating from it equally in all directions. The secondary disturbances from the neighboring points which were simultaneously disturbed by the initial wave coalesce to produce a net effect only along a surface which is the envelope of all the simultaneous neighboring secondary disturbances. This surface forms a new wavefront, which is further propagated in the same manner. Illuminance. Luminous flux incident per unit area. Metric units are the lux, one lumen per square meter, and the phot, one lumen per square centimeter. In the United States the lumen per square foot is commonly used. Unit illuminance

DEFINITIONS, STANDARDS, AND PHOTOMETRIC UNITS

6-5

is produced by a unit source at unit distance; hence the older names meter-candle for the metric unit the lux and the foot-candle, which is the same as the lumen per square foot. Index of Refraction. For any substance this is the ratio of the velocity of propagation of waves of light in a vacuum to its velocity of propagation in the substance. It is also the ratio of the sine of the angle of incidence to the sine of the angle of refraction. The index of refraction for any substance varies with the wavelength of the refracted light. Irradiance. Radiant power incident per unit area of a surface. The preferred symbol for this quantity is E; it is expressed in watts /m", Kirchhoff's Laws of Radiation. For each wavelength and temperature the emittance of any substance is equal to its absorptance. Lambert's Law of Absorption. Each layer of equal thickness of any homogeneous substance absorbs an equal fraction of the light which is incident upon that layer. Lambert's Law of Illumination. The illuminance of a surface on which light falls normally from a source small compared with its distance is inversely proportional to the square of the distance of the surface from the source. If the normal to the surface is inclined at an angle with the direction of the rays, the illuminance is proportional to the cosine of that angle. Lens Combination. If fl and /2 are the focal lengths of two thin lenses separated by a distance d, the focal length of the system is

Lens Formulas. The focal length F and distances p and q of pairs of conjugate foci (positive if convex) for a single thin lens which has index of refraction n and whose surfaces have radii of curvature rl and r2 are connected by

.!.

F

=

!p +!q =

(n - 1)

(1rl + 1) r2

If that lens has thickness t,

Lumen. See Luminous Flux. Luminance. The luminous flux per unit solid angle emitted per unit area as projected on a plane normal to the line of sight. The unit of luminance is that of a perfectly diffusing surface giving out one lumen per square centimeter and is called the lambert. The millilambert (0.001 lambert) is a more convenient unit. The candela per square centimeter is the luminance of a surface which has, in the direction considered, a luminous intensity of one candela per square centimeter of projected area. Luminosity. Ratio of the luminous flux in lumens to the total radiant flux in watts. Luminosity Maximum. 673 lumens per watt for 555 nm. Luminous Flux. The total amount of light emitted by a source per unit time is called the luminous flux from the the source. The unit of luminous flux, the lumen (symbol lm), is the flux emitted in a unit solid angle by a point source that has one candela luminous intensity. A one-candela point source that radiates uniformly in all directions thus emits 41r lumens into all space. Luminous Intensity. Luminous flux emitted per unit solid angle. The unit of luminous intensity is the candela. The symbol for luminous intensity is I.

6-6

OPTICS

The mean horizontal intensity is the average intensity measured in a horizontal plane passing through the source. The mean spherical intensity is the average intensity measured in all directions; it is equal to the total luminous flux in lumens divided by 411". Magnifying Power. In an optical instrument this is the ratio of the visual angle subtended by the image of the object seen through the instrument to the visual angle sub tended by the object when observed by the unaided eye. In the case of the microscope or simple magnifier the object when viewed by the unaided eye is supposed to be at a distance of 25 em. Minimum Deviation. The deviation, or change of direction, of light passing through a prism is a minimum when the angle of incidence is equal to the angle of emergence. If D is the angle of minimum deviation and A the angle of the prism, the index of refraction of the prism for the wavelength used is

n

= sin HA + D) sin

!A

Molecular Refraction. The molecular refraction of a substance can be computed by the following relation: M(n 2 - 1) N ::z d(n 2 + 2)

where N is the molecular refraction for a specified wavelength and temperature, M the molecular weight, d the density, and n the refractive index for the specified conditions. Nodal Points. Two points on the axis of a lens such that a ray entering the lens in the direction of one leaves as if from the other and parallel to the original direction. Optical Density. The common logarithm of the reciprocal of transmittance D

= log-t1

Polarized Light. Light which exhibits different properties in different directions at right angles to the line of propagation is said to be polarized. Specific rotation is the power of materials to rotate the plane of polarization. It is stated in terms of the rotation in degrees per decimeter per unit density or concentration. Principal Focus. For a lens or spherical mirror, this is the point of convergence of light coming from a source at an infinite distance. Radiance. The radiant power (flux) emitted in a specified direction, per unit projected area of surface, per unit solid angle. The preferred symbol for this quantity is L; it is expressed in watts per steradian per square meter. Radiant Energy. When a substance is excited-e.g., because it has a temperature above 0 K-it radiates energy, called radiant energy. This may be the amount of energy emitted during the entire radiating lifetime of the body, it may be the amount of energy for a given time period, or it may be the amount in a given volume of space. The preferred symbol for this quantity is Q; it is expressed in joules. Radiant Density. The radiant energy per unit volume of space is sometimes a useful quantity; it is called radiant density. The preferred symbol for this quantity is w, and it is expressed in joules /m". Radiant Exitance. Radiant power emitted into a full sphere (411" steradians) by a unit area of source. The preferred symbol for this quantity is M; it is expressed in watta/m>,

DEFINITIONS, STANDARDS, AND PHOTOMETRIC UNITS

6-7

Radiant Flux. The rate at which energy is radiated is called radiant power or flux. Radiant energy is the time integral of radiant flux. The preferred symbol for this quantity is If'; it is expressed in watts = joules/sec. Radiant Intensity. Radiant flux per unit solid angle, expressed in watts per steradian. The preferred symbol for radiant intensity is I. Radiation Formula, Planck's. The spectral exitance of a blackbody at wavelength ;\ and in a spectral range d;\ can be written

where M»; is watta/m"; Cl and C2 are constants with numerical values 3.7415 X 10- 16 watt· m 2 and 0.014388 m . K, respectively; A is the wavelength in meters; and T is Kelvin temperature. Radius of Curvature from Spherometer Readings. If 1 is the mean length of the sides of the nearly equilateral triangle formed by the points of the three legs, and d if; the normal distance from the mid-point of the triangle to the spherical surface on which the points rest, then the radius of curvature of the surface is

Reciprocal Dispersion. JI = (nD - l)/(nF - nc), where nc, n o, and nF are indices of refraction for the Fraunhofer lines C, D, F. The index nd for the Fraunhofer d lines is sometimes used instead of n o. The JI value is sometimes called the Abbe Number. Reflectance. The ratio of the reflected flux to the flux incident on a surface is called the reflectance; it may refer to diffuse or to specular reflection. In general, it varies with the angle of incidence and with the wavelength of the light. Symbol p. Reflection of Light at a Smooth Boundary between an Absorbing Medium and a Transparent Medium. At normal incidence, if no is the index of the transparent medium, and nl and k, are the index and extinction coefficients of the absorbing medium, the reflectance is p

=

+k + nIP + k

(no (no

nl)2

1

1

2

2

Reflection of Light by a Smooth Surface between Two Transparent Media (Fresnel's Formulas). If i is the angle of incidence, r the angle of refraction, nl the index of refraction of the medium from which the light is incident, n2 the index of refraction of the other, then for un polarized incident light the reflectance is R =

If i

!

[Sin 2 (i - r) 2 sin 2 (i + r)

+ tan

2

(i - r) ]

tan! (i

+ r)

where s~n ~ SIn t

=

~

n2

= 0 (normal incidence),

Refraction at a Spherical Surface. If u is the distance of a point object from a spherical surface separating two media, v is the distance of the point image or the intersection of a nearby refracted ray with the line defined by the object and the

6-8

OPTICS

center of curvature, nl and n2 are the indices of refraction of the first and second media, and r is the radius of curvature of the separating surface, then n2

v Refractivity.

+~

= n2 - nt

u

r

This is given by n - 1, where n is the index of refraction; the spe-

cific refractivity is given by (n - 1)/ d, where d is the density; molecular refractivity

is the product of the specific refractivity and the molecular weight. Relationships between Radiometric Units. In a nonabsorbing medium, for the geometrical arrangement in which the source and receiver areas are both perpendicular to the line joining their centers, the radiation quantities above are related as follows: cI>

= iJQ, at

M=~,

A,

L

=

M,

E

Wr

= La,

cI>

= IW r

where A, is source area, w, is the solid angle subtended by the source area at the receiver, Wr is the solid angle sub tended by the receiver area at the source, and r is the distance between the centers of the source and receiver areas. The corresponding relations connect the corresponding photometric quantities, which are distinguished by the root "lumi-" in place of "radi-." The same symbols are preferred for the photometric quantities as for the corresponding radiometric quantities. When symbols are needed for both photometric and radiometric quantities in the same context, the symbols for photometric quantities should be followed by the subscript v. The symbols of radiometric quantities should, in such cases, be followed by the subscript e. Resolving Power. For a telescope or microscope this is the minimum separation of two objects for which they appear distinct and separate when viewed through the instrument. Resolving power is often specified by the reciprocal, e.g., lines per millimeter. Rotatory Power, Molecular or Atomic. This is the product of the specific rotatory power by the molecular or atomic weight. Magnetic rotatory power is given by (J

t G cos a where G is the magnetic field strength, t is the thickness traversed, (J is the rotation of the plane of polarization by the Faraday effect, and a is the angle between the field and the direction of the light. Snell's Law of Refraction. If i is the angle of incidence, r the angle of refraction, v the velocity of light waves in the first medium, and v' the velocity in the second medium, the relative index of refraction n is

Specific Rotation. If there is n g of active substance in v em 3 of solution, and the light passes through 1 em, r being the observed rotation of the plane of polarization in degrees, the specific rotation (for 1 em) is [a]

=

TV

nl

DEFINITIONS, STANDARDS, AND PHOTOMETRIC UNITS

6-9

Spectral I rradiance. Irradiance per unit wavelength interval. The preferred symbol for this quantity is Ex; it is measured in units of watts per square meter per micrometer. Spectral Radiance. Radiance per unit wavelength interval. The preferred symbol for this quantity is Lx; it is measured in units of watts per steradian per square meter per micrometer. Spectral Series. Spectral lines or groups of lines which occur in an orderly sequence in the spectrum of an element. Spherical Aberration. When large surfaces of spherical mirrors or lenses are used, the light divergent from a point source is not focused exactly at a point. The phenomenon is known as spherical aberration. For oblique pencils it produces coma. Spherical Mirrors. If R is the radius of curvature, F is the principal focus, and 11 and /2 are any two conjugate focal distances, 1

1

1

2

-+-=-=/2 F R

11

If the transverse dimensions of the object and the image are 0 and I, respectively, and u and v their distances from the mirror,

Total Reflection. When light passes from a denser medium to one in which the velocity is greater, refraction ceases and total reflection begins, at a certain critical angle of incidence such that

where n is the index of the denser medium relative to that of the less dense. Transmissivity. The internal transmittance for unit thickness of a nondiffusing substance. Transmittance. If eJ>o and eJ> are the incident and transmitted luminous flux, respectively, the transmittance is given by eJ>/eJ>o. Transmittance, External. The external transmittance is the ratio of the flux that is transmitted through a sample to that which is incident on it. This is the quantity that is usually measured. The greater the losses by reflections at the surfaces, the smaller is the external transmittance; the greater the absorption, the smaller is the external transmittance. Transmittance, Internal. The ratio of the flux incident internally on the second internal surface of a sample to that leaving the first surface is the- internal transmittance. This is not a measurable quantity but is obtained from measurements of external transmittance corrected for reflection losses. Internal transmittance is related to sample thickness and absorption coefficient by Bouguer's law: Internal transmittance

= exp

(-ax)

Transmittance, Luminous. External transmittance, when flux is measured in photometric units (lumens). Transmittance, Radiant. External transmittance, when flux is measured in radiometric (powers) units. Transmittancy. The transmittancy is the ratio of the transmittance of a solution to that of a solvent.

6-10

OPTICS

Wein's Displacement Law. When the temperature of a radiating blackbody increases, the wavelength corresponding to maximum radiance decreases in such a way that the product of the absolute temperature and wavelength is constant. ArnaxT

= 0.0028978 m·K

Zeeman Effect. The splitting of a spectrum line into several symmetrically disposed polarized components, which occurs when the source of light is placed in a strong magnetic field. The directions of polarization and the appearance of the effect depend on the direction from which the source is viewed relative to the lines of force.

6a-2. Fundamental Standards Candela. The international standard unit of luminous intensity. It is -lo of the intensity of one square centimeter of a blackbody radiator at the temperature of solidification of platinum (2045 K). Primary Standard of Wavelength. The krypton " line whose vacuum wavelength is 6.057802106 X 10- 7 m. This is the unperturbed 2P w5d 5 transition of 86Kr. The actual definition was given by defining the standard meter as 1,650,763.73 vacuum wavelengths of the krypton line. Velocity of Light. An acceptable present value is 2.9979250 ± 10 X 108 meters per second (in SI units). This figure is taken from a paper by Taylor, Parker, and Langenberg, Rev. Mod. Phys., 41, 375 (1969). It should be considered an interim value pending completion of the work of the Task Group on Fundamental Constants, of the Committee on Data for Science and Technology, International Council of Scientific Unions. It is expected that the Task Group's recommended figure will be available in 1973.

6a-3. Photometric Quantities, Units, and Standards Apostilb, Unit of luminance. Ij1r cdjm 2• Symbol, asb. Blondel. Alternate name for apostilb. Candela. Unit of luminous intensity. It is io of the intensity of one square centimeter of a blackbody radiator at the temperature of solidification of platinum (2045 K). Symbol, cd. Efficiency of a Source of Light. The efficiency of a source is the ratio of the total luminous flux to the total power consumed. It is expressed in lumens per watt. Foot-Lambert. Unit of luminance equal to Ij1r candela per square foot. Symbol, fL. Lambert. Unit of luminance equal to Ij1r candela per square centimeter. Symbol, L. Ij1r sb. Least Mechanical Equivalent of Light. One lumen at the wavelength of maximum luminosity (555 nm) equals 0.00147 watt; 1 watt at the same wavelength equals 680 lumens. Lumen. The lumen is the unit of luminous flux. Symbol,lm. It is equal to the flux through a unit solid angle (steradian) from a one-candela point source or to the flux on a unit surface all points of which are at unit distance from a one-candela uniform point source. Luminous power of 1 talbot per second. Lux. Unit of illuminance. 1 lmym". Symbol, lx. Nit. Unit of luminance. 1 cdjm 2• Symbol, nt. Photo Unit of illuminance. 1 lm Zcm", Symbol, ph. Relative Luminosity. The relative luminosity for a particular wavelength is the ratio of the luminosity for that wavelength to the maximum luminosity. Values of the relative luminosity are given in Sec. 6j/ Colorimetry.

DEFINITIONS, STANDARDS, AND PHOTOMETRIC UNITS

6-11

Spherical Candlepower. The spherical candlepower of a lamp is the average intensity (candela) of the lamp in all directions. It is equal to the total luminous flux from the lamp, in lumens, divided by 41r. Stilb. Unit of luminance. 1 cd/cm 2 • Symbol, sb. Talbot. Unit of luminous energy, the product of lumens times seconds, Llm-sec. Troland. Unit of retinal illuminance. Illuminance produced on the retina of the human eye when a surface having luminance of 1 cd/m 2 is viewed through a pupil whose area is 1 mm", 0.4 times the illuminance produced on the retina when a surface having 1 millilambert luminance is viewed through a pupil having 1 millimeter diameter. Symbol, td.

6a-4. Photometric Equivalents Candela per Square Centimeter (Luminance). 1 stilb, 10,000 nit, 1r apostilbs, 3.1416 lamberts, 3,141.6 millilamberts. Candela per Square Inch (Luminance). 0.48695 lambert; 486.95 millilamberts. Foot-Candle (Illuminance). 1 lumen incident per square foot, 1.0764 milliphots, 10.764 lumens per square meter, 10.764 lux. Foot-Lambert (Luminance). 1.0764 millilambert. Lambert (Luminance). 0.3183 candela per square centimeter; 2.054 candela per square inch. One lumen is emitted per square centimeter of a perfectly diffusing surface having a luminance of 1 lambert. Lumen (Luminous Flux). Emitted by 0.07958 candela spherical intensity. A source of one candela spherical intensity emits 41r = 12.566 lumens. Lumen per Square Centimeter per Steradian (Luminance). 3.1416Iamberts. Lumen per Square Foot (Illuminance). One foot-candle, 10.764 lumens per square meter; 10.764 lux. Lumen per. Square Foot per Steradian (Luminance). 3.3816 millilamberts. Lumen per Square Meter (Illuminance). 1 X 10- 4 phot, 0.092902 foot-candle or lumen per square foot; 1.0 lux. Lux. 1 X 10- 4 phot, 0.1 milliphot, 0.092902 foot-candle. Meter-Candle (Illuminance). 1 lux, or 0.0929 lumen emitted per square foot (perfect diffusion). M illilambert (Luminance). 0.929 foot-lambert. Milliphot (Illuminance). 0.001 phot, 0.929 foot-candle; 10 lux. Photo 1,000 milliphots, 1.000 X 10 4Im/m 2, 10- 4 lx ; 929 candles. Stilb. 10,000 nit, 3.1416 lamberts, 31,416 apostilbs.

6b. Refractive Index of Special Crystals and Certain Glasses STANLEY S. BALLARD JAMES STEVE BROWDER JOHN F. EBERSOLE

University of Florida

Refractive indices for the following materials are given in this section: Ammonium dihydrogen phosphate (ADP) and Potassium dihydrogen phosphate (KDP) Barium fluoride Barium titanate Cadmium fluoride Cadmium iodide Cadmium selenide Cadmium sulfide Calcite Calcium fluoride Cesium bromide Cesium iodide Crystal quartz Cuprous chloride Diamond Fused silica Germanium Irtrans 1 to 6 Lanthanum fluoride Lead bromide Lead chloride Lead fluoride Lead selenide Lead sulfide Lead telluride Lithium fluoride Magnesium fluoride Magnesium oxide Muscovite mica Potassium bromide Potassium chloride Potassium iodide Rubidium bromide Rubidium chloride

Rubidium iodide Ruby Sapphire Selenium Silicon Silver chloride Sodium chloride Sodium fluoride Sodium nitrate Spinel Strontium titanate T-12 Tellurium Thallium bromide Thallium chloride Thallium bromide-chloride (KRS-6) Thallium bromide-iodide (KRS-5) Titanium dioxide Zinc sulfide Group III-Group V compounds: Gallium antimonide Gallium arsenide Gallium phosphide Indium antimonide Indium arsenide Indium phosphide N onoxide chalcogenic glasses: Arsenic-modified selenium glass Arsenic triselenide glass Arsenic trisulfide glass A telluride glass Texas Instruments Glass No. 1173 Special glasses: Cer-Vit Corning Vycor 6-12

6-13

REFRACTIVE INDEX OF CRYSTALS AND GLASSES

Refractive index, or index of refraction, can be defined in a number of ways. The complex refractive index, often written as n + ik, is defined and described in Sec. 6g. The real part of the refractive index of a substance can be defined as the ratio of the velocity of light in vacuo to the phase velocity of the light in the substance. Usually this quantity is called the absolute refractive index. Often the relative index-the ratio of the absolute refractive index of one substance to the absolute refractive index of another-is the more useful quantity. The refractive index relative to air is expecially useful, since most optical systems have air for both the initial and the final I Ge

4.0

~~Sb

Si

3.0

.

Ti02

x

w

Cl

~

'r\AS2S3 gloss

SrTi03

W

\

>

~

U

'i;~

....

~~

KRS-6 ........ ~

-

§ 0

~

lJ).

~ tu

er tv

CJ1

6-26

OPTICS

Dispersion equation:

TABLE

6b-13.

1 2 3 4

5

CONSTANTS OF THE DISPERSION EQUATION

0.00052701 0.02149156 0.032761 0.044944 25,921. 0

0.34617251 1.0080886 0.28551800 0.39743178 3.3605359

From W. S. Rodney, J. Opt. Soc. Am. 4.1,987 (1955) .

7.00

• - AVERAGE FOR 5 WAVELENGTHS X - VISIBLE DATA, AVERAGE OF 5 VALUES AT EACH WAVELENGTH

.p 8.00

r? 2

....~ 9.00

.g

10.00

FIG. 6b-4. The temperature coefficient of refractive index of cesium iodide. Rodneu, J. Opt. Soc. Am. 4:5,987 (1955).]

[From W. S.

The data for the region 0.185 to 0.76 pm were taken at 23°C by F. F. Martens, Ann. Physik 6, 603 (1901). Similar values are given by J. W. Gifford, Proc. Phys. Soc. (London) 70, 329 (1902), and by H. Trommsdorff, Z. Physik 2, 576 (1901). R. B. Sosman, "The Properties of Silica," Chemical Catalog Company, Inc., New York, 1927, gives a collation of the above data. The data for the wavelength region from 0.8325 to 2.30 ~m (at 20°C) are taken from A. Carvallo, Compt. Rend. 126, 728 (1898). For the region from 2.60 to 7.0 pm (at 18°C), the data are taken from H. Rubens, Wied. Ann. 64,488 (1895). The values fit together well (to a few parts in the fifth decimal place). They are, however, questionable at the extreme ends of the range (0.185, 5.00, 6.45, and 7.0 pm).

6-27

REFRACTIVE INDEX OF CRYSTALS AND GLASSES

Crystal Quartz

TABLE 6b-14. REFRACTIVE INDEX OF CRYSTAL QUARTZ A,.l'm

no

n.

A, I'm

no

n.

0.185 0.198 0.231 0.340 0.394 0.434 0.508 0.5893 0.768 0.8325 0.9914 1.1592 1.3070 1.3958 1.4792

1.65751 1.65087 1.61395 1. 56747 1.55846 1.55396 1.54822 1.54424 1.53903 1.53773 1.53514 1.53283 1.53090 1.52977 1.52865

1.68988 1.66394 1.62555 1.57737 1.56805 1.56339 1.55746 1.55335 1.54794 1.54661 1.54392 1.54152 1.53951 1.53832 1. 53716

1.5414 1. 6815 1.7614 1.9457 2.0531 2.30 2.60 3.00 3.50 4.00 4.20 5.00 6.45 7.0

1.52781 1.52583 1.52468 1. 52184 1.52005 1.51561 1.50986 1.49953 1.48451 1.46617 1.4569 1.417 1.274 1.167

1.53630 1.53422 1.53301 1.53004 1.52823

TABLE 6b-15. TEMPERATURE COEFFICIENTS OF REFRACTIVE INDEX dno/dT

dn./dT

x.. ~m

dno/dT

dn./dT

(l0-6;oC)

(lO-S;oC)

A,J,lffi

(10- 6;oC)

(10- 6;oC)

0.202 0.206 0.210 0.214 0.219 0.224 0.226 0.228 0.231 0.257 0.274 0.288

+0.321 0.253 0.193 0.124 0.074 0.017 -0.008 -0.027 -0.052 -0.186 -0.235 -0.279

+0.267 0.198 0.143 0.083 0.027 -0.048 -0.075 -0.093 -0.112 -0.265

0.298 0.313 0.325 0.340 0.361 0.441 0.467 0.480 0.508 0.589 0.643

-0.311 -0.348 -0.352 -0.393 -0.418 -0.475 -0.485 -0.499 -0.514 -0.539 -0.549

-0.415 -0.450 -0.469 -0.501 -0.521 -0.593 -0.601 -0.610 -0.616 -0.642 -0.653

-0.3~3

-0.385

From F. J. Micheli, Ann. Physik 4. 7 (1902).

Diamond

TABLE 6b-16. REFRACTIVE INDEX OF DIAMOND A,J,lffi

n

A,J,lffi

n

0.480 0.486 0.546

2.4368 2.4354 2.4235

0.589 0.644 0.656

2.4175 2.4114 2.4104

From von S. Rosch, Opt. Acta 12.253 (1965).

6-28

OPTICS TABLE

6b-17.

REFRACTIVE INDEX AT

20°C

FOR THREE SPECIMENS

OF FUSED SILICA

Measured difference X,l'm

Computed index

0.213856 0.214438 0.226747 0.230209 0.237833

C-D-G.E.*

Corning

Dynasil

General Electric

1.534307 1.533722 1.522750 1.520081 1. 514729

-27 - 2 +70 -21 + 1

-29 -11 +71 -28 +13

-42 -21 +68 -31 +23

-31 -22 +73 -23 +19

0.239938 0.248272 0.265204 0.269885 0.275278

1.513367 1.508398 1.500029 1.498047 1.495913

+ 3 + 2 -29 + 3 - 3

+ 6 + 6 -32 + 7 + 2

+ 2 - 1 -25 - 4 + 8

+ 9 + 7 -13 +11 +12

0.280347 0.289360 0.296728 0.302150 0.330259

1.494039 1.490990 1.488734 1.487194 1.480539

+ 1 +20 -14 - 4 - 9

- 4 +18 - 7 9 + 1

- 9 +22 -12 - 2 +10

-11 +20 - 4 +4 + 3

0.334148 0.340365 0.346620 0.361051

1.479763 1.478584 1.477468 1.475129

- 3 + 6 + 2 + 1

- 8 + 9 -17 + 3

- 1 + 2 -'-12 - 9

+ 9 - 8 -14 - 8

0.365015 0.404656 0.435835 0.467816 0.486133 0.508582

1.474539 1.469618 1.466693 1.464292 1.463126 1.461863

-19 + 2 - 3 + 8 + 4 + 7

-11 + 1 + 5 + 5 + 6 + 4

-15 - 1 + 1 + 3 + 5 + 1

-21 + 2 + 3 + 6 + 7 + 5

0.546074 0.576959 0.579065 0.587561 0.589262

1.460078 1.458846 1.458769 1.458464 1.458404

+ + + +

-

2 4 1 6 4

+ + + + +

4 5 6 3 6

+ 1 + 3 + 6 2 + 3

+ + + +

5 4 6 1 7

0.643847 0.656272 0.667815 0.706519 0.852111

1.456704 1.456367 1.456067 1.455145 1.452465

+ + + + +

6 3 3 5 5

+ 9 + 7 + 8 +10 + 8

+ 4 + 5 + 6 +12 + 3

+ + + + +

7 7 3 7 5

0.894350 1.01398 1.08297 1.12866 1.3622

1.451835 1.450242 1.449405 1.448869 1.446212

+ 5 + 8 - 5 + 1 -12

+11 + 6 + 8 + 7 - 6

+ 5 + 3 + 1 + 8 -14

+10 + 6 + 9 + 9 -12

1.39506 1.4695 1.52952 1.6606 1.681

1.445836 1.444975 1.444268 1.442670 1.442414

+ 4 - 5 + 2 -20 + 6

1 + 3 + 8 -14 2

-

-

+ 4 + 9 + 6 -19 -10

1.6932 1. 70913 1.81307 1.97009 2.0581

1.442260 1.442057 1.440699 1.438519 1.437224

0 + 3 +21 + 1 - 4

+ 7 0 7 + 6 - 3

-

- 6 + 3 - 7 +12 - 9

2.1526 2.32542 2.4374 3.2439 3.2668

1.435769 1.432928 1.430954 1.413118 1.412505

-29 -18 -24 +32 +25

-22 -10 -23 +21 +20

-25 - 3 -21 +29 +30

3.3026 3.422 3.5070 3.5564 3.7067

1.411535 1.408180 1.405676 1.404174 1.399389

+25 +20 -16 -24 -19

+32 +40 -26 -27 -22

+30 +42 -20 -29 -14

10.5

11.9

12.2

I

Average of absolute values of measured differences .............................

-

I I II

I

-

I

I

I

I

I

I

- 3 +10 0 -11 +8 + 1 - 1 + 6 +12 -11 -24 - 6 -14 +25 +25 +28 +37 -10 -18 - 9 11.7

* Difference for arithmetical mean table of values compiled from experimental data of Corning (C), Dynssil (D). and General Electric (G.B.). Adapted from 1. H. Malitson, J. Opt. Soc. Am. 1515, 1205 (1965).

REFRACTIVE INDEX OF CRYSTALS AND GLASSES

6-29

Dispersion equation: I _

n

_ 0.6961663A2 1 - A2- (0.0684043)2

+ A2

0.4079426A2 - (0.1162414)2

+A

0.8974794A2 (9.896161)2

2 -

The companies that submitted material for interspecimen comparison are Corning Glass Works, Dynasil Corporation of America, and the General Electric Company. They identify their brands as Corning code 7940 fused silica, Dynasil high-purity synthetic fused silica, and General Electric type 151. Each company submitted material from four different production runs. All specimens are considered to be of comparable optical quality, produced according to the highest standards of purity and uniformity. TABLE 6b-18. TEMPERATURE COEFFICIENT OF REFRACTIVE INDEX A,l£m

n,

n,

dn/dT

n,

dn/dT

26°C

471°C

(l0-6/0C)

828°C

(10- 6jOC)

0.23021 0.23783 0.2407 0.2465 0.24827

1.52034 1.51496 1.51361 1.50970 1.50865

1.52908 1.52332 1.52201 1.51774 1.51665

+19.6 +18.8 +18.9 +18.1 +18.0

1.53584 1.52985 1.52832 1. 52391 1.52289

+19.3 +18.6 +18.3 +17.7 +17.8

0.26520 0.27528 0.28035 0.28936 0.29673

1.50023 1.49615 1.49425 1.49121 1.48892

1.50763 1.50327 1. 50143 1.49818 1.49584

+16.6 +16.0 +16.2 +15.7 +15.6

1.51351 1.50899 1.50691 1.50358 1. 50112

+16.5 +16.0 +15.8 +15.4 +15.2

0.30215 0.3130 0.33415 0.36502 0.40466

1.48738 1.48462 1.48000 1.47469 1.46978

1.49407 1.49126 1.48633 1.48089 1.47575

+15.1 +14.9 +14.2 +14.0 +13.4

1.49942 1.49641 1.49135 1.48563 1.48033

+15.0 +14.7 +14.1 +13.6 +13.2

0.43584 0.54607 0.5780 1. 01398 1.12866

1.46685 1.46028 1.45899 1.45039 1.44903

1.47248 1.46575 1.46429 1.45562 1.45426

+12.7 +12.3 +11.9 +11.8 +11.8

1.47716 1.47004 1.46870 1.45960 1.45820

+12.9 +12.2 +12.1 +11.5 +11.4

1. 254* 1.36728 1.470* 1.52952 1.660*

1.44772 1.44635 1.44524 1.44444 1.44307

1.45283 1.45140 1.45031 1.44961 1.44799

+11.5 +11.4 +11.4 +11.6 +11.1

1.45700 1.45549 1.45440 1.45352 1.45174

+11.6 +11.4 +11.4 +11.3 +10.8

1.44230 1.43863 1.43430 1.42949 1.41995 1.41353 1.40990

1. 44733 1.44361 1.43933 1.43450 1.42495 1.41893 1.41501

+11.3 +11.2 +11.3 +11.3 +11.2 +12.2 +11.5

1.45140 1.44734 1.44306 1.43854 1.42877 1.42243 1.41915

+11.3 +10.9 +10.9 +11.3 +11.0 +11.1 +11.5

1.701 1. 981* 2.262* 2.553* 3.00* 3.245* 3.37*

I

• Wavelength determination by narrow-bandwidth interference filters. From J. H. Wray and J. T. Neu, J. Opt. Soc. Am. 69,774 (1969).

These values of dn/dT are for Corning No. 7940, ultraviolet grade.

6-30

OPTICS

Germanium TABLE 6b-19. REFRACTIVE INDEX OF GERMANIUM AT 27°C X, ,urn

Single-crystal n

Polycrystal n

2.0581 2.1526 2.3126 2.4374 2.577 2.7144 2.998 3.3033 3.4188 4.258 4.866 6.238 8.66 9.72 11.04 12.20 13.02

4.1016 4.0919 4.0786 4.0708 4.0609 4.0552 4.0452 4.0369 4.0334 4.0216 4.0170 4.0094 4.0043 4.0034 4.0026 4.0023 4.0021

4.1018 4.0919 4.0785 4.0709 4.0608 4.0554 4.0452 4.0372 4.0339 4.0217 4.0167 4.0095 4.0043 4.0033 4.0025 4.0020 4.0018

Adapted from C. D. Salzberg and J. J. Villa, J. Opt. Soc. Am. 48,579 (1958).

Resistivity is about 50 ohm-em. TABLE 6b-20. TEMPERATURE COEFFICIENT OF REFRACTIVE INDEX AT 24.5°C AND RELATIVE TEMPERATURE COEFFICIENT dn/dT

(l/n)(dn/dT)

X, ,urn

(l0-4;oC)

(1O- 4/oC)

1.934 2.174 2.246 2.401

5.919 5.285 5.251 5.037

1.432 1.287 1.280 1.231

From D. H. Rank, H. E. Bennett, and D. C. Cronemeyer, J. Opt. Soc. Am. 44, 13 (1954).

For computational purposes, a dispersion equation for the wavelength region 0.5 to 6.0 ,urn is given by M. Herzberger and C. D. Salzberg, J. Opt. Soc. Am. 62. 420 (1962) : n = A + BL + CL2 + D>..2 + EX' 1 where L = - - - X2 - 0.028

= 3.99931 B = 0.391707 C = +0.163492 D = -0.0000060 E = +0.000000053 A

Irtrans 1 to 6 TABLE

6b-21.

REFRACTIVE INDEX OF IRTRANS

1 to 6

X, p.m

Irtran 1 Irtran 2 Irtran 3 Irtran 4 Irtran 5 Irtran 6

A, p.m

Irtran 1 Irtran 2 Irtran 3 Irtran 4 Irtran 5 Irtran 6

1.0000 1.2500 1.5000 1.7500 2.0000

1.3778 1.3763 1.3749 1.3735 1.3720

2.2907 2.2777 2.2706 2.2662 2.2631

1.4289 1.4275 1.4263 1.4251 1.4239

2.485 2.466 2.456 2.450 2.447

1.7227 1.7188 1.7156 1.7123 1.7089

2.838 2.773 2.742 2.725 2.714

7.0000 7.2500 7.5000 7.7500 8.0000

1.2934 1.2865 1.2792 1.2715 1.2634

2.2304 2.2282 2.2260 2.2237 2.2213

1.3693 1.3648 1.3600 1.3550 1.3498

2.423 2.422 2.421 2.419 2.418

1.5452 1.5307 1. 5154 1.4993 1.4824

2.679 2.678 2.678 2.677 2.677

2.2500 2.5000 2.7500 3.0000 3.2500

1.3702 1.3683 1.3663 1.3640 1.3614

2.2608 2.2589 2.2573 2.2558 2.2544

1.4226 1.4211 1.4196 1.4179 1.4161

2.444 2.442 2.441 2.440 2.438

1.7052 1.7012 1.6968 1.6920 1.6868

2.707 2.702 2.698 2.695 2.693

8.2500 8.5000 8.7500 9.0000 9.2500

1.2549 1.2460 1.2367 1.2269

2.2188 2.2162 2.2135 2.2107 2.2078

1.3445 1.3388 1.3330 1.3269 1.3206

2.417 2.416 2.415 2.413 2.411

1.4646 1.4460 1.4265 1.4060

2.676 2.675 2.675 2.674 2.674

3.5000 3.7500 4.0000 4.2500 4.5000

1.3587 1.3558 1.3526 1.3492 1.3455

2.2531 2.2518 2.2504 2.2491 2.2477

1.4141 1.4120 1.4097 1.4072 1.4047

2.437 2.436 2.435 2.434 2.433

1. 6811 1. 6750 1.6684 1.6612 1.6536

2.691 2.689 2.688 2.687 2.686

9.5000 9.7500 10.0000 11.0000 12.0000

...... ......

2.2048 2.2018 2.1986 2.1846 2.1688

1.3141 1.3073 1.3002 1.2694

2.410 2.409 2.407 2.401 2.394

. ..... . ..... ......

~

4.7500 5.0000 5.2500 5.5000 5.7500

1.3416 1.3374 1.3329 1.3282 1.3232

2.2462 2.2447 2.2432 2.2416 2.2399

1.4019 1.3990 1.3959 1.3926 1.3892

2.433 2.432 2.431 2.430 2.429

1.6455 1.6368 1. 6275 1. 6177 1.6072

2.685 2.684 2.683 2.683 2.682

13.0000 14.0000 15.0000 16.0000 17.0000

6.0000 6.2500 6.5000 6.7500

1. 3179 1.3122 1.3063 1.3000

2.2381 2.2363 2.2344 2.2324

1.3856 1. 3818 1.3778 1.3737

2.428 2.426 2.425 2.424

1.5962 1.5845 1.5721 1.5590

2.681 2.681 2.680 2.680

18.0000 19.0000 20.0000

......

..... .

..... .

......

..... . . ..... . ...... ..... .

2.1508

..... .

. ..... . .....

.....

..... .

..... .

..0 . . .

. .....

..... . . .....

. .....

. .....

...... ...... ...... . ..... ...... 0

•••••

...... ......

2.386 2.378 2.370 2.361 2.352

. .....

...... . .....

. ..... . ..... . .....

. .....

tr.j ~

~

o> ~

H

-< tr.j

Z t:::I tr.j

X

o

~

2.673 2.672 2.672 2.669 2.666 2.663 2.660 2.657 2.655

2.343 2.333 2.323

From Kodak Pamphlet U-71. 1968.

Index of refraction values were experimentally determined at selected wavelengths between 1 and 10 p.m. Coefficients of an interpolation formula were established and reduced by least-square methods, and the values computed. All values beyond 10 p.m are extrapolated.

o

~

~

~

e-

Ul

>

Z

t:::I

o ~ Ul Ul

tr.j

Ul

151

BARIUM FLUORIDE SODIUM FLUORIDE

"2 + Cul. + G4jO

where x is the wavelength in micrometers, and L 1M. Herzberger, Opt. Acta 6, 197 (1959).

=

1/(>..2 - 0.028).

(6d-34)

6-102 TABLE

OPTICS

6d-2.

A REPRESENTATIVE SELECTION OF AVAILABLE OPTICAL GLASSES

Manufacturer*

Type

"

Schott ....... Schott ....... Schott ....... Schott ....... Schott ....... B &L ....... Schott ....... B &L ....... Schott ....... Schott ....... B &L ....... B &L ....... B &L ....... Schott ....... B &L ....... B &L ....... B &L ....... B &L ....... Schott ....... EK .......... B &L ....... B &L ....... Schott ....... B &L ....... B &L ....... Schott ....... B &L ....... Schott ....... Schott ....... EK .......... B&L ....... B&L ....... B &L ....... Schott ....... Schott ....... Schott ...•... B &L ....... B&L ....... Schott ....... B &L ....... B&L ....... Schott ....... Schott ....... EK .......... B&L .•••... B&L ....... EK .......... B &L ....... B &L ....... Schott ....... B &L ....... Schott ....... EK ....••.... Schott ....... Schott ....... Schott ....... B &L ....... Schott. " .... Schott ....... Schott ....... B &L ....... B&L ....... Schott ....... B &L ....... B &L ....... Schott ....... Schott ....... B&L ....... B &L ....... Schott ....... B &L ....... Schott ..... ,. Schott ....... Schott .......

FI(SOI FK05 PKSOI FK6 PSKSOI BSC PSKS6 BSC PSKI Kll DBC C DBC BaK2 C LBC DBC EDBC KI0 110 DBC LaC LaK18 CF EDBC BaLF5 LBF LaK19 KF6 210 CF LBF EDBC LaK17 SSK7 BaF5 LaF LaF LaF21 ELF BF BaF8 LaSFl 310 BF ELF 430 BF LF LFSI LaF BlLSF6 450 LaSF5 BaSFS6 BaSFlO DF BaSFS2 LaF13 FSI DBF DF' Bfl,SFI4 EDF EDF BaSFS7 SFS08 LaF EDF LaF9 EDF SFS3 SFS09 SFS06

81.61 70.34 69.69 67.28 67.25 67.0 65.41 63.5 62.88 61.59 61.2 60.5 60.3 59.66 68.6 57.4 57.2 57.2 56.46 56.15 55.5 54.8 54.67 54.6 53.9 53.61 53.4 53.24 52.16 51.18 51.0 51.0 50.9 50.48 50.36 49.25 48.0 47.5 47.37 47.3 47.2 47.04 46.76 46.42 46.0 45.5 44.69 43.6 42.5 42.19 42.0 41.88 41.80 41.00 40.99 39.31 38.0 37.99 37.83 37.06 36.6 36.2 34.95 33.8 32.2 32.15 31.30 31.0 29.3 28.39 27.8 26.10 23.83 20.36

* Schott B &L EK

I

nd.

0.5876

Jenaer Glaswerk Scuott & Bausch & Lomb. Eastman Kodak.

nA'. ~m

1.48523 1. 48749 1.52054 1.44628 1. 55753 1.49808 1. 60310 1. 51107 1.54771 1. 50013 1.58811 1. 51258 1. 62011 1.53996 1.52307 1. 57497 1. 61109 1.65709 1.50137

i:638io

1.69111 1.72875 1.52568 1.61711 1. 54739 1.58809 1. 75496 1.51742

.......

1.52408 1. 56210 1.65714 1.78847 1. 61847 1.60729 1.70012 1.72013 1. 78831 1.54110 1.67008 1.62374 1.80279

i:5839i

1.55860

i: 60542

1.57262 1. 54765 1. 72016 1.66755

i :88069

1. 70181 1.65016 1.60514 1.72340 1.77551 1.58407 1.65715 1. 62114 1.69968 1.64916 1.67269 1.73627 1. 61339 1.86725 1.72022 1.79504 1. 75084 1. 78470 1.84666 1.95250 Ul:lJ.

0.7682

~m

1. 48135 1.48282 1. 51556 1.44188 1.55205 1.49316 1.59704 1.50578 1.54198 1.49479 1.58184 1.50708 1.61342 1.53407 1.51729 1.56619 1.60423 1.64972 1.49560 1.68877 1.63074 1.68305 1.72004 1.51954 1.60980 1.54086 1. 58110 1.74574 1. 51105 1.72483 1. 51759 1.55518 1.64894 1.77841 1. 61069 1.1S9949 1.69098 1.71063 1.77767 1.53386 1.66123 1. 61541 1.79184 1.73491 1.57598 1.55086 1.76582 1.59682 1. 56425 1.53959 1.70957 1.65766 1.79180 1.86722 1.69108 1.63999 1.59538 1. 71160 1.76283 1. 57440 1.64616 1.61066 1.68749 1.63754 1.66012 1.72243 1.60174 1.85036 1.70555 1.77827 1.7a473 1.76688 1.82578 1.92545

nco

0.6563

nIl',

~m

1.48342 1.48534 1. 51824 1.44424 1.55'198 1.49577 1.60028 1.50860 1.54505 1.49765 1.58513 1.50999 1.61696 1.53720 1.52036 1.56956 1.60785 1.65362 1.49867 1.69313 1. 63461 1.68730 1.72469 1.52277 1.61368 1.54432 1.58479 1.75065 1.51443 1.72978 1. 52100 1.55879 1.65323 1.78375 1.61479 1.60359 1.69576 1.71561 1.78330 1.53768 1.66585 1. 61980 1.79763 1.74033 1.58013 1.55495 1. 77164 1. 60130 1. 56861 1.54382 1. 71508 1.66284 1. 79814 1.87430 1.69672 1.64529 1.60045 1.71779 1.76946 1.57945 1.65189 1.61610 1.69384 1.64355 1.66663 1. 72961 1. 60777 1.85910 1.71309 1.78695 1. 7430:i 1.77607 1. 83651 1.93U28

0.4861

I

nfl.

~m

1.48936 1.49227 1.52571 1.45088 1.56327 1.50320 1.60950 1.51665 1.55376 1.50577 1.59474 1.51846 1.62724 1.54625 1.52929 1.57953 1.61853 1. 66510 1. 50755 1.70554 1. 64611 1.69910 1.73802 1.53239 1. 62512 1.55453 1.59580 1.76483 1.52435 1.74417 1. 53127 1.56982 1.66614 1. 79937 1.62707 1.61592 1.71033 1.73077 1.79994 1.54912 1.68004 1.63306 1.81480 1. 75638 1.59282 1.56722 1.78902 1. 61518 1.58208 1.55680 1.73220 1.67878 1.81738 1.89578 1.71384 1.66183 1.61638 1.73683 1.78996 1. 59521 1.66984 1.63325 1. 71386 1.66275 1.68751 1. 75251 1.62737 1.88706 1.73766 1.81495 1.77005 1.80613 1.87204 1.98606

0.4047

I

I

I

~m

1.49520 1.49893 1.53295 1.45737 1. 57137 1. 51048 1.61857 1.52454 1.56230 1. 51379 1.60424 1.52685 1.63748 1.55528 1. 53819 1. 58951 1.62923 1.67649 1.51647 1. 71786 1.65772 1. 71248 1.75126 1. 54215 1.63670 1.56494 1.60697 1.77902 1.53446 1.75877 1. 54185 1. 58115 1. 67927 1.81514 1.63972 1. 62871 1.72536 1. 74645 1.81694 1. 56102 1.69472 1.64692 1.83239 1.77301 1.60615 1. 58010 1.80706 1.62987 1.59637 1. 57091 1. 74965 1.69579 1.83767 1.91825 1.73200 1.67968 1.63358 1. 75729 1.81201 1.61274 1. 68943 1.6.'>197 1.73599 1.68397 1. 71084 1. 77817 1. 65071 1. 91874 1.76542 ~.84675

1.80089 1.84085 1.91363 2.042811

6-103

GEOMETRICAL OPTICS

• 1.9

•

i.e

•

1.8 ..

1.7 I-nd

1.6 l-

1.5 ..

• •

•

1.4 90

•• • •• • • • •• • • • • • • • • •• • • • •• • • • • • • • • • •• • •• • • • • • • • • • • • • • •• • • • • •• • •

• I

I

I

,

80

70

60

50

40

I

I

30

20

lid

FIG. 6d-2. Graphical representation of

TABLE

c

D d

e F 0

0' h

TABLE

vs,

Vd

of the glasses shown in Table 6d-2.

UNIVERSAL FUNCTIONS FOR USE IN

A, ,urn

al

a2

0.76820 0.65630 0.58930 0.58760 0.54610 0.48610 0.43580 0.43410 0.40470

+1.000000 0.000000 -0.219082 -0.220644 -0.198539 0.000000 0.146293 0.145947 0.000000

0.000000 1.000000 0.951088 0.943152 0.652493 0.000000 -0.362709 -0.360970 0.000000

Line

--A'

6d-3.

nd

6d-4. j

EQ. (6d-33) a3

a4

0.000000 0.000000 0.317290 0.328101 0.619332 1.000000 0.835623 0.810864 0.000000

0.000000 0.000000 -0.049296 -0.050609 -0.073287 0.000000 0.380793 0.404160 1.000000

I

MATRIX OF COEFFICIENTS FOR DETERMINING UNIVERSAL FUNCTIONS

c.,

CZj

C3j

C4j

-10.181350 13.140533 2.192521 -0.149673

18.313606 -19.603381 -4.346029 0.311663

-9.815670 8.696877 3.108244 -0.267335

2.683413 - 2.234029 -0.954736 0.105345

-I 2 3 4

6e. Index of Refraction for Visible Light of Various Solids, Gases, and Liquids

6-104

fr-105

INDEX OF REFRACTION TABLE

6e-l.

INDEX OF REFRACTION OF SOME LIQUIDS RELATIVE TO

AIR·

Indices of refraction Substance

Density

Temp., °C

0397 pm 0.434 ",m 0.486 pm 0.589 pm 0.656 pm H F D 0' C

--- --- --- --- --- --- --Acetaldehyde, CH.CHO ......... Acetone, CH.COCH•........... Aniline, C.H.·NHs .............. Alcohol, methyl, CH,·OH ........ Alcohol, ethyl. C,H.·OH ......... Alcohol, ethyl. ................. Alcohol, ethyl, dn/dt . . . . . . . . . . . . Alcohol, n-propyl, C.H7'OH ..... Benzene, C.H•......••........ , Benzene, C.H. dn/dt ............ Bromnaphthalene, C lOH7Br...... Carbon disulfide, CB, .••........ Carbon disulfide ................ Carbon tetrachloride, CCk ...... Chinolin, C,H7N ...•••......... Chloral, CCI.·CHO ....•••...... Chloroform, CHCla............. Decane, CloHu ................. Ether, ethyl, C2H.·O·C,H•....... Ether, ethyl, dn/dt . . . . . . . . . . . . . . Ethyl nitrate, C2H.·O·NO•....... Formic acid, H·CO,H ........... Glycerine, C.HsO, .............. Hexane, CH.(CH2)4CH•......... Hexylene, CH.(CH,hCH·CH, ... Methylene iodide, CHsI, ........ Methylene iodide dn/dt ....... . . . Naphthalene, CIOHs............. Nicotine, ClOHuNI ............. Octane, CH.(CH2)SCH•...••.... Oil: Almond .....•.•.•....•...... Anise seed ..........•...•.... Anise ..................••... Bitter almond ................ Cassia ....................... Cassia .......... , ............ Cinnamon ................... Olive ........................ Rock ........................ Turpentine .................. Turpentine .................. Pentane, CHa(CH2hCH•........ Phenol, C.H.OH ............... Phenol. .......................

Styrene, C.H.CH·CH2. ......... Thymol, CIOHuO .............. Toluene, CHI·C6H•............. Water, H2O.................... Water ............ , ............ Water .... , .................... Water ..... , .....•..... , .......

0.780 0.791 1.022 0.794 0.808 0.800

..... 0.804 0.880

.....

1.487 1.293 1.263 1.591 1.090 1.512 1.489 0.728 0.715

..... 1.109 1.219 1.260 0.660 0.679 3.318

.....

0.962 1.012 0.707 0.92 0.99 0.99 1.06

..... .....

1.05 0.92

.....

0.87 0.a7 0.625 1.060 1.021 0.910 0.982 0.86

.....

..... ..... .....

20 20 20 20 0 20 20 20 20 20 20 0 20 20 20 20 20 14.9 20 20 20 20 20 20 23.3 20 20 98.4 22.4 15.1 0 15.1 21.4 20 10 22.5 23.5 0 0 10.6 20.7 15.7 40.6 82.7 16.6

......

1.3394 1.3359 1.3316 1.3298 1.3678 1.3639 1.3593 1.3573 1.6204 1.6041 1.5863 1.5793 1.3399 1.3362 1.3331 1.3290 1.3277 ...... 1.3773 1.3739 1.3695 1.3677 ...... 1.3700 1.3666 1.3618 1.3605 ...... -0.0004 -0.0004 -0.0004 -0.0004 1.3938 1.3901 1.3854 1.3834 1.5236 1.5132 1.5012 1.4965 ....... -0.0007 -0.0006 -0.0006 -0.0006 1.6582 1.6495 1.7289 1.704:1 1. 6819 1. 7175 1.6920 1.6688 1.6433 1.6336 1.6994 1.6748 1.6523 1.6276 1.6182 ...... 1.4729 1. 4676 1.4607 1.4579 ...... 1.6679 1. 6470 1.6245 1.6161 ...... 1.4679 1.4624 1.4557 1.4530 1.463 1.458 1.4530 1.4467 1.4443 ...... 1.4200 1.4160 1.4108 1.4088 ...... 1.3607 1.3576 1.3538 1. 3515 ...... -0.0006 -0.0006 -0.0006 -0.0006 ...... 1.395 1.392 1.3853 1.3830 ...... 1.3804 1.3764 1.3714 1.3693 ...... 1.4828 1. 4784 1.4730 1. 4706 ...... 1.3836 1.3799 1.3754 1.3734 ...... 1.4059 1.4007 1.3945 1.3920 1.7692 1. 7417 1.7320 1.8027 ........ ........ -0.0007 -0.0007 -0.0006 ........ 1.6031 1.5823 1.5746 ...... 1.5439 ........ 1.5239 1.5198 ...... 1.4097 1.4046 1.4007 1.3987

...... ......

...... ......

...... ......

...... ........ ........ ...... ........

1.6084

......

1.7039 1.6985

1.5775

........ ........

...... ........ ...... ........ ...... ........ 1.4939 ........ 1.4913 ........ ...... 1.3645 ...... 1.5684 ...... ........

....

...... 1.5816 ...... ........

20 20 0 40 80

1.3435 1.3444 1.3411 1.3332

• "SmithlJonian Physical Tables," 1954, Table 551.

......

1.5170 1.3404 1.3413 1.3380 1.3302

1.4847 1.5743 1. 5647 1.5623 1.6389 1. 6314 1.6508 1.4825 1.4644 1.4817 1.4793 1.3610 1.5558 1.5356 1.561>9 1.53S6 1.5070 1.3372 1.3380 1.3349 1.3270

1.4782 1. 5572 1. 5475

........ 1.6104 1.6026 1. 6188 1.4763 1.4573 1. 4744 1.4721 1.3581 1.5425

........ 1.5485

........ 1.4955 1.3330 1.3338 1.3307 1. 3230

1.4755 1.5508 1.5410 1. 5391 1.6007 1.5930 1.6077 1. 4738 1.4545 1.4715 1.4692 1.3570 1.536P 1. 5174 1.5419 1.5228 1.4911 1.3312 1.3319 1.3290 1.3313

6-106

OPTICS TABLE

6e-2.

INDEX OF REFRACTION FOR SOLUTIONS OF SALTS AND ACIDS RELATIVE TO AIR*

Indices of refraction for spectrum lines Density

Substance

1-----,.---------------

Temp.,

°C

c

D

F

1.37936 1.35050 1.44279 1.39652 1.37369 1. 41109 1.40181 1.40281 1.34278 1. 35179 1.36029 1.41334 1.37789 1.35959 1. 34191 1.38535 1.43669 1.42466 1.37009 1.33862 1.40222 1. 37515

1.38473 1.35515 1. 44938 1.40206 1.37876 1. 41774 1.40857 1.40808 1.34719 1.35645 1.36512 1. 41936 1.38322 1.36442 1.34628 1.39134 1.44168 1.42967 1.37468 1.34285 1.40797 1.38026

H

Solutions in Water Ammonium chloride ............ Ammonium chloride ............ Calcium chloride ............... Calcium chloride ............... Calcium chloride ............... Hydrochloric acid .............. Nitric acid ..................... Potash (caustic) ................ Potassium chloride .............. Potassium chloride .............. Potassium chloride .............. Soda (caustic) .................. Sodium chloride ................ Sodium chloride ................ Sodium chloride ................ Sodium nitrate ........... " .... Sulfuric acid ................... Sulfuric acid ................... Sulfuric acid ................... Sulfuric acid ................... Zinc chloride ................... Zinc chloride ...................

1.067 27.05 29.75 1.025 25.65 1.398 22.9 1.215 1.143 25.8 1.166 20.75 18.75 1.359 11.0 1.416 Normal solution Double normal Triple normal 21.6 1.376 1.189 18.07 1.109 18.07 18.07 1.035 1.358 22.8 1.811 18.3 1.632 18.3 1.221 18.3 1.028 18.3 26.6 1.359 26.4 1.209

1.37703 1.34850 1.44000 1. 39411 1.37152 1. 40817 1.39893 1.40052 1.34087 1.34982 1.35831 1.41071 1. 37562 1. 35751 1.34000 1.38283 1.43444 1.42227 1.36793 1.33663 1.39977 1.37292

.......

....... .......

....... '0

•••••

....... ....... .......

1. 39336 1.36243 1.46001 1. 41078 1.38666 1. 42816 1.41961 1.41637

1.35049 1.35994 1. 36890

.......

1.42872

1.38746 1.36823 1.34969

....... ....... .......

1. 40121 1.44883 1.43694 1.38158 1. 34938 1.41738 1.38845

1.36395 ....... 1.35986 . ...... . ...... 1. 361 . ...... 1.3705

1.37094 1.36662 1. 3759 1.3821

.0

•••••

.0

•••••

.0

•••••

.......

Solutions in Ethyl Alcohol Ethyl alcohol .................. Ethyl alcohol .................. Fuchsin (nearly saturated) ....... Cyanin (saturated) .............

.....

.....

..... .....

25.5 27.6 16.0 16.0

1.35971 1. 35971 1.35372 1.35556 1.3918 1.398 ....... 1. 3831

Note: Cyanin in chloroform also acts anomalously; for example, Sieben gives for a. 4.5 % solution = 1.4593, IoIB = 1.4695, loll' (green) = 1.4514, lJ.a (blue) = 1.4554. For a 9.9 % solution he gives lolA = 1.4902, 101, (green) = 1.4497, lola (blue) = 1.4597. lolA

Solutions of Potassium Perrnanganate in Water Wavelength, 101 m

Index Spec- Index Index Index Wavetrum for 1 % for 2 % for 3 % for 4 % length, sol line sol sol sol IJ.m

---- - - --- --- --- --0.687 0.656 0.617 0.594 0.589 0.568 0.553 0.527 0.522

B C

... ... D

...

... E '"

1.3328 1 3335 1.3343 1.3354 1.3353 1.3362 1.3366 1.3363 1.3362

1.3342 1.3348 1.3365 1.3373 1.3372 1.3387 1.3395

Index Index Index Spec- Index trum for 1 % for 2 % for 3 % for 4 % sol sol sol sol line

--- - - ---

...... 1.3382 0.516 1.3365 1.3391 1.3381 1.3410 1.3393 1.3426 . . . . . . 1.3426 1.3412 1.3445 1.3417 1.3438

1.3377 1.3388

• "Smithsonian Physical Tables," 1954, Table 552.

0.500 0.486 0.480 0.464 0.447 0.434 0.423

. .. ... F

. .. '"

. .. . .. '"

1.3368 1.3374 1.3377 1.3381 1.3397 1.3407 1. 3417 1.3431

--- --- --1.3385 1.3383 1.3386 1.3404 . ..... ...... 1.3408 1.3395 1.3398 1. 3413 1.3402 1. 3414 1.3423 1. 3421 1.3426 1.3439 . ..... ...... 1.3452 1.3442 1.3457 1.3468

~107

INDEX OF REFRACTION TABLE

6e-3.

LIQUIDS USED FOR DETERMINING REFRACTIVE INDEX BY TRANSMISSION METHOD

*

Liquid Trimethylene chloride . Cineole , . Hexahydrophenol . Decahydronaphthalene . Isoamylphthalate . Tetrachloroethane . Pentachloroethane . Trimethylene bromide . Chloro benzene . Ethylene bromide + chlorobenzene . o-Nitrotoluene . Xylidine . 0- Toluidine . Aniline , . Bromoform . Iodobenzene + bromobenzene . Iodobenzene + bromobenzene . Quinoline . a-Chloronaphthalene . a-Bromonaphthalene + o-chloronaphthalene . a-Bromonaphthalene + a-iodonaphthalene . Methylene iodide + iodobenzene . Methylene iodide . Methylene iodide saturated with sulfur . Yellow phosphorus, sulfur, and methylene iodide] (8: 1: 1 by weight). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..

ND,24°C 1.446 1.456 1.466 1.477 1.486 1.492 1.501 1.513 1.523 1.533 1.544 1.557 1.570 1.584 1.595 1.603 1.613 1.622 1.633 1. 640-1. 650 1.660-1.690 1. 700-1. 730 1.738 1. 78 2.06

• "Handbook of Chemistry and Physics," 36th ed., p, 2669, Chemical Rubber Publishing Company, 1954-1955. t Can be diluted with methylene iodide to cover range 1.74-2.06. For precautions in use, cf. West, Am. Mineralogist Sl, 245-249 (1936).

6-108

OPTICS TABLE

6e-4.

INDEX OF REFRACTION OF PLASTICS·

Optical Plastics Optical properties of polymer

Optical properties of polymer

I

Name of monomer

RecipRefrac- rocal tive diaperindex sive (N20) power

Name of monomer

RecipRe£rac- rocal tive diaperindex sive (NID) power

-p-Methoxy styrene ...................... tl-Amino-ethyl methacrylate .............. Methyl a-bromoacrylate ................. Vinyl benzoate ......................... Phenyl vinyl ketone ..................... Vinyl carbazole ......................... Lead methacrylate...................... 2-Chlorocyclohexyl methacrylate .......... 1-Phenyl-cyclohexyl methacrylate ......... Triethoxy-silicol methacrylate ............ p-Bromophenyl methacrylate ............. 2-3 Dibromopropyl methacrylate .......... Diethyl-amino-ethyl methacrylate ......... 1-Methyl-cyclohexyl methacrylate ......... n-Hexyl methacrylate ................ , .. 2-6-Dichlorostyrene ..................... p-Bromo-ethyl methacrylate .............. ~-Polychloroprene ....................... Methyl o-chloracrylate.................. tl-Naphthyl methacrylate ................ Vinyl phenyl sulfide ............... , ..... Methacryl methyl salicylate .............. Methyl isopropenyl ketone ............... Ethylene glycol mono-methacrylate ....... N-Benzyl methacrylamide ............ , ... p-Phenyl-sulrone ethyl methacrylate ....... N-Methyl methacrylamide............... N-Allyl methacrylamide ................. Methacryl-phenyl salicylate .............. N-tl-Methoxyethyl methacrylamide ....... N-tl-Phenylcthyl methacrylamide ......... Cyclohexyl a-ethoxyacrylate ............. 1-3-Dichloropropyl-2-methacrylate ........ 2-Methyl-cyclohexyl methacrylate ......... 3-Methyl-cyclohexyl methacrylate ......... 3-3-5-Trimethyl-cyc1ohexyl methacrylate .. N-Vinyl phthalimide .................... Fluorenyl methacrylate.................. a-Naphthyl-carbinyl methacrylate ........ p-pl-Xylylenyl dimethacrylate ............ Cyclohexanediol-l-4 dimethacrylate ....... Ethylidene dimethacrylate ............... p-Divinyl benzene....................... Decamethylene glycol dimethacrylate ..... Vinyl cyclohexene dioxide................ Methyl a-methylene butyrolactone ........ a-Methylene butyrolactone .............. 4-Dioxolylmethyl methacrylate ........... Methylene-a-valerolactone ............... o-Methoxy-phenyl methacrylate ........... Isopropyl methacrylate ......... , ........ TriBuoroisopropyl methacrylate ........... tl-Ethoxy-ethyl methacrylate ............. Name of polymer Condensation resin from di- (p-aminocyclohexyl) methane and sebacic acid ........ Columbia resin 39.......................

1.5967 1.537 1.5672 1.5775 1.586 1.683 1.645 1.5179 1.5645 1.436 1.5964 1.5739 1.5174 1.51'11 1.4813 1.6248 1.5426 1.5540 1.5172 1.629.8 1.6568 1.5707 1.5200 1.5119 1.59,65 1.5682 1.5398 1.5476 1.6Q06 1.52~6 1.5857 1.4969 1.5270 1.50~8

1.4947 1.485 1. 620P 1.631~

1.63 1.5559 1.5067 1.4831 1.6150 1.4990 1.5303 1.5118 1.5412 1.5084 1.5431 1.5705 1.4728 1.4177 1.4833 1.5199 1.5001

Allyl methacrylate ...................... Benzhydryl methacrylate ................ Benzyl methacrylate ...••............... a-Butyl methacrylate.................... Tert-butyl methacrylate ................. o-Chlorobenzhydryl methacrylate ......... a-(o-Chlorophenyl)-ethyl methacrylate .... Cyclohexyl-cyclohexyl methacrylate ....... Cyclohexyl methacrylate ................. p-Cyclohexyl-phenyl methacrylate ........ a-tl-Diphenyl-ethyl methacrylate ......... Menthyl methacrylate ................... Ethylene dimethacrylate ................. Hexamethylene glycol dimethacrylate ..... Methacrylic anhydride ................... Methyl methacrylate .................... m-Nitro-benzyl methacrylate ............. 2-Nitro-2-methyl-propyl methacrylate ..... a-Phenyl-allyl methacrylate .............. a-Phenyl-n-amyl methacrylate ............ a-Phenyl-ethyl methacrylate ............. p-Phenyl-ethyl methacrylate ............. Tetrahydro£ur£uryl methacrylate .......... Vinyl methacrylate ........ , , ........ , ... Styrene ....... , ........................ Vinyl formate .......................... Phenyl cellosclve methacrylate ........... p-Methoxy-benzyl methacrylate .......... Ethylene chlorohydrin methacrylate ....... o-Chlorostyrene ......................... Pentachlorophenyl methacrylate .......... Phenyl methacrylate.................... Vinyl naphthalene....................... Vinyl thiophene ......................... Eugenol methacrylate ....... , ... , ....... m-Cresyl methacrylate ................... o-Methyl-p-methoxy styrene .............. o-Methoxy styrene ...................... o-Methyl styrene ........................ Ethyl sulfide dimethacrylate ............. , Allyl einnamate ......................... Diacetin methacrylate ................... Ethylene glycol benzoate methacrylate .... Ethyl glycolate methacrylate ............. p-Isopropyl styrene .............. , ...... Bornyl methacrylate .................... Triethyl carbinyl methacrylate ........... Butyl mercaptyl methacrylate ............ o-Chlorobenzyl methacrylate ............. a-Methallyl methacrylate ................ tl-Methallyl methacrylate .......... , .. , ., a-Naphthyl methacrylate ................ Ethyl acrylate .......................... Cinnamyl methacrylate .................. Methyl acrylate ........................ 52.0 Terpineyl methacrylate .................. 58.8 Furfuryl methacrylate ................... 28 52.5 46.5 30.7 26.0 18.8 28 56 40 53 33 44 54 54 57 31.3 40 36 57 24 27.5 34 54.5 56 34.5 39 47.5 47 36 53 37 58 56 53 55 54 24,1 23.1 25 37 54.3 52.9 28.1 56.3 56.4 53.9 56.4 59.7 47.8 33.4 57.9 65.3 32.0

1.5196 1. 5933 1.5680 1.483 1.4638 1.6040 1.5624 1.5250 1.5064 1.5575 1.5816 1.4890 1.5063 1.5066 1.5228 1.4913 1. 5845 1.4868 1.5573 1.5396 1.5487 1.5592 1.5096 1.5129 1.5907 1.4757 1.5624 1.552 1.517 1.6098 1.608 1.5706 1.6818 1.6376 1.5714 1.5683 1.5868 1.5932 1.5874 1.547 1.57 1.4855 1.555 1.4903 1.554 1.5059 1.4889 1.5390 1.5823 1. 4917 1.5110 1.6411 1. 4685 1.5951 1.4793 1.514 1.5381

49.0 31.0 36.5 49 51 30 37.5 53 56.9 39.0 30.5 54.5 53.4 56 48.5 57.8 27.4 48 34.8 40 37.5 36.5 54 46 30.8 55 36.2 32.5 54 31 22.5 35.0 20.9 29 33 36.8 30.3 :l9.7 32 44 30 50 36.8 55 35 54.6 57 41.8 37 49 47 20.5 58 26.5 59 50 39.2

.. • H. C. Raine, Plastic Glasses, Proc, London Conf. Opt.Instruments 1950, 243.

6-109

INDEX OF REFRACTION TABI,E

6e-4.

INDEX OF REFRACTION OF PLASTICS·

(Continued)

Polystyrene Refractive index at Spectral line

Wavelength,

A

.!

7,679 6,563 5,896 4,861 4,358

C D1 F g

15°C

35°C

55°C

1.5812 1.587° 1.592 3 1.606 2 1. 617 6

1.578 6 1.584 3 1.589 7 1.603 4 1. 614 8

1.575 8 1. 581 6 1.586 9 1.600 6 1.612°

Polycyclohexyl Methacrylate Refractive index at Spectral line

Wavelength,

A

7,679 6,563 5,896 4,861 4,358

A C

D1 F g

15°C

35°C

55°C

1.501 6 1.504 4 1.507 1 1.513 4 1.518 4

1.499 2 1.502 1 1.5046 1. 5010 1. 516 0

1.496 4 1.499 2 1.5018 1.508 1 1.513 1

Polymethyl Methacrylate Spectral line

C D e F g

Wavelength, 6,563 5,896 5,461 4,861 4,358

A

Refractive index at 20°C 1.489° 1.4913 1.493 2 1.497' 1.501 11

6-110

OPTICS TABLE

6e-5.

(n - 1)10 3 t

Wavelength, ,urn

INDEX OF REFRACTION OF GASES AND VAPORS*

Air

O2

(n - 1)10 3

Wavelength,

N2

H2

,urn

Air

O2

t

CO 2

H2

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - I- - - 0.4861 0.2951 0.2734 0.3012 0.1406 0.4360 0.2971 0.2743 0.4563 o.141~ 0.5461 0.2936 0.2717 0.2998 0.1397 0.5461 0.2937 0.2704 0.4500 0.1397 0.1393 0.6709 0.2918 0.2683 0.4471 0.1385 0.5790 0.2930 0.2710 0.6563 0.2919 0.2698 0.2982 0.1387 6.709 0.3881 0.2643 0.4804 0.1361 8.678 0.2888 0.2650 0.4579 0.1361 ••••

* The

4

values are for O°C and 760 mm Hg.

t Cuthbertson, 1910. :\: Koch, 1909.

Substance

Kind of light

Indices of refraction

Kind of light

Substance

Acetone ............. D 1.001079-1.001100 Hydrogen ........... White Ammonia ........... White 1.000381-1.000385 Hydrogen ........... D Ammonia ........... D 1.000373-1.000379 Hydrogen sulfide .... D 1.000281 Argon .............. D D 1. 00170Q-l. 001823 Methane ............ White Benzene ............. D 1.001132 Methane ............ Bromine ............ D D Carbon dioxide ...... White 1.000449-1.000450 Methyl alcohol. ..... D 1.000448-1.000454 Methyl ether ........ Carbon dioxide ...... D D Nitric oxide ......... White Carbon disulfide ..... White 1. 001500 D 1.001478-1.001485 Nitric oxide ......... D Nitrogen ............ White Carbon monoxide .... White 1.000340 White 1.000335 Nitrogen ............ D Nitrous oxide ....... White Chlorine ............ White 1.000772 D 1.000773 Nitrous oxide ....... D Chlorine ......... , .. D 1.001436-1.001464 Oxygen ............. White Chloroform .......... Oxygen ............. Cyanogen ........... White 1.000834 D 1.000784-1.000825 Pentane ............ D Cyanogen ....... , ... D 1.000871-1.000885 Sulfur dioxide ....... Whitc Ethyl alcohol. ....... D 1.001521-1.001544 Sulfur dioxide ....... D Ethyl ether .......... D 1.000036 Water .............. White Helium ... , ......... D Hydrochloric acid .... White 1.000449 Water .............. D 1.000447 D

Indices of refraction

1.000138-1.000143 1. 000132 1.000644 1.000623 1.000443 1.000444 1.000549-1.000623 1.000891 1.000303 1.000297 1.000295-1.000300 1.000296-1.000298 1 . 000503-1 .000507 1. 000516 1.000272-1.000280 1.000271-1.000272 1. 001711 1.000665 1.000686 1.000261 1.000249-1.000259

* .. Smithsonian Physical Tables," 1954, Table 554. A formula was given by Biot and Arago expressing the dependence of the index of refraction of a gas on pressure and temperature. More recent The formula is nl - 1 = no - 1 L, where n, is the index of 1 at 760 refraction for temperature t, no for temperature zero, a the coefficient of expansion of the gas with t.emperature, and p the pressure of the gas in millimeters of mercuryexperiments confirm their conclusions.

+

6-111

INDEX OF REFRACTION AIR

D. H. Rank, in an article in "Advances in Spectroscopy," vol. I, indicates that the Edlen formula for the dispersion of air agrees with experimental data from the ultraviolet (2,000 A) to the near infrared (2.06 ,urn). The equations are for air free of carbon dioxide at standard conditions and for standard air (dry, 0.03 percent carbon dioxide), respectively: (n _ 1)108

=

6431 8 , .

(n _ 1)108 = 6,432.8

+ 2,949,330 + 25,536 146 _ 41 _ 0- 2

+ 2,949,810 + 146 -

0- 2

0-2

25,540 41 - 0- 2

is the wave number in ,urn-I. Furthermore, Rank reports the equation of Barrell and Sears for the change of index with temperature and pressure:

(T

nTp -

where T

1 =

p(l (nI5.760 -

1) 760(1

+ p{1T)(l + 15a) + 760{115)(1 + aT)

= temperature

p

= pressure

a

=

0.00366

{1T = (1.049 - 0.015 7T)IO- S

{116

= 0.813 6

X 10- 6

6f. Optical Characteristics of Various Uniaxial and Biaxial Crystals

6-112 TABLE

OPTICS 6f-1.

INDEX OF REFRACTION OF SELECTED UNIAXIAL MIN·ERALS.

Index of refraction Mineral

Formula

I

Ordinary Extraordinary ray ray

Uniaxial Positive Minerals Ice ............... Sellaite ........... Chrysocolla ....... Laubanite ......... Chabazite ......... Douglasite ........ Hydronephelite ... Apophyllite ....... Quartz ........... Coquimbite ....... Brucite ........... Alunite ........... Penninite ......... Cacoxenite ........ Eudialite ....... , . Dioptase .......... Phenacite ......... Parisite ........... Willemite ....... , . Vesuvianite ....... Xenotime ......... Connellite ......... Benitoite ......... Ganomalite ....... Scheelite .......... Zircon ............ Powellite ......... Calomel .... , ... , . Cassiterite ........ Zincite ........... Phosgenite ........ Penfieldite ........ Iodyrite. " ..... , . Tapiolite .......... Wurtzite .......... Derbylite ......... Greenockite ....... Rutile ............ Moissanite ........ Cinnabar .........

H 2O MgF 2 CuO·Si0 2·2H2O 2CaO·AbOa·5Si0 2·6H2O (Ca, Na2)O·AhOa·4Si02·6H20 2KCI·FeCI 2·2H2O 2Na20·3Al20a·6Si02·7H20 K 2O·8CaO·16Si02·16H2O Si0 2 Fe 2Oa·3S0 a·9H2O MgO·H 2O K 2O·3AhOa·4S0a·6H2O 5(Mg, Fe)O·AhOa·3Si0 2·4H2O 2Fe 2Oa·P206·12H2O 6Na 20'6(Ca, Fe)O·20(Si, Zr)02·NaCI CuO·Si0 2·H2O 2BeO·Si0 2 2CeOF·CaO·3C0 2 2ZnO·Si0 2 2(Ca, Mn, Fe)O·(AI, Fe) (OH, F)O·2Si0 2 Y 2Oa, P206 20CuO·SOa·2CuCI 2·20H2O BaO·Ti0 2·3Si0 2 6PbO·4(Ca, Mn)O·6Si0 2·H2O CaO·WO, Zr02·Si0 2 CaO·MoO, HgCI Sn02 ZnO PbO·PbCI 2·C0 2 PbO·PbCb AgI FeO·(Ta, Nbh06 ZnS 6FeO·Sb 2Oa·5Ti02 CdS Ti0 2 CSi HgS

1.309 1.378 1.460 ± 1.475 1. 480 ± 1.488 1.490 1.535 ± 1.544 1.550 1.559 1.572 1.576 1.582 1.606 1.654 1.654 1.676± 1.691 1. 716±

1.313 1.390 1.570 ± 1.486 1.482± 1.500 1.502 1.537 ± 1.553 1.556 1.580 1.592 1.579 1.645 1.611 1.707 1.670 1.757 1.719 1.721

1.721 1.724 1.757 1.910 1.918 1. 923 ± 1.974 1.973 1.997 2.013 2.114 2.130 2.210 2.270 2.356 2.450 2.506 2.616 2.654 2.854

1.816 1.746 1.804 1.945 1.934 1. 968 ± 1.978 2.650 2.093 2.029 2.140 2.210 2.220 2.420 (Li line) 2.378 2.510 (Li line) 2.529 2.903 2.697 3.201

OPTICAL CHARACTERISTICS 01 10. For small angles Eq. (6i-2) is combined with Snell's law, and the fractional change in wavelength is expressed as (6i-3) where no is the index of the incident medium in which cP is measured. As the fractional bandwidth of the filter is decreased, the flux must be more nearly perfectly collimated in order to maintain the fractional "angle shift" of the passband comparable to the Q-l of the filter. 5. Although it is theoretically possible to attain a high resolution by using cavity reflectors with a reflectance very close to 100 percent, this is usually undesirable for

GLASS, POLARIZING, AND INTERFERENCE FILTERS

6-175

several reasons: First, the effect of any absorption in cavity spacer or in the reflectors is greatly enhanced, and this drastically reduces T max' Second, the passband width does not decrease below a certain limit owing to a lack of planeness in the surface of the reflectors [22]. Single-cavity bandpass filters have also been constructed using a solid material for the cavity, as, for example, a slab of fused quartz [23] or a sheet of mica [24]. Compared with the conventional Fabry-Perot, these have the advantages of greater mechanical and thermal stability. They also have a smaller angle shift, as can be seen from the effect of n 2 in the denominator of Eq. (6i-3). However, the T max is smaller, because of the absorption of the spacer. A typical mica filter [24] has a T ntBX of 60 percent, ~A! of 0.15 nm, and an order number of 150 at Ao of 600 nm. Multilayer mirrors are usually used for the reflectors in both the "air-spaced" and the "solid spacer" types of Fabry-Perot filters. The bandpass filters which are fabricated entirely of thin films have several distinct features: (1) Multiple-cavity filters [25] can be constructed, which have the advantage of superior off-band rejection. (2) Metal films can be used to advantage in the

IJJ

u

z

n

0.8 -

~ 0.6....

:i (I') z 04 "(cP,8) =

±AU

::2

(cos! 8 - sin! 8)

(6i-ll)

The plus and minus signs apply, respectively, for positive and negative crystals. Let ~>..(cP) be the maximum acceptable shift. The corresponding q, at 8 = 0 or 7r/2 is (6i-12) This is a fairly stringent restriction. For example, in a filter for X = 6,563 (Hex) with 0>" = 0.5 A, ~>..(q,) = 0.1 A is a reasonable tolerance. Then q, = 9 X 10- 3 radian. Lyot invented a wide field elaboration of the simple filter in which each b element is made of two equal pieces of half the calculated thickness. The two are rotated 90 deg with respect to each other, and a 90-deg polarization rotator (usually a >../2 plate) is mounted between them. Then for a given light ray, 8 in the first half element becomes 8 + 7r/2 in the second half element, and by Eq. (6i-ll), the ~>..(q,,8)'s compensate. Since Eq. (6i-ll) neglects higher-order terms, the compensation is not

6--180

OPTICS

perfect, but Lyot's device does increase the radius of the useful field by factors of 26 and 6 for b elements of quartz and calcite. Another problem is the loss of light by absorption in the polarizers of filters with large finesse. A Polaroid film usually transmits about 80 percent of the desired light, which means an optical density of 0.091n + 0.39 for the filter as a whole. In some uses the loss of 95 percent of the light is serious. To alleviate the pain, Evans [2] devised a "split element" filter. Here half the b elements are cut into two equal halves and crossed as in Lyot's wide-field filter. The remaining elements are inserted between these equal halves with axes at 45 deg, and a unit of two birefringent elements can then be placed between successive polarizers. This reduces the optical density to O.091n/2 + 0.39, a very considerable improvement when n approaches 8 or 10. A better solution is to use more transparent polarizers like Rochon prisms, which may be no more expensive than the split-element construction. The prism polarizers are the only presently practical approach at wavelengths less than about 4,200 A, where the absorption of Polaroid film begins to become excessive. Beyond the limited slow tuning by temperature variation, each transmission band of a birefringent filter has a fixed central wavelength. It is feasible, however, to tune to any desired wavelength by adding phase shifters to the b elements. The condition for a transmission band at a given wavelength, ;>\}, is that I' be integral at ;>\} in all b elements. If each b element has a phase shifter which adds AI', adjustable from to 1, this condition can be satisfied. The elegant approach is a filter with b elements of adjustable thickness. Each element is a pair of wedges, one of which slides with respect to the other to vary the total thickness in the optical path. The AI' is then a function of the wedge position and wavelength, but at every wavelength the required AI' can be achieved. Hence the variable thickness tuning works at all wavelengths for which the polarizers are effective. So far, the mechanical problems of control in filters of 8 or 10 elements have prevented use of this method. However, one of the modern small control computers could deal with these problems quite easily. The second approach to filter tuning is relatively simple mechanically, but is effective only over a limited spectral range. Before entering the following polarizer, the light emerging from a b element is elliptically polarized. As A varies and I' goes through a range of 1, the elliptical figure goes through the cycle from vertical linear to right circular, horizontal linear, left circular, and back to vertical linear. If now we add a A/4 plate with its axis at 45 deg to the axis of the b element, elliptical polarization is converted to plane polarization rotated at an angle '!t = !I' to the axis of the A/4 plate. If now we rotate the following polarizer, we can adjust it to transmit any AI', regardless of the wavelength. In a simple filter the '!t's are simply proportional to the thicknesses of the preceding b elements, which progress in powers of two. The wavelength limitation is imposed by the fact that a simple A/4 plate is A/4 at only one wavelength. Light leaks develop in the wavelength intervals between principal bands as we depart from that wavelength. However, the leaks are tolerable for most purposes over a range of several hundred angstroms. The tuning range of the rotating polarizer filter can be greatly extended by the use of achromatic A/4 plates, which can now be constructed by known principles [4]. One such filter with a 0.25 A passband at A6,563, tunable from 4,200 to 7,000 A, is presently under construction. All commercially available LO filters have b elements of quartz with E - W rv 0.009, or calcite with E - W rv 0.18, or both. The use of other materials has been confined to a few experiments. A typical example has an aperture of 30 mm, a 0.5 Apassband at 6,563, with high-order calcite elements of wide field construction. The two thickest elements are tunable over a range of ± 2 A by rotating polarizers. The total length is about 16 em.

°

GLASS, POLARIZING, AND INTERFERENCE FILTERS

6-181

The Solc filter [3) consists of a pile of N plane-parallel birefringent plates placed between two polarizers. The plates are identical in thickness, and are cut with the optic axes parallel to the surfaces. Two basic arrangements give identical filtering characteristics. The folded filter has crossed polarizers, and the optic axes of the plates are set successively at angles of plus or minus 7r/4N to the electric vector of light from the first polarizer. The fan filter has parallel polarizers, and the orientations of successive b elements increase monotonically, 7r/4N, 37r/4N, 57r/4N, etc. The action of the pile on polarized light is not readily apparent, but can be understood qualitatively if one thinks of the pile as a device for producing N 1 different pathlengths, among which the light is distributed somewhat unevenly. The resulting transmission curve resembles that of a grating of N + 1 rulings, but has some significant differences. The transmission is

+

sin Nx

T

= -.-cos sin x

7r

X

tan 2N

(6i-13)

where x is defined by cos

X :;:

cos

7r

7r1'

cos 2N

and l' is the retardation of a single plate. The separation of successive transmission bands is approximately t..A

= u~

(6i-14)

l'

The bandwidth approaches (6i-15) as N increases. Equation (6i-15) is accurate within one percent when N ~ 5. The Sole and LO filters have the same band separation and bandwidth if l' = 1'1 and N = -vI3 X 2n - 1 • In its basic form, however, the Solc filter suppresses parasitic light much less effectively than the Lyot filter. S (Sole) increases with N. It is 0.22 for N = 16 and approaches an upper limit of 0.27. However, Solc [5) showed that S can be reduced to "=380 >"=770

Y

I I

T,.,P,.,X

= >"=380 >"=770

P,.,y

).=380 ).=770

Z

=

I I

T"'P",1.

),=380 ),=770

P,.,y

>"=380

Relative values of P,., are sufficient for determining tristimulus values X, Y, Z of material. For reflecting materials, substitute p,., for T,., in above formulas. For samples subtending more than 5-deg visual angle, the values of X10, Y10, 1.10 in Table 6j-5 are probably more appropriate than x, y, z, for colorimetry, but Y based on Ylo has no photometric significance. Data designed to facilitate manual computation of tristimulus values based on e, Y, 1. for illuminants A, B, and C; blackbody sources of 1000, 1500, 1900, 2360, 3000, 3500, 4800, 6000, 6500, 7000, 8000, 10,000, 24,000 K; and infinite temperature; for five phases of natural daylight and for three commercial sources of artificial daylight, are tabulated in "The Science of Color."! 1

Citation at bottom of Table 6j-1 (p. 6-184).

6-194

OPTICS

Chromaticity Coordinates. Horizontal tical coordinate y = Y I (X + Y + Z).

coordinate x = X I(X

z

y

0.4476 0.3484 0.3101 0.3127 0.3324 0.2990

0.4074 0.3516 0.3162 0.3290 0.3475 0.3150

Illuminant C.LE. C.LE. C.LE. C.LE.

standard standard standard standard

A B C D 6 50 0

. . . .

D 5500 . . • • • . . • • . . . . . . . . . . . . • . . • . D7500 • . . • • • . . . . • • . • • . . . . • . . . . . .

+ Y + Z).

Ver-

C.I.E. 1931 (x,y) DIAGRAM: Produced by plotting the chromaticity coordinates, x horizontally, y vertically, to equal scales. C.I.E. 1960 (u,v) DIAGRAM: Provisionally recommended for use whenever a projective transformation of the (x,y) diagram yielding more nearly uniform chromaticity spacing is desired; it is formed by plotting u horizontally and v vertically, to equal scales, where

4x u = 3 _ 2x + 12y'

v

=

6y 3 - 2x + 12y

v

=

X

Alternatively, 4X

u

=

X

+ 15 Y + 3Z'

6Y

+ 15Y + 3Z

C.I.E. 1964 U·, V·, W·, COORDINATE SYSTEM: Provisionally recommended for use whenever a three-dimensional color-coordinate system perceptually more nearly uniformly spaced than the (X, Y,Z) system is desired. It is formed by plotting U·, V·, and W* to equal scales along mutually orthogonal axes, where, with 1 ~ Y ~ 100 and Uo, Vo representing light that appears achromatic under the conditions prevailing in the application of interest (usually that is the illuminant),

W· = 25yl - 17

V* = 13W*(u - uo)

V* = 13W*(v - vo)

Curve obtained by plotting chromaticity coordinates x, y or u, v for all wavelengths listed in Table 6j-5. DOMINANT WAVELENGTH: Wavelength corresponding to the intersection of the spectrum locus with the straight line drawn from the point representing the light source or illuminant, through the point representing the light reflected from (or transmitted by) the sample. COMPLEMENTARY WAVELENGTH: 'Wavelength corresponding to the intersection of the spectrum locus with the straight line drawn from the point representing the light from the sample through the point representing the light source or illuminant (used when dominant wavelength is not determinate). PURITY: Ratio of distance from source point to sample point, compared with distance from source point to point on the spectrum locus representing the dominant wavelength (or, in case in which dominant wavelength is not determinate, ratio of distance from source point to sample point compared with distance from source point to collinear point on line joining extremities of the spectrum locus). PLANCKIAN LOCUS: Curve produced when x, y in Table 6j-8 or the corresponding values of u, v, are plotted. Correlated color temperature of an illuminant is the temperature corresponding to the point on the planckian locus which is at the foot of the perpendicular to that locus, from the point representing the illuminant in the C.LE. 1960 (u,v) diagram. C.LE. 1964 COLOR-DIFFERENCE FORMULA: For evaluating difference between two closely similar colors specified by and SPECTRUM LOCUS:

V:, V:, W:,

ilE = [(V: - U;)2

+ (V:

- V:p

U;, V:, W:,

+ (W:

- W:p]l

6-195

COLORIMETRY

This and three other formulas proposed for test for the same purpose were published in J. Opt. Soc. Am. 58, 291 (1968), which should be consulted for details. The following formulas, to the end of the section on colorimetry, are not recommended by the C.LE. or by any other organization. They are presented for trial and use by anyone who finds them to be applicable to his problems. GEODESIC TRANSFORMATION OF (x,y) CHROMATICITY DIAGRAM: This nonlinear transformation of the (x,y) diagram provides the most nearly uniform plane representation of small-color-difference data for 14 observers. 1 ~ =

+ 13,295b 3 + 32,327ab - 25,491a 2b - 41,672ab 2 + 10a - 5,227 V~ + 2,952 = 10x/(2Ax + 34y + 1) and b = 10y/(2Ax + 34y + 1). 11 = 404b - 185b 2 + 52b 3 + 69a(1 - b 2) - 3a 2b + 30ab 3

3,751a 2

10a 4

-

-

520b 2

3b

in which a

~

in which a = 10:r/(4.2y - x + 1) and b = 10y/(4.2y - z + 1). ~ and 11 are given in units of root-mean-square errors of color matching by the 14 normal observers. All straight lines in the (~,71) diagram represent paths (geodesics) of minimum accumulated color differences, as evaluated according to the observer data. According to the Schrodinger hypothesis," such geodesics [straight lines in the (~,71) diagram] drawn outward from the achromatic point should represent series of colors of constant hue. The point representing C.LE. standard illuminant D G5 is at ~ = 861.2, 11 = 395.7. CHROMATICITY DIFFERENCE between any two colors specified by (~l,111) and (~2,772) is Llc = [(~l -

~2)2

+ (711 -

712)2]t

of color specified by ~, 71, Y: 8 = WI [(~ - ~a)2 + (11 - 11a)2]l, where WI = 0.054 + 0.46yi (1 < Y < 80), and ~a and 71a are the specifications of the achromatic color, usually the illuminant. HUE (h) expressed as an angle clockwise from the vertical drawn downward from the point representing the achromatic color, SATURATION

h

where

0


.

= 0.65

,um*

Range of observed values

Probable value for the oxide formed on smooth metal

0.22-0.40 0.07-0.37 0.58-0.80 0.60--0.80

0.30 0.35

0.55-0.7I 0.60--0.80 0.63-0.98 0.10--0.43 0.85-0.96 0.20--0.57 0.32-0.60

0.18-0.43

0.70 0.75 0.70 0.70 0.70 0.20 0.90 0.50 0.50 0.30 0.70 0.60 0.40 0.87 0.70 0.87 0.90 0.83 0.78 0.75 0.84 0.80 0.85

0.25-0.50

The emittance of oxides and oxidized metals depends to a large extent upon the roughness of the surface. In general, higher values of emissivity are obtained on the rougher surfaces. * American Institute of Physics, "Temperature, Its Measurement and Control in Science and Industry," p. 1313, Reinhold Publishing Corporation, New York, 1941.

6-207

RADIOMETRY TABLE

6k-7.

SPECTRAL EMITTANCE OF OXIDES FOR X

= 0.665 #Lm·

Material

Tern perature, °C

Emittance

Year

Aluminum oxide. 99.5 % ...................... Beryllium oxide, white (hot pressed) ........... Magnesium oxide ............................ Nickel oxide, NiO ............................ Silicon dioxide ............................... Tantalum oxide .............................. Thorium oxide ...............................

1000-1600 927-1063 1000-1470 816-1204 1000-1600 816-1204 1268-1800

0.175 0.21 0.18 0.87-0.82 0.18 0.78 0.40

1952 1948 1957 1957 1952 1957 1952

The emittance of white oxides depends strongly on purity. • See ref. 13, p. 6-205.

TABLE

6k-8.

Only low values are shown.

THERMAL-CONTROL MATERIALS·

Material

Paints: White silicate on AI. , White epoxy. . . . . . . . . . . . . . . . . . . . . . . . . . .. Al-silicone . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. AI-acrylic..... . .. .. Black acrylic. . . . . . . . . . . . . . . . . . . . . . . . . . .. Black silicone. . . . . . . . . . . . . . . . . . . . . . . . . .. Optical solar reflector (second surface mirror, Ag) " . . . . . .. .. Stainless steel, sandblasted (AI 81410) , 6061 AI, rolled, chemically cleaned. . . . . . . . . .. Al foil, annealed. . . . . . . . . . . . . . . . . . . . . . . . . .. AI, sandblasted , AI, Reynolds wrap foil: Dull side..... . . . . . . . . . . . . . . . . . . . . . . . . . .. Shiny side. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Inconel quilted. . . . . . . . . . . . . . . . . . . . . . . . . . .. Inconel, X-foil. . . . . . . . . . . . . . . . . . . . . . . . . . . .. Hanovia gold on Rene 41 , Gold, high purity on AI. ,

Absorptancet a. at 70°F

Emittance E at 70°F

0.15 0 . 25 0 . 92 0.85 1 .06 1. 15

0.13 0.22 0.22 0.41 0.93 0.89

0.85 0.89 0.24 0.48 0.88 0.77

0.0625 0.88 2.7 2.4 2.0

0.05 0.75 0.16 0.12 0.42

0.80 0.85 0.06 0.04 0.21

5.0 6 .3 3.2 6.6 6.0 9.0

0.2 0.18 0.38 0.66 0.53 0.27

0.04 0.03 0.12 0.10 0.09 0.03

ailE

• Space Materials Handbook, Air Force Rept: AFML-TR 60-40, suppl, 2, 1966. additional materials, details on composition, and stability. t~.... absorptance for solar radiation.

See reference for

6-208

01>TICS

TABLE

6k-9.

RELATION BETWEEN BRIGHTNESS TEMPERATURE AND TRUE

TEMPERATURE FOR VARIOUS VALUES OF SPECTRAL

A = 0.65 pm·

EMISSIVITY AT

800 /1000

Brightness temp., °C .... Emissivity

E

I

1200

I

* American

1400

I

1600 11800

I

2000

True temp., °C

(0.65 pm)

0.05 0.10 0.15 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90

r

982 934 909 891 867 850 837 827 819 812 805

1265 1194 1156 1130 1095 1071 1053 1039 1027 1017 1008

1567 1467 1413 1377 1329 1296 1272 1252 1236 1222 1210

1846 1752 1681 1632 1567 1525 1493 1467 1447 1429 1413

2236 2054 1958 1895 1813 1757 1717 1685 1659 1636 1617

2609 2370 2248 2168 2064 1995 1944 1905 1872 1844 1821

3011 2704 2549 2451 2320 2236 2174 2125 2087 2054 2025

Institute of Physics, .. Temperature, Its Measurement and Control in Science and Industry," Reinhold Publishing Corporation, New York, 1941.

TABLE

6k-l0.

RELATION BETWEEN ApPARENT AND TRUE TEMPERATURE

FOR V ARIOUS VALUES OF THE TOTAL EMISSIVITY·

Apparent temp.,oC Total emissivity

0.05 0.10 0.15 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90

100

1200 I 400 I 600 I 800 11000 11200 11400 11600 11800 True temp., °C

Et

422 316 264 231 189 164 146 132 121 113 106

686 536 460 410 347 307 278 255 238 223 211

1137 913 799 725 630 568 523 489 461 437 417

1567 1275 1126 1029 904 823 763 718 680 649 623

1993 1632 1449 1330 1175 1075 1002 945 900 861 828

2317 1989 1771 1629 1446 1327 1240 1173 1119 1073 1034

2841 2345 2093 1929 1717 1579 1478 1400 1337 1284 1239

3264 2701 2415 2228 1987 1830 1716 1628 1556 1496 1445

3687 3057 2736 2527 2258 2082 1954 1855 1775 1707 1650

4110 3413 3058 2827 2528 2333 2192 2082 1993 1919 1855

* American Institute of Physics, .. Temperature, Its Measurement and Control in Science and Industry," Reinhold Publishing Corporation, New York, 1941.

6-209

RADIOMETRY TABLE

6k-ll.

EFFICIENCIES OF ILLUMINANTS· .--

Lamp Acetylene ................ Arc, electric: Carbon, enclosed d-e .... Carbon, open d-e ....... High intensity. " ....... Magnetite d-e .......... Gas burner, open flame .... Gas mantle, incandescent: High pressure .......... Low pressure ........... Incandescent electric carbon filament: First commercial ........ Squirted cellulose ....... Metalized .............. Tungsten filaments: Vacuum ............... Gas-filled .............. Gas-filled .............. Gas-filled .............. Gas-filled .............. Gas-filled .............. Fluorescent lamps: General line ............ General line ............ General line ............ Slimline ............... Slimline ............... General line ............ General line ............ General line ............ General line ............ Mercury lamps ...........

Rating, or specification 1.0 liters/hr

Eff.

Ab. eff.

0.67

0.0010

5.9 11.8 18.5 21.6 0.22

0.0087 0.0173 0.0272 0.0318 0.00032

0.578 lumen/(Btu. hr) 0.350 lumen/(Btu. hr)

2.0 1.2

0.0030 0.0018

............................... ...............................

1.6 3.3 4.0

0.0023 0.0048 0.0059

10.6 11.6 13.9 16.3 21.6 32.8

0.0156 0.0171 0.0204 0.0239 0.0318 0.0482

50.0 64.0 58.0 76.0 69.0 54.0 84.0 33.0 3.6 50.0 65.0 55.0

0.0735 0.0940 0.0850 0.1115 0.1015 0.0795 0.1235 0.0485 0.0053 0.0735 0.0955 0.0808

6.6 amp opal globe and reflector 9.6 amp clear globe 150 amp bare arc 6.6 amp Bray high pressure

............................... 25 watt 40 watt 60 watt 100 watt 1,000 watt 5,000 watt

120 volt 120 volt 120 volt 120 volt 120 volt 120 volt

(1,000 hr life) (1,000 hr life) (1,000 hr life) (750 hr life) (1,000 hr life) (75 hr life)

20 watt standard warm white (TI2) 40 watt standard warm white (TI2) 90 watt standard warm white (TI7) 96T8 (120 rna) standard warm white 96T12 (425 rna) standard warm white 40 W daylight (T12) 40 W green (TI2) 40 W blue (TI2) 40 W red (T12) 400 W (E1) 1,000 W (A6) Sodium .................. 10,000 lumen

The rating listed is the commercial rating of the lamp. The absolute efficiency is the equivalent power in light flux (0.556 #4m) per watt input. Efficiency is given in lumens per watt input. ~ "Handbook of Chemistry and Physics," 49th ed., p. E-196, Chemical Rubber Publishing Company, 1968-1969. Compiled by J. M. Smith and C. E. Weitz.

~210

OPTICS

TABLE 6k-12. ApPROXIMATE BRIGHTNESS OF VARIOUS LIGHT SOURCES·

Lam.. bertsj

Source Natural sources: Clear sky. . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sun (as observed from earth's surface) .. , Sun (as observed from earth's surface) .. , Moon (as observed from earth's surface). Combustion sources: Candle flame (sperm) Kerosene flame (flat wick) . . . . . . . . . . . . .. Illuminating-gas flame... . . . . . . . . . . . . . .. Welsbach mantle. . . . . . . . . . . . . . . . . . . . .. Acetylene flame. . . . . . . . . . . . . . . . . . . . . .. Incandescent electric lamps: Carbon filament . Metalized carbon filament (Gem) . Tungsten filament Tungsten filament Tungsten filament Fluorescent lamps: 20 watt T12 standard warm white 40 watt T12 standard warm white 96T12 standard warm white Electric-arc lamps: Plain carbon arc

Average brightness At meridian Near horizon Bright spot Bright spot Bright spot Fishtail burner Bright spot Mees burner

Vacuum lamp, 10 lumens per watt Gas-filled lamp, 20 lumens per watt 750-watt projector lamp, 26 lumens per watt

. . .

Positive crater 7 mm nonrotating High-intensity carbon arc. . . . . . . . . . . . .. Positive crater 8 mm nonrotating High-intensity carbon arc. . . . . . . . . . . . .. Positive crater 13.6 mm nonrotating High-intensity carbon arc. . . . . . . . . . . . .. Positive crater Mercury lamps: Low-pressure mercury arc. . . . . . . . . . . . .. 50-in. a-c rectified tube 400 W (H1) . 1,000 W (A6) Water-cooled Sodium lamps 10,000 lumens

2.5 519,000 1,885 0.8 3.1 3.8 1.3 20.0 34.0 165 300 650 3,800 7,500

1.67 2.10 2.052

55,000 125,000 220,000 314,000 6.6 440 94,000 18

'" "Handbook of Chemistry and Physics," 49th ed., pp. E-19a, 197, Chemical Rubber Publishing Company, 1968-1969. Compiled by J. M. Smith and C. E. Weitz. t To convert lamberta to foot-lamberts multiply by 929. To convert lamberts to candelas/cm t divide by ...

6-211

RADIOMETRY TABLE

Temp., K

300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400 2500 2600 2700 2800 2900 3000 3100 3200 3300 3400 3500 3600

Normal brightness new candela Zcm"

•••••

0

•••

.

........ ........ . ........ .

......... .

6k-13.

PROPERTIES OF TUNGSTEN*

Spectral emissivity

0.65

}Lm

0.467

Color emissivity

Total emissivity

0.032 0.042 0.053 0.064 0.076 0.088 0.101 0.114 0.128 0.143 0.158 0.175 0.192 0.207 0.222 0.236 0.249 0.260 0.270 0.279 0.288 0.296 0.303 0.311 0.318 0.323 0.329 0.334 0.337 0.341 0.344 0.348 0.351 0.354

}Lm

0.472

0.505

..... .0 .••

.....

.... . ..... . .... . .... .....

..... .... . .0

•••

........ . ........ .

.... .

.

. ....

0.0001 0.001 0.006 0.029 0.11 0.33 0.92 2.3 5.1 10.4 20.0 36 61 101 157 240 350 500 690 950 1260 1650 2100 2700 3400 4200 5200

0.458 0.456 0.454 0.452 0.450 0.448 0.446 0.444 0.442 0.440 0.438 0.436 0.434 0.432 0.430 0.428 0.426 0.424 0.422 0.420 0.418 0.416 0.414 0.412 0.410 0.408 0.406

0.486 0.484 0.482 0.480 0.478 0.476 0.475 0.473 0.472 0.470 0.469 0.467 0.466 0.464 0.463 0.462 0.460 0.459 0.458 0.456 0.455 0.454 0.452 0.451 0.450 0.449 0.447

....

. .... . .... .0

•••

. ....

. .... 0.395 0.392 0.390 0.387 0.385 0.382 0.380 0.377 0.374 0.371 0.368 0.365 0.362 0.359 0.356 0.353 0.349 0.346 0.343 0.340 0.336 0.333 0.330 0.326 0.323 0.320 0.317

Brightness temp. 0.65 }Lm

966 1059 1151 1242 1332 1422 1511 1599 1687 1774 1861 1946 2031 2115 2198 2280 2362 2443 2523 2602 2681 2759 2837 2913 2989 3063 3137

Color temp.

1007 1108 1210 1312 1414 1516 1619 1722 1825 1928 2032 2136 2241 2345 2451 2556 2662 2769 2876 2984 3092 3200 3310 3420 3530 3642 3754

* "Handbook of Chemistry and Physics," 49th ed., p. E-228, Chemical Rubber Publishing Company, 1968-1969. Roeser and Wensel, National Bureau of Standards.

6-212

OPTICS

TABLE

6k-14.

THE EMITTANCE OF WELL-DEFINED TUNGSTEN RIBBON AS A

FUNCTION OF WAVELENGTH AT TEMPERATURES BETWEEN AND

1600

2800 K* Emissivity

Wavelength, Jo'm

0.25 0.30 0.35 0.40 0.50 0.60 0.70 0.80 0.90 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.8 2.0 2.2 2.4 2.6

1600 K

1800 K

2000 K

2200 K

2400 K

2600 K

2800 K

0.447 0.482 0.479 0.481 0.469 0.455 0.444 0.431 0.413 0.390 0.367 0.344 0.322 0.300 0.281 0.264 0.234 0.210 0.190 0.176 0.164

0.442 0.478 0.476 0.477 0.465 0.451 0.440 0.426 0.4070.386 0.364 0.343 0.322 0.302 0.284 0.268 0.241 0.219 0.201 0.187 0.175

0.437 0.474 0.473 0.475 0.462 0.448 0.436 0.420 0.401 0.382 0.361 0.342 0.323 0.306 0.288 0.273 0.247 0.227 0.210 0.196 0.185

0.430 0.470 0.470 0.471 0.458 0.444 0.432 0.414 0.396 0.376 0.358 0.341 0.323 0.308 0.292 0.278 0.255 0.235 0.218 0.206 0.194

0.424 0.465 0.467 0.468 0.455 0.441 0.428 0.409 0.390 0.373 0.355 0.340 0.324 0.310 0.296 0.283 0.262 0.243 0.228 0.215 0.205

0.416 0.461 0.464 0.464 0.451 0.438 0.423 0.404 0.386 0.371 0.353 0.339 0.324 0.311 0.299 0.288 0.268 0.251 0.236 0.224 0.214

0.410 0.456 0.461 0.461 0.448 0.434 0.419 0.400 0.383 0.368 0.352 0.338 0.325 0.313 0.302 0.292 0.275 0.259 0.245 0.233 0.224

• J. C. De V08, PhyBica 10, 690 (1954).

20 z i= U w 0

-I

I.L

18

Ex20

GLOWER 1.3 AMP

16

W 0

14 a:: wo E @5 ::L U;z

w-

12

a:::I:

011-0

10

~!:: Q~ !i:(/)

8

-13= ~010

0

a::

6

c..

>-

4

z

2

~ w

LLI

5

7911

WAVELENGTH, pm FIG. 6k-1. Characteristics of globar and glower sources.

~213

RADIOMETRY

1.0 0.9 0.8

t 0.706

I

I

,

3;

I

\

I

A-EMISSIVITY OF GLOBAR B-REFLECTIVITY OF SINGLE CRYSTAL OF SiC

0.5 ~ 0.4 ~ 0.3

100 90 80

-----!.

A~

I

>-

: ,

""

"

r r

r r

-------_!....---.._----,.. ,;

0.2 0.1 0

EMISSIVITY OF GLOBAR

'"

'"

70 ::.!! 60 ::50 40 30

5; t; ~

20 ~ 10

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

WAVELENGTH, pm ~ FIG. 6k-2. Emissivity of globar.

6k-4. Stellar Radiation. Brightness of stars as seen by any photoreceiver may be expressed as a stellar magnitude, related to the effective irradiance I in watts/em! received from the star: Stellar magnitude m

= -2.5Iog 1o ToI

The effective irradiance I from the star as seen by a photoreceiver is I =

where J'A

fo

00

JC>-.)u('A) d'A

= spectral distribution of radiation received from the star, in watta/cm!

per wavelength increment dA. J (A) for stars approximates blackbody distribution for the assumed surface temperatures. u(A) = photoreceiver's spectral-response function normalized at the response peak. For visual magnitude 10

=

6 ~5

X

10-(24.18/2.5)

= 3.1 X 10- 13 W /cm 2

(Cf. definition of lumen, page 6-5; definition of stellar magnitude, "Smithsonian Tables," 8th ed., Table 798.) Star brightness as seen by photoreceivers other than the eye is also expressed as a stellar magnitude (e.g., bolometric magnitude, photographic magnitude). The magnitude scales are generally adjusted by setting 1 0 so that a class AO star (surface temperature 11,000 K) appears of the same magnitude to each photoreceiver. For stars at other temperatures the effective-irradiance integral can be evaluated to obtain an index, which when added to visual magnitude gives the star's magnitude as seen by other receivers. Early stellar photometry used the non-calor-sensitized (blue-sensitive) photographic plate; the difference between photographic and visual magnitude was called color index. Difference between bolometric and visual magnitude was called heat index. Indices for the principal spectral classes of stars and for several photoreceivers are given in Table 6k-15.

6-214

OPTICS

6k-15.

TABLE

COLOR INDICES OF VARIOUS STELLAR SPECTRAL CLASSES

Index Spectral class

Approx eff. surface ternp., K

BO........... AO........... FO ........... gGO .......... gKO .......... gMO ..........

20,000 11,000 7,500 5,000 4,200 3,400

Photographic, visual

Bolometric, visual

S4 photosurface, visual

PbS, visual

-0.30 0 +0.33 +0.70 +1.12 +1. 70

-1.4 0 +0.6 +0.4 +0.1 -0.8

-0.15 0 +0.30 +0.7 +1.0 +1.1

+0.2 0 -0.4 -1.0 -1.5 -2.6

Effective temperature: Kuiper, Astrophys. J. 88,464 (1938). 84 index: computed from manufacturers' data on 1P21 photomultiplier. Bolometric index: Kuiper, Astrophys. J. 88,452 (1938). Photographic index: "Smithsonian Tables," 8th ed. PbS index: computed from manufacturers' data.

6k-6. Luminance of a Blackbody and Tungsten.' The luminance of a blackbody and of tungsten ribbon can be represented as a function of temperature by the followng formulas: log L log L

=

7.2010 _ 1.137~ X 10

4

=

6.8045 _ 1.123~ X 10

4

+ 0.0061;2 X 10 + 0.0053;2 X 10

where L is the luminance and T is the temperature. 1

J. C. De Vos, Physica 20, 715 (1954).

8

for a blackbody 8

for a tungsten ribbon

6-215

RADIOMETRY

TABLE 6~-16. BRIGHTNESS OF STARS AS SEEN BY VARIOUS PHOTORECEIVERS

Star

Spectral type

Visual magnitude

S4 photosurface magnitude

Lead sulfide magnitude

Sirius ............... Canopus ............ a Centauri ........... Vega ................ Capella ............. Arcturus ............ Rigel ............... Procyon ............. Achernar ............ Betelgeuse (var.) ..... f3 Centauri. .......... Altair ............... a Crucis ............. Aldebaran ........... Pollux .............. Spica ............... Antares ............. Fomalhaut .......... Deneb .............. Regulus .......... " . f3 Crucis ............. Castor .............. "Y Crucis ............. E Canis Majoris ...... E Ursa Majoris ....... "Y Orionis ............ A Scorpii ............ E Carniae ............ E Orionis ............ f3 Tauri ............. f3 Carniae ............ a Triang. Aust....... a Persei ............. '1 Ursa Majoris ....... "Y {}eminorum ........ a Ursa Majoris ....... E Sagitarii ........... 6 Canis Majoris ...... 1 f3 Canis Majoris ......

AO FO GO AO GO KO B8p F5 B5 MO B1 A5 B1 K5 KO B2 MO A3 A2p B8 B1 AO M3 B1 AOp B2 B2 KO BO B8 AO K2 F5 B3 AO KO AO F8p Bl

-1.58 -0.86 0.06 0.14 0.21 0.24 0.34 0.48 0.60 0.7 ± 0.5 0.86 0.89 1.05 1.06 1.21 1.21 1.22 1.29 1.33 1.34 1.50 1.58 1.61 1.63 1.68 1. 70 1.71 1. 74 1. 75 1. 78 1.80 1.88 1.90 1.91 1.93 1.95 1.95 1.98 1.99

-1.6 -0.6 0.8 0.1 0.9 1.3 0.3 1.0 0.5 1.8 ± 0.5 0.7 1.0 0.9 2.1 2.2 1.1 2.3 1.4 1.4 1.3 1.4 1.6 2.7 1.5 1.7 1.6 1.6 2.7 1.6 1.7 1.8 2.9 2.4 1.8 1.9 3.0 2.0 2.6 1.9

-1.6 -1.3 -0.9 0.1 -0.8 -1.3 0.3 -0.2 0.7 -1.9 ± 0.5 1.1 0.7 1.3 -0.8 -0.3 1.4 -1.4 1.2 1.2 1.4 1.7 1.6 -1.4 1.8 1.7 1.9 1.9 0.2 2.0 1.8 1.8 0.2 1.2 2.1 1.9 0.5 2.0 1.1 2.2

6-216

OPTICS TABLE

x

Px

I

6k-17.

SOLAR SPECTRAL IRRADIANCE*

DX

x

Ph

Dx ..-

0.140 0.150 0.160 0.170 0.180

0.0000048 0.0000176 0.000059 0.00015 0.00035

0.00050 0.00059 0.00087 0.00164 0.00349

0.420 0.425 0.430 0.435 0.440

0.1758 0.1705 0.1651 0.1675 0.1823

11.19 11.83 12.45 13.06 13.71

0.190 0.200 0.205 0.210 0.215

0.00076 0.00130 0.00167 0.00269 0.00445

0.00760 0.0152 0.0207 0.0288 0.0420

0.445 0.450 0.455 0.460 0.465

0.1936 0.2020 0.2070 0.2080 0.2060

14.41 15.14 15.90 16.66 17.43

0.220 0.225 0.230 0.235 0.240

0.00575 0.00649 0.00667 0.00593 0.00630

0.0609 0.0835 0.1079 0.1312 0.1534

0.470 0.475 0.480 0.485 0.490

0.2045 0.2055 0.2085 0.1986 0.1959

18.19 18.95 19.72 20.47 21.20

0.245 0.250 0.255 0.260 0.265

0.00723 0.00704 0.0104 0.0130 0.0185

0.1788 0.2053 0.2375 0.2808 0.3391

0.495 0.500 0.505 0.510 0.515

0.1966 0.1946 0.1922 0.1882 0.1833

21.92 22.65 23.36 24.07 24.76

0.270 0.275 0.280 0.285 0.290

0.0232 0.0204 0.0222 0.0315 0.0482

0.4163 0.4960 0.5758 0.6752 0.8225

0.520 0.525 0.530 0.535 0.540

0.1833 0.1852 0.1842 0.1818 0.1783

25.43 26.12 26.80 27.48 28.14

0.295 0.300 0.305 0.310 0.315

0.0584 0.0514 0.0602 0.0686 0.0757

1.020 1.223 1.430 1.668 1.935

0.545 0.550 0.555 0.560 0.565

0.1754 0.1725 0.1720 0.1695 0.1700

28.80 29.44 30.08 30.71 31.34

0.320 0.325 0.330 0.325 0.340

0.0819 0.0958 0.1037 0.1057 0.1050

2.227 2.555 2.925 3.312 3.702

0.570 0.575 0.580 0.585 0.590

0.1705 0.1710 0.1705 0.1700 0.1685

31.97 32.60 33.23 33.86 34.49

0.345 0.350 0.355 0.360 0.365

0.1047 0.1074 0.1067 0.1055 0.1122

4.090 4.483 4.879 5.271 5.674

0.595 0.600 0.605 0.610 0.620

0.1665 0.1646 0.1626 0.1611 0.1576

35.11 35.72 36.33 36.93 38.11

0.370 0.375 0.380 0.385 0.390

0.1173 0.1152 0.1117 0.1097 0.1099

6.099 6.529 6.949 7.359 7.765

0.630 0.640 0.650 0.660 0.670

0.1542 0.1517 0.1487 0.1468 0.1443

39.26 40.39 41.50 42.00 43.67

0.395 0.400 0.405 0.410 0.415

0.1191 0.1433 0.1651 0.1759 0.1783

8.189 8.675 9.245 9.876 10.53

0.680 0.690 0.700 0.710 0.720

0.1418 0.1398 0.1369 0.1344 0.1314

44.73 45.78 46.80 47.80 48.79

6-217

RADIOMETRY TABLE

x

6k-17.

P~

SOLAR SPECTRAL IRRADIANCE* (Contt"nued) D~

X

3.6 3.7

0.00135 0.00123

98.720 98.816

3.8 3.9 4.0 4.1 4.2

0.00111 0.00103 0.00095 0.00087 0.00078

98.902 98.982 99.055 99.122 99.182

4.3 4.4 4.5 4.6 4.7

0.00071 0.00065 0.00059 0.00053 0.00048

99.238 99.289 99.335 99.376 99.414

4.8 4.9 5.0 6.0 7.0

0.00045 0.00041 0.000383 0.000175 0.000099

99.448 99.480 99.509 99.716 99.817

8.0 9.0 10.0 11.0 12.0

0.000060 0.000038 0.000025 0.0000170 0.0000120

99.876 99.912 99.935 99.951 99.962

13.0 14.0 15.0 16.0 17.0

0.0000087 0.0000055 0.0000049 0.0000038 0.0000031

99.969 99.975 99.9785 99.9817 99.9843

18.0 19.0 20.0

0.0000024 0.0000020 0.0000016

99.9863 99.9879 99.9893 100.0

0.730 0.740 0.750 0.800 0.850

0.1290 0.1260 0.1235 0.1107 0.0988

49.75 50.69 51.62 55.95 59.83

0.900 0.950 1.000 1.1 1.2

0.0889 0.0835 0.0746 0.0592 0.0484

63.30 66.49 69.42 74.37 78.35

1.3 1.4 1.5 1.6 1.7

0.0396 0.0336 0.0287 0.0244 0.0202

81.61 84.32 86.62 88.59 90.24

1.8 1.9 2.0 2.1 2.2

0.0159 0.0126 0.0103 0.0090 0.0079

91.58 92.63 93.48 94.19 94.82

2.3 2.4 2.5 2.6 2.7

0.0068 0.0064 0.0054 0.0048 0.0043

95.36 95.85 96.287 96.664 97.001

2.8 2.9 3.0 3.1 3.2

0.0039 0.0035 0.0031 0.0026 0.00226

97.305 97.579 97.823 98.034 98.214

3.3 3.4 3.5

0.00192 0.00166 0.00146

98.368 98.501 98.616

X...

Px

Dx

* NASA Rept. X-322-68-304, August, 1968. Based on measurements on board NASA·711 Galileo at 38,000 ft. 'A Wavelength, ~m Px Solar spectral irradiance averaged over small bandwidth centered at X, W /(cmt.~m). DX Percentage of the solar constant associated with wavelengths shorter than 'A Solar constant 0.013510 W /crn 2•

6-218

OPTICS TABLE

6k-18.

ENERGY DISTRIBUTION IN THE SPECTRA OF THE SELECTED STARS IN CGS UNITS·

E(X), erg!(cm 2'sec) per unit AX

No.

Xt

I

r Ori

a Leo

8

9

10

0.156 0.154 0.148 0.141 0.131

0.3b 0.301 0.281 0.261 0.242

0.314 0.288 0.278 0.259 0.238

0.180 0.172 0.164 0.157 0.148

0.23 6 0.233 0.230 0.220 0.208

0.179 0.199 0.198 0.195 0.186

0.22 1 0.199 0.197 0.190 0.179

0.217 0.195 0.192 0.184 0.174

0.219 0.259 0.258 0.251 0.238

0.603 0.559 0.510 0.478 0.448

0.189 0.172 0.153 0.143 0.134

0.170 0.156 0.141 0.132 0.123

0.163 0.148 0.133 0.124 0.117

0.158 0.143 0.129 0.121 0.113

0.219 0.199 0.179 0.168 0.158

0.0315 0.0300 0.0287 0.0274 0.0255

0.413 0.386 0.356 0.327 0.290

0.120 0.110 0.0990 0.0893 0.0796

0.111 0.102 0.0937 0.0857 0.0754

0.106 0.0964 0.0873 0.0791 0.0696

0.103 0.095 0 0.086 5 0.079 5 0.0700

0.142 0.130 0.118 0.107 0.094 1

0.0283 0.0263 0.0246 0.0225 0.0209

0.0233 0.0219 0.0208 0.0195 0.0186

0.261 0.243 0.230 0.218 0.206

0.0706 0.0643 0.058, 0.0530 0.0510

0.0666 0.060 8 0.056 4 0.051 6 0.0487

0.0624 0.0580 0.054 2 0.049 5 0.0478

0.060 2 0.0550 0.0500 0.046 0 0.042 6

0.083 6 0.0776 0.0730 0.0679 0.0639

6,500 6,563 6,600 6,700 6,800

0.0202 0.0198 0.0195 0.0189 0.0180

0.0181 0.0176 0.0173 0.0165 0.0156

0.198 0.192 0.188 0.176 0.165

0.0486 0.0460 0.0450 0.0421 0.0390

0.0470 0.0456 0.0448 0.0420 0.0392

0.0470 0.0453 0.0449 0.0412 0.0388

0.040 6 0.0393 0.0380 0.035 5 0.033 2

0.061 4 0.059 6 0.0588 0.0560 0.052 2

7,000 7,100 7,200

0.0160

0.0139

0.144 0.134 0.125

0.034 0.032 0.030

0.0339 0.0311 0.028 6

0.0337 0.0321 0.0300

0.0287 0.0266 0.0243

0.0448 0.0415 0.036 6

(3 Ari

r Per

(30ri

2

3

4

5

6

7

2 3 4 5

3,300 3,400 3,500 3,600 3,700

0.024 5 0.0244 0.0243 0.0244 0.0251

0.060 2 0.0577 0.0552 0.0528 0.0502

0.714 0.695 0.670 0.648 0.671

0.31 1 0.284 0.263 0.246 0.226

6 7 8 9 10

3,800 3,929 3,970 4,036 4,102

0.035 5 0.0539 0.0586 0.0600 0.0581

0.0510 0.0487 0.0475 0.0461 0.0442

0.74 4 0.710 0.696 0.673 0.649

11

12 13 14 15

4,221 4,340 4,500 4,600 4,700

0.0550 0.0527 0.0495 0.0475 0.0455

0.0410 0.0388 0.0364 0.0350 0.0335

16 17 18 19 20

4,861 5,000 5,150 5,300 5,500

0.0418 0.0384 0.0355 0.0333 0.0307

21 22 23 24 25

5,700 5,850 6,000 6,200 6,400

26 27 28 29 30 31 32 33

E:

Ori

{3 Tau

E

Ori

-I

-I

...... ......

. ..... . .....

6-219

RADIOMETRY TABLE

6k-18.

ENERGY DISTRIBUTION IN THE SPECTRA OF THE

SELECTED STARS IN CGS UNITS*

(Continued)

E(A), erg/(cm 2'sec) per unit ./lA

No.

At 'Y

UMa

T/UMa

a Oph

a Lyr

o Cyg

a Aql

a Cyg

a Peg

--.

2

11

12

13

14

15

16

17

18

2 3 4 5

3,300 3,400 3,500 3,600 3,700

0.029. 0.0296 0.0298 0.0300 0.0302

0.165 0.156 0.147 0.139 0.129

0.033 0.0344 0.0349 0.0354 0.0383

0.339 0.320 0.314 0.308 0.306

0.0249 0.0249 0.0248 0.0247 0.0246

0.123 0.124 0.126 0.128 0.135

0.103 0.106 0.109 0.112 0.158

0.033. 0.0336 0.0340 0.0339 0.0342

6 7 8 9 10

3,800 3,929 3,970 4,036 4,102

0.0518 0.0784 0.0804 0.0806 0.0770

0.143 0.161 0.163 0.157 0.150

0.0590 0.0750

0.0452 0.0620 0.0612 0.0596 0.0571

0.197 0.232

0.0896 0.0866

0.50 0 0.778 0.798 0.795 0.765

0.294 0.288

0.217 0.214 0.212 0.208 0.201

0.055 2 0.0874 0.0906 0.0873 0.0831

11 12 13 14 15

4,221 4,340 4,500 4,600 4,700

0.0710 0.0667 0.0615 0.0584 0.0552

0.137 0.127 0.114 0.107 0.0990

0.0830 0.0796 0.0758 0.0739 0.0712

0.709 0.655 0.598 0.564 0.531

0.0525 0.0484 0.0438 0.0413 0.0389

0.276 0.268 0.258 0.250 0.243

0.187 0.176 0.165 0.159 0.153

0.0770 0.0707 0.0642 0.0607 0.0570

16 17 18 19 20

4,861 5,000 5,150 5,300 5,500

0.0504 0.0471 0.0438 0.0406 0.0368

0.0890 0.082 0 0.0745 0.0680 0.0600

0.0650 0.0609 0.0571 0.0535 0.0491

0.484 0.449 0.413 0.382 0.345

0.0356 0.0332 0.0306 0.0285 0.0256

0.226 0.212 0.198 0.186 0.174

0.143 0.135 0.127 0.119 0.110

0.0520 0.0482 0.0443 0.0411 0.0371

21 22 23 24 25

5,700 5,850 6,000 6,200 6,400

0.0329 0.0304 0.0286 0.0266 0.0246

0.052 6 0.0480 0.044 3 0.0401 0.0377

0.0453 0.0425 0.0401 0.0379 0.0354

0.313 0.290 0.272 0.248 0.230

0.0230 0.021'2 0.0196 0.0180 0.0170

0.162 0.154 0.146 0.137 0.128

0.102 0.0952 0.0900 0.0833 0.0779

0.0333 0.0388 0.0286 0.0261 0.0245

26 27 28 29 30

6,500 6,563 6,600 6,700 6,800

0.0234 0.0225 0.0221 0.0208 0.0199

0.036 2 0.0350 0.034 0 0.032 0 0.029 5

0.0336 0.0324 0.0318 0.0300 0.0282

0.220 0.209 0.204 0.190 0.178

0.0166 0.0161 0.0156 0.0144 0.0133

0.122 0.119 0.117 0.112 0.107

0.0746 0.0726 0.0710 0.0675 0.0646

0.0234 0.0227 0.0221 0.0205 0.0190

31 32 33

7,000 7,100 7,200

......

0.026

..... . ..... .

...... ......

0.0245 0.023 0.021

0.154 0.145 0.136

0.0115 0.0105

0.095 0.090 0.086

0.0566 0.0526 0.0476

0.0162 0.0146 0.0131

1 -I

* Kharitonov,

..... .

A. V., Soviet Astron.-AJ 7, 258 (1963).

t Wavelength in angstroms.

•••••

0

.0

••

•

6-220 TABLE

x,

OPTICS

6k-19.

A

log j, t. W /(cm 2·A)

log U/E),t photons/ (ern 2' sec' A)

-11 -10.2 -9.6 -9.5 -9.4 -9.8 -9.8 -9.8

4.7 5.8 6.8 7.2 7.6 7.5 7.7 7.8

10 20 50 100 200 400 600 800

* Compiled by

SOLAR ULTRAVIOLET FLUX INCIDENT ON EARTH'S ATMOSPHERE*

x,

A

900 1,000 1,100 1,200 1,400 1,600 1,800 2,000

log j,t. W /(cm 2·A)

log U/E),t photons/ (cm 2·sec·A)

-9.4 -9.3 -9.8 -9.7 -9.3 -8.3 -7.6 -7.1

8.2 8.4 7.9 8.1 8.5 9.6 10.4 10.9

G. R. Cook, The Aerospace Corp.

t C. W. Allen, "Astrophysical Quantities," 2d ed.,

p, 173, Athlone Press, University of London, London, 1963. Mean solar intensity with spectrum lines smoothed less the dominant resonance lines:

t Photon energy E - he/X. TABLE

6k-20.

HI 1216 A HeI 584 A. Hell 303 A

LABORATORY VACUUM ULTRAVIOLET SOURCES*a

Gas

Name

6 X 10- 7 W /cm 2 0.1 X 10- 7 W /cm l 0.3 X 10- 7 W/cm l

Pressure, torrs

Wavelength,

A

Excitation method

Flux, photons/ (cm 2'sec'A)

Continua Hopfield................. Argon ................... Krypton ................. Xenon ................... Hydrogen ................ Lyman/90 % He + 10 % air Synchrotron .............. X-ray fluorescence ........

He Ar Kr Xe H2

...

.. . . "

50-200 50-200 50-200 50-200 1-2 0.02-0.05 ......... ........ ,

600-1,000 1,060-1,500 1,250-1,800 1,500-1,800 1,600-5,000

Condensed spark Condensed spark Condensed spark Condensed spark A-c or d-e glow 300 I"o.J 5,000 Condensed spark 100-5,000 180 MeV 10-100 Soft X-ray tube

10 1o-10 11b 10 1O-10 11b 10 9 -10 10b 10 9 -10 1ob 10 L10 8e d 108-1O~

I

Line Emission Hydrogen ................ Resonance line/He 10 %

+ Resonance line/Ar + 10 %. Resonance line / Ar + 10 % . Resonance line/Ar + 10 %. Spark spectra He + 10 % .. Hollow cathode ...........

* Compiled by G.

H2 Ar

1"o.J1

H2 02

1"o.J1 1"o.J1 1"o.J1

N2 Air He

1-2

0.05 0.1

R. Cook, The Aerospace Corp.

850-1,600 1,165,1,236 1,470, 1,295 1,216 1,302-1,306 1,743-1,745 200-1,500 231-1,640

A-c or d-e glow Microwave Microwave Microwave Microwave Condensed a-c D-c glow

1"o.J10 1111 10 1 41&

lO 13h 10 12h

lO 12h i

106-10 71

RADIOMETRY

6-221

Notes for Table 6k-20 a An account of this subject may be found in J. A. R. Samson, "Vacuum Ultraviolet Spectroscopy," chap. 5, John Wiley & Sons, Inc., New York, 1967. b Fluxes are approximate, and represent values that one may expect to obtain at the maximum of the continuum with a 1- or 2-m normal-incidence monochromator with a 600- or 1,200-line/mm grating. Absolute flux measurements have been reported by Metzger and Cook, J. Opt. Soc. Am. 55, 516 (1965), and by R. E. Huffman, J. C. Larabee, and Y. Tanaka, Appl. Opt. 4, 1581 (1965). The Ar, Kr, and Xe continua may also be excited with less intensity by microwaves. See P. G. Wilkenson and E. T. Byran, Appl. Opt. 4, 581 (1965). Greater intensity may be obtained in high-energy single-flash technique. See J. A. Golden and A. L. Myerson, J. Opt. Soc. Am. 48, 548 (1958). C At about 1,850 A.. See D. M. Packer and C. Lock, J. Opt. Soc. Am. 41, 699 (1951). d This source requires current densities of 30,000 A/cm 2 or more in the light-source capillary tubes. Flash tubes have been designed which produce a well-developed photographic spectrum after two or three flashes. See W. R. S. Garton, J. Sci. Lnsir, 36, 11 (1959), and M. Nakamura, Sci. Light (Tokyo) 16, 179 (1967). For wavelengths shorter than about 1,000 A. the continuum contains numerous emission lines. e These values are for the NBS 180-MeV, R = 83 em, electron synchrotron at a distance of about 2 m along the tangent to the orbit before entering the spectrograph with A = 304 A.. See K. Codling and P. Madden, J. Appl. Phys. 36, 380 (1956). For 6-GeV electrons in a 31.7-m orbit see R. Haensel and C. Kunz, Z. Angew. Phys. 23, 276 (1967). The wavelength of the maximum of the continuum decreases according to A = 2.35RI E3, where X is in A., R is in meters, and E in GeV. For 1 GeV and R = 31.7 m, the maximum of the continuum is at about 75 A. f Fluorescence in the 10- to 100-A. region is detected with proportional counters containing P-lO or methane gas. For analysis of the light elements Mg to Be typical counting rates vary from 30 to 7,200 per sec, with peak to background ratios between 4 and 55. See B. L. Henke in "Advances in X-ray Analysis," vol. 8, p. 269, Plenum Press, Plenum Publishing Corporation, New York, 1965. (/ This is the flux observed at A = 1215.6 with a I-m monochromator with the light source operated 400 rnA. See D. M. Packer and C. Lock, J. Opt. Soc. Am. 41, 699 (1951). A wavelength table of the H 2 and many line spectra with relative intensities has bean prepared by K. E. Schubert and R. D. Hudson, ATN-64 (9233)-2, October, 1963, The Aerospace Corp., P. O. Box 95085, Los Angeles, Calif. 90045. II About 50-W microwave power at 2450 MH coupled to the gas in a 13-mm OD capillary. See H. Okabe, J. Opt. Soc. Am. 54, 478 (1964). A table of wavelengths of emission lines from neutral and ionized atoms in the 6 to 2,000 A range has been prepared by R. L. Kelly, UCRL 5612, University of California, Lawrence Radiation Laboratory, Livermore,Calif. For each line there are one or more references to the original literature. i Current densities less than for the Lyman discharge allow pulse rates in the 50 to 400 per sec region. These rates are convenient for photoelectric detection. Details of this source have been published by P. Lee and G. E. Weissler, J. Opt. Soc. Am. 42, 80 (1952). i These are photon fluxes at the entrance slit of a 1-m grazing incident monochromator necessary to produce an output current of 10- 9 amp from a Bendix magnetic-type multiplier. See E. Hinnov and F. Hofmann, J. Opt. Soc. Am. 53, 1259 (1963). 0

61. Wavelengths for Spectrographic Calibration 1

TABLE

61-1.

Wavelength, A

WAVELENGTH STANDARDS FOR THE VACUUM ULTRAVIOLET*

Intensity

Spectrum

Estimated relative error

Wavelength,

A

Intensity

Spectrum

20 1 2 1 30 10 60 15 8 15 2 4 20 18

Si I Si I Si I Si I NI NIl NI NIl Si I Hg II NI Si I

4

Hg II Si I Si I Hg II Si I Si I Si I Hg II

(±mA)

1,942.273 1,930.902 1,900.284 1,880.969 1,870.547 1,869.548 1,867.590 1,864.742 1,862.806 1,861.750a 1,859.406 1,857.956 1,853.260 1,850.665 1,849.497 1,849.380 1,848.237 1,846.014 1,844.304 1,842.066 1,839.995 1,833.264 1,831.973 1,830.458 1,820.336 1,816.921 1,808.003 1,807.303 1,803.888 1,796.897 1,787.805 a 1,782.817 1,775.677

20 10 5 5 20 8 1 5 2 1 3 8 3 5 50Rb 5 5 8

10 1 4 1 5 4 20 8 5 30 2 15 10 15 1

Hg

II

01 Hg II Si I Hg II Hg II NIl NIl NIl Si I Ni I Ni I Si I Si I HgI Ni I Si I NIl NIl NIl Si I

0 NIl NIl Hg II Si II Si II NIl Hg II Hg II Si I Na III HgI

2 2 2 2 4 2 3 2 5 2 2 4 4 5 4 4 4 4 4 5 4 5 4 4 4 2 4 5 2 4 2 4 4

1,774.941 a 1,769.658a 1,753.113 a 1,749.771 a 1,745.246 1,743.322 1,742.724 1,740.327 1,736.582 1,732.142 1,730.874 1,727.332a 1,721.081 1,720.158 1,707.397 1,704.558 a 1,702.805 a 1,702.733 1,700.522 1,693.756 1,676.913 1,672.405 1,658.117 c 1,657.899 c 1,657.541 1,657.374c 1,657.243 1,657.00l c 1,656.923c 1,656.454 1,656.259 1,654.055 1,653.644

4 8 8 3

15 5 2 20 15 1 10 1 30 15 4 15 5 2

011 011

01 01 01 01 01 01 01 01 01 01 Hg

II

Estimated relative error (±mA)

4 4 3 5 3 4 3 3 4 4 3 3 3 4 4 4 4 4 4 4 4 3 1 4 5 1 5 1 1 4 1 3 3

1 This section presents calibration standards in the ultraviolet and infrared wavelength regions. For corresponding data on visible wavelengths, see Sec. 7.

6-222

WAVELENGTHS FOR SPECTROGRAPHIC CALIBRATION TABLE

61-1.

WAVELENGTH STANDARDS FOR THE VACUUM ULTRAVIOLET·

A

Intensity

Spectrum

1,649.932 1,640.474 1,640.342 1,630.180 1,629.931 1,629.830 1,629.366 1,613.251 1,605.321 1,602.598 1,592.245 1,589.607 1,574.035 1,561.433 1,561.339 1,560.687 d 1,560.301 1,504.474 1,494.673 1,492.824 1,492.624 1,485.600 1,481. 760 1,470.082 1,469.844 1,467.405 1,466.723 1,463.838 1,463.346 1,459.034 1,439.094 1,411.948 1,393.322 1,364.165 1,361. 267 1,357.140 1,355.598 1.354.292 1,350.074 1,335.692 1,335.184 1,334.520 1,331.737

10 80d 100d 2 4 4 4 4 1 15 4 2 1 20 5 15 2 5 60 30 80 8 30 5 15 20 5 40 40 20 10 30 1 8 8 5 2 8 4 80 8 60 20

Hg II He II Hell Si J Sil

Wavelength,

NIl Si I He II He II

CI Si I Si I

NIl CI CI CI CI Hg

III

NI NI NI Si II CI CI CI CI NI C CI CI Si II NI Hg III CI Hg II CI 01

CI Hg

II

CII Hg

CII Hg

II

Estimated relative error (±mA)

Wavelength, A

Intensity

4 4 2 3 4 4 4 4 3 3 3 3 3 2 4 12 5 4 4 4 5 2 3 3 4 3 4 3 2 4 2 3 2 4 4 2 3 3 2 5 3 5 4

1,329.590 1,329.108 1,328.836 d 1,327.927 1,326.572 1,321. 712 1,319.684 1,319.003 1,316.287 1,311. 365 1,310.952 1,310.548 1,309.278 1,307.928 1,306.036 1,304.872 1,302.173 1,288.430 1,280.852" 1,280.604" 1,280.403" 1,280.340" 1,280.140" 1,279.897" 1,279.230 1,277.727 1,277.551 1,277.282 1,276.754 1,265.001 1,261.5591 1,261.4301 1,261.1281 1,261.0001 1,260.9301 1,260.7381 1,259.523 1,253.816 1,251.164 1,250.586 1,248.426 1,246.738 1,243.309

40 40 15 10 15 20 30 20 1 20 25 25 3 10

25 30 30 5 10

8 5 15 8 10 8 20 50 40 3 1 15 8 8 8 8 8 10 5 8 4 5 1 15

Spectrum

CI CI CI NI NI Hg II NI NI NI CI NI NI Si II Hg II 01 01 01

CI CI CI CI CI CI CI CI CI CI CI NIl Si II CI CI CI CI CJ CI CJ CJ Si II Hg I Si II Si

II

NI

6---223

(Continued)

Estimated relative error (±mA

1 2 10 2 4 3 4 2 1 3 1 3 5 3 3 5 1 3 1 3 4 1 1 1 3 1 4 1 1 1 1 4 1 1 2 1 3 1 4 4 4 3 4

6-224 TABLE

OPTICS

61-1.

WAVELENGTH STANDARDS FOR THE VACUUM ULTRAVIOLET*

Wavelength,

A 1,243.179 1,229.172 1,228.790 1,228.410 1,225.372 1,225.028 1,215.662 1,215.167 1,215.086 1,200.708 u 1,200.226 u 1,199.718 u 1,199.551 u 1,194.496 1,194.060 1,193.674 1,193.388 d 1,193.243 1,193.013 1,189.628 1,189.244 1,188.972 1,177.694 1,176.626 1,176.508 1,170.276 1,169.692 1,168.537 1,168.334 1,167.450 1,164.322 1,163.884 1,158.138 1,158.030 1,152.149 1,134.988 1,134.426 1,134.176 1,101.293 1,100.362 1,099.259 1,099.153 1,098.264

Intensity

Spectrum

NI NI NI NI 10 NI 15 NI 100Rb H 5 Hen 5 Hen 30 NI 40 NI 2 NI 50 N I, C I Si I 5 3 CI 3 CI 3 CI CI 15 15 CI 5 NI 3 NI 5 NI 15 NI 3 NI 15 NI 1 NI NI 1 20 NI 8 NI 25 NI 8 NI 12 NI 1 CI 8 CI 2 01 25 NI 25 NI 20 NI 40 NI 30 NI 40 Hg II 25 NI 40 NI 20 1 10 5

Estimated relative error (±mA) 1 1

4 4 1 4 5 5 4 2 1 4 5 1 3 3 8 2 4 4 3 1 3 5 1 3 1 4 4 4 3 4 5 4 5 4 4 4 5 4 3 5 5

iContinued)

I

Wavele~gth, A

Intensity

Spectrum

1,098.103 1,097.990 1,097.245 1,096.749 1,096.322 1,095.940 1,085.707 1,085.546 1,085.442 1,084.970 1,084.910 1,084.579 1,083.990 1,070.821 1,069.984 1,068.476 1,067.607 1,041. 688 1,040.941 1,039.233 1,037.627 1,037.020 1,028.162 1,027.433 1,025.728 1,025.298 990.805 h 990.210 h 990. 132h 988. 776h 988. 661h •d 977.967 964.626 963.991 953.658 953.415 952.522 952.414 952.304 950.114 949.742 910.279 909.692

40 25 50 35 35 35 50 3 3 2 2 30 20

NI NI NI NI NI NI Nu Nu Nn Hen He n Nu Nil NI NI NI NI 01 01 01 0 CII 01 01 H Hell 01 01 01 01 01 01 NI NI NI NI NI 01 NI 01

°

30 35 35 1 15 20

°°8 20 60 2i 2 8 1 15 2 1 1 5 15 15 4 8 8

° °°

25

H

NI NI

Estimated relative error (±mA) 5 4 4 4 2 3 3 5 3 4 5 3 4 5 1 4 4 4 4 4 3 1 3 3 3 5 4 4 4 4 4 4 4 4 4 3 4 4 4 4 4 5 5

WAVELENGTHS FOR SPECTROGRAPHIC CALIBRATION TABLE

61-1.

WAVELENGTH STANDARDS FOR THE VACUUM ULTRAVIOLET*

Wavelength,

A

Intensity

Spectrum

906.722 906.426 906.202 905.829

1 15 10 5

NI NI NI NI

Estimated relative error (±mA)

2 4 3

4

Wavelength,

A

Intensity

893.079 888.363 888.019 875.092

0 0 0 5

Spectrum

Hg

NI NI NI

II

6-225

(Continued)

Estimated relative error (±mA)

2 2 4 5

* J. Opt. Soc. Am. 4.1, 10 (195.5). "Identification: A. Fowler, Proc, Roy. Soc. (London), ser. A, 128, 422 (1929); J. C. Boyce and H. A. Robinson, J. Opt. Soc. Am. 26, 133 (1936). b Self-reversed resonance line. e Resolved 2p2 ap - 38 1 p o multiplet. d Blended line. • Completely resolved 2p2 Ip - 4b apo multiplet. I Completely resolved 2p2 ap - 3d apo multiplet. Q Resolved 2pa 4S0 38 4p multiplet. A 2p4 ap - 38' aDo multiplet. i Diffuse lin".

~226

OPTICS TABLE

61-2.

PROPOSED INTERNATIONAL WAVELENGTH STANDARDS IN THE VACUUM ULTRAVIOLET

Wavelength,

Wavelength,

A,

Spectrum

this research

1,930.902 1,745.246 1,742.724 1,740.327 1,658.117 1,657.899 1,657.374 1,657.001 1,656.259 1,560.301 1,494.673 1,492.624 1,481.760 1,335.692 1,329.590 1,329.108 1,277.282 1,261.559 1,200.708 1,200.226 1,199.551 1,177.694 1,176.508 1,167.450 1,134.988 1,134.426 1,134.176 1,085.546 1,084.579 1,083.990 990.805 990.210

Wavelength.

Wavelength,

A

A,

I,

More and Rieke a

Boyce and Riekeb

Weber and Watsonc

.... . .... . .... . .... . .... . 0.909 .... . ..... 0.266 0.308 0.672 .... . 0.771 0.700 0.587 0.102 .....

0.900 0.246 0.734

0.889 0.255 0.733 0.320 0.127

CI NI NI NIl CI CI CI CI CI CI NI NI CI CII CI CI CI CI NI NI NI Ny NI NI NI NI NI NIl NIl NIl CI CI

..... 0.719 0.217 0.552 0.701 0.506 0.442 0.977 .....

..... ..... 0.584 ..... 0.790 0.198

..... 0.126 .... . 0.380 0.005

..... 0.316 0.669 0.630 .... . .... .

.... . 0.101 0.274 0.560 0.706 0.220 0.547

.... .

.....

..... 0.980 0.419 0.171 0.546 0.579 0.991 0.797 0.213

J

.....

"J. C. Boyce and C. A. Rieke,

A,

...... ......

1,930.897 1,745.249 1,742.730 1,740.321 1,658.123 1,657.900 1,657.378 1,657.001 1,656.260 1,560.308 1,494.670 1,492.630 1,481. 760 1,335.692 1,329.587 1,329.104 1,277.279 1,261. 561 1,200.708 1,200.219 1,199.552 1,177.691 1,176.504 1,167.449 1,134.981 1,134.420 1,134.172 1,085.546 1,084.580 1,083.990 990.797 990.207

...... 0.315 d

...... 0.891 6

...... 6.9986 0.2556

. .... . .... 0.693 0.215 0.557 0.677 0.498 0.454 0.980 0.416 0.169 0.546 0.582 0.990

..... .....

A.

mean value

. .... . .... .... . 0.668 0.634 ..... ..... ..... .... .

Wavelength,

other observers

0.381

K. R. More and C. A. Rieke, Phys. Rev. 10, 1054 (1936). Phys. Rev. 4.7, 653 (1935). GR. L. Weber and W. W. Watson, J. Opt. Soc. Am. 26, 307 (1936). d A. Fowler, Proc, Roy. Soc. (London), ser, A, 123,422 (1929) . • A. G. Shenstone, Phys. Rev. 72,411 (1947). IE. Ekefors, Z. Physik 63,437 (1930). II B. Edl~n, Z. Physik 98, 561 (1936); Nature 119, 129 (1947). 11 F. Paschen and G. Kruger, Ann. Phys. 7, 1 (1930).

a

Wavelength,

......

...... ...... 0.7501 0.684a 0.583h ...... 0.280h 0.565h ......

...... ...... ......

. ..... . ..... ...... . ..... . ..... . ..... ...... . ..... . ..... . .....

..-

6-227

WAVELENGTHS FOR SPECTROGRAPHIC CALIBRATION

TABLE 61-3. INFRARED STANDARD WAVELENGTHS \Vs..velength, #lm

State

0.54607 0.57696 0.57907 1.01398 1.12866 1.140 1.35703 1.36728 1.39506 1.52452 1.6606 1.671 1.69202 1.69419 1.70727 1.71090 1.81307 1.97009 2.008 2.150 2.1526 2.22 2.24929 2.3126 2.32542 2.37 2.4030 2.4374 2.439

Emission Emission Emission Emission Emission Liquid Emission Emission Emission Emission Liquid Liquid Emission Emission Emission Emission Emission Emission Gas Liquid Liquid Liquid Emission Liquid Emission Solid Liquid Liquid Gas

2.464 2.4944 2.5434 2.688 2.7144 2.765 2.79 2.996 3.2204 3.230

Liquid Liquid Liquid Gas Vapor Gas Solid Gas Solid Gas

3.2432 3.2666 3.3033 3.3101

Solid Solid Solid Solid

Description

AH-41amp AH-41amp AH-41amp AH-41amp AH-41amp

Substance

Mercury Mercury Mercury Mercury Mercury ................ Benzene AH-41amp Mercury AH-41amp Mercury AH-41amp Mercury AH-41amp Mercury 0.5-mm cell 1,2,4-Trichlorobenzene ................ Benzene AH-41amp Mercury AH-41amp Mercury AH-41amp Mercury AH-41amp Mercury AH-41amp Mercury AH-41amp Mercury ................ Carbon dioxide ................ Benzene 0.5-mm cell 1,2,4-Trichlorobenzene ................ Carbon disulfide AH-4lamp Mercury 0.5-mm cell 1,2,4-Trichlorobenzene AH-41amp Mercury 25-,um film Polystyrene 0.5-mm cell 1,2,4-Trichlorobenzene 0.5-mm cell 1,2,4-Trichlorobenzene ................ Carbon oxysulfide central min ................ Benzene 0.5-mm cell 1,2,4-Trichlorobenzene 0.5-mm cell 1,2,4-Trichlorobenzene ................ Carbon dioxide 5.0-cm cell Methanol ................ Carbon dioxide ................ Lithium fluoride 200-mm 5. O-cm cell Ammonia-zero branch 25-,um film Polystyrene Carbon oxysulfide central min 25-,um film Polystyrene 25-,um film Polystyrene 25-,um film Polystyrene 25-,um film Polystyrene

................

Ref.

9 9 9 9 9 6 9 9 9 9 9 6 9 9 9 9 9 9

9 9 9 9 9 Wright 9 9 8 5 9 9 Barker and Wu 9 Barker and Wu 9 2 9 8

j9

I~

fr-228

OPTICS TABLE

Wavelength,

61-3.

INFRARED STANDARD WAVELENGTHS

Description

State

(Continued)

Substance

Ref.

IJ

3.320 3.3293 3.4188 3.426

Gas Gas Solid Gas

5.0-cm cell 25-ttm film

3.465

Gas

· ...............

3.5078 4.258 4.613

Solid Gas Vapor

25-ttm film Atmospheric

4.866 4.875

Vapor Gas

5.0-cm cell

5.138 5.284

Solid Gas

50-ttffi film ................

5.292 5.549 5.847

Gas Solid Gas

50-ttm film ................

6.154 6.238 6.692 6.753 6.925 7.268 7.681 8.241 8.362 8.490 8.623 8.762 9.057 9.216 9.295 9.378 9.548

Gas Solid Solid Liquid Gas Liquid Gas Gas Gas Gas Gas Gas Gas Gas Gas Gas Gas

9.608 9.672 9.673 9.724 9.807 9.85

Vapor Vapor Gas Solid Vapor Gas

w

•••••••••••••••

· ...............

·............... ................

................

200 mm 5. O-cmcell 50-ttm film 5o-,um film

................ ................ 0.05-mm cell

................ 200-mm 20o-mm 200-mm 20o-mm 20o-mm 20o-mm 200-mm 200-mm 20o-mm

5. O-cm cell 5. O-cm cell 5. O-cm cell 5. o-cm cell 5. o-cm cell 5. O-cm cell 5. o-cm cell 5. O-cm cell 5. o-cm cell

................ ................ 5-cm cell

................ 50-ttffi film

................ ................

Methane-zero branch Methane Polystyrene Carbon oxysulfide central min Hydrogen chloride central min Polystyrene Carbon dioxide Carbon disulfide central min Methanol Carbon oxysulfide central min Polystyrene Carbon oxysulfide central min Ethylene central min Polystyrene Carbon oxysulfide central min Ammonia-zero branch Polystyrene Polystyrene Benzene Ethylene-zero branch Methylcyclohexane Methane-zero branch Ammonia Ammonia Ammonia Ammonia Ammonia Ammonia Ammonia Ammonia Ammonia Carbon oxysulfide central min Methyl chloride Methanol Ammonia Polystyrene Methyl chloride Ammonia

7 9 9 8

9 9 5 9 8 9 8 5 9 8 2 9 9 S. Silverman 5 9 3 2

2 2 2 2 2 2 2 2

8 4 9 Wright 9 4 Wright

WAVELENGTHS OR SPECTROGRAPHIC CALIBRATION TABLE

Wavelength, JoIm

61-3.

State

10.073 10.53 11.008 11.035 11.26 11.475 11. 793 11.862 12.075 12.381 12.732 12.809 12.885 12.961 12.99 13.69 13.883 14.29* 14.42

Gas Gas Gas Solid Gas Liquid Gas Liquid Gas Gas Gas Gas Gas Gas Gas Gas Gas Solid Liquid

14.98 15.48

Gas Liquid

17.40* 18.16 20.56

Liquid Liquid Liquid

21.52 21.80 22.76* 23.85

Liquid Liquid Liquid Vapor

INFRARED STANDARD WAVELENGTHS

Description

(Continued)

Substance

Ammonia Ethylene-zero branch Ammonia Polystyrene Ammonia Methylcyelohexane Ammonia Methylcyclohexane Ammonia Ammonia ................ Acetylene ................ Acetylene Acetylene ................ Acetylene ................ Ammonia ................ Acetylene Carbon dioxide Atmospheric Polystyrene 50-.um film ................ Toluene 1 % in carbon disulfide Atmospheric Carbon dioxide 0.05 mm (1:4 CS2) Unknown in technical grade of 1,2,4trichlorobenzene 0.025-mm cell 1,2,4-Trichlorobenzene o.025-mm cell 1,2,4-Trichlorobenzene 0.05-mm cell 1,2,4- Trichlorobenzene (sat. sol. in CS 2) Toluene o.05-mm cell o.025-mm cell 1,2,4- Trichlorobenzene 0.025-mm cell 1,2,4-Trichlorobenzene Atmospheric Water

200-mm 5. O-cm cell ................ 200-mm 5. O-cm cell 50-,um film 200-mm 5. O-cm cell o.05-mm cell 200-mm 5. O-cm cell 0.05-mm cell 200-mm 5. O-cm cell 200-mm 5. O-cm cell

•••••••••••••

°

0

"

'

6--229

Ref.

2 5 2 9 J. Opt. Soc. Am. 9 2 9 2 2 1 1 1 1 Wright 1 9 9 9 9 9

9 9 9 9 9 9 9

* Broad bands. References 1. Levin and Meyer: J. Opt. Soc. Am. 16, 137 (1928); Meyer and Levin: Phys. Rev. 29(2), 293 (1927). 2. Oetjen, Kao, and Randall: Rev. Sci. Instr, 13, 515 (1942). 3. Cooley: Astrophys. J. 62, 73 (1925). 4. Bennett and Meyer: Phys. Rev. 32, 888 (1927). 5. McKinney, Leberknight, and Warner: J. Am. Chem. Soc. 69, 481 (1937). 6. Liddel and Kaspar: J. Research Nat!. Bur. Standards 11, 599 (1933). 7. Nielsen and Nielsen: Phys. Rev. 48, 864 (1935). 8. Bartunek and Baker: Phys. Rev. 48, 516 (1935). 9. Plyler: J. Research Natl. Bur. Standards 46, 463.

6m. Magneto-, Electro-, and Elasto-optic Constants WILLIAM R. COOK, JR. AND HANS JAFFE

Gould, Inc.

6m-1. Magnetic Rotation (Faraday Effect). The most important interaction between magnetic field and light wave propagation is a rotation of the plane of polarization of a light wave traveling parallel to a magnetic field component a

=

(6m-l)

VHl

where H is magnetic field strength, and I the path length. This is the Faraday effect. The coefficient V is known as the Verdet constant. The Faraday effect results from a difference in propagation velocity for left and right circular polarized light. For a constant value of this difference, the Verdet constant is inversely proportional to wavelength. The tables give V in angular minutea/oersted-cm, Positive sign indicates rotation of the polarization plane in the same sense as a positive current in a coil producing the field. TABLE

Gasb

He Ar H2 N2 02 Air Cb HCI H 2S NHa CO CO2 NO CH4 n-C4H 10

(nD O -

X

1)

ros-

0.036 2.81 0.297 0.272 0.293 0.773. 0.447 0.63 0.376 0.34 0.45 0.297 0.444

6m-la.

VERDET CONSTANTS OF GASES AND LIQUIDS"

10 6Vo

Liquid

A, JLm

+ 0.40 + 9.36 + 6.2g + 6.46 + 5.69 + 6.27 +31.9 +21.5 +41.5 +19.0 +11.0 + 9.39 -58 +17.4 +44.0

P S H 2O. H2O D 20 HaP04 CS2 CCl4 SbCl5 TiCl4 TiBr4! Methanol Acetone Toluene Benzene Chlorobenzene Nitrobenzene Bromoform

0.589 0.589 0.546 0.589 0.589 0.578 0.589 0.578-0.589 0.578 0.578 0.578 0.589 0.578-0.589 0.578-0.589 0.578-0.589 0.589 0.589 0.589

t,OC

33 114 25 20 19.7 97.4 20 25.1 18 17 46 18.7 20.0 15.0 15.0 15 15 17.9

nD 2 O. ,tJ

10 2V

+13.3 1.929 1100 + 8.1 + 1.547 1.3330 + 1.309 200 1.3384 + 1.257 + 1.35 1.6255 + 4.255 150 1.463 + 1.60 140 1.601 + 7.45 1.61 - 1.65 - 5.3 1.3289 + 0.958 1.3585 + 1.116 1.4950 + 2.71 1.5005 + 3.00 1.5246 + 2.92 1.5523 + 2.17 1.5960 + 3.13

G Selected except as noted from R. de Malleman, "Tables des constantes selectionees; pouvoir rotatoire magnetique (effet Faraday)," Hermann &; Cie, Paris, 1951. b Vo for>. - 0.578 JIm as reduced to OOC and 760 mm Hg, • "Handbook of Chemistry and Physics," Chemical Rubber Publishing Co., Cleveland, Ohio. tJ Indices of refraction for organic chemicals from Eastman Kodak Co. Organic Chemicals List No. 39, 1954. • V. Sivaramakrishnan, Proc, Indian Acad. Sci. 39,31 (1954); J. Indian Lnst, Sci. 36, 193 (1954). I P. Fritsch, Compt, Rend. 217, 447 (1943).

6-230

6-231

MAGNETO-, ELECTRO-, AND ELASTO-OPTIC CONSTANTS

6m-lb. VERDET CONSTANTS OF SOLIDS (At room temperature except as noted)

TABLE

Solid

Oxide glasses 39ThO·61Si0 2(moles) 20TeO 2·80PbO 24Pr20a·76B 20 a 24Nd20a·76B20a 85BbOa·15B 20a 85PbO·15B20a 85TI20·15B20a 2.67Ce20a·P206 As2Sa

Solid

. . . . . . . . .

"

V 0.633 Ilm

V 0.700 Ilm

Ref.

0.12 0.14 -0.26 -0.14 0.10 0.115 0.122 -0.174 0.26

0.10 0.127 -0.22 -0.105 0.085 0.093 0.092 -0.132 0.194

8 8 8 8 8 8 8 10 9

n 0.54611lm V 0.54611lm n 0.5893 Ilm V 0.5893

Oxide glasses 1.4601 0.01664 1.4585 Si0 2................... Dense flint 18 .......... 1.8999 0.1180 1.8900 Lead glass (Corning 8363) 0.133 . ..... ...... Oxide crystal.Of NH.AI(SO.)d2H20 ..... 0.0151 1.4594 ...... KAI(SO.)d2H 20 ....... ...... 0.0144 1.4564 NH.Fe(SO.)2·12H20 at 1.4848 26°C ................ ...... -0.00145 ...... -0.0145 . ..... Same at -111°C ....... ...... 0.0256 NiSO.·6H 20 at 24°C .... w= 1.5109 Same at 1.36°K ......... ..... . 0.419 ...... MgAhO. (spinel) ....... ...... . ........ 1.7181 CaCOa (calcite) ......... ..... . ......... w= 1.6585 NaCIO a................ ...... 0.0105 1.5151 Si0 2 (quartz) ........... w= 1.5462 0.01952 1.5443 AhOa (corundum) ....... w= 1. 7712 0.0240 1.7685 Cubic halide crystals NaCI .................. ...... 0.0410 1.5443 NaBr .................. 0.0621 1.6412 KCI ................... ...... 0.0328 1.4904 KBr ................... 1.5641 0.0500 1.5600 KI .................... 1.6731 0.083 1.6664 NH.CI ................ 0.0430 1.6426 NH.Br ................ 0.0601 ...... 1.7108 CaF 2.................. 1.4338 ..... . ......... Tetrahedral cubic crystals C, diamond ............. 0.0278 2.4172 ...... CuCI .................. 1.793 ..... . 0.20 ± 0.03 ZnS ................... ...... 0.287 2.3683 •

0

••••

••••

0

•

~m

Ref.

0.01421 0.0969 0.107

3b 3b 9

0.0128 0.0124

3c 3c

-0.00058 -0.0111 0.0221

1 1 4 2 6 7 3c 3b 3d

. .....

0.021 0.019 0.0081 0.01664 0.0210 0.0345 ••

0

••••

0.0275 0.0425 0.070 0.0362 0.0504 0.00883 0.0233

......... 0.226

3c 3c 3c 3c 3c 3c 3c 3a

3a 5 3a

References to Table 6m-lb 1. Kaufmann, H.: Ann. Physik 18, 251 (1933). (Paramagnetic rotation.) 2. Levy and van den Handel: Physica 15, 717 (1951). (Paramagnetic rotation.) 3. Ramaseshan, S.: Proc. Indian Acad. Sci.: (a) 24, 104 (1946); (b) 24,426 (1946); (c) 28. 360 (1948); (d) 34, 97 (1951); (e) Current Sci. (India) 20, 150 (1951). 4. O'Connor, Beck, and Underwood: Pbu«. Rev. 60, 443 (1941). 5. Gassmann, G.: Ann. Physik 35, 638 (1939). A volume of 23.9 ems/mole is assumed to derive this value of V. 6. DuBois: Ann. Physik 51, 537 (1894).

6-232 7. 8. 9. 10.

OPTICS

Chauvin: J. Phys. 9, 5 (1890). Borrelli, N. F.: Personal communication; also, J. Chem, Phys. 41, 3289 (1964). Robinson, C. C.: Appl. Opt. 3, 1163 (1964). Berger, S. B., C. B. Rubinstein, C. R. Kurkjian, and A. W. Treptow: Phys. Rev. 133A, 723 (1964).

6m-2. The Kerr Effect. The lowest-order effect of an electric field on the refractive index of an isotropic material permitted by symmetry is quadratic in the electric field. The observed effect is an induced birefringence, the Kerr effect. It has substantial magnitude in polar liquids. (See also Sec. 6m-6 for ferroelectric crystals.) The Kerr constant K is defined by the relation

r

= (n p

-

n,)l = lKE2

(6m-2)

X

where r is the retardation (path difference in fractions of the wavelength X), n p and n. are the refractive indices parallel and normal to the applied field E, and 1 is the path length. As customary, Table 6m-2 gives K in electrostatic units. TABLE 6m-2. TABULATED CHARACTERISTICS OF LIQUIDS WITH KNOWN LARGE KERR CONSTANTS * Kerr constant K, 10-7 esu (X=0.589 ~m)

Liquid

Symbolt

Carbon disulfide................ Acetone....................... Methyl ethyl ketone ............ Pyridine ....................... Ethyl cyanoacetate.......... , .. o-Dichlorobenzene.............. Benzenesulfonyl chloride......... Nitrobenzene ................... Ethyl B-aminoerotonate ....... , . Paraldehyde ...................

C& C,HaO C4H80 C,H,N C,H7N02 CaH4Cb CaH,CI02S CaH,N02 CaHuNO. CaHl20.

+3.23 +16.3 +13.6 +20.4 +38.8 +42.6 +89.9 +326 +31.0 -23.0

Benzaldehyde ..................

C7HaO

+80.8

p-Chlorotoluene .....•..•....... o-Nitrotoluene ................. m-Nitrotoluene ..•.............. p-Nitrotoluene ................. Benzyl alcohol. ....•.....•......

C7H7CI C7H7NO. C7H7N02 C7H7NO. C7H80

+23.0 +174 +177 +222 -15.4

m-Cresol. ......................

C7H80

+21.2

m-Chloroacetophenone.......... Acetophenone..................

C8H7CIO CaR80

+69.1 +66.6

Quinoline...................... Ethyl salicylate ................. Carvone ....................... Ethyl benzoylacetate ............ Water .........................

CSH7N CSH100. CloH140 CuHl20, H 2O

+15.0 +19.6 +23.6 +16.0 +4.0

ShortwaveStatic Melting point, -o nD20/Hfj - Ha length dielectric eonstant] Boiling point, "C cutoff e X.o, nmi

2.6 21. 9 18.5 12.5 27.7 7.5

....

36.1

.... 14.5 12.0 18.0 14.1 6.4 27.4 23.8 18.7 13.0 10.8 13.0 5.0 18.3 15.8 9.0 8.6 11.2 12.8 81

-108.6/+46.3 -94.3/+56.1 -86.4/+79.6 -42/+115.3 -22.5/+206 -17.6/+179 +14.5/+247 +5.7/210.9 +33.9/210 +10.5/+124

1.6295/0.0343 1.3591/0.0068 1.3791/0.0071 1.509/0.0163 1.4179/0.0044 1. 549/0. 0176

-56.0/+179.5

1.5464/0.0232

4,000

+7.8/+162.5 -4.1/+222.3 +15.5/+231 +51.3/+238 -15.3/+205.8

1.521/0.0164 1.5462/ 1. 5475/ 1.5346/ 1. 5399/0.0173

3,200 4,600

+10/+202.8

1.540/0.0181

3,400

+19.7/+202.3

1.5339/0.0217

3,800

-19.5/+239.7 +1.3/+231.5

i=

en (5

IJJ

«

10~1....0......--'--'....................;--''-'-......................-:;---'--'....L.J....&..&..Ll''"--:--L-......................... 1

105

NOISE lC = CURRENT ON o = CURRENT OFF • = SIGNAL

~

su

1.0

iLl (I)

az

d0::

I00 ~

10' (I')

o o> a::

~

z o

'"

..........

-

r-,,-

It--I-o

t--..

........ ,,....,,,

Z

o

'"

0-

"

(I)

W

'\

a::

i\

-J

10

~ ~

(I)

.........

w >

r"oi

~

...J iLl

I

Ie>

103

10'

10 5

a::

FREQUENCY, Hz Signal VS. chopping frequency, and noise

FIG. 6p-3. PbSe detector at -195°C. frequeney.

VB.

6-257

RADIATION DETECTION

TABLE 6p-4. PHOTOTUBE TYPES, PHOTOSENSITIVE-DEVICE CLASSIFICATION CHART Phototubes Response

Single-unit Gas Vacuum 917 IP40 919 IP41 922 868 925 918 921 6570 923

Twin-unit Vacuum Gas 920 ....

Multiplier 7120

8-1 927 928 930 6405/1640 6953 8-3

926

1P29 1P37 5581 5582 5583 ... .

5652

8-4

1P39 929 934 5653 7043

8-5

935

S-8

....

8-9

IP42

8-10

. .. ,

.. , .

. ... . ... . ... . ...

1P21 931-A 6328 6472 7117

....

.. , .

. ...

1P28

... .

.., .

. ...

IP22

. ...

.. , .

. ...

6217

.... .. . .. . , ,

5584

8-11

. ..

. ...

.. , .

. ...

2020 5819 6199 6342-A 6655-A 6810-A 7264

Extended S-11

....

...

.

. ...

. ...

7046

,

8-13

."

.

... .

.., .

. ...

6903

S-17

... .

... .

. ...

....

7029

8-19

... .

... .

.. , .

. ...

7200

8-20

....

... .

. ...

'"

.

7265 7326

6-258

OPTICS

TABLE 6p-4. PHOTOTUBE TYPES, PHOTOSENSITIVE-DEVICE CLASSIFICATION CHART (Continued) Camera Tubes Image orthicons

Vidicons

Iconoscopes

5820 6474 6849 7198 7513

6198 6326 7038 7262 7263

1850-A

Image-converter Tubes Response

Infrared-sensitive types

B-1

6032 6032-A 6914 6914-A 6929

8-21

......

U1traviolet-sensitive types

7404

6p-2. Photoemissive Detectors. A tabulation of photoemissive detector tubes of single, twin, and electron multiplier types is shown in Table 6p-4. The multiplier types have sensitive surfaces ranging in diameter from about 1 to 11 em with 6, 10, or 14 stages. Table 6p-5 shows dark noise equivalent power data of some of the mort' sensitive types (ref. 4) with various spectral characteristics. The spectral characteristic curves of various photo surfaces are shown in Fig. 6p-4. TABLE 6p-5. THE DARK NOISE EQUIVALENT POWER OF VARIOUS PHOTOEMISSIVE DETECTOR TUBES Dark NEP at response pe k Type No.

IP21 7102t 7200 7264 7265

t

Spectral response

S-4 S-1 S-19 S-11 S- 0

At +25°C, watts 5 1.7 5 4 1.6

X X X X X

10- 16 10- 12 10- 16 10- 15 1O-1~

At temp. shown, watts at °C 5 5 3 1.2 2.3

X X X X X

10- 17 10- 14 10- 17 10- 15 10- 16

-55 -60 -78 -;0 -80

NI';P figures are for long-wavelength response peak at 0.8 ~m.

The dark NEP data apply only if there is no substantial amount of unchopped effective radiation reaching the photocathode. Otherwise the phototube becomes dominated by shot noise, and the NEP is then given by ... /

NEP

2eW j - /1)

='J C(/2

fr-259

RADIATIUN DETECTION

SPECTRAL SENSITIVITY CHARACTERISTIC OF PHOTOTUBE HAVING 5-3 RESPONSE

SPECTRAL SENSITIVITY CHARACTERISTIC OF PHOTOTUBE HAVING 5-1 RESPONSE

FOREOUAL VALUES OFRADIANT FLUX AT ALL WAVELENGTHS

FOR EOUALVALUES OF RADIANT FLUX AT ALL WAVELENGTHS

140 ~

140

:i

en

.'

~120 " Z ::;) rrlOO Cl:

a: 16 80 a:

~RANGE

OF MAX. VALUE-

I

~

I

I

1

-

AX VA!.UE

\

\ \

I

1\

\ 1\

\

1\

\

r\ \

r-,

ill

a:

SPECTRAL SENSITIVITY CHARACTERISTIC OF PHOTOTUBE HAVING S-5 RESPONSE

SPECTRAL SENSITIVITY CHARACTERISTIC OF PHOTOTUBE HAVING 5-4 RESPONSE

FOR EOUAL VALUES OF RADIANT FLUX AT ALL WAVELENGTHS

FOR EOUAL VALUES OFRADIANT FLUX AT ALL WAVELENGTHS

140

140

~120 Z ::;)

I!! I 20

~IOO Cl:

a:

~

iii

~ 80

Z :;)

7\

>-

f-RANGE OF \MAX. VALUE

I

~IOO

,

iii ~80 ~

~

~ 60

~60

1\

i=

~

iii

z

\ \ \

~ 40

~40

w

,

ill

>

20

..J

W

a: 30 00

520 w

a:

~

I.

_

5000 7000 9000 11000 13000 WAVELENGTH, ANGSTROMS

--..!!,..!o..' ,

..~~ ~~ Jr

;~~~5~ FIG.

'\ I

,/ ,•

, , I

,

;1

,

>

i=

o

r-~~~~~A~E

-/

~

>--

!;i

~~NGE OF

\,

J

5

,

t--

\

\ \

IJ

~ , ffien 40 ~20

~r

J

Cl:

ill

z

::;)

/ r\ 'I

,r' ,, ~ 60 , Ii

t:120

-

" " !'

\

\ i\

\ \

, -,

2000 4000 6000 8000

10000

WAVEhE~yT~, ~~GSTROMS

;11

6p-4. Spectral sensitivities of commercially available phototubes.

6--260

OPTICS

SPECTRAL SENSITIVITY CHARACTERISTIC OF PHOTOTUBE HAVING s-e RESPONSE

SPECTRAL SENSITIVITY CHARACTERISTIC OF PHOTOTUBE HAVING S-9 RESPONSE

FOR EQUAL VALUES OF RADIANT FLUX AT ALL WAVELENGTHS

FOR EQUAL VALUES OF RADIANT FLUX AT ALL WAVELENGTHS

140

140

~

~

ANGE OF H I-- MAX.VALUE

RANGE OF MAX.VALUE

,

{

\

II \

\ \

(

1\

\ \,

-',

I

I

I

1\

\

1\

\

I'... 3000 5000 7000 9000 11000 13000

3000 5000 7000 9000 11000 13000

WAVELENGTH, ANGSTROMS

WAVELENGTH. ANGSTROMS

~III

•

FOR EQUAL VALUES OF RADIANT FLUX AT ALL WAVELENGTHS

FOR EQUAL VALUES OF RADIANT FLUX AT ALL WAVELENGTHS

~ 80

~

IlJ \

I

a:

\

eX

>' .s

w >

~\

I

eo

\ \

E 60 VI

-oJ

1\

a:

1\

W

-l ~~~~~A~0~

~IOO

.iii

VI

~ 60

en ~120

FOR VALUE OF RADIANT SENSITIVITY I-II'AMP/~WATTlAT IOO-UNIT POINTSEE DATA SHEET FOR SPECIFIC TYPE

~

>-

~100 E VI

I

140

140

120

I I

SPECTRAL SENSITIVITY CHARACTERISTIC OF PHOTOTUBE HAVING S-II RESPONSE

SPECTRAL SENSITIVITY CHARACTERISTIC OF PHOTOTUBE HAVING S-10 RESPONSE

FOR VALUE OF RADIANT SENSITIVITY f- AT lOO-UNIT POINT. SEE DATA SHEET FOR SPECIFIC TUBE TYPE

II I I I

\

z

w

\ \

VI

40

20

UJ

>

\ \,

40

,

~

~20

a:

I\..

o

----

1\ 3000

FIG. 6p-4 (Continued)

5000 7000 9000 11000

WAVELENGTH, II I I

I

II

ANGSTROMS

6-261

RADIATION DETECTION SPECTRAL SENSITIVITY CHARACTERISTIC OF PHOTOTUBE HAVING 5-12 RESPONSE

SPECTRAL SENSITIVITY CHARACTERISTIC OF PHOTOTUBE HAVING S-19 RESPONSE

FOR EQUAL VALUES OF RADIANT FWX AT ALL WAVELENGTHS

140

~120 rr

FOR EQUAL VALUES OF RADIANT FLUX AT ALL WAVELENGTHS

140

FOR VAWE OF RADIANT SENSlTIVIT~L f-(I£AMP/I£WATTI AT 100- UNIT POINT SEE DATA SHEET FOR SPECIFIC TYPE

120

:J

~IOO

i=

~ 80

....>= s

ILl

(f)

ILl

i= 60

>

en z

~

ILl

60

...J ILl

(f)

40

\ 1\

a: 40

~

_V

20

V

'-

"

I

I

I

f\

o

3000 4000 5000 6000 7000 WAVELENGTH, ANGSTROMS

,

\

)

~O a:

o

r(-RANGE OF MAX. VALUE

'\ I \ I 1\ \

s

iii

a: et 80

>

"1

~loo

~

ILl

I FOR VALUE OF RADIANT SENSITIVITY AT IOO-UNIT POINT. SEE DATA SHEET FOR SPECIFIC TUBE TYPE

\

3000 5000 7000 9000 11000 WAVELENGTH, ANGSTROMS

I I I

Q~f3

I&lZII: 11:_

SPECTRAL SENSITIVITY CHARACTERISTIC OF PHOTOTUBE HAVING S-21 RESPONSE

SPECTRAL SENSITIVITY CHARACTERISTIC OF PHOTOTUBE HAVING S-20 RESPONSE FOR EQUAL VALUES OF RADIANT FLUX AT ALL WAVELENGTHS

14 0

FOR EQUAL VALUES OF RADIANT FLUX AT ALL WAVELENGTHS

140

FOR VALUE OF RADIANT SENSITIVITY AT IOO-UNIT POINT, SEE DATA SHEET FOR SPECIFIC TUBE TYPE

120

120

"1

~IO v

s

~\

i=

~80

J

V

llJ (f)

~100

~6 0

ti...J ILl

a:40

\' !

i=

I

(f)

I

ILl

>

fi...J

60

1\

\I

ILl

a: 40

\ J

J

~ 80

ILl

i\

20

-+1 f\t-~~~~~A~~E

s

1\ \ \

ILl

0

r- ~~~~~A~~E

20

r-,

1000 3000 5000 7000 9000 WAVELENGTH,ANGSTROMS

o

FIG. 6p-4 (Continued)

IJ

I\..

1000 3000 5000 7000 9000 WAVELENGTH, ANGSTROMS

6-262

OPTICS

70 J---+-+..3or---+---+---I----II----l---+--~

60 J---+--+---+---'I.,.---¥-- PHOTOVOLTAle EFFECT --+--~ c:(

ioon

:Lso J--f-~--_+---,I-__+_::lo,._-+_---l~-_+--_l_-__1

l.Li o o zs :c 4 0 J-~~--_+--_+_--~_--1f_-_+_--_+_-~ C> :::J

o

a:

i=30 ........'---+-+--+~-_¥_--+_---j~,-_+_--_+_-~ t:z w

a:

g;2.0H--~~.......:=>o,,

(.)

~300

o

z 200

100

(

~

~

/ 2000 LUMENS I FI!

rr :1

1300 LUMENS/FT

~

585

I

2

I

IIMEN~ IFT2

:'I~" IIIMENS/FT2

~ .,...

145 LUMENS /FT 2 ARK CURRENT

o

-10

-20 -30 VOLTAGE ACROSS DIODE. VOLTS

-40

-50

FIG. 6p-5. Germanium photodiode curves showing biased and unbiased photovoltaic characteristics.

RADIATION DETECTION

where

6-263

e,h,!1 = quantities defined under shot noise WI

= un chopped

background radiation reaching the photocathode, effective watts C = cathode sensitivity, amp per effective watt 6p-3. Germanium Photodiodes and Silicon Cells. The characteristics of germanium photodiodes are shown in Fig. 6p-5. Silicon photovoltaic cells (ref. 2) are used largely for the conversion of solar energy into electrical energy. Typical data are shown in Fig. 6p-6. 6p-4. Cadmium Sulfide, Cadium Selenide, and Selenium Detectors. CdS and CdSe cells (ref. 3), listed in Table 6p-6, are available in photoconductive surfaces, areas 1 to 100 mm", potted in transparent resin or sealed in glass envelope. Some CdSe cells have very low dark conductance:

~

70~--_+_----1+f-+--I-~~~~--+-_4_+_--_+_--__1

Z

W

~

601-----+---~..-+....f-Io--1f--4-otH__+_--+-_4__\_-_4--__1

::>

o w

W

501-----+-----If--I1I---++-......-\=lI,,...---4--I---'--4-----I

(/)

Z

o

a..

(/)

~40~---+----H--+~++--f--\+\=.....:....::;~f----\-+----I

W

>

~

...J W 0::

301----+--#-+-+--+--I--+---..--+'-"'-"---lf-A---+-----1

CL-405 I0

CL-404~~--+---+----+-~~+--~--+~---l~

CL-403

4000

5000

6000

WAVELENGTH,

7000

8000

9000

ANGSTROMS

FIG. 6p-7. Spectral response of CdS and CdSe photoconductive cells.

IMAGE ORTHICON TYPE

7198

DATA

t

Sensitive area Approximately 1.1 X 1.4 in. Spectral response. . . . . . . . .. S-10 Resolution Limited at high light level to approximately 600 lines; diminishes to approximately 75 lines at 2 X 10- 6 ft-c tSee ref. 6,

The light-transfer characteristics of this tube are shown in Fig. 6p-12; the effect of photocathode illumination on the signal-to-noise ratio is given in Fig. 6p-13. Other types (ref. 10) (5820, 6849, 7389A, 7513, 7611, and 4401) have similar sensitive area,

6-267

RADIATION DETECTION '000 500

o

200 100 50

~

~ 20

o

i

:t.

5 2

W

I

,

i,.-'

P'"

~ .5 1 /

;:

u

.2 .1

~ .05 ~ .02

u .01

k:::= ~=::;

2"""

~~~

~~ ~

~r-

_V

"'"

~

_10-

....

~

.........

/'

/"

5 2

L.oo'-

~P

~~

.....

5

...

~

I-

.--....

10

4 3 7

'-'"' ~I_1-1~ ~ "",

.--~

0eell • F X

°0

CONDUCTANCE F'ORM FACTOR (F) MAT'L TYPE--2 3 3A 4 5 7 400,600 I I 2 I I I 400L,600L - - 38 20 21 500 - 20 18 500L - - - 120 110 I I I1I1I11 1 ! III III I 2 5 10 20 50 100

-

.02

.05

.1

.2

.5

FOOT- CANDLES

FIG. 6p-8. Characteristics of CdS and CdSe cells.

w

(I)

Z

o

wOo

>(1) _UJ .... 0::

c::r

.J..J

w a... f::> 0

-l

."

/'fI"

I-

/

f-

2

/

Z t9

en 0.1 at-

t-

a::

6 l4

I-

I-

U

>-

/~

/'

6f4

...... ~

./

1.0 af-

99.5 98.4 98.4 89.0

0.985 0.86 0.86 0.86 0.65 0.94 0.86 0.90 0.90

. .....

96.4 97.9 98.0 96.6 96.0 89.0 63.0 33.0 0 · " .. •

0

...

...

0

....

.......

...

0

0

..

....

........

.......

. ...... .0

.....

.. ..

.....

••

0

..

...... ......

0.80 ........

...... 0.53 0.65 0.54 0.39 0.27

NRL

BM

......

>0.995 0.81 0.86 0.67

0.87 0.88 0.83 0.84 0.81 0.57 0.43 0.35

ILl

o :z

~

I-

~

(I)

0.50

~0.25 a::

I-

075 050 0.25

8M

100 300 500 1500 2500 3500 WAVE NUMBER, cm- 1 FIG. 6r-12. Transmittance of gratings. The DP polymethyl methacrylate grating and the NRL polyethylene grating were unaluminized and measured in unpolarized radiation. The BM metal-strip grating was measured in the high-transmission direction in polarized ra.diation.

6-293

FAR INFRARED

TABLE 6r-ll. TRANSMITTANCE OF PYROGRAPHITE POLARIZER PGPI FOR RADIATION WITH ELECTRIC FIELD IN THE C DIRECTION Wave number, cm- 1 r, ± 2 % 17.1 22.7 33.3 42.0 51.0 58.8 66.2 71.0 77.0 81.5

0.519 0.504 0.512 0.487 0.495 0.519 0.520 0.505 0.507 0.494

TABLE 6r-12. PERCENTAGE POLARIZATION OF PYROGRAPHITE POLARIZER PGPI Percentage polarization

Wave number, cm- 1

16.7 21.7 28.6 500 666.7 1,000 2,000

* T2 is the transmittance for

1.7 4.5 2.4 7.5 10.7 11.4 7.7

99.65 99.11 99.53 98.03 97.45 96.20 93.58

± ± ±

0.35 0.21 0.06

the unwanted direction of polarization.

A thin foil of pyrolitic graphite, which has a layered crystal structure, acts as a polarizer [4] in both the far and the near infrared. The transmittance for the desired polarization is rather low (about 50 percent), but the polarizance is above 99 percent. The results obtained by Rupprecht et al. [4] are summarized in Tables 6r-ll and 6r-12. References for Sec. 6r-6 1. 2. 3. 4.

Bird, G. R., and W. A. Schurcl ff: J. Opt. Soc. Am. 49, 235 (1959). Mitsuishi, A., Y. Yamada, S. Fujita, and H. Yoshinaga: J. Opt. Soc. Am. 50, 433 (1960). Hass, M., and M. O'Hara: Appl. Opt. 4, 1027 (1965). Rupprecht, G., D. M. Ginsberg, and J. D. Leslie: J. Opt. Soc. Am. 52, 665 (1962).

6r-6. Optical Constants of Far-infrared Materials. Precise values of refractive index and reasonably good values of absorption coefficient have been determined for far-infrared materials by two techniques. Both are basically interferometric: one is the use of a Michelson Fourier spectrometer with the sample in one arm [1,2], referred to as an "asymmetric Michelson"; the other is the analysis of the channelspectrum fringes (fringes of equal chromatic order) resulting from interference between the multiple beams produced by internal reflections in a plane-parallel sample of material [3]. In the asymmetric Michelson method, the sample is placed in one arm, and an interferogram is taken; the amplitude of the resulting spectrum gives the absorption coefficient while the phase gives the refractive index. The analysis of the channel spectra is based on the fact that the fringe position depends on the index only, whereas the amplitude depends on both index and absorption coefficient. The channel-spectrum fringes are revealed by spectra, which may be taken with either a conventional or a Fourier spectrometer. In spite of the fact that the absorption coefficient can in theory be derived by the above methods, in most of the data given below it is derived from analysis of a low-

6-294

OPTICS

resolution transmission spectrum, using the refractive index found in the interferometric method. This is so because discrepancies between absorption coefficients calculated from the asymmetric Michelson or channel spectrum and those calculated from the transmission measurements are always resolved in favor of the latter. The tables and graphs below list the optical constants for the following materials: Mylar (polyethylene terephthalate) Irtran VI (hot-pressed CdTe) Teflon (polytetrafluoroethylene) CdTe (crystalline) GaAs (crystalline)

Crystal quartz Sapphire Germanium Silicon Fused quartz

The quantites given are index and absorption coefficient ex which is related to k, the imaginary part of the complex refractive index, by ex

= 411" ku

where a = wave number of the radiation. Units of a and ex are em"? in all cases. Except where noted, measurements were made at room temperature. The optical constants of Mylar are labeled with subscripts 1 and 2. If Mylar is uniaxial, 1 denotes the ordinary optical constants, 2 the extraordinary. Mylar is probably biaxial, but it is difficult to determine this for the far infrared. The samples were aligned by using a polarizing microscope.

6-295

FAR INFRARED TABLE

6r-13.

OPTICAL CONSTANTS OF CRYSTAL QUARTZ FROM

* E.

no

ne

2lJ.2 25.2 30.2 35.3 40.3

2.1073 2.1076 2.1076 2.1083 2.1093

2.1541 2.1561 2.1560 2.1564 2.1573

0.0468 0.0485 0.0484 0.0481 0.0480

45.4 50.4 55.4 60.5 65.5

2.1105 2.1114 2.1124 2.1134 2.1147

2.1580 2.1590 2.1602 2.1615 2.1629

0.0475 0.0476 0.0478 0.0481 0.0482

70.6 75.6 80.6 85.7 90.7

2.1159 2.1175 2.1190 2.1209 2.1228

2.1644 2.1662 2.1679 2.1699 2.1718

0.0485 0.0487 0.0489 0.0490 0.0490

95.8 100.8 105.8 110.9 115.9

2.1248 2.1269 2.1291 2.1316 2.1343

2.1739 2.1762 2.1787 2.1815 2.1842

0.0491 0.0493 0.0496 0.0499 0.0499

120.9 122.0 123.0 124.0 125.0

2.1376 2.1383 2.1393 2.1400 2.1413

2.1872 (2.1877) § (2.1882) (2.1888) (2.1895)

126.0 127.0 128.0 129.0 130.0

2.1421 2.1426 2.1419 2.1408 2.1403

131.0 132.0 133.0 134.0 135.0

ne

TO

200

CM- I

*

Absorption coefficients, ~ cm ' !

Refractive indicest

Wave number, CT, crn "!

20

ao

a.

0.10

0.10

0.15

0.12

0.32

0.21

0.47

0.37

0.61

0.56

0.90

0.83

0.0496 0.0494 0.0489 0.0488 0.0482

1.2 1.3 1.3 1.9 2.5

1.1

2.1902 (2.1909) (2.1916) (2.1923) (2.1930)

0.0481 0.0483 0.0497 0.0515 0.0527

4.3 6.0 8.5 8.0 7.1

2.1406 2.1413 2.1419 2.1428 2.1434

2.1937 (2.1944) (2.1950) (2.1957) (2.1964)

0.0531 0.0531 0.0531 0.0529 0.0530

5.3 4.7 3.8 3.6 3.1

136.1 141.1 146.1 151.2 156.2

2.1441 2.1478 2.1515 2.1553 2.1592

2.1971 2.2009 2.2049 2.2089 2.2131

0.0530 0.0531 0.0534 0.0536 0.0539

2.8

1.3

2.8

1.9

161. 3 166.3 171. 3 176.4 181.4

2.1635 2.1678 2.1725 2.1773 2.1826

2.2177 2.2222 2.2273 2.2325 2.2381

0.0542 0.0544 0.0548 0.0552 0.0555

3.3

2.4

4.1

3.2

186.5 191. 5 196.5 201.6

2.1882 2.1941 2.2005 2.2072

2.2440 2.2502

0.0558 0.0561

-

no

I

E. Russell and E. E. Bell, J. Opt. Soc. Am. 57,341 (967). t The total, estimated probable error in the measured values of the refractive indices is ± 0.001 except at wave numbers less than 25 crn "! and greater than 175 crn :", where the error can be somewhat greater. t The estimated probable error in the measured absorption coefficients is approxima tely ± 100 % for u .--+---+---+--..!!F-=...j--+---+---+--+-__l-+-+--+-_+---f----l 2 0 1---i;;;;;;;;;;;;;..-lI!!!"'""a;:sp

-~E oC5~~~"'SP

~Sp

~

. .s/

3G

3H 55

5p

-~ ~I 50

5F

75

7p

70

7F

FIG. 7c-12. Energy-level diagram of Fe I. The spectrum of Fe I is one of the best studied and is of particular importance because of the use of iron lines for wavelength standards and other applications (see Table 7e-6). Eight valence electrons, ground-state configuration 3d 64s 2, which gives 16 multiplet levels, of which 9 are known (marked x in the figure). Other configurations leading to low-lying levels are 3d 748 (8), 3d 64s4p (8p), 3d 8 (d 8) , 3d 74p (p), 3d 54s 24p (S2p). If n values higher than for 3d, 4s, 4p are involved, they are indicated as, e.g., 3d 64s58 (S58).

7-24

ATOMIC AND MOLECULAR PHYSICS em-I

103

90

10 30

80

se"

5d'

I - - ~i=

70 ~S

60

f== I--

50

__ f--

,...

- 4f 4d

f--

--

~-_.

40

20

3247,3274 II I ,

10

o

..

.. ... 4p

--

~

"

l!tP

30

_5s'

-1--

--- ---4p

-.

'--

f-5

eFSs

5s ,

t:= 45

I~$

25

P

0

F G 25

P 0

F G·5

P 0

F G

FIG. 7c-13. Energy-level diagram of Cu 1. The arrangement of the outer electrons is 3d10482S in the ground state. If the 48 electron is excited, the levels are very similar to those of an alkali as shown, e.g., in Fig. 7c-5. These regular levels are indicated at the left. If one of the 3d electrons is excited, levels of more complicated structure arise as indicated at the right.

15

IpO

10

IFO 35

3pO 30

3FO

FIG. 7c-14. Energy-level diagram of Hg 1. This is the diagram of a typical two-electron spectrum with singlets and triplets. Because of the wide use of the mercury spectrum in many applications, the wavelengths of many transitions are indicated. Single triplet transitions are relatively strong. See also Table 7e-7 and Figs. 7e-5 and 7e-6.

42 ID~!/2

NO

L M===== /21/2

K~9/2

u-

~&

·II5~:~2

H'J

y--

z-

E,~=:=,~~'+z

36

4 T--G,'t

0 __

---~1p-·1

NM--

. L--

R~I/'

34

L_

O~n

,--~ ~~~~~:

32

e--p·1z B_-'l-.K-

A---.--'lZ J--

5-RQ--

30

,-W=

p--

1_

0 __

~J

H--

p'_ _

28

N 'H: O~

K--

K~''R

26

-GH--

!12. N - -

f--

•

M~.=~l\~.

~~4

0'-

L~ L~'~&

K-;'"

G. lH"z

1.......-

24

·K _ _•

H~V2 Sp

G~~

--I

22

J.......-. t~\

IF

1-'-' H-..--'i

2 'K.

--i..

-..:&11/2 -"--'G~''2

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•

F~9/2~~ 4 ~4 F '--r G_\ IH'~

•

F--

's

£""""='i$a [-..--Ita

18

16

14

D.~

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Fs/z

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w...... '+a

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U~

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6

0

--I

'F",

£---0;,-

4

I9/ Z

Nd

'r,

V--"l

_.

x-'.

__s

y...... }.

--I

z_

--I

6

Hs/z

~OX. . . . . I},

7

Fo

Pm Sm El,J

"....1\ --4

"_f

--I

__ I

--s

_.y.....'' a

-. 8

5

Gd

Tb

Dy Ho

Er

Tm Yb

FIG. 7c-15. Lowest energy levels of the three-valent ions as determined from the crystal absorption and fluorescence spectra. (In most cases the data are for anhydrous chloride.) The thickness of the levels indicates the amount of splitting of the free ion level in the crystal field. The ground state is indicated on the bottom; the excited states are designated by empirical letters A, B, C, etc., or by the equivalent 1"S coupling symbols like .D2. The J values are given at the sides. The data for Pm are tentative. The scheme is complete to about 25,000 cm. -1 A semicircle under a level shows that it is the upper state of fluorescenee transitdozw. (Sl)urce of data, The Johns Hopkins University.)

7-25

7d. Persistent Lines of the Elements

Table 7d-1 gives the strongest lines of each element and is useful for the spectroscopic identification of small traces of elements and spectrochemical analysis in general, when the elements in question occur in rather small concentrations. For the procedure of routine quantitative analysis with larger concentrations, see the special literature. A selection of strong lines is given both from the spectrum of the neutral atom and from the spectrum of the singly ionized atom. The former are most prominent with mild excitation (d-e arc at atmospheric pressure, glow discharge in a gas at moderate pressure, microwave discharge). The lines of the ionized atoms appear with stronger excitation (condensed spark, discharge in a gas at very low pressure, etc.). The relative intensities even in the same spectrum may depend very pronouncedly on the discharge conditions so that what is indicated as the .strongest line may be relatively weak at a particular condition. The data are taken from W. F. Meggers, C. H. Corliss, and B. F. Scribner, "Tables of Spectral-line Intensities," 2 parts, National Bureau of Standards Monograph 32, Government Printing Office. Washington, D.C., 1961. These tables list the relative intensities, obtained in a 10-A direct-current arc, of the lines of 70 elements mixed in a concentration of 0.1 atomic percent with copper. The lines of gaseous and unstable elements are from older sources. In general, wavelengths in Table 7d-1 and other tables of this section are wavelengths in standard air for x > 2,000 A and in vacuum for x < 2,000 A.

7-26

7-27

PERSISTENT LINES OF THE ELEMENTS TABLE

7d-l.

PERSISTENT LINES OF THE ELEMENTS

Neutral atoms Z

Singly ionized

Symbol Strongest line

Other strong lines

Strongest line

Other strong lines

-- - - I 2 3 4 5 6 7 8 9 10 11 12 13 14

15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54

H He Li Be B C N 0 F Ne Na Mg Al Si P S CI A K

Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr Rb Sr Y Zr Nb Mo Tc Ru Rh

Pd Ag Cd In Sn Sb Te I Xe

1,215.66 6,562.85 4,861. 33 584.33 5,875.62 3,888.65 ........ 303.78 6,707.85 6,103.64 ........ ........ 199.26 2,348.61 2,650.47 3,321.34 ........ 3,130.42 3,131.07 2,497.73 2,496.78 ........ ........ 1,362.463.451.41 1,657.01 2,478.57 ........ ........ 1,335.71 4,267.27 1,134.98 4,109.98 4,099.94 ........ 1,085.74 5,679.56 1,302.19 7,771.93 7,774.14 7,775.43 834.47 954.80 6,856.02 6,902.46 ........ 606.81 735.89 5,852.49 6,402.25 5,400.56 460.73 5,889.95 5,895.92 8,194.81 3,302.32 372.04 2,852.13 3,838.26 5,183.62 3,832.31 2,795.53 2,802.70 3,1J61.53 3 ,092. 78 3 , 944 . 03 3,082.161,670.81 2,669.17 2,516.11 2,881.60 2,524.11 2,528.51 1,817.0 1,774.94 2,535.65 2,553.28 ........ 1,542.32 1,807.31 9,212.91 9,228.11 4,694.13 1,259.53 1,347.2 ........ ........ ........ 1,071. 05 4,794.54 1,048.22 8,115.31 7,067.22 6,965.43 919.78 7,664.91 7,698.98 4,044.14 4,047.20 600.77 4,226.73 4,454.78 6,162.17 4,4;34.96 3,933.67 3,968.47 3,911. 81 3,907.49 4,020.40 5,081. 56 3,613.84 3,630.74 3,998.64 3,653.50 3,642.68 4,981. 73 3,349.41 3,234.52 4,379.24 3,183.98 ~,111. 78 4,384.72 3,093.11 3,102.30 3,578.69 3,593.49 4,254.35 3,605.33 2,835.63 2,677.16 4,030.76 4,033.07 2,794.82 4,034.49 2,576.10 2,593.73 3,734.87 3,581.20 3,719.94 4,045.82 2,599.40 2,611.87 3,453.50 3,405.12 3,502.28 3,569.38 2,388.92 2,528.62 3,414.76 3,524.34 3,515.05 3,619.39 2,394.52 2,216.47 3,247.54 3,273.96 5,218.20 5,105.54 2,135.98 2,700.96 2,138.56 3,345.02 4,SlO.53 4,722.16 2,061. 91 2,025.51 4,172.06 4,032.98 2,943.64 2,874.24 1,414.44 2,651.18 2,709.63 3,039.06 2,754.59 1,649.26 1,890.43 2,780.22 2,860.44 2,349.84 1,266.36 1,960.91 2,039.85 2,062.79 8,918.80 1,192.29 1,488.4 ........ ........ . ....... 1,015.42 4,704.86 1,235.82 5,870.92 5,970.29 .. , ..... 917.43 7,800.23 7,947.60 4,201. 85 4,215.56 741.4 4,607.33,6,408.47 4,962.26 5,480.84 4,077.71 4,215.52 4,102.384,077.383,620.94 4,643.70 3,710.30 3,600.73 3 , 601 . 19 3 , 519 . 60 3 , 835. 96 4,687.80 3,391.98 3,438 23 4,058.94 4,079.73 4,100.92 3,58027 3,094.18 3,130.79 3,798.25 3,864.11 3,132.59 3,902.96 2,775.40 2,816.15 3,636.10 4,297.06 4,262.26 ........ 2,543.24 2,610.00 3,728.13 3,4\)8.94 3,726.93 4,080.60 2,678.76 2,402.72 3,692.36 3,528.02 3,434.89 3,657.99 2,.520.53 2,490.77 3 ,404 . 58 3 , 609.55 3,634.70 3,421.'24 2,488.92 3,280.68 3,382.89 5,209.07 5,465.49 2,413.18 2,437.79 2,288.02 3,610.51 5,085.82 3,466.20 2,265.02 2,144.38 4,511.32 4,101. 77 3,256.09 3,039.36 1,586.4 2,839.99 2,863.33 3,034.12 2,706.41 2,152.22 2,598.05 2,528.52 2,877.92 3,232.52 1,606.98 2,385.76 2,383.25 2,142.75 ........ 1,161.52 1,830.4 ........ ........ ........ 1,233.97 2,062.38 1,469.62 4,671.23 4,624.28 ........ 1,100.42

2,836.71 5,666.64

2,816.18

4,810.06

4,819.46

3,179.33 4,246.83 3,372.80 3,110.71 3,843.25 2,605.69 2,598.37

8,542.09 3,572.53 3,383.76 2,908.82 2,849.84 2,949.20 2,404.88

2,192.26

4,785.50

4,816.71

3,464.46 3,774.33 3,496.21 2,927.81 2 ,84~L23 3,237.02(?)t

4,374.94 3,572.47 2,950.88 2,871.51

2,45~.57

2,71Q.31

2,246.41

5,464.61

7-28

ATOMIC AND MOLECULAR PHYSICS TABLE

7d-1.

N eu tral a toms Z

Singly ionized

Symbol Strongest line

Other strong lines

-- - - 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 102 103

(Continued)

PERSISTENT LINES OF THE ELEMENTS

Cs Ba. La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu Hf Ta. W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn Fr Ra. Ac Th Pa U Np Pu Am Cm Bk Cf Es Fm No Lw

Strongest line

Other strong lines

I

8,521.10 8,943.50 4,555.36,6,723.28 926.75 5,535.556,110.786,498.76('059.944, 554.034,934.09 6, 249. 93 5 , 177. 31 5, 234. 27 5, 501. 34 3 , 949. 10 4 , 086. 72 5,699.235,159.695,161.48 4,186.603,952.54 4,951.364,939.74 5,045. 53 695. 774, .79.42 4,222.98 4,924.53 4,883.81 4,634.24 5,620.54 4,303.584,061. 09 ................................ 3,892.163,910.26 4,296.7 45,071.205,175.424,336.143,568.273,592.60 4,205.053,819.673, 930,48 14, 907 .104,594.034,627.22 4,225.853,783.054,078.704,053.643,768.393,422.47 4,326.474,318. 85(, 765.144,338.453,509.173,702.85 4,211.724,045.994,186.784,194.853,531. 703,968.42 13, 3,796.753,810.73 02 14,053.933,456.003,891. 4,007. 97 3,862.82 ,151.10 3,906.3 43,372.76 1 13,892.69 4,094.194,105.84 3,717.92 3,462.203,848.02 14,187.62 1 3,987.983,464.36 5,556.487,699.49 3,694.193,289.37 1 3,281.7413,359.56:3,312.1113,376.5012,615.4212,911.39 2,866.37 13,072.88 48?, 940.7713.399.8013,561.66 12,916. 2'653.2'1"714.672'647.4712'6" .6' 3 ,012 .54 12 ,685.17 4,008.754,074.364,294.612,724.352,555.09 3,460.463,464.73 3,424.62 2,999.60 3,580.15 12,571.44 2,461.84 2, OOD. 06 3,058.663, 301. 56 260.85 ....... '12, 538. 00 3,220.782,543.973,133.323,800.12 ........ 3,731.36 3,064.71 2, 659 .45 702.40 14, 2,733. D6. ,777. OD 2,488.74 2,675.952,427.953,122.7812,748.26 1,740.472,802.19 1,849.682,536.524,358.355,460.741,649.96 3,519.245,350.46 12, 13,775.723,429.431,908.64 4,057.83 3,683.48 2,801 .99 2 , 833.06 1,726.75 2,203.51 3,067.72 3 , 897 . 98 2 , 938. 30 2 , 989.03 1,902.41 2,449.99 15,245.92

14,103.84

1

14

6,141.72 3,794.78 3,801.53 4,225.33 3,863.36 3,998.96t 3,885.29 4,661. 88 3,646.19 3,568.51 3,645.41 3,398.98 3,692.64 3,131.26 2,891.38 3,077.60 2,820.22 2,400.63 2,658.04 2,608.50 2,486.24 2,242.68

6,496.90 4,333.74 3,999.24 3,908.43 4,012.25 4,424.34 3,212.81 3,340.47 3,324.40 3,944.70 3,484.84 3,499.11 3,425.08 2,970.56 3,507.39 3,505.23 2,635.58 2,764.27 2,733.04

5,608.8

1,786.07 7,450.007,055.42 4,825.91

.w ••••••••••••••••••••••

3,814.42 4,682.28 3,649.55 3,863.12 3,469.92 3 ,OM'. 6 3,670.07 3,829.2 3,907.1 3,926.2

........ ........................ 4,168.40 4,088.40

3,719.44 3,803.073,304.243,967.39 4,019.13 2,837.30 2,743.9 2,743 3,812.00 3 , 854 . 88 3 , 871. 04 3 , 566 . 60 3,859.58 3,854.66 ........ ........ ........ ........ ........ 2,956.6 ........ ........ ........ ........ ........ 2,835.5 ........ ......... ........ ........ ........ 2,832.3

t Scribner, Bozman, Meggers, t Scribner, Bozman, Meggers,

I·· ..... ·1· .......

J. Research Natl. Bur, Standards 46, 85 (1951) (Pm). J. Research Natl. Bur. Standards 41, 476 (1950).

, Fred, Tomkins, J. Opt. Soc. Am. 19,357 (1949).

4,340.64 3,392.03 3,957.8'\[ 3,890.36 4,290.9'\[ 3,989.7'\[ 4,188.2'\[

7e. Important Atomic Spectra H. M. CROSSWHITE AND G. H. DIEKE

The Johns Hopkins University

7e-L, General. The tables and figures of this section furnish data on spectra which are often used for reference. These are chiefly the spectra of toe rare gases which can easily be obtained with simple discharge tubes (a neon advertising sign, for instance, is a good source for the neon spectrum); the iron spectrum which is the best source of standard lines for a spectrograph of moderate to high dispersion; and the mercury spectrum which, like that of helium, is particularly useful for spectrographs of low dispersion. Data on other spectra of varying degrees of accuracy and completeness can be found in the MIT tables;' Kayser, "Handbuch der Spectroscopie," vols. 5-8; Paschen und Gotse (1922); Fowler (1922); C. E. Moore, "Multiplet Tables" (1945); and Brode, Chemical Spectroscopy" (1943). An atlas of spectra is Gatterer and Junkes (1937 and 1945). For the solar spectrum, Minnaert, Mulders, and Houtgast (1940) is recommended. The various tables of spectra and figures presented in this section are as follows: (j

Spectrum Helium Neon Ne I Argon A I Krypton Kr I Xenon Xe I Iron Fe I Mercury Hg I

. . . . . . .

Table

Figure

7e-l 7e-2 7e-3 7e-4 7e-5 7e-6 7e-7

7e-l 7e-2 7e-3 7e-4 7e-5 7e-6, 7

The wavelengths and intensities are listed as completely as space permits. Special attention has been paid to lines which can be used as standards for wavelength measurements of high accuracy. The figures, which are direct photoelectric traces obtained at The Johns Hopkins University, will help to orient the reader in the particular spectra. The traces were made with a logarithmic amplifier and calibrated to compensate for variations in sensitivity of spectrograph and measuring devices. Furthermore, the intensity scale is the same for all spectra so that the values indicate relative brightnesses of the light sources. Intensities as read from the charts, however, are not meant for high accuracy. In a number of spectra numerical intensity values are given on a logarithmic scale. Also the conditions under which the spectra were produced are shown in each case. 1

See the references on p. 7-96a.

7-29

7-30

ATOMIC AND MOLECULAR PHYSICS

Without the knowledge of such conditions intensity tables have little meaning because the intensities vary greatly with the discharge conditions. In both figures and tables (except for helium) the intensities are standardized to give the energy flux from 100 em! of the light source per unit solid angle in ergs per second. In Figs. 7e-l through 7e-5, only whole numbers are given in the wavelength designations. Values accurate to several decimal places appear for many of these lines in Tables 7e-2 through 7e-7. 7e-2. Standard Wavelengths. Since October, 1960, the international standard of length is officially defined in terms of the orange line of the krypton isotope with mass 86. The anstrom unit (A) is exactly 10- 10 meter. The meter is defined as exactly 1,650,763.73 wavelengths in vacuo of the Kr 86 line, which has Avac Aair

= 6,057.80211 A = 6,056.12525 A

This line has the indicated wavelength when the atoms are free from interactions. If a lamp meets the following specifications, the wavelength is within 10- 4 A of the nominal value. 1. Purity of Kr 86 not less than 99 percent. 2. Temperature of the coldest point of the lamp not higher than 63 K (triple point of nitrogen). The Kr pressure is then about 0.03 mm of Hg. 3. The current density must not exceed 4 ma/mm 2. 4. For a hot-cathode d-e lamp the anodes should be toward the observer. Wavelengths of Kr 84, which is the predominant constituent of natural krypton, are approximately 0.001 A larger in the visible than the Kr 86 wavelengths. For accurate spectroscopic wavelength measurements wavelength standards should be used as follows: (1) For interferometric measurements of the highest accuracy, the primary standard. (2) For other interferometric measurements and grating measurements of exceptional accuracy, the primary standard and secondary standards of Kr 86 or natural Kr*, Ne*, A *, H g198*, Fe* (in a low-pressure source), and Th determined to four decimals. The values for the elements marked by an asterisk will be found in Tables 7e-2 to 7e-7 of this section. (3) For other grating measurements, in general those listed under (2) and many other lines produced by stable low-pressure light sources and measured reliability to at least three decimals. Note. Using lines of one order of the grating as standards for different overlapping orders mayor may not lead to errors, depending on the properties of the particular grating. Helium I. The He I spectrum (Table 7e-l) consists of singlets and triplets. The latter appear as double lines except under the most favorable conditions. This is because the 2 3P 2 and 2 3P 1 levels almost coincide, whereas the 2 3P O level is about 1 ern"! removed. The wavelengths are taken from the literature [see especially W. C. Martin, J. Research NBS 64, 19 (1960)]. The intensities II and 1 2 are quantitative measurements at the following conditions: II, discharge with external electrodes, frequency 15 MHz, pressure 7.5 mm; 1 2, same, pressure 0.25 mm; 1 o, estimates from the literature.

7-31

IMPORTANT ATOMIC SPECTRA TABLE

7e-1.

THE SPECTRUM OF HELIUM

I

AND

II

Classification

x

He II

243.027 256.317 303.781 522.2128 537.0296 584.331 591.4117 1,084.975 1,215.171 1,640.474 2,696.119 2,723.191 2,763.804 2,829.076 2,945.106 3,187.745 3,203.14 3,354.550 3,447.586 3,587.270 3,587.405 3,599.314 3,599.448 3,613.643 3,634.232 3,634.369 3,651. 990 3,652.130 3,705.005 3,705.148 3,732.865 3,733.010 3,819.6072 3,819.758 3,867.475 3,867.630 3,888.648 3,964.7289 4,009.268 4,023.973 4,026.1912 4,026.359 4,120.812 4,120.993

., .

. ..

... ... 18 18 18 18

.. .

. ... ...

.,

...

. .. 4P

., . . .. . ..

.

4~1

. . ..

2~1

" "

... . ..

. .. . . .. ., . ., . .,

. .. . .. .. .

. .

., "

.

. ..

28 28 28 28 28 28

9p 8p 7p 6p 5p 4p . ..

.,

28 28

7P 6P

. .. . ...

., .,

. . ... .. .

.. . .. . . .. . ..

2p 2p 2p 2p

9d 9d 98 98

28

5P

.. .

...

. ... ., . ... ., . ... ., .

. .. . .. ., .

2p 2p 2p 2p 2p 2p 2p 2p 2p 2p 2p 2p 28

8d 8d 88 88 7d 7d 78 78 6d 6d 68 68 3p

., .

.. .

.

.. . ... ., . ... .. . 28

.,

.

. ..

., .

. .. . ..

. .. . .. ... ., . . .. . ..

...

... 4P 7D 78 . ..

.. . ., .

... . ..

...

., .

2P 2P

3~1

2p

. .. . ..

.,

I.

II

3P 2P

.. . .. . ... ... ., . ., .

.,

Io

Triplets

Singlets

.,

., . ...

2p 2p 2p 2p

.

"

.. .

"

.

.. . 5d 5d 58 58

5~2 4~

3~ 6

2 2

•••

.' .. '" . . ... . ... . ... 3 . ... '" .

1 1 2 4 6 8

5~

.

2 2 2 1 1 1 3 2 1 1 1 3 1 1 1 4 1 2 1 10 4 1 1

'"

.

5

370

1,450

'"

.

1 3 1

90

480

. . ... . ... . ." . . ... '"

'"

. ...

. ... . ... ., .. . ... . ... . ... . ... . '"

. ...

. ... ." . . ... . ... ."

" '"

..

.

19

260

28

260

84

680

23

160

10,000 140 5

10,000 2,100 89

7-32

ATOMIC AND MOLECULAR PHYSICS TABLE

7e-l.

THE SPECTRUM OF HELIUM

I

AND

II (Continued)

Classification

x

He II Singlets

4,143.761 4,168.967 4,387.9294 4,437.551 4,471. 479 4,471.682 4,685.75 4,713.1455 4,713.376 4,921.9310 5,015.6799 5,047.738 5,411.551 5,875.621 5,875.966 6,559.71 6,678.151 7,065.190 7,065.707 7,281.349 10,123.77 10,829.088 10,830.248 10,830.337 12,784.79t 12,790.27 17,003.11 18,685.12 18,697.00 20,580.9

2P 2P 2P 2P

.. . .. . ., . .. . .. .

10

II

Is

Triplets

6D 6S 5D 5S

...

.. .

., . .. . .. . ., .

. .

2p 2p

4d 4d

. ... . . ...

.. .

. ..

4-+3

2p 2p

4s 4s

.. . " .

.. . . .. ... . ..

" "

"

.

"

.

"

.

2P 2S 2P

4D 3P 4S

.. . ... ... ...

... . .. .. . .. .

2P

3D

.,

. ., . 2P

"

.

...

" "

. .

'" " '"

.

.. .

'"

."

.

'"

.

.... ." . . ...

3d 3d

.. . " .

., .

6-+4

. ..

.. .

.. .

2p 2p

3s 3s

. . ...

3S

.. . .. .

.. . . ..

. .. . . ..

2s 2s 2s 3d

2po 2PJ

3D

5F

"

. ..

.. . .. .

. .. .

.

3p 3d

4d 4f

3D 28

4F

"

.

"

.

"

"

2P

.. . . "

~P2

5f

. ..

. ..

19 3 83 17 2,300

210 36 590 290 2,220

3 1 4 6 2

350

370

57 710 120

1,800 3,106 860

10 1

18,200

7,100

6 5 1 3*

2,400 7,100

1,850 1,450

500 1,500 2,500 lOt 1 20 70 10 5,000

105,000

7 -+ 4

2p 2p

.. . . .. ., . .. . .. .

2 1 3 1 6 1

. . ...

'"

'"

'"

.

....

1,450

5-+ 4 '"

.

'"

.

. ... '"

.

. ... . . . . '" '" '" '"

6,950

*

Change in the 10 scale. From here on National Bureau of Standards values. t Wavelengths and intensities from here on from Humphreys and Kostkowski, J. Research Naa. Bur. Standards 409,73 (1952).

The classification is indicated by capital letters for singlets, lower-case letters for triplets. A few of the He II lines are also listed. They have elaborate fine structures. Neon I. The neon spectrum is moderately rich in lines and may serve, like the other rare-gas spectra, as an easily obtained comparison spectrum. Any neon-sign manufacturer can produce a satisfactory tube. The wavelengths of the strong lines have been measured with great accuracy and have been adopted as international secondary standards;' often replacing the primary standard for interferometric measurements. Table 7e-2 lists the principal neon lines. The wavelengths are interferometric wavelengths when followed by a capital letter. B, Burns, Adams, Longwell, J. Opt. Soc. Am. 40,339 (1950) H, Humphreys, J. Research Natl. Bur. Standards 20, 17(1938) 1

Tram. Intern. Astron. UnionS, 86 (1935); 9.204 (1957); 10,229 (1958).

7-33

IMPORTANT ATOMIC SPECTRA TABLE

7e-2.

THE SPECTRUM OF NEON

I

Classification

10

Wavelength System.

log II

4pJ

.... . .....

ls 2 ls 4 l s, Is. Is.

5p. 4P4 4pG 4P2 4pI

7 8 9 5.5 6

.... . .... . . .... .....

ls& Is, Is&

4pg 4P3 4PIO 4pG 4P7

9

.... .

3s 11 3s 11

5p23 5poo 5pOl 5pI2 5p11

3,017.348 3,057.388 3,076.971 3 , 126. 1986 B 3 , 148.6107 B

3S11 3S~1 38~1 3S~1 3S~1

5p22 5p~o 5p;2 5poo 5P11

ls4 182 182

B B B B B

3S~1 38~1 3s12 3s 12 3s 12

5P22 5pOI 4p~2 4p~1 4p~1

3 ,417 .9031 B 3,418.0066 H

3s 11

3811

B B 3 ,450. 7641 B 3 ,454 . 1942 B

Is, Is 4 Is 4 ls 2

7PG.7 6p4 6pI 5Pl

lsi

3S~1 3s 11 3s12 3s~o 3s~o

6poo 5p12

2,982.663 2,992.420 2,992.438 3,012.129 3,012.955

3s 12

3s12

2,932.721 2,947.297 2,974.714 2,980.642 2,980.922

3,153.4107 3,167.5762 3,369.8076 3,369.9069 3,375.6489

3s 11 3s 11 3s~o

3s12

3s 11

38 12

3,423.9120 3,447.7022

B 3 ,464.3385 B 3,466.5781 B 3,472.5706 B 3,460.5235

3,498.0632

B

3,501. 2154 B 3,510.7207 B 3,515.1900 B 3,520.4714 B

5pJ2 5p~1 5p;1

log I.

--- ---

8 8 8 5 8

8PI 7p~2 7p;1 6p~o 5p~1

2,647.42 2,675.24 2,675.64 2,872.663 2,913.168

log I J

Paschen

ls4 Is,

~}

6 6

.....

..... ..... .....

..... . .... . .... .....

..... . .... . .... ..... ..... . .... . ....

4P8 4PI 4P4 4p. 4P7

..... .... .

. ....

9

8 8 7

.... .

..... .... .

..... . .... .....

ls 2 ls 2 ls& ls& ls&

4ps

6

4PIO 3p4 3P2 3p&

6

Is, ls 4 Is, Is, Is&

3p4 3P2 3p& 3pG 3p7

10

3s 11 3s 12 3s12

4p~2 4p~1 4p;1 4p12 4p11

3s 11 3s~o 3S12 3s~o 3S12

4poo 4p~, 4P22 4P;1 4P23

Is 4 Iss Is, Is. Is,

3p. 3P2

3s 11 3s 11 3s12 3s 11 3S~1 I

4pI2 4p11 4pOI 4P22 4p~o

Is, ls 4 Is,

184 182

ls 2

ls2

6

.. , ...

2.73 3.16 3.30 3.2? 3.6? 2.7 2.80 3.52 3.32 2.93 2.98 3.12 2.7 2.80 3.61 2.44

.... . .... . ..... . ..... .... .

..... ..... ..... . .... .....

2.4? 2.21 3.90 4.36 2.98

..... ..... ..... ..... .....

. .... . .... . .... . .... . ....

4.62 4.14 3.57 4.91 4.18

7 7 7 8 10

.....

. ....

..... .... . . ....

. .... .....

. .... .....

4.72 4.37 4.27 4.64 4.90

3pG 3p7 3PIO

7 8

..... .... . .... .

3ps

8 20

. .... ..... ..... ..... .....

4.45 4.53 3.85 4.55 5.32

3ps 3P6 3pg

3PI

10 15 6

6 6

8 6

6

.... .

.... . .... .

7-34

ATOMIC AND MOLECULAR PHYSICS TABLE

7e-2.

THE SPECTRUM OF NEON

I (Continued)

Classification 10

Wavelength System. 3,562.9551 B 3,593.5263 B 3,593.639 B 3,600.1694 B 3 ,609 . 1787 B

3811 38~1 38~1 38~1 38~0

4pol 4p~2 4p~1 4p~1 4pol

3,633.6643 B 3,682.2421 B 3,685.7351 B 3,701. 2247 B 3,754.2148 B

38~1 38~1 38~1 38~1 38~1

4poo 4P12 4p22 4pOI

4,270.2674 4,275.5598 4,306.2625 4,334.1267

3pOI

7d oo

3pol 3pol

6d;2

B B B B

4p1l

4,363.524 M

3pla

8812 78~1 9d u

4,381.220 M 4,395.556 M

3pu 3p22

10812 9d u

4,422.5205 B 4,424.8096 B

3pol 3pol

4,425.400 M

3pOI

4,433.7239 B

4,460.175 M

3p2a 3pu

4,466.8120 B

3p22

4,475.656 M 4,483.199 B

3p1l 3pOI

4.488.0926 B

3pOI

3pOI

8d.

2pI0 2p6 ~P. 2p7 2PI0

586 8" 81 8 ,,, 81

4,552.598 M 4,565.888 M

3p1l

4,582.4521 B

4,609.910 M 4,614.391 M

3P22 3p22 3p23

3p~1 3P22

3 4 8 8 7

2pe

2p8 2p7 2PIO

5d;2 7d23

4,582.035 M

&6

2plo

786

3pOI 3p23 3pu

7d u 9811 8d u 7d sa 6d;a 8812 7d~2 8811

4.28 4.21 4.08 4.06 3.42

4 5 5 5 5

8et.

4,537.7545 B 4,538.2927 B 4,540.3801 B

..... ..... .....

7d e 68"" 1 686 582 9d~

2PI0 2PI0 2pI0

2Pe

5d~1

.... . .... . .... . .... . .... .

7 7 7 7 6

2pe

3pOI

4.70 4.50 4.17 3.26

3pe 3p7 3P8 3pI0

3pa

2pI0 2pe 2pe 2p7 2pe

9d.

6d a 6d6

7" 81 58.

8d~' 58~

5·8"1 "

ts;

7d~ 78. 8d~

2p8

7d.

2ps

68'" 1 68 5 78"1 68.

2pe 2p6

2ps

---

..... ..... ..... .....

ls2 ls2 ls2 182 182

9812 8d 31 7d~2 7811

8d;a 8d 22

log L,

.... . .... . .... . .... .

18a

sa.,

7812 8d~2

log 1 2

3 10 9 7 6

3pe 3p2 3p6 3pI0

fide

3p~1 3p~2 3pn

4,575.0620B

3plo

6d 01 6d oo

4,500.182 M 4,517.736 M 4,525.764 M 4,536.312

3P12

18. 182 182 182

2pe 2P8 2pI0 2PIO 2PIO

6d 12

log II

Paschen

5 6 5 6 7 8 4 6 5 7

.....

.....

2.4GO 2.70

2.61

2.97 2.89

2.90 2.81

2.34

2.19

2.02

1.81

2.098 2.811

2.673

2.694

2.699

10 8 10 3 4.5

3.3

3.4

2.964

2.854

8 7 7 7 6

2.714 2.4 2.4 2.19 2.204

2.569 2.3 2.3

7-35

IMPORTANT ATOMIC SPECTRA TABLE

7e-2.

THE SPECTRUM OF NEON

I (Continued)

Classifieation

10

Wavelength System.

4,617.837 M 4,628.3113 B 4,636.125 M

3p22 3p~2

8812 7d~3 7d 22

2ps 2p. 2p7 2P7 2P7

686 78", 1

7d~'

4,645.4180B

3pu 3pu 3pu

4,649.904 M 4,656.3936B 4,661. 1054 B 4,670.884 M 4,678.218 M

3p22 3pOI 3pOI 3p~2 3p12

78~1 68~1 68~o 88~1 7d 23

2PI0 2p. 2pe

4,679.135 M 4,687.6724 B

3p12 3P12 3pOl 3pOI 3pOI

7d 12 6d~3

2pe

7d 3

2Pll

68'" 1

2PI0 2PI0

5d 2

2plo

5d 6

3pOI 3P23

5d oo 6du 6d u

2PI0 2pg 2pg 2pe 2ps

5d e 6d~ 6d:

2ps 2pg 2P6 2p. 2p.

6d.

4,636.630

4,702.526 4,704.3949 B 4,708.8619 B

4,710 .0669 B 4,712.0661 B 4,715.3466 B 4,725.145 M 4,749.5754 B

3p21

7d u

6d~2

5d u 5d 12 5d o1

3p12 3p22

8812

4,752.7320 B 4,788.9270 B 4,790.217 B 4,800.100 B 4,810.0640 B

3p22 3p23 3p~1 3p12 3p~2

6d 31

4,817.6386 B

3p1l 3p1l 3p22 3poo 3pOI

4,818.748 4,821. 9236 B 4,823.174 4,827.3444 B

4,827.587 B 4,837.3139 4,852.6571 4,863.0800 4,865.5009

B B B B

4,866.477 B 4,867.010 4,884.9170B 4 ,892 .1007 B 4,928.241 B

3p22 3pOI 3p~1

6d 22

7812 6d 22 7d21 6d~, 6d22

2ps

2pl0

7d 2

68"1 582 482 481 682 7d~

s«,

686 6d~

586 68"1 7d~

6'" 81 6d~'

6d u 7811

2P7 2P7 2ps

6d~1

2pI

68~

68u

2PI0

48.

7812 6812

2ps 2PI0 2P2 2pe 2P6

586 486 68"" 1

3p12 3p12

6d~2 6d 23 6d 12

3p12 3p~1 3p~2

6d u 78~o 78~1

3pu

7811

I 3p~1

78~1

log II

log 1 2

log i,

Paschen

2P6 2ps 2p. 2P7 2P2

6d 2

58.

6d~

6d , 6d.

583 582 58. 582

5 7 5 5 8

-----2.49 2.0 2.0 2.672

2.39

2.916 2.634

2.828 2.559

2.4

2.3

7 6 7 15 12

2.2 2.410 2.472 3.701 3.688

2.1 2.340 2.427 3.729 3.693

3.437 3.459

10 10 15 5 8

3.33 2.96 3.57

3.33 2.90 3.50

3.34 2.55 3.17

2.78

2.68

10 12 10 5 7

3.329 3.16 2.84

3.243 3.05 2.77

2.974

3.07

3.01

2.70

8 7 8 6 10

2.861 2.599 2.864 2.3 2.9

2.775 2.499 2.646 2.2 2.8

2.597 2.335 2.693

8 9 6 6 6

3.442 2.731 3.131

3.402 2.632 3.064

3.177

2.61 2.4 3.2 2.58

2.53 2.3 3.2 2.38

5 8 7 5 8

5 5 5 10 9 5

2.607 2.799

3.0

7-~6

ATOMIC AND MOLECULAR PHYSICS TABLE

7e-2.

I

THE SPECTRUM OF NEON

Classification

Wavelength System. 4,939.0457 B 4,944.9899 B 4,957.0335 B 4,957.123 B

4,973.538 4,994.913 B 5,005.1587 B 5,011.003 M 5,022.864 B 5,031.3504 B 5,035.989 5,037.7512B 5,074.2007 B 5,080.3852 B 5,104.7011 B

7812 7812

2pll 2pll

3pu

5d;2 5d;2

2P7 2p7 2P6

3p11 3p;1

6du

B B B B B

5,210.5672 5,214.3389 5,222.3517 5,234.0271 5,274.0393

B B B B B

5,280.0853 5,298.1891 5,304.7580 5,326.3968 5,330.7775

B B B B B

5 10 5 8 5

2.818 4.27 3.53 4.038 2.798

2.823 4.29 3.54 4.061 2.745

48~

7 8 8 10 5

3.475 4.11 3.6 3.9 2.9

3.654 4.36 3.6 4.0 2.9

3.326 3.92

5d~' 5d2 5d. 58~

3.595 3.292 2.5 3.087 3.813

3.597 3.286 2.5 3.094 3.898

3.352

486

7 6 6 6 8

58~

5 3.6

3.6

8 7

3.837 3.584

3.884 3.585

3.515

6 5 6 6 5.5

.... .

.....

2.860

2.777 3.549 3.161 2.767

2.745 3.431 3.125 2.649

2.962 3.492 3.255 3.388 4.547

2.899 3.396 3.154 3.540 4.771

6d2

3pu 3p21

5d21

2pe

5d~

3p21 3p21 3pu 3pu 3pu

5d12

5du 5du 5du 68~0

2pe 2pe

2ps 2ps

5d. 5d: 5d~ 5d4

2P7

48.

4d~1 4d~2 5d~2

2pI0 2PI0 2p6

5d;.

2pt 2pll

5du 5du

2P7 2p7 2p7 2p. 2pe

3pu 3pu 3pu 3poo 3p21

5,191.3223 5,193.1302 5,193.2227 5,203.8962 5,208.8648

2.365 3.13 2.208 2.506 3.665

2p.

5d12 5d~1

6812

3p~1 3p~1 3p~1

5d;2 5d;2

3P12 3P12

5d 12

3P12 3P12

5d01

3pu 3P22 3p;1

3p~1 3p~2 3pu 3pOI 3pOI

2ps

5d~1

5d21 5du 68u 6812 68~1

68~0 68~1

6811 4du 4d12

2p2 2P2 2p2

6d~

482

4" 81 5" 81 58'" 1 482

5" 81 5 ,,,, 81

2pll 2pll

5d~ 5d.

2pll 2pll 2ps

5d4 5d6

2P8 2P6 2p6 2P4 2P7 2PI0 2pI0

--- --2.462 2.517 3.4

2.451 3.10 2.279 2.592 3.634

5'" 81

68~1

2.626 2.641 3.3

log I.

10 4 4 9

2P4

2pll

3p12

6 6 10 7 6

log 1 2

2.406

6d21

3p~1 3p~2

log 11

2.496

5d;. 6d11

5,150.077 B B B B

6d~'

3p~2

3pOI 3pOI

5,154.4271 5,156.6672 5,158.9018 5,188.6122

584 586 5" 81 58"" 1

3P12 3poo

68~1

10

Paschen

3P12 3P12

5,113.6724 B 5, 116.5032 B 5,122.2565 B 5,144.9384 B

5,151. 9610 B

I (Continued)

484 486 482 48. 482 484 4d2

-ida

7ur

~}

6 8 7 7 12

2.89 3.58 3.374 4.01 3.27 3.803

3.519

3.592

2.660 3.300 3.088 4.360

7-37

IMPORTANT ATOMIC SPECTRA TABLE

7e-2.

THE SPECTRUM OF NEON

I (Continued)

Classification Wavelength System. 4d o1 4d oo

log 1 2

10

log 1 1

20 12 8 8 7

4.537 4.3 3.072 3.392 3.318 3.002 2.487 4.735 2.948 2.88

2.984 2.525 5.079 3.015 2.85

log L,

Paschen

2P1O 2P1O

4d 5 4d 6

2P2 2p6

482 484 486

--- ---

4.732 4.5 3.004 3.297 3.282

5,341.0938 5,343.2834 5,349.2038 5,360.0121 5,372.3110

B B B B B

3p01

3p12 3p12

6811 6812

5,374.9774 5,383.2503 5,400.5616 5,412.6490 5,418.5584

B B B B B

3poo

5d 11 5d o1

2P1

3p~1 3p~1

3p~o

2pa 2pa 184

5d 12 5d o1

2P2 2p2

5d a 5d 6

6 4 50 9 8

3p01 3p01 3p~1

58~1 58~o

2p10 2p6 2p4

2pa

9 8 6 7 6

3.349 3.077 2.843 2.738 2.625

3.377 3.169 2.745 2.720 2.532

3.223

6811 6812 6811

382 38a 484 485 484

2ps

4'" 81

10

48'''' 1 384 386

7 10 7 8

3.9 3.400 4.20 3.438 4.179

4.1 3.562 4.40 3.665 4.305

3.7 3.240 3.96

10 7 15 10

3.9 4.4 3.603 5.080 4.374

4.1 4.6 3.800 5.312 4.585

3.7 4.1

8 10 50 7 10

3.53 4.870 5.904 3.659 4.47

3.69 5.080 6.268 4.74

4.27

20 6 1.5 6 9

5.235 4.82

6.300 5.05

5.974 4.626

4.448 4.133

4.671 4.303

4.185 3.927

4.09 5.365 3.903 4.54 4.7

4.28 6.380 4.198 4.75 5.6

3.860 6.104 3.717 4.25

5,433.6513 B 5,448.5091 B 5,494.4158 B 5,533.6788 B 5,538.6510B

3p01 3p~1

3poo 3811

3p~2

3poo

4d~3 4d~1 4d~2

5,562.7662 5,652.5664 5,656.6588 5,662.5489 5,689.8163

B B B B B

5,719.2248 5,748.2985 5,760.5885 5,764.4188 5,804.4496

B B B B B

3p12 3p23 3p23 3p22

4d 23 4d 12 4d 24 4d 22

5,811.4066 B 5,820.1558 B

3p22 3p22

5 ,852 .4878 S 5,868.4183 B 5,872.8275 B

38~1 3p~1 3p~1

4d u 4d 3a

5 l881.8950 S

3812

5,902.4623 B 5,902.7835B 5,906.4294B 5,913.6327 B 5,918.9068 B 5,944.8342 S 5,961. 6228 B 5,965.4710 B 5,974.6273 B

3p22

68~1

3pu 3pu 3p01

3p01

3P2a

58u 5812 4d~a

3p~o 4d~1 4d~2

2ptl

2P1O

2p7 2P7 2pI0

2P1O 2po 2pa 2pa 2pa

5d2 5d 5

48~

4'" 81 4~

4d a

4~

2ps t-'td'i' 2ps 2ps 182

4d 2 4d 4 2p1

2p5 2p6

481 48'''' 1

10

3p~1

186

4d;a 4d;2 4d 22 4d u

2p4 2p4 2p7 2P7

2pa

48~

9

Is 6

2P4

10

3p~1 3p~1

4d~1 3p~2 4d~1 4d~2

48; 48"1

7 10

3p12

4d 23

2p2 2P2 2po

3p~2 3p~2

3pu 3pu 3poo

3812

2P2

481/' 1 48'''' 1

4d~' 4d 2

4~

10

3.936 2.810 3.129 2.196

4.832

3.949

4.868 4.12·J 4.638 6.442

4.34L

7-38

ATOMIC AND MOLECULAR PHYSICS TABLE

7e-2.

THE SPECTRUM OF NEON

I (Continued)

Classification Wavelength System. 3p~1 4d 12 4d u

6,000.9275 B 6,029.9971 S

3s 12 3P12 3P12 3P12 3s 11

6,046.1348 6,064.5359 6,074.3377 6,096.1630 6,128.4498

B B S S B

10

log 11

5.14 4.373 4.049 3.725 5.200

4d01 3p~1

Iso 2P6 2P6 2P6 Is 4

4d 4 4d o 2P2

*12 8 7 6 10

3p11 3P11 3s 11 3s 11 3s 11

5S~1 5s~0 3poo 3p12 3p~1

2P7 2P7 Is 4 Is 4 Is,

3S2 3s. 2p. 2p, 2p&

4 4 10 8 6

6,143.0623 S 6 ,163.5939 S 6,174.8829 B 6 ,182. 1460 B 6,189.0649 B

3s 12 3s~0 3P12 3pu

3P12 3p~1 4d 23 5S12 4d 12

Iso ls. 2P4

2pa 2P2

2pu

6,193.0663 B 6,205.7775 B 6,213.8758 B 6,217.2813 S 6,246.7294B

3P12 3poo 3P22 3s 12 3P22

S B S B B

S B S B 6,421. 7108 B

6,444.7118 6,506.5279 6,532.8824 6,598.9529 6,652.0925

5,975.5340 S

5,987.9074 B 5,991. 6532 B

3pll

4d u 4d 11 5s 11

2p4 2p4 2p,

2ps

3.249 3.613 5.411 5.428 4.908

3.961 3.995 6.490 6.550 5.580

6.093 6.161 5.024

3s o 4d,

10 12 5 7 5

5.48 5.231 3.9 3.610 3.544

6.63 6.488 4.3 4.737 3.846

4d, 4d 2 3s 4 2P7 3s&

4 6 7 15 6

..... 3.785 4.376 5.359 3.929

3.498 4.043 4.473 6.436 4.129

2p& 3s 2 2pa 3s, 3S2

15 6 6 7 8

5.336 3.683 5.422 3.899 4.424

6.606 3.900 6.391 4.151 4.546

6.156

2ps

10 6 12 20 6

5.567

6.679

6.281

5.503 5.93 3.701

6.684 6.83 3.893

6.221 6.389

7 15 6 15 7

4.094 5.635 5.381 5.736 4.279

4.191 6.709 6.531 6.691 4.681

3.823 6.287 6.094 6.213 4.203

6 9 2 10 9

5.840 5.765 5.965 5.436

6.806 6.712 6.783 6.068

6.393 6.286 6.421 5.568

4d1

Is&

2ps

3s~0 3p~o 3s 11 3p~o 3p~2

3p~1 5S~1 3P12 5s~o 5S~1

2p& Is 4 2p& 2p4

3812 3poo 3s 11 3s 12 3p~1

3p22 5S~1 3p11 3pu 5s 12

Is 5 2p. Is 4 Is 5 2P2

B S S S B

3P12 3s 11 38~o 3S~1 3S~1

5sn 3P22 3p11 3p~1 3poo

2pa

3s 5

184

2ps

Is,

2P7 2p2 2p,

6,666.8967 B 6,678.2764 S 6,717 .0428 S 6,929.4672 B 7,024.0500 B

3poo 3S~1 3S~1 38~1 38~1

5s 11 3p~2 3p~1 3pn

2pa 182 182 ls2 ls2

3Pll

18.

182 1s2

---

5.748

4da

5S12

6,334.4279 6,351.8618 6,382.9914 6,402.2460

log I.

6.05 4.601 4.237 3.925 6.266

2po

3Pll

6,266.4950 6,293.7447 6,304.7892 6,313.6921 6,328.1646

log 1 2

Paschen

3S2 2Pi

2pu 3s 5

3s 4 2P4 2P5 2pa 2p7

4.058 3.729

6.198 6.010 4.334

5.962

6.009

7-39

IMPORTANT ATOMIC SPECTRA TABLE

7e-2.

THE SPECTRUM OF NEON

I (Continued)

Classification Wavelength System. 7,032.4127 S

3812 3p01

3p01 3d~1 3d~2 3p22

10

log 1 1

10 5 7.5 10 10

5.732 4.286 4.868 5.793 5.751

log 1 2

log 1 3

Paschen

185 2P1O 2P1O 182 18.

2P1O

183 2P1O 2P1O 2P1O 2P1O

3d 2 3d 3 3d 6 3d 6

8 4 9 8 6

2P1 2p9 2ps 2ps 2ps

38. 381'" 38; 381" 38If' 1

10 30 40 70 200

2p10 38~ 38~

2P1O 38~

- --6.917 6.362 ..... .5.534 6.411 6.756

4.281 4.904 6.022 6.289

5.510 4.432 5.398 5.352 4.962

6.424 5.021 6.052 5.978 5.667

4.441 5.424 5.387 4.956

3.303

3.939

.....

. ....

3.487 4.718

4.043 5.412

3.19 3.48 4.040 4.725

200 100 60 300 30

4.676 4.452 3.916 5.047 3.467

5.203 5.030 4.633 5.718 4.038

4.629 4.419 3.85 5.029 3.34

4.327

.....

.....

5.387

4.280 4.691

38"" 1 3d; 3d 3

150 250 80 600 150

5.31 4.439

5.97

.....

5.316 4.415

3d~ 3d~ 3d~ 3d 2 3d 3

800 100 400 150 80

.....

. ....

5.957

3d 12

2p9 2ps 2ps 2ps 2ps

4.2 5.15 4.433 3.930

4.9 5.87 5.039 4.678

5.244 4.452 3.90

8,571. 3524 S 8,591.2587 S 8,634.6470 S

3p22 3p22 3p~1 3p~1 3Pll

3d n 3d o1 3d~1 3d~2 3d 22

2ps 2ps 2P6 2P6 2P7

3d. 3d 6 38~

500 60 100 400 600

5.703 4.014 4.332 5.436 5.3

6.324 4.752 5.012 6.057 6.0

5.764 3.98 4.330 5.450 5.386

8,647.0411 S 8,654.3831 S 8,655.5224 S

3P12 3p;2 3p;2

300 1,500 400 500} 500

4.709 5.56

5.235 6.26

5.747

3poo 3pu

2p. 2p. 2p. 2p3 2p7

381" 381If' 381""

8 1679.4925 S

3d;2 3d~3 3d~2 3d~1

5.2

5.8

7,051. 2923 S

38,"

7,059.1074 S 7 , 173.9380 B 7,245.1665 B

3811

3p01

7,438.8981 7,472.4386 7,488.8712 7,535.7741 7,544.0443

B

38~0

S S S S

3p01 3p01 3p01 3p01

3p01 3d u

7,724.6281 B 7,839.0546 S

3p~o 3p23 3p22 3p22 3p22

3d~3 3d~1 3d~2 3d~3

8,082.4576 B

38~1

3p01

182

8, 118. 5492 S 8,128.9108 S 8, 136.4057 S 8,248.6824 S

3pu

3P12

3d;1 3d;2 3d~2 3d~1

2P7 2p7 2p7 2P6

S S S S S

3p12 3p12 3p12 3p23 3p23

3d~2 3d~3 3d~2 3d 23 3d 12

2P6 2P6 2P6 2p9 2p9

38~ 3 8If' 1

8,377 .6065 S 8 , 417 . 1591 S 8,418.4274 S 8,463.3575 S 8,484.4435 S

3p23 3p22 3p22 3P22 3p22

3d 34 3d 23 3d 22

8,495.3598 S 8,544.6959 S

7 ,927 .1177 S 7,936.9961 S 7,943.1814 S

8,259.3790 8,266.0772 8,267.1166 8,300.3263 8,365.7486

8,681.9211 S

3p01 38~1

3Pll

3pu

3d 12

3do1 3doo 58u

3d u

3d u

2ps

2p1O

381"" 38~

381""

3d~

38~ 3d 2

5.016 5.075

7-40

ATOMIC AND MOLECULAR PHYSICS TABLE

7~-2. THE SPECTRUM OF NEON

I (Continued)

Classification Wavelength

10 System.

log 11

log 1 2

log II

Paschen

--- --3p11 3p~1

8,704.1116 8,771.6563 8,780.6210 8,783.7533 8,830.9072

S S S S S

8,853.8669 8,865.3060 8,865.7552 8,919.5007

S S S S

3p12

8,988.57 9,148.672 9,201. 759 9,220.058 9,221.580 9,226.690

S S S S' S

9,275.520 9,300.853 9,310.584 9,313.973 9,326.507 9,373.308 9,425.379 9,459.210 9,486.68 9,534.163

3P12

3d12 3d~1 3d 23 3d~3

2p7 2p2 2p6 2p2 2P6

3d 3 38~ 3d~

3p~1 3p12

3dn

3p12

3d12

3p12 3pOl

3d 33 48~1

2pIO

282

3d01

2P6

3d ti

2p6 2p6

381'" 3d 2

3dl 3d,

200 400 1,200 1,000 50 700 tOO} 500 300 200

4.243 4.845

4.992 5.467

3.606

4.258

5.233

5-.805 5.246

.....

.... . .... .

.....

5.0

,5.6

4.201 4.888 5.642 5.488 3.61

5.0

4.623 4.3tO

5.290 4.712

4.624 4.12

4.809 4.786 4.54 4.0 4.040

5.501 5.381 5.23 4.7 4.785

4.808 4.826 4.624

.....

3POl

48~0

2PIO

283

3p~1

3d 22

3P:l

3dn

2pti 2pti 2p, 2p4 2pti

3d:' 3d 2 3d:

3d a

600 600 400 200 200

2p, 2p, 2pti 2p, 2P3

3d 2 3d a 3d 6 3d, 3d 2

100 600 150 300 600

4.650 4.213 4.224 4.682

4.466 5.261 4.966 4.947 5.285

3.83 4.639 3.60 4.23 4.710

2p, 2p3 2p2

3d ti 3d ti 3d 3

200 500 300 500 500

4.008 4.472 4.211 4.793 4.555

4.712 5.225 4.969 5.280 5.319

3.96 4.47 4.15 4.76 4.567

300 1,000

4.241 5.:207

4.986 5.552

4.15 5.155

3p~2 3P:2 3P:l

3d 23 3d 22 3d 12

S S S S S

3P:2 3P:2 3P:l 3P:2 3poo

3dn

S S S

3P:2 3poo 3p~1

2pIO

28,

S

3p~1

3d01 3do1 3d12 4811 3d01

2p2

3d ti

9,547.405 S 9,665.424 S

3p~1

3d oo

2P2

3d 6

3pOl

4812

2PIO

285

3pOl

3d 12 3d oo 3d a3

3dn

3d~'

I

4.01

7-41

IMPORTANT ATOMIC SPECTRA TABLE

7e-2.

THE SPECTRUM OF NEON

I (Continued)

Classifieation Wavelength

10

System.

10,295.417 562.408 620.664 798.07 844.477

3p22 3p~0

11,143.02 177.533 390.439 409.134 522.745

3p21 3p21

11,525.02 536.345 601.536 614.11 688.002

3Pll 3pu 3P12

3pu

3p;1 3p;2

Paschen

48~1 3d~1 48~1 48~0 48~1

2ps

282

2Pl 2p; 2P1 2P6

38~

282 283 282

80 200 40 150 200

4811 4812 4812 4801

2ps

284 286 286 282 282

300 300 110 100 150

284

48~1

3pll

4811

3p~0 3poo 3p~1 3p~0

3d 11 48~1 48~o 3d o1

3p~1 3p12

48~1 4811 4812

11,766.792 789.05 789.895 984.94 12,066.340

3pu 3p~1 3p12

48~0

12,459.39 595.01 689.21 769.532 887.16

3P:l 3P:2 3poo 3p;1 3p~1

4811 4811 4811 4812 4811

12,912.021 13,219.248 15,230.713 17,161. 94

3P:2 3p~1 3p~o 3p~0

4812 4812

4812

48~1

4811

2P9

2ps 2P6 2p4 2P1 2p 2P3 2p5 2Pl

3d 5

90 50 25 80 10

2p2 2P6 2P1 2P2 2P6

282 284 285 283 286

60 50 10 10 15

2P5 2P4

2

2P5 2P2

284 284 284 285 284

2p4 2P2 2Pl 2Pl

285 285 282 284

2pa

3d 2

282 281

1

7-42

ATOMIC AND MOLECULAR PHYSICS

Neon Microwave 1.25 mm Pressure End-on View

J

~~~

~-

Co>

Co>

§ ~

Co>

ID CAl

tEJ Co>

g:

.1

Co>

Co>

-..I

S UI i! FIG. 7e-1. Photoelectric traces of the neon spectrum, microwave discharge at 1.25 mm. Wavelength range is 3,000 to 10,000 A.

Neon Microwave 1.25mm Pressure End-on View

4.0 - - - - - - - - - - - - - - - - - - - - - 3.5 - - - - - - - - - - - - - - - - - - - - - - - 3.0

2.5 - - - - - - - - - - - - - - - - - - - - - - - - - - -

I.

FIG. 7e-1 (Continued)

.

.~

~

-.::t'!

I t-

~ ~

8 ~

Co)

en

P-l Co)

'""' ::E 0 8

8

~

Z ~

~

8

::E

0 P-l t-t

CI1

~ ~ ~ ~ ~:>

~~? c:: E-g OIl'lLIJ CI1(\j

Z...;

III

rt)

I

C! rt)

I

·4712 ·4708 ·4704

I

4517

I

I

).......11( 4973

4944 4939

1]4957 4928

4800

4537

C! rt)

4788

Il'l

fli

4780

~

C!

4525

4552

04678

14687

tm·:~:

I ~

~

CI1

~

~ ~ ~

~~>

c::

E -g

t Q.. c:: :i E ? OIl'lLIJ CI1(\j

Z...;

o

.n

It)

.,j

0

-

I--

....."

5234 5222

5193 5188

5214 5208 5203

= -I"""'"

--

5022 5015 5011

5037 5031

5045 5042

5052

5090 5083 5080 5074

5104 5099

5122 5116 5113

....., 5163 ~ 5158 ===: , 5154 -~' 5151 5144

...-..

I-

--

-

~.

-

l"-

-

f--

fli

0

i ' - -=; 5005 It)

.:t fli

o

Il'i

It)

.,j

~

0

-

-l-

-=;

I--"",!

-I-

5418 5412

5433

5448

5494

-~

5383

5400

I-

- ~~

-

--~== -=;

5280

5304 5298

5330 5326 5320 5314

5341

5372 5366 5360 5355 5349

f--r-=

=

- ......

fli

0

-I-- 5274

-~

- -~

fli

Il'l

;::l

~ ~

.~ ~

S

co 000>

6.5 6.0 5.5

5.0 4.5 4.0

I

I

II I I

mis!--

.... ~

I

I

I

1_"!9

I

!a!a!9

i ;::!~:S. FIG. 7e-l (Continued)

r

7-46

ATOMIC AND MOLECULAR PHYSICS Neon Microwave 1.25mm Pressure End-on View

1.0

:~

58J s 00

~

........ "'''' ~~

t:JfI

w w'" "''''''' '" ~ 8w~ VI

6.0-----

1

1. ~

c:i

_

::~ :=J-rj----l------------... FIG. 7e-1 (Continued)

M, Meggers and Humphreys, J. Research Natl. Bur. Standards 13, 293 (1934) S, International secondary standard 1 The classification is expressed in two notations: Systematic (Modified Racah). Orbital angular momentum of the last electron (valence electron) is specified by the symbols s, p, d, etc. (not the angular momentum of the configuration as in L, S coupling). The first subscript is the angular momentum K of the atom exclusive of the spin of the valence electron minus t. The second index is the total angular momentum J of the atom (J = K ± t). The Ievels are primed if they converge to the 2Pt level of the ion which lies above the lowest ionization limit 2PJ. Paschen Notation. This is a semiempirical notation first used by Paschen and extensively used in the literature for the rare-gas spectra. It is now obsolete. The intensities are standardized in such a way that they give the energy flux from 100 ern! of the light source per unit solid angle in ergs per second. 11, glow discharge, 60 cycles, pressure 1.25 mm; 1 2, microwave discharge; pressure 10 mm; 1 3, hollowcathode discharge, pressure 3.5 mm, current 90 rna. Argon 1. Listed in Table 7e-3 are the strongest lines in the argon spectrum and some others for which accurate wavelength determinations have been made. Letters indicate origin of wavelengths: B, Burns and Adams, J. Opt. Soc. Am. 43, 1020 (1953) L, Littlefield and Turnbull, Proc. Roy. Soc. (London) A218, 577 (1953) M, Meggers and Humphreys, J. Research Natl. Bur. Standards 13, 293 (1934) There are systematic deviations between the wavelengths of different observers, and care should be exercised if the lines are to be used as wavelength standards. COLUMNS 2 TO 5: Classification, systematic (modified Raeah) and conventional Paschen designations (see Table 7e-2). COLUMNS 6 AND 7: Intensities (logarithmic scale): 11, intensity in 60-cycle a-c glow discharge; current 60 rna, argon pressure 3 mm; 1 2, hollow-cathode discharge with iron electrodes, current 150 rna, argon pressure 1 mm. 1

Trans. Intern. Astron. Union 6, 86 (1935).

7-47

IMPORTANT ATOMIC SPECTRA TABLE

7e-3.

THE SPECTRUM OF ARGON

Classification

I Intensities

>. System. 3,319.3446 3,373 .4823 3,554.3048 3,567.6550 3,572.2960

B B L L B

4s 12 4s 11 4s 12 4s 12 4S~1

7p12 7poo 6P12 6pn 7poo

3,606.5207 3,649.8310 3,834.6775 3,894.6609 3,947.5046

L L L L L

4s 11 4S~1 4S~1 4S~1 4s 12

6poo 6p~o 6poo 6p01 5p~2

3 ,948.9785 4,044.4176 4,045.9645 4,054.5259 4,158.5906

L L L L L

4s 12 4s 11 4s 11 4s 11 4s 12

5p~1 5p~2 5p~1 5p~1 5p12

4,164.1794 L 4,181. 8833 L 4,190.7126 L 4,191.0292 L 4 , 198 . 3174 L

4s 12

4s~o

5p~1

4s 12 4s~o 4s 11

5p22 5p~1 5poo

4,200.6745 4,251.1848 4,259.3615 4,266.2865 4,272.1688

L L L L L

4s 12 4s 12 4S~1 4s 11 4s 11

5pn 5p01 5p~o 5p12 5Pll

4,300. 1005 4,333.5611 4,335.3374 4,345.1679 4,363.7944

L L L L L

4s 11 4S~1 4S~1 4S~1 4s 11

5poo 5p~2 5p~1 5p~1 5p01

4,510.7332 4,522.3231 4,596.0963 4 ,628 .4406 4,702.3160

L L L L L

4S~1 4s~o 4S~1 4S~1 4S~1

5poo 5pOl 5p11 5p22 5pOl

4,768.6750 4,876.2610 4,887.9478 5,060.0793 5,151. 3943

B L B B B

4pOl 4pOl 4p01 4pn 4pOl

6d~2 7d 12 7d ol

5p11

Sdu 6d oo

Paschen ls 5

ls4 ls 5 ls 5 ls 2 Is,

ls2 ls 2 ls 2 ls 5 Is, Ls,

ls4 Is, ls 5

lsi lSI ls 6

lsi ls4 lSI lSI

ls2 Is, Is, Is. ls 2 ls 2

ls2 Is. ls 2

lsi ls 2 ls2 ls2 2PlO 2P1O 2PlO 2pu 2PlO

log 1 1

log 1 2

5pa 5pI 4pe 4pu 5p5 4P5 4P1 4p5 4PIO 3pI

2.18 1. 75 1.54

3P2 3pI 3P2 3p4 3pe

3.09 3.16 2.17 1.92 3.80

2.65

3p7 3p2 3pa 3p4 3pI

3.03 3.13

2.62 2.56 3.11

3pu 3P1O 3Pl 3pe 3P7

3.83 2.73 3.40 3.29 3.54

3P5 3pI 3P2 3p. 3P1O

3.40 3.32 2.95 2.91 1.89

3p5 3P1O 3p7 3pa 3PlO

3.13 2.62 2.65 2.42 2.74

6" Sl

1.63 1.80 1. 77 1.65 2.00

is, 7d ,

Sd. 6d e

....

3.56

3.53

3.11

3.00 2.52 2.59 2.30 2.92 2.19 2.20 2.27

7-48

ATOMIC AND MOLECULAR PHYSICS TABLE

7e-3.

THE SPECTRUM OF ARGON

I (Continued)

Classification

I

x System.

Paschen

Intensities log I 1

log I 2

5,162.2847 5,187.7467 5,221.2690 5,252.7857 5,373.4951

L L L L B

4p01 4pOl 4P23 4P22 4Pll

6d o1 5d~2 7d u 7d 33 7d 22

2pI0 2pI0 2pu 2ps 2P7

6d 6 5" 81 7d~ 7d~'

2.47 2.53 2.17 1.85 1.45

5,410.4750 5,421. 3492 5,439.9903 5,451. 6506 5,457.4158

B L B L B

4p12 4p23 4pOI 4pOl 4P22

7d 23 8812 7811 7812 8811

2ps 2pu 2P10 2pI0 2ps

7d~ 586 48. 486 58.

2.49 2.0~ 1.6 2.42 1.09

5,467.1626 5,473.455 5,495.8728 5,506.1105 5,524.9576

B B L L L

4p22 4p22 4p23 4P22 4p23

8812 78~1 6d u 6d 33 5d~3

2ps 2ps 2pu 2ps 2pu

586 482 6d~ 6d. 58'" 1

1.28 1.45 2.72 2.00 1. 70

5,558.7015 5,572.5406 5,588.7213 5,597.4783 5,606.7328

L L B B L

4pOl 4p22 4P22 4p~2 4pOl

5d 12 5d~3 5d~2 6d~3 5d o1

2pI0 2ps 2ps 2p3 2PI0

5d a 58 rrr 1 581"" 11 6/ 81 5d 6

2.84 2.35 1.55 1.58 2.84

2.48 2.09

5,650.7042 5,659.1278 5,681. 8976 5,739.5191 5 , 772 . 1143

L B L L L

4pOl 4P12 4P12 4P11 4P12

5d oo 8812 6d 23 5d~2 5d~3

2P10 2ps 2ps 2P7 2pG

5d s 586 6d~ 58III 1 58", 1

2.54 1.61 1. 78 2.25 1.83

2.21

5,802.0802 5,834.2640 5,860.3098 5,882.6245 5,888.5830

L L L L L

4P12 4P12 4p01 4p01 4p2a

6d o1 5d~2 68~1 68~o 7$12

2ps 2ps 2p10 2p10 2pu

6d 6 581" 382 38a 486

1.69 2.01 2.19 2.41 2.78

5,912.0848 5,928.8119 5,942.6676 5,987.3027 5,999.0004

L L L B B

4p01 4p22 4P22 4p23 4p22

4d~1 7s 11 7812 5d 33 5d 22

2PI0 2ps 2ps 2pu 2ps

48~ 48. 486 5d. 5d~'

2.82 2.43 1.96 2.10 1.90

6,005.7246 6,013.6790 6,025.1515 6,032.1273 6,043.2232

B B B L L

4p~2 4p23 4p~2 4P23 4p22

8811 5d 12 78~1 5d u 5d aa

2P3 2pu 2pa 2pu 2ps

58. 5d 3 482 5d~ 5d.

1.33 1. 75 1. 97 3.33 2.88

t.u

2.01

2.00

2.39 1.98 1.43

2.56

1.43 1.93 1.71

1. 75 2.05 1.98 2.34 2.62 2.17 1.84 1. 75

2.91 2.46

7-49

IMPORTANT ATOMIC SPECTRA TABLE

7e-3.

THE SPECTRUM OF ARGON

I (Continued) Intensities

Classification

x

System.

Paschen

4p11 4p~1 4p~2

4d~2 4d~2 7811 5d~2 4d~a

2PI0 2PI0 2P7 2p4 2ps

48'''' 1 4" 81 484 58'''' 1 58t rr 1

2.28 2.59 2.10 2.28 2.25

7s 11 5d~1 7s 12 5d u 5d 23 5d~2

2pa 2p4 2pa 2P7 2pa 2pa

4s 4 5" 81 485

1.93

L L L B

4pll 4p~1 4P12 4p11 4P12 4p~2

5d~ 5" SI

2.25 2.30 2.26 2.01

6,296.8739 L 6,307.6561 L 6,364.8940 L 6,369.5756 L 6,384.7160 L

4p~1 4P12 4p11 4P12 4pOI

5d~t 5d 12 5d oo 5d o1 6s 11

2P2 2P6 2P7 2P6 2PI0

5" SI 5d a 5d a 5d 5 3s 4

2.18 2.36 1. 75 2.05 2.60

6,416.3064 6,431.5553 6,466.5498 6,538.1118 6,604.8542

L L L L B

4pOI 4pu 4poo 4P23 4P22

6S12 6S~1 5d 11 4d~a 4d~a

2pI0 2ps 2P6 2pv 2ps

385 382 5d 2 48rrr 1 48r t r 1

3.36 1.60 1.64 2.18 2.43

6,660.6784 6,664.0533 6,677.2812 6,698.8752 6,719.2193

B B B B B

4p11 4P22 4s 11 4P12 4poo

6S~1 4d~2 4p~o 6S~1 5d o1

2P7 2ps ls 4 2pa 2P6

38a 48'''' 1 2pl 382 5d 6

2 12 2.16 3.40 1.97 1.92

6,752.8347 6,766.6134 6,827.2529 6,871.2898 6,888.1704

B B B B B

4pOI 4P12 4p~2 4pOI 4p11

4d 12 4d~1 5d o1 4d o1 4d~2

2PI0 2pa 2pI 2PI0 2P7

4d a 48~ 5d 5 4d 6 4" 81

3.60 2.27 1.89 3.53 2.45

6,937.6658 6 •965 .4304 7,030.2519 7,067.2175 7,107.4777

B B B B B

4pOI 4s 12 4P23 4812 4P22

4d oo 4p~1 6812 4p~2 6812

2PI0 ls 6 2pg 186 2ps

4d a 2P2 386 2ps 385

3.15 5.06 3.57 5.01 2.79

7,125.825 B 7,147.0408 B 7,206.9812 B 7,272.9349 B 7,311.724 B

4p~1 4s 12 4p~2 4s 11 4p11

68~1 4p~1 68~1 4p~1 6s 11

2p4 1s 6 2pI Is. 2P7

382 2p4 3s 2 2P2 3s.

2.47 4.42 2.93 4.71 2.89

L L B L L

4pOI

6,155.2393 B

6,052.7230 6,059.3723 6,098.8046 6,105.6346 6,145.4406

6 , 170 . 1734 6,173.0949 6,212.5015 6,215.9423

4p~1

5d~'

log I.

log II

I I

1.84 2.25 2.05 2.81 1.93

2.71 1.97

2.09

2.34 2.87

3.01

3.26

3.26

2.86 4.75 3.19 4.75

3.83 4.23

7-50

ATOMIC AND MOLECULAR PHYSICS TABLE

7e-3. THE

SPECTRUM OF ARGON

I (Continued)

Intensities

Classification

x Paschen

System.

7,353.316

2p4 2Pl 2Pfi 2pG 2p7

2.86 5.35 5.22 5.53 5.44

5.28 5.07 5.36 5.19

2pG Iss Is, ls fi ls 4

4d a 2p4 2pG

3.60 5.13 5.23 5.30 5.31

5.13 5.06 5.29 5.30

4P23 4p~1 4p~2 4p22 4p~1

ls fi ls 2 ls2 Is, ls 2

2pe 2P2 2pa

5.58 5.28 5.36 5.35 5.18

5.59 5.07 5.35 5.48 5.09

4p~2

4d 12

4poo

4do1

4.52

4.64

4d u 4d 34 4p~2 4d;2 4d;s

7,471.1676 7,503.8685 7,514.6514 7,635.1056 7,723.7599

B B B B B

4s 11 4S~1 4s 11 4s 12 4s 12

4p~1 4p~o 4P12 4p11

ls2 ls 4 ls fi ls fi

7,891.0777 B 7 ,948 .1755 B 8,006.1566 B 8,014.7853 B S,103.6920 B

4P12 4s~o 4s 11 4s 12 4s 11

4d 12 4p~1 4P12 4p22 4p11

8,115.3108 8,264.5221 8,408.2094 8,424.6473

4s 12 4S~1 4S~1 4s 11 4S~1

B B B B 8,799.082 B 9,122.9660 B 9,194.636 B 9,224.4955 B 9,354.218 M 9,657.7841 M 9,784.5010 M

10,470.051 M

log 1 2

4SI"" 4'" SI

4p22 4p23 4s 11 4p~1 4p~2

8,605.7790 8,620.4602 8,667.9438 8,761.6907

II

3.32 3.76 5.02 2.55 2.48

2ps

7,372.1189 B 7,383.9796 B 7,412.334 B 7,425.290 B

B B B B 8,521. 4428 B

log

4poo

2pe Is, 2p4

2pa Ls,

4d 4 4d: 2ps

2ps 2p7

2ps 2p4

3.44 5.03

4s~o 4p~1 4p~2

4p11 4d 12

2pa 2Pfi ls a 2P2

4do1

2pa

4d s 4d fi 2P7 4d a 4d fi

4s 12

4pOl

Is,

2P1O

....

5.58

2pI0 ls 2 ls 2 Is,

2s 2 2p6 2p7

'" . ....

2P1O

.,

..

5.19 4.18 5.36

ls 2 ls 3

2ps 2P1O

.,

..

4.72

4pOl 4S~1 4S~1 4s 11 4S~1 4s~o

5s~o 4P12 4p11

4pOl 4P22

4pOl

7-51

IMPORTANT ATOMIC SPECTRA

7e-3. THE SPECTRUM OF ARGON I (Continued) Vacuum Argon Wavelengths in the Near Infrared"

TABLE

Classification

x

10 System.

10,676.489 684.698 11 ,081. 901 671. 903 12,115.639

H H H H H

4pOI 4p23 4p22

12,346.770 H 406.2184 R 442.724 H 459.523 H 491.0793 R

4P22 4P11 4pOI 4p22 4P23

5811 5812

12,705.755 H

4p~1 4p22

3d~1 3d 22

4pOl

3d01 58~1 3doo

806.2474 R 960.2029 R 13,011.8209 R 217.606 H

13,231.727 H 276.2656 316.8552 370.7679 507.8818

R R R R

13,603.051 H 626.3909 682.2918 722.3286 16,945.2129

R R R R

4p12 4P23

4P:2

4pOl 4p23 4P:2 4P:l

4P12 4P22

5812 3d~3 3d~2 3d~2 3d 23 3d 23 3d 11 3d 12

3d 33 3d~3 3d;2 3d 23 3d 33

4P:2 4P11 4p~1 4P23

3d~2 3d 22 3d~2

4P12

3d 12

3da 4

Paschen 2PI0 2P9

2ps 2P6 2p9

2ps 2P7 2PI0

285 38III 1 381111 1 381II

500 200 200 100 300

3d~ 3d 2 3d 3

150 400 500 400 700

3d~

2P5

28. 286

2P2

38~

2ps 2PIO

3d 5

2ps

2P3 2plO 2P9 2P3 2P4 2P6

2ps 2p3 2P7 2p2 2P9 2p6

3d~'

282 3d 6 3d.

38III 1 381/1/ 1 3d; 3d.

38II/I 1 3d~'

381/I

3d~ 3d a

150 300 250 200 150 200 750 600 800 850 55 500 300 1000 100

• From Report of Commission 14 of the International Union, December, 1960. H measured by Humphreys and Paul, J. phys. 19,424 (1958); R measured by Littlefield and Rowley in the abovementioned report.

7-52

ATOMIC AND MOLECULAR PHYSICS

Argon Microwave 6.5mm Pressure End-on View

l

I

A

~'

w www

~

10000 5000 2000

Ow w w w

§

...,~

is

l000AL::&1'

w

~~~

l! !l$

C7\

lS

w

ww

s

8m

50000

~

20000 10000 5000

~2ooo 1000

4J

.- 0

I.

~~I!:l OVl~

,

?Pi

~

ii

w

~

I

FIG. 7e-2. Photoelectric traces of the argon spectrum, microwave discharge at 6.5 mm pressure. Wavelength range is 3,500 to 10,000 A.

50000 20000 10000 5000 2000 1000 500 I

200 100 50 20 0

I II

A

8 II,)

i

•

.s» ... u...

\,..0'01

0

~

20000 10 000 5 000 2 000 1 000 500

I

'-

...... \Iw

...........

I

II

200 100 50 20 0

FIG. 7e-2 (Continued)

i

"\1\..

l.~

~

t.!.

Q

~

8

riI P4 00

Q .... ::g o -
-1

7e-6.

THE SPECTRUM OF IRON I

Classification

>-2

5,110.4139

. 4120 J

5,123.7231 5,127.3624 5,133.692 5,150.8425

.7192 .3585 .6885 J .8385

5,166.2841 5,167.4905 5,168. ()O03 5,171. 5987 5,191. 4615

.2814 .4878 .8974 .5955 .4544

J

5,192.3509 5,194.9441 5,198.7149 5,202.3395 5,204.5840

.3437 .9410 .7108 .3364 .5822

J J

5,216.2770 5,225.531 5,227.1911 5,232.9474 5,235.392

.2738 .5253 .1876 9400 .3858

J J

5,236.204 5,242.4955 5,247.065 5,250.211 5,250.6490

.4903 J .0494 J .216 .6449

5,263.3134 5,266.5626 5,269.5402 5,270.3602 5,281.7970

.3038 . 5548 .5363 .3557 .7896

5,283.6283 5,302.3073 5,307.3633 5,324.1864 5,328.0418

(Continued)

E'

log 12

log 13

z7D. (zIH5) zoFI z6F6 f6Ge zoFa

19,562 48,383 27,666 26,875 53,169 27,395

4.238

.....

3.323 3.002 3.577 2.506

z7D6 z3Da

3.901 5.37 3.926 4.651 3.701

..... .....

z3F. e7DI

19,351 31,323 19,757 31,307 43,764

Z7P3 a 3Fa aOPI a 5Pa a 5D2

e7Da z3F3 y6P2 y5Pa z7D2

43,435 31,805 37,158 36,767 19,913

a 3F2 a 6D I a 3F. Z7P. b 3F a e3F .

z3F2 z7DI

a 6D• (aIH.) a 6F I a 6F4 yW6 a 6F2 a 6Dt a 3F. a 6D3 a 3F. Z7P2

I

log I.

I

log vA v

3.613

-0.85

3.415 3.212 3.786 3.322

0.18 -0.14 3.89 0.50

..... ....

3.190 4.71R 3.48r 4.23R 4.080

-1.50 -1.67 -1.03 1.25 2.93

3.914 4.275 2.39 2.85 3.464

.... ..... ..... ..... .....

3.250 3.88r 3.32 3.725 2.86

2.05 0.96 1.30 1.77 -1.74

4.171 2.90 5.02 4.436 2.73

..... ..... ..... ..... .....

3.78

1.08 -1.78

e 7D6 x 6Da u 3Da

32,134 20,020 31,686 42,816 39,970 51,969

e3F 2 aile a 6D2 a 6D o a 6P2

81 zlH$ z7Da z7DI y6Pa

52,858 48,383 19,757 20,020 36,767

1.83 3.20 2.89 2.44 2.78

..... ..... ..... .....

J J J J J

ZoD2 Z7Pa a oF6 a 3F2 Z7P2

e6D2 e7D• z6D. z3DI

45,334 43,163 25,900 31,937 43,435

3.195 4.033 5.058 4.914 3.477

..... ..... ..... ..... .....

3.60 4.281 4.68r 3.832

2.65 3.06 1.45 1.48 2.63

.6203 .2991 .3604 .1784 .0386

J

z6Da z5DI a 3F2 z6D. aoF.

e5D3 e oD2 z3Fa

45,061 45,335 31,805 44,677 26,140

3.811 3.423 3.337 4.182 4.867

.....

..... ..... ..... .....

4.045 3.736 3.00 4.393 4.70R

3.07 2.79 0.26 3.36 1.29

5,328.5336 5,332.9020 5,339.9371 5,341.0255 5,364.874

.5309 .8987 .9286 .0236 .8717

J

a 3Fa a 3F3 z6D2 a 3F2 z5G2

zaDa z3F. e6D3 z3D2

»n,

31,323 31,307 45,061 31,686 54,491

4.507 3.951 3.874 4.65 3.384

..... ..... ..... ..... .....

4.20r 3.155 3.846 4.00r 3.64

1.19 0.36 2.87 1.11 3.91

5,367.470 5,369.965 5,371.4926

.4671 H . 9621 H .4892 H

vo,

54,237 53,874 26,340 54,379 53,353 25,900

..... ..... .....

3.79 3.91 4.61R

4.02 4.10 1.10

.3689 H .1272 H

e6H4 e5H6 z5D2 (e 3G3) e6He z6D.

3.564 3.725 4.622

5,383.374 5,397.1311

z6G• a 6Fa (Z3G.) z6G6 a 6F.

3.844 4.459

..... .....

4.11 4.43R

4.23 0.81

5,404.144 5,405.7781 5,424.072 5,429.6999 5,434.5268

. 1185 .7744 .0686 .6963 .5237

z3G• a 6F2 z6Ge a 6Fa a 5FI

e3H o z6DI e5HI z5Da z5Do

54,267 26,479 53,275 26,140 26,550

3.819 4.353 3.842 4.414 4.048

.....

4.08 4.49R 4.08 4.48R 4.28R

0.86 4.19 0.89 0.72

H J

H J

J J

H H J

.......

H H H J

H H H J

J

H H H H

v»,

z3D~

«t»,

»o, z5Da

' 0 ' ••

..... ..... .0.0.

.0

•••

..... .....

..... .....

..... 4.93 4.61r 2.96

3.326

..... ..... 3.402

.....

2.95

3.73 -2.00 -1.93 1.32

7-91

IMPORTANT ATOMIC SPECTRA TABLE

"I

7e-6.

THE SPECTRUM OF IRON I

Classification

}.2

5,446.9197 5,455.6131 5,497.5196 5,501.4686 5,506.7824

.9168 . 6093 . 5159 . 4633 .7785

H H H H H

5,569.6256 5,572.8501 5,586.7634 5,6Hi.6521 5,624.5501

.6174 .8419 .7555 .6434 .5417

H H H H H

5,658.8247 5,662.525 7,187.341 7,445.776 7,495.088

.8156 H .516

7,511.045 7,586.044 7,780.586 7,937.166 7,998.972

....... ....... ....... ....... .......

8,046.073 8,220.406 8,248.151 8,327.063 8,331.941

....... ....... ....... ....... .......

8,387.781 8,661.908 8,688.633 8,824.227

....... ....... ....... .......

.......

....... .......

E'

log

12

(Continued) log l a

log 14

log

vA~

a 6F2 a 6FI a 6FI a 6Fa a 6F2

z6D2 z6DI z6D2 z6D4 z6Da

26,340 26,479 26,340 25,900 26,140

4.337 4.144 3.374 3.299 3.494

..... ..... ..... ..... .....

4.42R 4.42R 3.60 3.46 3.68

0.82 0.72 0.12 -0.06 0.17

z6F2

e6D! e6D2 e6D a e6Dt e6D2

45,509 45,334 45,061 44,677 45,334

3.541 3.806 4.074 4.262 3.319

..... ..... ..... ..... .....

3.807 4.06 4.43 4.375 3.574

2.89 3.11 3.26 3.35 2.62

z6F a

eo,

y6F6 y6D. y6Fa y6F.

g6Dl e6F6 e6Fa e6F4

45,061 51,351 47,006 47,756 47,378

3.22 3.661 3.53 3.48 3.53

..... .....

3.597 3.241

2.62 3.09

y6F6 z6G.

taF.

eaF2 e6F. e6Fa

47,006 47,961 48,928 47,378 47,756

3.66 3.39 3.28 4.040 3.26

z6G. z6G. a 6Pa z3G6

e3F2 e6F6 e6F4 Z6PI e6F.

48,532 47,006 47,378 29,773 47,378

3.36 3.69 3.34 3.61 3.11

a 6Pa a 6PI a 6Pa a 5Pa

z·Pa z6Pa z·Pa z6Pa

29,469 29,469 29,056 29,056

3.79 3.75 4.161 3.76

z6Fa

z6F. z6F6 z6F2

zaGa

Z6G6 z6Gl

vo,

e6F2

7-92

ATOMIC AND MOLECULAR PHYSICS

M ercuru 1. This spectrum is very useful because of the ease with which it can be obtained. Any low-pressure mercury tube gives sharp lines; for example, a commercial so-called bactericidal lamp is suitable. High-pressure lamps give broader lines and very high pressure lamps (commercial type H6) a continuous spectrum. The mercury spectrum is useful as a general reference spectrum. Under high dispersion most lines show elaborate isotopic and hyperfine structure because there are six isotopes with considerable abundance: 196 (0.15 percent), 198 (10.12 percent), 199 (16.84 percent), 200 (23.13 percent), 201 (13.2 percent), 202 (29.80 percent), and 204 (6.85 percent). The two odd ones have lines with hyperfine structure. The structure of the lines is sometimes useful for obtaining the resolving power of spectrographs (for details of structure, see Schuler and Burns and Adams"). An example is shown in Fig,7e-5.

o 1

lI)

~

N

I'

':+'

lI)

en

=t:

'It

CD N

I'

FIG. 7e-5. High-dispersion photoelectric trace of the 5461-A line of ordinary mercury showing isotope and hyperfine structure. Resolving power was 400,000.

Pure H g 1 98 can be obtained by irradiation of gold with neutrons. Lamps with this isotope are now commercially available and the spectrum shows very sharp single lines. Meggers has proposed to adopt the wavelength of the green line (5,461) of Hg 198 as a primary standard of length. International adoption of this proposal, however, awaits investigation of the variability of the wavelength with discharge conditions. In the meantime most of the strong lines of Hg 198 , particularly those marked S in Table 7e-7, may be used as standards for interferometric wavelength measurements. Hg202 is the most abundant isotope in natural mercury. Tubes with nearly pure Hg202 are also available and their wavelengths may also be used as standards. Table 7e-7 gives the wavelengths of natural mercury, H g 1 98 and Hg202. All values listed between 2,300 and 6,900 A are recent interferometric wavelengths; those outside this interval are known with much less accuracy. 1 Schiller and Keyston, Z. Physik 72, 423 (1931); Schiller and Jones, Z. Physik 79, 631 (1932); Burns and Adams. J. Opt. Soc. Am. 42, 716 (1952).

7-93

IMPORTANT ATOMIC SPECTRA TABLE

Classifieation

6 18 618 6 18

7e-7.

THE SPECTRUM OF MERCURY

X H g 202

log I

............

. ..........

....................

.. ............

(4) (20)

.....................

45.4400 78.3246

. .......... 45.4369 78.3224

5.33 6.60

X Hg198

X (Hg nat.)

I

6 3Po 6 3P O

1038 8 3D 1

1,402.72 1,849.52 2,296.97 2,345.433 2,378.316

6 3P 1 6 3P O 6 3P 1 6 3P 1 6 3P I

1038 938 8 3D 2 8 3D 1 8 1D 2

2,446.895 2,464.057 2,481. 996 2,482.710 2,483.815

46.8998 64.0636 81.9993 82.7131 83.8215

46.8974 64.0614 81.9971 82.7112 83.8196

4.44 4.31 5.43 4.94 5.23

6 3P O 6 18 6 3P I 6 3P 1 6 3P 1

7 3D 1 6 3P 1 918

2,534.764 2,536.517 2,576.285 2,652.039

34.7662 36.5277 63.8584 76.2882 52.0399

6.35 8.95

938 7 3D 2

34.7691 36.5063 63.8610 76.2904 52.0425

5.00 6.20

73D I

2,653.679 2,655.127 2,698.828 2,752.778 2,759.706

53.6827 55.1305 98.8314 52.7828 59.7103

53.6809 55.1284 98.8293 52.7801 59.7077

6.75 5.63 5.35 5.58 4.0

2,803.465 2,804.434 2,805.344 2,806.759 2,856.935

03.4706 04.4378 05.347 06.765 56.9389

03.4678 04.4357 05.3474 06.7630 56.9357

5.25 4.56 3.49 3.52 4.30

93.5982 25.4135 67.2832

93.5952 25.4104 67.2819

5.88 4.82 6.52

21.4996

21.4973

6.09

6 3P 1 6 3P I 6 3P 2 6 3P o 6 3P 2

6 1P 7 1P 7 3P 2

7 1D 9 3D 3

8 38 1038

...............

0 0 0 0 0

6 3P 2 6 3P 2 6 3P 2 6 3P 2 6 3P I

8 3D 3 8 3 D2 8 3D 1

6 3P 1 6 3P 2 6 3P O 6 3P O 6 3P 2

8 38 9 38 6 3D 1 6 1D 73D3

2,893.594 2,925.410 2,967.280 2,967.543 3,021.498

6 3P 2 6 3P 2 6 3P 2 6 3P 1 6 3P 1

7 3D 2 7 3D 1 7 1D 6 3D 2 6 3D 1

3,023.475 3,025.606 3,027.487 3,125.6681 3,131.5485

23.4764 25.6080 27.4896 25.6698 31.5513

23.4739 25.6056 27.4874 25.6675 31.5480

5.45 4.43 4.76 6.62 6.48

6 3P I 6 3P 2 6 3P 2 6 3P 2 6 3 P2

6 1D 8 38 6 3D 3 6 3D 2 6 3D 1

3,131. 8391 3,341.4766 3,650.1533 3,654.8363 3,662.879

31.8423 41.4814 50.1564* 54.8392 62.8826

31.8394 41.4766 50.1532 54.8361 62.8801

6.56 5.85 6.94 6.51 5.70

8 1D 8 18

7-94

ATOMIC AND MOLECULAR PHYSICS TABLE

Classification

7e-7.

THE SPECTRUM OF

X (Hg nat.)

MERCURY

I (Continued)

X H g 198

X H g 20 2

log I

6 3P 2 6 1P 6 1P 6 3P O 63P 1

6 1D 9 1D 8 1D 738 7 18

3,663.2793 3,704.1655 3,906.371 4,046.5630 4,077.8314

63.2808 04.1698 06.3715 46.5712* 77.8379

63.2778 04.1712 06.3715 46.5619 77.8284

6.35 3.94 4.56 7.09 6.00

6 1P 6 1P 6 1P 63P 1 6 1P

918 73 D 2 7 1D 738 8 18

4,108.054 4,339.2232 4,347.4945 4,358.3277 4,916.068

08.0574 39.2244 47.4958 58.3375 16.0681

08.0572 39.2251 47.4967 58.3257 16.0677

4.74 5.17 7.07 4.35

63P 2 6 1P 1 6 1P 1 6 1P 738

738 63 D 2 63D 1 6 1D 2 8 1P

5,460.7348 5,769.5982 5,789.664 5,790.6630

60.75328 69.59848 89.669 90.66288 6,072.7128

60.7355 69.6000 89.671 90.6648 72.6260

718 7 18 7 38 738 738

9 1P 8 1P 83P 2 8 3P 1 83P O

6,234.4020 6,716.4289 07.4612

34.3776 16.3253 07.4675

6 1P 738 718 7 38 7 38

718 73P 2 7 1P 7 3P 1 7 3P O

.

6 1D

5 1F

13,570.700 13,673.090 13,950.750 15,295.25 0 16,918.3 0

............ ............ ............

7 3P 2 63D 1 73P 2 6 3 D2

7 3D 3 54F 2 7 1D 53F3

16,920.970 16,942.330 17,072.670 17,109.570

63D3 7 3P o 7 3P 1 7 3P 2

53F . 17,202.080 838 22,499.290 838 23,253.470 0 838 36,261

........... ........... ........... 6,907.520 7,082.01 0 7,092.200 10,139.750 11 ,287.040

6.76 6.02 4.41 5.97

. ...... ...... . ...... . ...... . ...... . ......

6.20 5.98 5.36 5.53 5.26 5.78

............ ............

. ...... . ...... . ......

4.72 4.90 4.74

............

.. .

4.49

............

............ ............

............

.'

.

7-95

IMPORTANT ATOMIC SPECTRA

Values obtained by Blank.' for Hg198 are 3,650.1569, 4,046.5716, and 4,358.3376. Intensities are rough photoelectric values obtained at The Johns Hopkins University with a low-pressure neon-mercury discharge. The scale is the same as for neon (Table 7e-2). Intensities may be considerably different for other discharge conditions.

Mercury Tube

9.0 8.0 7.0 6.0

7.0 6.0 5.0 4.0

I

3

....0>

~

s

....

~

,~

....

~

U1

~

~

~.

CD"

7.0 6.0 5.0 4.0

m 011

Fig. 7e-6. Photoelectric traces of the mercury spect.rum, low-pressure mercury tube, 60 Hz discharge. Wavelength range 2400 to 5800 A. In order to bring out the weaker lines, the sensitivity was increased so that the ghosts of the strong lines show.

Notes on Table 7e-7. All wavelengths are interferometric values by Burns," except where otherwise noted. Those marked 0 (natural mercury) are older values, sometimes of questionable accuracy. The values of H g198 marked by * or S are averages, the latter proposed for international standards. Blank, J. Opt. Soc. Am. 40, 345 (1950). Burns, Adams, and Longwell, J. Opt. Soc. Am. 40, 339 (1950); Burns and Adams, J. Opt. Soc. Am. 42,56 (1952); 42, 716 (1952). 1

2

7-96

ATOMIC AND MOLECULAR PHYSICS

References Brode, W. R.: "Chemical Spectroscopy," 2d ed., 677 pp, John Wiley & Sons, Ine., New York; 1943. Fowler, A.: "Report on Series in Line Spectra," Fleetway Press, London, 1922. Gatterer, A., and J. Junkes: "Spektren der seltenen Erden," 2 vols., text and plates, Specolar Vaticana, 1945. Kayser, H.: "Handbuch der Spektroscopie," 8 vols., S. Hirzel Verlag, Leipzig. Volumes 1-6 (1912) are now out of date but are still the chief source for the earlier developments in spectroscopy. Volumes 7 (1934) and 8 (1932) are more recent but also not quite up to modern standards. This handbook contains the most detailed compilation of spectroscopic data. Minnaert, M., G. F. W. Mulders, and J. Houtgast : "Photometric Atlas of the Solar Spectrum," Amsterdam, 1940. Moore, C. E.: A Multiplet Table of Astrophysical Interest: I, Table of J\\ultiplets; II, Finding List, Contrib. Princeton Univ. Obs, 20, 1945. Paschen, F., and R. Gotze: "Seriengesetze der Liniensprektren," 154 pp., Springer-Verlag OHG, Berlin, 1922. This and the similar book by Fowler, though now largely out of date nevertheless contain material on the simpler spectra not found conveniently anywhere else.

7f. X-Ray Wavelengths and Atomic Energy Levels I. A. BEARDEN AND J. S. THOMSEN

The Johns Hopkins University

Tables 7f-1 and 2 list the wavelengths of virtually all experimentally observed X-ray emission lines (excluding satellites) and absorption edges. These are taken from a review by J. A. Bearden [1] and are expressed in terms of the A* unit, which is defined [2] in terms of the W Kcx1line by setting Xw Kal = 0.2090100 A*. This figure was chosen to make the A* unit as close to unity as possible i the difference was then estimated to be zero with a probable error of 5 ppm (parts per million). However the conversion factor must remain an experimentally determined quantity. A number of prominent X-ray reference lines (Or KCX2' Cu KCXl, Mo Kat, and Ag KCXl) were carefully remeasured in terms of the W KCXl standard [3]. An extensive survey of all experimental X-ray wavelength measurements was made, and the necessary corrections have been applied, as far as possible, to put each one on a basis consistent with the above set of reference values. When two or more values of comparable accuracy were available for the same wavelength, appropriate weighted averages were taken. The same procedure was followed with absorption edges. In all cases estimated probable errors were included. A thorough recheck of the five reference lines is currently in progress. It now appears that at least one of the crystals used in the original work [3] contained significant imperfections. As a result of this redetermination some of the reference wavelength ratios may be shifted by as much as 10 ppm. Furthermore, a recent reevaluation of the atomic constants by Taylor et al, [4}, which includes the highly

7-97 between A'"

X-RAY WAVELENGTHS AND ATOMIC ENERGY LEVELS

precise a-c Josephson effect work, indicates that the conversion factor units and angstroms may differ from unity by about 20 ppm. As a result of these two developments most of the wavelengths listed below must be considered to have probable errors of no less than 10 ppm in terms of A'" units and perhaps somewhat larger errors in terms of angstroms. Bearden and Burr [5] combined the emission line data of this table with the photoelectron measurements of Hagstrom, Nordling, and Siegbahn [6] to obtain a revised set of X-ray atomic energy levels. A separate least-squares adjustment was carried out for each element to obtain the values most consistent with all available data. The results are given below in Table 7f-3. While the reviews [1,5] cited above outline the general principles of the wavelength and energy-level evaluations, full details are found only in the original separately published reports [7,8]. These must be consulted for references to all of the original papers used and for details of the procedures employed in the evaluations. References

1. Bearden, J. A.: Rev. Mod. Phys. 39, 78 (1967). 2. Bearden, J. A.: Phys. Rev. 137, B455 (1965). 3. Bearden, J. A., A. Henins, J. G. Marzolf, W. C. Sauder, and J. S. Thomsen: Phys. Rev. 135, A899 (1964). 4. Taylor, B. N., W. H. Parker, and D. N. Langenberg: Rev. Mod. Phys. 41,375 (1969). 5. Bearden, J. A., and A. F. Burr: Rev. Mod. Phys. 39, 125 (1967). 6. Hagstrom, S., C. Nordling, and K. Siegbahn: "Alpha-, Beta-, and Gamma-ray Spectroscopy," vol.l, p. 845, K. Siegbahn, ed., North-Holland Publishing Company, Amsterdam, 1965. 7. Bearden, J. A., and collaborators: X-ray Wavelengths, AEC Rept. NYO-10586, 1964. Price $8.45. (Available from Clearinghouse for Federal Scientific and Technical Information, National Bureau of Standards, U.S. Department of Commerce, Springfield, Va. 22151.) 8. Bearden, J. A., and A. F. Burr: Atomic Energy Levels, AEC Rept. NYO-2543-1, 1965. Price $6.00. (Available from Clearinghouse for Federal Scientific and Technical Information, National Bureau of Standards, U.S. Department of Commerce, Springfield, Va. 22151.)

TARLE

7f-1.

X-RAY WAVELENGTHS IN

A*

UNITS AND IN

-:J

KEV

I

'-0 00

Designation

Wavelength,

p.e.f

keY

Wavelength,

A*

keY

Designation

A* 3 Lithium

a KL

p.e.f

keY

p.e.f

A* 4 Beryllium

I 1 I 0.0543 114

228

Wavelength,

I 1

5 Boron

I

I

6 Carbon

{31 LIIM rv l LrrrM r al,2 LrIlMrv,v

p.e.f

keY

A*

21 Scandium (Cont.)

0.1085

Wavelength,

31.02 35.59 31.35

I

2 3 3

I

0.3996 0.3483 0.3954

22 Titanium (Cont.)

27.05 31.36 27.42

I

2 2 2

I

0.4584 0.3953 0.4522

>8 o ~

l-I

(1

a KL

67.6

I 3 I 0.1833

44.7

I 3 I 0.277 80xy(}en

7 Nitrooen.

23 Vanadium a2 KLII

KLrrr {31,3 KMrr.IIr {35 KMyv,y {33.~ LrMn,ur n LrrMr {31 LnMrv l Liu Ms al,2 LrIlMlv,v Mu,rIlMrv, v al

a KL

31.6

I 4

I

0.3924

23.62

9 Fluorine al,2 Kl.u.iu {3 KllJ

18.32

I

2

10 Neon

0.6768

I

11 Sodium al,2 KLII,YII {3 KM Lrr.IIyM LrLrr,III

11.9101 11. 575 407.1 376

I

9 2 5 1

I

a2 KLu

KLuy {3 KM Lrr,rrr LrLrLur

8.34173 8.33934 7.960 171. 4 290

9 9 2 5 1

14.610 14.452

I

3 5

0.8486

I 0.8579

12 Mtumesium.

1. 0410 9.8900 1. 0711 9.521 0.03045 251.5 0.0330 317

13 Aluminum

al

I 3 I 0.5249

1.48627 1. 48670 1.5574 0.0724 0.0428

2 2 5 1

1.25360 1.3022 0.0493 a2 KLII 0.0392 al KLrrr I {3I,3 KMrr,ur {3~ KMyv,y 14 Silicon {33,4Lr Mu,m 7.12791 9 1.73938 Tf LuMr 7.12542 9 1.73998 {31 LIIMyv 6.753 1 1.8359 l LmM y 135.5 4 0.0915 al.2 LrryMyv.v Mu.IIrkfrv, v

I

2.50738 2.50356 2.28440 2.26951 21. In 27.34 23.88 27.77 24.25 337

2 2 2 6 9 3 4 1 3 9

4.94464 4.95220 5.42729 5.4629 0.585 0.4535 0.5192 0.4465 0.5113 0.037

24 Chromium

2.293606 2.28970 2.08487 2.07087 18.96 24.30 21.27 24.78 21.64 309

3 2 2 6 2 3 1 1 3 9

5.40551 5.41472 5.94671 5.9869 0.654 0.5102 0.5828 0.5003 0.5728 0.040

>~ t;

~

o

e-

trl

(1

Lj

t"'

>-

~

'"d

::r:

~

25 AI anqanese

2.10578 2.101820 1. 91021 1.8971 17.19 21.85 19.11 22.29 19.45 273

2 9 2 1 2 2 2 1 1 6

5.88765 5.89875 6.49045 6.5352 0.721 0.5675 0.6488 0.5563 0.6374 0.045

to

26 Iron

1.939980 1.936042 1.75661 1. 7442 15.65 19.75 17.26 20.15 17.59 243

9 9 2 1 2 4 1 1 2 5

l-I

(1

6.39084 6.40384 7.05798 7.1081 0.792 0.628 0.7185 0.6152 0.7050 0.051

c:

a2

KLII

al KLnl

{3KM {31 KM {3z KM Ln.IIIM l, fJ Ln.mMI

6. ieor 6.f57t 5.796

1 1 2 4

103.8

2.0127 2.0137 2.13'90

5.37496 5.37-216

8 7

2.30664 a2 KLn 2.30784 al KLIII

5.0316 5.0233

2 3

2.4640 2.4681

0.1194 3

4.7307 4.7278 4.4034

1 1 3

2.62078 2.62239 2.8156

9 9

0.1841 0.1826

{31,3 KMn,nl

TJLIIMI

l LmMI

67.33 6:.90

19 Potassium KLn al KLm a2

{31.3 KMn,lIr {35 KMrv,v

LnMr

TJ

3.7445 3.7414 3.4539 3.4413 47.24

2 2 2 4 2

{31

l

Lttt M:

al.2 LruMrv,v Mn,urNr

1

47.74

9

692

3.3111 3.3138 3.5896 3.6027 0.2625

a2

KLn

al KLrn {31,3 KMn,nr {35 KMrv,v

11 LrrMr

1 1 2 3 2

4.19474 4.19180 3.8860 55.9t 56.3t

4.0861 4.0906 4.4605 4.4865 0.3529

LnMI 13'1 LnMlv 1 LmMI

5 5 2 1 1

al.2 LlnMlv.v

2.95563 MII,lIIMIV,v 2.95770 3.1905 0.2217 0.2201

KLn al KLIII e, KMII a2

{31,3 KMn,ln {32 KNn,II 20 Calcium {35 KMlv,v 3.68809 (33,4 Lr M n .1I 3 3.36166

3.35839 3.0897 3.0746 40.46 35.94 0.25971 40.96 36.33 0.0179 525

21 Scandium

3.0342 3.0309t 2.7796 2.7634 35.13

0.1487

18 Argon

17 Chlorine KLn al KLln {3KM a2

{31.3 KM n. n l {35 KMlv.v {33,4 LIM n.III TJ

83.4

22

2.75216 2.74851 2.51391 2.4985 30.89

3 2 3 2 2 2 2 9

28 Nickel

27 Cobalt

16 Sulfur

15 Phosphorus

3.69168 4.0127 4.0325 0.3064 0.3449 0.3027 0.3413 0.0236

TJ LnMr 8 1 LuMlv 1 LmMI

al,2 LnlMrv, v

MlI,ruMrv,v

a2

KLn KLrn KMn KMm KNn,m KMrv,v LrMn LrMm

al {33 Titanium {31 4.50486 {32 2 4.51084 {35 2 4.93181 {34 2 4.9623 {38 2 0.4013 {33.4 LrMn,rn 3

1.792850 1.788965 1.62079 1. 60891 14.31 17.87 15.666 18.292 15.972 214

9 9 2 3 3 3 8 8 6 6

6.91530 6.93032 7.64943 7.7059 0.870 0.694 0.7914 0.6778 0.7762 0.058

2 2 1 9

8.02783 8.04778 8.9029 8.90529

8.9770 1.38109 3 1.0228 12.122 8 0.832 2 14.90 0.9498 3 13.053 0.8111 15.286 9 0.9297 3 13.336 0.072 3 173 31 Gallium 1.34399 1.340083 1.20835 1.20789 1.19600 1.1981 10. 359t

8 8 8 4 1 3

6 9 3 2

7.4608 9 7.4781 5 8.2641: 6 8.3281: 0.941 0.762 0.8688 0.7427 0.851~

0.065]

1 9 5 2 2 2

9.22482 9.25174 10.2603 10.2642 10.3663 10.348

8

1.197

1.439000 1. 435155

8 7

9 9 9 2 2 1 2 2

I

~ ~

~

~ trj

tr.j

8.615i 8 Z 8. 638~ 6 0

t-3

9.572( 2 1.29525 9. 658( 2 1.28372 1 9.6501 1.2848 7 1.107( 11. 200 2 13.68 0.906 3 1.034i 11. 983 2 0.884 14.02 3 1. 011i 12.254 3 0.079 157 32 Germanium 1. 258011 1.254054 1.12936 1.12894 1. 11686 1.1195 9.640 9.581

~

e-

30 Zinc

29 Copper

1.544390 1.540562 1.3926 1.392218

1. 661747 1. 657910 1.500135 1.48862 13.18 16.27 14.271 16.693 14.561 190

9. 855~ 9.8864 10. 978( 10.982] 11. 100~ 11.074t 1. 286] 1. 294]

t The probable error (p.e.) is the error in the last digit of wavelength. Designation indicates both conventional Siegbahn notation (if applicable) and transition, e.g., 111 Lu Mtv denotes a transition between L1I and Mi» levels, which is the LlJi line in Siegbahn notation. t This is an interpolated value. In some instances, no experimental values were available; in others, experimental measurements appeared clearly inconsistent with other data, as indicated by a Moseley diagram.

:Il tn

>

Z

t:1

> t-3 o

a:: '"'1

o

trj

Z trj

::0

o

~

t"4

trj ~ trj

t"4 tn ~

I

~

TABLE

7f-1.

X-RAY

WAVEL}~NGTHS IN

A*

UNITS AND IN KEV

~

(Continued)

f--'

o

Designation

Wavelength,

p.e.f

keY

31 Gallium (Cont.) 7J LnMr

l LmMr al.2

Iau Msv,v

12.597 11. 023 12.953 11. 292

I

0.9842 1. 1248 0.9572 1.09792

2 2 2 1

33 Arsenic

a2 KLrr KLrn KMn KMm KNrr,m KMrv,v /33,4 LrMn,IIr TJ LnMr /31 LIIMrv l u;«. al,2 Lnr1lfrv,v MvNrrr

al

/33 /31 /32 /35

1. 17987 1. 17588 1. 05783 1.05730 1.04500 1.0488 8.929 10.734 9.4141 11. 072 9.6709

1 1 5 2 3 1 1 1 8 1 8

a2 KLrr KLrrr /33 KMII /31 KMm /32 KNn,IIr /35 KMrv,v {34 KNrv,v

keY

Designation

1.04382 1.03974 0.93327 0.93279 0.92046 0.9255

2 2 5 2 2 1

11.8776 11. 9242 13.2845 13.2914 13.4695 13.396

Wavelength,

p.e.']

keY

A*

11. 609 10.175 11.965 10 .4361 34

36

0.9841 0.9801 0.8790 0.8785 0.8661 0.8708 0.8653

1.0680 MrM rn 2 1 1. 2185 MirMrv 4 1. 0362 MIINr 1.18800 .MmMrv.v 8 MIIrN r S2 MrvNII Selenium MrvN m S2 ll-1 rvNn,IIr 11.1814 Sl MvNm 2 2 11. 2224 12.4896 5 12.4959 3 12.6522 a2 KLrr 5 al KLrn 1 12.595 /33 1.490 9 1 1.2446 /31 KMm 1.41923 /32 KNrr,rII 5 1.2044 /35 KMrv.v 1 1.37910 /34 KNrv.v 5 0.0538 /34 Li Ms: 2 /33 LrMnr )'2,3 LrNII,rII Krypton TJ LrMr /31 LrIIMrv 1 12.598 )'5 LIINr 1 12.649 )'1 Lu Ntv 1 14.104 l Lui M: 1 14.112 a2 LrrrMrv 1 14.315 al Lr.rMv 2 14.238 /36 Ltu Ns 14.328 2 {32,15

xu«

144.4 91. 5 57.0 96.7 59.5 127.8 126.8 128.7

Wavelength,

o p.e.f

keY

A*

37 Rubidium (Cont.)

32 Germanium (Cont.)

10.50799 1. 10882 10.54372 1.10477 0.99268 11. 7203 11.7262 0.99218 11.8642 0.97992 11. 822 0.9843 1.3884 8.321t 1.1550 9.962 8.7358 1. 3170 1.1198 10.294 1.2820 8.9900 230

35 Bromine al

p.e.']

A*

A*

/31 LnMrv

Wavelength,

38 Strontium (Cont.)

3 2 2 2 2 2 2

0.0859 0.1355 0.2174 0.1282 0.2083 0.0970 0.0978

85.7 51.3 91.4 53.6

2 1 2 1

0.1447 0.2416 0.1357 0.2313

2

108.0 0.0964 108.7

2 1

0.1148 0.1140

39 Yttrium

1 1 3 2 4 1 5 3 3 3 3 3 3

14.8829 14.9584 16.7258 16.7378 17.0154 16.879 17.036 2.0600 2.0722 2.3468 1.76095 1.99584 2.1102

7.3563 6.4558 6.4488 6.0942

3 3 2 3

1.68536 1. 92047 1.92256 2.0344

a:: H

o

>-

0.79015 0.78593 0.70228 0.70173 0.68993 0.6959 0.68901 5.6681 5.6330 4.9536 6.6069 5.8360 5.4977 5.3843 6.9185 6.0778 6.0705 5.7101 5.5863

1 1 4 3 4 1 5 3 3 3 3 3 3 3 3 3 2 3 3

Z

t1

a::

o

40 Zirconium

0.83305 0.82884 0.74126 0.74072 0.72864 0.7345 0.72776 6.0186 5.9832 5.2830 7.0406 6.2120 5.8754

>-

1-3

o

~

15.6909 15.7751 17.654 17.6678 17.970 17.815 17.994 2.1873 2.2010 2.5029 1.87654 2.1244 2.2551 2.3027 1.79201 2.0399 2.04236 2.1712 2.2194

tr.J

o d

~

>-

::d

"d ~ ~

UJ H

o

UJ

e, io;« (3. LrMnr (33,4 LrMn,rII

LIIMr (31 LnMrv 1'5 l Ltn M: al.2 Ltu Miv,» 'TJ

7.304 7.264 9.255 8.1251

9 1 5

1.596 1..3396 1.52590

9.58J> 8.3746

1 5

1.2935 1.48043

3 3 3 2 3 3 2 3 2

0.0672 0.0753 0.1133 0.1613 0.1089 0.1554 0.06488 0.0654 0.06437

7.767f

(36

LIINnr MyM II MrMIIr MnMrv MnNr MnrMrv.v f2 MrvNn MrvNnr rl MvNnr

184.6 164.7 109.4 76.9 113.8 79.8 191.1 189.5 192.6

37 Rubidium a2KLn al KLrn (33 KMn (31 KMm fJ2 KNn,nr fJ. KMyv.v (34 KNrv,v (34 LrMn (33 LrMnr 1'2.3 Lt Nti.ut 11 LnMr (31 LnMrv 1'5 LnNrv l LmMr a2 LruMrv al LyuMv (36 LmNr

0.92969 0.925553 0.82921 0.8286S 0.81645 0.8219 0.8154 6.8207 6.7876 6.0458 8.0415 7.0759 6.7553 8.3636 7.3251 7.3183 6.9842

1 9 3 2 3 1 2 3 3 3 4 3 3 4 3 2 3

13.3358 13.3953 14.9517 14.9613 15.1854 15.085 15.205 1. 81771 1.82659 2.0507 1. 54177 1. 75217 1.83532 1.48238 1.69256 1. 694-13 1. 77517

5 5

1.697 1.707

7.576: 7.279

3 5

1.6366 1.703

7.817: 7.510 7.250

3 4 5

1.5860 1. 6510 1.710

38 Strontium

0.87943 0.87526 0.78345 0.78292 0.77081 0.7764 0.76989 6.4026 6.3672 5.6445 7.5171 6.6239 6.2961 7.8362 6.8697 6.8628 6.5191

1 1 3 2 3 1 5 3 3 3 3 3 3 3 3 2 3

14.0979 14.1650 15.8249 15.8357 16.0846 15.969 16.104 1.93643 1. 94719 2.1965 1.64933 1. 87172 1.96916 1.58215 1.80474 1.80656 1. 90181

MlIMrv MnNr MrIIMv AlnrNr MmMrv.v t Mrv.vNtr,nr M rv, vOn.rII

81.5 46.48

2 9

0.1522 0.267

48.5 86.5 9"3.4

2 2 2

0.256 0.1434 0.1328

41 Niobium a2 KLn al KLlIr {33 KM II {31 KM nr {32 II {32 KNn,yn {34 KNrv.v {35II KMrv {35 r KMv {34 KNrv.v {34 LrMn {33 LrM nr 1'2.3Lr Nn.nr 11 LnMy {31 Lu Msv 1'5 LnNr 1'1 LnNrv l LmMr a2 LnrMyv al LnrMv {36 {32.15 Liu Niv,v MnMrv MnNy MnN rv MIl r A-I v MurNy l' MmNrv, v t Myv,vNn,nr Mrv,vOn.nr

u.»,

1 1 3 2

16.5210 16.6151 18.6063 18.6225

0.65416 0.65318

4 5

18.953 18.981

3 3 2 3 3 3 3 3 3 2 3 3 3 3 2 2 2 2 9 2

2

0.1617

80.9

3

0.1533

82.1 70.0

2 4

0.1511 0.177

42 AIolybdenum

0.75044 0.74620 0.66634 0.66576

5.3455 5.3102 4.6542 6.2109 5.4923 5.1517 5.0361 6.5176 5.7319 5.7243 5.3613 5.2379 72.1 38.4 33.1 78.4 40.7 34.9 72.19 61.9

76.7

0.713590 0.709300 0.632872 0.632288 0.62107 0.62099

0.62708 0.62692 0.62001 2.3194 5.0488 2.3348 5.0133 4.3800 2.6638 1.99620 5.8475 2.2574 5.17708 2.4066 4.8369 2.4618 4.7258 1.90225 6.1508 5.41437 2.1630 2.16589 5.40655 5.0488 2.3125 4.9232 2.3670 0.1718 68.9 0.323 35.3 0.375 0.1582 74.9 0.305 37.5 0.356 0.1717 64.38 0.2002 54.8

6 1 9 9 5 2 5 5 9 3 3 2 3 8 2 2 3 8 8 5 2 2 3

17.3743 17.47934 19.5903 19.6083 19.963 19.9652 19.771 19.776 19.996 2.4557 2.4730 2.8306 2.1202 2.39481 2.5632 2.6235 2.01568 2.28985 2.29316 2.4557 2.5183 0.1798 0.351

1 2

0.1656 0.331

7 2

0.1926 0.2262

~ I

~

> ~

~

~ ~

t""

t'j

Z

4)

'"3

:I:

Ul

>

Z

t:::I

> 8 o

a= H

o t'j

Z

l"'.1

::tl

4) ~

e~

~

l"'.1 t""

Ul

-:J

I

~

o

~

TABLE

Designation

Wavelength.

p.e.']

7£-1.

keV

A*

Wavelength.

A*

keV

p.e.']

UNITS AND IN KEV

Designation

A*

43 Technetium

0.67932t 0.67502t 0.60188t 0.6013ot 0.59024t

3 3 4 4 5

18.2508 18.3671 20.599 20.619 21. 005

III

4.8873t

5. 1148t

8

3

2.5368

2.4240

tv.v

,v t.nr II

45 Rhodium a

X-RAY WAVELENGTHS IN

0.6176301 4 0.613279 4

I 20.0737 20.2161

Wavelength.

(Continued)

p.e.f

keV

A*

44 Ruthenium 0.647408 0.643083 0.573067 0.572482 0.56166 0.5680 0.56785 0.56089 4.5230 4.4866 3.8977 5.2050 4.fi2058 4.2873 4.1822 5.5035 4.85381 4.84575 4.4866 4.3718 62.2 32.3 25.50 68.3 26.9 52.34 44.8

5 4 4 4 3 2 9 9 2 3 2 2 3 2 2 3 7 5 3 2 1 2 9 1 1 7 1

19.1504 19.2792 21.6346 21.6568 22.074 21. 829 21.834 22.104 2.7411 2.7634 3.1809 2.38197 2.68323 2.8918 2.9645 2.2528 2.55431 2.55855 2.7634 2.8360 0.1992 0.384 0.486 0.1814 0.462 0.2369 0.2768

LrNIT )'3 LrNrn

)'2

LTTMr {31 LTTM rv )'!, LuNr )'1 LIIINlv l Lrrr1VIr az LrrrAfrv 7]

al

LrTTMv

{36 Lin N: {3z.15 LruNlv.v {310 LIM IV (39 LIM v

MrNu,rTT MTTMrv MTTNI MrrN l v .MmAfv ]vImNr

)' MTTINrv, v MrvOlI,Iu .I M IV, vNn,m MvN I MvO m

Mrv. vOn,TTI

p.e.']

keV

tV

A*

0.48598 3.87023 3.83313 3.31216 3.30635 4.4183 3.93473 3.61638 3.52260 4.7076 4.16294 4.15443 3.80774 3.70335 3. ei iss 3.60497 18.8 54.0

3 5 9 9 9 2 3 9 4 2 5 3 9 3 9 9 2 1

20.66 60.5 26.0 21.82

7 1 1 7

39.77 24.4

7 2

33.5

3

48 Cadmium (Cant.) 25.512 3.20346 3.68203 9 3.36719 3.23446 3.64495 9 I 3.40145 3.7432 2 3.1377 3.9513 3.7498 2.8061 4.19315 9 2.95675 3.15094 3.73823 4 3.31657 3.42832 3.42551 9 3.61935 3.51959 3.33564 6 3.71686 2.6337 4.48014 9 2.76735 2.97821 3.96496 6 3.12691 2.98431 3.95635 4 3.13373 3.25603 3.61467 9 3.42994 3.34781 3.51408 4 3.52812 3.43287 3.4367 2 3.6075 3.43917 3.43015 9 3.61445 0.658 0.2295 52.0 2 0.2384 22.9 2 0.540 0.600 19.40 7 0.639 0.2048 58.7 2 0.2111 0.478 24.5 1 0.507 0.568 20.47 7 0.606 1 30.4 0.408 0.3117 36.8 1 0.3371 0.509 30.8 1 0.403 0.370

1,9 Indium

I 21.0201 I az 21.1771

~

o

47 Silver (Cant.) {34 KNrv,v {34 LrMIT {33 LrMm

I,B Palladium

0.5898211 3 0.585448 3

~ Wavelength,

al

KLTT KLm

0.5165441 3 0.512113 3

I 24.0020

24.2097

50 Tin

0.4950531 3 0.490599 3

I 25.0440 25.2713

...,~ o

~ H

o ~

Z

tj

~

o

r-

M

o

Q t" ~

::0 '"d

P:: ~

tn H

o

in

63 61

KMII KM IlI

62II KNu 62 KNILIlI (3.u KM r v (3.r KM v

(34

KN rv. v

0.546200 0.545605 0.53513 0.5:3.5e);3 0.54118 0.54101 0.5:34J1

4 4 5 2 9 9 9

4.2888 4.2522 3.6855 4.9217 4.37414 4.0451 :3.9437 5.2169 4.G0545 4.59743 4.2417 4.1310

2 2 2 2 4 2 2 :3 9 9 2 2

(3. KllJrv,v (34 LrMu (33 LrllIIII

Y2,a LINrLIII rt L"A!I (31 LIIMIV

1'5 L"NI 1'1 L"Nrv ~ LrII1IJ, ~2 LrrrAIrv ~1 LIlIA[ V (36

u.»,

(32,1" LrIINIV. V 610 LI1Y!IV (39

LIM v

MrN".rII MIIM rv M"Nr MIIN r v MuM v

MIIINI )' lY[IlI Nrv.v r Mrv.vNll.III M r v, VOII.III

59.3 28.1

1 2

65.5 29.8 25.01 47.67 40.9

1 1 9 9 2

22.0089 22.7236 23.168 23.1728 22.9Of) 22.917 23.217

0.521123 0.520520

4 4

123.7911 23.8187

0.510228

4

24.2991

(32 KN II. III KOILIrr .B5 1r KM I V (35 1

0.5093 0.51670 4.0711 2.8908 2.9157 4.034G 3.4892 3.3640 2.5191 4.6605 2.83441 4.14622 3.8222 3.0650 3.14:38 3.7246 2.3765 4.9525 2. ()9205 4.37588 2.69674 4.36767 4.0162 2.9229 3.90887 3.0013 3.7988 3.7920 20.1 0.2090 56.5 0.442 26.2 22.1 0.1892 62.!J 0.417 27.9 0.496 23.:H 0.2601 43.6 0.303 37.4

47 Silver

{33 KMII (31 J(M IlI

2 9

2 2 2 2 5 2 2 3 7 5 2 4 2 2 2 1 2 1 1 1 1 1 2

24.346 23.995 3.0454 3.0730 3.553:3 2.6603 2.99022 3.2437 3.3287 2 ..5034 2.83:329 2.83861 3.0870 3.17179 3.2637 3.2696 0.616 0.2194 0.474 0.560 0.1\)70 0.445 0.5:31 0.2844 0.332

KM v (34 KN 1v. v (34 Lrlv!,r (33 L,M IlI

)'2.aLr NrLI,r )'~ LrOlI."1

LlIMI ,.BILlI Mrv )'5 L"N, )'1 LIIl'VrV l LJlIM, 0'2 LrIlMrv 0'1 L"r A! V (36 Liu N: 7J

(32.15 LIIrNrV.V (37 LIlIa' (310 LrMIV (39 LrMv

0.455181 0.454545 0.44500 0.44374 0.45098 0.45086 0.44393 :3.50697 3.46984 2.9800 2.9264 3.98:327 :3.555:31 3.24907 3. lG213 4.26873 3.78073 3.77192 3.43606 3.33838 3.324 3.27404 3.26763

4 4 1 3 2 2 4 9 ~

2 2 9 4 9 4 9 6 4 9 3 4 9 9

27.2377 27.2759 27.8608 27.940 27.491 27.499 27.928 3.5353 3.5731 4.1605 4.2367 3.11254 3.48721 3.8159 3.92081 2.90440 ~> • 27929 3.28694 3. (j0823 3.71:381 3.730 3.7868 3.7942

M"M,v lV!IINI M"Nr v MIlIM v MmNr

)' MmNIV.V ilhvOrLIIr r khv.V NII.1lI Jl;[ vallI

(33 (31 (32 (3.

KM II KMIlI KNII,III KM r v. v

0.563798 0.5594075 O. 4~)7685 0.497069 0.487032 0.49306

4 6 4 4 4 2

5 5 8 3 3 3 3 9 3 2 2 9 3 9 3 9 4 3 9 3 3 9 9 1 1 5 1 1 5 1 9 1

28.4440 28.4860 29.1093 29.195 28.710 28.716 29.175 3.7083 3.7500 4.3768 4.4638 3.27234 3.66280 4.0192 4.13112 3.04499 3.43542 3.44398 :3.7926 3.90486 3.9279 3.9716 3.9800 0.2621 0.619 0.733 0.2287 0.575 o. e91 0.491 0.397 0.483

48 Cadmium 51 Antimony

Cl'2 KLII Cl'1 J(LrII

0.435877 0.435236 0.425915 0.42467 0.43184 0.43175 0.42495 3.34335 3.30585 2.8327 2.7775 3.78876 3.38487 3.08475 3.00115 4.07165 3.60891 3.59994 3.26901 3.17505 3.1564 3.12170 3.11513 47.3 20.0 16.93 54.2 21. 5 17.94 25.3 31.24 25.7

21. 9903 22.16292 24.9115 24.9424 25.4564 25.145

0.539422 0.535010 0.475730 0.475105 0.4G5328

3 3 5 6 7

22.9841 23.1736 26.0612 26.0955 26.6438

KLII KLrII KM II KM m (32 KNII.III 0'2 0'1 (33 (31

0.474827 0.470354 0.417737 0.417085 0.407973

3 3 4 3 5

26.1108 26.3591 29.6792 29.7256 30.3895

52 Tellurium

0.455784 0.451295 0.400659 0.399995 0.391102

3 3 4 5 6

27.2017 27.472:3 30.9443 30.9957 31.7004

~ I

~

>-~

~

~

t":l

e-

t":l

Z

Q

8

~

[f)

>Z

t:t

>8 o ~ ,...

o

tr1

Z

tr1 ~

Q

~

t"l t":l

-

Z

t:'~

o

rl"!j

(1

q

r-

>-

~

"i:l

:I: ~

....

rJ2 (1

rJ2

53 Iodine az al {33 {31

e,

KLII KLuI KMIT KMIlI

KNII,ur {34 LrMIT {33 LrMIlI /'2.3 LrNrI.IIr /'4 LrOII.IIr ." LIIMr {31 LIlMIv /'0 /'1

LIl N[ LITNIV

l LIIIM I az LITrJ,[rv o i LIUMV {36 LmNI {32,loLIIINrv.v {37 LIlIOI {3JO LOlli V {39 LIMV

0.437829 0.433318 0.384564 0.383905 0.37523t 2.91207 2.87429 2.4475 2.3913 3.27979 2.93744 2.65710 2.58244 3.55754 3.15791 3.14860 2.83672 2.75053 2.7288 2.72104 2.71352

7 5 4 4 2 9 9 2 2 9 6 9 8 9 6 6 9 8 3 9 9

54 Xenon

28.3172 28.6120 32.2394 32.2947 33.042 4.2575 4.3134 5.0657 5.1848 3.7801 4.22072 4.6660 4.8009 3.48502 3.92604 3.93765 4.3706 4.5075 4.5435 4.5564 4.5690

0.404835 0.400290 0.355050 0.354364 0.34611

2.6666 2.6285 2.2371 2.2328

4 4 4 7 2

2 2 2 2

2 2 2 2 3

29.458 29.779 33.562 33.624 34.415

30.6251 30.9728 34.9194 34.9869 35.822

4.6494 4.7167 5.5420 5.5527

e»

KM rv

{3oI KM v {34 KNrv,v {34 LrMIT {33 LrMIII /'2 LINII /'3 LINur /'4 LIO IL rII ."LIIM I {31 LuM IV /'0 Lu Ni /'1 LuN rv /'8 LITOr

3.0166t

2

4.1099

l LIIIM r az L III 11if r v al LIITM v {36 LIIINr {32,10 Liu Niv,v {37 LmOr {310 LrMrv

{39L IM v 56 Barium

55 Cesium a2 KLIT al KLITr {33 KM IT {31 KM m {32 KNu,IIr KOrLrrr {33 Il KM rv {3or KM v {34 KNrv,v {34 LIM u {33 LrMrrr /'2 LIN II /'3 L I llf ITr

0.42087t 0.41634t 0.36941t 0.36872t 0.36026t

{32 KNrr,III KOu,m

0.389668 0.385111 0.341507 0.340811 0.33277 0.33127 0.33835 0.33814 0.33229 2.5553 2.5164 2.1387 2.1342

5 4 4 3 1 2 2 2 2 2 2 2 2

/' MITrNrv.v {3 MrvNvr

SMVNIII a MvNvI.VII M VOIT,III

31.8171 32.1936 36.3040 Ns», vOu.IIr 36.3782 37.257 37.426 36.643 la2 KLII 36.666 al KLur 37.311 {33 KM II 4.8519 {31 KM m 4.9269 {32 KNII,m 5.7969 {34 Lr M rr 5.8092 {33 LrMm

0.3201171 0.31864 0.32563 0.32546 0.31931 2.4493 2.4105 2.0460 2.0410 1.9830 2.740 2.45R91 2.2056 2.1418 3.006 2.67533 2.66570 2.3790 2.3030 2.275 2.290 2.282 12.08 14.51 19.44 14.88 152.6

7 2 2 2 2 3

3 4 4 4 3 5 4 3

38.7299 38.909 38.074 38.094 38.828 5.0620 5.1434 6.060 6.074 6.252 4.525 5.0421 5.621 5.7885

3 5 5 4 3 3 3 3 4 5 5 5

4.124 4.63423 4.65097 5.2114 5.3835 5.450 5.415 5.434 1.027 0.854 0.638 0.833

6

0.0812

59 Praseodymium

0.30816 0.30668 0.31357 0.31342 0.30737 2.3497 2.3109 1.9602 1.9553 1. 8991 2.6203 2.3561 2.1103 2.0487 2.0237 2.8917 2.5706 2.5615 2.2818 2.2087 2.1701 2.1958 2.1885 11. 53 13.75 18.35 14.04 14.39 144.4

1 2 2 2 2 4 3 3 3 4 4 3 3 4 4 4 3 2 3 2 2 5 3 1 4 4 2 5 6

40.233 40.427 39.539 39.558 40.337 5.2765 5.3651 6.3250 6.3409 6.528 4.7315 5.2622 5.8751 6.052 6. 126 4.2875 4.8230 4.8402 5.4334 5.6134 5.7132 5.646 5.6650 1. 0749 0.902 0.676 0.883 0.862 0.0859

60 Neodymium

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Z

tj

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o

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o

t'i

Z

t"1 :::0

o

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0.348749 0.344140 0.304975 0.304261 0.29679 2.2550 2.2172

2 2 5 4 2 4 3

35.5502 36.0263 40.6529 40.7482 41. 773 5.4981 5.5918

0.336472 0.331846 0.294027 0.293299 0.286It 2.1669 2.1268

2 2 3 2 1 3 2

36.8474 37.3610 42.1665 42.2713 43.33 5.7216 5.8294

t;

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Z

o

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e-

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P:1

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m

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o

U2

LrOrv,v L[[M[[ {j17 LrrM[[I LrrMv LrrNn

Lu Niu.

u.«,

v LrrNvI LrrO rr LrrOm t LmM rr 8 LUIMrrI Ltu Nis LmN[[I u LlrrNvr.V[[ LmOrr,Irr

sc.s«.

MrOlI,Irr MrrN r MrrNrv Mvu N: MrrrNlv "y MrrrNv MrrrO r M[[rOIV,V f2 MlvNn MIVNrrI {j MIVNvI MlvO n ft MvNm a MvNvr.vrr a2 MvNVI at MvNvrr MvOrrI NrrNIV NIVNvI NvNvr. VII NvN v1 NvN v II

1.06192 1.43048 1.3864 1. 31897 1. 1600 1.1553 1.13687 1. 1158 1. 11789 1. 11693 1.67265 1. 61264 1. 3167 1.3086 1. 25778 1.2601 5.40 5.570 7.612 6.353 6.312 5.83 5.67 9.330 8.90 7.023 7.09 9.316 7.252 7.30 58.2 61.1

9 9 1 9 2 1 9 1 9 9 9 9 1 1 4 3 2 4 9 5 4 2 3 5 2 1 2 4 1

11.6752 8.6671 8.9428 9.3998 10.688 10.7316 10.9055 11.1113 11. 0907 11.1001 7.4123 7.6881 9.4158 9.4742 9.8572 9.839 2.295 2.226 1.629 1.951 1.964 2.126 2.19 1.3288 1.393 1.7655 1.748 1.3308 1.7096

2

1.700

1 2

0.2130 0.2028

1.0250

2

12.095

1. 3387 1.2728 1.1218 1. 1149

2 2 3 2

9.261 9.741 11. 052 11.120

1.0771

1

11.510

1.0792 1.6244 1.5642 1.2765 1.2672 1.21868 1. 2211 5.172 4.44 6.28 5.357 7.360 6.134 6.092 5.628

2 3 3 2 2 5 9 2 2 4 8 4 3 8

11. 488 7.632 7.926 9.712 9.784 10.1733 10.153 2.397 2.79 1.973 2.314 1.684 2.021 2.035 2.203

8.993 8.573 6.757 6.806 8.91)2

5 8 1 9 4

1.3787 1.446 1.8349 1.822 1.3835

6.992 6.983 7.005 54.0 55.8

2 1 9 2 1

1. 7731 1. 7754 1.770 0.2295 0.2221

59.5 58.4

3 1

0.208 0.2122

2

{jtO LrMrv {j9 LIM v LINI LINIV 1'1tLI NV LIOr LIOlv.v LrrMrr {j17 Lu Mv: Lti M» LrrNrr LIINrrI v LrrN v I LuOm t Lm.Mrr 8 LlrrMlrr LmNI

Lni Niu u Lns Nv i, vrr MrN m Mrr N r MrrNlv MmNr MrrINlv I'MrrrNv r2 MnrNrr MrvN m {j MIVN v I rt MvNlrr a Mv Nvi.vsi NIVNVI

1.17218 1. 16487 1.0420 1.0119 1. 0108 0.9965 0.9900 1.3366 1.2927 1.2305 1.0839 1. 0767 1.0404 1.0397 1.5789 1. 5178

5 4 1 1 1 1 1 1 1 1 1 1 1 1 1 1

10.5770 10.6433 11. 899 12.252 12.266 12.442 12.524 9.2761 9.5910 10.0753 11. 438 11.515 11.917 11. 925 7.8525 8.1682

1.2283 1.1815

1 1

10.0933 10.4931

5.931 5.885 8.664 8.239 6.504 8.629 6.729

5 2 5 8 1 4 1

2.090 2.1067 1.4310 1.505 1.9061 1.4368 1.8425

Nv Nvi.vii 77 Iridium a2 KLrr at KLlrr {j3 KMrr {jt KMm

0.195904 0.191047 0.169367 0.168542

2 2 2 2

63.2867 64.8956 73.2027 73.5608

1.13353 1. 12637

5 6

10.9376 11. 0071

0.9772 0.9765 0.96318 0.95603 1.2934 1.2480 1.18977

3 3 7 5 2 2 7

12.687 12.696 12.8721 12.9683 9.586 9.934 10.4205

1.03973 1.0050 1.0047 1.5347 1. 4735 1.20086

5 2 2 2 2 7

11. 9243 12.337 12.340 8.079 8.414 10.3244

1.14537 4.79 5.81 4.955 6.89 5.724 5.682 8.359

7 2 2 4 2 5 4 5

10.8245 2.59 2.133 2.502 1.798 2.166 2.182 1. 4831

1 4 1 1 2

1.9783 1.4919 1. 9102 0.2388 0.2266

6.267 8.310 6.490 51.9 54.7

78 Platinum

0.190381 0.185511 0.164501 0.163675

4 4 3 3

65.122 66.832 75.368 75.748

~ I

~

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~

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Z

Q

1-:3

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Z

tl

>

1-:3

o

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o

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Z

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TABLE

Designation

{j2II

KNII {j2I KNm KOn.III {jon KMIV {joI KM v {j4 KNIV.V

e, LIMn

e, LIMm

1'2 LrNn 1'3 LrNm 1"4 LrOn 1'4 LrOm '7 LnMr

{jl Lu.Msv 1'0 Lu N; 1'1 Ln.Ntv 1'8 LnOr 1'6 LnOrv 1 LIIlMr a2 LrnMrv al LIIrJl;[v

e, u.»,

{jloLnr Nrv

e. Ltu Nv

{j7 LmOr {35 LmOrv. v LrMr {jl0 LrMrv {jg LrMv LrNr LrNrv

Wavelength,

p.e.j

7f-1.

keY

X-RAY WAVELENGTHS IN

Wavelength,

p.e.f

keY

A*

A*

77 Iridium (Cont.)

78 Platinum (Cont.)

0.16415 0.163956 0.163019 0.16759 0.167373 0.16352 1. 17958 1.14085 0.96545 0.95931 0.92831 0.92744 1.28448 1. 15781 1. 02175 0.99085 0.97409 0.96708 1.54094 1.36250 1. 35128 1.17796 1.13707 1.13532 1.11489 1.10585 1. 2102 1.09702 1.08975 0.9766 0.9459

1 7 5 2 9 2 3 3 3 5 3 3 3 3 5 3 3 4 3 5 3 3 3 3 3 3 2 4 5 2 2

75.529 75.619 76.053 73.980 74.075 75.821 10.5106 10.8674 12.8418 12.9240 13.3555 13.3681 9.6522 10.7083 12.1342 12.5126 12.7279 12. &201 8.0458 9.0995 9.1751 10.5251 10.9036 10.9203 11. 1205 11. 2114 10.245 11. 301Q 11.377D 12.t>95 13.108

A*

UNITS AND IN KEV

Designation

(Continued)

Wavelength,

p.e.f

keY

A* 1 1 1 2 3 2 5 5 5 5 4 4 2 2 2 3 1 2 2 2 3 5

77.785 s, KMrrr 77.878 {j2II KNII 78.341 {j2I KNm 76.199 KO n. m 76.27 KLr {jon KM I V 78.069 10.8543 {joIKMv 11. 2308 {jo KMIV.V 13.2704 {j4 KN I V. v 13.3613 e, LIMn 13.8145 {j3 LrMm 13.8281 '}'2 LrNn 9.975 1'3 LrNIn 11.0707 1"4 LIOn 12.552 '}'4 Lr'OnI 12.9420 13.173 {jl LnMrv 13.271 '}'o LnNI 8.268 '}'1 LnNrv 9.3618 '}'8 LnOr 9.4423 '}'6 LnOIv 10.8418 1 LmMI

1.10200 1.08168 1.0724 1. 16962 1. 06183 1.05446 0.9455

3 3 2 9 7 5 2

11.2505 11.4619 11. 561 10.6001 11.6762 11.7577 13.113

." u.u.

a2 Lut Msv al Lni M» {j6 Liu N: {jlo Liit Nsv {j2 LrrrN v f37 LmOr {35 LmOrv. v LrM r (jIO LrMrv

0.158982 0.15483 0.154618 0.153694 0.18672 0.158062 0.157880 0.154224 1. 10651 1.06785 0.90434 0.89783 0.86816 0.86703 1.20273 1.08353 0.95559 0.92650 0.90989 0.90297 1. 45964 1.28772 1.27640 1. 11092 1. 07188 1.07022 1.04974 1.04044 1.13525 1.02789

I:\:)

p.e.f

keY

A*

79 Gold (Cont.)

0.15939 0.15920 0.15826 0.16271 0.16255 0.15881 1.14223 1. 10394 0.93427 0.92791 0.89747 0.89659 1.2429 1. 11990 0.9877 0.95797 0.9411 0.9342 1.4995 1.32432 1. 31304 1.14355

Wavelength,

jl ,.... ,....

3 2 9 7 4 7 5 5 3 9 3 5 4 4 3 3 3 3 5 3 9 3 3 3 5 3 8 3 5 7

77.984 80.08 80.185 80.667 66.40 78.438 78.529 80.391 11.2047 11. 6103 13.7005

13.8090 14.2809 14.2996 10.3083 11. 4423 12-:9743 13.3817 13.6260 13.7304 8.4939 9.6280 9.7133 11. 1602 11.5667 11. 5847 11.8106 11.9163 10.9210 12.0617

80 Mercury (Cont.)

0.154487 0.15040 0.15020 0.14931

3 2 2 2

80.253 82.43 82.54 83.04

2 2 7 7 7 7 7 7 1 5 7 5 7 7 1 7 5 7 7 7 7 7 2 2

80.75 82.78 11.5630 11.9953 14.162 14.265 14.757 14.778 10.6512 11.8226 13.410 13.8301 14.090 14.199 8.7210 9.8976 9.9888 11. 4824 11.9040 11.9241 12.1625 12.2769 11. 272 12.446

>

1-3

o

So:: ~

(1

> Z

0.15353 0.14978 1.07222 1. 03358 0.87544 0.86915 0.84013 0.83894 1. 1640 1.04868 0.92453 0.89646 0.87995 0.87319 1.4216 1.25264 1.24120 1. 07975 1. 04151 1. 03975 1. 01937 1. 00987 1.0999 0.9962

t:j

~

o

e-

t:rJ

(1

d

r>

~

~

~

~

U1 ~

(1

U1

'Yll LINv LrOlv.v LIOI LIOlv LIOv

0.9446 0.9243

LuMu

1.2502 1.2069 1. 1489 1. 0120 1.0054 0.97161 0.96979 1.4930 1.4318 1. 16545 1. 1560 1. 11145 l.t0923 4.631t 4.780 6.669 5.540 5.500

{317 LuMm

LuMv

LuNIl Lu Nvit v LuN VI LuOm

t LruMu 8 LluMul LmNu

LluNur u LruNvI.vu LurOlI,m MIN m

MuNlv MmNr

MIIINlv 'Y MIrrNv

2 3

3 2 2 2 3 6 5 3 2 5 3 4 6 9 4 9 5 4

13.126 13.413

9.917 to. 273 10.791 12.251 12.332 12.7603 12.7843 8.304 8.659 to. 6380 to. 725 11. 1549 11.1772 2.677 2.594 1.859 2.238 2.254

MmO I

MUIOIV.V

f2 MIVNII MlvNm {3 MIVNvI ft MvNm a2 MvNvl at MvNvIl MvO m

NIVNVI NvNvI.VII

4.869 8.065 7.645 6.038 8.021 6.275 6.262 50.2 52.8

9 5 8 1 4 3 1

2.546 1. 5373 1.622 2.0535 1.5458 1. 9758 1.9799

1 1

0.2470 0.2348

79 Gold a2 KLrr at KLIII {3a KMu

0.185075 0.180195 0.1598tO

2 2 2

0.9143

2

13.560

0.8995 0.8943 0.8934 1. 213 1.1667 1. 1129 0.9792 0.97173 0.93931

2 1 1 1 1 2 2 4 5

13.784 13.864 'Yll LINv 13.878 LrOI to. 225 LrOrv.v to. 6265 LIlM II 11. 140 {317 Ln Mss: 12.661 LuMv 12.7588 Ln Ntu 13.1992 v LuNvr

1.4530 1.3895 1. 13tO 1. 1226 1.07896 1.0761 4.460 4.601 6.455 5.357 5.319 4.876 4.694 7.790 7.371 5.828 7.738 6.058 6.047 5.987 48.1 50.9

2 2 2 2 5 3 9 4 9 5 4 9 8 5 8 1 4 3 1 9 2 1

8.533 8.923 to.962 11. 044 11. 4908 11. 521 2.780 2.695 1.921 2.314 2.331 2.543 2.641 1.592 1.682 2.1273 1.6022 2.047 2.0505 2.071 0.258 0.2436

80 Mercury

66.9895 68.8037 77.580

{39 LIM v

LIN I LINlv

0.179958 0.175068 0.155321

3 3 3

68.895 70.819 79.822

LUOIl LuOm t LmMu 8

LluMul

Lui Ns: Lin Nut u LIIINVI.VIl

1.02063 0.9131 0.88563 0.88433 0.87074 0.86400 1.1708 1.12798 1. 0756 0.9402 0.90837 0.90746 0.90638 1.41366 1.35131 1.09968 1.09026 1.04752

7 1 7 7 5 5 1 5 2 2 5 7 7 7 7 7 7 5

12.1474 13.578 13.999 14.020 14.2385 14.3497 10.5892 10.9915 11. 526 13.186 13.6487 13.662 13.679 8.7702 9.1749 11.2743 11.3717 11.8357

u' LUINvI u LuINvII

LIIIOU,IU

1.0450

2

'Y MIIINv

MurOI

MUIOIV,V

f2 Msv Nts MIVNUI {3M I VNvl ft MvNm at MvNvI at MvNvIl MvOm

NlvNvl NvNvI.VII

1. 03876 4.300 4.432 6.259 5.186 5.145 4.703 4.522 7.523 7.tOl 5.624 7.466 5.854 5.840 5.767 46.8 49.4

7 9 4 9 5 4 9 6 5 8 1 4 3 1 9 2 1

2 2

12.560 14.045

0.85657 0.8452 0.8350 1.1387 1. 0916

7 2 2 5 5

14.474 14.670 14.847 to. 888 11.358

0.90894 0.87885 0.8784 0.8758 1.3746 1.3112 1.0649 1.0585

7 7 1 1 2 2 2 1

13.640 14. t07 14.114 14.156 9.019 9.455 11. 642 11. 713

1.01769 1.01674

7 7

12.1826 12.1940

:>

1. 01558 1.01404

7 7

12.2079 12.2264

:> t-3 o

11. 865

LIlIOu LmOm

LIU PII.I11 MINIII MUNIV MIIINI MUINlv

0.9871 0.8827

11.9355 2.883 2.797 1.981 2.391 2.410 2.636 2.742 1.648 1.746 2.2046 1.6605 2.118 2.1229 2.150 0.265 0.25tO

~ ~

:> ~

~

~

t':1 ~

t':1

Z

ot-3

:r:

l/1

Z

t:l

a:: ~

Q

6.09

2

2.036

4.984t

2

2.4875

t':1

~ ~

o ~

6.87 5.4318t

2 9

1.805 2.2825

5. 6476t

9

2.1953

3 3

0.274 0.259

et':1 -< t':1 ~

45.2t 47.9t

l/1

j'I ..... .....

W

TABLE

7f-1.

X-RAY WAVELENGTHS IN

x.*

UNITS AND IN KEV (Continued)

-:J

I

~

Designation

Wavelength,

p.e.f

keY

A*

KLn KLnI {33 KMn {31 KMm {32u K N u {32 I KNuI KOu.m KP {3~ KMrv. v {3P KM I V {35 I KMv {34 KNIv.v {34 LIMn {33 LIMm /'2 LINn /'3 LrNm a2

/,' 4

t.o.,

LIOm 'T/ LuMr {31 LUMIV /'5 LUNI /'4

/'1 Lu.Niv /'~ LnOI /'6 LIIOIV LrrPI l LmMI a2 LnIMrv al LnIMv

{36 Lui Ni {315 LmNIv {32 Liu Nv {37 LmOI

p.e.t

Designation

keY

0.175036 0.170136 0.150980 0.150142 0.14614 0.14595 0.14509 0.14917

2 2 6 5 1 1 1 1

70.8319 72.8715 82.118 82.576 84.836 84.946 85.451

82 Lead

0.170294 0.165376 0.146810 0.145970 0.14212 0.14191 0.141012 0.1408

2 2 4 6 2 1 8 1

72.8042 74.9694 84.450 84.936 87.23 87.364 87.922 88.06

2 3 3 5 4 5 5 3 4 4 3 2 2

85.19 11.9306 12.3904 14.6251 14.7368 15.2482 15.2716 lO.9943 12.2133 13.8526 14.2915 14.564 14.685

1. 38477 1. 21875 1.20739 1.04963 1. 01201 1. 01031 0.99017

3 3 4 5 3 3 5

8.9532 10.1728 10.2685 11.8118 12.25lO 12.2715 12.5212

0.14512 0.14495 0.14155 1.0075 0.96911 0.82lO 0.8147 0.78706 0.7858 1. 09241 0.98291 0.86655 0.83973 0.82365 0.81683 0.81583 1.34990 1.18648 1. 17501 1.02lO 0.98389 0.98221 0.9620

2 3 3 1 7 2 1 7 1 7 3 5 3 5 5 5 7 5 2 1 7 7 1

85.43 85.53 87.59 12.306 12.7933 15.101 15.218 15.752 15.777 11. 3493 12.6137 14.3075 14.7644 15.0527 15.1783 15.1969 9.1845 lO.4495 10.5515 12.143 12.6011 12.6226 12.888

MvN v1 MvNvn MvO m NrvNvI

a2 al

Nv Nvtvt:

NvrO l v NvrO v

NvuO v

keY

p.e.f

KLn al KLllr {33 KM II {31 KMm {32 U KNu {32 r KNm KO II. m {35 KMIV.v {34 KNIV,V {34 LIM u {33 LIMm /'2 LINn /'3 LINnI /,'4 LIOll /'4 LIOIIl /'13 LIPn.III 'T/ LnMI {31 LnMIv /'5 LnNr /'1

Lu Nsv

/'8 LnOr

~ngth.

p.e.f

keY

1-1=>-

A*

5.472 5.460 46.5 115.3 113.0 117.7

5.299 5.286 5.168 42.3 0.267 45.0 O. lO75 lO2.4 O. lO968 lOO.2 O. lO530 lO4.3

2 2 1 1

0.165717 0.160789 0.142779 0.141948 0.13817 0.13797 0.13709 0.14111 0.13759 0.97690 0.93855 0.79565 0.78917 0.76198 0.76087 0.75690 1.05856 0.951978 0.83923 0.81311 0.7973

2 2 7 3 1 1 1 1 2 4 3 3 5 3 3 3 3 9 5 2 1

82 Lead (Cont.)

2.2656 2.2706

2 1

83 Bismulh a2

~

Wav.e-

81 Thallium (Cont.)

83.114

0.14553 1.03918 1.00062 0.84773 0.84130 0.81308 0.81184 1.12769 1.01513 0.89500 0.86752 0.8513 0.8442

Wavelength,

A*

A* 81 Thallium

al

Wavelength,

74.8148 77. lO79 86.834 87.343 89.733 89.864 90.435 87.860 90.11 12.6912 13.2098 15.5824 15.7lO2 16.2709 16.2947 16.3802 11.7122 13.0235 14.7732 15.2477 15.551

2 1 9 2 1 1 2 1

2.3397 2.3455 2.399 0.293 0.2756 0.1211 0.1237 0.1189

84 Polonium

0.16130t 0.15636t 0.13892t 0.13807t 0.13438t 0.13418t

1 1 2 2 2 2

76.862 79.290 89.25 89.80 92.26 92.40

>-

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(1

>-

~

t'

~

o

t"' t':l

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L;

r-

>-

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,...

Ul

0.9475 0.9091 0.772

3 3 1

13.086 13.638 16.07

0.9220

2

13.447

0.78748

9

15.744

(1

u:

'135 LmOIV, V LIMI {:JIOLIMIV {:J9LIM v LINI LINIV /'ll LINv LINvI,VII LIOI LIOlv,v

u.»«

LlIMm LIIM v LIIN II LIIN II I LIINv :v LIIN v I LIIO Il LlIOm t LmMII {:J17

s

LIIIMII I

LIIINII LIIINIII ·u LII I N VI. VII LmOlI LIIIOLI

LmPIl,m MINm MIIN I MIINlv MIIIN I "~hIlNIV

./' MmNv

0.98058 1.0644 0.96389 0.95675 0.8549 0.83001 0.82879

3 2 7 7 1 7 5

12.6436 11. 648 12.8626 12.9585 14.503 14.937 14.9593

0.8158 0.80861 1.0997 1.05609 1.00722 0.882 0.87996

1 5 1 7 5 2 5

15.198 15.3327 11.274 11.7397 12.3093 14.057 14.0893

0.8504'3 0.8490

5 1

14.5777 14.604

1. 34154 1.27807

5 5

9.2417 9.7007

1.0286 0.9888 0.98738 0.98538 0.97926 4.013

1 1 5 5 5 9

12.053 12.538 12.5566 12.5820 12.6607 3.089

4.116 5.8'34 4.865 4.823

4 8 5 4

3.013 2.107 2.548 2.571

4.216 7.032

6 5

2.941 1.763

5.249 5.196 6.974

1 9 4

2.3621 2.386 1.778

MIll 0 1

MIl 01\', V MIVNII MlvN m .{3 MIVNvI MIVOII !l MvNm

·r2

I/'6 LlIOIV

0.9526 1.0323 0.9339 0.9268 0.82859 0.80364 0.80233 0.7884 0.7897 0.78257 1.0644 1.0223 0.9747 0.8585 0.85192 0.8382 0.82327

1 2 2 1 7 7 9 1 1 7 2 1 1 3 7 2 7

13.015 12.010 13.275 13.377 14.963 15.427 15.453 15.725 15.699 15.843 11. 648 12.127 12.720 14.442 14.553 14.791 15.060

0.8200 1.30767 1.24385 1. 01040 1.0005 0.96133 0.9586 0.9578 0.95118 3.872 4.655 3.968 5.704 4.715 4.674 4.244 4.069 6.802 6.384 5.076 5.004 6.740

1 7 7 7 1 7 1 1 7 9 8 5 8 3 1 9 6 5 7 1 9 3

15.120 9.4811 9.9675 12.2705 12.392 v LIINvI 12.8968 LIIOm 12.934 tLHIMII 12.945 8 Liu Mvn 13.0344 £lIl N lI 3.202 LmNm 2.664 u. LIIINvI.vlI 3.124 LmOIl 2.174 LIIIOm 2.630 LmPII,l1I 2.6527 MIN II 2.921 MUVIII 3.047 MIIN I V 1.823 MmNI 1.942 MIIINlv 2.4427 /' MIIINv 2.477 MIIIOI 1.8395 MIIIOIV.V

l LmMI

0'2 LIIIMI V 0'1 LllIMV {:J6 LmNI ' /315

Lui Nsv

{:J2 LmNv {:J7 LmOI {:J5 LmOlv,v LIM I {:JIOLIMIV {:J9LIMv LINI LINIV /'ll LINv LINvl,vII LIOIV,V LIIM II {:J17 LIIM II I LIIM v LIIN II LIIN m

0.79043 1.31610 1.15536 1. 14386 0.99331 0.95702 0.95518 0.93505 0.92556 1.0005 0.90495 0.89791 0.8022 0.7795 0.77728 0.7641 0.75791 1.0346 0.98913 0.94419 0.8344 0.8248 0.79721 0.79384 1. 2748 1. 2105 0.98280 0.97321 0.93505 0.9323 0.9302 0.92418 3.892 3.740 3.834 5.537 4.571 4.532 4.105 3.932

3 7 1 2 3 5 4 5 3 9 4 3 1 5 5 5 5 9 5 5 9 1 9 5 1 1 5 5 5 2 2 4

9 9 4 8 5 2 9 6

15.6853 9.4204 10.73091 10.8388 12.4816 12.9549 12.9799 13.2593 13.3953 12.39 13.7002 13.8077 15.456 15.904 15.951 16.23 16.358 11.98 12.5344 13.1310 14.86 15.031 15.552 15.6178 9.7252 10.2421 12.6151 12.7394 13.2593 13.298 13.328 13.4159 3.185 3.315 3.234 2.239 2.712 2.735 3.021 3.153

0.7645 1.2829 1. 12548t 1. 11386 0.9672 0.9312 0.92937

2116.218 5 9.664 5 11.0158 4 11.1308 2 12.819 2 13.314 5 13.3404

0.8996

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TABLE

Designation

Wavelength,

p.e.']

7f-1.

keY

Wavelength,

p.e.']

keY

A*

A*

89 Actinium (Cont.)

90 Thorium (Cont.)

51

NnOlv NIIPI

Ntut)» NlvN v I NvNvI,vII

NVIOlv NVIOv NVIIOV

OmPlv.v Olv,vQII,ln 91 Protactinium

Designation

0.134343t 0.129325t 0.11523t 0.114345t 0.11129t O.l1107t

9 3 2 8 2 2

92.287 95.868 107.60 108.427' 111. 40 111.62

KOn.I1I {35 KMIV,V {34 KNlv,v {34 f33 LIM m

ut««

0.7699 0.73230

1 5

16.104 16.930

Wavelength,

.5 2 9 9 7 7 5 7 1 9 9 1 1 1 3 5 i

2.364 2.987 2.9961 3.29R 1. 313 1.1319 1.072 1.120 0.897 0.3693 0.3414 0.2505 0.2572 0.2479 0.1817 0.068

92 Uranium

0.130968 0.125947 0.112296 0.111394 0.10837 0.10818 0.10744 0.11069 0.10780 0.747985 0.71029

4 3 4 5 1 1 1 1 2 9 2

94.665 98.439 110.406 111. 300 114.40 114.60 115.39 112.01 115.01 16.5753 17.4550

j:I

(Continued)

p.e.f

..... .....

Wavelength,

keY

MINn l

MIIO IV MulN r

MnlN l v l'

MlnNv

MIIIO I MIIIOIV,V 52 MlvN n MlvN m {3 MlvNvl MlvOu 51 MvNm a2 MvNvI

MvNVII

3.441 2.910 2.527 4.450 3.614 3.577 3.245 3.038 5.193

5 2 4 4 2 1 9 2 2

3.603 4.260 4.906 2.786 3.430 3.4657 3.82 4.081 2.3876

3.827 3.691 5.092 4.035 4.022

1 2 2 3 1

3.2397 3.359 2.4350 3.072 3.0823

keY

92 Uranium (Cont.)

MINn MIO m MIPm MIINI MIINl v

00 p.e.']

A*

91 Protactinium (Cont.)

al

KLn KLnl {33 KM n {31 KM m {32 n KNn {32 r KN m

a2 al

AND IN KEV

A*

5.245 4.151 4.1381 3.760 9.44 9.40 11.56 11.07 13.8 33.57 36.32 49.5 48.2 50.0 68.2 181

MvN m MvNvI MvN v II MvPm NIPn NrPm a2 al

A* UNITS

X-RAY WAVELENGTHS IN

NIO m NIP n

».r.« NnPI NmOv NlvNvr

Nv Nvt.vi: Nivtrtv NvlO v NIPIV,V

I

2.92 2.753 2.304 2.253 3.329 2.817 2.443 4.330 3.521 3.479 3.115 2.948 5.050 4.625 3.716 3.576 4.946 3.924 3.910 10.09 8.81 8.76 10.40 12.90 31.8 34.8 43.3 42.1 8.60

2 8 7 6 4 2 4 2 2 1 7 2 2 5 1 1 2 1 1 7 7 7 7 9 1 1 2 2

7

4.25 4.50 5.38 5.50 3.724 4.401 5.075 2.R63 3.521 3.563 3.980 4.205 2.4548 2.681 3.3367 3.4666 2.507 3.1595 3.1708 1.229 1. 41 1. 42 1. 192 0.961 0.390 0.357 0.286 0.295 1. 44

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0.6239 0.6169

1 1

19.872 20.098

0.5937

1

20.882

0.8295 0.74232 0.6550 0.63358

1 5 1 9

14.946 16.702 18.930 19.568

0.6133

1

20.216

l Lau M: a2 LrrrMrv al LnrMv /36 Liu Ni /31; LrrrNrv

1.0908 0.94482t 0.93284 0.8079

1 5 5 1

11. 366 13. 1222 13.2907 15.347

/32 Liu Nv /37 LIlIOr {3; LrrrOrv.v

0.7737 0.7546 0.7452

1'2 LrNII

LrNrrr 1"4 LrOrr 1'4 Lstru.n: ")'3

")'13

LnMr {31 Lrr 21frv 1'5 LrrNr 1'1 LIINrV 1'8 LrrOr 1'6 LnOrv 71

Ltil"i»

LrrrPr LrrrPrv,v {310 LrMlv {jg LrM v LrNlv I'll LrNv LrOrv.v {l17 Ln Mitt

u,»,«

v LnNvI Luitln: LnPn,In t LlnMn 8 LnrMIII Liu Ns:

LmNm u LnrNvr.vn Liuttn

Liutru: LrnPn .nr

0.7088 0.7018

1 2 2 2 1

16.024 16.431 16.636 17.492 17.667

0.605237 0.598574 0.576700 0.57499 0.5706 0.80509 0.719984 0.63557 0.614770 0.60125 0.594845 0.59203 1.06712 0.922558 0.910639 0.78838 0.756642 0.754681 0.73602 0.726305 0.72521 0.72240 0.68760 0.681014 0.59096 0.58986 0.5725 0.74503 0.6228 0.6031 0.59728 0.5930 1. 0347 0.9636 0.78017 0.7691 0.738603 0.7333 0.7309 0.72426

9 9 9 9

1 2 8 2 9 5 9 5 2 9 9 2 9 9 6 9 5 5 5 8 5 5 1 5 1 1 5 2 1 1 9 1 9 1 1 5

20.4847 20.7127 {34 LrMrr 21. 4984 {33 LrMrrr 21. 562 ")'2 LrN Il 21.729 ")'3 L,N rrr 15.3997 17.2200 ")"4 LrOrr 19.5072 ")'4 LrOrr.rrr 71 Lrr M, 20.1671 {31 LrrM,v 20.621 20.8426 1'5 Ln Ns 1'1 LrrNrv 20.942 11. 6183 1'8 13.4388 ")'6 LrrOrv 13.6147 l LrrrMr 15.7260 a2 Ltu Ms» m Lm M.v 16.3857 {36 LrrrNr 16.4283 {31S Lui Niv 16.845 Liu N» 17.0701 {32 {37 LrrrO r 17.096 {3s LrrrOrv. v 17.162 {310 LrMlv 18.031 {39 LrM v 18.2054 u LrrrNvr.vn 20.979 21. 019 21. 657 16.641 {34 LrMn 19.907 {33 LrMm 20.556 1'2 Lt Ns: 20.758 {31 LnMlv 20.906 1'1 Lu Niv 11.982 ")'6 LrrOlv 12.866 l LII1MI 15.892 a2 LlnMrv 16.120 al LmMv 16.7859 {36 Liii N: {31;, LrrrNrv 16.907 16.962 {32 Liu N» 17.118 {3s LmOlv,v

93 Neptunium

0.72671 0.6892ot 0.5873 0.5810

2 9 5 5

17.0607 17.989 21. 11 21.34

0.5585 0.7809 0.698478 0.616 0.596498

5 2 9 1 9

22.20 15.876 17.7502 20.12 20.7848

0.57699 1.0428 0.901045 0.889128 0.769

5 6 9 9 1

21. 488 11. 890 13.7597 13.9441 16.13

0.736230

9

16.8400

0.70814

2

17.5081

95 Americium

0.68639 0.64891 0.5544 0.657655 0.561886 0.54311 1.0012 0.860266 0.848187 0.73418 0.70341 0.701390 0.67383

2 2 2 9 9 2 6 9 9 2 2 9 2

18.0627 19.1059 22.361 18.8520 22.0652 22.8282 12.384 14.4119 14.6172 16.8870 17.6258 17.6765 18.3996

94 Plutonium

0.70620 0.66871 0.57068 0.564001 0.5432 0.5416 0.7591 0.67772 0.5988 0.578882 0.5658 0.55973 1.0226 0.88028 0.86830 0.75148 0.7205 0.71851 0.7003 0.69068 0.6482 0.6416 0.7031

2 2 2 9 1 1 1 2 1 9 1 2 1 2 2 2 1 2 1 2 1 1 1

17.556 o 18.540 5 21. 725 21.982 4 22.823 22.891 16.333 18.293 20.704 21. 417 21. 914 22.150 12.124 14.084 14.278 16.498 17.208 17.255 17.705 17.950 19. 126 19.323 17.635

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0.12807 0.129325 0.13052 0.13069 0.13072 0.130968 0.13155 0.132813 0.13418 0.13432 0.134343 0.13438 0.13517 0.136417 0.13694 0.13709 0.13759 0.137829 0.13797 0.13807 0.13817 0.13892 0.14014 0.1408 0.140880 0.141012 0.14111 0.14141 0.14155 0.14191 0.141948 0.14212 0.142779 0.14399 0.14495 0.14495 0.14509 0.14512

5 3 4 5 4 4 5 2 2 4 9 2 4 8 1 1 2 2 1 2 1 2 2 1 5 8 1 2 3 1 3 2 7 3 1 3 1 2

87 91 85 86 85 92 86 90 84 85 91 84 85 89 83 83 83 90 83 84 83 84 88 82 82 82 83 89 82 82 83 82 83 87 81 82 81 82

Fr Pa At Rn At U Rn Th Po At Pa Po At Ac Bi Bi Bi Th Bi Po Bi Po Ra Pb Pb Pb Bi Ac Pb Pb Bi Pb Bi Fr Tl Pb Tl Pb

K{33 KOlI K{32 1 K{31 K{32 II K0l2 K{33 KOlI K{32 I K{31 K0l2 K{32 II K{33 KOlI K

KMn KLm KNm KMrrr KNu KLII KMn KLIII KNIll KMm KL!I KN n KM n KLm Abs, edge KO Il •1II

K{34 K0l2 K{32 1 K{31 K{32 II K{33 KOlI K

KNIv.v KLII KNIll KM IIl KN II KMII KLm KP Abs. edge KO n.I11

K{3s K0l2 K{34 K{32 1 K{31 K{32 rr K{33 KOlI K K{3sI

KMIv.v KLlI KNIV.V KNIll KMm KN rr KMII KLm Abs. edge KM v KOn.III

K{3sII

KM1v

96.81 95.868 94.99 94.87 94.84 94.665 94.24 93.350 92.40 92.30 92.287 92.26 91.72 90.884 90.534 90.435 90.11 89.953 89.864 89.80 89.733 89.25 88.47 88.06 88.005 87.922 87.860 87.67 87.59 87.364 87.343 87.23 86.834 86.10 85.533 85.53 85.451 85.43

0.15920 0.15939 0.159810 0.160789 0.16130 0.16255 0.16271 0.16292 0.163019 0.16352 0.163675 0.163956 0.16415 0.164501 0.165376 0.165717 0.167373 0.16759 0.16787 0.16798 0.16842 0.168542 0.168906 0.16910 0.169367 0.170136 0.170294 0.17245 0.17262 0.17302 0.17308 0.173611 0.17362 0.174054 0.17425 0.174431 0.175036 0.175068

1 1 2 2 1 3 2 1 5 2 3 7 1 3 2 2 9 2 1 1 2 2 6 1 2 2 2 1 1 1 1 3 2 6 1 3 2 3

78 Pt 78 Pt 79 Au 83 Bi 84 Po 78 Pt 78 Pt 77 Ir 77Ir 77 Ir 78 Pt 77Ir 77 Ir 78 Pt 82 Pb 83 Bi 77 Ir 77 Ir 76 Os 76 Os 76 Os 77Ir 76 Os 76 Os 77 Ir 81 Tl 82 Pb 76 Os 76 OS 75 Re 75 Re 76 Os 75 Re 75 Re 75 Re 76 Os 81 Tl 80 Hg

K{32 I K{32 II K{33 KOlI K0l 2 Kfh I K{3sII

K

KNIll KN H KMn KLIII KLu KM v KM 1V Abs. edge KOrr.Irr

K{34 K{31 K{32 I K{32 U K{33 KOlI K0l 2 K{3sI K{3sII

K

KNIV.V KMm KNIll KNn KM rr KLrrr KLII KMv KM 1V Abs. edge KO rr. rr I

K{34 K{31 K{32 I K{32 II K{33

x«.

K0l 2 K{3sI K{3sII

K

KNIV.V KM Irr KNrrI KNu KMrr KLIII KLrr KMv KMIV Abs. edge KO rr•1rr

K{31 K{34 K{32 1 K{32 II K{33 K0l2 KOlI

KM III KNIV.V KNlrr KNrr KM u st.« KLnr

77.878 77.785 77.580 77 .1079 76.862 76.27 76.199 76.101 76.053 75.821 75.748 75.619 75.529 75.368 74.9694 74.8148 74.075 73.980 73.856 73.808 73.615 73.5608 73.402 73.318 73.2027 72.8715 72.8042 71. 895 71.824 71. 658 71. 633 71. 413 71. 410 71.232 71.151 71. 077 70.8319 70.819

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p. 7-99.

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TABLE

7f-2.

WAVELJ;~NGTHS OF X-RAY EMISSION LINES AND ABSORPTION EDGES: IN NUMERICAL ORDER

-:J I

(Continued)

I--' ~

Wavelength,

A*

p.e.f

0.17766 0.17783 0.17837 0.178444 0.178880 0.17892 0.179421 0.17960 0.179697 0.179958 0.180195 0.183092 0.183264 0.18394 0.184031 0.184374 0.18451 0.185011 0.185075 0.185181 0.185188 0.185511 0.18672 0.188757 0.188920 0.18982 0.190089 0.190381 0.1908 0.190890 0.191047 0.19585 0.19589

1 1 1 5 3 2 7 1 3 3 2 7 5 1 7 2 1 8 2 2 9 4 4 6 6 5 4 4 2 2 2 5 2

Designation

Element

keY

Wavelength,

~

A*

p.e.f

0.22855 0.229298 0.23012 0.23048 0.23056 0.23083 0.2317 0.234081 0.23618 0.236655 0.23788 0.23841 0.23858 0.23862 0.2397 0.241424 0.244338 0.24608 0.24681 0.24683 0.24687 0.24816 0.249095 0.252365 0.25275 0.25460 0.25534 0.25553 0.255645 0.256923 0.257110 0.260756 0.263577

3 2 2 1 3 2 2 2 3 2 2 1 3 2 2 2 2 2 1 2 3 3 2 2 3 2 2 1 7 8 2 2 5

Element

Designation

keY

----

75 75 74 74 75 74 74 74 75 80 79 74 74 73 73 74 73 73 79 74 73 78 79 73 73 72 73 78 72 73 77 71 71

Re Re W W Re W W W Re Hg Au W W Ta Ta W Ta Ta Au W Ta Pt Au Ta Ta Hi Ta Pt Hi Ta Ir Lu Lu

K{j5 I K{js'! K K{31 K{34 K{j2 I K{32" K{j3 Ka2 Kal K{j5 I K{35" K K{jl K{34 K{32[ Ka2 K{33 K{32"

x«.

K{j5 1 K{j5 II K K{31 Ka2 K{j2 K{j3 Kal K

KM v KMIv Abs. edge KO".III KM II, KNIV.V KNm KN" KNI" KL" KL", KM v KM IV Abs. edge KO",TII KMm KN,v.v KNm KLII KM" KN" KLm KL, KM v KM[v Abs. edge KMm KL,[ KN".I" KM u KLuI Abs. edge KO".m

69.786 69.719 69.508 69.479 69.310 69.294 69.101 69.031 68.994 68.895 68.8037 67.715 67.652 67.403 67.370 67.2443 67.194 67.013 66.9895 66.9514 66.949 66.832 66.40 65.683 65.626 65.31 65.223 65.122 64.98 64.9488 64.8956 63.31 63.293

67 71 67 66 66 67 66 71 66 70 66 65 65 66 65 70 69 65 64 65 64 64 69 68 64 64 64 63 63 63 68 67 63

Ho Lu Ho Dy Dy Ho Dy Lu Dy YbDy Tb Tb Dy Tb Yb Till Tb Gd Tb Gd Gd Till Er Gd Gd Gd Eu Eu Eu Er Ho Eu

K{j5

s», K{31 K K{33 K{j2 Ka2 K{35 Kal K{31 K K{j3 K{32 Ka2 Kal K{31 K K{33 K{32 Ka2 Kal K{35 K{31 K{33 K K{321 Ka2 Ka1 K{31

KM,v.v KLm KMIfI Abs, edge KO".I"

«u.,

KN".m KL" KM,v.v KLm KA-f m Abs. edge KO".III KM" KN".III KL" KLm KMIII Abs. edge KM II KOII.III KNII.,,[ KL" KLIII KA-hv.v KM m KM" Abs. edge KO".I" KN II • II [ KL" KLIII KM m

54.246 54.0698 53.877 53.793 53.774 53.711 53.47 52.9650 52.494 52.3889 52.119 52.002 51.965 51.957 51. 68 51. 3540 50.7416 50.382 50.233 50.229 50.221 49.959 49.7726 49.1277 49.052 48.697 48.555 48.519 48.497 48.256 48.2211 17 .5467 47.0379

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0.195904 0.19607 0.196794 0.19686 0.1969 0.20084 0.201639 0.20224 0.20226 0.20231 0.202781 0.20309 0.2033 0.20739 0.207611 0.20880 0.20884 0.20891 0.2090100 0.2096 0.2098 0.213828 0.21404 0.215497 0.21556 0.21567 0.21581 0.21592 0.21636 0.2167 0.220305 0.22124 0.222227 0.22266 0.22291 0.22305 0.22341 0.2241 0.227024

2 3 2

77Ir

4

72 Hi

2 2 2 5 2 3 2 4 2 2 1 5 8 2 8td.

71 Lu 71 Lu 76 Os 70 Yb 70 Yb 71 Lu 75 Re 71 Lu 70 Yb 70 Yb 75 Re 69 Tm 70 Yb 69 Tm 74 W 70 Yb 69 Tm 74 W 69 Tm 73 Ta 69 Tm 68 Er 68 Er 74 W 69 Tm 68 Er 73,Ta 68 Er

1

2 2 2 4 2 1 3 4 2 2 8 3 3 2 1 3 2 2 3

72 Hi

76 Os

72 Hi

68 67 67 68 67

Er Ho Ho Er Ho

72 Hi

Ka2 K{jl Kal K{ja K{j2 K{j5 Ka2 K K{jl Kal K{ja K{j2 K{j5 Ka2 K K{jl

s«, K{ja Kfh Ka2 K{js Kat K{3t K K{ja K{32 Ka2 K{j5 Kat K{jl K

tee, K{32 Ka2

KLu KM m KLm KM n KNu.UI KMIV.v KLn l

.

Abs, edge KOn.I1I KM m KLm KM n KNn.UI KMIV,V KLu

Abs. edge KM m KOIl.IU KLm KM u KNu,UI KLu

KMIV,v KLm KMm

Abs. edge KOn.uI KLI KMu KNn.UI KLn

KMlV,V KLm KMm

Abs. edge KOn,III KM n

KNu.III KLn

63.2867 63.234 63.0005 62.98 62.97 61.732 61.4867 61.30 61.298 61. 283 61.1403 61.05 60.89 59.782 59.7179 59.38 59.37 59.346 59.31824 59.14 59.09 57.9817 57.923 57.532 57.517 57.487 57.450 57.42 57.304 57.21 56.277 56.040 55.7902 55.681 55.619 55.584 55A94

55.'32 54.6114

0.264332 0.26464 0.26491 0.265486 0.2662 0.269533 0.27111 0.27301 0.27376 0.274247 0.27431 0.2759 0.278724 0.28290 0.283423 0.28363 0.28453 0.2861 0.288353 0.293038 0.293299 0.294027 0.29518 0.29679 0.298446 0.303118 0.304261 0.304975 0.30648 0.30668 0.30737 0.30816 0.309040 0.31342 0.31357 0.313698 0.315816 0.316520 0.31844

5 5 3 2 1 2 3 2 2 2 5 1 2 3 2 4 5 1 2 2 2 3 5 2 2 2 4 5 5 2 2 1 2 2 2 2

2 4 5

63 Eu 628m 628m 67 Ho 628m 66 Dy 628m 628m 628m 66 Dy 61 Pm 61 Pm 65 Tb 61 Pm 65 Tb 61 Pm 60 Nd 60 Nd 64 Gd 64 Gd 60 Nd 60 Nd 59 Pr 59 Pr 63 Eu 63 Eu 59 Pr 59 Pr 58 Ce 58Ce 58 Ce 58 Ce 628m 58 Ce 58 Ce 628m 58 Ce 58 Ce 57 La

K{ja K Ka2 K{j2 Kal K{j5 K{jl K{ja Ka2 K K{j2 Kat KfJI Ka2 K{ja K K{j2 Kat Ka2

tee,

K{ja K K{j2 Kat Ka2 K{jt K{3a K K{34I K{32 Kat K{35I K{j5 I1 Ka2 K{jt K{3a K

KMu

Abs. edge KOn.In KLn KN u.I1I KLm KMIv,v KMm KMu KLu

Abs. edge KNu.m KLm KMm KLu KMu

Abs, edge KNu.UI KLm KLu KMm KMu

Abs. edge KNu.UI KLm KLu KMm KMu

Abs. edge KOn.nI KNIV,V

KNn.III KLm KMv KMIV KLu KMm KMu

Abs. edge

46.9036 46.849 46.801 46.6997 46.57 45.9984 45.731 45.413 45.289 45.2078 45.198 44.93 44.4816 43.826 43.7441 43.713 43.574 43.32 42.9962 42.3089 42.2713 42.1665 42.002 41.773 41. 5422 40.9019 40.7482 40.6529 40.453 40.427 4{L337

40.233 40.1181 39.558 39.539 39.5224 39.2573 39.1701 38.934

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o :>

z

t:l ~

o

et:r:1

o q

t"

:> ~

"'tl

P:1 H1

ta H

o

W

0.37523 0.375313 0.383905 0.384564 0 ..885111 0.389668 0.38974 0.38974 0.391102 0.399995 0.400290 0.400659 0.404835 0.40666 0.40668 0.40702 0.407973 0.41378 0.41388 0.41634 0.417085 0.417737 0.42087 0.424,67 0.42467 0.42495 0.425915 0.43175 0.43184 0.433318 0.435236 0.435877 0.437829 0.44371 0.44374 0.~4393

0.44500 0.45086 0.45098

I

2 2 4 4 4 5 1 1 6 5 4 4 4 1 1 1 5 1 1 2 3 4 2 3 1 3 8 3 3 5 5 5 7 1 3 4 1 2 2

53 57 53 53 56 56 52 52 52 52 55 52 55 51 51 51 51 51 51 54 51 51 54 50 50 ,50 50 50 50 53 50 50 53 49 49 49 49 49 49

I La I I Ba Ba Te Te Te Te Cs Te Cs Sb Sb Sb Sb Sb Sb Xe Sb Sb Xe Sn Sn Sn Sn Sn Sn I Sn Sn I In In In In In In

K{32 Ka2 K{31 K{3a Kal Ka2 K K{32 K{31

x«.

K{3a Ka2 K K{34I K{32 K{361

K{36 n Kal K{31 K{3a Ka2 K K{34I K{32 K{361

KNII.ln KLn KMm KMn KLm KLII

KOn.nI Abs. edge KNII.nI KMm KLm KMIl KLn KOIl.1I1

Abs, edge KNlv.v KNn.nI KMv KMlv KLm KMm KMn KLn

KOn,nI Abs. edge KNIV.V

KNn.ln KMv

K{36 n

KMIv

Kal K{31 K{3a Ka2 K

KLm KMnI KMn KLn

K{3i K{32 K{3s1

K{36 n

Abs. edge KOlI,In KNIV.V

KNn.In KMv KMIV

33.042 33.0341 32.2947 32.2394 32.1936 31. 8171 31.8114 31.8114 31. 7004 30.9957 30.9728 30.9443 30.6251 30.4875 30.4860 30.4604 30.3895 29.9632 29.9560 29.779 29.7256 29.6792 29.458 29.195 29.1947 29.175 29.1093 28.716 28.710 28.6120 28.4860 28.4440 28.3172 27.9420 27.940 27.928 27.8608 Z7.499 27.491

0.54101 0.54118 0.5416 0.54311 0.5432 0.545605 0.546200 0.5544 0.5572 0.5585 0.5594075 0.55973 0.56051 0.56089 0.56166 0.561886 0.563798 0.564001 0.5658 0.56785 0.5680 0.5695 0.5706 0.57068 0.572482 0.5725 0.573067 0.57499 0.576700 0.57699 0.578882 0.5810 0.585448 0.5873 0.58906 0.589821 0.58986 0.59024 0.59096

9 9 1 2 1 4 4 2 1 5 6 2 1 9 3 9 4 9 1 9 2 1 1 2 4 1 4 9 9 5 9 5 3 5 1 3 5 5 5

45 45 94 95 94 45 45 95 94 93 47 94 44 44 44 95 47 94 94 44 44 92 92 94 44 92 44 92 92 93 94 93 46 93 43 46 92 43 92

Rh Rh Pu Am Pu Rh Rh Am Pu Np Ag Pu Ru Ru Ru Am Ag Pu Pu Ru Ru U U Pu Ru U Ru U U Np Pu Np Pd Np Te Pd U Tc U

K{3s1 K{3sIl L'Y4 L'Y6 L'Yl K{31 K{3a L'Y2

KMv KMIV LIOm LnOlv LIOn KM nr KM n LINn

Ln

Abs. edge LIOn.nI

L'Y4 Kal L'Y6 K J({34 K{32 L'Yl Ka2 L'Ya L'Y8 K{3s1

xe»

LI L'Y13 L'Y2 K{31 K{3a L'Y4 L'Yl L'Y6 L'Yl L'Ya Kal L'Y2 K Ka2 L'Yll K{32

KLIII LIIOIV

Abs. edge KN rv• v KNn.III LnNIv KLn

LINIn LnOI KMv

KM IV Abs. edge LIPn. n I LINn KMnI LIOIV.V KMn LIOm LIOn LnOlv

LnNlv LINIn KLIII LINn

Abs. edge KLn LINv KNn,nI LINIV

22~917

22.909 22.891 22.8282 22.823 22.7236 22.6989 22.361 22.253 22.20 22.16292 22.1502 22.1193 22.104 22.074 22.0652 21. 9903 21. 9824 21. 914 21. 834 21. 829 21. 771 21. 729 21.1251 21. 6568 21. 657 21. 6346 21. 562 21.4984 21. 488 21. 4173 21.34 21. 1771 21.11 21.0473 21.0201 21. 019 21.005 20.979

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Z

trJ

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trJ t"

[f).

j:I I-'

t\:)

I;Il

TABLE

7f-2.

WAVELENGTHS OF X-RAY EMISSION LINES AND ABSORPTION

EDGJ

;:d

Iod

~ ~

U2 l-t

o

U2

0.62636 0.62692 0.62708 0.6276 0.6299 0.62991 0.6312 0.6316 0.632288 0.63258 0.632872 0.63358 0.63557 0.63559 0.6356 0.6369 0.63898 0.64064 0.6416 0.64221 0.643083 0.6445 0.64513 0.6468 0.647408 0.64755 0.6482 0.64891 0.64965 0.65131 0.6521 0.65298 0.65313 0.65318 0.65416 0.6550 0.657655 0.6620 0.6654

9 5 5 1 1 9

1 1 9 4 2 9 2 4 1 1

5 9 1 4 4 1

5 1 5 5 1 2

5 5 1 1 3

5 4 1 9 1 1

90 42 42 90 90 90 90 90 42 90 42 91 92 90 90 90 90 90 94 90

Th Mo Mo Th Th Th Th Th Mo Th Mo Pa U Th Th Th Th Th

Pu

Th 44 Ru

L'Yl1 K{3sr

K{3sII LII

Abs. edge

K{31 L-Y6 K{33

Ltii':» LuPu.ru LuPr KMm LuOrv KMn

L-Yl L-ys

L-Y3 L-Y8 Lv L{39 L-Y2 Kal

88 Ra 88 Ra 88 Ra

Lr L-Y13

44 Ru 90 Th 94 Pu 95 Am 88 Ra 88 Ra 90 Th

Ka2

41 90 41 41 91 95 90

LrNv KMv KMrv Lt Nsv

L{3l0

L{33 L'Y4 L-y4'

Ln Nvv

u,».

Ia Niu

LnOnr LuOn LnOr LrrNvr LrMv Li N'u KLru Abs. edge LrPu.ur LrOrv,v KL II LrN r LrMrv LrMur LrOru

t..o«

LuNv

Nb

K

Th

L-Yl

Nb Nb

K{34 K{32

Pa Am Th

L-ys

KNrv,v KNu,rII LuNr

L{3l

Lu.Msv

L'Yll

LnNru LrNv

88 Ra

Abs. edge Ln Nt»

19.794 19.776 19.771 19.755 19.683 19.682 19.642 19.629 19.6083 19.599 19.5903 19.568 19.5072 19.507 19.506 19.466 19.403 19.353 19.323 19.305 19.2792 19.236 19.218 19.167 19.1504 19.146 19.126 19.1059 19.084 19.036 19.014 18.9869 18.9825 18.981 18.953 18.930 18.8520 18.729 18.633

0.7003 0.701390 0.70173 0.7018 0.70228 0.7031 0.70341 0.7043 0.70620 0.70814 0.7088 0.709300 0.71029 0.713590 0.71652 0.71774 0.71851 0.719984 0.7205 0.7223 0.72240 0.7234 0.72426 0.72521 0.726305 0.72671 0.72766 0.72776 0.72864 0.7301 0.7309 0.73230 0.7333 0.73418 0.7345 0.73602 0.736230 0.738603 0.73928

1 9 3 1 4 1 2 1 2 2 2 1 2 6 9 5 2 8 1 1 5 1 5 5

9 2

5 5 4 1 1

5 1 2

1 6

9 9 9

94 95 40 91 40 94 95 88 94 93 91 42 92 42 87 88 94 92 94 92 92 90 92 92 92 93 39 39 39 90 92 91 92 95 39 92 93 92 86

Pu Am

Zr Pa

Zr Pu Am

Ra Pu Np Pa Mo U Mo Fr

L{37 L{32 K{3l L{39 K{33 Lu L{315 L{34 L{3s L{3l0

Ra Pu

Kal L{33 Ka2 L'Yl L'Ys L{32

U

L{3l

Pu

L{315 Lru

U

U Th U

L{39

U U Np

Y Y Y Th U Pa

L{3s L{34 K

K{34 K{32 L{310

L{33

U Am

Y U Np U

Rn

L{36 K{3s L{37 L{32 Lu L-Yl

LIlIOr LmNv KMIlI LrMv KMn Lui N vr. vrr Lni Nsv

?

Lu Ni u LrMn LurOrv.v LrMrv KLIlI LrMru KLrr LnNlv Ln.Ni LmNv LrrMrv Liu Ntv Abs. edge LuiPiv,v

LrMv LrnPrr,In LrrrPr LurOrv,v LrMu Abs. edge KNrv,v KN n . u r LrMrv LurOnr LrMur LIlIOn LIlINr KMrv,v LIlIOr LrnNv LurNvr,vrr LuNrv

17.705 17.6765 17.6678 17.667 17.654 17.635 17.6258 17.604 17.5560 17.5081 17.492 17.47934 17.4550 17.3743 17.303 17.274 17.2553 17.2200 17.208 17.165 17.162 17.139 17.118 17.096 17.0701 17.0607 17.038 17.036 17.0154 16.981 16.962 16.930 16.907 16.8870 16.879 16.845 16.8400 16.7859 16.770

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t".j

Z

o 8

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t"

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l' ~

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TABLE

7f-2.

WAVELENGTHS OF X-RAY EMISSION LINES AND ABSORPTION EDGES: IN NUMERICAL ORDER

jl

(Continued)

~

Wavelegth,

A* 0.74072 0.74126 0.74232 0.74503 0.7452 0.74620 0.747985 0.75044 0.75148 0.7546 0.754681 0.75479 0.756642 0.75690 0.7571 0.7579 0.75791 0.7591 0.7607 0.76087 0.76087 0.76198 0.7625 0.76289 0.76338 0.7641 0.7645 0.76468 0.765210 0.76857 0.769 0.7690 0.7691

p.e.f Element

2 3 5 5 2 1 9 1 2 2 9 3 9 3 1 1 5 1 1 9 3 3 2 9 5 5 2 5 9 5 1 1 1

39 39 91 92 91 41 92 41 94 91 92 90 92 83 83 90 83 94 90 90 83 83 90 85 90 83 84 90 90 88 93 90 92

Y Y Pa U Pa Nb U Nb Pu Pa U Th U Bi Bi Th Bi Pu Th Th Bi Bi Th At Th Bi Po Th Th Ra Np Th U

Designation

K{3l K{33 L{3l L{317 L{36 Kal L{34 Ka2 L{3& L{37 L{32 L{33 L{316 L-Y13 LI

KM m KM u LnMIv

LuMnI LnIOIv.v KLIII LIMn KLn

LUINI LInOI LmNv LIMm LmNlv

L1Pu,ru

Abs. edge

L."

LnMv LIOIV,V LnMI

LUI

Abs. edge

L-Y4 L-yl

LIOnI LIOU

LnIPIv,v LUIPn,IlI L-Yl

LnNIv LIUPI LINvI,vu

L-y& L{36 L{31

LIIO IV LnIOIv,v

L{3~

L{3&

LnMIv LIM v LmNI LIIIOm LUINIII

keV

16.7378 16.7258 16.702 16.641 16.636 16.6151 16.5753 16.5210 16.4983 16.431 16.4283 16.4258 16.3857 16.3802 16.376 16.359 16.358 16.333 16.299 16.295 16.2947 16.2709 16.260 16.251 16.241 16.23 16.218 16.213 16.2022 16.131 16.13 16.123 16.120

Wavelength,

A*

p.e.f

0.7973 0.-8022 0.80233 0.80273 0.8028 0.80364 0.8038 0.8050 0.80509 0.80627 0.8079 0.8081 0.8082 0.80861 0.81163 0.81184 0.81308 0.81311 0.81375 0.8147 0.81538 0.8154 0.81554 0.8158 0.81583 0.8162 0.81645 0.81683 0.8186 0.8190 0.8200 0.8210 0.8219

1 1 9 5 1 7 1 1 2 5 1 1 1 5 9 5 5 2

5 1 5 2 5 1 5 1 3 5 1 2 1 2 1

Element

83 83 82 88 88 82 88 88 92 88 91 81 90 81 90 81 81 83 88 82 82 37 37 81 82 88 37 82 88 90 82 82 37

Bi Bi Pb Ra Ra Pb Ra Ra U Ra Pa Tl Th Tl Th Tl Tl Bi Ra Pb Pb Rh Rh Tl Pb Ra Rb Ph Ra Th Pb Pb Rb

Designation

L-Y8 L-Yll L{3a

LnOI LINI LINv LIMm

LUI

Abs, edge LINIV

LInPn,nI LInPI L." L{36 L{3&

LnMI

LI

Abs. edge

L-Y4 L-yl L-Yl L{3l L-Y3 Ln K{34 K L{37 K{32 L-y& Lu

L-Y2 K{35

LUIOIV.V LIUNI LUINIu LIOIV,V LIMI LrOm LIOIl L,INIV LIlMIV LINm

Abs, edge KNIV.V

Abs, edge LIOI LUPI LIIlOI KNn ,III LUOIV LIIIN VI.VII LIIINlI LUOIII LINII KMIV.V

keV

15.551 15.456 15.453 15.4449 15.444 15.427 15.425 15.402 15.3997 15.3771 15.347 15.343 15.341 15.3327 15.276 15.2716 15.2482 15.2477 15.2358 15.218 15.2053 15.205 15.2023 15.198 15.1969 15.190 15.1854 15.1783 15.146 15.138 15.120 15.101 15.085

tV 00

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1-4

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a::

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t'"

t?:l

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d

t'"

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Ul

1-4

C

Ul

0.76973 0.7699 0.76989 0.77081 0.7713 0.772 0.7737 0.77437 0.77546 0.7764 0.77661 0.77728 0.77822 0.77954 0.78017 0.7809 0.78196 0.78257 0.78292 0.78345 0.7858 0.78593 0.78706 0.78748 0.78838 0.7884 0.7887 0.78903 0.78917 0.7897 0.79015 0.79043 0.79257 0.79257 0.79354 0.79384 0.79539 0.79565 0.79721

5 1 5 3 1 1 1 4 5 1 5 5 9 5 9 2 5 7 2 3 1 1 7 9 2 1 1 9 5 1 1 3 4 4 3 5 5 3 9

38 91 38 38 90 84 91 90 88 38 90 83 89 83 92 93 82 82 38 38 82 40 82 84 92 82 83 89 83 82 40 83 90 90 90 83 90 83 83

Sr Pa Sr Sr Th Po Pa Th Ra Sr Th Bi Ac Bi U Np Ph Ph Sr Sr Ph Zr Pb Po U Pb Bi Ac Bi Pb Zr Bi Th Th Th Bi Th Bi Bi

K L(j4 K(j4 K(j2

Ahs. edge LIMn KNIV.V KNn.In

LnIOn L'Y2 L(j2 L{37

t.s.; K(j5 Lu

t.-« L(j3 L." LI K(jr K{33 L'Y4 Kal L'Yl L'Yl L(j6

LINn LUINv LnIOr LIM IV KM IV.V

Lan Nvi.vu LINv LIM m LINIV LIIINn LnMr

Ahs. edge LrOrv,v KM m KM n LIOm KLm

LrOn LnNiv

LnrN I Lt N'vuvt:

Ln L(jr L'Y3 Ka2 L'Y6 L{34 L{317 L{32

Abs. edge LnMrv LIN n r LIOI KLn

LnOIv LIMn

LnMnr LmMv

LuOnI L{315 L'Y2 Lv

LnIN1v LINn LnNvI

16.107 16.104 16.104 16.0846 16.074 16.07 16.024 16.0105 15.988 15.969 15.964 15.951 15.931 15.904 15.892 15.876 15.855 15.843 15.8357 15.8249 15.777 15.7751 15.752 15.744 15.7260 15.725 15.719 15.713 15.7102 15.699 15.6909 15.6853 15.6429 15.6429 15.6237 15.6178 15.5875 15.5824 15.552

0.82327 0.82365 0.8248 0.82789 0.82790 0.82859 0.82868 0.82879 0.82884 0.82921 0.8295 0.83001 0.83305 0.8338 0.8344 0.8350 0.8353 0.83537 0.83722 0.8382 0.83894 0.83923 0.83940 0.83973 0.84013 0.84071 0.84130 0.8434 0.8438 0.8442 0.8452 0.84773 0.848187 0.8490 0.85048 0.8512 0.8513 0.85192 0.85436

7 5 1 9 8 7 2 5 1 3 1 7 1 1 9 2 1 5 5 2 7 5 9 3 7 5 4 1 1 2 2 5 9 1 5 1 2 7 9

82 82 83 87 90 82 37 81 39 37 91 81 39 90 83 80 80 88 88 82 80 83 87 82 80 88 81 81 88 81 80 81 95 81 81 88 81 82 86

Ph Ph Bi Fr Th Ph Rh Tl Y Rh Pa Tl Y Th Bi Hg Hg Ra Ra Ph Hg Bi Fr Ph Hg Ra Tl Tl Ra Tl Hg Tl Am Tl Tl Ra Tl Ph Rn

Lv L'Y8 L{33 L{36 K{3r L'Yll Kar K{33 LTJ Ka2

Lr L{32 L(j15

LnNvI

LnO I LnNnI LIMnI LmNI LrNI KMm LIN v KLm KM n LnMI LINrv KLn LnMn LnNn LrOIv,v

Abs. edge LUINv

LrnNrv Lu Nv

L'Y4 L'Y5 L{31 L'Yl L'Yl L(j4 L'Y3 Lu L{317 L'Y6 L'Y2 t.«.

LrOnr LnNI LnMrv LnNrv

LrOn Lt Mv: LINrII

Abs. edge LnMur LnOrv LI0I LINn LruMv

LuOn Lv L'Y8 L(j3

LuNvr

Lui Ntit LnOI LuNnr LrMrn

15.060 15.0527 15.031 14.976 14.975 14.963 14.9613 14.9593 14.9584 14.9517 14.946 14.937 14.8829 14.869 14.86 14.847 14.842 14.8414 14.8086 14.791 14.778 14.7732 14.770 14.7644 14.757 14.7472 14.7368 14.699 14.692 14.685 14.670 14.6251 14.6172 14.604 14.5777 14.566 14.564 14.553 14.512

~ I

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t':l t"4 t':l

Z

o

8

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tn

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t1

>8 o ~ ~

o

t':l

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t':l ~

o

~

t"4 t.".l ~

t':l t"4

tn

j.:I

......

I:\:)

~

TABLE

7f-2.

WAVELENGTHS OF X-RAY EMISSION LINES AND ABSORPTION EDGES: IN

NUMERICAL ORDER

~

(Continued)

I

~

Wavelength,

A.*

p.e.f

0.85446 0.8549 0.85657 0.858 0.8585 0.860266 0.8618 0.86376 0.86400 0.8653 0.86552 0.86605 0.8661 0.86655 0.86703 0.86752 0.86816 0.86830 0.86915 0.87074 0.8708 0.87088 0.8722 0.87319 0.87526 0.87544 0.8758 0.8784 0.8785 0.87885 0.8790 0.87943 0.87995

4 1 7 2 3 9 1 5 5 2 1 9 1 5 4 3 4 2 7 5 2 5 1 7 1 7 1 1 1 7 1 1 7

Element

90 81 80 87 82 95 88 79 79 36 36 86 36 82 79 81 79 94 80 79 36 88 80 80 38 80 80 80 36 80 36 38 80

Th Tl Hg Fr Pb Am Ra Au Au Kr Kr Rn Kr Pb Au TI Au Pu Hg Au Kr Ra Hg Hg Sr Hg Hg Hg Kr Hg Kr Sr Hg

Designation

L." LYll L{j2

LnMI LINI LINv

LmNv

La2

LnNn LmMlv LIlINn

LI

Abs. edge

K{j4 K L{j1 K{j2 LY5 LY4 LYI Lyl Lai LY3 K{j5 L{je Ln Lye Kal LY2 K{j1 Lv K{j3 Ka2 LY8

LIOIV.V KNlv.v

Abs. edge LnMIv

KNn,nI LIINI

LIOln LnNIv LIOn LInM v

LINnI LIOI KMlv.v LInNI

Abs. edge LnOIv KLm LINn LnOm LnOn KMm LnNvI KMn KLn L1I0I

keY

14.5099 14.503 14.474 14.45 14.442 14.4119 14.387 14.3537 14.3497 14.328 14.3244 14.316 14.315 14.3075 14.2996 14.2915 14.2809 14.2786 14.265 14.2385 14.238 14.2362 14.215 14.199 14.1650 14.162 14.156 14.114 14.112 14.107 14.104 14.0979 14.090

Wavelength,

1*

p.e.j

0.9234 0.9236 0.92413 0.9243 0.92453 0.9255 0.925553 0.92556 0.92650 0.9268 0.92744 0.92791 0.92831 0.92937 0.92969 0.9302 0.9312 0.9323 0.93279

1 1 4 3 7 1 9 3 3 1 3 5 3 5 1 2 2 2 2 5 5 2 5 2 5 5 5

0.93~84

0.93327 0.9339 0.93414 0.9342 0.93427 0.93505 0.93505 0.93855 0.93931 0.9402 0.9411 0.94419 0.9446

3

5 2 1 5 2

Element

83 Bi 77 Ir 83 Bi 77 Ir 80 Hg 35 Br 37 Rb 83 Bi 79 Au 82 Pb 77Ir 7R Pt 77 Ir 84 Po 37 Rb 83 Bi 84 Po 83 Bi 35 Br 91 Pa 35 Br 82 Pb 78 Pt 78 Pt 78 Pt 83 Bi 83 Bi 83 Bi 78 Pt 79 Au 78 Pt 83 Bi 77Ir

Designation

LnI LI

LY5 K{j5 Ka1 L{j5 . LYI L{jg LY4 LY3 Lyl L{j2 Ka2

Abs. edge Abs. edge LlnPn,nI LIOIV,V LnNI KMIV.V KLm

Lintliv,»

LnNIv LIMv LIOm LINm LIOn Liu.Nv KLn

LIIIOIII L{j15 K{j1

Ltu Nt» LmOn KMm

t.«;

Lui M»

K{ja

KMIl LIMIV

Ln LYe LY2 L{jr Lu L{j3 Lv

Abs. edge

t.s.,

LnOlv LINn LmOr Lnr N VI.VII LIMIn LnNvI

Ln Nitt LY8 LYll

LIIOI LnMv L1Nv

keY

13.426 13.423 13.4159 13.413 13.410 13.396 13.3953 13.3953 13.3817 13.377 13.3681 13.3613 13.3555 13.3404 13.3358 13.328 13.314 13.298 13.2914 13.2907 13.2845 13.275 13.2723 13.271 13.2704 13.2593 13.2593 13.2098 13.1992 13.186 13.173 13.1310 13.126

ce o

> 8 o

a:: H

o

>

Z

t:::1 ~

o

t'"

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t'"

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l"d

=n

~ U1 H

o

U1

0.879'96 0.88028 0.88135 0.8827 0.88433 0.88563 0.8882 0.889128 0.8931 0.8934 0.89349 0.8943 0.89500 0.89646 0.89659 0.89747 0.89783 0.89791 0.8995 0.8996 0.901045 0.90259 0.90297 0.90434 0.90495 0.90638 0.90742 0.90746 0.90837 0.90894 0.9091 0.90989 0.910639 0.9131 0.9143 0.9204 0.92046 0.9220 0.922558

5 2 9 2 7 7 2 9 1 1 9 1 4 5 4 4 5 3 2 2 9 5 3 3 4 7 5 7 5 7 3 5 9 1 2 1 2 2 9

81 94 85 80 79 79 81 93 78 78 85 78 81 80 78 78 79 83 78 84 93 79 79 79 83 79 88 79 79 80 84 79 92 79 78 35 35 84 92

TI Pu At Hg Au Au Tl Np Pt Pt At Pt TI Hg Pt Pt Au Bi Pt Po Np Au Au Au Bi Au Ra Au Au Hg Po Au U Au Pt Br Br Po U

La2 L{j3 L'Yll Lal Lr L{jl L'Ys L'Yl L'Y4 L'Yl L'Y3 L{ju L{j5 La2 Lrr L'Y6 L'Y2 L{jlO L71 Lv L{j3 L'Y8 t.«.

L'Yll K K{j2 L{jl La2

Lu Ntti LnrMrv LrMnr LrNr LrNv LrNrv LIIMII Lvu Mv Abs. edge

t..o,

LrrMrv LrOrv LIINr LrrNIv

iso«. LrOn

us,« LrMv LrO r LIIrOrv,v Liu Mt.v Abs. edge LIIOrv LrNu LrMrv LrrOrrr

u.u.

LIIOrr LIINvr LIIN IIr LrMIII LIIOr LrIIMv LIN I LINv Abs. edge KNII,III LIIMIV LrIIMIv

14.0893 14.0842 14.067 14.045 14.020 13.999 13.959 13.9441 13.883 13.878 13.876 13.864 13.8526 13.8301 13.8281 13.8145 13.8090 13.8077 13.784 13.782 13.7597 13.7361 13.7304 13.7095 13.7002 13.679 13.6630 13.662 13.6487 13.640 13.638 13.6260 13.6147 13.578 13.560 13.470 13.4695 13.447 13.4388

0.94482 0.9455 0.9459 0.9475 0.95073 0.95118 0.951978 0.9526 0.95518 0.95559 0.9558 0.95600 0.95603 0.95675 0.95702 0.9578 0.95797 0.9586 0.95931 0.95938 0.96033 0.96133 0.9620 0.96318 0.9636 0.96389 0.96545 0.96708 0.9671 0.9672 0.96788 0.96911 0.96979 0.97161 0.97173 0.97321 0.97409 0.9747 0.9765

5 2 2 3 5 7 9 1 4 3 1 3 5 7 5 1 3 1 5 8 8 7 1 7 1 7 3 4 1 2 2 7 5 6 4 5 3 1 3

91 Pa 78 Pt 77 Ir 84 Po 82 Pb 82 Pb 83 Bi 82 Pb 83 Bi 79 Au 76 Os 90 Th 76 Os 81 Tl 83 Bi 82 Pb 78 Pt 82 Pb 77Ir 76 Os 76 Os 82 Pb 82 Pb 76 Os 92 U 81 TI 77 Ir 77 Ir 77Ir 84 Po 90 Th 82 Pb 77 Ir 77 Ir 78 Pt 83 Bi 77 Ir 82 Pb 76 Os

La2 L{j4 LrII L{jl L{js L{j2 L'Ys Lr Lal L{ju L{j16 L'Yl L'Y3 L'Y4 L'Yl Lu L{j7 L8 L{jlO L'Y2 L"Y6 LII L{j6 La2

ce, Lv

L'Y8 L'Yll

LIIrMrv LrNr LrNrv LrMII Abs. edge LrnPII,III LIIMrv LruOrv,v LrnNv LIINr Abs. edge Lui M» LIOrv,v LrMv LIlINrv LIIIOIIr LrrNrv LIlIOrr LrNrrr LrOrrr

uo«

LruNvI,vII LIlIOI LIOr LmMIIr LrMrv LrNrr LrrOrv Abs, edge LmNr LnrMrv

uu,«

LrrOrII LIINvr LIINnr LIIINIII LIIOI LIIM v LINv

13.1222 13.113 13.108 13.086 13.0406 13.0344 13.0235 13.015 12.9799 12.9743 12.972 12.9687 12.9683 12.9585 12.9549 12.945 12.9420 12.934 12.9240 12.923 12.910 12.8968 12.888 12.8721 12.866 12.8626 12.8418 12.8201 12.820 12.819 12.8096 12.7933 12.7843 12.7603 12.7588 12.7394 12.7279 12.720 12.696

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TABLE

7£-2.

WAVELENGTHS OF X-RAY EMISSION LINES AND ABSORPTION EDGES: IN

NUMERICAL ORDER

l'

(Continued)

~

Wavelength,

A*

p.e.f

0.9766 0.97690 0.9772 0.9792 0.97926 0.9793 0.97974 0.97992 0.97993 0.9801 0.98058 0.98221 0.98280 0.98291 0.98389 0.9841 0.9843 0.98538 0.9871 0.98738 0.9877 0.9888 0.98913 0.9894 0.9900 0.99017 0.99085 0.99178 0.99186 0.99218 0.99249 0.99268 0.99331

2 4 3 2 5 1 1 5 5 1 3 7 5 3 7 1 1 5 2 5 2 1 5 1 1 5 3 5 5 3 5 5 3

Element

77 83 76 78 81 81 34 34 89 36 81 82 83 82 82 36 34 81 80 81 78 81 83 75 75 81 77 89 76 34 75 34 83

Ir Bi Os Pt

TI TI Be Be Ae Kr

TI Pb Bi Pb Pb Kr Be Tl Hg

Designation

LrNr L{34

LrNrv Lu Nii

Lm K K{32 Lal Kal L{35 L{32

L{31 L{315 Ka2 K{35 L{39

TI Pt

TI Bi Re Re Tl Ir Ac Os Be Re Be Bi

Lt Mv:

L'Y5 Lu L{317 Lr L{37 L'Yl La2 L'Y3 K{31 L'Y4 K{33 L{36

LrrrPII,rrr Abs. edge Abs. edge KNII.IIr LrIIM v KLm LrIIOIv.v LIIrNv LrIINrr LrrMrv LIlrNrv KLrr KMrv,v LIrrO m LrMv LrrIOrr Lu.Ni LrrrNvI,vrr LrrMm Abs. edge LrO rv. v LmOr LrrNrv LrrrM rv Ls Nu: KM m LIOrrr

«u«

Liu Nt

keY

12.695 12.6912 12.687 12.661 12.6607 12.660 12.6545 12.6522 12.6520 12.649 12.6436 12.6226 12.6151 12.6137 12.6011 12.598 12.595 12.5820 12.560 12.5566 12.552 12.538 12.5344 12.530 12.524 12.5212 12.5126 12.5008 12.4998 12.4959 12.4920 12.4896 12.4816

Wavelength,

A*

p.e.j

Element

1.0250 1.02503 1.02613 1. 02775 1.02789 1.0286 1.02863 1.03049 1.0317 1.03233 1.0323 1.03358 1.0346 1.0347 1.03699 1. 0371 1.03876 1.03918 1.0397 1.03973 1. 03974 1. 03975 1.04000 1.0404 1.04044 1.04151 1.0420 1.04230 1.0428 1.04382 1.04398 1.0450 1.0450

2 5 7 3 7 1 3 5 3

74 W 76 Os 75 Re 74 W 79 Au 81 TI 74W 87 Fr 74W 75 Re 82 Pb 80 Hg 83 Bi 92 U 75 Re 75 Re 79 Au 81 TI 75 Re 76 Os 35 Br 80 Hg 79 Au 75 Re 79 Au 80 Hg 75 Re 87 Fr 93 Np 35 Br 75 Re 79 Au 33 As

5 2 7 9 1 9 1 7 3 1 5 2 7 5 1 3 7 1 5 6 2 5 2 1

Designation

L'Yl L'Y3 L'Y4 L{310 L'Yl t.«.

L'Y2 L{33 Lt L'Y6 L rr L{34 Kal L{32 Lm Lv L{35 L{315 La2 Ll Ka2 L'Y8 K

LrOrv,v Lrr N rv Lt N'u: LrOm LrMrv LrIINIII LIOn LmMv LIOr LINn Lr M r Lt Mt u LrMrr LmMrr LrrOIv Abs. edge LnrPrr,rrr Lrr M rr LrrOrrr LrrN n r KLm LmNv Abs. edge LrrNvr Ltutriv,v LmNrv LrNr LmMrv LrnMr KLII

u.o,

LrrrOrr,rrr Abs. edge

keY

12.095 12.0953 12.0824 12.0634 12.0617 12.053 12.0530 12.0313 12.017 12.0098 12.010 11. 9953 11.98 11. 982 11.956 11. 954 11. 9355 11.9306 11. 925 11.9243 11. 9242 11. 9241 11.9212 11. 917 11. 9163 11. 9040 11. 899 11.8950 11.890 11.8776 11.8758 11. 865 11. 865

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0.99334 0.9962 0.9965 0.99805 1.0005 1.0005 1.00062 1. 00107 1.0012 1.0014 1.0047 1.00473 1.0050 1.0054 1.00722 1.0075 1.00788 1. 0091 1.00987 1.01031 1. 01040 1. 0108 1.0112 1.0119 1.0120 1.01201 1.01404 1.01513 1.01558 1.01656 1.01674 1. 01769 1. 01937 1.02063 1.0210 1.02175 1.0223 1.0226 1.02467

5 2 1 5 1 9 3 5 6 1 2 5 2 3 5 1 5 1 7 3 7 1 1 1 2 3 7 4 7 5 7 7 7 7 1 5 1 1 5

75 80 75 76 82 83 81 76 95 76 76 88 76 77 81 82 76 80 80 81 82 75 90 75 77 81 80 81 80 88 80 80 80 79 82 77 82 94 74

Re Hg Re Os Pb Bi Tl Os Am Os Os Ra Os Ir Tl Pb Os Hg Hg Tl Pb Re Th Re Ir Tl Hg Tl Hg Ra Hg IIg Hg Au Pb Ir Pb Pu W

L-yl

LfJlo L-Y2 LfJa L-Y6 Ll

Ln

u« Lv LfJ4 L-ys Lm LfJs LfJ2

LIOn LIM l v LIOI LINn LUINnl LIMI LIMnl LnOrv

LmMI Abs, edge LIIOm LnlMv LnNvl Lu Niu LnMv LIMn LnOI Abs. edge

LnlOrv,v LmNv

LUINn L-Yll L8

LINv

LnlMnl LINlv Ln N n

LfJ15

LUIN l v LUIOln

LfJl

LuMl v

La2 Lu LU' LfJ7 LfJg LfJ6 L-ys L{317 Ll

LI

LUIOn LlnMlv LUIN vu Ltu Nvr LUIOI LIM v LmNI LuNI

LIIMnl LmMI Abs, edge

12.4813 12.446 12.442 12.4224 12.392 12.39 12.3904 12.3848 12.384 12.381 12.340 12.3397 12.337 12.332 12.3093 12.306 12.3012 12.286 12.2769 12.2715 12.2705 12.266 12.261 12.252 12.251 12.2510 12.2264 12.2133 12.2079 12.1962 12.1940 12.1826 12.1625 12.1474 12.143 12.1342 12.127 12.124 12.0996

1.04500 1.0458 1.0468 1.04752 1.04868 1.0488 1.04963 1. 04974 1.05446 1.05609 1.05693 1.05723 1.05730 1.05783 1.0585 1.05856 1.06099 1.0613 1.06183 1. 06192 1.06200 1. 06357 1.0644 1.0644 1. 06467 1.0649 1.06544 1.06712 1. 06771 1.06785 1.06806 1.06899 1.07022 1.07188 1.07222 1.0723 1.0724 1. 07448 1. 0745

3 1 2 5 5 1 5 8 5 7 5 5 2 5 1 3 5 1 7 9 6 9 2 2 3 2 3 2 9 9 3 5 3 5 7 1 2 5 1

33 As 74W 74W 79 Au 80 Hg 33 As 81 Tl 79 Au 78 Pt 81 Tl 76 Os 86 Rn 33 As 33 As 80 Hg 83 Bi 75 Re 73 Ta 78 Pt 73 Ta 74 W 73 Ta 82 Pb 81 Tl 73 Ta 80 Hg 73 Ta 92 U 73 Ta 79 Au 74 W 86 Rn 79 Au 79 Au 80 Hg 78 Pt 78 Pt 74 W 74 W

KfJ2

L'Yll Lu

io,

tee,

LfJ6 LfJ7 LfJg LfJ17

L-ys t.«. KfJI

«e,

KNu,Iu LIN v LINlv LInN VI.VII LnMlv KMlv.v LmNI

LlnOI LIMv Ln Mst: LnNI LmMv KMnl KMn

LmNl1I LTJ L-Yl

Lr

t.s., L-ya

LnMI LnNlv Abs. edge LIMlv LIOlv,v

LINIn LINvI.vu LnMu LrMI

L-Y4

LrO rn LUINn

L1'l Ll

LIOn LmMI LIOI LrMm LINu

LfJa L1'2 La2 L{32

L{3ls L{34

Lrn L{3s L1'6

LII

LrllMlv LmNv Lau Niv

Li Mv: Abs. edge LuitJtv,» LIIOIV Abs, edge

11. 8642 11. 856 11. 844 11. 8357 11.8226 11.822 11.8118 11. 8106 11.7577 11.7397 11. 7303 11. 7270 11. 7262 11. 7203 11.713 11. 7122 11. 6854 11. 682 11. 6762 11.6752 11. 6743 11. 6570 11. 648 11.648 11. 6451 11. 642 11.6366 11. 6183 11.6118 11. 6103 11. 6080 11.5979 11. 5847 11. 5667 11. 5630 11. 562 11. 561 11. 5387 11.538

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1. 10394 1. 10477 1.1053 1.1058 1.10585 1.10651 1.10664 1.10882 1.10923 1. 11092 1. 11145 1.1129 1. 1137 1. 11386 1.11388 1.11489 1. 1149 1.11508 1. 11521 1. 1158 1. 11658 1.11686 1. 11693 1. 11789 1. 1195 1. 11990 1.1205 1.12146 1.1218 1.12250 1. 1226 1.12548 1.12637 1.12769 1.12798 1.12894 1. 12936 1. 1310 1.13235

5 2 1 1 3 3 9 2 6 3 4 2 1 4 3 3

2 4 9 1 5 2 9 9 1 2 1 9 3 9 2 5 6 3 5 2 9 2 3

78 34 73 77 77 79 72 34 77 79 77 78 73 84 73 77 74 90 73 73 32 32 73 73 32 78 73 72 74 72 78 84 76 81 79 32 32 78 74

Pt Se Ta Ir Ir Au Hf Se Ir Au Ir Pt Ta Po Ta Ir W Th Ta Ta Ge Ge Ta Ta Ge Pt Ta Hf W Hf Pt Po Os Tl Au Ge Ge Pt W

L{33 Kal L'Y2

Lui L{3; L{34 Ka2 L{36 Lu

Lu Lal L'Y6 L{37 Ll Lv K K{32 K{35 L{3l L'Y8 L'Yll

LrMm KLm

Lt Ni« Abs, edge LrnOIv.v LrMn LrOr KL n LurOn.In LmNr Liu N VI.VII LuMv Abs. edge LmMv LnOIv LmOI LuNrn LmMI LrNr LuNvr Abs. edge KNn.ur LuOur LuOn KMrv.v LuMrv LuOr LrN v LuNn Li N'iv

Ltu Nvn La2 L{3g L11 L{317 K{3l K{33 L'Y5

LmMIv LrMv LIIM r LuMnr KMm KM rr Liu Nii LIIN r

11. 2308 11. 2224 11.217 11.212 11.2114 11. 2047 11.2034 11.1814 11.1772 11. 1602 11. 1549 11. 140 11. 132 11.1308 11. 1306 11. 1205 11. 120 11.1186 11.1173 11.1113 11.1036 11.1008 11.1001 11. 0907 11. 0745 11. 0707 11. 0646 11.0553 11. 052 11. 0451 11. 044 11.0158 11. 0071 10.9943 10.9915 10.9821 10.9780 10.962 10.9490

1. 16545 1. 1667 1.16719 1. 16962 1.16979 1.1708 1.17167 1. 17218 1. 1729 1. 17501 1. 17588 1.17721 1. 1773 1.17788 1. 17796 1. 17900 1. 17953 1. 17955 1. 17958 1. 17987 1.1815 1. 1818 1.1827 1.1853 1.1853 1.18610 1. 18648 1.1886 1.18977 1.1958 1. 19600 1.19727 1. 1981 1. 1985 1. 1987 1.20086 1. 2014 1.20273 1.2047

5 1 5 9 8 1 5 5 1 2 1 5 1 9 3 5 4 7 3 1 1 1 1 1 2 5 5 1 7 1 2 7 2 1 1 7 1 3 1

77 78 88 78 76 79 76 75 73 82 33 75 75 72 77 72 71 76 77 33 75 70 70 70 71 75 82 70 76 31 31 76 31 71 71 76 71 79 71

Ir Pt Ra Pt Os Au Os Re Ta Pb As Re Re Hf Ir Hf Lu Os Ir As Re Yb Yb Yb Lu Re Pb Yb Os Ga Ga Os Ga Lu Lu Os Lu Au Lu

LmNn

L{3l7 Ll

Lu Mvu LurMI

L{32

LrM I LmNv

L{315 L{310 L'Y5

c«.

Kal L{35 Lm L{36 L'Yl L'Y3 L{33 L{34 Ka2 Lu Lr L'Y4 L'Y2 L{37 La2

u.««

LmNrv LrM rv LnNI LmMv KLm LmOrv.v Abs. edge LnNv LIIlNr LnNIv

us.«

LrAfrn LrMn KLu Lrn N vr ,VII Abs. edge LrOrv.v LrOn.m LrNn Luit):

LmMIv LrOr

u.u,

K K{32 L{31 K{35 LII L'Y6 L11 L'Y8

Abs. edge KN rr.m LnMrv KMrv.v Abs. edge LnOrv LIIlNu LuOn.rrr LnMr LnOr

I

10.6380 10.6265 10.6222 10.6001 10.5985 10.5892 10.5816 10.5770 10.5702 10.5515 10.54372 10.5318 10.5306 10.5258 10.5251 10.5158 10.5110 10.5108 10.5106 10.50799 10.4931 10.4904 10.4833 10.4603 10.460 10.4529 10.4495 10.4312 10.4205 10.3682 10.3663 10.3553 10.348 10.3448 10.3431 10.3244 10.3198 10.3083 10.2915

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1.2429 1.24385 1.24460 1.2453 1. 24631 1.2466 1.2480 1.24923 1.2502 1. 25100 1.25264 1.2537 1.254054 1.2553 1.2555 1.25778 1. 258011 1. 25917 1.2596 1. 2601 1.26269 1.26385 1.2672 1.26769 1.2678 1.2706 1.2728 1. 2742 1. 2748 1. 2752 1.27640 1.2765 1.27807 1. 281809 1.2829 1.2834 1.28372 1.28448 1.28454

2 7 3 1 3 2 2 5 3 5 7 2 9 1 1 4 9 5 1 3 5 5 2 5 2 1 2 2 1 2 3 2 5 9 5 1 2 3 2

78 82 74 70 74 73 76 70 77 75 80 73 32 73 73 73 32 75 71 73 74 73 74 70 69 68 74 69 83 68 79 74 81 74 84 30 30 77 73

Pt Pb W Yb W Ta Os Yb Ir Re Hg Ta Ge Ta Ta Ta Ge Re Lu Ta W Ta W Yb Tm Er W Tm Bi Er Au W TI W Po Zn Zn Ir Ta

LTJ L8 L{3z L{3I5 L{39 L{3I7 L-Y8 L{36 Laz L{3I0 Kat Lur L{35 Lu Kaz L{34 L-Y5 L{33 L{37 L-YI L-Y3 LI L-yz Lt L-Y4 Lm L8 L{3I Ll K K{3z LTJ L{3z

LuMr LruMu I Lsu Nv LnOu,ur LmNrv LIMV LuMur LuOr LuMu Iau N: LurMIv LrMrv KLm Abs. edge LrrIOrv,v LurNvr,vu KLu LIMu LnNr LIUOU,UI LrMm Luit): Lvu Nstt

Lu Nsv LINm Abs. edge LuMv LrNu LIUMU LIOrr,II[ LrnMv LmNu LruMur LuMrv Ltu M: Abs. edge KNn,ur Lu Ms LIUNv

9.975 9.9675 9.9615 9.9561 9.9478 9.946 9.934 9.9246 9.917 9.9105 9.8976 9.889 9.88642 9.8766 9.8750 9.8572 9.85532 9.8463 9.8428 9.839 9.8188 9.8098 9.784 9.7801 9.779 9.7574 9.741 9.730 9.7252 9.722 9.7133 9.712 9.7007 9.67235 9.664 9.6607 9.6580 9.6522 9.6518

1.32698 1.32783 1.32785 1.33094 1.3358 1.3365 1.3366 1.3386 1.3387 1.3397 1.340083 1.3405 1. 34154 1. 34183 1.3430 1.34399 1.34524 1. 34581 1.34949 1.34990 1.35053 1. 35128 1.35131 1.35300 1.3558 1.35887 1.36250 1.3641 1.3643 1.3692 1.3698 1.37012 1.3715 1. 37342 1. 37410 1.37410 1. 37459 1.3746 1.38059

3 5 7 8 1 3 1 1 2 3 9 1 5 7 2 1 9 3 5 7 9 3 7 5 2 9 5 2 2 1 2 3 1 5 5 5 7 2 5

73 72 76 73 71 74 75 68 74 68 31 71 81 71 71 31 71 73 71 82 72 77 79 72 69 72 77 68 67 66 67 71 71 75

Ta Hf Os Ta Lu W Re Er W Er Ga Lu TI Lu Lu Ga Lu Ta Lu Pb Hf Ir Au Hf Tm Hf Ir Er Ho Dy Ho Lu Lu Re

72 Hi

72 66 80 29

Hf Dy

Hg Cu

L{3I L{3I5 LTJ L{36 L{39 Lrr L{317 L-Y6

s:«.

Lru Lt L{35 L{3I0 Kaz L{34 L{37 Ll

LUMIV LmNrv LrrMI LmNr LrMv L IM I LuMn Abs, edge LrrM u r LuOrv

su«

Abs. edge Liu Ms: Lautliv,» LrMrv KLu LUIOu,ur LIMu LmOr LmMr

Iau Nvu LOll L8 L{33 L-Y5 Laz L-YI L-Y3 LI L-yz L{3z LpI5 LTJ L{3I L{36 L-Y4 Lt K

LruMv LIrrMur LrMm Lu.N: LUINn Lsu Mvv Ln.Ns» LrNru Abs. edge LINrr LmNv Lui Niv LuMr Lu.Msv LrnNr LIOILIU LrnMrr Abs, edge

9.3431 9.3371 9.3370 9.3153 9.2816 9.277 9.2761 9.2622 9.261 9.255 9.25174 9.2490 9.2417 9.2397 9.232 9.22482 9.2163 9.2124 9.1873 9.1845 9.1802 9.1751 9.1749 9.1634 9.144 9.1239 9.0995 9.089 9.087 9.0548 9.051 9.0489 9.0395 9.0272 9.0227 9.0227 9.0195 9.019 8.9803

XI

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TABLE

7£-2.

WAVELENGTHS OF X-RAY EMISSION LINES AND ABSORPTION EDGES: IN NUMERICAL ORDER

-

~

(Continued)

C \j

Wavelegth,

A*

p.e.f

Element

1.38109 1.3838 1.38477 1.3862 1.3864 1. 38696 1.3895 1.3898 1.3905 1. 39121 1. 3915 1.39220 1.392218 1.3923 1.3926 1.3948 1.3983 1. 40140 1.40234 1.4067 1.41366 1.41550 1. 41640 1. 4174 1. 4189 1. 42110 1.4216 1.4223 1.42278 1.4228 1.42359 1.4276 1.43025

3 1 3 1 1 7 2 1 1 5 1 5 9 2 1 1 2 5 5 3 7 5 7 2 1 3 1 1 7 3 3 2 9

29 Cu 70 Yb 81 TI 70 Yb 73 Ta 70 Yb 78 Pt 70 Yb 67 Ho 76 Os 70 Yb 72 Hf 29 Cu 67 Ho 29 Cu 70 Yb 67 Ho 71 Lu 76 Os 68 Er 79 Au 70 Yb 66 Dy 67 Ho 71 Lu 74W 80 Hg 65 Tb 66 Dy 65 Tb 71 Lu 65 Tb 72 Hf

Designation

K{32 L{39 Ll LnI L{317 L{3. L8 Ln Lal L{3l0 L{3. K{3l,3 L"(6 K{33 L{37 L"(f; L{33 La2 L"(5 Lt L{32,l. L"(3

i-« L{36 L.,., Ll Lr L"(2 L{3l L"(4

KMIV,V LrMv LmMr Abs, edge LnMm LnrOrv.v LrIIMrII LnrOrLrn Abs. edge LInMv LrMrv LrMn KMn,m LnOrv KMn LmOI LnOI LIM n i Liu Mvv LnNI LmMn Liu Niv,v LINIII LnNIv LmNr Lu M:

Lmi'!I Abs. edge LINrr LrOrv,v LnMIv LrOn,m LIMI

keY

8.9770 8.9597 8.9532 8.9441 8.9428 8.9390 8.923 8.9209 8.9164 8.9117 8.9100 8.9054 8.90529 8.905 8.9029 8.8889 8.867 8.8469 8.8410 8.814 8.7702 8.7588 8.7532 8.747 8.7376 8.7243 8.7210 8.7167 8.7140 8.714 8.7090 8.685 8.6685

Wavelength,

A* 1. 4941

1.4941 1.4995 1. 500135 1.5023 1.5035 1.5063 1.5097 1.51399 1.5162 1. 5178 1. 51824 1. 52197 1.52325 1.5297 1.5303 1.5304 1.53293 1. 5331 1.53333 1.5347 1.5368 1.5378 1. 5381 1.540562 1.54094 1.5439 1.544390 1.5448 1.5486 1. 5616 1.5632 1.5642

p.e.j

Element

3 3 2 8 1 2 2 2 9 2 1 7 2 5 2 2 2 2 2 9 2 1 2 1 2 3 1 9 2 3 1 1 3

68 Er 68 Er 78 Pt 28 Ni 65 Tb 65 Tb 69 Tm 65 Tb 68 Er 69 Tm 75 Re 66 Dy 73 Ta 72 Hf 64 Gd 65 Tb 69 Tm 73 Ta 64 Gd 71 Lu 76 Os 67 Ho 67 Ho 63 Eu 29 Cu 77 Ir 63 Eu 29 Cu 69 Tm 67 Ho 68 Er 64 Gd 74W

Designation

L{37 L{3l0 Ll K{3l,3 Ln L"(6 L{33 L"(8 L{32,l. L{36 L8 L"(. Lal L.,., L"(3 L"(l L{3l La2 L"(2 Lt LUI L{3. LI Kal Ll L"(4 Ka2 L{34 L{310 L{33 Ln L8

LmOI LIM rv LIIlMI KMn,In Abs, edge LnOrv LIM In LnOI LmNIv,v LmNr LmMnI

u.»,

LnrM v LnMr LrNm LnNIv LnMIv LmM Iv LINn Ln Mv: LmMIl Abs. edge LmOrv,v Abs. edge KLm LmMr LIOn,In KLu LIMn LIM l v LIM rri Abs, edge LnIMnI

keY

8.298 8.298 8.268 8.26466 8.2527 8.246 8.231 8.212 8.1890 8.177 8.1682 8.1661 8.1461 8.1393 8.105 8.102 8.101 8.0879 8.087 8.0858 8.079 8.0676 8.062 8.0607 8.04778 8.0458 8.0304 8.02783 8.026 8.006 7.9392 7.9310 7.926

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o

t'"

t'j

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t'4

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o

tn

1.43048 1.4318 1.43290 1.4334 1.4336 1.4349 1.435155 1.43643 1.439000 1.44056 1. 4410 1. 44396 1.4445 1. 44579 1.45233 1.4530 1.45964 1. 4618 1.4640 1.4661 1. 47106 1. 4718 1.47266 1. 4735 1.47565 1. 4764 1. 47639 1. 4784 1.48064 1.4807 1.4835 1.4839 1.4848 1.4855 1.48743 1.48807 1.48862 1. 49138 1.4930

9 2 4 1 3 2 7 9 8 5 3 5 1 7 5 2 9 2 2 1 5 2 7 2 5 2 2 1 9 3 1 2 3 5 2 1 4 3 3

73 77 75 69 69 69 30 72 30 71 69 75 66 66 70 78 79 67 69 70 73 65 66 76 70 65 74 64 72 64 68 64 68 68 74 28 28 70 77

Ta Ir Re Tm Tm Tm Zn Hf Zn Lu Tm Re Dy Dy Yb Pt Au Ho Tm Yb Ta Tb Dy Os Yb Tb W Gd Hf Gd Er Gd Er Er W Ni Ni Yb Ir

LnMn

L8 Len

u..«.«

Lm

Abs. edge

L{jg

LIM v LmOlv.v KLm

t.e, Kal L{j17 Ka2 L{j4

L{jlO

LmMv

LnMnI KLn LrMn LrMlv

La2 Ln L""6 L{j3 Lt Ll L.."s L{j2.1S L{j6 LTJ L""3 L""l L8

LrnMrv Abs. edge LnOrv

to.

LIIMlv LINII LmMv

L""2 Lal LI

LIMm

LnrMn LmMr LnNr Liu Nsv,v

LlnNI

u.u.

LrNrrr LnNrv

LrrrMnI

Abs. edge LIIMn LrOlv.v

Abs. edge LrOn.III LrnOrv.v

Lrn L""4 L{j5 L{jg La2 K

LlnMlv Abs. edge

L{j4 Lt

KMrv.v LIMn LIn MIl

tea,

LIM v

8.6671 8.659 8.6525 8.6496 8.648 8.641 8.63886 8.6312 8.61578 8.6064 8.604 8.5862 8.5830 8.5753 8.5367 8.533 8.4939 8.481 8.468 8.4563 8.4280 8.423 8.4188 8.414 8.4018 8.398 8.3976 8.3864 8.3735 8.373 8.3575 8.355 8.350 8.346 8.3352 8.33165 8.3286 8.3132 8.304

1.5644 1.5671 1. 5675 1.56958 1. 5707 1.5779 1.5787 1.5789 1.58046 1.58498 1.5873 1.58837 1.58844 1.5903 1. 5916 1.5924 1. 5961 1.59973 1.6002 1.6007 1. 60447 1.60728 1. 60743 1. 60815 1. 60891 1. 61264 1.61951 1.6203 1.62079 1.6237 1.62369 1.6244 1. 6271 1.6282 1.63029 1.63056 1.6346 1.63560 1. 6412

2 2 2 5 2 1 2 1 5 7 1 7 9 2 1 2 2 9 1 1 7 3 9 1 3 9 3 2 2 2 7 3 1 2 5 5 2 5 2

64 Gd 67Ho 68 Er 72 Hf 64 Gd 71 Lu 65 Tb 75 Re 72 Hf 76 Os 68 Er 66 Dy 70 Yb 63 Eu 66 Dy 64 Gd 63 Eu 66 Dy 628m 68 Er 66 Dy 628m 66 Dy 27 Co 27 Co 73 Ta 71 Lu 67 Ho 27 Co 67 Ho 66 Dy 74 W 63 Eu 63 Eu 71 Lu 75 Re 63 Eu 70 Yb 64 Gd

L.."e

uu.« t.e, u« L""8 L1'/ L.."s Lt La2 Ll

i.s, L{js

L""3

Lrn L""l L""2 L{jg Lr L{j4 L{j7 L""4

LnOlv LmNlv.v

LmNI LmMv

LnOI LnMI LnNr LmMn LmMrv LIIIM I LnMlv LmOrv.v LnMIl

LrNrn Abs. edge LnNrv LINn LrMv

Abs. edge LrMn LIIIOr

LrOn.rn

L{jlO

LIM rv

K K{j5 L8 Lal L{j3 K{jl.3 L{j6 L{j2.15 Lt Ln L""6 La2 Ll L""8 LTJ L""5

Abs. edge KMrv,v LrrrMm LmMv LrMm

KM n. n I LmNI

LurNiv,v LIIIMn Abs, edge LnOlv Lui Msv LrnMI

LnOI LnMI LnNI

7.925 7.911 7.909 7.8990 7.894 7.8575 7.8535 7.8525 7.8446 7.8222 7.8109 7.8055 7.8052 7.7961 7.7897 7.7858 7.7677 7.7501 7.7478 7.7453 7.7272 7.714 7.7130 7.70954 7.7059 7.6881 7.6555 7.6519 7.64943 7.6359 7.6357 7.6324 7.6199 7.6147 7.6049 7.6036 7.5849 7.5802 7.5543

:- ~ ~

>

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Z

o

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~

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Z

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is:: o ~

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U2

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TABLE

Wavelength,

7f-2.

WAVELENGTHS OF X-RAY EMISSION LINES AND ABSORPTION EDGES: IN NUMERICAL ORDER

A*

p.e.']

Element

1.6475 1.6497 1.6510 1. 65601 1.6574 1. 657910 1.6585 1.6595 1.66044 1. 661747 1.66346 1.6673 1.6674 1. 67189 1.67265 1.6782 1.68213 1.6822 1.68285 1.6830 1.6953 1.6963 1.6966 1.7085 1. 71062 1.7117 1.7130 1.7203 1. 72103 1.72305 1.7240 1.72724 1.7268

2 1 2 3 2 8 2 2 6 8 9 3 5 4 9 1 7 2 5 2 1 2 9 2 7 1 2 2 7 9 3 3 2

67 Ho 65 Tb 65 Tb 628m 63 Eu 28 Ni 65 Tb 67 Ho 628m 28 Ni 72 Hf 65 Tb 61 Pm 70 Yb 73 Ta 74 W 66 Dy 66 Dy 70 Yb 65 Tb 628m 69 Tm 628m 63 Eu 66 Dy 64 Gd 64 Gd 64 Gd 66 Dy 72 Hf 64 Gd 628m 69 Tm

Designation

L{31 Lt u L{3. L"{3 L"{l Kal L{37 L{34 L"{2 Ka2 L8 L{310 Lr Lal Lt Ll L{36 L{33 La2 L{32.1. Ln L.,., L"{6 L"{. L{31 LnI L{3. L{37 L{34 Lt L{39 L"{l Lal

LnM rv Abs. edge LrnOrv.v Lt N'ui LnNrv KLm LIIIOr LrM n LrN II KLII LurMIIr LrMrv Abs. edge LIIIM v LrIlM n LrnMr LnrNr LrM IIr LrnMrv Lau Nsv,v Abs. edge LIiMr LnOrv LnNr LnM rv Abs. edge LUIOrv.v LIIIOr LrMn LrIlM u LIMV LnNIv LrnMv

keY

7.5253 7.5153 7.5094 7.487 7.4803 7.47815 7.4753 7.4708 7.467 7.46089 7.4532 7.436 7.436 7.4156 7.4123 7.3878 7.3705 7.3702 7.3673 7.3667 7.3132 7.3088 7.308 7.2566 7.2477 7.2430 7.2374 7.2071 7.2039 7.1954 7.192 7.178 7.1799

Wavelength,

r

(Continued)

~ ~

A*

p.e.f

Element

1.8450 1.8457 1.8468 1.84700 1.8540 1.8552 1. 8561 1.85626 1. 86166 1.86990 1.8737 1.8740 1.8779 1.8791 1. 8821 1.8867 1.8934 1. 89415 1.89643 1.8971 1. 89743 1. 8991 1. 90881 1. 91021 1. 9191 1. 91991 1.9203 1.9255 1.9255 1.9355 1.936042 1.9362 1.939980

2 1 2 9 2 5 2 3 3 3 2 4 2 4 3 2 5 5 5 1 7 4 3 2 1 3 2 2 5 4 9 4 9

67 Ho 628m 64 Gd 628m 64 Gd 60 Nd 67 Ho 628m 628m 628m 63 Eu 59 Pr 60 Nd 59 Pr 628m 63 Eu 58 Ce 70 Yb 25 Mn 25 Mn 66 Dy 58 Ce 66 Dy 25 Mn 61 Pm 66 Dy 63 Eu 63 Eu 59 Pr 60 Nd 26 Fe 59 Pr 26 Fe

Designation

Len Lnr L{31 L{3. L{34 L"{8 La2 L{37 L{39 L{310 L{36 L"{3 L"{l L"{2 L{32.1. L{33 Lr Ll K K{3. L.,., L"{4 Loa K{3I.3 Lrn La2 L{31 L{34 LII L"{5

s:«,

L"t8 Ka2

LrnMv Abs. edge LnMrv LrnOrv.v LrMn LnOr Litt Msv

LIIIOr LrMv LrMrv LmNr LrNIIr LIINrv LrNn LrnNrv.v LrMm Abs. edge LmMr Abs. edge KM rv•v LIIMr Lr On.I1r LmMv KMn.rIl Abs. edge LrIlM rv LuMrv LrMu Abs. edge LnNr KLm LIIOI KLn

keY

6.7198 6.7172 6.7132 6.7126 6.6871 6.683 6.6795 6.679 6.660 6.634 6.6170 6.616 6.6021 6.598 6.586 6.5713 6.548 6.5455 6.5376 6.5352 6.5342 6.528 6.4952 6.49045 6.4605 6.4577 6.4564 6.4389 6.439 6.406 6.40384 6.403 6.39084

o

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8

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o

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Z

tl ~

o

t"4

tr.j

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o

tn

1. 72841 1.7315 1.7381 1.7390 1. 7422 1. 74346 1. 7442 1. 7445 1. 7455 1.7472 1.75661 1.7566 1.7676 1. 7760 1. 7761 1. 7768 1.7772 1.77934 1. 78145 1.78425 1. 7851 1.7864 1.788965 1. 7916 1.792850 1.7955 1.7964 1.7989 1.7993 1.8013 1.8054 1.8118 1.8141 1. 8150 1. 8193 1.8264 1. 83091 1.8360 1.8440

5 3 2 1 2 1 1 4 2 2 2 1 5 1 1 3 2 3 5 9 2 2 9 3 9 2 4 9 3 4 2 2 5 2 4 2 9 1 1

73 Ta 64 Gd 69 Tm 60 Nd 65 Tb 26 Fe 26 Fe 60 Nd 64 Gd 65 Tb 26 Fe 68 Er 61 Pm 71 Lu 63 Eu 65 Tb 63 Eu 628m 72 Hf 68 Er 63 Eu 65 Tb 27 Co 63 Eu 27 Co 68 Er 60 Nd 61 Pm 63 Eu 60 Nd 64 Gd 63 Eu 59 Pr 64 Gd 59 Pr 67 Ho 70 Yb 71 Lu 60 Nd

Ll L(310 La2 LI L(3s K K(3s LY4

L(32.1S

LmMI LIMIv

LIIIMIV Abs. edge LmNI

Abs. edge KM I V.V

LIOn,nI LnINIv,v LIMnI

L(33 K(3I.3 LTJ Ln Lt

LmMn

LnI

Abs. edge

L(31 L(3s

LnMIV

Lys

LnNI LmMI LInMv LmOI LIMn KLm LIM v KLn LmMIv LINm LnNIv LIMIV LINn

Ll Lal L(37 L(34 Kal L{39 Ka2 La2

Lya LYI L(310 LY2 L(3s L(32,1& LI L(33 L"(4 LTJ Lt Ll Ln

«v«,«

LnMI

Abs. edge

LnIOIv.v

LnINI LmNIV,V

Abs. edge LIMm

LI On,IlI LIIM I

LInMn LInMI Abs. edge

7.1731 7.160 7.1331 7.1294 7.1163 7.11120 7.1081 7.107 7.1028 7.0959 7.05798 7.0579 7.014 6.9810 6.9806 6.978 6.9763 6.968 6.9596 6.9487 6.9453 6.9403 6.93032 6.920 6.91530 6.9050 6.902 6.892 6.890 6.883 6.8671 6.8432 6.834 6.8311 6.815 6.7883 6.7715 6.7528 6.7234

1.94643 1.9550 1.9553 1.9559 1.9602 1. 9611 1.96241 1.9730 1.9765 1.9780 1.9830 1. 9875 1.9967 1.99806 2.00095 2.0092 2.0124 2.015 2.0165 2.0205 2.0237 2.0237 2.0360 2.0410 2.0421 2.0460 2.0468 2.0487 2.0494 2.0578 2.0678 2.07020 2.07087 2.0756 2.0791 2.0797 2.08487 2.0860 2.0919

3 2 3 6 3 3 3 2 2 5 4 2 1 3 6 3 5 1 3 4 4 3 3 4 4 4 2 4 1 2 5 5 6 3 5 4 2 2 4

628m 69 Tm 58 Ce 61 Pm 58 Ce 59 Pr 628m 65 Tb 65 Tb 57 La 57 La 65 Tb 60 Nd 628m 628m 60 Nd 58 Ce 68 Er 60 Nd 59 Pr 58 Ce 60 Nd 60 Nd 57 La 61 Pm 57 La 64 Gd 58 Ce 64 Gd 64 Gd 56 Ba 24 Cr 24 Cr 56 Ba 59 Pr 61 Pm 24 Cr 67 Ho 59 Pr

L(3s Ll LY3

LmNI LmMI LINm

L(32.1S

Lm Nvv;v

LY2

LINn LIINIV

LYI L(33 LTJ Lal LI LY4 La2 LUI L(31 L(34 L(37 Ln Ll L(39

Lys LY8 L(310 L(32.lf> LY3 L{33 LY2 t:«.

LYI LTJ La2 LI K K(3& LY4

Lm L(31 K(31,3 Ll L(37

LIMnI LnMI LmMv

Abs. edge LIOn,III LInMIv

Abs. edge LnMIv LIMn LmOI

Abs. edge LInMI LIMv LnNI LnOI LrMIv

LnINIv,v Lt Nti: LIMm LINn LJIlMv LIINI V LnMI

LInMIv Abs. edge Abs. edge KilfIV, v LIOn,In Abs. edge LnMIv

KMn,III Lut.M: LmOI

6.3693 6.3419 6.3409 6.339 6.3250 6.3221 6.318 6.2839 6.2728 6.268 6.252 6.2380 6.2092 6.2051 6.196 6.1708 6.161 6.152 6.1484 6.136 6.126 6.1265 6.0894 6.074 6.071 6.060 6.0572 6.052 6.0495 6.0250 5.996 5.9888 5.9869 5.9733 5.963 5.961 5.94671 5.9434 5.927

~ I

~

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:a ~

~

e-

~

Z

l:;:l

8

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Z

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o

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Z

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l:;:l ~

t' ~

< ~ t'

U1

j1 ~

I+:>-

~

TABLE

7f-2.

WAVELENGTHS OF X-RAY EMISSION LINES AND ABSORPTION EDGES: IN NUMERICAL ORDER

-..:I

(Continued)

I

....... tv ~

Wavelength,

A*

p.e·t

Element

2.1004 2.101820 2.1039 2.1053 2.10578 2.1071 2.1103 2.1194 2.1209 2.1268 2.1315 2.1315 2.1342 2.1387 2.1418 2.15877 2.166 2.1669 2.1669 2.1673 2.1701 2.1741 2.1885 2.1906 2.1958 2.1998 2.2048 2.2056 2.2087 2.21062 2.2172 2.21824 2.2328

4 9 3 5 2 4 3 4 2 2 2 2 2 2 3 7 1 3 2 5 2 2 3 4 5 2 1 4 2 3 3 3 2

59 Pr 25 Mn 60 Nd 57 La 25 Mn 59 Pr 58 Ce 59 Pr 63 Eu 60 Nd 63 Eu 63 Eu 56 Ba 56 Ba 57 La 66 Dy 58 Ce 60 Nd 60 Nd 55 Cs 58 Ce 55 Cs 58 Ce 59 Pr 58 Ce 62 Sm 56 Ba 57 La 58 Ce 62 Sm 59 Pr 62 Sm 55 Cs

Designation

L{39

««.

L{36 Ln K'a2 L{310 L'Y5 L{32.15 t.«.

L{33 L." La2 L'Y3 L'Y2 L'Yl Ll LnI L{34 L{31 LI L{37 L'Y4 L{39 L{36 L{310 t.«.

Ln L'Y5 L{32.15 La2 L{33 L." L'Y3

LIM v KLm LmNI Abs, edge KLn Lt'MIV LrrNI Ltu Nsv;v Lni Mv LIMm LnMI LmMlv LIN m LINn LnNlv LIIIllIy Abs. edge LIMn LnMlv Abs. edge LIlIOI LIOn.ln LIMv LmNI LIMlv Lin M.v Abs. edge LnNI LIIINIV.V LlnMlv LIMm LIlM I LINIn

keY

5.903 5.89875 5.8930 5.889 5.88765 5.884 5.8751 5.850 5.8457 5.8294 5.8166 5.8166 5.8092 5.7969 5.7885 5.7431 5.723 5.7216 5.7216 5.721 5.7132 5.7026 5.6650 5.660 5.646 5.6361 5.6233 5.621 5.6134 5.6090 5.5918 5.589 5.5527

Wavelength,

A*

p.e.j

2.4094 2.4105 2.4174 2.4292 2.442 2.443 2.4475 2.4493 2.45891 2.4630 2.4729 2.4740 2.4783 2.4823 2.4826 2.4849 2.4920 2.49734 2.4985 2.50356 2.50738 2.5099 2.5113 2.5118 2.512 2.51391 2.5164 2.527 2.5542 2.5553 2.5615 2.5674 2.56821

4 3 2 1 9 4 2 3 5 2 3 1 2 4 2 2 2 5 2 2 2 1 2 2 3 2 2 4 5 2 2 2 5

Element

60 57 55 54 90 92 53 57 57 59 59 55 55 62 56 55 55 22 22 23 23 52 52 55 59 22 56 91 53 56 58 52 56

Nd La Cs Xe Th U I La La Pr Pr Cs Cs Sm Ba Cs Cs Ti Ti V V Te Te Cs Pr Ti Ba Pa I Ba Ce Te Ba

Designation

L." L{3a L'Y5 Ln L'Y2,3 L{34 L{31 Lal La2 LIn L{39 Ll L{36 L{37 L{310 K K{35 tc«.

Ka2 LI L'Y4 L{32,15 L." K{31,3 L{33 Ln L{34 i.«.

L'Y2.3 L{31

LnMI LIM n I LnNr Abs. edge MIO m MnO rv LINn,In LIMn LnMlv Lsu Mv LInMIv Abs. edge LIM v LmMI LmNI LmOI LIMlv Abs. edge KMIV,V KLm KLn Abs. edge LIOn.nI LmNlv.v LnM I KM n. n I LIMm MnO lv Abs. edge LIMn LIIIM v LINn. n I LnMlv

keY

5.1457 5.1434 5.1287 5.1037 5.08 5.075 5.0657 5.0620 5.0421 5.0337 5.0135 5.0113 5.0026 4.9945 4.9939 4.9893 4.9752 4.96452 4.9623 4.95220 4.94464 4.9397 4.9369 4.9359 4.935 4.93181 4.9269 4.906 4.8540 4.8519 4.8402 4.8290 4.82753

> l-3 o ;s;:

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o

rJ2

2.2352 2.2371 2.2415 2.253 2.2550 2.2588 2.261 2.2691 2.26951 2.2737 2.275 2.282 2.2818 2.2822 2.28440 2.28970 2.290 2.2926 2.293606 2.3030 2.304 2.3085 2.3109 2.3122 2.3139 2.3480 2.3497 2.3561 2.3629 2.3704 2.3764 2.3790 2.3806 2.3807 2.3869 2.3880 2.3913 2.3948 2.40435

2 2 2 6 4 3 1 1 6 1 3 3 3 3 2 2 3 4 3 3 7 3 3 2 1 2 4 3 1 2 2 4 2 3 2 5 2 2 6

65 55 56 92 59 59 57 23 23 54 57 57 58 61 23 24 57 61 24 57 92 56 58 64 55 55 58 58 56 60 56 57 56 60 56 53 53 63 56

Tb Cs Ba U Pr Pr La V V Xe La La Ce Pm V Cr La Pm Cr La U Ba Ce Gd Cs Cs Ce Ce Ba Nd Ba La Ba Nd Ba I I Eu Ba

Ll L"{2 i-, L{34 L{31 Lnl K K{35 LI L{37 L{3g L{36 t.«.

K{31,3 Kal L{310 La2 Ka2 L{32,15 L"{5 L{33 Ll LII L"{l L{34 L{31 LIn t.«.

L{3g L{36 L{37 La2 L{310 Lr L"{4 Ll L{32, 15

LmMI LINn LnNlv MIPm LIMn LnMlv Abs. edge Abs. edge KMlv,v Abs, edge LmOr LIMv LmNI LmMv KMn,nr KLm LrMrv Ltu Ms» KLn LmNlv,v MIO rn

u.».

Li Msi: LmMI

Abs. edge LIINrv LIMn LIIkIrv Abs. edge LmMv LIMv LmNI LmOI LruMrv LrMlv Abs. edge LrOII,IIr LmMr LmNrv,v

5.5467 5.5420 5.5311 5.50 5.4981 5.4889 5.484 5.4639 5.4629 5.4528 5.450 5.434 5.4334 5.4325 5.42729 5.41472 5.415 5.4078 5.405509 5.3835 5.38 5.3707 5.3651 5.3621 5.3581 5.2804 5.2765 5.2622 5.2470 5.2304 5.2171 5.2114 5.2079 5.2077 5.1941 5.192 5.1848 5.1772 5.1565

2.5706 2.58244 2.5926 2.5932 2.618 2.6203 2.6285 2.6388 2.6398 2.65710 2.66570 2.6666 2.67533 2.6760 2.6837 2.6879 2.6953 2.71241 2.71352 2.7196 2.72104 2.7288 2.740 2.74851 2.75053 2.75216 2.753 2.762 2.7634 2.77595 2.7769 2.7775 2.7796 2.7841 2.78553 2.79007 2.817 2.8294 2.8327

3 8 1 2 5 4 2 1 2 9 5 2 5 4 2 1 2 6 9 5 9 3 3 2 8 2 8 1 3 5 1 2 2

4 5 9 2 5 2

58 Ce 53 I 54 Xe 55 Cs 90 Th 58 Ce 55 Cs 51 Sb 51 Sb 53 I 57 La 55 Cs 57 La 60 Nd 55 Cs 52 Te 51 Sb 52 Te 53 I 53 I 53 I 53 I 57 La 22 Ti 53 I 22 Ti 92 U 21 Se 21 Se 56 Ba 50 Sn 50 Sn 21 Se 59 Pr 56 Ba 52Te 92 U 51 Sb 50 Sn

La2 L"{l Lm L{36 LTJ L{33 Lr L"{4 L"{5 i.«.

L{34 La2 Ll L{31 Ln L"{2,3 L"{l L{3g LUI L{310 L{37 LT] Kal L{32,15 Ka2 K K{35

t.s,

LI L"{4 K{31,3 Ll La2 L"{5 LII L"{2,3

LnlMlv Ln Ni» Abs. edge LIIINI MIIOIV LnMr LIM m Abs. edge LIOn,ln LnNr LrnMv LrMn

Iau Msv Liu M': LIIM rv Abs. edge Lt Nvi.u: LnNlv LrMv Abs. edge LIMlv LmOr LnMr Klaii Lni Nsv,v KLn MINm Abs. edge KMrv,v LrIIMv Abs. edge LIOn,rn KMn,nr

Lsn M: LmMrv LnNr MIINrv Abs. edge LrNn,lII

4.8230 4.8009 4.7822 4.7811 4.735 4.7315 4.7167 4.6984 4.6967 4.6660 4.65097 4.6494 4.63423 4.6330 4.6198 4.6126 4.5999 4.5709 4.5690 4.5587 4.5564 4.5435 4.525 4.51084 4.5075 4.50486 4.50 4.489 4.4865 4.46626 4.4648 4.4638 4.4605 4.4532 4.45090 4.4437 4.401 4.3819 4.3768

XI

~

;> t--

A*

p.e.']

Element

3.27404 3.27979 3.283 3.28920 3.29846 3.30585 3.30635 3.31216 3.3237 3.324 3.3257 3.329 3.333 3.33564 3.33838 3.34335 3.346 3.35839 3.359 3.36166 3.38487 3.42551 3.43015 3.43606 3.4365 3.4367 3.437 3.43832 3.43941 3.441 3.4413 3.44840 3.4539

9 9 9 6 9 3 9 9 1 4 1 4 5 6 3 9 5 3 5 3 3 9 9 9 1 2 1 9 4 5 4 6 2

49 In 53 I 90 Th 52 Te 52 Te 50 Sn 47 Ag 47 Ag 49 In 49 In 48 Cd 92 U 92 U 48 Cd 49 In 50 Sn 81 Tl 20 Ca 8"3 Bi 20 Ca 50 Sn 48 Cd 48 Cd 49 In 19 K 48 Cd 46 Pd 52 Te 51 Sb 91 Pa 19 K 51 Sb 19 K

Designation

L~lO

LYJ

LIMlv LnMy

MlnO y i:«. La2 L~3

LY3 LY2

tIll

LmMv LmMlv LyM m LIN m LINn

Ln

Abs. edge LIIIOI Abs. edge

Myv LYI

Abs. edge Ln Ntv

L~2,l5 L~4

LuyNyv,v

L~7

MuNy

MI Kal

Mu Ka2

LIMn Abs. edge KLm

Abs. edge KLlY

cs,

Lu Msv

Lys

LnNI LIMv LmNI

L~9 L~6

K

Abs. edge

L~lO

LIM IV

LI L." t.«.

tee, La2

xe«,

Abs. edge LuMI LmMv MIIN I KM l v• v

LIUMIv KMu,IU

keY

3.7868 3.7801 3.78 3.76933 3.7588 3.7500 3.7498 3.7432 3.7302 3.730 3.7280 3.724 3.720 3.71686 3.71381 3.7083 3.705 3.69168 3.691 3.68809 3.66280 3.61935 3.61445 3.60823 3.6078 3.6075 3.607 3.60586 3.60472 3.603 3.6027 3.59532 3.5896

~

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o

tn

3.011 3.0166 3.02335 3.0309 3.0342 3.038 3.04661 3.068 3.0703 3.0746 3.07677 3.08475 3.0849 3.0897 3.094 3.11513 3.11513 3.115 3.12170 3.131 3.1355 3.1377 3.1473 3.14860 3.15258 3.1557 3.1564 3.15791 3.16213 3.17505 3.19014 3.217 3.22567 3.245 3.24907 3.2564 3.2670 3.26763 3.26901

2 2 3 1 1 2 9 5 1 3 6 9 1 2 5 9 9 7 9 3 2 2 1 6 9 1 3 6 4 3 9 5 4 9 9 1 2 9 9

90 54 51 21 21 91 52 90 20 20 52 50 48 20 83 50 51 92 50 90 56 48 49 53 51 50 50 53 49 50 51 82 51 91 49 47 55 49 50

Th Xe Sb Se Se Pa Te Th Ca Ca Te Sn Cd Ca Bi Sn Sb U Sn Th Ba Cd In I Sb Sn Sn I In Sn Sb Pb Sb Pa In Ag Cs In Sn

MIINyv LOll Lfh15 Kal Ka2 LfJ.

Mnr K KfJs LfJl L'}'s Ly KfJl,3

LruMv

Lui Nsv,» KLIIY KLII MmOrv. v LrMn

Abs. edge Abs. edge KMrv,v

Lu Mvv Ln Ns Abs. edge KMIJ.rn

Mr

Abs. edge

LfJg LfJ6

LrM v LmNr

MilrOy LfJIO

LrMrv

MurOrv,v Ll L'}'2 Ln Lal LfJ3

Lur LfJ7 La2 L'}'l LfJ2.1S LfJ4 MI

ce,

L'}'s Lr Ll LfJg LfJ6

LIIIMy LrNn

Abs. edge LrIlM v LIMn y

Abs. edge LnrOr LIITMI V LnNIv Ltit Nvv,v

LIMn

Abs. edge LnMIv MIll 01 LnNI

Abs. edge LmMr LIM v LUINI

4.117 4.1099 4.10078 4.0906 4.0861 4.081 4.0695 4.041 4.0381 4.0325 4.02958 4.0192 4.0190 4.0127 4.007 3.9800 3.9800 3.980 3.9716 3.959 3.9541 3.9513 3.9393 3.93765 3.9327 3.9288 3.9279 3.92604 3.92081 3.90486 3.8364 3.854 3.84357 3.82 3.8159 3.8072 3.7950 3.7942 3.7926

3.46984 3.478 3.479 3.4892 3.492 3.497 3.5047 3.50697 3.51408 3.5164 3.521 3.52260 3.537 3.55531 3.557 3.55754 3.576 3.577 3.59994 3.60497 3.60765 3.60891 3.61158 3.614 3.61467 3.61638 3.616 3.629 3.634 3.64495 3.679 3.68203 3.6855 3.691 3.6999 3.70335 3.716 3..71696 3.718

9 5 1 2 5 5 1 9 4 1 2 4 9 4 5 9 1 1 3 9 9 4 9 2 9 9 5 5 5 9 2 9 2 2 1 3 1 9 3

49 80 92 46 82 92 48 49 48 47 92 47 90 49 90 53 92 91 50 47 51 50 47 91 48 47 79 45 81 48 90 48 45 91 47 47 92 52 90

In Hg U Pd Pb U Cd In Cd Ag U Ag Th In Th I U Pa Sn Ag Sb Sn Ag Pa Cd Ag Au Rh Tl Cd Th Cd Rh Pa Ag Ag U Te Th

Lfh

LrMIJY

My

Abs. edge

M'}' L'}'2,3

MIl Mv Lrn

MmN v

LrNn.nr Abs. edge Abs. edge Abs. edge

LfJ. LfJ2.1S Ln

LyMn Ltu Ntv,v

L'}'l

LnNyv

Abs. edge MmNyv MnNy

LfJl

LnMrv

Mrv

Abs. edge LnrMr

Ll

MrvOn M'}' t.«. LfJg L7] La2 LfJlO LfJ6 L'}'s My Lr Mn LfJ3 M'}' LfJ4 L'}'2.3

Msn.N» Lni M» LrMv LnMr LmMyv L1Mrv MllrNIv LInNy LnNI

Abs. edge Abs. edge Abs. edge LIMnI

MlnNv LIMn

LrNn.nI MlvOn

LUI LfJ2,lS MfJ Ll

Abs. edge LllrNrv.v MIVNVI LIIIMI

MlnNlv

3.57311 3.565 3.563 3.5533 3.550 3.545 3.5376 3.53528 3.52812 3.5258 3.521 3.51959 3.505 3.48721 3.485 3.48502 3.4666 3.4657 3.44398 3.43917 3.43661 3.43542 3.43287 3.430 3.42994 3.42832 3.428 3.417 3.412 3.40145 3.370 3.36719 3.3640 3.359 3.35096 3.34781 3.3367 3.33555 3.335

XI

~

>~

~

~

t':1 t'i

t':1

Z

o~

= tn

>-

Z

~

>-~

o

~ H

o t'j

Z

t':1

~

o

~

t'i

t':1

~

t':1 t'i

rn

~ I-" ~

01

TABLE

7f-2.

WAVELENGTHS OF X-RAY EMISSION LINES AND ABSORPTION EDGES: IN NUMERICAL ORDER

~

(Continued)

~

Wavelength,

A*

p.e.f

3.7228 3.7246 3.729 3.73823 3.740 3.7414 3.7445 3.760 3.762 3.77192 3.78073 3.783 3.78876 3.7920 3.7988 3.80774 3.808 3.8222 3.827 3.83313 3.834 3.835 3.87023 3.87090 3.872 3.8860 3.88826 3.892 3.8977 3.904 3.9074 3.90887 3.910

1 2 5 4 9 2 2 9 5 4 6 5 9 2 2 9 4 2 1 9 4 5 5 5 9 2 9 9 2 5 1 4 1

Element

46 46 90 48 83 19 19 90 78 49 49 80 50 46 46 47 90 46 91 47 83 44 47 18 82 18 51 83 44 83 46 46 92

Pd Pd Th Cd Bi K K Th Pt In In Hg Sn Pd Pd Ag Th Pd Pa Ag Bi Ru Ag A Pb A Sb Bi Ru Bi Pd Pd U

Designation

Ln L"(l Mv

Abs. edge Lu Nsv Abs. edge

io,

Ln Mv«

MINnI Kal Ka2

KLm KLn MvPm

MI

Abs. edge Liu.M.» LnlMlv Abs. edge

t.«, La2 MIl L.,., LfJv LfJlO LfJ6

LnMI Li M.» LrMIv LmNI

MrvOn L"(5 MfJ LfJ3

LnNI MlvNvl

LIMnr MnNIv

LI LfJ4 K KfJI,3 Ll L"(2,3 M nI LnI LfJ2,l6 Mal

Abs. edge LrMn

Abs, edge MINnI KMn,In LmMr MINn LINn , I1I

Abs. edge Abs. edge LIIINIV,v MvNvn

keY

3.33031 3.3287 3.325 3.31657 3.315 3.3138 3.3111 3.298 3.296 3.28694 3.27929 3.277 3.27234 3.2696 3.2637 3.25603 3.256 3.2437 3.2397 3.23446 3.234 3.233 3.20346 3.20290 3.202 3.1905 3.18860 3.185 3.1809 3.176 3.17298 3.17179 3.1708

Wavelength,

~

A*

p.e.f

Element

4.198 4.216 4.236 4.2417 4.244 4.2522 4.260 4.26873 4.2873 4.2888 4.300 4.304 4.330 4.355 4.36767 4.369 4.3718 4.37414 4.37588 4.3800 4.3971 4.4034 4.407 4.4183 4.432 4.433 4.436 4.44 4.450 4.460 4.48014 4.4866 4.4866

1 6 5 2 9 2 5 9 2 2 9 5 2 1 5 1 2 4 7 2 1 3 5 2 4 5 1 2 4 9 9 3 3

81 TI 81 Tl 75 Re 45 Rh 82 Pb 45 Rh 77 Ir 49 In 44 Ru 45 Rh 79 Au 42 Mo 92 U 80 Hg 46 Pd 44 Ru 44 Ru 45 Rh 46 Pd 42 Mo 17 CI 17 CI 74W 47 Ag 79 Au 76 Os 43 Te 74 W 91 Pa 78 Pt 48 Cd 44 Ru 44 Ru

Designation

MI

Abs. edge MmOlv,v Abs. edge

LfJ3

LmNI Mill 01 LIMm

Mnl

t.s, Mn Ll L"(5 LfJ4 LI

Abs. edge LlnMI LnNI LIMn MrNm

Abs. edge MmNI

M rn

Abs. edge

t.«, Lm LfJ2,l5 LfJI La2 L"(2,3 K K(3

LmMv

Mr

Abs. edge

L.,.,

LnMr MnNrv

Mn

Abs. edge Abs. edge MIOn.ln

Ln

Ll LfJ3 LfJa

Abs. edge LrnNlv,v LnMrv Lmkfrv

LINn,rn Abs, edge KM

MlnNI MrNnI LlnMI LIMm LmNr

keY

2.9535 2.941 2.927 2.9229 2.921 2.9157 2.910 2.90440 2.8918 2.8908 2.883 2.881' 2.863 2.8469 2.83861 2.8377 2.8360 2.83441 2.83329 2.8306 2.81960 2.8156 2.813 2.8061 2.797 2.797 2.7948 2.79 2.786 2.780 2.76735 2.7634 2.7634

O':l

>

8

o

s::: >-1 o

>

Z

t::1

s:::

o

~

t':l

o q e-

>

::t1 Iod

::z:

~ lfl

>-1

o

in

3.915 3.924 3.932 3.93473 3.936 3.941 3.9425 3.9437 3.95635 3.96496 3.968 3.98327 4.013 4.0162 4.022 4.0346 4.035 4.0451 4.047 4.058 4.069 4.0711 4.071 4.07165 4.093 4.105 4.116 4.1299 4.rnO 4.1381 4.14622 4.151 4.15443 4.16294 4.180 4.1822 4.19180 4.19315 4.19474

5 1

6 3 5 1 5 2 4 6 5 9 9 2 1 2 3 2 1 5 6 2 5 9 5 9 4 5 2 9 5 2 3 5 1 2 5 9 5

77 Ir 92 U 83 Bi 47 Ag 79 Au 90 Th 45 Rh 45 Rh 48 Cd 48 Cd 82 Pb 49 In 81 Tl 46 Pd 91 Pa 46 Pd 91 Pa 45 Rh 82 Pb 43 Te 82 Pb 46 Pd 76 Os 50 Sn 78 Pt 83 Bi 81 Tl 45 Rh 45 Rh 90 Th 46 Pd 90 Th 47 Ag 47 Ag 44 Ru 44 Ru 18 A 48 Cd 18 A

MI Ma2

Abs. edge MvNvI MnIOIv,V

Lfjl Mu Mfj Ln L'Y1 LOll La2

LnMIv

Abs. edge MIVNvI Abs. edge LnNIv LmMv LmMIv

MnNIv L." Lfj6 Mal Lfja Ma2 L'Y5

MIll LI Lfj4 MI Ll Mn

Lnl Lfj2,l5 Mal Lfjl Ma2 Lal La2 Ln L'Y1 Ka1 L." Ka2

LnMI MINn I

LInNI MvNvn LIMm

MvNvI LnNI

Abs. edge Abs. edge MnIOIv,V LIMn

Abs. edge LmMI

Abs. edge MmOI MnNIv Abs. edge

Lin Nsv,v MvNvn LnMlv MvNvI LmMv

Iau Msv Abs. edge LnNIv KLm LIIMI KLn

3.167 3.1595 3.153 3.15094 3.150 3.1458 3.1448 3.1438 3.13373 3.12691 3.124 3.11254 3.089 3.0870 3.0823 3.0730 3.072 3.0650 3.0632 3.055 3.047 3.0454 3.045 3.04499 3.029 3.021 3.013 3.0021 3.0013 2.9961 2.99022 2.987 2.98431 2.97821 2.9663 2.9645 2.95770 2.95675 2.95563

4.518 4.522 4.5230 4.532 4.568 4.571 4.572 4.575 4.585 4.59 4.59743 4.601 4.60545 4.620 4.62058 4.625 4.630 4.631 4.6542 4.655 4.6605 4.674 4.686 4.694 4.703 4.7076 4.715 4.719 4.7258 4.7278 4.7307 4.757 4.764 4.780 4.79 4.815 4.823 4.823 4.8369

1 6 2 2 5 5 5 5 5 2 9 4 9 5 3 5 1 9 2 8 2 1 1 8 9 2 3 1 2 1 1 5 5 4 2 5 3 4 2

79 Au 79 Au 44 Ru 83 Bi 90 Th 83 Bi 83 Bi 41 Nb 73 Ta 83 Bi 45 Rh 78 Pt 45 Rh 75 Re 44 Ru 92 U 43 Tc 77 Ir 41 Nb 82 Pb 46 Pd 82 Pb 78 Pt 78 Pt 79 Au 47 Ag 82 Pb 42 Mo 42 Mo 17 Cl 17 Cl 82 Pb 83 Bi 77Ir 76 Os 74 W 83 Bi 81 Tl 42 Mo

MIn

Abs. edge MmOIv,v

Lfj4 M'Y

LIMn

MInNv MmNI MmNIv

M IV LI MI

Loa La2 Mn

Abs. edge Abs. edge Abs, edge MIvPn,In LnIMv MnNIV LmMIv

Abs. edge

t.e,

LIIMIV

LUI

MIVNIU Abs. edge

L'Y2,a L." M'Y

Min Ll Ln L'YI Kal Ka2

M IV Mv

MINm LINn,IIl MuNI LnMI

MInNv Abs. edge MmOlv,v MIlIOI LmMI

MInNlv Abs. edge LnNIv KLm KLn

Abs. edge Abs, edge MnNlv MINm

MIl

Abs. edge MlvOn

M'Y L'Y5

MmNv LnNI

2.7439 2.742 2.7411 2.735 2.714 2.712 2.711 2.710 2.704 2.70 2.69674 2.695 2.69205 2.684 2.68323 2.681 2.6780 2.677 2.6638 2.664 2.6603 2.6527 2.6459 2.641 2.636 2.6337 2.630 2.6274 2.6235 2.62239 2.62078 2.606 2.603 2.594 2.59 2.575 2.571 2.571 2.5632

~ I

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:a ~

t?'.1

to"

t?'.1

Z

o

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==

r:J).

>

Z

t::1

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I-l

o

t?'.1

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t?'.1 ~

o

~

to"

t?'.1

-< t?'.1

~

tn

jl """'"

~

.....:J

TABLE

7f-2.

WAVELENGTHS OF X-RAY EMISSION LINES AND ABSORPTION EDGES: IN NUMERICAL ORDER

~

(Continued)

~

t+:o-

Wavelength,

A*

p.e.']

Element

4.84575 4.85381 4.861 4.865 4.869 4.876 4.879 4.8873 4.909 4.911 4.913 4.9217 4.9232 4.946 4.952 4.9525 4.9536 4.955 4.955 4.984 5.004 5.0133 5.0185 5.020 5.0233 5.031 5.0316 5.0361 5.043 5.0488 5.0488 5.050 5.076

5 7 1 5 9 9 5 8 1 5 1 2 2 2 5 3 3 4 5 2 9 3 1 5 3 1 2 3 5 3 5 2 1

44 Ru 44 Ru 77 Ir 81 TI 77 Ir 78 Pt 40 Zr 43 Tc 83 Bi 90 Th 42 Mo 45 Rh 42 Mo 92 U 81 TI 46 Pd 40 Zr 76 Os 82 Pb 80 Hg 82 Pb 42 Mo 16 S 73 Ta 16 S 41 Nb 16 S 41 Nb 76 Os 42 Mo 42 Mo 92 U 82 Pb

Designation

Lal La2 MIll

LIIIMv

LIIIM IV Abs. edge MIIIN I V

MIIIOIV,V MmO I LI

Abs. edge

L~l M~

LIIMI V MIVNvI MIVNIII

LIII L." L~2,15

su,

MIV Ll L'Y2,3

Abs. edge LIIM I LIIINIV.V MvN m

Abs. edge LIIIM I

LINII.III MIIN I V

Mv M'Y L~3

K MIl

tee;

Abs. edge MIIINv MIVOII

LIMIII Abs. edge Abs. edge KM

LII

Abs. edge

K~l

KM LIINIV

L'YI

MIll

Abs. edge

L~4 L~6

LIM II LmNI MIVNn MrvNvI

Mr2 M{3

keY

2.55855 2.55431 2.5505 2.548 2.546 2.543 2.541 2.5368 2.5255 2.524 2.5234 2.5191 2.5183 2.507 2.504 2.5034 2.5029 2.502 2.502 2.4875 2.477 2.4730 2.47048 2.470 2.4681 2.4641 2.46404 2.4618 2.458 2.4557 2.4557 2.4548 2.4427

Wavelength,

A*

p.e.f

5.40655 5.41437 5.4318 5.435 5.460 5.472 5.4923 5.4977 5.500 5.5035 5.537 5.540 5.570 5.579 5.584 5.5863 5.59 5.592 5.624 5.628 5.6330 5.6445 5.6476 5.650 5.6681 5.67 5.682 5.704 5.7101 5.724 5.7243 5.7319 5.756

8 8 9 1 1 2 3 3 4 3 8 5 4 1 5 3 1 5 1 8 3 3 9 5 3 3 4 8 3 5 2 3 1

Element

42 42 80 74 81 81 41 40 77 44 83 77 73 40 79 40 78 38 79 74 40 38 80 73 40 73 76 82 40 76 41 41 39

Mo Mo Hg W Tl Tl Nb Zr Ir Ru Bi Ir Ta Zr Au Zr Pt Sr Au W Zr Sr Hg Ta Zr Ta Os Pb Zr Os Nb Nb Y

Designation

Lal La2 M~

Lui M.v

LIIIMI V 1'ffrv N vI

MIll Mal Ma2

Abs. edge MvN vII MvN vI

L~l

LIIMIV LIINI MIIINv LIIIMI MIIIN I MIIINI V MIINI V

L'Ys M'Y Ll

LIII Mv

Abs. edge Abs. edge

L~2.15

LIIINIV.V

MIV LI

Abs. edge Abs. edge

M~

A-hvN vI MmO I

L~3

LIMm

L'Y2,3 Mal

LINII,III MvN v II

MIn

Abs. edge

L~4

LIMII

MIIIOIV,V M'Y L~6

Lal La2

La

MIIIN v MmNI LIIINI MInNIV LIIIMv

LmMIv Abs. edge

keY

2.29316 2.28985 2.2825 2.2811 2.2706 2.2656 2.2574 2.2551 2.254 2.2528 2.239 2.238 2.226 2.2225 2.220 2.2194 2.217 2.217 2.2046 2.203 2.2010 2.1965 2.1953 2.194 2.1873 2.19 2.182 2.174 2.1712 2.166 2.16589 2.1630 2.1540

00

> 8

o

~

H

C

>

Z

c;

~

o rt:rJ

o q

t'i

>

;0

"t1

P::

~ U2 H

C

U2

5.092 5.1148 5.118 5.130 5.145 5.1517 5.153 5.157 5.168 5.172 5.17708 5.186 5.193 5.196 5.2050 5.217 5.2169 5.230 5.234 5.2379 5.245 5.249 5.2830 5.286 5.299 5.3102 5.319 5.340 5.3455 5.357 5.357 5.36 5.3613 5.37216 5.374 5.37496 5.378 5.3843 5.40

2 3 1 2 4 3 5 5 9 9 8 5 2 9 2 5 3 1 5 3 5 1 3 1 2 3 4 5 3 4 5 1 3 7 5 8 1 3 2

91 Pa 43 Tc 83 Bi 83 Bi 79 Au 41 Nb 81 Tl 80 Hg 82 Pb 74 W 42 Mo 79 Au 91 Pa 81 Tl 44 Ru 39 Y 45 Rh 41 Nb 75 Re 41 Nb 90 Th 81 Tl 39 Y 82 Pb 82 Pb 41 Nb 78 Pt 90 Th 41 Nb 74W 78 Pt 80 Hg 41 Nb 16 S 79 Au 16 S 40 Zr 40 Zr 73 Ta

Mrl

MvNu I LUIMv MvNvu

Lal Mal Ma2 M-y L-Y5

MmNv LnNI

Mv MIV

Abs. edge Ahs. edge

L{31 Mr2 L." LI Ll LUI

MUI L{32,15

Mrl M{3 L-Y2.a Mal Ma2 L{ja M-y Mr2 L{j4

Mvl1lvI

MvO n I MINIn LUMIV MnlNIv MIvNn MIVOU LuMI

Abs. edge LUIM I Abs, edge Abs. edge LUINIV,V MvNuI MIVN vI

LIN n. Iu MvNvn MvN v I

LIMnI MInN v MIVNu LIMn

MnN Iv MInNlv

Mv

Abs. edge

L{36

s:«.

LmNI KLm

MIV

Abs, edge

Ka2 Lu L-YI

Abs, edge

KLn LnNIv MINu I

2.4350 2.4240 2.4226 2.4170 2.410 2.4066 2.406 2.404 2.399 2.397 2.39481 2.391 2.3876 2.386 2.38197 2.377 2.3765 2.3706 2.369 2.3670 2.364 2.3621 2.3468 2.3455 2.3397 2.3348 2.331 2.322 2.3194 2.314 2.314 2.313 2.3125 2.30784 2.307 2.30664 2.3053 2.3027 2.295

5.767 5.784 5.796 5.81 5.81 5.828 5.83 5.83 5.8360 5.840 5.8475 5.854 5.8754 5.884 5.885 5.931 5.962 5.9832 5.987 6.008 6.0186 6.038 6.0458 6.047 6.05 6.058 6.0705 6.073 6.0778 6.09 6.092 6.0942 6.134 6.1508 6.157 6.160 6.162 6.173 6.2109

9 1 2 2 1 1 2 1 3 1 3 3 3 8 2 5 1 3 9 5 3 1 3 1 1 3 2 5 3 2 3 3 4 3 1 1 8 1 3

79 Au 15 P 15 P 76 Os 78 Pt 78 Pt 73 Ta 77 Ir 40 Zr 79 Au 42 Mo 79 Au 39 Y 81 Tl 75 Re 75 Re 39 Y 39 Y 78 Pt 37 Rb 39 Y 77 Ir 37 Rb 78 Pt 77 Ir 78 Pt 40 Zr 76 Os 40 Zr 80 Hg 74 W 39 Y 74 W 42 Mo 15 P 15 P 83 Bi 38 Sr 41 Nb

MvOm K K{3

Mv M{3

M IV L{3l Mal L." Ma2 L-Y5 M-y LIU L{33 LI L{34 M{j L-Y2,3 Mal

Abs. edge KM MnNI

Abs. edge MIv N vI MIll 01 Abs, edge LlIMIV

MvNvu LUMI MVNVI LnNI MI/IN I MmNv MIIINIV

Abs. edge LIMuI MVOUI

Abs, edge LIMu MIVN v I

LINn,nI MvNvu

Mv

Abs, edge

Ma2 Lal MIV La2

MvN v I

M-y L{36 Ll

x«,

Ka2 Lu L."

Ltn Mv

Abs. edge LnIMIV MUIN I MmNv LmNI MnINIV LUIM I KLuI KLu MIvNm

Abs. edge LuMI

2.150 2.1435 2.1391 2.133 2.133 2.1273 2.126 2.126 2.1244 2.1229 2.1202 2.118 2.1102 2.107 2.1067 2.090 2.0794 2.0722 2.071 2.063 2.0600 2.0535 2.0507 2.0505 2.048 2.047 2.04236 2.042 2.0399 2.036 2.035 2.0344 2.021 2.01568 2.0137 2.0127 2.012 2.0085 1.99620

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6.738 6.740 6.7530 6.755 6.757 6.768 6.7876 6.802 6.806 6.8207 6.83 6.862 6.8628 6.8697 6.87 6.87 6.89 6.9185 6.959 6.974 6.983 6.9842 6.992 7.005 7.023 7.024 7.032 7.0406 7.0759 7.09 7.101 7.11 7.12542 7.12791 7.168 7.250 7.252 7.264 7.279

1 3 1 3 1 6 3 5 9 3 1 1 2 3 1 2 2 3 5 4 1 3 2 9 1 8 5 3 3 2 8 1 9 9 1 5 1 5 5

14 82 14 37 74 71 37 82 74 37 74 37 38 38 73 80 76 40 35 81 74 37 74 74 73 70 81 39 37 73 79 73 14 14 36 36 73 36 36

Si Pb Si Rb W Lu Rb Pb W Rb W Rb Sr Sr Ta Hg Os Zr Br Tl W Rb W W Ta Yb TI Y Rb Ta Au Ta Si Si Kr Kr Ta Kr Kr

K Mrl K{3 L-ys M{3 M-y L{33

Mr2 L{34

Mv LnI LOll L0l2 MIv 0 Ll LI Mrl Mal L{36 M0l2 M{3 M-y

Mr2 LTf L{3l

Mv

s:«, K0l2 Lu MOl L{33 L-ys

Abs. edge MvNnI KM LnNIv MIVN v I MInNV LIMnI MIvN n MIvOrr LIMn Abs. edge Abs. edge Liu M» LInMIv Abs. edge MIvNn I MmN I LInMI Abs. edge MvNm MvNvrr LmNI MvNvI MvO In MIVNVI MnrNv MIvNrr LrrMI LnMIv MIvOn,III MIVNIII Abs. edge KLIII KLn Abs, edge LnNuI MvNvI.vn LIMrrI LrrNI

1.8400 1.8395 1.83594 1.83532 1.8349 1.832 1.82659 1.823 1.822 1. 81771 1. 814 1.8067 1.80656 1.80474 1.804 1.805 1.798 1. 79201 1.781 1.778 1.7754 1.77517 1. 7731 1.770 1.7655 1.765 1.763 1.76095 1. 75217 1. 748 1.746 1. 743 1.73998 1.73938 1.7297 1.710 1.7096 1.707 1.703

7.984 8.021 8.0415 8.065 8.107 8.1251 8.144 8.149 8.239 8.249 8.310 8.321 8.33934 8.34173 8.359 8.3636 8.3746 8.407 8.470 8.48 8.486 8.487 8.573 8.592 8.60 8.601 8.629 8.646 8.664 8.7358 8.76 8.773 8.81 8.82 8.844 8.847 8.90 8.929 8.962

5 4 4 5 1 5 9 5 8 7 4 9 9 9 5 4 5 1 9 1 9 5 8 3 7 5 4 1 5 5 7 1 7 1 9 5 2 1 4

35 77 37 77 33 35 66 70 75 69 76 34 13 13 76 37 35 34 70 69 65 69 74 68 92 68 75 34 75 34 92 32 92 68 64 68 73 33 74

Br Ir Rb Ir As Br

Dy Yb Re Tm Os Se Al Al Os Rb Br Se Yb Tm Tb Tm W Er U Er Re Se Re Se U Ge U Er Gd Er Ta As W

Lm Mrl LTf

Mr2 LI L(3l M-y MOl M{3 Mrl L{33,4 Ka l K0l2

Abs. edge MvNIrr LnMI MIvNrr Abs. edge LnMIv MmNIv,v MvNvI,vrr MrvNnr MIVNVI MvN m LrMn,Irr KLm

«u.

Mr2

ftfIvNrr

Ll L0l1,2 Lrr

LmMI

MOl M-y

Mv M{3

MIv

LIUMIV,V Abs. edge MmNI MvNvr,vIl

MUINIv,v Abs. edge MrvNnI MrvNvr NIPIV,V Abs. edge

L{3l

MvNI rr Abs. edge MIvNrr LnMIv

LI

NIPnI Abs. edge

Mrl

LUI Mr2

NIPn MOl M-y

Mv L(33,4 Mrl

MvNvI,vn MnINIV,V Abs. edge MIvNru LrMrr,III MvNIII

1.5530 1.5458 1. 54177 1.5373 1.5293 1.52590 1.522 1.5214 1.505 1.503 1.4919 1.490 1.48670 1.48627 1. 4831 1.48238 1.48043 1.4747 1.464 1.462 1. 461 1.4609 1.446 1.4430 1. 44 1. 4415 1.4368 1.4340 1.4310 1. 41923 1.42 1.4132 1. 41 1.406 1.402 1. 4013 1.393 1.3884 1.3835

XI

::c

~ ~

:a ~

t?:l

t'i

t?:l

Z

o 1-3 P:1

Ul

~

Z

t1

~

1-3

o

~ ~

C1

t?:l

Z

t?:l

::c

o ~

t'i

t?:l

""1 t?:l

t'i tn

~ ~

Clt ~

TABLE

7f-2.

WAVELENGTHS OF X-RAY EMISSION LINES AND ABSORPTION EDGES: IN NUMERICAL ORDER

~

(Continued)

~

Wavelength,

A*

C1l

p.e.f

Element

4 5 5 1 2 9 1 4 5 6 1 7 8 7 1 5 2 2 1 2 9 2 8 7 7 6 2 1 1 2 7 1 1

67 Ho 348e 74W 33 As 67 Ho 63 Eu 35 Br 73 Ta 73 Ta 66 Dy 33 As 90 Th 33 As 90 Th 12 Mg 31 Ga 12 Mg 32Ge 35 Br 66 Dy 628m 32 Ge 33 As 72 Hf 72 Hf 65 Tb 12 Mg 32 Ge 34 Be 65 Tb 92 U 32 Ge 32 Ge

Designation

keY

Wavelength,

A*

t-:)

p.e.f

Element

Designation

keY

----8.965 8.9900 8.993 9.125 9.20 9.211 9.255 9.316 9.330 9.357 9.367 9.40 9.4141 9.44 9.5122 9.517 9.521 9.581 9.585 9.59 9.600 9.640 9.6709 9.686 9.686 9.792 9.8900 9.924 9.962 10.00 10.09 10.175 10.187

M{3 Lal.2 Mt2 Ln Ma M-y LTI Mtl Mt2 M{3 Lm

L{31 K Lr K{3 L{33 Ll Ma M-y L{34 Lal.2 Mt2 Mtl M{3 Kal,2 Ln LTI Ma

L{31 LUI

MIVNvI LnrMIv.v MrvNn Abs. edge MvNvr.vn Msu Nsv;» LnMI MvNrlI MIvNrr MrvNvr Abs, edge NIPIn LnMIv NIPn Abs. edge Abs. edge KM LIMm LIIIMI MvNvI.VII MIIINIV.V LIMn LrIIMIv.v MIvNn MvNm MIVNVI KLn.rn Abs. edge LnMI Mv Nvi.vt: NIO m LlIMIV Abs. edge

1.3830 1.37910 1.3787 1.3587 1.348 1.346 1.3396 1.3308 1.3288 1.3250 1.3235 1.319 1. 3170 1.313 1.30339 1.3028 1.3022 1.2941 1.2935 1.293 1.291 1. 2861 1.2820 1. 2800 1.2800 1. 2661 1.25360 1.2494 1.2446 1.240 1.229 1.2185 1.2170

12.131 12.254 12.43 12.44 12.459 12.597 12.68 12.737 12.75 12.90 12.953 12.98 13.014 13.053 13.06 13.122 13.18 13.288 13.30 13.336 13.343 13.394 13.57 13.68 13.75 13.8 14.02 14.04 14.22 14.242 14.271 14.3018 14.31

1 3 2 2 5 2 2 5 3 9 2 2 1 3 2 5 2 1 6 3 5 5 2 2 4 1 2 2 2 5 6 1 3

30 30 66 60 60 31 60 60 56 92 31 65 29 29 59 59 28 29 83 29 59 59 64 30 58 90 30 58 63 28 28 10 27

Zn Zn Dv Nd Nd Ga Nd Nd Ba U Ga Tb Cu Cu Pr Pr Ni Cu Bi Cu Pr Pr Gd Zn Ce Th Zn Ce Eu Ni Ni Ne Co

Lm L al.2 Mt M{3

M rv LTI Ma

Mv M-y Ll Mt

Ln L{31 M{3

MIV L{33.4 LIIl Lal.2 Ma

Mv Mt LTI M{3

Abs. edge LInMIv.v MvNm MIVNVI Abs. edge

u.».

MvNvr.vII Abs. edge MnINl\'.v NmOv LmMr MvNm Abs. edge LnMrv

MrvNvr Abs. edge L IMn. 1I1 Abs, edge NrPn.nr L1nMrv.v MvNvr.vn Abs. edge MvNm

Lu.Ms MrvNvr NmOv

Ll Ma Mt

LIrrMr MvNvI.vn

Ln

Abs. edge LnMIv Abs. edge LrMn.III

L{31 K L{33.4

»-s,«

1. 02201 1.0117 0.998 0.997 0.9951 0.9842 0.978 0.9734 0.973 0.961 0.95-72 0.955 0.95268 0.9498 0.950 0.9448 0.941 0.93306 0.932 0.9297 0.9292 0.9257 0.914 0.906 0.902 0.897 0.884 0.883 0.872 0.8706 0.8688 0.866889 0.870

>

8

o

a=

1-4

o

>

Z

t'

a= o

e-

t:rj

o

Ll

t'4

>

~

'"tI

=

~ U1 1-4

o

U1

10.254 10.294 10.31 10.359 10.40 10.4361 10.46 10.48 10.505 10.711 10.734 10.750 10.828 10.96 10.998 11. 013 11. 023 11.072 11.07 11.100 11. 200 11.27 11. 288 11. 292 11. 37 11. 47 11. 53 11. 552 11.56 11. 569 11. 575 11. 609 11. 862 11.86 11.9101 11. 965 11. 983 12.08 12.122

6 1 1 9 7 8 3 1 9 5 1 7 5 3 9 5 2 1 7 1 7 1 5 1 1 3 1 5 5 1 2 2 1 1 9 2 3 4 3

64 Gd 348e 30 Zn 31 Ga 92 U 32 Ge 64 Gd 70 Yb 60 Nd 63 Eu 33 As 63 Eu 31 Ga 63 Eu 59 Pr 63 Eu 31 Ga 33 As 90 Th 31 Ga 30 Zn 628m 628m 31 Ga 68 Er 628m 58 Ce 628m 90 Th 11 Na 11 Na 32 Ge 30 Zn 67 Ho 11 Na 32 Ge 30 Zn 57 La 29 Cu

Mfj Ll LI

ui«,

MIvN vI LIUMI Abs. edge LIMn,III NnP I

Lal,2 Ma M?; My

M IV L71 Mfj Ln Ma My

Mv ui. Ll

LUIMIv,v MvNvI,VII MvNIn MIIINIV,V Abs. edge LnMI

MIVN vI Abs. edge MvNvI.vn MnINIV,V Abs. edge LnMlv LnIM I NnPI

LnI t.a«, Mfj

Mlv Lal,2 M?; Ma My

Mv K Kfj L71 Ln M?; Kal,2 Ll Lfjl My Lfja, 4

Abs. edge LIMn,nI MIVNVI Abs, edge LlnMIv,v ft{vNm

MvNvI,vn MnINIv,v Abs, edge NnO Iv Abs, edge KM LUMI

Abs. edge MvNm KLn,III

LIUMI LnMIv MUINIV,V LIMn,III

1. 2091 1.2044 1.197 1.197 1.192 1.18800 1.185 1.183 1.180 1. 1575 1.1550 1.1533 1.1450 1.131 1.1273 1.1258 1.1248 1.1198 1.120 1. 1169 1.1070 1.0998 1.0983 1.09792 1. 0901 1.081 1.0749 1.0732 1.072 1. 07167 1. 0711 1.0680 1.04523 1.0450 1.04098 1.0362 1.0347 1.027 1.0228

14.39 14.452 14.51 14.525 14.561 14.610 14.88 14.90 14.91 15.286 15.56 15.618 15.65 15.666 15.72 15.89 15.91 15.915 15.93 15.972 15.98 16.20 16.27 16.46 16.693 16.7 16.92 16.93 17.19 17.202 17.26 17.38 17.525 17.59 17.6 17.87 17.94 17.9 18.292

5 5 5 5 3 3 5 2 4 9 1 5 4 8 9 1 5 5 4 6 5 5 3 4 9 1 4 5 4 5 1 4 5 2 1 3 5 1 8

58 Ce 10 Ne 57 La 28 Ni 28 Ni 10 Ne 57 La 29 Cu 628m 29 Cu 56 Ba 27 Co 26 Fe 27 Co 56 Ba 56 Ba 56 Ba 27 Co 52 Te 27 Co 518b 56 Ba 28 Ni 60 Nd 28 Ni 24 Cr 518b 508n 25 Mn 26 Fe 26 Fe 59 Pr 26 Fe 26 Fe 52 Te 27 Co 508n 24 Cr 27 Co

MvOn,In Kfj Mfj

LUI Lal,2 K al,2 Ma L71 M?; Ll

MIv Lu

t.s;, Lfjl

Mv LnI My Lal,2

L71 M?; Ll LI My

i.e«, Ln Lfjl M?;

LnI Lal,2 L71 My Ln Ll

KM

MIVNvI Abs, edge LInMIv,v KLu,IU MvNvI,vn LUMI

MvNnI LmMI

Abs, edge Abs. edge LIMu.In LnMlv MlvOln Abs. edge MlvOn Abs. edge MmNlv,v LlnMIv,v MnNlv MvOIn LnMI MvNm

LIUMI Abs, edge MnINIv,v MuNIV LIMn,III Abs. edge LuMIV MVNUI Abs, edge LIUMIV,V MUNI LnMI

MUINlv,v Abs. edge LInMI

0.862 0.8579 0.854 0.8536 0.8515 0.8486 0.833 0.832 0.831 0.8111 0.7967 0.7938 0.792 0.7914 0.789 0.7801 0.779 0.7790 0.778 0.7762 0.776 0.765 0.762 0.753 0.7427 0.741 0.733 0.733 0.721 0.7208 0.7185 0.714 0.7074 0.7050 0.703 0.694 0.691 0.691 0.6778

~ I

~

> ~ ~

~

tr.J tot tr.J

Z

Q

1-3

::x:

tn

>

Z

t::1

> 1-3 o

s:: H

C

tr.J

Z

tr.J ~

Q

~

tot

~ tr.J

~

ta

(I ~

Cl

W

TABLE

7f-2.

WAVELENGTHS OF X-RAY EMISSION LINES AND ABSORPTION EDGES: IN NUMERICAL ORDER

j:I .....

(Continued)

Con

Wavelength,

.A* 18.32 18.35 18.8 18.8 18.96 19.11 19.1 19.40 19.44 19.45 19.66 19.75 20.0 20.1 20.15 20.2 20.47 20.64 20.66 20.7 21.19 21.27 21.34 21.5 21.64 21.78 21.82 21.85 22.1 22.29 22.9 23.32 23.3

Designation

p.e.f Element

2 4 1 2 4 2 1 7 5 1 5 4 1 2 1 1 7 4 7 1 5 1 5 1 3 5 7 2 1 1 2 1 1

9F 58 Ce 51 Bb 47 Ag 24 Cr 25 Mn 52 Te 48 Cd 57 La 25 Mn 53 I 26 Fe 56 s» 46 Pd 26 Fe 51 Bb 48 Cd 56Ba 47 Ag 24 Cr 23 Va 24 Cr 52 Te 50 Bn 24 Cr 52 Te 47 Ag 25 Mn 46 Pd 25 Mn 48 Cd 80 46 Pd

Ka Mr

i.s«, L{Jl

Mr Lal,2 MIV,V L." Ll M-y Mr

LIII

t.s«, L{Jl Lal,2 M-y L." Ll K M-y

KL MvNIII MIINI MINII.III LIMII.IU LUMIV MmNI MIINIV MvNm LIIIMIv,v Abs. edge LnMI MIINI MINII,UI LmMI MmNI MmNlv,v MvNm MIINIV Abs. edge LIMn.III LIIMIV M IVOIl,III MmNI LIUMlv,v MvOm MIIINlv,v LIIMI MIINIV LIIIMI MIINI Abs, edge MmNlv,v

keV

0.6768 0.676 0.658 0.658 0.654 0.6488 0.648 0.639 0.638 0.6374 0.631 0.628 0.619 0.616 0.6152 0.612 0.606 0.601 0.600 0.598 0.585 0.5828 0.581 0.575 0.5728 0.569 0.568 0.5675 0.560 0.5563 0.540 0.5317 0.531

Wavelength,

.A* 33.1 33.5 33.57 34.8 34.9 35.13 35.13 35.3 35.49 35.59 35.63 35.94 36.32 36.33 36.8 37.4 37.5 38.4 39.77 40.46 40.7 40.9 40.96 42.1 42.1 42.3 43.3 43.6 43.68 44.7 44.8 45.0 45.2

~

p.e.f

Element

2 3 9 1 2 2 1 3 1 3 1 2 9 2 1 2 2 3 7 2 2 2 2 2 1 2 2 1 1 3 1 1 3

41 Nb 47 Ag 90 Th 92 U 41 Nb 21 Be 20 Ca 42 Mo 20 Ca 21 Be 20 Ca 20 Ca 90 Th 20 Ga 48 Cd 46 Pd 421\10 41Nb 47 Ag 20 Ca 41 Nb 45 Rh 20 Ca 92 U 19 K 82 Pb 92 U 46 Pd 6C 6C 44 Ru 82 Pb 80 Hg

Designation

MIINIv MIV.VOIl.I1I NIVNVI

Nv Nvt.vts M-y L." LII LnI Ll LII.nI L{Jl L al.2 Mr

Mr L." Ll

Ln.I11 Mr K Ka

MIIINIV.v LIIMI Abs, edge MIINI Abs, edge LmMI Abs. edge LIIMI V NvNvl.VII LnIMIV.V M IV.vNII.1I1 MIV.VOIl,III MmNI MnN I M lv.vNII.1I1 LnMI MnINI MIv,vOn.III LIIIM I NvlO v Abs. edge NIv N vI NVIOIV M I v. vNn.I11 Abs. edge KL MIv.vOn.I1I NVNVI.VIl NIVNvI

keV

0.375 0.370 0.3693 0.357 0.356 0.3529 0.3529 0.351 0.34931 0.3483 0.34793 0.3449 0.3414 0.3413 0.3371 0.332 0.331 0.323 0.3117 0.3064 0.305 0.303 0.3027 0.295 0.2946 0.293 0.286 0.2844 0.28384 0.277 0.2768 0.2756 0.274

>-~ o

~ ~

(1

>-

Z

t:::l

~

o

~

t>;j (1

d

~

>-

~

"tf

::= I- Z e > ""3 o

a:: ~

(1

tr:l

Z

tr:l

~

o to
-

~

I-d

~ ~ U2 H

Q

U2

TABLE

Level

K .......

17

7f-3.

cr

2822.4 ± 0.3

RECOMMENDED VALUES OF THE ATOMIC ENj -

K .......

6539.0 ± 0.4 [6539.0]c

Lt . ...... LIl ......

(6538.) 769.0 ± 0.4 [769.0jd 651.4 ± 0.4

29 Cu

8978.9 ± 0.4 [8978.9jc,u

(8980.3) 1096.1 ± 0.4 [1096. Old 951.0 ± 0.4

32 Ge

9658.6 ± 0.6 [9658.6I u (9660.7) 1193.6 ± 0.9

10367.1 ± 0.5 [10367.1ju (10368.2) 1297.7 ± 1.1

~ ..... o

1042.8 ± 0.6

1142.3 ± 0.5

11103.1 ± 0.7 [11103.8ju (11103.6) 1414.3±0.7 [1413.6ju 1247.8±0.7

(1045.) 1019.7±0.6

1115.4 ± 0.5

(1249.) 1216.7 ± 0.7

::0

(1117 .) 158.1 ± 0.5 106.8 ± 0.7 102.9 ± 0.5

(1217.0) 180.0 ± 0.8 127.9 ± 0.9 120.8 ± 0.7

et';j 1-3 o ~ H

(1

0.3 0.3 0.4 0.4 0.3 0.3 0.3

28.7 ± 0.4

>Z o ~

o rt".l

(1

d

t"

>-

~

Level

41 Nb

42 Mo

43 Tc

44 Ru

46 Pd

45 !th

47 Ag

Iod

48 Cd

~

~

K .......

Lt ....... LIl ...... LII! . . . . .

U2

18985.6 ± 0.4 (18987. ) 2697.7 ± 0.3 [2697.7]1

19999 . 5 ± O. 3 (20004.) 2865.5 ± 0.3 [2866.0]1

21044.0 ± 0.7

2464.7 ± 0.3 [2464.7]'

2625.1 ± 0.3 [2624.5)' (2627.) 2520.2 ± 0.3 [2520.2)' (2523.2)

2793.2 ± 0.4 12973.2)'

2370.5 ± 0.3 [2370.6]'

3042.5 ± 004 [3042.5)1

2676.9 ± 004 [2676.9)'

22117.2 ± 0.3 (22119. ) 3224.0 ± 0.3 [3224.3)1 2966.9 ± 0.3 [2966.8)1 (2966.3) 2837.9 ± 0.3 [2837.7)1 (2837.7)

23219.9 ± (23219.8) 3411.9 ± [3412.0)' (3417.) 3146.1 ± [3146.3)' (3145.) 3003.8 ± [3003.5)0,

(3002.)

0.3 0.3

I

24350.3 ± 0.3 (24348.) 3604.3 ± 0.3 [3604.6)' (3607.)

0.3

3330.:t± 0.3

0.3

[3330.3)1 (3330.3) 3173.3 ± 0.3

25514.0 ± 0.3 (25516.) 3805.8 ± 0.3 [3806.2]'" (3807.) 3523.7 ± 0.3 [3523.6)0,01 (3526.) 3351.1 ± 0.3

26711.2 ± (26716. ) 4018.0 ± [4018.1]'" (4019.) 3727.0 ± [3727.1]'" (3728.) 3537.5 ±

[3173.0)0,'

[3350.8)0

[3537.3)0

(3173.0)

(3351.0)

(3537.6)

0.3

H

(1

U2

0.3 0.3 0.3

Mr. ..... Mn ..... Mnr. .... MIV ..... Mv .. . . . NI ......

Z~~rl ...

NIV.V ...

Level

468.4 378.4 363.0 207.4 204.6 58.1

± 0.3 ± 0.4 ± 0.4 ± 0.3 ± 0.3 ± 0.3

504.6 409.7 392.3 230.3 227.0 61.8

± 0.3 ± 0.4 ± 0.3 ± 0.3 ± 0.3 ± 0.3

33.9 ± 0.4

34.8 ± 0.4

3.2 ± 0.3

1.8 ± 0.3

49 In

............... 444.9 ± 1.5 425.0 ± 1.5 256.4 ± 0.5 252.9 ± 0.4 ...............

38.9 ± 1.9 ...............

± 0.3 ± 0.3 ± 0.3 ± 0.3 ± 0.3 ± 0.3

43.1 ± 0.4 2.0 ± 0.3

52 Te

51 Sb

50Sn

585.0 482.8 460.6 283.6 279.4 74.9

± 0.3 0.3 ± 0.3 ± 0.3 ± 0.3 ± 0.3

669.9 559.1 531.5 340.0 334.7 86.4

±

47.9 ± 0.4

51.1

±

627.1 521.0 496.2 311. 7 307.0 81.0 2.5

±

±

0.4

53 I

0.3 ± 0.3 ± 0.3 ± 0.3 ± 0.3 ± 0.3 0.4

1.5 ± 0.3

717.5 602.4 571.4 372.8 366.7 95.2 {62.6 55.9 3.3

±

0.3 ± 0.3 ± 0.3 ± 0.3 ± 0.3 ± 0.3 ± 0.3 } ± 0.3 ± 0.3

55 Cs

54 Xe

770.2 ± 0.3 650.7 ± 0.3 616.5 ± 0.3 410.5 ± 0.3 403.7 ± 0.3 107.6 ± 0.3 66.9 9.3

± ±

0.4 0.3

LI ....... Ln ...... LIn .....

MI ...... Mn ..... MIn ..... MIV ..... Mv .. . . . NI ......

Zn }...

II! N,v} Nv ...

~

:a ~

56 Ba

Z

Q

27939.9 ± 0.3

29200.1 ± (29195. ) 4464.7 ± [4464.5j1 (4464.8) 4156.1 ± [4156.2j· (4157.) 3928.8 ± [3928.8j (3928.8) 883.8 ± 756.4 ± 714.4 ± 493.3 ± 484.8 ± 136.5 ±

0.4

30491.2 ± (30486.) 4698.3 ± [4698.3jm (4698.4) 4380.4 ± [4380.6jm (4382.) 4132.2 ± [4132.2j. (4132.3) 943.7 ± 8119 ± 765.6 ± 536.9 ± 527.5 ± 152.0 ±

0.3

4237.5 ± 14237.7jm (4237.3) 3938.0 ± [3937.8jm (3939.3) 3730.1 ± [3730.0j. (3730.2) 825.6 ± 702.2 ± 664.3 ± 450.8 ± 443.1 ± 121.9 ±

0.3

±

0.4

88.6 ± 0.4

98.4 ± 0.5

16.2 ± 0.3

23.9 ± 0.3

31.4 ± 0.3

77.4

0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3

0.3 0.3 0.3 0.3 0.4 0.3 0.3 0.3 0.4

0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3

0, .......

0.1 ± 4.5

0.9 ± 0.5

6.7±0.5

gI! } ....

0.8 ± 0.4\

1.1 ± 0.5

2.] ± 0.4

nt

I

~

:>

t.".1 t" t?'.1

--K .......

~

33169.4 ± 0.4 (33167.) 5188.1 ± 0.3 [5188.1ji

31813.8 ± (31811.) 4939.2 ± [4939.3jm (4939.7) 4612.0 ± [4612.0jm (4612.6) 4341.4 ± [4341.2j. (4341.8) 1006.0 ± 869.7 ± 818.7 ± 582.5 ± 572.1 ± 168.3 ±

0.3

±

0.5

122.7 ± 0.5

39.8 ± 0.3

49.6 ± 0.3

110.2

0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3

11.6±0.6 2.3

±

0.5

4852.1 ± 0.3 [4852.0ji 4557.1 ± 0.3 [4557.1ji 1072.1 930.5 874.6 631. 3 619.4 186.4

± 0.3 ± 0.3 ± 0.3 ± 0.3 ± 0.3 ± 0.3

34561. 4 ± 1.1 (34590.) 5452.8 ± 0.4 (5452.8) 5103.7 ± 0.4 (5103.7) 4782.2 ± 0.4 (4782.2) .............. 999.0 ± 2.1 937.0 ± 2.1 .............. 672.3 ± 0.5 .............. 146.7

±

3.1

. .............

13.6 ± 0.6

..............

3.3 ± 0.5

..............

35984.6 ± (35987.) 5714.3 ± [5712.7ji (5721.) 5359.4 ± [5359.5ji (5358.) 5011.9 ± [5012.0ji (5011.3) 1217.1 1065.0 997.6 739.5 725.5 230.8 {172.3 161.6 { 78.8 76.5 22.7 { 13.1 11.4

0.4 0.4 0.3 0.3 0.4 0.5 0.5 0.4 0.5 0.4 0.6 0.6 0 . .'5 0.5 0.5 0.5 0.5

37440.6 ± (37452.) 5988.8 ± [5986.8ji (5996.) 5623.6 ± [5623.6ji (5623.3) 5247.0 ± [5247.3ji (5247.0) 1292.8 ± 1136.7 ± 1062.2 ± 796.1 ± 780.7 ± 253.0 ± 191.8 ± 179.7 ± 92.5 ± 89.9 ± 39.1 ± 16.6 ± 14.6 ±

0.4

1-3.

~

tn 0.4

:>

0.3

ztj

0.3

o

:> 1-3.

s:: ~

0.4 0.5 0.5 0.3 0.3 0.5 0.7 0.6 0.5 0.5 0.6 0.5 0.5

o

t?'.1

Z

t.".1 ~

Q ~

rt?'.1

~

t.".1 t"

U!

-:J

I

~

OJ ~

TABL]7.2 ± 0.4 [2457.4]"

2550.7 ± 0.3 [2550.5)" (2550.5)

2743.0 ± 0.3 [2743.1)1' (2744.0)

(14842. ) 14208.7 ± 0.7 (14215.) 12283.9 ± 0.4 [12284.0)',1' (12286. ) 3561.6 ± 1.1 3278.5 ± 1. 3

o

t:1

Z

t:1

;:d

o

~

et:1

~

t:1 t"4

2847.1 ± 0.4 [2847.1)1'

U1

,

-:J I-l

0:> W

TABLE

7f-3.

73 Ta

Level

RECOMMENDED VALUES OF THE ATOMIC ENERGY LEVELS, AND PROBABLE ERRORS IN

74 W

75 Re

76 Os

77 Ir

78 Pt

MIV .....

1793.2 ± 0.3 [1793.1jp

1871.6 ± 0.3 [1871.4jP

1948.9 ± 0.3 [1948.9jp

2030.8 ± 0.3 [2031.0jp

2116.1 ± 0.3 [2116.1Jp

2201.9 ± 0.3 [2201. 9Jp

Mv .....

1735.1 ± 0.3 [1735.2Jp

1809.2 ± 0.3 [1809.3Jp

1882.9 ± 0.3 [1882.9Jp

1960.1 ± 0.3 [1960.2Jp

2040.4 ± 0.3 [2040.5Jp

2121.6 ± 0.3 [2121. 6Jp

83.7 ± 0.6 58.0 ± 1.1 45.4 ± 1.0 ...............

690.1 ± 0.4 577.1 ± 0.4 494.3 ± 0.6 311.4±0.4 294.9 ± 0.4 { 63.4 ± 0.4 60.5 ± 0.4 95.2 ± 0.4 63.0 ± 0.6 50.5 ± 0.6 3.8 ± 0.4

722.0 ± 0.6 609.2 ± 0.6 519.0 ± 0.6 330.8 ± 0.5 313.3 ± 0.4 74.3±0.4 71.1±0.5 101.7±0.4 65.3 ± 0.7 51.7 ± 0.7 2.2 ± 1.3

84 Po

85 At

86 Rn

0.7

93105 . 0 ± 3. 8

95729.9 ± 7.7

98404. ± 12.

0.4

16939.3 ± 9.8

17493. ± 29.

18049. ± 38.

NI ...... NIl ...... NIlI. .... Nrv ..... Nv ...... NVI } ... NVIl 01 ....... OIl ... . . . DIll . . . . .

OIV,V....

Level

565.5 464.8 404.5 241.3 229.3

± ± ± ± ±

0.5 0.5 0.4 0.4 0.3

25.0 ± 0.4 71.1±0.5 44.9 ± 0.4 36.4 ± 0.4 5.7 ± 0.4

595.0 ± 0.4 491.6 ± 0.4 425.3 ± 0.5 258.8 ± 0.4 245.4 ± 0.4 { 36.5 ± 0.4 } 33.6 + 0.4 77.1±0.4 46.8 ± 0.5 35.6 ± 0.5 6.1 ± 0.4

82 Pb

81 Tl

625.0 517.9 444.4 273.7 260.2

± ± ± ± ±

0.4 0.5 0.5 0.5 0.4

40.6 ± 0.4 82.8 45.6 34.6 3.5

± ± ± ±

0.5 0.7 0.6 0.5

83 Bi

654.3 546.5 468.2 289.4 272.8

± ± ± ± ±

0.5 0.5 0.6 0.5 0.6

46.3 ± 0.6

EV*

"I

(Continued)

79 Au

2291.1 ± 0.3 [2291.2Jp (2307.) 2205.7 ± 0.3 [2206.1Jp (2220.) 758.8 ± 0.4 643.7 ± 0.5 545.4 ± 0.5 352.0 ± 0.4 333.9 ± 0.4 86.4 ± 0.4 82.8 ± 0.5 107.8 ± 0.7 71.7±0.7 53.7 ± 0.7 2.5 ± 0.5

87 Fr

I--' ~

H::.

80 Hg

2384.9 ± 0.3 [2384.9jP 2294.9 ± 0.3 [2294.9jP

>

1-3

800.3 676.9 571.0 378.3 359.8 102.2 98.5 120.3 80.5 57.6 6.4

± ± ± ± ± ± ± ± ± ± ±

1.0 2.4 1.4 1.0 1.2 0.5 0.5 1.3 1.3 1. 3 1.4

o

s::: H o

>

Z

tj

s:::

o

t'4 tr.l

o

1208.4

30.

886.

[678.9]1'

± 0.4

~ ~

[805.3]1'

406.6

3791.8 ± 1. 7

2798.0 ± 1.2

[938.7]1'

Nlv .....

3663. ± 40.

[2687.4]1'

[2585.5]1'

[2485.2]1'

3301.9

92 U

93 Np

94 Pu

96

95 Am

± ± ± ± ± ± ±

em

::t:

2.4

tn

2.1 2.0 2.0

>

1.7

> 1-3 o

2.2 1.8

Z e:;,

~

8

t'.j

Z

K ...... '1106755.3 ± 5.31109650.9 ± 0.9 LI....... 19840. ± 18. 20472.1 ± 0.5

112601. 4 ± 2.4 21104.6 ± 1.8

115606.1 21757.4

(20464.) 19693.2 ± 0.4 (19683. ) 16300.3 ± 0.3 [16299. 6]q (16299.) 5182.3 ± 0.3

(21128.) 20313.7 ± 1.5 (20319. ) 16733.1 ± 1.4

(21771. ) 20947.6 (20945.) 17166.3

(16733.) 5366.9

(17165. )

Ln ..... '119083.2

LIIl.....

MI. ..... I

Mu.....

± 2.8

15871.0 ± 2.0 (15871. 0) (5002.)

± ±

1.6 0.3

118678. ± 33. 22426.8 ± 0.9

121818. ± 44. 23097.2 ± 1.6

±

0.3

±

0.3

17610.0 ± 0.4

(23109. ) 22266.2 ± 0.7 (22253.) 18056.8 ± 0.6

0.4

(17606.2) 5723.2 ± 3.6

(18053.1) 5932.9 ± 1.4

21600.5 ± 0.4

[17168.5]r

± 1.6

5548.0

±

5182.2

±

125027. ± 55. 23772.9 ± 2.0 (23772.9} 22944.0 ± 1.0

23779

18504.1 ± 0.9

18930

I (18504.1) 6120.5 ± 7.5

[5182.3]q

4656.

±

18.

4830.4

± 0.4

[4830.6]q

5000.9 ± 2.3

[5180.9]r

0.4

5366.2 ± 0.7 [5366.4]'

5541.2 ± 1.7 I

128220 24460

5710.2

±

2.1

t'.j ~

o

~

et'.j

< t'.j t'"

W

6288 5895

[I ~

~

C;t

-a TABLE

7f-3.

Level

89 Ac

Mrll .....

3909. ± 18.

Mrv .....

3370.2 ± 2.1

RECOMMENDED VALUES OF THE ATOMIC ENERGY LEVELS, AND PROBABLE ERRORS IN EV*

90 Th

91 Pa

4046.1 ± 0.4

4173.8 ± 1.8

[4046.1]q

(4041. ) 3490.8 ± 0.3

3611.2 ± 1.4

[3490.7]q

Mv .....

3219.0 ± 2.1

(3485.) 3332.0 ± 0.3

(1269. )

(3325.) 1329.5 ± 0.4

(3608.) 3441.8 ± 1.4

[3332.1]q

Nr ......

(3436.) 1387.1 ± 1. 9

[1329.8]q

NIl ......

1080. ± 19.

N'ut .....

890. ± 19.

1168.2 ± 0.4

1224.3 ± 1.6

[1168.3)q

967.3 ± 0.4

1006.7 ± 1. 7

[967.6)q

Nrv ..... Nv ...... Nvr .....

674.9 ± 3.7

714.1 ± 0.4

743.4 ± 2.1

[714.4)q

..............

676.4 ± 0.4

708.2 ± 1.8

[676.4]q

..............

344.4 ± 0.3

371.2 ± 1.6

93 Np

92 U

4303.4 ± [4303.6]' (4299. ) 3727.6 ± [3728.1]r (3720.) 3551. 7 ± [3551.7]' (3545.) 1440.8 ± [1441.3)' 1272.6 ± [1272.5)' 1044.9 ± [1044.9)' 780.4 ± [779.7)r 737.7 ± [737.6]' 391.3 ±

..............

Or ....... all ......

.............. ..............

Onr .....

..............

335.2 ± 0.4 [335.0)q

290.2 ± 0.8

229.4 ± 1.1

I

181.8 ± 0.4

Osv .....

..............

4556.6 ± 1.5

4667.0 ± 2.1

4797

0.3

3850.3 ± 0.4 [3849.8]-

3972.6 ± 0.6 [3972.7]1

4092.1 ± 1.0

4227

0.3 0.4 0.3 0.3 0.3 0.3 0.6

380.9 ± 0.9

309.6 ± 4.3

323.7 ± 1.1 fS9.3 ± 0.5

222.9 ± 3.9

195.1 ± 1.3

Ov ......

..............

{'Os.o ±

94.3 ± 0.41

[94.4]q

87.9 ± 0.3

94.1 ± 2.8

0.5

96.3 ± 1.4

[88.1]q

.............. Pit ...... .............. Pur ... , . .............. Pr .......

59.5 ± 1.1 49.0 ± 2.5 43.0 ± 2.5

I:::::::::::::::

96 em

4434.7 ± 0.5 [4434.6]'

359.5 ± 1.6

[181.8)q

95 Am

~

~ ~

0.3

[344.2)q

NVIl ....

94 Pu

I

(Continued)

70.7 ± 1.2 42.3 ± 9.0 32.3 ± 9.0

3971

> 8

o

3665.8 ± 0.4 [3664.2]-

3778.1 ± 0.6 [3778.0]1

3886.9 ± 1.0

1500.7 ± 0.8 [1500.7]1327.7 ± 0.8 [1327.7]1086.8 ± 0.7 [1086.8)815.9 ± 0.5 [817.1)770.3 ± 0.4 [773.2]415.0 ± 0.8 [415.0)404.4 ± 0.5 [404.4]............... 283.4 ± 0.8 [283.4]' 206.1 ± 0.7 [206.1]109.3 ± 0.7 [108.8)101.3 ± 0.5 [101.4]'

1558.6 ± 0.8

1617.1±1.1

1643

>

1372.1 ± 1-.8

1411.8 ± 8.3

1440

tj

1154

~

1114.8 ± 1.6 848.9 ± 0.6 [848.9]1 801.4 ± 0.6

~

(1135.7)

Z

o t"4

878.7 ± 1.0

t;rj

o

827.6 ± 1.0

q

[801. 4)t

t"4

>

445.8 ± 1. 7

~

432.4 ± 2.1 351. 9 ± 2.4 274.1±4.7

~

o

""d

................

385

:::t:

~ Ul ~

oin

206.5 ± 4.7 116.0 ± 1.2

115.8 ± 1.3

105.4 ± 1.0

103.3 ± 1.1

TABLE

7f-3.

RECOMMENDED VALUES OF THE ATOMIC ENERGY LEVELS, AND PROBABLE ERRORS IN EV*

(Continued)

~ I

~

Level

97 Bk

98 Cf

99 Es

IOOFm

IOIMrl

I02 No

I03Lw

--K ....... [131590 ± 40]" Lr ....... [25275 ± 17)" Ln .. . . . . [24385 ± 17]" [19452 ± 20]u Lrn [6556 ± 21]" MI ...... [6147 ± 31]u Mn [4977 ± 31]" MIlr ..... 4366 Mrv ..... 4132 Mv ..... [1755 ± 22]u Nr ...... 1554 NIl .. . . .. 1235 Nrn ..... [398 ± 22]u Or .......

135960 26110 25250 19930 6754 6359 5109 4497 4253 1799 1616 1279 419

139490 26900 26020 204IO 6977 6574 5252 4630 4374 1868 1680 1321 435

143090 27700 268IO 20900 7205 6793 5397 4766 4498 1937 1747 1366 454

146780 28530 276IO 21390 7441 7019 5546 4903 4622 20IO 1814 14IO 472

150540 29380 28440 21880 7675 7245 5688 5037 4741 2078 1876 1448 484

154380 30240 29280 22360 7900 7460 5710 5150 4860 2140 1930 1480 490

~ ~

~

~t?:j

et?:j

Z

o 8 :r: rJ2 ~

Z

t; ~

J. E. Mack, 1949, as given in C. E. Moore, "Atomic Energy Levels" (U.S. National Bureau of Standards, Washington, D.C., 1949), vol. I, p. 1. b G. Herzberg, 1957, as given in C. E. Moore, "Atomic Energy Levels" (U.S. National Bureau of Standards, Washington, D.C., 1958), vol. 3, p. 238. c S. Hagstrom and S. E. Karlsson, Arkiv Fysik 26, 451 (1964); and S. Hagstrom, Z. Physik 178,82 (1964). d A. Fahlrnan, D. Hamrin, R. Nordberg, C. Nordling, and K. Siegbahn, Phys. Rev. Letters 1', 127 (1965); R. Nordberg, K. Hamrin, A. Fahlman, C. Nordling, and K. Siegbahn, Z. Physik 192,462 (1966). • E. Sokolowski, Arkiv Fysik 11, 1 (1959). I S. Hagstrom, C. Nordling, and K. Siegbahn, Al.pha-, Beta-, and Gamma-Ray Spectroscopy, K. Siegbahn, Ed. (North-Holland Publ. Co. Amsterdam, 1965), Vol. I, p, 845. o C. Nordling, Arkiv Fysik 11,397 (1959). h E. Sokolowski, C. Nordling, and K. Siegbahn, Arkiv Fysik 12, 301 (1957). i C. Nordling and S. Hagstrom, Arkiv Fysik 16, 515 (1960). f I. Andersson and S. Hagstrom, Arkiv Fysik 27, 161 (1964). a

M. O. Krause, Phus. Rev. 140, A1845 (1965). I A. Fahlman, O. Hornfeldt, and C. Nordling, Arkiv Fysik 23, 75 (1962). m P. Bergvall, O. Hornfeldt, and C. Nordling, Arkiv Fysik 17, 113 (1960). n P. Bergvall and S. Hagstrom, Arkiv Fysik 17, 61 (1960). -s. Hagstrom, Z. Physik 178, 82 (1964). P A. Fahlman and S. Hagstrom, Arkiv Fysik 27, 69 (1964). q C. Nordling and S. Hagstrom, Z. Physik 178,418 (1964). r C. Nordling and S. Hagstrom, Arkiv Fysik 11,431 (1959). • S. Hagstrom, Bull. Am. Phys. Soc. 11,389 (1966). I A. Fahlman, K. Hamrin, R. Nordberg, C. Nordling, K. Siegbahn, and L. W. Holm, Phu«. Letters 19, 643 (1966). u J. M. Hollander, M. D. Holtz, T. Novakov, and R. L. Graham, Arkiv Fysik. 28,375 (1965). v J. A. Bearden, Rev. Mod. Phys. 39,78 (1967). J. A. Bearden, X-Ray Wavelengths, NYO I0586 (National Technical Information Service, U.S. Dept. of Commerce, Springfield, vs. 22151). k

8

o

~

I-l

o

t'i

Z t'i

~

o

~

rt'i

~ t.:rj

t"

rJ2

jl ~

0;>

-....l

7g. Constants of Diatomic Molecules K. P. HUBER

National Research Council of Canada

Explanation of Columns in Table 7g-1 (1) Identification of molecule. (2) Mass numbers of the constituent atoms to which the data refer. If, in the original paper, the mass numbers are not clearly specified, or, if the data refer to the normal isotopic mixture, the mass numbers for the most abundant isotope are given in parentheses. (3) Reduced mass p. in unified atomic mass units (12C = 12.0000000). Precise atomic masses were taken from the 1961 nuclidic mass table [L. A. Konig, J. H. E. Mattauch, and A. H. Wapstra, Nucl. Phys. 31, 18 (1962)]. (4) Designation of the ground state of the molecule. For multiplet II, .6., ••• states the spin-orbit coupling constant A has been added. (5) (6) (8) (9) Rotational constant Be. Rotation-vibration interaction constant a6 (from B; = Be - ae(v + -!) + ...). Vibrational frequency We' Anharmonic constant WeXe (from G(v) = We(V

+ -!) -

weXe(V

+ -!p + ...).

All constants in em-I. They are derived from the analyses of molecular spectra in the microwave, infrared, visible, and vacuum uv region. For 12: states, the constants in these columns correspond to the coefficients Y OI , - Y u, Y I O, and - Y 20, respectively, in the Dunham series expansion for the term values

T VJ

=

l

Y1m(v

+ i)IJm(J + l)m

lm

(7) Equilibrium internuclear distance r, in

A,

calculated without correction from

(10) Dissociation energy Do0 in electron-volts (eV). Data obtained by a large variety of both spectroscopic and thermochemical methods have been included. Uncertain quantities are enclosed in parentheses ( ). Quantities in square brackets [ ] in columns (5) and (8) refer to B« and .6.G(i) respectively. • after We and w.xe indicates that these numbers are for the natural isotopic mixture rather than for the isotope specified in column (2). The physical constants and conversion factors given in Appendix VII of the following book have been used throughout: G. Herzberg, "Electronic Spectra and Electronic 7-168

CONSTANTS OF DIATOMIC MOLECULES

7-169

Structure of Polyatomic Molecules," D. Van Nostrand Company, Inc., Princeton, N.J., 1966. The data included in the table are taken from a new compilation of vibrational and rotational constants for the electronic states of all known diatomic molecules. This compilation is presently being prepared by G. Herzberg and K. P. Huber and will provide further details and the literature references. A critical table of dissociation energies has recently been published by A. G. Gaydon in his book "Dissociation Energies and Spectra of Diatomic Molecules," 3d edition, Chapman & Hall, Ltd., London, 1968.

TABLE

7g-1.

-:J

I

CONSTANTS OF DIATOMIC MOLECULES

i-'-

-..J

ml

m2

p.

Ground state

B.

a.

r.

w.

WtXtJ

Doo

(1)

(2)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

Ag2 ............ AgAl ........... AgAu .......... AgBr ........... AgCl ........... AgCu ......... , AgF ............ AgGa .......... AgH. '" .......

107 107 (107) 107 107 (107) 107 (107) 107 107 107 107 107

109 27 197 79 35 (63) 19 (69) 1 2 127 115 16

53.94779 21.544070 (69.29476) 45.402072 26.349782 (39.611998) 16.131608 (41. 90678g) 0.99841288 1. 97685795 58.02466 55.38014 13.9132425

............

............

. ...........

...........

(107) (107) (107) 27 27 27 27 27 27 27 27 27 27 27 27 27 27 40 40 75 75 75 75

(80) (120) (130) 27 197 79 35 19 1 2 1 127 16 31 32 (80) (130) 40 40 75

(45.73067,) (56.51557) (58.64437) 13.4907675 23.7307671 20.1070870 15.2301443 11.1484731 0.97153601 1.87419812

AgI ............ AgIn ........... A!!:O ............ AgSe ........... AgSn ........... A!!:Te........... Ah ............. AIAu ........... AlBr ........... AICI ........... AlF ............ AlH ............ AIH+ ........... All ............. AIO ............ AlP ............ AIS .. '" ....... AISe ........... AlTe .......... , Ar2 ............ Ar2+ ............ A82............ A82+........... AsCi ........... A8F ............

.............. 22.2507357 10.0419499 14.4200738 14.6327874 (20.1712771) (22.341268) 19.9811919

.............. 37.460790

(~~) I . (23:S4iiiS)" 19

15.1553527

1~+

............ 1~+ 1~+

............ 1~+

0.12796

............ 0.06483378 0.122983860

............ 0.2657

............

............

1~+

6.449 3.2572 0.044876

1~+ 1~+

............ 2£1(r) A = (+135) (2II)

............ (2II)

............ 0.3028

............ . ........... ............

2~+

0.2054 0.1299la 0.1591 0.2439267 0.552468 6.39066 3.3186 6.763

1~+

............

3~U-

1~+(O+) 1~+

1~+ 1~+ 1~+

1~+

2~+

............ 2~+

(2~)

(22:) (1~u+)

............ l~u+

(2~"+) (3~-) (3~-)

0.64136

............ 0.2799

............ ............ ............ ............ 0.10165

............ ............

............

0.00076

2.4728

............

. ..........

0.00023597 o.000595405

2.3931 2.2808

. ........... 0.0019

. ........... 0.201 0.0722 0.0001473

. ...........

. .......... 1.983

. .......... 1.6181 1. 6180 2.5444

. .......... 2.000

0.0025

. ........... . ........... . ........... 0.0012 0.000668 0.000853 0.0016021 0.004950 0.18581 0.0697 0.398

............ 0.00580

............ 0.0018

. ........... ............

. ........... . ........... 0.00034

............ . ............

............

........... . .......... . .......... 2.4665 2.3384 2.296 2.1302 1.6544 1. 6478 1.6463 1.6018

. .......... 1. 6178

........... 2.0288

........... ........... ............

........... 2.1040

........... ........... ..

...........

192.4 256.60 (200) 250.49 343.49 229.5 513.45 184.7 1759.9 1250.7 206.52 155.8 490.4*

0.643 1.13

. ..........

1.63 (1. 7g) 2.06 3.0 3.21 1. 76 3.63

0.6871 1.17 1 2.59 0.65 34.06 17.17 0.445 0.42 3.0*

(2.4)

.... .......

. ..........

1.3/

195.3 350.01 333.00 378.0 481.30 801.9 5 1682.563 1211.95

0.30 2.022 1.163 1.28 1. 95 4.70 29.090 15.138

1.86 3.31 4.43 5.0s 6.8g 2.91 2.94

316.1 979.23

1.0 6.97

(233)

2.41 2.4, 2.62

o

:> 1-3

o s= H

o :>

z

t:t

s= o

t'"

tr1

o r: e:> ~

'"0'

~

to
Z e ~

o

et:r:l o q

~

>-

;t1

"tf

::r:

..q rJ) H

o rJ)

CaH ........... Cal ............ CaO ............ CaS ............ CBr ............

(40) (40) (40) (40) 40 12

1 2 127 16 32 (79)

22:+ 22:+ (22:+) 12:+ 12:

(0. 9~303388) (1.91746266) (30.392038) (11 .4229222) 17.7617688 (10.4161613)

2ITr

4.2778 2.196

............ 0.4444 0.17667 [0.4872]

0.0963 0.035

............ 0.0034 0.000837

. ...........

2.0022 2.001

. .......... 1.822. 2.3178 (1.82261

1299 242.0 733.4 462.23

. ..........

19.5

:51.70

0.64 5.28 1. 78

(3.3) 4.0. 3.4. :54.11

(6.2)

(3.8)

...........

A = +466 CCl. ...........

12

35

8.9341385.

2ITr

Ao Cd2 ............ CdBr .......... , CdCl. .......... CdF ........... CdH ...........

(112) (114) (114)

(U.4)

(56.44717) (46.618567) (26.754971) (16.2825730) (0.99898613) (1.97910660)

.............. ..............

Cdl ............ CdO ............ CdS ........... , CeO ............

(114) (114) (114) (114) (114) (114) (114) (140)

(79) 35 19 1 2 1 2 127 16 (32) 16

CeS ............ CF .............

(140) 12

(32) 19

(26.0247312) 7.3545996.

CdH+ ..........

(114)

(60.02651) (14.0253977) (24.964643) (14.3538823)

12

1

0.92974056

+135

............ (22:) 22: (22:) 22:+ 22:+ 12:+ 1~+

22:

............ ............. (1IcI»

............ 2ITr

Ao CH .............

=

=

0.6970

............

............

............ ............ 5.437 2.788 6.071 3.075

............ ............ ............

0.0067

. ........... ............

............ ............ 0.218 0.168 0.189 0.0682

............ . ........... ............

1.645.

........... . .......... . .......... . .......... 1.7617 1. 748 1.6672 1.664

. .......... . ..........

...........

[0.35687] ............ [1. 8141] (constants for n = 3 component)

. ...........

. ...........

. ..........

[866.1]

. .......... 230.0 330.5 (535) 1430.7

............ 1775.4 1262.5 178.5

. ..........

. .......... (830)

. ..........

........... 0.50 1.2 46.3

........... 37.3 19.01 0.625

. .......... . .......... . ..........

. ..........

0.08 (1.6) 2.1 0.678 0.704 (2.0) (1.4) :53.8 :52.0 8.18

0.01840

1.2717

1308.1

11.10

14.457

0.534

1.1199

2859.1

63.3

3.47

7.808 14.1776 0.24407 0.2696 0.5164802 [0.620525]

0.212 0.4917 0.00153 0.00166 0.004358:;

1.1189 1.1309 1. 9875 1.891 1.6283 [1.5733]

2099.0 [2739.70] 559.71 645.2 786.34 868

34.1

3.52 4.09 2.47950 4.01 2.56 2.746

1. 41720

A = +28 CH+ ........... Cb ............. Clt+ ............ CIF ............ CIO ............

12 12 35 35 35 35

2 1 35 35 19 16

CN ............ CN+ ...........

12 12

14 14

CO ............. CO+ ............ C02 ............ CoBr ........... CoCl. .......... CoH ...........

12 12 59 59 59 59 59

16 16 59 (79) (35) 1 2

1.72463608

.............. 17.484427.

.............. 12.3102870 10.9749310 6.46219328

.............. 6.85620870

.............. 29.4665946 (33.738542) (21.946552.) 0.99088003 1. 94754291

2ITr

1};+ l};g+

2ITg ,'

12:+ 2IT. A = -282 22:+ 12: 12:+ 22:+

............ ............ ............ (14))4 (14))4

. ...........

. .......... 2.70 3.002 6.23 7.5

zrp. 1-3

>

Z

1-3

rp.

o

~

t:l

~

5.90 5.42

+77 2ITr

o

o

> 1-3

o

~ ~

o

~

o

~

t;j

o d

~

1.8992 1.8964

0.01701 1.1720 2068.745 0.0188 1.1728 2033.05 (constants for lowest observed 1}; state) 1. 931271 0.017513 1.1283 2169.8233 1.97720 0.01896 1.1151 2214.24

............

. ...........

..............

. ............ ............

............ [7.151] [3.7221

. ...........

........... . .......... . ..........

...............

[1.5424] [1.52501

........... (320) (420) (1890)

13.134 16.14

7.91 4.9.

13.2939 15.164

11.091 8.34 1.68

. ..........

t;j

tn

j:I J-O

-

1.97 3.43 3.82 4.42 2.73 2.76

FeBr ........... FeCI ...••......

(56) (56)

(79) 35

(32. 734038) (21.5170410)

............

Gal ............ GaO ........... GaTe ........... GdO ...........

(56) (56) (69) 69 69 69 (69) (69) 69 69 (69) (158)

16 (32) (71) 81 35 19 1 2 127 16 (130) 16

Ge2 ............ GeBr ...........

(74) 74

(72) 79

FeO ............ FeS ............ Ga2 ............ GaBr ........... GaCl ........... GaF ............ GaH ...........

(12.4381535) (20. 343723Q) (34.955486) 37.220627 23.199027 14.8932794 (0.99330126) (1.95691837) 44.666126 12.9822500 (45.032443) (14.5239010) (36.453870) 38.169026

GeCI ...........

74

35

23.738983

GeCo ........... GeCr ........... GeCu ......... , GeF ............

(74) (74) (74) (74)

59 (52) (63) 19

(32.79086,) (30.50573;) (33.99198I) (15.1139760)

GeFe ........... GeH ........•..

(74) 72

(56) 1

(31.84120,) 0.99389792

72 (74) (74) 74 74 (74) (74) 74 1 1 2 1

2 127 (58) 16 32 (80) (28) 130 1 2 2 1

1 . 91)923560 (46.71177 D) (32 . 479607) 13.1496247 22.318826 (38.40100 3) (20.295639) 47.11256 0.50391261 0.67171136 1. 00705110 ..............

Gel ............ GeNi ........... GeO ............ GeS ............ GeSe ........... GeSi ........... GeTe ........... H2 ............. H2+ ............

.

........... [0.8828]

. ........... ............

[~1.01O]

(0.01)

. ........... ............ ............ 0.51271 . ........... ............ 0.0818393 0.149895 0.3590; 6.137 [3.083] 0.056934 7 [(0.4271)]

............ ............

............ . ...........

............ 2II, A = +1150 2II, A = +975 ............

............ ............

........... . ...........

(3~) l~+

1~+ 1~+

12;+ 1~+

12;+ 2~

............

............ 2II, A =' +935 ............. 2II, A = +891 2II, 211! ............ 1~+

12;+ 1~+

............ 1~+

12;0 + 1~0+

12;0+

22;.+

.

.

[1. 4178] [:::;1. 326]

. ........... . ........... . ........... 0.00376 . ........... . ........... 0.0003207 0.000776 0.00282 0.181 ............ 0.000189 ............ . ........... . ...........

(62;) or (42;) 5(7)2;0 .............

. ..........

.. ..........

. .......... . .......... 1.625, ........... ..... ...... 2.3525 2.2018 1.7755 1.6629 [1.671/;] 2.5747 [(1.7436)]

. .......... . .......... ........... . ..........

.......... [891.8,,]

. .......... (15.6)

~1073

9

(300) 406.6 397.0 880.53 . .......... . .......... 263.1 365.3 622.2 1604.52

1.2 1.6 4.63 . .......... . .......... 0.81 1.2 3.2 28.77

216.6 767.5 ........... 841.0 or 830.0 ........... 295.4

0.5 6.24 . .......... 3.70 2.25 . .......... 0.72

5.80 1.60 3.2,

3.92 3.31 (1.2) 4.31 4.92 5.9B 2.87 3.47 3.91 2.6 7.50

. ........... ............ . ........... ............

. . .

........... ........... ........... . ...........

........... . .......... . .......... . ..........

. .......... . .......... . .......... 665.2

. .......... . .......... 2.80

. ........... 6.727

............

. .......... 1. 587~

.

.......... 1908

. .......... 37

2.14 2.95

.

0.193

3.413 ............

. ........... 0.48.56961 0.1865653 ............ . ........... 0.06533820 60.864 45.6378 30.442 29.8

...........

. ..........

406.6

1.30 . ..........

Z

U2

~

Z

""3

U2

o

~

2.81

Z 8 w o

~

t1 ~

> 8 o ~

~

o

(1.26)

2II o . i

8.68388223 0.94808710 Ao

OH+

(1.09)

2.9v 3.75 6.507

o

>944 1580.36ls 1903.85

5.4 12.0730 16.18

1108 I 9 [1028.5] in Ar matrix 3739.94 I 86.350 2716.1 [2955] [2187] 780.89

42.15 (85) (51) 2.820

[~733. 7]

256.5 207.5

2.96 0.50

(5.1) 5.1155 6.67. 4.10 4.39. 4.457 4.81 4.86 4.76 5.031 (3.7) 1.00 2.5

~

o

etr.:l

o q

t-


Z

t::l

a::

o et."'.l

. ..........

(3.0s)

o

[2299.60]

...........

3.06

[1666] 1337.24 1233.33

::c>

6.983 6.57

...........

1405 (820) 739.1 844.6 ........... 1051.18 [2293.50] . .......... 256.2 57.28 169 228* 376*

(5) . .......... 2.96 3.3

. .......... 4.87

...........

. .......... 0.71 0.096 0.46 0.92 1.9

6.36 ~6.15

7.88 (5.6) (6.6) 4.91 6.30 (3.6) 3.82 0.490 4.00 4.40 5.10

~ ~

""d

~

~ tn ~

o

ta

RbH ........... RbI ............ RhC ........... RhO ........... RuC ........... RuO 8 2.............. Sb2............. 8bBi ........... SbBr ........... ShCI ........... SbF ............ SbH ........... ,

(85) 85 103 103 (102) (102) 32 (121) (121)

SbN ........... , SbO ............

(121) (1:l1) (12-1) (121)

1 127 12 16 12 16 32 (123) 209 (7lJ)' 35 19 1 2 14 16

SbSe' ........... SbTe ........... Se2............. SeF ............ SeO ............ SeS ............ Se2............. SeF ............

(121) (121) 45 45 ,45 45 80 (80)

(80) (130) 45 19 16 (32) 80 19

SeH ............

(80)

1

(HH) (121) (lin)

12:+ 12:+ '2:

(0.99600356) 50.872750 10.7467886 13.8~3208

(lQ .7:J5'774«) (13.824938) 15.9860369 (60.94787) (76. 59 208) (47. 75009~) (27. 123853) (16.418463) (0: 99949368) (1.98109960) (12.5495816) (14.1261071)

.............

............

............. l2:g -

22.477~596

13.3546989 11.7974776 (18.684147«) 39.958256 (15.349416.)

............

............

............ 0.29547

............ 1~+

............

12:12:'n~

on ) ('ITt)

............ 12:+ '2:+ (22:+) 0 0+

'IT. 'IT. = -1600

SeO ............

80

16

13.3274820

'2:-

SeS ............ SH .............

(80) 32

(32) 1

(22.836079.) 0.97702732

............

SH+ ............ SiI ............. SiBr ............

32 32 28 (28)

2 1 28 (79)

(28~

..............

11.3148106

(28) 28

(79) 12 35

BiF ............

28

19

'IT. Ao =- -377 'IT. 12)12:/1-

13.988463G (20.654728) (8.39792224) 15.5422821

0.001570

............ ............ ............ ............. . ........... . ........... . ........... . ........... . ...........

Ao

S;Br+ ........... SiC ............ SiCl. ...........

............ .............

............ ............

............

............ ............ [5.87] [2.94]

............ ............

............ ............ 0.3950 [0.51340]

............ 0.08992 [0.363]

A = -560

1.89474167

. ...........

............

(0.99527385)

..............

0.072 0.00010946 0.00396

............

12: 0 +

12:+

............

A = +2272

(48.113701) (62.62182)

3.020 0.03283293 0.6027

'IT

r

A = +418 12:+

............

'IT 'IT = +162 r

[7.98]

............ . ...........

0.00266

............ ............ 0.000288

............ ............

0.4704 0.00326 (constants for F2 levels)

............

. ...........

2.367 3.1769 1.6133

. ...........

. .......... . .......... 1.8892 . .......... . ..........

. .......... .. .......... . ..........

936.9« 139 1049.87

14.21 0.34 4.94

. .......... . ..........

........... . ..........

880.8 725.647 269.85 220.0 (242.1) (369.0) (614.2)

13.1 2.844 0.59 0.50 (0.56) (0.92) (2.77)

(1.9) 3.47 6.01 4.3 6.55 5.3 4.38 3.06 (3.0) (3.2) (4.6) (4.2)

942.0 817

5.6 5.0

(4.8) (4.1)

326.1 (284)

1.04 (0.2)

[1.696] [1.701]

...........

........... . .......... . ..........

~

...........

. ..........

. ..........

1.7876 [1.6683]

735.6 971.55

3.8 3.95

........... 2.1660 [1.73.] [1.457]

. .......... 385.3028 (2400)

. .......... 0.96363

...........

(3.1) 2.78 1.65 6.06 6.96 4 ..92 3.410

1.6398

915.43

4.52

4.34

...........

. ..........

. ..........

[9.4611]

(0.300)

[I.3504]

(2702)

(60)

[4.900.] [9.1340] 0.2390

. ...........

(0.111)

[1.3474] [1.3744] 2.245

(1940)

(31)

3.576

............ . ........... ............

. ........... . ...........

. .......... . ...........

510.98 425.4

2.02 1.5

3.10 (3.7)

1.6

0.25619

0.00163

2.0576

535.89

2.29

(5.5) 4.6« (4.5)

0.58138

0.00490

1.6008

857.20

4.74

5.57

. ............

. ..........

535.8

. ..........

. ..........

A = +207 r

A

>

Z

~

UJ

o

IozJ

t1 ~

> ~ o ~

3.2

(3.90) 3.53

0.0013

o

o zrJ)

~

o is:

o

t'4

l;j

o

~

~

to

jl ~

00

~

~

1--4

TABLE m1

(1)

m2

~ ~

JJ.

7g-1.

Ground state

(3)

SiH ............

(28)

1

(0.97278225)

Sil ...........' ..

(28) 28

2 127

(1.8788414,) 22.9233244

28 28

14 16

(4) 2Il. +143 2II. 2II! A = +(757) 22:+ 12;+

A

SiN ............ SiO ............ SiO+ ........... SiS ............. SiSe ............ SiTe ........... SmO ........... Sn2 ............. SnBr ...........

9.3321338 10.1767074

.. ,

...

. .............

28 28 28 (152) (120) (120)

32 80 (130) 16 (118) (79)

14.9206887 20.7224688 (23.019425) (14.4712976) (59.44677) (47.593076)

SnCI ...........

(120)

35

(27.073116)

SnF ............

118

19

16.361890

SnH ............

(120)

SnI ....•....... SnO ............ SnS ............ SnSe ........... SnTe ........... SO ............. SrBr ........... SrCI ............ SrF ............ SrH ............ SrI. ............ SrO ............ SrS ............

(120) (120) 120 120 120 (120) 32 (88) (88) (88) (88) (88) (88) 88 (88)

1 2 127 16 32 80 (130) 16 79 35 19 1 2 127 16 (32)

(0.99942466) (1.98082846) (61.65195) 14.112333\ 25.241415 47.954285 (62.35204) 10.6613029, (41. 584947) (25.017065) (15.622111) (0.99640162) (1.96898851) (51.93244) 13.5325857 (23.444936)

CONSTANTS OF DIATOMIC MOLECULES

=

12:+ 12:+ 12:+

............ ............ ill.

A

=

A

=

+2467 ill.

+2361 2II. A = +2317 2II. A = +2178 2II. 2II 12:+ 12:+ 12:+ 12: 12:22:+ 22:+ 22:+ 22:+ 22:+ (22:+) 12;+ (12:)

B. (5)

00

(Continued)

~

a.

T.

w.

waf

Doo

(6)

(7)

(8)

(9)

(10)

7.4979

0.2149

1.5203

2045

36

3.06

3.8849

0.0801

1. 5197

1471 360.5

19 1.01

3.09

............

............

. ..........

0.00567 0.7310 0.0050385 0.7267514 Spectrum previously attributed 0.0014736 0.3035290 0.0007767 0.1920116

............

1.5720 1151.680 6.5600 1.5097 1241.44 5.92 to SiO+ now known to be due to SiN. 1.9293 749.6, 2.58 2.0583 580.0* 1.78* ........... 481.2 1.30

............ ............ ............ .............

............

. ........... ............

...........

............

............

........... 1.942

........... ...........

354.0

1.1

$4.25

q

586.1*

2.76*

4.7,

>

. .......... 247.7

. ..........

. ..........

5.383

0.137

1.7701

1715

30

2.7195

0.049

1.7690

1218 199.0 822.1 487.26 331. 2* 259.5 1148.19 216.5 302.3 500.1 1206.2

15 0.55 3.73 1.358 0.736* 0.50 6.116 0.51 0.95 2.21 17.0

............ 0.720817

............ ............ 0.25045 3.6751 1.8609

............. 0.33798

............

............

. ..........

0.002142, 0.0005063 0.00017048

1.8325 2.2090 2.3256

............ 0.005736

............ ............ 0.00148 0.0814 0.0292

. ........... 0.00219 . ...........

........... 1.4811

........... ........... 2.0757 2.1456 2.1449

........... 1. 9198

>

Z

0.62

. ..........

0.0011

0.3557190 0.136861, 0.06499776

i:= 1-4 o

6.37 5.45 4.60 6.16 1. 9, (3.0)

0.2733

............

(6.2) 8.26

> 8 o

...........

. ..........

173.9 653.2*

0.42 3.92*

........... ........... . ...........

2.60 (2.2) 5.49 4.77 4.09 3.65 5.358 (3.9) 4.25 5.58

~

"d

II:

~ tn ~

o

tn

7h. Constants of Polyatomic Molecules G. HERZBERG

National Research Council of Canada L. HERZBERG

Communications Research Center, Ottawa, Canada

7h-1. Introduction. The following tables present some of the more important data on simple polyatomic molecules derived from infrared, Raman, and microwave spectra. Tables 7h-l through 7h-4 give the fundamental vibrational frequencies (in cm- I ) of most triatomic and four-atomic molecules for which these quantities are available and for a few important five- and six-atomic molecules. The point groups to which the molecules belong are indicated in the last column. The numbering of the vibrations is in accordance with the practice followed by many authors in recent years! and now established by international agreement.t For most molecules listed the fundamentals are active in both the infrared and the Raman spectrum. However, for molecules of high symmetry, certain vibrations cannot occur in the Raman spectrum, others cannot occur in the infrared spectrum, and a few in neither one: for triatomic linear symmetric molecules (D oo" ) , Vi is Raman active and V2 and va infrared active; for four-atomic linear symmetric molecules (Dec")' VI, V2, and V4 are Raman active and va and Vs infrared active; for four-atomic planar molecules with a threefold axis (D ah ) , Vi is Raman active, V2 infrared active, and va and V4 are both Raman and infrared active; for five-atomic tetrahedral molecules (T d ) all vibrations are Raman active but only va and V4 are infrared active; for linear symmetric six-atomic molecules, the vibrations VI, V2, va, V6, P7 are Raman active and the remaining ones are infrared active; for six-atomic molecules with three mutually perpendicular planes of symmetry (V,,), the vibrations V7, Vg, VIO, Vll, V12 are infrared active and all others, except V4, are Raman active; for six-atomic molecules of C 2h symmetry, VI, V2, va, V4, vs, and V8 are Raman active, and the others are infrared active. Tables 7h-5 through 7h-15 give the rotational constants A rOl, B [OJ, C [OJ of selected triatomic, four-atomic, five-atomic, and six-atomic molecules. These rotational constants are, apart from the factor h/81r2 c, the reciprocal moments of inertia, and therefore from them the geometrical parameters of the molecule can be determined if a sufficient number of isotopes have been investigated. The geometrical parameters thus obtained are also listed in Tables 7h-5 through 7h-15. The constants A ro), B[oJ, C[OI refer to the lowest vibrational level which still includes the zero-point vibration. In the few cases in which these constants have been determined for the true equilibrium positions, the equilibrium contants A e, Be, C, are also listed. Microwave spectra give the constants in megahertz while infrared and Raman 1 G. Herzberg. "Molecular Spectra and Molecular Structure. II. Infrared and Raman Spectra of Polyatomic Molecules," D. Van Nostrand Company, Inc., Princeton, N.J., 1945. 2 R. S. Mulliken, JCP 13, 1997 (1955).

7-185

7-186

ATOMIC AND MOLECULAR PHYSICS

spectra give them in cmr". Here all microwave values have been converted to cm- I by dividing by c = 2.997925 X 10 10 em/sec. In the alphabetical order used, D is counted as an H in order to have the deuterated molecules appear with the corresponding nondeuterated ones. Element symbols without mass numbers refer to the most abundant isotope. Many of the data have been taken from the books by Heraberg"; by Gordy, Smith, and Trarnbarulo": by Townes and Schawlow "; and the more recent compilations of Shimanouchi' and Starck". In addition, some of the literature up to 1968 has been included. For detailed tables of microwave data reference should be made to the Microwave Spectral Tables prepared by Cord, Petersen, Lojko, and Haas."

7h-2. Fundamental Vibrations TABLE

Molecule

1'1 cm " !

1'2 cm- I

B02 ..... B0 2- .... BrCN ... Ca ....... CF2..... CICN .... ChO ..... CI02 ..... CNC ....

1070 1070t 575 (1230)t 1102 714 640 945.5

464 610t 341.5 63.1 667 378.4 (300) 447.4 321

7h-1.

I'a cm "!

TRIATOMIC MOLECULES

Point group

Molecule

1'1 cm " !

1'2 cm- I

HPO ... , H2S ..... HDS .... D2S ..... H2Se ..... HDSe ... D2Se ..... HSiBr ... HSiCI ... ICN .... , KrF2 .... N a- ...... NFL .... NH2 ..... N20 ..... N 20+ .... N02 ..... N02- .... N02+ .... NOCl. ... NOF ... , 03 ....... OCN- ... OCS .... , SCN- .... SeCN- ... SiCC .... S02 ...... U02++ ... XeF2 ....

........

1187 1182.7 1090 855.5 1034.2 912 741.4 771. 4 805.6 321* 232.6 630*

---

C02 ..... C02+ .... CS2 ...... FCN .... F20 ..... HCF .... HCN .... DCN .... HCO .... HCP ... , HF 2- .... HgBrs ...

HgCh ... HgI2 ..... HNO .... H 2O..... HDO .... D 2O..... HOCl. ... DOCl. ...

........ { 1388.2 1285.5t 1280 658.0 (2294) 928

........ 2096.9 1925.3 (2700) 3216.9 (595)t 225 360 156 3596 3656.7 2726.7 2671.5 3609.2 2666.0

1322 D""h 1970t D""h 2198.3 Coo. 2040 D""h (1222) C 2• 2215.6 Coo. 686 Ch 1110.5 C2v . ..... Dooh

667.4

2349.2

Dooh

......

(1469) 1533 1076.5 831

D""h Dooh

396.7 451.3 461 1403 712.0 569.0 1820. % 674.3 1240t 41 70 33 1562 1594.8 1402.2 1178.3 1242 911

. .....

c-; C2. C.

3311. 5 c-: 2630.3 C"". 1083.0 C. 1278.2 C"". Coo,,(?) 1500t 293 Dooh 413 Dooh (235) Dooh 1110 C. 3755.8 C2. 3707.5 C. 2788.0 C2v 739 C. 739 C.

2614.6

........ 1896.4 2344.5 1691 1686.7 1547.8

........ 470* 449 1350* 1074.3

........ 1284.9 1736.6 1318 1345* 1400* 1799 1844.0 1110 2180* 2062.2 2066* 2051. 5* 1742 1151.4 860t 515

(573)t

1497.2 588.8 461.2 749.8 816* 538* 596 765.9 705 870* 520.4 483* 575*

......

517.7 (252)t

213.2

I'a cm " !

Point group

---

---

985 2627 (2684) 1910 2357.8 2352 1697.4 408.0 522.4 2158* 588 2080* (931)t .0

••••

2223.8 1126.4 1617.8 1236* 2358* 332 521 1042.2

......

859.0 750* .0

••••

591 1361.8 930t 558

C. C2. C. C2. C2. C. C2. C. C. Coo. Dooh Dooh C2. C2v

c.;

C"".

Ch

C2. (Dooh) C. C. C2. C""" Coo. Coo. Coo. Coo. C2v C2. Dooh

(

) Values in parentheses are uncertain or have been obtained indirectly. liquid. t Fermi resonance between '''1 and 2"2. t Observed in crystal or solid matrix.

* Observed in

1 G. Herzberg, "Molecular Spectra and Molecular Structure," vol. II, "Infrared and Raman Spectra of Polyatomic Molecules," 1945, vol. III. "Electronic Spectra and Electronic Structure of Polyatornic Molecules," D. Van Nostrand Company, Inc., Princeton, N.J., 1945, 1966. 2 W. Gordy, W. V. Smith, and R. F. Trambarulo, "Microwave Spectroscopy," John Wiley & Sons, Inc., New York, 1953. 3 C. H. Townes and A. L. Schawlow, "Microwave Spectroscopy," McGraw-Hill Book Company, New York, 1955. 4 T. Shimanouchi, Tables of Molecular Vibrational Frequencies, parts 1-3, NaC. Standard Ref. Data Ser, NBS 6, pp. 11, 17, 1967-1968. 6 B. Starck, in Landolt-Bornstein New Series Group II, vol. 4, 1967. 6 M. S. Cord, J. D. Petersen, M. S. Lojko. and R. H. Haas, Microwave Spectral Tables, NBS Monoqraph. 70, vols. 3, 4, and 5, 1968.

7-187

CONSTANTS OF POLYATOMIC MOLECULES TABLE

7h-2.

FOUR-ATOMIC MOLECULES

cm- I

V2 cm " !

V3 cm'"!

V4 cm- I

VO cm'"!

AsCb ........... 410 AsF3 ........... 740.3 AsH a........... 2116.1 1523.1 AsD a........... BBr3 ........... 279 471 BCb ........... BI a............. 189* 888 BF3 ............ 288 BiCb ........... Br03- .......... 803* CH a............ ...... . CD a............ ...... . C 2H2........... 3372.7 C 2HD .......... 3335.6 C 2D2........... 2703.8 2113 C 2J 2...... " .... C 2N2........... 2329.9 1827 ChCO .......... C12CS .......... 1139 CIFa ........... 752 CIO a- .......... 940* CO a-- .......... 1063* F 2BO ........... 1369 FCiCO ......... 1868 F 2CO ........... 1942 HC 2Br ... , .. " . 3325 HC 2CI.......... 3340 DC 2Cl. ......... 2612 HC 2F .......... 3355 HC02- ......... 2825* H 2CO .......... 2766.4 HDCO ......... 2845 D 2CO .......... 2055.8 HFCO .......... 2981. 0 HN3 ........... 3335.6 HNCO ......... 3531 HNCS .......... 3537.9 cis-HN0 2. . . . . . . 3426 trans-HN02 . . . . . 3590 cis-DN0 2. . . . . . . 2530 trans-DN0 2. . . . . 2650 H 20 2........... 3599 D 202 ........... 2510* 2513* H 2S2........... 10 3- ........... 779* NCh ........... 535* NFa ............ 1032 trans-N 2F 2...... (1636) NH3 ........... 3336.7 NH 2D.......... NHD 2.......... ....... ND 3........... 2420.4 N2H2 ........... NO a- ........... 1048* P4. ............ 606 PBra ........... 380 PCb ............ 507

193 336.5 906 660.0 372 460 305* 691.4 130 428*

370 702.2 2123 1529.3 802 956 692* 1453.7 242 828*

159 262.3 1003 714 151 243

......

......

..... . ..... . . ,. ..

611t 463t

. ...... . ......

..... . ......

1973.7 1853.8 1763.8 191 854.2 .567 503 527 617* 878* 856.0 1095 965 2085 2110 1980 2255 1584* 1746.1 2120.5 1700 1836.9 2139.8 2274 1973 1639 1698

3294.9 2583.6 2439.2 718 2157.8 285 288 326 988* 1415* 491.0 776 584 618 756 742 1055 1386* 1500.6 1723.3 1105.7 1342.5 1263.7 1527 999 (1370) 1264 . ...... 1018 880 878* 510* 826*

611. 7 518.4 510.7 301 507.2 580 471 703 479* 680*

Molecule

VI

•

•

0

0

•••••

••

0.'

....... 1690 (1380) 1009* 882* 390t 347* 647

6~7*

(lOlD)

950.4 ••••••

0

2418 747.5 1481* 824* 363 162 260

905 (592) 3443.8 1592 1234 2564.0 •••

0

•••

1357* 465 400 493

480.4 96 350*

..... . 501 774 618 604 472 578 1352* 2843.4 1399 2159.7 1064.8 1150.5 777.1 615 856 793 816 739 309 229 416 330* 254* 493 360 1626.8 884 813 1191. 2 3120.1 720* •

'0

0"

116 189

..... . ..... . ..... . ..... . ...... '

..... . ...... . ..... 729.2 677.8 536.4 (115) 233.1 849 818 434

.. , ... ...... ...... 415 1249 295 326 (312) 367 773* ]251.2 1041 990 662.5 534.2 659.8 467 620 598 (591) 591 3608 2482* 2577

..... . ..... . ......

V6 cm- I

Point group

. ......

CJl)

....... 0

••••••

....... .0 ...... . ...... "

eo

•

••

0"

.......

.......

....... ....... ....... 440 292 364 .0

0

••

0

1286*

. ...... 667 626

....... ........ ....... ....... 1069* 1167 1074 938 (1175) 607.0 577.5 834 638 544 508 416 1266 1004* 886 ., .....

....... •••••

0

••

•

••••

. ... •

•

0

••

0.0

••

.......

.

•••

....... .0

••

0

•••••

. ......

•

0

. 0

••

0

•••••

••

0

C3c D 3h Dah D~h

Dah Ca,. Ch Dah Dah D'7:Jh C'7:Jl' D'7:Jh D'7:Jh D'7:J,h C 2l'

c;

1464

2556 '

••

421

...... •

0·

.0.' .•.

989 •••

•••

....... ....... .......

c., c..

••

o

•

•••

0

.0.0

•••

••••

0

••

C. Cal' Dah C 2l' C. C 21' C'7:Jr C'7:J1' C'7:Jl' C'7:JV C 2l' C 2v C. C 2v

C. C. C. C. C. C. C. C.

C2 C2 C2 C3v Cal' Cac C2h C av C. C. C av C2h Dah Td C3l' CJc

7-188

ATOMIC AND MOLECULAR PHYSICS

7h-2.

TABLE

Molecule

PFs ............ PFBn .......... PFCh .......... PF2Cl. .. " ..... PFClBr ......... PHs ............ PH2D .......... PHD2 .......... PD s............ 8bCb ........... 8bHs ........... Sb Ds ........... 82Cb .... " ..... 80s ............ 80Bn .......... 80Cb .......... 80F2 ........... (

cm- l

892 817 827 860 822 2322.9 .......

0

..

..

2320 1694 360 1890.9 1358.8 448 1067 1121 1230 1333

V2

cm- l

487 421 524 527 503 992.0 1700 ........

730 165 781.5 561.1 438 498 405 490 808

vs cm- l

860 ••

0

cm'"!

344

. . . . . . . .. .0

/'4

...

........

..

415 2327.7 1097 906 1700 320 1894.2 1362.0 206 1391. 2 267 344 530

••••

cm'"!

V6

.....

0

...... .....

(Continued)

0

......

.. ..

..

0

...

0

....

1118.3 892

...... ......

.....

..

0

..

806 134 830.9 592.5 102 531 120 194 (410)

..

393 496 833

..

..

0

......

...

0

0

cm'"!

V6

........ ........ . ......... .. ........ ......... ••

........

C.

980

C.

0

.....

...

0

....

...

0.0

0

......

..

...

...

..

..

......

....

......

•••

0

....

242

538 .....

0

379 445 748

Csv C. C. C. Cl C3v

..

..

0.0

Point group

..

....

) Values in parentheses are uncertain or have been obtained indirectly. liquid or solution. Observed in crystal or solid matrix.

* Observed in t

VI

FOUR-ATOMIC MOLECULES

..

•••••

223 284 390

0

..

c.; c; Csv Csv (C2) Ds,. C. C. C.

7-189

CONSTANTS OF POLYATOMIC MOLECULES TABLE

7h-3.

SOME FIVE-ATOMIC MOLECULES

Va cm- l

V, cm'"!

V5 cm- 1

Vft cm- 1

em'"!

V2 cm'"!

1533.6 1091. 9

3018.9 2259.3

1306.2 995.6

2200.0 2142 435.0

1300

3016.9

1471

1155

CHD a........... CF4 .............

2916.7 2108.9 2973} t 2914 2993 908.5

2263 631. 7

1291

1036

CCl •............

459.0

221

CBr4 ............ CI4 ............. SiH4, ........... SiF4 ............. SiCI4............ SiBr4 ............ SiI4 ............. GeH4. ........... GeF 4............ GeCI4 ........... GeBr4. " ..... , .. GeI4 ............ SnH4 ............ SnCI4. ........... SnBr4 ........... CHaF ........... CRaCI ........... CIt~Br ... , ......

267* 178t 2187.0 800 425 249* 168 2106 (740) 396* 235* 159

122* 90t 974.6 268 149 90* 63 930.9 (200) 134* 79* 60 758 104 64 1460.5 1354.9 1305.9 1250.8 1139.5 671.1 541 385* 782 ,762 741 990 949 930 903 497 358* 859.0 848 833 812

1003 1283.0 794.3} t 756 671* 555t 2190.6 1031.8 619.0 487* 405 2113.6 800 453* 327* 264 1901. 1 403 279 1048.6 732.1 611. 1 533.2 697.0 364.8 222 145* 475 350 285 872 551 430 (355) 250* 169* 689.1 423 305 248

Molecule

VI

CH4. ............ CD4 ............. CHaD ...........

ousr.... " .... "

CHFa ........... CnCh ........... C1I:13ra ...........

em, ............

CFiiCI ........... CF~Br ........... CFaJ ............ SiH.aF........... SiHiCI .......... Sill~Br .......... SiHal. ...........

smoi, ..........

SiRl3ra .......... GelI aF .. , ., ..... GeRaCI. .... " ... GeHaBr ......... Ge1I aI. ..........

.0

•••••

366 220 2964.5 2966.7 2972 2953.2 3034.5 3032.0 3042 (3040)* 1104 1083 1073 2206 2201 2200 2191.8 2274 2232* 2120.6 2121 2116 2112

310.0 182* 123t 914.2 389.4 221.3 137* 94 819.3 260 172* 112* 80 677 13~

88 3005.8 3042.4 3056.6 3060.3 1377.5 1218 1149 1064* 1217 1208 1185 2196 2195 2196 2205.6 810 769* 2131.8 2129.1 2127.0 2120.6

••

0

•••

••••

••

0

•••

••

0

•••

t Observed in

crystal or solid matrix.

..0 ... •

•••

0

•

. ..... . ..... ..0 ....

••

0

•••

••

0

•••

••

0

••

0

•••

••

0·

...

0

•••

••

0

••

0

•••

•

•••

0

•

••

0

•••

••••

0

..

••

0.0.

••

0.0

..

...

0

••

0

•••

..... .. ••

0.0.

••

0

•••

..... . . ......

......

••••

..

0.

1466.5 1452.1 1442.7 1437.4 1152 768 669 581* 559 549 540 (956) 954.4 950.4 941.0 600 473* 874.2 874.7 871. 4 853.0

( ) Values in parentheses are uncertain or have been obtained indirectly. • Observed it) liquid or solution.

t Fermi resonance.

0.

•••

....

••••

••

...

....

0

•

0·0

•

...... ...

..

0

•••

.....

••

0

•••

...... 1182.4 1011.3 954.7 882.4 508 256 155 92* 351 305 267* 728.1 664.0 632.6 592.4 179* 111* 642.5 603.9 578.1 558.7

Point group

Td Td

c., c; Td Td Td (Td) Td Td Td Td Td Td Td Td Td Td Td Td Td

c.. c; C av c.; Cav

C av C av

c.; c., c.; Cav c.,

Cav C av Cav

c., c;

Ca" Ca"

c.. C",

l' ~

CO TABLE

Molecule

HC=C-C=CH

C 2H 4........... C 2D 4........... C 2F4........... C2C14.......... C 2Br4.......... C 214 ........... H 2C : CF 2.......

cis-C 2H 2 F 2. . . . . . irans-C 2H 2 F 2 •••• H 2C : C Ch ......

cis-C 2H,Ch . . . . . trans-C 2H 2Ch . . . H 2C:CBr2 ...... -:is-C 2H2Br2.....

lrans-C 2H 2B r 2 N 20 4. ......... N 2H 4.......... CHaCN ........ CHaNC ........ CHaOH ........ CHaSH ........

PI

P2

cm'"!

cm'"!

Pa cm- I

(3293)* 3026.4 2251* 1872 1571* 1546* 1448* 3058.3 3135

2184 1622.6 1515* 778 447* 266* 181* 1728.5 1715

874 1342.2 981* 394 237* 144* 106* 1410 1266

......

.

3035* 3086 3071* 3023* 3084 3089* 1360 3325 2965.3 2965.8 3682 2946

••••

0

•

1627 1591 1576* 1593* 1584* 1581* 813 3261* 2267.3 2166.0 2977 2869

• •• 0"

1400 1179* 1270* 1379* 1150* 1250* 283 1493 1400.0 1410.0 2844 2607

7h-4.

P4

......

925.3 1014

...... 603 711* 844* 467* 580* 745*

...... 1098 919.9 944.6 1477 1475

SOME SIx-ATOMIC MOLECULES

cm- I

P5

P8

P7

P8

cm'"!

cm'"!

cm" !

cm- I

2020 3102.5 2305 1340 1000* 886* 780* 550 (255)

627 1222 (1009) 551 347* 211* 146* 590 (866) 874 686* 876* 898 668* 866 899 500* 780 1454.0 1466.9 1340 1070

482 949.3 720.0 407 288* 245* 225t 3099.8 (482) 325 3130* 406* (192) 3108* 372*

......

630 943 780 510 512* 463* (418) 1302 3135 774 1095 3072 758* 1065* 3059* 736*

680 377 1041.0 1129.3 1056 803

3350 361.0 263 1034 704

(220) 3105.5 2345 1337 908* 766* 638* 955 1376 3115 800 1303 3090 696* 1264 3099 1749 3314

cm- I

3329 1023 (726) (190) (110) (66)

o

•

0

••••

299 173* 349* 184* 109* 217* 1724* 873* 3009.0 3014.3 1455 1335

( ) Values in parentheses are uncertain or have been obtained indirectly. • Observed in liquid only. .:t Observed in crystal or solid matrix.

. .....

PIO

P11

P12

cm'"!

cm'"!

cm" !

Point group

. .....

D"""

P9

••

0

••••

...... . (2977) 2999

•••

0

••

826.0 (586) 218 176* 119* 94t 438 1127 1274 372 857 1200 322* 757 1163 380 1628 ••

0.0

••••

1477 1430

0

•

•

.00·

••

2988.7 2201.0 1186 777* 635* 525* 801 768 1159 875 571 827 886* 466 688 1265 1275 •

•••

0

•

..0 ... 1171* 955

1443.5 1077.9 558 310* 188* 129t 613 756 (410) 460 697 265* 405* 670 (192) 752 950 •

•••

0

•

•

•••

0

•

270 (600)

V" V" V" V" V" V"

C 2v C 2v C 2" C 2v C 2v

C~" C 2v C2v C 2"

>~

o

~ ~

o

>-

Z

t;

~

o

t'" t."'.J

o q

t'"

>-

;:d ~

V"

l:Il

C2 C3v Cav C. C.

U2

t-20 7.2716 9.0156 4.843 7.7272 8.86621 6.0970 7.24s 12.942

C[O) (em-I)

Point group

9.2869 6.4173 4.8458

C"j C.

4.7315 3.140 3.9013 } 1. 98e14 3.0361

C2l} Cs

6.00s 8.169

C2 c C2v

C2v

C2v C2v

HCO ..... 22.365 DCO ..... 13.641

1.494. 1.28h

1. 4008} 1. 171 2

C8

HNO ..... 18.4792 DNp ..... 10.5222

1.4115 1.2920

1.3071 } 1.1462

C8

HPO ..... 8.855 HCF ..... 15.55 HCCL ... 15.75 N02 ...... 8.00251

0.7024 1.221 0.6054 0.433665

0.6488 1.126 0.5882 0.410493

C8 C. C. C2v

Geometrical parameters

10(OH)

2.94736

0.41719

0.36469

C 2v

SiF 2......

1.02076

0.29433

0.22784

C2v

0, .......

3.55345

0.445276 0.394749

C2v

S02 ......

2.02736

0.34417

0.293535

C2v

S20 ......

1. 39811

0.168753

0.15034 2

C8

NOF .....

3.175189

0.395077 0.350519

C.

NOClu ... NOCI37... NOBr 71... NOBr 81... NS32F .... NS34F .... Cp 60 2....

2.8493 2.8486 2.7799 2.7799 1. 65841 1. 61101 1.73718

0.191383 0.186825 0.12499 0.12417 0.290615 0.290245 0.331971

F 20 ......

1.960777

0.363466 0.305792

0.179343 } 0.175327 0.11962 0.11886 0.246607 } 0.245262 0.277992

}

C. C. C.

C 2t· C2v

.A; ~o(HOH)

= 0.9572 .A; ~.(HOH) 104.52° r~(HS) = 1.3356.A; ~6HSH = 92.1° r.(HSe) = 1.4605 .A; ~.HSeH = 90.9° ro(HTe) = 1.653 ~; ~HTeH = 90.25° ro(BH) = 1.18.A; o~HBH = 131 0 ro(NH) = 1.024 A; ~HNH == 103.4° (',(eH) - 1.08 A(assumed) : "i:HCO == 119.5° ro(CO) == 1.19s .A t(NH) = 1.063 A ron'~'O) == 1.212 .A; ~HNO == 108.60 r.(OH)

=

ro(NO)

134.1°

CF 2......

= 0.9568

== 105.05°

== 1.193 .A; ~ONO ==

= 1.300 .A; ~FCF == 104.94° ro(SiF) = 1.59~ .A; ~FSiF == 101.0° ro(O'O) == 1.278 .A; ~OO'O == 116.8° ro(SO) = 1.432.A; ~OSO == 119.56° ro(SO) = 1.465 .A; r(SS) == 1.88.; "i:SSO = 118.0~ ro(Nq) == 1.13 A; ro(NF) == t52 A; ~ONF :;: 110° ro(NCI) = 1.975 A; ro(NO) == 1.139 .A; "i:CINO = 113.3° ro(NBr) = 2.14.A; ro(NO) = 1.15 .A; "i:BrNO == 114° ro(SF) = 1.646 .A; ro(SN) == 1.446 .A; ~NSF == 116.9° ro(ClO) = 1.473 .A; ~OCIO = 117.6° ro(OF) = 1.409 .A; ~FOF = 103.3° ro(CF)

7-193

CONSTANTS OF POLYATOMIC MOLECULES TABLE

7h-7.

FOUR-ATOMIC LINEAR MOLECULES

C 2H 2............

{1.1766

C 1HD ...........

{0.991O B. = 0.9948 {0.84787 R = 0.85076 0.15712 } 0.14774 0.189606 } 0.185874 0.173020 0.169592

C 2N214 • • • • • . • • • • • C 2N216........... HC 212CIS6 ........ HC 212C}37 ........ DC2 12C136........ DC2 12C}3i ........ FCCH .......... FCISCH ......... FCCISH ......... FCCD ........... FCISCD ......... FCClSD .........

0.323764 0.323579 0.312681 0.291403 0.291332 0.283071

TABLE

AsCh s6... ....... AsCla S7... AsF s ..... ....... AsHs .... ....... AsDs .... ....... BFs ...... 0.17635 N14Fs .... NI6Fs .... NH a..... 6.196 NDa ..... 3.117 PCla S6.... PCla S7.... PFs ...... .0.0 .•. PHa ..... PD a ..... Sb 12 1Cla.. SbusCla .. Sb 121Hs .. Sb I2SHs .. Sb 121Ds .. Sb I2SDa .. 0

•••

•••

0

•••

•••

0

•••

•••

0

•••

•••

0

•••

•••

••

0

00

•••

••

•••••

.0.0

.0

•••

•••

0

•••

0'0

_ ..- ..,

•

0.

•••••

•••

•••••

. UQ..-...

7h-8.

A[o] or CrO] cm- 1

•••

0

D., I c.;

B.= 1.1817

C 2D 2............

Molecule

Point group

Brol cm- l

Molecule

•

•

.....__ .._..

2. 93643} 2.93588 1. 49081 1.49027

-

= =

1. 208 1. 057

A; r.(CC) = A; r.(CH) =

1. 204 1.059

A A

D«>h

c.;

c.;

ro(C-C)

=

1.389

r,(CH) - 1.052 ro(CC) = 1.211 r o(CCI) = 1.632 r,(CH) ro(CC) ro(CF)

= = =

1.053 1.198 1.279

A;

ro(C==N)

1.154 A (assumed)

=

A A A A A A

FOUR-ATOMIC SYMMETRIC Top MOLECULES

0.071623 } 0.068204 0.1961013 3.75154 } 1. 91723 0.3527 0.356261 } 0.354557 9.9443 } 5.1423 0.087305} 0.082974 0.260847 4.45236 } 2.31728 0.05850 } 0.05840

..

{ro(CC) ro(CH)

D«>h

I

B[OI cm'"!

, _,"

Geometrical parameters

Point group

Geometrical parameters

= 2.161 A; ~CIAsCl = 98.4° ~ F AsF = 102° (assumed) ~HAsH = 91.7°

CS v

ro(AsCI)

Cs v

D Sh

= 1.712 A; ro(AsH) = 1.517 A; ro(BF) = 1.295 A

Cs v

ro(NF)

= 1.371 A; ~FNF = 102.16°

C s,.

ro(NH)

= 1.017 A; ~HNH = 107.8°

c.:

ro(PCI)

C3v

ro(PF)

= 2.043 A; = 1.535 A;

~FPF

CSv

ro(PH)

= 1.419 A;

~HPH

Cav

ro(SbCl)

=

CSv

ro(SbH)

= 1.704 A; ~HSbH = 91.1°

Cs v

ro(AsF)

2.325

........

~CIPCI

A;

= =

~C1SbCl

....

100.1°

= 100.1° (assumed) 93.3°

=

99.5°

_.....'

7-194

ATOMIC AND MOLECULAR PHYSICS TABLE

Molecule

A[o)

7h-9.

cm- 1

FOUR-ATOMIC ASYMMI'~TRIC Top MOLECULES

B,oj crn "!

CrOj crn "!

Point group

CChuO ..... CCIUCIJ70 .. CUF20 16... , CUF20 16 .... CUF 20I8 ....

0.264141 0.262440 0.394054 0.39409.'i 0.394055

0.115913 0.0804639 0.112743 0.0787704 0.392037 0.196166 } 0.39.1847 0.196129 0.362869 0.188574

C2v C. C2v

Geometrical parameters

= 1.166 A; ro(CCl) = 1.746 A 1:CICCI = 111.3° rO(CF) = 1.312 4 ro(CO) = 1.174 A 1:FCF = 108.0° {ro(CH) = 1.102 A; ro(CO) = 1.210 A; 1:HCH = 121.1° {ro(CO)

CH20 .......

9.4053

1.29536

1.13426

Ch

CUHFOI6 ... CUHFOI6 ... CUDFOu ... C12HFOIl ...

3.04056 2.95221 2.17117 2.99439

0.39227 0.39211 0.39233 0.37035

0.34680 0.34548 0.33162 0.32901 j

C.

{rO(CF) = 1.3384; ro(CO) = 1.181 A ro(CH) = 1.095 A; 1:FCO = 122.8°; 1:HCO = 127.3°

Cl·.FI ...... , CIIIF, .......

0.458573 0.455421

0.153830 0.115039 } 0.153836 0.114840

C.

' CIF2F:

HN,u ....... 20.34 HN1lNI U • • • (20.58) HN2 UN 1 6... (20.58) DN1u ....... 11.47

0.401416 0.389187 0.388327 0.378603

0.392988j 0.381192 0.380432 0.365769

C.

liNCO ...... DNCO ......

0.369289 0.344025

0.363938 } 0.336221

C.

HNC 12sa ... 44.90 HNC 12SU... .......... DNC12SI2 .. 23.5 8

0.196250 0.194989} 0.191626 0.19042, 0.183477 0.181634

C•

H20:l

0.8740

C2

30.59 17.3.

10.068

cis N2Ft ..... cis NUNuF2.

0.656682 0.643874

0.8384

0.265075 0.188510 } 0.263556 0.186677

TABLE

7h-1O.

r'CIF) ~ 1.698

A; ~FCIF ~

175.0° ro(ClF') = 1.598 A; 1:F'CIF = 87.5° HN'N"N"': 1.00 A; (180°) (assumed) ro(N'N") = 1.237 A ro(N"N"') = 1.133 A; 1:HN'N" = 114.1 ° rO(HN) = 0.987 A; 1:HNC = 128.1°: ro(NC) = 1.207 A; ro(CO) = 1.171 A 1: NCO = (180°) (assumed)

{'"'N'H) ~

0

~N'N"N'" ~

rO(NH) = 0.989 A; ro(NC) = 1.216 A; ro(CS) = 1.561 A; 1:HNC = 135.0° 1: NCS = 180° (assumed)

C2v

{ro(OH) = 0.950 A; ro(OO) = 1.475 A; 1: OOH = 94.8°; dihedral angle = 119.8° {ro(NF) = 1.384 A; ro(NN) = 1.214 A 1: FNN = 114.5°

FIVE-ATOMIC LINEAR MOLECULES

Molecule

B[o]. ern'"!

Point group

HC12C12C12N14 ...... " . HC12CltC13N14 ......... HC12Cl3C12N14 ... , " ... HC13C12C12N14 ......... HC12C12cuN15 ... , " " . DCltC12C12N14 ......... DC 12C12Cl3N H • • • • • . . . . DCltC13C12N14 .... " ... DC l3C 12CUN H • . • . . . . . . DC12CltC12N15 .........

0.151740\ 0.151112 ) 0.151099 O. 14705~r 0.147332 > 0.140817 0.140181 1 0.140350 0.137002 0.136775

c.;

ro(CH) = 1.057 A;oro(C=C) ro(C-C) = 1.382 A; ro(CN)

o.;

{ ro(CO)

C.O t .................. 0.07321

Geometrical parameters

ro(CC)

= 1.160 A (assumed) = 1. 280 A

= 1.203 A = 1.157 A

7-195

CONSTANTS OF POLYATOMIC MOLECULES TABLE

7h-ll.

FIVE-ATOMIC SYMMETRIC AND SPHERICAL Top MOLECULES

Molecule

AIO] or CIOj. em-I

CFIBr 7t ••••••• CF IBr 81....... CFICln ....... CFaCII7 .......

.......... .......... .......... ..........

Brol. cm "!

0.069984 0.069331 0.111262 0.108458

CFaI ..........

0.1910

0.050809

CH•.......... CHaD ........ CHD•........ CD •.......... CHBra 79 •••••• CHBra 81....... CDBra 79....... CDBra 81....... CI2H.Br 7t ••••. CuH.Br 81..... CUH aBr 7t • . . . • CUH.Br 81... , . CUD aBr 79... , . CuD.Br 81..... CHCla n ....... CHCla n ....... CDCla 15 ••••••• CI2H.Cla6 ... ,. CuH aCI17 ..... CuHICln ..... CuHICI17 ..... CI2DICln ... ,. CuD aCl·7 ..... C12H.Cl·8 ..... CI2HF•....... CI2DF a ....... C"HFI ....... CuHaF ....... CUH.F ....... CuD.F ....... CuHII. ....... CuH.I. ....... CuD.I. .......

..........

5.2412 3.878 3.2795 2.6329 0.041616 0.040605 0.041344 0.040345 0.319160 0.317947 0.304194 0.302971 0.257332 0.256218 0.110146 0.104389 0.108414 0.443402 0.436574 0.426835 0.419957 0.361647 0.355528 0.439892 0.345196 0.330940 0.347640 0.851794 0.829318 0.682132 0.250215 0.237465 0.201482

Ge 7°F algC)U ... Ge 7°F auCla7 ... Ge 72Fa uClu ... Ge 72Fl uC117 ... Ge HF.UC\35 ... Ge HFl uCla7 ... GeH •......... GeD •......... GeHDa ....... GeH.D ....... Ge 7°H aBr 79 •••• Ge 7°HaBr 81.... Ge 72HaBr 79 •••• Ge72HaBr81.... Ge aH.Br 79 •• ,. Ge 7·HaBr81.... Ge76H3Br79.... Ge76HaBr81.... Ge 7°HCI335 .... Ge 72HClaa5.... Ge 7·HCl la5.... Ge 7°HC!a37 .... Ge 72HCla37.... Ge 74HCl aa7 ....

5.243

.......... .......... ..........

.......... .......... .......... } 5.129 {

.......... .......... } 2.591 {

...........

.......... ., ......... (5.14)

........... 5.124

..........

.......... .......... .......... .......... .......... .......... 5.081

.......... .......... 5.134

.......... .......... .......... .......... .......... .......... .......... .......... .......... ..........

.......... .......... .......... ..........

.......... .......... .......... .......... .......... .......... .......... .......... ..........

.......... .......... ..........

} }

Point group

c.. c.; C."

I I} }

I}

Geometrical parameters

= 1.33 1; 1: (FCF) = 108° (assumed) = ],908 A {ro(QF) = 1.328..\; 1: (FCF) = 108° (assumed) ro(CCl) = 1.740 A {ro(CF) = 1.33 A (~ssumed) i 1:FCF = 108° { ro(CF)

ro(CBr)

(alllumed) ro(CI) = 2.134 A

= 1.0940.A = 1.085 A = 1.0918 A

T, } Ca. Ca. Td

rO(CH)

c..

{roCOH) ro(CBr)

= =

c.,

{ ro(PBr) rotCH)

Civ

{ ro(CBr) ro(CD)

Ca.

{ ,.u(CH) ro(CCl)

= 1.939 A; 1: (HCH) = 110°58' = 1.096 A = 1.9391 A; 1: (DCD) = 111°26' = 1.104 A = 1.073 A; ~(CICCl) = 110°24' = 1.76,7 A

Ca.

{ -srccn ;:: ro(CH) =

1. 7810 Ai ~(HCH) 1.113 A

=

110°31'

Ca.

{ ro(CCl) ro(CD)

= =

1.7810.A; ~(DCD) 1.164 A

=

110°43'

{ ro(CH) ro(CF)

= =

1.098 Ai 1: (FCF) 1.332 A

=

108°48'

{ro(CH) ro(CF)

= = = =

1.10g Ai 1: (HCN) 1.385 A

=

110°0'

r.(CH)

ro(CD)

1.068 A; 1: (BrCBr) 1.9;J0 A

=

110°48'

CIv

} } c.; Us»

}

Ca. C«•

1.106 A; 1: (HCH) = 111°10' {ro(CH) ro(CI) 2.1396 A ro(CI) = 2.1392 A; ro(CD) = 1.104; ~(DCD) = 111°37'

0.072334 }

0.070320 0.072301 0.070283 0.072270 0.070248 2.70 a 1.3512 1.669 1.969 0.081342 0.080395 0.080269 0.079322 0.079251 0.078303 0.078282 0.077332 0.072475

1.688 A: 1: (FGeF) 2.067 A

{ ro(GeF) ro(GeCl)

Td Ca•

T'l

ro(GeH)

c.,

{ ro(GeH) ro(GeBr)

= 1.55 Ai = 2.297 A

c..

{ro(GeCl) ro(GeH)

= 2.113.9 A; = 1.55 A

=

107°42'

=

112°0'

= 1.5~4 A

o..

J 1: (HGeH)

1

0.0723586}

0.0722445 0.0688389 0.0687284 0.0686207

= =

C,,,

~(ClGeCl)

=

108°17'

7-196 TABLE

ATOMIC AND MOLECULAR PHYSICS

7h-ll.

FIVE-ATOMIC SYMMETRIC AND SPHERICAL

Top

MOLECULES

(Continued) Molecule

Alo] or Cro), cm ?

Ge 7nHaCla5 .... Ge 74H aCI35 .... Ge 74H aCla7.... Ge 76H aCla7.... Ge 7°H aF ...... MnOaF ....... POC!a 35 ....... POClaa7 ....... POI6F•........ POI8F, ........ Psa2C!a35...... PS32CI;37...... pS34C!aa6 ...... PSa2F a........ PSaaFa ........ PS34F a........ Re 1S60aCI 35 .... Re 1a60aCI37.... Re I870aCla6 .... Re I870aCI37.... SiFaBr 71....... SiFiBr S1....... SF aCla5........ SiFaCla7 ....... Si 2SH4......... SiHD a........ Si2SHaBr71..... Si28HaBr81..... Si 2IHaBr71..... Si 2IHaBrS1..... Si aoHaBr 7l . . . • . Si 30HaBr S1..... SiHCl aa6 ....... SiHClaa7 ....... Si 2sHaCla6 ..... Si 30H aCla5..... Si 28H aCla7..... Si 28D aCla5..... Si 29DaCla5..... Si aoD aCla5..... Sj78DaCla7..... Si 28HFa ....... Si 2lHF a ....... SiaoHF a....... Si 28H aF ....... Si 2IH aF ....... SiaoHaF ....... Si 28D aF ....... Si 29D aF ....... Si'oDaF ....... SiH a!. ........ SnH .......... HnSD a .......

.......... 2.603

.......... .......... .......... .......... .......... .......... ..........

.......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... ..........

.......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... ..........

Blo]. cm- 1

0.146825 0.144563 0.139359 0.13831 0.33699 0.137732 0.067220 0.064457 0.153248 0.146610 0.046787 0.045222 0.045702 0.088650 0.087218 0.086052 0.069856 0.067547 0.069834 0.067525 0.051702 0.051173 0.082650 0.080491 2.864 1.7755 0.144159 0.143187 0.141196 0.140220 0.138409 0.137431 0.0824732 } 0.0782564 0.22261 0.21634 0.21723 0.19739 0.19515 0.19303 0.19256 0.240435 0.240021 0.239622

Point group

I

c.: c.; o.:

} }

1.52 A; 1: (HGeH) = 111°4' 2.1471

{ ro(PCl) ro(PO)

= 1.99 A; 1:: (ClPCl) = 103°36' = 1.45 A = 1.52 A; 1: (FPF) = 102°30'

{ro(PF) ro(PO) = 1.45

C3.

{ro(PCl) ro(PS)

C3• Ca•

}

Ca•

= =

2.02 1.85

{ro(PF) = 1.53

ro(PS)

=

{ ro(ReO)

ro(ReCl)

1.87

= =

A. A.; 1:: (CIPC1) = 100°30' A A.; 1: (FPF) = 100°18' A

1.761 2.230

A.; A.

1: (OReO) = 108°20'

{ro(SiF) = 1.560 A.; ro(SiBr) = 2.153 1: (FSiF) = 108°30' (assumed) {ro(SiF) = 1.560 A; ro(SiCl) = 1.989 1: (FSiF) = 108°30' (assumed)

A. A.

Td Ca•

}ro(SiH)

=

1.480

Cav

{ ro(SiH) ro(SiBr)

= =

1.57 A.: 1: (HSiH) = 111°20' 2.209 A.

Ca.

{ ro(SiH) = 1.47 A.: 1: (ClSiCI) ro(SiCl) = 2.021 A.

Ca.

{ro(SiCl) ro(SiH)

= 2.048 A.; = 1.50 A.

Ca.

{ ro(SiF) ro(SiH)

= =

Ca•

{ro(SiR) = 1.503 A.; ro(SiF) = 1.593 A 1:: (HSiH) = (111°) (assumed)

}

0.477927 0.473550 } 0.469411 0.408732 0.406120 0.403678 0.10726 2.161 1.3573

ro(GeCl)

Ca•

C3.

I}

}

= =

{ ro(GeH)

Ca"

} }

~

Geometrical parameters

Ca. Td}

c.;

A

=

109°22'

1: (HSiH) = 110°57'

1.565 A.; 1:(FSiF) = 108°17' 1.455 ..\ (assumed)

ro(SnH) = 1.701

A.

7-197

CONSTANTS OF POLYATOMIC MOLECULES TABLE

Molecule

7h-12.

AroJ, cm- 1 B[o],cm-1

[ A - B+C] 2-

CH2Br2 .............. CH2CO .............. CHDCO............. CD2CO .............. CH2Chl i . . . . . . . . . . . . . CH2ClIiCI17 ........... CH2Ch17 . . . . . . . . . . . . . CHDChl i . . . . . . . . . . . . CHDCIIiCII7.......... CD2CI~ ............. CD7ClIiCII7........... CH2Cffir.............

FIVE-ATOMIC ASYMMETRIC Top MOLECULES

9.37

........ ........ 1. 06746 1.063344 1.0592 0.9072 0.90364 0.78976 0.78661

0.343347 0.321790 0.304237 O. Il076 0.10779 0.1048 0.Il02 0.10732 0.1095 0.10666

[ A - B+C] 2-

C[o], cm- 1

= 0.821

Point group

C2V

0.330758 0.306032 0.285286 0.10224 0.099677 0.09713 0.1010 0.09845 0.09985 0.09740

C. C2v C.

C'c. "l

= 0.8975

C. C2v

0.3537

0.3085

0.377109 0.334984 0.402Il2 0.402138 0.392356 0.403610 0.377355 0.169218 0.169Il7 0.26024 0.24842

0.361759 } C2. 0.3Il764

........

= 1.907 A;

~ (HCB)

= Il2°

(elec.diffr.)

ro(CCl) To(CH)

= 1.7724 Ai ~ (CICCI) = 111°47' = 1.068 A; 1:(HCH) = Il2°0'

C2v C.

CH2N2............... CD7N2............... HC02H .............. DC02H.............. HC0 2D.............. HNOJ...........•.... DNO, ................ 8n07F2 .............. 8U02F2 .............. Si28H2F2 .............. Si28D7F2 ..............

2.58548 1.9250 2.2052 0.434005 0.432656 0.171261 0.171243 0.82359J 0.629925

To(CBr)

C.. ) C, . {To(CH) = 1.075 A; ~ (HCH) = 122.0° , TO(CO) = LUI A (assumed); TO(CC) =- 1.315 A C2v

CH2F2 ............... 1.6391 9.Il2

GeometricalparameterB

e.'''''') 0.332087 C. 0.332565 0.208831 } C. 0.201301 0.168685 } C2V 0.168586 0.21272 C2. 0.20435

}

{To(CBr) = 1.9Il A; TO(CCI) = 1.7ll6 A (uBumed) ~ (HCH) = 112° (elec.diffr.) {To(CH) = 1.09 A; ~ (HCH) = Il2° To(CF) = 1.36 A; ~ (FCF) = 1080 {To(NN) = 1.12 A; To(CN) = 1.32 A; To(CH) = 1.08 A; ~HCH = 12r r,(CR) ~ 1.097A: ,,(CO) - 1.202, I.... A To(OH) = 0.972 A; ~OCO = 124.go; ~HCO == 124.1°; ~COH = 106.3°

{To(NO) = 1.199. 1.2Il, 1.406 A; To(OH) = 0.964

~ONO = 130.3°, 113.85°; ~NOH = 102.ho {TO(SO) = 1.405 A; ~ 080 = 124.0° To(8F) = 1.530 A; ~FSF = 96.1° {To(SiH) 0;. 1.470 A; To(SiF) = 1.577 A; ~ FSiF = 107.9°

Ai

7-198

ATOMIC AND MOLECULAR PHYSICS TABLE

7h-13.

Point group

B[OI,

Molecule

cm- l

C4H 2........... C4D 2........... C4H 2+..........

0.14689 0.12767 0.14013

TABLE

} o.; o.;

7h-14.

Geometrical parameters

{ro(C-C) = 1.37~ A, assuming ro(C=C) = 1.205 ro(CH) = 1.046 A

SIX-ATOMIC SYMMETRIC Top MOLECULES

Point group

Molecule

BIOHaCO BllHaCO BIODaCO BllDaCO,

0, 299544 } 0.288773 C 0.251185 at' 0.244721

CFaCN H •••••• , , 0.0982523 } C CFaCNI6 , . 0.0952611 av C 12HaC12N14 C12HaC12NI6 C12HaClaN14 C13HaCI2N14 C12D aCI2N14 CIIDaClaN14.,

0.306842 0.297599 0.306686 0.297977 0.262119 0.261798

Cav

I

CHaH gl98Br 8l, .. 0.03754 CHaHg202Br79... O.03802 CH aHg202Br 8l, .. 0.03743 CH aH gl98ClJ 5 , CH aH gl98ClJ7 , CHaH glUC13 5 CH aH gIIl9Cla7 CH sHg2ooCla6 CH aH g200ClJ7 CHaHg202C135 CH sHg202C13 7 CH aH g204Cla5 CH aHg204C13 7 , CH aNC12 CHaNCla CD aNCI2 CDsNC 13 • • • • • • • SiHaCN SiDaCN

SIX-ATOMIC LINEAR MOLECULES

I

(

1

}cav

1.194 A 1.540 1: (HBH) = 113°52' 1.131 A 1.335 A 1.158 A (assumed); = 108° (assumed) 1.464 A

+;

r O(C H ) = 1.092 A ro(CC) = 1.460 ~; 1: (HCH) = ro(CN) = 1.158 A

I

= 2.406 A ro(CH) = 1.092 A (assumed); 1: (HCH) = 109°7' (assumed) ro(CHg) = 2.07 A

T o(HgBr)

{

I

0.16587 , . 0.15127

r O(B H ) = ro(BC) = roCCO) = r O(C F ) = ro(CN) = {• 1: (FCF) ro(CC) =

C3t'

0.069296 1\ 0.066918 \ 0.069286 I 0.066906 I' 0.069275 1\ 0.066895 Cav 0.069255 0,066872 0.069234 0.066849 II 0.335328 0.323420 0.286266 0.276150

Geometrical parameters

r O(C H ) = 1.092 ro(CHg) = 2.059 ro(HgCl) = 2.282

I

A (assumed); A

1: (HCH) =

A

r O(C H ) = 1.094 ~ ro(C-N) = 1.427 A; 1: (HCH) = 109°46' ro(N=C) = 1.167 A r O(SiH ) = 1.47 A (assumed); 1:HSiC = 108° (assumed) ; ro(SiC) = 1.848, ro(CN) = 1.156 A

I I

0

A

7-199

CONSTANTS OF POLYATOMIC MOLECULES TABLE

7h-15.

SIX-ATOMIC ASYMMETRIC Top MOLECULES

CrO] cm- 1

Point group

Aro] cm- 1

Bro] em"!

C2H4. ............ CzD, ...........

4.828 2.432

1.0012 0.7369

}

Vh

CHzCFz ......... CDzCFz.........

0.367003 0.35324

0.347873 0.17830; } 0.29998 0.16199

c«

CHzCFCl" ...... CHzCFCI17 ...... CHzCHBr7g...... CHzCHBrS1 .•..•.

0.35630 0.35629 ........ ........

0.17019 0.16528 0.13886 0.13804

CHzCHC!"...... CHzCHCla7 ......

........ ........

0.201138 0.181635} 0.196922 0.178165

C,

CHzCHI. .......

........

0.10870

0.10229

C.

CHaOH......... CDaOH......... CHaOD.........

........ ........

o 82299

0.79263 0.64272 o 73309

C.

Molecule

........

CHISH......... (5.68) CHISD......... (3.04) CDISH......... (4.03) HCzCHO........ 2.26912 DCzCHO........ 2.22715 HCzCDO........ 1.72668 DCzCDO........ 1.70368 NzH,...........

3.981,

NHzCHO....... NHzCDO....... NDzCHO.......

2.42555 1. 83288 1. 99191

0.66186 0.78273 0.4305, 0.42227 0.3516a 0.160985 0.148895 0.159825 0.147739

0.8282 0.5630

0.11503 0.11276 0.12885 0.12816

} }

0.41309 0.391h 0.339&

1

o0.139359 150091} 0.146060 0.135747

Bo + Co = 1.60633

Geometrical parameters

ro(C=C)

(~(CH) ~ (1.080 A); 1:HCH ~ 121.8" ro(CF) ro(CC)

32802 o0, 31421 0.29055

1

= (1.325 A); = (1.313 A.)

1: FCF

= 108.9°

C. C•

(,,(CH) ~ 1.07, A; ,,(CH') ~ 1.090 A; ,,(CC) ~ 1.33, A

C.

ro(CCl) = 1.726 A; 1: CCH 1: CCCI = 122.3°

= 119.5°,

123.8°, 121.0°;

{"(C-O)=

~ 1.425 A; 1: COH ~ 108.S' ro(CH) 1.094 A; 1:HCH = 108.6° ro(OH) = 0.945 A. methyl tilt 3.3° ('"(CH) ~ 1.104 A".(SH) ~ 1.329 A ro(CS) = 1.818 A.; 1:HCH = 110.3° 1: CSH = 100.3°

(,,(C=C) ~ 1.215 A; ,,(C""C) ~ 1,"" A C.

= 1.445 A; ro(CH) = 1.106 A, 1.055 A. = 123.7°, 1:CCC = 178.4° r(NH) ~ 1.02 A (assumed): ,,(NN) ~ 1.45 A (assumed) 1:HNH = 106°; 1:HNN = 112° Dihedral angle = 90.0° ro(NH') = 1.014 A.; ro(NH") = 1.002 A.; ro(CN) = 1.376 ~t ro(CH) = 1.102 A ro(CO) = 1.193A; 1:H'NH" = 118.9°; 1: H"NC = 120.6° 1:H'NC = 117.15°; 1:NCO = 123.8°; 1: NCH = 113.2° 1:0CH = 123.0°; 1:H'NC - NCO = 7°; 1:H"NC - NCH = 12° ro(C-C)

1:CCO

Cz

I 0.37939 0.37936 0.34002

= 1.086 A; :~ HCH = 117.6° = 1.339 A

{'o(CH)

Cl

I

7i. Atomic Transition Probabilities' w.

L. WIESE AND B. M. GLENNON

National Bureau of Standards

In the following tables, we present selected critically evaluated atomic transition probabilities for the 20 lightest elements. For this group of elements many data of moderate or sometimes even high accuracy are available from various experimental and theoretical sources. The material selected here is obtained principally from Hartree-Fock calculations (which partly include the effects of configuration interaction), from the Coulomb approximation, from the nuclear charge expansion method, and, experimentally, from emission measurements, with stabilized arcs, from lifetime experiments (with delayed coincidence techniques as well as with the Hanle effect method) and from anomalous dispersion measurements. 1. Guideposts for the Selection 01 Data. The listed data are mostly the same as those chosen by us for two recent comprehensive critical data compilations [1,2] which are several times larger than the present table. For the inclusion of data into this much more compact table we have used the following guideposts: Only lines with uncertainties estimated not to exceed 50 percent are included; only the more prominent lines of a spectrum, that is, the lines of at least moderate strength, are listed (even if reliable data are known for weak lines); and normally only those lines are included which have been observed before, i.e., which are listed in multiplet or other spectral line tables [3-6]. However, we have not been too rigid about the last requirement, especially for spectra of higher stages of ionization. These spectra have recently come into prominence, but are as yet rather incompletely represented in present multiplet tables. For these spectra we have thus listed the most prominent lines-when good f-value data are available-even in cases when we had only calculated wavelengths at our disposal. (In order to indicate that the calculated wavelengths are normally much more uncertain than the measured ones, the former are given in square brackets.) We believe that with the greatly expanded scale of research in plasma physics and astrophysics it will be only a short time before many of these lines are observed and may be needed for diagnostic studies. 2 As stated above, most of the data for this tabulation have been taken from two recent comprehensive compilations published in 1966 (H through Ne [1]) and in 1969 (Na through Ca [2]). But, in addition, we have also evaluated and included the most recent material through early 1970. Especially for the spectra of He, Li, Be, B, C, Ne, and Si we have found quite a bit of newer, more accurate data. In such cases we present the new data, list the individual references and indicate there which particular experimental or theoretical method the author has used. 2. Definitions, Units, and Conversion Factors. In the current literature several equivalent expressions for the atomic transition probability have found widespread Contribution of the National Bureau of Standards, not subject to copyright. We have usually not listed any data for stages of ionization beyond six. Some material for still higher stages of ionization is found in Wiese et al, [1,2]. 1

2

1-200

7-201

ATOMIC TRANSITION PROBABILITIES

acceptance. Not only the transition probability (per second) for spontaneous emission Aki from upper atomic state k to lower state i, but also the (absorption) oscillator strength or f value and the line strength S are widely used. In addition, the log (Jf is often employed in the astrophysical literature «(J is the statistical weight). For the present tables, where we have to restrict ourselves to one quantity to achieve a compact presentation, we have chosen to list Aki. Quantum theory yields for it the expression (7i-I)

where the summation in the squared matrix element is over the position vectors r of all p electrons of the atom, and Pik is the frequency.

TABLE 7i-1. NUMERICAL CONVERSION FACTORS FOR ALLOWED LINES The transition probability is listed in units 8- 1, and the f value is dimensionless. The wavelength A must be used in angstroms, and (Ji and (Jk are the statistical weights of the lower and upper states, respectively. (Note that in the tables, with the exception of hydrogen, Aki is given in units 108 8- 1 ) .

Transition probability

Transition probability Aki

=

Oscillator strength jn, = Line strength

s=

Oscillator strength 6.6702 X 10 1 5 a. -jik A2 o»

1.4992 X 10- 16 A2 fJ!:.

4.9356 X 10- 19 (JkA3Aki

3.2921 X 10-

2.0261

x

10 18 S

(Jk A 3

303.75 S

-

Aki

(Ji

Line strength

(Ji A 3

(JiAf,k

-

The f value and the line strength S are numerically related to A k i by the formulas given in Table 7i-l (see also [2]). The line strength is as usual given in atomic units, which are for allowed (or electric dipole) transitions

The statistical weights, which are listed for all presented lines, are related to the inner or total angular momentum quantum number J by (J = 2J + 1. Aside from the quantities listed in Table 7i-I, the transition probability for induced or stimulated emission Bioi and the transition probability for absorption B i k may become important in special fields, for example, in laser research. These quantities are numerically related to the transition probability for spontaneous emission by

and

Bioi

=

6.01>-3Aki

(7i-2)

Bi,

=

6.01>-3 fJ.!: A k i

(7i-3)

where A is the wavelength in angstroms.

(Ji

7-202

ATOMIC AND MOLECULAR PHYSICS

Occasionally the emission oscillator strength fie; has been employed. is related to the normally used (absorption) oscillator strength by

This quantity

3. Discussion of Data Tables. In this compilation we list the transition probabilities of individual spectral lines, whenever the nearest known neighboring lines differ by at least a few parts in 10 4 in wavelength." We often present several lines of a multiplet, usually the stronger ones, but omit the weaker ones. In the relatively few cases where the lines of a multiplet are all so closely grouped together that they are difficult or impossible to resolve, we list the multiplet value (as well as the multiplet statistical weights) instead of the individual line data. These data are marked by a dagger. If just a portion of the lines in a multiplet (or lines from different multiplets) differs in wavelength by less than one part in 10 4, we have omitted these lines, since they would overlap completely under most experimental conditions so that they might be mistaken for a single line. For hydrogen, we list "average" transition probabilities A;i' which are needed for most practical applications. These (calculated) transition probabilities are exact values for the number of digits given. For hydrogen, all states with the same principal quantum number are degenerate, so that only a single line having an "average" transition probability is observed for all possible combinations involving the principal quantum numbers i and k. The only assumption entering into the application of average transition probabilities is that the atomic substates must be occupied according to their statistical weights [1,7], which is the case for any plasma which is not too dilute. The spectra of hydrogen-like ions are not included jn this tabulation, since their transition probabilities may be obtained simply by scaling the hydrogen values AH according to (7i-5) where Z is the nuclear charge. For all other tabulated spectra we give accuracy estimates for the transition probabilities and present for purposes of identification all available multiplet numbers as given by Moore [3-51. The evaluation of the accuracy of the presented material is the most crucial (and normally the most time-consuming) part of a critical data compilation. We have therefore discussed our evaluation procedures extensively in the general introductions to our larger compilations [1,21, from which-as was mentioned before-we have extracted most of the data presented here. Because of limitations of space we have to refer here to these discussions and may also state that we have used in this compilation exactly the same procedures for the evaluation of all newer material. In addition to the allowed lines, we also list transition probabilities for some prominent forbidden lines because they are of interest in astrophysics and atmospheric physics. We always present total transition probabilities, i.e., the sum of the magnetic dipole and electric quadrupole values for a given line (in [1,21, on the other hand, we have listed the separate values). For a number of magnetic dipole lines the line strengths are essentially given by straight numbers. In some of these cases, furthermore, the transition probabilities of the respective electric quadrupole lines at the same wavelength are smaller by several orders of magnitude for all the ions covered in this table. The principal reason for this is that the wavelengths are relatively large (detailed estimates are given by Naqvi 1

In cases where only moderate spectral resolution is achieved, the multiplet tables [3-6]

or [1,2] should be checked for the existence of other nearby lines.

ATOMIC TRANSITION PROBABILITIES

7-203

as well as Shortley, Aller, Baker, and Menzel [8]). The total transition probabilities in such instances, if the wavelength X is known, may thus simply be obtained from (7i-6) where X is in angstroms, and the magnetic dipole line strength Sm is in atomic units. The Sm values for these lines are tabulated in Table 7i-2. TABLE 7i-2. LINE STRENGTHS FOR SOME FORBIDDEN TRANSITIONS Configuration

Line

S, atomic units

nsnp*

3POO_3Plo 3Plo_ 3P2o 2P!O_2PjO 3P1_3P 2

2.00 2.50

np np2 np3 np· np5

* Complete shell!", like 1s 228 2 , are omitted.

2DJO_2D jo W!o_2pio

3P2_3P 1 2PJO_2P!O

1. 33

2.50 2.40 1.33

2.50 1.33

The principal quantum number n has the values n

=a

2,3.

4. Availability of Data for Heavier Elements. For most other elements not included in this table, with the exception of the alkalies and some selected lines for elements of the iron group and the alkaline earths, the accuracy and reliability of atomic transition probabilities-if there are any available at all-are still rather poor and at the present time hardly worth a detailed critical compilation such as this. Thus, until more and especially more accurate material becomes available, we have to refer to the following sources: (1) Bibliography on Atomic Transition Probabilities, NBS SpecialPubl. 320, B. M. Miles and W. L. Wiese, 1970. This is an annotated bibliography which lists literature references ordered by elements and stages of ionization and indicates the various experimental or theoretical methods that have been employed. (2) Experimental Transition Probabilities, NBS M onograph 53, by C. Corliss and W. Bozman, 1962. This tabulation lists about 25,000 atomic oscillator strengths, mostly for heavier elements, obtained from arc intensity measurements which are generally of moderate or rather poor quality, as many comparisons with other data have shown. The data of Corliss and Bozman show many large discrepancies with other material, especially for the alkalies and alkaline earths and for lines from higher excited levels of the iron group elements. Thus great caution should be exercised when employing these data. (3) A special critical evaluation of transition probability data is available for the spectra of Ba I and II, NBS Tech. Note 474, by B. M. Miles and W. L. Wiese, 1968. 5. Regularities and Systematic Trends. Some remarks are in order about the recently detected regularities in atomic oscillator strengths, because these are of great value for evaluating the reliability of existing data as well as for determining additional numerical values by simple interpolation techniques. Three principal regularities have been detected (for detailed discussions see [9-11]), which may be briefly stated in the following way: DEPENDlj;NCE OF fVALUES ON NUCLEAR CHARGE Z. This dependence may be readily derived from conventional perturbation theory, with the result that f may be represented by a power series in Z-l:

7-204

ATOMIC AND MOLECULAR PHYSICS

where the first term ao is a hydrogenic I value [9,10) which vanishes for all transitions which do not involve a change in the principal quantum number. Three graphical examples exhibiting this systematic trend for different physical situations are given in Figs. 7i-l to 7i-3, where the I value is plotted against liZ. SYSTEMATIC TRENDS OF I VALUES WITHIN SPECTRAL SERIES. Within a spectral series, the dependence of I on the principal quantum number n (or the effective quantum number n *) is found to be always a smooth one, in an analogous fashion as for hydrogen. For lower values of n the I value is not always monotonically decreasing 1.0 r------.,-------,------"""T"""-----,

t.l-seouence

2s 25 -2p 2 po 0.8

0.6

0.4

•

Weiss, 45-term confio. interact. wavefcts.

o

Weiss, Hartree-Fock wavefcts.

)(

Berkneret 01., lifetime measurements

_._- Cohen a.Da1oarna,charoe expansion calc.

t

f-value

0.2

LiI 01

0.2

0.3

1/2FIG. 7i-1. Oscillator strengths vs. 1/ Z for the 2s-2p transition of the lithium isoelectronic sequence. (From Ref. [10], where the quoted authors and methods are discussed in detail.)

(see Fig. 7i-4), but for higher n the I values gradually tend to obey the hydrogenic dependence I '" (n *)-3. Two examples for these trends are given in graphical form (Figs. 7i-4 and 5), where n *31 is plotted against n *. HOMOLOGOUS ATOMS. The third principal regularity concerns homologous atoms, i.e., atoms with the same outer electron structure. Here we have found that for certain analogous groups of spectral lines the I values remain approximately constant throughout a family of homologous atoms. For example, the principal resonance lines of the alkalies, i.e., 2s-2p for Li, 3s-3p for Na, 4s-4p for K, etc., are all close to unity. This behavior is readily understood on the basis of the Wigner-Kirkwood partial I-sum rule. If it is assumed that most of the strength of a spectral series is concentrated in its leading transition (for example, 3s-3p has the dominant strength in a 3s-np series), then it follows that for this dominant transition array the mean I value is approximately given by the value obtained from the partial I-sum rule. Further-

7-205

ATOMIC TRANSITION PROBABILITIES

BORON SEQUENCE

252 2p 2 po- 2 5 2p~ 2 D o

Weiss(conf, interact. wavefcts.)

X Lawrence and Savage.(Ufetime)

o Heroux (Llfeflrne)

0.12 f -

-

• Bickel (Lifetime)

0.08

-

f-value

t

f-

-

0.04

-

f-

-

I-

I

I

0.05

0.10

en

om: Nm

Ne1ZI

I

BI

I

I'

J

0.20

0.15

I/Z-+ FIG. 7i-2. Oscillator strength!'! vs, 1/ Z for the 2s 2 2p 2po_2s2p2 2D transition of the boron isoelectronic sequence. (From Ref. [9], where the quoted authors and methods are discussed in detail.)

No-SEQUENCE

~

Hydrogen value: \ \

f=0.485

0.3

f-

,

,,

35 2S-4p 2po

\,

"

Prokof'ev (central field approximation)

•

Stewart end Ro.enberg (ThomasFermi potential)

'\ ., \

0.2 ....

'Weiss (SCF cdleulation) 6 Douglas and Garstang (SCF calculation) '-, 0 Coulomb approximation " C!) Hinnov and Kohn (Emission experiment)

-

,,

,.

f

i-,

f-value 0.1 -

, "

,

Fe:I2L I

0.02

II

-

'~,

0,

o

-

X

0.04

,

'6 Sint,...,

CoX I

,,

I

0.06

I

... .l~ •

0.08

_~

"I ...

0.1

I/ZFIG. 7i-3. Oscillator strengths vs. 1/ Z for the 3s 2S-4p 2po transition of the sodium isoelectronic sequence. (From Ref. [10], where the quoted auihore and methods are discussed in detail.)

10,..----------------------

LiI

7

2s-np SERIES 5

x Weiss (variational calculation) o Fillipov (hook,relativejnormalized to Weiss) • Anderson and Zilltls (semi-empirical calculation)

3

2

1.0 0.7 0.5

,..- _..-...... -e--.-----.- ...--.

0.3

,ff'

0.2

I I I

I I

I

0.1 L -........_ _L............_ _L............- - ' _........- - ' _........- - ' _......- - '_ _...... I

3

5

7

9

II

13

15

n*~ FIG. 7i-4. Oscillator strengths multiplied by n*3 vs. effective principal quantum number n* for the resonance series 2s-np of Li I. (From Ref. [10], where the quoted authors and methods are discussed in detail.) TABLE

7i-3.

COMPARISON OF MULTIPLET IN SOME DOMINANT

Transition

+

+

+

+

+

+

f

+

VALUES FOR HOMOLOGOUS ATOMS

TRANSITION ARRAYS·

Uncertainty, %

f value

l)p . . . . . . 1)8 - (n 2S_2PO . . . . . . . . . . . . . " .. np(n l)s - np(n l)p .. 3po_3D .. . , .... " ....... 3PO_3P................. 3PO_3S . . . " ............ IPO_ID ................. IPO_lS ................. l)p np2(n + 1)8 - np2(n 4P-4Do ................. 4P_4PO.. . , ............. 4P_4S0 . . . . . . . . . . . . . . . . . 2P_2PO.. . , .......... " . l)p n p3(n l)s - np3(n °SO_5P ................. 3S0_3P ..... . . . . . . . . . . . . (n

s-p

Boron (n = 2) 1.21 25 I Carbon (n = 2) 0.50 50 0.31 50 0.10 50 0.42 50 0.11 50 Nitrogen (n = 2) 0.36 25 0.23 25 0.088 25 0.318 25 Oxygen (n = 2) 0.922 10 0.898 10

.. The data are the adopted "best" values.

I

Uncertainty, ~

f value

Aluminum (n 1.41 I Silicon (n = 0.61 0.39 0.13 0.67 0.12 Phosphorus (n 0.57 0.36 0.13 0.39 Sulfur (n =

I

1.1 1.1

I

= 3)

25 3) 50 50 50 50 50 = 3)

50 50 50 50 3) 50 50

Data from experimental sources are in italics.

7-206

7-207

ATOMIC TRANSITION PROBABILITIES

5.0,---,.------r----,-----...,------,

or

rpf

f.

3p - ns SERIES

4.0

/1 Triplet (3p"_3S )

o Quintet (&po-Ss)

3.0

2.0

1.0

o

~O

4~

~o

6~

zo

n*~ FIG. 7i-5. Oscillator strengths multiplied by n*3 VB. effective principal quantum number n* for the 3p-ns .series of 0 1. The solid circles and triangles indicate that experimental values are involved in the data. (From Ref. [10], where the quoted authors and methods are discussed in detail.)

more, in all homologous atoms the breakdown of the total strength of a transition array into multiplets and individual lines remains the same as long as the coupling scheme remains constant. It follows therefore that for all lines of dominant transition arrays in homologous atoms the f values should stay approximately constant. An example is given in Table 7i-3. More extensive comparisons are found in lID]. References 1. Wiese, W. L., M. W. Smith, and B. M. Glennon: Atomic Transition Probabilities, vol. 1, Hydrogen through Neon, Natl. Standard Ref. Data Ser, NBS 4, 19(\6. 2. Wiese, W. L., M. W. Smith. and B. M. Miles: Atomic Transition Probabilities, vol. 2, Sodium through Calcium, Natl. Standard Ref. Data Ser, NBS 22, 1969. 3. Moore, C. K: A Multiplet Table of Astrophysical Interest, rev. ed., NBS Tech. Note 36, 1959. 4. Moore, C. E.: An Ultraviolet Multiplet Table, NBS Circ. 488, sec. 1, 1950. 5. Moore, C. E.: Selected Tables of Atomic Spectra, sees. 1 and 2, Si I, II, III, IV, Natl. Standard Ref. Data Ser, NBS 3, 1965, 1967. 6. Kelly, R. L.: "Atomic Emission Lines Below 2000 A," u.s. Government Printing Office, Washington, D.C., 1968. 7. Bethe, H. A., and E. E. Salpeter: "Quantum Mechanics of One- and Two-electron Atoms," Academic Press, Ine., New York, 1957,

7-208

ATOMIC AND MOLECULAR PHYSICS

8. Naqvi, A. M.: Thesis, Harvard University, 1951; G. Shortley, L. H. Aller, J. E. Baker, and D. H. Menzel: A3trophys. J. 93, 178 (1941). 9. Wiese, W. L.: "Beam Foil Spectroscopy," vol, 2, p. 385, S. Bashkin, ed., Gordon and Breach, Science Publishers, Inc., New York, 1968. 10. Wiese, W. L., and A. W. Weiss: Phys. Rev. 175,50 (1968). 11. Wiese, W. L.: Appl. Optics 7, 2361 (1968).

Explanations for Main Data Tables 7i-4: and 7i-6. A dagger (t) before a row of data indicates that multiplet values are given, for example, the averaged multiplet wavelength. WAVELENGTH COLUMN: The wavelengths are given in angstroms. Values in square brackets [ ] are calculated and are likely to be less accurate than observed ones. MULTIPLET COLt1.MN: The numbers refer to the multiplet numbers of C. E. Moore, "A Multiplet Table of Astrophysical Interest," revised editipn, Nat. Bur. Standards Tech. Note 36, 1959; or, if "uv" is added, to C. E. Moore, An Ultraviolet Multiplet Table, Natl. Bur. Standards Circ. 488, sec. 1, 19.50; or, for Si I, II, III, and IV, to C. E. Moore, "Selected Tables of Atomic Spectra," NSRDS-NBS 3, sees. 1 and 2. (Preceded by "UV," if in the ultraviolet.) All are available from the U.S. Government Printing Office, Washington, D.C. 20402. STATISTICAL W:EIGHTS COLUMN: The statistical weight gk of level k is related to the inner quantum number J by

The J's are listed in C. E. Moore, Atomic Energy Levels, Nail. Bur. Standards Cire. 467, vol. III, 1958, U.S. Government Printing Office, Washington, D.C. 20402. TRANSITION PROBABILITY COLUMN: Normally, the Ads are listed in units 108 r l • But for hydrogen and the forbidden lines, they are listed in units 8- 1 and the number given in parentheses ( ) indicates the power of ten by which the transition probability values have to be multiplied. ACCURACY COLUMN: The accuracy ratings are to be understood in the sense of "estimated extent of possible errors." Since it is at present not feasible to give specific numerical error limits for each evaluated f value, the data are assigned to one of several levels of accuracy which differ by about factors of three. Further details are found in [1,2]. SOURCE COLUMN: The numbers refer to the references given below. n indicates normalization to an absolute scale different from the one in the listed reference. References for Tables

7i-~

and 7i-5

1. Wiese, W. L., M. W. Smith, and B. M. Glennon: Atomic Transition Probabilities, vol. 1, Hydrogen through Neon, Natl. Standard Ref. Data Ser, NBS 4, 1966. 2. Wiese, W. L., M. W. Smith, and B. M. Miles: Atomic Transition Probabilities, vol. 2, Sodium through Calcium, Natl. Standard Ref. Data Ser. NBS 22, 1969. 3. Green, L. C., N. C. Johnson, and E. K. Kolchin: Astrophys. J. 144.,369 (1966). (Central field approximation with exchange and configuration mixing.) 4. Cohen, M., and P. S. Kelly: Can. J. Phys. -~5: 1661 (1967). (Self-consistent field calculation.) 5. Cohen, M., and P. S. Kelly: Can. J. Phys. ~5, 2079 (1967). (Self-consistent field calculation.) 6. Weiss, A. W.: Phys. Rev. 188, 119 (1969) and to be published. (Self-consistent field calculation with configuration mixing.) 7. Bergstrom, 1., J. Bromander, R. Buchta, L. Lundin, and 1. Martinson: Physics Letters 28A, 721 (1969). (Lifetime measurement.) 8. Froese, C.: J. Chern. Phys. U, 4010 (1967). (Self-consistent field calculation.) 9. Pfennig, H., P. Steele, and E. Trefftz: J. Quant. Spectr, & Radiative Transfer I, 355 (1965). (Self-consistent field calculat.ion.) 10. Lawrence, G. M., and B. D. Savage: Phys. Rev. Hl, 67 (1966). (Lifetime measurement.)

ATOMIC TRANSITION PROBABILITIES

7-209

11. Hese, A., and H. P. Weise: Z. Physik 215, 95 (1968). (Lifetime measurement.) 12. Warner, B. : Monthly Notices Roy. Astron: Soc. 139, 1 (1968). (Scaled Thomas-Fermi approximation with limited configuration mixing.) 13. Weiss, A. W.: Phys. Rev. 162, 71 (1967). (Self-consistent field calculation with configuration mixing.) 14. Roberts, J. R., and K. L. Eckerle: Phys. Rev. 153, 87 (1967). (Relative emission measurement. ) 15. Steele, R., and E. Trefftz: J. Quant. Spectr. & Radiative Transfer 6, 833 (1966). (Selfconsistent field calculation with configuration mixing.) 16. Curnette, B., W. S. Bickel, R. Girardeau, and S. Bashkin: Phys. Letters 27A, 680 (1968). (Lifetime measurement.) 17. Warner, B.: Monthly Notices Roy. Astron. Soc. 141, 273 (1968). (Scaled ThomasFermi approximation.) 18. Heroux, L.: Phys. Rev. 153, 156 (1967). (Lifetime measurement.) 19. Bickel, W. S., R. Girardeau, and S. Bashkin: Phys. Letters 28A, 154 (1968). (Lifetime measurement.) 20. Lewis, M. R., T. Marshall, E. H. Carnevale, F. S. Zimoch, and G. W. Wares: Phys. Rev. 164, 94 (1967). (Lifetime measurement.) 21. Gaillard, M., and J. E. Hesser: Astrophys. J. 152,695 (1968). (Lifetime measurement.) 22. Lawrence, G. M.: Bull. Am. Phys. Soc. II, 13, 424 (1968). (Lifetime measurement.) 23. Bickel, W. S.: Phys. Rev. 162,7 (1967). (Lifetime measurement.) 24. Bickel, W. S., and S. Bashkin: Phys. Letters, 20,488 (1966). (Lifetime measurement.) 25. Bridges, J. M., and W. L. Wiese: Phys. Rev. A2, 285 (1970). (Emission measurement.) 26. Lilly, R. A., and J. R. Holmes: J. Opt. Soc. Am. 58, 1406 (1968). (Relative emission measurement. ) 27. Hesser, J. E.: Phys. Rev. 174,68 (1968). (Lifetime measurement.) 28. Hofmann,_W.: Z. Naturforsch, 24a, 990 (1969). (Emission measurement.)

~ ~

o

TABLE

Wavelength,

A

Statistical weights Transition (J,

o«

I

7i-4.

TRANSITION PROBABILITIES FOR ALLOWED LINES

Average transition probability Aki*,

,,-1

Source*

Wavelength,

A

Statistical weights Transition

a,

Hydrogen

Average transition probability Aki*.

I

(Jk

,,-1

Source*

> ~

o a:: 1-1

o

>

Hydrogen (Continued)

Z

~

914.039 914.286 914.576 914.919 915.329

1-20 1-19 1-18 1-17 1-16

2 2 2 2 2

800 722 648 578 512

3.928(+3) 5.077(+3) 6.654(+3) 8.858(+3) 1. 200 ( +4)

1 1 1 1 1

8467.26 8502.49 8545.39 8598.39 8665.02

3-17 3-16 3-15 3-14 3-13

18 18 18 18 18

578 512 450 392 338

3. 444( +3) 4. 680( +3) 6.490( +3) 9.211(+3) 1. 343( +4)

1 1 1 1 1

a:: o

915.824 916.429 917.181 918.129 919.352

1-15 1-14 1-13 1-12 1-11

2 2 2 2 2

450 392 338 288 242

1. 657( +4) 2.341( +4) 3.393(+4) 5.066( +4) 7 .834( +4)

1 1 1 1 1

8750.47 8862.79 9014.91 9229.02 9545.98

3-12 3-11 3-10 3- 9

18 18 18 18 18

288 242 200 162 128

2.021( +4) 3.156(+4) 5.156(+4) 8.905(+4) 1. 651( +5)

1 1 1 1 1

> ::c

3- 8(P e)

t" trj

o d

t"

~

::r: 0


~

~

"'1 tn

~

o

rJ:J

4168.97 4387'.93 4437.55 t4471. 5 4713.2

52 51 50 14 12

3 3 3 9 9

1 5 1 15 3

0.0181 0.0899 0.0022 0.257 0.0934

10 10 10 10 10

3 3 3 3 3

4921. 93 5015.68 5047.74 t5875.7 6678.15

48 4 47 11 46

3 1 3 9 3

5 3 1 15 5

0.199 '0.1338 0.0670 0.706 0.638

10 1 10 3 3

3 1 3 1 1

t7065.3 7281. 35 1'9463.57 9603.42 t9702.66

10 45 67 75

9 3 3 1 9

3 1 9 3 3

0.278 0.181 0.00561 0.00586 0.00871

3 3 10 10 10

1 1 3 3 3

74 73 1 79 84

9 9 3 15 5

15 3 5 21 7

0.0201 0.0145 0.1022 0.0212 0.0212

10 10 1 10 10

3 3 1 1 1

t10311 t10667.6 10830.3 t10912.9 10917.0 11013.1 11045.0 11225.9 t11969.1 t12528

71

70 88 87 72 -

t12785 12790.3 t12846 12968.4 (13411. 8]

-

15083.7 t17002

-

-

1 3 3 9 3

3 5 1 15 9

0.00928 0.0184 0.0113 0.0349 0.00608

10 10 10 10 10

3 3 3 3 1

15 5 9 3 3

21 7 3 5 1

0.0462 0.0461 0.0274 0.0336 0.0205

10 10 10 10 10

1 1 3 3 3

1 9

3 15

0.0137 0.0664

10 10

1 3

• For references see pp. 7-208 and 7-209.

t3232.63 t3985.5 t4132.6 "t4273.1 t4'602.9 t4971.7 t6.l03.6 t6707.8 t8126.4 t1051O.6 t11032.1 t12237.7 t12793.3 t13557.8 t17546.1

2

-

6

5 4 1 3

-

-

-

2 6 6 6 6

6 2 10 2 10

0.0117 0.0250 0.106 0.0460 0.236

10 10 10 10 10

1 1 1 1 4

6 6 2 6 6

2 10 6 2 10

0.106 0.716 0.372 0.349 0.0194

10 10 3 10 10

4 1 1 1 1

6 6 10 6 6

2 10 14 2 10

0.0144 0.0341 0.0463 0.0276 0.0719

10 10 10 10 10

1 1 1 1 4

14 6 2 10 6

0.138 0.00481 0.0774 0.00819 0.0377

10 10 10 10 10

1 4 4 1 1

0.00922 0.0136 0.00286 0.0225 0.00778

10 10 10 10 10

1 1 1 1 4

3 3 10 10 10

1 1

:> 8

o

is: ~

o 8

~

:>

z

to 8

~

t18703.1 t19274.8 t 24464.7 t[25197] t26877 .8

-

10 10 6 6 2

t[28417] t[38081] t[41791] t[54633] t[68592]

-

6 6 10 6 2

2 10 6 2 6

1 1 3 1 9

3 3 9 3 15

Li II: 178.015 199.282 t[944.72] [1093.2] t1132.1

-

-

2 uv 1 uv -

-

77.9 256 1.39 1.38 3.90

i5

~

o

Z "0

~

ob:j

:>

b:j ~

t'"

~

8 t':l

~

rn

~

tS

1-4

W

TABLE

Wavelength,

A-

Multiplet no.

Statistical weights

o.

I

7i-4.

TRANSITION PROBABILITIES FOR ALLOWED LINES

Transition probability Aki, 10 8 S-1

Accuracy, %

Source*

Wavelength,

A-

Multiplet no.

(Continued)

a.

o»

Lithium (Continued) t1166.4 t1198.09 [1237.4] 1253.3 1420.89

-

t1493.0 t1653.1 1681. 66 1755.33 t2674.43

-

-

4 uv

3 9 5 1 3

1.07 2.88 3.16 0.784 2.82

10 3 10 10 3

5 1 5 5 1

9 9 3 3 3

15 3 5 1 9

11. 2 2.96 10.1 2.03 0.192

3 10 3 10 10

1 5 1 5 1

3 15 3 21 7

0.202 0.549 0.318 0.739 0.736

10 10 10 10 10

1 1 1 1

0.528 0.252 0.295 0.351 1.11

10 10 10 10 10

1 1 5 5 5

2.21 2.21 1. 17 0.0895 0.738

10 10 10 10 10

1 1 5 5 5

-

1 9 9 15 5

[3250.1] [3306.5] t3684.1 4156.3 t4325.7

2 3 5

3 3 3 1 9

5 1 9 3 15

t[4671.81 [4678.4] [4787.5] t[4840.8] t4881.3

4

15 5 3 15 9

21 7 5 9 3

s

I

~

Transition probability Aki. 10 8 S-1

Accuracy, %

Source*

Ok

Boron

9 3 3 3 1

[2952.5] t[3029.1] t[3155.4] t[3195.8] [3199.4]

~ ,.....

Statistical weights

1

BI: t1826.2 t2089.3 2496.77 2497.72 8667.2 8668.6 t11661 15625 15629 t16243

3 uv 2 uv 1 uv 1 uv -

-

6 6 2 4 2 4 2 2 4 6

10 10 2 2 2

2.23 0.494 0.65 1.30 0.0162

2 6 2 2 10

0.0324 0.196 0.051 0.103 0.119

25 25 25 25 25 25 25 25 25 25

6,10 6, 10, 11 6,7 6,7 1 1 6 1 1 6

~

c

>

Z

t::l

a:: o et;j C

q

r-

>

~

B II: 1362.46 t1624.0 [1842.8] 3451. 41 t4121.95

> 1-3 o a::

1 uv 3 uv 1 2

1 9 3 3 15

3 9 1 5 21

11.1 10.0 6.8 0.64 2.11

25 25 50 25 25

10 10 1 7 7

6 10 2 6 10

12.5 56.8 16.3 1. 91 1.11

10 10 10 3 10

1 1 1 1 1

14 6

10 10

1 1

BIll: -

t518.25 t677.09 t758.60 t2066.3 t4243.60

1

2 6 6 2 6

t4487.46 t7838.5

2 -

10 2

-

I

2.10 0.222

"'t1 ~ ~

U2 ~ C

U2

[5038.7] t5484.8 [9562.2] t[57324]

1

3 3 1 9

I

1 9 3 15

0.533 0.228 0.0518 0.00110

10 3 3 3

I

5 1 1 1

Beryllium

Be I: 2348.61 t2494.6 t2650.6 t3321. 2 [3455.2] 3515.54 3813.40

1 uv 3 uv 2 uv 1

-

7 5

1 9 9 9 3 3 3

3 15 9 3 1 5 5

5.3 1.4 4.29 1.6 2.09 0.13 0.23

25 50 25 50 25 50 50

6,7 9 6,7 7,8 1, 7 1 1

Be II: t1036.31 t1512.4 tl776.2 t3130.6 t3247.7 t3274.64 t4360.9 t4673.46 t5270.7 t12094

1 uv 4 uv 3 uv 1 5 2 4 6 3

-

2 6 6 2 6 2 6 10 6 2

6 10 2 6 2 6 10 14 2 6

1.66 11.4 4.22 1.15 0.410 0.133 1.12 2.21 1.00 0.128

10 10 10 3 10 10 10 10 10 10

1 1 1 1 1 4 4 1 4 1

B IV: 52.682 60.313 t[344.19] [381.13] t2823.4 [4499.4]

I

I

1 1 3 1 3 1

3 3 9 3 9 3

1080 3720 54.6 51.0 0.455 0.125

3 3 3 3 3 3

1 1 1 1 1 1

Carbon ~

9 7 6 5 4

uv uv uv uv uv

8

9 9 5 9 9

9 15 7 9 9

1.2 1.6 0.11 0.82 1.4

50 50 50 50 50

1 1 1 1 1

o

r:n

~ ~

o 8

~

> Z

65 65 65 38 37

uv uv uv uv uv

5 5 5 5 5

7 5 3 3 7

1.5 1.4 1.3 0.37 2.1

50 50 50 50 50

1 1 1 1 1

36 34 3 2 62

uv uv uv uv uv

5 5 9 9 1

3 5 15 9 3

0.46 0.33 1.25 3.20 0.87

50 50 25 25 50

1 1 10 10 1

o b:l > b:l e-

33 uv 61 uv 16 14 13

5 1 3 3 3

3 3 5 3 1

3.1 0.33 0.0032 0.0097 0.046

50 50 50 50 50

10,13 10,13 1 1 1

r:n

12

3 3

5 3

0.017 0.016

50 50

1 1

~

8

~

o

Z "'d

~

~ ~

8

~

Be III: 88.314 100.254 [398.19] t[583.01] t[3721.8] [6141. 2]

-

1 1 1 3 3

3 3 3 9 9

-

1

3

-

...For references see pp. 7-208 and 7-209.

362 1220 42.8 16.5 0.342 0.0877

3 3 3 3 3

1 1 1 1 1

3

1

11

t."'.l

jl ~ I-l

Con

TABLE

Wavelength;

A-

Multiplet no.

Statistical weights

7i-4.

Transition probability Ak.,

Oi

I

TRANSITION PROBABILITIES FOR ALLOWED LINES

108

S-1

Accuracy, %

Source*

Wavelength,

A-

Multiplet no.

Ok

9062.53 9078.32 9088.57 9094.89 9111. 85 9603.09 9620.86 9658.49 10124 10548.0

22 10 3 3 3 3 3 3 2 2 2

-

20

3 3 3 1 3 3 5 5 1 3 5 3 3

3 1 5 3 3 1 5 3 3 3 3 3 3

0.024 0.32 0.065 0.083 0.062 0.25 0.19 0.11 0.024 0.074 0.12 0.171 0.010

50 50 50 50 50 50 50 50 50 50 50 25 50

1 1 1 1 1 1 1 1 1 1 1 1 1

5 3 5

0.13 0.10 0.18 0.072 0.043

50 50 50 50 50

1 1 1 1 1

3 3 5 5 5

5 3 7 5 3

0.OO9Q 0.0492 0.0073 0.0453 0.0163

25 25 25 25 25

1 1 1

1

3

1 1 1 1

1

11602.9 11609.9 11619.0 11631. 6 11638.6

25 25 25 25 25

~

Transition probability

108 S-1

Aki'

I

Accuracy, %

Source*

Ok

> t-3

Carbon (Continued)

5 3 7 3 5

10683.1 10685.3 10691. 2 10707.3 10729.5

Statistical weights

O'

Carbon (Continued)

6587.75 8335.19 9061.48

~.....

(Continued)

1 1

4371. 59 4372.49 4374.28

45 45 45

2 4 6

4 6 8

0.83 1.99

25 25 25

1 1 1

t4411.4 5143.49 5145.16 5151.08 5640.50

39 16 16 16 15

10 4 6 6 2

14 2 6 4 4

2.11 0.72 0.60 0.385 0.109

25 25 25 25 25

1 1 1 1 1

5648.08 5662.51 t5890A 6578.03 6582.85

15 15 5 2 2

4 6 10 2 2

4 4 6 4 2

0.217 0.325 0.337 0.361 0.361

25 25 25 25 25

1 1 1 13 13

6783.75 6787.09 6791.30 6800.50 7231.12

14 14 14 14 3

6 2 4 6 2

8 2 4 6 4

0.370 0.307 0.195 0.110 0.362

25 25 25 25 25

1 1 1 1 13

C III: 386.203 t459.57 977.026 tU75.7 1247.37

2 6 1 4 9

1 9 1

3 15 3 9 1

50 50 25 50 50

8 9 15 1 1

lAO

o

a:: ~

o

>

Z

~

a:: o et:r.J

C

q

e>

;0

'"d

= rn ~

uv uv uv uv uv

9

3

25 95 16.1 13 12

~

o

tn

[11653] 11656.0 11677.0 11747.5 [11778]

29 29 25 24 24

3 3 7 3 5

1 3 5 5 5

0.157 0.158 0.0101 0.202 0.0375

25 25 25 25 25

1 1 1 1 1

11801.8 11849.3 11863.0 11880.4 12551.0

24 23 23 23 30

7 5 3 3 1

7 5 3 1 3

0.0266 0.017 0.029 0.11 0.0352

25 50 50 50 25

1 1 1 1 1

12582.3 12602.6 12614.8 16890

30 30 30

3 5 5 5

5 3 5 7

0.0262 0.0435 0.078 0.123'

25 25 25 25

1 1 1 1

25 25 25 25 25

13 13 13 13 13

o rr

-

t687.25 t904.09 tlOlO.2 t1036.8 t1323.9

5 3 7 2 11

uv uv uv uv

t1335.3 2509.11 2511. 71 2512.03 2836.71

1 14 14 14 13

uv

6 6 12 6 10

10 6 4 2 10

uv uv uv uv uv

6 2 4 4 2

10 4 4 6 4

2.65 0.63 0.126 0.75 0.359

25 25 25 25 25

10, 13, 13, 13, 13,

2837.60 t3876.7 3918.98 3920.68 4074.53

13 uv 33 4 4 36

2 28 2 4 6

2 36 2 2 8

0.359 2.66 0.62 1. 24 1. 96

25 25 25 25 25

13, 14 1 1, 14 1, 14 1

4076.00 t4267.2

36 6

8 10

10 14

2.28 2.46

25 25

1 1

28.0 41.6 34.3 22.2 5.3

13 14 14 14 14

10 12 15

3 1 9 3 15

5 3 15 3 21

1. 20 0.325 0.95 0.82 1. 81

25 25 25 25 25

7, 16 1 1 1 1

4056.06 4122.05 4325.70 4388.24 t4516.5

;24 17 7 14 9

5 3 3 7 9

7 5 5 5 3

1.45 1.04 1.08 0.224 1.66

25 25 25 25 25

1 1 1 1 1

4647.40 4663.53 4665.90 4673.91 5249.6

1 5 5 5 23

3 3 5 5 5

5 1 5 3 3

0.68 0.84 0.63 0.347 0.52

25 25 25 25 25

7 1 1 1 1

5253.55 5272.56 6727.1 6730.7 6744.2

4 4 3 3 3

3 5 1 3 5

3 3 3 5 7

0.194 0.320 0.149 0.201 0.266

25 25 25 25 25

1 1 1 1 1

2296.89 3170.16 t3609.3 3703.52 t3887.1

8 uv 8

> ""3 o ~ 1-4

o 8

;:l;l

>

Z

W

1-4

8

1-4

o

Z ~

;:l;l

o

t:d

6;

C IV:

t244.907 t259.52 289.143 296.857 296.951

3 10 9 8 8

uv uv uv uv uv

2 6 2 2 4

6 10 4 2 2

312.418 312.455 384.032 419.525 419.714

2 2 7 6 6

uv uv uv uv uv

2 2 2 2 4

4 2 4 2 2

22.3 27.6 49.5 5.27 10.5 45.7 45.5 148 14.3 28.5

10 10 10 10 10

4 17 4 4 4

10 10 10 10 10

1 1 1 1 1

1-4

t'4

1-4

""3 1-4 t':j

W

jl tv

• For references see pp. 7-208 and 7-209.

~

-a

TABLE

Wavelength.

A-

Multiplet no.

Statistical weights

a.

I

7i-4.

TRANSITION PROBABILITIES FOR ALLOWED LINES

Transition probability A~i, 10 8 S-1

Accuracy, %

Source·

Wavelength,

A-

Multiplet no.

o»

1 1 14 13 12

uv uv uv uv uv

2 2 10 10 2

4 4 14 6 2

2.65 2.63 6.62 0.673 1.17

3 3 10 10 10

1 1 17 17 17

2698.70 t3936 5021 5023 5801. 51

12 uv 2 3 3 1

4 2 2 4 2

2 6 2 2 4

2.33 0.330 0.464 0.930 0.319

10 10 10 10 10

17 17 17 17 1

CV:

2

2

0.316

Source"

Ok

10

1

6 4 4 6 4

0.0149 0.106 0.161 0.063 0.092

25 25 25 25 25

1 1 1 1 1

8216.32 8223.12 8242.37 8590.01 8629.24

2 2 2 8 8

6 4 6 2 4

6 2 4 2 4

0.160 0.202 0.102 0.190 0.238

25 25 25 25 25

1 1 1 1

o

!

q

8680.27 8683.40 8686.16 8703.26 87] 1. 71

1 1 1 1 1

6 4 2 2 4

8 6 4 2 4

0.191 0.133 0.079 0.171 0.101

25 25 25 25 25

1 1 1 1 1

1 15 15

6 2 6 2 2

6 2 8 4 4

0.054 0.255 0.269 0.257 0.183

25 10 10 10 25

1 1 1 1 1

4 6 8 2 4

6 6 8 4 6-

0.218 0.0542 0.101 0.262 0.281

25 10 10 10 10

1 1 1 1 1

>

Z

a::

~ ~ C".} ~

>

~

~

::t= ~

(f) ~

2550 8870 142 124 136

3 3 10 10 3

1 1 5 5 1

8718.84 9028.92 9045.88 9060.72 9386"18-1-

[247.31] t248.71 267-.26 t2273.9 [3540.8]

-

1 9 3 3 1

3 15 5 9 3

128 425 396

3 3 3 3 3,

1 1 1 1 1

939-2.79 9822.75 9R63.33 10105.1 +-010&.9

165:-

a::

1-4

C".}

t:'

3 3 15 5 9

o 565

> 8 o

6 4 6 4 2

1 1 9 3 3

f)

Accuracy, %

29 3 3 2 2

-

-

1-1

Transition probability Aki, 10 8 S-1

6945.22 7442.30 7468.31 8184.85 8188.01

34.973 40.270 t186.72 197.02 t227.22

-

I

~ 00

Nitrogen (Continued)

1548.20 1550.77 t2524.40 t2595.14 2697.73

1

Statistical weights

0.

Carbon (Continued)

5812.14

(Continued)

7

7 1~

19 18 18

o

(f)

Nitrooen

N I: 1134.17 1134.42 1134.98 t1164.0 t1167.9

1199.55 1200.22 1200.71 t124~.3

t1310.7 t1411.94 1494.67 t1743.6 4099.95 4109.96

2 2 2 7 6

uv uv uv uv uv

4 4 4 10

1 uv 1 uv 1 uv 5 uv 13 uv

4 4 4

10 uv 4 uv 9 uv 10 10

10

10

6

2 4 6 10 14 6

4 2 10 10

6 4 6 2 4

10 2 6 4 6

1.82 1.82 1.60 0.343 0.87

25 25 25 25 25

In, 10 In, 10 In, 10 In, 10 In, 10

4.01 3.86 4.01 3.35 0.95

25 25 25 25 25

In, In, In, In, In.

0.379 3.65 1.46 0.034 0.040

25 25 25 50 50

10 10 10 10 10

In, to In, 10 In, 10

1 1

4214.73 4215.92 4230.35 4914.90 4935.03

5 5 5 9 9

4 2 6 2 4

6 4 4 2 2

0.022 0.031 0.033 0.00759 0.0158

50 50 50 10 10

1 1 1 1 1

[5197.8] [5201.8] 5281.18 5328.70 5401.45

14 13 -

2 2 6 6 2

2 4 6 8 2

0.023 0.023 0.00282 0.00254 0.00369

50 50 25 25 25

1 1 1 1 1

5411. 88 6644.96 6646.51 6653.46 6656.51

20 20 20 20

4 8 2 6 4

2 6 2 4 2

0.0075 0.0311 0.0194 0.0244 0.0193

25 25 25 25 25

1 1 1 1 1

* For references Bee pp. 1-208 and 7.209.

10112.5 10114.6 10128.3 10147.3 10164.8

18 18 18 18 18

6 8 4 6 8

8 10 4 6 8

0.321 0.374 0.104 0.0898 0.0523

10 10 10 10 10

1 1

10500.3 10507.0 10513.4 10520.6 10539.6

28 28 28 28 28

2 4 2 4 6

4 6 2 4 8

0.0652 0.132 0.174 0.162 0.242

10 10 10 10 10

1 1 1 1 1

103

10549.6 10591. 9 10644.0 10653.0 10713.6

28

6 6 4 2 4

6 8

10 10 10 10 10

1 I

o

4 6

0.126 0.326 0.107 0.0532 0.0376

1 1 1

>

10718.0 10757.9 11291. 7 11294.2 11313.9

-

6 6 8 2 6

4 6 6 2 4

0.0564 0.0868 0.117 0.0731 0.0920

10 10 25 25 25

1 1 1 1 1

-

-

17 17 17

2

1 1 1

11997.9 12074.1 12186.9 [12330] [12384]

37 37 27 34 34

4 6 6 4 4

4 6 6 4 6

0.054 0.055 0.054 0.124 0.123

25 25 25 25 25

1 1 1 1 1

12461. 2 12467.8

36 36

4 6

6 8

0.202 0.217

25 25

1 1

3 5 9

3 3 9

25

18 18 18

>

o

a::: ~

103

:::c

z

rJ2

~

103 ~

o Z

I'tl

:::c

o

~

~ ~

t"l '103 ""'"

't:':j ""'"

N II: 644.825 645.167 t671.48

4 uv 4 uv 3 uv

30.2 51 9.9

25 25

rJ2

~ ~

CO

TABLE

7i-4.

TRANSITION PROBABILITIES FOR ALLOWED LINES

(Continued)

-1

Statistical weights

o

~

I:\:)

Wavelength,

A

Multiplet no.

Statistical weights

Transition probability Aki,

o.

I

10

8 8- 1

Accuracy,

Source*

%

Wavelength,

A

Multiplet no.

Aki,

a,

a»

Transition probability

I

10 8 8 - 1

Accuracy,

Source*

%

o»

> 1-3

Nitrogen (Cuntinued)

t916.34 t1085.1

2 uv 1 uv

9 9

9 15

10.4 3.56

25 25

3006.86

14 uv 15 uv 23 uv 22 uv 18

3 3 5 5 3

3 5 3 7 3

0.52 0.49 0.353 0.35 0.54

50 50 25 50 25

1 1 1 1 1

3328.79 3330.30 3331. 32 3437.16 3593.60

22 22 22 13 26

7 3 5 3 3

5 1 3 1 5

0.93 1.11 0.83 2.40 0.231

25 25 25 25 25

1 1 1 1 1

3609.09 3829.80 3838.39 3919.01 3995.00

26 30 30 17 12

3 3 5 3 3

3 5 5 3 5

0.228 0.175 0.52 1.00 1.58

25 25 25 25 25

1 1 1 1 1

4026.08 t4040.9 4124.08 4133.67 4145.76

40 39 65 65 65

7 21 3 5 7

9 27 5 5 5

0.90 2.64 0.276 0.458 0.64

25 25 25 25 25

1 1 1 1 1

4176.16 4227.75

42 33

5 5

7 3

2.19 1.06

25 25

1

1886.82 2206.10 2461.30 2709.R2

Nitrogen (Continued)

18 10,18

1

o

~

5940.25 5941. 67

28 28

3 5

3 7

0.235 0.564

25 25

1 1

6167.82 6170.16 6173.40 6242.52 6340.57

36 36 36 57 46

9 5 7 7 7

7 3 5 5 5

0.333 0.362 0.320 0.341 0.258

25 25 25 25 25

1 1

6356.55 6357.57 6482.07 6504.61 6532.55

46 46 8 45 45

5 3 3 7 5

3 1 3 7 5

0.229 0.304 0.365 0.052 0.0404

25 25 25 25 25

6610.58 6629.80 6809.99 6834.09 6941.75

31 41 54 54 53

5 5 5 3 5

7 3 3 3 5

N III: 685.513 685.816 t990.98 1804.3 1805.5

3 uv 3 uv 1 uv 22 uv 22 uv

2

4 6 2 4

2 4 10 2 2

0.59 0.283 0.199 0.118 0.065 39.0 48.8 4.20 2.26 4.51

1 1

1

;...j

o

>

Z

t::::l

~

o

t" tr.l

o

1

d

1

>

1 1 1

25 25 25 25 25

1 1 1 1 1

25 25 25 25 25

18 18 18 1 1

t"

~

""d

~.

~ U1 ;...j

o

U1

t4239.4 4447.03 4530.40

48 15 59

15 3 7

21 3 9

2.14 1.30 1. 69

25 25 25

1 1 1

4552.54 4601.48 4607.16 4613.87 4621.39

58 5 5 5 5

7 3 1 3 3

9 5 3 3 1

0.76 0.270 0.340 0.196 0.90

25 25 25 25 25

1 1 1 1 1

4630.54 4643.09 4677.93 4779.71 4788.13

5 5 62 20 20

5

5 3 3 5

5 3 5 3 5

0.84 0.466 1.65 0.269 0.248

25 25 25 25 25

1 1 1

4803.27 5104.45 5338.66 5340.20 5351.21

20 34 69 69 69

7 1 5 7 7

7 3 7 5 7

0.313 0.189 0.139 0.194 0.275

25 25 25 25 25

1 1 1 1 1

5478.13 5480.10 5495.70 5526.26 5530.27

29 29 29 63 63

3 5 5 3 5

5 3 5 5 7

0.100 0.167 0.298 0.198 0.377

25 25 25 25 25

1 1 1 1 1

5543.49 5666.64 5676.02 5679.56 5686.21

63 3 3 3 3

5 3 1 5 3

5 5 3 7 3

0.327 0.423 0.310 0.56 0.231

25 25 25 25 25

1 1 1 1 1

5710.76 5927.82 5931.79

3 28 28

5 1 3

5 3 5

0.137 0.315 0.425

25 25 25

1 1 1

• For-reterences see PI>. 7·208 and 7·209.

1

1

t1885.25 tI908.11 2063.50 2063.99 2972.60

24 27 30 30 25

uv uv uv uv uv

10 10 6 8 2

14 14

[2977.3] [2978.8] 2983.58 3365.79 3367.36

25 uv 25 uv 25 uv 5 5

4 2 4 4 6

2 4 4 2 6

S

10 2

11.9 11.0 10.9 11.3 0.93

25 25 25 25 25

1 1

0.461 0.230 1.14 1.45 1.22

25 25 25 25 25

1 1 1 1 1

1 1 1

3374.06 3745.83 3754.62 3771.08 3934;41

5 4 4 4 8

6 2 4 6 2

4 4 4 4 4

0.78 0.209 0.416 0.61 0.80

25 25 25 25 25

1 1 1 1 1

3938.52 3942.78 4097.31 4103.37 4195.70

8 8 1 1 6

4 4 2 2 2

6 4 4 2 4

0.96 0.160 0.96 0.97 0.84

25 25 25 25 25

1 1 1 1 1

4200.62 4215.69 4348.36 4514.89 4518.18

6 6 10 3 3

4 4 8 6 2

6 4 8 8 2

1.00 0.165 0.198 0.70 0.58

25 25 25 25 25

1 1 1 1 1

4523.60 4861.33 4873.58 4884.14 6445.05

3 9 9 9 14

4 6 6 8 2

4 8 6 8 4

0.372 9.54 0.152 0.089 0.181

25 25 25 25 25

1 1 1 1 1

6450.78 6453.95

14 14

2

4

2 6

0.362 0.304

25 25

1 1

> o

1-3

a::....

Q

1-3

l;l:l

> Z

....

Ul

1-3 .... o

Z

'"d

l;l:l

o

t:z:l

....~ ....t'"

1-3 .... ~

Ul

~

I:'>:l

.....

TABLE

7i-4.

TRANSITION PROBABILITIES FOR ALLOWED LINES

1

(Continued)

l\:) l\:)

Wavelen~th,

A

Multiplet no.

Statistical weights

Transition probability Aki

a:

I

10 8,

S-l

Accuracy, %

Source*

Wavelength,

A

Multiplet no.

N IV: t225.17 247.05 t283.53 335.050 765.140

921. 982 922.507 923.045 923.211 923.669 924.274 1718.52 3463.36 3478.69 3482.98 3484.90 3747.66 4495 4528 [4685.4]

4 6 6

14 14 14 6 uv 2 uv 5 uv 10 uv 1 uv 3 3 3 3 3

uv uv uv uv uv

3 uv 7 uv 7 1 1 1 8 6 6 11

4 8 6

9 1 9 3 1

15 3 15 5 3

3 1 3 5 3

5 3 3 5 1

0.232 0.432 0.129 92 110 264 200 20.5 3.57 4.82 3.58 10.7 14.4

tv

Transition probability Aki

a.

(Jk

Nitrogen (Continued)

6463.03 6466.86 6478.69

Statistical weights

I

108.

8- 1

Accuracy, %

Source*

(]k

Nitrogen (Continued)

25 25 25

1 1 1

25 50 25 25 25

1 9 9 18 15

25 25 25 25 25

18 18 18 18 18

5 3 5 3 3

3 5 5 5 3

5.9 3.23 0.94 1.09 1.09

25 25 25 25 25

18 19 1 9,20 9,20

3 3 3 5 3

1 5 3 3 3

1.07 1.06 0.189 0.305 0.089

25 25 25 25 25

9,20 1 1 1 1

[185.09] 1896.82 1907.34 1907.87 [2914.6]

-

3 3 3 3 1

-

5 5 3 1 3

825 0.683 0.672 0.671 0.206

3 3 3 3 3

1 1 1 1 1

t4368.30 t5330.0 5435.16 5435.76 5436.83

5 12 11

5 5 3 1 5

5 3 3 3 15

5.3 3.14 1. 94 0.61 0.00326

25 25 25 25 25

11

3 15 3 5 7

9 25 5 5 5

0.0066 0.0197 0.0061 0.0102 0.0142

25 25 25 25 25

1 1 1 1 1

t6046.4 t6157.3 t6259.6 6453.64 6454.48

22 10 50 9 9

9 15 21 3 5

3 25 27 5 5

0.0234 0.0701 0.063 0.0142 0.0237

25 10 25 10 10

1 1 1 1 1

6456.01 6653.78

9 65

7

5 1

0.0331 0.600

10

1

3

10

1

11

uv uv uv uv

>-

Z

t1

o

01:

6 2 2 2 3

~

H

()

~

Oxygen

11.52.16 1302.17 1304.87 1306.04 t3947.29

>8 o

21 21,22 21,22 21,22 1

t'" trl

o d

t'"

>-

~

""d ~ ~

00 H

o

00

4733 4752 5236 5245 5734 6383 7109.48 7123.10 NV: t162.562 t186.13 t209.28 247.563 266.192

266.375 1238.81 1242.80 t3161 t4335 4603.83 4619.9 t4751 t4933 t5273 N VI: 24.898 28.787 t161.22 [173.34] t173.92

11 11 5 5 9

5 7 3 5 3

2 4 4 3 6 2 5 4

1 3 5 uv uv uv uv uv

4 uv 1 uv 1 uv 2 3 1 1 5 7 4

-

-

* For references see

2 6 2 2 2 4 2 2 6 2 2 2 6 10 6 1 1 3 1 9

5 7 5 7 5 3 5 7 6 10

6 4 2 2 4 2 2 6 4 2 10

14 2 3 3 9 3 15

pp. 7 ·208 and 7-209.

0.081 0.102 0.261 0.345 0.178 0.193 0.107 0.142 57.2 142 120 357 30.2 60.6 3.38 3.36 3.06 0.368 0.415 0.411 0.958 1. 62 1.40 5160 18100 285 269 876

25 25 25 25 25 25 25 25 10 10 10 10 10 10

3 3 10 10 10

10 10 10 10

3 3 3 3 3

1 1 1 1 1 1 9 9 17 17 1 1 1 1 1 1 17 17 1 1 17 1 17 1 1 1 1 1

t7002.1 7156.80 t7254.4

21 38 20

9 5 9

15 5 3

0.0325 0.473 0.062

25 10 25

1 1 1

7471.36 7473.23 7476.45 7477.21 7479.06

55 55 55 55 55

5 5 5 3 3

3 5 7 3 5

0.0114 0.102 0.408 0.170 0.306

10

1 1 1 1 1

7480.66 7771. 96 7774.18 7775.40 7886.31

55 1 1 1 64

1 5 5 5 3

3 7 5 3 5

0.226 0.340 0.340 0.340 0.370

10 10

~939.49

7.943.15 7950.83 7952.18 7995.12

35 35 35 35 19

7 7 5 5

5 7 7 5 7

8227.64 8232.99 8235.31 t8446.5 8508.63

34 34 34 4 -

5 3 3 3 3

8820.45 t9263.9 tI 1287 11295.0 11297.5

37 8

11302.2 t13164

7

10 10 10

10

>

8

o

10

1 1 1 1 1

0.00165 0.0417 0.331 0.313 0.29

25 25 25 25 50

1 1 1 1 1

Z

3 3 5 9 3

0.0834 0.261 0.0432 0.280 0.289

10 10 10

10 25

1 1 1 1 1

5 15 9 3 5

7 25 15 5 5

0.261 0.419 0.235 0.054 0.091

25 25 25 25 25

1 1 1 1 1

7 9

5 3

0.127 0.188

25 25

1 1

3

10 10

~ H

o 8

~

>

U2 H

8

H

o

Z "'0

-

7 7

-

~

o

b:1

> b:1

H

t" H 8 H

trj

W.

~

~ ~

TABLE

Wavelength,

A

Multiplet no.

Statistical weights g.

I

7i-4.

TRANSITION PROBABILITIES FOR ALLOWED LINES

Transition probability A". 10 8, S-1

Accuracy,

Source·

%

Wavelength,

A

Multiplet no.

Statistical weights g.

gk

~ t--:l

(Continued)

I

lot:o-

Transition probability Ak. 10\ S-1

Accuracy,

Source*

%

g"

>1-3 o

Oxygen (Continued) Oxygen (Continued)

011:

2733.34 2747.46 3122.62 3129 44 3134.32

20 uv 20 uv 14 14 14

2 2 6 4 2

4 2 6 4 2

0.37 0.36 0.278 0.493 0.77

50 50 25 25 25

1 1 1 1 1

3134.82 3138.44 3139.77 3277.69 3287.59

14 14 14 23 23

8 6 4 4 6

6 4 2 6 6

1.23 0.96 0.76 0.259 0.60

25 25 25 25 25

1 1 1 1 1

3290.13 3305.15 3306.60 3377.20 3390.25

23 23 23 9 9

2 6 4 2 2

4 4 2 2 4

0.356 0.379 0.70 1.88 1.86

25 25 25 25 25

1 1 1 1 1

3470.42 3470.81 3712.75 3727.33 3739.92

27 27 3 3 31

4 6 2 4 4

2 4 4 4 6

1.24 1.12 0.280 0.59 0.267

25 25 25 25 25

1 1

3749.49 3762.63 3777.60

3 31 31

6 4 4

4 4 2

0.90 0.269 0.252

25 25 25

1 1 1

1 1

1

a:: ~

4650.84 4661.64 4676.23 4861.03 4871.58

1 1 1 57 57

2 4 6 2 4

2 4 6 4 6

0.82 0.52 0.257 0.366 0.435

25 25 25 25 25

1 1 1 1 1

[4872.2] 4890.93 4906.88 4924.60 4941.12

57 28 28 28 33

4 4 4 4 2

4 2 4 6 4

0.073 0.68 0.68 0.67 0.83

25 25 25 25 25

1 1 1 1 1

4943.06 4955.78 5160.02 5176.00 5190.56

33 33 32 32 32

4 4 2 4 2

6 4 2 2 4

1.06 0.256 0.350 0.171 0.137

25 25 25 25 25

1 1 1 1 1

5206.73 6640.90 6721. 35 6895,29 6906.54

32 4 4 45 45

4 2 4 10 8

4 2 2 8 6

0.391 0.098 0.189 0.298 0.272

25 25 25 25 25

1 1 1 1

6908.11 6910.75

4.5 45

4 6

2 4

0.332 0.267

25 25

1 1

1

o

>-Z

t:::1

a::

o e-

t"'1

o

d

e-

>-

~

'"d

tIl ~

iJ).

~

C':l

ti:

~8O::L 14 3919.29

34 17

4 4

4 2

0.55 1.40

25 25

1 1

3945.05 3954.37 3973.26 3982.72 t4060.8

6 6 6 6 97

2 2 4 4 14

4 2 4 2 18

0.217 0.95 1. 27 0.447 2.20

25 25 25 25 25

1 1 1 1 1

4072.16 4075.87 4078.86 4153.86 4169.54

10

6 8 4 4 6

8 10 4 6 4

1. 70 1.98 0.55 0.77 0.157

25 25 25 25 25

1 1 1 1 1

6 8 22 6 6

0.220 2.43 2.63 1.08 0.398

25 25 25 25 25

1 1 1 1 1

10

10 19 19

o III: 2454.99 2558.06 2597.69 2605.41 2695.49

19 21 20 20 23

2983.78 2996.51 3004.35 3017.63 3035.43

3 7 5 3 3

1 5 3 3 5

4.00 1.16 0.97 0.58 2.09

25 25 25 2.5 25

1 1 1 1 1

6 10 10 10 4

3 3 5 7 3

5 3 5 7 3

2.24 0.51 0.472 0.59 0.51

25 25 25 25 25

1 1 1 1 1

3043.02 3047.13 3059.30 3083.65 3084.63

4 4 4 26 26

3 5 5 7 7

1 5 3 7 5

2.03 1. 52 0.84 0.311 0.248

25 25 25 25 25

1 1 1 1 1

3088.04 3115.73 3121.71 3132.86 3200.95

26 12 12 12 31

9 3 3 3 3

9 1 3 5 3

0.52 1.39 1.38 1.36 0.499

25 25 25 25 25

1 1 1 1 1

5

25 25 25 25 25

1 1 1 1 1

25 25 25 25 25

1 1 1 1 1

uv uv uv uv uv

4169.28 4185.46 t4253.9 t[4272.3] 4395.95

19 36 101 26

6 6 18 2 6

4414.91 4416.98 4443.05 [4443.7] [4447.7]

5 5 35 35 35

4 2 6 6 8

6 4 6 8 6

1.15 0.95 0.57 0.0212 0.0282

25 25 25 25 25

1 1 1 1 1

4448.21 4452.38 4489.48 4491. 25 4590.97

35 5 86 86 15

8 4 2 4 6

8 4 4 6 8

0.57 0.154 1. 51 1. 81 1.11

25 25 25 25 25

1 1 1 1 1

3207.12 3215.97 3260.98 3265.46 3267.31

31 31 8 8 8

5 7 5 7 3

7 9 5

0.460 0.58 1.84 2.07 1. 73

4602.11 4609.42 4638.85 4641.81 4649.14

93 93 1 1 1

4 6 2 4 6

6 8 4 6 8

1. 70 1.82 0.422 0.79 1.04

25 25 25 25 25

1 1 1 1 1

3382'.69 [3383.5] 3383.85 3384.95 3394.26

27 27 27 27 27

5 5 5 7 7

7 3 5 9 7

0.97 0.363 0.85 1.45 0.480

-

~ ..... o

1-3

;:0

>

Z

ro ~

1-3 ~

I

• For references see pp. 7-208 and 7-209.

> t-3

o

7

o

Z "'d

~

o

l:l:1

~ ~

~ ~

t-3 ~

t"J

ro

~ tv

C)l

TABLE

Wavelength,

A

Statistical weights

Multiplet no.

o,

I

7i-4.

TRANSITION PROBABILITIES FOR ALLOWED LINES

Transition probability Aki, 10 8 s-1

Accuracy,

Source*

Wavelength,

A

%

Multiplet no.

27 24 24 24 24

[3555.3] 3556.92 3638.70 3645.20 3646.84

24 24 35 35 35

I

I

~

l:-..J ~

Transition probability Aki, 108 S-1

Accuracy,

Source*

%

Ok

Oxygen (Continued)

7 1 3 3 3

5 3 1 3 5

0.096 0.493 1. 47 0.367 0.366

25 25 25 25 25

1 1 1 1 1

5 5 5 5 3

3 5 7 5 5

0.60 1.08 1.40 0.347 1.04

25 25 25 25 25

1 1 1 1 1

3650.70 3653.00 3961.59 [4072.3] 4073.90

35 35 17 23 23

3 1 5 1 3

3 3 7 3 5

0.58 0.77 1. 28 0.52 0.71

25 25 25 25 25

1 1 1

4081. 10 4440.1 4447.82 4461.56 5268.06

23 33 33 33 19

5 5 5 5 1

7 5 7 3

0.94 0.495 0.492 0.486 0.311

25 25 25 25 25

1 1 1 1 1

5500.11 5592.37

16 5

5 3

5 3

0 . .112 0.328

25 25

1 1

3

Statistical weights

Oi

Ok

Oxygen (Continued)

[3395.5] [3520.7] [3530.7] [3532.8] [3534.3]

(Continued)

1

1

4783.43 4794.22 4798.25 4813.07 5305.3

9 9 9 9 11

4 4 6 6 4

6 4 8 6 4

0.213 0.161 0.303 0.090 0.069

25 25 25 25 25

1 1 1 1 1

5362.4

11

6

6

0.069

25

1

o

> o

1-3

a:: J-4

Q

>

Z

t:;

a::

o

V:

~

9 3 1 5 3

15 5 3 5 5

6 5 5 8 8

3 3 5 5 7

5 3 3 5 7

4135.9 4158.76 4554.28 5114 5343

11 11 7 1 13

3 3 3 1 1

3

5352 5376

13 13

3 3

t192.85 220.352 629.732 760.445 1371. 29

5 10 1 3 7

3058.68 3239 3275.67 3717 3747

uv uv uv uv uv

600 450 25.2 16 7.4

25 25 25 50 25

9 9 15 1 24

1.30 0.342 0.55 0.109 0.136

25 25 25 25 25

1 1 1 1

0.261 0.257 0.233 0.273 0.304

25 25 25 25 25

1

5 5 3 3

1 8 1

1 3

0.91 0.223

25 25

1 1

tEl

Q

d

~

>

~

'"d

1

1

~ ~

rf). J-4

Q

tn

o IV:

25

2 2

4.87 0.97 5.8 1.02 2.01

2l)

23 23 23 1 1

4 2 6 8 4

1 1-3 o

a::

>-4

o VI:

o

3349.11 3354.31 3362.63 3375.50 3385.55

4 8 8 8 3

4 4 4 4 6

6 2 4 6 8

1.23 0.69 0.69 0.68 1.06

25 25 25 25 25

1 1 1 1 1

3390.37 3396.83 3411. 76 3489.84 3560.42

3 3 2 14 12

2 4 4 4 4

2 4 6 6 6

0.88 0.56 1.15 0.99 1.08

25 25 25 25 25

1 1 1 1 1

1031.95 1037.63 t3068 t3314 t3426

1 uv 1 uv 2 4 6

2 2 2 6 10

4 2 6 10 14

4.09 4.02 0.865 2.01 3.34

3 3 10 10 10

1 1 17 17 1

::tI

3563.36 3729.03 3744.73 3758.45 3995.17

12 6 6 6 10

6 6 6 8 6

8 8 6 8 6

1.15 0.69 0.194 0.112 0.215

25 25 25 25 25

1 1 1 1 1

t3509 t3622 3811.35 3834.24

5 3 1 1

10 6 2 2

6 2 4 2

0.868 2.70 0.513 0.503

10 10 10 10

17 17 1 1

....b:1t" ....8t:ri

t4568 [4652.5] [4685.4] 4772.57 4779.09

15 13 13 9 9

14 2 2 2 2

10 2 4 4 2

0.124 0.301 0.295 0.128 0.254

25 25 25 25 25

1 1 1 1 1

-

1 1 3 1 9

3 3 9 3 15

3 3 3 3 3

1 1 1 1 1

• For references see pp. 7-208 and 7-209.

t129.84 t150.10 172.935 183.937 184.117

o VII:

I

18.627 21. 602 t120.331 [128.25J t128.46

5 2 4 3 3

-

uv uv uv uv uv

6 2 2 2 4

10 6 4 2 2

292 259 737 56.7 113

9370 33000 533 504 1620

10 10 10 10 10

17 1 1 1 1

1-3

~

>

Z

UJ >-4

'"3

>-4

o Z

"'d

o

b:1

>

t--f

U1

~

tV tV 'l

TABLE

Wavelength,

A-

Multiplet no.

Statistical weights

O.

I

7i-4.

TRANSITION PROBABILITIES FOR ALLOWED LINES

Transition probability Aki, 10 8 S-1

Accuracy, %

Source'"

Wavelength,

A-

Multiplet no.

-

3 3 3 3 1

-

5 5 3 1 3

1530 0.805 0.784 0.781 0.246

I

tv 00

Transition probability AM, 10 8 S-1

Accuracy, %

Source·

Ok

:>

Fluorine (Continued)

OxYoen (Continued) (135.77] 1623.29 1637.96 1639.58 [2475.4]

Statistical weights

O.

Uk

~

(Continued)

3 3 3 3 3

1 1 1 1 1

Fluorine

F I: 6239.64 6348.50 6413.66 6773.97 6834.26

3 3 3 2 2

6 4 2 6 4

4 4 4 6 4

0.29 0.18 0.090 0.14 0.24

50 50 50 50 50

1 1 1 1 1

6856.02 6870.22 6902.46 6909.82 6966.35

2 2 2 2 6

6 2 4 2 4

8 2 6 4 2

0.45 0.38 0.31 0.18 0.16

50 50 50 50 50

1 1 1 1 1

~

3039.75 3113.58 3115.67

3 1 1

4 2 4

6 4 6

2.56 0.67 1.1

25 50 50

1 1 1

3121.52 3124.76 3134.21 3142.78 3145.54

1 1 1 4 1

6 2 4 2 4

8 2 4 4 2

1.6 1.3 0.84 1.16 0.26

50 50 50 25 50

1 1 1 1 1

3146.96 3154.39 3156.11 3174.13 3174.73

1 4 4 2 2

6 4 4 4 2

6 6 4 6 4

0.47 1.38 0.230 1.7 1.4

50 25 25 50 50

1 1 1 1 1

3213.97

2

4

4

0.27

50

1

o

~

~

o :> Z t:'

~

o ~ o d

~ ~

~

~ r:fJ 1-4

o

Neon

7037.45 7127.88 7202.37 7311.02 7331. 95

6 6 6 5 1

4 2 2 4 6

4 2 4 2 4

0.38 0.30 0.072 0.27 0.17

50 50 50 50 50

1 1 1 1 1

Ne I: 735.89 743.70 3454.19 3472.57 3520.47

7398.68 7425.64 7489.14

1 1 5

6 4 2

6 2 2

0.25 0.30 0.13

50 50 50

1 1 1

5433.65 5852.49 5881.90

r:fJ

2 uv 1 uv 2 2 7

1 1 3 5 3

3 3 1 7 1

6.6 0.476 0.085 0.099 0.073

25 25 25 25 25

1 1 1 1 1

6 1

-

3 3 5

3 1 3

0.0029 0.706 0.102

50 10 10

26n 25 25

-

5 5

3 5

5975.53 6030.00 6046.13 6064.54 6074.34

1 3 3

5 3 3 3 3

6096.16 6118.03 6128.45 6143.06 6163.59

3 3 1 5

6217.28 6266.50 6293.74 6304.79 6313.69

1 5

7552.24 7573.41

1 1

4 2

6 4

0.10 0.14

50 50

1 1

5939.32 5944.83

7754.70 7800.22

4 4

4 2

6 4

0.35 0.29

50

50

1 1

F II: 3202.74 t3504.0 [3535,2] 3536.84 [3538.6]

8 3 6 6 6

5 15 3 5 3

·5 25 1 3 3

1.4 2.86 2.1 1.5 0.51

50 25 50 50 50

1 1 1 1 1

3541.77 [3544.5] t3641. 7 3847.09 3849.99

6 6 11 1 1

7 5 21 5 5

5 5 21 7 5

1.7 0.31 0.147 1.3 1.3

50 50 25 50 50

1 1 1 1 1

3851.67 4024.73 4025.01 4025.50 t4103.4

1 2 2 2 4

5 3 3 3 9

3 5 1 3 15

1.3 1.2 1.2 1.2 2.05

50 50 50 50 25

1 1 1 1 1

4109.17 4116.55 [4117.1J [4118.8] 4119.22

5 5 5 5 5

7 5 5 3 3

7 5 3 5 3

1.6 1.2 0.45 0.27 1.3

50 50 50 50 50

1 1 1 1 1

t4246.16 4299.18 t4446.9

9 7 10

25 5 15

35 7 21

2.47 1.7 2.35

25 50 25

1 1 1

FIll: 3034.54 3039.25

3 3

6 6

6 8

0.184 2.75

25 25

1 1

• For references see pp. 7.208 and 7.209.

1

~-

-

3

-

I

0.0021 0.112

50 10

26n 25

3 3 3 1 1

0.0349 0.0512 0.0024 0.0026 0.583

10 10 50 5€ 10

26n 26n 25

3 5 3 5 1

5 3 3 5 3

0.179 0.0065 0.0070 0.285 0.141

10 50 25 10 10

25 26n 25 25 25

5 1 3 3 3

3 3 3 5 1

0.0601 0.254 0.0069 0.0424 0.0053

10 10 50 10 50

25 25 26n 25 26n

5 5 1 3 5

3 5 3 3 7

0.037 0.180 0.0037 0.316 0.506

50 10 50 10 10

26n 25 26n 25 25

25 25

6328.'16 6334.43 6351.86 6382.99 6402.25

3 1

6421.71 6506.53 6532.88 6598.95 6678.28

3 5 6 6

3 3 1 3 3

1 5 3 3 5

0.0033 0.298 0.106 0.225 0.231

50 10 10 10 10

26n 25 25 25 25

6717.04 6929.47 7032.41 7173.94 7245.17

6 6 1 6 3

3 3 5 3 3

3 5 3 5 3

0.217 0.174 0.253 0.0321 0.100

10 10 10 10 10

25 25 25 25 25

1

-

>

1-3

o

a=....

o

1-3 ~

> Z

.... 1-3 .... o rfJ

Z

"'d

~

o

b:I

> b:I e....

....tr11-3

rfJ

I' tv tv

~

TABLE

7i-4.

TRANSITION PROBABILITIES FOR ALLOWED LINES

(Continued)

j1 tv

Wavelength,

A

Multiplet no.

Statistical weights

Transition probability Aki.

a.

I

10 8

S-l

Aecuracy, %

Source*

Waveloep.gth, Multiplet no. A

(Jk

5 12 18

1 1 3 7 5

3 3 5 9 7

0.0030 0.0242 0.349 0.51 0.357

50 10 25 25 25

25 1 1 1

8654.38

33

5

7

0.445

25

1

-

6 6 6 2 2

6 6 4 4 2

0.91 0.11 0.46 0.43 0.52

50 50 50 50 50

1 1 1 1 1

[2955.7] 3001. 65 3034.48 3037.73 3045.58

4 4 8 8 8

6 4 6 4 2

4 4 8 4 2

1.2 0.78 3.1 2.0 2.5

50 50 50 50 50

1 1 1 1 1

3047.57 3054.69 3118.02 3169.30 3248.15

8

6 4 6 4 4

1.8 0.93 0.11 0.17 0.14

50 50 50 50 50

1

16 16 15

4 2 8 6 4

3255.39 3263.43

23 15

6 2

4 4

0.12 0.36

50 50

26n

Ne II:

8

I

10 8

S-l

Aceuracy, %

Source*

o»

> ~

Neon (Continued)

7304.82 7438.90 7488.87 8377.61 8495.36

-

o Transition probability Ah.

(Ji

Neon (Continued)

[2858.0] [2870.0] [2873.0] [2910.4] [2925.7]

Statistical weights

C;.j

1 1

1 1 1 1

o [4292.4] [4346.9]

57 57

10 8

10 8

0.20 0.33

50 50

1 1

4379.50 4385.00 4391. 94 4397.94 4409.30

56 56 57 56 57

8 6 8 10 6

8 6 10 10 8

0.20 0.18 2.2 0.24 2.0

50 50 50 50 50

1 1 1 1 1

4413.20

57

4

6

2.0

50

1

-

>

Z

tj

~

o

~

~

o

~ ~

>~

Ne III:

2086.96 2087.44 2088.92 2089.43 2095.54

~

o""'"

3 5 3 5 7

3 3 5 5 7

2.96 0.99 0.59 2.73 3.47

25 25 25 25 25

1 1 1 1

t2413.0 2590.04 2593.60 2595.68 2610.03

11 uv 11 uv 11 uv -

9 5 5 5 7

15 7 5 3 9

4.87 1. 69 1. 69 1. 69 2.01

25 25 25 25 25

1 27 27 27 27

2613.41 2615.87 t2678.2

12 uv

5 3 3

7 5 9

1. 78 1. 68 2.70

25 25 25

27 27 27

~

~ ~

tn

o""'" m

3297.74 3323.75 3453.10

2 7 21

6 4 4

6 4 4

0.53 1.56 0.59

50 25 50

3456.68 3503.61 3551.52 3557.84 3561.23

28 28 24 6 31

2 2 2 2 4

4 2 4 2 6

1.0 1.9 0.055 0.51 0.11

50 50 50 25 50

3565.84 3568.53 3571. 26 3590.47 3594.18

34 9 31 32 34

4 6 4 4 4

4 8 4 6 2

0.82 1.14 0.43 0.087 1.3

50 25 50 50 50

3612.35 3628.06 3632.75 3659.93 3664.09

26 41 33 33 1

2 4 4 4 6

4 4 4 6 4

0.22 0.57 0.090 0.11 0.51

50 50 50 50 25

3679.80 3694.22 3697.09 3701.81 3709.64

41 1 41 40 1

4 6 2 4 4

2 6 2 6 2

0.36 0.73 0.34 0.25 0.84

50 25 50 50 25

3713.09 3766.29 3800.02 3818.44 3829.77

5 1 39 39 39

4 4 4

6 6 4 4 6

1.19 0.245 0.35 0.69 0.88

25 25 50 50 50

4219.76 4231. 60 4290.40

52 52 57

* For references see

2

4 8

6 10

8 6 12

pp. 7-208 and 7-209.

0.33 0.22 2.5

50 50 50

1 In, 27

1 1 1 1 In, 27

1 1 In, 27 1 1 1 1 1 1 1 In, 27

1 In, 27

1 1 In, 27 In, 27 In, 27

1 1 1 1

1 1

Ne IV:

541.124 542.076 543.884 2018.44 2022.19

1 uv 1 uv 1 uv -

4 4 4 4 6

2 4 6 4 6

[2174.4] [2176.1] 2203.88 [2206.4] 2220.81

-

2 4 6 4 6

4 6 6 2 4

-

2258.02 2262.08 2264.54 2285.79 2293.49

-

2350.84 2352.52 2357.96 2372.16 2384.95

15.2 15.2 15.2 3.7 3.8 1.3 0.96 2.2 2.5 1.4

25 25 25 50 50

23 23 23 1 1

50 50 50 50 50

1 1 1 1 1

8 6 4 8 6

2.7 2.7 2.7 2.8 2.6

50 50 50 50 50

1 1 1 1 1

-

2 4 6 4 6

4 6 8 4 6

1.0 1.7 2.5 1.3 0.72

50 50 50 50 50

1 1 1 1 1

1 uv 1 uv 1 uv 1 uv 1 uv

1 3 3 5 5

3 3 5 5 7

6.7 4.97 8.9 2.94 11. 7

25 25 25 25 25

23 23 23 23 23

-

5 7 3 1 5

7 9 5 3 7

0.13 0.20 1.7 1.2 2.2

50 50 50 50 50

1 1

-

Ne V:

568.418 569.759 569.830 572.106 572.336 2227.42 2232.41 2259.57 2263.39 2265.71

-

-

~ ~

6 6 6 6 4

-

> l-3 o o

l-3

~

>

Z

tn ~ l-3

~

o Z

"'d

~

o

b:l

~ ~

~ ~

l-3 ~

t'=j

rn

1

1 1

~

c,..., ~

-3 TABLE

7i-4.

TRANSITION PROBABILITIES FOR ALLOWED LYNES

I

(Cont£nued)

~

e,.." ~

Wavelength,

A

Multiplet no.

Statistical weights

OJ,

I

Transition probability Aki. 10 8 8- 1

Accuracy,

Source*

%

Wave!ength, A

Multiplet no.

o»

OJ,

-

3 5

Ne VI: t122.62 2042.38 2055.93 {2213.1]

-

6 2 2 2

Ne VIII: t88.1l t98.20 tI03.00 770.409 780.324

-

2 6 6 2 2

3 5 10

4 2 4 6 10

2 4 2

t[2860.1] t{8454.3]

-

2 6

10

Ne IX: [11. 558] 13.44 t74.4 [82.010] t[1297.5] {190!. 5]

-

1 1 3 3 3 1

3 3 9 5 9 3

6

I

Transition probability Aki. 10 8 S-l

Accuracy,

Source*

%

Ok

:> t-3

Sodium (continued)

Neon (Continued)

2282.61 2306.31

Statistical weights

0.89 0.52 1400 2.73 2.68 1.54 853 2760 462 5.72 5.50 0.696 0.0214 24800 88700 1460 4180 0.980 0.329

50 50 50 25 25 25 10 10 10 10

10 10 10

3 3 10

3 3 3

1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1

22083.7 23348.4 [91380] Na II: 300.151 301.432 372.069 NaIll: 1752.65 1849.58 1856.73 1935.54 1939.32

1951.21 1965.04 [1976.4] 1985.58 1995.62 [2004.8] [2011. 9] [2028.6] [2036.9] [2045.5]

-

2 2 4

2 4 2

4 uv 3 uv 2 uv

1 1 1

3 3 3

0.062 0.056 0.00156

o 25 25 25

2 2 2

50 50 50

2 2 2

....a::

(")

:>

z

t:t

30 9.5 3.1

t:::

o

t"

t::1

o

-

6 6 4 4 6

6 8 6 6 8

3.3 7.2 5.1 7.0 7.6

50 50 50 50 50

2 2 2 2 2

6 8 4 4 6

4

50 50 50 50 50

2

6 4 6

2.7 8.8 8.3 1.7 2.0

2 2 2 2

4 8 8 2 6

4.6 8.4 1.7 4.4 1.1

50 50 50 50 50

2 2 2 2 2

2 6 8 2 6

10

d

t"

:>

::c

Iod

tI:

-
8

o

~ ~

o 8

~

;>

Z

r:n I-! 8

H

o

Z

-

170 23 76

""d

~

o

to'

~

I-!

-

4 2 4 4 6

2 2 2 2 10

270 52 100 120 11

50 50 50 50 50

2 2 2 2 2

-

4 4 4 4

2 4 6 4

31 31 31 68

50 50 50 50

2 2 2 2

-

tot H 8

H

t"j

r:n

j:I tv W W

TABLE

7i-4.

TRANSITION PROBABILITIES FOR ALLOWF;D LINES

~

(Continued)

~

Wavelength,

A

Multiplet no.

Statistical weights

Transition probability Aki,

a,

I

108

S-1

Accuracy,

Source·

%

Wavelength,

A

Multiplet no.

(Jk

Statistical weights

Aki.

0.

Mtumeeium.

~

Transition probability

I

108

S-1

Accuracy,

Source*

%

(Jk

> 1-3 o

Ma(Jnesium (Continued)

MgJ;

Mg III:

2025.82 2736.54 2776.69 2778.27 2781. 42

2 9 6 6 6

uv uv uv uv uv

1 5 3 1 3

3 7 5 3 1

1.2 0.207 1. 31 1. 76 5.3

50 25 25 25 25

2 2 2 2 2

2782.97 2846.72 2938.47 2942.00 3091.07

6 5 3 3 5

uv uv

5 1 3 5 1

3 3 3

2.16 0.15 0.052 0.086 0.313

25 50 50 50 25

2 2 2 2 2

uv uv

3

3

186.510 187.194 231. 730

1459.52 1490.41 [1525.2] [1548.1] 1658.92

4 4 4 3 14

1 3 5 1 3

3 3 3 3 5

0.034 0.10 0.17 0.940 0.21

50 50 50 10 50

2 2 2 2 2

4702.99 5167.32 5172.68 5183.60 5528.40

H

5

2 2 2 9

3 1 3 5 3

3 3 5

0.16 0.116 0.346 0.575 0.14

50 10 10 10 50

2 2 2 2

1680.02 1698.83 [1703.4] 1874.59 1893.87

t7657.8 8806.76 8923.57

22 7 25

3 3 1

9 5 3

0.0148 0.14 0.011

25 50 50

2 2 2

1906.71 1946.20 1956.58

2

1 1 1

3 3 3

170 100 87

50 50 50

2 2 2

a::

~

o

>

Z

~

Mg IV:

[1230.3] [1245.2] [1246.6] [1253.7] [1375.4]

3329.92 3332.15 3336.67 3829.35 4351. 91

3

4 uv 3 uv 2 uv -

-

-

-

-

-

-

-

-

6 6 2 4 4

4 6 4 6 4

4.1 5.9 3.4 2.6 4.5

6 4 4 4 6

4 4 4 6 6

4.6 2.8 6.7 6.4 1.8

4 4 2 6 6

4 6 4 4 6

4 4 2

2 6 4

a::

2 2 2 2 2

o

50 50 50 50 50

2 2 2 2 2

~

3.1 3.9 2.4 1.8 2.8

50 50 50 50 50

2 2 2 2 2

3.2 1.1 1.5

50 50 50

2 2 2

50 50 50 50 50

~

t:".l

o

c:; ~

>

'"t1

::t:

~

r.tl ~

o

r.tl

9255.78 9414.96

27 38

5 15

7 21

0.089 0.022

25 25

2 2

t10811.1 10953.3 11828.2 12083.7 t14817.6

37 35 6 26 -

15 1 3 5 15

21 3 1 7 21

0.0452 0.025 0.26 0.170 0.105

25 50 50 25

2 2 2 2

25

2

tl5031 17108.7

-

3 1

9 3

0.139 0.094

25 25

2 2

Mg V: 276.581 312.311 351.089 352.202 3~3.094

353.300 354.223 355.326

-

-

-

5 1 5 3 5

3 3 3 1 5

200 27 50 120 88

50 50 50 50 50

2 2 2 2 2

3

3 3 5

29 40 29

50 50 50

2 2 2

1 3

Aluminum

uv uv uv uv uv

10 2 2 2 2

14 4 4 2 2

0.38 3.94 2.68 2.66 1.07

50 10 10 10 25

2 2 2 2 2

2936.51 t3104.8 4384.64 4427.99 4433.99

2 uv 6 10 9 9

4 10 2 2 4

2 14 4 2 2

2.15 0.81 0.14 0.107 0.214

25 25 50 25 25

4481.2 t5264.3 t6346.8 7877.05 8213.99

4 17 16 8 7

]0 10 2 2

14 14 14 4 2

2.25 0.125 0.216 0.66 0.260

8234.64 9218.25 9244.27 9632.2 10951.8

7 1 1 15 3

4 2 2 10 4

2 4 2 14 2

0.52 0.359 0.356 0.413 0.166

2928.63

8

s::: o "'"4

Mg II: t2660.8 2790.77 2795.53 2802.70

:>

o

4 3 1 1 2

* For references see

10

pp. 7.208 and 7-209.

Al I:

2145.56 2168.83 2367.05 2373.12 2373.35

9 uv 4 uv 4 uv

2 2 2 2 2

2567.98 2575.10 2652.48 2660.39 3082.15

10 25 25 25 25

2 2 2 2 2

3944.01 3961. 52 6696.02 6698.67 7835.31

25 25 25 25 25

2 2 2 2 2

8772.87 10873.0 10891. 7 11253.2 13123.4

4 uv

2 2 2 4 4

4 4 4 6 4

2 uv 2 uv 1 uv 1 uv 3

2 4 2 4 2

4 6 2 2

1 1 5 5 10 9 12 12 8 4

-

0.233 0.306 0.71 0.85 0.14

25 25 25 25 50

2 2 2 2 2

4

0.221 0.264 0.133 0.264 0.6-1

25 25 25 25 25

2 2 2 2 2

2 4 2 2 4

2 2 4 2 6

0.493 0.98 0.0169 0.0169 0.057

25 25 25 25 50

2 2 2 2 2

4

6 2 2 6 4

0.098 0.011 0.022 0.166 0.182

50 50 50 25 25

2 2 2 2 2

4

4 4 2

8

~

:>

z

tn "'"4

8

~

o Z

'"d

~

o

b:f

:>

b:f "'"4 t"4 "'"4 8 "'"4

tr.j

W

1 tv

CJ,j

0'

TABLE

Wavelength, A

Multiplet no.

Statistical weights

o:

I

7i-4.

TRANSITION PROBABILITIES FOR ALLOWED LINES

Transition probability A ki • 10 8 8- 1

Accuracy.

Source*

%

Wavelength,

A

2 2 4 4

4

-

-

o»

a.

2 4 6 4

0.181 0.085 0.101 0.017

1761. 98 1765.81 1767.60 1855.95 1858.05 1862.34 t1908.7 1931. 05 t1963.0 1989.85 t2193.8 2816.19 t2996.8 3088.52 t3653.0

-

9 3 1 1 3

15 5

2 2 2 2

uv uv uv uv uv

4 uv -

3 5

1.7 8.8 14.6 6.79 3.30

50 50 10 10 25

2 2 2 2 2

1 3 5 1 3

3 1 3 3 3

4.38 13.1 5.4 0.832 2.48

25 25 25 10 10

2 2 2 2 2

-

5 9 3 9 3

3 9 1 15 5

4.12 8.1 10.8 12 14.7

10 50 25 50 25

2 2 2 2 2

14 20 12

15 3 9 3 9

21 1 15 5 15

3.1 3.83 0.11 0.15 0.27

50 25 50 50 50

2 2 2 2 2

10 uv 2 uv 6 uv 5 uv

5 5 5 4 4

8 uv

3

I

~

CI:) 0)

Transition probability Aki 108 S[-I]

Accuracy,

Source*

%

Ok

>-

Aluminum (Continued)

25 25 25 50

Al II:

t1191.0 1539.74 1670.81 1719.46 1760.10

Statistical weights

Multiplet no.

Aluminum (Continued)

13150.8 16719.0 16750.6 16763.4

(Continued)

8

37]3.10 3980.56

4 12

4 10

2 14

2.27 0.229

25 25

2 2

t4150.1 4357.24 4512.54 4903.71 5696.47

5 9 3 11 2

10

2.19 0.070 2.15 0.351 0.882

25 50 25 25

2

14 4 4 14 4

10

2 2 2 2 2

5722.65

2

2

2

0.870

10

2

-

1 1 1

2 2 10

a::

H

a

>-

Z

t;:;

~

o

t'I

t:r.1

a d

t'I

Al IV:

129.729 [130.37 160.073

o

-

3 3 3

340 630 170

50 50 50

2 2 2

>-

l:!:l "d

::r: 10 ""3

o

~ ~

o

""3

;:0

>

Z

00 ~

""3

~

o Z

'"d ;:0

o

to

~ ~

to' ~

""3 ~

t"j 00

-l

I

l"-'

* For references see pp. '1-208 and '1-209.

C\j

--I

TABLE

Wavelength,

Multiplet

A-

no.

Statistical weights

o.

I

7i-4.

TRANSITION PROBABILITmS FOR ALLOWJ~D LINES

Transition probability A k i , 108 8 - 1

Accuracy,

Source*

%

Wavelength,

A-

Multiplet no.

o»

11 10 10 17 9

5 3 5 3 1

3 1 5 1 3

Statistical weights

a.

Silicon (Continued)

5684.48 5701. 11 5708.40 5772.15 5780.38

(Continued)

0.039 0.031 0.025 0.080 0.011

I

-:J

I tv

Transition probability AAi. 108 8- 1

I

W 00

Accuracy, %

Source*

{Jk

> 1-3

Silicon (Continued)

50 50 50 50 50

12 12 12 12 12

5793.07 5797,86 5948.55 6721. 85 6976.52

9 9 16 38 60

3 5 3 3 3

5 7 5 5 5

0.014 0.014 0.044 0.034 0.023

50 50 50 50 50

12 12 12 2 2

7003.57 7005.88 7680.27 7918.39 7932.35

60 60 36 57 57

5 7 3 3 5

7 9 5 5 7

0.024 0.027 0.062 0.054 0.054

50 50 50 50 50

2 2 2 2 2

1250.43 1251.16 1260.42

UV 13.05 UV 8 UV 4

6 6 2

6 4 4

35 19 25

o 50 50 50

28 2 2

~

J-l

o

>

Z 1304.37 1309.27 1526.72 1533.45 t2072.4

UV UV UV UV UV

3 3 2 2 9

2 4 2 4 10

2 2 2 2 14

3.6 7.0 3.73 7.4 1.0

50 50 25 25 50

2 2 2 2 2

UV 18 UV 17 7 6 6

4 4 2 2 4

6 6 4 2 2

0.38 0.67 0.39 0.15 0.30

50 50 50 50 50

2 2 2 2 2

t::;

~

o

t"'

t':l

o d

2500.93 2904.28 3203.87 3333.14 3339.82

e-

>

~

"'d

:r: ~

rJ2 H

7944.00 8093.24 94.l3.51 10288.9 10371. 3

57 34 14 6 6

7 3 3 1 3

9 3 1 3 3

0.049 0.012 0.29 0.027 0.081

50 50 50 50 50

2 12 12 2 2

3856.02 3862.60 4128.07 t4621.5 5041. 03

1 1 3 7.05 5

6 4 4 10 2

4 2 6 14 4

0.25 0.28 1. 32 0.16 0.98

50 50 25 50 50

2 2 2 2 2

10585.1 10603.4 10661. 0 10689.7 10694.3

6 5 5 53 53

5 3 1 3 5

3 5 3 5 7

0.19 0.048 0.089 0.12 0.12

50 50 50 50 50

12 12 12 2 2

t5466.6 5957.56 5978.93 6347.10 6371.36

7.03 4 4 2 2

10 2 4 2 2

14 2 2 4 2

0.26 0.42 0.81 0.70 0.69

50 50 50 25 25

2 2 2 2 2

o

rJ2

10727.4 10749.4 10786.9 10827.1 10843.9

53 5 5 5 31

7 3 3 5 3

9 3 1 5 5

0.12 0.10 0.24 0.19 0.098

50 50 50 50 50

2 12 12 12 12

10869.5 10979.3 11984.2 11991. 6 12031. 5

13 5 4 4 4

3 5 3 1 5

5 3 5 7

0.24 0.042 0.15 0.11 0.18

50 50 50 50 50

12 12 12 12 12

Si III: 883.398 994.787 997.389 1108.37 1140.55

UV UV UV UV UV

12103.5 12270.7 15557.8 15884.4 15888.4

4 4 42.21 42.21 11.12

3 5 5 3 3

3 5 5 3 3

0.061 0.033 0.013 0.020 0.082

50 50 50 50 50

12 12 2 2 12

1141. 58 1142.28 1144.31 1144.96 1155.00

15960.0 16060.0 16094.8

42.21 42.21 42.21

7 3 5

5 1 3

0.070 0.083 0.060

50 50 50

2 2

1155.96 1156.78 1158.10 1160.26 1161. 58

2 2 2 4 4

4 4 2 4 2

50 50 50 50 50

2 2 2 2 2

Si II: 989.867 1190.42 1193.28 1194.50 1197.39

UV UV UV UV UV

6 5 5 5 5

3

1223.91 1224.25 1227.60 1229.39 1246.74

UV UV UV UV UV

8.02 8.02 8.02 8.01 8

4 4 6 6 2

2 4 6 8

1248.43 1250.09

UV 8 UV 13.05

4 4

6.7 7.2 29 35 14

2

6818.45 7113.45 7125.84 7848.80

1207.52 1294.54 1296.73 1301.15 1303.32

7.20 7.19 7.19 7.02

50 50 50 ·50

2 2 2 2

63 7.89 13.1 16.2 22

50 10 10 10 50

2 2 2 2 2

5 3 7 5 3

30 16 39 9.7 7.5

50 50 50 50 50

2 2 2 2 2

1 3 5 3 5

22 5.2 5.5 9.1 16

50 50 50 50 50

2 2 2 2 2

2 2 4 4

4 2 2 6

27 6 6 5 32

5 3 5 1 1

7 3 3 3 3

UV UV UV LTV UV

32 32 32 32 31

3 3 5 5 1

UV UV UV UV UV

31 31 31 31 31

3 3 3 5 5

UV UV UV UV UV

22 4 4 4 4

5 3 1 3 5

5 5 3 1 3

4

20 11 24 36 6.3

50 50 50 50 50

28 28 28 28 2

1328.81 1362.37 1417.24 1435.78 1588.95

UV UV UV UV UV

48 38 9 61 59

1 3 3 5 5

3 1 1 7 3

4 4

13 38

50 50

2 28

1778.72 1842.55

UV 35 UV 20

7 5

9 3

I • For references see pp, 7-208 and 7-209.

0.11 0.051 0.098 0.39

19 5.62 7.46 22.2 9.18 27 11 26.0 21 11 4.4 2.61

50 10 10 10 10

2 2 2 2 2

50 50 25 50 50

2 2 2 2 2

50 25

2 2

>'-3 o

s:: H

(1

'-3

::0

>-

Z

tn H '-3 H

o

Z "d

::0

o

to

>to

H

~

H

'-3

H

trJ

rn

-.:J I

G:l

C;.:I

CD

TABLE

Wavelength,

A

Multiplet no.

Statistical weights

7i-4.

Transition probability Aki,

a.

I

TRANSITION PROBABILITIES FOR ALLOWED LINF.S

108

8- 1

Aceuracy,

Source*

%

Wavelength,

A

Multiplet no.

Silicon (Continued)

~

o Transition probability Aki,

I

10 8

S-1

Accuracy. %

Source*

Ok

> ""3 o ~ .....

Silicon (Continued)

t2449.48 2528.47 2546.09

UV 78 UV 81 UV 56

15 5 5

21 7 5

1.2 0.81 0.61

50 50 50

2 2 2

2559.21 3233.95 3241. 62 t3486.91 3590.47

UV 55 6 6 8.06 7

5 3 5 15 3

7 3 3 21 5

7.7 1.3 2.3 1.8 3.9

50 50 50 50 50

2 2 2 2 2

3681.40 3791. 41 4338.50 4341.40 4494.05

10.09 5 3 46 15

5 1 1 3 3

3 3 3 1 3

0.33 2.0 0.147 1.8 0.46

50 50 25 50 50

2 2 2 2 2

4552.62 4554.00 4567.82 4574.76 4619.66

2 15 2 2 13

3 5 3 3 3

5 3 3 1 5

1.26 0.76 1.25 1.25 0.33

25 50 25 25 50

2 2 2 2 2

4638.28 4665.87 4683.02

13 13 13

1 3 5

3 3 5

0.43 0.32 0.95

50 50 50

2 2 2

I

Statistical weights

o:

(Jk

~ ~

(Continued)

2120.18 2127.47 t2287.04 t2675.2 t2723.81 3149.56 3773.15 4088.85 4116.10 t4212.41

UV UV UV UV UV

18 18 22 25 32

2 4 10 14 10

2 2 14 10 14

3.0 6.0 6.4 0.280 1.1

25 25 25 25 50

2 2 2 2 2

2 3 1 1 5

2 4 2 2 10

4 2 4 2 14

4.02 2.36 1. 56 1.54 1. 72

25 25 10 10 25

2 2 2 2 2

4314.10 4328.18 t4403.73 6667.56 t6998.36

4 4 14 3.02 12

2 4 10 2 10

2 2 14 4 14

1.08 2.14 0.41 1. 14 0.55

25 25 50 25 25

2 2 2 2 2

7068.41 7630.50 7654.56 t8240.61 8957.25

4.01 9 9 15 3.01

4 2 4 14 2

2 2 2 10 4

1.00 0.440 0.88 0.126 0.421

25 25 25 25 25

2 2 2 2 2

9018.16

3.01

2

2

0.413

25

2

(1

>

Z

e

~

o

rt':'J

(1

q

t'"

>

~

'"d

::I: ~

U1

.....

(1

U1

Phosphorus

4683.80 4716.65

13 8.09

3 5

1 7

1.3 2.8

50 50

2 2

4730.52 5473.05 5490.11 5539.93 5696.50

13 12.08 12.08 12.08 8.17

5 5 3 5 5

3 7 3 5 3

0.52 0.79 0.33 0.19 0.20

50 50 50 50 50

2 2 2 2 2

PI: 1774.99 1782.87 1787.68 t1859.2. 2136.18

5704.60 5716.29 5739.73 6169.84 6314.46

8.17 8.17 4 22 10.02

7 9 1 5 3

5 7 3 7 1

0.18 0.19 0.47 0.12 1.2

50 50 50 50 50

2 2 2 2 2

2149.14 2152.94 2533.99 2535.61 2553.25

4 9 8 8 8

6521. 49 6831. 56 7612.36 8262.57 8265.64

17 10.07 10.01 10.06 10.06

3 5 3 5 5

5 3 5 7 5

0.32 0.74 1.1 0.91 0.23

50 50 50 50 50

2 2 2 2 2

8269.32 8341. 93 9799.91

10.06 44 8.08

3 3 5

5 5 3

0.70 0.26 0.39

50 50 50

2 2 2

Si IV: t645.759 t749.941 815.049 818.129 t1066.63

UV UV UV UV UV

15 13 4 4 11

10 10 2 4 10

14 14 2 2 14

7.0 14.5 12.3 24.4 39.1

50 25 25 25 25

2 2 2 2 2

1122.49 1393.76 1402.77 t1533.22 1727.38

UV UV UV UV UV

3 1 1 24 10

2 2 2 10 4

4 4 2 14 2

22.2 9.20 9.03 3.57 5.5

25 10 10 25 25

2 2 2 2 2

* For references see

pp, 7-208 and 7-209.

4 4 4 10 6

6 4 2 10 4

2.17 2.14 2.13 2.81 2.83

25 25 25 25 25

2 2 2 2 2

uv uv uv uv uv

4 2 2 4 2

2 4 4 4 2

3.18 0.485 0.200 0.95 0.71

25 25 25 25 25

2 2 2 2 2

2554.90 8046.79 8090.08 8637.62 8741. 54

8 uv

-

4 8 6 2 2

2 6 4 2 4

0.300 0.023 0.020 0.079 0.091

25 50 50 50 50

2 2 2 2 2

9175.85 9304.88 9525.78 9563.45 9593.54

3 3 3 2 2

2 4 6 4 2

4 4 4 6 4

0.050 0.096 0.14 0.081 0.11

50 50 50 50 50

2 2 2 2 2

9750.73 9790.08 9796.79 9903.74 9976.65

2 4 2 4 2

4 2 6 2 6

2 4 6 2 4

0.22 0.045 0.18 0.18 0.11

50 50 50 50 50

2 2 2 2 2

4 4 1 1 1

4 4 2 4 6

4 2 4 6 8

0.21 0.083 0.088 0.15 0.21

50 50 50 50 50

2 2 2 2 2

10084.2 10204.7 10511.4 10529.5 10581. 5

1 uv 1 uv 1 uv 5 uv 4 uv

-

-

:> 8

o

~

~

o 8

~

:> ~

(J2

~

8

o'"'"

~

'"d

~

g

:> t::l:I ..... r..... 8 ..... tr:I

(J2

~ t-:) ~ 1-0'-

TABLE

7i-4.

TRANSITION PROBABILITIES FOR ALLOWF:D LINF:S

-a

(Continued)

I t+:o-

l:-.:>

Wavelength,

A

Multiplet no.

Statistical weights

0,

I

Transition probability Ak', 10 8 S-1

Accuracy,

Source*

%

Wavelength,

A

Multiplet no.

Oi

Ok

P II: 1301. 87 1304.47 1304.68 1305.48 1309.87

1310.70 1535.90 1542.29 4385.35 4402.09 4414.28 4417.30 4420.71 4424.07 4463.00 4467.98 4475.26 4483.68 4499.24 4530.81

2 4 6

1 1 1 2 2 2 2 2

uv uv uv uv uv

2 uv 1 uv 1 uv

-

-

-

-

-

1 3 3 3 5 5 3 5 3 1

2 4 6 3 1 3 5 3 5 5 7 3 3

0.17 0.11 0.060 0.53 1.57 0.392 0.392 0.65 1. 17 0.096 0.127 0.40 0.73

I

l:-.:>

Transition probability Aki. 10 8 s-1

Accuracy,

Source*

%

Ok

> ""3

Phosphorus (Continued)

Pho8phorus(Continued)

10596.9 10681.4 10813.0

Statistical weights

50 50 50 25 25 25 25 25 25 25 25 50 50

3 3 3 3 5

5 3 1 1 5

0.18 0.55 1.6 0.73 0.54

50 50 50 50 50

1 5 3 5 3

3 7 3 7 5

0.25 1.3 0.19 1.4 1.0

50 50 50 50 50

2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

2 2 2

2

5583.27 5588.34 5727.71

-

6024.18 6034.04 6043.12 6055.50 6087.82

-

6165.59 7735.06 7845.63

-

-

-

-

5 3 3

3 5 3

0.19 0.15 0.15

50 50

3 1 5 5 3

5 3 7 3 3

0.51 0.37 0.68 0.69 0.27

50 50

50

50

50 50

2 2 2 2 2 2 2 2

o

~ ,...

o

>

Z

~

~

o

r-

t":j

5 1 3

5 3 3

0.16 0.11 0.33

50 50 50

2 2 2

3.9 1.8 0.34 0.68 0.97

50 50 50 50 50

2 2 2 2 2 2 2 2

PIlI: 3219.32 t3280.22 3717.63 3744.22 3802.08

4 6 10 10 10

2 10 4 6

4 14 4 4 4

3895.03 3904.79 3951. 51 3957.64 3997.17

9 9 9 9 9

4 2 4 6 6

6 4 2 6 4

0.54 0.75 1.4 1.2 0.76

50 50 50 50 50

4057.39 4059.27

1 1

4 6

4 4

0.10 0.90

50 50

2

2 2

2 2

o d

r>

;:0 ." ~

~

to

(=)

t»

4533.96 4554.83 4565.27 4582.17 4588.04

-

5 3 3 5 5

3 5 1 5 7

0.31 0.96 0.96 0.33 1.7

50 50 50 50 50

2 2 2 2 2

4589.86 4602.08 4626.70 4628.77 4658.31

-

3 7 5 3 7

5 9 5 3 7

1.6 1.9 0.30 0.97 0.21

50 50 50 50 50

2 2 2 2 2

4864.42 4927.20 4935.62 4943.53 4954.39 4969.71 5040.80 5152.23 5191. 41 5253.52 5296.13 5316.07 5344.75 5378.20 5386.88 5409.72 .5425.91 .5450.74 .5483.55 .5499.73 .5507.19 .5541. 14

-

-

-

-

-

-

-

-

5 3 1 7 3

5 3 3 5 1

0.11 0.19 0.63 0.63 0.78

50 50 50 50 50

2 2 2 2

3 5 3 3 5

0.58 0.40 0.12 0.35 1.0

50 50 50 50 50

2 2 2 2 2

5 3 1 3 3

3 5 3 5 3

0.55 0.24 0.32 0.11 0.23

50 50 50 50

2 2 2 2 2

3 5 5 1 5

1 5 5 3 3

0.93 0.69 0.33 0.15 0.37

50 50 50 50 50

2 2 2 2 2

3 3

3 1

• For references see pp. 7-208 and 7-209.

0.11 0.45

50 50

1 3 3

4 2 2

2 4 2

0.99 1.5 1.4

50 50 50

2 2 2

t4587.91

7

14

10

0.11

50

2

1 3 5 3 1

3 3 3 1 3

5.5 16.5 27.3 24.2 26.3

25 25 25 25 10

2 2 2

3 5 3 5 1

5 7 5 5 3

48 66 84 26 39.4

50 50 50 50 10

2 2 2

>-

2 2

1-3 I-l

1 3 1 3 5

3 5 3 1 3

29.0 7.7 10.1 29.9 12.4

25 25 25 25 25

2 2 2 2 2

P IV: 628.983 629.914 631.765 776.366 823.181

4 uv 4 uv 4 uv

-

3 uv

2

2

2

5 5 1 3 3

50

4080.04 4222.15 4246.68

2 2

846.999 849.764 [855.05J 866.84 950.662

-

5 uv 1 uv

>o

8

is:

1-4

o

1-3 =0

Z

"(J) 1-4

o 963.993 1025.58 1028.13 1033.14 1035.54

-

2 2 2 2

uv uv uv uv

Z

;S

g G; t: 1-1

t1090.0 1118.59 [1847.5J 3347.72 3364.44 3371. 10 [3719.3J 3728.67 4249.57

-

1 1 1 3

3 2

15 3 5 3 3

9 1 7 5 3

18 32.4 7.3 2.13 2.09

50 25 50 25 25

2 2 2 2 2

3

1 5 3 3

2.1 2.0 1.8 0.84

50 50 50 25

2 2 2 2

7 5 1

~

t;I:j U2

~

~ C;.j

TABLE

wavel~u.th.1 A

Multiplet

Statistical weights

no.

o.

I

7i-4.

TRANSITION PROBABILITmS FOR ALLOWED LINES

Transition probability Ah, 10 8 S-1

Accuracy,

Source*

%

Wavelength,

A-

Multiplet no.

o«

542.567 544.914 t673.90 865.435 [997.53]

-

2 4 10 2 4

-

-

-

2 2 14 4 4

25 49 97 31.0 1.7

25 25 25 25 25

2 2 2 2 2

4 4 2 2

15 16 12.0 11.6 6.6

25 25 25 25 25

2 2 2 2 2

13

25 25 25 25 25

2 2 2 2 2

-

1385.11 [2424.3] [2440.8] [2441. 1] 3175.16

-

2

1

4 2 4 4 2

4 4

6.4 7.4 1.2 2.34

3204.06

1

2

2

2.28

25

2

4.8 2.4 1.3 1.1 4.8

50 50 50

2 2 2 2 2

6 4 2 2 2

-

-

-

2

4 J

I

H::oH::o-

Transition probability Aki. 10 8 S-1

Accuracy,

Source*

%

{Jk

>

Sulfur (Continued)

997.641 1000.36 1117.98 1128.00 [1379.7]

-

Statistical weights

{Ii

Phosphorus (Continued) PV:

1 lV

(Continued)

Sulfur

8

o

t8684.2 t9036.7 9212.91

6 13 1

15 9 5

25 15 7

0.12 0.029 0.30

50 50 50

2 2 2

9228.11 9237.49 10455.5 10456.8 10459.5

1 1 3 3 3

5 5 3 3 3

5 3 5 1 3

0.28 0.28 0.22 0.22 0.22

50 50 50 50 50

2 2 2 2 2

uv uv uv uv uv

2 4 2 4 4

4 4 2 2 4

0.84 3.1 2.7 1.1 0.048

50 50 50 50 50

2 2 2 2 2

1250.50 1253.79 1259.53 3567.17 3616.92

1 uv 1 uv 1 uv 56 56

4 4 4 4 6

2 4 6 4 6

0.46 0.42 0.34 0.35 0.36

25 25 25 50 50

2 2 2 2 2

3892.32 3933.29 4032.81 4142.29 4145.10

50 55 59 44 44

6 6 4 2 4

6 8

0.63 2.0 1.2 1.7 1.8

50

2 2 2 2 2

S II:

1124.39 1125.00 1131.05 1131. 65 1234.14

8 8 8 8 7

S I:

1295.66 1296.17 1302.34 1302.87 1303.11

9 9 9 9 9

uv

uv uv uv uv

5 5 3 3 3

5 3 5 3 1

50 50

6

4 6

50

50 50 50

s::

~

o

>

Z

t:::1

s::

o

t"

t?:j

o d r-

>-

;:0 lod ~ ~

.... o W W

-

3

1.9 1.7 0.94 0.91 0.50

50 50 50 50 50

2 2 2 2 2

4153.10 4162.70 4165.11 4259.18 4294.43

44 44 64 66 49

6 8 6 6 6

8 10 6 8 8

2.0 2.3 0.74 1.5 1.7

50 50 50 50 50

2 2 2 2 2

1 9 5 5 5

3 15 3 7 5

0.16 3.6 6.9 1.6 0.57

50 50 50 50 50

2 2 2 2 2

4463.58 4483.42 4552.38 4656.74 4716.23

43 43 40 9 9

8 6 4 2 4

6 4 2 4 4

0.53 0.31 1.3 0.12 0.23

50 50 50 50 50

2 2 2 2 2

uv uv uv uv uv

3 3 1 1 5

5 3 3 3 5

1.2 0.75 0.023 0.89 5.8

50 50 50 50 25

2 2 2 2 2

4792.02 4815.52 4824.07 4885.63 4917.15

46 9 52 15 15

6 6 6 2 2

6 4 4 4 2

0.37 0.64 0.76 0.13 0.55

50 50 50 50 50

2 2 2 2 2

uv uv uv uv

1 1 5 3 1

3 3 3 3 3

0.94 1.5 4.1 2.2 0.73

50 50 25 25 25

2 2 2 2 2

4924.08 4925.32 4942.47 4991.94 5009:54

7 7 7 7 7

4 2 2 4 4

6 4 2 4 2

0.22 0.24 0.15 0.15 0.70

50 50 50 50 50

2 2 2 2 2

2 2 2 4 9

5 5 5 3 3

7 5 3 9 5

0.0076 0.0074 0.0072 0.0038 0.0057

50 50 50 50 50

2 2 2 2 2

5014.03 5027.19 5032.41 5047.28 5103.30

15 1 7 15 7

4 4 6 4 6

4 2 6 2 4

0.72 0.26 0.66 0.32 0.50

50 50 50 50 50

2 2

6408.13 6415.50 t6751. 2 7679.60 7686.13

9 9 8 7 7

5 7 15 3 5

5 5 25 5 5

0.0095 0.013 0.079 0.012 0.020

50 50 50 50 50

2 2 2 2 2

5142 ..33 t5208.0 5320.70 5400.67 5428.64

1 39 38 61 6

2 10 6 4 2

2 10 8 4 4

0.19 0.79 0.84 0.40 0.38

50 50 50 50 50

2 2 2 2 2

7696.73 t8451. 6

7 14

7 9

5 3

0.028 0.050

50 50

2 2

5432.77 5453.81

6 6

4 6

6 8

0.61 0.78

50 50

2 2

1303.42 1305.89 t 1320 . 0 1401. 54 1409.37

9 8 6 6

uv uv uv uv

5 1 9 5 3

3 3 15

1412.90 t1429.1 1448.25 1474.01 1474.39

6 5 12 3 3

uv uv uv uv uv

1483.04 1483.23 1485.61 1487.15 1666.69

3 3 4 3 11

1687.49 1782.26 1807.34 1820.36 1826.26

-

13 2 2 2

4694.13 4695.45 4696.25 t5278.7 6403.58

3

2

2 2

>-~ o a::: 1-1

C ~

=:c

>-

zrp 1-1

~

1-1

o

Z

;g g ~

1-1

e-

1-1

~

1-1

• For references see pp. 7-208 and 7-209.

t:r.1 rp

~ I:'-J

~

CJ1

TABLE

Wavelength,

A

Multiplet no.

Statistical weights

a,

I

7i-4.

TRANSITION PROBABILITIES FOR ALLOWED LINES

Transition probability Aki, 10 8 S-1

Accuracy,

Source*

%

Wavelength,

A

Multiplet no.

5536.77 5564.94 5578.85 5606.11 5616.63

2 4 8

6 6 1l

4 6 6 10 4

11

6 11 11 11

5639.96 5646.98 5659.95 5664.73 6305.51

14 14

6312.68 7967.43 8314.73

2 4 8 6 6 6 8 4

0.74 0.39 0.081 0.066 0.16 0.074 0.30 0.083

50 50 50 50 50 50 50 50

2 2 2 2 2 2 2 2

19

6 4 4 2 6

0.75 0.68 0.34 0.38 0.18

50 50 50 50 50

2 2 2 2 2

26 12 12

6 2 4

4 2 2

0.20 0.080 0.16

50 50 50

2 2 2

SIll:

2460.50 2489.59 2496.24 2499.08 2508.15

17 17 17 17 17

uv uv uv uv uv

5 3 7 3 5

5 3 5 1 3

Statistical weights

~

I

t+:o-

Transition probability Aki, 10 8 8- 1

Accuracy,

Source*

%

ale

>-

Sulfur (Continued)

4 2 6 4 8

11 11

~ t-:J

a:

(J"

Sulfur (Continued)

5473.59 -5509.67 5526.22

(Continued)

0.45 0.77 2.5 3.1 2.3

50 50 50 50 50

2 2 2 2 2

4332.71 4340.30 4361. 5:3

4 4 4

1 3 5

3 3 5

1 1

2 2 2

2 4 2

8

0.64 0.48 0.28

50 50 50

2 2 2

25 50 50

2 2 2

o

>-

S IV:

551. 17 3097.46 3117.75

o ~ .....

20.6 2.6 2.5

Z

t:1 ~

o

~

M

S V:

437.37 438.19 439.65 658.262 786.476

4 4 4 3 1

uv uv uv uv uv

1 3 5 1 1

3 3 3 3 3

11. 2 33.3 55 36.2 52.5

25 25 25 10 10

2 2 2 2 2

849.241 852.185 857.872 860.462

2 2 2 2

uv uv uv uv

3 1 3 5

5 3 1 3

10.7 14.1 41. 4 17.1

25 25 25 25

2 2 2 2

5 3 3 3 1

uv uv uv uv uv

10 2 4 4 2

14 4 6 4 4

202 41.7 48.5 8.1 16.3

25 25 25 50 25

2 2 2 2 2

1 uv

2

2

15.7

25

2

S VI:

t464.654 706.480 712.682 712.844 933.382 944.517

o q

~

>-

::0

~

:I: ~

in

..... o

Ul

2636.88 2665.40 2680.47 2691.68 2702.76

19 19 19 19 19

uv uv uv uv uv

3 5 1 3 3

5 5 3 3 1

0.45 1.4 0.62 0.46 1.9

50 50 50 50 50

2 2 2 2 2

2718.88 2721. 40 2726.82 2731. 10 2741.01

16 19 20 16 16

uv uv uv uv uv

3 5 3 5 5

3 3 5 5 3

1.2 0.77 0.60 1.1 0.39

50 50 50 50 50

2 2 2 2 2

2756.89 2775.25 2785.49 2856.02 2863.53

16 16 20 15 15

uv uv uv uv uv

7 7 3 5 7

7 5 3 7 9

1.4 0.24 0.61 5.1 5.7

50 50 50 50 50

2 2 2 2 2

2872.00 2904.31 2950.23 2964.80 2985.98

15 15 18 18 18

uv uv uv uv uv

3 7 3 5 5

5 7 5 7 5

4.7 3.0 4.0 0.99

50 50 50 50 50

2 2 2 2 2

3662.01 3717.78 3778.90 3831. 85 3837.80

6 6 5 5 5

3 5 3 1 3

3 3 5 3 3

0.64 1.0 0.44 0.56 0.42

50 50 50 50 50

2 2 2 2

3838.32 3860.64 3899.09 4253.59 4284.99

5 5 5 4 4

5 3 5 5 3

5 1 3 7 5

1.3 1.6 0.67 1.2 0.90

50 50 50 50 50

2 2 2

* For references see

pp, 7-208 and 7-209.

O.fH

2

2

2

Chlorine

Cl I: 1201. 36 1335.72 1347.24 1351.66 1363.45

2 2 2 2

4323.35 4363.30 4369.52 4379.90 4438.48

2 4 4 2 2

4 2 4 2 4

2.39 1. 74 4.19 3.23 0.75

25 25 25 25 25

2 2 2

9 8 8 7 6

4 4 2 4 6

4 6 4 4 6

0.011 0.0067 0.0070 0.Oi2 0.014

50 50 50 50 50

2 2 2 2 2

4469.37 4475.31 4526.20 4601.00 4661.22

15 7 15 15 15

4 4 4 2 2

2 6 4 2 4

0.016 0.0043 0.041 0.039 0.010

50 50 25 25 50

2 2 2 2 2

4691.53 4976.62 5099.80 7256.63 7414.10

-

4 4 2 6 6

2 4 2 4 4

0.011 0.0035 0.0085 0.19 0.047

50 50 50 50 50

2 2 2 2 2

7547.06 7717.57 7744.94 7769.18 7821. 35 7830.76 7878.22

-

-

5 4 5 4 5 -

3

uv uv uv uv

2 2

:> 1-3

o

~

I-
Z

U1 I-
1-3 o ~ .... C":J

1-3

;:0

:> Z rn .... 1-3

oZ '"d ;:0

o

ttl

:> ttl ....

....t'"

1-3 .... t:j

tn

2

~ l\:) Con

pp. 7-208 and 7-209.

.....

TABLE

Wavelength,

A

Multiplet no.

Statistical weights

0.

I

7i-4.

TRANSITION PROBABILITIES FOR ALLOWED LINES

Transition probability Aki,10 8s- 1

Aeeuracy, %

Source*

Wavelength, Multiplet no. A

7383.98 7435.33 7503.87

-

3 5 3

5 5 1

0.087 0.0094 0.472

25 50 25

2 2

7514.65 7635.11 7723.76 7724.21 7948.18

-

3 5 5 1 1

1 5 3 3 3

0.430 0.274 0.057 0.127 0.196

25 25 25 25 25

2 2 2 2 2

8006.16 8014.79 8103.69 8115.31 8264.52

-

3 5 3 5 3

5 5 3 7 3

0.0468 0.096 0.277 0.366 0.168

25 25 25 25 25

2 2 2 2 2

8408.21 8424.65 8521.44 8605.78 8667.94 8761.69 9122.97 9194.64 9224.50 9291.53

-

-

-

-

3 3 3 5 1 3 5 3 3 3

5 5 3 5 3 5 3 3 5 1

0.244 0.233 0.147 0.0108 0.0280 0.0099 0.212 0.0198 0.059 0.0366

I

CJl ~

Transition probability Aki, 10 8 S-1

Accuracy,

Source*

%

Ok

Aroon (Contt'nued)

Aroon (Continued)

-

Statistical weights

0.

Ok

~

(Continued)

25 25 25 25 25 50 25 25 25 25

2

2 2

2 2 2 2 2 2 2 2

13499.2 13504.0 13573.6

-

5 5 3

13599.2 13622.4 13678.5 13825.7 14093.6

-

5 3 3 5 1

14596.3 14634.1 14786.3 15046.4 15172.3 15302.3 15402.6 15899.9 15989.3 16436.9 16549.8 16940.4 23844.8 Ar II: 718.091 723.361

-

-

-

-

0.027 0.12 0.051

50 50 50

2 2 2

5 5 5 5 3

0.025 0.082 0.070 0.033 0.048

50 50 50 50 50

2 2

Z

2

a:: o

2 2

5 7 5 1 1

12 16 12 3 3

0.053 0.090 0.0021 0.058 0.015

50 50 50 50 50

2 2 2 2 2

7 7 3 1 3

16 9 5 3 5

0.054 0.014 0.077 0.021 0.059

50 50 50 50 50

2 2 2 2

-

-

3 5 9

8 5 7

0.016 0.028 0.012

50 50 50

2

4 uv 4 uv

4 4

2 4

50 50

2 2

-

-

-

-

> 8 o

3 7 1

9.5 23

2

2 2

== (') ~

> t:;;

~

tJj

o

~

e:>

~

"tl

~

to< m ~

o

m

9657.78 9784.50 10470.1 10478.0 10506.5 10673.6 11393.7 11441. 8 11668.7 11719.5

-

-

-

-

-

11943.5 12112.2 12139.8 12343.7 12356.8

-

12402.9 12439.2 12456.1 12487.6 12702.4

-

-

-

3 3 1 3 5

3 5 3 3 12

0.060 0.0161 0.0117 0.0274 0.0158

25 25 25 25 25

2 2 2 2 2

3 3 5 5 5

5 1 3 5 3

0.049 0.0249 0.0156 0.0423 0.0107

50 25 25 25 25

2 2 2 2 2

3 7 3 5 5

8 7 3 7 12

0.046 0.035 0.051 0.022 0.0135

50 50 50 50 25

2 2 2 2 2

3 3 5 7 3

3 5 3 5 3

0.12 0.055 0.10 0.12 0.080

50 50 50 50 50

2 2 2 2 2

5 3 5 3 3

5 3 5 1 3

0.012 0.022 0.064 0.11 0.083

50 50 50 50 50

2 2 2 2 2

-

5 3 3 5 3

3 1 3 7 5

0.10 0.091 0.046 0.17 0.15

50 50 50 50 50

2 2 2 2

-

3 9

3 20

0.034 0.065

50 50

12733.6 12746.3 12802.7 12933.3 12956.6

-

13008.5 13214.7 13231. 4 13273.1 13313.4

-

13367.1 13406.6

-

* For references see

pp, 7-208 and 7-209.

725.550 730.929 919.782

4 uv 4 uv 1 uv

2 2 4

2 4 2

19 4.5 1. 41

50 50 25

2 2 2

932.053 3000.44 3028.91 3093.40 3139.02

1 uv 69

2 4 2 4 6

2 4 4 6 6

0.67 1.5 2.3 4.4 1.0

25 50 50 50 50

2 2 2 2 2

2 4 6 6 4

4 6 4 4 4

1.8 0.82 0.63 0.24 0.40

50 50 50 50 50

2 2 2 2 2

3161. 37 3169.67 3181.04 3194.23 3204.32

-

47 -

47 47 46 71

3236.81 3243.69 3249.80 3263.57 3273.32

83 47 47 46 71

2 4 2 2 4

4 2 4 4 2

0.52 2.0 1.0 0.35 0.37

50 50 50 50 50

2 2 2 2 2

3281. 70 3293.64 3307.23 3350.93 3366.59

47 83 83 109 83

2 4 2 6 4

2 4 2 6 2

0.73 1.7 3.4 1.5 0.41

50 50 50 50 50

2 2 2 2 2

1.5 1.9 0.22 0.32 0.45

50 50 50 50 50

2 2 2 2 2

0.37 1.34 2.5

50 25 50

2

>-~

o

~

H

C1 ~

~

>-

Z

tr: H

~

H

o

Z ~

~

o t:l:j

>-t:l:j

H

t"

H

3376.44 3388.53 3429.62 3432.59 3454.10

109 96 107 107 44

8 2 8 6 6

8 4 6 4 4

3464.13 3476.75 3509.78

70 44 44

6 6 2

6 6 2

~ .... t::j

to

2

2 2

I

2 2

~

c.n

Ct,j

TABLE

7i-4.

TRANSITION PROBABILITIES FOR ALLOWED LINES

~ tv

(Continued)

ell t+;o.

Wavelength,

A

Multiplet no.

Statistical weights

o.

(Jk

Transition probability

I A". 10' ,-'

Accuracy, %

Source*

Wavelength,

A

Multiplet no.

Statistical weights

o.

I

44 56

4 6

6 6

1. 23 0.80

Aecuracy,

Source*

%

(Jk

I

> 8 o

Ar(Jon (Continued)

Ar(Jon (Continued)

3514.39 3520.00

Transition probability Aki, 10 8 S-1

50 50

2 2

4266.53 4275.16 4277.52

7 77 32

6 2 6

6 4 4

0.156 0.26 1.0

25 50 50

2 2 2

....s::

o

>

Z 50 50 50 50 50

2 2 2 2 2

4337.07 4348.06 4352.20 4362.07 4370.75

113 7 1 39 39

2 6 2 4 4

4 8 2 6 4

0.34 1. 24 0.228 0.057 0.65

50 25 25 50 25

2 2 2 2 2

3535.32 3548.52 3559.51 3561.03 3565.03

44 56 70 106 57

2 4 6 8 2

4 4 8 10 4

0.82 1.1 3.9 4.0 1.1

3576.61 3581.61 3582.36 3588.45 3600.22

56 56 56 56 115

6 2 4 8 4

8 4 6 10 4

2.77 1.8 3.72 3.39 2.2

25 50 25 25 50

2 2 2 2 2

4371.33 4375.95 4379.67 4400.10 4400.99

1 17 7 1 1

6 4 2 4 8

4 2 2 4 6

0.233 0.200 1.04 0.164 0.322

25 25 25 25 25

2

-3622.14 ~639. 83 3650.89 3655.28 3671. 01

42 116 43 82 115

4 4 2 4 4

2 6 4 6 2

0.64 1.4 0.12 0.23 0.71

50 50 50 50 50

2 2 2 2 2

4426.01 4448.88 4481. 81 4545.05 4564.42

7 127 39 15 85

4 6

0.83 0.65 0.494 0.413 0.29

25 50 25 10 50

2

4 4

6 6 6 4 2

3678.27 3680.06 3718.21 3724.52 3729.31

42 116 131 131

6 2 4

4 4 6 6 4

0.25 1.2 2.0 0.34 0.60

50 50 50 50 50

2 2 2 2 2

4579.35 4589.90 4609.56 4657.89 4721. 59

17 31 31 15 85

2 4 6 4 4

2 6 8 2 4

0.82 0.82 0.91 0.81 0.15

25 25 25 25 50

2 2 2 2 2

10

6 6

6

2

2 2 2

tl

~

o

t'

t".1

o

c::

r>

~

I-d

~

~

U2

2 2 2 2

....

o

U2

2 2 2 2 2

4726.86 4735.91 4764.86 4806.02 4847.82

14 6 15 6 6

4 6 2 6 4

4 4 4 6 2

0.50 0.58 0.575 0.79 0.85

25 25

0.98 0.41 0.94

50 50 50 50 50

10

2

25 25

2 2

6 4 6 6 4

0.25 0.23 1.5 0.44 0.76

50 50 50 50 50

2 2 2 2 2

4865.92 4879.86 4933.21 4965.07 5009.33

85 14 6 14 6

4 4 4 2 4

6 6 4 4 6

0.15 0.78 0.143 0.347 0,147

50 25 25 25 25

2 2 2 2 2

90 54

6 4 4 4 4

6 2 4 6 4

0.15 0.27 0.47 1.9 0.19

50 50 50 50 50

2 2 2 2 2

5062.04 6638.23 6639.74 6643.'72 6684.31

6 20 20 20 20

2 6 4 10 8

4 4 2 8 6

0.221 0.129 0.181 0.167 0.113

25 25 25 25 25

2 2 2 2 2

54 105 10 90 105

2 6 2 4 8

2 4 4 4 6

0.22 1.4 0.30 1.1 1.4

50 50 50 50 50

2 2 2 2 2

3979.36 4013.86 4033.82 4042.90

89 90 2 52 33

4 4 8 4 4

4 2 8 2 4

0.35 1.3 0.107 0.98 1.4

50 50 25 50 50

2 2 2 2 2

4072.01 4131. 73 4156.09 4218.67 4222.64

33 32 52 64 77

6 4 4 4 4

6 2 4 4 2

0.57 1.4 0.39 0.36 0.69

25 50 50 50 50

2 2 2 2 2

4226.99 4228.16

113 8

4 4

6 6

0.41 0.130

50 25

2 2

3737.89 3763.50 3765.27 3770.52 3780.84

131 54 42 42 54

6 8 6 2 8

8 6 6 4 8

3796.60 3799.38 3803.17 3809.46 3825.68

129 54 129 42 128

4 6 6 4 6

3826.81 3841. 52 3850.58 3868.52 3872.14

54 54

3880'.34 3925.72

39~.63

3932.55 3946.10 395~.73

10

* For references see

pp. 7-208 and 7-209.

2.3

I 0.14

~

2

~ ......

o

t-3

~

;>

Z

Ul

...... t-3

......

Ar III: uv uv uv uv uv

5 3 5 3 1

3 1 5 3 3

1. 20 2.81 2.09 0.69 0.91

25 25 25 25 25

2 2 2 2 2

887.404 3024.05 3054.82 3064.77 3078.15

1 uv 4 4 4 4

3 5 3 3 1

5 7 5 3 3

0.68 2.6 1.9 1.0 1.4

25 50 50 50 50

2 2 2 2

3285.85 3301. 88 3311. 25 3336.13 3344.72

1 1 1 3 3

5 5 5 7 5

7 5 3 9 7

2.0 2.0 2.0 2.0 1.8

50 50 50 50 50

871. 099 875.534 878.728 879.622 883.179

;> t-3

o

1 1 1 1 1

2

o

Z

'"d

~

o

t::d ;> t::d ...... t" ...... t-3 ...... t::.l

Ul

2 2

2 2 2

-.:J

I

tv Cll Cll

TABLg

7i-4.

TRANSITION PROBABILITIES FOR ALLOWED LINES

~ l\:I

(Continued)

~

0)

Wavelength,

A

Multiplet no.

Statistical weights

O'

I

Transition probability Ak'. 10 8 S-1

Accuracy,

Source·

%

Wavelength,

A

Multrplet no.

o»

Statistical weights

O.

I

Transition probability Aki, 10 8 S-1

Accuracy,

Source·

%

o»

>

~

o a::

Aroon (Continued) 3 7 3 5

5 7 3 5

1.6 1.6 1.3 1.2

50 50 50 50

2 2 2 2

uv uv uv uv uv

4 6 6 2 4

6 6 8 4 6

2.67 2.2 2.8 1.1 2.5

25 50 50 50 50

2 2 2 2 2

4 uv 4 uv

4 6

6 8

1.9 2.6

50 50

2 2

3358.49 3480.55 3499.67 3503.58

3 2 2 2

Ar IV: 850.602 2640.34 2757.92 2776.26 2784.47

1 5 6 4 6

2788.96 2809.44

7698.98 [8904.1]

3 3

1 1

-

.2 2 2 4 2 2 4

4 2 2 4

0.0124 0.0124 0.0272 0.054 0.387

25 25 25 25 10

2 2 2 2 2

2 6

0.382 0.020

10 50

2 2

2

joool

o

>

KIll: 2550.02 2635.11 2689.90 2938.45 2986.20

8 8 8 7 7

uv uv uv uv uv

6 4 2 6 4

4 4 4 6 4

2.0 1.2 0.60 0.77 1.3

50 50 50 50 50

2 2 2 2 2

2992.24 [3023.4] 3052.07 3056.84 [3061. 2]

7 7 7 7 5

uv uv uv uv

6 2 4 2 4

8 2 6 4 2

2.5 2.1 1.7 1.0 0.88

50 50 50 50 50

2 2 2 2 2

3201. 95 3209.34 3278.79 3289.06 3322.40

5 5 1 4 1

4 2 6 4 6

4 2 4 6 6

1.8 1.5 0.86 2.0 1.3

50 50 50 50 50

2 2 2 2 2

[3358.5] 3364.22 3421. 83 3468.32 3513.88

1 5 4 1 1

4 2 2 4 2

2 4 4 6 4

1.5 0.32 1.5 0.48 0.65

50 50 50 50 50

2 2 2 2 2

Z

tl

s::: o t" t"'.J

o d

t"

> ;:0 "d

~

~

Potassium K I: 4044.15 4047.21 [6911.1] [6938.8] 7664'.91

Potassium (Continued)

W

joool

o

W

9597.76 t11022.3 11690.2

10 9 6

11772.8 12432.2 12522.1 {l2526] {12540]

6 5 5

13377 .9 13397.1 15168.4 t16963 [17939]

-

-

-

[18000] t18627 t21945 [27068] [27185]

-

[27206] [27226] t31162 [31381] [31591]

-

[36363] [36613] [37072] [37333] [37348] [62068] [62436]

-

-

-

0.033 0.066 0.220

50 50 25

2 2 2

2

6 14 4

4 2 4 2 2

6 2 2 4 2

0.259 0.079 0.156 0.0045 0.0045

25 25 25 50 50

2 2 2 2 2

6 4 4

4 2 6 14 2

0.0037 0.0041 0.15 0.0060 0.0056

50 50 50 50 50

2 2 2 2 2

4 10

10

2

2 6

2 14 14 4 4

0.011 0.0088 0.014 0.046 0.0025

50 50 50 50 50

2 2 2 2 2

2 4 10 6 4

2 2 14 4 2

0.045 0.0029 0.020 0.014 0.015

50 50 50 50 50

2 2 2 2 2

4 10 10

(j

0.016 0.032 0.029 0.0057 0.034

50 50 50 50 50

2 2 2 2 2

4 2

0.0078 0.0083

50 50

2 2

2 4 2 4 4

2 2 4 4

6 4

Calcium

Ca I:

7 uv 5 uv 17 17 17

1 1 1 3 3

3 3 3 5 3

0.153 0.167 0.367 0.241 0.279

25 25 25 25 25

2

3000.86 3006.86 3009.21 3150.75 t3220.5

17 17 17 15 13

3 5 5 5 9

1 5 3 7 15

1.58 0.75 0.430 0.086 0.15

25 25 25 50 50

2 2 2 2 2

3344.51 3487.60 3624.11 3870.48 3973.71

11 9 26 6

1 5 1 3 5

3 3 3 5 3

0.151 0.078 0.212 0.072 0.175

25 50 25 50 25

2 2 2 2 2

4092.63 4108.53 4226.73 4283.01 4289.36

25 39 2 5 5

3 5 1 3 1

5 7 3 5 3

0.11 0.90 2.18 0.434 0.60

50 50 25 25

2 2 2 2 2

4298.99 4302.53 4307.74 4318.65 4355.08

5 5 5 5 37

3 5 3 5 5

3 5 1 3 7

0.466 1.36 1. 99 0.74 0.19

25 25 25 25 50

2 2 2 2 2

4425.44 4434.96 4435.69 4454.78 4455.89

4 4 4 4 4

1 3 3 5 5

3 5 3 7 5

0.468 0.63 0.356 0.86 0.208

25 25 25 25 25

2 2 2 2 2

2200.73 2398.56 2994.96 2997.31 2999.64

10

10

2 2 2 2

>

1-3

o

~

1-1

o

1-3 ~

> Z

Ul

1-1

1-3 1-1

o

Z ~

~

o

txt

&; 1-1

tot

1-1

1-3 1-1

l"j

tu

~

tv

* For references see

pp. 7-208 and 7-209.

~

"'"

-:J TABLE

Wavelength,

A

Multiplet no.

Statistical weights

7i-4.

TRANSITION PROBABILITIES FOR ALLOWED LINES

Transition probability Ak" 10 8

0,

I

S-1

Accuracy, %

I Source "

Wavelength,

A

Multiplet no.

Statistical weights

CJl 00

I

Accuracy. %

Transition probability Aki. 10

0;

o»

I tv

(Continued)

8 S-1

Sourcev

o»

> ~

o

a::

Calcium (Continued)

Calcium (Continued)

~

3 3 1 9 5

0.231 0.056 0.22 0.53 0.090

25 50 50 50 50

2 2 2 2 2

4526.94 4578.55 4685.27 4878.13 5041. 62

36 23 51 35 34

5 3 3 5 5

3 5 5 7 3

0.41 0.176 0.080 0.188 0.33

50 25 50 25 50

2 2 2 2 2

6122.22 6163.76 6166.44 6439.07 6449.81

3 20 20 18 19

3 3 3 7 5

5188.85 5261. 71 5262.24 5264.24 5265.56

49 22 22 22 22

3 3 3 5 5

5 3 1 5 3

0.40 0.15 0.60 0.091 0.44

50 50 50 50 50

2 2 2 2 2

6462.57 6471. 66 6493.78 6499.65

18 18 18 18

5 7 3 5

7 7 5 5

0.47 0.059 0.44 0.081

50 50 50 50

2 2 2 2

-

6 6 6 6 4

0.459 0.66 1. 01 1.59 0.412

25 25 25 25 25

2 2 2 2 2

4 6 6 2 2

0.081 0.486 2.44 0.155 0.308

25 25 25 25 25

2 2 2 2 2

Ca II:

>

Z

t:1

a::

o

t'"

tr1

o

~

r>

:::c

5270.27 5581. 97 5588.76 5590.12 5594.47

22 21 21 21 21

7 5 7 3 5

5 7 7 5 5

0.50 0.060 0.49 0.083 0.38

50 50 50 50 50

2 2 2 2 2

[1329.8] [1368.4] 1433.1 1553.5 1807.74

11 uv

4 4 4 4 2

5598.49 5601. 29 5602.85 5857.45 6102.72

21 21 21 47 3

3 7 5 3 1

3 5 3 5 3

0.43 0.086 0.14 0.66 0.077

50 50 50 50 25

2 2 2 2 2

[1814.6] 1815.04 1838.08 1843.6 1851. 10

11 uv 11 uv 4 uv 10 uv 10 uv

4 4 4 2 4

• For references see pp. 7-208 and 7-209.

I

o

-

7 uv 6 uv

"'d

:I: to< tn

~

o

rn

TABLE

Wavelength.

A

Multiplet no

Statistical weights

a,

[

7i-4.

TRANSITION PROBABILITIES FOR ALLOWED LINES

Transition probability Aki' 10 8 S-1

Accuracy. %

Source*

Wavelength.

A

Multiplet no.

(Continued)

Statistical weights

(Ji

(Jk

I

Transition probability A::i. 10 8 S-1

Accuracy, %

Source*

> 8 o

(Jk

~

~

2103.24 2112.76 2113.19 2131. 43 2132.25 2197.79 2208.61 3158.87 3179.33 3181. 28

9 9 9 3 3

uv uv uv uv uv

8 uv 8 uv 4 4 4

2 4 4 6 4

4 6 4 4 2

0.93 1.10 0.182 0.018 0.020

25 25 25 50 50

2 2 2 2 2

2 4 2 4 4

2 2 4 6 4

0.313 0.62 3.05 3.59 0.60

25 25 25 25 25

2 2 2 2 2

3706.03 3736.90 3933.66 3968.47 4097.12

3 3 1 1 17

2 4 2 2 2

2 2 4 2 4

0.84 1. 65 1.50 1.46 0.099

25 25 25 25 50

2 2 2 2 2

4109.83 4110.33

17 17

4 4

6 4

0.12 0.019

50 50

2 2

* For references see

pp. 7-208 REd 7-209.

o

Calcium (Continued)

Calcium (Continued)

5001. 49 5019.98 5285.34

15 15 14

2 4 2

4 6 2

0.20 0.23 0.078

50 50 50

2 2 2

8

:;0

>

Z

lfl ~

5307.30 8203.2 8250.2 8256.1 8498.02

14 13 13 13 2

4 2 4 4 4

2 4 6 4 4

0.15 0.51 0.61 0.10 0.0111

50 25 25 25 25

2 2 2 2 2

8542.09 8662.14 9856.7 9933.3 11836.4

2 2 12 12 5

6 4 2 4 2

4 2 2 2 4

0.099 0.106 0.19 0.38 0.23

25 25 50 50 50

2 2 2 2 2

8

~

o

Z

IoIj

:;0

o t:l:1 > ~

t"

~

8

~

t"l

lfl

11947.0

5

2

2

0.23

50

2

-:J

I

t>..:l 0"1

~

TABLE

Wavelength,

A

IMult.iplet

Statistical weights

no.

o.

I

7i-5.

TRANSITION PROBABILITIES FOR FORBIDDEN LINES

I probability 'I'ransit.ion I Accu- I I Wavelength, IMUlti-j racy, Source* A plet Aki,

Ok

%

S-1

no.

2F IF IF

Neon (continued) 5 1 2.80 5 5 1.70(-1) 3 5 5.2 (-2)

4 2 4 6 4

1.33 5.3 (-1) 5.6 (-3) 5.9 (-4) 4.01(-1)

25 25 25 50 25

1 1 1 1 1

2 4 2

1.10(-1) 4.37(-1) 3.89(-1)

25 25 25

1 1 1

4.20 6.8 (-3) 2.60 1.38(-1) 3.82(-1)

25 50 25 25 25

1 1 1 1 1

Hudrooen.

1420.4 MHzt

I

-

I

1

I

3

12.87(-15)

I

3

I

1

3342.9 3868.74 3967.51

1 1 1 1 1

Ne IV: [1608.8] [1609. OJ [2438.6] [2441.3] 4714.2.5

IF

4 4 4 4 6

1

4715.61 4724.15 4725.62

IF IF IF

6 4 4

1 1

Ne V: [1575.2] [1592.7] 2972 3345.9 3425.8

Carbon

C I: 4621. 5 4627.3 8727.4 9823.4 9849.5 C III: [2000.0]

2F 2F 3F IF IF

-

3 5 5 3 5 1

1 1 1 5 5 3

2.60( -3) 1. 9 (- 5) 5.0 (-1) 7.8 (-5) 2. 31( -4) 1. 42( -3)

25 50 25 25 25 25

Nitro(Jen

N I: 5198.5 5200.7

IF IF

4 4

4 6

1. 63( -5) 6.9 (- 6)

25 25

NIl: 3063.0 3070.8 5754.8 6548.1 6583.6

2F 2F 3F IF IF

3 5 5 3 5

1 1 1 5 5

3.40( -2) 1. 6 (-4) 1.08 1.03( -3) 3.04(-3)

25 50 25 25 25

1 1 1 1 1

N IV: (1573.4]

-

1

3

1.18(-2)

25

1

Oxygen 01: (2958.4] 2972.3 5577.35 6300.23 6363.88

2F 2F 3F IF

IF

5 3 5 5 3

1 1 1 5 5

3.7 (-4) 6.7 (-2) 1.34 5.12(-3) 1. 64( -3)

50 25 25 25 25

I 1 1 1 1

1- pmh.b~\ty I

Statistical weights (Ji I 01:

Transition Ah.

S

I

Accuracy, %

ISomee*

25 25 25

1 1 1

I

~ Cj;)

0

I

>

8

0

s::

H

(1

>

Z

~

~

0

r-

3 5 5 3 5

2F IF IF

1 1 1 5 5

Na III: [73294]

t"J, (1

d

t'"

>

~

1'0 ~

Sodium

~

l/2

-

Na IV: [1497.5] [1522.7] [2803.3] 3319.3 3445.9 [90391] Na V: [1379.4] [1380.2]

-a

4

-

5 3 5 5 3 5

IF IF -

I

-

2

I

4 4

1 1 I 5 5 3

I

4 2

4.56(-2)

I

1. 2 (-2) 7.6 3.5 5.6 (-1) 1.67(-1) 3. 04( -2)

I 4.3 1.7

3

I

50 25 25 25 25 10

I

25 25

2

l/2

2 2 2 2 2 2

I

~

(1

2 2

011: 3726.16 3728.91 7318.6 7319.4 7329.9 7330.7

o Ill: [2321.1] [2331. 6] 4363.21 4958.91 5006.84 o V: [1304.2]

IF IF 2F 2F 2F 2F

4 4 6 6 4 4

4 6 2 4 2 4

1.70(-4) 4.84(-5) 6.1 (-2) 1. 15( -1) 1.00( -1) 6.1 (-2)

25 25 25 25 25 25

1 1 1 1 1 1

-

3 5 5 3 5

1 1 1 5 5

2.30(-1) 7.1 (-4) 1.60 7.1 (-3) 2.10(-2)

25 50 25 25 25

1 1 1 1 1

FIll: [2930.0] [2933.1] F IV: [1875.5] [1889.3] 3532.2 3996.3 4059.3

2F IF IF

-

1

3

6.4 (-2)

25

1

-

2F IF IF

5 3 5 5 3

1 1 1 5 5

1. 6 (-3) 4.90(-1) 2.10 3.82(-2) 1. 21( -2)

50 25 25 25 25

1 1 1 1 1

4015.3 4017.5 4021. 6

IF

4 4 6

4 6 4

1. 26( - 2) 1.2 (-3) 9.0 (-1)

25 50 25

2 2 2

IF IF IF

4 6 4

4 2 2

1.30 1.3 (-1) 9.3 (-1)

25 50 25

2 2 2

-

Mg I: 3848.91 3853.96 3854.97 Mg IV: [44911] MgV: [1286.8] [1317.01 [2416.8] [2750.4] [2892.0] [56164]

-

3

-

5 5

3 5 3

1.8 (+1) 2.5 (+1) 5.3 (+1)

50 50 50

2 2 2

-

4

2

1.98(-1)

3

2

-

4 4

-

2F IF IF

3 5 5 3 5

4 6 1 1 1 5 5

1.42(-3) 1.31( -4) 1.10 2.3 (-3) 2.10 3.42( -2) 9.8 (-2)

25 50 25 50 25 25 25

1 1 1 1 1 1 1

-

* For references see

5 3

1 1

5.1 (-3) 2.20

50 25

1 1

AlII: [4451.6] Al V: [29062

:> 8

o

a: ~

-

-

-

5 3 5 5 3 5

1 1 1 5 5 3

2.7 (-2) 2.3 (+1) 4.2 1.90 5.5 (-1) 1.27(-1)

50 25 25 25 25 10

2 2 2 2 2 2

-

1

3

o 8

::c :> z

rJ).

~

8

~

o

z

;g

obj

Aluminum

Neon NeIll: [1793.8] [1814.8]

-

Maoneaium

Fluorine F II: [2225.5] [2246.6] 4157.5 4789.5 4869.3

[2100.4 [2101.5] 4011. 2

2. 88( -3)

25

2

1; ~

e-

~

-

4

2

7.31(-1)

3

2

8 ~ t':1

tn

Silicon Si I: 6526.78 6589.61 10991.4 16068.3 16454.5

IF IF

2F O.OlF O.OIF

3 5 5 3 5

1 1 1 5 5

3.55(-2) 1. I (- 3) 8.0 (-1) 9.7 (-4) 2.74(-3)

25 50 50 25 25

2 2 2 2 2

-.::J

I

~

0:-

pp. 7-208 and 7-209.

t For this line the frequency in megahertz is listed.

~

TABLE

Wavelength

A

IM~lti-I pet no.

Statistical weights

a, !

7i-.5.

I

o»

Transition probability Aki. S-1

I

Accuracy, %

I

Source *

Waveleugth

A

I

MUlti-I plet no.

Silicon (continued)

-

1

3

1. 82( -2)

25

2

Phosphorus PI: 5332.4 5339.7 8787.6 8799.1 {13533] {13562] [13580] {13609] P II: 4669.5 4736.6 7869.5 11483.2 11898.2 P IV: {2681.7]

2F 2F IF IF

-

2F 2F 3F IF IF

-

4 4 4 4 4

4 2 6 4 4

1. 08( -1) 4.26(-2) 2.0 (-4) 2.97(-4) 7.5 (-2)

25 25 50 25 25

2 2 2 2 2

6 4 6

4 2 2

1.13(-1) 1.01(-1) 5.3 (-2)

25 25 25

2 2 2

3 5 5 3 5 1

1 1 1 5 5 3

2.20( -1) 6.3 (-3) 2.0 6.3 (-3) 1. 70( -2) 7.8 (-2)

25 50 50 25 25 25

2 2 2 2 2 2

Sulfur S I: 4506.9 4589.26 7725.04 10819.8 11305.8

2F 2F 3F IF IF

5 3 5 5 3

1 1 1 5 5

7.3 (-3) 3.5 (-1) 1. 78 2. 77( -2) 8.0 (-3)

50 25 25 25 25

2 2 2 2 2

S II: 4068.60 4076.35

IF IF

4 4

4 2

3.41(-1) 1.34(-1)

Statistical weights

a,

Transit.ion probability

o»

i

A k i, S-1

Accuracy, %

I

ISource*

-:J I

tv

O':l

tv

Chlorine (continued)

Si Ill: [3314.7]

(Continued)

TRANSITION PROBABILITIES FOR FORBIDDEN LINES

25 25

2 2

Cl IV: 3118.3 3203.3 5323.29 7530.54 8045.63 Cl V: [67000]

2F 2F 3F IF IF

Ar IV: [2853.6] [2868.2] 4711. 33 4740.20 7170.62 7237.26 7262.76 7332.0 Ar V: [2691.1] [2786.1] 4625.54

1 1 1 5 5

2.61 3.8 (- 2) 3.2 8.0 (-2) 1. 97 (- 1)

I

25 50 50 25 25

!

2 2 .,

>-

2 2

8 0

2

8 >-

r::::

-

Ar II: [69842] Ar III: 3005.1 3109.0 5191.82 7135.80 7751.06 [89896]

3 5 5 3 5 2

4 Arqon.

2. 98( - 2)

2

5. 26( - 2)

3

Z d

4

3

2

~

0

2F 2F 3F IF IF -

5 3 5 5 3 5

1 1 1 5 5 3

4.3 (-2) 4.02 3.10 3.35( -2) 8.3 (-2) 3.08(-2)

50 25 25 25 25 10

2 2 2 2 2 2

r-

~

C1

C

t"

>-

::tl "'tt

~

-

>-
~

o

~ ..... H

Q

~ I

Chlorine Cl II: 3583.2 3675.0 6152.9 8579.5 9125.8

6435.10 7005.67 [78905]

2F 2F 3F IF IF

5 3 5 5 3

1 1 1 5 5

1. 8 (- 2) 1.34 2.29 1.04( -1) 2. 94( -2)

50 25 25 25 25

2 2 2 2 2

Cl III: 3342.7 3353.4 5517.66 5537.6 8433.7

2F 2F IF IF 3F

4 4 4 4 4

4 2 6 4 4

9.6 (-1) 3.74(-1) 1.0 (-3) 7.1 (- 3) 3.90(-1)

25 25 50 25 25

2 2 2 2 2

8481. 6 8501. 8 8550.5

3F 3F 3F

6 4 6

4 2 2

3. 64( -1) 3.51(-1) 1.08(-1)

25 25 25

2 2 2

KV: [2495.3] [2515.3] 4122.63 4163.30 6223.4 6316.6 6349.5 6446.5

~

IF IF 2F

4 2 6 4 4

6.5 2.40 6.9 (-3) 1.11( -1) 2.26

25 25 50 25 25

2 2 2 2 2

o Z

2F 2F 2F

6 4 6

4 2 2

1.46 1.50 1. 9 (-1)

25 25 25

2 2

o

-

2

Calcium Ca IV: [32090]

>

4 4 4 4 4

-

Z

U2 H

~

H

-e

~

t:d

>

t:d H

t'I

4

2

5.43( -1)

3

2

H

~

H

Ca V: [2280.0] [2412.3] 3996.3 5309.18 6086.92 [41551]

M

U2

-

2F IF IF -

5 3 5 5

3 5

1 1 1 5 5 3

1. 6 (-1) 2.4 (+1) 4.6 1. 94 4.31(-1) 3.11(-1)

50 25 25 25 25 10

2 2 2 2 2 2 -::J

* For references see pp, t

'1-208 and '1-209. For this line the frequency in megahertz is listed.

I

t>..J OJ W

Section 8

NUCLEAR PHYSICS J. B. MARION, Editor The University of Maryland

CONTENTS 8a. 8b. 8c. 8d. 8e. 8f. 8g. 8h.

Nuclear Constants and Calibrations : . . . . . . . . . . . . . . . . . . . . . . . .. Properties of Nuclides Atomic Mass Formulas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Passage of Charged Particles through Matter Gamma Rays. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Neutrons.......................................................... Nuclear Fission. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... . . . . . . . . . .. Elementary Particles and Interactions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. sr. Health Physics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. , 8j. Particle Accelerators

8-1

8-2 8-6 8-92 8-142 8-190 8-218 8-253 8-277 8-291 8-316

8a. Nuclear Constants and Calibrations JERRY B. MARION

University of Maryland

This section collects the various nuclear quantities that are useful in designing or analyzing experiments in nuclear physics. For an extensive collection of graphs and tables, the reader is directed to Marion and Young [1]. 8a-1. Nuclear Constants in the MeV System. A complete list of fundamental physical constants and derived quantities is to be found inside the front cover of this volume. For many nuclear physics calculations, however, it is convenient to have certain of these quantities already expressed in Me V energy units. The following list has been generated by using the fundamental constants of Taylor, Parker, and Langenberg [2]. moc2 = 0.5110043 MeV M pc 2 = 938.2595 Me V M nc2 = 939.5529 Me V c2 = 931.481 MeV/amu h = 4.13.5705 X 1O-2~ Me V-sec ft = 6.582180 X 10- 22 MeV-see ftc = 1.973288 X 10- 11 MeV-em ft2 c2 = 389.387 Me V2-barn e = 3.794703 X 10- 7 (MeV-em)! e2 = 1.439977 X 10- 13 Me V-em elhc = 1.923036 X 10 4 (Me V-cm)-! (e/hc)2 = 3.698066 X 10 8 (MeV-cm)-1 ft/moc 2 = 1.288087 X 10- 21 sec 8a-2. Natural Units.

If ft

=

1 and c

=

1, then

Mass, energy, and impulse are in units of em'< Angular momentum is dimensionless e = llV137 1 MeV = 0.506 X 1011 cm- 1 If h = 1, c = 1, and mo = 1, then 1 sec = 7.764 X 1020 natural units 1 em = 2.58 X 1010 natural units 1 Me V = 1.96 natural units 8a-3. Alpha-particle Calibration Energies. Listed in Table 8a-l are the values for alpha-particle momenta and energies recommended by Wapstra [3]. The energies have been calculated for Wapstra's Bp values by using the expression

E

= a(Bp )2

+ b(Bp) 4 + C(Bp)6 8-2

NUCLEAR CONSTANTS AND CALIBRATIONS

8-3

where a, b, and care [1] a

48225.33 X 10- 12 keY (G-cm)-2

=

b = -311.98 X 10- 24 keY (G-cm)-4 c = 4.04 X 10- 38 ke V (G-cm)-8 TABLE

8a-1.

ALPHA-PARTICLE CALIBRATION ENERGIES

Source

Bo ; G-cm

Energy, keY

P0210................ Bi 211 ................ P0211................ Bi 212(ThC ao) Bi 212(ThC a1)* . . . . " . Po212(ThC/) ......... Bi 214 ....... " .... " . P02U ................ P0215................ P0218................ P0218................ Rn 2u ............... Rn 220............ " . Rn 222............ " . Ra 223....... " ...... Ra 224 ....... " ...... Ra 228............... Th 227............... Th 228............... Th 230. " .... " ......

331,722 ± 15 370,720 ± 40 393,190 ± 50 354,326 ± 20 355,475 ± 20 427,060 ± 20 338,170 ± 70 399,488 ± 16 391,490 ± 40 375,050 ± 40 352,870 ± 70 376,160 ± 40 361,260 ± 60 337,410 ± 70 349,010 ± 50 343,450 ± 40 314,99.0 ± 80 354,070 ± 60 335,570 ± 60 311,960 ± 160

5304.5 ± 0.5 6621.9 ± 1.4 7448.1 ± 1.9 6049.6 ± 0.7 608S.9 ± 0.7 8785.0 ± 0.8 5510.9 ± 2.3 7688.4 ± 0.6 7383.9 ± 1.5 6777.3 ± 1.5 6000.1 ±2.4 6817.5 ± 1.5 6288.5 ± 2.1 5486.2 ± 2.3 5869.6 ± 1.7 5684.2 ± 1.3 4781.8 ± 2.4 6040.9 ± 2.0 5426.6 ± 2.0 4690.3 ± 4.8

*.......

• Intenaity ratio: ao/al= 2.57.

8a-4:. Gamma-ray Calibration Energies. Listed in Tables 8a-2 to 8a-4 are the weighted mean values of the energies of gamma rays frequently used as calibration standards [4]. (A more comprehensive list may be found in ref. 4.) Also, relative intensities are given for C058 since the gamma rays from this nucleus span such a wide energy range and are therefore of great value for both energy and efficiency calibrations. Gamma rays from both radioactive sources and nuclear reactions are given. 8a-6. Accelerator-energy Calibration Points. In order to know with precision the energy of the beam from an accelerator, unless an absolute instrument of some type is available, the beam-analyzing system must be calibrated against some accurately known energy points. One method frequently used to calibrate such analyzers is to measure a number of gamma-ray resonances and neutron thresholds to establish several points of the energy scale. Listed in Tables 8a-5 to 8a-7 are a number of energy points suitable for . calibration purposes. Only the weighted mean values are given; more complete details can be found elsewhere [5].

8-4

NUCLEAR PHYSICS TABLE

8a-2.

GAMMA RAYS FROM RADIOACTIVE SOURCES

Energy, keY

Source

moc 2 • • • • • Be 7...... Na 22.....

Na H . . . . . Cr 51..... Mn 54.... C060 ..... Zn 65..... yss ......

511.006 477.57 1274.55 { 1368.526 2753.92 320.080 834.81 { 1173.23 1332.49 1115.40 { 898.04 1836.13

± ± ± ± ± ±

±

± ± ± ± ±

Half life

0.002 0.05 0.04 0.044 0.12 0.013 0.03 0.04 0.04 0.12 0.04 0.04

TABLE

Energy, keY

733 . 79 787.92 846.76 977.47 1037.97 1175.26 1238.34 1360.35 1771.57 1964.88

15.0 h 27.8 d 314 d 5.26 Y 246 d

± 0.05

± 0.07 ± 0.13 ± 0.09 ± 0.09 ± 0.10 ± 0.45

8a-4.

Nucleus

8a-3.

Tpos ..... (ThC") .. Am 241 ....

{

GAMMA RAYS FROM

0.076 0.009 0.06 0.09 0.13 + 0.020 ± 0.023 ± 0.10 ± 0.010 ± 0.015

30 y 2.70 d

± ± ± ± ±

30 y (1.91y) 433 y

C0 56

Energy, keY

2015.49 2035.03 2113.00 2598.80 3009.99 3202 . 25 3253.82 3273.38 3452.18 3548. 11

± ± ± ±

±

± ± ± ± ±

Relati ve intensity

0.20 0.12 0.10 0.12 0.24 O. 19 0.15 0.18 0.22 O. 25

2.93 ± 0.16 7.33 ± 0.30 0.37 ± 0.08 16.77 ± 0.57 0.84 ± 0.16 3.15 ± 0.16 7.70 ± 0.34 1. 55 ± 0.11 0.88±0.10 0.18 ± 0.10

GAMMA RAYS FROM NUCLEAR Rj;~ACTIONS

)I-ray energy, ke V

F17.......... FIs .......... 0 17 • • • • • • • • • • BI2 .......... Bu ...... " .. NI4 .......... Be l o... " .... NI4 .......... Be lo...... " . CI2 ..........

Bi 207.....

661. 635 411. 795 (569.62 1063.44 1769.71 ( 510.723 583.139 2614.47 26. 348 59.543

106.6 d

0.1 ± 0.05 0.40 ± 0.11 100 1.52±0.16 13.02 ± 0.35 1.86 ± 0.23 69.35 ± 1.47 4.38 ± 0.16 15.30 ± 0.53 0.72 ± 0.08

± 0.13

CSI37..... Au I9s ....

Half life

I

Relative intensity

± O. 19 ± 0.15

TABLI~

53 d 2.60 y

Energy, keY

Source

495.33 658.75 870.81 953.10 1673.52 2312.68 2589.9 2792.68 3367.4 4439.0

± ± ± ±

±

0.10 0.7 a 0.22 0.60 0.60

± o.to± 0.25< ± 0.15 d ± 0.2" ± 0.2 1

Nucleus

CI3 ......... N14..... , ... 0 15......... NI5 ......... NI5 ......... 0 16......... Be I O •• , •• " • 0 16......... Pb 209........ N14..... , ... NI5 .........

)I-ray energy, ke V

4945.46 5104.87 5240.53 5268.9 5297.9 6129.3 6809.4 7117.02 7367.5 9173 10829.2

± ± ± ±

0.17" 0.18 0.52 0.2 ± 0.2 0 ±0.4 ± 0.4" ± 0.49

+

I"

±I

h

± 0.4"

I

From 1.70-1.04 MeV decay. b Doppler shifted unless formed in 014(~+)NH. c From 5.96-3.37 MeV decay (thermal neutron capture). d From 5.10-2.31 MeV decay. • From thermal neutron capture. / Doppler shifted unless formed in B12(~-)C12. g Doppler shifted unless formed in Olb(~-)N15 or by thermal neutron capture. h Calculated from C13(p,I')NH resonance energy (1747.6 ± 0.9 keV) and 1964 masses; value given for observation at 0 deg to beam direction. a

NUCLEAR CONSTANTS AND CALIBRATIONS TABLJo~

Reaction

r, keY

ER, keY

Flt(p,a"Y)016 . Flt(p,a"Y)016 . Al27(p,"Y)Si 28 . C13(p,"Y)Nu . 018(p,p)018.......• C12(V,p)C12 . II

8-5

PROTON RJo~SONANCJo; ENJo~RGlES

8a-5.

340.46 872.11 991. 90 1747.6 12714 14233

± 0.04 ± 0.20 ± 0.04 ± 0.9 ±8 ±8

2.4 4.7 0.10 0.077

0

± 0.2 ± 0.2 ± 0.02 ± 0.012

2.8

0.232

~

~

UJ ~

C")

W

58 59 60rn

60 61 62 62

63 64rn

28

Ni

Nickel

64 56

57

31 32

... 33 34

...

.......... 2+

71.3 d 100% 10.47 m

-66.189

5.26 y

-64.248 -66.811

-67.56

2+ 7

~-

5+ 7

~-

99m

.......... (H,2+) 1.55 m

35

-66.05

(4+,5+) 13.9 m

36

-66.41

(%-,i-)

...

37 28

29

.......... (4+) -64.5 -57.88

-60.23

(1+) 0+

3

2-

52 s 28 s ~

. ..

2.6

1.68

2.3 130

0.9 6 1.08

0.099

71

41

-72.28

(1-)

2.4 m

........... ...........

~2.61(80). 2.10(14).

2.61

0.512(13), 0.92(3), ' • ,

0.457

0.145(92). 0.193(8), 0.016(8), ' ..

.. . 31

Ga

Gallium

72

42

-73.14

0+

46.5 h

· . . . . . . . . . . ...........

63 64

32 33

-61. -63.26

(~-)

0+

33 a 2.6 m

........... ...........

........... ·

~0.296(90). 0.25(10)

~5.5

tt+

......... tt+2.89(33). 6.05(22).

7.08

. . . • t(2) 65 66

34 3.5

-67.27

........

.......... ........... P+2.12(53),2.03(10),

15.2 m

-68.39

0(+)

94h

·

. . . . . . . . . . ..........

3.26

2.24(7)•... , t(10) tt+4.153(5l), 0.94(3), . . . , t(42) t(100)

5.175

67

36

-71. 78

3

2-

78 h

+1.850

+022

68

37

-72.01

1+

68.3 m

±0.0117

±0.031

69 70

-74.420 -73.973 -75.294 -73.63

3

2-

60.~%

+2.016

+0.19

1+

3-

21.1 m 39.6% 14.1 h

..........

72

38 39 40 41

73

42

-74.87

(l-)

4.8 h

........... ...........

~1.19(85). 0.40(9).

74

43

-72.92

(3-)

7.9 m

........... ...........

~2.6(52).

5.5

75 76 77 78 65 66

44 45 46 47 33 34

1.9m 32 s ......... (3-) . . . . . . . . . . .......... 17 s ~4 s . . . . . . . . ....... ........ 1.5m -60. 2.4 h -66.15 0+

~3.3

3.3

67

35

-67.6

68 69

36 37

-71.60 -72.034

0+

70 71

38 39

-75.749 -75.044

0+

71

.,3

....

+2.562 -0.1322

1.00

tt+1.90(88),O.82(1). t(10)

2.92

....................

tJ-0.95(28),0.66(21). 0.64(15). 3.15(10).

1. 66 .

32

Ge

Germanium

-73.6

........

........ ........

~-

........... ........ .......... . ..........

-....

. .. . .

· .. ....

5.3, 2.2, •.•

........ e: ...... ~ . ..... . ........... tt+5.5, 3.8•... · . . . . . . . . . . ........... tt+1.3. 2.0••..• t

..........

19m

...........

.

275 d 39 h

........... · ..........

........... ...........

20.52% lid

~5.8,

tl+3.24(51). 1.6(12). 2.3(8)•...• t(6) t(100) tJ+ 1.21(32)•..•• t(63)

1.8

1.04(0.5),0.173(0.2)

. . . . . . . . .....

... .. .. ..

4.000

0.834(95), 2.201(29). 0.630(23), 2.508(14).

1. 55

0.296(87), 0.325(13), 0.742(7), ... 0.596(85), 2.35(49). 0.609(13), ... 0.58,0.36 1.12, 0.560•...

5

~7

tr.:l

~

"'3 ~

t:j

u:

o":::j

. ..

l.47(9), . . .

1.16(5)•... 4.3, . . .

"'j

::0

o

"'j

.................... ......... ..................... P-1.65(99.5), ...

+012 +0.59

0.9{)2(46).3.366(17). 0.809(14),0.919(8) • 2.375(8). ' .. 0.115(51)).0.061(15). 0.153(9).0.752(7), • , • 1.039(40).2.748(25). 0.828(6),2.190(6) •... 0.0933(70), 0.1845(2). 0.300(15),0.393(4), ... 1.078(3)•...

2: C

o

s::

C' t:j

rJ).

6.5 3.0

4.43

0.67(3), 1.72(2) 0.044(441.0.382(29), 0.109(17). 0.273(12). 0.338(10).0.065(8), . . . 0.167(90).0.915(10). 1.48(9)•...

~.7

2.227

.......... .......... .................... ......... +0.546 · . . . . . . . . . . t(I00) 0.235

1.107(26).0.574(12). 0.872(9), ... . ...................

0.28

cr ~

ec

TABLE (1)

(2)

(3)

(4)

(5)

Name

Mass number

ber of neutrons N

Num-

Atomic Symnumber

Z

hoi

A

--32

-Ge

Germanium

72 73m

8b-1.

PROPERTIES OF NUCLIDES

(6)

(7)

(8)

Mass excess. amu X 10- 3

Spin and parity

% abundance or half life

cr

(Continued)

~

(9)

(10)

(11)

(12)

(13)

(14)

Magnetic moment. nuclear rnagnetons

Quadrupole moment. barns

Mode of decay. energy. and intensity. MeV (%)

13-decay Qvalues, MeV

Energy and intensity 01 ")'-ray transitions. MeV (%)

2.200-m/s neutronabsorption cross section, barns

---- - - 0+ (~-)

27.43% 0.53 s.

.......... · . . . . . . . . . . .................... ......... . . . . . . . . . . . . . . . . . . . . . 0.98 ........... . .......... . ................... ......... ITO.OG33(99). 0.0670(1).

!+ 0+ . . . . . . . . . . (~+) -77.12~(-)

7.76% 36.54% 46 s 83 m

.................... ......... . .................... 14 ........... ........... .................... . . . . . . . . . ..................... 0.45 ........... ........... .................... . ........ ITO.l3311(0) ........... ~1.I9(87). 0.919(11). 1. 189 0.2646(11).0.199(1)• . . . ±0.51

40

-77.918

...

.........

41 42

-76.536-78.821

o

0.0135(99) 73 74 75m 75 76 77m 77

... 43 44

... 45

-78595 0+ ......... - .. (~)-76.39

(~+)

-0.8792

-0.28

... 7.76% 53 s

........... . ..........

~2.90(52)•..•

II.3 h

........... ...........

(:J

3il

As

Arsenic

46 47 35 36 37

-77.0

-69.07

4(+)

7I

38 39

-72.89 -73.24

(~)2-

72

73 74m

40

...

0+

. ........ ITO.159(26). 0.215(22).

...

2.76

-76.17

(!-)

.......... (5)

52 m

64 h

........... ...........

26 h

........... ........... tt+2.50(60).3.34(18).

4.357

0.834(78). 2.201(20). 2.508(10).0.630(8) • . . .

76 d

...........

1.87(5) • (10) .(100) ...........

0.341

0.0533(99). 0.0135(99). 0.0670(1)

...........

........... . ................... ......... ITO.283(100)

8s

........... . .......... · . . . . .. . . . . ·.......... ...........

0.263(50).0.210(32), 0.215(28). 00417(25). 0.558(18) • . . . 0.278(100)

........... ........... ........... . .......... ...........

1.5h

.......... 50 s . . . . . . . . ........ ~7m -67.77 ........ 15 rn 74.5

(:J0.70(100) (:J

Li t"'

tr:l

,, 7S 79 68 69 70

Z

(1

0.98 4.3

fJ+ 13+2.9•• 13+2.144(74). 1.44(10). 2.89(6) ••(10)

3.9 6.22

e(66). tt+0.812(33)• . . .

2.009

....................... 0.23 0.23 1.040(80). 0.668(26). 0.595(24). 0.760(24). 1.I4(24).1.708(23) • . . . 0.175(99\ I.IO(3) •..•

>~ ~

::t:

~

'(J2 ~

(1 '(J2

74

41

-76.069

2-

17.7 d

...........

...........

e(33), p+0.91(28),

2.56

0.596(58),0.635(16), ••.

1.51(4), tr1.36(19),

0.72(16)

~(-)

75 76

42 43

-78.400 -77.602

77 78

44 45

-79.35 -78.1

"2-

79

46

-79.1

2-

100% 26.4 h

+1.439 -0.905

+0.29 ±7

1.354

.................... ......... ..................... tr2.97(52), 2.41(29),

2.972

(2-)

38.8 h 1.5h

........... ........... ........... ...........

1.76(10), ..• trO.686(97), •.• tr4. l( 25), 1.4(25), •..

0.686 4.1

(!)-

9.0m

........... ...........

tr2.14(95), 1.70(2),

2.24

3

4.3

0.5593(41), 0.657(6), 1.216(5), ... 0.239(2), ... 0.641(56), 0.695(21), 1.310(14), .•• 0.36(2), 0.43(2), •.•

1.80(1.5), 1.25(1.5),

34

Se

Selenium

...

80

47

-77.0

1+

155

........... ...........

81 82 83 84 85 70

48 49 50 51 52 36

-77.9

(~-)

325 155 14.5 65 2.15 39 m

........... ........... ........... ...........

tr3.8(100) tr ........... ........... tr ........... ........... tr ........... ........... tr, n

........... ...........

e:

71 72

37 38

-68. -73.

........... ...........

p+3.4

...........

.......... -

........... ........... P+4.1(60), .•.

...........

2: d

o

~

........... .................... .........

........... ........... ........... +2.05 +1.643

0.221(25), 0.568(21), 1.533(11), 0.498(11), 1.472(10),0.904(7), .•. 0.120(65),0.536(48), 1.11(48), . . . 0.108(65), 0.509(25) 0.14(50), ..•

t(76), tJ+O.80(l1), 1.67(10) p-0.8!l(3)

4.17 1.0

0.7768(13), 1.38i(1), . . . 0.52l(46),0.530(30\••.. ......... ITO.464(52),O.216(48) • 0.250(48) 2.680 0.883(73\ •..• 0.886

toe ::I: ~

if!. ~

o

tn

48

-88.200

5

86

49

-88.822

2-

87

50

-90.814

3

88

51

-88.7

2-

85 86m

89

2-

... .......... ........

52

-87.72

2-

........

72.15% 1.02 m 18.66 d 5 X 1010 y 27.85% 17.8 m 15.4 m

+1.3524 .................... ......... ..................... +0.26 ........... ........... .................... ......... ITO.56(loo) -1.691 ........... tr1.78(91),0.70(9) 1.078(9) 1. 78 +2.7500 ±0.51

+0.12

...........

........... ...........

•(0.005) trO.274(100)

0.52 0.274

tr5.2(76), 2.5(14),

5.2

3.4(4), ... tr1.26(38), 2.21(32),

4.49

4.49(18), 1.92(4), ...

90 90

38

Sr

Strontium

91 92 93 94 95 96 97 80 81 82 83

..

,

53

54 55 56 57 58 59 60 42 43 44 45

.......... ........ -8!i.2 -84. -81. -78.

.......... .......... .......... ..........

.......... -77. -81. -82.3

(2-)

85m

85 86 87m

87 88 89 90 91

46

-86.570

........ 573

........

4.43 ........ 5.93 ........ 2.73 ........ 0.363 ........ 0.233 .......... 0.143 1.7h 0+ ........ 29m 25 d 0+ 33 h i+

.. ,

..........

47 48

-87.06 -90.724 .......... -91.108 -94.372 -92.53 -92.25 -89.84

...

49 50 51 52 53

0+ (!-)

(!+) 0+

!-

!+ 0+

~+ 0+

~+

1.0

1.863(21), 0.898(13), 2.68(2), ... 1.03(60), 1.25(47), 2.19(17),2.57(12), 0.659(10), 0.949(10),

...

4.3m 2.6m

........... ...........

tr6.6, 5.8, 4.4, 2.2, •..

........... ........... tr4.6 ........... ........... tr ........... ........... tr, n ........... ........... tr, n ........... ........... tr, n ........... ........... (J, n ........... ........... tr,n ........... ........... .(100) ........... ........... fJ+ ........... ........... .(100) ........... ........... .(SO),fJ+1.l5(11),

6.6

I"d

0.83(61), 4.34(18), 3.34(15), ..•

~

o

I"d l".:l

5.7 ~7.9

~

~7

8

I-l

t.%J rJ:i:

o

I:I=J

. ........ 0.58

Z d

~4

o

~0.6

2.21

0.81(7), ..• 8'

.....................

0.45

t'f

0.763(43),0.385(35), 0.040(23), ...

.....................

I-l

t::1

0.56% 70m

........... ........... .................... .........

64 d 9.86% 2.83 h 7.02% 82.56% 52 d 28.1 y 9.67 h

........... ........... .(100) 1.11 ........... ........... .................... . ......... ..................... 0.8

. .......... ...........

. ...........

...........

-1.093

+0.3

.(14)

.(1)

.........

.........

ITO.007(85),0.231(85), 0.150(14),0.237(1) 0.514(100)

t.%J

tn

ITO.388(99)

............. ........... ..................... ......... ..................... ........... ........... tr1.46(99.9), .•• 1.463 0.91(0.01) ............ ............ trO.546(loo) ..................... 0.546 ........... ............ tr1.09(33), 1.36(29), 1.025(30),0.748(27), 2.67 2.67(26), 0.62(7), 2.04(4)

0.88

0.645(15), 1.413(5), 0.93(3)

0.005 0.5 0.9

:c ~

TABLE (1)

(2)

(3)

(4)

(5)

8b-1.

PROPlmTIES OF NUCLIDES

(7)

(6)

(8)

(9)

(Continued)

(10)

(11)

(12)

(13)

(14)

Energy and intensity of ")'-ray transitions, MeV (%)

2,200-m/s neutronabsorption cross section, barns

t

~

Num-

Atomic number

Z

--38

Symhoi

Name

Mass number

A

Mo:.ss

ber of neutrons N

excess, amu X 10-'

Spin and parity

-- --- --Sr

Strontium

% abundance or half life

92 93

54 55

-89.0 -85.8

0+

2.71 h

94 95 96 97 82 83 84

56 57 58 59 43 44 45

-84.6 -81.

0+

1.3m 26 s 4.0 s

. . . . . . . 8m

Magnetic moment, nuclear magnetons

Quadrupole moment, barns

Mode of decay, energy, and intensity, MeV (%)

. . .. .. .. ... ....... trO.55(90), 1.5(10) ........... . . . . . . . . . . . tr2.9(65), 2.6(25).

~-decay

Q values,

MeV

1.9 4.3

1.37(90),0.44(4),0.23(3) 0.60, 0.8, 1.2, •••

3.5

1.42(100)

3.9(14), ••.

39

Y

Yttrium

85m

...

........ .......... ........ .......... .......... ~O.4s .......... ........ Short -78. ........ 7.5 m ........ 41 m -79.11

.......... .. ........ ........... . ..........

........... ........... ........... ...........

tr2.1

tr tr

~5.7

Z

tr

d

(1

to"

........... ...........

e, (t+3.5, 2.9

. . . . . . . . . . (~-)

2.8 h

........... ........... (t+1.54(50), 1.1, .•• ,

(~+)

4.9 h

........... ...........

0.795(100), 0.982(100), 1.041(50), •.. ......... 0.92(9),0.503,0.70,0.77 6.3

.(45) 85

46

-83.56

0.231(13),2.16(9). 0.77(8), ..• ........... ........... .................... ......... iTO.I02(loo),0.208(100) 1.077(82), 0.63(37), 5.27 ........... ........... E(73), (t+1.2(1l), .•• 1.16(35). 0.778(21), ••• ........... ........... (t+(5) ......... ITO.381(99) 0.483, 0.388 1.9 ........... ........... E(99.7), (t+0.7(0.3) 3.621 1.836(100), 0.898(91) ........... ........... e(99.8), (t+0.76(0.2) ........... ........... .................... ......... ITO.91(loo) 0.001 -0.1373 ........... .................... ......... ......... 110.202(99.6), 0.483 ........... ........... tr(0.4) (99.6) 1.75(0.2) -1.63 -0.15 tr2.27(99.8), .•• 2.27 1.4 ........... ........... .................... ......... ITO.551(100) 1.21(0.3) 1.545 ±0.164 ........... tr1.545(99.7), .•• 0.934(14), 1.40(5)•••. 3.63 ........... ........... tr3.63(86), ..• 0.267(6),0.94(2), 2.89 ........... ........... tr2.89(90), •.. 1.90(2), . . . 5.0 0.92(43),0.56(6)•••• ...................... tr5. 0(50), .•. (t+2.24(55), 2.1(10),

3.26

1.1(4), . . . , E(30)

86m

86 87m

87 88 89m

89 90m

90 91m

91 92 93 94

... 47

. . 48 49

.

. . . . . . . . . 5-

-85.05 .

'

....... (~+)

-89.09

(~-)

~90.49

(4-)

-94.133

.)-

~+

'"

50

... 51 '"

4-

1

.......... (7+) -92.84 -

2-

. . . . . . . . . ~+

52 53 54

-92.71 -91.07 -90.45

55

-88.3

1

2-

2(~-)

........

48 m 14.6 h 14 h 80 h 108 d 16 s 100% 3.1 h 64.2 h 50 m 58.8 d 3.53 h 10.2 h 20.3 m

•

•••••••••••

4

••••••••

t.'::l

>

~

~

~ 10-04

(1

U'l

95

56

-87.2

(1-)

10.7 m

........... ...........

~U3(82). 1.31(5),

4.43

0.86(4), •••

40

Zr

Zirconium

96 97 99 81 82

83 84 85 85 86

57 58 60 41 42 43

44 45 45 46 47 48

87 88 89m 89

...

90m

...

to 91 92 93

"

95

96 97

49

50 51 52 53 54 55 56 57

2.3 m l.11s -o.8s -10m 9.5m 5-10 m 16 m 15m 1.4 h 16.5 b

........... ........... ........... ............ ........... ...........

~3.5

........... ........... ........... ........... ........... ...........

e, fJ+ e, fJ+

1.6b 85 d 4.l8'm 78.4 b 0.81s

........... ...........

fJ+2.10(83), e(17)

0+ i+ 0+ i+ 0+ i+

51.46'k 11.23% 17.11% 1.5 X 10'y

........... ........... -1.303 ........... ........... ........... ........... ............. ........... ........... ........... ...........

0+

2.10%

........... ........... .................... ......... .. ..................

17.0 h

........... ...........

........ .......... .......... ..........

-84.

-82.

.......... ........ .......... 0+

.......... ........ .......... 0+ .......... ........ ........ -78. -84.

0+

-85.33 -90.8

0+

........

.......... (!-) -91.091

(t+)

.......... 5-95.300 -94.358 -94.961 -93.552 -93.680 -91.965 -91.718 -89.03

0.953,2.175,1.323,2.631, 3.576, .•• e.7. 1.0, 1.5, •••

........

17.~0%

65 d

-7 --6

~ ~

......... -5 -1

e(loo)

...........

0.243(96), 0.028(20), 0.612(5)

3.50 -0.7

........... ........... e(loo)

........... ........... ........... ...........

0.04

e(5), fJ+0.89(1), ••• e(78), fJ+0.9O(22)

........... ....................

.................... ......... . ................... .................... ......... ..................... ..................... ......... ..................... ..................... 0.063 ~0.060(95), . . . .................... ......... ..................... ~

~0.362(55). 0.399(43).

1.121

0.88(1)• . . .

~

2.67

0.743(95), 0.508(5)

41

Nb

Niobium

98 99 100 101 88 89m 89

58 59 60 61 47

... 48

-87.25 -84. -83. -78. -82.

.......... ........... ........... ........... ........... ........... ........... ........... ........... ...........

~2.1

..........

(~-)

42m 1.9h 20 s 14.6 h

........... ...........

p+3.1, e

62 d Long 10.16 d

........... ........... e(3) ........... . . . . . . . . . . . .no» .. ........ . . . . . . .. ., e(99.9). fJ+

-86.9

(l+) .......... (4)-88.74 (8+)

OOm 90

.. ,

91m 91 92m

.. ,

.......... (-~-)

50 .. ,

-93:00

49

(~+) .......... 2+

2.2 -4.5 -3 -6.5

~

tr ~ fJ+3.~,

0.05 1.0 0.15

0.47,0.63,1.1,2.19,1.60,

I' I'

0.307(91),0.545(8),

q

~4.5

• • • • • • • • • •. .•••••.••••

1.63

o

0.778(100),0.851(100;, 0.81(84), 1.12(16), 0.32(5) ITO.0965(100)

1'1.32(90),1.07(10) 1'4.4 1'2.2

. .. . .. .. . ..

~

2,200-m/s neutronb ti a sorp I?n cross section, barns

~0.3

.. +5.68

(14)

~-decay Energy and intensity Q va1 ft iti ues, 0 ,-ray ransi IOns, MeV MeV (%)

~ "'d

:::r: ~

U1 1-4

o

U1

105

57 1-91.

106 107 108 109 110

58 59 60 61 62

...

111m

111 112

63 64

113m

I Indium

1.32% 6.5 h 0.88% 453 d 12.39% 48.6 m

-93.537 -93.388 -95 811 -905050 -96.990

0+ i+ 0+

......

11 -2--

-95 814 -97.238

0+

24.070/"

11

0+

~+

~+

12.7~%

·.........

-2--

14y

-95.592 -96.637

~+ 0+

12.26% 21.H% 43 d

-0.74

+0.5

........... ........... -06144

+0.8

........... ........... --0.8270

+0.8

~1.69•.•.

.................... f(99.7), ~0.302(0.3)

.................... . ........

-1.11 -0 ..5943

-1.0

......... ..................... ......... IT? ........ ..................... .......... ....... ............ ......... ..................... ......... 0.935(2), 1.29(1)•... -0.6 tJ1.62(97). 0.68(1.6).

-0.8 -1.087 tJO.58(100) -0.6217 ........... ....................

53.5 h

-0.6477 ........... (Jl.l1(60J,O.58(31),

116

68 1-95.238

I 0+ 11

7.51% 3.4 h

.......... ........... .................... ........... · . . . . . . . . . . tJO.67. 0.41

117

69 1-92.76

I ~+

118

70

-93.08

0+

...

lIn 121 106

71 73 57

107

58

108m 108 100m2 109ml 109

I

... 59 ...

I

...

60

12,4 h

... ... . . .. -1.040

-86.30 -89.6

........

32 m

...........

3n ill 56m

. .......... ...........

0.21 s 1.3m 4.3 h

.......... ... .... ...

1~90:3""1 ~~.;t) 1 .......... 1

(_>:1..+)

........

(2-\

-92.88

~+

+5.53

10.06 20.000 0.34

........... tJ ........... tJ3.5 · . . . . . . . . . . s-s.s ........... e: ........... p+4.89.2.7

"'d

~

0

"'d

US

2.52

1.2l(l1), 0.880(10). 1.433(10),1.408(8)•... I 0.273(31), 1.303(19). 0.34.)(18), 1.577(17). 0.314(16),0.897(7\, ...

--0.8

.........

tr.j ~

0.336(95). 0.526(26), 0.492(10), •..

......... ..................... ......... 0.27~(18). 1.998(15).

I...........I.. ...... ..I tJO.65, 0.79; 2.23••.. I

........ ........ 10m ........ 138 ........ 5.3 m

.. .. .. . -90.4 ·........ ·

0.1

..

.. .

........... . .......... ........... . .......... . ..........

.50m 2.7 m

.....................

........... ........... ....................

I !+ -2--

O.088 CiOO) ............\ ~~

.................... . ........ ITO.150.0.247

67 1-94 ..57

..........

0.182

........... ........... ....................

115

11 .......... -2'--

0.31.0.34.0.35,0.43,0.61, 1.9,2.0.2.3 ......... ..................... 11.0 0.093(100). . . . 1.417

--2.8

«io»

6.5 66

119m

I In

55m

113 114 115m

117m

49

Ii

0.8?

3.5

0.077

0-3 .... tr.J

W

0

"2j

Z L1 0

....to"

t1

tr.j

W

0.53. 0.63, 0.86, 1.66. 0.99, ... 0.22(46\,0.32,0.73.0.84. 3.5 ........... P+2.2• • • . • e 0.94. 1.05. 1.2.5, .. 0.383. 0.633, 0.842 5.15 · . . . . . . . . . . P+3.50. 2.66, 2.28. e 0.633,0.842,0.872.0.243. 5.11 · . . . . . . . . . . P+1.29. f 0.150•.. ........... .................... . ........ ITO.68(lOO), 1.44(80) . . . . . . . . . .................... . ........ ITO.658(l00\ 0.205, 0.28, 0.35. 0.65. 2.02 f(94). ~0.79(6) +0.86 0.91 6.7

00

I

Co...:> ~

TABLE (1)

(2)

Atomic Symnumber

hoi

Z

(3)

(4)

Name

Mass number A

--In

49

Indium

110m 110 111m

111 112m 112

Number of neu-

trons N

63

PROPERTIES OF NUCLIDES

(Continued)

114

'"

64

... 65

(9)

(10)

(11)

(12)

(13)

(14)

Mass excess. amu X lO- a

Spin and parity

% abundance or half life

Magnetic moment. nuclear magnetons

Quadrupole moment. barns

Mode of decay. energy. and intensity. MeV (%)

tI-decay

Q values.

Energy and intensity of -y-ray transitions. MeV (%)

2.200-m/s neutronabsorption cross Set tion, barns

+10.4 or -10.7 +4.36

-0.21 or +0.22 +036

-92.77

7(+)

4.9 h

2+

67 m 7.3 m 2.81 d 20.7 m 14 m

.........

........

-94.93

9

. ..

.. ...

-94.46

24 4+

1+

......

e,

tr?

P+2.20(71). . . . • (29)

1 . . . . . . . . . . 2-

-95.91

........

!+ 5+

-95.10

1+

..........

1 2

-96.13

~+

100 m 4.28% 50.0 d 72 s

116m2 116mJ

... 66

...

...

-

.......... . ....... .......... 5+

4.50 h 6 X 1014 y 95.72% 2.16 s 54.0m

MeV

. ....... 3.93

+5.53

.....

+0.85 - ...........

+2.81

+0.089

.(00)

-0.210 +5.523 +4.7

~0.66(44)

........

0.658(99)• . . .

........... +0.83

~O.83(5)

~0.49(100)

i

...

118 119m

... ..........

'"

68

...

69

-94.74

14 s .......... 1. 93 h -95.47 44 m !+ .......... .......... 8.5 s .......... (4.5+) 4.4 m 1+

1.986 1.44

!-

-93.9

1+

(~-) 2"

5s 18 m

........... ...........

~3.3(99)• . . .

3.27

t."'.1

10.7

>~ ~

~

0.724(3.5).0.556(3.5) 1.30(0.2)

~ H

. ........ ITO.335(95) 0.49 .....................

. .......... ........... .................... . ........ ........... P-1.00(49).0.87(40). . ........ +4.3

........... ........... -0.2515 . .......... ........... ........... . .......... ........... . .......... ...........

t'1

0.617(6) . . . . . . . . . ITO.393(100)

ITO.164(1001 1.293(80). 1.09(53)• 0.417(36).2.ll1(20). 0.819(17). 1.508(11). "

67

Q

0.66 2.59

0.60(11) ••.•

116 117m 117 118m2 118m

zq

0.247(94).0.173(89)• . . . TTO.156(100)

.................... +0.82 ..................... ......... ..................... . .......... e«0.02) . ........ ITO.1916(96.5).

........... ........... P-1.986(98), . . . -0.244 5.534

0.83

.................... . .......

~

0:>

0.66.0.91

... . . . . . . . . . . . .................... . ........ ITO.S39

• (2). P+O.4(O.OO4) 115m 115

I

(8)

.(34). tI+1.56(21) 113m 113 114m

00

(7)

----... .......... ... ... ... ...

8b-1.

(6)

(5)

.

1.293(1)• . . . ~1.77(37). 1.62(16) . ........ ITO.314(47).0.158(16) ~0.74(100) 1.47 0.56(100). 0.158(100) ~1.8(1) . ........ ITO. 138(99) ~1.3(53). 2.0(32)••.. ......... 1.23(97). 1.05(80)• 0.69(41) • . . . ........... P-4.2(8O). 3.0(16) •.•. 4.2 1.23(15) ........... ~2.7•...• (95) . . . . . • . .. 0.023. 0.91. ITO.30(5)

Q

W 198

119 120m? 120

.50

Sn

Tin

121 121 122 123 124 108 109,']i 109

70 '"

71

113m

117m

119m

119 120

'"

63 64 65 66 '"

121m

121 122 123m

123 124 125m

67 68 '

..........

........

-92.13 -92.24

62

11'1 118

-92.

2.4 m 3.29 469

60 61

'"

113 114 115 116

(1H (4,5+)

59

72 73 74 75 58

112

(~+)

.........

3.1 m 309 ........ 89 ........ 36 s ........ 4s 9m 0+ .......... .......... 1.5m -8.9 ........ 18.1 m

'"

110 111

-94.2

..

-92.1 -89. -89. -86.8 -88.

...... ,.

0+

........

-95.17

0+

-10 5

........... ........... . ......... ...........

-94.26 -94.717

11

-2--

0+

· . . . . . . . . . (~-+)

12.5

75

-92.21

126 127

76

-92.34 ·

. . . . . . . . . ........

4m

y

0.82(95).0.73(5) 1.17(-15) 1.171(100).1.02(61) 1.28(14);0.090(12). 0.71(12).0.94(12) •..•

~3.7

~ ~5 ~4..t ~5

3.4 .....,7 4.4 7.4

0.59 2.52

0.94 0.99.1.14 1.13, 0.99, 3.21 0.28,0.42 IT 1.12(50),0.65(44). 0.33(26), 1.55(18), . . . 0.283(95) 1.14(2). 0.75(1). 1.89(1),

'"d

~

o

'"d

...

........... ........... .................... ......... . .................... · . . . . . . . . . . , .......... t(9) . ........ ITO.079(9l) ±0.88 ........... f(100) 0.76 0.393(100), 0.255(1)

11 -2--

i+ 0+

5.6

-4

........... ........... . .......... , ..........

.......... (~+ )

...

........... tJ+ ........... f (80). tJ+1.52(20)

24.03% -250 d 8.58% 32.85% 76 y 27 h 4.'12% 40m 129 d 5.94% 9.7 m 9.6 d

-95.762 -96.549

~2.2(4l). 3.1(27),

.......... ........... f . .......... ........... t(70), tJ+1.51(30)

4.0 h 35 m

2.35

.........

-2

0+

11 .......... -r-

~1.6(100) ~-5.6(-85)

........... f

'1~61%

8 d

-95.574 -96.688

l+ 0+

6."% 11.'fl% l09d

. . . . . . . . . . (J:l--)

75

-94.79

(~-+)

9.3 h

76

-95.532

0+

31.79%

'"

........... ........... «io» 0.1>73(80),0.508(18), . . . -1. ........... ........... .................... ......... . . . . . . . . . . . . . . . . . . . . . 3.1 ........ . .......... . ................... . . . .. .. ITO.088(100), 0.159(100) -0.7359 . . . . . . . . . . . .(100) 0.06 . .................... 140 ........... ........... .................... · . . . . . . . . . . . .......... .................... -0.8871 ........... .................... · . . . . . . . . . . ........... .................... ........... . .......... P-(1) ........... ........... P-0.69(W.7), . . .

......... .. . . . . . ......... ......... . ....... .

0.69

..................... ITO.I094-(1oo), 0.031>5(100)

..................... .....................

34 d

........... ........... .................... . ........ ..................... . .......... ........... 8-1.60(30), 0.91(6), . ........ ITO.1056(64), 0.696(6),

.. .

0.22

0.730, . . . 0.027(19), 0.460(15), 1.08(2), . . .

129

77

-93.40

i+

69 m

........... ...........

130

78

-93.768

0+

It.ta%

........... ........... .................... ..... ... .....................

1.48

1.56 1.02

ITO.0887(lOO) 0.417(0.3), . . .

.......... J,!1.._

P-1.45(89), 1.00(9), 0.37(1), ...

68

0.22

~

""d

p:: ~

u:

'"'"

(1

tn

131m

I

Iodine

..........

J 1.2

30 h

........... ........... .......... -

,a-0.42(43), 0.57(311, 0.22(4),2.46(4), . . .

131

79

-91.45

~+

25 m

...........

13~

80

-91.46

0+

78 h

........... ...........

11-0.22(100)

..........

(Jl--)

Mm

........... ...........

11-1.3, 2.4(87)

133m

53

- ..

...

133

81

-8g.0

(!+)

12.5 m

...........

134

82

-89.

0+

42 ru

...........

135 136 115 116 117 118m

83 84 62 63 64

...

........

2g s

0+

~33s

-S3. -84. -86.8

........ ........ ........

..........

.

1.3m

~

"'d

::t: ~

tn

~

o u:

117 118 119 120 121 122 123

12. 125m

68

-80. -84. -84.8 -88. -88.5 -91.

69

-91.6

70

-93.9

63

64 65 66

67

...

........ 0+

........

0+

........

0+

........ 0+

.......... e,}--)

125

71

-9a.5

(!+)

126

72

-95.71

0+

127m

...

..........

~

Iod

~ ~

tr:

.....

D

rIl

60

Nd

Neodymium

142

83

-89.91

2-

19.2 h

143 144

84 85

-89.14 -86.65

i+ 0-

13.6 d 17.3 m

145

86

-85.45

(i+)

146

87

-82.5

147

88

-81.0

148 149 135 136 138 139m

89 90 75 76 78

-78. -76.6

139 140 141m 141 1'2 1'3 1'4

... 79 80 '"

81 82 83 84

2.16

1.57(4)

18

0.931 2.996

. ....................

89

0.696(1),2.186(0.7), ...

5.98 h

tr2.16(96),O.59(4), e(O.OI) ........... ........... trO.931 ........... ........... tr2.996(98), 2.296(1), 0.806(1), ... ........... ........... tr1.805(98), ...

1.805

0.674(0.5), 0.749(0.4),

(3)-

24.2 m

........... ...........

trl.1(40),2.1(29), 3.6(11), ..•

4.08

........

12m

........... ...........

tr2.10(45), 1.45(35),

2.0m 2.3 m 12 m 55 m 5.2 h 5h

........... ........... tr4.2

........ ........ .......... ........ .......... 0+

-88.

0+

.......... . .......

-ss. -90.4

........ 0+

.......... -90.36 -92.23 -90.14 -89.87

!+ 0+

7

145 1'6 147

85 86 87

-87.39 -86.85 -83.87

U8 149

88 89

-83.07 -79.85

7

'Z-

0+ 'Z-

0+ 5

2-

0+ 5

2-

30m 3.3 d 63 s 2.5 h 27.11% 12.17% 2.1 X 1015 y 23.85% 8.30% 17.22% 11.06 d

5.73% l.72h

±0.25

±0.03

...

........... ........... s-s.o ........... ........... (J+ ........... ........... [J+1.32, 2.97, 6 ........... ........... e, [J+1.0 ........... ........... e, fJ+3.1

90 91

-79.09 -76.11

0+

........

5.62% 12 m

"'t1 ~

o

"0

t-1 ~

8t-< l".1

.........

0.73, 0.114, 0.983, 0.327, 1.03, 0.90, ... , ITO.23 ........... ........... [J+, e ......... 0.41 ........... ........... e(100) 0.47 . .......... ........... .................... ......... ITO.755(100) ........... ........... e(97), [J+0.79(3) 1.14(2), 1.30(1), ... 1.80

.................... . ........ ..................... -0.48 -1.08 ................... ......... ..................... ........... ........... a1.83 . ........ ..................... ........... ...........

U2

o

"".f

Z

18.8 32.0 4.0

q

o

et-< t:'

t:':1

-0.66

-0.25

.................... ......... ..................... ......... .....................

........... ........... .................... ±0.59

...........

...........

trO.807(81), 0.365(16), 0.21(2), 0.408(1), . . .

0.898

1.67

48 1.4

U2

0.0911(27),0.531(13), 0.440(1),0.275(1), ...

........... .................... . ........ .....................

........... ........... tr1.42(38), 1.02(30),

1.13(26), 1.55(6), . . .

150 151

. ..

0.454(49), 1.526(18), 0.736(8),0.790(8), 1.378(6), ... 2.7 0.565(29), 0.645(16), 1.26(11),0.61, 1.18, 0.078, ... ~5 0.31 0.11,0.14,0.17,0.30,0.74 3.0 ......... 0.21,0.44 ......... 0.109, 0.553, 0.540, 0.576

2.5

0.210(27), 0.27(26), 0.114(18),0.541(10), 0.424(9), 0.654(9), ...

........... ........... .................... ......... ..................... ........... ........... s-s.i, 1.8, 1.6, 1.2 2.46 0.118(40),0.174(10), 1.180(9),0.138(6), 0.086(5).0.737(5), .••

1,3

!

~

8b-1.

TABLE (I)

Atomic number Z

(2)

Sym-

hoI

(3)

(4)

Name

Mass number

A

(5) Number of neu-

trons

N

-61

(6)

(7)

(8)

Mass excess, amu

Spin and parity

% abundance

or hall life

X 10-3

(9)

(10)

Magnetic moment, nuclear magnetons

Quadrupole moment, barns

c;o

(Continued)

PROPERTIES OF NUCLIDJ ~

~ ;3 .....

Q U2

62

Sm

Samarium

]40 ]41

78 79

-82.

.......... ........ ........

14m 23 m

........... ......... . ........... ...........

tr e, tr

142 143m 143

80

-84.9

0+

f(94), tr1.03(6)

..........

3.48(0.003) a3.37 a2.87 ,(98), tJ+0.85(2), . . .

~2.0

3.0 0.8 ~2.1

2.10

........... ........... ,(100) 1.36 ........... ........... .................... . . . . . . . . . ........... · . .. ..... t(100) 0.365 ........... · - ........ .................... ........ -0.46 +2.3 .................... ........ ........ .......... .................... ......... +0.64 +2.5 .................... ......... ........... .. ........ . - ................. -to:: . .......... ........... .................... . .......... ........... (J-0.89(2), 1.0(0';,) . .... ±0.50 ......... , . tJ-1.3\8::l), 1.2(15), 1.30 0.3(1), . . .

t-3 .... tT.j

0.39 0.145 0.257 0.081, 0.100, 0.255, . . .

U1

o

~

Z d o

0.227(68), 0.664(3), 1.090(3), 1.000(3), 0.905(2), . . .

....t;jrtT.j U1

0.326(91\• . . .

. ....................

96

0.058(4), . . .

. ...................

..................... . .................... ..................... . .................... IT ITO.108(97),0..514(2\,... O.09fi(4), . . .

55 585 200 140

2,600

cr

Ql Ql

TABLE (1)

(2)

Atomic number

Sym-

(3)

(4)

(5)

M_

ber of

Num-

Z

hoi

Name

number

neu-

A

trona N

67

PROPERTIES OF NUCLIDES

(6)

(7)

(8)

(9)

Ma!lS excess. amu X 10- 1

Spin alld parity

% IIbutldance

Magnetic moment. nuclear

or half life

magnetons

(Continued)

(10)

(11)

(12)

(13)

(14)

Quadrupole moment. barns

Mode of decay. energy. and intensity. MtV (%)

~-d('(;ay

Energy and intensity of 'Y ray transitions. MeV (o/c)

2,200-m/s neutronabsorption crosssection, barn.

Q values, MeV

cr C,)l

~

-----

--66

8b-1.

Dy Ho

Dysprosium Holmium

-67,17

85 86

........ .......... ........ ........ -68. ........ -68 .• ........ -69.60 ........

87 88

-69.35 -71.

1 "2"

81.5 h 4 .• m -20s 42 s 36 s 52 s 2.4m 9m 12 m 50m

89

-70.

1

55m

166 167 150 151 151 152 152 153 154 155

100 101 83

156

... 84

...

0+

.......... ........

-66.

5

........... . .......... . .......... ........... ........... ........... ........... . .......... ...........

........... ...........

~2.1.~

6.4 4.3 5.8 -3

........... ...........

e, tJ+1.8O, 1.3. 2.9

-5

........... ~0.40(92). 0.48(5) •... 0.482 ........... ~ . .......... e, tJ+ -7

0.082(12)• . . .

...........

e, ~. a4.60(30) e, tJ+. a4.5l(20) . .......... e, ~. 0:4.45(19) ........... ~,~. a4.38(30) ........... e, fJ+, a3.95(0.1) ........... ~.~. a3.91

...........

Z d

-5

o

~

t".:1 0.335 0.092.0.138,0.117.0.209, 0.243. 0.326 0.138(100), 0.266(99). 0.367(23). 0.685. 0.89.

Loll, ... 157 158m

158

90

... 91

"2"

7

14 m

........... ...........

~.~

..........

2-

29 m

. .......... ...........

~1.32. ~

-71.29

5+

11m

........... ...........

~

7

"2"

6.9 s 33 m

........... ........... .................... . ........ ........... ........... -1.7

25+

5.0 h 2.6m

. .......... ...........

1+

6s 2.5 b

........... ...........

-72.

0.087.0.152.0.100.0.227, 0.71.1.20•... . ........ lTO.067, 0.098. 0.218• 0.32, . . . 3.98 0.098. 0.218. 0.320. 0.52.

-2.5

"

159m 159

160m 160

161m 161

'"

92

.......... -72.

....... .......... 93

'"

94

-71.64

.......... -72.15

l-

.

ITO.206(lOO) ~ 0.057, 0.080, 0.17, 0.25. 0.309• . . . ........... ~(34) . ........ ITO.06O(66) ........... ~(99.8). ~0.57(O.2)•... 2.92 0.729(50). 0.97(35)• 0.880(26). 0.65(20), 0.197(20).0.539(5) • . . . ........... .................... ......... ITO.211(100) ........... ~(10:l) 0.82 0.026(23). 0.075(15), 0.176(2).0.157(1)••••

>-

~

~

~

r:J) ~

o

r:J)

...

..........

164

97

61+ . . . . . . . . . . l+ 7 -71.23 ~.......... 6 -69.73 1

165

98

-69.64

162m

162 163m

163 164m

95 '"

96

...

-70.83

......... 11'0.0578, 0.383(63) E(37) 0.081(8) 2.16 ........... E(95), ~1.10, . . . ........... .................... ......... 11'0.30(100)

68m 15 m 1.1 8 33 y 38m 25m

........... ...........

100% 1.2 X 101 y

.................... ......... ..................... ......... 0.184(90),0.810(60), ........... ........... ,s--0.07, ...

........... ........... ........... ........... ...........

........... E

E(43) 166m

...

7

2-

.......... (7-)

+4.12

0.01

........... .................... . . . . . . . . . 11'0.046, 0.052, 0.037 0.091(5) 0.97 .......... ,s--0.9i(35). 0.88(22) 1.11

0.073(5)

+3.0

65

0.711(58),0.081(12), 0.412(12),0.532(12) •

.. . 166

99

-67.69

0-

26.7 h

........... ...........

167

100

-66.9

(~-)

3.1 h

........... ........... P-0.30(44),O.62(21),

3.3 m 4.6 m

........... .......... ........... ........... 8-1.20(75),1.95(25)

,s--1.84(52), 1.76(47),

1.84

0.C81(5),1.380(0.1), . . .

0.97

0.347(58), 0.079(14), 0.208(13),0.084(9), ... 0.85 0.065(60), 0.78(30), 0.075(18),0.850(13), 0.150(13), 0.760(11),

I'd ;:0

0.3i1(I), . . . 0.97(16),0.89(14), ... 168 169

101 102

-64.1 -63.1

(~-)

,s--2.2

2.8 2.2

o

I'd t.%J

;:0

1-3 ~ t.%J

m

...

~8

Er

Erbium

170 152 153 154 155 157 158

103 84 85 86 87 89 90

-60.5 -65. -65. -67. -66.6 -68.

........ 0+

........

........ 3

2"

458 118 36 s 4.5 m 5.3 m 24m

........... ........... ........... ........... ........... ...........

-70.

0+

2.3 h

..........

3

........... .......... . ......... ........... ........... ...........

,s--3.1 a4.80(90), E, ~ a4.67(75), E, 13 a4.15 a4.01

s», E

. .......... E.~1J.8

3.7

q

~2

o

~4 ~4

~1.5

2"

36 m

........... ........... "~

~3

160 161

92 93

-71. -70.

0+

29 h 3.1 h

........... ........... ........... ...........

---0.8 2.0

162 163

94 95

-71.17 -69.92

0+

0.136% 75 m

........... ........... .................... ......... .....................

1" 165

96 97

-70.76 -69.21

0+

5

5

~-

1.56% 103 h

+1.1

+3.9

E(99.9), ~O.19(0.004),

.. .

1.21

±2.2

E(1oo)

0.37

t:'

tn

0.206, 0.627, 1.20, 1.80, 2.60, ... 0.826(63),0.211(9), 0.592(8),1.17(8), 1.37(5), 0.305(3), . . . 160

0.44(0.06), 1.11(0.05),

...

........... ........... .................... ......... ..................... ±0.65

~

t.%J

. ..

-69.

2"-

t"'

0.117, 0.386, 1.32, 1.66, 1.82,2.0 0.072, 0.067, 0.315, 0.387,

91

E E(99), ~1.2(l)

~

Z

~5

159

(!-)

o

0.43

~3

13

f

~

-...:r

TABLE

(1)

(2)

Atomic Symnumber bol Z

69

PROPERTIJ

::0 ~

l:I:

~ U1 ~

o

U1

...

51 s

........... . .........

+8+(99+), a5.02(0.OOO6) .... . ......... E + ff'"(99+), .. ,,4.82(0.02) ........... ..... E + ff'"(99+), a4.72(0.00l)

181

103

-36.

...

182

104

-38.

0+

3m

183

105

-38.

."

6m

184m

...

184 185 186 187

106 107 108 109

-40. -39 -40. -39.

....... ........ ........

42 m 20 m l.1h 2.8 h 23 h

.......... ........... ........ ........... · . . . . . . . . . .. . . . . . . . . ......

188

110

-40.50

10.2 d

...........

189

111

-39.

...... 0'

_._

0+

(~-

i-\

190

112

-40.03

0+

191

113

-38.29

(~-)

192

114

-38.92

0+

115 116

-36.96 -37.29

193m

193 194 195m

195 196

Jl+

117 118

-35.19 -35.03

ic+ (!;t'!+)

197m

197 19B

0+

119 120

-32.65 -32.11

!(-I

0+

199m

199

121

-2fi.42

I··

11h

5 X 10" y 0.0127% 3.0 rl 0.78% 4 3d 16 y 32.9% 4.1 d

. . . . ..

....

...........

. .........

...........

........... ..........

E

~5

~4

~5

........

E E.

a4.47

E E E

-2.5 -4 -2 -3 054

E

~2

E

122 123

-29. -25.2

0+ ....

0.065,0.140,0.190 0.1064,0.1101, 0.1795, 2.01,0.1391,0.1840, ... 0.1376(41),0.1951(41), . 0.0547(11),0.3816(9), 0.0419(5),0.424(4), ... 0.082H5lJ), 0.0942(33), 0.1138(17), 0.1411(17), 0.1867(9),0.721(8), ...

"d

~

o

"d

t."J

~

1-:3 ....

. . . . . . . . . a3.18

t."J

rJ).

.........

· . . . . ......

.(100)

1.00

· . . . . . . . . . . .................. ...... . ..... .................. ..... .... . ........

....

..

. ....... ...........

o

~

..................

0.039, 0.123, •••

~

~ ~

r:tJ 1-4

C

r:tJ

0.163,0.189,0.352,0.493, 0.530

0.22(13), .••

0':050(40),0.080(13), 0.234(4), . . .

88

89

Ra.

Ac

Radium

Actinium

224 225 226 206 207 208 209 210 211 212 213

137 138 139 118 119 120 121 122 123 124 125

214 215 216 217 218 219 220 221

126 127 128 129 130 131 132 133

222 223 (AcX)

134 135

224 (ThX) 225 226 (Ra) 227 228 (MaTh.) 229 230 209 210 211

136

........ 23. .......... .......... .......... .......... 5. 4. 2. 2. 0.5 0.8 -0.3 0.1 -0.03 2.74 3.49 6.32 7.15 10.08 11.03 13.93

15.38 18.53

20.20

0+

........ 0+

........ 0+

........ 0+

........ ........ ........

0+

........ 0+

........ 0+

........

0+ (!+)

0+

137 138

23.63 25.44

0+

139 140

29.20 31.10

0+

141 142 120 121 122

35. 37. 10. 10. 8.

(i)-

........ ........ ........ ........ ........ ........

5 X

240 228 or 227 ~29

230

.......... ........ 36.25 37.79 38.27 40.

...........

Fission 14

06.89 a6.66 06.29 . .......... ........... e ........... ........... t(99+) a5.M(O.001) ........... ........... e(99+), tJ+0.8(0.05)

::::.SOm ::::.13 m 35m

........... ........... 10l

y

e(99+), 05.02, 5.10, • .. (0.002)

. .......... ........... tr?

"'d

~

6.0 480

147

239

Np

........... ...........

0.36

........... ........... .................... ......... -0.35 +4.1 a4.396(57), 4.3611(18), ......... ........... ........... 40216(5.7),4.597(4.6), . ........

26.1 m 7.1 X 108 y

2_ 146

+3.5

Fission 25

. ..

0.0057% t+ 7 2-

0.72% 144 145

+0.54

0.072(0.5),0.231(0.2),

o

"'d

t?:l

~

1-3 ""'t?:l"

rI1

o

~

Z d o

t"I ""'l::'" t?:l

rI1

2.7 1.1 1.80

1.56(20), 1.53(12), 1.60(10), 1.44(7), 1.19(6), 1.57(6), .•.

Fission 900

0.113

......... .....................

2,800

00

r1

~

8b-1.

TABLE

(1)

(2)

(3)

(4)

(5)

Num-

Atomie n Imber Z

Sym-

hoI

--

--

93

Np

94

Pu

Name

Mass number

A

ber of neutrons N --

Neptunium

Plutonium

237

144

PROPERTIES OF NUCLIDES

(7)

(8)

(9)

(10)

(11)

(12)

(13)

(14)

Mass excess, amu X 10- 3

Spin and parity

% abundance or half life

Magnetic moment, nuclear n.agnetons

Quadrupole moment, barns

Mode of decay, energy, and intensity, MeV (%)

l'1-decay Qvalues, MeV

Energy and intensity of 'Y-ray transitions, MeV(%)

2,200-m/s neutronabsorption cross section, barns

48.19

~+

2.14 X 106 y

+3.3

145

50.97

2(+)

2.1 d

...........

23J

146

52.95

~+

2.35 d

...........

240m

...

7.3 m

...........

240

147

........

67 m

...........

241 241 232 233 234

148 138 139 140

.......... ........ .')8.3 ........

3.4 h 16m 36m

235 236

141 142

237m 237 238

143 144

239 240

...

145

146

00

~

---

238

...

cr

(Continued)

(6)

.......... 1(-) 56.08

11.17 42.99 43.33 45.28 46.05

0+

0+

. . . . . . . . . . (~+) (~-)

4.76(8),4.64(7), 4.66(5), 4.87(3), . . . ........... trl.25(45),O.26(38), 0.20(15)•••. ........... a-0.437(48). 0.332(32). 0.393(7).0.713(7). 0.654(4)•••. ........... ~2.18(41). 1.60(32), 1.30(10).0.7(7), •.. ........... 1'1-0.89

........... ...........

0.18s 45.6 d 86 y

........... . . . . . . . . . . . .................... ........... ........... E(99+.), a5.37. 5.66 ........... ........... a5.50(72), 5.46(28), •••

52.18

~+

2.44 X

0+

6,580 y

101

y

+0.200

...........

0.029(14), 0.087(14), 0.145(1)••.•

169 Fission 0.019

1.29

1.01(42). 0.044, •.•

Fission 2,000

0.723

0.106(23), 0.278(14), 63 0.228(12),0.209(4), •..

2.1

E(99+1, a5.86(0.003) a5.77(69), 5.72(31), 5.62(0.2)••..

0.92(3), 1.5(3), •.. 0.56, 0.160, 0.245. 0.290. 1.00. 1.16, •.•

~

::r:

~ ....

r:n

1.12

.........

........... a5.157(73),5.144(15),

. ........

5.107(11), . . . ........... a5.17(76),5.12(24), 5.02(0.1), . . .

.........

~

(J

. ........ 0.048(0.3), 0.109(0.01)

0.22

C':1

~

1.4 1.1 2.0 0.39

.........

z (J ~

>

. ........ 0.56(21), 0.60(13),

. ..

. .......... ........... ........... ...........

0+

.........

e:

26.lD, 2.85 y

48.43 49.58

53.8!

a4.79(49), 4.77(26),

........... ........... 1'1-1.4 ........... ........... E(98). a6.59(2) ........... ........... E(99+). a6.31(0.1) ........... ........... E(94), a6.20(4), 6.19(2),

0+ .... ·1 ~~o~ ........

-

Fission 170

ITO.145(100) 0.060(5),0.033.0.044, ••• Fission 2.500 0.043(0.04)•••• 577 Fission 16.5 0.052(0.02), 0.039(0.007), 1,005 ... Fission 736 0.045•... 290 Fission 0.05

241

95

Am

Americium

14.0 y

-0.73

+5.6

~-0.C208(99+).

a4.90(0.002) •... ........... a4.90(76). 4.86(24) ........... ~-0.58(61). 0.49(38).

58.77 62.03

0+ (1+)

3.79 X 106 y 4.98 h

........... ..........

244 24,) 246

150 151 152

64.24 67.83 70.13

0+

8 X 107 y 10.5 h 10.9 d

........... ........... a ........... ........... ~-0.93(48). 1.2•... ........... ........... ~-0.15(90). 0.33(10)

237 238

142 143

50. 52.

239

144

53.04

243

Curium

~+

148 149

242m2 242m! 242

Cm

56.87

242 243

240 241

96

147

145 146

55. 56.85

........ 0+

........

~1.3

........

1.9h

. .......... ........... .(99+). a6.02(O.005) . .......... ........... .(100)

12.1 h

...........

(i-)

5

2-

'"

.......... ........

'"

..........

147 148

59.57 61.39

.. .

5(-) 1(-) 5

2-

h

51 h 433 y 0.014 s 152 y 16.0 h 7.37 X 103 y

...........

........... ......... . +1.59

+4.9

........... . ..........

.(99+). a5.78(O.005)

.(100) a5.49(86). 5.44(13). 5.39(1).5.55(0.3)•...

+1.4

±2.8 +4.9

.....................

......... ..................... 0.59

0.084(21).0.381(0.7),

...

......... ..................... 1.26 0.37

0.327(49)•... 0.044(30). 0.224(25). 0.180(10)

0.81

1.4

.........

0.98(80). 1.35(76). 0.58(29). 0.36(12) 0.228(18). 0.278(17). 0.209(5). 0.068. 0.057. 0.049, . . . 1.00(77). 0.90(23). 1,40 0.060(36). 0.026(3)•.•. 787

~-0.62(50), 0.66(34)

.(16) a5.28(88). 5.23(ll). 5.18(1)•... (r1.50(8O) •... , (20) .(0.04)

......... 0.66 0.75

.........

(1-)

26 m

........... ...........

244

149

64.31

(6-)

10.1 h

........... ........... s-e.asmo»

1.43

245

150

66.48

(~+)

2.05 h

........... ...........

0.91

~-0.91(78). 0.65(1i).

.........

0.60(5)

ITO.048(99.5), •.. 0.042 Fission 2.100 0.045 0.075(61),0.044(5) • . . . 189 0.043•... 0.746(66).0.900(25). Fission 2.300 0.154(19).0.099(5)•... 0.253(20). 0.240(1). 0.296(1) 0.680,0.205,0.154.0.757.

39 m

........... ...........

(2+)

25.0 m

........... ...........

(r1.31(79), 1.60(14). 2.10(7)

........

22 m 2.5 h 2.9 h

........... ........... ........... ........... . .......... ...........

~-

~1.6

1.079(32).0.799(29). 1.063(19). 1.037(14). 1.086(2). 0.834(2), . . . 0.285. 0.227

.(90), a6.51(1O) .(100)

....-0.9 1.7

0.188

246

151

69.72

247 238 239

152 142 143

72. 53.03 55.

0+

........

~-

~

~

o

-e

trj ~

8

1-4

trj lfl

..........

.......... ........

Fission 196 1.8 260

Fission 3.3

...

'"

Fission i.on 20 271

1.5 ~2.3

244m

246m

1.371

SF

........... ........... a5.21(0.4) •... ±0.382

0.0208

......... 2.30

oIo%j Z d

o

t" t::l

1-4

t'=.i

lfl

. ..

cr

00

[J).

f

~ I-'

Be. Atomic Mass Formulas PHILIP A. SEEGER

Los A lamos Scientific Laboratory

8c-1. Introduction. The nuclear or atomic mass is a direct measure of the total binding energy of the nucleus, and thus of the ground state of the nuclear Hamiltonian. If the Hamiltonian were known, the mass-law problem would be solved: it would be possible in principle to write the binding energy in terms of the atomic number Z and the mass number A = N + Z. Note that the mass is B(Z,A) (8c-I) M(Z,A) = A . u + Z . t..M H + (A - Z) . t..Mn - -c-2where u is the atomic mass unit = 931.487 MeV /c 2, t..MH = 7.82519 mu is the mass excess of the hydrogen atom, t..Mn = 8.66520 mu is the neutron mass excess, and B(Z,A) is the binding energy in MeV. Even an incomplete nuclear theory can be used to predict the forms of some terms in the mass law. Weizacker [1] pointed out that arbitrary multipliers could be used with such terms to gain insight both for the theory and the masses. His mass law, as simplified by Bethe and Bacher [2], has formed the basis for most subsequent studies. Many recent formulations and summaries are given in proceedings of topical conferences held at Vienna [3], Lysekil [4], and Winnipeg [5]. 8c-2. Uses of the Mass Law. The complexity of a mass law depends on its intended use. For instance, in the calculation of nuclear kinematics, the mass number A is often a sufficient approximation, whereas for nuclear reaction theory quite sophisticated treatments are required. Uses may be classed as theoretical or experimental. Theoretical uses include the comparison of calculated coefficients to values fitted to experimental data. Another use is an indirect determination of arbitrary constants in the theory: e.g., parameters in a proposed form of the nucleon-nucleon interaction can be found by calculating mass-law terms as functions of the interaction [6]. A third theoretical use is subtraction of the smoothly varying part of the mass law from the experimental data to isolate the small terms. The mass law is used "experimentally" to estimate binding energies for use in other calculations or experiments. Fur "interpolation"-finding binding energies in the region of known data-the mass law should be discarded whenever practical in favor of tabulated experimental values. If it is necessary to use a mass law, a formula such as that of Zeldes et al. [7], which uses a large number of parameters to reproduce the experimental data as well as possible, may be used. Extrapolation to unknown masses requires the mass law. If the extrapolation is only a short distance from known data, and if only a few binding energies are needed, the values given by the mass law should be corrected by comparison of calculated and experimental data in the neighborhood, or a local extrapolation should be made. If a long extrapolation or a large number of calculations must be performed, a sophisticated 8-92

8-93

ATOMIC MASS FORMULAS

mass-law formula must be used, and it should then be used for all binding energies in the problem, including known data. Two suitable formulas are those of Myers and Swiatecki [8] and of Seeger [9]; the latter is presented below. 8e-3. Terms in the Mass Law. Mathematically, the function B(Z,A) can be expanded in terms of any two functions of Z and A which remain small over the ranges of Z and A to be considered. Since the binding energy per particle is nearly constant for A > 10, it is convenient to expand B(Z,A)IA. The range of nuclear force being short compared to the nuclear radius, a convenient expansion parameter is Constancy of nuclear density implies that Rr-« At, and so the usual expansion parameter is 11Ai. The distance of Z from the line of beta stability is a possible choice for the other parameter. In deriving terms from a model of the nucleus, however, the betastability line is not explicitly known, and it is more natural to expand about the symmetry line Z = A12; from the statistical model [2] the form is [(A - 2Z)IAj2. There are some terms in the nuclear binding energy which it is not convenient to expand. The Coulomb force, for example, does not have a short range, and the Coulomb energy can be included explicitly if the charge distribution is assumed; for a uniformly charged sphere of radius roAl,

un.

The binding energy can be expressed quite generally as B(Z,A)

=

2Z)2,A-I ] -

AA - A·f [( -

E,

(8c-2)

where f is a power series in its arguments, and E; represents Coulomb energy and any other terms which are not expanded. Although the original derivation was in terms of the liquid-drop model, the terms can be calculated analytically or numerically from any model. A calculation for infinite nuclear matter with N = Z will yield the zero-order term in the expansion, the volume term aA. (Adjustable multipliers are denoted by Greek letters.) A mass law of this simple form, with one parameter determined by least-squares fit to known odd-A binding energies [10, 11] and the Coulomb energy derived from electron-scattering experiments [12], is illustrated in Fig. 8c-la; it is clear from the figure that finite nuclei cannot be adequately represented by infinite nuclear matter. The two first-order terms are the symmetry and the surface terms of the liquid drop: -,8(A - 2Z)2IA - "YAi. These can be found for other models by calculating respectively infinite nuclear matter with N ~ Z and semi-infinite matter with a plane surface. The negative signs indicate decreased binding energy. Inclusion of these terms completes the Weizsacker formula [2]; the residual discrepancies following a least-squares fit to odd-A nuclides with A > 40 are shown in Fig. 8c-1b. The calculated binding energies are accurate to about percent; the error is greater than 1 percent for only nine of the lightest nuclides included. Myers [6], using a nuclear force with constants determined by fitting to the fourparameter mass law above, has carried the expansion of Eq. (8c-2) to second-order terms: At, (A - 2Z)2/A~, and (A - 2Z)4/A3. The expressions become very complicated because the Coulomb force affects the density distribution of protons compared to neutrons. Only one of the second-order terms, the surface-symmetry term '1(A - 2Z)2IA~, is commonly included in the mass law, and its effect is so weak that the coefficient is determined only poorly.

t

8-94

NUCLEAR PHYSICS

G.

••

••••

• ••••

• •••••• •• • ••••••• •• ••• •••••• • ••• •••• • • •••••••• •• •• •• • ••• ••• •••••••••••••••••••••••• ••••• •••• •••••••••••••••••••• • • • • •• • • •• •• • • •••••• • ••••••••••••••••••••••••••••• •••••••• •••• •••• • • •••••••• •• • • • • •

••••• ••• -:» •....• :.:.. . . . ..••••••• ...... . . . .... . . •.•.. ..- ............... .. . . .."'••••••""• • • • • • • • • • • . ;,-:........ r : . r -:

•

~

~"'~

!I~

'"

>

• :I:

••

b.

.; C)

~

•

0::: IIJ

z.

.1Ij. ...

... ....

...........

IIJ

.lJ!.'" -. -."

....

C)

Z

C z

iii

.........

.

..J

.......... .. .............

set

•• •

fa

~

•••

;:)

0

~ 0::: 0 0::: 0:::

IIJ

2

•

-2

+

40

60

80

100

12\>

140

160

180

260

MASS NUMBER A

FIG. 8c-1. Errors of calculated binding energies versus mass number A: (a) for mass law with volume term and Coulomb energy only, fitted with 1 parameter to odd-A binding energies; (b) for 4-parameter liquid-drop mass law; (c) residual errors for odd-A nuclides, for Eq. (8c-3) fitted to 1,148 odd- and even-A nuclides; (d) same mass law, residual errors of eveneven (+) and odd-odd (0) nuclides.

8-95

ATOMIC MASS FORMULAS

The expansion of Eq. (8c-2) is accurate only to the extent that the discrete levels occupied by nucleons can be represented by a smooth distribution, and the structure apparent in Fig. 8c-lb is due principally to the breaking down of this assumption. A correction term to the liquid-drop mass law can be constructed by comparing a single-particle-level diagram such as that of the Nilsson model to a smoothed average of the same levels. The method used is that of Strutinsky, extended by Tsang [13], who has shown that the results reach a limit which is independent of the details of the smoothing. The calculations [9] yield two functions aU N(N,E) and aU Z(Z,E), where E is a measure of the spheroidal deformation of the nucleus. The coefficients of these functions in the mass law depend only on the radii of the neutron and proton distributions, rNAl and roAl, respectively. The parameter r» is new, but ro is the same radius constant which describes the proton charge distribution in the Coulomb energy. Pairing correlation energy cannot be included in an average nuclear potential. It is calculated by applying the Bardeen-Cooper-Schrieffer (BCS) formalism to the single-particle levels, using as the average pairing matrix element G I/A. For a given value of the one adjustable parameter GNrN2 = Gpro2, the BCS ground-state energy for each particle number is found, and the difference in binding energy between it and the sum of the Nilsson levels is called PN(N,E) or P Z(Z,E) [9]. Since the presence of an unpaired particle decreases the binding energy of the BCS solution, the evenodd mass difference is calculated directly with no additional parameters. (A simple alternative phenomenological form for the even-odd difference is ± a/A!, where the + sign is for even-even nuclides, - for odd-odd, and the term is omitted for odd A. The least-squares determined value for a is 10.6 ± 1.1 MeV.) It is known that many nuclei, e.g., the rare earths and actinides, have nonspherical equilibrium shapes which are represented approximately in the Nilsson model by spheroids. The terms 5 U and P are explicit functions of the deformation parameter E; the surface and Coulomb terms in the liquid-drop mass law can also be expanded in powers of E. Then by maximizing total binding energy with respect to E, the equilibrium deformation EO is found; the results [9] agree qualitatively with experiment. Several other small terms are included in the mass law. In the Coulomb energy there are an exchange term [2] and a correction for the diffuseness of the nuclear surface [8]. A first-order term in (A - 2Z) / A seems to be required to represent extra binding of nuclei with N = Z; a rapidly decreasing exponential is used [8]. The binding of the atomic electrons [14] is included, although small, to prevent falsification of other terms. The complete formula is, in MeV, f'o..I

B(Z,A) = a A _ ~(A -A 2Z)2 _ [ 'Y

3

- 5e

2 Z2

roAl

(1

-

Al _?l(A A! - 2Z)2] (1 + ~ 45

0.76361

2.453

zr- - ro2AJ -

4

2

45 EO

-

92 2,835

+ 7 exp ( - 61A ~ 2Z + 14.33 X 1O-6Z2.38 + 5UN(A - z, + 5U Z(Z,EO) + PN(A - z, The value used for !e is 0.864 MeV-fm. I

EO)

2+ ~ 3) 2,835

EO

EO

3) EO

)

EO)

+ PZ(Z,EO)

(8c-3)

2

8c-4. Determination and Testing of Coefficients. The principal method used to determine coefficients is least-squares fitting to tables of experimentally derived binding energies. From a statistician's [15] point of view, this is not a valid procedure because there are correlations among the data of the mass table. Therefore Eq. (8c-3) has been fitted both to the mass table and to the raw experimental data. Other methods, e.g., fitting the Coulomb radius to a fission barrier [8], have also been used. In this mass law, the four parameters of the Nilsson model were chosen [9] by trial and error to reproduce known level structures as well as possible. The value for the BOS

8-96

NUCLEAR PHYSICS

parameter was found by solving the problem with several values of the BCS parameter, iterating to find the solution which minimized the sum of residuals. The least-squares solution fitting the remaining six parameters to 1,148 binding energies from the 1964 [10] and 1967 [11] mass tables is given in the second column of Table 8c-1, and the solution fitted to 552 mass-spectroscopic doublets [16] and 957

TABLE

Parameter

a, MeV {J, MeV

. . . . . .

MeV " MeV TO, fm TN, fm Gp T 0 2 , MeV-fm 2 .•• 0"1, MeV . 0"2. MeV . ')I,

'17.

8c-1.

MASS-LAW COEFFICIENTS

Fitted to mass table

Fitted to doublets and reactions

15.8089 ± 0.0170 30.157 ± 0.142 20.230 ± 0.052 47.66 ± 0.94 1.18729 ± 0.00229 1. 2285 ± O.0070 28.70 0.805 0.464

15.8570 ± 0.0322 31.402 ± 0.168 20.337 ± 0.105 53.52 ± 0.92 1.17641 ± 0.00376 1. 1983 ± 0.0078 27.67 1.916 0.449

nuclear reaction Q values [11,16]is given in the third column. The standard deviation 0"1 is the fit to total binding energies, and 0"2 is the fit to the doublets and reaction energies. The quoted errors in Table 8c-1 are the square roots of the diagonal elements of the error matrix adjusted to force x 2 = degrees of freedom. For the first column they show only the relative uncertainties ih the determination of the parameters; for the second column they are a more accurate estimate of statistical uncertainties. The values of the coefficients are slightly different from those in the "Winnipeg Proceedings" [9] because of the elimination ~ ~

::r: ~

U2

.....

o

24: Chromium

350.2 366.0 381.1 395.4 409.1 420.5 431.3 441.6 451.3 460.6 469.4 477.7 485.5 492.9

z

U2

5.2 3.5 7.5 5.3 8.0 5.7 7.2 3.0 4.4 3.4 6.4 4.9 6.6 4.2

352.5 366.3 383.5 396.3 412.2 422.4 435.7 445.3 457.2 464.6 474.2 480.2 489.2 494.0

31 32 33 34 35 36

52 53 54 55 56 57

442.4 44S.3 453.7 458.7 463.3 467.6

-1.8 -2.4 -3.5 -4.2 -5.0 -5.4

1.1 3.0 1.8 3.9 2.3 4.4

441.6 448.8 451.7 458.2 460.4 466.3

4.8 3.6 7.0 5.1 7.4 5.0 6.6 3.2 4.0 3.4 6.0 4.5 6.2 4.4 7.8 5.8 8.0 6.0 7.6

347.9 360.3 376.1 385.7 398.5 407,,3 419.3 427.5 438.1 444.2 452.4 457.1 464.8 468.3 475.5 478.3 484.8 487.2 493.1

2.8 1.4 4.8 2.7 5.0 2.4 4.4 1.1

348.3 361.4 377.9 390.1 403.6 413.1 425.7 434.7

Z "'" 22: Titanium

20 21 22 23 24 25 26* 27 28 29 30 31 32 33 34 35 36 37 38

42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

346.4 360.7 374.3 385.5 396.0 406.0 415.5 424.5 432.9 440.8 448.2 455.2 461.7 467.8 473.5 478.7 483.6 488.1 492.2

-3.3 -3.9 -5.3 -4.9 -4.9 -3.7 -2.9 O. 1.2 0.1 -1.7 -2.6 -3.1 -3.7 -5.8 -6.2 -6.7 -6.9 -6.7

Z = 23: Vanadium

20 21 22 23 24 25 26 27*

43 44 45 46 47 48 49 50

348.7 363.8 378.1 391.8 403.0 413.7 423.9 433.5

-3.3 -3.7 -5.1 -4.4 -4.5 -2.9 -2.6 0.3

34 35 36 37 38 39 40 41

499.8 506.3 512.4 518.1 523.4 528.3 532.9 537.2

58 59 60 61 62 63 64 65 Z

20 21 22 23 24 25 26 27 28 29 30* 31 32 33 34 35 36 37 38 39 40 41 42 43

=

350.9 367.4 383.2 398.2 412.6 426.3 437.8 448.7 459.1 469.1 478.5 487.4 495.8 503.9 511.4 518.5 525.2 531.5 537.4 543.0 548.1 552.9 557.4 561.5

45 46 47 48 49 50 51 52 53 54

55 56 57 58 59 60 61 62 63 64 65 66 67 68

I

47 48

I

8.4 6.3 8.6 6.2 7.9 6.3 8.0 6.1

502.4 506.5 514.3 517.8 524.9 527.9 534.5 537.1

2.6 1.0 4.7 2.4 5.0 2.2 4.5 0.6 1.9 1.0 3.8 2.4 4.1 1.9 5.7 3.5 5.6 3.8 5.4 3.9 5.7 3.9 6.0 4.4

351.6 366.2 397.6 414.2 426.8 440.7 450.9 463.5 471.6 481.8 488.4 498.1 503.6 512.6 517.4 525.7 529.8 537.5 541.2 548.3 551.5 558.1 561.0

2.3 6.1

369.4 387.9

25: Manganese

Z

21 22

-5.8 -6.0 -6.7 -6.5 -6.4 -6.7 -6.4 -6.1

368.0 384.5

-1.9 -2.1 -3.9 -3.0 -3.4 -1.7 -1.6 1.8 2.4 1.6 -0.5 -1.4 -1.8 -1.9 -4.5 -4.6 -5.1 -5.4 -5.2 -5.7 -5.4 -5.2 -5.3 -4.9

=

3R4.0

>1-3 o s:: .... o s:: >-rn

rn ~

o ~ s:: d

~

>-

tn

26: Iron

I

-0.9 -2.6

I

I

co I

~ ~

TABLE

Number of neutrons N

Mass number A

Liquid drop

8c-2.

Shell correction

I Z

23 24 25 26 27 28 29 30 31* 32 33 34 35 36 37 38 39 40 41 42 43 44

49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70

= 26:

22 23 24 25 26

49 50 51 52 53

BCS pairing energy

Total binding energy

Number of neutrons N

=

385.0 401.4 417.1 432.2 446.6

-2.3 -2.5 -1.5 -0.4 2.9 3.8 2.8 0.7 -0.1 -0.6 -1.0 -3.5 -4.0 -4.6 -4.4 -4.3 -4.6 -4.4 -4.1 -4.5 -4.1 -3.6

I .......

o Mass number A

Liquid drop

Shell correction

BCS pairing energy

Total binding energy

o

Z = 28: Nickel (Continued)

4.2 6.6 4.5 5.8 1.9 3.1 2.3 5.1 3.6 5.3 3.2 7.1 5.2 7.4 5.1 6.8 5.1 6.9 5.1 7.6 5.8 7.6

402.2 419.4 432.7 448.8 459.6 472.9 481.5 492.4 499.7 510.0 516.0 525.7 531.0 539.9 544.7 552.9 557.1 564.8 568.6 575.7 579.1 585.7

2.1 0.5 2.1 0.1 1.5

387.3 402.3 420.2 434.2 450.8

27: Cobalt 0.4 0.7 1.2 2.2 3.0

00

MEV (Continued)

Iron (Continued)

400.2 415.3 429.6 443.4 455.0 466.0 476.6 486.6 496.2 505.2 513.9 522.0 529.8 537.1 544.0 550.4 556.6 562.3 567.7 572.7 577.4 581.7 Z

CALCULATIW BINDING ENERGIES IN

39 40 41 42 43 44 45 46 47 48

67 68 69 70 71 72 73 74 75 76

580.8 587.7 594.2 600.3 606.1 611.5 616.6 621.4 625.9 630.0

-0.7 -0.6 -0.9 -0.9 -0.5

O. 0.9 2.1 3.9 5.5

2.4 4.2 2.8 5.0 3.3 4.9 3.2 4.2 1.7 2.5

582.5 591.3 596.1 604.4 608.9 616.5 620.7 627.7 631.5 638.0

53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69

418.6 434.9 450.6 465.6 480.0 493.9 505.8 517.1 528.0 538.4 548.4 557.9 566.9 575.6 583.8 591.6 599.0

0.8 1.8 2.5 4.0 5.5 4.1 3.0 1.9 1.3 0.2 -0.6 -1.4 -1.7 -2.4 -2.6 -3.0 -3.1

o

t"i t.".1

>

~

"t1

Z = 29: Copper

24 25 26 27 28 29 30 31 32 33 34 35* 36 37 38 39 40

zq

l:I: 2.1 0.2 1.6 -0.3 -0.2 -0.3 1.4 0.3 2.2 1.0 3.1 1.6 3.6 2.1 4.0 2.7 4.6

421.3 436.6 454.6 469.0 485.4 497.5 510.1 519.3 531.4 539.4 550.7 557.9 568.6 575.1 585.1 591.0 600.3

~ "'"I

o

U2

27 28 29 30 31 32* 33 34 35 36 37 38 39 40 41 42 43 44 45

54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71

72

460.4 472.0 483.2 493.9 504.0 513.7 523.0 531.7 540.1 548.0 555.4 562.5 569.2 575.5 581.4 587.0 592.2 597.1 601.7

4.3 5.8 4.5 3.4 2.2 1.5 0.5 -0.2 -1.0 -1.4 -2.1 -2.4 -2.8 -2.8 -2.6 -2.2 -1.5 -0.4 0.5

-0.4 -0.2 -0.4 1.4 0.3 2.3 1.0 3.1 1.5 3.5 2.0 4.2 2.8 4.7 2.9 4.5 2.4 3.6 1.7

464.1 477.6 487.1 498.5 506.4 517.4 524.2 534.3 540.3 549.8 555.1 564.0 568.8 577.1 581.4 589.1 593.0 600.1 603.7

Z = 28: Nickel

23 24 25 26 27 28 29 30 31 32 33 34* 35 36 37 38

51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66

401.8 418.2 433.9 449.0 463.4 477.2 489.0 500.2 511.0 521.3 531.1 540.5 549.4 557.9 565.9 573.6

1.6 1.7 2.6 3.8 5.9 7.9 6.2 4.8 3.9 3.5 2.0 0.6 -0.2 -0.7 -0.7 -0.5

1.5 3.5 1.6 2.7 -0.2 O. -0.2 2.1 0.7 2.3 1.2 4.1 2.5 4.6 2.5 4.0

404.9 423.5 438.1 455.5 469.0 485.1 495.0 507.1 515.6 527.1 534.3 545.2 551.8 561.8 567.7 577.1

41 42 43 44 45 46 47 48 49

70 71

72 73 74 75 76 77 78

606.1 612.7 619.0 625.0 630.6 635.9 640.9 645.5 649.9

-2.9 -2.5 -1.8 -0.8 O. 1.2 2.7 3.9 5.9

2.9 4.5 2.5 3.7 1.9 2.9 0.9 1.8 -0.3

605.8 614.5 619.6 627.7 632.4 639.9 644.3 651.2 655.4

5.9 2.3 3.2 2.6 5.2 3.8 5.4 3.6 7.1 5.4 7.5 5.3 6.9 5.3 7.0 5.4 7.7 6.0 7.7 6.1 7.1 4.4 5.4 2.4 2.9 2.5

456.7 471.6 488.7 501.4 516.1 525.8 538.4 546.9 558.9 566.7 577.8 584.9 595.4 601.9 611.8 617.8 627.1 632.7 641.3 646.6 654.6 659.5 667.0 671.5 678.3 680.8

Z = 30: Zinc

26 27 28 29 30 31 32 33 34 35 36 37* 38 39 40 41 42 43 44 45 46 47 48 49 50 51

56 57 58 . 59 60 61 62 63 64 65 66 67 68 69 70 71

72 73 74 75 76 77 78 79 80 81

451.4 467.1 482.1 496.6 510.5 522.4 533.9 544.9 555.4 565.5 575.1 584.3 593.1 601.4 609.4 617.0 624.2 631.0 637.5 643.7 649.5 654.9 660.1 665.0 669.5 673.8

-0.6 2.3 3.4 2.2 0.4 -0.4 -0.9 -1.5 -3.7 -4.2 -4.7 -4.6 -4.5 -4.8 -4.6 -4.5 -4.8 -4.3 -3.9 -3.2 -1.9 0.2 1.4 4.2 5.9 4.6

> 1-3

o

~ ~

o

~

>

rJ2 rJ2 I'2j

o

~

q

~

>

rJ2

f

J-l

o

J-l

TABLE

8c-2.

CALCULATED BINDING ENERGIES IN ME V

cr

(Continued)

~

Number of neutrons N

Mass number A

Liquid drop

Z

=

27 28 29 30 31 32 33 34 35 36 37 38* 39 40 41 42 43 44 45 46 47 48 49 50 51 52

58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83

467.9 483.5 498.5 513.0 526.9 539.0 550.5 561.6 572.3 582.4 592.2 601.5 610.4 618.9 627.1 634.8 642.2 649.2 655.8 662.1 668.1 673.8 679.1 684.2 688.9 693.4

29 30

61 62

499.8 514.8

BCS pairing energy

Shell correction

Total binding energy

I

o Mass number A

31: Gallium

I

O. -2.3

Liquid drop

Shell correction

BCS pairing energy

Total binding energy

tv

Z = 33: Arsenic (Continued)

1.1 1.9 1.0 -0.9 -1.7 -2.2 -2.5 -4.5 -4.8 -5.2 -5.7 -5.5 -6.0 -5.9 -5.7 -5.6 -5.3 -4.7 -4.3 -3.0 -0.9 0.2 3.0 4.5 3.3 1.5

1.0 2.0 1.3 3.8 2.5 4.1 2.2 5.4 3.5 5.5 3.9 5.4 4.0 5.9 4.2 6.1 4.5 6.0 4.7 5.6 3.0 4.2 1.2 1.8 1.4 3.4

469.7 487.4 500.7 515.9 527.6 540.8 550.0 562.5 570.8 582.6 590.3 601.3 608.4 618.8 625.4 635.2 641.3 650.5 656.2 664.8 670.2 678.1 683.2 690.5 693.5 698.3

3.6 6.5

503.2 519.0

Z = 32: Germanium

I

Number of neutrons N

I

I

41* 42 43 44 45 46 47 48 49 50 51 52 53 54

55 56

74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89

644.7 653.4 661.8 669.8 677.5 684.8 691.8 698.5 704.8 710.8 716.5 721.9 727.0 731.8 736.4 740.6 Z

30 31 32 33 34 35 36 37 38 39 40

64 65 66 67 68 69 70 71

72 73 74

=

516.3 531.9 547.0 561.5 575.5 587.8 599.6 611.0 622.0 632.5 642.6

-5.2 -7.9 -7.4 -7.0 -6.3 -5.0 -2.9 -1. 7 1.0 2.7 1.4 -0.3 -1.3 -2.2 -2.6 -3.1

3.4 7.1 5.4 7.1 5.5 6.5 3.8 4.9 2.0 2.4 2.1 4.0 3.2 4.4 2.9 3.9

641.9 652.6 659.8 670.0 676.8 686.3 692.7 701.6 707.7 715.9 719.9 725.6 728.9 734.0 736.6 741.4

6.0 4.7 6.6 4.7 6.4 5.0 6.9 5.2 7.0 4.8 6.9

519.1 532.6 548.8 561.1 576.4 586.5 599.8 609.2 621.9 630.6 642.5

34: Selenium -3.2 -4.0 -4.5 -4.4 -4.8 -5.8 -5.9 -5.8 -6.0 -5.0 -5.9

z

q

Q

et.".l

>

!:O

~

::r: ~

w H Q

w

i:Sl 32 33 34 35 36 37 38 39 40* 41 42 43 44 45 46 47 48 49 50 51 52 53 54

63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86

529.3 543.2 555.4 567.0 578.2 588.9 599.2 609.1 618.6 627.6 636.3 644.5 652.4 659.9 667.1 673.9 680.4 686.5 692.4 697.9 703.1 708.1 712.7 717.1

-3.0 -3.5 -3.3 -6.3 -5.6 -6.0 -6.8 -6.4 -6.2 -6.8 -6.6 -6.7 -6.4 -6.1 -5.6 -4.4 -2.0 -1.0 2.0 3.4 2.3 0.3 -0.6 -1.5

=

33: Arsenic

500.3 515.9 530.9 545.4 559.5 571.6 583.4 594.7 605.6 616.0 626.0 635.5

-1.2 -3.0 -3.7 -4.2 -3.8 -6.9 -5.1 -5.3 -5.4 -5.8 -5.2 -5.7

Z

29 30 31 32 33 34 35 36 37 38 39 40

62 63 64 65 66 67 68 69 70 71 72 73

5.0 6.7 4.4 8.4 5.6 7.6 6.2 7.6 5.9 8.1 6.4 8.3 6.8 8.7 7.3 8.3 5.3 6.6 3.4 4.1 3.5 5.7 4.8 6.1

2.1 4.6 3.2 4.8 2.7 6.5 3.1 5.1 3.5 5.3 3.3 5.3

531.3 546.4 556.1 569.1 578.1 590.3 598.6 610.2 617.8 628.7 635.8 646.1 652.8 662.5 668.7 677.8 683.6 692.1 697.7 705.4 708.9 714.1 716.9 721.6

501.1 517.5 530.4 546.1 557.7 571.2 580.7 593.6 602.5 614.6 622.8 634.2

41 42* 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57

75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91

652.3 661.5 670.4 678.9 687.1 694.9 702.4 709.5 716.3 722.8 729.0 734.8 740.4 745.7 750.7 755.4 759.9 Z

32 33 34 3.') 36 37 38 39 40 41 42 43 44* 45 46 '7 48 49 50

67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85

= 35:

547.8 562.9 577.5 591.6 603.9 615.9 627.3 638.4 648.9 659.1 668.9 678.3 687.2 695.9 704.2 712.2 719.8 727.1 734.0

-5.5 -6.3 -5.5 -6.3 -6.5 -5.3 -3.0 -2.0 0.4 2.4 0.9 -0.6 -1.6 -2.4 -2.9 -3.4 -4.5

5.1 7.3 5.4 7.8 7.0 7.9 5.1 6.3 3.8 3.8 3.7 5.4 4.6 5.8 4.4 5.3 4.9

650.7 661.9 669.6 680.3 687.5 697.6 704.4 713.8 720.4 729.0 733.5 739.7 743.4 749.0 752.1 757.3 759.8

a: H

o ~

Bromine

-4.8 -4.2 -4.3 -4.4 -4.7 -3.4 -4.5 -3.3 -4.2 -4.0 -4.8 -4.4 -6.3 -5.7 -4.8 -3.2 -2.4 -0.1 1.7

>-

1-3

o

>-

4.7 2.8 4.4 2.9 4.6 2.3 4.5 2.2 4.1 2.5 4.6 2.9 5.7 4.0 5.3 3.2 4.5 2.1 2.3

547.3 560.2 576.1 588.1 601.9 612.0 625.1 634.5 646.8 655.5 667.1 675.3 686.4 694.1 704.6 712.0 721.9 729.0 738.0

U1 U1 ~

o

l:d ~

d

r-

>-

U1

cr I-"

o

c..J

TABLE

Number of neutrons N

Liquid drop

Mass number A

Z

51 52 53 54 55 56 57 58 59

86 87 88 89 90 91 92 93 94

= 35:

33 34 35 36 37 38 39 40 41 42 43 44 45* 46 47 48 49 50

69 70 71 72 73 74 75 76 77

78 79 80 81 82 83 84 85 86

Shell correction

BCS pairing energy

Total binding energy

Number of neutrons N

= 36:

563.6 578.7 593.3 607.4 619.9 631.8 643.4 654.4 665.2 675.4 685.3 694.8 703.9 712.7 721.1 729.2 737.0 744.4

0.4 -1.1 -1.9 -2.7 -3.4 -4.2 -2.6 -3.1 -1.9

.-

Liquid drop

Mass number A

I-'"

o Total binding energy

BCS pairing energy

Shell correction

~

Z = 37: Rubidium (Continued)

2.1 3.8 2.8 3.9 2.8 4.1 2.2 3.6 1.9

743.0 749.6 753.8 759.9 763.5 769.2 772.1 777.7 780.7

Krypton

-5.0 -4.8 -4.1 -4.3 -2.9 -3.3 -2.8 -3.7 -3.5 -5.8 -6.0 -6.2 -6.2 -5.9 -3.5 -3.0 -0.2 1.3

cr

(Continued)

CALCULATED BINDING ENERGIES IN MEV

Bromine (Continued)

740.6 747.0 753.0 758.7 764.2 769.4 774.4 779.0 783.5 Z

8c-2.

4.9 6.2 4.2 5.8 3.4 5.0 3.3 5.2 3.6 6.7 5.4 7.1 5.9 7.6 4.8 6.4 3.6 4.0

562.4 578.8 591.3 606.8 617.4 631.0 640.9 653.7 662.9 675.0 683.7 695.2 703.5 714.5 722.3 732.7 740.2 749.7

61 62

I

98 99

I

821.2 825.7

I

0.1 0.1

I

0.6 1.7

I

818.2 823.8

Z = 38: Strontium

35 36 37 38 39 40 41 42 43 44 45 46 47 48* 49 50 51 52 53 54 55 56 57 58 59

73 74 75 76 77

78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97

594.9 610.0 624.6 638.7 651.3 663.3 675.0 686.2 697.1 707.5 717.6 727.3 736.7 745.8 754.5 762.8 770.8 778.5 785.9 793.0 799.8 806.3 812.6 818.5 824.3

...,...1.9 -1.6 -0.8 -0.4 -0.8 -1.7 -1.8 -4.1 -3.9 -6.4 -6.1 -5.5 -3.7 -2.7 -0.6 1.5 -0.1 -1.4 -2.3 -3.1 -3.8 -4.9 -2.6 -2.7 -0.5

2.6 3.9 1.8 2.9 1.8 3.7 2.3 5.2 3.8 7.1 5.5 6.9 4.6 5.8 3.6 3.4 3.4 5.0 4.1 5.2 4.0 5.9 3.2 4.4 1.9

592.6 609.1 622.0 637.7 648.6 662.3 672.5 685.5 695.1 707.6 716.7 728.7 737.5 748.8 757.3 767.7 774.1 782.1 787.7 795.1 800.0 807.0 811.3 818.2 822.6

z

q

o

~

t::1

> ;0 't1

::= ~ ~

o

tn

51 52 53 54 55 56 57 58 59 60

87 88 89 90 91 92 93 94 95 96

751.5 758.3 764.8 771.0 776.8 782.5 787.8 793.0 797.9 802.4

0.2 -1.6 -2.4 -3.3 -3.7 -4.2 -5.4 -3.5 -1.5 -1.1

755.2 762.3 766.9 773.5 777.4 783.6

3.6 5.6 4.6 5.8 4.4 5.4 5.1 5.1 2.9 3.7

793.0 796.4 802.0

72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97

594.5 609.0 623.2 635.6 647.7 659.3 670.5 681.2 691.6 701.5 711.1 720.4 729.3 737.9 746.1 754.0 761.6 768.8 775.7 782.4 788.7 794.8 800.7 806.2 811.5 816.5

-2.8 -2.5 -1.8 -1.5 -1.9 -2.4 -2.4 -3.6 -3.7 -6.0 -6.8 -5.7 -3.9 -2.9 -0.6 1.2 -0.1 -1.6 -2.5 -3.3 -3.9 -4.4 -2.5 -2.4 -0.9 -0.3

1.9 3.1 1.2 2.4 1.2 2.9 1.4 3.5 2.3 5.3 4.4 5.6 3.2 4.4 2.0 2.2 2.0 3.7 2.8 3.9 2.7 4.3 1.9 2.9 1.0 1.7

590.7 606.7 619.1 633.1 643.6 656.8 666.6 679.0 688.2 700.1 708.7 720.2 728.6 739.4 747.4 757.4 763.4 770.9 776.0 783.0 787.4 794.0 798.0 804.5 808.5 814.5

98 99 100 101 102

78"1.0

Z = 37: Rubidium

35 36 37 38 39 40 41 42 43 44 45 46 47* 48 49 50 51 52 53 54 55 56 57 58 59 60

60 61 62 63 64

829.7 834.9 839.8 844.4 848.8

0.3 0.9 0.9 1.2 1.2

2.5 1.3 2.3 1.2 2.0

829.0 833.2 839.1 842.7 848.1

0.3 1.2 0.1 2.1 0.7 2.3 1.9 5.0 2.7 4.7 3.0 4.0 2.2 2.2 2.1 3.4 2.6 3.6 2.8 4.8 1.7 2.7 0.5 1.0 0.2 1.3 0.2 0.9 0.2 1.2

621.6 637.7 650.4 664.3 675.1 688.3 698.4 711.2 720.9 733.2 742.5 754.2 763.2 774.0 781.0 789.3 795.4 803.3 808.6 816.1 821.0 828.4 833.3 840.2 844.8 851.1 855.2 861.0 864.5 869.7

Z = 39: Yttrium

37 38 39 40 41 42 43 44 45 46 47 48 49 50* 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66

76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105

625.5 640.1 654.3 666.8 678.9 690.6 701.9 712.8 723.4 733.6 743.4 752.9 762.1 770.9 779.3 787.5 795.3 802.9 810.1 817.0 823.8 830.1 836.3 842.2 847.8 853.0 858.1 862.9 867.4 871.7

0.3 0.8 0.8 -0.6 -0.7 -1.7 -3.3 -5.6 -4.1 -4.8 -3.6 -2.6 -0.9 0.9 -0.4 -1.6 -2.3 -3.0 -4.1 -5.1 -2.4 -2.1 0.1 1.0 1.2 1.2 1.4 1.6 1.2 0.9

>-

8

o

....o~ ~

>-

U1 U1 ~

o

~

~

d

e-

>-

U1

Cf

I-l

o

c.n

TABLE

8c-2.

cr

(Continued)

CALCULATED BINDING ENERGIES IN MEV

I-"

o

Number of neutrons N

Mass number A

Liquid drop

Z

38 39 40 41 42 43 44 45 46 47 48 49 50 51* 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67

78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107

=

Shell correction

scs pairing energy

Total binding energy

Number of neutrons N

Z

40: Zirconium

640.5 655.2 669.3 681.9 694.1 705.9 717."3 728.3 739.0 749.4 759.3 768.9 778.2 787.1 795.7 804.0 811.9 819.6 827.0 834.1 840.9 847.5 853.8 859.8 865.5 870.9 876.1 881.0 885.7 890.2

-0.8 -1.3 -2.1 -2.1 -4.1 -3.8 ....,5.9 -6.0 -5.9 -3.9 -3.6 -0.8 0.6 -0.4 -2.2 -2.9 -3.7 -4.3 -4.7 -2.5 -3.0 -0.9 -0.3 0.6 0.5 0.9 0.9 0.7 0.3 -0.1

3.1 2.0 4.0 2.5 5.2 3.7 6.7 5.4 7.3 4.8 6.6 3.8 4.3 3.8 5.8 4.7 5.9 4.5 5.7 3.1 4.5 2.2 2.8 1.5 2.5 1.4 2.2 1.4 2.5 1.7

639.5 652.6 668.3 679.5 693.4 704.0 717.4 727.5 740.4 750.2 762.3 771.7 783.1 790.4 799.3 805.8 814.1 819.8 827.7 832.9 840.6 845.8 853.0 8Q8.0 864.7 869.1 875.3 879.2 884.8 888 2

Liquid drop

Mass number A

46 47 48 49 50 51 52 53 54 55* 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71

96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113

42 43

85 86

= 42:

95

Z

I

I

O';l

Molybdenum (Continued)

747.9 759.1 770.0 780.5 790.7 800.5 810.0 819.1 827.9 836.5 844.7 852.6 860.3 867.7 874.8 88'1.6 888.1 894.4 900.3 906.1 911.5 916.7 921.7 926.5 931.0 935.3

88 89 90 91 92 93 94

Total binding energy

BeS pairing energy

Shell correction

=

-5.5 -3.2 -3.3 0.1 0.8 0.2 -1.9 -2.5 -3.4 -3.7 -3.9 -4.4 -3.7 -1.4 -1.4 -0.2 -0.3 0.2 -0.1 O. -0.3 -0.5 -1.0 -1.2 -1.4 -1.4

749.7 760.4 773.5 783.8 796.0 804.2 814.0 821.3 830.5 837.2 845.9 851.9 860.3 866.1 874.2 879.8 887.3 892.5 899.5 904.2 910.6 914.8 920.9 924.7 930.3 933.7

7.4 4.6 6.8 3.4 4.5 3.6 6.0 4: 8

6.0 4.4 5.2 4.2 5.1 2.3 3.3 1.7 2.7 1.6 2.6 1.6 2.6 1.7 2.9 2.1 3.0 1.9

43: Technetium

699.8 714.0

I

-3.3 -3.0

I

3.6 1.9

I

698.6 711.6

z ~

Q

~

t:;j

> ~ "'d

=::

to
-'"3

o

e::

~

c

e::

>-

\fl \fl

"%j

o

~

e:: d

e>rn

= 44: Ruthenium

728.6 741.5 754.0 766.2 777 .9 789.3

-4.6 -6.4 -5.1 -2.2 -2.0 1.6

Cf o """""

r:tJ

Z = 48; Cadmium

4.0 5.2 2.0 2.8 2.2

774.2 789.0 801.0 815.0 825.0

49 50 51 52 53

97 98 99 100 101

799.2 811.9 824.3 836.4 848.1

6.3 8.3 6.8 5.4 4.4

cr......

o

~

TABLE

8c-2.

CALCULATED BINDING ENERGIES IN MEV

~

(Continued)

~

~

Number of neutrons N

Mass number A

Liquid drop

Shell correction

BCS pairing energy

Total binding energy

Number of neutrons N

o Mass number A

Z = 48: Cadmium (Continued)

54 55 56 57 58 59 60 61 62 63 64* 65 66 67 68 69 70 71

72 73 74 75 76 77 78 79 80 81 82

102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130

859.4 R70.4 R81.1 891.5 901.5 911.3 920.7 929.9 938.8 947.4 955.7 963.8 971.5 979.1 986.3 993.3 1000.1 1006.6 1012.9 1018.9 1024.7 1030.3 1035.7 1040.9 1045.9 1050.6 1055.2 1059.5 1063.7

3.6 3.1 2.7 1.1 -0.6 -1.5 -2.9 -3.7 -4.1 -4.6 -4.4 -3.4 -3.5 -2.5 -2.7 -1.8 -2.1 -1.3 -1.8 -0.8 -1.3

O. O. 1.9 3.1 4.5 6.0 7.8 9.6

Liquid drop

Shell correction

energy

Total binding energy

2.0 0.7 1.5 0.9 3.5 2.5 4.6 3.5 5.0 3.7 5.0 3.9 5.7 4.4 6.2 4.6 6.2 4.7 5.7 4.0 4.8 2.8 3.7 1.7 2.2 1.0 1.3 -0.1

873.5 883.4 895.4 904.3 916.1 924.6 935.8 943.8 954.4 962.0 972.2 979.3 989.2 996.0 1005.4 1012.0 1021.0 1027.3 1036.0 1042.0 1050.4 1056.1 1064.1 1069.7 1077 .4 1082.9 1090.0 1095.3

BCS pairing

Z = 5'): Tin (Continued) 3 J)

1.7 2.5 2.0 4.5 3.4 5.6 4.6 5.9 4.7 5.9 3.7 5.0 3.0 4.5 2.6 4.2 2.6 4.3 2.6 4.6 2.9 4.6 2.5 3.2 1.9 2.3 0.9 1.0

866.0 875.2 886.3 894.5 905.5 913.1 923.5 930.8 940.6 947.5 956.9 963.5 972.5 978.8 987.4 993.4 1001.6 1007.2 1015.0 1020.3 1027.9 1033.0 1040.3 1045.2 1052.2 1057.0 1063.5 1068.2 1074.3

54 55 56 57 58 59 60 61 62 63 64 65 66 67* 68 69 70 71 72

73

74 75 76 77 78 79 80 81

104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131

864.7 876.6 888.0 899.2 910.1 920.6 930.8 940.8 950.4 959.8 968.8 977.6 986.1 994.4 1002.4 1010 .1 1017.6 1024.9 1031. 9 1038.6 1045.2 1051.5 1057.5 1063.4 1069.0 1074.5 1079.7 1084.7

6.7 6.2 5.8 4.2 2.6 1.5 0.3 -0.5 -1.1 -1.5 -1.6 -2.2 -2.7 -2.8 -3.1 -2.7 -2.7 -2.3 -1.5 -0.6 0.4 1.9 2.9 4.6 6.1 7.4 9.0 10.7

z

q

o

t"i t:rJ

>-

~ ~

~

~ Ul H

o

Ul

Z=4 9: Indium 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66* 67 68 69 70 71 72

78 79 80 81 82 83 84

100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133

826.1 838.5 850.6 862.4 873.8 884.9 895.7 906.1 916.3 926.1 935.7 944.9 953.9 962.6 971.0 979.1 987.0 994.7 1002.0 1009.2 1016.0 1022.7 1029.1 1035.3 1041.2 1047.0 1052.5 1057.8 1062.9 1067.8 1072.5 1077.0 1081.3 1085.4

52 53

102 103

840.1 852.6

73

74 75 76 77

8.3 6.9 5.9 5.0 4.5 4.1 2.5 0.9 -0.2 -1.4 -2.2 -2.7 -3.2 -3.3 -3.8 -4.3 -3.8 -3.9 -3.1 -3.2 -2.6 -2.6 -1.6 -1.1 0.6 1.3 3.1 4.5 5.9 7.4 9.1 10.9 9.6 8.4

-0.2 1.5 0.8 1.9 0.6 1.4 0.9 3.4 2.4 4.5 3.4 4.9 3.6 4.9 3.9 5.6 3.9 5.4 3.5 5.0 3.5 5.0 3.4 4.6 2.4 3.6 1.5 2.1 0.9 1.2 -0.2 -0.1 -0.2 1.0

834.1 846.9 857.2 869.3 878.9 890.5 899.0 910.4 918.5 929.2 936.9 947.1 954.4 964.2 971.0 980.4 986.9 996.0 1002.2 .1010.9 1016.8 1025.1 1030.8 1038.8 1044.2 1051.9 1057.1 1064.4 1069.6 1076.4 1081.4 1087.8 1090.8 1094.8

1.6 0.9

850.2 861.0

Z = 50: Tin

I

I

I

8.6 7.6

I

I

82 83 84 85

132 133 134 135

I

1089.6 1094.2 1098.6 1102.9

12.5 11.2 10.0 9.1

O.

I

-0.1 1.1 0.6

I

1102.1 1105.3 1109.7 1112.6

Z = 51: Antimony

54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69* 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85

105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136

866.5 878.7 890.6 902.2 913.4 924.3 935.0 945.3 955.3 965.0 974.5 983.7 992.5 1001. 2 1009.5 1017.6 1025.5 1033.1 1040.4 1047.5 1054.4 1061.0 1067.5 1073.7 1079.6 1085.4 1091.0 1096.3 1101.5 1106.4 1111.2 1115.8

5.0 4.3 3.8 2.3 1.0

O. -0.9 -1.7 -2.2 -2.5 -3.1 -2.8 -3.0 -2.4 -2.6 -1.8 -1.8 -0.8 -0.9

O. 0.4 1.4 1.9 3.1 4.3 5.6 7.2 8.8 10.6 9.4 8.3 7.4

1.6 0.5 1.5 0.9 3.0 2.0 3.8 2.8 4.3 3.1 4.8 3.1 4.5 2.8 4.2 2.4 3.8 2.0 3.4 1.9 3.1 1.6 2.8 1.4 2.1 0.8 1.1 -0.2 -0.1 -0.1 0.8 0.3

873.1 883.5 895.8 905.3 917.4 926.3 937.8 946.2 957.3 965.3 975.9 983.6 993.7 1001.1 1010.8 1017.8 1027.1 1033.8 1042.7 1049.1 1057.7 1063.9 1072.1 1078.1 1086.0 1091.8 1099.3 1105.0 1112.0 1115.6 1120.3 1123.5

>-

~

o

~ ~

Q

~

>-

W

w "'J

o

::d ~

d

t""

>w

1209.3 1213.0 1218.6 1222.6 1228.2 1232.1 1237.3 1241.0

~

Cerium -0.1 -0.3 -0.7 -0.9 -1.1 -1.0 -0.8 -1.5 -2.0 -2.3

2:

oo

"'d

~ I-

::0

"tI

::q

~

U1 H

o

U1

75 76 77

78 79 80 81 82 83 84* 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102

135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162

1119.6 1129.0 1138.2 1147.1 1155.8 1164.3 1172.5 1180.6 1188.4 1196.0 1203.4 1210.6 1217.6 1224.4 1231.0 1237.5 1243.8 1249.8 1255.7 1261.4 1266.9 1272.2 1277.3 1282.3 1287.0 1291.6 1296.1 1300.4 Z

71

72 73 74 75 76 77 78

132 133 134 135 136 137 138 139

-1.7 -2.4 -2.8 -4.0 -3.8 -2.2 -0.4 1.2 0.3 -1.1 -1.5 -2.8 -2.4 -4.0 -3.8 -3.0 -1.6 -0.8 0.1 0.6 1.2 1.6 2.2 2.6 2.6 2.6 2.8 2.9

1.9 3.2 2.8 5.0 4.6 4.9 3.4 3.6 3.3 4.6 3.8 5.0 3.5 5.0 3.5 3.8 2.1 2.3 1.1 1.7 0.9 1.4 0.5 0.9 0.5 1.1 0.5 1.0

1118.1 1128.7 1137.4 1147.8 1156.6 1166.9 1175.5 1185.4 1192.0 1199.5 1205.6 1212.8 1218.5 1225.4 1230.6 1237.2 1242.4 1249.1 1254.3 1260.8 1265.7 1271.9 1276.5 1282.2 1286.5 1291.8 1295.8 1300.7

0.2 0.7 0.2 1.6 0.8 1.7 1.4 2.9

1079.5 1091.1 1100.6 1111.7 1120.8 1131.5 1140.5 1151.0

= 61: Promethium

1081. 9 1092.6 1103.2 1113.3 1123.2 1133.0 1142.4 1151.6

1.1 1.1 0.6 -0.6 -1.2 -1.5 -2.2 -3.0

75 76 77 78 79 80 81 82 83 84 85 86 87 88* 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106

137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168

1126.3 1136.3 1146.1 1155.6 1165.0 1174.1 1183.0 1191. 6 1200.1 1208.3 1216.4 1224.2 1231.8 1239.2 1246.4 1253.5 1260.4 1267.0 1273.5 1279.7 1285.8 1291.7 1297.4 1302.9 1308.2 1313.4 1318.4 1323.3 1327.9 1332.4 1336.7 1340.9 Z

74 75 76 77

137 138 139 140

=

1118.2 1128.8 1139.1 1149.2

-1.1 -1.4 -2.0 -3.0 -3.4 -3.1 -1.3 0.3 -0.6 -2.0 -2.1 -2.8 -2.9 -2.8 -2.3 -1.5 -0.7

O. 0.7 1.1 1.6 2.0 2.6 3.0 3.0 3.0 3.1 3.3 3.5 3.5 2.8 2.5

1.6 2.4 2.1 3.8 3.9 5.2 3.7 4.0 3.6 4.9 3.8 4.5 3.5 3.7 2.5 2.7 1.6 2.0 1.1 1.6 0.9 1.4 0.5 0.9 0.5 1.1 0.6 1.0 0.4 0.7 0.5 1.2

1124.7 1135.7 1145.0 1155.8 1165.1 1176.1 1185.3 1195.9 1203.1 1211.2 1218.0 1225.8 1232.1 1239.6 1245.5 1253.0 1258.9 1266.4 1272.2 1279.3 1284.8 1291.5 1296.8 1303.1 1308.0 1313.8 1318.3 1323.7 1327.9 1332.9 1336.5 1341.1

1.5 0.8 1.4 0.9

1116.8 1126.5 1137.8 1147.2

:> 8 o

s:: ~

o

s::

:>

tn

Ul ~

o

~ d

~

:>

tn

63: Europium 0.1 -0.7 -0.8 -1.5

cr

I-' I-'

"'-J

TABLE

8c-2.

CALCULATED BINDING ENERGIES IN

cr

MEV (Continued)

~ ~

Number of neutrons N

Mass number A

Liquid drop

Shell correction

BCS pairing energy

Total binding energy

Number of neutrons N

Mass number A

Z = 63: Europium (Continued)

78 79 80 81 82 83 84 85 86 87 88 89* 90 91 92 93 '94 95 96 97 98 99 100 101 102 103 104 105 106 107

141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170

1159.1 1168.7 1178.1 1187.3 1196.3 1205.1 1213.6 1222.0 1230.1 1238.0 1245.8 1253.3 1260.7 1267.8 1274.8 1281.5 1288.1 1294.4 1300.6 1306.5 1312.3 1317.9 1323.4 1328.7 1333.7 1338.7 1343.4 1348.0 1352.5 1356.8

-2.0 -3.0 -3.5 -1.6

O. -0.9 -2.4 -1.8 -2.1 -2.5 -1.8 -1.3 -0.7

O. 0.7 1.2 1.5 1.9 2.4 2.8 3.2 3.2 3.2 3.3 3.5 3.6 3.7 3.0 2.7 2.3

Liquid drop

Shell correction

BCS pairing energy

Total binding energy

4.1 2.9 3.1 2.7 3.8 1.9 2.1 1.7 1.6 0.6 1.2 0.4 0.9 0.3 0.9 0.3 0.8

1185.3 1195.6 1206.9 1215.1 1224.2 1232.0 1240.7 1248.1 1256.6 1263.7 1272.3 1279.2 1287.5 1294.3 1302.2 1308.7 1316.2 1322.3 1329.4 1335.2 1341.8 1347.2 1353.4 1358.4 1364.2 1368.6 1374.0 1378.0 1383.1 1386.8

00

Z = 65: Terbium (Continued)

2.1 2.4 4.3 2.8 2.9 2.7 4.0 2.5 2.8 2.1 2.1 1.0 1.5 0.5 1.0 0.3 0.9 0.3 0.7

O. 0.4

O. 0.6 0.1 0.5 -0.1 0.1

O. 0.7 0.2

1158.2 1167.8 1178.9 1188.5 1199.3 1206.8 1215.3 1222.4 1230.5 1237.2 1245.1 1251. 5 1259.4 1265.7 1273.5 1279.7 1287.1 1293.0 1300.0 1305.5 1312.1 1317.2 1323.4 1328.2 1333.8 1338.3 1343.5 1347.4 1352.3 1355.8

80 81 82 83 84 85 86 87 88 89 90 91 92 93* 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109

145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174

1184.6 1194.4 1204.1 1213.4 1222.6 1231.6 1240.3 1248.8 1257.2 1265.3 1273.3 1281.0 1288.5 1295.8 1302.9 1309.8 1316.6 1323.1 1329.5 1335.6 1341. 6 1347.4 1353.1 1358.6 1363.9 1369.0 1374.0 1378.8 1383.5 1387.9

-3.3 -1.7 -0.2 -1.0 -2.2 -1.0 -1.2 -1.9 -1.0 -0.3

O. 0.4 1.0 1.3 1.7 2.0 2.4 2.9 3.2 3.2 3.3 3.4 3.5 3.7 3.8 3.1 2.8 2.4 2.2 1.6

O. 0.4

O. 0.6 0.1 0.5 -0.1 0.1 -0.1 0.6 0.2 0.7 0.3

z ~

o

t"l t.".1

~ ~

'"d

t:I: ~

tn

~

o

Ul

110 111

Z .. 64: Gadolinium

76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91* 92 93 94 95 V6 97 98 99 100 101 102 103 104 105 106 107 108 109

140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173

1141.4 1151.8 1162.0 1171.9 1181. 6 1191. 2 1200.5 1209.5 1218.4 1227.0 1235.5 1243.7 1251.7 1259.6 1267.2 1274.7 1281.9 1288.9 1295.8 1302.4 1308.8 1315.1 1321. 2 1327.1 1332.8 1338.3 1343.7 1348.9 1353.9 1358.8 1363.5 1368.1 1372.4 1376.7

-0.6 -1.4 -2.2 -3.0 -3.5 -1.8 O. -1.1 -2.3 -1.8 -2.1 -2.5 -2.0 -1.4 -0.5 0.1 0.7 1.2 1.6 2.0 2.4 2.9 3.3 3.3 3.3 3.4 3.6 3.7 3.8 3.1 2.8 2.4 2.1 1.5

1140.9 1150.7 1162.1 1171. 9 1183.4 1193.3 1204.4 1212.2 1221. 0 1228.4 1236.8 1243.9 1252.0 1258.6 1266.8 1273.4 1281.4 1287.8 1295.5 1301.6 1308.9 1314.7 1321. 6 1327.0 1333.4 1338.5 1344.4 1349.2 1354.6 1358.8 1363.9 1367.7 1372.5 1376.0

1.9 1.6 3.1 3.4 5.2 4.0 3.9 3.9 4.9 3.4 3.8 3.0 3.1 1.9 2.1 1.0 1.5 0.7 1.4 0.7 1.2 0.4 0.8 0.4 1.0 0.5 0.9 0.3 0.5 0.3 1.0 0.6 1.1 0.7

Z = 65: Terbium 78 79

143 144

I

1164.4 1174.6

I

-1.1 -2.3

I

I

1163.6 1173.7

175 176

I

1392.3 1396.5

I

1.3 0.9

I

0.9 0.4

1391.6 1395.0

5.3 3.8 4.2 3.7 5.0 2.7 2.9 2.5 2.6 1.4 1.9 0.9 1.5 0.7 1.4 0.7 1.2 0.4 0.8 0.4 1.0 0.5 0.9 0.3 0.5 0.3 1.0 0.5 1.0 0.6 1.3 0.8 1.4 0.9

1188.9 1199.4 1211 .1 1219.6 1228.9 1237.0 1246.1 1253.7 1262.5 1269.7 1278.5 1285.7 1294.3 1301.2 1309.5 1316.2 1324.0 1330.3 1337.7 1343.7 1350.7 1356.3 1362.8 1368.0 1374.1 1378.8 1384.4 1388.8 1394.1 1398.1 1403.2 1406.8 1411.6 1415.1

Z = 66: Dysprosium

II 1.5 2.0

I

II

80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95* 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113

146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179

1187.0 1197.2 1207.1 1216.8 1226.3 1235.5 1244.6 1253.4 1262.0 1270.4 1278.7 1286.7 1294.6 1302.1 1309.5 1316.7 1323.7 1330.6 1337.2 1343.6 1349.9 1356.0 1361.9 1367.7 1373.2 1378.6 1383.9 1388.9 1393.9 1398.6 1403.2 1407.7 1412.0 1416.2

81 82

148 149

Z = 67: Holmium 1199.4 -1.1 1209.6 0.1

I

I

-3.4 -1.6 -0.1 -0.8 -2.3 -0.9 -1.0 -1.7 -1.2 -0.7 -0.1 0.4 0.9 1.3 1.7 2.0 2.4 2.9 3.3 3.3 3.3 3.4 3.5 3.7 3.8 3.2 2.9 2.5 2.2 1.7 1.4 0.9 0.6 0.3

I

>

1-3

0

~

H

o ~

>

U1 U1

""J

0

~

~

d

t"'

>

U1

00

I

I

2.6 3.2

I

1200.9 1212.9

~ ~

~

TABLE

Number of neutrons N

Mass number A

Liquid drop

8c-2.

Shell correction

CALCULATED BINDING ENERGIES IN

BCS pairing energy

Total binding energy

Number of neutrons N

MEV (Continued)

Mass number A

Z = 67: Holmium (Continued)

83 84 85 86 87 88 89 90 91 92 93 94 95 96* 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114

150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181

1219.6 1229.4 1239.0 1248.3 1257.4 1266.4 1275.1 1283.6 1291. 9 1300.0 1307.9 1315.6 1323.1 1330.4 1337.5 1344.4 1351.1 1357.7 1364.0 1370.2 1376.2 1382.1 1387.7 1393.2 1398.6 1403.8 1408.8 1413.6 1418.4 1422.9 1427.3 1431. 6

I

-0.2 -2.0 -0.2

O. -0.9 -0.6 -0.2 0.2 0.7 1.1 1.5 1.8 2.1 2.5 2.9 3.3 3.3 3.3 3.4 3.5 3.7 3.8 3.2 2.9 2.5 2.3 1.8 1.5 1.0 0.8 0.4 0.2

Liquid drop

cr Shell correction

BCS pairing energy

Total binding energy

I-l l\:)

o

Z = 69: Thulium (Continued)

2.3 3.9 1.3 1.3 1.1 1.6 0.6 1.2 0.3 0.9 0.2 0.9 ' 0.2 0.8

O. 0.3

O. 0.6 0.1 0.5 -0.1 0.1 -0.1 0.6 0.1 0.6 0.2 0.8 0.3 1.0 0.4 1.0

1221.7 1231.3 1239.7 1249.1 1257.0 1266.2 1273.8 1283.0 1290.5 1299.4 1306.6 1315.2 1322.1 1330.3 1336.9 1344.6 1350.8 1358.0 1363.9 1370.7 1376.2 1382.5 1387.5 1393.4 1398.0 1403.6 1407.8 1413.2 1417.1 1422.1 1425.8 1430.6

87 88 89 90 91 92 93 94 95 96 97 98 99 100* 101 102 103 104 105 106 107 108 109 110

III 112 113 114 115 116 117 118

156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187

1263.9 1273.4 1282.7 1291.8 1300.7 1309.4 1317.8 1326.1 1334.1 1342.0 1349.7 1357.1 1364.4 1371.5 1378.4 1385.1 1391.7 1398.0 1404.2 1410.3 1416.1 1421.8 1427.3 1432.7 1438.0 1443.0 1448.0 1452.7 1457.3 1461.8 1466.1 1470.3

O. -0.2 -0.3 -0.1 0.2 0.4 0.8 1.1 1.4 1.7 2.2 2.6 2.6 2.6 2.7 2.8 3.0 3.1 2.7 2.4 2.1 1.9 1.4 1.2 0.9 0.7 0.3

O. -0.2 -0.2 -0.3 -0.4

0.7 1.4 0.8 1.4 0.6 1.2 0.4 1.1 0.4 0.9

O. 0.4

O. 0.7 0.1 0.6 -0.1 0.2 -0.1 0.5

O. 0.6 0.1 0.7 0.2 0.8 0.3 1.0 0.4 0.9 0.3 0.8

1264.2 1273.8 1281.9 1291.5 1299.5 1308.8 1316.6 1325.6 1333.1 1341. 7 1348.8 1357.1 1363.8 1371.6 1378.0 1385.3 1391.4 1398.3 1403.9 1410.3 1415.5 1421.6 1426.5 1432.3 1436.8 1442.4 1446.6 1452.0 1456.0 1461.1 1464.9 1469.9

z

q

(1

t"

tz:j

i>

~

"'d

:Il ~

lFl H

(1

in

Z = 68: Erbium

83 84 85 -86 87 88 89 '90 '91 '92 '93 94 95 96 97 98* 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116

151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184

1221.9 1232.0 1241. 9 1251.5 1260.9 1270.1 1279.1 1287.9 1296.6 1304.9 1313.1 1321.1 1328.9 1336.5 1343.9 1351.0 1358.0 1364.8 1371.5 1377.9 1384.2 1390.3 1396.3 1402.0 1407.6 1413.1 1418.3 1423.5 1428.4 1433.2 1437.9 1442.4 1446.8 1451.0

Z = 70: Ytterbium

3.2 4.6 2.1 2.3 1.8 2.4 1.7 2.0 0.9 1.4 0.6 1.2 0.5 1.0 0.2 0.5 0.1 0.8 0.2 0.7

0.2 -1.5 0.2

O. -0.6 -0.7 -0.8 -0.3 0.4 0.9 1.4 1.7 2.1 2.5 3.0 3.4 3.4 3.4 3.5 3.6 3.8 3.9 3.3 3.0 2.6 2.3 1.8 1.5 1.1 0.9 0.4

O. 0.3 0.1 0.7 0.3 0.8 0.4 1.1 0.6 1.2 0.7 1.5 1.0 1.7

O. -0.3 -0.6

157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190

1266.3 1276.1 1285.7 1295.1 1304.3 1313.2 1322.0 1330.5 1338.9 1347.0 1355.0 1362.7 1370.2 1377 .6 1384.8 1391.8 1398.6 1405.2 1411.7 1418.0 1424.1 1430.0 1435.8 1441. 5 1447.0 1452.3 1457.4 1462.5 1467.3 1472.1 1476.6 1481.1 1485.4 1489.5

1245.7 1255.7

89 90 91

160 161 162

Z = 71: Lutetium 1288.2 O. 1297.9 -0.4 1307.3 -0.5

Z = 69: Thulium

85 86

154 155

1244.3 1254.2

I

1.0 0.8

I

0.9 1.1

I

0.4 0.2 -0.2 -0.4 -0.3

1225.2 1235.2 1243.9 1253.5 1261.7 1271. 0 1278.8 1288.1 1295.8 1304.9 1312.4 1321.2 1328.4 1336.8 1343.7 1351.6 1358.1 1365.6 1371.8 1378.8 1384.6 1391.2 1396.5 1402.6 1407.5 1413.4 1417.9 1423.5 1427.8 1433.1 1437.0 1442.1 1445.8 1450.7

87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102* 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120

I

I

O. 0.4 0.7 1.1 1.3 1.8 2.3 2.2 2.2 2.3 2.4 2.6 2.7 2.4 2.2 1.8 1.6 1.3 1.1 0.8 0.6 0.2

O. -0.1 -0.2 -0.1

O. O. O.

I

I

1.5 1.9 1.3 2.1 1.3 2.0 1.1 1.7 1.0 1.5 0.7 1.0 0.7 1.3 0.8 1.3 0.6 0.8 0.5 1.0 0.6 1.1 0.6 1.1 0.6 1.2 0.8 1.5 0.9 1.5 0.8 1.4 1.0 1.8

1267.9 1277.8 1286.0 1295.7 1303.8 1313.4 1321.3 1330.6 1338.3 1347.2 1354.6 1363.1 1370.1 1378.1 1384.8 1392.4 1398.7 1405.9 1411.7 1418.5 1423.9 1430.4 1435.5 1441. 6 1446.4 1452.3 1456.8 1462.5 1466.8 1472.3 1476.4 1481. 7 1485.9 1491.0

0.8 1.7 1.0

1288.3 1298.3 1306.5

I

>-~

0

~

H

0

~

>-

l/2 l/2

'%J

0

;:0

~

d

~

I>

l/2

00 I

I--L t\:) I--L

TABLE

Number of neutrons N

Liquid drop

Mass number A

Z

92 93 94 95 96 97 98 99 100 101 102 103 104· 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122

163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193

= 71:

8c-2.

Shell correction

CALCULATED BINDING ENERGIES IN MEV

BCS pairing energy

I I

Total binding energy

Number of neutrons N

Mass number A

1316.3 1324.4 1334.0 1341.9 1351.0 1358.6 1367.4 1374.7 1383.0 1389.9 1397.8 1404.4 1411.8 1418.0 1425.0 1430.8 1437.5 1442.9 1449.4 1454.5 1460.6 1465.4 1471.4 1476.0 1481.7 1486.1 1491.7 1496.1 1501.5 1505.9 1510.8

94 95 96 97 98 99 100 101 102 103 104 105 106 107* 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125

167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198

-0.5 -0.2

O. 0.5 0.8 1.3 1.7 1.8 1.7 1.8 1.9 2.2 2.2 1.9 1.7 1.4 1.2 0.9 0.9 0.6 0.4

O. -0.2 -0.2 -0.2

O. 0.2 0.4 0.7 1.0 1.1

Liquid drop

.....

Shell correction

BCS pairing energy

Total

tv tv

bil'diD~

energy

Z = 73: Tantalum (Continued)

Lutetium (Continued)

1316.6 1325.6 1334.4 1343.1 1351. 5 1359.7 1367.7 1375.6 1383.2 1390.6 1397.9 1405.0 1411. 9 1418.6 1425.2 1431.5 1437.7 1443.8 1449.7 1455.4 1461.0 1466.4 1471.7 1476.8 1481.8 1486.6 1491. 3 1495.8 1500.2 1504.5 1508.6

00 I

(Continued)

1.8 0.9 1.5 0.6 1.2 0.3 0.7 0.3 1.0 0.4 0.9 0.2 0.5 0.1 0.6 0.2 0.7 0.2 0.7 0.3 0.9 0.5 1.2 0.6 1.1 0.4 0.9 0.4 0.8 0.6 1.3

1340.7 1349.9 1358.9 1367.7 1376.2 1384.6 1392.8 1400.8 1408.6 1416.2 1423.6 1430.9 1437.9 1444.9 1451.6 1458.2 1464.6 1470.8 1476.9 1482.8 1488.6 1494.2 1499.6 1505.0 1510.1 1515.2 1520.0 1524.8 1529.4 1533.9 1538.2 1542.4

-0.4

O. 0.3 0.7 1.0 1.1 1.0 1.1 1.1 1.4 1.5 1.4 1.3 1.1 0.9 0.8 0.8 0.6 0.4 0.2 0.1 0.1 0.2 0.6 1.0 1.6 2.1 2.5 2.8 3.3 3.7 4.1

1.8 0.9 1.3 0.5 0.9 0.4 1.2 0.6 1.2 0.3 0.7 0.3 0.8 0.3 0.9 0.4 0.8 0.4 1.0 0.6 1.3 0.7 1.2 0.4 0.9 0.1 0.6 0.2 0.8 0.5 1.1 1.0

1340.7 1349.0 1358.7 1366.7 1376.0 1383.8 1392.6 1400.1 1408.5 1415.5 1423.6 1430.3 1437.9 1444.3 1451.6 1457.6 1464.6 1470.2 1477.0 1482.3 1488.9 1494.0 1500.3 1505.3 1511.5 1516.5 1522.5 1527.4 1532.9 1.537.6 1512.9 1547.5

z ~

o etr:l

;>

::c

"d ~

~

w. o tn ~

Z

162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195

90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105* 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123

I

165 166

I

=

1321.7 1331.4

Z

72: Hafnium

1300.1 1309.9 1319.4 1328.7 1337.8 1346.8 1355.4 1363.9 1372.2 1380.4 1388.2 1396.0 1403.5 1410.9 1418.0 1425.0 1431.8 1438.5 1444.9 1451.2 1457.4 1463.4 1469.2 1474.9 1480.4 1485.8 1491.0 1496.0 1501.0 1505.8 1510.4 1514.9 1519.3 1523.5 Z

92 93

=

-0.6 -0.5 -0.7 -0.5 -0.2 0.2 0.5 0.9 1.3 1.4 1.3 1.4 1.4 1.7 1.8 1.6 1.5 1.2 1.0 0.8 0.8 0.5 0.3

2.6 1.7 2.5 1.6 2.2 1.3 1.8 1.0 1.4 0.9 1.7 1.1 1.6 0.8 1.2 0.8 1.2 0.8 1.4 0.9 1.3 0.9 1.6 1.1 1.9 1.3 1.9 1.1 1.6 0.9 1.5 1.2 1.9 1.6

O. -0.2 -0.2 -0.2 0.1 0.4 0.9 1.2 1.6 1.8 2.3

1301.6 1310.0 1320.0 1328.3 1338.1 1346.2 1355.6 1363.5 1372.5 1380.0 1388.6 1395.8 1404.0 1410.7 1418.5 1425.0 1432.3 1438.3 1445.3 1451.0 1457.8 1463.1 1469.6 1474.7 1480.9 1485.8 1491.8 1496.5 1502.5 1507.1 1512.9 1517.5 1522.9 1527.3

94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109* 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 120 127

168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201

1343.1 1352.6 1361.8 1370.9 1379.7 1388.4 1396.8 1405.1 1413.2 1421.1 1428.7 1436.3 1443.6 1450.8 1457.7 1464.6 1471.2 1477.7 1484.0 1490.2 1496.2 1502.1 1507.8 1513.3 1518.8 1524.0 1529.2 1534.2 1539.0 1543.7 1548.3 1552.7 1557.1 1561.2

1322.2 1330.7

96 97 98

171 172 173

1364.3 1373.6 1382.7

Z

73: Tantalum

I

-0.6 -0.5

I

1.9 1.2

I

=

I

74: Tungsten

= 75:

-0.4

O. 0.3 0.6 0.9 1.0 0.9 1.1 1.0 1.3 1.4 1.4 1.3 1.2 1.0 1.0 1.0 0.8 0.7 0.5 0.4 0.6 0.8 1.0 1.3 1.8 2.6 3.3 3.3 4.3 4.7 5.3 5.9 5.3

2.3 1.3 1.8 1.0 1.4 0.9 1.7 1.0 1.7 0.8 1.3 0.7 1.2 0.7 1.3 0.7 1.2 0.7 1.4 0.9 1.6 1.0 1.5 0.9 1.6 0.9 1.2 0.7 1.7 1.0 1.5 1.3 1.4 1.2

1343.9 1352.4 1362.3 1370.6 1380.2 1388.1 1397.3 1405.0 1413.7 1420.9 1429.3 1436.3 1444.2 1450.8 1458.4 1464.7 1472.0 1477.9 1484.9 1490.6 1497.4 1502.9 1509.5 1514.8 1521.4 1526.6 1532.9 1538.1 1544.0 1548.9 1554.5 1559.4 1564.4 1567.7

1.4 0.4 1.0

1364.6 1373.0 1382.9

> t-3 o ~ ~ C

~

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t» rJ)

I:Ij

o

~

~

~

t"4 ;>

U2

Rhenium

0.2 0.6 0.8

f

~

~

C;.j

TABLE

8c-2.

CALCULATED BINDING ENERGIES IN MEV

f

(Continued)

~

Number of neutrons N

Liquid drop

Mass number A

Z

99 100 101 102 103 104 105 106 107 108 109 110 111* 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129

174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204

= 75:

Shell correction

BCS pairing energy

Total binding energy

Number of neutrons N

Mass number A

1391. 0 1400.5 1408.3 1417.4 1424.9 1433.6 1440.8 1449.1 1455.9 1463.8 1470.4 1478.0 1484.2 1491.5 1497.4 1504.5 1510.3 1517.3 1523.0 1529.8 1535.3 1541.8 1547.2 1553.3 1558.4 1564.2 1569.2 1574.5 1578.0 1582.2 1585.5

101 102 103 104 105 106 107 108 109 110 111 112 113 114* 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132

178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209

Z

Rhenium (Continued)

1391.7 1400.4 1408.9 1417.2 1425.4 1433.3 1441.1 1448.7 1456.1 1463.4 1470.5 1477.4 1484.1 1490.7 1497.1 1503.4 1509.5 1515.4 1521. 2 1526.9 1532.4 1537.8 1543.0 1548.1 1553.1 1557.9 1562.5 1567.1 1571. 5 1575.8 1579.9

1.0 0.7 0.9 0.8 1.2 1.2 1.5 1.4 1.3 1.1 1.2 1.2 1.0 0.8 0.7 0.4 0.6 0.9 1.3 2.1 2.9 3.8 4.4 5.0 5.5 6.3 6.8 7.5 6.7 6.0 5.5

Liquid drop

0.3 1.2 0.5 1.2 0.3 0.8 0.1 0.6 0.1 0.8 0.2 0.7 0.2 1.1 0.6 1.4 0.7 1.4 0.7 1.0 0.1 0.4 -0.1 0.2 -0.1 0.1 -0.1 -0.1 -0.1 0.5 0.2

= 77:

Shell correction

BCS pairing energy

Total binding energy

0.9 1.6 0.7 1.3 0.3 0.7 0.2 1.0 0.2 0.8 0.3 1.5 0.9 1.5 0.8 1.5 0.6 0.8 0.1 0.4 O. 0.4 -0.1 0.1 -0.1 -0.1 -0.1 0.6 0.3 0.8 0.3 0.7

1414.9 1424.,5 1432.5 1441.8 1449.4 14-58.4 1465.7 1474.2 1481.3 1489.5 1496.2 1504.1 1510.6 1518.4 1524.7 1532.4 1538.5 1545.9 1551. 9 1558.9 1564.8 1571.3 1577.0 1583.2 1588.8 1594.5 1598.5 1603.1 1606.8 1611.3 1614.8 1619.0

tv

~

Iridium (Continued)

1415.0 1423.9 1432.5 1441.0 1449.3 1457.4 1465.4 1473.2 1480.8 148~.2

1495.4 1502.5 1509.4 1516.2 1522.8 1529.2 1535.5 1541. 7 1547.7 1553.5 1559.2 1564.8 1570.2 1575.5 1580.6 1585.6 1590.5 1595.2 1599.8 1604.3 1608.6 1612.8

0.4 0.3 0.6 0.7 1.2 1.4 1.4 1.3 1.4 1.6 1.4 0.7 0.9 1.1 1.5 1.9 2.6 3.5 4.2 5.0 5.7 6.2 6.9 7.7 8.3 8.9 8.1 7.3 6.8 6.3 5.9 5.5

Z

G C1

~

t'1

>

~

'"d

~ ~

U2' H

C1 U2

=

76: Osmium

1385.2 1394.5 1403.4 1412.2 1420.8 1429.2 1437.4 1445.5 1453.3 1461.0 1468.5 1475.9 1483.0 1490.0 1496.8 1503.5 1510.0 1516.4 1522.5 1528.6 1534.5 1540.3 1545.9 1551.4 1556.7 1561.9 1566.9 1571.8 1576.6 1581.2 1585.7 1590.1 1594.4 1598.5

1.0 1.2 0.9 1.1 1.0 1.3 1.4 1.8 1.8 1.7 1.5 1.6 1.5 1.3 0.8 0.7 0.8 1.1 1.5 2.4 3.5 4.0 4.6 5.3 6.0 6.8 7.7 8.3 9.0 8.1 7.3 6.6 6.0

=

77: Iridium

Z

174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207

98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113* 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131

Z

99

I

~-

176 177

I

1396.7 1405.9

Z

O. 0.1

O. O. O. 0.7 0.4 1.1 0.7

5.5

I

0.4 0.1

1386.0 1394.4 1404.1 1412.3 14Z1. 6 1429.3 1438.3 1445.8 1454.3 1461.4 1469.6 1476.4 1484.3 1490.7 1498.4 1504.6 1512.0 1518.1 1525.5 1531.4 1538.6 1544.5 1551.3 1556.9 1563.3 1568.7 1574.8 1580.1 1585.6 1589.3 1593.7 1597.2 1601.4 1604.7

1.3 0.5 1.5 0.7 1.4 0.5 1.1 0.2 0.7 0.2 1.0 0.3 0.9 0.5 1.6 1.2 1.8 1.0 1.5 0.4 0.6 0.2 0.8 0.2 0.6

101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116* 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134

=

I

I

1396.6 1406.6

103 104

I

182 183

-0.1

1417.3 1426.4 1435.4 1444.1 1452.7 1461.1 1469.3 1477.3 1485.1 1492.8 1500.3 1507.7 1514.8 1521.8 1528.7 1535.4 1541.9 1548.3 1554.5 1560.6 1566.6 1572.4 1578.0 1583.5 1588.9 1594.1 1599.2 1604.2 1609.0 1613.7 1618.3 1622.7 1627.0 1631.2

179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212

Z

0.8 1.8

78: Platinum

I

1437.7 1446.7

O. 0.2 0.4 0.9 1.2 1.3 1.2 1.5 1.7 1.5 1.4 1.6 1.8 2.2 2.5 3.1 3.8 4.6 5.4 6.0 6.3 7.1 7.8 8.3 9.0 8.2 7.3 6.8 6.1 5.7 5.2 5.2 4.7

=

1.3 2.1 1.1 1.8 0.6 1.1 0.5 1.3 0.4 1.0 0.6 1.6 0.9 1.6 0.8 1.5 0.7 1.1 0.2 0.5 0.1 0.7 0.1 0.4 0.3 0.4 0.2 1.1 0.7 1.3 0.9 1.4 0.6 1.2

1417.6 1427.6 1435.7 1445.3 1453.2 1462.4 1470.0 1478.9 1486.2 1494.7 1501.7 1510.0 1516.7 1524.7 1531.3 1539.1 1545.4 1553.0 1559.2 1566.5 1572.6 1579.4 1585.2 1591.8 1597.5 1603.5 1607.7 1612.6 1616.5 1621.2 1624.9 1629.4 1632.8 1637.1

1.2 1.9

1437.5 1447.4

79: Gold

I

-0.7 -0.6

I

I

>

~

0

~ ~

Q

~

>

U1 U1 ~

0

~

a:: e> U1 q

cr

......

tv

W Ul

~

0 ::0

s::

q

r-

>

r.J1

= 83: Bismuth 00

107 108

I

188 189

I

1478.0 1486.8

I

-1.4 -1. 7

I

1.4 2.7

I

1477.7 1487.5

111 112

I

194 195

I

1517.7 1526.2

-1.3 -1.4 I

I

I

r ......

tv --l

TABLE

8c-2.

CALCULATED BINDING ENERGIES IN MEV

(Continued)

..

Number of neutrons N

Liquid drop

Mass number A

Z

113 114 115 116 117 118 119 120 121 122 123 124 125 126* 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144

196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227

= 83:

Shell correction

BeS pairing energy

Total binding energy

Number of neutrons N

Mass number A

Bismuth. (Continued)

1534.6 1542.9 1550.9 1558.8 1566.6 1574.2 1581.6 1588.9 1596.0 1603.0 1609.8 1616.4 1623.0 1629.3 1635.6 1641.7 1647.6 1653.4 1659.1 1664.6 1670.0 1675.3 1680.4 1685.5 1690.3 1695.1 1699.7 1704.3 1708.6 1712.9 1717.1 1721.1

-0.6 -0.3 0.6 1.4 2.2 3.3 3.8 4.5 5.1 5.8 6.6 7.4 8.0 8.7 7.8 7.0 6.5 5.9 5.5 5.1 4.8 4.5 4.4 4.3 3.0 1.8 0.8 -0.3 -0.9 -1.7 -2.0 -2.5

Liquid drop

Z

1.2 2.1 1.0 1.4 0.4 0.6 0.1 0.6 0.1 0.5 -0.1 0.1 -0.1

O. -0.1 0.6 0.3 0.8 0.4 0.9 0.3 0.7 -0.1 0.1

O. 1.6 1.3 2.6 2.0 3.1 2.3 3.3

1535.0 1544.6 1552.4 1561. 5 1569.1 1578.0 1585.5 1593.9 1601. 2 1609.2 1616.3 1623.9 1630.8 1637.9 1643.3 1649.3 1654.4 1660.1 1665.0 1670.6 1675.1 1680.5 1684.8 1689.8 1693.3 1698.5 1701.8 1706.6 1709.7 1714.3 1717.4 1721.8

116 117 118 119 120 121 122 123 124 125 126 127 128 129* 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147

201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232

= 85:

Shell correction

BeS pairing energy

Total binding energy

1.9 1.0 1.3 0.8 1.3 0.8 1.3 0.7 1.0 0.8 0.9 0.8 1.5 1.2 1.8 1.3 1.8 1.2 1.6 0.7 1.0 0.8 2.6 2.0 3.4 2.6 3.7 2.5 3.0 0.9 1.3 1.0

1566.0 1574.1 1583.4 1591.4 1600.3 1608.0 1616.5 1624.0 1632.1 1639.5 1647.1 1652.8 1659.3 1664.8 1671.1 1676.3 1682.4 1687.4 1693.2 1697.9 1703.4 1707.3 1712.9 1716.6 1721.9 1725.5 1730.5 1734.0 1738.8 1742.4 1747.2 1750.8

cr ~

~

00

Astatine (Continued)

1564.9 1573.2 1581.2 1589.1 1596.8 1604.4 1611.9 1619.1 1626.3 1633.2 1640.1 1646.8 1653.3 1659.7 1665.9 1672.1 1678.0 1683.9 1689.6 1695.2 1700.6 1705.9 1711.1 1716.2 1721.1 1725.9 1730.6 1735.2 1739.7 1744.1 1748.3 1752.5

-0.7 0.1 0.9 1.5 2.1 2.8 3.4 4.2 4.9 5.4 6.1 5.3 4.5 4.0 3.4 3.0 2.5 2.4 2.0 2.0 1.8 0.6 -0.8 -1.5 -2.7 -3~0

-3.8 -3.6 -3.6 -1.9 -1.6 -1.4

zo

o

et:9 > ~

~

~ ....

o

m

Z = 84: Polonium 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127* 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145

196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229

1528.5 1537.2 1545.6 1554.0 1562.1 1570.1 1577.9 1585.6 1593.1 1600.4 1607.6 1614.7 1621. 6 1628.3 1634.9 1641.4 1647.7 1653.9 1659.9 1665.8 1671.6 1677.2 1682.7 1688.0 1693.3 1698.4 1703.3 1708.2 1712.9 1717.5 1722.0 1726.4 1730.6 1734.7

114 115

199 200

1548.0 1556.6

Z

-1.9 -1.3 -1.5 -0.5 -0.1 1.0 1.9 2.5 2.9 3.6 4.3 5.3 6.0 6.6 7.3 6.5 5.6 5.0 4.3 3.9 3.4 3.3 3.0 3.1 2.9 1.7 0.2 -0.6 -2.0 -2.4 -3.5 -3.5 -4.3 -3.2

2.7 1.7 3.1 1.8 2.6 1.4 1.8 1.2 1.9 1.4 1.8 1.0 1.3 1.1 1.2 1.1 1.9 1.6 2.3 1.9 2.4 1.7 2.1 1.0 1.3 1.1 3.0 2.4 4.1 3.3 4.8 3.6 4.8 2.8

1529.1 1537.4 1547.1 1555.1 1564.6 1572.4 1581.6 1589.3 1598.0 1605.5 1613.7 1621.0 1628.9 1636.1 1643.4 1648.9 1655.2 1660.5 1666.5 1671. 5 1677.4 16$2.1 1687.7 1692.2 1697.5 1701. 2 1706.6 1710.0 1715.1 1718.4 1723.2 1726.4 1731.1 1734.2

Z = 85: Astatine

I

I

I

-1.5 -1.1

I

2.0 1.3

I

1548.2 1556.5

117 118 119 120 121 122 123 124 125 126 127 128 129 130 131* 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148

203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234

1575.8 1584.0 1592.2 1600.1 1608.0 1615.6 1623.1 1630.5 1637.7 1644.7 1651. 6 1658.4 1665.0 1671.5 1677.8 1684.0 1690.1 1696.0 1701.8 1707.5 1713.0 1718.4 1723.7 1728.8 1733.9 1738.7 1743.6 1748.3 1752.9 1757.4 1761. 7 1765.9 Z

119 120 121 122

206 207 208 209

=

=

1594.8 1603.0 1611.0 1618.9

86: Radon -0.7

O. 0.5 0.9 1.7 2.1 3.1 3.7 4.3 4.9 4.2 3.3 2.8 2.1 1.7 1.2 1.1 0.7 1.0 0.6 -0.4 -2.1 -2.6 -4.1 -4.0 -5.0 -4.0 -2.2 -1.9 -1.7 -1.5 -1.2

1.7 2.2 1.7 2.4 1.8 2.4 1.6 2.1 1.9 2.0 1.8 2.7 2.3 3.0 2.6 3.1 2.3 2.8 1.7 2.1 1.7 3.8 3.0 4.8 3.5 4.8 2.9 2.1 1.5 2.0 1.8 2.2

1576.6 1586.2 1594.4 1603.5 1611.4 1620.2 1627.9 1636.3 1643.9 1651. 7 1657.6 1664.4 1670.1 1676.6 1682.0 1688.3 1693.5 1699.6 1704.5 1710.2 1714.3 1720.1 1724.1 1729.5 1733.3 1738.5 1742.3 1747.4 1751.4 1756.5 1760.5 1765.3

1.1 1.5 1.0 1.8

1595.6 1605.0 1613.2 1622.1

>

8

o

a:: ......

o

~

>

U1 U1 ":.j

o

~

a::

d

r-

>

U1

87: Francium -0.2 0.5 1.2 1.4

cr ~

tv

CO

TABLE

8c-2.

CALCULATED BINDING ENERGIES IN MEV

(Continued)

err> ~

Number of neutrons N

Mass number A

Liquid drop

BeS pairing energy

Shell correction

Total binding energy

Number of neutrons N

Mass number A

Z == 87: Francium (Continued)

Z

121 122

I

209 210

2.3 2.8 3.3 4.0 3.3 2.4 1.9 1.2 0.9 0.4 0.3 -0.1 0.1 -0.3 -1.3 -2.9 -3.3 -4.7 -4.4 -4.7 -2.4 -2.1 -2.0 -1.8 -1.6 -1.2 -0.4 -0.2

1626.7 1634.2 1641.7 1648.9 1656.1 1663.1 1669.9 1676.6 1683.2 1689.6 1695.9 1702.0 1708.0 1713.9 1719.6 1725.2 1730.7 1736.1 1741.3 1746.4 1751.6 1756.5 1761.3 1765.9 1770.5 1774.9 1779.2 1783.3

210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237

123 124 125 126 127 128 129 130 131 132 133* 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150

I

=

1613.6 1621.8

Liquid drop

Z

1.1 1.6 1.5 1.6 1.3 2.2 1.8 2.5 2.0 2.5 1.7 2.3 1.2 1.7 1.3 3.3 2.4 4.1 2.7 3.3 1.0 1.4 1.1 1.6 1.3 1.6 0.8 1.0

1630.1 1638.6 1646.5 1654;5 1660.7 1667.6 1673.6 1680.3 1686.0 1692.5 1697.9 1704.2 1709.3 1715.3 1719.6 1725.6 1729.8 17354 1739.5 1744.9 1749.2 1754.7 1759.0 1764.3 17'68.5 1773.5 1777.6 1782.3

129 130 131 132 133 134 135 136 137* 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152' 153 154

0.5 0.6

1.7 2.7

1615.9

I 1625.0

125 126

I

215 216

0.4 -0.3 -0.7 -1.2 -1.2 -1.7 -1.4 -1.8 -2.7 -4.5 -4.7 -6.2 -3.2 -2.5 -2.2 -2.1 -1.8 -1.5 -0.9 -0.6

1760.6 1766.0 1771.3 1776.6 1781.6 1786.6 1791. 3 1796.1 1800.6 1805.0 1809.3 1813.6 1817.6

I

iJ,)

o

Actinium (Continued)

l'i55.0

Z

I

Shell correction

1678.3 1685.4 1692.4 1699.3 1706.0 1712.6 1719.0 1725.3 1731.5 1737.5 1743.4 1749.2

218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243

88: Radium

I

= 89:

Total binding energy

BeS pairing energy

=

1650.9 1658.8

1680.8 1687.9 1694.1 1701.0 1706.9 1713.5 1719.1 1725.5 1730.3 1736.7 1741.3 1747.4 1752.3 1758.4 1763.4 1769.4 1774.2 1779.9 1784.6 1790.1 1794.6 1799.7 1804.0 1808.6 1812.5 1816.9

2.0 2.8 2.3 2.9 2.0 2.7 1.5 2.0 1.5 3.6 2.6 4.4 1.3 1.5 0.9 1.6 1.2 1.6 0.9 1.2 0.7 0.9 0.7 0.8 0.7 1.0

O. 0.2 0.3 0.3 0.1 -0.1 90: Thorium

I

1.3 1.9

I

2,5 2.6

I

1654.6 1663.3

z oo etJ:1

>

;t1 ~

= ~

rp

~

C"}

rp

123 124 125 126 127 128 129 130 131 132 133 134 135* 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152

211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240

1629.7 1637.5 1645.2 1652.7 1660.1 1667.3 1674.3 1681.2 1688.0 1694.7 1701.2 1707.5 1713.7 1719.8 1725.8 1731.6 1737.3 1742.9 1748.4 1753.8 1759.0 1764.1 1769.1 1774.0 1778.7 1783.3 1787.9 1792.2 1796.4 1800.5 Z

123 124 125 126 127 128

212 213 214 215 216 217

= 89:

1632.3 1640.4 1648.3 1656.0 1663.6 1671.0

1.5 2.0 2.5 3.1 2.5 1.5 1.1 0.4 O. -0.5 -0.5 -1.0 -0.7 -1.1 -2.0 -3.8 -4.0 -5.6 -4.5 -3.1 -2.3 -2.1 -2.0 -1.8 -1.4 -1.0 -0.3 -0.1 O. 0.1

2.0 2.5 2.4 2.5 2.2 3.1 2.6 3.4 2.9 3.5 2.6 3.3 2.1 2.6 2.1 4.2 3.1 5.0 3.0 2.5 1.5 2.1 1.8 2.3 1.8 2.1 1.4 1.6 1.4 1.6

1633.2 1642.0 1650.0 1658.3 1664.7 1671.9 1678.1 1685.0 1690.9 1697.6 1703.3 1709.7 1715.1 1721.3 1725.8 1732.0 1736.4 1742.3 1746.6 1752.4 1757.1 1762.8 1767.4 1772.9 1777 .4 1782.6 1786.9 1791. 8 1796.0 1800.4

127 128 129 130 131 132 133 134 135 136 137 138 139* 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156

217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246

Actinium 0.8 1.3 1.8 2.4 1.8 0.8

1666.6 1674.3 1681.8 1689.2 1696.4 1703.5 1710.4 1717.2 1723.8 1730.3 1736.7 1743.0 1749.1 1755.2 1761.2 1766.9 1772.6 1778.1 1783.5 1788.8 1793.9 1798.9 1803.8 1808.5 1813.2 1817.7 1822.1 1826.4 1830.6 1834.6 Z

1.4 1.9 1.8 1.9 1.6 2.5

1634.5 1643.5 1651. 8 1660.3 1667.0 1674.4

128 129 130 131 132 133

219 220 221 222 223 224

= 91:

1677.1 1684.9 1692.5 1699.9 1707.2 1714.3

1.2 0.3 -0.1 -0.8 -1.0 -1.6 -1.5 -2.2 -2.0 -2.3 -3.3 -5.0 -5.1 -3.6 -2.7 -2.0 -1.9 -1.7 -1.4 -1.0 -0.5 -0.2 0.3 0.6 0.6 0.7 0.5 0.3 -0.1 -0.5

2.4 3.2 2.7 3.4 2.8 3.5 2.6 3.4 2.3 2.7 2.3 4.4 3.3 2.8 1.6 1.8 1.4 2.0 1.5 1.9 1.3 1.6 1.1 1.2 1.1 1.2 1.1 1.4 1.3 1.9

1670.2 1677.8 1684.5 1691.8 1698.2 1705.3 1711.4 1718.3 1724.1 1730.7 1735.7 1742.3 1747.2 1753.6 1758.9 1765.3 1770.6 1776.8 1781.8 1787.8 1792.7 1798.3 1803.1 1808.3 1812.9 1817.7 1821.8 1826.3 1829.9 1834.4

2.6 2.1 2.9 2.6 3.0 1.9

1679.5 1686.4 1693.9 1700.5 1707.9 1714.2

> ~ c ~ .... o

~

>

W

W ~

o l:O a;: d

e-

>

tr:

Protactinium -0.2 -0.7 -1.4 -2.0 -2.3 -2.0

cr.....

~

.....

TABLE

8c-2.

CALCULATED BINDING ENERGIES IN MEV

Cf

(Continued)

"""'" CI:l Number of neutrons N

Liquid drop

Mass number A

Total binding energy

BCS pairing energy

Shell correction

Number of neutrons N

Mass number A

225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248

-2.7 -2.6 -2.7 -4.0 -5.4 -3.5 -2.9 -2.3 -1.7 -1.4 -1.2 -0.9 -0.6 -0.2 0.2 0.6 0.8 0.9 1.0 0.8 0.6 0.3 -0.1 -0.4

1721. 3 1728.2 1734.9 1741. 5 1748.0 1754.5 1760.7 1766.9 1772.8 1778.7 1784.4 1790.0 1795.5 1800.8 1806.0 1811.1 1816.0 1820.8 1825.6 1830.2 1834.6 1839.0 1843.3 1847.4

1721.3 1727.3 1734.2 1739.4 1746.2 1751.6 1758.4 1764.0 1770.7 1776.2 1782.6 1787.9 1794.0 1799.2 1805.0 1810.0 1815.4 1820.2 1825.2 1829.4 1834.1 1838.0 1842.6 1846.3

2.7 1.7 1.9 1.8 3.6 1.5 1.7 0.8 1.0 0.7 1.2 0.8 1.1 0.6 0.9 0.5 0.6 0.5 0.6 0.5 0.8 0.6 1.2 0.8

Z = 92: Uranium

130 131 132

I

222 223 224

I

1695.3 1703.0 1710.5

I

-1.6 -1.6 -2.3

I

Shell correction

~

Z = 93: Neptunium (Continued)

Z = 91: Protactinium (Continued)

134 135 136 137 138 139 140 141* 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157

Liquid drop

Total binding energy

BCS pairing energy

3.4 2.7 3.3

I

1697.1 1704.0 1711.5

141 142 143 144 145* 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161

234 235 236 237 238 239 240 241 24,2 243 244 245 246 247 248 249 250 251 252 253 254

1776.9 1783.3 1789.5 1795.6 1801.6 1807.5 1813.2 181S.8 1824.3 1829.6 1834.9 184.0.0 1845.0 1849.8 1854.6 1859.2 1863.8 1868.2 1872.5 1876.7 1880.8

-1.4 -0.8 -0.7 -0.4 -0.2 0.2 0.6 1.0 1.3 1.6 1.6 1.7 1.5 1.3 1.0 0.7 0.4 0.2 0.1 0.1 0.1

0.5 0.8 0.5 1.0 0.6 0.9 0.4 0.6 0.3 0.4 0.3 0.4 0.3 0.6 0.4 0.9 0.6 1.1 0.7 1.0 0.4

I

I

1774.4 1781.5 1787.5 1794.3 1800.1 1806.6 1812.1 1818.4 1823.7 1829.6 1834.7 1840.1 1844.7 1849.8 1854.1 1859.0 1863.1 1867.8 1871. 7 1876.2 1879.9

Z = 94: Plutonium

134 135 136 137 138 139

228 229 230 231 232 233

1731.2 1738.7 1746.0 1753.4 1760.6 1767.7

-3.8 -4.0 -4.3 -3.0 -2.3 -2.0

3.5 2.9 3.3 1.7 1.9 1.4

1730.9 1737.6 1745.0 1751.4 1759.0 1765.6

zq o

to"

t".l

> ~ "'d ~ ~

(fl H

o

t»

133 134 135 136 137 138 139 140 141 142 143* 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159

225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251

1717.8 1725.0 1732.1 1739.1 1745.9 1752.7 1759.3 1765.8 1772.1 1778.3 1784.3 1790.2 1796.0 1801. 7 1807.2 1812.6 1817.9 1823.0 1828.1 1833.0 1837.8 1842.5 1847.0 1851.5 1855.8 1860.0 1864.2

-2.4 -2.9 -3.1 -3.0 -4.7 -3.9 -2.9 -2.3 -1.8 -1.1 -1.0 -0.8 -0.5 -0.2 0.2 0.6 0.9 1.2 1.2 1.3 1.1 1.0 0.7 0.3 0.1 -0.1 -0.2

2.7 3.3 2.6 2.6 3.0 3.0 1.6 1.9 1.1 1.3 1.0 1.6 1.2 1.5 1.0 1.3 0.9 1.0 0.9 1.0 0.9 1.2 0.9 1.5 1.2 1.6 1.2

1718.1 1725.4 1731. 6 1738.6 1744.1 1751.1 1757.0 1764 .1 1769.9 1776.9 1782.6 1789.2 1794.7 1801.0 1806.4 1812.4 1817.6 1823.2 1828.2 1833.4 1837.8 1842.7 1846.8 1851.6 1855.4 1860.0 1863.7

Z = 93: Neptunium

132 133 134 135 136 137 138 139 140

225 226 227 228 229 230 231 232 233

1713.3 1720.9 1728.3 1735.6 1742.8 1749.9 1756.9 1763.7 1770.4

-2.2 -2.6 -3.1 -3.6 -3.8 -3.6 -2.7 -2.4 -1.9

2.3 1.9 2.4 2.0 2.2 1.6 1.6 0.9 1.3

1713.3 1720.1 1727.5 1734.0 1741.2 1747.3 1754.7 1760.9 1768.3

140 141 142 143 144 145 146 147* 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163

234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257

1774.5 1781.3 1787.8 1794.3 1800.6 1806.8 1812.8 1818.7 1824.5 1830.2 1835.8 1841.2 1846.5 1851.7 1856.8 1861. 7 1866.6 1871.3 1875.9 1880.4 1884.8 1889.1 1893.3 1897.3

-1.4 -0.9 -0.3 -0.2

O. 0.3 0.7 1.0 1.4 1.7 2.0 2.0 2.2 1.9 1.8 1.5 1.2 0.8 0.6 0.5 0.4 0.5 0.6 0.3

1.7 0.9 1.2 0.8 1.3 0.9 1.2 0.7 1.0 0.6 0.7 0.6 0.7 0.6 0.9 0.7 1.2 0.9 1.4 1.0 1.4 0.8 1.0 0.8

1773.2 1779.5 1786.9 1793.0 1800.0 1806.0 1812.7 1818.5 1824.9 1830.5 1836.5 1841. 8 1847.4 1852.3 1857.5 1862.0 1867.1 1871.3 1876.3 1880.3 1885.1 1888.9 1893.4 1897.1

230 231 232 233 234 235 236 237 238 239 240 241

1741.3 1749.0 1756.6 1764.0 1771. 2 1778.3 1785.2 1791. 9 1798.6 1805.1 1811.5 1817.7

-4.2 -2.7 -2.2 -1.8 -1.4 -0.8 -0.4 0.1 0.3 0.5 0.8 1.2

s=

1-4

o

~

>-

tn tn

~

o

~

~

Z = 95: Americium

135 136 137 138 139 140 141 142 143 144 145 146

> o

1-3

t"1

2.2 1.6 0.8 1.5 0.7 1.1 0.3 0.6 0.2 0.8 0.3 0.6

1739.2 1747.1 1754.0 1762.1 1768.8 1776.7 1783.2 1790.8 1797.2 1804.4 1810.6 1817.5

>-

U2

f....... C/.j

ce

TABLE

8c-2.

CALCULATED BINDING ENERGIES IN MEV

00 I

(Continued)

~

CI:i

Number of neutrons N

Mass number A

Liquid drop

Shell correction

BCS pairing energy

Total binding energy

Number of neutrons N

Mass number A

242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259

1823.8 1829.8 1835.7 1841.5 1847.1 1852.6 1858.0 1863.2 1868.4 1873.4 1878.4 1883.2 1887.9 1892.5 1896.9 1901.3 1905.6 1909.8

1.5 1.9 2.2 2.5 2.5 2.6 2.3 2.2 1.9 1.7 1.3 1.1 0.9 0.9 0.9 1.0 0.7 0.5

0.1 0.4 O. 0.2 O. 0.1 O. 0.3 0.1 0.6 0.3 0.8 0.4 0.8 0.2 0.4 0.1 0.6

1823.4 1830.1 1835.8 1842.1 1847.6 1853.4 1858.4 1863.9 1868.5 1873.8 1878.2 1883.3 1887.6 1892.5 1896.5 1901.2 1905.0 1909.4

1.8 0.9 1.3 0.5 0.8 0.5 1.0 0.5 0.8

1765.7 1772.7 1780.7 1787.5 1795.3 1801.8 1809.3 1815.6 1822.8

Z = 96: Curium

138 139 140 141 142 143 144 145 146

234 235 236 237 238 239 240 241 242

1766.9 1774.3 1781.5 1788.6 1795.6 1802.4 1809.1 1815.7 1822.2

-1.2 -0.7 -0.2 0.2 0.7 0.8 1.1 1.3 1.7

Shell correction

BCS pairing energy

Total binding energy

Z = 97: Berkelium (Continued)

Z = 95: Americium (Continued)

147 148* 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164

Liquid drop

J+:o.

157 158 159 160 161 162 163 164 165 166 167

254 255 256 257 258 259 260 261 262 263 264

1891.2 1896.4 1901. .5 1906.4 1911. 3 1916.0 1920.7 1925.2 1929.7 1934.0 1938.2

2.2 1.9 1.7 1.6 1.5 1.7 1.5 1.4 1.2 1.1 0.8

0.2 0.8 0.4 0.8 0.3 0.4 0.1 0.4 0.1 0.4 0.1

1891.8 1897.3 1901.8 1907.1 1911.5 1916.6 1920.7 1925.5 1929.4 1934.0 1937.6

~

q

(1

et:tj >

~

~

::I1

Z = 98: Californium

~ tn ,..;

142 143 144 145 146 147 148 149 150 151 152 153 154* 155 156 157

240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255

1801. 6 1808.9 1816.0 1823.0 1829.8 1836.6 1843.2 1849.6 1856.0 1862.2 1868.3 1874.2 1880.1 1885.8 1891.4 1896.9

1.3 1.4 1.6 1.9 2.3 2.7 3.1 3.3 3.6 3.6 3.7 3.5 3.3 3.0 2.8 2.5

0.9 0.6 1.1 0.6 0.9 0.4 0.6 0.3 0.4 0.3 0.4 0.3 0.6 0.4 0.8 0.6

1802.0 1809.0 1816.8 1823.6 1831.1 1837.6 1844.9 1851.2 1858.0 1864.1 1870.5 1876.1 1882.2 1887.4 1893.3 1898.2

(1

to

147 148 149 150* 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165

243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261

1828.5 1834.7 1840.8 1846.7 1852.5 1858.2 1863.8 1869.3 1874.6 1879.9 1885.0 1890.0 1894.9 1899.6 1904.3 1908.9 1913.3 1917.7 1921. 9 Z

140 141 142 143 144 145 146 147 148 149 150 151 152* 153 154 155 156

237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253

=

2.1 2.5 2.7 3.0 3.0 3.1 2.9 2.8 2.5 2.2 1.9 1.7 1.4 1.4 1.4 1.6 1.2 1.1 0.9

0.3 0.6 0.2 0.4 0.2 0.3 0.2 0.5 0.3 0.8 0.5 1.0 0.7 1.0 0.4 0.6 0.4 0.8 0.4

1828.9 1835.7 1841.7 1848.1 1853.8 1859.8 1865.0 1870.7 1875.6 1881.0 1885.6 1890.9 1895.3 1900.4 1904.6 1909.5 1913.5 1918.1 1921.8

97: Berkelium

1784.4 1791. 7 1798.8 1805.9 1812.8 1819.6 1826.2 1832.8 1839.1 1845.4 1851.6 1857.6 1863.5 1869.2 1874.9 1880.5 1885.9

0.1 0.5 0.9 1.1 1.3 1.6 2.0 2.3 2.7 3.0 3.2 3.3 3.4 3.1 3.0 2.7 2.5

1.0 0.3 0.6 0.2 0.7 0.2 0.6 0.1 0.3

O. 0.1 O. 0.1 O. 0.3 0.1 0.5

1783.5 1790.5 1798.5 1805.2 1812.9 1819.4 1826.8 1833.1 1840.2 1846.3 1853.0 1858.9 1865.0 1870.4 1876.3 1881. 3 1887.0

158 159 160 161 162 163 164 165 166 167 168 169

256 257 258 259 260 261 262 263 264 265 266 267

1902.3 1907.6 1912.8 1917.8 1922.7 1927.6 1932.3 1936.9 1941.4 1945.8 1950.1 1954.3 Z

144 145 146 147 148 149 150 151 152 153 154 155 156* 157 158 159 160 161 162 163 164 165 166 167

243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266

=

2.3 2.0 1.9 1.9 1.9 1.8 1.9 1.6 1.4 1.1 0.9 0.5

1.1 0.7 1.1 0.6 0.9 0.4 0.7 0.4 0.7 0.5 0.9 0.6

1903.9 1908.6 1914.1 1918.6 1923.9 1928.2 1933.3 1937.3 1942.1 1945.9 1950.4 1954.0

99: Einsteinium

1818.8 1826.0 1833.0 1840.0 1846.7 1853.4 1859.9 1866.3 1872.6 1878.8 1884.9 1890.8 1896.6 1902.3 1907.9 1913.3 1918.7 1923.9 1929.0 1934.1 1939.0 1943.8 1948.5 1953.1

2.0 2.3 2.8 3.1 3.5 3.7 4.0 4.0 4.1 3.9 3.7 3.4 3.2 2.9 2.7 2.5 2.4 2.3 2.3 2.3 2.4 2.1 1.8 1.5

0.7 0.2 0.5

O. 0.2 -0.1 0.1 -0.1

O. -0.1 0.3 O. 0.5 0.2 0.7 0.3 0.8 0.3 0.6 O. 0.2 O. 0.4 0.1

1819.6 1826.6 1834.3 1841.1 1848.5 1855.1 1862.1 1868.4 1874.9 1880.7 1887.0 1892.4 1898.4 1903.6 1909.5 1914.4 1920.0 1924.7 1930.2 1934.7 1939.9 1944.2 1949.1 1953.1

> 8 o

a::

~

o

a::

>

1jl 1jl

l%J

o

~

a:: ~

t'"

> 1jl

,....,

co

~

CJ1

TABLE

8c-2.

cr

(Continued)

CALCULATED BINDING ENERGIES IN MEV

~

0"

Number of neutrons N

Mass number A

Z

168 169 170 171

I

267 268 269 270

Liquid drop

= 99:

246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268

Number of neutrons N

Mass number A

Einsteinium (Continued)

1957.6 1961.9 1966.3 1971.0 Z

146 147 148 149 150 151 152 153 154 155 156 157 158* 159 160 161 162 163 164 165 166 167 168

Total binding energy

BCS pairing energy

Shell correction

=

1835.8 1842.9 1849.9 1856.8 1863.5 1870.1 1876.6 1882.9 1889.2 1895.3 1901.3 1907.2 1913.0 1918.6 1924.2 1929.6 1934.9 1940.1 1945.2 1950.2 1955.1 1959,8 1964,5

I

1.4 0.9 0.7 1.7

I

Z

0.5 0.2 0.7

O.

I

1957.8 1961.5 1966.1 1969.6

100: Fermium 3.3 3.6 4.0 4.2 4.5 4.5 4.6 4.4 4.2 3.9 3.7 3.4 3.2 3.0 2.8 2.7 2.7 2.7 2.8 2.5 2.3 2.0 1.8

0.5 0.1 0.3

O. 0.1

O. 0.1

O. 0.3 0.1 0.5 0.2 0.7 0.4 0.8 0.4 0.6 0,1 0.3 0.1 0.5 0.2 0.6

1837.7 1844.7 18.52.3 1859.0 1866.2 1872.7 1879.4 1885.4 1891.9 1897.5 1903.7 1909.1 1915.1 1920.2 1926.1 1931.0 1936.6 1941.3 1946.7 1951.1 1956.2 1960.4 1965.3

153 154 155 156 157 158 159 160 161 162* 163 164 165 166 167 168 169 170 171 172 173 174 175 176

Liquid drop

= 102:

255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278

153 154 155

I

256 257 258

I

=

~

Nobelium (Continued)

1889.9 1896.5 1903.0 1909.4 1915.7 1921.8 1927.8 1933.8 1939.6 1945.2 1950.8 1956.3 1961. 6 1966.9 1972.0 1977.0 1982.0 1986.8 1991.5 1996.1 2000.4 2004.8 2009.1 2013.3 Z

Total binding energy

BCS pairing energy

Shell correction

4.4 4.2 3.9 3.7 3.4 3.2 3.0 2.9 3.0 3.1 2.8 2.7 2.5 2.5 2.1 1.9 1.5 1.3 1.1 0.9 -0.1 0.1 -0.6 -0.5

0.1 0.4 0.2 0.6 0.4 0.9 0.5 0.9 0.3 0.5 0.2 0.6 0.2 0.5 0.2 0.6 0.3 0.8 0.4 0.7 0.7 0.9 1.2 1.4

1892.7 1899.5 1905.5 1912.2 1917.9 1924.3 1929.8 1936.1 1941.4 1947.4 1952.4 1958.2 1963.0 1968.5 1973.0 1978.3 1982.6 1987.6 1991.7 1996.6 2000.6 2005.5 2009.5 2013.9

-0.1 0,2 0,

1895.5 1902.5 1908.7

103: Lawrencium

1892.8 1899.6 1906.3

I

4,3 4.2 3.9

I

I

z

q

o

t"f

tzj

>~ "0

::r:

r< tn H

o

tn

169 170 171 172 173

269 270 271 272 273

1969.0 1973.5 1978.5 1982.7 1987.0

1.3 1.1 2.2 2.3 2.2

0.3 0.8 0.1 0.4 0.1

1969.2 1973.9 1977.8 1982.5 1986.2

-0.1 0.1 -0.1

0.4 0.1 0.5 0.2 0.7 0.2 0.6 0.1 0.7

1861.9 1869.3 1876.0 1882.9 1889.1 1895.7 1901. 5 1908.0 1913.5 1919.8 1925.1 1931.1 1936.2 1942.0 1946.9 1952.5 1957.1 1962.4 1966.8 1971.8 1975.9 1980.8 1984.7 1989.4 1993.2 1997.9

0.1 0.2

1879.2 1886.3

Z = 101: Mendelevium

149 150 151 152 153 154 155 156 157 158 159 160* 161 162 163 164 165 166 167 168 169 170 171 172 173 174

250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275

1859.7 1866.6 1873.4 1880.1 1886.6 1893.1 1899.4 1905.6 1911. 7 1917.6 1923.4 1929.2 1934.8 1940.3 1945.7 1951.0 1956.1 1961. 2 1966.2 1971.0 1975.7 1980.4 1984.9 1989.4 1994.3 1998.5

4.1 4.4 4.4 4.6 4.3 4.2 3.9 3.7 3.4 3.1 2.9 2.8 2.7 2.8 2.7 2.8 2.5 2.3 2.0 1.8 1.4 1.2 0.9 0.8 1.7 1.5

O. -0.1 0.3

O. 0.5 0.2 0.7 0.4 0.8 0.3 0.5

O. 0.2

O.

Z = 102: Nobelium

151 152

I

253 254

I

1876.3 1883.2

I

4.5 4.6

I

I

156 157 158 159 160 161 162 163 164* 165 166 167 168 169 170 171 172 173 174 175 176 177 178

259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281

1912.9 1919.3 1925.6 1931.8 1937.9 1943.9 1949.8 1955.5 1961. 2 1966.7 1972.2 1977.5 1982.7 1987.8 1992.8 1997.7 2002.5 2007.0 20.11.5 2916.0 2020.4 2024.7 2028.9

3.7 3.4 3.1 3.0 3.0 3.0 3.1 2.9 2.7 2.5 2.5 2.1 1.9 1.6 1.3 1.1 0.9 0.4 0.5

O. O. -0.4 -0.2

0.5 0.2 0.7 0.3 0.7 0.1 0.3

O. 0.4 0.1 0.3 0.1 0.5 0.2 0.6 0.2 0.6 0.1 0.4 0.4 0.8 0.7 0.8

1915.5 1921.4 1928.0 1933.8 1940.2 1945.7 1951.9 1957.1 1963.0 1968.1 1973.7 1978.5 1983.9 1988.4 1993.6 1997.9 2002.9 2007.0 2012.0 2016.2 2020.8 2024.8 2029.2

259 260 261 262 263 264 265 266 267 268 269 270 271

1909.1 1915.9 1922.5 1929.0 1935.4 1941. 7 1947.9 1953.9 1959.9 1965.7 1971.4 1977.0 1982.5

~

1-4

o

~

>-

U1 U1 ~

o

~

~

Z = 104

155 156 157 158 159 160 161 162 163 164 165 166* 167

>8 o

q 4.0 3.8 3.4 3.3 3.1 3.1 3.1 3.3 3.0 2.8 2.6 2.6 2.2

0.2 0.6 0.4 0.8 0.5 0.8 0.2 0.4 0.1 0.6 0.2 0.5 0.2

1911.8 1918.8 1924.9 1931.8 1937.7 1944.3 1950.0 1956.4 1961.8 1967.9 1973.1 1978.9 1983.9

~

>-

U1

cr

I--' ~

""-l

TABLE

8c-2.

CALCULATED BINDING ENERGIES IN

Cf

l\IEV (Continued)

I-" C\j

Number of neutrons N

Mass number A

Liquid drop

Z

168 169 170 171 172 173 174 175 176 177 178 179 180

272 273 274 275 276 277 278 279 280 281 282 283 284

=

Shell correction

BCS pairing energy

Total binding energy

262 263 264 265 266 267 268 269 270 271 272 273 274 275

Liquid drop

Mass number A

1987.9 1993.2 1998.4 2003.4 2008.3 2013.1 2017.8 2022.5 2027.1 2031.5 2035.9 2040.1 2044.3

2.0 1.7 1.5 1.0 0.7 0.5 0.7 0.2 0.1 -0.1

O. -0.7 -0.8

1925.3 1932.0 1938.6 1945.1 1951.4 1957.7 1963.8 1969.8 1975.7 1981.5 1987.2 1992.8 1998.2 2003.6

3.3 3.2 3.1 3.1 3.1 3.3 3.0 2.8 2.6 2.6 2.3 2.0 1.7 1.5

Shell correction

Z

104 (Continued) 0.6 0.3 0.8 0.5 0.9 0.8 0.9 1.1 1.4 1.3 1.4 1.7 1.9

1989.5 1994.2 1999.6 2004.0 2009.4 2014.0 2019.1 2023.5 2028.3 2032.5 2037.1 2041.0 2045.4

Z = 105

157 158 159 160 161 162 163 164 165 166 167 168* 169 170

Number of neutrons N

0.3 0.7 0.3 0.6

O. 0.2

O. 0.4

O. 0.3 0.1 0.5 0.2 0.6

1927.6 1934.6 1940.7 1947.5 1953.4 1960.0 1965.7 1971. 9 1977.3 1983.3 1988.5 1994.3 1999.1 2004.7

269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292

162 163 164 165 166 167 168 169 170 171 172* 173 174 175 176 177 178 179 180 181 182 183 184 185

1963.9 1970.4 1976.8 1983.0 1989.2 1995.2 2001.1 2006.9 2012.6 2018.22023.7 2029.0 2034.3 2039.5 2044.6 2049.6 2054.5 2059.3 2063.9 2068.5 2073.0 2077.4 2081. 7 2085.9 Z

164 165 166

II

272 273 274

=

I

1979.6 1986.1 1992.4

I

Total binding energy

0.2 -0.1 0.2 0.3 0.1 0.6 0.3 0.7 0.2 0.5 0.2 0.2 0.3 0.5 0.3 0.5 0.7 0.9 1.5 2.1 1.8 1.9 1.6

1966.3 1972.4 1979.0 1984.8 1991. 2 1996.7 2002.9 2008.2 2014.3 2019.6 2025.5 2030.7 2036.4 2041.4 2046.7 2051.4 2056.5 2061.0 2065.9 2070.1 2074.8 2078.8 2083.2 2086.8

0.5 0.2 0.4

1982.2 1988.3 1994.9

00

107 3.1 2.9 2.9 2.6 2.5 2.2 1.9 1.6 1.5 1.6 1.6 1.7 2.1 1".8 1.8 1.6 1.6 1.1 1.1 0.2 -0.4 -0.4 -0.4 -0.7

=

BCS pairing energy

O.

108 2.9 2.7 2.7

I

I

2: q o

t"f t."'.l

> ::c "'t1

~ ~

rJ). H

o

m

171 172 173 174 175 176 177 178 179 180 181 182

276 277 278 279 280 281 282 283 284 285 286 287

2008.8 2013.8 2018.8 2023.8 2028.6 2033.3 2038.0 2042.5 2046.9 2051.3 2055.5 2059.7

1.1 1.0 0.9 1.1 0.7 0.6 0.5 0.6

O. -0.1 -1.2 -1.4 Z

160 161 162 163 164 165 166 167 168 169 170* 171 172 173 174 175 176 177 178 179 180 181 182 183

266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289

1948.0 1954.6 1961.0 1967.3 1973.5 1979.6 1985.5 1991.4 1997.1 2002.7 2008.2 2013.6 2018.9 2024.1 2029.2 2034.2 2039.2 2044.0 2048.7 2053.3 2057.8 2062.2 2066.5 2070.8

=

0.3 0.6 0.3 0.4 0.4 0.8 0.5 0.7 0.9 1.1 1.8 2.0

2009.4 2014.9 2019.6 2025.0 2029.5 2034.5 2038.8 2043.6 2047.6 2052.2 2056.1 2060.3

106 3.2 3.2 3.4 3.1 3.1 2.8 2.6 2.3 2.1 1.7 1.3 1.1 1.2 1.2 1.5 1.2 1.2 1.0 1.0 0.4 0.3 -0.6 -0.9 -1.1

0.7 0.1 0.3 0.1 0.4 0.1 0.5 0.2 0.6 0.4 1.0 0.6 1.0 0.7 0.8 0.8 1.1 0.9 1.2 1.4 1.7 2.3 2.7 2.5

1950.8 1956.8 1963.6 1969.5 1975.9 1981.5 1987.7 1993.0 1999.0 2004.1 2009.9 2015.0 2020.8 2025.8 2031.3 2036.1 2041.3 2045.8 2050.7 2055.1 2059.8 2063.9 2068.3 2072.2

167 168 169 170 171 172 173 174* 175 176 177 178 179 180 181 182 183 184 185 186 187

275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295

1998.6 2004.7 2010.7 2016.5 2022.3 2028.0 2033.5 2039.0 2044.4 2049.6 2054.8 2059.8 2064.8 2069.7 2074.4 2079.1 2083.7 2088.1 2092.5 2096.8 2101. 0

2.4 2.1 2.0 2.0 2.1 2.2 2.3 2.6 2.4 2.3 2.2 2.0 1.6 1.3 1.0 0.6 0.4 0.4 0.1 -0.6 -0.6

0.2 0.8 0.4 0.8 0.4 0.8 0.5 0.6 0.6 0.9 0.8 1.2 1.3 1.8 1.8 2.4 2.1 2.3 2.0 3.0 2.3

2000.6 2007.0 2012.7 2019.0 2024.5 2030.7 2036.2 2042.0 2047.2 2052.7 2057.6 2062.9 2067.7 2072.7 2077.2 2082.0 2086.2 2090.8 2094.6 2099.1 2102.8

275 276 277 278 279 280 281 282 283 284 285 286 287 288 289

1995.2 2001.6 2007.9 2014.1 2020.1 2026.1 2031. 9 2037.6 2043.3 2048.8 2054.3 2059.6 2064.8 2070.0 2075.0

o

~

t-I

Q

~

>

r:n.

ta

~

Z = 109

166 167 168 169 170 171 172 173 174 175 176* 177 178 179 180

> ~

o

~

2.9 2.6 2.5 2.4 2.5 2.6 2.8 3.0 3.3 3.1 3.1 3.0 2.8 2.5 2.2

0.1

O. 0.4 0.1 0.4 O. 0.3 O. 0.1 0.1 0.3 0.1 0.5 0.6 1.0

1997.7 2003.7 2010.3 2016.2 2022.7 2028.4 2034.8 2040.4 2046.5 2051.8 2057.5 2062.6 2068.0 2072.9 2078.2

~

q

t"'t

>

tn

cr......

W CO

TABLE

Number of neutrons N

Mass number A

290 291 292 293 294 295 296 297 298

Shell correction

Liquid drop

Z

181 182 183 184 185 186 187 188 189

= 109

CALCULATED BINDING ENERGIES IN MEV

278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295

2010.7 2017.0 2023.2 2029.4 2035.4 2041.3 2047.2 2052.9 2058.5 2064.0 2069.4 2074.7 2079.9 2085.0 2090.0 2094.9 2099.7 2104.4

BCS pairing energy

Total binding energy

Number of neutrons N

Mass number A

Cf

(Continued)

1.1 1.6 1.3 1.5 1.2 2.2 1.6 2.2 1.5

2082.8 2087.8 2092.2 2096.9 2100.9 2105.6 2109.4 2113.8 2117.5

= 110 2.9 2.9 3.2 3.1 3.4 3.6 3.9 3.7 3.7 3.5 3.4 2.8 3.0 2.8 2.5 2.4 2.4 2.0

Liquid drop

Z

(Continued)

1.9 1.5 1.3 1.3 1.0 0.3 0.3 -0.1 0.1

2079.9 2084.7 2089.5 2094.1 2098.7 2103.1 2107.5 2111.8 2115.9 Z

168 169 170 171 172 173 174 175 176 177 178* 179 180 181 182 183 184 185

8c-2.

I--l ~

I

i

0.5 0.2 0.4 0.3 0.5 0.3 0.4 0.4 0.7 0.6 1.1 1.4 1.4 1.4 1.8 1.6 1.7 1.5

2013.7 2019.8 2026.6 2032.6 2039.2 2045.1 2051.3 2056.9 2062.8 2068.1 2073.8 2078.9 2084.3 2089.2 2094.3 2098.9 2103.8 2107.9

177 178 179 180 181 182* 183 184 185 186 187 188 189 190 191 192 193 194

289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306

= 112

288 289 290 291 292 293 294 295 296

2062.7 2068.8 2074.8 2080.8 2086.6 2092.3 2097.9 2103.4 2108.8

Total binding energy

5.1 5.0 5.0 5.3 5.1 4.8 4.7 4.7 4.3 3.7 3.5 3.1 3.0 2.8 2.7 2.6 2.8 2.6

0.5 0.9 0.8 0.8 0.7 1.1 0.8 1.0 0.8 1.7 1.3 1.9 1.4 1.9 1.4 1.8 1.2 1.6

2077.2 2083.3 2088.8 2094.6 2099.8 2105.3 2110.2 2115.4 2119.9 2125.1 2129.4 2134.3 2138.5 2143.3 2147.2 2151.9 2155.7 2160.2

6.1 6.2 6.2 6.3 6.4 6.6 6.4 6.2 6.1

-0.1 0.1 O. 0.2 -0.1 O. -0.1 0.2 -0.1

2068.6 2075.1 2080.9 2087.2 2092.9 2098.8 2104.2 2109.8 2114.8

o

(Continued)

2071. 6 2077.4 2083.0 2088.6 2094.0 2099.3 2104.6 2109.7 2114.8 2119.7 2124.6 2129.4 2134.0 2138.6 2143.1 2147.5 2151.8 2156.0 Z

175 176 177 178 179 180 181 182 183

BCS pairing energy

Shell correction

= 113

z

~ Q

rt?:l :> ~

~

:I: ~

7Jl H

Q 00

186 187 188 189 190 191

I

296 297 298 299 300 301

2109.1 2113.6 2118.0 2122.4 2126.6 2130.8

1.3 1.2 0.8 0.8 0.6 0.6

2.4 1.9 2.6 2.0 2.4 1.9

2112.8 2116.7 2121.4 2125.2 2129.6 2133.3

3.6 4.0 4.2 4.4 4.4 4.4 4.3 4.3 4.1 4.2 4.0 3.6 3.5 3.5 3.1 2.4 2.4 2.0 2.0 1.9 1.9 1.6

0.1 0.3 0.2 0.1 0.3 0.2 0.5 0.4 0.5 0.5 0.9 0.7 0.9 0.6 1.5 1.0 1.6 1.0 1.4 0.9 1.4

2035.9 2042.7 2048.7 2055.1 2060.9 2066.9 2072.4 2078.3 2083.5 2089.1 2094.2 2099.5 2104.2 2109.3 2113.5 2118.6 2122.7 2127.5 2131.5 2136.1 2139.9 2144.4

4.8 5.0 5.1 5.1

0.4 0.6 0.4 0.7

2052.7 2059.3 2065.2 2071.5

Z = 111

171 172 173 174 175 176 177 178 179 180* 181 182 183 184 185 186 187 188 189 190 191 192

282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303

2032.3 2038.5 2044.6 2050.6 2056.5 2062.3 2068.0 2073.6 2079.1 2084.4 2089.7 2094.9 2100.0 2104.9 2109.8 2114.6 2119.3 2123.9 2128.4 2132.8 2137.1 2141.3

O.

Z = 112

173 174 175 176

285 286 287 288

2047.5 2053.7 2059.8 2065.8

184* 185 186 187 188 189 190 191 192 193 194 195 196

297 298 299 300 301 302 303 304 305 306 307 308 309

6.0 5.5 5.2 4.9 4.7 4.5 4.4 4.3 4.2 4.2 4.2 4.2 4.4

2n4.2 2119.4 2124.5 2129.5 2134.4 2139.3 2144.0 2148.7 2153.2 2157.7 2162.0 2166.3 2170.5

0.1

O. 0.6 0.3 0.8 0.4 0.8 0.3 0.7 0.2 0.5 -0.1

O.

2120.3 2124.9 2130.3 2134.7 2139.9 2144.2 2149.1 2153.3 2158.1 2162.1 2166.7 2170.5 2174.9

Z = 114

>-~ o ~ H

177 178 179 180 181 182 183 184 185 186* 187 188 189 190 191 192 193 194 195 196 197 198

291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312

2077.7 2083.7 2089.7 2095.6 2101.4 2107.1 2112.7 2118.2 2123.6 2128.8 2134.0 2139.1 2144.1 2149.0 2153.8 2158.5 2163.2 2167.7 2172.1 2176.5 2180.7 2184.9

7.4 7.7 7.7 7.9 7.7 7.5 7.4 7.5 6.9 6.4 6.1 5.8 5.6 5.4 5.3 5.2 5.3 5.3 5.5 5.8 4.9 4.1

O. 0.1 O. O. O. 0.3

O. 0.1

O. 0.8 0.5 1.1 0.7 1.1 0.7 1.0 0.4 0.7

O. O. O. 1.2

(1

2085.1 2091. 6 2097.5 2103.6 2109.1 2114.9 2120.1 2125.7 2130.5 2136.0 2140.6 2145.9 2150.4 2155.5 2159.8 2164.8 2168.9 2173.7 2177.6 2182.3 2185.6 2190.1

~

>-

W W

~

o

~

~

d

~

>-

W

cr

...... ~ ......

8-142

NUCLEAR PHYSICS

6. Myers, W. D.: "Winnipeg Proceedings," p. 61; W. D. Myers and W. J. Swiatecki: Annals of Physics 55, 395 (1969). 7. Zeldes, N.: "Lysekil Proceedings," p. 361. Calculations are tabulated by N. Zeldes, A. Grill, and A. Simievic: Mat. Fys. Skr. Dan. Vid. Selsk. 3(5), (1967). 8. Myers, W. D., and W. J. Swiatecki: "Lysekil Proceedings," p. 343; Nucl. Phy.~. 81 (1966). A table of calculated values is included in report UCRL-11980. 9. Seeger, P. A.: "Winnipeg Proceedings," p, 85; P. A. Seeger and R. C. Perisho, report LA-3751. 10. Mattauch, J. H. E., W. Thiele, and A. H. Wapstra: Nucl. Phys. 67, 1 (1965). 11. Wapstra, A., C. Kurzeck, and A. Anisimoff: "Winnipeg Proceedings," p. 153. 12. Hahn. B., D. G. Ravenhall, and R. Hofstadter: Phys. Rev. 101, 1131 (1956). 13. Nilsson, S. G., C. F. Tsang, A. Sobiczewski, Z. Szymanski, S. Wycech, C. Gustafson, 1. L. Lamm, P. Moller, and B. Nilsson: Nucl. Phys. A131, 1 (1969). 14. FoIdy, L. L.: Phys. Rev. 83,397 (1951). 15. Breitenberger, E.: "Vienna Proceedings," p. 91. 16. Mattauch, J. H. E., W. Thiele, and A. H. Wapstra: N1lcl. Pbus. 67, 73 (1965). 17. Wing, James: "Winnipeg Proceedings," p. 194. 18. Seeger, P. A.: "Lysekil Proceedings," p. 495: "Winnipeg Proceedings'," p R5. 19. Talbert, W. L., Jr., A. B. Tucker, and G. M. Day: Phys. Rev. 177, 1805 (1969). 20. Green, A. E. S.: "Nuclear Physics," Mc-Graw-Hill Book Company, New York, 1955.

8d. Passage of Charged Particles Through Matter! HANS BICHSEL

University of Washington

8d-t. Introductory Note. This section presents some of the commonly used formulas and principal data on the passage of fast charged particles through matter. Because of space limitations, much useful material has been omitted. The bibliography includes mainly the newest available references. Most of the technical reports cited are available from the National Technical Information Service, Springfield, Virgina 22151. Anextensive review of the field is found in Publication 1133 of the National Academy of Sciences-National Research Council (NA67). The Bibliography of Atomic and Molecular Processes (ORNL-AMPIC 13, UC-34-Physics for JanuaryDecember, 1969), is published annually by the Atomic and Molecular Processes Information Center, Oak Ridge National Laboratory, Oak Ridge, Tennessee. It contains sections concerned with energy losses, ionization, particle range, etc. The Information Center at JILA (Joint Institute for Laboratory Astrophysics), University of Colorado, Boulder, Colorado 80302, also disseminates information of this nature. A number of papers concerned with particles at the lowest energies considered in this article have appeared in the Proceedings of an International Conference on Atomic Collisions and Penetration Studies with Energetic Ion Beams, Chalk River, Ontario, September 18-21, 1967 (DA68), in the abstracts of the V International Conference of the Physics of Electronic and Atomic Collisions (FL67), and of the Sixth Inter1 This work was supported by Public Health Service Grant CA-08150 from the National Cancer Institute and in part by the U.S. Atomic Energy Commission Contract AT(04-3)-136.

PASSAGE OF CHARGED PARTICLES THROUGH MATTER

8-143

national Conference on the Physics of Electronic and Atomic Collisions, M.LT., July 28-August 2 (1969), (The Massachusetts Institute of Technology Press, Cambridge, Massachusetts 02142). The seventh Conference took place in Amsterdam, July 26-30, 1971. 8d-2. Atomic Collision Cross Sections. The following notation will be used. The kinetic energy of particles will be denoted by T, the energy of a secondary electron (delta ray) by E or by W if expressed in atomic shell units [Eq. (8d-3)]. Thicknesses s are usually measured in g cm- 2 (s = px, z thickness in em, p density in g cm :s). The stopping power (usually called dE/dx) will then be denoted as S = -dT/ds. Except for particles with very small or extremely large velocities v, the interaction between energetic charged particles (of charge ze) and matter leads mainly to the excitation and ionization of atoms or molecules (F A63). The probability for a collision leading to an atomic state of energy En is described by the collision cross section a«. Relatively little information is available about the details of Un (e.g., FC68, RU68, OL67, ES69). In energy-loss experiments, the quantities observed are usually averages over En and Un (e.g., the stopping power dT Ids is "T,nEnUn) , and even a coarse approximation of «« will give satisfactory answers. Frequently, the free-electron approximation is used for a description of a «. The energies En then are continuously distributed and are equal to the energy E of the electron after the collision. The collision cross section is differential with respect to E and is given, nonrelativistically, by (see, e.g., BI68) ndu'

=

(~;)

E-2 dE

(8d-l)

= 27rz2me2r02N 01 A = 0.15354 X Z2/ A MeV /(g/cm 2) z = charge number of incident particle

where P

{3

= v/e, velocity of incident particle relative to velocity of light [see Eq. (8d-37)]

r02

m No e E A

= e 4/m 2e4 = 7.9408 X 10- 26 em" (square of "classical electron radius") =

rest mass of electron, me" = 0.511004 MeV

= Avogadro's number = 6.02217 X 1023

= electron charge

= energy of electron after collision = atomic weight of stopping material, in grams Z = atomic number of stopping material

n = number of electrons in a thickness s = 1 g/cm 2 Using the Born approximation, Bethe (BE30, IN71) has given the nonrelativistic quantum mechanical derivation of do for bound electrons: (8d-2) where J, is called the excitation function (WA56). Electron energies Wand equivalent particle energies 71i are measured in atomic shell units:

~,)2RI/

W = (Z _ me 2{32 71. = 2RI/(Z _ d.)2

(8d-3)

=

18,800{32 (Z _ d.)2

(8d-4)

where R li = Rydberg = 13.60 eV d, = electron defect, depending on the atomic shell i (i = K, L, M, ... shell) d«

= 0.3

dt. = 4.15

8-144

NUCLEAR PHYSICS

The excitation functions J: have been evaluated, using hydrogenic wave functions, for the K, L, and M shells (WA51, WA52, WA56, BI67, KM66, KH68). Whereas J K probably is reasonably correct for all Z, it appears that J L is acceptable without modifications for Z > 30 only, and J M will have to be recalculated with more realistic wave functions. An appreciation of the difference between the two approximations, do' and du, can be obtained from a study of a plot of J i W2 versus W (Fig. 8d-l). Further comments will be made later at appropriate places (see also BI69). Generally, the Born approximation is valid for (3 » z/137 (protons with (3 = 1/137 have a kinetic energy of 25 keY). Some tests have been made for small-particle velocities: for protons incident on helium, the Bethe-Born approximation is valid for energies above 450 keY (TH67), while for the vacuum ultraviolet emission of hydrogen 100

·10

40

"1L"3~1\ L-SHELL

~ 0.7" 0.41'....~ ~ r\

1.5r'\..

20 10 7

0.2 0.1

.................. ~ ~

1000 MeV for protons) nuclear interactions absorb most of the particles, and range becomes a rather meaningless term. While the straggling in pathlength can be represented approximately by a gaussian (see Sec. 8d-7), the asymmetry of multiple scattering (the zigzag path taken by a particle can only be longer than the foil thickness, see Sec. 8d-8), and the residual skewness of the electron-loss straggling causes an asymmetry in the range straggling. The median range therefore, is different from the mean range. The total median range Rm(T) (equal to the foil thickness), neglecting the straggling asymmetries, can be obtained from the computed mean pathlength Rt(T) by the application of the multiple-scattering correction t..R:

The relative correction of t..R/R for several elements is plotted in Fig. 8d-5. Further discussion is given in BU60, BF61, BZ67, and TB68. No discussion of the relation of mean and median range seems to be available (see Sec. 8d-7). 8d-5. Shell Corrections and I Values. In principle, the stopping power 8 can be calculated theoretically using atomic collision cross sections [Eq. (8d-5)). At present, no complete sets of cross sections for all shells are available, and the expression Eq. (8d-ll) is used for the calculation of 8. The unknown functions B K , B L , . • • are then replaced by one unknown constant, I = laY' and the unknown functions

TABLE 8d-3A. LOW-ENERGY PROTON STOPPING POWER

T, MeY

H2

----0.01 0.02 0.03 0.04 0.05

.. ..

... . ... . ... . 3800

S

IN MEV /(G/CM 2 )

FOR SEVERAL SUBSTANCES: ACCURACY

Ni Ai A Ne 02 C N2 -- -- -- -- -- -260 . .. 100 .. . .. . ., . .. . 440 . .. . , . 145 .. . 360 .. . 560 . .. . .. .... . , . . , . 177 .. . 410 .. . . .. . , .. . .. .. . 640 .. . 200 440 .. . ., . .. . ., . ., . . , .. 700 He

o

Li

Be

•••

1050

.. .

690

720

750

600

350

460

480

220

Cu

Kr

Ag

70 160 190 200 210

.. . .. . .. .

.. . 270

., . ., . ., . ., . ., .

Air

H2O

. .. . .. ... .. . . ..

· .. ·.. · ., . "

240

22 44 60 75 85

;>

o

t."'.1

...

730

890

122 127 127 120 113

730 650 580 520 480

910 830 740 660 600

., .

...

151 142 134 128

142 134 127 121

152 143 134 127 121

104 98 93 88 84

106 100 95 90 86

430 410 380 350 330

540 500 460 430 400

122 113 105 99 94

115 107 100 94 89

115 106 98 92 87

81 75 70 66 63

83 77 71 67 63

310 280 260 240 220

380 340 310 290 260

99 94 90 87 84

89 85 82 79 75

85 81 78 75 71

82 78 75 72 69

60 57 54 53 51

60 58 55 53 52

210 198 186 177 168

260 230 220 210 197

81 76 72

72 68 64

68 65 61

66 62 59

49 47 44

50 47 45

160 147 136

188 172 159

700 640 570 510 460

710 650 580 540 490

780 690 610 530 480

610 600 540 500 450

440 440 420 390 360

440 390 340 320 310

480 430 380 330 300

260 270 260 250 230

220 220 220 210 200

290 250 220 198 182

. . ., . ., . ., .

0.35 0.40 0.45 0.50 0.55

1560 1410 1280 1180 1090

600 550 510 480 450

450 420 390 340

430 390 370 350 330

460 430 390 370 350

440 400 370 350 320

410 380 360 340 320

340 320 300 290 270

290 280 270 250 240

270 250 230 220 210

220 210 193 182 173

192 183 175 168 161

169 159 150 143 137

0.60 0.70 0.80 0.90 1.00

1020 910 810 740 680

420 380 340 310 290

320 290 260 240 230

310 280 260 240 220

330 290 270 250 230

310 280 250 240 220

300 270 250 230 220

260 210 198 185

230 210 197 185 173

200 184 171 160 150

165 151 141 133 126

155 144 135 128 121

132 123 116 109 104

1.1 1.2 1.3 1.4 1.5

630 590 550 520 500

270 250 240 220 210

220 210 200 195 188

210 198 187 179 170

220 200 192 183 175

210 194 185 176 168

200 192 182 173 165

174 164 156 149 144

163 155 147 140 134

142 134 127 121 116

120 115 110 106 101

114 109 104 99 95

1.6

470 430 390

200 183 168

184 173 164

161 148 137

167 154 143

160 148 137

157 144 134

137 127 119

129 119 111

112 103 95

97 91 85

92 85 80

., ,

'"d

;> r.J2

U2

105 112 119 116 110

750 680 610 550 500

2.0

Ph

230 210 192 176 163

1090 960 830 740 660

1.8

Au

10%

. .. ... . .. . .. . ..

.

3500 2800 2300 1990 1740

2~0

Xe

TO

-- -- ---- -- ---- -- --

0.10 0.15 0.20 0.25 0.30

360

Sn

2

o

"%.1

(1

0::

;> ~

o

t."'.1

t:1

~

~

>-3 ~

(1 ~

t."'.1 r.J2

>-3

~

~

o d

c

~

~ ;> >-3 >-3 t."'.1

~

00

I ......

c..n ec

TABLE

8d-3B.

EXPERIMENTAL PROTON STOPPING POWER

cr ~

S IN MEV /(G/CM 2) *

~

o T, MeV

Be

Al

Ca

Sc

Ti

V

Cr

-- --

--- --- --- --- - -

Mn

--

Fe

Co

Ni

-- -- --

Cu

Zn

Zr

Ag

--- - - - - - -

Gd

Ta

-- --

Pt

Au

--

---

2.00 2.25 2.50 2.75 3.00

134.25 122.70 113.21 105.19 98.35

110.67 101. 92 94.68 88.52 83.19

107.21 98.91 92.03 86.15 81.09

96.58 89.24 83.15 77.94 73.40

93.19 86.11 80.23 75.20 70.87

90.61 83.73 78.02 73.14 68.91

89.57 82.93 77.41 72.69 68.60

86.51 80.07 74.72 70.13 66.16

87.30 80.83 75.45 70.85 66.84

83.74 77 .64 72.56 68.18 64.37

86.45 80.14 74.89 70.35 66.41

81.09 75.19 70.28 66.07 62.44

80.89 75.02 70.13 65.92 62.32

71.49 66.56 62.44 58.83 55.70

63.74 59.63 56.18 53.16 50.46

55.31 51. 65 48.58 45.87 43.51

49.27 46.20 43.62 41.3.5 39.35

45.43 42.85 40.67 38.71 36.97

45.78 43.12 40.87 38.89 37.11

3.25 3.50 3.75 4.00

92.42 87.24 82.65 78.57

78.56 74.51 70.94 67.76

76.65 72.76 69.30 66.18

69.45 65.97 62.87 60.08

67.11 63.78 60.81 58.15

65.22 61.93 59.04 56.44

65.01 61.82 58.98 56.42

62.66 59 . .59 56.86 54.40

63.32 60.21 57.45 55.00

61.04 58.09 55.46 53.10

62.96 59.97 57.28 54.88

59.25 56.43 53.91 51.65

59.16 56.36 53.85 51.60

52.92 50.42 48.20 46.20

48.07 45.94 44.02 42.28

41.42 39.57 37.91 36.42

37.59 36.02 34.60 33.32

35.39 33.96 32.66 31.47

35.52 34.09 32.79 31.62

4.25 4.50 4.75 5.00 5.25

74.90 71.60 68.58 65.87 63.36

64.85 62.21 59.80 57.59 55.56

63.38 60.83 58.51 56.37 54.41

57.57 55.29 .53.21 51.30 49.53

55.74 53.54 51.53 49.68 47.98

54.09 51.9.5 50.00 48.21 46.56

54.09 51.97 50.04 48.25 46.61

52.19 .50.16 48.31 46.62 45.05

52.79 .50.78 48.94 47.24 45.67

50.97 49.03 47.26 45.62 44.11

52.69 50.70 48.86 47.17 45.61

49.60 47.72 45.99 44.42 42.95

49.55 47.69 45.99 44.42 42.97

44.40 42.74 41.23 39.84 38.55

40.70 39.26 37.93 36.71 35.58

35.06 33.83 32.69 31.65 30.69

32.15 31.07 30.07 29.15 28.29

30.39 29.40 28.49 27.65 26.85

30.55 29.56 28.65 27.79 27.00

5.50 5.75 6.00 6.50 7.00

61.06 58,93 56.96 53.42 50.34

53.68 51.93 50.31 47.38 44.81

52.59 50.91 49.35 46.53 44.04

47.90 46.38 44.97 42.4I 40.17

46.40 44.93 43.56 41. 10 38.92

45.03 43.61 42.29 39.90 37.80

45.09 43.68 42.37 39.98 37.89

43.60 42.25 40.99 38.72 36.71

44.22 42.87 41.60 39.31 37.28

42.72 41. 41 40.20 38.00 36.06

44.16 42.82 41. 57 39.30 37.29

41.59 40.33 39.15 37.01 35.12

41. 61 40.36 39.19 37.07 35.19

37.36 36.25 35.22 33.35 31.69

34.53 33.55 32.63 30.97 29.48

29.80 28.96 28.18 26.77 25.50

27.49 26.75 26.06 24.79 23.66

26.12 25.43 24.79 23.60 22.54

26.25 25.56 24.91 23.72 22.67

7.50 8.00 8.50 9.00 9.50

47.62 45.21 43.05 41.10 39.34

42.52 40.47 38.64 36.97 35.46

41.83 39.85 38.08 36.47 35.00

38.17 36.38 34.77 33.31 31.98

36.99 35.27 33.71 32.30 31.02

35.93 34.26 32.75 31.39 30.15

36.02 34.35 32.85 31.49 30.25

34.92 33.32 31.88 30.57 29.38

35.47 33.85 32.39 31.06 29.85

34.33 32.78 31.37 30.09 28.92

35.51 33.90 32.45 31.14 29.95

33.44 31.93 30.57 29.33 28.21

33.52 32.01 30.65 29.41 28.29

30.21 28.89 27.69 26.60 25.60

28.14 26.94 25.85 24.86 23.95

24.37 23.36 22.43 21.59 20.82

22.65 21. 73 20.89 20.13 19.42

21. 58 20.72 19.94 19.22 18.56

21.73 20.85 20.06 19.34 18.67

10.00 10.50 11.00 11.50 12.00

37.74 36.27 34.93 33.69 32.54

34.08 32.82 31.66 30.58 29.58

33.66 32.43 31.30 30.25 29.28

30.76 29.65 28.61 27.66 26.77

29.84 28.77 27.77 26.85 26.00

29.01 27.97 27.01 26.12 25.30

29.11 28.06 27.10 26.21 25.37

28.28 27.28 26.35 25.49 24.69

28.74 27.72 26.78 25.90 25.09

27.85 26.87 25.96 25.12 24.33

28.84 27.83 26.89 26.02 25.21

27.17 26.22 25.35 24.54 23.78

27.26 26.30 25.42 24.61 23.85

24.69 23.85

23.11 22.34

20.11 19.46 18.85 18.29 17.77

18.77 18.17 17.62 17.10 16.62

17.95 17.39 16.88 16.39 15.93

18.06 17.49 16.97 16.48 16.02

z

q

o

to"

t'j

>

~ ~

* From AR67, AS68. and AV69.

23.0'1 21.62

22.35 21. 68

20.96 20.34

~ ~

U1 H

o

U1

PASSAGE OF CHARGED PARTICLES THROUGH MATTER TABLE

8d-4.

CALCULATED CSDA RANGES

R

OF KINETIC ENERGY

T, MeV ----

Be

Graphite

Water

Al

8-161

IN G/CM 2 FOR PROTONS

T

eu

I

Ag

Ph

1.0 1.1 1.2 1.3 1.4

0.0029 0.0034 0.0039 0.0044 0.0050

0.0039 0.0043 0.0048 0.0053 0.0059

0.0039 0.0043 0.0047 0.0051 0.0056

0.0042 0.0048 0.0054 0.0061 0.0068

0.0061 0.0070 0.0078 0.0088 0.0098

0.0080 0.0091 0.0103 0.0115 0.0128

0.0116 0.0133 0.0151 0.0169 0.0188

1.5 1.6 1.7 1.8 1.9

0.0055 0.0062 0.0068 0.0075 0.0082

0.0064 0.0070 0.0076 0.0083 0.0089

0.0061 0.0066 0.0071 0.0077 0.0083

0.0075 0.0083 0.0091 0.0099 0.0108

0.0108 0.0118 0.0129 0.0141 0.0153

0.0141 0.0154 0.0168 0.0183 0.0198

0.0208 0.0228 0.0248 0.0270 0.0291

2.0 2.1 2.2 2.3 2.4

0.0089 0.0097 0.0105 0.0113 0.0121

0.0096 0.0104 0.0111 0.0119 0.0127

0.0089 0.0095 0.0101 0.0108 0.0115

0.0117 0.0126 0.0136 0.0146 0.0156

0.0165 0.0178 0.0190 0.0204 0.0218

0.0213 0.0229 0.0245 0.0262 0.0279

0.0314 0.0336 0.0360 0.0384 0.0408

2.5 2.6 2.7 2.8 2.9

0.0130 0.0139 0.0148 0.0158 0.0167

0.0135 0.0143 0.0152 0.0161 0.0170

0.0122 0.0130 0.0137 0.0145 0.0153

0.0166 0.0177 0.0188 0.0200 0.0211

0.0232 0.0245 0.0261 0.0276 0.0291

0.0296 0.0314 0.0332 0.0351 0.0370

0.0433 0.0458 0.0484 0.0511 0.0538

3.0 3.1 3.2 3.3 3.4

0.0177 0.0188 0.0198 0.0209 0.0220

0.0180 0.0189 0.0199 0.0209 0.0220

0.0161 0.0170 0.0178 0.0187 0.0196

0.0223 0.0236 0.0248 0.0261 0.0274

0.0307 0.0323 0.0340 0.0357 0.0374

0.0390 0.0409 0.0430 0.0450 0.0471

0.0565 0.0593 0.0621 0.0650 0.0680

3.5 3.6 3.7 3.8 3.9

0.0232 0.0243 0.0255 0.0267 0.0279

0.0230 0.0241 0.0252 0.0263 0.0275

0.0205 0.0215 0.0225 0.0234 0.0245

0.0287 0.0301 0.0315 0.0329 0.0344

0.0392 0.0409 0.0428 0.0446 0.0465

0.0493 0.0515 0.0537 0.0559 0.0582

0.0709 0.0740 0.0771 0.OR02 0.0834

4.0 4.1 4.2 4.3 4.4

0.0292 0.0305 0.0318 0.0331 0.0345

0.0287 0.0299 0.0311 0.0323 0.0336

0.0255 0.0265 0.0276 0.0287 0.0298

0.0358 0.0373 0.0389 0.0404 0.0420

0.0484 0.0504 0.0524 0.0544 0.0564

0.0605 0.0629 0.0653 0.0677 0.0702

0.0866 0.0899 0.0932 0.0965 0.0999

4.5 4.6 4.7 4.8 4.9

0.0359 0.0373 0.0387 0.0402 0.0416

0.0349 0.0362 0.0375 0.0389 0.0403

0.0309 0.0321 0.0332 0.0344 0.0356

0.0436 0.0453 0.0469 0.0486 0.0503

0.0585 0.0606 0.0628 0.0649 0.0672

0.0727 0.0753 0.0778 0.0805 0.0831

0.1034 0.1069 0.1104 0.1140 0.1176

5.0 5.5 6.0 6.5 7.0

0.0432 0.0510 0.0595 0.0686 0.0782

0.0417 0.0490 0.0569 0.0653 0.0742

0.0369 0.0433 0.0502 0.0575 0.0653

0.0521 0.0612 0.0709 0.0812 0.0922

0.0694 0.0810 0.0934 0.1066 0.1205

0.0858 0.0997 0.1145 0.1302 0.1466

0.1213 0.1403 0.1603 0.1814 0.2035

7.5 8.0 8.5 9.0 9.5

0.0884 0.0992 0.1106 0.1225 0.1349

0.0837 0.0937 0.1042 0.1152 0.1266

0.0736 0.0824 0.0915 0.1012 0.1112

0.1038 0.1160 0.1288 0.1421 0.1561

0.1351 0.1504 0.1664 0.1831 0.2005

0.1639 0.1820 0.2008 0.2205 0.2409

0.2267 0.2508 0.2759 0.3019 0.3289

8-162

NUCLEAR PHYSICS TABLE

8d-4.

CALCULATED CSDA RANGES OF KINETIC ENERGY

T. MeV

Be

Graphite

Water

R

IN G/CM'2 FOR PROTONS

T (Continued)

Al

eu

Ag

Ph

10.0 10.5 11.0 11.5 12.0

0.1479 0.1614 0.1755 0.1901 0.2052

0.1386 0.1511 0.1641 0.1775 0.1915

0.1217 0.1327 0.1440 0.1558 0.1680

0.1706 0.1857 0.2013 0.2175 0.2343

0.2186 0.2373 0.2567 0.2768 0.2975

0.2620 0.2840 0.3066 0.3300 0.3541

0.3568 0.3856 0.4154 0.4460 0.4776

12.5 13.0 13.5 14.0 14.5

0.2208 0.2370 0.2536 0.2708 0.2885

0.2059 0.2207 0.2361 0.2519 0.2682

0.1807 0.1937 0.2072 0.2211 0.2353

0.2516 0.2695 0.2879 0.3068 0.3263

0.3188 0.3408 0.3635 0.3867 0.4106

0.3790 0.4045 0.4308 0.4578 0.4855

0.5100 0.5433 0.5775 0.6125 0.6484

15.0 15.5 16.0 16.5 17.0

0.3067 0.3254 0.3446 0.3643 0.3845

0.2849 0.3021 0.3198 0.3379 0.3564

0.2500 0.2651 0.2806 0.2965 0.3128

0.3463 0.3668 0.3879 0.4095 0.4316

0.4351 0.4602 0.4860 0.5123 0.5393

0.5138 0.5429 0.5726 0.6030 0.6341

0.6851 0.7226 0.7610 0.8002 0.8403

17.5 18.0 18.5 19.0 19.5

0.4052 0.4264 0.4481 0.4702 0.4929

0.3755 0.3949 0.4148 0.4351 0.4559

0.3295 0.3465 0.3640 0.3819 0.4001

0.4542 0.4773 0.5009 0.5251 0.5497

0.5668 0.5950 0.6237 0.6530 0.6830

0.6659 0.6983 0.7314 0.7651 0.7995

0.8811 0.9228 0.9652 1.0085 1.0525

20.0 21.0 22.0 23.0 24.0

0.5160 0.5637 0.6132 0.6646 0.7179

0.4771 0.5209 0.5663 0.6135 0.6624

0.4187 0.4571 0.4970 0.5385 0.5814

0.5748 0.6266 0.6804 0.7361 0.7937

0.7135 0.7762 0.8412 0.9086 0.9781

0.8346 0.9066 0.9812 1.0584 1.1'380

1.0974 1.1894 1.2845 1.3826 1.4838

25.0 26.0 27.0 28.0 29.0

0.7731 0.8301 0.8889 0.9495 1.0119

0.7129 0.7651 0.8190 0.8745 0.9317

0.6258 0.6717 0.7190 0.7678 0.8180

0.8533 0.9148 0.9782 1.0434 1.1106

1.0499 1.1240 1.2002 1.2786 1.3591

1.2201 1. 3047 1.3918 1.4812 1.5730

1.5880 1.6952 1.8052 1.9182 2.0341

30.0 31.0 32.0 33.0 34.0

1.0760 1.1420 1.2096 1.2791 1.3502

0.9904 1.0508 1.1127 1.1763 1. 2414

0.8696 0.9227 0.9772 1.0330 1.0903

1.1795 1.2503 1.3229 1. 3974 1.4736

1.4418 1.5266 1.6135 1.7025 1.7935

1.6672 1.7638 1.8627 1.9640 2.0675

2.1529 2.2744 2.3988 2.5259 2.6.558

35.0 36.0 37.0 38.0 39.0

1.4231 1.4977 1.5740 1.6520 1.7316

1.3081 1.3763 1.4461 1.5174 1.5903

1.1489 1.2089 1.2703 1.3330 1. 3971

1. 5516 1. 6313 1.7129 1. 7961 1. 8811

1.8867 1.9818 2.0791 2.1783 2.2795

2.1733 2.2814 2.3918 2.5043 2.6191

2.7885 2.9239 3.0620 3.2027 3.3462

40.0 41.0 42.0 43.0 44.0

1.8129 1.8959 1.9805 2.0668 2.1546

1.6646 1. 7405 1.8178 1.8967 1.9770

1.4625 1.5292 1.5972 1.6666 1.7373

1.9679 2.0563 2.1465 2.2383 2.3319

2.3827 2.4879 2.5951 2.7042 2.8152

2.7361 2.8553 2.9766 3.1002 3.2258

3.4922 3.6409 3.7922 3.9461 4.1025

45.0 46.0 47.0 48.0 49.0

2.2441 2.3353 2.4280 2.5223 2.6182

2.0588 2.1421 2.2268 2.3129 2.4006

1.8092 1.8825 1.9570 2.0329 2.1099

2.4271 2.5239 2.6224 2.7226 2.8244

2.9282 3.0431 3.1599 3.2786 3.3992

3.3537 3.4836 3.6157 3.7498 3.8861

4.2615 4.4231 4.5871 4.7537 4.9228

8-163

PASSAGE OF CHARGED PARTICLES THROUGH MATTER TABLE

8d-4.

CALCULATED CSDA RANGES OF KINETIC EN"~RGY

T, MeV

Be

Graphite

Water

R

IN

G/CM 2 FOR PROTOSS

T (Continued) Al

eu

Ag

Pb

----

50.0 52.5 55.0 57.5 60.0

2.7156 2.9661 3.2263 3.4960 3.7752

2.4896 2.7184 2.9560 3.2023 3.4571

2.1883 2.3897 2.5988 2.8156 3.0400

2.9278 3.1934 3.4690 3.7545 4.0496

3.5216 3.8359 4.1617 4.4988 4.8470

4.0244 4.3792 4.7466 5.1266 5.5188

5.0943 5.5339 5.9886 6.4583 6.9426

62.5 65.0 67.5 70.0 72.5

4.0637 4.3614 4.6681 4.9839 5.3086

3.7204 3.9921 4.2720 4.5602 4.8563

3.2718 3.5111 3.7576 4.0113 4.2722

4.3544 4.6686 4.9922 5.3251 5.6671

5.2063 5.5764 5.9573 6.3487 6.7507

5.9233 6.3398 6.7682 7.2083 7.6601

7.4415 7.9547 8.4821 9.0235 9.5786

75.0 77.5 80.0 82.5 85.0

5.642 5.984 6.335 6.694 7.062

5.161 5.473 5.792 6.120 6.455

4.540 4.815 5.097 5.386 5.681

6.018 6.378 6.747 7.124 7.511

7.163 7.586 8.018 8.461 8.914

8.123 8.598 9.083 9.580 10.088

10.147 10.729 11. 325 11.933 12.555

87.5 90.0 92.5 95.0 97.5

7.438 7.822 8.215 8.615 9.024

6.798 7.149 7.506 7.871 8.244

5.983 6.292 6.607 6.929 7.257

7.905 8.309 8.720 9.140 9.568

9.376 9.848 10.330 10.821 11.322

10.606 11.135 11.675 12.225 12.785

13.189 13.836 14.495 15.167 15.852

100.0 105.0 110.0 115.0 120.0

9.440 10.297 11.184 12.101 13.048

8.623 9.404 10.212 11. 047 11.910

7.592 8.279 8.992 9.729 10.489

10.004 10.901 11.828 12.787 13.776

11.832 12.879 13.962 15.081 16.233

13.355 14.527 15.738 16.988 18.276

16.548 17.976 19.452 20.973 22.539

125.0 130.0 135.0 140.0 145.0

14.024 15.029 16.061 17.121 18.208

12.799 13.713 14.654 15.619 16.608

11.273 12.080 12.909 13.760 14.633

14.795 15.843 16.919 18.024 19.156

17.420 18.640 19.893 21.177 22.493

19.601 20.963 22.361 23.794 25.262

24.150 25.803 27.499 29.236 31.015

150.0 155.0 160.0 165.0 170.0

19.322 20.462 21.627 22.817 24.032

17.622 18.659 19.720 20.803 21.909

15.527 16.442 17.378 18.334 19.309

20.315 21.500 22.712 23.950 25.212

23.840 25.217 26.623 28.059 29.524

26.763 28.298 29.865 31. 464 33.095

32.833 34.691 36.587 38.521 40.492

175.0 180.0 185.0 190.0 195.0

25.272 26.536 27.823 29.133 30.466

23.037 24.186 25.357 26.549 27.761

20.304 21.319 22.352 23.404 24.474

26.500 27.812 29.147 30.507 31.889

31.017 32.538 34.086 35.661 37.262

34.757 36.449 38.171 39.922 41.702

42.500 44.544 46.622 48.735 50.882

200.0 205.0 210.0 215.0 220.0

31.821 33.199 34.598 36.018 37.460

28.994 30.247 31.519 32.811 34.122

25.562 26.668 27.791 28.932 30.089

33.294 34.722 36.171 37.643 39.135

38.888 40.541 42.218 43.920 45.646

43.510 45.346 47.210 49.100 51.018

53.063 55.276 57.521 59.798 62.106

225.0 230.0 235.0 240.0 245.0

38.922 40.404 41. 907 43.429 44.971

35.451 36.799 38.165 39.549 40.951

31. 262 32.452 33.659 34.880 36.118

40.649 42.183 43.737 45.312 46.906

47.396 49.169 50.965 52.784 54.625

52.961 54.930 56.924 58.943 60.987

64.444 66.813 69.211 71.638 74.094

8-164

NUCLEAR PHYSICS TABLE

8d-4.

CALCULATED CSDA RANGES OF KINETIC ENERGY

T. MeY

Be

Graphite

"Yater

---

..

R

IN G/CM 2 FOR PROTONS

T (Continued)

Al -----

eu

Ag

Ph

250.0 255.0 260.0 265.0 270.0

46.531 48.111 49.709 51. 325 52.960

42.370 43.806 45.258 46.727 48.213

37.371 38.639 39.921 41. 219 42.531

48.520 50.152 51.804 53.473 55.161

56.489 58.373 60.279 62.206 64.154

63.054 65.145 67.260 69.397 71. 557

76.578 79.090 81.630 84.196 86.789

275.0 280.0 285.0 290.0 295.0

54.612 56.282 57.968 59.672 61.392

49.714 51. 232 52.765 54.313 55.876

43.857 45.197 46.551 47.918 49.299

56.867 58.591 60.332 62.090 63.865

66.121 68.109 70.116 72.143 74.188

73.739 75.943 78.169 80.416 82.683

89.408 92.052 94.722 97.416 100.135

300.0 310.0 320.0 330.0 340.0

63.129 66.651 70.236 73.883 77.588

57.455 60.655 63.912 67.225 70.591

50.693 53.520 56.397 59.323 62.297

65.657 69.289 72.984 76.741 80.558

76.253 80.437 84.692 89.017 93.410

84.971 89.608 94.322 99.113 103.978

102.877 108.434 114.081 119.818 125.641

350.0 360.0 370.0 380.0 390.0

81.352 85.171 89.045 92.972 96.951

74.010 77.479 80.998 84.565 88.178

65.318 68.383 71.492 74.644 77.836

84.434 88.365 92.352 96.392 100.484

97.868 102.389 106.973 111.616 116.317

108.914 113.920 118.993 124.131 129.333

131. 548 137.535 143.601 149.744 155.960

400.0 410.0 420.0 430.0 440.0

100.980 105.058 109.183 113.355 117.572

91.837 95.540 99.286 103.074 106.902

81.070 84.342 87.653 91.000 94.384

104.626 108.818 113.057 117.342 121.673

121.075 125.889 130.756 135.675 140.644

134.597 145.304 150.743 156.237

162.249 168.607 175.033 181. 525 188.081

450.0 460.0 470.0 480.0 490.0

121.832 126.136 130.481 134.866 139.291

110.770 114.677 118.621 122.602 126.619

97.803 101. 256 104.742 108.261 111.812

126.048 130.465 134.924 139.423 143.962

145.663 150.731 155.844 161.003 166.207

161.785 167.384 173.035 178.734 184.482

194.699 201.378 208.115 214.909 221. 758

500.0 510.0 520.0 530.0 540.0

143.754 148.255 152.792 157.365 161. 972

130.670 134.755 138.873 143.023 147.205

115.393 119.005 122.645 126.314 130.011

148.539 153.154 ]57.805 162.492 167.213

171.453 176.741 182.070 187.439 192.846

190.276 196.115 201.999 207.925 213.893

228.662 235.618 242.624 249.681 256.785

550.0 560.0 570.0 580.0 590.0

166.614 171.288 175.994 180.732 185.501

151. 417 155.658 159.929 164.228 168.555

133.735 137.486 141.262 145.063 148.889

171. 967 176.755 ]81. 574 186.425 191.306

198.291 203.773 209.290 214.842 220.428

219.902 225.951 232.038 238.162 244.323

263.937 271.134 278.375 285.660 292.987

600.0 610.0 620.0 630.0 640.0

190.299 195.126 199.982 204.865 209.775

172.908 177.288 181.693 186.124 190.579

152.739 156.612 160.508 164.426 168.365

196.216 201.156 206.124 211.119 216.140

226.047 231.697 237.380 243.093 248.835

250.520 256.751 263.017 269.315 275.645

300.355 307.763 315.211 322.696 330.218

650.0 660.0 670.0 680.0 690.0

214.712 219.675 224.662 229.675 234.711

195.057 199.559 204.083 208.630 213.198

172.326 176.308 180.309 184.330 188.371

221.188 226.262 231.360 236.482 241.628

254.607 260.406 266.234 272.088 277.968

282.006 288.397 294.819 301.269 307.747

337.776 345.369 352.996 360.657 368.349

1~9.921

8-165

PASSAGE OF CHARGED PARTICLES THROUGH MATTER TABLE

8d-4.

CALCULATED CSDA RANGES OF KINETIC ENERGY

R

IN

G/CM 2

ron

PROTONS

T (Continued)

T, MeV

Be

Graphite

Water

700.0 710.0 720.0 730.0 740.0

239.770 244.853 249.957 255.084 260.231

217.787 222.396 227.026 231.676 236.344

192.430 196.507 200.603 204.715 208.845

246.797 251. 989 257.202 262.437 267.693

750.0 760.0 770.0 780.0 790.0

265.400 270.589 275.797 281.025 286.272

241.031 245.737 250.460 255.201 259.959

212.991 217.154 221.332 225.526 229.736

800.0 810.0 820.0 830.0 840.0

291.537 296.821 302.122 307.440 312.775

264.733 269.524 274.330 279.152 283.989

850.0 860.0 870.0 880.0 890.0

318.127 323.494 328.878 334.276 339.690

900.0 910.0 920.0 930.0 940.0

Al

eu

Ag

Ph

283.874 289.805 295.760 301.739 307.741

314.253 320.785 327.344 333.928 340.537

376.074 383.829 391.614 399.428 407.270

272.969 278.265 283.581 288.916 294.269

313.765 319.812 325.880 331.968 338.078

347.170 353.827 360.507 367.209 373.933

415.140 423.037 430.960 438.909 446.8&2

233.960 238.198 242.451 246.717 250.997

299.640 g05.029 310.435 315.858 321.297

344.207 350.355 356.523 362.709 368.913

380.679 387.445 394.232 401.039 407.864

454.880 462.902 470.946 479.013 487.102

288.841 293.708 298.588 303.483 308.391

255.290 259.596 263.914 268.245 272.588

326.752 332.223 337.710 343.211 348.727

375.134 381.373 387.628 393.900 400.188

414.709 421.572 428.454 435.352 442.268

495.212 503.343 511.494 519.665 527.855

345.119 350.562 356.019 361.489 366.973

313.312 318.246 323.193 328.151 333.123

276.943 281. 309 285.686 290.075 294.474

354.257 359.802 365.359 370.930 376.514

406.492 412.810 419.144 425.492 431.854

449.200 456.149 463.113 470.093 477 .088

536.064 544.291 552.536 560.798 569.077

950.0 960.0 970.0 980.0 990.0

372.470 377.981 383.503 389.038 394.585

338.105 343.100 348.105 353.122 358.149

298.883 303.303 307.733 312.173 316.622

382.111 387.720 393.341 398.974 404.619

438.230 444.619 451. 022 457.437 463.865

484.098 491.122 498.160 505.211 512.276

577.373 585.684 594.012 602.354 610.711

1000.0

400.143

363.187

321.081

410.275

470.305

519.354

619.083

Cc; which are important only at small energies. If extensive experimental data are available, the shell corrections, C/Z = '1;iCi/Z, can be determined experimentally (AN69), together with the I value. Usually, experimental uncertainties and limited coverage in energy do not permit this approach. In a modification of an earlier approach (BI6!), it is suggested now, that, for 8 ~ Z ~ 25, Walske's shell corrections (WA52, WA56, BI67, KH68) be used in modified form:

C

:z-

CK

+ VCL(H{32) Z

(8d-I5)

with parameters H, V, and I determined in a least-squares fit to experimental data. Similarly, for Z ~ 8, CjZ = VC K{H(32). For Z 2: 25, Bonderup's shell corrections C B (B067) are used, also in a modified form:

C

Z-

VCB{Hv2jvo2Z) Z

(8d-I6)

8-166

NUCLEAR PHYSICS

Good fits to experimental data for protons and deuterons are obtained as long as CB 2:: o. Values for H, V, and I may be found in BJ67. Typically, for Z 2:: 47, H = 0.755, V = 0.68, and lAg = 476 eV, [Au = 780 eV. For Z = 29, H = 0.55, V = 0.61, and [eu = 319.5 eV. These fits include effects due to the higher Born approximations and are therefore valid only for particles of charge +e. It was found that the least-squares fits do not show singular and distinct minima. For experimental data covering a limited energy range, different local minima will give almost the same x 2• This is fairly obvious from Eq. (8d-ll): for a limited velocity range, an increase in I can be almost entirely compensated by a decrease in the shell corrections (BH69). 100%

5

0.6

B

Z "-'6.9

where B is the stopping number, Eq. (8d-8), and -B =

Z

!((3) - In I -

~l > 0.4 T1 T > 0.4

IC'Z

-!

i

PASSAGE OF CHARGED PARTICLES THROUGH MATTER

8-173

1.10

1.05

-N

1.001-----r---Hr-+,4I--+--....L------1...-.-.l----L..--.l-----l..-......J.----.J

::E

"

N

::E 0.95

FIG. 8d-7. The ratio M2IM 2' of the second moments of the quantum-mechanical [Eq. (8d-2)] and the free-electron cross sections [Eq. (8d-1)] for the L shell. The curves apply for silicon (Wmin = 0.093), copper (0.115) silver (0.135), and lead (0.167).

-,.,

::E

",.,

::E

FIG. 8d-8. The ratio M a/ M 2' of the third moments for the L shell (see Fig. 8d-8 for the elements). Notice that the asymmetry (skewness) is reduced at lower energies.

For larger energy losses, TS68 should be consulted. For the asymmetry of the curves, the third moment should be studied. Tschalar uses' the skewness parameter 'Y~ = C a/C 2 ! for this purpose. From his results it is found that the expression for thin absorbers, 'Y; = 8M;/(8M~)J, is accurate to a few percent for BIZ """'2.3and Tt/T> 0.5 and for BIZ,...,., 6 and TIlT> 0.7. It may be noted that the distribution func-

8-174

NUCLEAR PHYSICS

99.5%

99 98

97 96

~--------_-.J= 19 0 88

__- - - - - -

-----------~85

___

-------~80

__-------...J 75 ~----------l70

P

60

0 50

.--------- --

40

30 25 20

-1

15 12 10 8 6

-----

4 3 2

-2

----

/32=0.04 0.5 0.2 -3 -2

-1 I

I

0.01 FIG.

J

0.1

0 I

0.2

J

I

0.4 0.7 1

1 I

I

I

2

4

7 10

8d-9. Contour lines for the straggling distribution function 4>

I

---CD

log X

X

[(~u) =

(Au

} 0

f(~)

de

where f(~) is the Vavilov function] in silicon for particles of velocity {32 = 0.04 (T 1'0./ 20 MeV for protons). The curves are similar for other velocities. The Vavilov theory has been

PASSAGE OF CHARGED PARTICLES THROUGH MATTER

8-175

tions for the cases discussed above are approximately given by the Vavilov functions for the value K v = 0.251'3- 2 of the Vavilov parameter K v = ~/Emax (SB67). For the ranges R of particles with a mean value R the second central moment, also called the mean-square fluctuation 0"2 is defined by 0"2 = (R2) - R2

(8d-32)

The distribution feR) is usually approximated by a gaussian: feR)

~ ~ exp [ _ _(R_-_R_-_)2] O"V27r

(8d-33)

20"2

and the probability p of finding a particle with range between Rand R + dR is p dR = feR) dR. The deviations from a gaussian are small, but not negligible. They are discussed in LE52 and TT68. Their influence on the Bragg curve has not been studied yet (VK69).

--'--~t-t-~t--,-:-p..~~-------l1.4

~ '---~1-----'~'7t-~~---" percent of the incident particles. The actual energy loss is .1 = Li + pa , where Li is the mean energy loss (Li = sS), and 0" is the standard deviation 0"2

= 78,250sz 2 (1 - (32/2) /(1 - (32) keV".

40-MeV protons, 8 = 0.02 g cm- 2, (32 = 0.08, xv = 0.22, Li = 0.02 X 11.72 = 0.234 MeV, 0" = 40 keY. For.1 = Li, p = 0, and about 58 percent of all the protons lose less than 234 keY. The exact answer is 61.6 percent. On the other hand, for cI> = 96 percent, p "" 2.0, and A - 234 80 ke V - 314 ke V. Thus. 4 percent of the protons lose more than 314 keY (the exact answer is 315 keY), EXAMPLE:

+

8-176

NUCLEAR PHYSICS

values calculated by Sternheimer (ST60), but they are still slightly larger than experimental values (BU60), which were evaluated neglecting the skewness of the range straggling curves. The observed straggling in range-energy measurements is composed of the energy-loss straggling, and an additional asymmetric contribution caused by the multiple-scattering process (BU60, BI60). 8d-8. Coulomb and Multiple Scattering, and Nuclear Interactions. Coulomb Scattering. The differential cross section for Coulomb scattering of a charged particle of kinetic energy T (in MeV), momentum p, velocity v, and charge ze by a nucleus of charge Ze and mass number A into the solid angle 271" sin 0 do is given by the Rutherford formula:

+

271"e 4z 2Z(Z 1) . d4.>(O) = 4 p 2V 2 sin 4 (0/2) sm 0 dO

~ 0.814z Z (Z T2 2

+ I)

sin 0 do X 10-26 2 sin! (0/2) em

(8d-35)

where 0 is the angle of scattering from the incident direction. The above formula assumes that the mass of the incident particle is negligible compared with the mass of the nucleus. Deviations from the Rutherford formula will occur at large angles as the particles begin to feel the influence of nuclear forces. An estimate of the minimum energy T m for which a deviation can be expected at 0 = 180 deg can be obtained from T

=

zZ(A

+ 3)-1

(8d-36)

MeV

A detailed discussion is found in EP61 and JA68. At small angles, the cross section will be smaller than given by Eq. (8d-35) because the atomic electrons will shield the nuclear charge. The Rutherford cross section is reduced by 10 percent at an angle Oq given by (from M047) and by 50 percent at Or

where and ex

=

00 (2.75 0.244Z!

+ 1O.85ex 2)1

00 = ---=-=-=-= pc (MeV)

=

Zz/137f3.

0.244Z1

V2Moc2T

For large kinetic energies, pc

=

(T2

+ 2TM oc2)1, and with r = T/M oc2, 2 _ r +2 f3 - r (r + 1)2

IO-MeV alpha particles in Au: from Table 8d-l, f3 1.05/(74,600)! = 3.84 X 10- 3 deg. Finally,

EXAMPLE.

00

=

e, =

3.84 X 10- 3(61.7

+ 105,000)1

(8d-37) =

0.073, ex = 15.8.

= 1.25 deg.

This reduction is of great importance in the derivation of the multiple-scattering formulas. Multiple Scattering in Thin Absorbers. Multiple Coulomb scattering in thin foils will cause a parallel beam of particles to spread out into a cone. Recent discussions are found in HF68, SC63, and GD68. Moliere's theory (M048, BE53, and M055) is a small-angle approximation to the general problem (BR59, NS61, and TM59) which is in agreement with experimental results, with the possible exception of electrons in heavy elements and also possibly at small energies (f32 < 2 X 10- 3) . The characteristic quantity occurring in the theory is the angle 00 , defined by 00 = OIBt where S_ 02 = 0157 Z(Z + I)Z2_ (8d-38) I· A (pV)2

PASSAGE OF CHARGED PARTICLES THROUGH MAT'J'ER

8-177

61 is in radians; s is the foil thickness in g Zcm", p the momentum, and v the velocity of the particle (pv in MeV); z, Z, and A have the same meaning as in Sec. 8d-2. B is defined in M048; for practical purposes it can be obtained from MZ67 or from Table 8d-6, for particles with charge 1 with an accuracy of better than 5 percent. A few values are listed for z > 1. It is not obvious whether z* or z should be used for a computation of the multiple scattering of heavy ions. The use of z* is suggested. For z ~ 6 and Z ~ 50, all values B({3,z) are larger than 0.98 X B({3 = 0, z = 1); and for z ~ 6 and Z ~ 20, all values B({3,z) ~ 0.95 X B({3 = 0, z = 1), but less than B(O,I).

TABLE 8d-6. B OF MOLIERE'S THEORY FOR Z = I, 2, AND 6, VARIABLE {3, AND THICKNESS s* z Z

8,

=

1

z

=

2

z

=6

g/cm 2 (32

=0

--

0.005 0.01 0.02 0.05 0.1 0.2 0.5 1.0 0.1 1.0 0.1 1.0 --

-- - - - - - - - - - - - - - - - - - -

3

10- 3 10- 2 10- 1 1

10.5 13.0 15.4 17.9

8.8 8.3 7.6 6.6 5.7 4.9 11.5 10.8 10.2 9.2 8.5 7.7 14.0 13.3 12.8 11.7 11. 0 10.3 16.4 15.8 15.2 14.2 13.5 12.8

3.8 6.6 9.2 11.8

2.8 5.7 8.5 11.0

10

10- 3 10- 2 10- 1 1

8.2 10.7 13.3 15.7

8.0 7.7 7.4 6.7 10.5 10.3 9.9 9.25 13.0 12.8 12.4 11.8 15.4 15.2 14.8 14.3

5.2 8.0 10.5 13.1

4.2 7.0 9.6 12.1

3.2 7.2 6.2 9.8 8.8 12.3 11.4 14.8

4.9 7.7 10.3 12.8

8.1 7.2 10.6 9.7 13.1 12.3 15.5 14.7

20

10- 3 10- 2 10- 1 1

6.8 9.4 12.0 14.4

6.7 6.6 6.5 9.3 9.3 9.2 11.9 11.8 11.7 14.4 14.3 14.2

6.2 5.8 5.2 8.9 8.5 7.9 11.4 11.0 10.5 13.9 13.5 13.1

4.2 7.1 9.7 12.2

3.5 6.4 9.0 11.5

6.5 9.2 11.7 14.2

5.0 7.8 10.3 12.8

6.8 9.4 11.9 14.4

6.4 9.1 11.6 14.2

50

10- 3 10- 2 10- 3 1

4.7 7.5 10.0 12.5

4.7 4.7 4.6 4.6 4.5 7.5 7.5 7.4 7.4 7.3 10.0 10.0 10.0 10.0 9.9 12.5 12.5 12.5 12.5 12.4

4.3 7.2 9.7 12.2

3.7 6.6 9.2 11.8

3.2 4.6 6.0 7.5 8.8 10.0 11.3 12.6

4.1 7.0 9.6 12.1

4.7 7.5 10.1 12.5

4.6 7.4 10.0 12.5

100

10- 3 10- 2 10- 1 1

3.1 6.0 8.7 11.2

3.1 3.1 3.1 6.0 6.0 6.0 8.7 8.7 8.7 11.2 11. 2 11.2

3.0 3.0 6.0 5.9 8.7 8.6 11.2 11.1

3.0 5.9 8.6 11.1

2.8 5.7 8.4 10.9

2.5 5.4 8.2 10.7

2.9 5.8 8.5 11.0

3.1 6.0 8.7 11.2

3.1 6.0 8 7 11.2

6.0 8.7 11.2 13.7

* For any value of z at fJ = 0, B is the same as for z = 1. Linear interpolation for Z or fJ2 will give sufficient accuracy. for 8.

7.4 4.6 10.0 7.4 12.5 10.0 14.9 12.6

3.1 6.0 8.7 11.2

.........

7

10 T,MeV

~

§

...... :=.:..-:- :-.:---r- •• _

----

20

1---

40

.-

70100

FIG. 8d-l1. Calculated electron-mass stopping power S, including collision and radiation loss for different materials (BS67). The stopping power for NaI is within 1 percent of S for Ag,

maximum of a straggling distribution may amount to more than 50 percent of the mean energy loss. Multiple scattering (VV68) and backscattering contribute to the problem. Comparison of mean energy losses calculated from Eq. (8d-41) with experimental data (e.g., HU57, HA59, HR68) can be expected to be accurate to better than 10 percent only if a detailed study of straggling etc., has been made. A comparison of experiment and theory for 1- and 2-MeV electrons in silicon is found in 8167. Electron Ranges and Energy Deposition in Thick Absorbers. For electrons traversing thick absorbers, lateral and backscattering will be very important, and electron distri-

8-182

NUCLEAR PHYSICS

bution functions will extend over wide ranges in space, angle, and energy. A general treatment is found in BE63, KK68, R068, SP55, and SP54. Practical results for many substances are given in SP59, KE66, BS67, LP57, and PE62 and KK68. Detailed investigations have been performed for 5- to 30-keV electrons (CT65), and for 40- to 160-keV electrons (GF59). For higher energies, see, e.g., BH58. Electron ranges calculated by the use of Eq. (8d-14) do not have a simple relation to any observed quantity: see Table 8d-IO. TABLE

8d-1O.

THE COMPARISON OF IVL>\XIMUM ELECTRON RANGES WITH SPENCIII 10

104

~

0::

UJ

z

TF=

103

UJ

0::

8

103

E (eV), TF (,usec/m)

z

0

I-

7W

102

102

101

101

::> UJ

z

10° 0.01

0.1

1.0

10

10° 100

NEUTRON VELOCITY, meters/microsecond NEUTRON TIME OF FLIGHT, microseconds/meter

, FIG. 8f-1. Variation of neutron velocity and neutron time of flight with energy for the neutron energy range 1 eV to 10 MeV.

8-220

NUCLEAR PHYSICS NEUTRON TEMPERATURE, oK

10 6

y

10 3

>u 10 2

~

a: w z w 10'

sa:

~

107

10 8

~

1

E=8.6171 xlO-5T

E(eVl. T(OK)

..... ;:)

w 10°

z

10-1

10-2

~

~

~ t

->

10 4

103

NEUTRON TEMPERATURE, oK

FIG. 8£-2. Variation of neutron temperature with energy for the neutron energy rang 0.001 eV to 10 keY.

NEUTRON WAVE NUMBER,cm'l (xl0 9 )

10

4 100

o

~

~

10 3

---r:-----i Ie!' en ~

~

10 2 I-------+----:>.,,---+----r---:;.,L-+-----~

~

105 ~ a:

~

.....

Cl

a: w z 10' f------+---------"'

~

"'d

::q

~ U1 H

o

U1

13

Al

14

Si

15

P

16

S

17

CI

18

Ar

19

K

20

Ca

25 26 27 27 28 28 29 30 31 31 32 32 33 34 35 36 37 35 36 37 38 36 37 38 39 40 41 39 40 41 42 40 41 42 43 44 45 46 47

13 14 15 14 15 14 15 16 17 16 17 16 17 18 19 20 21 18 19 20 21 18 19 20 21 22 23 20 21 22 23 20 21 22 23 24 25 26 27

7,330 11,098 6,443 13,056.7 7,723 17,175.4 .8,476 10,617.2 6,594 12,312 7,936.6 15,092 8,646 11,422.3 6,985.1 9,879 4,420 12,635 8,583 10,316.6 6,110 15,252 8,790.8 11,838.7 6,591 9,872 6,098 13,089 7,801.5 10,096.0 7,535 15,619 8,364 11,471 7,927.8 11,135 7,420.3 10,401 7,281

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

1 1 1 2.6 1 3.5 1 4.3 5 8 2.4 11 1 3.7 2.9 8 70 6 2 4.1 8 17 2.5 2.4 6 6 2 10 2.7 0.8 2 23 1 8 4.8 5 4.9 10 11

29

Cu

30

Zn

31

32

Ga

Ge

59 60 61 62 63 64 65 63 64 65 66 64 65 66 67 68 69 70 71 69 70 71 72 70 71 72

73

33

As

34

Se

74 75 76 77 75 76 74 75 76 77 78 79

31 32 33 34 35 36 37 34 35 36 37 34 35 36 37 38 39 40 41 38 39 40 41 38 39 40 41 42 43 44 45 42 43 40 41 42 43 44 45

8,999.2 11,387.4 7,817.4 10,596.2 6,835.7 9,658.8 6,099 10,840.5 7,916.3 9,911 7,065.2 11,855.1 7,979.2 11,051 7,052.4 10,198.1 6,482.2 9,195 6,050 10,324 7,640 9,311 6,516 11,529.0 7,413.2 10,750.9 6,785.2 10,200.0 6,489 9,445 5,986 10,244 7,334 12,072 8,025 11,161 7,415 10,492 6,971.3

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.6 2.7 2.9 1.5 2.8 2.0 5 4.5 0.8 4 0.7 3.5 0.8 5 0.7 0.5 0.9 8 50 4 7 7 6 4.5 4.8 4.7 1.5 1.6 19 19 32 5 5 19 6 8 6 5 4.4

Z tr.J q '-3 ~

o Z

U1

cr

tv tv

CJ,.j

TABLE

Atomic no.

Element

Z 34

Se

35

Br

36

Kr

37

Rb

38

Sr

39

Y

40

Zr

Mass no.

A=N+Z 80 81 82 83 79 80 81 82 78 79 80 81 82 83 84 85 86 87 85 86 87 88 84 85 86 87 88 89 89 90 90 91

8f-I.

TABLE OF NEUTRON SEPARATION ENERGIES

Number of neutrons

N 46 47 48 49 44 45 46 47 42 43 44 45 46 47 48 49 50 51 48 49 50 51 46 47 48 49 50 51 50 51 50 51

Separation energy B n , keY

9,902.8 6,715 9,262 5,970 10,698 7,876.0 10,164 7,601 12,010 8,340 11,520 7,850 10,980 7,467 10,519 7,122 9,848 5,511 10,475 8,637 9,940 6,130 11,580 8,482 11,522 8,437 11,113 6,393 11,477 6,857 11,997 7,194

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

4.9 6 9 50 6 4.4 6 8 50 8 9 100 100 6 5 6 7 8 6 9 7 90

± ± ± ± ± ± ± ± ±

31 31 5 1 8 8 2 6 5

Atomic no.

Mass no.

Element

A=N+Z

46

Pd

47

Ag

106 107 108 109 110 111 107 108 109 110 106 107 108 109 110

Z

48

Cd

III

49

In

50

Sn

~ l\:)

(Continued)

112 113 114 115 116 117 113 114 115 116 112 113 114 115 116 117

Number of neutrons

N 60 61 62 63 64 65 60 61 62 63 58 59 60 61 62 63 64 65 66 67 68 69 64 65 66 67 62 63 64 65 66 67

Separation energy e; keY

9,544 6,532 9,227 6,150 8,807 5,740 9,531 7,267 9,182 6,810 10,870 7,929 10,334 7,381 9,856 6,975.4 9,399.6 6,538.2 9,039 6,143 8,694 5,764 9,427 7,312 9,034 6,725 11,080 7,744 10,320 7,537 9,563 6,941

± ± ± ± ± ± ± ± ± ±

4 7 8 9 14 50 9 1 9 1

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

7 7 7 7 4.5 4.8 3.8 1 9 9 13 12 12 10 23 200 17 16 9 7 5

l\:) ~

z

q

o

e-

trl

>

::0

"'C ~ ~

lf1 ;-;

ou:

41

Nb

42

Mo

43

44

Tc

Ru

45

Rh

46

Pd

92 93 94 95 96 97 93 94 95 92 93 94 95 96 97 98 99 100 101 97 98 99 100 96 97 98 99 100 101 102 103 104 105 103 104 102 103 104 105

52 53 54 55 56 57 52 53 54 50 51 52 53 54 55 56 57 58 59 54 55 56 57 52 53 54 55 56 57 58 59 60 61 58 59 56 57 58 59

8,634 6,750 8,198 6,468 7,838 5,575 8,844 7,229.5 8,510 12,580 8,053 9,692 7,373 .8 9,154.2 6,816.1 8,642.8 5,918 8,300 5,390 9,450 7,350 8,880 6,590 10,124 8,040 10,250 7,469 9,671 6,806 9,216 6,248 8,887 5,976 9,312 6,999.3 10,360 7,608 10,023 7,091

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

2 6 6 6 7 22 8 1.5 15 50 13 13 3.8 0.5 3.4 1.0 9 9 19

± ± ±

200 60 37

± ± ± ± ± ± ± ± ± ± ± ± ±

5 6 6 5 20 20 16 9 1.5 50 23 20 12

51

Sb

52

Te

53

I

54

Xe

118 119 120 121 122 123 124 125 121 122 123 124 120 121 122 123 124 125 126 127 128 129 130 131 127 128 129 130 124 125 126 127 128 129 130 131 132 133 134

68 69 70 71 72 73 74 75 70 71 72 73 68 69 70 71 72 73 74 75 76 77 78 79 74 75 76 77 70 71 72 73 74 75 76 77 78 79 80

9,331.1 6,484 9,110.1 6,181 8,804 5,957 8,506 5,732 9,250 6,806.0 8,975 6,468 10,283 6,976 10,058 6,925 9,425 6,630 9,117 6,290 8,754 6,116 8,385 5,907 9,153 6,826 8,865 6,498 10,500 7,610 10,240 7,200 9,640 6,913 9,259 6,603 8,932 6,531 8,460

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

4.6 3 4.3 6 7 5 11 5 8 1.5 7 2 24 47 45 3 2 3 5 3 10 10 10 2 8 3 10 31

± 350 ± 350 ± 7 ± 7 ± 6 ± 6 ± 36 ± 36

zt?'.j d

"':3 ~

o

Z

[fl

f

~ ~

CJ1

TABLE

Atomic no.

Mass no.

Element

A=N+Z

-54

Xe

55

Cs

56

Ba

135 136 137 133 134 135 136 130 131 132 133 134 135 136 137 138 139 138 139 140 136 137 138 139 140 141 142 143 141 142 142 143 144 145

Z

57 58

La Ce

59

Pr

60

Nd

8f-I.

TABLE OF NEUTRON SEPARATION ENERGIES

Number of neutrons

N 81 82 83 78 79 80 81 74 75 76 77

78 79 80 81 82 83 81 82 83 78 79 80 81 82 83 84 85 82 83 82 83 84 85

-

Separation energy e: keY

6,560 7,880 4,460 9,038 6,705 9,050 6,610 10,260 7,695 9,560 7,257 9,252 6,974 9,106.4 6,904 8,611.1 4,723.4 7,260 8,792 5,161.0 9,990 7,840 9,470 7,508 9,039 5,428.6 7,159 5,182 9,386 5,843.6 9,809 6,123 7,817.2 5,760.4

± ± ± ± ± ± ±

100 100 100 27 15 110 70

± ± ± ± ± ± ± ± ±

12 280 42 16 3 0.8 4 0.8 0.7

± 20 ± 1.0 ± ± ± ± ± ± ± ± ± ± ±

26 48 0.6 8 10 18 1.2 9 2 1.8 1.9

Atomic no,

Z

Dy

67

Ho

68

Er

69

Tm

70

Yb

71

Mass no.

Element

66

Lu

(Continued)

A=N+Z --100--161 162 163 164 165 165 166 167 162 163 164 165 166 167 168 169 170 171 169 170 168 169 170 171 172 173 174 175 176 177 175 176 177

I

Number of neutrons

N 94 95 96 97 98 99 98 99 100 94 95 96 97 98 99 100 101 102 :i03 100 101 98 99 100 101 102 103 104 105 106 107 104 105 106

~ ~

Separation energy e: keY

8,590 6,448 8,193 6,270 7,654 5,715 8,043 6,243 7,290 9,200 6,840 8,795 6,645 8,549 6,436.2 7,771. 2 5,997 7,190 5,676 8,055 6,595 8,980 6,867.2 8,550 6,616 8,023 6,365 7,465 5,819 6,640 5,565 7,801 6,293.2 6,890

± ± ± ± ± ± ± ± ±

O':l

30 12 3 3 3 2 36 3 100

± ± ± ± ± ± ± ± ± ± ±

90 42 40 33 0.5 0.5 12 70 10 35 2.5

±

0.5

± 3 ± 3 ± 3 ± 3 ± 3 ± 80 ± 16 ± 42 ± 1.2 ± 2

z

q o t"

trj

> ~ "'d

~ ~

rJJ.

I-t

o

rJJ.

61

Pm

62

Sm

63

64

Eu

Gd

65

Tb

66

Dy

146 147 148 149 150 151 147 148 144 145 146 147 148 149 150 151 152 153 154 155 151 152 153 154 152 153 154 155 156 157 158 159 160 161 159 160 156 157 158 159

86 87 88 89 90 91 86 87 82 83 84 85 86 87 88 89 90 91 92 93 88 89 90 91 88 89 90 91 92 93 94 95 96 97 94 95 90 91 92 93

7,570.2 5,293.2 7,333.7 5,042 7,332 5,309 7,684 5,904 10,616 6,763 8,411 6,371 8,140.0 5,846.2 7,985.2 5,609 8,224 5,867.0 7,904 5,819 7,933 6,305 8,544 6,439 8,510 6,480 8,606 6,456 8,527 6,347 7,929.4 6,031 7,376 5,650 8,177 6,377 9,890 6,830 8,840 6,851

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± +

2.1 4.0 4.8 12 11 15 23 11 36 11 19 17 1.2 4.8 0.8 15 16 0.4 12 11

23 4 12 2 13 20 9 5 5 3.7 27 28 70 25 2

34

72

Hf

73

Ta

74

W

75

Re

76

Os

77

Ir

78

Pt

174 175 176 177 178 179 180 181 181 182 183 180 181 182 183 184 185 186 187 185 186 187 188 184 185 186 187 188 189 190 191 192 193 191 192 193 194 190 191 192

102 103 104 105 106 107 108 109 108 109 110 106 107 108 109 110 111 112 113 110 111 112 113 108 109 110 111 112 113 114 115 116 117 114 115 116 117 112 113 114

8,700 6,910 8,110 6,370 7,622 6,098 7,383 5,693 7,640 6,063.0 6,929 8,400 6,947 8,035 6,191 7,413 5,754 7,206 5,467 7,800 6,178 7,290 5,872.2 8,000 6,820 8,310 6,220 7,837 6,000 7,793.5 5,890 7,630 5,480 8,250 6,145 7,786 6,103 8,680 6,680 8,360

± 70 ± 3 ± 3 ± 3 ± 3 ± 21 ± 0.8 ± 11 ± 36 ± 21 ± 2 ± 4 ± 2 ± 43 ± 2 ± 5 ± 60 ± 1.5 ± 70 ± 70 ± 60 ± 19 ± 90 ± 1.5 ± 90 ± 80 ± 60 ± 180 ± 9 ± 46 ± 27

z t';j

d

""3

;:0

o Z

Ul

Cf tv tv

""-l

TABLE

Atomic no.

Element

Z 78

Pt

79

Au

80

Hg

81

82

Tl

Pb

83

Bi

88

Ra

Mass no.

A=N+Z 193 194 195 196 197 198 199 197 198 196 197 198 199 200 201 202 203 204 205 203 204 205 206 202 203 204 205 206 207 208 209 208 209 210 226 227

8f-1.

TABLE OF NEUTRON SEPARATION ENERGIES

Number of neutrons

N 115 116 117 118 119 120 121 118 119 116 117 118 119 120 121 122 123 124 125 122 123 124 125 120 121 122 123 124 125 126 127 125 126 127 138 139

Separation energy B n , keY

6,288 8,384 6,126 7,920.9 5,854 7,561 5,570 8,084 6,513.2 8,810 6,637 8,634 6,652.8 8,028.8 6,226.5 7,755.1 5,987 7,499 5,540 7,696 6,654 7,534 6,504 8,870 6,930 8,244 6,734.2 8,082 6,736.4 7,367.7 3,944 6,867 7,453.6 4,599.7 6,387 4,586

± 48 ± 20 ± 13 ± 1.5 ± 14 ± 19 ± 19 ± 12 ± 0.8 ± 42 ± 41 ± 4.9 ± 0.5 ± 4.6 ± 1.5 ± 7 ± 7 ± 100 ± 23 ± 2 ± 7 ± 3 ±

± ± ± ± ± ± ± ± ± ± ±

39 12 1.5 6 1.5 1.5 9 6 4.4 4.8 6 21

Atomic no.

Element

Z 90

Th

91

Pa

92

U

93 94

95

96

Np Pu

Am

em

(Continued) Mass no.

A=N+Z 229 230 231 232 233 231 232 232 233 234 235 236 237 238 239 236 237 238 238 239 240 241 242 243 244 245 241 242 243 244 245 246 247 248 249

Number of neutrons

N 139 140 141 142 143 140 141 140 141 142 143 144 145 146 147 143 144 145 144 145 146 147 148 149 150 151 146 147 148 149 149 150 151 152 153

00 I

Separation energy ts; keY

5,233 6,787 5,129 6,431 4,787 6,803 5,567 7,270 5,737 6,840 5,307 6,545 5,129 6,144 4,803.4 5,715 6,591 5,486 7,002 5,657 6,533.7 5,243 6,305 5,034 6,018 4,750 6,660 5,535 6,376 5,355 5,524 6,452 5,156 6,209 4,713

l'.:) l'.:)

00

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

12 4 4 4 5 21 23 50 12 4 4 2 4 4 2.4 16 16 9 7 4 1.5 3 4 7 13

±

9 9 5 4 4 8 8 6

±

± ±

± ± ± ±

Z d

o

r-

ttj

»>

~

""d

P::

~ U1 H

o

U1

NEUTRONS

8-229

where the Ii are the abundances Cr.fi = 1) of the individual isotopes with coherent amplitudes tu, The index of refraction for a noncapturing medium can be calculated from the coherent scattering amplitude as n2 =

2

1 _ 'A N acoh 11"

where 'A is the neutron wavelength, and N is the number of nuclei per em", Table 8f-2 lists the coherent scattering amplitudes for those elements, or particular isotopes, for which experimental values have been determined. The amplitude values are given in femtometers (== 10- 13 em) and are preceded by a positive or negative sign. The standard convention adopted here is that positive amplitude represents hardsphere scattering, i.e., a phase shift of 180 deg. For two values the sign is omitted, since no explicit experimental assignment has been made, but both cases are probably positive. 8f-4. Recommended 2,200-m/sec Cross Sections for Fissile Isotopes. In Table 8f-3, which is taken from G. C. Hanna, C. H. Westcott, H. D. Lemmel, B. R. Leonard, Jr., J. S. Story, and P. M. Attree, Atomic Energy Rev. 7, (4) 3 (1969), IAEA, Vienna, the results of a careful study of relevant experimental measurements are presented. A least-squares fitting procedure was used, and both direct and indirect measurements of the quantities listed were considered. The quantities appearing in the table have the following meanings: Ua Absorption cross section: u(n,-y) + u(n,f) = Utot - Uscat U/ Fission cross section: u(n,f) u"'{ Radiative capture cross section:u(n,-y) a Ratio: u(n,-y)/u(n,f) T/ Number of neutrons produced per absorption event: prompt + delayed iiT Number of neutrons produced per fission event: prompt + delayed The II value for Cf 252 , which is the standard used in the fissile II measurements, was evaluated to be 3.765 ± 0.012. 8f-6. s-wave Neutron Strength Functions, Observed Resonance Spacings, and Average Radiation Widths. Neutron cross sections of most nuclides exhibit individual resonances in the energy region from 0.1 eV to 100 ke V. These resonances correspond to excited states of the compound nucleus at an excitation energy just above the neutron separation energy. The resonances can be described by the following parameters: Eo Resonance energy r Total width r n Neutron width r"'{ Radiation width I' F Fission width l Angular momentum of the neutron, 8, p, d, etc. J Spin of the compound nucleus Since the parameters of over 10,000 resonances have now been measured, it is not possible to present a complete listing of these parameters in this section. The detailed parameters may be found in the many volumes of the report BNL-325 (1958, 1960, 1964-1966). However, for many purposes the average of the parameters for each nuclide are sufficient. Some of these averages for s-wave interactions which are predominant in the energy region 10 ke V are listed in Table 8f-4. The s-wave neutron strength function for a nuclide is defined as r:/D. r: is the average of the reduced neutron widths of s-wave resonances of the same spin and parity, where is equal to rn/VE o (in eV). D is the average level spacing for resonances of the same spin and parity. s-wave strength functions can be determined from the parameters of resolved resonances or from the energy dependence of the

:s

r:

r:

TABLE

Atomic no.

Element

Z 1 2 3

H He Li

Mass no.

A=N+Z 1 2 3

.. . ... 6 7

4 5

Be B

... ...

10 11

6

C

...

N 0 F Ne Na Mg Al Si P S CI Ar K Ca

· .. ... ... ... ... ... ... ... ... ... ... ...

13

7 8 9 10 11 12 13 14 15 16 17 18 19 20

· .. · ..

40 44

21 22

Sc Ti

· ..

... 46 47

8f-2.

%

COHERENT SCATTERING AMPLITUDES

Coherent amplitude acoh. fm

-3.719 +6.21 +4.7 +3.0 -1.94 +1.8 -2.1 +7.74 +5.40 +6.53 +6.1 +6.656 +6.0 +9.14 +5.80 +5.6 +4.60 +3.5 +5.2 +3.5 +4.1646 +5.1 +3.1 +9.9 +1.89 +3.70 +4.88 +4.9 +1.8 +11.8 -3.5 +4.8 +3.3

± ± ± ± ±

0.002 0.04 0.3 0.5 0.05

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.07 0.04 0.35 0.1 0.004 0.8 0.10 0.05 0.1 0.05 0.1 0.1 0.3 0.0022 0.1 0.2 0.6 0.02 0.04 0.07 0.2 0.1 1.0 0.1 0.2 0.2

Atomic no.

~

Element

Z 47

Ag

Mass no.

A=N+Z

... 107 109

48 49 50

Cd In Sn

... ... ...

116 117 118 119 120 122 124 51 52

Sb Te

·.. · ..

120 123 124 125 130 53 54 55 56 57 58

I Xe Cs Ba La Ce

...

... ... ... ... ...

140 142 59 60

Pr Nd

... · ..

142 144 146

Coherent amplitude acoh. fm

+6.1 +8.3 +4.3 +3.32 +3.8 +6.1 +5.8 +6.4 +5.8 +6.0 +6.4 +5.5 +5.9 +5.4 +5.6 +5.3 +5.8 +5.5 +5.6 5.7 +5.2 +4.62 +4.9 +5.3 +8.3 +4.84 +4.7 +4.5 +4.4 +7.2 +7.7 +2.8 +8.7

±0.4 ± 0.5 ±0.4 ± 0.20 ± 0.1 ±0.4 ± 0.1 ± 0.25 ± 0.1 ± 0.25 ± 0.1 ± 0.3 ± 0.2 ± 0.1 ± 0.4 ± 0.1 ± 0.7

o

z

q

o

~

tr.1

> ~ I'tf

::I:

~ ~

o

1ft

± 0.6 ± 0.3 ± 0.09 ± 0.3 ± 0.3 ± 0.6 ± 0.06 ± 0.2 ±0.4 ±0.4 ± 0.6 ± 0.6 ± 0.6 ±0.4

48 49 50

23

V

24

Cr

25 26

Mn Fe

... ...

52

· ., ...

54

56 57

27 28

Co Ni

...

· ..

58 60 61 62 64

29

Cu

...

63 65

30 31 32 33 34 35 36 37

Zn Ga Ge As 8e Br Kr Rb

38 39 40 41 42 43 44 45 46

8r Y Zr Nb Mo Tc Ru Rh Pd

...

... ·.. · .. ... ·.. ... ...

85

... · .. ... ... ... 99 ... ... ...

-5.8 ± 0.3 +0.8 ± 0.2 +5.5 ± 0.3 -0.5 ± 0.1 +3.52 ± 0.06 +4.9 ..:....3.7 ±O.2 +9.2 ± 0.2 ± 0.3 +4.2 ± 0'.2 +10.1 +2.3 ± 0.1 +2.5 ± 0.3 ± 0.2 +10.3 ± 0.2 +14.4 +3.0 ± 0.3 +7.60 ± 0.06 -8.7 ±0.4 -0.38 ± 0.07 +7.7 ± 0.3 +6.72 ± 0.15 ± 0.2 +11.1 +5.7 ± 0.1 +7.2 ± 0.1 +8.4 ± 0.5 +6.4 ± 0.1 +7.79 ± 0.14 +6.7 ± 0.5 7.44 ± 0.15 +8.5 ± 0.1 +8.3 ± 0.1 +6.83 ± 0.07 +7.88 ± 0.05 +7.0 ± 0.2 +6.9 ± 0.2 +6.7 ± 0.2 +6.8 ± 0.3 +7.3 +6.0 ± 0.7 +5.9

61 62

Pm 8m

63 64 65 66

Eu Gd Tb Dy

152 154

... ... ... ...

160 161 162 163 164 67 68 69 70 71

Ho Er Tm Yb Lu

72

Hf

73

Ta

74 75 76

W

Re Os

... · .. ·..... ... .,. · .. · .. · .. . ..

189 190 192 77 78 79 80 81 82 83 90 92 93 94

Ir Pt Au Hg

Tl Pb Bi Th U

. . .. ... ... . .. .,

. ..

. ..

... . ..

235

Np Pu

...

239 240

-5 +8 +6.3 +15 +7.56 +16.9 +6.7 +10.3 -1.4 +5.0 +49.4 +8.5 +7.9 +7.20 +12.90 +7.3 +.7.77 +7.0 +4.66 +9.2 +10.7 +11.0 +11.4 +11.9 +10.6 +9.5 +7.6 +12.68 +8.9 +9.34 +8.5239 +9.8 +8.4 +9.8 +10.57 +7.5 +3.8

±2 ±2 ± 0.3 ±2 ± 0.20 ±0.4 ±0.4 ±0.4 ± 0.5 ±0.4 ± 0.5 ± 0.2 ±0.4 ± 0.06 ± 0.07 ± 0.2 ± 0.14 ± 0.5 ± 0.09

Z

t:r:J

d

8

~

o

Z

U1

± ± ± ± ± ± ± ± ± ± ±

0.6 0.1 0.02 0.9 0.02 0.001 4 0.1 0.2 0.6 0.06 0.3

Cf

~ ~

.....

8-232

NUCLEAR PHYSICS

TABLE 8f-3. RECOMMENDED 2,200-M/SEC CROSS SECTIONS FOR FISSILE ISOTOPES Parameter I

eTa eTl

0'';; a 1]

iiT

U 2 33 577.6 530.6 47.0 0.0885 2.2844 2 .4866

± 1.8 ± 1. 9 ± 0.9 ± 0.0018 ± 0.0063 ± O. 0069

I

U230

PU 2 3 9

PU 24 l

678.5 ± 1. 9 580.2 ± 1.8 98.3 ± 1.1 o. 1694 ± O. 0021 2.0719 ± 0.0060 2.4229 ± 0.0066

1012.9±4.1 741.6 ± 3.1 271.3 ± 2.6 0.3659 ± 0.0039 2.1085 ± 0.0066 2.8799 ± 0.0090

1375.4 ± 8.6 1007.3 ± 7.2 368.1 ± 7.8 0.3654 ± 0.0090 2.149±0.014 2.934 ± 0.012

I,

total cross section averaged over many resonances. The values with standard deviations listed in Table 8f-4 were taken principally from a compilation by K. K. Seth, Nuclear Data A2, 299 (Sept. 1966). Standard deviations are given for values where the errors are less than 50 percent of the value. A few spin-i target nuclides have s-wave strength functions which are different for the two compound nucleus spin states 1 and 2. For these nuclides the s-wave strength function for the resonances with J = 2 is approximately twice that for J = 1 resonances. The values for the observed resonance spacings with standard deviations for s-wave neutrons D o b a listed in Table 8f-4 were taken principally from a summary by J. E. Lynn, "The Theory of Neutron Resonance Reactions," Clarendon Press, Oxford, 1968. For zero-spin target nuclides, the average level spacing D for resonances with J = j- is equal to D ob • • For nonzero-spin target nuclides, D for the two spin states is greater than D ob • and may be computed from the formula

21

I

+1

+1 where 1 = spin of target nucleus J = spin of compound nucleus J = 1 ± j- for s-wave resonances For example, for 1 = j-, D J _ o = 4D o b • and D J _ l = -!D ob s ' Several of the values listed as lower limits were determined from the energy of only the lowest resonance. The values of the average radiation widths with standard deviations for s-wave neutrons roy listed in Table 8f-4 were determined principally from the resonance data tabulated in BNL-325 (1958, 1960, 1964-1966). The standard deviation includes both the experimental errors in the measurements of the radiation widths of the individual resonances and the standard deviation arising from the width of the distribution of r'Y' For heavy nuclides the width of the distribution is ",,10 percent corresponding to a chi-squared distribution with 200 degrees of freedom, while for light nuclides the width is ",,30 percent which corresponds to "-'22 degrees of freedom. Values denoted with an asterisk are based on data for only one or two resonances and sometimes are computed from thermal capture cross sections or resonance capture integrals. These values with an asterisk may not include the standard deviation arising from a poor sampling from the distribution of r'Y' Hence, the correct 'f''Y for these nuclides might be different from the value listed by "-'10 to ""30 percent. A few nonzero-spin target nuclides have average radiation widths which are different for the two spin states of the compound nucleus. For these nuclides values are listed for both spin states. Sf-G. Infinite-dilution Resonance Integrals;' The neutron cross sections for most nuclides exhibit resonance structure. The incident neutron energy range in which D J = 2 D ob • 2J

1 We should like to express our appreciation to Dr. M. K. Drake, of the Gulf General Atomic Corporation (now at Brookhaven National Laboratory), for supplying the information contained in this section and in Table 8f-5.

NEUTRONS

8-233

the individual resonances can be observed varies from nuclide to nuclide; but for most of the heavier nuclides, this energy range begins at near-thermal neutron energies and extends to approximately 10 keY. The resonance integral is a quantity that is frequently used to characterize the magnitude of the neutron cress section for the resonance energy region. The resonance integral has been found to be particularly useful in characterizing the absorption cross section for materials used in reactor physics analysis. When a resonance absorber is placed in a moderator at near-zero concentrations, the resonance absorption integral is not affected by energy self-shielding or by Doppler broadening. Under these conditions, the material absorbs neutrons in the slowingdown spectrum of the moderator. The resonance integral is expressed as R.T. =

~

Em ax

Eo

u(E)'P(E) dE

where u(E) is the neutron cross section as a function of energy E. In the case where the absorber is at near-zero concentrations in a moderator, the weighting function 'P(E) (neutron flux distribution) is proportional to 1/E for neutron energies greater than a few tenths of an electron volt. The upper limit of the integral is generally taken as a few MeV. The lower-energy limit is generally taken as the cutoff, between where the neutron flux distribution can be treated as being I/E and where a Maxwellian distribution can be used. In most experimental measurements of the resonance integral, E; is determined by the type and thickness of the filter used to absorb the neutrons in the Maxwellian portion of the spectrum. Cadmium is the material generally used as the filter, and an appropriate thickness of the material results in a cutoff energy of 0.5 eV. In Table Sf-5 are listed recommended infinite-dilution resonance integrals. The values given in this table have been taken from various sources. In most cases the recommended values have been taken from experimental integral measurements. In other cases the values have been obtained by integrating experimentally measured, differential cross-section data. Resonance integrals for several reaction mechanisms, i.e., (n,'Y), (n, fission), and (n, absorption), are included. The particular reaction mechanism is given in the Reaction column. In certain cases the (n,'Y) reaction produces two or more different states of the residual nucleus, and this information is also given in the Reaction column. The recommended resonance integrals (R.I.) at infinite dilution are given in the final column. In all cases the cutoff energy, E c has been taken as 0.5 eV, and the upper energy limit E m a x has been taken to be 15 MeV. Also, the integrals given in Table Sf-5 contain the contribution from the l/v part of the low-energy cross sections. 8f-7. Neutron Flux Standards. Because of the uncharged nature of the neutron, its direct detection is difficult. For many cross-section measurements a knowledge of the incident neutron flux, either absolute or relative, is required, and many techniques are employed to accomplish this end. For absolute flux measurements, techniques used include the production of known flux by means of source reactions (see Sec. Sf-9), the utilization of the reasonably well-known characteristics of the interactions of neutrons with protons (the n-p interaction), and the invocation of certain well-determined cross sections as standards for measurement of other lesser-known cross sections. The n-p interaction is, of course, only a special case of the last technique. The total n-p cross section has been measured to high precision at a number of neutron energies. These data have been fitted by an analytical form based on effective range theory. The resulting equation, which gives the total cross section UT in barns for an incident laboratory neutron energy E in Me V, seems to fit the high-

TABLE

8f-4.

8-WAVE NEUTRON STRENGTH FUNCTIONS

i\o/D,

8-WAVJ

~

"tl

::r:

~

U2 ~

o

170 150 150 130 100 120

26

60 5 >100 8 ±

165 200 290 155

10 30

± ±

155 100

±

3 14

± ± ± ±

± ±

30* 30* 30* 30* 40* 20

± ±

20* 20 50* 5

±

10 15*

± ± ±

U2

28 Ni 58 60 61 62 64

29 Cu 63 65 30 Zn

31 Ga

64 66 67 68 69 71

32 Ge

33 As 34 Se

70 72 73 74 76 75 74 76 77

78 80 82 35 Br 79 81 36 Kr 37 Rb

(J

{I.

80 83 85 87

* Based on t

2.4 3.0 2.8 2.8 2.9 2.0 1.9 2.5 1.7 1.7 1.1 1.5 3.1 3.0 1.2 1.5 1.4 1.8 1.3 2.0 0.8 1.8 0 2.5 1.3 2.6 1.7 1.6 1.0 1.4 1.0 0.9 { 1.9 1.5 1.3 0.24 1.1 2.0

± ± ± ± ±

0.9 0.7 0.6 0.8 0.7

(2.7 (2.3 (2.4 (1.9 (2.8

± 0.5) X 10 4 ± 0.4) X 10 4 ± 0.6) X 10 3 ±0.3)X10 4 ± 0.4) X 10 4

± ± ± ±

0.8 0.7 0.8 0.6

(1.2 (1.7

± 0.8 ± 0.5 ± 0.7 ± 0.5 ± 0.7 ± 0.3 ± 0.6t

± 0.6 ± 0.8

± 0.5

± 0.4 ± 0.8

± 0.3 ± 0.4t ± 0.6

±0.4 ± 0.4

107 109 48 Cd 800

± 200*

± 0.3) X 10 3 ± 0.3) X 10 3

510 340

± 50 ± 40

(2.6 (5.0 600 (1.0 340 170

± 0.9) X 10 3 ± 1.3) X 10 3 ± 300 ± 0.2) X 10 4 ± 95 ± 63

300 200 400 180 210 350

± 30*

(1. 7 (2.1

± 0.3) X 10 3

(8.5 (8

± 1.0) X 10 3 ± 1) X 10 3

87

± 14

290

±

70 ± 150 ± 25 ± 200 ± 400 ± 1) X 10 3

260 230 380 220 220

57 51

± 19 ± 26

340 300

± 20 ± 30

530 200 180 1600

± 280 ± 150 ± 30 ± 400

400 220 215 145

± ± ± ±

370 700 100 1000 1200 (7

±

50* ± 70* ± 30* ± 50* ± 110*

110 111 112 113 114 49 In 113 115 50 Sn 112 114 115 116 117 118 119 120 122 124

± 0.4) X 10 3

± 20

51 Sb

± 50*

52 Te

±

40*

±

50*

121 123

± 30* ± 50*

53 I

122 123 124 125 126 128 130 127 129

54 Xe 90* 60* 20* 30*

129 130 131 135

± 0.1 ± 0.3 ± 0.15

30 13

± 10

0.35 0.45 0.4 0.6 0.4 0.6 ± 0.3 0.3 ± 0.15 0.2 ± 0.1 0.5 ± 0.2 0.7 0.3 0.26 ± 0.05 0.16 ± 0.03 0.4 ± 0.2 0.08 ± 0.03 0.12±0.06 0.4 0.10 0.4 ± 0.1 0.5 0.6 0.5 ± 0.2 0.8 ± 0.2 1.0 ± 0.2 0.7 ± 0.2 0.49 ± 0.10 0.30 ± 0.10 0.25 ± 0.10 0.14 ± 0.04 0.6 ± 0.1 0.3 1.0

26 200 25 160

± 5 ± 50 ± 5

0.4 0.8 0.4

±

3 >45

2.0

±

6.5 6.7 25 150 50 150 25 180 30 200 400 400 14 28 130 26 147 38 210 260 870 13.0 31

±

± ±

50 2.0 2.0

± 7 ± 60 ± 30 ± 20 ± 5

±

50

± 8 ± 70 ± 200 ± 200

± 4 ± 12 ± ± ± ± ± ± ± ± ±

± ±

130 95 90 110 150

± 40* ± 20*

70 76

± 20* ± 5*

±

4 3

30*

± 5* ± 50*

110

±

30*

70 70 79 70 100 130

± ± ± ± ± ±

30* 15 14* 30* 50* 60*

'"3 ~

92 90

± 4 ± 20

5

104

±

150

± 80*

11

o

Z

00

4

20 30 90 0.5 10

3*

40

± 15

120

±

7*

31

± 16

113 91

± ±

8* 1*

0.7

Z

t"J d

15

data for only one or two resonances (sometimes computed from thermal-capture cross sections or resonance-capture integrals). (J = 2).

=- 1) and

141 133

cr

l'V

c,..:) ~

TABLE

8£-4.

S-WAVE NEUTRON STRI

~

'"tJ ~

rJ). H

±

7

±

2* 1*

52 70 { 93 118 120 150

± ± ± ± ± ±

8* 15* 6t 20* 30*

125

±

4

220 135

± 100* ± 15

5.1

±

1.2

90

3.1 8.2

± ±

0.6 1.6

87

±

150 200

± 60 ± 100

± 0.7 ± O.4t

12

±

1

±0.4 ± 0.6t ± 0.5

16.8

±

1.6

90

>50 ± 30

............ 1.0

z

± 0.5

196 198 79 Au 197 80 Hg 196 198

cr

D obe,

I'')' (Continued)

71

10

o rJ).

65 66

67 68

152 154 155 156 157 158 160 Tb 159 Dy 161 162 163 164 Ho 165 Er 162 164 166 167 168 170

69 Tm 169 70 Yb 168 170 171 172 173 174 176 71 Lu 175 176 72 Hf 174 176 177

178

* Based on

4.6 2.4 2.2 1.8 2.3 1.5 2.6 1.9 1.0 1.8 2.5 1.7 1.2 1.9 1.9 2.1 1.5 1.7 2.2 1.4 1.4 1. 4 { 1.3 1.3 2.4 1.5 1.1 1.6 0.9 1.8 1.9 1.7 2.5 2.8 1.4 2.0 2.1

± 1.8 ± 1.0 ± 0.3 ± 0.6 ± 0.3 ± 0.5 ± 1.0 ± 0.6

15 15 1.9 47 5.6 85 170 3.9

± ± ±

± ± ±

± ±

2 2 0.2 4 0.8

9 20 0.6

15* 15* 2 12

103

± ± ± ± ±

89 98 87

± ±

13 15 2

57 63 109 82

\

±0.4 0.9 0.5 ±0.4 ± 0.3 ± 0.5 ± 0.7 ± 0.5 ± 0.5 ±0.4 ±0.4 ± 0.5 ± 0.4 ± 0.2t

± ±

± 0.5 ± 0.3 ±0.3 ±0.4 ± 0.4 ± 0.6 ±0.7 ± 0.7 ± 0.5 ± 0.5

±

0.7

± ± ±

0.4 15

200 5.0

± ±

50 1.0

6

± ± ± ± ± ± ±

2 8 5 0.3 17 50

± ±

2.9 72 10

20 49 4.3 130 250 7.3 15 37 6.3 62 7.5 230 190 3.7 2.3 16 32 2.3 60

±

± ± ±

± ± ±

2

110 155 110 55 77

± ± ±

±

± ±

4

2

83 Bi 88 Ra 90 Th

0.5

85

±

2

10 6 0.6 10 0.8 50 50 0.7 0.4

70

±

10*

73

±

5

10

3 10*

91 Pa 92 U

74

72 59.0

± ± ±

9'3 Np 94 Pu

6

2* 0.2*

70

±

200

2.1

(2.2

201

1.4

± ±

202

82 Pb

± ± ±

2.0

81 Tl

10 15* 10 3*

90 87 80

199

95 Am

1.2 203 205 204 206 207 208 209 226 229 230 232 231 233 232 233 234 235 236 238 237 238 239 240 241 242 241 243 m

± ±

7

± ±

0.3 20

3

243

64

±

96 3*

em 244

246

100

±

(2.4 0.4 (2

0.55 ± 0.2 1.8 0.3 0.5

± 0.2

0.62 ± 0.25 1.3 ± 0.5 0.9 ± 0.1 0.85 ± 0.15 1.9 1.4 ± 0.6 0.9 ± 0.2 1.2 ± 0.4 0.95 ± 0.10 1.2 ± 0.3 0.9 ±0.1 1.0 ± 0.15 1.3 ± 0.2 1.2 ± 0.2 1.05 ± 0.16 1.lO±0.2 0.9 ± 0.3 1.1 ±0.2 1.4 0.84 ± 0.25 0.76 ± 0.30 0.5

(1.0 (2.7

20

230 { 300

± ±

30*

460 { 290

± ±

30* 20*t

640

±

70*

5500

±

900*

0.7) X 10 3 40

15t

± 1.3) X 103

±

1)

X 103

±0.3) X 10' ± 0.5) X 103 ,......,5 X 10'

(3.5 0.60 11 17.5 0.45 0.8 5.3 0.62 13 0.53 15 17.7 0.57 13 2.39 13.5 1.2 15 0.43 0.6 1.4 13 30

,......,8 X 10 3 >3.5 X 10 5 ± 1.2) X 103 ±

±

0.15 3

± 0.7 ± 0.07 ± 0.2 ± 1.0 ± 0.05 ± 2 ± 0.03 ± 2 ± 0.[ ± 0.U6

±

4

± 0.12 ± 1.0 ± 0.2 ± 2 ± 0.07 ± 0.2 ± 0.3

± ±

3 15

data for only one or two resonances (sometimes computed from thermal-capture cross sections or resonance-capture integrals). t (J = 1) and (J = 2). : (J = 0) and (J = 1).

~

"'t1 ~ ~

rJ2 H

o m

18 Ar 19 K

35 37 40 41

20 Ca 21 Be 22 Ti

45

23 V 24 Cr

25 Mn 26 Fe 27 Co

50 52 53 55 58m 59

28 Ni 29 Cu 63 65 30 Zn 64 68 68 68 31 Ga 33 As 34 Be 35 Br

69 71 75 79 81

n, 'Y n, 'Y n, 'Y Abs. n, 'Y n, 'Y Abs, n, 'Y n, 'Y Abs. n, 'Y Abs. n, 'Y Abs, n, 'Y n, 'Y n, 'Y n, 'Y n, 'Y n, 'Y n, 'Y n, 'Y Abs. n, 'Y Abs. n, 'Y n, 'Y n, 'Y n, 'Y n, 'Y n, 'Y (n,y) 69g Zn(51 min) (n,')') 69m Zn(l3. 8 hr) n, 'Y n, 'Y n, 'Y n, ')' n, ')' n, 'Y n, 'Y n, 'Y

17.0 ± 1.0 0.30 ± 0.03 0.41 ± 0.03 3.0 ± 0.5 2.0 ± 1.0 0.96 ± 0.05 1.65± 0.2 0.45 ± 0.1 11.0 ± 1.0 3.0 ± 0.2 2.9 ± 0.2 2.6 ± 0.2 2.54 ± 0.25 1.6 ± 0.1 1.5 ± 0.1 7.5 ± 0.2 0.43 ± 0.04 9.5 ± 0.5 14.4 ± 0.4 2.25 ± 0.2 (2.5 ± 1.0) X 10 5 72 ± 3 2.8 ± 0.1 2.2 ± 0.1 4.3 ± 0.4 4.2 ± 0.3 5.1±0.2 2.3 ± 0.2 1.6 ±,0.2 1.6 ± 0.2 2.0 ±.,0.4 1.8±0.4 0.21 ± 0.03 8.0 ±2.0 6.4 ± 2.0 10.5 ± 2.0 80 ± 5 12 ± 3 75 ± 20 110 ± 30 41 ± 2

45 Rh

101 102 104 106 103 103 103 105

46 Pd 102 104 105 106 108 110 47 Ag 107 109 109 111 48 Cd 106 108 110 111 112 113 114 116 49 In 113 115 115 115 50 Sn 112 114 115 116 117 118

n, 'Y n, 'Y n, 'Y n, 'Y (n,'Y) 104m Rh (n,'Y) 104g Rh n, 'Y n, 'Y n, 'Y n, 'Y n, 'Y n, 'Y n, 'Y n, 'Y n, 'Y n, 'Y n, 'Y (n,'Y) 110m Ag n, 'Y n, 'Y n, 'Y n, 'Y n, 'Y n, 'Y n, 'Y n, 'Y n, 'Y n, 'Y n, 'Y n, 'Y n, 'Y (n,'Y) 116m In(54 min) (n,')') 1161( In(13 sec) n, ')' n, 'Y n, ')' n, ')' n, 'Y n, 'Y n, 'Y n, 'Y

85 ± 10 5 ± 1 6 ± 2 2.0 ± 0.6 82 ± 4 1,080 ± 40 1,160 ± 40 (1.8 ± 0.5) X 10 4 95 ± 15 14 ± 4 20 ± 5 90 ± 20 16 ± 5 250 ± 30 16 ± 5 760 ± 60 120 ± 15 50 ± 5 1,460 ± 80 100 ± 20 68 ± 10 7 ± 3 8±3 40 ± 5 45 ± 5 15 ± 5 380 ± 20 23 ± 3 2 ± 1 3,200 ± 100 840 ± 60 2,650 ± 100 650 ± 30 3,300 ± 100 7.5±1.0 30 ± 3 7.5 ± 2.0 3.8 ± 1.0 16 ± 2 17 ± 2 6.5 ± 1.0

zt'j

q

1-3 ~

o

Z

tn

rr ~

W

-

O

Z d

o

~

trJ

>

~

~

= ~

to

~

o

m

56 Ba 130 132 134 135 136 137 138 140 57 La

58 Ce 59 Pr

138 139 140 140 142 144 141 143 144

60 Nd

61 Pm

142 143 144 145 146 148 150 147 147 147 148m 148g

628m 144 147 148 149 150 151 152 154

n, "Y "Y n, "Y n, "Y n, "Y n, "Y n, "Y n, "Y n, "Y n, "Y n, "Y n, "Y n, "Y n, "Y n, "Y n, "Y n, "Y n, "Y n, "Y n, "Y n, "Y n, "Y n, "Y n, "Y n, "Y n, "Y n, "Y n, "Y (n,"Y) 148m Pm (n,"Y) 148g Pm n, "Y n, "Y n, "Y n, "Y n, "Y n, "Y n, "Y n, "Y n, "Y n, "Y n, "Y 71,

9±2 15 ± 3 6±3 15 ± 5 100 ± 20 18 ± 2 5 ± 1 0.25 ± 0.05 14 ± 2 12.3 ± 1.0 330 ± 30 12 ± 1 70 ± 5 0.45 ± 0.05 2.5 ± 0.5 2.6 ± 0.3 18.3 ± 1.0 190 ± 40 60,000 ± 30,000 45 ± 5 12 ± 2 115 ± 10 10 ± 2 260 ± 15 12 ± 2 18 ± 1 16 ± 2 2,300 ± 400 1,200 ± 300 1,100 ± 300 30,000 ± 10,000 40,000 ± 10,000 1,400 ± 150 10 ± 5 590 ± 20 20 ± 10 3,200 ± 100 350 ± 50 2,450 ± 300 3,100 ± 100 40 ± 20

174 176 71 Lu 175 176 72 Hf 174 176 177 178 179 180 73 Ta 180 181 74W 180 182 183 184 186 75 Re 185 187 76 Os 187 189 77 Ir 191 193 78 Pt

79 Au 80 Hg

190 192 194 195 196 198 197 196 198

n, n, n, n, n, n, n, n, n, n, n, n, n, n, n, n, n, n, n, n, n, n, n, n, n, n, n, n, n, n, n, n, n, n, n, n, n, n, n, n, n,

"Y "Y "Y "Y "Y "Y "Y "Y "Y "Y "Y "Y "Y "Y "Y "Y "Y "Y "Y "Y "Y "Y "Y "Y "Y "Y "Y "Y "Y "Y "Y "Y "Y "Y "Y "Y "Y "Y "Y "Y "Y

36 ± 4 14 ± 2 670 ± 70 660 ± 70 950 ± 100 2,000 ± 200 450 ± 50 800 ± 80 7,300 ± 200 1,900 ± 200 625 ± 50 45 ± 5 740 ± 40 100 ± 30 740 ± 40 350 ± 30 1O±1O 590 ± 10 380 ± 15 13 ± 2 490 ± 50 850 ± 50 1,770 ± 100 310 ± 20 210 ± 20 250 ± 30 760 ± 100 2,050 ± 150 3,100 ± 200 1,400 ± 100 140 ± 10 80 ± 30 90 ± 10 14 ± 2 380 ± 20 5 ± 2 50 ± 5 1,565 ± 40 90 ± 10 1,350 ± 200 70 ± 10

ztrj d 8

~

o

Z

U1

Cf

l\:)

l+>-

I--'

TABLE

Target nucleus Z A

199 200 201 202 81 TI 203 205 82 Pb

83 Bi 89 Ac 90 Th 91 Pa 92 U

204 206 207 208 209 227 230 232 233 231 233 232 2~1

93 Np

232 233 233 233 234 235 235 235 236 238 237 237 237 238

Reaction

n, 'Y 'Y 'Y 'Y 11., 'Y 11., 'Y 11., 'Y 11., 'Y 11., 11., 11.,

11., 'Y 11., 'Y 11., 11., 11., 11., 11.,

'Y 'Y 'Y 'Y 'Y

11.,

'Y

11., 'Y 11., 'Y 11., 'Y

n, 'Y Fiss. Abs. 11., l'

Fiss. Abs. 11., l' 11., l'

Fiss. Abs, 11., 'Y

n, 'Y 11., 'Y

Fiss. Abs. 11., l'

8f-5.

TABLE OF INFINITE-DILUTION RESONANCE INTEGRALS

Resonance integral, barns

410 20 40 6 12 40 0.7 0.18 2.7 0.12 0.45 0.015 0.31 1,300 1,050 84 500 510 890 240 320 560 138 780 918 650 144 280 424 400 275 850 7 860 750

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

50 5 10 2 2 5 0.1 0.02 0.3 0.02 0.05 0.005 0.03 50 100 2 200 50 50 40 40 60 8 20 25 50 6 15 20 80 10 200 3 200 250

Target nucleus Z A

94 Pu

95 Am

96 Cm

97 Bk 98 Cf 99 Es

238 238 239 238 238 238 239 239 239 240 241 241 241 242 241 241 241 241 242m 243 243 243 244 244 244 245 245 245 246 248 249 250 251 253

(Continued)

Reaction

Fiss. Abs, 11., 'Y 11., 'Y Fiss. Abs. 11., 'Y Fiss. Abs. 11., 'Y 11., 'Y

Fiss. Abs. 11., 'Y 11., 'Y

(n,'Y)242ffi Am (n,'Y) 242g Am

Fiss. Fiss, 11., 'Y (n,'Y) 244ffi Am (11.,1') 244g Am 11., 'Y Fiss. Abs, 11., 'Y Fiss. Abs, 11., 'Y 11., 11., 11., 11.,

l' l' l' l'

11.,

'Y

Resonance integral, barns

750 1,500 450 145 24 169 190 310 500 8,200 160 590 750 1,200 2,400 300 2,100 20 1,600 2,300 2,200 110 650 20 670 250 500 750 250 350 1,200 5,300 1,000 3,500

± 250 ± 500 ± 300 ±8 ±4 ± 10 ± 10 ± 15 ± 20 ± 600 ± 20 ± 30 ± 40 ± 100 ± 800 ± 100 ± 700 ±5 ± 200 ± 400 ± 400 ± 20 ± 60 ±4 ± 60 ± 50 ± 100 ± 100 ± 50 ± 50 ± 200 ± 500 ± 100 ± 600

Cf tv ~

tv

Z

d

o

~ t':j

>-

~

"d

::0 to


~

I%J ~ tn

to ~

o Z

0.29 0.23 0.11 0.021 0.0039 6.8 X 10- 5

Cf

t-.:l 0:>

-...l

8-268

NUCLEAR PHYSICS

!!

'c ::J

e

~

:e

.s en

I-

z

=>

0

u u, 0

a: w al ~

=>

z

NL NH

1 H,P H

L,P L

PULSE HEIGHT (arbitrary units)

FIG. 8g-14. Shape parameters for Cf m fission-fragment pulse-height distribution.

TABLE 8g-5. AVERAGE FRAGMENT ENERGIES AND MASSES FOR THERMAL-NJ ~ II)

6" "6

0.1

f-

~

.""

-:

·6

.....

"6

£

.

.

'lit.

-e-

loe

0.01 F-

-: 6. 6 6

0.001

I

0

I

I

2

Energy

I

5

4

3 ~

6

(MeV)

FIG. 8g-18. The center-of-mass neutron spectrum ¢(7/) divided by 7/. the neutron energy in the center-of-mass system. The dots represent neutrons emitted in the direction of the light fragments; the triangles represent neutrons emitted in the direction of the heavy fragments. The curve for the light fragments was reduced by the factor 1.16, the ratio of the number of neutrons from light fragments to the number from heavy fragments if all neutrons are emitted from moving fragments. See Fig. 8g-17 for reference.

2.2

2.0

>cu ~

t

I~

••

• ••••• t 1.2 I.OL...-_......._ ......_ _I . . - - _......._ - . . L_ _L - _ . . . I o - _ - - L _ - - - . l " " -_ _ 160 140 120 eo 100

A

FIG. 8g-19. The average center-of-mass neutron kinetic energy as a function of fragment mass, corrected for mass resolution. For reference, see Fig. 8g-17.

8-274

NUCLEAR PHYSICS

AL 126 122 lIS

114

110

106 102 98

94

90

86

I

-

65-

1

I

• •

4~

i

•

3~

• • •

I

I

I

-

I

\

Averooe

-

50-

-

40

-

..

30

...

20I

I

I

I

...-

I

I

I

126 130 134 /38 142 146 150 154 158 162

AH FIG. 8g-20. Total number of neutrons v and total energy E u appearing in the form of neutrons as a function of fragment mass. For reference, see Fig. 8g-17.

8

o

7

tt

..J W

~

6

~

~

tt t tt I

t

1, we have enlarged the error of the mean, OX, i.e., ox --> S ox. This convention is still inadequate, since if S »1, the experiments are probably inconsistent, and therefore the real uncertainty is probably even greater than S ox. See text and ideogram in data card lietings, UCRL-8030. II Quoted upper limits correspond to a 90 % confidence level. b In decays with more than two bodies, Pmax is the maximum momentum that any particle 'can have. C See data card listings, (UCRL-8030) for energy limits used in measuring this branching ratio. d Theoretical value; see also data card listings, UCRL-8030. • See note in data card listings, UCRL-8030. I Predicted from SU 3. II Assumes rate for Z- --> 2;0 er» small compared with Z- --> Ae-".

t'=.l ~

t'=.l ~ tr.J

Z

"'3

~ ~ ~ 'ij

~ ~

"'3

I-f

o

~

t'=.l

U2 ~

Z

I:;f

I-f

Z

"'3 t'=.l

~ ~

o

"'3

I-f

o

Z

U2

cr

t>.J 00 \0

8-290

NUCLEAR PHYSICS

particles called quarks and an antimultiplet (antiquarks) . (It is not known whether quarks exist in nature or only as a mathematical explanation.) The quarks "exist" as an I-spin doublet (such as nand p), and a singlet (such as A). In their simplest form they would have surprising fractional quantum numbers, B = i, Q = -i or + i, etc. Mesons are then tightly bound states of quark + antiquark (qq); baryons "contain" three quarks (qqq) held together by the strong interaction. The mathematics of how three primitive objects can be combined into larger groups is called group theory, and the particular combination that correctly explains nature is called, in group theory, SUa; hence the title for this section: tlSU a Classification."

a(a) Stable Baryons, JP =

1+(arf)

(b)Slable Mesans,JP=O-

(0)

(c) Unslable Mesons. JP = 1-

tP • = Slales known before Jon 61 when Ihe Eillhtfald way was formulaled.

o V=D

(13B5 MeV)

y=-,

(1530MeV)

Y =-2'

(1676 MeVll

(d)

= States predicted by Eightfold way and laler verified experimenlally.

Unstable Baryons, JP=t+

FIG. 8h-1. The asterisks labeled n', P'. and A' are a possible set of primitive particles called "quarks," from which the mesons and baryons can be formed.

The algebraic rules of SU 3 explain much more than the size of multiplets-they also explain quite well the masses and decay modes of particles and resonances (see any textbook on particle physics [3]). 8h-6. Further Reading. There are many textbooks on particle physics. A sample of them are listed in ref. 3. Two fairly recent and complete books are those by Gasiorowicz [3J and by Frazer [3J. Many excellent semipopular articles can be found in the Scientific American [4J, and more technical review articles in the Annual Review of Nuclear Science [5J. A mild apology to the reader-this text is rather compact and not too easy to read; two articles which cover much of the same material but in a more leisurely fashion have been written by Ne'eman [6J and Rosenfeld [7J. A more extended but nonmathematical discussion of the subject can be found in a readable book by Ford [8]. Acknowledgement. We wish to thank Dr. LeRoy Price of the Berkeley Particle Data Group for his help and criticism.

HEALTH PHYSICS

8-291

References 1. Weber, J.: Phys. Rev. Letters 22, 1320 (1969). 2. Particle Data Group: Rev. Mod. Phys. 41, 109 (1969). 3. (i) Gasiorowicz, S.: "Elementary Particle Physics," John Wiley & Sons, Inc., New York, 1966. (ii) Frazer, W.: "Elementary Particles," Prentice-Hall, Inc., Englewood Cliffs, N.J., 1966. (iii) Bernstein, J.: "Elementary Particles and Their Currents," W. H. Freeman and Company, San Francisco, 1968. (iv) Gell-Mann, M., and Y. Ne'eman: "The Eightfold Way," W. A. Benjamin, Inc., New York, 1964. (v) Kallen, G.: "Elementary Particle Physics," Addison-Wesley Press, Inc., Cambridge, Mass., 1964. (vi) Sakurai, J. J.: "Invariance Principles and Elementary Particles," Princeton University Press, Princeton, N.J., 1964. (vii) Adair, R. K., and E. C. Fowler: "Strange Particles," Interscience Publishers, a division of John Wiley & Sons, Inc., New York, N.Y., 1963. (viii) Levi-Setti, R.: "Elementary Particles," University of Chicago, 1963. (ix) Yang, C. N.: "Elementary Particles," Princeton University Press, Princeton, N.J., 1962. (x) Williams, W. S. C.: "An Introduction to Elementary Particles," Academic Press, Inc., New York, 1961. 4. Scientific American Articles: (i) The Overthrow of Parity, P. Morrison, April, 1957. (ii) Pions, R. Marshak, January, 1957. (iii) Elementary Particles, Gell-Mann and Rosenfeld, July, 1957. (iv) The Weak Interactions, S. B. Treiman, March, 1959. (v) Two Neutrino Experiment, L. Lederman, January, 1962. (vi) Strongly Interacting Particles, Chew, Gell-Mann, and Rosenfeld, February, 1964. (vii) The Omega-Minus Experiment, W. B. Fowler and N. P. Samios, October, 1964. (viii) Violations of Symmetry in Physics, E. P. Wigner, December, 1965. 5. (i) Lee, T. D., and C. S. Wu: Ann. Ret'. Nucl. Sci. 15, 381(1965); 16, 471(1966). (ii) Tripp, R. D.: ibid. 15, 325 (1965). (iii) Feinberg, G., and L. M. Lederman: ibid. 13, 431 (1963). 6. Ne'eman, Y.: "Science Year (the World Book Science Annual), 1968. 7. Rosenfeld, A. H.: Elementary Guide, UCRL-ll 100 (unpublished). 8. Ford, K. W.: "The World of Elementary Particles," Blaisdell Publishing Company, a division of Ginn and Company, Waltham, Mass., 1963.

8i. Health Physics 1 KARL Z. MORGAN AND JAMES E. TURNER

Oak Ridge National Laboratory

8i-1. Introduction. The practice of health physics utilizes knowledge gained in all sciences to furnish an understanding of the mechanisms of radiation damage and to provide adequate and reasonable limits for exposure, measurements of exposure, and the specification of conditions and procedures to ensure protection. It embodies 1 Work sponsored by the U.S. Atomic Energy Commission under contract with Union Carbide Corporation.

8-292

NUCLEAR PHYSICS

the application of many scientific and technical disciplines, i.e., physics, biology, chemistry, engineering, etc., to the end that any situation involving possible radiation hazard to man can be analyzed correctly, and suitable steps can be taken to prevent harm to man or to his environment. Health physics involves research, engineering, educational, and applied activities. It deals with the scattering and loss of energy of ionizing radiation and the damage produced by the passage of this radiation through matter. Thus, in addition to applied activities, there are many health-physics research and engineering problems such as (1) shielding, (2) dosimetry, (3) studies of physical parameters relating to dosimetry (e.g., stopping power, attachment coefficient, energy to produce an ion pair, etc.), (4) radioactive-waste disposal, (5) studies of human exposures, (6) determination of permissible exposure values, (7) studies of effects of ionizing radiation on the environment, etc. A health physicist is a person engaged in and dedicated to a study and practice of problems of providing radiation protection. He is concerned with obtaining an understanding of mechanisms of radiation damage and with the development and implementation of instruments, methods, and procedures so that he can determine the existence of hazardous ionizing radiation and provide protection to man and his environment from its unwarranted deleterious effects. 8i-2. Definition of Units and Terms Used in Health Physics. 1 Absorbed Dose: the amount of energy imparted by ionizing radiation to a sample of matter per unit mass. The unit of absorbed dose is the rad (= 100 ergs/g). Absorption CoejJicient (J.I. - us): the difference between the attenuation coefficient and that for Compton scattering. This quantity, which is used to a good approximation to describe photon energy absorption, excludes the part of the original photon energy that escapes as a degraded photon from the site of interaction. The dimension of J.I. - Us is reciprocal distance (e.g., cm :"). Activity: the disintegration rate of a radionuclide. The unit of activity is the curie (1 Ci corresponds to 3.7 X 10 1 0 disintegrations/sec). Attenuation Coefficient J.I. (Macroscopic Cross Section): the probability of interaction per unit distance traveled. The dimension of J.I. is reciprocal distance (e.g., cm"), EXAMPLE: The relative number of photons of a given energy that do not experience an interaction in traveling a distance x is e-jJ.X. In terms of a i, the total microscopic cross section (e.g., ern"), J.I. = NUt, where N = number of electrons per unit volume. The Bragg-Gray principle and applications of it are used as the basis of many measurements of ionizing radiation. According to this principle the energy absorbed per unit mass (dE/dm)b in a given medium b is related to the ionization in a small gas-filled cavity in that medium by the expression (8i-l) Here Pi, is the relative mass stopping power of the medium b with respect to the gas g,

W g is the average energy required to produce an ion pair in the gas, and J g , the quantity that is usually determined experimentally, is the number of ion pairs produced per unit mass of the gas in the cavity. It should be emphasized that, in order for this principle to hold always, the gas cavity must be small compared with the range of the ionizing particles, and both W g and Pi. must be independent of the energy of the radiation. When the walls of the chamber and the gas are made of the same material, e.g., air- or tissue-equivalent substances, the Bragg-Gray principle also applies with a cavity large compared with the range of the ionizing particles. 1 More detailed discussions are given in Radiation Quantities and Units, report lOa of the International Commission of Radiological Units and Measurements, Natl. Bur. Standards Handbook 84, 1962.

HEALTH PHYSICS

8-293

Curie, Ci: unit of activity: 1 Oi = 3.7 X 10 10 disintegrations/sec. The millicurie (1 mOi = 10- 3 Ci), microcurie (1 JLOi = 10- 6 Ci), nanocurie (1 nOi = 10-9 Oi), and picocurie (l pOi = 10- 12 Ci) are often used. Dose Equivalent: defined for purposes of radiation protection as the product of the absorbed dose and relevant modifying factors, such as those for radiation quality (e.g., QF, which relates to LET, and the H factor, which relates to the damage from internally deposited, bone-seeking radionuclides relative to that of radium). The unit of dose equivalent is the rem. Dose equivalents from different sources of radiation are additive in protection work. Exposure: the amount of charge (of either sign) produced in air by X- or gamma-ray photons per unit mass of air. The unit of exposure is the roentgen (= 2.58 X 10- 4 coul/kg). Fluence: the ratio of the number of particles or photons that enter a small, imaginary test sphere placed in a radiation field and the cross-sectional area of the sphere. The dimension of fluence is the square of reciprocal distance (e.g., cmr"). Flux Density: fluence per unit time. The dimensions of flux density are reciprocal area times reciprocal time (e.g., cm- 2 sec""). Linear Energy Transfer, LET: linear rate of energy loss along the track of a particle. LET is often expressed in keV /JLm or MeV/cm (1 keV /JLm = 10 MeV/em). Mass-absorption Coefficient, (JL - 0'8) / p; the quotient of the absorption coefficient and the density of a material. Dimensions are area times reciprocal mass (e.g., ems/g). M ass-attenuation Coefficient, JL/ p.: the quotient of the attenuation coefficient and the density of a material. Dimensions are area times reciprocal mass (e.g., cm 2/g). M ass Stopping Power, P / o: the stopping power of a material divided by its density. Often expressed in MeV/(g/cm 2) or ergs/(g/cm 2) . See Sec. 8i-3.1 and Fig. 8i-1. Quality Factor, QF: numerical linear-energy-transfer-dependent factor, depending on the kind of incident radiation and its energy. The product of QF and absorbed dose gives the dose equivalent used for purposes of radiation protection. See tables given in Sec. 8i-13. Rad: Unit of absorbed dose: 1 rad = 100 ergs/g. Relative Biological Effectiveness, RBE: the biological effectiveness of any type and energy of ionizing radiation in producing a specific biological effect (e.g., a certain incidence or degree of leukemia, anemia, sterility, carcinomas, cataracts, shortening of life-span, etc.) relative to damage produced by X rays, having an energy of about 200 ke V or a linear energy transfer in water of about 3 ke V/ J.lm delivered at a rate of about 10 rads /min. Gamma radiation from 60 0 0 is often used as the reference standard. The RBE is given frequently as an average value in the common energy range of a particular type of ion and/or throughout the medium under study. Rem: roentgen-equivalent-man. Unit of dose equivalent. Roentgen, R: unit of exposure: 1 R = 2.58 X 10- 4 coul/kg. This quantity is numerically the same as that implied by the older definition of the roentgen as that quantity of X or gamma radiation that produces 1 esu of charge of either sign per 0.001293 g of dry air (1 cc at 0°0 and 760 mm Hg). Stopping Power, P or -dE/dx: mean rate of energy loss of a charged particle per unit distance traveled. The stopping power of a medium for a given particle is numerically equal to LET. Often expressed in ergs/em or MeV/cm. (See mass stopping power.) Specific Ionization S: the average number of ion pairs produced per unit distance along the track of a particle. W Value: the average energy needed to produce an ion pair. (See page 8-296.) 8i-3. Useful Data and Equations. Stopping Powers. Figure 8i-l shows the stopping powers of water for a number of particles. These values differ only slightly

8-294

NUCLEAR PHYSICS

2r--------------------------------. i-l04

N

e

~

5

G

~

ffi

2

~

103

~

5

~

0:: IIJ

~

2

~

102

if

5

~

101

z

~ (/) ~

2

i 2

100 ~-L.-• ...L....-.I...-:--...J.....-..J.--L.::__.L---L..-..L..:_--'-""""'--~-'--....L----I...",.........L.....-...J.....--J 10-2 2

FIG. 8i-l. Mass stopping power of water for several particles. The dashed curve shows the contribution of radiation (bremsstrahlung) to the mass stopping power for electrons.

from those of muscle or other soft tissue. sources:

These curves are based on the following

Barkas, W. H., and M. J. Berger: Studies in Penetration of Charged Particles, U. Fano ed., Natl. Acad. Sci.-Natl. Res. Council Publ. 1133, 1964. Berger, M. J., and S. M. Seltzer: Studies in Penetration of Charged Particles, U. Fano, ed. See above. We are grateful to Dr. Berger for furnishing the positron data. Bichsel, H.: "American Institute of Physics Handbook, 3d ed., D. W. Gray, ed., McGrawHill Book Company, New York, 1972. (This volume.) Neufeld, J., and W. S. Snyder: in "Selected Topics in Radiation Dosimetry," International Atomic Energy Agency, Vienna, 1961. Steward, P. G.: Stopping Power and Range for any Nucleus in the Specific Energy Interval 0.01-500 MeV / AMU in any Nongaseous Material, LRL Rept. UCRL-18127, 1968. Whaling, W.: "Encyclopedia of Physics," vol. 34(2), p. 214, Springer-Verlag OHG, Berlin, 1958.

Stopping powers of a number of materials for different charged particles can be calculated over a wide range of energies from the information given by H. Bichsel in Sec. 8d of this Handbook. Average stopping power P (Me V j em) of particle of energy E (Me V) over its range R (em):

- E P=71

(8i-2)

Average mass stopping power (MeV cmv/g) is Pjp, where p is the density (gZcm') of the medium traversed. Ranges. The mean ranges of electrons, protons, and alpha particles in water, muscle, bone, and lead are shown in Fig. 8i-2. The ranges of these particles in air are given in Fig. 8i-3. These figures are based on the following sources: Barkas, W. H., and M. J. Berger: ibid. Berger, M. J., and S. M. Selzer: ibid. Bethe, H. A., and J. Ashkin: "Experimental Nuclear Physics," vol. I, E, Segre, ed., John Wiley & Sons, Inc., New York, 1953.

8-295

HEALTH PHYSICS

Evans, R. D.: "The Atomic Nucleus," McGraw-Hill Book Company, New York, 1955. Snyder, W. S., and J. Neufeld: On the Energy Dissipation of Moving Ions in Tissue, Oak Ridoe Natl. Lab. Rept. ORNL-1083, Oak Ridge, Tenn., 1951. Steward, P. G.: ibid.

These mean ranges have been calculated at high energies without allowance for nuclear cascades, i.e., absorption of a proton by a nucleus. Except at low velocities, where capture and loss of electrons by a moving ion occurs, the ranges of other heavy particles (e.g., muons, pions, deuterons, tritons) can be found from the range-energy curves given in Fig. 8i-2, since energy loss depends in a 3 10

r-------r--------r-------.---------.------~

2

t-------+-------4------+-------+---...:;:,....,,~--,J

10

to' 1-------+-------4------+--~~-___+~~--J---/,..___~

ALPHA PARTICLES

10- 1

---:r-tlt--:"t=:=jr::::=---- Pb

1--------1---'''--#-

'~----BONE II_~-- MUSCLE,

100

H20

to'

ENERGY (MeV)

FIG. 8i-2. Mean ranges of electrons, protons, and a particles in water, muscle, bone, and lead. See text for determining ranges of other heavy particles. Ranges in other materials can be approximated from the water and lead curves by interpolating on the basis of average atomic number.

8-296

NUCLEAR PHYSICS

known way on charge and velocity. For example, the ranges R1(v) and R 2(v) of two heavy particles, moving with the same speed v in a medium and having charges Zl and Z2 and masses M 1 and M 2, are related by the equation (8i-3) Nonrelativistically, the range Ri(E) of one particle at energy E is given by (8i-4) where R 2(M 2E/M 1) is the range of the other particle at energy (MdM1)E. Electron and positron ranges are approximately the same. W Values. The average energies needed to produce an ion pair in a number of gases are given in Table 8i-1. Although these values, regarded for simplicity as TABLE 8i-1. W VALUES He.............. Ne.............. Ar.............. Kr.............. Xe..............

42 37 26 24 22

H 2• N2•

36 36 31 35

• • • • • • • • • • • • • • • • • • • • • • • • • •

02.............. Air..............

IN

EV FOR SEVERAL GASES· CO 2 •

• • • •••••

CH4. C2H2............ C2H4............ C2H6............ CaH s....... .. .. . C4Hio...... .. .. . BFa..... . . . . . . . .

34

28 27 27 26 26 26 36

/ • Based on data summarised by L. W. Cochran in chap. 5, "Principles of Radiation Protection," K. Z. Morgan and J. E. Turner, eds., John Wiley & Sons, Inc., New York, 1967.

being independent of the type and energy of radiation, are appropriate in most health physics applications (e.g., with X rays, radiation from radioactive sources, and most types of accelerators), W values for slow-moving heavy ions (i.e., at ion velocities lower than that of the electron in first Bohr orbit) may be much larger than the values given in the table. A lpha Rays. Specific ionization (ion pairs/em) in air.' (8i-5) where E is in MeV. «10 percent error for alpha energies 2 ~ E ~ 50). See Table 8i-2 for numerical values. Limited portions of the range R-energy E curve in Fig. 8i-3 can be fit by the formula R = AEk

(8i-6)

where A and k are constant over a particular portion. With R in em and E in MeV, for example, the measured range in the neighborhood of 5 to 10 Me V is given accurately by R = 0.31E1.5. Beta Rays, Electrons, and Positrons. Range (em) of electrons of energy E (Me V) in medium of density p (g/cm 3) :1 R 1

~

1 - [0.54E - 0.13(1 - e- 4E )]

p

Empirical formula developed by K. Z. Morgan.

(8i-7)

HEALTH PHYSICS

8-297

105 . . . - - - - - - . . . , . - - - - - - - . , . - - - - - - . , . . . . - - - - - - - - - -.........----.

t - - - - - - - - + - - - - - - - + - - - - - - + - -__~--_+_.l_-------l

104

ELECTRONS

3

10

E 2

cr the phase of the field at the moment of particle transit. A particle is synchronous with the rf field if it crosses each gap at the same phase ct>.. A fundamental requirement for a resonance accelerator like the linac is the existence of phase stability which assures that nonsynchronous particles (ct> different from ct>.) are not lost during the acceleration process. Simple consideration shows that this is achieved only if ct>. lies in the phase interval where E. is increasing, i.e., -1r/2 < ct>. < O. In this case particles crossing the gaps at phases different from ct>. are forced into phase oscillations about ct>., provided the starting phase is within certain limits. Unfortunately this principle of phase stability is incompatible with the requirements of transverse focusing. The electric fields in the gaps constitute electric lenses which are focusing only if the transverse field components in the entrance region (see Fig. 8j-8b) are stronger than the defocusing components in the exit half of the gap, i.e., if 0 < ct> < 1r /2. This dilemma was solved in earlier designs by the use of grids (Fig. 8j-8c), reducing the defocusing field components, and/or the use of solenoidal magnetic lenses incorporated in the drift tubes. The latest linacs, however, generally employ magnetic quadrupole lenses as proposed by Blewett [131, which provide the most effective means of focusing resulting in only negligible beam loss. One of the greatest drawbacks of any linear accelerator is the high power required, which is in the range of megawatts. It is therefore necessary to operate linacs in a pulsed scheme with relatively low (macroscopic) duty factor to keep power losses at a manageable level. The largest existing proton linac in the world is the 100-MeV injector for the Serpukhov 75-Ge V synchrotron. (The 70-MeV linac at Minnesota which was the largest machine in the past, has recently been shut down.) A 800-MeV proton machine is being built at Los Alamos. Electron Linacs. In the electron linac the electron velocity is practically equal to the speed of light, which permits operating the cavity as a waveguide in a travelingwave mode. No drift tubes are necessary since the electrons are riding on the crest of the wave, being continuously accelerated to full energy. However, the phase velocity of a traveling wave in an empty waveguide is greater than the speed of light, and to reduce it to the value c, it is necessary to load the cavity with disk-shaped irises spaced at intervals of X/4. The first successfully operating electron linacswere developed in 1945 to 1947 by W. W. Hansen and collaborators at Stanford and D. W. Fry and coworkers at the Telecommunications Research Establishment in England [14]. In contrast to the proton linac, transverse focusing poses no great problem in electron linacs. This is due to the fact that, at the much higher frequencies of the electron linacs, the azimuthal magnet field B fJ resulting from the time-varying electric field produces a focusing force vBfJ which is comparable to the defocusing qEr term.

8-328

NUCLEAR PHYSICS

The net defocusing force is proportional to 1 - {32 and thus goes to zero as {3 approaches 1. The largest electron accelerator in the world is the 2-mile linac at Stanford which is designed for electrons of 20-Ge V energy. 8j-G. The Conventional Cyclotron. The cyclotron, invented by Lawrence in 1930, was the first successful circular accelerator. It is based on the fact that a magnetic field B forces charged particles into circular orbits with angular frequency w = qB [m. (Eq. 8j-7) and orbit radius R = vlw (Eq. 8j-6). During each revolution the particles

MAGNET

POLE TIP

FIG. 8j-9. Cyclotron.

pass through an acceleration gap across which a r-f voltage V = V m cos w.t is maintained. When the radio frequency is in "resonance" with the circulating ions, i.e., when w. = w, continuous acceleration occurs, and the ions travel on an expanding spiraling orbit from the center of the magnetic field (R = 0) to some maximum energy and radius determined by the size of the pole shoes of the magnet. The r-f system consists of a large pillbox-type structure split into two halves, which are shaped like a D and therefore called "dees" (see Fig. 8j-9). Each dee is part of a quarter-wave resonance system. The two resonators are oscillating in a push-pull mode (180 deg out of phase); i.e., VI = V o cos wet, V 2 = V o cos (w.t + 11"), and the peak voltage across the acceleration gap is V m = 2Vo• The dees are located in the gap between the poles of an electromagnet and are enclosed by a vacuum chamber. The ions

PARTICLE ACCELERATORS

8-329

are produced in a low-pressure gas-discharge tube at the center of the magnetic field. Ion source design and technology have been considerably improved over the years; the "open-arc source" of the early days was replaced by the "hooded" structure, and today most cyclotrons use the "chimney"-type source with reflector developed by R. S. Livingston and R. J. Jones at Oak Ridge [15]. The magnetic field in the conventional cyclotron must decrease slightly with radius to produce the required force component toward the median plane, which serves to focus the beam during the many revolutions from center to maximum radius. The equation of motion for the z direction (perpendicular to the median plane) is

z = !L vB r

(8j-19)

m

Using the linear term of the Taylor expansion, B, or aBr/az = aBz/ar, we can write ..

z =

q

"in v

=

dB qB w r dB dr z = Tn B d1 z

r

(aBr/az)z, and div B

=

0,

(8j-20)

where B = Bz(r) is the field in the median plane. Introducing the "field index" n = - (r/B) dB/dr, and azimuth angle (J = wt, Eq. (8j-20) can be written in the form (8j-21) where

(8j-22)

If n > 0, or dB/dr < 0, the particles perform stable oscillations about the median plane. These oscillations are known as betatron oscillations because they were first investigated in connection with the betatron [16]. The parameter V z measures the number of betatron oscillations per revolution. A similar equation can be derived for the radial motion, yielding for the radial betatron frequency the relation (8j-23) with the stability condition n < 1. Thus simultaneous stability in both vertical and radial directions can exist only if

o = 271'"(w e - w)/w, is negative (w > We); the ion phase cf> with respect to the radio frequency reaches a minimum cPmin < 0 at r e , then increases in the region r > r: (where I::.cf> > 0), goes through the peak-voltage phase cf> = 0, and reaches a maximum value cf>max close to 71'"/2 at the final radius. At this point, just before. deceleration would occur, the particles have reached the maximum energy attainable and enter an electrostatic deflector which extracts them out of the magnet for bombardment of an external target. The maximum energy attainable in this type of cyclotron depends on the number of revolutions, which is inversely proportional to the peak dee voltage. The largest conventional machine is the 86-in. cyclotron at Oak Ridge National Laboratory, which accelerates protons to 24 MeV (with a dee-to-ground voltage of 250 k V, or

8-330

NUCLEAR PHYSICS

V m = 500 kV!). With the development of the sector-focusing cyclotrons, conventional cyclotrons are no longer built, and many existing machines are being converted or shut down. 8j-7. The Microtron. Cyclotrons are only capable of accelerating protons or heavy ions since the orbital frequencies of these particles are low enough to permit the use of quarter-wave resonators where the wavelength A is substantially larger than the magnet pole diameter. Electron frequencies for magnetic fields between 10 and 20 kG are in the range of several thousand MHz, and quarter-wave resonance systems are impractical (A is too small). Besides, the relativistic mass increase of electrons begins at much lower energies (1 percent increase at 5 ke V!) than that for protons. The microtron, or electron cyclotron, first proposed by Veksler [6] is a cyclotrontype device for the acceleration of electrons. It employs a small microwave cavity near the periphery of the magnetic field, through which the electron beam passes once per revolution. The orbits form a family of circles of increasing radius with a common tangent at the point where they intersect the cavity gap. Resonance acceleration occurs if the electrons cross the gap at the same voltage phase in each revolution. The rotation period of the electrons is given by T

=

27r ~

27rE

27rEo

= eBc 2 = eBc 2 I' =

TO'Y

(8j-25)

Resonance exists if the electron rotation period on the first revolution T1 and the difference ~T = T n+1 - Tn between consecutive orbits are each equal to some integral multiple of the r-f period TTf, i.e., Ekl) = kTrf (8j-26) T1 = TO')'l = TO ( 1 + Eo ~T

=

Tn+1

-

Tn

=

TO~')'

where k and m are positive integers. If E k1 = ~Ek, we find by elimination of ~Ek

Trf

=

s», TO

X

= mra

(8j-27)

the relation m

X=k-m

(8j-28)

In contrast to the cyclotron, the energy gain in a microtron cannot be arbitrary but must occur in fractions of the rest energy Eo as determined by the choice of the integers k and m in Eq. (8j-28). Note also that k must be larger than m (minimum k value is 2) in order for ~Ek to be finite and positive. For k = 2, m = 1 the energy gain must be equal to the rest energy. It should be pointed out that the magnetic field in a microtron is practically uniform,27rE o/eBc 2 = TO = const, which implies that there is little or no vertical focusing. However, if the number of orbits is not too large, this is not a serious problem. Microtrons for electron energies between 1 and 30 Me V have been built at many places. However, very little is known about operating experience and performance characteristics. 8j-8. The Synchrocyc1otron. In 1945 McMillan and Veksler independently proposed the synchrotron and synchrocyclotron [6] which made it possible to get beyond the energy limits of the conventional cyclotron. The two basic ingredients in this new accelerator concept are (1) the modulation of the electric frequency (and in the synchrotron also the magnetic field) with time to achieve synchronism between radio frequency and circulating particles; (2) the existence of phase stability which assures the continuous acceleration of nonsynchronous particles within certain limits. The synchrocyclotron employs a cyclotron-type r-f system with frequency w. modulated by the use of a rotating capacitor, tuning fork, or other means, such that We is a function of time, decreasing in synchronism with the orbital frequency of the ions. After a group of ions is accelerated to full energy, the radio frequency returns

PARTICLE ACCELERATORS

8-331

to its starting value and begins another cycle of acceleration. The major drawback of this scheme is that beam intensities are down by a factor of 10 2 to 10 4 compared to those of the fixed-frequency cyclotrons. On the other hand, the substantial increase in particle energy more than outweighs this disadvantage. Many synchrocyclotrons were built throughout the world, the largest machines producing protons of more than 600 MeV. The time variation of the electric frequency in a synchrocyclotron is determined by the rate of change of the orbital frequency of the synchronous particle: ds», w s2 K qV cos cPs (jj = 211"E s

where

K

= 1

+ (1

n _ n){3s2

(8j-29) (8j-30)

and q V cos cPs is the energy gain per turn, and E, the total energy of the synchronous particle. A particle which passes the acceleration gap at a phase cP different from cPs will gain a different amount of energy, and, therefore, its orbital radius will be slightly different from that of the synchronous particle. If tip/p is the fractional difference in momentum between nonsynchronous and synchronous particles, then the corresponding difference in revolution time is given by the relation tiT

1

1 tip

T=~--::;'p

(8j-31)

where a = 1 - n, 'Y = E/E o. In synchrocyclotrons the values of a and 'Yare such that tiT /T has the same sign as tip/po This implies that phase stability exists only in the phase interval 0 < cPs < 11"/2 where the voltage falls: A particle crossing the gap at a phase 1> > cPs gains less energy, i.e., tip < 0; as a result has a shorter revolution time than the synchronous particle; and arrives, therefore, earlier at the next gap crossing. A similar argument can be made if cP < cPs. In both cases the phase cP oscillates about the synchronous phase cPs. The differential equation for these phase oscillations is d ( e. d ) di w 2K dt s

cP

=

qV 211" (cos 1> - cos cPs)

(8j-32)

Ion capture takes place only during a small time interval tit at the beginning of each modulation cycle. With a few simplifying assumptions Bohm and Foldy derived the expression [17] tit = i- - /1I"E s L(cPo,cPs) (8j-33) W s '1 Kq V cos cPs where L(cPo,1>s) is a function of starting phase cPo and synchronous phase cPs. As was first pointed out by McKenzie [18], the beam current that can be accelerated in a synchrocyclotron is space-charge limited. If l.p.eh. denotes the maximum (direct) current that can pass through the available beam space within the dees under spacecharge conditions, the captured average current in a synchrocyclotron is given by I

= l.p.eh.

tit ticPo T ~ m

=

ticPo i;». titfm ~

(8j-34)

ticPo/211" is the microscopic, tit/T m the macroscopic duty factor (see Fig. 8j-4). l.p.eh. is roughly proportional to the voltage V and the square of the vertical focusing frequency, v z 2 in the center [10,20J. Since the repetition rate fm is proportional to V, and tit is proportional to V-!, the beam current in a synchrocyclotron is in this crude approximation proportional to V! or some similar power of V. In all existing synchrocyclotrons the dee voltage is very small (5 to 20 k V) to minimize r-f power losses. The low voltage also necessitates the use of an open-arc source since ions would not

8-332

NUCLEAR PHYSICS

be able to clear the chimney-type structure of the type of ion source used in fixedfrequency machines. All these factors explain the very low internal beam currents (down by a factor 10 2 to 10 3 compared to fixed-frequency cyclotrons), poor beam quality, and poor extraction efficiency (a few percent compared with typically 40 to 90 percent in FF cyclotrons). After the successful development of sector-focusing cyclotrons, several synchrocyclotrons are being modified and improved to remain competitive with the new type of machines. All these synchrocyclotron conversion programs (a survey is given by Blosser in [21]) involve an increase of the dee voltage and thus the repetition rate, the installation of a "chimney"-type ion source used in other cyclotrons, and an improvement of the vertical focusing in the center through use of magnetic bumps or sectors. aj-9. Sector-focusing (Isochronous) Cyclotrons. In 1938 L. Thomas had shown in a theoretical study that it should be possible to build a cyclotron with constant ion frequency w by employing a magnetic field which varies sinusoidally with azimuth angle. The average magnetic field increases with radius to compensate the relativistic mass increase, thus keeping w = qB/m a constant, while at the same time vertical focusing is provided by the azimuthal field variation (called "flutter"). Because of World War II and the invention of the synchrotron, this idea was not acted upon until 19,1'>0 when a group at the Lawrence Radiation Laboratory began a study and built an electron model which proved the feasibility of the new cyclotron concept [9]. Similar studies were soon started at other places in the United States and Europe, and since then a large number of sector-focusing cyclotrons have been built and are now in operation. Details of the theory, design, and performance characteristics of sector-focusing cyclotrons can be found in J. R. Richardson's monography [22] and in the proceedings of several international conferences [23]. Most sector-focusing cyclotrons employ a wedge-shaped rather than a sinusoidal variation in azimuth. Besides, in most cases the pole-shoe sectors or "hills" are spiral-shaped rather than straight, which provides additional focusing, as was first proposed by the MURA group (Midwestern Universitities Research Association) in 1955 [24]. In this general case the median-plane magnetic field is of the form B(r,O)

=

B(r) [ 1

+

L

In(r) cos n (0 - cPn(r» ] (n

=

N, 2N, 3N, etc.)

(8j-35)

n

The number of sectors or periods N is 3 or 4 in most existing cyclotrons. The average magnetic field B(r) increases with radius according to the relativistic mass change: B(r) =

e,

(1 + ;:) = B o(l -

i3 2) - ! = B o

(1 _r:o) -!

(8j-36)

Then w

=

Wo

qB = - o = const mo

(8j-37)

Calculation of the betatron frequencies for such a sector field leads to rather complicated analytical expressions. (For high accuracy, numerical orbit integration by computer is required.) Neglecting a number of less important terms, first-order theory gives the following approximate results: (8j-38)

(8j-39) where

(8j-40)

PARTICLE ACCELERATORS a

8-333

is the (effective) spiral angle defined by tan a = r dl/J/dr

(8j-41)

More accurate formulas are given in the literature ([22,24] for example). Equation (8j-38) for the radial frequency is identical with Eq. (8j-23) except that in this case Ur ~ 1 as k is positive. With respect to the vertical frequency (Eq. 8j-39), the spiral angle a and flutter amplitude F must be large enough to compensate for the defocusing average field and, in addition, provide a net focusing effect such that Uz > 0 (in most cases u. is between 0.1 and 0.2). At small radii, sector focusing ceases to be effective since the azimuthal field amplitude, measured by F(r), goes to zero as (r/g)N, where g is the magnet gap width, and N the number of sectors. To achieve good focusing at small radii, the number of sectors should be small, i.e. three or four (fields with fewer than three sectors are unstable for the radial motion). The problem can be further alleviated by utilizing electric focusing through careful programming of the particles' phase history with respect to the radio frequency [25] and, if necessary, employing a small magnetic bump with negative k. Improved central-region design (source position, beam optics, space-charge compensation, defining slits, etc.) is one of the main reasons for the excellent beam quality in sector-focusing cyclotrons [26]. It is also possible to control the pulse width to a certain extent and achieve microscopic duty factors of 10 to 20 percent and higher or get narrow nanosecond pulses for time-of-flight experiments by employing phase-selection slits in the center. Sector-focusing cyclotrons are limited in energy by resonances in the radial motion which arise whenever the betatron frequency Ur passes through certain critical values. Under the condition of isochronism, k = and hence, approximately,

')'2 -

1

(8j-42) (8j-43)

Thus Ur starts at unity and increases linearly with energy. According to the theory of resonances in sector fields, a stop band occurs in the radial motion whenever Ur = N /2, where N is the number of sectors. A two-sector field is therefore intrinsically unstable. According to Eq. (8j-43), in a three-sector cyclotron the stop band Ur = j occurs at a proton energy of 469 MeV, while N = 4 (ur = 2) leads to a limit of 938 Me V. If terms neglected in Eqs. (8j-38) and (8j-43) are taken into account, the stopband energy limits are found to be considerably lower than these values. The resonance problem as well as practical considerations such as achieving the desired field shapes put an upper limit for isochronous cyclotrons at a proton energy of about 800 to 1000 MeV. The largest sector-focusing machine built so far is the isochronous cyclotron at the University of Maryland, which is capable of accelerating protons to a maximum energy of 140 MeV. At energies above about 200 MeV, new design concepts must be invoked. Several projects in this category are presently under study or construction: A 500-MeV sector-focusing "meson factory" designed as a ring accelerator with a 70-MeV isochronous cyclotron as injector, is presently under construction at Zurich, while a somewhat similar ring machine for 200-MeV protons is being designed at Indiana University. The concept of a separated-orbit cyclotron (SOC) has been studied at Oak Ridge National Laboratory, and a negative-hydrogen cyclotron (H-) for 500 MeV, called TRIUMF, is being built at Vancouver, Canada. One of the outstanding features of most existing isochronous cyclotrons is the variability of energy and the possibility of accelerating different types of particles. The r-f system can be tuned over a wide range of frequencies, and the desired magnet-

8-334

NUCLEAR PHYSICS

field profiles at various excitation levels are achieved by means of a system of trimming coils. Extraction of the beam out of the cyclotron [27] is generally accomplished by inducing a coherent radial oscillation at the Vr = 1 resonance, which occurs at the transition from the isochronous field to the fringe field. In traversing the resonance, the radial amplitude, and thus separation between consecutive turns, is increased sufficiently so that the beam can enter an electrostatic deflector (or a combination of electric and magnetic deflector channels) which bends it into the external beam pipe. Extraction efficiencies of 40 to 90 percent have been achieved in existing machines for proton currents between 10 and 100 p.A. The energy spread of the extracted beam is in the range of 0.1 to 0.3 percent while the emittance in radial and vertical direction is typically between 10 and 30 mm mrad. Sector-focusing cyclotrons are, therefore, excellent tools for nuclear-structure physics in the intermediate-energy range of 10 to 200 Me V for light nuclei. 8j-tO. Constant-gradient Synchrotons. For acceleration of protons to energies above 1 Ge V, linacs and cyclotrons are impractical, as the size of such machines would become prohibitively large. The only type of accelerator that has been capable so far of generating protons in the billion-volt energy range is the synchrotron, which is based on the principle of phase-stable synchronous acceleration proposed by Veksler and McMillan. Fundamentally the synchrotron is an extension of the synchrocyclotron, the main difference being that the orbit radius is kept constant, and the guiding magnetic field is provided by a number of individual magnets placed along the orbit. The particles are first preaccelerated in a Van de Graaff, Cockcroft-Walton, or linac, and then injected into the synchrotron ring. To keep the orbit radius constant in the synchrotron, the magnets are pulsed such that B = B (t) increases from a minimum value at injection to the maximum given by the final energy of the particles. Orbit stability is provided by constant-gradient focusing as in cyclotrons. Magnets and pole shoes have to be designed carefully to keep the field index n = - (r / B)dB / dr within acceptable limits over the entire range of variation of the magnetic field. The orbital frequency of the particles is determined by the radius of curvature R in the magnets and the length l of the straight drift section between the magnets. With N straight sections, the circumference of an orbit is L = 21rR + Nl, and substituting Eq. (8j-4) for v = {3c, one gets (8j-44) or, in view of Eq. (8j-6) 21rC W

=

BRqc

L [(BRqc)2

+E

(8j-45) 02]!

The particles are accelerated by r-f resonators located in the straight sections between magnets. From Eq. (8j-6) the rate of energy increase dE/dt is determined by dB/dt: (8j-46) The corresponding energy gain per turn fj.E = q V cos cP obtained from Eqs. (8j-44) and (8j-46), and is given by

(w/21r)dE/dt, is then

(8j-47) Since accurate timing of the magnet pulse is exceedingly difficult at such high power levels, no predetermined time schedule can be set up for the variation of B, fj.E, and Wrf with time. Instead, Wrf and fj.E are controlled electronically to follow the rate of

PARTICLE ACCELERATORS

8-335

change of the magnetic field. A pickup loop in the magnetic field supplies a signal proportional to dB/dt, from which B is obtained at any given time through electronic integration. A computer solves Eq. (8j-45), and the values for wand V are sent to the control circuits of the r-f oscillators. The required frequency bandwidth of the oscillators is porportional to the range of velocities between injection and full energy; it is the smaller, the higher the energy of the preaccelerator. As in the synchrocyclotron, phase stability in the constant-gradient synchrotron is obtained when the phase of the synchronous particle lies in the interval of decreasing voltage amplitude. Electron synchrotrons differ from proton machines in several aspects. Because of the smaller rest mass, electron velocities at energies above a few Me V are essentially equal to the speed of light. The orbital frequency is thus higher than for the proton machines but practically constant, so that frequency modulation is unnecessary. In addition, energy losses due to electromagnetic radiation of the accelerated electrons are substantially higher than for the protons where they are practically negligible. However, these losses are automatically compensated for by the mechanism of phase stability: A decrease in momentum due to radiation losses causes a shrinkage of the orbit radius, so that the electron arrives earlier at the acceleration gap and thus gains additional energy which compensates for these losses. Historically the electron synchrotron preceded the proton synchrotron by several years. The largest constant-gradient electron machine is the 1.3-0e V synchrotron at Cornell University, while the largest proton synchrotron with constant gradient is the 10-0e V accelerator at Dubna. The focusing forces in constant-gradient synchrotrons are inherently weak, and, consequently, the amplitudes of the betatron oscillations are relatively large. This necessitates the use of magnets with large gap dimensions to contain the beam, and makes an accelerator of this kind prohibitively expensive if the energy exceeds more than a few Ge V. (The magnets for the 10-0e V "Synchrophasotron" at Dubna weigh 36,000 tons!) The invention of the alternating-gradient or strong-focusing principle was, therefore, a major breakthrough in high-energy accelerator design. Alternatinggradient synchrotrons can be built with smaller magnets and have better beam quality and higher beam intensities than constant-gradient machines. 8j-I!. Alternating-gradient Synchrotrons. The principle of strong focusing was independently discovered first in 1949 by Christofilos, whose work was not published then, and shortly after that by Courant, Livingston, and Snyder in 1952. This new concept is most easily understood in terms of its well-known optical analog, the combination of focusing and defocusing lenses. If two lenses of focal lengths II and /2 are combined, with a separation d between them, the focal length F of this system is given by 111 d (8j-48) -=-+---

F

Ii

12

Id2

In the special case of a converging and diverging lens of equal, but opposite, strength, one has 12 = -iI, and hence (8j-49) The focal length of such a two-lens system is thus always positive (focusing). The application of this idea to synchrotrons implies the combination of scrongly focusing and defocusing magnets. According to the theory of betatron oscillations, Eqs. (8j-20) to (8j-24), a magnet with negative gradient, dB /dr < 0, is focusing vertically while defocusing radially if n > 1. A radially increasing field (n < 0), on the other hand, focuses the particles only in the radial direction and is defocusing with respect to the vertical motion. The alternating-gradient synchrotron ring consists of a

8-336

NUCLEAR PHYSICS

succession of magnets arranged in such a way that a magnet with large positive gradient is followed by one with a negative gradient of equal strength. The absolute values of n are typically in the range of 200 to 300, as compared to 0.5 in the conventional weak focusing machines. Consequently, the frequencies of the corresponding radial and vertical oscillations are between one and two orders of magnitude larger than in constant-gradient accelerators. The strong focusing forces reduce the required beam space and the size of the magnets, and thus result in substantial reduction of costs and in improvement of beam quality. With regard to synchrotron oscillations and phase stability, the alternating-gradient machines are distinctly different from the weak focusing accelerators. The theory shows that the parameter a in Eq. (8j-31) is always greater than 1, and hence l/a < 1, in contrast to the constant-gradient machines. At low energies, where )'2 < a, an increase in momentum causes a decrease in revolution time. This implies that stability exists if the synchronous particle crosses the accelerating gaps when the voltage is rising. As)' increases, a critical transition energy occurs where v! = a. Above that energy ()'2 > a), particles behave as in the synchrocyclotron and constantgradient synchrotron; i.e., the synchronous phase must be in a region of falling voltage. This means that in AG synchrotrons provisions must be made to shift the phase of the accelerating voltage at the point where the particles pass through the transition energy. If the injection energy is, however, higher than the transition energy, this difficulty can be avoided. A major problem in the design of strong focusing synchrotrons is the existence of resonances which occur whenever the values of the betatron frequencies are integers or integral fractions. The operating point must be carefully chosen, taking into account the effects of misalignments and space-charge forces. The electric and magnetic self-fields of the circulating beam produce a net defocusing force which is equivalent to an effective change of the field index n given by (8j-50) where Q is the total charge, and R is the major and a the minor radius of the toroidal ring of circulating beam. If Iln denotes the maximum tolerable change in field index (to stay away from a resonance or avoid defocusing), then the maximum number of particles Nu« which can be contained in the ring is given by (8j-51) where Eo is in MeV, a and R in m. (A detailed analysis of space-charge effects, including image effects in surrounding walls, was made by Laslett [28].) For electrons at extremely relativistic energies ()'» 1) the total current hm = qNlimV/2'1T-R contained in the ring is given by the relation I = 8,500

(~) 2 )'3 Iln

(8j-52)

By proper choice of the n values and careful alignment of the magnets it was possible to overcome the difficulties imposed by resonances and space-charge effects. Several AG synchrotrons are now operating successfully. The presently largest proton accelerator in the world is the 70-GeV alternating-gradient synchrotron at Serpukhov (U.S.S.R.) which went into operation during 1968. In second and third place follow the 33-GeV AGS at Brookhaven (U.S.A.) and the 28-GeV proton synchrotron at CERN, the European Nuclear Research Center at Geneva, Switzerland.

PARTICLE ACCELERATORS

8-337

The largest alternating-gradient synchrotron for the acceleration of electrons is the 1O-GeV accelerator built at Cornell University. Other large electron machines are the 7-GeV synchrotron (DESY) at Hamburg, Germany, which began operation in 1964; the 6-0eV machine at Cambridge, Massachusetts, operating since 1962; and a 6.5-MeV accelerator in the Soviet Union. Although synchrotron radiation losses put an upper limit in the range of 10 Oe V to electron synchrotrons, proton machines with energies up to 1000 Ge V appear to be within the reach of technical feasibility. Preliminary studies of a 1000-0eV accelerator have been carried out in the United States and are in progress in the U.S.S.R. At the National Accelerator Laboratory at Batavia, Illinois, a 200-Oe V alternatinggradient synchrotron is being constructed, with provisions to extend the energy to 500 Ge V at a later time. Acceleration in this project will take place in three stages: A 200-MeV linac will inject the beam into a 10-0eV booster synchrotron (diameter of 150 m), from which the particles are steered into the main ring (diameter of 2,000 m) for acceleration to full energy. COILS

ELECTRON BEAM

VACUUM CHAMBER

FIG. 8j-lO. Betatron.

8j-12. Betatrons. The betatron differs from other circular accelerators in that the electromotive force for accelerating the particles is generated by the time variation of the magnetic flux. It is only suitable for the acceleration of electrons. The magnet structure of a betatron (Fig. 8j-1O) resembles that of a cyclotron; the major difference is in the design and shape of the core part with the pole shoes. As in a synchrotron, the orbit radius of the circulating electron beam is kept constant throughout the acceleration process. This implies that the increase in energy due to the changing magnetic flux linked by the circulating electrons must be precisely in step with the increase of the magnetic field strength at the orbit radius. The accelerating electric field E along the circular orbit is determined by Maxwell's second equation

f In cylindrical coordinates, if B

E . dL = -

ata f B . dS

(8j-53)

= Be, and increasing in time, E

21rRE = -a

at

JR 21rBR dR 0

dB

= 1rR2-

dt

-Earp, and thus (8j-54)

B is the average magnetic field inside the circular orbit with constant radius R. rate of change of momentum of the electron is given by d

di (mv)

= eE =

d

dt (eBR)

= eR

dB

di

The

(8j-55)

8-338

NUCLEAR PHYSICS

Elimination of E from Eqs. (8j-54) and (8j-55) gives the fundamental betatron relation dB = 2 dB (8j-56) dt

dt

which says that the change in the space-averaged field inside the orbit B must equal twice the change in the field at the orbit B(R). If both the average core field and the field at the orbit are zero when the acceleration process starts, as is usually the case, integration of (8j-56) gives B = 2B (8j-57) The average core field must thus be twice as high as the field at the orbit ("two-toone" rule) which explains the shape of the magnet core and pole shoes in Fig. 8j-1O. The magnet is driven with an ac power supply which generates a sinusoidally varying current at a frequency in the range of 30 to 60 Hz. To minimize eddy currents the magnet structure is laminated. The electrons are injected from an electron gun close to the equilibrium orbit, with a starting energy between 10 and 100 keV. The acceleration process then takes place during the quarter cycle during which the field rises from the value (close to zero) that corresponds to the injection energy to the peak value, where the electrons have reached the maximum energy. Radial and axial stability of the beam during acceleration is maintained by constantgradient focusing; i.e., the field near the orbit is decreasing with radius such that the index n has values between 0 and 1. In fact, the resulting oscillations are known as betatron oscillations because the theory of gradient focusing was first developed in connection with the betatron by Kerst and Serber. At the end of each acceleration cycle the electron beam is displaced from the equilibrium orbit by a perturbation in the magnetic field. This is accomplished by additional coils which disturb the "two-to-one rule," resulting in an increase of the orbit radius and thereby forcing the beam to hit the internal target or deflecting it out of the magnetic field for external use. Most betatrons are used primarily for production of hard X rays from internal targets. Electromagnetic radiation emitted by the circulating electrons sets an upperenergy limit to betatron-type acceleration. In the relativistic electron-energy range above a few Me V, the rate of energy loss due to radiation is proportional to the fourth power of the kinetic energy and inversely proportional to the orbit radius, 1~.Erad =

8.8 X 10

-8

E k 4. I f

(8j-58)

where flEr ad is in electron volts per revolution, Ek in Me V, and R in meters. The betatron was invented by Wide roe, but the first successful machine was built by Kerst. Today a large number of betatrons are in operation in hospitals, for industrial applications as well as for scientific use. The largest betatron is the 300-MeV machine at the University of Illinois, Urbana. 8j-1S. New Developments. Accelerator technology is advancing at a rapid rate in many areas. New design concepts have been proposed or are being investigated, and in all likelihood new types of accelerators will be built in the future. It is impossible to survey all these developments, but below a few examples will be discussed briefly to illustrate major present trends. Heavy-ion Accelerators. In principle all the existing types of accelerators with the exception of the betatron and microtron are capable of accelerating ions of heavy elements. The main problem in practically every instance is that a high charge state is either required to facilitate acceleration or desired to obtain a sufficiently high energy per nucleon. Most ion sources, however, which are utilizing a gas discharge produce ions with only a few electrons removed (typically 1 to ,5). However, to

PARTICLE ACCELERATORS

8-339

accelerate heavy ions (M > 20) with low charge state (Z < 4) in a cyclotron, for example, the wavelength of the r-f system would have to be impractically large, or operation at a very high harmonic, Wrf/w = N » 1, would be necessary, which again is not feasible. There are basically two solutions to this problem: One is to develop new types of ion sources which yield higher charge states; the other approach is to accelerate ions with low charge state to some intermediate energy, then remove more electrons by stripping in a foil or gas cell, and accelerate further. Thus a negatively charged heavy ion can be injected into a tandem where stripping takes place in the positive-voltage terminal, followed by several steps of acceleration and stripping until the ions with various charge states and energies arrive at ground potential. If desired, one ion component can then be injected into a cyclotron for acceleration to even higher energies. Similar possibilities exist with a multistage linear accelerator or combination of linac and synchrotron. Various schemes of this kind are discussed in the Proceedings of the 1969 Accelerator Conference in Washington, D.C. High-energy Cyclotrons. Several sector-focusing cyclotron projects in the 200- to 500-MeV range are under construction (Indiana, Zurich, Vancouver), and should come into operation in the 1970s. In addition, the improvement of existing synchrocyclotrons is of great interest as currents in such converted machines should be close to those achieved in isochronous cyclotrons. The 600-MeV synchrocyclotron at CERN is being improved by a change of the rf system (higher dee voltage and repetition rate) and of the ion source and central region. The 385-MeV synchrocyclotron of Columbia University, New York, is being converted into a 500-MeV machine by changing rf voltage, repetition rate, and central region, as in the CERN case, but also adding sector focusing in the magnetic field. These modifications should increase internal beam currents by a factor of 10 to 20 and external beams by 100. The Collective-ion or Electron-ring Accelerator (ERA). First proposed by Veksler in 1956 [29], the ERA involves an entirely new acceleration concept which holds great promise for the acceleration of protons to superhigh energies. The basic idea involves the formation of a relativistic high-density electron ring (typically 1013 to 1014 particles, major radius 5 em, minor radius 1 mm, energy 20 to 25 Me V) in a strong magnetic field. After formation of the ring, gas is admitted, the ions formed by collisions with the electrons are trapped in the deep potential well of the electron cluster, and the ring with ions is subsequently accelerated to high energies. Since the ions travel with the same speed as the electrons, their final kinetic energy is substantially larger than that of the electrons. If Mic" is the rest energy of the ions, E eo the total energy of the ring electrons before and Eel after acceleration, the final total ion energy is given by Eil = (EetfEeo)Mic2. Thus to obtain a proton energy of 1 GeV, requires Eel ~ 2Eeo, and if the initial energy of the ring electrons is E eo = 25 Me V, an additional amount of 25 Me V must be added by acceleration of the ring. If the energy is gained at a rate of 40 ke V/cm, the accelerator needs only a length of a little more than 6 m to produce the I-GeV protons. The size of a multi-Ge V proton accelerator would therefore be substantially smaller than that of a synchrotron, which explains the attractiveness of the electron-ring accelerator concept. At the same time the ERA holds great promise also as an accelerator for heavy ions. The various design problems and prospects of the ERA are discussed in the proceedings of a symposium in Berkeley [30]. Compressed electron rings in a pulsed magnetic field were obtained during 1968 in experiments at Dubna, Berkeley [31], and the University of Maryland ]32]. A promising alternative to a pulsed system is the formation of the electron ring in a static magnetic field [33]. For further information on the ERA see the article by D. Keefe in the journal Particle Accelerators [341. Other interesting developments in the accelerator field, such as storage rings, superconducting linacs, and the racetrack microtron, are reviewed in the proceedings of the latest accelerator conferences listed in the general bibliography.

8-340

NUCLEAH PHYSICS

General Bibliography 1. Livingood, John J.: "Principles of Cyclic Particle Accelerators," D. Van Nostrand Company, Inc., Princeton, N.J., 1961. 2. Livingston, M. S., and J. P. Blewett: "Particle Accelerators," McGraw-Hill Book Company, New York, 1962. 3. Kollath, R.: "Particle Accelerators," Sir Isaac Pitman & Sons, Ltd., London, 1962. 4. Kolornensky, A. A., and A. N. Lebedev: "Theory of Cyclic Accelerators," NorthHolland Publishing Company, Amsterdam, 1966. 5. Persico, E., E. Ferrari, and S. E. Segre: "Principles of Particle Accelerators," W. A. Benjamin, Inc., New York, 1968. 6. Nuclear Instrumentation I, "Encyclopedia of Physics," vol. 44, Springer Verlag OHG, Berlin, 1959. 7. Proc. CERN Symp. Hi{}h Ener{}y Accelerators and Pion Phys. 1, E. Regenstreif, ed., CERN, Geneva, 1956. 8. Proc. Intern. Conf. Hi{}h Ener{}y Accelerators and Instrumentation, L. Kowarski, ed. CERN, Geneva, 1959. 9. Proc. Intern. Conf, Hioh. Energy Accelerators, 1\1. H. Blewett, ed., Brookhaven, 1961. 10. Proc, Intern. Con]. High Energy Accelerator s, Dubna, 1963, A. A. Kolomensky, chief ed., Atomizdat, 1964. 11. Proc, Intern. Con], High Energy Accelerators, Frascati, 1965. 12. Proc. 6th Intern. Conf, Hiqh. Energy Accelerators, Cambridge, Mass., 1967. 13. First National Particle Accelerator Conference, IEEE NS-12(3), June, 1965. 14. U.S. National Particle Accelerator Conference, IEEE N5-14(3). June, 1967. 15. 1969 Particle Accelerator Conference, IEEE NS-16(3), June, 1969.

References 1. Wideroe, R.: On a New Principle for Production of High Potentials, Arch. Elektrotech. 21,387-406 (1928). 2. Van de Graaff, R. J.: A 1,500,000 Volt Electrostatic Generator, Phys. Rev. 38, 1919 (1931). 3. Lawrence, E. 0., and N. E. Edlefsen: On the Production of High Speed Protons, Science 72, 376-377 (1930). Lawrence, E. 0., and M. S. Livingston: The Production of High Speed Light Ions without the Use of High Voltages, Phys. Rev. 40, 19-35 (1932). 4. Cockroft, J. D. and E. T. S. Walton: Experiments with High Velocity Positive Ions, Proc. Roy. Soc. (London), ser. A, 136, 619-630 (1932). 5. Kerst, D. W.: The Acceleration of Electrons by Magnetic Induction, Phys. Rev. 60, 47-53 (1941). 6. McMillan, E. 1\1.: The Synchrotron: a Proposed High Energy Particle Accelerator, Phys. Rev. 68, 143-144 (1945). Veksler, V.: A New Method of Acceleration of Relativistic Particles, J. Phys. (U.S.S.R.) 9, 153-158 (1945). 7. Christofilos, N.: Focusing System for Ions and Electrons, U.S. Patent 2,736,799 (filed March 10, 1950, issued Feb. 28, Hl56). E. D. Courant, 1\1. S. Livingston, and H. S. Snyder: The Strong-Focusing Synchrotron: a New High Energy Accelerator, Phys. Rev. 88, 1190-1196 (1952). 8. Thomas, L. H.: The Paths of Ions in the Cyclotron, Phys. Rev. 54,-580-588 (1938). 9. Kelly, E. L., P. V. Pyle, R. L. Thornton, J. R. Richardson, and B. T. Wright: Two Electron Models of a Constant Frequency Relativistic Cyclotron, Rev. Sci. Instr. 27, 493-503 (1956). 10. Livingston, M. S., and J. P. Blewett: "Particle Accelerators," McGraw-Hill Book Company, New York, 1962. 11. Schenkel, 1'1.: Eine neue Schaltung fur die Erzeugung hoher Gleichspannungen, Elektrotech. Z. 40, 333-334 (1919). H. Greinacher: Uber eine neue Methode, Wechselstrom mittels elektrischer Ventile und Kondensatoren in hochgespannten Gleichstrom zu verwandeln, Z. Physik 4, 195-205 (1921). 12. Alvarez, L. W.: The Design of a Proton Linear Accelerator, Phys. Rev. 70, 799-800 (1946). L. W. Alvarez, H. Bradner, J. V. Frank, H. Gordon, J. D. Gow, L. C. Marshall, F. Oppenheimer, W. K. H. Panofsky , C. Richman, and J. R. Woodyard: Berkeley Proton Linear Accelerator, Rev. Sci. Instr. 26, 111-133 (1955). 13. Blewett, J. P.: Radial Focusing in the Linear Accelerator, Phys. Rev. 88, 1197-1199 (1952). 14. Ginzton, E. L., W. W. Hansen, and W. R. Kennedy: "Linear Electron Accelerator," Rev. Sci. Instr. 19,89-108 (1948). D. W. Fry, R. B. R. Shersby-Harvie, L. B. Mullet, and W. Walkinshaw: Traveling Wave Linear Accelerator for Electrons, Nature 160, 351-352 (1947).

PARTICLE ACCELERATORS

8-341

15. Livingston, R. S., and R. J. Jones: High Intensity Ion Source for Cyclotrons, Rev. Sci. Lnstr, 26, 552-557 (1954). 16. Kerst, D. W., and R. Serber: Electronic Orbits in the Induction Accelerator, Phys. Rev. 60, 53-58 (1941). 17. Bohm D., and L. Foldy: Theory of the Synchro-cyclotron, Phys. Rev. 72, 649-661 (1947). 18. McKenzie, K. R.: Space Charge Limits and Cyclotron Beam Enhancement, N ucl, Lnstr, Methods 31, 139-146 (1964). 19. Blosser, H. G., and M. M. Gordon: Performance Estimates for Injector Cyclotrons, Nucl. Instr, Methods 13, 101 (1961). 20. Reiser, M.: Space Charge Effects and Current Limitations in Cyclotrons, IEEE Trans. Nucl. Sci. NS-13 (4) , 171-178 (1966). 21. Blosser, H. G.: Synchrocyclotron Improvement Programs, IEEE Trans. Nucl. Sci. NS-16(3) , June, 1969. 22. Richardson, J. R.: Sector Focusing Cyclotrons, in "Progress in Nuclear Techniques and Instrumentation," vol. I, North-Holland Publishing Company, Amsterdam, 1965. 23. Conference on Sector Focused Cyclotrons, Sea Island, Ga., February, 1959, Nail. Acad. Sci. Publ. 656, 1959. Proceedings of the International Conference on Sectorfocused Cyclotrons, Los Angeles, Calif., April, 1962, in N'ucl, Lnstr, Methods 18, 19 (1962), Proceedings of the International Conference on Sector-focused Cyclotrons and Meson Factories, Geneva, Switzerland, April, 1963, CERN Rept. 63-19, May 29, 1963. International Conference on Isochronous Cyclotrons, Gatlinburg, Tenn., May, 1966, in IEEE Trans. NS-13 (4) , (1966). 24. Symon, K. R., D. W. Kerst, L. W. Jones, and K. M. Terwilliger: Fixed-field Alternating Gradient Accelerators, Phys. Rev. 98, 1152-1153 (1955). K. R. Symon, D. W. Kerst, L. W. Jones, L. J. Laslett, and K. M. Terwilliger: Fixed-field Alternating Gradient Particle Accelerators, Phys. Rev. 103, 1837-1859 (1956). 25. Smith, W. I. B.: Improved Focusing near the Cyclotron Source, Nucl. Inetr, Methods 9, 49-54 (1960). M. Reiser: Ion Capture and Initial Orbits in the Karlsruhe Isochronous Cyclotron, Nucl. Lnstr, Methods 13, 55-69 (1961). 26. Reiser, M.: Central Orbit Program for a Variable Energy Multi-particle Cyclotron, Nucl. Ineir, Methods18,19, 370-377 (1962). H. G. Blosser: Problems and Performance in the Cyclotron Central Region, IEEE Trans. Nucl. Sci. NS-13(4), 1-14 (1966). 27. The various extraction methods are discussed in papers by Gordon, Kim, Hagedorn and Kramer, Paul and Wright in IEEE Trans. NS~13(4), 48-83 (1966). 28. Laslett, L. J.: On Intensity Limitations Imposed by Transverse Space Charge Effects in Circular Particle Accelerators, Proc, 1963 Summer Study on Storage Rings, Accelerators, and Experimentation at Super-high Energies, BNL 7534, 1963. 29. Veksler, V. I.: Proc. CERN Symp. on High Energy Accelerators, p. 80, 1956. 30. Proceedings of. the Symposium on Electron Ring Accelerators, LRL Rept, UCRL18103, February, 1968. 31. Keefe, D., et al.: Experiments on Forming Intense Rings of Electrons Suitable for the Acceleration of Ions, Phys. Rev. Letters 22, 558-561 (1969). 32. Trivelpiece, A. W., R. E. Pechacek, and C. A. Kapetanakos: Phys. Rev. Letters 21, 1436 (1968). 33. Berg, R. E., Hogil Kim, M. P. Reiser, and G. T. Zorn: Possibilities of Forming a Compressed Electron Ring in a Static Magnetic Field. Phys. Re», Letters 22, ~19-421 (1969). See also papers by Laslett and Sessler, Christofilos, Berg, et al. in Proceedings of 1969 Accelerator Conference, Washington, D.C., IEEE Trans. NS-16 (3) 19·69. 34. Keefe, D.: Research on the Electron Ring Accelerator, Particle Accelerators 1, 1-13 (1970).

Section 9

SOLID-STATE PHYSICS H. P. R. FREDERIKSE, Editor

The National Bureau of Standards

CONTENTS 9a. Crystallographic Properties...... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 9b. Structure, Melting Point, Density, and Energy Gap of Simple Inorganic Compounds 9c. Electronic Properties of Solids. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 9d. Properties of Metals ge. Properties of Semiconductors " 9f. Properties of Ionic Crystals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 9g. Properties of Superconductors 9h. Color Centers and Dislocations 9i. Luminescence 9j. Work Function and Secondary Emission. '"

9-2 9-16 9-26 9-38 9-56 9-74 9-127 9-148 9-158 9-172

9a. Crystallographic Properties J. D. H. DONNAyl

The Johns Hopkins University W. P. MASON AND E. A. WOOD 2

Bell Telephone Laboratories, Inc.

9a-l. Crystal System, Space Group, Cell Content, Lattice Constants, Structure Type. These data are presented for all the chemical elements (Table 9a-2) and for certain selected compounds (Table 9a-3). In each table the first column contains the chemical formula, with mention of the polymorphic form, if necessary, and of the temperature, if known, at which the lattice constants have been determined. c

FIG. 9a-1. Coordinate axes (= "crystallographic axes").

FIG. 9a-2. Coordinate axes for the hexagonal system (can also be used for the rhombohedral system).

The crystal system, listed in column 2, is based on the point symmetry of the lattice! of the crystal structure. It is given by the initial letter of its name (see Table 9a-l). The ~oordinate axes x, y, z are taken along three concurrent cell edges that form a right-handed system (a, b, c in Fig. 9a-l; ai, a2, c in Fig. 9a-2). Symmetry governs the relative values of the unit lengths a, b, c and of the interaxial angles a, (3, 'Y. The symmetry requirements entail a specialization of the lattice constants (Table 9a-l) and a corresponding reduction in the number of values that must be listed in the tables of data. The space group is given (Tables 9a-2 and 9a-3, column 3) in both Schoenflies and and Hermann-Mauguin notations. The symbols of the 32 crystal point groups, needed for comparison with the space-group symbols, will be found in Table 9a-l, where the Crystallographic Data. Tensor Properties of Crystals. 3 "Lattice" 8.8.: triperiodic assemblage of points, the termini of the vectors L(uvw) Ull + vb + we, where u, v, w take all integral values-the geometrical expression of a translation group, described by a repeating parallelepiped ("cell") whose edges are preferably chosen along symmetry axes of the lattice. 1

2

9-2

9-3

CRYSTALLOGHAPHIC PROPERTIES

Hermann-Mauguin symbol is given for every orientation and the Schoenflies symbol follows between parentheses. A Hermann-Mauguin point-group symbol states what symmetry a specified discontinuous vectorial property possesses along certain directions of the crystal. These directions are those of the symmetry axes of the lattice (Table 9a-l, column 2). They are grouped in sets of equivalent directions, some being chosen as cell edges as shown in Table 9a-1 (column 3). An Arabic numeral represents a rotation axis of symmetry along one direction (examples: any 2 in 222, the 3 in 3m) or along each direction of a set (the 2 in 42m, either 2 in 622, the 3 in m3m). Surmounted by a bar the numeral indicates a rotatory-inversion axis. Example: the 4 axis stands for a cyclic group in which the first power of the symmetry operation is a 90 deg rotation followed by an inversion through a point! on the axis-the fixed point in the point group. The I axis 4 ~m

~ ~ ~2 ~ .

:\:: '

.:

""

2

(b)

(0)

(e) (d)

FIG. 9a-3. Examples of macroscopic crystal symmetry (point groups): (a) tetragonal, 4lmmm; (b) monoclinic, 21m; (c) orthorhombic, mm; (d) tetragonal, 42m. (After W. P. Ma80n and E. A. Wood.)

is not defined in direction: it symbolizes the center of symmetry. A mirror plane of symmetry, designated m, is perpendicular to the direction it describes. Example: in 61mmm the first m is perpendicular to the c axis, the second m and the third m represent three mirrors each that are perpendicular to aI, a2, a3 and the bisectors, respectively. The following point groups contain the center of symmetry: mmm (= 21m 21m 21m), m3m (= 4/m 321m), m3 (= 21m 3), 3, and N [m, where N is an even number. Figure 9a-3 illustrates the assemblages of symmetry elements in four selected point groups, which express the morphological symmetry of well-formed crystals. A Hermann-Mauguin space-group symbol begins with a capital letter that tells the lattice mode: primitive (P), body-centered (I), one-face-centered (e, A, or B), all-facecentered (F), rhombohedral (R). Additional symmetry elements appear. In a 1

Note that this point is not a center of symmetry.

I TABLE

Name

Lattice symmetry (holohedry)

9a-1.

THE SEVEN CRYSTAL SYSTEMS BASED ON THE POINT SYMMETRY OF THE LATTICE

Symmetry direotions-

Restrictions imposed by symmetry

Tabulated values

Anorthic ...... I (C.,) (= triclinic) Monoclinic .... 2/m(C2h) Orthorhombic. mmm(D2h) (= rhombic) Tetragonal .... 4/mmm(D4h)

None

None

a, b, c, a, (3, l'

b (a) (b) (c)

l' = a = 90° a = (3 = l' = 90°

a, b, c, (3

(c) (ab) (bisectors)"

b = a, a = (3 = l' = 90°

a, c

Hexagonal ..... 6/mmm(D6h)

(c) (ala2aa) (bisec.)"

b = a, a = (3 = 90°, l' = 120°

a, c

b = a, a = (3 = 90°, l' = 120°

a, c

b = c = arh, (3 = l' = a b = c = a, a = (3 = l' = 90°

arh, a a

Rhombohedral" 3m(Dad) Cubic ......... m3m(Oh) (= isometric)

a, b, c

Merohedries (subgroups of the lattice symmetry in each system") l(C l )

;

U2

m(C.), 2(C2) mm2[2mm][m2m](C211), 222(D 2)f;

'0 I

rC)(a,a",.l ................ (abc) (b. d.) (f.d.)d

42m[4m2](D2d), 4mm( C 411), 422(D4); 4/m(C4h), 4(84), 4(C4);

rm2l62ml(D"l'

6mm(C•• J, 622(D.);

6/m(C6h) , 6(Cah), 6(C6); 3m1[31m](Dad) , 3m1(31m](Cat:), 321[312](Da) 3(Cai), 3(Ca)l1; 3m(Call), 32(Da); 3(Cai), 3(Ca)l1; 43m(Td), 432(0); m3(Th), 23(T)

a Symmetry directions in the lattice (in the same sequence as in the Hermann-Mauguin symbol), and how cell edges are chosen from them. A rhombohedral lattice can be described by means of a triple cell, which has the same shape as the cell of a hexagonal lattice (e,c) but has additional points at 1 aI, a2, e, respectively), or by means of the primitive rhombohedral cell (a,h,a). Both descriptions are given in Tables 9a-2 and 9a-3. e Bisectors of the angles between the axes: aOb, aOo(T) and alOiia, aaOa2, a20al(H). (Fig.9a-2) Ii The four body diagonals (b. d.) and the six face diagonals (f. d.) of the cube, • Semicolons separate the 11 Laue classes. I Alternat,e orientations, shown between brackets, are needed in space-group symbols. 11 All five trigonaZ point groups appear in both hexagonal (H) and rhombohedral (R) systems. b

i i and f 1 i (fractions of

o e-

1-4

U2 ~

> ~

tr.l ""d

l:Il

~ U2 1-4

o

U2

9-5

CRYSTALLOGRAPHIC PROPERTIES TABLE

9a-2.

Formula (temp., °C, for the lattice constants given)

CRYSTALLOGRAPHIC DATA FOR THE ELEMENTS

Crystal system

Space group«

Ar (extrapolated, OK). ....... Ag (25). ... . .......... ....... Al (24.8) ............... ...... As (26) ........... .. ........

Cub. Cub. Cub. Rhdr.

Au (25) .......... ......... . . B .................... ....... Ba (26) ..................... Be (18) ................ . . . . . . Be (630)(stable 500-700) ....... Bi (25) ......................

Cub. Tetr. Cub. Hex. Hex. Rhdr.

Oho-Fm3m D4h 12_P42! nmn Oh9-Im3m D6h 4-P63/ mmc ............. D3do-R3m

Br2 (-150) ................... C (diamond) (26) . ............ C (graphite) (14.6) ............. C (graphite) ... ........... .. ,

Orth. Cub. Hex. Rhdr.

D2h 18-Bmab Oh7-Fd3m D6h 4-P63/mmc D3d o-R3m

(a) (electrolytic) ........... (-y)(above 464) .. ..... (26) ......... ... ...... .... (-y)................ .. .... ({3). ......................

Cub. Cub. Hex. Cub. Hex. Cub. Cub. Tetr. Hex. Cub. Cub. Cub. Cub. Cub. Hex. Hex. Cub. Cub. Cub. Cub. Orth. Orth. Hex. Cub. Hex. Hex. Hex. Hex. Rhdr.

O"o-Fm3m OhLlm3m D6h 4-P63/mmc Oh5-Fm3m D6h 4-P63/mmc Oho-Fm3m Oh9-Im3m D4h 16-P42/ncm D6h4-P63/mmc Oh5-Fm3m Tda-I43m Oh9-Im3m Oh9-Im3m Oh o-Fm3m D6h4-P6a/mmc D6h4-P63/mme Oh9-Im3m Oh9-Im3m Oho-Fm3m Oh9-Im3m

Hex. Orth. Tetr. Cub. Cub. Cub. Cub. Hex. Cub. Cub.

D6h4-P6a/mmc D2h Fl-Bmab D4h 17-I4/mmm Oho-Fm3m Oh9-Im3m Oho-Fm3m Oho-Fm3m ............. Oho-Fm3m Oh9-Im3m

Ca Ca Cd Ce Ce Ce Ce Cb Co Co

(a) ....... .. ..... ........ (0) (stable above 730) .... ...

(-185) .......... '...

(a)(20) .. , ............... (20) ........... ....... .... Cr........ , .................. Cr (25) ............ . . . . . . . . . . . Cs (-100) ....................

Cu (25) ......................

Dy (99.8% pure) ...... , ....... Er Eu Fe Fe Fe Ga Ga Gd Ge

(99.8% pure) .............. (98-99 % pure) ............. (a)(20)(stable to 900) ...... (,.)(stable 900-1400) ....... (0) (stable above 1400) ... ... (unstable form) ( -16.3) ..... (stable form) ......... .... (99.7% pure) .... .......... (24.6) .... . . . . . . . . . . . . . . . . . Hi (above 1.30 K). ........... He a (3.48 K, 163 atm) ......... He 4 (3.95 K, 129 atm) ........ Hf (26) ...................... Hg (5K) .....................

Ho (99.4 % pure) .............. 12 (26 ± 1) ................... In (26) ....................... Ir (26) ....................... K (20) ....... ................ Kr (-252.5) .................. Kr (89 K) .................... La (a)(99.8 % pure) ............ La ({3)(stable above ca. 260) .... La (,.)(stable above 864 C) .... Li 7 (20) .................... } LiB (20) .................... Li (-195) .... . . . . . . . . . . . . . . . Li(-195) .............. ....... Li (-195), ...................

Cub.

O,.o-Fm3m Oho-Fm3m Oho-Fm3m D3i;-R3m

Dn.-Amani

D2h 18-Abam D6h 4-P63/mmc OI/-Fd3m D6h4-P63/mmc D6h 4-P63/mmc D6h4-P63/mmc D6h-P63/mmc D3d5-R3m

Oh 9-Im3m

Z

Lattice constants.s a, b, Cj a, {3, ,.

4 4 4 6 2 4 50 2 2 ca. 60 6 2 4 8 4 6 2 4 2 2 4 2 4 2 8 2 4 58 2 2 4 2 2 2 2 4 2 4 8 2 8 2 2 2 2 3 1 2 4 2 4 2 4 4 4 4 2

5.3109 ± 0.0001

"'d ~

H

C

constants the same, except

= o. = C25,

Cab

=

Cba

and

C62

=

o "'d

C45 C46

C5B

= Cu, resulting in 7 constants.

2M 5 2 K constants the same as C constants except 2M 4 1 K u = K 23, resulting in 6 constants. M ll - M l 2

Mu Mu

M 45 Mu

C

~

o

"'d

t?=.:l

~

1-3 H

constants the same except Cab = Cba, 2C41 = Cl4 = C56. 6 constants. K constants the same as the C constants except K 4 4 = K 23 • 5 constants.

C

constants the same except Cl3 = C31, Cl6 = C61, = O. 7 constants. K constants the same except K 44 = K 23, K 66 = K 12 • 5 constants.

t?=.:l

u:

C

C45

ep ,.... ~

Group VII Tetragonal 4mm, 42m, 422, 4/mmm 7 constants Group vm Hexagonal 6,6,6/m 8 constants

Group IX Hexagonal 6m2, 622, 6mm, 6/mmm 6 constants

Group X Cubic 23, m3 4 constants

GrC1Up XI Cubic 43m, 432, m3m 3 constants

Group XII Isotropic 2 constants

I

M12 Ml1

M 31

M 31

0 0 0

0 0 0

M 11

Ml2 M 11

M M

M

M 33 0 0 0

M

I I

I

I

I

TABLE 9a-7. FOURTH-RANK TENSORS (Continued) 0 0 0 c constants the same except Cn = C31. 6 conM 18 0 stants. 0 0 M 33 0 0 K constants the same except K u = K 2 3, K 6 6 = 0 Mu 0 0 K 12 • 4 constants. 0 0 0 Mu 0 0 0 M 66 0

Mn M12

12

M 31 0 0 M 62

31

0 0 -M 6 2

M13

13 13

M 11

M

M l2 Mal

M 11

M 13

Mal

M aa

0 0 0

0 0 0

0 0 0

12

M 11

M

MIa M 12

M 11 M 13 0 0

0 0 0 M l1 M l2 M l2

0 0 0

M 11 M 12 M l2

0

0 0

12

0 M l2

M 11 M 12 0 0 0 M 12 M 11 M 12 0 0 0

M 13

M 13 M l2

M ll 0 0 0

M M

0 0 0 M 45 M 44 0

0 0 0 M 44 0 0

0 0 0 0 M 44 0

0 0 0 M 44 0 0

0 0 0 0 M 44 0

Mu

0 0 0

0 0 0 0 M 44 0

0 0 0 0 0 M 44

0 0 0 0

0 0 0 0 0

12

M 11 0 0 0

Mu 0 0

M 12

0 0 0

M l2

M 11 0 0 0

M 11

-

0 0

M

12

M ll

-

0

M 12

I

.......

I+>-

2M 6 2 c constants the same except Cl3 = cn, C61 = 0, -2M 62 5 constants. C45 = o. 0 K constants the same as C constants except K 44 0 K 2 3 • 4 constants. 0 M ll - M 12

0 0 0 M 44 -M 4 5 0

12

CD

0 0 0 0 0

M ll

-

C constants the same except

-

=

l/)

C31.

5 con-

stants. K constants the same as C constants, except K 4 4 = K 2 a • 4 constants.

a e~

t:;! I

tn >-3

> >-3

M l2

c constants the same except Cl2 = C13. 3 constants. K constants the same as C constants except K 4 4 = K 12 • 2 constants.

0 0 0 0 0

.ilI11

C13

t':1 ~

~ ~ tr: ~

o w

IKc constants the same. 3 constants. constants the same as constants c

K u = K 12•

I c and

M

12

2 constants.

K constants the same.

2 constants.

except

CRYSTALLOGRAPHIC PROPERTIES

9-15

relations, one can Interchange the ij with the kl moduli, and this reduces the number to 21. When it is not permissible to interchange ij with kl as in the magnetostrictive equations, (9a-8) there are 36 possible constants. Table 9a-7 for fourth-rank tensors shows how the crystal symmetries affect the number and relations among the independent constants. Type c relations indicated are for the case that ij can be interchanged with kl. A TABLE 9a-8. GLOSSARY OF TENSOR TERMS Symbol Meaning tiQ Increment of heat tiT Increment of temperature tiS Increment of entropy B, Magnetic flux density C,jkl Elastic stiffness constants D Electric displacements Do Electric displacement at optical frequencies dn,j Piezoelectric constants e Electronic charge emkl Piezoelectric constants E Electric fields gnij Piezoelectric constants h, Flow of heat per unit area hnkl Piezoelectric constants Hj Magnetic fields I, Electric current densities kij Thermal conductivities mijmn Photoelastic constants M i j kl Magnetostrictive constants p«, Pi Pyroelectric or pyromagnetic constants P, Polarization qn. q, Pyroelectric or pyromagnetic constants q,jkl Electrostrictive constants

Symbol T,j

Rid S,jkl

S,j T

T kl z, a';j

aijkl

{3,j Vmno

Eii Eiik

J.l.ii 7riikl

n., P';i fT';j

~ik

Meaning Thermal resistive constants Hall-effect constants Compliance constants Strain components Absolute temperature Stress components Length variable Temperature-expansion coefficients Magnetoresistive constants Dielectric or magnetic impermeabilities Electrooptic constants Dielectric constants Rotation tensor (see ref. 4, p.393) Temperature coefficients of stress at constant volume Electrochemical potential Magnetic permeability constants Piezoresistive constants Peltier thermoelectric coefficients Electrical resistivity constants Electrical conductivity constants Thermoelectric coefficients (Thomson)

third type of symmetry for fourth-rank tensors occurs when all the indices i, j, k, and l are interchangeable. Such a case occurs when the elastic moduli satisfy the Cauchy relationship. This is denoted by type-K symmetry in Table 9a-7. Table 9a-8 shows the symbols used in the above equations and their meaning. References for Section 9a-2 1. Mason, W. P.: "Piezoelectric Crystals and Their Application to Ultrasonics," D. Van

Nostrand Company, Inc., Princeton, N.J., 1640. 2. Nye, J. F.: "Physical Properties of Crystals," Oxford University Press, New York, 1957. 3. Huntington, H. B.: The Elastic Constants of Crystals, Solid State Phys. 7 (1958). 4. Mason, W. P.: "Physical Acoustics and the Properties of Solids," D. Van Nostrand Company, Inc, Princeton, N.J. 1958.

9b. Structure, Melting Point, Density, and Energy Gap of Simple Inorganic Compounds H. P. R.

FREDERIKSE

The National Bureau of Standards

Table 9b-1 lists the following properties of inorganic compounds: Crystal structure (see also Sec. 9a) Space group (see also Sec. 9a) Melting point (see also Sees. 4d and 4j) Density (see also Sees. 2b, 3f, and 4c) Energy gap (for definition see Sec. 9c-1) The compounds are listed not alphabetically but according to the location of the constituent elements in the periodic table (see Sec. 7b). The bulk of the table presents data on binaries; a few ternaries are also listed. Compounds are listed in groups beginning with the constituent elements from the first column and the seventh column and successively progressing toward the middle of the periodic system as follows (Roman numerals refer to columns):

lA-VII lA-VI IA-V IB-VII IB-VI IB-V IB-IV IIA-VII IIA-VI IIA-V IIA-IV lIB-VII

lIB-VI IIB-V IIIB-VI IIIB-V IVB-VII IVB-VI IVB-V IVB-IV VB-VI Transition metal oxides, sulfides, etc. Transition metal phosphides, arsenides, etc. Ternaries Noble gas compounds

With a few exceptions only those compounds have been listed for which at least one of the four properties has been measured. The list of compounds is, of course, far from complete; the cutoff is by necessity somew hat arbitrary. There is often some disagreement among authors or sources. For an evaluation of the reliability of a particular figure one should go back to the original literature. For further information the reader is referred to the references at the end of the table. Abbreviations cub cubic tetr tetragonal hex hexagonal orth orthorhombic mon monoclinic tricl triclinic rhomb rhombohedral Z zinc blende W wurzite per perovskite

d b.p. tr liq s ign calc met

decomposes boiling point transition (the compound listed is stable below the transition temperature) liquid sublimes ignites calculated metallic (conduction)

9-16

ENERGY GAP OF SIMPLE INORGANIC COMPOUNDS TABLE

9b-1.

CLASSIFICATION AND PROPERTIES OF INORGANIC COMPOUNDS

Structure

Compound IA- VII (alkali halides (ref. 7): LiF ........... LiCl. ......... LiBr .......... LiI ........... NaF .......... NaCI ......... NaBr ......... NaI .......... KF ........... KCI ...... ... KBr ..... ..... KI ........... RbF ..... ... RbCI ......... RbBr ......... RbI .......... CsF .......... CsCI. ...... CsCI (fJ) ...... CsBr ..... .. , CsI. ... .... ... IA- VI: LhO. - , ., . .. . Li2S. . . . . . . . . . Li2Se. . . . . . . . . Li2Te. Na20 .. . . . . . . .. Na2S .... Na,Se ........ Na2Te. ..... . K 2O.......... K 2S........ ,. lA-V: Li.N .......... NaN •......... NaN, ...... '" KN •.......... Rb,N ......... Li 3P .......... Na.P ......... Lis As ......... Na3As .. ...... K.As ......... Li.Sb ......... NaSb ......... NaaSb ........ KSb .......... KaSb ......... Cs 3Sb ......... Na 3Bi. ....... K,Bi ......... Cs 3Bi ......... IE-VII: CuCI (1) ...... CuCI (2) ...... Cu Br (1) ...... CuBr (2) ...... CuI .......... AgF .......... AgCl ......... AgBr ......... AgI (1) ....... AgI (2) ....... AgI (a) (146558°C) ...... "

9-17

Density, g/cm 3

(NaCI) (CsCI) (CsCI)

Fm3m Fm3m Fm3m Fm3m Fm3m Fm3m Fm3m Fm3m Fm3m Fm3m Fm3m Fm3m Fm3m Fm3m Fm3m Fm3m Fm3m Pm3m Fm3m Pm3m Pm3m

870 614 547 446 992 800 755 651 880 790 730 723 760 715 682 642 683 tr 460 646 636 621

2.601 2.068 3.464 4.061 2.79 2.164 3.210 3.665 2.505 1. 9917 2.754 3.114 2.88 2.76 3.35 3.55 3.586 3.988 3.54 (calc.) 4.43, 4.51

(CaF2) (CaF2) (CaF2) (CaF2) ..... (CaF2) (CaF2) (CaF2) (CaF2) (CuF 2) (CaF2)

Fm3m Fm3m Fm3m Fm3m Fm3m Fm3m Fm3m Fm3m Fm3m Fm3m

>1700

2.0b 1.66 2.91 3.24 2.27 1.856 2.58 2.90 2.32 1.80.

cub cub cub cub cub cub cub cub cub cub cub cub cub cub cub cub cub cub cub cub cub

(NaCl) (NaCI) (NaCI) (NaCI) (NaCl)

cub cub cub cub cub cub cub cub cub cub

(NaCI) (NaCI) (NaCI) (NaCI) (NaCI) (NaCI) (NaCI) (NaCl) (NaCI) (NaCI) (NaCI)

hex (fJ AhO,) cub hex hex cub

P6/mmm ..... . . . . . . R32 or R3m I4/mcm I4/mcm P6,/mmc P6J!mmc P6./mmc P63/ m mc P6./mmc P63/ m mc P2 1/n P63/ mmc . .... ..... P6 3/mmc Fd3m P6./mmc P63/mmc Fd3m

cub hex cub hex cub cub cub cub cub hex

F43m P63m C F43m P6,mc F43m Fm3m Fm3m Fm3m F43m P63mc

hex orth (?) hex tetr tetr hex (fJ Ah0 3) hex hex hex hex hex mon hex (fJ AhO,)

.......... ..

cub

Melting point, °C

Space group

(Z) (W) (Z) (W) (Z) (NaC!) (NaC!) (NaCI) (Z) (W)

. .......

"

.......

................. ................. s 950 >875

................. ................. 471 840 19 d 340 350

...........

Energy gap, eV

",12 ",10 "'8.5 ~5.9 ~1O.5 8. i

7.7 ~5.8

10.9 8.5 7.8 >6.2 10.4 8.2 7.7 ~6.1

10.0 ~8.0 ~7.5

7.0-8.0 ~6.3

2-3

tr

................. ................. d

................. . ................ ................. >950 465 856 605 812

................. 773

................. ................. tr 407 422 tr 382 488 605 435 455 430

................. 558

I

1.853 2.038 2.788 1.43 1.74 (calc) 2.42 (calc) 2.328 2.14 (calc) 2.96 (calc) 4.03 (calc) 2.67 (calc) . ........ " 2.35 (calc) 5.01 (calc) 3.70 (calc) 2.98 (calc) 5.01 (calc)

,....Q.8 0.9 0.8 0.8 0.5-0.6

4.136

3.31

4.72

2.98

5.667 5.852

3.06

...........

........... 6.0 5.68

3.0 2.9 2.8

9-18

SOLID-STATE PHYSICS TABLE

9b-1.

CLASSIFICATION AND PROPERTIES OF

INORGANIC COMPOUNDS

Compound

IE-VII (Cant.): AuOI .......... AuBr ......... AuI .......... IE-VI: CuO .......... CU20 ......... CuS .......... CU1.8S........ CUtS (a) ...... CU28 ({3) ...... CuSe ......... CU2Se ({3)..... Cu 2Te ........ AgO .......... Ag20 ......... Ag2S (fJ) ••••.. Ag2S (a) .. .. " Ag2Se ({3). . . . . Ag2Se (a) . . . . . Ag2Te (a) ..... AuTe2 ........ IE-V: CusN ........ , CUsP ......... CusAs ........ Cu2Sb ........ Cu 3Sb ........ Ag 3Sb ........ AuSb2 ........ Au2Bi ......... IE-IV: AuSn ......... Au2Pb ........ IIA-VII: BeF2 ......... BeCh ......... BeBr2 ......... BeI2 .......... MgF2 ......... MgBrq ........ MgCh ........ Mg Is ......... CaF2. ........ Ca.Cl s......... Ca Brs . . . . . . . .

CaIs .......... SrF2 .......... SrCh ......... Sr Br s......... Srh .......... BaF2 ......... BaCh (1) ... ,. BaCh (2) ..... BaBrs ........

BaI2 .......... IIA-VI: BeO .......... BeS .......... BeSe ......... BeTe ......... MgO .........

Melting point, °c

Structure

Space group

.............

............. ............. P42/n

............. .............

cub (CaF 2) hex cub (CaF2) hex cub cub (CU20) man cub (CsCI) man cub (CsCl) man man

A2/a Pn3m P6s/mmc Fm3m(?) cmma} Cm2a (?) C2ma Fm3m(?) P63/mmc Fm3m P6/mmm ? Pn3m P2t/n Pm3m P21/n Pm3m P2t/n C2/m

cub hex hex tetr hex orth cub (FeS2) cub (spinel)

? ? P3c P4/nmm ? ? Pa3 Fd3m

hex (NiAs) cub

P63/m mc Fd3m F4132 } ?

man cub hex cub (NaCI?) orth

............. .............

P4/mnm P3m1 P3ml P3m1 Fm3m Pnnm

tetr (Sn02) hex (CdI2) hex (CdI2) hex (Cdh) cub orth ............. hex cub (CaF2) cub (CaF2) orth ............. cub (CaF2) mon cub (CaF2) orth orth

Fm3m Fm3m Pbnm . ............ Fm3m ? Fm3m Pnam Pnam

hex cub cub cub cub

P6smc F43m F43m F43m Fm3m

(W) (Z) (Z) (Z) (NaCI)

p~~"""'"

.

Density, g/cm s

6.40 6.0 4.681 5.6 (170°C) 5.8

1100 ................. 1148 1125 d >100 d 300 tr 175 825 ................. 897 955 464

5.6 5.99 6.75 7.41 (calc) 7.44 7.143 7.326 7.31 . .......... 8.187 8.350 9.31 (calc)

9.74 9.98 15.46

418

11.6

2550 ................. .. , .............. . , ........ ....... 2800

~1.95

2.2

~1.3

met ~0.075

met (?) 0.17

6.12 (calc) 7.15 7.85

830 585 687 559(?) 460(?) 373

800 s 405 s 488 480 1263 711 714 d 1418 782 760 575 1400 875 643 402 1320 tr925 962 850 740

Energy gap, eV

7.4 7.9 8.25

d 1236 tr 103 ................. tr 105

d 300

Ibam

............. .. ...... .....

tr 170 (...... AuCIa) d 115 d 120

.................

.............

tetr orth

(Continued)

2.01 1.90 3.465 4.36 (calc) 3.148 3.72 2.32 4.43 3.18 2.22 3.353 3.956 4.18 3.052 4.216 4.549 4.893 3.856

I

~11

~1O

4.886 5.236 3.01-3.09 2.36 4.32 (calc) 5.09 (calc) 3.65

-

7.3

ENERGY GAP OF SIMPLE INORGANIC COMPOUNDS TABLE

9b-1.

CLASSIFICATION AND PROPERTIES OF

INORGANIC COMPOUNDS

Compound

II A- VI (Cont.): MgS .......... MgSe ......... MgTe ........ CaO .......... CaS .......... CaSe ......... CaTe ......... SrO .......... SrS ........... SrSe .......... SrTe ......... Baa .......... BaS .......... BaSe ......... BaTe ......... IIA-V: BeaN2 ....... , Be.P2 ......... MgaN2 ........ MgaP2 ........ MgaAS2. ...... MgaSb2 ....... Mga Bi2 ....... CaaN2. ....... Ca aP2......... CaaAS2........ Ca aSb2........ Ca aBi2....... , lIA-IV: Be2C ......... Mg2Si ........ Mg2Ge ........ Mg2Sn ........ Mg2Pb ........ Ca2C ......... Ca2Si. ........ CaSi2 ......... CB2Ge ........ Ca2Sn ........ Ca2Pb ........ lIB-VII: ZnF 2.......... ZnCh ......... ZnBn ........ Znh .......... CdF2......... CdCh. ........ CdBr2 ........ CdI 2.......... HgF2 ........ , Hg2F2 ........ HgCh ....... , Hg2C12 ........ HgBr2 ........ Hg2B r2 ....... HgI2 ......... HgI2 .......... Hg2h ......... lIB-VI (refs. 11, 12): ZnO .......... ZnS ({J) ....... ZnS (a) ..... . . ZnSe ......... ZnTe .........

Space group

Structure

cub cub hex cub cub cub cub cub cub cub cub cub cub cub cub

(NaCI) (NaCl) (W) (NaCI) (NaCI) (NaCI) (NaCI) (NaCI) (NaCI) (NaCI) (NaCI) (NaCI) (NaCl) (NaCl) (NaCl)

Fm3m Fm3m P6mc Fm3m Fm3m Fm3m Fm3m Fm3m Fm3m Fm3m Fm3m Fm3m Fm3m Fm3m Fm3m

cub cub cub cub cub hex hex cub cub cub cub cub

(ThO a) (ThO a) (TI20a) (TI20a) (ThO a)

la3 la3 la3 la3 la3 pam pam la3 la3 (?) la3 (?) la3 (?) la3 (?)

(ThO a) (ThO a) (ThO a) (ThOa) (ThO a)

9-19

(?) (?) (?) (?)

cub (CaF2) cub (CaF 2) cub (CaF2) cub (CaF 2) cub (CaF2) tetr tetr hex orth tetr .............

Fm3m Fm3m Fm3m Fm3m Fm3m

(Continued) Melting point,

°c

Density, g/om 3

2.82

d

................. 2600

................. ................. 2415 ................. ................. ................. 1923

.................

"'2200

................. d 1500

................. 800 930 715 1195 >1600 d

3.86 (calc) 2.62 2.80 7.59a 3.9-4.8 3.7 4.53 (calc) . .......... 4.7-5.7 4.25

2.70 9 2.234 2.71 2.05 6 3.148 4.09 5.94 2.63 2.51 2.50

1.9 1.88 3.09 3.591 3.29

d >2100 1102 1115 778 550 920 1220

...........

............. . ............

1122 1150

........... ...........

tetr (Sn02) hex (CdCh) hex (CdCI2) (?) hex (CdCh) cub (CaF2) hex (rhomb) hex (rhomb) hex (W) cub (FeS2) cub orth tetr orth tetr tetr orth tetr

P4/mnm Ram Ram (?) Ram Fm3m Ram Ram P6mc Pa3 l4/mmm Pmnb I4/mmm Bb2m I4/mmm P4/nmc ............. l4/mmm

872 262 394 446 1110 568 568 387 d 645 570 277 s 400 241 s 345 tr 126 259 s 140

hex cub hex cub cub

P6mc F43m P6mc F43m F 43 m I

6-7

"'6 "'2 "'2 "'4.8

0.82 met (1)

928

............. Ram Pnam

(W) (Z) (W) (Z) (Z)

Energy gap, eV

0.77 0.6-0.7 0.3 met (1) 1.9

2.456

,

1975 tr 1020 1850 (150 atm) "'1500 1238

4.84 2.91 4.21g 4.696 6.64 4.047 5.192 5.4-5.6 8.95 8.73 5.6 6.47 6.05a 7.307 6.28 6.271 7.70 5.7 4.102 4.08 5.65 5.54-6.39

0.9 0.4-0.5

>6.0

3.436 3.84 3.91 2.83 2.39

9-20

SOLID-STATE PHYSICS TABLE

9b-1.

CLASSIFICATION AND PROPERTIES OF

(Continued)

INORGANIC COMPOUNDS

Compound

lIB-VI (refs. 11, 12) (Cont.) : CdO .......... CdS (fJ) ....... CdS (a) ....... CdSe ........ , CdTe ......... HgO .......... HgS (a) ....... HgS (fJ) ....... IigSe ......... HgTe ......... lIB-V (ref. 13): Zn aN2 ........ ZnaP2 (1) .... ' ZnaP2 (2) ...... ZnaAS2 (1) ..... ZnaAS2 (2) ..... ZnSb ......... CdaN2. ....... Cd aP2 (1) ..... Cd aP2 (2) ..... Cd aAs2 (1) .... Cd aAB2 (2) ... , Cd aSb2........ CdSb ......... IIIB-VII: B2F4 .......... BCla .......... BBra ......... BI a........... AIF a.......... AICla ......... AlBra ......... GaF a......... GaCI2 ......... Gaia .......... InFa .......... InCI~ ......... InCl a......... InBr .......... InI ........... TIF .......... TICI .......... TICla ......... TlBr .......... TlI .......... TlI .......... IIIB-VI )ref. 8): B 2Oa.......... B 2S5 • • • • • • • • • • B 2Sa.......... B2Sea ......... AhOa (a) ...... AhOa (fJ) ...... AhOa h) ...... AhSa ......... AhSea ........ AhTea ........ Ga20a ........ Ga20 ......... Ga2Sa (fJ) ... . . , Ga2Sa (a) ..... GaS .......... Ga2S ......... Ga2Sea (fJ) .....

Structure

Energy Density, I gap, eV g/cm 3 I - - - - -------1··----_·-

Melting point,

Space group

°c

cub (NaCI) cub (Z) hex (W) hex (W) cub (Z) orth hex cub (Z) cub (Z) cub (Z)

Fm3m F43m P6me P6me F43m Pmnn P3121 F43m F43m F43m

cub cub tetr cub tetr orth cub cub tetr cub tetr mon orth

Ja3 Pn3m P4/nme Pn3m P4/nme Pben Ja3 Pn3m P4/nme Pn3m P4/nme ............. Pben

mon hex hex hex hex mon mon hex orth orth hex orth mon orth orth orth cub mon cub orth cub

P21/n P6a

cub cub cub cub hex hex cub hex hex hex hex

s 1559 s 685 1750 (100 attn) >1258 1098 d 100 tr 386 s 583 798 670

?

C2/m Amam Amam Fmmm Pm3m C2/m Pm3m Amam Pm3m

(Fe20a)

P6mc P6me R3e

P3l

............. .............

R~~"""'"

.

............. .............

.............

hex (W) P6me cub (Z) ........ F43m hex P6/mmc

.............

.............

hex (W)

P6me !

1015

................. 544

................. ................. ... ............. 721 421 456 56 -107 - 46 43 1040 s 178 97.5 >1000 170.5 212 1170 235 s 400 220 351 b.p.300 430 25 460 tr 175 440

?

P6 a/mme P413

>420

-

P6a R32 A2/m P21/a R3e Penn Amma R3e

or hex (?) or hex (?) or hex (?) or hex (?) (Fe20a) (NiAs) (spinel)

................. .................

294 390 310 d 2050 2040 tr to a 1118

................. 900 1740 >660 1255 tr 550 965 >800 1020

8.15 4.87 4.82 5.81 6.20 11.23 8.176 7.65 8.24 (calc) 8.12 (calc)

I

2.2 (?) 2.5 2.582 1.84 1.007 2.5 met met

6.4 (calc) 4.678 (calc) 4.54 (calc) 5.578 4.21-4.76 6.383

1.0 0.56

5.956 (calc) 5.956 6.21 4.25

0.6

6.92

0.48

0.13

1.92 (calc) 1.80 (calc) 3.41 (calc) 3.197 (calc) 2.48 (calc) 3.205 2.74 ? 3.64 4.96 5.39 (calc) 8.23 7.02 7.54

I

3.41 3.02

7.45 (calc) 2.44 1. 85 1. 55 3.99 3.30 3.619 2.32 3.21 4.54 6.44 (calc) 4.77 3.67 (calc) 3.63 3.86 4.18 4.92

8.3 4.1 3.1 2.5 4.4 ~2.5

2.85 ~2.9

9-21

ENERGY GAP OF SIMPLE INORGANIC COMPOUNDS

9b-1.

TABLE

CLASSIFICATION AND PROPERTIES OF

INORGANIC COMPOUNDS

Structure

Compound

Space group

(Continued) Melting point, °C

Density, g/cm 3

Energy gap, eV

.................

...........

-1.9 2.04

lIIB-VI (ref. 8) (Cant.):

Ga2Sea (a) ..... GaSe ......... Ga2Se ......... Ga2Tea (fJ) . . , . Ga2Tea (a) .... GaTe ......... In20a ......... InO .......... In20 .......... In2Sa ......... InS ........... In2S .......... In2Sea (fJ) .... · In2Se (a) ...... InSe .......... In2Se ......... In2Tea (a) ..... InTe ......... In2Te ......... TI20a ......... ThO .......... ThSa ......... TIS ........... ThS .......... ThSea ........ TISe .......... ThSe ........ , ThTes ........ lIIB-V (refs. 9, 10): BN ........... BP ........... AIN .......... AlP .......... AlAs .......... AISb .......... GaN .......... GaP .......... GaAs ......... GaSb ......... InN .......... InP .......... InAs .......... InSb .......... InBi .......... TISb .......... TIBi .......... IVB-VII: CBr4 (a) ...... CBr4 (fJ).··· .. CI4 ........... SiBn Sik .......... GeBn .. GeBr4 ........ GeI4 .......... SnCb ......... SnCI4 ......... SnBr2 ......... SnBr4 ......... SnI2 .......... SnI4 ..........

cub (Z) hex

F43m P63/m mc

hex (W) cub (Z)

P6mc F43m

cub (ThO a)

la3

............. .............

.............

.............

.............

.............

cub

Fd3m

hex

P6a/ mmc

............. ............. ............. ............. .............

cub (Z) tetr

.............

. ............ . ............ . ............ . .............

F~3~""""

.

14/mcm

.............

. ................ 790 tr 670 824 d 850 2650-700 (in vac) 1050 692 653 890 tr 196 660

. ................ 667 696 460 717 300 260

cub

la3

tetr hex

I4/mcm R3 or R3

.................

tetr

14/mcm

.................

............. .............

............. ............

cub cub hex cub cub cub hex cub cub cub hex cub cub cub tetr cub cub

(Z) (Z) (W) (Z) (Z) (Z) (W) (Z) ........ (Z) (Z) (W) (Z) (Z) ........ (Z)

............. . ............

. ............

.............. F43m F43m P6smc F43m F43m F43m P6mc F43m F43m F43m P6mc F43m F43m F43m

.............

(CsCI) (CsCI)

mon cub cub

.............

cub (FeS2?)

.............

.............

cub (FeS2) orth

.............

orth orth mon cub (FeS2)

Pm3m Pm3m

............. P43m P43m . ............ Pa3

............. .............

Pa3

............. ............. ............. ............. .............

Pa3

5.03 5.02

960

5.57 5.44 7.18

1.2 or 1.5 1.7 -2.8

6.99 4.63 5.18 5.87

""'2.0

5.48 5.55 6.17 5.75 6.29 6.47 10.19

1.2 1.05 -1.0

7.62 8.0

448

-1.0 0.57

5.175

398 428

3.26 2.424 (calc) 3.598 4.34 6.10

................. 1600 1060

................. ~1350

1280 728

................. 1055 942 525 110

4.6

2.20

s 3000 ign 200 >2200

........... 44

4

•••

••

4

•••••

44.44

•••

6.88

........... 4

•••••

4.4

4.4.4

•••••••

230 tr 47 90 d 171 5 120.5 122 26.1 144.0 247 -33 232 31 320 145

•

........... 3.42 4.32 2.814 3.132 4.322 3.9 2.23 (liq) 5.12 3.34 (liq) 5.21 4.46

-3.3 2.5 2.3 1.55 2.35 1.35 0.7 2.4 1.3 0.35 0.17 met

9--22

SOLID-STATE PHYSICS TABLE

9b-1.

CLASSIFICATION AND PROPERTIES OF

INORGANIC COMPOUNDS

Structure

Compound

IVB-VII (Cont.): PbFa ......... PbFa ......... PbC12 ......... Pb Cl s .....••.. PbBra ........ PbI .......... Pb Is .......... IVB-VI: SiOa: a-Cristohalite ..... /3-Cristohalite ..... a-Quartz .... /3-Quartz .... a-Tridymite. I /3-Tridymite. Fused silica. SiSa .......... SiS ........... GeOL ........ GeSz .......... GeS .......... GeSe ......... GeSez ......... GeTe ......... Sn02 ......... SnO .......... SnSa .......... SnS ........... SnSea ......... SnSe .......... SnTe ......... PbOa ......... PbO (red) ..... PbO (yellow) .. PbaO ......... PbS .......... PbSe ......... PbTe ......... IVB-V: SnAs ......... SnaAsz ........ SnSb ......... IVB-IV: SiC ........... SiC (carborundum) ....... VB- VI (ref. 8): ASaOa (1) ..... Asa03 (2) ..... AszSa ......... AsaSe •........ AsaTe •........ SbaO a (1) .... , SbaO a (2) ..... SbaSI ......... SbaSes ........ SbaTel ........ BiaOI (1) ...... BizOa (a) ...... BizOa ({3)...... BiaS a ......... BizSe•........ BitTe•........

orth cub (CaFs) orth ............. orth

.............

Space group

,

Melting point, °C

tr 200

Pnam Fm3m ? . ...

(Continued)

........

Pnam

. ............

822 501 -15 373 d 300 402

Density, g/cm l

8.37 7.66 5.85 3.18 6.71 (calc) 6.18

hex

P3m1

pseudocub.

P212121

cub hex hex orth hex tetr orth

P213 P3221 or P3121 P6222 or P6,22

1728 tr 600

.............

1680

2.3

1090

2.02 1.85 4.7 3.01 4.01

............. hex orth orth orth orth cub (NaCl) tetr tetr (PbO) hex (W) orth

............. orth cub (NaC!) tetr (SnOz) tetr orth cub (CU20) cub (NaCl) cub (NaC!) cub (NaCl)

.................

Energy gap, eV

""5.0

2.57

2.30 2.32 2.66

P6s/mme [bam . ............. P3221 Fdd2 P6nm P6nm

.............

Fm3m P4/mnm P4/nmm P6me (?) P6nm

............. .............

Fm3m P4/mnm P4/nmm Pca2 Pn3m Fm3m Fm3m Fm3m

cub (NaCl) orth cub (Na.Cl)

Fm3m

.............

Fm3m

hex (W)

Pb anc

cub (Z)

F43m

mon cub mon hex (rhomb) mon cub orth orth orth hex (rhomb) orth cub tetr orth hex (rhomb) hex (rhomb)

P21n Fd3m P21n R3m (?) P2rn (?) Fd3m Pnaa Pbnm Pbnm R3m (?)

............. Pn3m P4b2 Pbnm R3m (?) R3m

................. 1115 ,..,800 625 780 707 725 d 1127 d 700-950 d

880 650 860 800 d 290 888

................. d

1114 1065 905

...........

1.8 1.0

4.56 7.0 6.45 4.5 5.08 5.0 6.18 6.48 9.33-9.44 9.13 9.52 8.35 7.5 8.1-8.2 8.16

2.3 ,..,1.1 ,..,1.0 1.3 0.3 ,..,2.6 0.37 0.27 0.33

600 585 425 ,..,2700

................. 315 s 193

300 360 362 656 656 550 611 629 820 tr 704 ................. 850 (?)

710 580

3.17-3.22

3.1

3.216

2.86

4.14 3.874 3.43 4.75 ...........

5.1-5.8 ,..,5.7 4.64 5.8

1.3 1.0-1.2

...........

1.7 1. 2-1.35 0.3

8.9 8.2 9.14 7.39 6.82 7.65

1.1-1. 3 0.35 0.15

.:mNERGY GAP OF SIMPLE INORGANIC COMPOUNDS TABLE

9b-1.

CLASSIFICATION AND PROPERTIES OF

INORGANIC COMPOUNDS

Compound

9-23

Structure

Space group

I

(Continued)

Melti~tPoint.

---------Dgi~~;'

Transition Metal Oxides, Sulfides, Selenides, and Tellurides SC20, ........... Ti02 (rutile) ..... Ti 20, ........... TiO ............ V201 ........... , V20•........... VaO, ............ Cr20, ........... Mn02 ........... Mn20, .......... MnO ........... MnaO •.......... MnSa ........... MnS ............ MnSe2 ........ ,. MnSe ........... MnTe' .......... MnTe ........ ,. FeaOa (hematite) Fe,O, ('Y) . . . . . . . FeO ............ Fe,O. (magnetite) FeS ............ FeS. (1) (pyrite) . Sz (2) ......... - Se ............ FeSez ........... CoO ............ CoS ............ CoS•............ Co,S•........... CoSe ........... CoTe ........... NiO ............ NiS (millerite) ... NiS ({j) ......... NiSz ............ NiSe ............ NiTe ........... Zr02 (1) ........ Zr02 (2) ........ Nb20 •.......... Nb20a .......... Mo02 ........... MoO, ........... MoS2 (molybdenite) .......... Ta 20 •........... W02 ............ WO, ............ Th02 ........... U02 ............

la3 P4/mnm Rae Fm3m Pnm2 P4/mnm Rae Rae P4/mnm la3 Fm3m l4/amd Pa3 Fm3m Pa3 Fm3m Pa3 P6,/mmc Rae P4,3 or P213 Fm3m Fd3m P6,/mme Pa3 Pnnm P6a/mmc Pa3 Fm3m P6,/mmc Pa3 Fd3m P6 a/mmc P6a/ mmc Fm3m

cub (ThO a) tetr (Sn02) hex (Fe20a) cub (NaCI) orth tetr (Sn02) hex (Fe20a) hex (Fe20,) tetr (Sn02) cub (ThO,) cub (NaCl) tetr cub (FeSz) cub (NaCI) cub (FeS2) cub (NaCI) cub (FeSz) hex (NiAs) hex cub cub (NaCI) cub (spinel) hex (NiAs) cub orth hex (NiAs) cub (FeSz) cub (NaCI) hex (NiAs) cub (FeSz) cub (spinel) hex (NiAs) hex (NiAs) cub (NaCl) hex hex (NiAs) cub (FeS.) hex (NiAs) hex (NiAs) cub (CaF2) mon orth

..............

P6a/mmc Pa3 P6 ,/mmc P6,/mmc Fm3m P2I/a

............. .............

.............

tetr (Sn02) orth

P4/mnm Pbnm

hex (NiAs) orth tetr (Sn02) tricl cub (CaF2) cub (CaF2)

P6,/mmc

.............

P4/mnm

.............

Fm3m Fm3m

................. 1835 2130 1750 700-800 1967 1970 1990 d 535 d 1080 1650 1705 d d

.................

................. ................. 1565

................. 1420 d 1538 1193 1171 tr 450

................. 1935 >1116

................. ................. .................

3.861 4.283 4.6 4.93 3.577 4.4 4.78 5.215 5.026 4.5 or 4.8 5.4 4.8 3.46 3.95

. .......... 5.59 6.15 (calc) 5.24 4.59 5.7 5.17 4.84 5.005 4.92

6.7-6.9 5.41 4.6 4.3 (calc) 8.46

2715 2700 1520 1772

5.35 5.82 4.5-4.6

................. 795 1185 d 1470 ign 1470 3050 2227

4.92 8.736 12.11 7.16 9.87 10.9

I

hex hex (NiAs) orth orth hex (NiAs) tetr hex (NiAs) cub (FeSO orth hex (NiAs)

............. P6a/mmc Pnam Pnam P6a/mmc P4/nmm P6a/mmc P2,3 Pnam P6 a/mmc

. ................ 1100 1190 d 400 809 948 1280 >1000 1020

1.2

--4.0

6.44-6.47 4.5

Transition Metal Phoaphides, Arsenides, etc. CrAs ........... CrSb ........... MnP ........... MnAs ........... MnSb ........... Mn2Sb ......... MnRi ........... MnSi. .......... FeP ............ FeAs ('I) ........

0.15 2.5

5.0 5.7-6.7 5.45 4.27 4.86 7.65

2090 797 797

................. .................

3.05 met

6.35 5.49 --6.2

5.9 5.2 or 6.07 7.83

",1.0

9-24

SOLID-STATE PHYSICS TABLE

9b-1.

CLASSIFICATION AND PROPERTIES OF

INORGANIC COMPOUNDS

Compound

Space group

Structure

(Continued) Melting point,

Density, g/cm a

°c

Energy gap, eV

Transition Metal Phosphides, Arsenides, etc. (Cant.): FeSb ........... FeSi ............ NiAs ........... NiSb ........... NiSi ............

hex (NiAs) cub hex hex cub (FeSi)

P6 a/mmc P213 P6a/mmc P6a/mmc P213

-WOO 1410 968 1158 1000

6.21 7.72 7.54

Ternaries (refs. 17, 18) CuFeS2 (chalcopyrite) ........ CuAIS2. ........ CuInS2 ......... CuInSe2 ......... CuInTe2 ........ CuTIS2 ......... AgInS2 ......... AgInSe2 ......... AgInTe2 ........ ZnSiAs2 ......... ZnGeP2 ......... CdGeP2 ......... ZnGeAs2 ........ CuaSbSa ......... CuaAsSa ......... AgaSbSa ......... AgaAsSa ......... AgSbS2 ......... AgSbSe2 ........ AgSbTe2 ........ MgAh04 (spinel). ZnFe204 ........ CuFe204 ........ NiFe204 ......... MnFe204 ........ ZnAhS4 ......... CaIn2S4 ......... HgIn2S4. ........ CaTiOa (perovskite) ... BaTiO a (1) ...... BaTiOa (2) ...... SrTiOa .......... PbTiOa (2) ...... FeTiO a......... PbZrOa (2) ...... KNbO a (1) ...... KNbO a (2) ...... KTaOa (1) ...... Na.NbOs (1) ..... LaMnOa ........ NaCIO a......... NaBrOa ......... NaIOa .......... KCIO •..........

tetr tetr tetr tetr tetr tetr tetr tetr tetr tetr tetr tetr tetr

I42d 142d 142d 142d 142d 142d 142d 142d 142d 142d 142d 142d 142d

................. ................. ................. ................. ................. .................

cub cub hex hex mon cub cub cub cub (spinel) cub (spinel) cub (spinel) cub (spinel) cub (spinel) cub (spinel) cub (spinel)

143m 143m R3c R3c A2/a

................. ................. .................

............. .............

Fd3m Fd3m Fd3m Fd3m Fd3m Fd3m Fd3m Fd3m Pm3m Pm3m P4/mmm Pm3m P4/mmm R3 P4/mmm Pm3m

cub cub (per) tetr cub (per) tetr hex tetr cub (per) orth cub (per) cub (per) pseudo cub (distorted per) cub (FeSi) cub (FeSi) orth mon

.............

Pm3m Pm3m

.............

P213 P213 Pnma P21/m

1085

................. 950 990 790

.... ............. 850

550 640

611 555 2135 1590

................. ................. ................. ................. ................. ................. 1915 1618 tr 120 1910 tr 490 1470 tr 233 1039 tr 434 1357 1450

................. 248 381

... . ............ 368

4.1-4.3 3.45 4.71 5.65 6.00 6.07 4.97 5.80 6.08

. .......... 4.04

........... 5.26 4.4-5.1 -4.5 5.85 5.69 (calc) 5.2-5.3 6.64 7.12 3.57 5.29 5.42 5.268 4.52 3.30 4.10 5.79 -4.0 "'6.0 6.02 (calc) 5.11 (calc) 7.94 (calc) 4.4-4.9 8.10 (calc) 4.634 (calc) 7.022 (calc) 4.609 (calc) 6.89 (calc) 2.49 3254 -4.26 2.32

Noble gas compounds (ref. 19): XeF2 ........... tetr XeF4 ........... mon XeFe ........... ............. XeO •........... orth

14/mmm P21/n

. ............

P212121 .._-

_.~

140 -114 46

.................

4.32 (calc) 4.04 (calc) 4.55

0.53 2.5 1.2 0.92 0.95 1.9 1.18 0.96 2.1 2.2 1.8 >0.6 -1.0 -1.0 -1.9 -2.0 -0.7 -0.6

3.7 3.5 3.4

3.5

ENERGY GAP OF SIMPLE INORGANIC COMPOUNDS

9-25

References to Table 9b-1 General References 1. "Handbook of Chemistry and Physics," 46th ed., Chemical Rubber Publishing Company, Cleveland, Ohio, 1966. 2. "Lange's Handbook of Chemistry," McGraw-Hill Book Company, New York, 1952. 3. NBS Circ. 500. 4. Donnay, J. D. H.: "Crystal Data," 2d ed., American Crystallographic Association, 1963. 5. Wyckoff, R. W. G.: "Crystal Structures," 2d ed., vols. 1-3, Interscience Publishers, a division of John Wiley & Sons, Inc., New York, 1963-1965. 6. Hansen, M. and Anderko, K.: "Constitution of Binary Alloys," 2d ed., MeGraw-Hill Book Company, New York, 1958.

Specific References 7. Eby, Teegaarden, and Dutton: Phys. Rev. 116, 1099 (1959) (energy gap). 8. Aigrain, P., and 1\1. Balkanski: "Selected Constants of Semiconductors," Pergamon Press, New York. 1961. 9. Hannay, N. B., ed.: "Semiconductors," Reinhold Publishing Corporation, New York, 1959. 10. Willardson, R. K., and A. C. Beer, eds.: "Semiconductors and Semimetals," vols. 1-3, Academic Press, Inc., New York, 1966-1968. 11. Reynolds, D. C., et al.: Phys. Stat. ssua: 9,645 (1965); 12,3 (1965). 12. Harman, T. C.: "Proceedings International Conference on II-VI Compounds" D. G. Thomas, ed., W. A. Benjamin, Iric., New York, 1966. 13. Turner, W. J., et al: Phys. Rev. 121, 759 (1961). 14. Morin, F. J.: ref. 9, p. 600. 15. Levin, E. M.: H. F. McMurdy, and F. P. Hall: "Phase Diagrams for Ceramists," vols. 1 and 2, American Ceramic Society, Columbus, Ohio, 1956, 1959. (Oxides, melting points) 16. Hutson, A. R.: ref. 9, p. 541. 17. Hahn, Harry, et al.: Z. Anorg. Allqem; Chem. 271, 153 (1953); ibid. 279, 241 (1955). (Chalcopyrites: structure) 18. Winkler, U.: Helv. Phys. Acta 28, 633 (1955). (Appendix 2: selected semiconductors: energy gaps) 19. Hyman, Herhert H., ed.: "Noble Gas Compounds," University of Chicago Press, Chicago, 1963.

9c. Electronic Properties of Solids H. P. R. FREDERIKSE 1

The National Bureau of Standards J. C. SLATER 2

University of Florida

DEFINITIONS AND FORMULAS Dc-I. Energy-band Theory of Solids (refs. 1, 2, and 3). According to quantum theory an electron bound to an atom can exist in only a limited number of discrete energy states. A large number of noninteracting identical atoms will all have the same set of allowed discrete energy states. If, now, these atoms are brought closer together and finally to their actual distances in a solid, they begin to interact and the energy levels will split. In a periodic array of atoms (crystalline solid), the allowed states tend to cluster into continuous groups of energy levels called energy bands. These energy bands mayor may not overlap. The solid may also consist of two, three, or more kinds of different atoms (compounds). Metal: A material in which the highest occupied energy band is only partly filled. The resistivity of metals increases with temperature; the temperature dependence is close to linear except at low temperatures. Semiconductor (refs. 1, 2, and 3): A material in which the highest occupied energy band (valence band) is completely filled at absolute zero. The energy gap between the valence band and the next higher band (conduction band) is between zero and 4 or 5 eV. The resistivity decreases in certain temperature ranges exponentially with increasing temperature. Insulator: A material in which the highest occupied energy band is completely filled. The difference between insulators and semiconductors is only gradual. Materials with energy gaps larger than 4 or 5 eV are usually called insulators. The resistivity of pure insulators at room temperature is extremely high. At elevated temperature ionic conduction often dominates electronic conduction. Effective MaSs (refs. 1, 2, and 3). Near the top or the bottom of a band the energy is generally a quadratic function of the wave vectors, so that by analogy with the expression g = p2/2m = fl. 2k 2/ 2m for free electrons we can define an effective mass m * such that o2e/ok 2 = 1I. 2/ m* (p = momentum, k = wavevector, ", = Planck's constant X 1/211"). The effective mass of electrons is positive. Near the top of a band m* is negative, so that the motion corresponds to that of a positive charge (hole). Dc-2. Distribution Function, Fermi Energy, etc. The probability that a given state of energy g is occupied is given by 1

f =&-&, ---

.v + 1

1

2

Definitions and Formulas. Bibliography of Energy Band Calculations.

9-26

ELECTRONIC PROPERTIES OF SOLIDS

9-27

This is called the Fermi-Dirac distribution function. SF is the Fermi energy. At absolute zero SFo has the significance of a cutoff energy. All states with energy less than SFo are occupied, and all states with energy greater than SFo are vacant. The distribution is called degenerate when SF » kT and nondegenerate when SF «kT. In the latter case the distribution function becomes

This is known as the Maxwell-Boltzmann or classical distribution function. The density of states (or number of states with energy s) per unit volume is given by

_ 41T"(2m*)1 l

g (S ) -

h3

S

(for spherical energy surfaces). The Fermi energy or Fermi level is determined by the total number of electrons per unit volume (no). One calculates for Fermi-Dirac statistics:

where and for Maxwell-Boltzmann statistics: n oh 3

SF

= kT In 2 (21T"m *kT)1

9c-3. Transport Properties. Electrical Conductivity. duction occurs, the current density J is given by

J

=

In a solid where ohmic con-

uE

where u is the conductivity and E the applied electric field. In a homogeneous isothermal crystal u is a tensor having the symmetry of the crystal. Mobility. The drift mobility of charge carriers is defined as the drift velocity per unit applied electric field (vD/E). The relation to the collision time Tc is given by p.(D)

=

eTc

m*

Hall Effect. When a magnetic field is applied to a conductor carrying a current density J, an electric field En (Hall field) is developed given by the relation En = RJ X B

R is called the Hall coefficient and B is the magnetic induction. When the current density is in the length direction of the sample (J z ) and the field in the z direction, the Hall coefficient (for electrons or holes) is

R=+.!-

where n e p.

= =

=

a = r =

ne carriers/ em 3 1.6 X lO-u coul cmt/volt-sec (ohm-em):'! a scattering factor of the order of 1

+~ u

9-28

SOLID-STATE PHYSICS

Hence R = cm f.L is called the Hall mobility and is usually somewhat different from the drift mobility. M agnetoresistance. The resistance of a metal or semiconductor is altered by the presence of a magnetic field. The relative change in resistance is 3/couI.

t!t.p = aB2 1 + J.'2B2 p The theory for a single isotropic energy band gives no change in resistance for metals. For semiconductors (with one type of carrier scattered by acoustical lattice vibrations) one finds at low fields that a = 0.38f.L2 X 10-16

where the mobility f.L is measured in cm 2/volt-sec and B in oersteds. Seebeck Effect (Thermoelectric Power). If two different conductors are joined together at both ends and the two junctions kept at different temperatures, an electromotive force is set up which is proportional to the temperature difference (for small t!t.T). The thermoelectromotive force per degree centigrade is called the thermoelectric power (Q). For metals:

Q = 1r 2k 2T

3e

(a logasO"(S)

&=&p

where O"(S) is the electrical conductance due to charge carriers of energy B. For semiconductors see Sec. ge-4. Thomson Effect. When an electric current J passes between two points of a homogeneous conductor, with a temperature difference t!t.T existing between these points, an amount of heat O"TJ t!t.T is emitted or absorbed in addition to the Joule heat. The parameter O"T is called the Thomson coefficient. Peltier Effect. If two conductors are joined together and kept at a constant temperature while a current J passes through the junction, heat is generated or absorbed at the junction in addition to the Joule heat. The Peltier coefficient TI12 is defined so that the heat emitted or absorbed per second at the junction is nuJ. Kelvin Relations

Nernst Effect (ref. 4). If a temperature gradient is maintained in an electronic conductor (J = 0) in the presence of a transverse magnetic field, a transverse electric field develops which is given by

QN is called the isothermal N ernst coefficient. For semiconductors (one type of carrier, classical statistics, and acoustical lattice scattering): QN

= -

31r k 16ef.L

Ettinghausen Effect (ref. 4). If a temperature difference is maintained across an electronic conductor perpendicular to a current of density J in the presence of a magnetic field, a transverse temperature gradient is established given by vlT =

PJ X B

P is called the Ettinghausen coefficient. The Ettinghausen coefficient P, the Nernst coefficient QN, and the thermal conductivity K are related by the expression

ELECTRONIC PROPERTIES OF SOLIDS

9-29

Righi-Leduc Effect (ref. 4). If a temperature difference is maintained in an electronic conductor in the presence of a magnetic field in which J = 0, a transverse temperature gradient is established: VtT

=

SB X vT

S is called the Righi-Leduc coefficient. Thermal Conductivity. If a temperature difference is maintained across a solid, the heat transported per unit time and unit cross-sectional area is q =

K

\IT

where" is the thermal conductivity. The thermal conductivity of an electronic conductor can be written as the sum of two compounds; «i is due to heat transport via the lattice, and K~ stems from the electronic heat transport: « =

Kl

+

Ke

=

+ LuT

Kl

where u is the electrical conductivity and L the Lorenz number or Wiedemann-Franz ratio. For degenerate free electrons,

L = ~ (~)2 3 e

=

8

2.45 X 10- watt-ohm deg!

For nondegenerate free electrons and acoustical lattice scattering,

Thermionic Emission. temperature T is

The current density of electrons emitted from a metal at

This is the Richardson-Dushman equation. cP is the work function, A = 4n-mek2/h 3 = 120 ampycmv/deg-. 9c-4. Specific Heat. The specific heat of an electronic conductor consists of two terms C, = "IT + BT3 where the first term is the electronic and the second the lattice contribution. former can usually be observed only at very low temperatures. For degenerate free electrons: 2 2 = 7r- k erga/deg!

"I

...

SF

The

per electron

For nondegenerate free electrons: 'Y

3 k

= 2 T erga/deg! per electron

9c-5. Magnetic Properties of Electrons. Cyclotron Resonance. Current carriers in a solid when accelerated by a microwave electric field perpendicular to an externally applied static magnetic field H will spiral about the magnetic field. For sufficiently large mean free path l or collision time r-the condition is WeT> I-a resonance absorption is observed for a frequency We

=

eH m*c

where c is the velocity of light. This technique provides a direct measurement of the effective mass electrons (or holes) m",

9-30

SOLID-STATE PHYSICS

Magnetic Susceptibility of Charge Carriers. Charge carriers contribute a diamagnetic effect through their translational motion and a paramagnetic effect due to their spin. For nondegenerate conductors (semiconductors),

where n is the concentration of free carriers and IJ.B the Bohr magneton. If m· is small (Ge), the susceptibility is mainly diamagnetic. If m * is large (Ti0 2) , the paramagnetic effect dominates. For degenerate conductors (metals, semimetals, and impure semiconductors) at low temperature,

Transition metals have a large m *, and consequently they show a high magnetic susceptibility (Pauli paramagnetism); semimetals with small m * (e.g., Bi) have a diamagnetic susceptibility. Knight Shift. Polarization of conduction electrons will produce a shift in frequency at which nuclear magnetic resonance absorption will occur for a given type of nucleus in a metal relative to a particular nonmetallic solid. 9c-6. Optical Properties of Electrons. Optical Absorption. Electromagnetic radiation of wavelengths in the ultraviolet, visible, or infrared region will be absorbed by a semiconductor or metal through the excitation of electrons and phonons. As far as the electronic excitation is concerned, three mechanisms can be distinguished: 1. Electronic transition between different energy bands 2. Electronic transitions within an energy band ("free carrier absorption") 3. Electronic transitions between a localized state of an imperfection and an energy band

The absorption coefficient a is deduced from the measured transmission by means of the following expression: (1 - R2)e- a d 1 - R2e- 2a d 10 where 10 == incident light intensity I = transmitted light intensity d = thickness of sample R = reflectivity = [(n - 1)1 + k 2]/ [(n + 1)2 + k 2] n = refractive index k = extinction coefficient = a X wavelengtb /de Photoconductivity: An increase of electrical conductivity under illumination due to excitation of electrons or holes into conducting states. The resulting current is given by

T=l

J = elVIJ.T

£2

where I = absorbed light intensity V = applied voltage IJ. = carrier mobility T = carrier lifetime L = length of sample

ELECTRONIC PROPERTIES OF SOLIDS

9-31

Photovoltaic Effect: The generation of a voltage (due to optical excitations) when a semiconductor is illuminated at the electrodes or at internal barriers or p-n junctions. Carrier Lifetime: The length of time that an electron (hole) spends in conducting states before being captured by a hole (electron) or imperfection. The decay of excess carriers follows the law

dn

no - n

dt

T

where no is the equilibrium density of carriers and T the carrier lifetime. Exciton: A bound electron-hole pair in an insulator or a semiconductor. The exciton energy levels are states in the forbidden energy gap, below the conduction band. The exciton may move through the crystal, transporting energy but no electrical charge, because it is neutral. Specific References 1. 2. 3. 4.

Herman, F.: Proc. IRE 43, 1703 (1955). Lax, B.: Rev. Mod. Phys. 30, 122 (1958). Brooks, H.: Advan. Electron. Electron Phys. 7, 120 (1955). Scanlon, 'V. W.: "Methods of Experimental Physics," vol. 6B, p. 166. L. Marton. ed., Academic Press, Inc., New York, 1959.

General References 1. Condon, E. U., and H. Odishaw: "Handbook of Physics," McGraw-Hill Book Company, New York, 1958. II. Seitz, F.: "The Modern Theory of Solids," McGraw-Hill Book Company, New York, 1940. III. Wilson, A. H.: "Theory of Metals," 2d ed., Cambridge University Press, London, 1954. IV. Kittel, C.: "Introduction to Solid State Physics," 3d ed., John Wiley & Sons, Inc., New York, 1966. .. V. Shockley, W.: "Electrons and Holes in Semiconductors," D. Van Nostrand Company, Inc., Princeton, N.J., 1950. VI. Van Vleck, J. H.: "The Theory of Electric and Magnetic Susceptibilities," Oxford University Press, New York, 1932. VII. Wannier, G. H.: "Elements of Solid State Theory," Cambridge University Press, London, 1959. VIII. Ziman, J. M.: "Electrons and Phonons," Oxford University Press, New York, 1960.

BIBLIOGRAPHY OF ENERGY BAND CALCULATIONSI This bibliography contains most of the principal papers dealing with detailed energy-band calculations. The references are arranged chronologically under each type of crystal. 9c-7. Alkali Metals Wigner, E., and F. Seitz: Phys. Rev. 43, 804 (1933); 46, 509 (1934). Sodium, cellular. Slater, J. C.: Phys. Rev. 45, 794 (1934). Sodium, cellular. Millman, J.: Phys. Rev. 47, 286 (1935). Lithium, cellular. Seitz, F.: Phys. Rev. 47, 400 (1935). Lithium, cellular. Gombas, P.: Z. Physik 113,150 (1939). Na, K, Rb, Cs, pseudopotential. I Updated version of bibliography in J. C. Slater, "Quantum Theory of Molecules and Solids," vol. 2, pp. 300--305, McGraw-Hill Book Company, New York. 1965.

9-32

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von der Lage, F., and H. Bethe: Phys. Rev. 71, 612 (1947). Sodium, cellular. Sternheimer, R.: Phys. Rev. 78, 235 (1950). Cesium, cellular. Silverman, R. A.: Phys. Rev. 86, 227 1952). Lithium, k . p. Parmenter, R. H.: Phys. Rev. 86, 552 (1952). Lithium,OPW. Howarth, D., and H. Jones: Proc. Phys. Soc. (London), ser. A, 66, 355 (1952). Sodium, cellular. Kohn, W., and J. Rostoker: Phys. Rev. 94, 1111 (1954). Lithium, Green's function. Schiff, B.: Proc. Phys. Soc. (London), ser. A, 67, 2 (1954). Lithium, cellular. Callaway, J.: Phys. Rev. 103,1219 (1956). Potassium, OPW and cellular. Miasek, M.: Bull. Acad. Polan. Sci., Cl. III, 4,453 (1956). Sodium, variation. Callaway, J., and E. L. Haase: Phys. Rev. 108, 217 (1957). Cesium, OP\V and cellular. Brown, E., and J. A. Krumhansl: Phys. Rev. 109, 30 (1958). Lithium, modified OPW. Glasser, M. L., and J. Callaway: Phys. Rev. 109, 1541 (1958). Lithium, OPW. Callaway, J.: Phys. Rev. 112, 322 (1958). Sodium, pseudopotential. Callaway, J., and D. F. Morgan, Jr.: Phys. Rev. 112, 334 (1958). Rubidium, cellular. Callaway, J.: Phys. Rev. 112, 1061 (1958). Cesium, cellular, terms in k 2 • Cohen, M. H., and V. Heine: Advan. Phys. 7,395 (1958). Alkali metals. Bassani, F.: J. Phys. Chem. Solids 8, 375, 379 (1959). Sodium in diamond lattice, OP\V. Bassani, F., and V. Celli: Nuovo Cimento 11, 805 (1959). Lithium in diamond lattice, OPW. Callaway, J.: Phys. Rev. 119, 1012 (1960). Potassium, cellular, terms in ». Cornwell, J. F., and E. P. \Vohlfarth: Nature 186, 379 (1960). Lithium, pseudouotent.ial. Callaway, J.: Phys. Rev. 123, 1255 (1961). Sodium, cellular, terms in k 2 • Callaway, J.: Phys. Rev. 124, 1824 (1961). Lithium, OPW, and comparison of various results. Cornwell, J.: Proc. Roy. Soc. (London), ser. A, 261:551 (1961). Alkali metals and beryllium, pseudopotential. Callaway, J., and W. Kohn: Phys. Rev. 127, 1913 (1962). Lithium, cellular, terms in k», Ham, F. S.: Phys. Rev. 128, 82 (1962). Alkali metals, Green's function. Ham, F. S.: Phys. Rev. 128, 2524 (1962). Alkali metals, Green's function. Kenney, J. F.: Quart. Proqr, Rept. 53, p. 38, Solid-state and Molecular Theory Group, MIT, July 15, 1964. Lithium, sodium, APW. De Leener, M., and A. Bellemans: J. Chem. Phys. 43, 3075 (1965). Alkali metals, freeelectron approximation, cohesion. Meyer, A., and W. H. Young: Phys. Rev. 139, A401 (1965). Lithium, pseudopotential. Lafon, E. E., and C. C. Lin: Phys. Rev. 162,579 (1966). Lithium, tight-binding. Kenney, J. F.: Quart. Proqr . Rept. 66, Solid-State and Molecular Theory Group, l\UT, Oct. 15, 1967. Rubidium, cesium, APW.

9c-8. Divalent and Trivalent Elements Manning, M. F., and H. Krutter: Phys. Rev. 51,761 (1937). Calcium, cellular. Herring, C., and A. G. Hill: Phys. Rev. 58, 132 (1940). Beryllium, OPW. Matyas, Z.: Phil. Mruj. 30,429 (1948). Aluminum, tight-binding. Jones, H.: Phil. Afag. 41, 663 (1950). Magnesium, nearly free electrons. Donovan, B.: Phil . .Mag. 43, 868 (1952). Beryllium, cellular. Trlifaj, M.: Czech. J. Phys. 1, 110 (1952). Magnesium, APW. Antoncik, E.: Czech. J. Phys., 2, 18 (1953). Aluminum, APW. Heine, V.: Proc. Roy. Soc. (London), ser. A, 240, 340, 354, 361 (1957). Aluminum,OPW. Harrison, W. A.: Phys. Rev. 116, 555 (1959); 118, 1182 (1960). Aluminum, nearly free electrons, pseudopotential. Segall, B.: Phys. Rev. 124, 1797 (1961). Aluminum, Green's function. Cornwell, J. F.: Proc. Roy. Soc. (London), ser. A, 261, 551 (1961). Beryllium, pseudopotential. Falicov, L. M.: Phil. Trans. Roy. Soc. London, ser. A, 256, 55 (1962). Magnesium,OPW. Harrison, W. A.: Phys. Rev. 126, 497 (1962); 129, 2503, 2512 (1963). Zinc, pseudopotential. Segall, B.: Phys. Rev. 131, 121 (1963). Aluminum, Green's function. Loucks, T. L., and P. H. Cutler: Phys. Rev. 133, A819 (1964). Beryllium, OPW. Loucks, T. L., and P. H. Cutler: Phys. Rev. 134, A1618 (1964). Beryllium,OPW. Terrall, J. H.: Phys. Letters 8, 149 (1964). Beryllium, APW. Kimball, J. C., R. W. Stark, and F. :M. Mueller: Phys. Rev. 162, fOO (1967). Magnesium, pseudopotential. Vasvari, B., A. E. O. Animalu, and V. Heine: Phys. Rev. 154, 535 (1967). Calcium, strontium, barium under pressure, pseudopotential. Snow, E. C.: Ph'lls. Rev. 158, 683 (1967). Aluminum, APW,

ELECTRONIC PROPERTIES OF SOLIDS

9-33

9c-9. Diamond, Silicon, Germanium, 3-6 Compounds Kimball, G. E.: J. Chem, Phys. 3, 560 (1935). Diamond, cellular. Hund, F., and B. Mrowka: Sachsieche Akad. Wiss. Leipzig 87,185,325 (1935). Diamond, cellular. Mullaney, J. F.: Phys. Rev. 66, 326 (1944). Silicon, cellular. Morita, A.: Sci. Rept. Tohoku Univ., 33 :92 (1949). Diamond, tight-binding. Holmes, D. K.: Phys. Rev. 87, 782 (1952). Silicon, cellular. Herman, F.: Phys. Rev. 88, 1210 (1952). Diamond, OPW. Hall, G. G.: Phil. Mag. 43, 338 (1952); Phys. Rev. 90, 317 (1953). Diamond, equivalent orbital tight-binding. Herman, F., and J. Callaway: Phys. Rev. 89, 518 (1953). Germanium, OPW. Yamaka, E., and T. Sugita: Phys. Rev. 90, 992 (1953). Silicon, cellular. Herman, F.: Phys. Rev. 93,1214 (1954). Diamond and germanium, OPW. Herman, F.: Physica 20,801 (1954). Germanium,OPW. Jenkins, D. P.: Physica 20, 967 (1954). Silicon, cellular. Bell, D. G., R. Hensman, D. P. Jenkins, and L. Pincherle: Proc. Phys. Soc. (London), ser. A, 67, 562 (1954). Silicon, cellular. Herman, F.: Proc, Lnst, Radio Engrs. 43, 1703 (1955). Silicon and germanium, OPW. Herman, F.: J. Electron. 1, 103 (1955). General discus ion, OPW and experiment. Woodruff, T. 0.: Phys. Rev. 98,1741 (1955); 103,1159 (1956). Silicon,OPW. Jenkins, D. P.: Proc, Phys. Soc. (London), ser. A, 69,548 (1956). Silicon, cellular. Kobayasi, S.: J. Phys. Soc. Japan 11, 175 (1956); 13, 261 (1958). Carborundum, tightbinding, OPW. Bassani, F.: Phys. Rev. 108, 263 (1957). Silicon, OPW, tight-binding, interpolation. Callaway, J.: J. Electronics 2, 330 (1957). GaAs, perturbation of Ge. Kane, E. 0.: J. Phys. Chem. Solids 1, 82 (1957). Germanium, silicon, k . p. Kane, E. 0.: J. Phys. Chem. Solids 1, 249 (1957). InSb, k . p. Hall, G. G.: Phil. Mag. 3,429 (1958). Diamond, silicon, germanium, equivalent orbital tight-binding. Morita, A.: Progr. Theoret. Phys. (Kyoto) 19, 534 (1958). Diamond type, semilocalized combination of orbitals. Kleinman, L., and J. C. Phillips: Phys. Rev. 116, 880 (1959). Diamond, pseudopotential. Phillips. J. C.: J. Phys. Chem. Solids 8, 369, 379 (1959). Silicon, germanium, pseudopotential. Segall, B.: J. Phu«. Chem. Solids 8, 371, 379 (1959). Germanium, Green's function. Gubanov, A. I., and A. A. Nranyan: Fiz. Tverd. ~ Tela 1, 1044 (1959). 3-5 compounds, tight-binding and equivalent orbitals. Bassani, F.: Nuovo Cimento 13, 244 (1959). Silicon, tight-binding. Kleinman, L., and J. C. Phillips: Phys. Rev. 117,460 (1960). BN, pseudopotential. Kleinman, L., and J. C. Phillips: Phys. Rev. 118, 1153 (1960). Silicon, pseudopotential. Nranyan, A. A.: Fiz. Tverd. Tela 2,1650 (1960). 3-5 compounds, tight-binding equivalent orbitals. Gashimzade, F. M., and V. E. Khartsiev: Fiz. Tverd. Tela 3, 1453 (1961). Silicon, germanium, GaAs, OPW. Phillips. J. C.: Phys. Rev. 125, 1931 (1962). Silicon and germanium, general discussion. Braunstein, R., and E. O. Kane: J. Phys. Chem. Solids 23, 1423 (1962). 3-5 compounds. Coulson, C. A., L. B. Redei, and D. Stocker: Proc. Roy. Soc. (London), ser. A, 270, 357 (1962). 3-5 compounds, OPW. Redei, L. B.: Proc. Roy. Soc. (London), ser, A, 270, 373,383 (1962). Diamond, OPW. Stocker, D.: Proc. Roy. Soc. (London), ser, A, 270, 397 (1962). 3-5 compounds, OPW. Bassani, F., and M. Yoshimine: Phys. Rev. 130, 20 (1963). Group 4 elements and 3-5 compounds, OPW. Braunstein, R.: Phys. Rev. 130, 869 (1963). Germanium-silicon alloys. Bassani, F., and L. Liu: Phys. Rev. 132, 2047 (1963). Gray tin. Cohan, N. V., D. Pugh, and R. H. 'I'redgold: Proc Phys. Soc. (London) 82, 65 (1963). Diamond, tight-binding, equivalent orbitals. Brust, D.: Phy'. Rev. 134, A1337 (1964). Germanium and silicon, pseudopotential. Herman, F.: "Proceedings International Conference on the Physics of Semiconductors," M. Hulin, ed., Dunod, Paris, 1964. Diamond-type crystals, OPW. Kreher, K.: Fortschr. Physik 12, 489 (1964). Gallium arsenide. Cardona, M., F. H. Pollak, and J. G. Broerman: Phys. Letters 19, 276 (1965). Gallium arsenide, spin-orbit splitting. Chow, P. C., and L. Liu: Phys. Rev. 140, A1817 (1965). 3-5 compounds, relativistic effect, perturbation. .

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Doggett, G.: Proc. Phys. Soc. (London) 86, 393 (1965). Diamond, excited states, tight-binding, equivalent orbitals. Harrison, W. A.: Physica 31, 1692 (1965). Silicon, pseudopotential. Nakayima, M.: J. Phys. Soc. Japan 20,56 (1965). Semiconductors; effect of homogeneous deformation on band structure. Shindo, K., A. Morita, and H. Kamimura: J. Phys. Soc. Japan 20,2054 (1965). Crystals with zincblende and wurtzite structure, spin-orbit coupling. Cardona, M., and F. H. Pollak: Phys. Rev. 142, 530 (1966). Germanium and silicon, k . p method. Cohen, M. L., and T. K. Bergstresser: Phys. Rev. 141, 789 (1966). 14 semiconductors, pseudopotential. Doggett, G.: Phys. Chem. Solids 27, 99 (1966). Spin-orbit splitting, 4-4 and 3-,5 compounds, tight-binding. Herman, F., R. L. Kortum, C. D. Kuglin, and R. A. Short: "Proceedings International Conference on the Physics of Semiconductors," Kyoto, 1966. Diamond-type crystals, OPW. Herman, F., R. L. Kortum, C. D. Kuglin, and R. A. Short: "Quantum Theory of Atoms, Molecules, and the Solid State," Academic Press, Inc., New York, 1966. Silicon, germanium, gray tin, OPW. Kane, E. 0.: Phys. Rev. 146, 558 (1966). Silicon, pseudopotentia!. Keown, R.: Phlls. Rev. 150, 568 (1966). Diamond, APW. Pollak, F. H., and M. Cardona: Phys. Chem, Solids 27, 423 (1966). Germanium and gallium arsenide, k . p method. Saslow, W., T. K. Bergstresser, and M. L. Cohen: Phys. Rev. Letters 16, 354 (1966). Diamond, pseudopotential. Dresselhaus, G., and M. S. Dresselhaus: Phys. Rev. 160, 649 (1967). Silicon and germanium, tight-binding. Wiff, D. R., and R. Keown: J. Chem, Phys. 47, 3113 (1967). Boron nitride, APW.

9c-10. Transition and Other Elements with f.c.c., b.c.c, or Hexagonal Structure Krutter, H. M.: Phys. Rev. 48, 664 (1935). Copper, cellular. Tibbs, S. R.: Proc. Cambridqe Phil. Soc. 34, 89 (1938). Copper, silver, cellular. Chodorow, M. L: Phys. Rev. 55, 675 (1939). Copper, APW. Manning, M. F., and M. I. Chodorow: Phys. Rev. 56, 787 (1939). Tungsten, cellular. Manning, M. F.: Phys. Rev. 63, 190 (1943). Iron, cellular. Greene, J. B., and M. F. Manning: Phys. Rev. 63, 203 (1943). Iron, fcc, cellular. Fletcher, G. C., and E. P. Wohlfarth: Phil. Mao. 42, 106 (1951). Nickel, tight-binding. Fletcher, G. C.: Proc. Phus. Soc. (London), ser, A, 65, 192 (1952). Nickel, tight-binding. Howarth, D. J.: Proc. Roy. Soc. (London), ser. A, 220, 513 (1953). Copper, cellular. Koster, G. F.: Phys. Rev. 98, 901 (1955). Nickel, tight-binding. Howarth, D. J.: Phys. Rev. 99,469 (1955). Copper, APW. Callaway, J.: Phys. Rev. 99, 500 (1955). Iron,OPW. Schiff, B.: Proc, Phys. Soc. (London), ser. A, 68, 686 (1955); 69, 185 (1956). Titanium, cellular. Fukuchi, M.: Proqr . Theoret. Phys. 16,222 (1956). Copper,OPW. Altmann, S. L., and N. V. Cohan: Proc, Phys. Soc. (London) 71, 383 (1958). Titanium, cellular. Altmann, S. L.: Proc, Roy. Soc. (London), ser. A, 244, 141,153 (1958). Zirconium, cellular. Stern, F.: Phys. Rev. 116, 1399 (1959). Iron, tight-binding. Belding, E. F.: Phil. Ma{}. 4, 1145 (1959). Cr, Fe, Ni, tight-binding. Wood, J. H.: Phys. Rev. 117, 714 (1960). Iron, APW. Segall, B.: Phys. Rev. Letters 7, 154 (1961). Copper, Green's function. Burdick, G. A.: Phys. Rev. Letters 7, 156 (1961). Copper, APW. Asdente, M., and J. Friedel: Phys. Rev. 124, 384 (1961); 126, 2262 (1962). Chromium, tight-binding, 4s omitted. Knox, R. S., and F. Bassani: Phys. Rev. 124, 652 (1961). Argon, tight-binding and OPW. Cornwell, J. F.: Phil. Mao. 6, 727 (1961). Noble metals, pseudopotential. Segall, B.: Phys. Ren., 125:109 (1962). Copper, Green's function. Wood, J. H.: Phys. Rev. 126, 517 (1962). Iron, APW. Asdente, M.: Phys. Rev., 127, 1949 (1962). Chromium, tight-binding. Altmann, S. L., and C. J. Bradley: Phys. Letters 1, 336 (1962). Zirconium, cellular. Cornwell, J. F., and E. P. Wohlfarth: J. Phys. Soc. Japan 17 (suppl, B-1), 32 (1962). Iron. Glasser, M. L.: Rev. Mex. Fis. 11,31 (1962). Silver. Lomer, W. M.: Proc. Phys. Soc. (London) 80, 489 (1962). Chromium, general discussion. Burdick, G. A.: Phys. Rev. 129, 138 (1963). Copper. APW.

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Yamashita, J., M. Fukuchi, and S. Wakoh: J. Phys. Soc. Japan 18, 999 (1963). Nickel, tight-binding and Green's function. Mattheiss, L. F.: Bull. Am. Phys. Soc., ser. II, 8, 222 (1962). 3d transition elements to Cu, Zn, APW. Fowler, W. B.: Phys. Rev. 132, 1594 (1963). Krypton, tight-binding and OPW. Mattheiss, L. F.: Phys. Rev. 133, A1399 (1964). Argon, APW. Mattheiss, L. F.: Phys. Rev. 134, A970 (1964). Iron transition series, APW. Mattheiss, L. F., and R. E. Watson: Phys. Rev. Letters 13, 526 (1964). Tungsten, spinorbit parameters. Wakoh, S., and J. Yamashita: J. Phys. Soc. Japan 19, 1342 (1964). Nickel, KKR and APW. Abate, E., and IV1. Asdente: Phys. Rev. 140, A1303 (1965). Iron, tight-binding. Altmann, S. I.., and C. J. Bradley: Proc. Phys. Soc. (London) 86,915 (1965). Hexagonal metals, cellular. Dimmock, J. 0., A. J. Freeman, and R. E. Watson: J. Appl. Phys. 36, 1142 (1965). Gadolinium, APW. Gandelman, G. IV1.: Zh. Eksperim. i. Teor. Fiz. 48, 758 (1965). Argon, transition to metallic state under pressure, statistical method. Harrison, W. A.: Phys. Rev. 139, A179 (1965). Lead, pseudopotential. Hodges, L., and H. Ehrenreich: Phys. Letters 16, 203 (1965). Ferromagnetic nickel, pseudopotential. Katsuki, S., and M. Tsuji: J. Phys. Soc. Japan 20, 1136 (1965). Cadmium, pseudopotential. Lomer, "V. N.: "Proceedings International Conference on Magnetism," p. 127, London, 1965. Chromium, magnetic properties. Loucks, T. L.: Phys. Rev. Letters 14, 693 (1965). Tungsten, APW. Loucks, T. L.: Phys. Rev. 139, A1181 (1965). Chromium, molybdenum, and tungsten, APW. Loucks, T. L.: Phys. Rev. 139, A1333 (1965); 143,506 (1966). Tungsten, APW. Mattheiss, L. F.: Phys. Rev. 138, A112 (1965). VaX type compounds, APW. Mattheiss, L. F.: Phys. Rev. 139, A1893 (1965). Tungsten, APW. Nagamiya, T., K. Motizuki, and K. Yamasaki: "Proceedings International Conference on Magnetism," p. 195, London, 1965. Chromium, spin-density waves. Wakoh, S.: J. Phys. Soc. Japan 20, 1894 (1965). Copper and nickel, APW and KKR. Beeby, J. L.: Phys. Rev. 141,781 (1966). Transition metals, ferromagnetism. Chatterjee, S., and S. K. Sen: Proc. Phys. Soc. (London) 87, 779 (1966). Silver, OPW. Freeman, A. J., J. O. Dimmock, and R. E. Watson: "Quantum Theory of Atoms, Molecules, and the Solid State," Academic Press, Inc., New York, 1966. Rare earths, APW. Freeman, A. J., A. M. Furdyna, and J. O. Dimmock: J. Appl. Phys. 37, 1256 (1966). Palladium, APW. Hermanson, J., and J. C. Phillips: Phys. Rev. 150, 652 (1966). Excitons, pseudopotential. Hermanson, J.: Phys Rev. 150, 660 (1966). Rare-gas solid, excitons, pseudopotential. Hodges, I.., H. Ehrenreich, and N. D. Lang: Phys. Rev. 152, 505 (1966). Noble and transition metals, interpolation method. Keeton, S. C., and T. L. Loucks: Phys. Rev. 146, 429 (1966). Thorium, actinium, and lutecium, APW. Loucks, T. I..: Phys. Rev. 144, 504 (1966). Yttrium, APW. Snow, E. C., J. T. Waber, and A. C. Switendick: J. Appl. Phys. 37, 1342 (1966). Nickel, APW. Spicer, W. E.: J. Appl. Phys. 37, 947 (1966). Copper, nickel, silver, and iron, density of states from experiment. Switendick, A. C.: J. Appl. Phys. 37, 1022 (1966). Chromium, APW. Williams, R. W., T. L. Loucks, and A. R. Mackintosh: Phys. Rev. Letters 16, 168 (1966). Rare earth metals, APW and experiment. Yamashita, J., S. Wakoh, and S. Asano: "Quantum Theory of Atoms, Molecules, and the Solid State," p. 497, Academic Press, Inc., New York, 1966. Iron, nickel, chromium, CoFe, KKR. Asdente, M., and M. Delitala: Phys. Rev. 163, 497 (1967). Iron, tight-binding. Connolly, J. W. D.: Phys. Rev. 159, 415 (1967). Nickel, APW. Deegan, R. A., and W. D. Twose: Phys. Rev. 164, 993 (1967). Niobium, OPW. De Cicco, P. D., and A. Kitz: Phys. Rev. 162, 486 (1967). Iron, APW. Falicov, L. M., and M. J. Zuckermann: Phys. Rev. 160, 372 (1967). Antiferromagnetic metals, pseudopotential. Faulkner, J. S., H. L. Davis, and H. W. Joy: Phys. Rev. 161, 656 (1967). Copper, KKR. Heine, V.: Phys. Rev. 153, 673 (1967). Transition metals, pseudopotential. Loucks, T. L.: Phys. Rev. 159, 544 (1967). Zirconium, APW. Mueller, F. M.: Phys. Rev. 153, 659 (1967). Noble metals, interpolation method.

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Mueller, F. M., and J. C. Phillips: Phys. Rev. 157, 600 (1967). Copper, interpolation method. Snow, E. C., and J. T. Waber: Phys. Rev. 157, 570 (1967). Copper, APW. Sokoloff, J. B.: Phys. Rev. 161, 540 (1967). Magnetic impurities in copper. Stark, R. W., and L. M. Falicov: Phys. Rev. Letters 19, 795 (1967). Zinc and cadmium, pseudopotential. Tsui, D. C.: Phys. Rev. 164, 669 (1967). Nickel, comparison with experiment.

9c-H. Graphite Wallace, P. R.: Phys. Rev. 71, 622 (1947); 72, 258 (1947). Tight-binding. Coulson, C. A.: Nature 159,265 (1947). Tight-binding. Coulson, C. A., and R. Taylor: Proc. Phys. Soc. (London), ser. A, 65,815 (1952). Tightbinding. Carter, J. L., and J. A. Krumhansl: J. Chem. Phys. 21, 2238 (1953). Tight-binding. Ariyama, K., and S. Mase: Proqr, Theoret. Phys. 12, 244 (1954). 'I'ight-blnding, Lorner, W. M.: Proc. Roy. Soc. (London), ser. A, 227, 330 (1955). Tight-binding. Johnston, D. F.: Proc. Roy. Soc. (London), ser. A., 227, 349 (1955); 237, 48 (1956). Tightbinding. McClure, J. W.: Phys. Rev. 108, 612 (1957). k· p. Yamazaki, M.: J. Chem. Phys. 26, 930 (1957). Tight-binding. Corbato, F.: "Proceedings 1957 Carbon Conference," p, 173, Pergamon Press, New York. Tight-binding. Slonczewski, J. C., and P. R. Weiss: Phys. Rev. 109, 272 (1958). k· p. Haering, R. R.: Can. J. Phys. 36, 352 (1958). Tight-binding. Mase, S.: J. Phys. Soc. Japan 13,563 (1958). Tight-binding. Peacock, T. E., and R. McWeeny: Proc. Phys. Soc. (London) 74, 385 (1959). Tightbinding. Barriol, J.: J. Chim. Ph.us. 57, 837 (1960); J. Barriol and J. Metzger, J. Chim. Phys. 57, 848 (1960). Tight-binding. Anno, T., and C. A. Coulson: Proc. Roy. Soc. (London), ser. A, 264, 165 (1961). Tightbinding (semiempirical). Dresselhaus, G., and M. S. Dresselhaus: Phys. Rev. 140, A401 (1965). Graphite, spinorbit interaction, perturbation method. Linderberg, J.: Arkiv Fysik 30, 557 (1965). Graphite.

9c-l2. Elements with Other Crystal Structures Jones, H.: Proc. Roy. Soc. (London), ser, A, 147,396 (1934). Bismuth, nearly free electrons. Morita, A.: Sci. Rept. Tohok:a Univ. 33, 144 (1949). Bismuth, tight-binding. Reitz, J. R.: Phys. Rev. 105, 1233 (1957). Selenium, tellurium, tight-binding. Gaspar, R.: Acta Phue. Hung. 7, 289 (1957). Selenium and tellurium, tight-binding. Ridley, E. C.: Proc. Roy. Soc. (London), ser. A, 247, 199 (1958). Uranium, cellular. Mase, S.: J. Phys. Soc. Japan 13, 434 (1958); 14, 584 (1959). Bismuth, tight-binding. de Carvalho, A. P.: Compt. Rend. 248, 778 (1959). Tellurium, tight-binding. Harrison, W. A.: J. Phys. Chem. Solids 17, 171 (1960). Bismuth, pseudopotential. Miasek, M.: Bull. Acad. Polan. Sci., Ser. Sci. Math. Astron. Phys. 8, 9 (1960). White tin,OPW. Bergson, G.: Arkiv Kemi, 16, 315 (1960). Sulfur, tight-binding. Behrens, E.: Z. Physik, 161, 279 (1961). Bismuth, tight-binding. Behrens, E.: Z. Physik, 163, 140 (1961). Selenium, tight-binding. Miasek, M.: Phys. Rev. 130, 11 (1963). White tin, OPW. Wood, J. H.: Bull. Am. Phys. Soc., ser. n, 8,222 (1963). Gallium, APW. Golin, S.: Phys. Rev. 140, A993 (1965). Arsenic, OPW. Beissner, R. E.: Phys. Rev. 145, 479 (1966). Tellurium, pseudopotential. Falicov, L. M., and P. J. Lin: Phys. Rev. 141, 562 (1966). Antimony, pseudopotential. Lin, P. J., and J. C. Phillips: Phys. Rev. 147, 469 (1966). Antimony, pseudopotentis l.

9c-l3. Compounds, Other Than 3-6 Jones, H.: Proc, Roy. Soc. (London), ser. A, 144, 225 (1934). Alloys, ')'-phase, nearly free electrons. Slater, J. C., and W. Shockley: Phys. Rev. 50, 705 (1936). Sodium chloride, general discussion. Shockley, W.: Phys. Rev. 50, 754 (1936). Sodium chloride, cellular. Ewing, D. H., and F. Seitz: Phys. Rev. 50, 760 (1936). LiF and LiH, cellular. Tibbs, S. R.: Trans. Faraday Soc. 35, 1471 (1939). Sodium chloride, cellular.

ELECTRONIC PROPERTIES OF SOLIDS

9-37

Morita, A., and C. Horie: Sci. Rept. Tohoku Univ. 36, 259 (1952). Barium oxide, tightbinding. Bell, D. G., D. M. Hum, L. Pincherle, D. W. Sciama, and P. M. Woodward: Proc. Roy. Soc. (London), ser. A, 217, 71 (1953). PbS, cellular. Casella, R. C.: Phys. Rev. 104, 1260 (1956). Sodium chloride, tight-binding. Yamazaki, M.: J. Chem. Phys. 27, 746 (1957). Boron carbide, tight-binding. Kucher, T. 1.: Zh. cksperim. i Tcor. Fiz., 34:394 (1958); 35:1049 (1958). NaCl, tightbinding. Birman, J. L.: Phys. Rev. 109, 810 (1958). ZnS, cellular. Shakin, C., and J. Birman: Phys. Rev. 109, 818 (1958). ZnS, cellular. Howland, L. P.: Phys. Rev. 109, 1927 (1958). Potassium chloride, tight-binding. Tolpygo, K. B., and O. F. Tomasevich: Ukr. Fiz. Zh. 3, 145 (1958). Sodium chloride, tight-binding. Birman, J. L.: Phys. Rev. 115, 1493 (1959). ZnS, tight-binding. Birman, J. L.: J. Phys. Chem. Solids 8, 35 (1959). ZnS, general discussion. O'Sullivan, W.: J. Chem. Phys. 30, 379 (1959). BeO, tight-binding. Kudinov, E. K.: Fiz. Tverd. Tela 1, 1851 (1959). Bi 2Teg, tight-binding. Flodmark, S.: Arkiv Fiz. 14,513 (1959); 18,49 (1960). Type Bl\I6, tight-binding. Balkanski, M., and J. des Cloizeaux: J. Phys. Radium 21, 825 (1960); Abhandl. Deut. Akad. Wiss. Berlin, Kl. Math. Phys. Tech. 76 (1960). CdS, spin-orbit interaction. Kucher, T. I., and K. B. Tolpygo: Fiz. Tverd. Tela 2, 2301 (1960). Sodium chloride, tight-binding. Tolpygo, K. B., and O. F. Tomasevich: Fiz. Tverd. Tela 2, 3110 (1960). Sodium chloride, tight-binding. Kudinov, E. K.: Fiz. Tverd. Tela 3, 317 (1961). BbTeg, tight-binding. Zhilich, A. G., and V. P. Makarov: Fiz. Tverd. Tela, 3 :585 (1961). Cuprous oxide, Green's function. Wood, V. E., and J. R. Reitz: J. Phys. Chem, Solids 23,229 (1962). Cesium gold, cellular. Gashimzade, F. M., and V. E. Khartsiev: Fiz. Tverd. Tela 4, 434 (1962). SnS-type compounds,OPW. Evseev, Z. Ya., and K. B. Tolpygo: Fiz. Tverd. Tela 4, 3644 (1962). Sodium chloride, t.igh t-binding. Johnson, L. E., J. B. Conklin, and G. W. Pratt, Jr.: Phys. Rev. Letters 11, 538 (1963). PbTe, relativistic APW. Evseev, Z. Ya.: Fiz. Tverd. Tela 5, 2345 (1963). Sodium chloride, tight-binding. Lee, P. M., and L. Pincherle: Proc. Phys. Soc. (London) 81,461 (1963). Bismuth telluride, APW. Yamashita, J.: J. Phys. Soc. Japan 18, 1010 (1963). TiO and NiO. Tight-binding. Mackintosh, A. R.: J. Chem. Phus., 38, 1991 (1963). Tungsten bronzes. Beleznay, F., and G. Biczo: J. Chem. Phys. 41, 2351 (1964). DNA, Huckel approximation. Harman, T. C., et al.: Solid State Commun. 2, 305 (1964). Hg'I'e and HgTe-CdTe alloys. Kahn, A. H., and A. J. Leyendecker: Phys. Rev. 135, A1321 (1964). Strontium titanate, tight binding. Kahn, A. H., H. P. R. Frederikse, and J. H. Becker: From "Transition Metal Compounds," p. 53, Gordon and Breach, Science Publishers, Inc., New York, 1964. Sr'I'i Os and Ti0 2 • Ladik, J., and K. Appel: J. Chem. Phys. 40, 2470 (1964). Polynucleotides, Huckel approximation. Pratt, G. W., Jr., and L. G. Ferreira: "Proceedings Internal Conference on Physics of Semiconductors," M. Hulin, ed., Dunod, Paris, 1964. PbTe, k . p method. Sandrock, R., and J. Treusch: Z. Naturforsch. 19a, 844 (1964). Chalcopyrite structure, k· p. Conklin, J. B., Jr., L. E. Johnson, and G. W. Pratt, Jr.: Phys. Rev. 137, A1282 (1965). PbTe, relativistic APW. Ern, V., and A. C. Switendick: Phys. Rev. 137, A1927 (1965). TiC, TiN, TiO, APW. Frei, V., and B. Velicky : Czech. J. Phys. B15, 43 (1965). CdSb, symmetry and pseudopotential. Gorzkowski, W.: Phys. Stat. Solidi 11, K131 (1965). HgTe, k . p. Hassan, S. S. A. Z.: Proc. Phys. Soc. (London) 85, 783 (1965). Sodium-chloride type, plane-wave approximation. Johnson, K. H., and H. Amar: Phys. Rev. 139, A760 (1965). Ordered beta brass, KKR. Ladik, J., and G. Biczo: J. Chern. Phys. 42, 1658 (1965). DNA, Huckel approximation. Miyakawa, T., and S. Oyama: Mem. Defense Acad. Japan 5, 161 (1965). NaCl-type crystal, plane wave method. Scop, P. M.: Phys. Rev. 139, A934 (1965). AgCl. AgBr, APW. Amar, H., K. H. Johnson, and K. P. Wang: Phys. Rev. 148, 672 (1966). Beta-phase alloys, KKR.

9-38

SOLID-STATE PHYSICS

Dahl, J. P., and A. C. Switendick: Phys. Chern. Solids 27, 931 (1966). Cuprous oxide. APW. Onodera, Y., M. Okazaki, and T. Inui: J. Phys Soc. Japan 21, 1816 (1966), Potassium iodide, relativistic Green's function. Oyama, S., and T. Miyakawa: J. Phys. Soc. Japan 21, 868 (1966). KC1, plane wave method. Yamashita, J., S. Wakoh, and S. Asano: J. Phys. Soc. Japan 21, 53 (1966) CoFe superlattice, KKR. Amar, H., K. H. Johnson, and C. B. Sommers: Phys. Re-o. 153, 655 (1967). Beta-brass, KKR. Arlinghaus, F. J.: Phys. Rev. 157,491 (1967). Beta-brass, APW. Bergstresser, T. K., and 1\'1. L. Cohen: Phys. Rev. 164, 1069 (1967) CdSe, CdS, and ZnS pseudopotential. Cho, S. J.: Phys. Rev. 157, 632 (1967). EuS, APW. De Cicco, P. D.: Phys. Rev. 153,931 (1967). KCI, APW. Eckelt, P" O. Madelung, and J. Treusch: Phys. Rev. Letters 18, 656 (1967). ZnS, KKR Euwema, R. N., T. C. Collins, D. G. Shankland, and J. S. De Witt: Phys. Rev. 162, 710 (1967). CdS, OPW. Gray, D., and E. Brown: Phys. Rev. 16 ,567 (1967). CU3Au, OPW. Kunz, A. B.: Phys. Rev. 159, 738 (1967. Alkali halides, spin-orb t effects.

9d. Properties of Metals JULIUS BABISKIN

U.S. Naval Research Laboratory J. ROBERT ANDERSON

University of

~1 aryland

9d-1. Electrical Resistivity and Hall Coefficient. The temperature-dependent ideal resistivity values Pi for very pure metals are listed in Table 9d-l at 0 and 22°C where these Pi values are closely equal to the measured resistivity values P of pure metals. Pi was obtained either by subtracting Po, the residual resistivity at very low temperatures due to impurities and imperfections, from P or by choosing the lowest reported values of P for high-purity metals. The ratio of the resistivity at 100,000 kg/ ems (pp) to that at zero pressure (p) at 20°C and the Hall coefficient (R) at 20°C are also listed in Table 9d-1. 9d-2. Ideal Electrical Resistivity at Low Temperatures. M atthiessen's rule states that the measured resistivity P at a given temperature T is composed of the temperature-dependent ideal resistivity Pi due to electron scattering by lattice vibrations and the temperature-independent residual resistivity Po caused by impurities and imperfections; that is, P = Pi + po. At higher temperatures, Pi a: T for T :> 0.258, where 8 is the Debye characteristic temperature. At very low temperatures, Pi a: T» where n = 5 for a free-electron metal. For many transition metals, n ~ 2 to 3 at low T owing to electron-electron interactions. Tables 9d-2a and 9d-2b list values for Pi at various temperatures below 273 K, while Table 9d-l lists values for Pi at

9-39

PROPERTIES OF METALS TABLE

9d-1.

Metal

Pi,

SOME ELECTRICAL PROPERTIES OF PURE lVIETALS

* microhm-em

Pi,

* microhm-em

O°C

22°C

2.50, 2.44 a 37.6 26 36 2.71 105 6.73 3.08b 79, 76.7< 18.0 12.1 d 5.15 d 1. 55 d , 1. 545 a 87.5,56 c 77 86 127.5 13.65 2.01 d 28.0 d 74.5 8.0 4.65 d 8.7 d 75,62.4 c 19.3,19.2 a 8.494 49 3.94 136 d , 91 e 94.1 4.84 d 56.5 116 6.20 d 13.5 d 8.35 d 9.70 d 9.59 d 144 42 6.447, 6.1 e 64 16.9 d 4.36 d 11.25 6.69 d 95, 88 c 42.9 1.47 d 4.289 19.8 12.1 d 109 15 14.0, 13e 58

2.74 41.3 29 39 3.25 116 7.27 3.35b 81 19.96 12.9 d 5.80 d 1.70 d 90 81 89 134.1 14.85 2.20 d 30.6d 77.7 8.75 5.07 d 9.8 d 79 21.0 9.32 53 4.30 136 d 95.9 5.33 d 59 118.5 7.04 d 14.5 d 9.13 d 1O.55d 10.42d 143 46 7.19 67 18.6 d 4.78 d 12.51 7.37 d 99 46.8 1. 61 d 4.75 21.5 13.1 d 111 16.4 15. 62

pp/p,tat 100,000 kg/cm 2

R,:j: cm 3/coul X 10 4

0.770 0.605 0.928 2.618 0.876 0.474 0.658 4.399

-0.30

.---_._--

Aluminum ........ Antimony ........ Arsenic ........... Barium ........... Beryllium ........ Bismuth .......... Cadmium ........ Calcium .......... Cerium ........... Cesium ........... Chromium ........ Cobalt ........... Copper ........... Dysprosium ...... Erbium .......... Europium ........ Gadolinium ....... Gallium .......... Gold ............. Hafnium ......... Holmium ......... Indium ........... Iridium .. '" ..... Iron ............. Lanthanum ....... Lead ............. Lithium .......... Lutecium ......... Magnesium ....... Manganese ....... Mercury (liq.) .... Molybdenum ..... Neodymium ...... Neptunium ....... Nickel ........... Niobium ......... Osmium .......... Palladium ........ Platinum ......... Plutonium ........ Polonium ......... Potassium ........ Praseodymium .... Rhenium ......... Rhodium ......... Rubidium ........ Ruthenium ....... Samarium ........ Scandium ........ Silver ............ Sodium .......... Strontium ........ Tantalum ........ Terbium .......... Thallium ......... Thorium ......... Thulium .........

.....

5.33 0.558 0.951 0.866 ..... ••

w

••

+2.44 +0.60 +0.181 -7.8 -1.33 -0.55 -1.3 -0.34

.....

-0.95

0.816

-0.72

0.493 0.886 0.841

-0.07

.....

0.487 1.704 0.767 0

••••

0.555 0.892 .....

+0.245 -0.8 +0.09 -1. 7 -0.94 -0.93 +1.26 +0.97

0.858 0.894

-0.611

0.847 .861

-0.68 -0.24

0.596

-4.2 -0.71

..... 0.872 2.95

370

0.802 0.479 1. 810 0.882

-0.84 -2.5

0.265 0.821

+0.24

+1.01

9-40

SOLID-STATE PHYSICS

TABU';

9d-1.

SOME ELECTRICAL PROPERTIES OF PURE METALS

Metal

Tin .............. Titanium ......... Tungsten ......... Uranium ......... Vanadium ........ Ytterbium ........ yttrium .......... Zinc .............. Zirconium ........

Pi,* microhm-em Pi,

o-c

* microhm-em

x

100,000 kg/cm 2 0.548 0.916 0.895 0.724 0.878

+1.18

0.679 0.9836

+0.33

10.1

11.0 43.1 d 5.33 d

24.1

25.7

18.3

R,t

22°C

39.0 d 4.82 d d

pp/p,tat

(Continued)

19.9

d

25.5 53.7 5.45

26.4 58.5 5.92

38.6d

42.4 d

cm t /coul

10 4

-0.04

* Unless otherwise indicated, most of the Pi values were taken from G. T. Meaden, "Electrical Resistance of Metals," Plenum Press, Plenum Publishing Corporation, New York, 1965. t pp/p taken from P. W. Bridgeman, Proc. Am. Acad. Arts Sci. 81, 165 (1952). t R taken from J. Bardeen, "Handbook of Physics," pp. 4-74, E. U. Condon and H. Odishaw, eds., McGraw-Hill Book Company, New York, 1958. a L. A. Hall, "Survey of Electrical Resistivity Measurements on 16 Pure Metals in the Temperature Range 0 to 273°K," NBS Tech. Note 365, February, 1968. b F. X. Kayser and S. D. Soderquist, J. Phys. Chem. Solids, 28,2343 (1967). c J. A. Gibson et al.: "The Properties of Rare Earth Metals and Compounds," Battelle Memorial Institute, Columbus, Ohio, 1959. d G. K. White and S. B. Woods, Phil. Trans. Roy. Soc. London, ser. A, 261,273 (1959). e R. B. Stewart and V. J. Johnson, eds., A Compendium of the Properties of Materials at Low Temperatures (Phase II), W ADD Tech. Rept. 60-56, part IV, chap. 6, Wright-Patterson Air Force Base, Ohio: Aeronautical Systems Division, Air Force Systems Command, December, 1961.

273 K (DOC) and at 295 K (22°C). Table 9d-2a lists Pi, 8, and n for the noble metals (Group IB) and the transition metals (Groups IVA, VA, VIA, VIlA, and VIIIA). Table 9d-2b lists Pi and 8 for the remaining groups of metals other than the noble and the transition metals. 9d-3. Electronic Structure of Metals. The metals listed in Table 9d-3 are divided into three groups, simple metals, transition metals, and semimetals. The reference list is not complete, but the numbers next to the element names refer to recent papers which contain fairly complete references. A recent review article (1] gives rather complete references to de Haas-van Alphen effect studies up to 1968. In the first column under the name of the metal are given the lattice constants in angstroms and the crystal structure. Values of the lattice constants are given at low temperatures, approximately 4.2 K, where these are available. In some cases these have been estimated from low-temperature thermal expansion data. Where lowtemperature data are not available, room-temperature (R.T.) values are listed. One useful reference is Pearson's compilation (2]. In the next four columns the Fermi surface description IS given. For most metals the identifications are based upon band structure calculations, and in some cases the descriptions are extremely tentative. The letters in the description refer to symmetry points in the Brillouin zone following the standard convention as given, for example, by Koster (3]. The names of the parts of Fermi surface are taken from the appropriate references. e and h refer to electrons and holes, respectively. In the majority of cases the type of carrier has been determined from band structure calculations rather than from actual experiments. The magnetic field direction is given in column 6 and refers to the normal to an extremal Fermi surface cross section. The frequencies given in column 7 were obtained from de Haas-van Alphen effect measurements. When

TABLE

T)

9d-2a.

Group IB

eu

Ag

Group IVA

Au

-- --- - - - 250 220 200 180 160 140 120 100 90 80

1.40 1.20 1.06 0.92 0.775

1. 34 1.16 1. 04 0.92 0.795

IDEAL ELECTRICAL RESISTIVITIES IN MICROHM-CM OF PURE METALS AT

1. 83 1.60 1.44 1. 28 1.12

Ti

Zr

Group VA

Hf

V

Nb

Group VIA

Ta

Cr

Mo

0.635 0.490 0.350 0.280 0.21 5

0.675 0.545 0.420 0.355 0.290

0.955 0.790 0.630 0.545 0.460

14.8 11.2 7.9 6.35 4.85

0.153 0.09.5 0.050 0022 0.0063t

0.230 0.17 0.11 0.058 0.020

0.38 0.29 0.20 0.12 0.050

3.5 2.3t 1.4 0.65 0.20

34.u 29.4 26.1 22.6 19.3 16.0 12.8 9.5. 7.90 6.4

25.3 21. 7 19.3 16.9 14.5 12.2 9.9 7.6 65 5.4

16.65 14.5 12.9 11. 2 9. .5

12.3 10.8 9.8 8.7 7. .55

11.0 9.6 8.6 7.65 6.65

10.95 9.05 7.75 6.4 5.2

7.75 6.0 4.3 3.50t 2.65

6.4 .5.2 3.95 3.30 2.6s

5.6 4.6 3.5. 3.03 2.50

3.9 2.66 1. 62 1.18 0.81

1. 90 1.2, 0.75 0.3s 0.14

2.0; 1.5 0.9; 0.56t 0.25

1. 96 1.4 3 0.95 0.51 0.2 3t

0.52 0.30 0.165 0.07st 0.029

4. 3~ 3.64 3. Is 2.7; 2.2; 1. 82 1. 36 0.92 0.714

TEMPERATURES

Group VIlA

W

Mn

Re

4.32 3.66 3.22 2.7, 2.33

133 131 131 130 127

15.2 12.9 5 11.45 9.95 8.4

*

Group VIllA

Fe

- - - - - - - - --- --- --- - - - - - - - - - 34.8 29.3 25.7 22.1 18. .5

Low

7 .•55 6.2 .5.3 4.40 3.55

Ru

Os

Co

Rh

Ir

Ni

Pd

-- --

-- -- -- -- --

5.96 .5.02 4.3s 3.75 3.10

4.50 3.72 3.2 3 2.75 2.26

7.•50 6.45 .5.70 5.00 4.22

o.si,

1. 88 ! .44 1.02 0.82 0 0.600

125 123 121 120 121

6.9 5.35 3.9 5 3.2 2.53

2.7 3 1. 95 1. 24 0.92 0.64

2.4s 1. 85 1. 25 0.91 0.64

3.50 2.70 1. 90 1. .50 1.10

0.3.54 0.216t 0.11. 0.04; 0.0],

0.42 5 0.27\ 0.151 o 06et 0.022

122 122 117 105 82

1. 80 1.2; 0.7; 0.3; 0.11

0.42 0.25 0.135t 0.060 0.022

0.43 0.24 0.10.\ o 03st 0.010

0.79 0.50 0.26

1. 78 1.32 0.91 0.72 0.54

3 90 3.31 2.92 2 . .52 2.1,

4. ]g 3.50 320 2.80 2.3s

5.40 4.3G 3 72 3.10 2.52

8.82 7.6, 6.90 606 .5. ]g

Pt

-8.70 7.54 (j 76 .5.97 .5.18

1. 71 1. 28 0.89 0.695 0.51

1. 96 1. .55 1.10 0.90 0.72

1. 97 1.45 1.00 0.7.5 0.5.5

4.33 3.4G 2.60 2.17 1. 7,

4.375 3.56 5 2.74, 2.326 1. 909

0.34 0.204 0.105 0.043 0.01l5t

0.53 0.35 020 0.10 OOM

0.38 0245 0.15 0073 0.03ot

1. 30 0.92 0.58 0.32 0.13

1.497 1.094 0.719 0.396 o 160

I"d

;:d

o

'"tl

M

;:d

8 H M

[f).

o

~

70 60 50 40 30

4.90 3.50 2.2 5 1.2 0 0.47t

4.3 3.2 2·It 1.25 0.5\

0.38 0.25 0.145 o.ur 0.072t 0.028 0.02;

~

trj

8

> t'

[f).

25 20 15 10

O,K n

00025 0.0008 0.0001;

..... 310 5.1

0.010t 00038 0.0011 0.0002

0.027 0.0125t 0.0037 0.0006

0.075 0.020

220 4.7

18.5 5.1

360 5.3

.. ....

0.235 0.090 0.02 5

.....

0.26 0.105 0.027 0.005

.....

. ....

250 4.5

210 4.7

390 3.4

250 2.7

0.076 0.03; 0.014

0.15 0.08 0.035

I

0.], 0.051 0.01; 0.0032

. .....

230 3.8

480 3.2

0.01.55 0.0046 0.0115 0007, ..... 000.56 0.002; . .... 0.0024

.,. 380 5.1

. .... 315 4.0

65 46 28 12t 410 2.0

0.04;t 0.0125 0.005 O.Ob 0.014 00049 0.0145 0.017 0.074 0016 5 0.00; .... ...... 0.006r. 000Is 0.0050 0.009 o 036t .O.OOL 0045 0.014 5 0.004" . ..... ...... ...... 0.002; . ..... ...... ...... ...... O.OOlt . ...... ..... , ..... 0.004

o

280 4.6

400 3.3

.500 4.7

400 4.7

380 3.3

3.50 4.6

290 4.7

390 3.1

29.5 3.2

0.0837 0.03.59 0.01l6t 0.0029 225 3.7

* Data taken from

t Values for Oi

G. K. White and S. B. Wood~: Phil. Trans. Roy. Soc. London, ser. A, 251, 273 (19591. at which Oi ~ po (or p ~ 2po).

c.o

I t+:o-

i--L

9-42 TABLE

SOLID-STATE PHYSICS

9d-2b.

IDEAL ELECTRICAL RESISTIVITIES IN MICROHM-CM OF PURE METALS AT

Metal

20 K

Low

50 K

TEMPERATURES*

80 K

100 K

---- ---Group IA: Li ................ Na ................ K ................. Rb ................ Cs ................ Group IlA: Be ................ Mg ............... Ca ................ Sr ................ Ba ................ Group IlIA: Sc ................ y .................

Group lIB: Zn ................ Cd ................ Hg ................ Group IIIB: AI ................ Ga ................ In ....... , ........ Tl ................ Group IVB: Sn ................ Pb ................ Group VB: As ................ Sb ................ Bi ................ Rare-earth metals: La ................ Pr ................ Nd ............... Sm ............... Eu ................ Gd ............... , Tb ................ Dy ............... Ho ................ Er ................ Tm ............... Yb ................ Lu ................ Actinide metals: Th ................ U ................. Np ............... Pu ................

0.015 0.0165 0.1074 0.433 0.882

0.27 0.317 0.719 1.57. 2.656

0.995 0.805 1.389 2.700 4.424

1. 714 1.145 1.836 3.461 5.637

0.0004 0.0086 0.03 0.48 0.73

0.0077 0.1 2 0.25 2.5 3.5

0.0389 0.55 0.57 4.6 7.8

0.090 7 0.89 0.87 6.3 10.7

0.16 0.36

2.9 4.8

11.2 15.4

0.052 0.13 1.24

0.49 0.87 3.96

1.16 1.7 6.6.

0.05

0.0006 0.09 0.16 0.42 0.10 0.56

.......

0.94 2.0 0.96 2.76

150 K

200 K

--- ---

250 K

e.

Kt

--- --

3.708 1.994 3.00,5 5.466 8.780

5.704 2.874 4.281 7.648 12.22

7.613 3.821 5.720 10.01 16.06

0.436 .. .. , 1. 52 ...... ......

1. 151 2.6 2.14 14.1 25

2.156 1160 ...... 400 2.74 230 ...... 147 ...... 110

20.7 26.6

29.8 37.6

38.8 48.6

214t

1.62 2.3 8.6

2.72 3.6 13.3

3.84 4.9 18.4

4.9. 6.2 92.2

310 188 80

0.25 2.7 3 1. 80 3.6

0.47 3.96 2.38 4.7

1.0 6 6.8 3.84 7.5

1. 66 9.56 5.4. 10.36

2.24 12.3 7.16 13.5

428 320 108 87

a.r,

2.96 6.5

4.96 10.2

7.0 13.9

9.1 17.6

178 110

8 11.2

4.97

,

370 158 90 52

54t

1.9 3.2 19

4.6 7.2 30

6.4 10.0 37

...... 17.9 55

......

. .....

285t

25.9 74

34.0 96

207 119

29 23 25 52 61 29.7 27 26.6 31 39 25.5 10.8 11. 9

36 36 29.6 64 78 41.2 38 40 .• 43 42 29 13. ; 16

49.6 46 38.6 73 75 69.0 64 72.6 56 52 38 17 .. 26

61 54 46 82 78 95.6 93 81 64 63 46 21.6 36

71 61 53 91 83 119.0 108 85 71 73 5.5 24.4 45

142

0.7.

17 8.6 17 33 33 12.6 12. 6 11.8 15 24 21 6 .• 6.0

0.19 0.52 1.91 20

1.67 4.54 24.2 116

3.34 7.4 49.8 153

4.4 9.4 63.1 156

7.2 14.0 87.3 153

9.94 18.3 102.5 148

12.7 22.3 112.7 145

170 200

0.29 0.42 5.8 3.3 ....... 8.3 14 8.6 1.0 0.96 1.1 3.4 4.6 2.1 I..

74t

152t 158t 140

166t

* Except for calcium, the pi values were taken from G. T. Meaden, "Electrical Resistance of Metals," Plenum Press, Plenum Publishing Corporation, New York, 1965. The pi values for calcium were taken from F. X. Kayser and S. D. Soderquist, J. Phys. Chem, Solids, 28, 2343 (1967). t Unless otherwise indicated, most of the e values were taken from G. T. Furukawa and T. B. Douglass, "American Institute of Physics Handbook," 2d ed., pp, 4-61, D. E. Gray, ed., McGraw-Hill Book Company. New York, 1963. t These (J values were taken from F. J. Blatt: "Physics of Electronic Conduction in Solids,': pp, 48-49, McGraw-Hill Book Company, New York, 1968.

PROPERTIES OF METALS

9-43

extremal areas A were given in angstroms or atomic units, the conversion to frequency F was made, using the following relations: F (gauss) = A (a.u.r") X 3.741 X 108 F (gauss) = A (angstroms") X 1.04728 X 10 8

An sign is used for values estimated from graphs. Error estimates are not given here, but can be obtained from the references. If no reference is indicated for a specific measurement, the first reference given for that element is implied. In columns 8 and 9 are given cyclotron mass values obtained from de Haas-van Alphen effect and cyclotron resonance measurements. No attempt has been made to give a complete listing of the values obtained from cyclotron resonance even though more accurate measurements are usually obtained by this technique. In the final column are listed other experiments that have been performed on these metals, using the following abbreviations: r-..J

ASE

CR GM H KE

Anomalous skin effect Cyclotron resonance Galvanomagnetic Helicons Kohn effect

MA

Magnetoacoustic

MT Magnetothermal PA SE

Positive annihilation Size effect

Descriptions of these experiments can be found by referring to the references given in this table.

co TABLE

9d-3.

Car-

1. SIMPLE METALS 1. Aluminum [4] f.c.c. a = 4.0236 [5]

Band

Description

1 2

Full Large closed surface centered at I'

3

Multiply connected surface of [110] arms

rier

Orbit description

h

...............

e

Central sections through K Minimum arm cross sections Arm joints

2. Beryllium [9J h.c.p, a = 3.5814 c = 2.2828

1 and 2 6-cornered coronet

3and4

3. Cadmium [11] h.c.p. a = 2.9684 [12] c = 5.5261 [12]

Cigars

1 and2 Pinched-off monster

4. Calcium [17] f,c,c, a "" 5.57 (R.T.)

h

e

Neck B, belly B2 belly Inner circle Waist central 'Waist noncentral Long section

h

...............

e

AIIL plane Belly ...............

Band 1 caps at H Band 2 undulating cylinder along K-H 3and4 Lens-shaped centered at r ....... Data from polycrystalline samples only

Ii::. Ii::. Mass values, m*/m

Fermi surface nomenclature Metal

I

ELECTRONIC STRUCTURE OF METALS

"Hyperboloidal surface"

Magnetic field direction

[110] [111] [100] [110] [111] [IOO] [110] [100] [111] [100]

uio:

[1120] [1120] [1010] [0001] [0001] [0001] [1010] [1120J [000 I] [1120] [1010] [0001] [0001] [0001] [1120] [lOIoJ

. ...........

F (in 10 6 Gauss)

436.6 [6, 7] 411 [7] 680 [7] 2.86 3.44 3.89 .....0 .26 0.28 0.36 0.466 .....0.51 0.109 12.4 14.82 381 [10] 9.42 9.72 53.5 53.1 5.98 [14] 12.7 [I5] 11.4[I5J .....6 .4 [14] .....61 [14] 196 [15] 64 [1.')] 63 [15J 3.3 13 17.6

de Haasvan Alphen

Cyclotron resonance

. .........

. .........

1.3 [6, 7] 0.130 0.150 0.180

1.3 [8]

Other experiments

GM, MA, SE, ASE, KE, II U1

o r-

0.161 [8] 0.183 [8]

~

c:; I

~0.09

U1 ~

0.091 0.102 0.118 0.0196 0.25 0.34

>-

f-1

t'j

..

........

GM, PA, MT

"U

P:: ~

U1 ~

()

0.164 0.174

............

............ ............ ............ 0.35 0.62 0.65

U1

. ...........

1.23 [l6J .....0 .59 [l6] .....0 .59 [I6]

OM, MA, CR, SE

5. Cesium [181. [106] b.c.c, IJ = 6.045 6. Gallium [19J

1

Free-electron-like spherical surface

....... De Haas-Van Alphen frequencies and masses have not been completely correlated with band structure

e

. ..

, ............... ...............

[110] [100] [111J [100J

136.4 -139 -140 0.135 0.495 0.855 23.5 56.7

[010]

0.345 0.725 19.2 22.5 30.0 63.5 0.20 0.22 0.765 8.3 13 20.5

[001]

7. Indium [21] f.c.t, a = 4.5557 c = 4.9342

1

Full

2

Large closed surface centered at I'

3

Rings of [110] arms

Lead [24J f.c.c, a = 4.90

1 2

Full Large closed surface centered at I'

3

Multiply connected surface of [110] arms

............ ............

0.09730.896 [20J

............

0.05130.728 [20J

............

............

............

GM, MA, SE

"d ;0

0.0630.772 [20]

o

"d

trJ

;0

~

H

trJ

m h

e

Central Noncentral Central Central Central Arm cross section Centered at K Arm junction

s.

1.25-1.40

h

...............

e

Arm cross sections centered at K Junction of arms centered at W Inside four arms

[110] [110] [011] [001] [111] [110] [011] [100] [100] [011] [110]

295 [23] 339 [23J 332 [23] 476 [23] 317 [23] 4.59 8.25 6.05 0.092 0.148 0.140

[110J [111] [l00] [110] [100] [111] [100]

159 [26] 156 [26J 204 [28] 18.1 [26J 24 [26] 22.4 [26] 51.3 [26J

[100]

36.0 [26]

-1.2 [22J

1.17 [23]

-1.3 [22J

1.34 [23J 2.07 [23] 1.54 [23] 0.202 [23] 0.36 [23J 0.27 [23J

............

-1.5 [22] 0.204 0.36

........

. . . .

0.20 0.18 1.09 1.11 1.47 0.51 0.70 0.65 1.20

GM, MA, SE

oI'%j ~ trJ ~

>-

t"4

m

0.18 [23] [25J [25J [25] [25] [25] [25J [25]

0.87 [25]

1.12 1.15 1.58 0.56 0.75 0.70 1.23

[27] [27J [27J [27J [27] [27J [27]

GM, MA, SE, ASE, KE

co

J..

01

TABLE

9d-3.

ELECTRONIC STRUCTURE OF METALS

co

(Continued)

J..

0)

Fermi surface nomenclature

Mass values, Carrier

Metal

Orbit description

Description

Band

Magnetic field direction

F (in 10 6 Gauss)

m*/m

de Haasvan Alphen

Cyclotron resonance

...........

. ...........

Other experiments

I. SIMPLE METALS 9. Magnesium [29] h.c.p, a = 3.20 (R.T.) c - 5.20

1

Cap

h

...............

[0001]

2

Monster

h

Necks tilted ~28. 7° from r A zone line in (1010) Waists

[0001] [1010] [1120] [1120] [1010) [0001]

3

Cigar Lens

3 and 4

10. Mercury [3D, 31] a, b = 2.9863 c = 70°44.6' Rhomb

1

Magnetic breakdown couples 3d-band butterfly and 4thband pockets Multiply connected cylinders parallel to [001)

e e

e

...............

............... ...............

[1120] [0001] [1010] [1120) [0001) [loIo] [1120)

.

GM, MA, CR, ASE

0.11

tn

o

0.138 0.162 0.10

~

H

tj I

tn

8

;>

8 t".J

0.42 0.42 0.49

'"d ~ ~

0.32

tn H

h

...............

Larger orbits

11. Potassiume [321. [106] a = 5. 225 a [33) b.b.c,

norot

1.18 0.804 1.92 1.53 2.70 3.16 2.24 11.7 10.7 115 27.2 27.16 13.9 8.64 7.78

2

Surfaces centered at L

e

...............

1

Nearly spherical, centered at r

e

...............

[011) [2IIl [100) [111) [10Il [2 II) [100] [I oIl [100) [1oIl [Ill) [2III [110] [100) [110) [123)

0.94 1.07 0.735 1.06 1.34 19.3 21.5 15.8 34.0 32.0 34.5 40.0 32.2 182.7 182.4 [34) 182.4 [34)

............

0.20 0.23 0.16

GM, CR, PA

0.15 0.90

1.18-1.25 [34)

I

1. 21 [35)

GM, MA, SE, II

o

tn

12. Sodiume [36] a = 4.225 [33] b.c.c. 13. Rubidiums [34] a = 5.585 [331 b.c.c, 14. Thallium b [371. [1111. [112) a = 3.438 [38] c = 5.478 h.c.p,

1

Nearly spherical, centered at I'

e

...............

Arbitraryb

281.8 b

1.24 (341

. ...........

1

Nearly spherical, centered at I'

e

...............

Average of several diree-

160.3

1.28

.

CR, SE

tions 1 and 2 3 4

15. Tin b [41], [l05] a = 5.80 [42J e = 3.15 b.c.t,

...........

GM, CR, PA, H

Full Crown

h

Hexagonal network

e

1 and 2

Full

...

3

Dumbbells centered at X

h

4

5

Multiply connected intersecting tubes centered at I'

h

Crossed convex lensshaped reentrant region centered at I' Multiply connected tilted tubes with alternate top-up and top-down pearshaped pieces

e

Central Central Central arm Noncentral arm Central ...............

Central Noncentral ...............

...............

Molar-shaped surface centered at I'

[0001] [1120] [1120] [10IoJ [OOOIJ [OOOIJ . ........... [001] [001] [100] [110) [001) [001) [100) [110) [001)

93.5 [39] 98.9 [39] 209 [39] 27.4 [39J 37.6 [39J 218 [39] 1.8 [40] .

...........

1. 72 3.25 15.8 16.7 112 103 32.9 25.6 34.1

............

0.25 [40] . ........... 0.16 [43]

............

GM,MA

10M ~

. ...........

GM, MA, CR, SE

o

'1J

t?;j ~

1-3 .....

t?;j

rfl

0.56 [43) 0.51 (43)

oI'%j ~

t?;j

J-3

e

Large part of pear Smallest cross section of pear inside of tilted tube network Pear section Tilted tubes

6

[1120J

no10]

e

...............

[001] [001) [OOlJ

68.1 63.2 52.8

[110) [110) [100J [100) [OOlJ [110) [100J

80.4 67.7 20.6 20.9 4.45 5.87 4.54

o Low-temperature lattice constant may be in error owing to strained 'Samples [32). • The possibility of a martensitic transformation at the low temperatures makes interpretation difficult.

> t'4

m 0.57 [43)

0.55 [43)

0.31 [43J

1:

-:r

TABLE

9d-3.

Fermi surface nomenclature Metal

Band

Description

I. SIMPLE METALS (Coni.): 16. Zinc [44, 45] ....... ................. a = 2.651 2 Monster c = 4.838 h.c.p,

ELECTRONIC STRUCTUHE OF METALS

Carrier

'"

h

F (in 10 6 Gauss)

............

............

Orbit description

...............

Arms minimum

28° from [0001]

4-arm orbit

[0001] [1120]

Waists

[1120] [1010] [0001] [1120] [1120]

noroi

3

Cigar

e

...............

Lens

e

...............

[lOID] La, Barium [108]

a = 5.000 [118] bee II. TRANSITION METALS 1. Chromium [48], [103] b.c.c.s La, Cobalt [104,110]

a = 2.5071 c = 4.0686 (R.T.) h.c.p, 2. Copper [49J a = 3.603 [50J

.......

3a, Iridium [109,116) a = 3.8387 (R.T.) I,c.c,

. ..

[OOOlJ [111] [l11J [100]

a

(3 'Y

De Haas-van Alphen data not tabulated. See [48] ....... Preliminary results .......

...

. ..............

'"

. ..............

.

...........

4.44 [46] 5.13 [46] 26.6 [46] 33.0 0.446 [46] 1.11 [46] 0.0157 [46] 0.265 [46] 73.5 [46] 73.5 [46J ............ 3.29 4.56 19.5 ~0.2-40

co

Mass values. m*lm de HaasCyclotron van Alphen resonance . ........... ............

. ........... .

...........

I

Other experiments

1+>0-

00

GM, MA, CR, SE, MT

0.44 [44] ~0.11

0.13 0.0075 0.09 ~0.54 [44J ~0.59 [44J . ........... 0.37 0.42 0.92 .

...........

tn

~0.55

[47, 16J [47, 16] 1.20 [47,16]

o

~0.57

t"

...-t

t::1 I

tn

1-3

>-

.

...........

GM

1-3 tr.J "t1

[1123] [0001]

::r:

~4.9

~

~3.8

tn

...-t

o

1

I.c.c.

3. Gold [49] a = 4.065 [50] f.c.c.

.................

(Continued)

Magnetic field direction

1

.......

Sphere with necks touching [111] Brillouin zone faces

Sphere with necks touching [111] Brillouin zone faces

.................

e

Neck

...

Belly

e

Dog's bone 4-cornered rosette Neck

...

Belly

h

Dog's bone 4-cornered rosette . ..............

e

[111] [111J [100]

21. 77 [97J

[100J [111]

581.4 [97J 599.8 [97J 251.4 [97J 246.2 [97J 15.32

[111] [100] (110) (100) (100) (100) [111) [110] [100]

449.3 485.0 [97J 193.8 [97J 200.3 [97J 37.8 55.3 46.3 41.9 205

nio:

0.45 [51]

....... " ....

GM, MA, CR, ASE, PA, MT

............

GM, MA, CR

1.5 [50] 1.4 [51] [51] ~0.29 [47] ~1.3

~1.1

~1.1 ~1.0 ~1.1

[52) [52J [52J [50J

U'l

4. Iron [53, 54] a = 2.86 b.c.c,

5. Lutetium [96] 6. Molybdenum [55] [98, 100] a = 3.147 (R.T.) b.c.c,

...... .

. ..

Ellipsoids

Surface (1) centered at I' Surface (2) centered at I' Octahedron centered at H Surface centered at I' (minority) ? ....... Preliminary results ....... Ellipsoids centered at N

Octahedron centered at II Jack cen tered at

r

Lenses lying along

rH

7. Nickel [57,58] a = 3.5172 [5,59] f.c,c.

...............

...

...............

...

...............

...

...............

[100] [010] [111] [110] [101] [100J [111] [111] [l1OJ [111]

. ,.

...............

[111]

51.8

'"

···············1

[111] [0001] [100]

11.3 3.8 23

. .. h

h

e

e

............... ...............

............... Neck Waists ...............

....... Pockets centered at X

h

. ..............

Necks centered at L

e

...............

c Linearly polarized spin-density wave QII[OOl]. d The dimensions of the hole pockets depend on the orientation of the magnetic field. ellipsoidal model. See Hodge et al. [.'58].

[001] [110] [011] [101] [111] [111] [100] [110] [111] [100] [110] [111] [111] [100] [001] [110] [101] [111] [100] [010] [110] [101] [111] [110] [111]

3.84 4.08 4.11 3.89 4.10 23.8 28.0 369 347 154

31 26 "'29 "'39 24 31 154 [56] '-""116 110 ,-...,12 "'32 36.5 80 [56] ,-...,5.3 ,-...,8.4 ",5.0 "'5.8 5.5 10 .12t"i

,-...,0.44

tn

1.0 1.9 1.4 1.35 0.36 0.25

Thus the de Haas-van Alphen frequencies cannot be referred to a simple rigid

CO ~

~

TABLE

9d-3.

Fermi surface nomenclature Metal

Band

ELECTRONIC STRUCTURE OF METALS

Carrier

Orbit description

Ma.gnetic field direction

Ellipsoids centered at N

. ..

. ..............

. ...........

Jungle gym

...

Similar to Ruthenium

. .. ...

Description

(Continued)

F (in 10 6 Gauss)

CD

Mass values, m*/m de HaasCyclotron van Alphen resonance

I

Other experiments

C,)l

o

II. TRANSITION METALS (Cont.):

8. Niobium [60], [62]. [99] a = 3.29 (R.T.) b.c.c, 9. Osmium [63] a = 2.7304 (R.T.) c = 4.3097 h.c.p. 10. Palladium [64. 65] a = 3.884 f.c.c,

.......

....... .......

Minimum-arm cross section

. .............. . ..............

Closed surface centered at r

e

. ..............

Ellipsoids centered a.t X

h

...............

Open surface 11. Platinum [66]. [107] a = 3.907 [5] f.c,c.

~[111]

....... Closed surface cen-

h

...............

e

. ..............

tered at I' h

...............

Open surface

h

...............

5

Ellipsoids centered at L

h

...............

6

Dumbbells centered

h

...............

Ellipsoids centered ~X

12. Rhenium [68] a = 4.447 [69] c = 2.758 [69] h.c.p,

atL Rotated 60° Rotated 60° 7

Closed surface centered at L

h

...............

Rotated 60° Rotated 60°

[100] [0001] [0001] [0001] [100] [110] [Ill] [100] [001] [110] [101] [Ill] [100] [110] [100] [110] [Ill] [100]

rOOn

[111] [100] [110] [101] [0001] [1010] [1120] [0001] [0001] [1010] [1010] [1120] [1120] [1010] [1010] [1120]

63-86 [62]

............

[61] 1. 28 (62]

. ...........

GM

2.0 2.31 1.95 1.05 0.625 1.05 0.770 0.862 2.37 6.2 2.44 [651 3.16 [651 2.06 [651

. ...........

GM

~1.0

14.5 [62] ~21O ~150 ~3

275 309 244 8.95 5.71 8.95 6.84 7.49 27

............ 290 [65] 324 [65] 260 [65] 1. 11 [671 1. 7 [671 1.45 [65] 27.9 [65] 81.6 [65] 68.1 [65] 4.56 0.77 2.63 7.6 15.6 16.2 14.3 13.6 15.5 79.7 64.8 68

r.n o

t'" ..... tj I

o: ""3

>

""3 tr.J

"'d

. ...........

GM

::r:

~ 00

.....

(1

r.n

0.363 [65] 1.53 [65] 3.32 [651 3.62 [651

8

Open cylindrical surface

..

13. Rhodium [70, 71] a = 3.8044 (R.T.) f.c.c,

l4. Ruthenium [72]' a = 2.69844 (R. T.) c = 4.27305 h.c.p,

.......

I.c.c.

16. Tantalum [62], [75] a = 3.30 (R.T.) b.c.c. 17. Thorium [78] a = 5.084 (R.T.)

.

[0001] ~[1120]

...

Ellipsoids along I'-X

'"

................

Closed surface along I'-X (tentative) Closed surface centered at I' (tentative) ....... Closed surface probably centered at I'

...

...............

[100] [110] [101] [111) [111] [100] [001] [110] [101] [111] [110]

...

...............

[Ill]

h

e

Surface centered on line M-L

...

....... Distorted ellipsoids centered at N

...

...............

............... ...............

e

Neck Belly

'"

Dog's bone 4-cornered rosette ...............

...

Butterfly-shaped pieces along [110]

e

• Identification of orbits tentative.

. ..............

...

Jungle gym

I.c.c.

90 300 3.34 2.69 5.07 2.32 4.25 15.6 24.6 17.5 26.3 18.9 48.5 180

0.20 0.14 0.22 0.12 0.30 0.35 0.42 0.43

I

~0.5

0.43 1.2

""d

1.65

~

o

Two closed surfaces centered at I'

....... Sphere with necks touching [Ill] Brillouin zone faces

.......

...............

Ellipsoids along I'-L

..... ...... ....

Surface centered at L L5. Silver [73] a = 4.069 [50]

e

. ..

............... . ..............

7 and 8

Minimum-arm cross section ...............

[0001] [1 00] [1120] [0001] [1010] [1120J [OOOlJ [10IOJ [1120] [1010] [1120J [111J [l11J [100] [110J [lOOJ ............ [100] [100] [100] [110] [110] [111]

""d

~8

t?:j ~

~15

t-:l

~15

H

160-210 130-190 130-200

t?:j

W

o

~20

l"'.J

~7.5 ~8.0

~

~3.5

t?:j

~4

t-:l

8.921 [49] 460.0 [49] 474.6 [97] 201.6 [97] 196.3 [97) 45-63 [62J ~29

~0.4

[74J

~0.9

[74J

~1.0

[74J

~0.8

[76] (1.1-1.25) [77]

............

............

OM. MA, CR. ASE. MT

>

t'"

W

OM

[62]

10.0 11. 9 2.0 9.6 11.7

[79] [79] [79] [79] [79]

0.66 [79] 0.58 [79] 0.58 [79]

co I

Dl ~

TABLE

9d-3.

Fermi surface nomenclature Metal

Carrier

Orbit description

Quasi-spherical surface centered at I'

h

...............

Dumbbell-shaped pieces centered at L with axes along [111) ....... Ellipsoids centered at N

h

...............

h

. ..............

Band

Description

(Continued)

ELECTRONIC STRUCTURE OF METALS

Magnetic field direction

F

(in

10 6

Gauss)

co

Mass values, m*/m de HaasCyclotron van Alphen resonance

I

Other experiments

CJl

I:\J

II. TRANSITION METALS (Cont.):

18. Tungsten [80. 81) a == 3.162 (80)

b.c.c,

Octahedron centered at H Jack centered at

r

h

e

............... Necks Ball of jack

19. Vanadium [96) a = 3.0259

....... Preliminary results

. ..

Central orbit around jack body Two-ball orbit Four-ball orbit Ellipsoids at N

.......

. ..

. ..............

b.c.c, 20. Ytterbium [17], [83] a = 5.486 (84)

f.c.c. 21. Zirconium [851. [1141.

3

.................

Surface centered at r

h

[115) a = 3.23 c = 5.146 (R.T.) h.c.p. 4

h

...............

[llO) (111) (100)1 (110) (111) [111) [110] [101] (011) (111) [111] [100] (001) (100) [111) (110) [100) [111) (110) [100] [110) [112) [111) [100) [110) [110) [110) [110) [100) [100) (110) (112) [111) [0001) [1120) (1010)

[00011

24.8 (79) 24.8 (79) 22.1 (79) 19.9 (79) 22.5 (79) 10.9 (79) 6.87 8.03 9.22 7.03 7.66 5.93 8.54 143.5 98.8 106.9 6.12 23.03 19.5 21.81 22.84 69.1 63.8 178.4 120.4 66.75 55.5 52.7 60.3 ~52

~0.17 ~0.17

1.4-1.8 (86) ~37 [86) ~36 [86)

~34.5

~50

1861

0.75 (79) 0.58 (79) 0.27 0.32 0.36 0.287 0.287 [55] 0.28 [55) 0.37 0.93 0.60 0.67 0.25 0.75 [55) 0.58 0.60 0.9

............ ............ 1.782.3

0.27 [82] 0.32 (82) 0.36 [82]

GM, MA, CR, SE Ul

o

0.23 0.33 1.05 0.57 0.67

(82) (82) [82) [82) [82)

....tjt"I I

Ul

1-3

> 1-3 t?=.l

'"d 0.54 [82) O. 55-0 . 58 [82) 0.83 [82) 2.86 [82) 1.83 [82)

:::r:

~

u: ....

o

to

5

Multiply connected

e

...............

[0001) [0001) [0001)

"-110 [86) "-77 [86) "-59 [861

III. SEMIMETALS 1. Antimony [87) a = 4.3007 c = 11.222 [88) (hexagonal axes) trigonal

....... Closed pockets cen-

Six equivalent e llipsoidal pockets centered on the mirror plane

2. Arsenic [89, 90) trigonal

3. Bismuth [91], [113) a - 4.53 c - 11. 797 (hexagonal axes) trigonal

.......

h

Three closed centrosymmetric pockets tilted 86.4° from trigonal

e

Six pockets connected by long thin necks

h

....... Ellipsoids with one axis parallel to the binary axis and the other two tilted ~6° from the trigonal and bisectrix axes, respectively Ellipsoid

4. Carbon (graphite) [93) ....... Ellipsoidal surface a = 2.46 centered at K along K-H c = 6.70 hex Ellipsoidal surfaces along K-H Caps at ends of electron surfaces above (minority carriers) J

e

tered at L

e

Minimum cross section Maximum cross section

87.7°(/

0.68

174.0°(/

4.35

Binary 53.0°(/ Minimum cross section 148.8°(/ Maximum cross section Binary ............ 86.4°(/ Minimum cross section -9.0°(/ Maximum cross section Binary ............ -9.6°(/ Neck minimum cross section Trigonal Neck 37.25°(/ Principal pockets minimum cross section ............... Binary Binary Bisectrix Bisectrix Trigonal

3.6 0.613

.............

. ...........

GM, MA, CR, MT

. ...........

MA,' R

0.084 0.069

1.98 2.16 2.13

0.163 0.130

'"d

9.58

!:d

o

7.68 0.0258

'"d t"'.1

!:d 8

0.028 1.49 0.189 0.0139 0.0240 0.012 0.084

~

t"'.1 tn 0.14 [92) ............ ............ 0.009 [92) 0.11 [92]

. ........... . ........... . ...........

ol'%j ~ t"'.1 8

.> ~

h

...............

hh

...............

eh

...............

eh

...............

m

Binary Bisectrix Trigonal lie ..ie

0.223 0.223 0.0635 0.0625 [94J 0.77 [94J

0.067 0.057 [94J 0.68 [94]

lie ..ie lie ..ie

0.046 [94J 0.67 [94J 0.0074 [94J 0.067 [94J

0.039 [94] 0.47 [94J 0.0023 [94J 0.017 [94J

. ...........

Frequencies associated with dumbbell and quasi-sphere merge at [100].

o Tilt from trigonal in trigonal-bisectrix plane. h

GM, CR, MA, MT, H, SE, ASE

Experiments on py rolytic graphite [95] suggest that the surfaces attributed to holes should be attributed to electrons and vice versa.

GM, MA, CR

co I

01 Cl,j

9-54

SOLID-STATE PHYSICS

References for Section 9d and Table 9d-3 1. Gold, A. V.: "Solid State Physics," vol. 1, pp. 120-126, J. F. Cochran and R. Haering, eds, Gordon and Breach, Science Publishers, Inc., New York, 1968. 2. Pearson, W. B.: "Lattice Spacings and Structure of Metals and Alloys," Pergamon Press, New York, 1958. 3. Koster, G. F.: Solid StatePhys. 5,173-256 (1957). 4. Larson, C. 0., and W. L. Gordon: Phys. Rev. 156,703 (1967). 5. Armstrong, R. W.: Private communication. 6. Priestley, M. G.: Phil. Mag. 7, 1205 (1962). 7. Anderson, J. R, and S. Lane: Phys. ne« B2, 298 (1970). 8. Spong, F. W., and A. F. Kip: Phys. Rev. 137, A431 (1965). 9. Tripp, J. H., W. L. Gordon, P. M. Everett, and R. W. Stark: Phys. Letters 26A, 98 (1967). 10. Watts, B. R: Proc. Roy. Soc (London), ser. A, 282, 521 (1964). 11. Alekseyevsky, N. E., and V. S. Yegorov: Zh. Eksperim. i Teor. Fiz. 55, 1153 (1968). 12. Jones, R C., R. G. Goodrich, and L. M. Falicov: Phys. Rev. 174,672 (1968). 13. Naberezhnykh, V. P., A. A. Mar'Yakhin, and V. L. Mel'Nik: Soviet Phys.-JETP 25, 403 (1967). 14. Tsui, D. C., and R W. Stark: Phys. Rev. Letters 16, 19 (1966). 15. Grassie, A. D. C.: Phil. Mag. 9,847 (1964). 16. Shaw, M. P., T. G. Eck, and D. A. Zych : Phys. Rev. 142,406 (1966). 17. Condon, J. H., and J. A. Marcus: Phys. Rev. 134,A 446 (1964). 18. Okumura, K., and I. M. Templeton: Proc. Roy. Soc. (London), ser. A, 287,89 (1965). 19. Goldstein, A., and S. Foner: Phys. Rev. 146,442 (1966). 20. Moore, T. W.: Phys. Rev. 165,864 (1968). 21. Hughes, A. J., and J. P. G. Shepherd: Journal of Physics C (Solid State Physics) 2, 661 (1969). 22. O'Sullivan, W. J., J. E. Schirber, and J. R Anderson: Phys. Letters 27A, 144 (1968) 23. Mina, R T., and M. S. Khaikin: Soviet Phys-JETP 24,42 (1966). 24. Anderson, J. R, and A. V. Gold: Phys. Rev. 139, A1459 (1965). 25. Phillips, R. A., and A. V. Gold: Phys. Rev., 178,932 (1969). 26. Anderson, J. R, W. J. O'Sullivan, and J. E. Schirber: To be published. 27. Mina, R T., and M. S. Khaikin: Soviet Phys.-JETP 18, 896 (1964). 28. Anderson, J. R., and D. C. Hines: Phys. Rev. B2, 4752 (1970). 29. Stark, R W.: Phys. Rev. 162, 589 (1967). 30. Brandt, G. B., and J. A. Rayne: Phys. Rev. 148, 644 (1966). 31. Dishman, J. M., and J. A. Rayne: Phys. Rev. 166,728 (1968). 32. Thomas, R L., and G. Turner: Phys. Rev. 176,768 (1968). 33. Barrett, C. S.: Acta Cryst. 9, 671 (1956). 34. Shoenberg, D., and P. J. Stiles: Proc. Roy. Soc. (London), ser. A, 281, 62 (1964). 35. Grimes, C. C., and A. F. Kip: Phys. Rev. 132, 1991 (1963). 36. Lee, M. J. G.: Proc. Roy. Soc. (London), ser. A., 295,440 (1966). 37. Aleksandrov, B. N.: Soviet Phys. JETP-26, 508 (1968). 38. Barrett, C. S.: Phys. Rev. 110, 1071 (1968). 39. Priestley, M. G.: Phys. Rev. 148, 580 (1966). 40. Anderson, J. R., J. E. Schirber, and D. Stone: Grenoble High Pressure Conference Proceedings 188, 131 (1970). 41. Craven, J. E., and R. W. Stark: Phys. Rev. 168,849 (1968). 42. Statleu, M. D., and A. R de Vrooman: Phys. Stat. Solidi 23, 675, 683 (1967). 43. Vaughan, R W., and D. D. Elleman: Bull. APS 13, 1454 (1968). 44. Ventsel, V. A., A. I. Likhter, and A. V. Rudnex: Soviet Phys-JETP 26, 73 (1968). 45. Ventsel, V. A.: Zh. Eksperim. i Teor. Fiz. 55, 1191 (1968). 46. Higgins, R J., J. A. Marcus, and D. H. Whitmore: Phys. Rev. 137A, 1172 (1965). 47. Shaw, M. P., P. I. Sam path, and T. G. Eck: Phys. Rev. 142,399 (1966). 48. Graebner, J., and J. A. Marcus: Phys. Rev. 175, 659 (1968). 49. Jan, J. P., and I. M. Templeton: Phys. Rev. 161, 556 (1967). 50. Shoenberg, D.: Phil. Trans. Roy. Soc. London, ser, A, 255, 85 (1966). 51. Joseph, A. S., A. C. Thorsen, E. Gertner, and L. E. Valby: Phys. Rev. 148,569 (1966). 52. Joseph, A. S., A. C. Thorsen, and F. A. Blum: Phys. Rev. 140, A2046 (1965). 53. Panousis, P. T.: USAEC Rept. IS-T-175, 1967; and to be published. 54. Gold, A. V.: J. Appl. Phys. 39, 768 (1968). 55. Sparlin, D. M., and J. A. Marcus: Phys. Rev. 144, 484 (1966). 56. Meyers, A., and G. Leaver: "Proceedings 10th Conference on Low Temperature Physics," vol. 3, p. 290, Viniti Publishing House, Moscow, 1967. 57. Tsui, D. C.: Phys. Rev. 164, 669 (1967).

PROPERTIES OF METALS 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. 75. 76. 77. 78. 79. 80. 81. 82. 83. 84. 85. 86. 87. 88. 89. 90. 91. 92. 93. 94. 95. 96. 97. 98. 99. 100. 101. 102. 103. 104. 105. 106. 107. 108. 109. 1l0. 111. 112.

9-55

Hodges, L., D. R Stone, and A. V. Gold: Phys. Rev. Letters 19, 655 (1967). Heumann, T.: N aturioissenschaften 32, 296 (1944). Fawcett, E., W. A. Reed, and R. R. Soden: Phys. Rev. 159,513 (1967). Thorsen, A. C., and T. G. Berlincourt: Phys. Rev. Letters 7, 244 (1961). Halloran, M., J. H. Condon, J. E. Graebner, J. E. Kunzler, and F. S. L. Hsu, Phys. Rev. lB, 366 (1970). Kamm, G. N., and J. R Anderson, Phys. Rev. B2, 2944 (1970). Vuillemin, J.: Phys. Rev. 144, 396 (1966). Windmiller, L. R., J. B. Ketterson, and S. Hornfeldt, J. Appl. Phys. 40, 1291 (1969). Windmiller, L. R, and J. B. Ketterson: Phys. Rev. Letters 21, 1076 (1968). Stafieu, M. D., and A. R DeVroomen: Phys. Letters 19, 81 (1965). Thorsen, A. C., A. S. Joseph, and L. E. Valby: Phys. Rev. 150,523, (1966). Matteiss, L. F.: Phys. Rev. 151, 450 (1966). Coleridge, P. T.: Proc. Roy. Soc. (London), ser. A, 295,458 (1966). Ketterson, J. B., L. R Windmiller, and S. Hornfeldt: Phys. Letters 26A, 115 (1968). Coleridge, P. T., Phys. Letters 22,367 (1966) and Journal of Low Temperature Physic8 1,577 (1969). Lewis, P. E., and P. M. Lee: Phys. Rev. 175, 795 (1968). Joseph, A. S., and A. C. Thorsen: Phys. Rev. A138, 1159 (1965). Fawcett, E., W. A. Reed, and R R. Soden: Phys. Rev. 159,533 (1967). Thorsen, A. C., and T. G. Berlincourt: Phys. Rev. Letters 7, 244 (1961). Condon, J. H.: Bull. Am. Phys. Soc. 11, 170 (1966). Thorsen, A. C., A. S. Joseph, and L. E. Valby: Phys. Rev. 162,574 (1967). Boyle, D. J.: USAEC Rept. IS-T-261, 1968; D. J. Boyle and A. V. Gold: Phys. Rev. Letters 22, 461 (1969). Girvan, R. F., A. V. Gold, and R. A. Phillips: J. Phys. Chem. Solids 29, 1485 (1968). Girvan, IL F.: USAEC Rept: IS-T-103, 1966. Walsh, W. M., Jr.: In "Solid State Physics, vol. 1, p. 160, J. F. Cochran and R. Haering, eds., Gordon and Breach, Science Publishers, Irio., New York, 1968. Tanuma, S., Y. Ishizawa, H. Nagasawa, and T. Sugawava: Phys. Letters 25A, 669 (1967) . Gschneidner, K. A., Jr.: "Rare Earth Alloys," D. Van Nostrand Company, Inc., Princeton, N.J., 1961. Loucks, T. L.: Phys. Rev. 159, 544 (1967). Thorsen, A. C., and A. S. Joseph: Phys. Rev. 131, 2078 (1963). Windmiller, L. R.: Phys. Rev. 149,472 (1966). Barrett, C. S., P. Cucka, and K. Haefner: Acta Cryst. 16,451 (1963). Vanderkooy, J., and W. R. Datars: Phys. Rev. 156, 671 (1967). Priestley, M. G., L. R. Windmiller, J. B. Ketterson, and Y. Eckstein: Phys. Rev. 154, 671 (1967). Bhargava, R. N.: Phys. Rev. 156, 785 (1967). Kao, Y. H.: Phys. Rev. 129,1122 (1963) McClure, J. "Y., and W. J. Spry: Phys. Rev. 165,809 (1968). Soule, D. E.: IBM J. Res. Deoelop, 8, 268 (1964). Schroeder, P. P., IVI. S. Dresselhaus, and A. Javan: Phys. Rev. Letters 20, 1292 (1968). Phillips, R. A.: Private communication. O'Sullivan, W. J., A. C. Switendick, and J. E. Schirber: Phys. Rev. lB, 1443 (1970>' Boiko, V. V., V. A. Gasparov, 1. G. Gverdtsiteli, Soviet Phys. JETP 29, 267 (1969). Scott, G. B., and M. Springf'ord, Proc. Roy. Soc. (London) A320, 115 (1970). Leaver, G., and A. Myers, Phil. Mag. 19,465 (1969). Henmann, R., Phys. Stat. Sol. 25, 661 (1968). Cucka, P., and C. S. Barrett, Acta Crust, 15, 865 (1962). Arko, A. J., J. A. Marcus, and W. A. Heed, Phys. Rev. 185,901 (1969). Reed, W. A., and E. Fawcett, Proc. oj the Int'l Conf, on Magnetism (Inst. of Phys. and Phys. Soc., London) 120 (1964). Vaughan, R. W., D. D. ElJeman, and D. G. McDonald, J. Phys. Chem. Solids 31,117 (1970). Glinski, R., and 1. M. Templeton, Jour. of Low Temp. Phys. 1, 223 (1969). Ketterson, J. B., and L. R. Windmiller, Phys. Rev. 2B, 4813 (1970). McEwen, K. A., Phys. Letters 30A, 77 (1969). Volkenshtein, N. V., V. A. Vovosy dov, V. E. Startsev, Soviet Phys. JETP 31,862 (1970). Anderson, J. R., and D. R. Stone-private commuuicat ion. Ishizawa, Y., and A. E. Dixon, Bull. Am. Phys. Soc. 16,82 (1971). Capocci, F. A., P. M. Holtham, D. Parsons, and M. G. Priestley, Jour. of PhysicB C (Solid State Physics) 3, 2081 (1970).

9-56

SOLID-STATE PHYSICS

Brown, Rodney D., III, Phys. Rev. B2, 928 (1970). Everett, P. M., Bull. Am. Phys. Soc. 16, 336 (1971). Schirber, J. E., Phys. Letters 33A, 172 (1970). Grodski, J. J., and A. E. Dixon, Bull. Am. Phys. Soc. 16,82 (1971). Tanuma, S., W. R. Datars, H. Doi, and A. Dunsworth, Solid State Comm. 8, 1107 (1970). 118. Barrett, C. S., J. Chem, Phys. 25, 1123 (1956).

113. 114. 115. 116. 117.

ge. Properties of Semiconductors H. P. R. FREDERIKSE

The National Bureau of Standards

ge-1. Introduction. This chapter contains a number of numerical values of semiconductor parameters collected from the literature up to November, 1968. Our knowledge is, however, still very uneven. In some cases very detailed information about band structure, transport properties, etc., is available, while for other semiconductors even the energy gap has not yet been determined unambiguously. The data in this chapter are therefore limited to a few groups: elemental semiconductors, III-V compounds, some II-IV compounds, some II-VI compounds, the lead compounds, and a few others. For definitions of electronic parameters and some simple formulas the reader is referred to Sec. 9c. ge-2. Band Structure. In order to illustrate concepts like anisotropic effective mass, spin-orbit splitting, etc., the electronic energy band structure of Ge and Si will be briefly discussed (refs. 1 to 5). Germanium. CONDUCTION BAND. The constant-energy surfaces near the bottom of the conduction band consist of four symmetrically equivalent ellipsoids, whose lengths are oriented along the (111) directions. The four minima (valleys) are located at the edge of the Brillouin zone. Each of these ellipsoids can be described by the following energy-momentum relation:

=

8

px

2

+

PlI Zm,

2

+ 'E.!..2

Znu

where m, and m; are the transverse and longitudinal effective masses, respectively. The effective mass m * in any particular direction of momentum space is given by 1 _ cos! () m *2 - ----rnT

+ sin?

() mtml

where () is the angle between the chosen direction and the longitudinal axis of the ellipsoid. Experiments (ref. 2) indicate that m, m;

=

=

(1.59 (0.082

± 0.03)mo

±

0.0003)mo

9-57

PROPERTIES OF SEMICONDUCTOR,S

At the center of the zone (r 2 ' ) , ~

m*

0.034mo

The density-of-state effective mass m(N) (or average effective mass), which is obtained from conductivity and Hall-effect experiments, is given by

where v is the number of ellipsoids. The value of this parameter for the conduction band of germanium is m/ N ) = 0.55mo. VALENCE BAND. The energy-band structure at the top of the valence band consists of three nearly spherical (warped) surfaces. The maxima are located at the center of the zone [k = 0]. Two of the surfaces are degenerate at the center point. The third is somewhat lower in energy owing to spin-orbit interaction. (The spin-orbit interaction results from coupling between the magnetic dipole fields of the spin and the orbital motion of an electron.) Close to the band edge the energies of the two degenerate surfaces VI and V 2 can be described by 0J,2 =

-

1 -2 mo

IAp 2 ±

[B2p4

+ C 2(Px2p y2 + P1l2p~2 + P22p z2)]1}

and that of the split-off band V 3 by 03 =

-~

1 2mo

_ _-A p 2

where ~ is the spin-orbit splitting energy. The plus sign in the expression for ~h.2 refers to light holes, and the minus sign to heavy holes. In Ge the parameters have the following values: ~ = 0.29 ev mV1 = 0.34mo A = -13.3 ± 0.2 mV 2 = 0.043 mo B = ±8.6 ± 0.1 mV a = 0.08mo C = ±12.5 ± 0.2 For further details see Fig. ge-1. 5

3 5.4eV

.

2

>

.

.s

4.3eV

-3

k=2a.".(t~t)

k=O

k=~ (lOO)

ge-1. The band structure of germanium near the band gap. Energy as a function of wave vector k for the (111) and (100) directions. (After Charles Kittel, "Introduction to

FIG.

Solid State Physics," 3rd ed., John Wiley & Sons, Inc., New York, 1966.)

9-58

SOLID-STATE PHYSICS 5

Si

3.4eV

>

•

t

.!:

Eg-1.0B eV

3.2eV

t

o

4.1eV

-2 -3 L..---;-:-:,.......,.....,

k-

~-----.J>..------~x..

.L.-

Zf(ttt)

k=O

k=2a1T(lOO)

1(111)oxis •I• (l00) oxi 5 • I FIG. ge-2. The band structure of silicon near the band gap. Energy as a function of wave vector k for the (111) and (100) directions. (After Charles Kittel, "Introduction to Solid State Physics," 3d ed., John Wiley & Sons, Tnc., New York, 1966.)

Silicon. CONDUCTION BAND. The constant-energy surfaces near the bottom of the conduction band consist of three symmetrically equivalent ellipsoids whose length axes are oriented along (100) directions. The six minima (valleys) are inside the Brillouin zone. The effective electron mass values are tru = (0.98 m, = (0.19

± 0.04)mo ±

O.Ol)mo

The density-of-states effective mass is me(N)

=

1.lmo

VALENCE BAND. The constant-energy surfaces are similar to those of germanium at the top of the valence band. The parameters for Si are

A A B C

= =

= =

0.044 eV -4.0 ± 0.2 ± 1.1 ± 0.2 ±4.1 ± 0.5

mV l

= 0.52mo

mV 2

=

mV3

=

0.16m o 0.25mo

For further details see Fig. ge-2. References on Band Structure of Ge and Si: 1. Geballe, T. H.: "Semiconductors," p. 313, N. B. Hannay, ed., Reinhold Publishing Corporation, New York, 1959. 2. Kittel, C.: "Introduction to Solid State Physics," 3d ed., p. 316, John Wiley & Sons, Inc., New York, 1966. 3. Cohen, M. L., and T. K. Bergstresser: Phys. Rev. 141, 789 (1966). 4. Aigrain, P., and M. Balkanski, eds.: "Selected Constants of Semiconductors," Pergamon Press, New York, 1961. 5. Putley, E. H.: "The Hall Effect and Related Phenomena," Butterworth & Co. (Publishers), Ltd., London, 1960.

9-59

PROPERTIES OF SEMICONDUCTORS

I II- V Compounds. The bandstructures of the III-V compounds are similar to those of Ge and Si. However, most of the III-V compounds have the maximum of the valence band and the minimum of the conduction band at the center of the Brillouin zone (k = 0). Values of the energy gap Eo, effective masses (electron mass light and heavy hole masses ml~ and h , mass of the "split-off" valence band m:h' free-electron mass mo), and spin-orbit splitting fls.o. are listed in the first seven columns of Table ge-1.

m:,

m:

TABLE ge-1. CHARACTERISTICS OF III-V COMPOUNDS

Eo

Effective masses

at T = 0 K, eV

Lls.o. eV

Compound Direct

m,*/mo mlh*/mo mhh*/mO m.h*/mo

Indirect

--- --- --- --InSb ....... InAs ...... InP ..... InN ...... GaSb ....... GaAs ...... , GaP ...... GaN ........ AISb ........

... .... 0.23 6 0.36 ... . " 1. 29 .. , . ... 2.4 ... 0.81 4 1.85 (XH 1.52 2.88 (I')t 2.32 (X)t 3.3 2.20 (I')t 1. 65 (X)t

AlN ......... 4.6 BP .......... 6.0 (?) Ref ..........

p..

Impurity activation energy, eV

P.h

--- --- --- ---

0.015 0.026 0.073

0.021 0.025 0.078(c)

0.39 0.41 0.4

O.ll(c) 0.08 3 0.15(c)

~0.2

0.047 0.07 0.13(c)

0.06 0.12 O.14(c)

0.3 0.68 0.86(c)

0.14(c)

~.8

0.20 0.24(c)

O.ll(c)

O.ll(c)

0.9

0.22(c)

2.0 1,2

Mobilities, cm2/voIt-sec at 300 K

3

~0.9

78,000 33,000 4,600

750 460 150

0.007 (Zn,p)

4,000 8,800 300

1,400 400 100

0.024 (Zn,p)

0.34 0.13 0.75

200

550

0.43

4

5

0.07 (Te,n) 0.16 (Se,n)

6,7

tAt 77 K. (c) = calculated.

Other Compounds and Elemental Semiconductors. Somewhat less is known about the band structure of other semiconducting compounds and elements. Values for energy gaps, effective masses, and mobilities can be found in Table ge-2. Temperature and Pressure Dependence of the Energy Gap. For most semiconductors the energy gap decreases with increasing temperature. Exceptions are the lead compounds. The change is nearly linear with temperature except at low temperatures. The energy gap also changes with pressure. The thermodynamic relationship between the two is O) ( aG aT

p

=

(aGo) aT v

+ (aaTV)

p

(ap) (aGo) aV T oP T

Temperature and pressure coefficients for a few materials are listed in Table ge-3. References for Table ge-l 1. Willardson, R. K., and A. C. Beer, eds.: "Semiconductors and Semimetals," vol. I, p. 7, Academic Press, Inc., New York, 1966-1968. 2. InN: Ormorrt, B. F.: Zh. Neorqan, Khim. 4, 2176 (19S9); transl.: Russ. J. Lnoro, Chem, 4, 988 09S9). GaN: Grimmeis, H. G., et al.: Z. Naiurforsch: 159,799 (1960). AIN: Ivey, H. F.: Advan. Electron Electron. Phys., suppl. 1, 169 (1963). BP: Archer, R. J., et al.: Phys. Rev. Letters 12, 538 (1964). 3. Reference 1, vol. 2, p. lSI. 4. Reference 1, vol. 2, p. 141. 5. Reference 1, vol. 1, p. 16. 6. Hannay, N. B., ed.: "Semiconductors," p. 389, Reinhold Publishing Corporation. New York, 19S9. 7. AISb: Turner, W. J., and W. E. Reese: Phys. Rev. 117, 1003 (1960).

TABLE

ge-2.

f

CHARACTERISTICS OF SEVERAL ELEMENTAL AND COMPOUND SEMICONDUCTORS

~

o Mobilities at 300 K, cm 2/volt-sec

Effective masses Cornpound

Structure

Ea' eV (T = 0 K)

References

me/mo

Diamond.

cub

Graphite .. hex Se ........ trig Te ....... trig a-Sn ...... cub SiC ....... hex cub MgzSi ..... antifluorite MgzGe .... antifluorite MgzSn .... antifluorite hex tetr monocl orth

Mg3Sbz ... Zn3As2 .... ZnAsz ..... ZnSb .....

5.4 0.0 1.8 (T = 300 K) 0.33 O.Ot 3.0 1.9 0.78 0.57 0.185 (indirect) o.35 (direct) 0.82 0.93 0.9o(llc),O.93(..lc) 0.56

Cd3As 2 ••. tetr CdAs 2 • • • • tetr

-t-3

8,11 9, 12, 13

I-d

14 15 15 9 16 15,17 8

550

600

18a, 18b, 9

1,020

930

18a, 18c, 9

1,620

750

18a, 18d, 9

tr:l

::r1 ~

U1

.... o

U1

ZnO ...... hex ZnS ...... W§ ZnS ...... Z§ ZnSe ...... W§ ZnSe ..... Z§ ZnTe ..... Z§ CdS ...... W§ CdSe ..... CdTe ..... HgSe ..... HgTe ..... AS2Sea.... AS2Tea.... Sb2Sa ..... Sb2Sea .... Sb2Tea .... Bi2Sa ..... Bi2Sea ..... Bi2Tea .... CU20 ..... Ti0 2...... SrTi03 ...

W§

W§ Z§ Z§ Z§ amorph. monocl. ort.horh.

orthorh. rhornb.

orthorh. rhomb. rhomb. cub tetr. cub

3.436 3.910 3.84 2.795 2.83 2.39 2.582

=

0.38 0.27, mil

= 0.28 .................. .

m.l

to.o

••••••••••••••

•

0.1

.................. . m, = 0.171mo, mi = 0.15mo

1.840 1.607

0.13

.................. .

-0.24~

.....................

-0.30~

=

m.l

1.8 0.58, mil

.............................. to

..........................

..............

•••

0

00

••••••••

•••••••••••••

•

•

.................. .

00

•••••

...................... . ...................... . m.l = 5mo, mil = 0.7mo

=

m.l to

0.17t 0.35t to

..................

0

........

0

••

0

0

••••••••

•••••••••••••

0

•••••

.................. . = 1.5mo, mi = 6.0mo

m,

0"

.,

0

•••••

•••••••••••••••

0

0

••••

0

0

0

0.

..........

•

.0

•••

....

0'

0

•••••••

0

•••

00.

0

••••••

o

••

•••••

...........

to

0

to

•••••••

o

....

........

_0.0

to

1.0(llc); 0.2(1.c) 5

t:tj

.0 . . . . . . . . . .

80 45 270

e

••••••••••

0

0

~

26

515 100 e

m a:

........... ...........

••

""d

8~

............ }25

••

""d

~

0

t:tj ~

•

......

•••••••••••

00

19 (Eg,m*) 20-22 23, 24 (p.)

75 [24] ....

600 1,250

•

•

.0 ..•......

............. ............ . ............ .

O'

•••••

_0

••••

...........

170 15

•

0.51 0.5 •••

•

••••••••

600 {22) 900 [23)

0.

••••••••••••••

0.45 0.5

•••••

..................

...............................

.0.0

•

••

••••••

t

0

210 [8]

...........

••••••

•

••••

0.45, mil ~ mo

••

•

0

•

r",

••

............ .

...........................

.................. . ••••••••••••••

•

••••••••

••

.t'

100 [9)

...................... . ...................... .

0

0

0.6

..

..

100 [20] 140 (21)

?

••••••••••••••••

0.027t

1.6 1.0 "-'1.7 "-'1. 2 0.3 1.3 0.35 0.2 2.172 113 . 03; 1. 3 . 04 3.4

=

••••••••

1 26,27 28a, 28b, 8 • 9, 29 30, 31

t:tj

a::

~

0

0

Z

tj

q 0

8 0

~

tn tAt k = O. t Density-of-states mass. § W = wurzite; Z = zincblende. 'If HgSe and HgTe are semimetals.

The "energy gap" quoted is E(re) - E(rs) which is negative.

f

~

......

9-62

SOLID-STATE PHYSICS

References for Table ge-2 1. 2. 3. 4. 5. 6. 7. 8. 9. lOa.

lOb. 11. 12. 13. 14. 15. 16. 17. 18a. 18b. 18c. 18d. 19. 2). 21. 22. 23. 24. 25. 26. 27. 28a. 28b. 29. 30. 31.

Mitchell, E. J. W.: J. Phys. Chem. Solids 8,444 (958). Clark, C. D.: Proc. Roy. Soc. (London), ser. A, 277, 312 (964). Rauch, C. J.: Phys. Rev. Letters 7, 83 (1961). Rauch, C. J.: "Proceedings International Conference on the Physics of Semiconductors," p. 276, Exeter, Institute of Physics, L ndon, 1962. Redfield, A. G.: Phys. Rev. 94, 526 (954). Soule, D. K, and J. W. :McClure: J. Phys. Chem. Solids 8, 29 (959). Soule, D. K: Phys. Rev. 112, 698 (1958). Putley, K H.: "The Hall Effect and Related Phenomena," Butterworth & Co. (Publishers), Ltd., London, 1960. Aigrain, P., and IVI. Balkanski, eds.: "Selected Constants of Semiconductors," Pergamon Press, New York, 1961. Groves, S., and W. Paul: "Proceedings of the International Conference on the Physics of Semiconductors," p. 41, M. Hulin, ed., Dunod, Paris, 1964. Morris, IL G., R. D. Redin, and G. C. Danielson: Phys. Rev. 109, 1909 (1958). Lott, L., and D. Lynch: Phys. Rev.Hl, 681 (1966). Lipson, H. G., and A. Kahan: Phys. Rev. 133, 800 (1964). Lawson, W. D., et al.: J. Electron. 1, 203 (1955). Busch, G., et al.: Helv. Phys. Acta 27, 249 (1954). Turner, W. J., et al.: Phys. Rev. 121, 759 (1961). Haidemenakis, K D., et al.: J. Phys. Soc. Japan 21, 189 (1966). Turner, W. J., et al.: J. Appl. Phys. 32, 2241 (1961). Mitchell, K D., et al.: "Proceedings International Conference on the Physics of Semiconductors," p. 325, M. Hulin, ed., Dunod, Paris, 1964. Cuff, K. F., et al.: ref. 18a, p. 677. Berman, S.: Phys. Rev. 158, 723 (1967). Numata, H., and Y. Uemara: J. Phys. Soc. Japan 19, 2140 (1964). Reynolds, D. C., et al., Phys. Stat. Solidi 12, 3 (1965). Thomas, D. G.: J. Phys. Chem. Solids 10, 47 (1959). Aven, M., and C. A. Mead: Appl. Phys. Letters 7, 8 (965). Heinz, D. M., and E. Banks: J. Chem. Phys. 24, 391 (1956). Segall, B., et al.: Phys. Rev. 129, 2471 (1963). Yamada, S.: J. Phys. Soc. Japan 17,645 (1962). Harman, T. C.: "Proceedings of the International Conference on II-V Compounds," p. 982, D. G. Thomas, ed., W. A. Benjamin, Inc., New York, 1967. Black, et al.: J. Phys. Chem. Solids 2, 240 (1957). Drabble, J. R.: Proc. Phys. Soc. (London) 71, 430 (1958); ibid., 72, 380 (1958). Knox, IL S.: Solid State Phys. suppl, 5, 53 (1963). Gross, E. F.: J. Phys. Chern, Solids 8, 172 (1959). Frederikse, H. P. R.: J. Appl. Phys. 32 (suppl.}, 2211 (1961). Cohen, M. 1., and R. F. Blunt: Phys. Rev. 168, 929 (1968). Frederikse, H. P. R., et al.: J. Phys. Soc. Japan 21, (suppl.), 32 (1966.

9-63

PRO PERTIES OF SEMICONDUCTORS TABLE

ge-3.

TEMPERATURE AND PRESSURE DEPENDENCE OF THE ENERGY GAP

(fJtO/oT)p,

C .................. Si ................. Ge ................ a-Sn ............... Se ................. Te ................. SiC ................ InSb ............... InAs .............. InP ................ GaSb .............. GaAs .............. GaP ............... AISb ............... ZnO (W) ........... ZnS (W) ........... ZnSe (W) ......... . . CdS (W) ........... CdSe (W) .......... PbS ............... PbSe ............... PbTe ..............

2.3 (X)

-

3.7

-

-

-

+ '"'-/

'"'-/

3.5

9.5 3.8 7.2 5.0 4.6 3.7 4.0 4.0


< 111 > directions in germanium. [After Brockhouse and Iyengar, J. Phys. Chem. Solids 8, 400 1959.]

Data on WT, WL, e*, 00, and elastic constants for a number of semiconductors are assembled in Table ge-9. References 1. Born, :1\1., and V. Huang: "Dynamical Theory of Lattices," p. 114, Oxford University Press, New York, 1954. 2. Brockhouse, B. N., and P. K. Iyengar: Phys. Rev. 111, 747 (1958).

ge-9. Refractive Index and Dielectric Constant. The dielectric constant in ionic lattices depends on frequency. Neglecting dissipative forces this dependence is given by ( ) E W

=

Est -

E""

+1_

E""

(w/ W T )2

where WT is the lattice vibration frequency for long-wavelength transverse waves. For high frequencies W » WT: E = E"", the optical dielectric constant; for low frequencies E = Est, the static dielectric constant. The optical dielectric constant is related to the refractive index by the following expression: For nonpolar materials Est = E"". The dielectric constants of Ge and Si are 16 and 11.8, respectively, Values of nand Estforother semiconductors are given in Table ge-9.

TABLE

ge-9.

LATTICE PROPERTIES OF SEMICOND UCTORS

1011 N/m 2 at 300 K WT,

cm" !

WL,

cm " !

e

Ref.

E.

e*

n

Ref.

-- -Diamond ......... Si ................ Ge ............... InSb ............. InAs ............. InP .............. GaSb ............. GaAs ............. GaP .............. A1Sb ............. BN .............. ZnS(Z) ........... CdS(W) .......... PbS .............. PbSe ............. PbTe ............. Ti02 .............

1,333 518 309 180 218.9 303.7 230.5 268.2 366.3 318.8 820 339 261 238 65

...... . 31 125-167 400-533

.......

....... . ...... 191.3 243.3 345 240.3 290.5 401.9 339.6 835 298 295

....... 223

1a 1a 1a 1b 1b 1b Ib 1b 1b 1b 1b 6a 6a

. .. 9

44 8 10 110 360-400 } 15 770-823

1.25 0.639 0.483 0.367 0.453

10.76 1.656 1.288 0.672 0.833 •

0

•••••

•

••

•

.......... .

•

0

•••

••••

•

•

•

0

•

0

•••••

•

•••••

•

••

0.442

0.894 ••

•

..........

•

.

1.08 0.273 Cn = 0.149

•

0

••••••••

•

0.077 0.176 C33 = 0.484

645 374 203 247 321 266 344

. .......... 0.433 0.594 •

0

••••••••

.....

•

292

0.415 •

0.653 1.046 0.581 0.907 Cl3 = O. 510lC33 = 0.938 0.298 1.27 0.38 1.02

.......... .

2240

5.76 0.796 0.671 0.302 0.396

0.404 0.538

0.885 1.188

0

•••••

~

~

C44

C12

Cll

Ref.

•••

.....

•

0.461 0.150 }

315

..... 227

0.248 0.25

.......... .

0.134 0.125 C 6 6 == 0.194

..... 138 125 } "'758 ....

.

I

5.5 11.7 15.8 17.88 14.55 12.37 15.69 13.13 10.18 11.2 7.1 ..... 8.3 6b Ell = 9.4} 6b E33 = 10.3 205 11, 14 12 280 14 400 13, 14 16 173 (e) } 89 (a) ..... Ie 4 4 3 3 3 3 3 3 3

2.4 3.44 3.97 3.96 3.44 3.1 3.8 3.3 2.9 3.14 2.1 2.24 2.29

0 0 0 0.42 0.56 0.66 0.33 0.51 0.58 0.48 1.14 0.48

1d 1d 1d 2 2 2 2 2

o

'"d trj

~

~

H

trj

W

o

I"'.:l tn trj

~

2

H

o Z

...

2 2 5 6a

17.4

. ...

8

23.6 5.63

. ... 0.55

8 5

.... .

....

15

.

o

tj

q

o ~ o ~

u:

I

c.o I

-l

~

9-74

SOLID-STATE PHYSICS

References for Table ge-9

la. Cowley, R. A.: Proc. Phys. Soc. (London) 88 (II) , 463 (1966). lb. Hass, Marvin: in "Semiconductors and Semimetals," vol. I, p. 7, R. K. Willardson and A. C. Beer, eds., Academic Press, Inc., New York, 1966-1968. Ic. McSkimin, H. J., and W. L. Bond: Phys. Rev. 105, 116 (1957). Id. Aigrain, P., and M. Balkanski, eds.: "Selected Constants of Semiconductors," Pergamon Press, New York, 1961. 2. Hass, Marvin: In "Semiconductors and Semimetals," vol. I, p. 14, R. K. Willardson and A. C. Beer, eds., Academic Press, Inc., New York, 1966. 3. Drabble, J. R.: in "Semiconductors and Semimetals," vol. 2, p, 110, R. K. Willardson and A. C. Beer, eds., Academic Press, Inc., New York, 1967. 4. McSkimin, H. J.: J. Appl. Phys. 24, 988 (1953). 5. Burstein, E.: In "Lattice Vibrations," p. 315, R. Wallis, ed., Pergamon Press, New York, 1965. 6a. Reynolds, D. C., et al.: Phys. Stat. Solidi 12, 3 (1965). 6b. Berlincourt, D., et al.: Phys. Rev. 129, 1009 (1963). 7. Zemel, J. N., et al.: Phys. Rev. 140, A330 (1965). 8. Burstein, E., et al.: "Proceedings of the International Conference on the Physics of Semiconductors," p. 1065, M. Hulin, ed., Dunod, Paris, 1964. 9. Elcombe, M. 1'.1.: Proc. Roy. Soc. (London), ser. A, 300, 210 (1967). 10. Cochran, W., et al.: Proc. Roy. Soc. (London) ser. A, 293,433 (1966). 11. Bhagavantam, S., and T. S. Rao: Nature 168, 42 (1951). 12. Ramachandran, G. N., and N. A. Wooster: Acta Cryst. 4, 335 (1951). 13. Houston, B., et al.: J. Appl. Phys. 39, 3913 (1968). 14. Parkinson, D. H., and J. E. Quarrington: Proc. Phys. Soc. (London), ser. A, 67, 569 (1954). 15. Cronerneyer, D. C.: Phys. Rev. 112, 800 (1958). 16. Values corrected by F. Birch from work by Verma, R. K.: J. Geophys. Res. 65. 757 (1960) .

9f. Properties of Ionic Crystals R. J. FRIAUF 1

University of Kansas K. F. YOUNG 2

The National Bureau of Standards W. J. MERZ 3

RC A Laboratories Zurich, Switzerland

IONIC CONDUCTIVITY AND DIFFUSION IN IONIC CRYSTALS 9f-1. Ionic Conductivity and Diffusion. These phenomena are ascribed to the presence of ionic defects-vacancies where ions are missing from normally occupied positions and ions in interstitial positions in the structure. Schottky defects are comIonic Conductivity and Diffusion. Dielectric Constants of Inorganic Crystals. 3 Piezoelectric and Pyroelectric Properties; Ferroelectric and Antiferroelectric Properties. I

2

PROPEHTIES OF IONIC CRYSTALS

9-75

binations of cation and anion vacancies, as in the alkali halides and alkaline earth oxides. Frenkel defects are combinations of vacancies and interstitial ions, for cations as in the silver halides, or for anions as in the alkaline earth halides. At high temperatures the defects exist in thermodynamic equilibrium in the crystal; for Schottky defects in 1\1X crystals, for example, the concentration or mole fraction increases with temperature according to (ref. 23) X =

Xo

exp ( -

hf ) 21 kl'

Xo

=

exp ( :21

Sf)

k

(9f-1)

where h f and Sf are the enthalpy and entropy of formation of a pair of defects. At lower temperatures the mole fraction is usually controlled by the presence of aliovalent impurities. The random jumping of a defect gives rise to a microscopic diffusion coefficient for the defect of do =

i/la 2 exp (~s)

(9f-2)

where /I is an attempt frequency, a is the jump distance, and Sh. and tJ.s are the activation enthalpy and entropy for the jump. (The factor t is appropriate for a cubic lattice.) In an electric field there is also a drift mobility M = Mo exp ( -

:~)

(9f-3)

Here Mo has been obtained from do with the microscopic Einstein relation

d

kl'

M

q

(9f-4)

The conversion factor is kle = 0.862 X 10- 4 volt/K with din crn-/sec and Min cm 21 volt-sec. Equations (9f-1) to (9f-3) are used to express the observed conductivity and diffusion coefficients in the following sections. Ionic crystals covered in these tables include halides, simple inorganic radicals (such as nitrates and azides), binary oxides, and the other chalcogenides (sulfides, selenides, and tellurides). Excluded from consideration are III-V compounds, ternary oxides (such as spinels and perovskites), and glasses and zeolites. Conductivity and selfdiffusion coefficients are given for pure crystals only, but some information from experiments on doped crystals is contained in Table 9f-2. The effect of high pressure on conductivity and data for mixed electronic and ionic conductors are also presented. Space limitations prevent any consideration of the extensive recent literature on dielectric and anelastic relaxation, thermoelectric phenomena, and effects of radiation and plastic deformation on conductivity and diffusion. Similarly the diffusion of all foreign ions is excluded because of the proliferation of results. Many of the excluded topics are discussed in some of the books and review articles given in the general references. 9f-2. Conductivity for Ionic Conductors. The conductivity can be determined by passage of direct current through the sample if sufficient precautions are taken. More recently, however, most measurements have been made with current pulses of the order of 10- 2 to 10- 3 sec duration or alternating currents at frequencies of 1 to 10 kHz, in order to avoid large polarization effects at the electrodes. In most cases a plot of log a vs. 1 IT is approximately a straight line, at least for a limited temperature range, allowing an empirical representation of the data as (9f-5)

9-76

SOLID-STATE PHYSICS

The parameters 0"0 and Ware listed in Table 9f-1. The conductivity at the melting temperature has been calculated from Eq. (9f-5) if it is not given in the references. The values for 0"0 and Ware not always so accurate as the number of significant figures would indicate. With good single-crystal or polycrystalline samples of high purity a careful worker can reproduce results within a few percent, but data from different laboratories may differ by 5 to 10 percent, and discrepancies of 50 percent are not uncommon. Hence W may be reliable to a few percent in favorable circumstances or to perhaps 10 percent in less favorable cases, and a discrepancy of 50 percent in 0"0, which is very sensitive to the choice of W, is not surprising. For this reason several representative sets of data, if available, have been given for each substance. 9f-3. Concentration and Mobility of Defects in Ionic Crystals. The conductivity of a crystal containing several types of defects is (9f-6) where N is the number of molecules per unit volume of the perfect crystal, and qj is the magnitude of the charge of the jth defect. If only one type of defect makes an appreciable contribution to the conductivity, the use of Eqs. (9f-l) and (9f-3) gives the observed form of Eq. (9f-5). In the intrinsic region for temperatures near the melting point W i n tr = ihl + tJ.h and 0"0 = N qXo/LO, and in the extrinsic region for lower temperatures We x tr = Sh. and 0"0 = Nqcu« since x is maintained constant at the impurity concentration c. This simple explanation corresponds to the frequent observation of two different temperature ranges with different slopes in the plot of log 0" vs. liT, especially for the initial observations on a substance, and the two slopes are often combined to obtain hI and Sh. from the expressions for W i nt r and We x t r ' This is presumably the extent of the analysis when only activation enthalpies are given in Table 9f-2. Recent work has shown, however, that such an analysis is at best only tentative because of contributions of other types of ions, association and precipitation of impurities, and overlapping of the different temperature regions. In early work many transport number determinations were made by electrolysis in order to identify the ions carrying the current. When only one type of ion contributes to the conductivity, these experiments have, in fact, verified Faraday's laws of mass transport to an accuracy of 1 percent. When several types of ions, or both ions and electrons, however, make appreciable contributions, such experiments have not given very reliable results, presumably because of experimental difficulties at the electrodes and at the interfaces between the several samples involved. Hence only a handful of these experiments have been reported in the last ten years, and no separate table of results is provided. In a few recent investigations of alkali halides an attempt has been made to separate cation and anion contributions to the conductivity by fitting a sum of two terms of the form of Eq. (9f-5) to the observed total conductivity, as indicated by Eq. (9f-6), and some results are given in this form in Table 9f-1. Often measurements of tracer diffusion coefficients allow evaluation of ionic transport numbers, but even these may not be completely unambiguous if vacancy pairs contribute noticeably to diffusion (ref. Nel). The most reliable results are obtained from analysis of measurements on crystals intentionally doped with aliovalent impurities, with due account taken of mass-action laws, association of charged defects and impurities, and long-range DebyeHuckel interactions (ref. Bel). Most of the results in Table 9f-2 have been obtained in this way. The temperature dependences of x and /L are given by Eqs. (9f-l) and (9f-3). It should be observed, however, that /Lo contains a factor liT, which is also carried over into 0"0. For this reason do is listed rather than /Lo in Table 9f-2; the conversion is obtained immediately from Eq. (9f-4). When the factor of liT is not explicitly

9-77

PROPERTIES OF IONIC CRYSTALS

removed from Mo or 0"0, the apparent activation energy is smaller than the correct value by kT, which is of the order of 0.05 to 0.15 eV for temperatures from 300 to 1500°C. 91-4. Effect of Pressure on Conductivity. When the effect of high pressure is taken into consideration, Eqs. (9f-l) and (9f-3) are modified to give x

=

Xo exp (

-

hf

+ PVf) 2kT

M = MO

exp ( -

t.h

+kTP t.v)

(9f-7)

where Vf is the change in volume of the crystal when a pair of Schottky defects is formed, and t.v is the activation volume when a defect moves from one position to another. If only one type of defect contributes appreciably to the conductivity, the pressure dependence of the conductivity is given by (9f-8) where t. Vintr = iVf + t.v, for instance, in the intrinsic range. The pressure dependence of the original data is expressed by a pressure coefficient a

= -

(a ~~O")

T

(9f-9)

The corresponding free volume from Eq. (9f-8) is t. V = RTa = 82.0 X T X a with t. V in em 3 /rnole and a in atm -1. Values of pressure coefficients and free volumes are given for a number of substances in Table 9f-3. 9f-6. Mixed Electronic and Ionic Conductors. Many ionic crystals have an appreciable electronic conductivity in addition to their ionic conductivity. Exclusive ionic conductivity occurs for nearly all halides (the cuprous halides being the only noteworthy exception) and for crystals with simple inorganic radicals. Beryllia also has mainly ionic conductivity, but the other alkaline earth oxides show progressively larger amounts of electronic conductivity, especially at higher temperatures. The only other predominantly ionic conductors are crystals with the fluorite structure such as calcia-stabilized zirconia and even sodium sulfide, perhaps some rare-earth-type trioxides such as scandia and neodymia, and a new class of complex sulfides typified by AgaSI. Appreciable, but not exclusive, ionic conductivity is displayed by the cuprous halides, some simple metal oxides such as alumina and tetragonal zirconia, and most rare-earth oxides such as ceria and dysprosia. Traces of ionic conductivity (a few percent) are present in the copper and silver chalcogenides. Electronic conductivity (by electrons or holes) is dominant in transition-metal oxides such as Cr 20a, and in all other divalent chalcogenides such as ZnO and PbS. It should be clear that a fairly complicated situation exists when both electronic and ionic defects are present to an appreciable extent in a crystal. The treatment of the various interactions (refs. 21 and 22) shows that the defect structure may be profoundly influenced by the atmosphere surrounding the crystal or by deviations from stoichiometry of the crystal. Hence conductivity results are practically meaningless unless these conditions are specified, and similar remarks apply to diffusion. Fortunately much more attention has been devoted in recent years to control and measurement of the environment, and this information is provided where pertinent in Tables 9£-5 and 9f-6 in one of three ways: saturation of one constituent by contact with the metal or high vapor pressure of a volatile component, measurement of the oxygen partial pressure, or determination of the deviation from stoichiometry. Several experimental techniques have been used to distinguish between electronic and ionic conductivity (ref. 56). (1) The earliest was direct determination of mass

9-78

SOLID-STATE PHYSICS

transport by electrolysis, but this has often been unreliable (ref. He1) and is seldom used at present. (2) Polarization effects are often observed; namely, the a-c conductivity at moderately high frequencies like 100 kHz is considerably less than the d-e conductivity. The simplest assumption is that the a-c value is due to the electronic conductivity only, whereas the d-e value represents the total conductivity (ref. Ve3). Despite the appeal of this interpretation the results are usually ambiguous, and much clarification is needed to make this method reliable (ref. Mc1). (3) If the potential drop between the electrodes is kept below the decomposition voltage of the sample, it may be assumed that an ionic current cannot flow to the electrode, and the remaining current is then ascribed to electronic conductivity (refs. Wa5, Wa6). This method appears to be fairly reliable in some cases, but note must be taken of the range of chemical potentials occurring in such experiments. (4) If the conductivity is completely ionic, an emf that can be calculated from thermodynamic data should be established when the ends of the sample are at different chemical potentials (ref. Wa2), and this has been amply verified for calcia-stabilized zirconia, for instance. If some electronic conductivity is also present, part of the emf is effectively short-circuited out, and hence the reduction of the observed emf below the thermodynamic value gives an indication of the amount of electronic transport (ref. Sc6). This method is the most commonly used, especially for oxides, and appears to give a reliable estimate of the average transport number if care is taken to establish a well-defined chemical potential at each end of the sample and to ensure thermodynamic equilibrium. An unfortunate aspect of this method is that it does not distinguish between electrons and holes for the electronic part of the conductivity, or between different types of ions for the ionic conductivity, but often other information is available. (5) The amount of ionic conductivity can be calculated from tracer diffusion coefficients with the Einstein relation if the charge on the defect and the correlation factor are known (see Sec. 9f-7). Since the last two items require a rather detailed knowledge of the diffusion mechanism, this approach is most often useful to establish an order of magnitude, especially when the ionic conductivity is very much smaller than the electronic part. Table 9f-4 gives in most cases the total conductivity, which can often be determined more accurately than the transport numbers. Table 9f-5 gives the ionic transport numbers, which are defined as the fraction of the total current carried by ions. The two tables should be used together to obtain an estimate of the magnitude and nature of the conductivity for a particular substance. Substances have been listed only when there is some information about the ionic part of the conductivity; thus the numerous articles dealing solely with semiconducting behavior in ionic crystals such as ZnO and CdS are not included. 9f-6. Diffusion. The tracer diffusion coefficient for an ion which can diffuse by means of several types of defects is (9f-1O) where j', is the correlation factor (see Sec. 9f-7) and x, and d, are given by Eqs. (9f-1) and (9f-2). When only a single mechanism is important, the temperature dependence is given by

(9f-11) and this form is usually used to represent experimental results. Empirically determined values of Do and Ware given in Table 9f-6. In the intrinsic region the parameters in Eq. (9f-11) are given by and

W

=

!h l

+ Ah

(9f-12)

PROPERTIES OF IONIC CRYSTALS

9-79

Theoretical estimates indicate that W should be several electron volts, as observed. and that ~Sf + Lls should be at most a few entropy units, leading to a value of Do "-' 10- 3 to 10 em 2 /sec. When an appreciably different value of Do is obtained empirically, it is usually an indication that some disturbing influence, such as impurities or grainboundary diffusion, is dominating over the assumed thermodynamic equilibrium for volume diffusion. Since the temperature dependence is the same for all types of defects, indirect methods must be used to distinguish a particular type of defect; this has been done with considerable success in many instances, as indicated in Table 9f-6. Some of these methods are (1) determination of the influence of aliovalent impurities in doped crystals, (2) study of correlation effects as described in Sec. 9f-7, and (3) observation of the effect of varying the stoichiometry or ambient pressure of one of the constituents of the crystal. Among experimental methods for measuring diffusion coefficients with radioactive or isotopic tracers, sectioning is the most direct and reliable. Surface counting, gaseous exchange, and solution exchange are more sensitive but sometimes less reliable. Other methods of detection involve changes in optical absorption, X-ray emission, and semiconducting properties or observation of additive coloration or electrotransport. The line width in nuclear magnetic resonance allows a determination of the temperature dependence and an estimate of the magnitude of diffusion for stable nuclei. The rate of oxidation and sintering processes can also be used to evaluate diffusion coefficients when the process is sufficiently well understood. The remarks concerning the accuracy of the results for ionic conductivity apply here with even more need for caution. For most halides pure single crystals are available, the melting points are not excessively high, and the influence of the surrounding atmosphere is often unimportant (ref. 50); hence in favorable cases an accuracy approaching that for the conductivity may be realized. For the usually semiconducting and often refractory chalcogenides, however, the situation is much less favorable. The high melting temperatures and difficulties of obtaining pure materials suggest that very few intrinsic properties have yet been observed for these substances (ref. 54). Furthermore the influence of grain boundaries is just beginning to be investigated, and yet a number of measurements have been made on sintered or pressed powder samples with porosities up to 5 or 10 percent. Finally the defect structure is strongly influenced by any excess or deficit of the constituents, as discussed in Sec. 9f-5. The data in Table 9f-6 may nonetheless be useful both as a survey of existing experimental efforts and as a stimulus to better understanding. 9f-7. Correlation Effects in Diffusion. Both the ionic conductivity and diffusion of a charged defect are caused by the jumping of the defect through the crystal, and the connection of these two phenomena is given by the microscopic Einstein relation in Eq. (9f-4). If a single type of defect is responsible for all the observed conductivity and diffusion, Eqs. (9f-6) and (9f-10) may be combined (without the correlation factor) to give a macroscopic Einstein relation that defines Dconductivity. Dconductivily

=

C~~2)

(J'

(9f-13)

III. many instances this relationship is at least approximately satisfied, but there are (1) There may be another contribution to tho conductivity, such as an electronic part or another type of ionic defect. (2) There may be neutral complexes of defects, such as vacancy pairs in the alkali halides, which COT. tribute to the diffusion but not to the conductivity. (3) In the diffusion of tracers '.b.e:. c are correlations in the random-walk motion of tracer atoms that lead to correlation factors, as first described by Bardeen and Herring (ref. Ba2). (4) In interstitialcy ...a echaiiams there are also different displacements for the tracer atom and for the

lour ways in which deviations may occur.

9-80

SOLID-STATE PHYSICS

charge of the defect. This displacement effect is usually included with the genuine correlation effects to give an overall correlation factor for interstitialcy mechanisms. The experimental correlation factor is defined by

f =

Dtracer Dconductivit)

Theoretical correlation factors may be calculated by considering the geometry of the diffusion mechanism and of the lattice (see refs. below). Comparison of experimental and theoretical values will then often point to a particular mechanism for diffusion. Experimental and theoretical correlation factors are presented in Table 9f-7.

Guide to references on theoretical correlation factors. General treatment: 24, Ba2, Co2, Co3, HolO Vacancy mechanisms: Ba2, Co2, Frl, 8c8 Interstitial and interstitialcy mechanisms: Co3, Fr2, Mc2 Vacancy pairs and impurity complexes: Co2, HolO, LeI, Lil Anisotropic lattices: Co2, Ghl, Hul, Hu2, Mdl, Mu3 Disordered lattices: Ri2, Yo3 Diffusion by nuclear magnetic resonance: Ei2, 8t5 Isotope effects: Le2, Thl

9-81

PROPERTIES OF IONIC CRYSTALS TABLE

9f-1.

CONDUCTIVITY FOR IONIC CONDUCTORS

[The conductivity is given as Substance

Form

r-; -c

u(Tm), (ohm-em)"!

(T

=

(TO

T range,

-c

exp (- W jkT).] uo,

(ohm-ern)"!

W,eV

Specific reference

Other references

--- --ALKALI HALIDES LiH ....................

sc

688

LiD .................... LiF ....................

sc se

.......

..........

842

2.4 X lO- a

LiCI ...................

LiBr ...................

LiI ....................

NaF ................... NaCI ..................

4

X 10- 2

sc

.......

1.5 X lO- a

so po

606

.......

9 X lO- a 1.8 X lO- a

se pe

.......

sc se pc

.......

pc se

992 800

550

....... 452

1.8 X 10- 2 1.4 X 10"-2

.......... 5 7

X 10- 2 X 10- 2

X lO- a 1.0 X 10- 3

3

1.2 X lO- a

NaBr ..................

Nal ...................

sc

755

1.2 X lO- a

se

.......

2.1 X lO- a

pe

661

2.1 X lO- a X

10- 4

KF ....................

se

846

6

KCI ...................

se

768

2.4 X 10- 4

sc se

....... .......

10- 4

KEr ...................

KI. ....................

RhCl ..................

1.4 X 4.5 X 10- 5

se

728

1.3 X 10- 4

sc

....... .......

2.1 X 10- 4 1.0 X 10- 4 1.0 X lO- a

se se se se

680

...... 717

2.1 X 10- 4 1.3 X 10- 5 10- 5

681 684

3.4 X 1.1 X lO- a

636

6.1 X 10- 6 7 X 10- 6

RbBr .................. CaF ...................

se

CsCI (a) ...............

...... tr. 469 ... ..

CsBr ...................

se pe se se se

636

2.6XlO-a

pc

... ....

CsI. ...................

se

621

4 X 10- 4 1.9 X lO- a

se

... ....

2.1 X lO- a

sc

....... ....... .......

..........

CsCI (f3) ..• . • . . • • . . . . . .

MONOVALENT HALIDES NH4CI. ................ NH 4Br................. NHd ..................

pc

...... .... . ...... ..

2.07 0 2.19 1. 92 0.65 1.68 0.84 1.64 0.80 1.23 0.60 2.34 1.02 1.66< 2.36 0 1. 90 1. 88

Ma6 Ma6 Ho8 Ho8 Ph1 Ph1 Ka1 Ka1 Fu4 Fu4 Mi4 Al4

1. 91< 2.21 0 1. 93 1. 97

1.8 X 10 1. 6 X 105 2 1.0 X 108jT 1 8.0 X WjT 1.0 X 102 2.5 X 106 2.5X1Q4 1 X loa 2.2 X 105 1.4 X 104 1.1 X 106

2.55 0 2.03 1.55 0.85 1. 67 0.95 1.33 1.05 1.44 1.28 1.15 1.43 1.25 1.37

Da9 Da9 Ro4 Ho9 Pel Pel Ka1 Fu3 Fu3 Le5 Ha6 Ha6 Ar3 Ha6 Ar3 Mo7 Ly1 Ly1 Ha6 Ly1 Ly1 Ho7

4.4 X 106 2.6 1.9 X 107

1.15 0.83 1.23

He4 He4 He4

4 X 107 1 1 X 107 6 X 109jT 5 X 10IT 1.6 X 109jT 4.5 X 10IOjT 2.5 X 106 2.5 X 105 1.2 1.4 X 106 4.2 X 105 33 8 X 10- 2 9.6 X 105 1.8X105 1.4 X 10- 1 1.3 X lOa 4.7 X 108jT 1.2 KI09jT 2.4 X 1010jT 9.2 X 108jT

450-700 300-450 610-730 490-570 350-600 170-350 660-790 400--500 570-750 570-750 340-640 480-680

2.1>< 108jT 3.5 X 102jT 2.3 X 1081T 3 X 102jT 8.1 6 2 4 4.1 5.6 2.3 5.9

X X X X X X X X

lOa 10- 2 107 10- 1

300--700 300--700 440-680 560-680 430-600 430-600 450-650 550-700 550-700

3.1 7.1 1.1 7.9 1.4 1.6 1.6

X X X X X X X

108fT 109IT

..... .. 550-660 330-550 480-610 470-580 250-480 150-460 475-590 300-475 340-620 480-595 300-480 300-550

1. 72 0.53 1.72 2.07 0.70 1. 99 1. 65 1.47 1.42 0.59 1.29 1.22 0.56 0.43 1.05 0.92 0.36 1.42

Prl Pr1 Pr1 Ja6 Ja6 Ba7 Ba7 Ha19 Gil Gil Ha19 Gil Gil Al3 Ha19 Gil Gil Ph1 Fu3 Fu3 Ne1 Ne1 Ne1

480-630 240-480 480-630 540-720 340-540 560-750 330-560 480-570 400-550 30-350 440-540 350-500 30-300 160-360 340-420 250-350 30-150 330-980 520-740 520-740 720-800 550-650 275-425

31T

106jT 101°IT 108jT WIT

106 105

WjT 1012jT 106

3.6X1Q6jT 8.8 X 10IljT 6

1.86 e

i.es-

2.31 0 1.87

1.58 e

OTHER

pp pp

.......... ..........

40-170 70-150 0-130

Be7, Be8, Ha19, Le5, St7 Le5

Le5 Bi2, Br5, Do6, Dr2, Etl, Ja4, Ka4, Ko1, La4, Ma6, Le1 Le5, Ph1. Se2

Le5 Le5 As3, Be2, Bi4, Gr4, He4, Le5, Me2, Ph2, Pel, Wa4 Gr4, Le5, Pel, Ph2

Bi4, Eel, He4, Le5, Ph2 Le5, Pi1

Ar2 Ha6, Ha9, He4, Ho6

BelO, Eel, Ha6

9-82

SOLID-STATE PHYSICS TABLE

9£-1.

Substance

CONDUCTIVITY FOR IONIC CONDUCTORS

Form

r.; -c

T range,

~

tn

P0 2 (atm)

DIVALENT OXIDES

BeO

!I a axis

sfc

MONOVALENT OXIDES

Ou20

.

eation disorder

Mil, MU4,

set set

SIMPLE INORGANIC RADICALS 1

::::::::::::::::::::: I

Fr2 Fr2 Fr2 TalO TalO J03 N04 J03 La2 La2 J03 Zi1 Zit

1

se pc

sp MgO .•••••••••••••••••••••••••••. \

7Be 7Be 7Be

se

180

so

28Mg

sc

18 0

pc

180

1720-1960 1. 2 X lO-s 1500-1760 1. 3 X 10- 3 nco-rsoo 3.2 X 10-3 1500-2130 5.9 X 10-6 1560-1730 3.0 X 10--6 1400-1600 2.5 X 10-1 1000-1150 4.3 X 10- 6 750-1000 4.8 X 10- 1• 1650 D < 10--1•

1.56 2.78 2.73 2.12 2.97 3.42 3.56 1.31

VBe" VBe" VBe" VBe"

set set set set gsx

set

0 .. ' 0;'

gsx gsx

ard

Ar Ar vacuum

Dc/Da = 1.3 10- 1

4.1 X air (1 - 120) X 10- 1 (1 - 120) X 1Q-1 1.6 X 10- 1

Ro6 R06 H02

De2 Au2 Hi3, Se4 0i2

co I

CO ~

(0

TABLE

9f-6.

DIFFUSION IN IONIC CRYSTALS

I

(Continued)

~

t+::>Substance

Form

Isotope

T range,

-c

Do, cm'/sec

W,eV

Defect

Method

Environment

Comments

Specific reference

Other references

--

CaO ...........•................. BaO ............•.....•..........

se se

45Ca 14°Ba

1000-1400 1080-1230 330-1080

se pw sc

0 55Zn 55Zn

se se se sp pp pw pc

55Zn 18 0 18 0 119Sn 210Pb 180 mpb

AhO •............................

sp so

25Al 180

In201 ............................ Bi203 ............................

pf pp

In 21°Bi

Y201.............................

91y

Zr02:CaO (16%) ..................

sp sp se sc pf pc

Zr02:CaO (14%) .................. Nb 205 {a) ........................

se se

ZnO ..........•.•.•.•..•.........

CdO ............................. Sn02 ............................. PbO (a) .......................... PbO (IJ)..•...................•... POLYVALENT OXIDES

Ti02 ............................. Zr02 .............................

6.5 X 1011 3.8 X 105 1 X 105 4 X 109 5.4 X 10- 5 1.6 X 10- 11

1.50 11 12 0.44 0.3 2.8 3.32 3.25 0.87 1.9 7.15 3.99 5.14 3.5 0.93 0.56

{VCa") IBa: x )

{VB,,"} {Ba. x )

I VBa"} Vox 2ni'

........... {Zn,"}

set set set set set ade gsx sfe sfe set

[disloc ]

gsx

Vo' .

gsx

.............

............. .............

.............

sfc sfe gsx sfe

P0 2 (atm) 1. 3 X 10- 4

...........

.....................

........... ...........

.....................

........... ........... ........... D ex: PZnO. 55 ........... ...........

.....................

....................

Ba(g) Zn(g)

.................... ..................... .

O2 1 (to 10- 1) 1 (to 10- 1) air air 02 air

1

D ex: Po 2' D ex: Po 2- A . .......... ...........

........... ...........

Gu2 Re2 Re2 Re2 Re2 Sp2 Se5 Mu2 Mu2 Mo5 Mo5 Ha17

r.no Da2 Th3 Li9

Li6 Be12, Del

Le4, Li5, Pa4, Ro2, Ro3, Se1. Se2, Se4, Spl Ha14, Ha15 Si4 Li8

pf

0 180 180 0 95Zr 45Ca 18 0 180 18 0 0

1670-1905 1500-1780 1200-1620 308- 407 720- 780 600- 700 1400-1800 1000-1500 710-1300 800--1000 300- 390 1700-2150 1700--2100 780-1100 850-1200 850, 900 540- 840

2.8 X 10 1.9X101 6.3 X 10- 8 7.8 X 10-' 4.5 X 10- 1 4.3 X 10- 5 2.4 X 10- 4 7.2 2.0 X 10-' 9.7 X 10- 3 9 X 10- 4 3.5 X 10- 2 4.4 X 10- 1 1.8 X 10- 1 1.2 X 10--' Dli/DJ. = 60,190 1.0

4.95 6.6 2.5 1.35 2.00 0.90 1. 90 2.54 2.60 2.43 1. 24 4.01 4.35 1.35 2.14

..... 1.85

VAl'" Vo" Vo" In;"' . VBi'"

VBi'''

............. .............

Vo" Vo" Vo" Vzr'''' VCa" Vo' . Vo" 02 IVo")

set gax gsx oxy

sfe sfe set oxy gsx

gsx oxy

set set set gax ard oxy

air 2.0 X 10- 2 2.0 X 10- 2 5 X 10- 4 air air vacuum air (2 - 6) X 10- 1 4 X 10- 1 1 H2 H2 air 1 (to 10-1) 10- 17,10-1 1 to 10-1

........... ...........

........... on InSb

........... ........... . ..........

DJ./Dil = 1.6 ...........

........... ...........

o disorder ex: Po 2 [0101axis

D

i

...........

r:n

o

~

H

tj I

r:n

8 ;»8 l"'.J

~

::I:

P0 2 (atm)

so

Nba05 ('Y)..•..••••••••••••••••.•.

800-1300 720- 840 940-1025 850- 940 1000-1250 1100-1300 630- 855 980-1380 600- 680 500- 650 200-- 460

8.8X10--jJ 1 X 102g 1 X 1011 1 X 10-' 3 X 10- 1• 2.5 X 101 4 X 10- 1 5.0 3.0 X 10-9 1.3 X 10- 1

~

Pal Oil Oil Ro5 Pa3 Pa3 Be6 Wi2 Ha18 Mal Sm2 Rh1 Rh1 Si3 Ch6 Sh1 Sh2

U1 H

Col, He6

Ha16 De4, D04 Mol Mol Ha2, Sml CM, D05, Sh2

o

U1

I'RANSITION METAL OXIDES Cr20S ............................ MnO............................ FeO.............................

pc sp

pc pe

Fe20s (a) ... . . . . . . . . . . . . . . . . . . . . .

sp

FeaO•............................

pe pe

sc sp

sc CoO.............................

pc

se COsO•............................ NiO.............................

ttARE EARTH OXIDES PnOs............................ Nd20a........................... 3m20a........................... Er20a............................ U02.............................

MONOVALENT CHALCOGENIDES Na2S ............................. CUzS ............................ Cu2Se ............................ Ag2S (a) ........ . . . . . . . . . . . . . . . . . Ag2S ({J)....••••• • • • • • • • • • • • • • • • • AgSbS2 ........•.•••.•.•.•••......

61Cr 61Cr 18 0 64Mn .9Fe 66Fe .9Fe 18 0 66Fe 56Fe 69 Fe 18 0 6OCO I~O

so

180 63Ni 61Ni 180

pw pc pc pw se sp pw

0 18 0 18 0 0 233U 236U 180

sp

UNa

sp

36S 64Cu Cu IIOAg 86S HoAg llOAg 368 Ag Sb llOAg

pc

sc se

... pc pc pc pc pw pw pc

... Ag2Se............................ ThSe...................•........

(atm) N2 PH20/PH2 = 2 to 18 1.6 X 10- 1 10-12 (to 10-14) FeO.9170 FeO.9210 air 1.6 X 10-1 Fe2.99aO. Ar PC02/PCO = 10 to 101.6 H20(g) 1 2.1 X 10- 1

P0 2

sp sc

pc pe

204Tl 76Se

1040--1550 1300 1100--1450 900--U50 7QO-U2a 700-1000 950--1050 900--1250 750--1000 850--1075 1115 300- 550 1010--1340 1150--1500 830-- 860 1()()()-1470 1000--1400 1100-1500 700- 990 700-1000 700-1000 850--1250 1450--1700 1500 550-- 850 320-- 500 520-- 700 400-- 520 420-- 800 140-- 450 580-- 750 200-- 400 650--1000 95- 175 25- 70 120-- 141 400 400 150-- 280 150-- 300 150-- 300

1.4 X 10-1

D

a: (PH20/PH2)0-4

1.6 7.4 1.1 1.4 1.3 2.0 5.2 6

D

a:

3.2 2.2 9 2.4 1.8 4.4 6.2

X X X X X

10 10- 7 1~:l. 10-2

106

X 106 (PC02/PCO)O.; X 10- 14 X 10-S X 10 X 1022 X 10-3 X 10-4 X 10-4

4.5 X 10-2 1.3 X 10-4 6.0 X 10-6 1.2 4 X 10-7 D = 1. 6 X 10- 11 X yl.V 1.2 X 108 2.1 X 10-3 8.3 X 102 1.6 X 10-3 3.8 X 10-3 2 X 10-4 9 X 10-4 2.8 X 10-4 2.4 X 10-4 6 X 10-8 9.3 X 10-3 2.4 X 10-1 D = 4 X 10- 7 D=3XlO-H 2.1 X 10-4 1.2 X 10-8 2.2X10-1

2.64

..... 4.38 0.79 l.a! 1.31 4.35 3.38 2.38 3.64

VCr'" or Cr.' .. VCr'" ............. VMn" VFe"

VFe" ............. {Yo' .}

l/:SX

VFe"

sic set

.......

.....

.....

VFe" 0.74 ............. 1.50 Vco" ............. 4.2 7.6 1. 98 VNi" 1. 92 VNi" 2.49 {O;"}

1.82 1.34 0.93 2.07 3.04

..... 2.83 1.29

set set gsx set set set set

Vo"

.............

............. ............. {Vu""l U02+Y 0/' 0/'

1.66 ............. ............. 0.77 1. 77 ............. ............. 30 18.6 33.5 26.3 20.8 26 8il 168 25.9 280 14.3 205 400 12.1 11.05 4.9 9.27 900 9.11 11.03 5.6 80 81 141a 81 5.8 275 5.2 9 65 82 5.46 10' 18.0 ± 0.5 6.5 14.0-1 25.6 30.6 5.4 6.9-1 7.3!1 6.2 4.1 3.6

21 24 30 18 3 40.1 37 49 10 24 66 66 66 39 11

66 66 66 37 53

18 18 7 18 49 18 24 66 66 66 28 18 51 28 63 63 28 37 37 37 54 51 18 1 18 63 18 30 68

14 34 34 32 32 63 63 63 37 49

9-111

PROPERTIES OF IONIC CRYSTALS TABLE

9f-8.

Name

Formula

Potassium bromate ............ .. Potassium bromide. . . . . . . . . . . . .. Potassium carbonate ........... Potassium chlorate.............. Potassium chloride............

KBrOa KBr K2COa KCIOa KCI

Potassium chromate............. Potassium cyanide... ........ .... Potassium dihydrogen arsenate .... Potassium dihydrogen phosphate. Potassium fluoride.... ...... .... Potassium iodate..... ..... ...... Potassium iodide..... ... ........ Potassium nitrate .... .. , ...... Potassium perchlorate. ..... ...... Potassium orthophosphate....... Potassium monohydrogen orthophosphate.................... Potassium dihydrogen orthophosphate ....... . . . . . . . . . . . . . . . . . Potassium sulfate....... ........ Potassium tantalate-niobate (KTN) ................ .......

K2CrO, KCN KH2AsO, KH2PO, KF KIOa KI KNOa KCIO, KaPO,

Potassium thiocyanate ......... .. Potassium thionates: Potassium trithionate .... ... Potassium tetrathionate ..... ... Potassium pentathionate .. .... Potassium hexathionate ... ... Rubidium bromide (NaCI structure) ..... . . . . . . . . ........... Rubidium bromide (CsCI structure) .. ... ... .... .... . ... .. Rubidium carbonate...... ....... Rubidium chloride,......... . . . . . Rubidium fluoride. . . . . . . . . . Rubidium iodide.. ..... ... Rubidium indium sulfate.... Rubidium nitrate ...............

(Continued)

INORGANIC SOLIDS-CRYSTALLINE

t,OC

",Hz

r.t.

_lEv 106 106 106 106

105 105 105 106 105 105

7.3 4.78 4.96 5.1 4.64 4.80 7.3 6.15 31 46 6.05 16.85 4.94 4.37 5.9 7.75

57 28 51 57 27 27

r .t . r.t.

2X 2X 2X 2X 105 106 6X 2X 2X 103 2X 2X 2X 2X 2X 2X

9.05

57

r.t,

18

r.t. 29.5 80

...... .. r.t.

r.t. ... ..... . .. .... r.t,

....

..,

20

107 105 105

r.t.

2 X 106

KH2PO, K2S0,

r.t. r.t .

2 X 106 2 X 106

KTao.56Nbo, 34Oa

-1 0 20

K2HPO,

KSCN K2Sa06 K2S,06 K2S506·H2O K2S606

RbBr Rb2CO a RbCI RbF RbI Rbln(S04)2 RbN0 3

r.t,

Silicon carbide. ........... .. .. Siliconnitride.. .......... ... Silver bromide. ....... ..... Silver chloride... ..... .... Silver cyanide.. ...... .... Silver nitrate ............ Sodium ammonium tartrate tetrahydrate ... ......... Sodium bromide.. ..... Sodium carbonate .. Sodium carbonate decahydrate ... Sodium chlorate.. Sodium chloride.. .. ....

SiC SiaN, AgBr AgCl AgCN AgNOa

Sodium cyanide, . , . . . . . . . . . Sodium fluoride. ' .... .. , ..

NaCN NaF

NaNH,(C,H,OG)-4H 2O NaBr Na2COa Na2CO,'lOHlJ NaCIO, NaCI

1.8 X 106 1.8 X 106 1.8X106 1.8 X 106

20 20 20 20

r.t,

Selenium, amorphous...... Se Silicon monoxide ...... ... ' " .. SiO Silicondioxide (a-quartz) ..... ... Si02

104

............ . . . . . . ..... 2 X 106

r.t.

RbBr

Selenium............. .......... Se

Ref.

o

•

130-215 215-265 25 25 25 25

r.t . r.t.

. ... r.t . . ...... . .. . .. 20

•

•

•

•

•

. ...

19

..... ... .... .... ... ... .....

•

2X 2X 2X 2X

I

..

......

•

•

•

•

•

. .... 106 106 106 106

. ...

106 106 3 X 108 3 X 1O~ 2 X 1010 102---10 l C 103

........ ..... 106

loa 2 X 106 2 X 106 106 5 X 106

lOa 2 X 106 18

2 X 106 6 X 107

20 25 85 20 19

2 X 105 102---10 7 10'-10 7 106 2 X 106

... ....

.........

57 57 37 28 57 28 51 57 57

>31 6.4

57 57

6,000 34,000 6,000 7.9

12

57

5.7 5.5 7.8 7.8

50 50 50 50

4.9

25

6.5 6.73 5.0 5.91 5.0 6.85 20-380 30 11.0 10.4 7.5 6.00 5.8 4.5..L 4.6'1 10.2[1 4.2 13.1 12.3 5.6 9.0

25 51 28 28 28 19 16 16 63 63 63 63 22

9.0 5.99 8.75 5.3 5.28 5.62 5.9 5.98 7.55 6.0

37 28 51 30 31 28 63 63 58 28

9 26 22 28.18 28,18 18

9-112

SOLID-STATE PHYSICS TABLE

9f-8.

INORGANIC SOLIDS-CRYSTALLINE

Name

Formula

Sodium iodide. . . . . . . . . . . . . . . . . .. Na1 lI~aNOa Sodium nitrate Sodium nitrite NaN02

t,OC

r.t. NaCI04 Na2S04 Na2S0dOH20 Na2U02(C204)2 Sn02

Strontium carbonate. . . . . . . . . . . .. Stront!um chlor!de... 'c' . . . . . . . .. Strontium chloride hexahydrate .. , Strontium fluoride Strontium formate dihydrate , Strontium nitrate , Strontium oxide Strontium sulfide Strontium titanate

SrCOa SrCh SrCh'6H20 SrF2 Sr(COOHk2H 20 Sr(NOa)2 SrO SrS SrTiOa

Sulfur (100)...... . .. .. .. .. .. (010)

S

(00l)

Sublimed... . Tantalum pentoxide (a)'

.

,

.

. .

Tantalum pentoxide (m " Thallous bromide. . . . . . . . . . . . . . .. Thallous chloride Thallous iodide (orthorhombic).... (cubic)... .. . . . . . .. . .. .. .. .... (orthorhombic).. .. . . . . . . . . . . .. Thallous nitrate

Ta20& TIEr TICI Til Til Til TINOa

Thallous sulfate. . . . . . . . . . . . . . . . Thorium dioxide........... .. . ..

ThS04 Th02

r.t. r.t. 18

Uranium dioxide Ytterbium sesquioxide Zinc malonate Zinc monoxide Zinc selenide Zincsulfide Zinc telluride Zirconiumdioxide

. . . . . . . .

U02 Yb20a Zn(CaH204) ZnO ZnSe ZnS ZnTe Zr02

Ref.

2 X 105 5 X 10 5 X 105 5 X 105 103 5

104-1010 IG4 - 1010

2 X 10&

2 X 106

19 25 -195 25 25 25 25 -196 -196 19 25 20 20 193 20 20 r.t,

Tin antimonide '" SnSb Titanium dioxide (rutile). . . . . . . .. Ti02

Hz

2 X 106 19 r.t. r.t,

Sodium perchlorate Sodium sulfate Sodium sulfate decahydrate Sodium uranyl oxalate. . . . . . . . . .. Stannic dioxide

P,

(Continued)

r.t. r.t. r.t. r.t. 20 25 25 25 r.t,

lOa 2 X 10& 2 X 106 7.25 X 106 lOa 103 102-lO a 102-103 102-10 3 102- 103 103 103 103 103-101 2 X 106 1C4 1C4

101 5 X 105 27-37 X 109 5 X 105 3 X 105 2 X 106 104-106

103 5 X 10& 104 104 104

2 X 106

6.60 6.85 6.8a 6.4b 7.8e 5.76 7.90 5.0 5.18 9.0 ± 0.511 14 ± 2.1.

8.85 9.19 8.52 7.69 6.1 5.33 13.3 11.310 332 2,080 3.75 3.95 4.44 3.69 30.1. 6511 24 30.3 31.9 21.2 ± 0.2 29.6 ± 0.5 37.3 16.5 13.5 25.5 18.9 ± 0.4 10.6 147

89 a 173 c 24 5.0 5.6 8.14 9.12 8.37 10.10 12.5

28 51 55

37 30 30 20 60 60 51 30 30 28 37 51 28 52 65 65 63 63 63 63 42 42 42 63 28 47 47 63 18 33 18 2

24 32 41 41 2 22 13 4 4 4

24

References for Table 9f-8 1. Afanaev, Popova, and Metsik: Izv. Vysshikh Uchebn. Zavedenii Fiz. 1962, (6), 64. 2. Axe and Pettit: Phys. Rev. 151, 676 (1966). 3. Belyaev, Belikova, Dobrzhanskii, Netesov, and Schaldin: Fiz. Tverd. Tela 6, 2526-2528 (1964). 4. Berlincourt, Jaffe, and Shiozawa: Phys. Rev. 129, 1009 (1963). 5. Bever and Sproull: Phys. Rev. 83, 801 (1951). 6. Bosman and Havinga: Phys. Rev. 129, 1593 (1963). 7. Bosomworth: Phys. Rev. 157, 709 (1967). 8. Brown and Koenig: Phys. Letters 2, 309 (1962). 9. Cady: "Piezoelectricity," McGraw-Hill Book Company, New York, 1946. 10. Campbell and Lawson: J. Phys. Chern. Solids, 30, 775-776, 1969. 11. Chan, Davidson, and Whalley: J. Chern. Phys. 43, 2376 (1965). 12. Chen, Geusic, Kurtz, Skinner, and Wemple: J. Appl. Phys. 37, 388 (1966).

PROPERTIES OF IONIC CRYSTALS 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37.

9-113

Collins and Kleinman: J. Phys. Chem, Solids, 11, 190-194 (1959). Crevecoeur: Private communication. Curie: Ann. Chim. Phys. 17, 385 (1889). Dantsiger and Fesenko: Soviet Phys.-Cryst. 10, 272 (1965). Demau: J. Phys. Radium 24,284 (1963). Eucken and Buchner: Z. Physik. Chem, 27(B), 321 (1934). Ezuchevskaya, Syrkin, and Deichman: Zh. Neorq. Khim. 9, 1495 (1964). Ezuchevskaya, Syrkin, and Shchelokov: Zh. Neorg. Khim. 9, 1758-1759 (1964), Fang and Brower: Phys. Rev. 129, 1561 (1963). Feldman and Hacskaylo: Rev. Sci. Lnstr, 33, 1459 (1962). Gibbs and Hill: Phil. Mag. 9, 367-375 (1964). Guntherschultze and Keller: Z. Physik 75, 78 (1932). Havinga and Bosman: Phys. Rev. 140, A292 (1965). Hofman, Lely, and Volger ; Physica 23, 236 (1957). Hliljendahl: Z. Physik. Chem. 20(B), 54 (1933). Hojendahl : Kgl. Danske Videnskab. Selskab Mat.-Fys. Medd. 16, 1-132 (1938). Jaeger: Ann. Physik 53, 409 (1917). Kamiyoshi and Miyamoto: Sci. Rept. Res. Inst. Tohoku Univ., ser. A, 2, 370 (1950). Kiriyama: Science (Japan) 17,239 (1947). Kir'yashkina, Popov, Bilenko, and Kir'yashkina: Soviet Phys. 2, 69-73 (1957). LeFevre and Ritchie: J. Chem, Soc. 1963, 4933. Liebisch and Rubens: Sitzber. Preuss. Akad. Wiss. Pliueik-M'ath, Kl. 1919, 876. Lorimer and Spitzer: J. Appl. Phys. 36, 1841 (1965). Malone and Ferguson: J. Chern, Phys. 2, 99 (1934). Mason: "Piezoelectric Crystals and Their Application to Ultrasonics," D. Van N ostrand Company, Inc., Princeton, N.J., 1950. 38. Morgan and Lowry: J. Phys. Chem. 34, 2385 (1930). 39. Nakano, Satuka, ana Saruwatari: Nippon Kagaku Zasshi 84, 902-909 (1963). 40. Naragamo Rao: Proc. Indian Acad. Sci. 30A, 82 (1949). 40.1. Noguet: J. de Phys., 31,393 (1970). 41. Parker: Phys. Rev. 124, 1719 (1961). 42. Pavlovic: J. Chem. Phys. 40,951-956 (1964). 43. Reynolds, et al.: Phys. Stat. Solidi 12, 3 (1965). 44. Romich and Nowak: Sitzber. Akad. Wiss. Wien, Math.-Naturw. Kl. 7011, 380 (1875). 45. Rubens: Sitzber. Preuss. Akad. Wiss., Phys.-Math. Kl. 1915, I, 4. 46. Rubens: Z. Physik 1, 11 (1920). 47. Samara: Phys. Rev. 165, 959 (1968). 48. Schmidt: Ann. Physik 9, 919 (1902). 49. Schmidt: Ann. Physik 11, 114 (1903). 50. Schmidt and Sand: J. Lnortj, Nucl. Chem. 26, 1189-1190 (1964). 51. Schupp: Z. Physik 75, 84 (1932). 52. Sharma and Gupta: Indian J. Phys. 37,33 (1963). 53. Simhony: J. Phys. Chem. Solids 24, 1297-1300 (1963). 54. Sonin and Zheludev: Kristallografiya 8, 283 (1963). 55. Sonin and Zheludev: Kristallografiya 8,285 (1963). 56. Starke: Ann. Physik 60, 629 (1897). 57. Steulmann: Z. Physik 77, 114 (1932). 58. Tables of Dielectric Materials, vol. 6, MIT Lab. for Lnsul, Res. Tech. Rept. 126, June, 1958. 59. Tambovtsev, Skorikov, and Zheludev: Kristallografiya 8, 889-893 (1963). 60. van Daal: J. Appl. Phys. 39, 4467 (1968). 61. Unruh: Phys. Letters 17, 8-9 (1965). 62. Voigt: "Lehrbuch der Kristallphysik," p. 459. 63. Von Hippel: "Dielectric Materials and Applications," John Wiley & Sons, Inc., New York, 1954. 64. Wappler: Z. Phys. Chem. 228, 33 (1965). 65. Weaver: J. Phys. Chem. Solids 11, 274 (1959). 66. Willardson and Beer: "Semiconductors and Sernirnet.als;" vol , 1, p. 14, Academic Press, Inc., New York. 67. Young and Frederikse: J. Appl. Phys., July, 1969. 68. Yousef and Farag: Physica 31, 706 (1965).

9-114

SOLID-STATE PHYSICS

9£-9. Piezoelectric and Pyroelectric Constants TABLE

9£-9.

PIEZOELECTRIC STRAIN CONSTANTS·

Substance

Formula

dll

dB

d21i

------1----

1. Aluminum phosphate .............•.. AlP04 2. Ammonium dihydrogen arsenate 3. Ammonium dihydrogen phosphate

4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.

Ammonium ditartrate '" Barium formate " Benzil. " Benzophenon. . . . . . . . . . . . . . . . . . . . . .. Beryllium sulfate tetrahydrate. . . . . . .. Cadmiumtel1uride................... Cesium tartrate.. . . . . . . . . . . . . . . . . . .. Deutero ammonium dideuterium phosphate Dextrose plus sodium bromide .. , .. '" Dextrose plus sodium chloride Dextrose plus sodium iodide " Galliumarsenide Heavy rochelle salt

17. Hexametbylentetramine 18. Iodic acid. . . . . . . . . . . . . . . . . . .. '" 19. Lithium ammonium tartrate monohydrate..... .... 20. Lithium potassium tartrate monohydrate

21. 22. 23. 24.

±3.3 +1.4

NH 4H2As04 NH4H2P04

+1.5 +1.7 -1.6

NH4HC4B"40a Ba(HCOO)2 C14HlO02 (CaHIil!CO BeSOdH20 CdTe (-196°C) CS2C4H40a

H.O

" "

2.7

ND4D2P04 CaH1206+ 2NaBr C6H1206 + 2NaCI C6Hl206 + 2~aI GaAs KNaC4D2H20dD20

-3.7 -7.0 -3.8

(CH2)6N4 HIOa

LiKC4H406'H20

28. Potassium dihydrogen phosphate .... "

KH2P04

, " . ". KHC 4H406 29. Potassium ditartrate K 2S20Ii 30. Potassium dithionate 31. Quartz. . . . . . . . . . . . . . . . . . . . . . . . . . Si0 2 32. Rochelle salt

KNaC4H40dH20

Rubidium dihydrogen phosphate " Rubidium tartrate . Selenium.. . . . . . . . . Sodium ammonium tartrate tetrahydrate " 37. Sodium bromate .

RbH2P04 Rb2C4H40. Se NaNH4C 4H40dH20

33. 34. 35. 36.

38. Sodium chlorate

"

39. Strontium formate dihydrate 40. Zinc selenide " 41. Zinc sulfide (zincblende). . . . . ..

+19.1

Cl liH260 KD2P04 KH2As04

NaBrOa

.

NaClOa

"

Sr(HCOOk2H 20 ZnSe ZnS

42. Zinc telluride , ZnTe 43. Zinc sulfate heptahydrate. . . . . . . . . . .. ZnS04'7H20

+12.3 7 +1.7 0.17 10 -1.8 +0.3 +0.7 +2.6 Very large (see Table 9f-1O) +17.5 ±18.9

H.4

LiNH4C4H406·H20

27. Potassium dihydrogen arsenate ..... "

7.0 ±2.7

+8.0

Magnesium sulfate heptahydrate " MgS04'7H20 Mercury sulfide. . . HgS Nickel sulfate heptahydrate. . . . . . . . . NiS04'7H20 Nickel sulfate hexahydrate " NiS04'6H20

25. Patchouli camphor 26. Potassium dideuterium phosphate

±1.5 Small +41 -1.5

7.7 +3.2 +2.0 2.1 -2.1 -1.7 -2.0 -5.3 ±6.0

+2.0

.

1.4 +2.31 +2.3 -2.25

+1.1

-3.2 +3.2 +0.9 -1.9

29* 12* 12* 12* 40 29* 35 29* 42 45 12* 9* 12*

75

-73

+13.3

±15.3

.. . ... ±23.5

18* 29*

±6.5 -5.3 +11.2 -9.4 10.0 -2.7 -2.9

3.4

-56 -53

+2.7 65 +18.7 ±19 -2.6 -2.4 +27 -1.75 +2.0 ±8.5

· .' . .. ..... +31 +48 -45.6 +49 -0.4 ±4.7 ...... +20.3 · ,. ·. . .... . .

31 29* 29* 29* 15 30

+0.05

+23.5 26.6 +1.3 1.4 +1.3 -4.3 2.0 -0.73 -0.67 +0.85 Very large (see Table 9f-10) 4.5

1~IRef.

-49.8 ±31.7

± 11.5

-3.5

29* 35 29* 35 12* 40 11* -32 40 40 29* 42 2* +51. 7 37 +58 12* +22 22.4 33 -20.9 40 29* 23 12* +21 -1.0 35 12* 4 13,40 29* +11.8 29* +11.7 13 12* 37 42 17 +9.4 28 ±10.3 29 4 40 29* 4,40 29* ±2.3 29* 9* 24 9* 9* 40 ±4.9 6.8 ±7.6 +66 6.8 -3.8

9-115

PROPERTIES OF IONIC CRYSTALS TABLE

9f-9.

PIEZOELECTRIC STRAIN CONSTANTS*

(Continued)

Formula

Substance

d31

daa

Ref.

-------------1------- --- --- - - --- -- --- .-44. 45. 46. 47.

Aluminium nitride , , Ammonium pentaborate tetrahydrate Antimony sulfoiodide " Barium antimonyl tartrate

48. Barium titanate 49. 50. 51. 52. 53.

Barium titanate ceramic . Beryllium oxide . Boracite . Cadmium selenide . Cadmium sulfide . 54. Cesium nitrate , '" . 55. Lithium gallium oxide . 56. Lithium niobate . 57. Lithium trisodium chromate hexahydrate , , . 58. Lithium trisodium molybdate hexahydrate . 59. Potassium lithium sulfate . 60. Potassium pentaborate tstrahydrate 61. Resorcinol. . 62. Sodium calcium aluminosilieate . 63. S~dium lithium sulfate 64. Sodium nitrite 65. Terpine monohydrate 66. Tourmaline

,

. . . .

67. Zinc oxide. . . . . . . . . . .. . . . . . . . . . ..

+13

392

270 ....... ...... ........ ...... ..... ................. ....... .. , . . ...... -10.5 ...... ...... CdSe -14.3 ...... ...... CdS ....... . , ..... ... . . CsNOa +5.9 ...... +5.1 LiGa02 BaTiO a BeO

LiNbOa

......

+20.8

+74

5.0 -1.9 -6.6 +6.9 ~150 1,300

23· 16· 10·

........ ..... +3.7 -37 .. .. . 84 -34.5 85.6 -79 . 191 -0.12..... +0.24 ........ +0.6 -3.9 +7.8 -3.7 +10.7 ....... +0.5 -2.8 -2.4 -0.86 ..... +16.2

42· 14· 7· 7· 1· 39 9· 22· 38 11* 43

±2.9

29*

LiNaa(Mo04)2'6H20 ........ ±2.5 . .... ..... ..... KLiS04 +0.9 KB50dH20 +1.7 ....... +9.5 C6H4(OH)2 +18.0 . . . . . . . +18.4 (Na2Ca)4(AlSi04)s +9.0 . . . . . . . ...... COa(H20)o_a . . ...... 0.85 .. .... NaLiS04 . ,. ... -20.2 +9.3 NaN02 C!OH11(OHkH20 +43 .... .. +5.8 variable +3.7 -0.23 ..... -3.6 -033 ...... -10 to ....... ...... ZnO -13 '

Formula

Substance

...... +6.7 ..... ,

AlN NH4B50~'4H20 SbSI Ba(SbO)2 (C4H406kH20 BaTiOa

du

......

68. Anthracene .... , . ....... CuH!O 69. Cane sugar ............. CI2H220U 70. Diammonium tartrate ... (NH4hC4H406

d2l

dl6

+1.2 +3.1 +3.3

d22

± 1.3 . .... -2.35 .' ." -5.4 20g PbScl-CrtNbiO. (ceramic) .. PbFetNbiOa (ceramic) .. PbMgiNbi()a 0

0

•

0

0

•

0

•

0

0

•

0

0

0

•••••••••••••••••••

0

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0

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...............

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Structure at room temp.

Ferroelectric axis

orthorh.

...........

Curie point, K

tetrag. trigonal trigonal

e c c

423 513 763 1468 891-938

.......

...........

. ........

trigonal orthorh. orthorh. cubic hexag, hexag. hexag.

c c c c c c c c c c c c c c c

hexag. hexag. hexag. orthorh. orthorh. orthorh. orthorh. orthorh. orthorh.

monocl.

b ...........

rhomb. tetrag. tetrag.

...........

tetrag.

e

tetrag. orthorh. tetrag. orthorh. orthorh.

c c c

........... c

........... ...........

orthorh. tetrag.

............

.......

. .......... . ..........

rhomb. cubic

c

c

485 691 397 13

......... ......... ......... 973-998 933 434 432 463 430 70- >90 148 max. 120 max. 1.98 23 127 max. 94 max. 0.0049t 0.504t 0.00195t 0.420t >1.5 >0.7 >2.3 . ... . ..... >0.7 0.45 1.1 0.53 0.56 2-6.9t 4.5t >30 0.12 0.515 156§ o.00043-0 . 00236 0.005-0.0775 0.425 1.850 0.325 1.425 0.275 1.175 0.375 0.090 3.55 >14-138 138

5.75-7.88 .

"

..

5.3 4.7 7.07 7.20 7.49

O.·02·9·t· 0.024t 0.050 0.062 0.078

.

. ..

.,

5.31

=5.9

1 . 7-4.1

~0.8 ~0.75 ~0.45

"'0.30 0.238 0.227 0.185 0.165

• Temperature of critical field measurement. t Extrapolated. t: Linear extrapolation. , Parabolic extrapolation.

.,

19'9t ...... 172t "'34 "'28 "'25 17.3 14.3 8.2 3.8 108 max. "'3.4 "'3.15

"'2.2 "'1.2

>34

Tob••

K*

4.2 14.15 15 16 17 4.195 4.2 4.2 1.2 4.2 1.2 1.2 4.2

o o

4.2 4.2 4.2 4.2

o o 3.7 0.012-0.079 1.3 2.27 2.66 3.72 4.2 1.2 1.2

o

8-44

.

Vo.U Z r o . 7 4 . . . . . . . . . . . . . .

W (film). . . . . . .

H e 2 , kg

0.170

Nbo.lTau... .. . . Nb0.2Tao.s Nbo. e.-0.71Tao.02_0.10Z rO.25 NbzTh_z ..... Nb0.222UO.77S. NbzZrl_z ...

Hoi, kg

AND

T obs (Continued)

2.7

4.2 4.2

28.1 16.4 12.7 6.8

4.2 4.2 4.2 4.2 4.2 4.2 4.2 1.2 1. 79

o o

2

3 4

1.05 1. 78 3.04 3.5 1

9h. Color Centers and Dislocations C. C. KLICK

U.S. Naval Research Laboratory

9h-L General Properties of Color Centers. Color centers are imperfections in transparent solids that give rise to optical absorption. Most of these centers are associated with crystalline defects, but centers arising from the incorporation of chemical impurities are frequently also considered to be color centers. Work on this subject has progressed farthest in the alkali halides; and only these materials will be discussed here. Related centers appear in most transparent solids, but their atomic identification is uncertain in many cases. The conditions under which each center appears will be discussed in more detail below for the various centers. The most common treatments (ref. 1) are exposure to ionizing radiation such as X rays, heating in the alkali metal vapor which leads to centers with trapped electrons, and heating in halogen vapor which leads to centers with trapped holes. It is frequently useful to relate the number of centers to the strength of the absorption band produced. If the absorption band is gaussian in shape, then an approximate relation is (ref. 2) (9h-1) where No is the concentration of centers per cubic centimeter, f is the oscillator strength, n is the index of refraction of the material at the wavelength of the absorption band, am is the absorption coefficient at the maximum of the band in reciprocal centimeters, and W is the width of the absorption band in electron volts at an absorption coefficient one-half that of the maximum. If it is possible to measure the concentration No by some method such as chemical analysis or magnetic susceptibility, then the oscillator strength can be obtained. Knowledge of this factor for a particular center allows the determination of the density of that center from optical measurements alone and also gives a measure of the degree to which the optical transition is an allowed one. If the curve is Lorentzian in shape, then the constant in Eq. (9h-l) is 12.9. This form of the equation, often called Smakula's equation, is used in much of the older work, but the Gauss curve is a better (refs. 3 and 4), but not perfect, fit to the observed bands. Oscillator strengths given here will be in terms of Eq. (9h-l); they can be converted to Smakula's equation by multiplying by 1.48. 9h-2. F-center and Other Trapped Electron Centers. The most widely investigated color center is the F-cenier now known to consist of an electron trapped at a negative ion vacancy. If an alkali halide crystal is heated in the vapor of the alkali metal for several hours and then quenched to room temperature, the F-band appears. To the short-wavelength side of the F-band there also appear several weak absorption bands which have been designated K-, L 1- , L 2- , and Ls-bande. It is believed that these are more highly excited states of the F-center and show a dependence of wavelength on lattice constant which is similar to that of the F-band (ref. 5). 9-148

9-149

COLOR CENTERS AND DISLOCATIONS

If the F-band is bleached with light at low temperatures (-150°C for KBr, for example) a new broad band grows to the long-wavelength side of the F-band. This absorption is due to the F'-center and arises from an F-center that has captured an additional electron (ref. 6). Irradiation with light in the F-band at room temperature causes the F-band to decrease and produces the M-band which arises from a pair of F'-ceniers, and then the Rl- and R 2-bands arising from a cluster of three F-centers. The peak position of the absorption of these centers at room temperature is given in Table 9h-1. Wavelengths are given throughout this article in millimicrons (mu), TABLE 9h-1. WAVELENGTH OF ABSORPTION OF ELECTRON TRAP CENTERS (In millimicrons)

L3

L2

Ll

-180°C

-180°C

-180°C

·.. · .. .. . ·.. ·. ..

... .. , .. . ... .. . . . ..

. ..

F

K

Rl

R2

M

Width at half maximum of

F-band, eV -180°C 20°C 20°C 20°C 20°C 20°C

---LiF ...... LiCl ..... NaF ..... NaCI. ... NaBr .... NaI ..... KF ...... KCI. .... KBr ..... KI ...... RbCI. ... RbBr .... RbI ..... CsCI. ... CsBr ....

"

.. .

251 276 326 279 300 338

.. .

.. .

"

.

. ..

., . ., .

. .. . ..

.,

344 374 447 402 435 506

457 525 585 523 593 646

.. . .. .

"

288 316 382 335 362 413

. .. .. .

. .. ., .

.. . .. .

., . . ., .

.,

.,

.

.

250 385 341 458 540 588 455 556 625 689 609 694 756 605 680

313

... . ..

545

.. . .. .

658 735

.. . .. .

805

. .,

380 580 415 596 ., . 570 727 790

...

... 859 ...

444 650 505 725

0.82 0.62 0.62 0.47 0.52

...

0.41 0.35 0.345 0.345 0.31 0.28 0.35

...

825 892

. .. . ..

957

...

The values are somewhat approximate, since different workers report results varying by as much as 20 mu, Also given in Table 9h-1 are the widths at half maximum of the F-band at room temperature. It has been noted that the wavelengths of the absorption bands vary with the distance a between nearest neighbors of the alkali halides. Equations (sometimes called Ivey relations) governing these bands are as follows (ref. 7): F-center: Rj-center Rs-eenter: M-center:

Aab. = 703 a 1. 8 4 Aab. = 816a 1.84 Aab. = 884 a 1. 8 4 Aabe = 1,400a1.58

Both A and a are in angstroms. The variation of the maximum of the F -center absorption band as a function of temperature is shown in Fig. 9h-1 (ref. 16). The width W at half maximum of the F-band absorption also varies with temperature and fits an equation of the form W

( hll)t

= W o coth 2kT

(9h-2]

9-150

SOLID-STATE PHYSICS

where Wo is the width at absolute zero, h is Planck's constant, 11 is a frequency related to the lattice vibrations of the solid, k is Boltzmann's constant, and T is the absolute temperature. At low temperatures (less than about 25° absolute) W is a constant; at high temperatures (above room temperature) W increases with the square root of the 2.4 2.0 1.6 temperature. Table 9h-2 lists the values ENERGY (ELECTRON VOLTS) of W 0 and 11 which give the best fit to FIG. 9h-1. Effect of temperature on the experiment (ref. 17). Wand W o are given position of the F-band maximum. in units of electron volts. Direct measurements of oscillator strengths have been made for some of the F-centers using chemical techniques, electron-spin resonance measurements, and measurements 450

TABLE 9h-2. HALF WIDTH OF F-BAND AS A FUNCTION OF TEMPERATURE [Constants for Eq. (9h-2)] Wo, eV

LiF ............

NaCI ........... KCl. ........... KBr ........... KI .............

0.43 0.29 0.18 0.20 0.18

11,

4.1 4.4 2.6 2.6 3.6

Hz

X X X X X

10 12 1012 10 12 10 12 1012

of paramagnetic susceptibility. The agreement among these various methods is relatively poor. Oscillator strengths of the following values have been reported: F-center F-center F-center F-center

in in in in

NaCI: 0.5(8), 0.58(9), 0.5(10), 0.57(11) KCI: 0.55(8), 0.54(12), 0.57(9), 0.44(10), 0.78(13), 0.61 (11) KBr: 0.47(10), 0.57(11) KI: 0.31 (10)

From measurements on the growth of the M-band as the F-band is bleached by light, values of 0.2 (refs. 14 and 15) have been obtained for the oscillator strength of the M-band in KCI. The effect of pressure on the position of the F-center maximum has been measured (ref. 18) in the range up to 50,000 atm. Data obtained at room temperature for the F-band in NaCI, KCI, and CsBr are shown in Fig. 9h-2. In the case of KCI the sharp 0

3.3 3.2 No CI u.~ 3.1 ~S? zz 3.0

~~

m(f)

00 -0:

2.9 !::I(f)U ow Q....J 2.8 ::.c W < [ - 2.7

w Q.

o

/2.3

2.4

K CI

Cs Br

2.2

2.1 2.0 1.9 1.8

10 20 30 40 50 0 10 20 30 40 50 0 10 20 30 40 50 PRESSURE (THOUSAND ATMOSPHERES)

FIG. 9h-2. Effect of pressure on the position of the F-band maximum.

9-151

COLOR CENTERS AND DISLOCATIONS

break in the curve occurs as the lattice changes from the normal N aCI type to that of CsCI at high pressures. When color centers are excited, the stored energy may be released as luminescence. If only F-centers are present and measurements are made at liquid-nitrogen temperatures or below, F-center luminescence is observed (ref. 19). When Mecenters are present, then excitation in both the F-band and M-band gives rise to M-center emission. Finally, when the R-centers arise, only emission characteristic of these centers can be observed. In general only the M-center emission can be seen on exciting at room temperature. From measurements of the polarization of luminescence emission as a function of the polarization of the exciting light, the symmetry of the centers can be obtained. The F-center is found to be isotropic, but the M- and R-centers are asymmetrical and have their major axis along the (110) directions. Table 9h-3 gives the luminescence TABLE 9h-3. LUMINESCENCE OF ELECTRON TRAP CENTERS AT 77 K F-center

Peak tion, mil

Half width, eV

.... .

. ...

1,200 1,010 1,320 1,470 1,120

0.31 0.20 0.22 0.16 0.23

posi-

M-center

Peak position, mil

Half width, eV

R-center

Peak

P

posi-

tion, mil

Half width, eV

P

--LiF ....... NaC!. .... KCl ...... KBr ...... KI ........ RbCI. ....

....

670 1,070 1,080

0.20 0.21

0.60 0.60 0.60

1,180 1,240

0.19 0.15

0.20 0.20

peak positions and half widths for various centers and gives also the polarization P of the luminescence of the M- and R-centers (ref. 20). This polarization is measured with the exciting light, polarizer, sample, analyzer, and detector in line. If the polarizer is set parallel to a (110) direction, then the luminescence measured with the analyzer parallel to the polarizer is III and with the analyzer crossed is 11.' The polarization P is defined as P = III - 11. III

+ 11.

For simple dipoles along the (110) direction, the value of P should be 0.66. Electron-spin resonance has been observed for the F-center in many of the alkali halides. Table 9h-4 gives the g-values of the resonance (compared with a value of 2.023 for the free electron) and the width !::.H of the resonance absorption. This value is expressed in gauss for measurements in which the magnetic field is approximately 3,000 gauss and the frequency is approximately 9,000 MHz. 9h-3. Hole Trap Centers. A group of centers exists in the alkali halides characterized by having trapped a hole. Transfer of an electron from an electron trap center to one of these hole trap centers destroys them both. These centers do not follow an Ivey relation. Although some of them are formed by additive coloration at high temperature, the best-understood ones are formed at low temperatures by X-raying and show very detailed paramagnetic spectra. The peak position of the absorption bands for some of these centers is given in Table 9h-5.

9-152

SOLID-STATE PHYSICS

The H-center is formed by X-raying at liquid-helium temperatures. From a study of its detailed paramagnetic resonance spectrum (ref. 25), the H-center is found to be three halide ions and a halogen atom squeezed into the position normally occupied by three halide ions along a face diagonal. The center bleaches thermally at 56 K in KCI. X-raying at 77 K produces the V I-center, an H-center near an impurity. Also at 77 K a weak absorption band, called the X 2--band, is formed. The number of these centers is much larger if small amounts of Ag, TI, or Pb are in the crystals (ref. 26). From a study of the paramagnetic resonance spectra (ref. 27) it is concluded that the X 2--center consists of a hole trapped between two halogen ions which have been displaced toioani each other slightly from their equilibrium positions. TABLE 9h-4. ELECTRON-SPIN RESONANCE OF THE F-CENTER Material

u-value

t:.H

Ref. ---

LiF ............. NaF ............ NaCI. .......... KCL ........... KBr ............ KI ............. RbCl ........... RbBr ........... RbI ............

2.003 2".002 1.987 1.995 1.980 1.971 2 2 2

120 50 180 61 162 200 400 380 640

21 21 22 22 22 23 24 24 24

TABLE 9h-5. WAVELENGTH OF ABSORPTION OF HOLE TRAP CENTERS (In millimicrons) H

VI

X2-

V2

4K

17K

17K

300 K

I

Va

300 K

--- ---------

LiF ............. NaCl ........... KCI. ........... KBr ............ KI .............

.. .

...

330 335 380

345 356 410

.. .

...

348

...

365 385 404

223 230 265

210 212 231

The V 2- and Va-centers are formed in alkali halides by heating them in halogen vapor and quenching to room temperature. 9h-4. Perturbed Lattice Transitions. Two bands, the a- and {3-bands, have been found in alkali halides near the edge of the fundamental absorption band upon X-raying at liquid-nitrogen temperatures (ref. 28) (Table 9h-6). The strength of the a-band is correlated with the presence of negative ion vacancies and the {3-band with F -centers. It is believed that both bands arise from transitions similar to those in the fundamental band of pure crystals but modified by the proximity of the various imperfections. The oscillator strength of the {3-band is approximately unity, and that of the a-band somewhat less. 9h-6. Colloid Centers. Colloid centers are formed in crystals that have been colored by heating in alkali vapor and are then held at temperatures between 300 and 600°C. An absorption band to the long-wavelength side of the F-band appears. As "Ile temperature increases over this range, the F-band intensity increases, the colloid

9-153

COLOR CENTERS AND DISLOCATIONS

band decreases, and its peak position shifts to longer wavelength. It is believed that these bands are due to colloid metal particles of from 10 to 50 A in diameter. 9h-6. Impurity Absorption Bands. Alkali halide crystals containing hydrogen show an absorption band known as the U-band. The U-center consists of a hydride ion substituting for a normal halide ion. Irradiation with light in the U-band produces the F-center and a new center, the Us-center, due to interstitial hydrogen atoms. Interstitial hydrogen ions give rise to the Us-center (ref. 29). The absorption peak positions of the U-bands are given in Table 9h-7. For KCI the Uj-band occurs at 236 m}.' and the UI-band is a broad band near 275m}.'. TABLE 9h-6. ABSORPTION OF a- AND I3-BANDS (Absorption peaks in millimicrons)

NaF.. . . . . . . . . . . NaGl. .. .. . . . . . . . NaBr.. . . .. .. .. . KGl. .. . KBr... . . .. KI.............. RbBr.......... . RbI........ .....

a

13

131 173 199 178 201 238 205 240

127 168 170 192 226 196 229

TABLE 9h-7. ABSORPTION BANDS FROM U-CENTERS, HYDROXIDE CENTERS, ZI- AND Z2-CENTERS (In millimicrons)

NaGl ........... NaBr .•........ KG!. ........... KBr ........... KI ............. RbGl. .......... RbBr ..........

U-band

OH--band

Zl band

z, band

192 210 214 228 244 229 242

185

505

512

204 214

590

635

Incorporation of OH- in alkali halides gives rise to the hydroxide center absorption bands shown in Table 9h-7, which follow an Ivey relation (refs. 30 and 31). The presence of these bands influences the amount of F-center coloration by X rays at room temperature and the formation of colloids (ref. 32). Z-centers are formed from additively colored crystals that are doped with divalent impurities such as strontium, barium, or calcium (ref. 33). The ZI-center can be formed by irradiating an additively colored crystal in the F-band at room temperature. The Z2-center is formed by heating a crystal containing F- and ZI-centers to approximately lOO°C. Positions of these absorption bands are given in Table 9h-7. The Z2-center in KCI is luminescent and emits at 1,140 mu; the emission does not appear to be polarized (ref. 34). The addition of heavy metal ions to the alkali halides produces absorption and emission bands largely characteristic of the ions. Table 9h-8 shows the optical properties of the centers due to incorporation of TI, Pb, Ag, and Cu.

9-154 TABLE

SOLID-STATE PHYSICS

9h-8.

ABSORPTION AND EMISSION BANDS DUE TO TI,

Pb, Ag,

AND

Cu

(In millimicrons)

i

I

TI abs,

TI ernis,

Pb abs,

Pb emis.

Ag abs,

Ag ernis.

\ I --- --- --- --- --- ---

---

---

249

255

358

...

219

263

259

...

365 438

196 273

346

215

272

265

396

223 302 265

.. .

...

. ..

265

393

199 254

288

193 274

NaBr ..............

216 267 234 293 195 247

295 308

220

250 305 475 318 350 415 315

198

NaI ................ KCl. ...............

210 261 236 287 195 245 212 259 240 286 196 248 214 263 241 269 299

KBr ............... KI ................. RbCI ............... RbBr .............. RbI ................ CsCI ............... CsBr ............... CsI ................

Cu emis,

210

NaCI ...............

...

Cu abs,

.. .

318 384 453

.. .

. ..

. ..

I

References for Sees. 9h-l through 9h-6 There are a series of survey articles and books on color centers each of which gives an excellent summary of the field at the time of its publication. They are listed below in chronological order. Pohl, R. W.: Proc. Phys. Soc. 49, (extra part), 3 (1937). Mott, N. F., and R. W. Gurney: "Electronic Processes in Ionic Crystals," Oxford University Press, New York, 1940. Seitz, F.: Revs. Mod. Phy.~. 18, 384 (1946). Przibram, K.: "Verfarbung und Lumineszenz," Springer-Verlag OHG, Berlin, 1953; "Irradiation Colours and Luminescence," Pergamon Press, Ltd., 1956. Seitz, F.: Revs. Mod. Phys. 26, 7 (1954). Stockmann, F.: In "Landolt-Bornstein," 6th ed., vol. 1, pt. 4 entitled Kristalle, p. 981, Springer-Verlag, Berlin, 1955. Schulman, J. H., and W. D. Compton: "Color Centers," Pergamon Press, Ltd., 1963. Markham, J. J.: "F-Centers in Alkali Halides," Academic Press, Inc., New York, 1966. Fowler, W. B. ed.: "Physics of Color Centers," Academic Press, Inc., New York, 1968. 1. Schulman, J. H., and H. W. Etzel: In "Methods of Experimental Physics," vol. 6, p. 324, Academic Press, Inc., New York, 1959. 2. Dexter, D. L.: Phys. Rev. 101,48 (1956). 3. Hesketh, R. V., and E. E. Schneider: Phys. Rev. 95, 837 (19M). 4. Markham, J. J.: Rev. Mod. Phys. 31,956 (1959). 5. Luty, F.: Z. Phys., 160, 1 (1960). 6. Pick, H.: Ann. Physik 31, 365 (1938). 7. Ivey, H. F.: Phys. Rev. 72,341 (1947). 8. Pick, H.: Ann. Physik 31, (5),365 (1938). 9. Silsbee, R. H.: Phys. Rev. 103, 1675 (1956). 10. Rauch, C. J., and C. V. Heer: Phys. Rev. 105, 914 (1917). 11. Doyle, W. T.: Phys. Rev. 111. 1072 (1958).

9-155

COLOR CENTERS AND DISLOCATIONS 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34.

Kleinschrod, F. G.: Ann. Physik 27 (5), 97 (1936). Scott, A. B., and M. E. Hills: J. Chem. Phys. 28, 24 (1958). Hirai, M.: J. Phys. Soc. Japan 14, 1400 (1959). Okura, H.: J. Phys. Soc. Japan 12, 1313 (1957). Mollwo, E.: Z. Physik 85, 56 (1933). Russell, G. A., and C. C. Klick: Phys. Rev. 101, 1473 (1956). Maisch, W. G., and H. G. Drickamer: J. Phys. Chem. Solids 5, 328 (1958). Botden, Th. P. J., C. Z. van Doorn, and Y. Haven: Philips Res. Repts. 9, 469 (1954). Lambe, J., and W. Dale Compton: Phys. Rev. 106, 684 (1957). Lord, N. W.: Phys. Rev. 105,756 (1957). Kip, A. F., C. Kittel, R. A. Levy, and A. M. Portis: Phu«. Rev. 91, 1066 (1953). Noble, G. A.: Bull. Am. Phys. Soc., ser. 2, 3, 178 (1958). Wolf, H. C., and K. H. Hausser: Naturwissenschaften 23, 646 (1959). Kanaig, W., and T. O. Woodruff: J. Phys. Chem. Solids 9, 70 (1959). Delbecq, C. J., B. Smaller, and P. H. Yuster: Phys. Rev. 111, 1235 (1958). Castner, T., and W. Kanzig: J. Phys. Chem. Solids 3, 178 (1957). Delbecq, C. J., P. Pringsheim, and P. H. Yuster: J. Chem. Phys. 19, 574 (1951); 20, 746 (1952). Delbecq, C. J., B. Smaller, and P. H. Yuster: Phys. Rev. 104, 599 (1956). Rolfe, J.: Phys. Rev. Letters 1, 56 (1958). Etzel, H. W., and D. A. Patterson: Phys. Rev. 112, 1112 (1958). Etzel, H. W.: Phys. Rev. 118, 1150 (1960). Pick, H.: Ann. Physik 35, 73 (1939); Z. Physik 114, 127 (1939). West, E. J., and W. Dale Compton: Phys. Rev. 108, 576 (1957).

9h-7. Dislocations. There are two important simple types of dislocations in crystals: the edge dislocation and the screw dislocation. Figure 9h-3 illustrates an edge dislocation. In this case one portion of the crystal has partially slipped with respect to the other. The plane along which the slip has occurred is plane ABeD. If the slip has been one atom distance, then all the atoms are once again in order except for those along the line AD. This line, along which the crystal is badly distorted, is I

000 0 000 000 000 0 0 0 0 0 ~ 0 00000 0 0 0 0 0 000 000 0 0 ~ 0 I o 0 0 0 0 0 0 0 0 0 o 000 0 000 ~ 0

0 0 0 0 0 0

0 0 0 0 0 0

000 0 0 0 0 0 0 0 0 0 000 000 0 0 0 0 0 0 0 0 0 0 0 0

OOOOOOOO~OOOOOOOO ------+-----o 0 0 0 0 0 0 0 \0 0 0 0 0 0 0 0

o

000 000 0 0

0 0 000 0 0

o 000 0 0 0 0 000 0 0 0 0 0

o

0 0 0 0 0 0 0 000 0 0 0 0 0

o 000 0 000 0 0 0 0 0 0 0 0

o

000 0 0 0 0 00000 0 0 0

FIG. 9h-3. A n edge dislocation. (After W. T. Read, "Dislocations in Crystals," McGraw-Hill Book Company, New York, 1953.)

0 0 0 0 0 0 0 0 000 000 0 0

FIG. 9h-4. View of the surface of a crystal with an edge dislocation. (Reprinted with permission from W. Shockley, J. H. Hollomon, R. Maurer, and F. Seitz: "Imperfections in Nearly Perfect Crystals," John Wiley & Sons, Inc., New York, 1952.)

the dislocation. The direction of displacement of the atoms due to the formation of the dislocation is b, the Burgers vector, and for an edge dislocation b is always perpendicular to the dislocation line. Figure 9h-4 shows an end view of the crystal where the dislocation line comes through to the surface at A. The slip plane is represented by the horizontal line. It is seen that the edge dislocation can also be thought of as consisting of the partial introduction of an extra vertical plane of atoms. The end of this plane is the dislocation line.

9-156

SOLID-STATE PHYSICS

A screw dislocation is illustrated in Fig. 9h-5, and the surface of the crystal I through which it appears is shown in I I Fig. 9h-6. Here the Burgers vector b is I I parallel to the dislocation line. " I I " More general forms of dislocation lines "r--7 L/ " are possible. A ring, for instance, con/" sists of portions which are pure edge and / " pure screw dislocations connected by segments which have both edge and ,//' B screw character. / / The Burgers vector can be obtained in general by making a circuit around a disFIG. 9h-5. A screw dislocation. (After location. Starting in an undistorted part W. T. Read, "Dislocations in Crystals," ~McGraw-Hill Book Company, New York, of the crystal we might proceed by count1953.) ing up l atoms, then left r atoms, then down l atoms, and right r atoms. If this bounded surface does not contain a dislocation, one arrives at the starting point. If a dislocation line does pass through the surface, the circuit will not close on the origin. The vector necessary to close the circuit is the Burgers vector. The large amount of slip observed along single planes necessitates that there be a source for the creation of many dislocations within a strained crystal. One such model is the Frank-Read source illustrated in Fig. 9h-7. The line is a dislocation pinned at both ends by the presence of an impurity atom, for instance. Under stress I

I 1

A.~~~~'"

(Reprinted with permission from W. T. Read, "Dislocations in Crystals," McGraw-Hill Book Company, New York, 1953.)

FIG. 9h-6. View of the surface of a crystal with a screw dislocation.

the line bows out and finally curls back on itself to touch. One loop continues on; the other returns to the original configuration from which the process may be repeated. A jog in a dislocation is a sidewise step, usually of one atomic distance, of a dislocation line. Dislocations have been made visible in silver halides and alkali halides by appropriate treatment. It is found that they generally appear to form a hexagonal network. A convenient way to determine the number of dislocations in a crystal is to

COLOR CENTERS AND DISLOCATIONS

faJ

9-157

flJJ

etch the surface and count the ends of dislocation lines which appear as etch pits The density of dislocation lines is given as those passing through a square centimeter. Normal crystals have approximately 10 5 to 10 9 dislocations per square centimeter, and this may be reduced in very carefully prepared crystals to a few hundred or less. Etching also allows the motion of a single dislocation to be followed as stress is applied and thus permits studies of the mobility of dislocations. Dislocations have made it possible to understand the growth of crystals under conditions of very low supersaturation. If a screw dislocation intersects the surface, as in Fig. 9h-6, then the atoms can easily continue to build on the spiral. When examined carefully with the microscope, a great many crystals show this spiral growth pattern. Another problem solved by dislocations is that of the plastic flow of metals which occurs at stresses less by a factor of 104 than those calculated for a pure crystal. The relatively easy motion of dislocation lines has now been used to explain a large variety of mechanical properties. In recent years it has been possible to obtain dislocation-free crystals. These are usually in the form of thin small needles called whiskers. It can be shown experimentally that these whiskers have the mechanical properties expected of the pure materials. Whiskers of many materials have been prepared, including Fe, Cu, CdS, p-toluidine, and the potassium halides. While most of the whiskers are straight, a commonly observed defect is a sharp bend, or kink, in the crystal. References for Sec. 9h-7 A number of detailed expositions of dislocations are available. Cohen, M., ed.: "Dislocations in Metals," American Institute of Mining and Metallurgical Engineers, New York, 1954. Cottrell, A. H.: "Dislocations in Plastic Flow in Crystals," Oxford University Press, London, 1953.

9-158

SOLID-STATE PHYSICS

Fisher, J. C., W. G. Johnston, R. Thomson, and T. Vreeland, Jr., eds.: "Dislocations and Mechanical Properties of Crystals," John Wiley & Sons, Inc., New York, 1957. Read, W. T., Jr.: "Dislocations in Crystals," ~;JcGraw-Hill Book Company, New York, 1953. Van Buerew, H. G.: "Imperfections in Crystals," 2d ed., North Holland Publishing Company, Amsterdam, 1961. Verma, A. R.: "Crystal Growth and Dislocations," Academic Press, Inc., New York, 1953.

9i. Luminescence FERD WILLIAMS

University of Delaware

9i-1. General Phenomena and Definitions. Luminescence is the phenomenon of light emission in excess of thermal radiation. This definition must be qualified, however, in order to exclude the Raman effect, Compton and Rayleigh scattering, and Cherenkov emission; and this is achieved by limiting luminescence to phenomena involving a time delay of emission after excitation which is long compared with the period of the emitted radiation, Alc or approximately 10- 14 sec. Luminescent emission involves optical transitions between electronic states characteristic of the radiating material. For ordinary luminescence the emission occurs by the Einstein spontaneous transition probability and is therefore incoherent; at high-excitation intensities the emission for laser materials occurs predominately by the Einstein induced transition probability and is therefore coherent. Although most investigations of luminescence have been concerned with visible emission and the term implies luminous or visible radiation, the same basic processes may yield infrared or ultraviolet radiation. Therefore, luminescence is also applied to such emission as is in excess of thermal radiation. Solid materials which luminesce when suitably excited are called phosphors. In many crystalline phosphors the luminescent emission originates in impurity systems called activators. The general phenomenon of luminescence has been subdivided on the basis of the duration of the emission following excitation. Most investigators (refs. 1, 2, and 3) have made this subdivision by considering the mechanisms responsible for the afterglow. When the excitation is removed, there is invariably an exponential afterglow which depends on the lifetime of the emitting state of the activator. This spontaneous afterglow is called fluorescence. The time constant for the fluorescent emission may be as short as 10- 8 or as long as 10- 1 sec, depending on the phosphor, particularly on the identity of the activator. Frequently, there is an additional component to the afterglow which decays more slowly and with more complex kinetics. This component is called phosphorescence. In some phosphors, phosphorescence is attributed to metastable states of the activator; in others, to electron or hole traps spatially removed from the activator. Because thermal activation of the metastable activator or trap is prerequisite to emission, phosphorescence is strongly dependent on temperature. Phosphorescence may persist for times as short as milliseconds or as long as days or longer. During continuous excitation both the fluorescent and phosphorescent mechanisms contribute to the luminescent emission in proportions depending on the steady-state kinetics of these processes. Some authors (ref. 4) have chosen to define fluorescence

LUMINESCENCE

9-159

as luminescent emission during excitation, and phosphorescence as emission after the excitation has been removed. Luminescence has also been subdivided according to type of excitation. This subdivision is indicated by a prefix. For example, photoluminescence refers to luminescence excited by photons, electromagnetic radiation in the visible, ultraviolet, or infrared. Cathodoluminescence involves excitation by cathode rays, energetic electrons impinging on the phosphor. Electroluminescence involves the excitation of luminescence as a result of the existence of an applied electrical potential difference in the phosphor. This phenomenon may occur by several different mechanisms: excitation involving the injection of minority electronic charge carriers in semiconducting phosphors is designated injection electroluminescence; excitation involving the impact excitation of activators by electrons which have been accelerated to high kinetic energies in high applied fields is designated collision-excitation electroluminescence. Mechanical excitation such as grinding is termed triboluminescence. The conversion of the energy of a chemical reaction into luminescent emission is chemiluminescence, whereas the excitation of luminescence by biological processes is bioluminescence. Thermoluminescence, however, does not refer to thermal excitation but rather to the thermal stimulation of luminescence. The phenomenon is essentially phosphorescence measured during conditions of increasing temperature. The stimulation of luminescence by the visible or infrared is described as optical stimulation. Double prefixes are used to describe more complex luminescent phenomena. The first prefix refers to the control of the luminescence which has been excited in accordance with the mechanism described in the second prefix. For example, elecirophotoluminescence refers to the modulation of photoluminescence by an applied electric field, whereas photoelectroluminescence refers to the control of electroluminescence by incident photons. 9i-2. The Representation of Absorption and Emission Spectra. Most luminescent solids exhibit broad, bell-shaped absorption bands near the fundamental absorption edge and emission bands corresponding to smaller transition energies. The emission bands of many luminescent solids are also broad and structureless; however, the emission of some, particularly of solid-state lasers, are narrow bands. The photoluminescent excitation spectrum usually coincides with the absorption bands. The excitation and emission spectra are determined by the characteristics of the activator systems. The energies of the discrete, localized states of the activator system are a function of the nuclear coordinates of the crystal. Since the atoms which are near the activator interact differently, depending on the electronic states of the activator, the transition energy between these discrete states depends on the internuclear coordinates of these atoms. This effect combined with the Franck-Condon principle accounts for the Stokes' shift of the emission to smaller transition energies compared with absorption in the activator system and for the breadth of the absorption and emission bands. This is of course for systems in which the transition for emission is the inverse of the transition for photoexcitation except for differences in interaction with the lattice for excited and unexcited activator. For systems in which there is a nonradiative transition between quite different excited electronic states of the activator following photoexcitation, the Stokes' shift originates mainly from the difference in energies of these excited states, and the emission may be narrow bands. We shall first consider the origin and representation of the spectra of phosphors with broad and structureless absorption and emission bands. For simple activator systems, describable in terms of a single internuclear coordinate q, the probability of the transition involving a photon of wave number s per wave-number interval Pj, has been shown to be (ref. 5): K)' [ - K q2 ] dq (9i-l) P v = M2 ( 27rkT exp 2ko coth (OIT) d;;

9-160 TABLE

SOLID-STATE PHYSICS

9i-1.

ACTIVATOR' ABSORPTION AND EMISSION BANDS OF ALKALI HALIDE PHOSPHORS·

Absorption maxima, Po X 10- 4 em"!

Phosphor

NaCl:Tl. ....... KCl:Tl ......... RbCl:Tl. ....... CsCl:Tl ........ NaBr:Tl. ....... ;KBr:Tl. ........ RbBr:Tl. ....... CsBr:Tl. ....... NaI:Tl ......... KI:Tl .......... llbI:Tl. ........ CsI:Tl .... '" .. NaCl:Pb ....... KCl:Pb ........ RbCl:Pb ....... NaBr:Pb ....... KBr:Pb ........ NaCl:Sn ........ KCl:Sn ......... RbCl:Sn ........ NaBr:Sn ....... KBr:Sn ........ RbBr:Sn ....... LiI:Sn .. , ...... NaI:Sn ......... KI:Sn .......... RbI:Sn ........ NaCl:Ga ....... KCl:Ga ........ KBr:Ga ........ NaCl:ln ........ KCl:ln ......... NaBr:ln ........ KBr:ln ......... KI:ln .......... NaCl:Ge ....... KCl:Ge ........ KBr:Ge ........ NaCl:Cu ....... KCl:Cu ........ NaBr:Cu ....... KBr:Cu ........ KI:Cu ......... ~aCl:Ag....... KCl:Ag ........ NaBr:Ag ....... KI:Ag ......... Na.Br:Eu ....... KBr:Eu ........ KI:Eu .........

5.02 5.10 5.13 5.10 4.63 4.76 4.72 4.67 4.27 4.24 4.17 4.15 5.18 5.10 5.05 4.54 4.44

4.7 4.84.8 4.8 ...... .. ...... .. .. ...... ........

......

..

........

......

..

3.7

4.25 d

...... .. ...... .. ........ ........ ........ ...... ..

4.31

......

.... .. ..

.....

3.86 d

.... .. .... ..

.. ..... 3.47 d

....

..

4.60 4.61 4.42 4.18

4.35 d 4.00 4.10 3.82

4.30 d 4.54 d 3.98 d

3.94 3.883.86 3.77 3.75 4.76 4.554.56

3.70 d .... . 4.00 d

.... .

..

.. ...... ...... .. ...... .. ...... .. .. ...... ...... .. ...... .. ...... ...... ...... ...... ...... ......

.. .. ..

..

I

Emission maxima, Po X 10- 4 cm- 1

3.94 4.05 4.08 4.03 3.74 3.83 3.86 3.80 3.41 3.48 3.50 3.34 3.65 3.66 3.68 3.29 3.30 3.51

3.38 d 3.13b

.. ..........

2.42 2.39 2.30 1.68 3.13 2.89

............

............

............

.......... .......... ............

...... 3.28 d

............ .. ..........

..

.... .. .... .. .....

..

..........

..

..........

............ .. ..........

2.85 d ..

3.75 .... .. 3.643.40

2.25 2.01 1.93 2.15 1.93 1.84 1.89 1.85 1. 78 1. 73 2.44

............

. .....

..

.. .......... ............

3.22 a

3.56 d

....

............

3.35 3.27 3.16

...........

4 04 a ,b

I

.. .......... .......... .. .. .......... ..

......

.... ..

........

.......... ..........

2.41 2.30

3.39 d

........

2.28

...... .. ...... .. ...... .. ...... .. ...... ..

3.74

..........

2.121.85 1. 75 2.81 2.53

... . ... .

. ....

.. ..

3.51 d

...... ..

....

... . . ...

. .....

. ..... ......

.... ..

..

........... ............ ..

........

............

.... .

..... .

......

2.52 2.48

. ....

...... ......

2.30 2.36 2.28

3.03 d

. ....

. .....

I

I

..

2.80b 2.08b

..........

2.62 b ,c 2.89b 2.80b

I

2.67

2.17

..........

........

..........

1.99 1.99 1. 78

......

1.91

..

• The data of this table were assembled by P. D. Johnson, General Electric Research Laboratory• .. Excitation in large ~ absorption band. b Observed at low temperature. • Observed with high activator concentration• .. Multiple band. • Disagreement in literature.

9-161

LUMINESCENCE

where M is the electronic part of the matrix element for the transition, K is the force constant for the displacement q from equilibrium in the initial state, and ko is the zeropoint energy for the vibration associated with displacement q. If we make the harmonic approximation, that is, that M is independent of q, and also if we assume that the force constants for the initial and final states are equal, then Pj, is found to be gaussian in ii. TABLE 9i-2. PHOTOLUMINESCENT SPECTRA OF ZINC SULFIDE PHOSPHORS * Phosphor

Band

iio

X 10- 4 cm- 1 h X 10- 4 cm "

Hex. ZnS: Ag,CI. Silver blue Hex. ZnS:Cu,Cl. Copper blue

2.29 2.22

0.12 0.15

Hex. ZnS:I. .... Self-activated blue Hex. ZnS:Cu,I .. Copper blue

2.19

0.19

2.19

0.16

2.19

0.12

2.21 2.18

0.14 0.14

2.13

0.18

2.09

0.19

1. 92

0.12 0.12 0.23 0.24 0.20 0.22

Hex. ZnS ....... Self-activated blue Cub. ZnS: Ag,CI. Silver blue Cub. ZnS: Cu,CI. Copper blue

Cub. ZnS ....... Self-activated blue Cub. ZnS:Al .... Self-activated blue Hex. ZnS:Cu,CI. Copper green Cub. ZnS:Cu,Cl. Copper green Hex. ZnS:Ag,In. Silver red Cub. ZnS: Cu .... Copper red Cub. ZnS:Cu .... Copper red Hex. ZnS: Au,Ib . Gold infrared

1.88 1.56 1.49 1.39 1.20

Comments

Band skewed to small ii because of copper green

Copper blue and self-activated blue resolvable at low temperature

Band skewed to small ii because of copper green

Spectrum at 77 K Spectrum at 77 K Spectrum at 77 K

*

Spectra at 298 K unless otherwise indicated. The author is indebted to J. S. Prener, General Electric Research Laboratory, for evaluating these data.

This is not found to be precisely the situation experimentally, and actually the radiant energy of wave number ii per unit wave-number interval E: was empirically found to be the more accurately gaussian in ii (refs. 6 to 9)

Eji = b exp [ -

(ii -

)2]

iio

1.44h 2

(9i-2)

where 2h is the half width of the band with maximum at Po. P p and E-p are, of course, related as follows: E-v = hctrP», The parameters iio and h of Eq. (9i-2) are used to characterize the emission spectra ill Tables 9i-l to 9i-6. This permits the most precise representation of the spectra with two parameters and also permits the straightforward transformation to and from

9-162

SOLID-STATE PHYSICS

the wavelength scale. The latter is of some importance, because many of the spectral data on phosphors are given as radiant energy of wavelength X per unit wavelength interval E).. The relation between E-v and E). is as follows: E-v = - X2E).. The maximum at Xo in the plot of E). vs. X does not coincide with the maximum jio in the TABLE 9i-3. EMISSION SPECTRA AND QUANTUM EFFICIENCIES OF FLUORESCENTLAMP PHOSPHORS * jio X 10- 4

h X 10- 4

em"?

cm- 1

'It

(Ca,Zn),(PO.h: TI ........... BaSi 20.: Pb ................. Ca.(PO.h: Ce................ CaWO•..................... Ca.(PO.h: Cu,Sn ............. Caa(POch:Cu ................ 3Ca.(PO.h·Ca(F,C1)2:Sb,Mn ..

3.18 2.88 2.74 2.21 2.07 2.05 2.04 1.69

0.17 0.18 0.17 0.29 0.18 0.18 0.28 0.11

0.9

MgWO •..................... 3Sr.(PO')2·Ca(F,Cih:Sn,Mn ..

2.01 1.93 1. 76

0.29 0.28 0.10

Zn 2SiO.: Mn (willemite) .......

1.89

0.09

CaSiO.:Pb,Mn ...............

2.80 1. 74 1.60

0.33 0.10 0.10

(Sr, Mg) , (PO.h: Sn ....•...... Cd 2B20.:Mn ................

1.58 1.58

0.13 0.11

Phosphor

Comments

0.7 0.7

0.8-0.95 Evidence of additional Mn emission at small ji; relative intensities depend on Sb and Mn concentrations; jio depends slightly on F ICI composition 0.9 ........ Relative intensities of Sb and Mn bands depend on Sb and Mn concentration Slightly skewed to 0.8 small ji ........ R = 0.42 for overlapping Mn bands; R depends on Mn concentrations 0.7

• Excitation predominantly by 2,537-A radiation. The spectra, from which the;o and h were derived, 'Were provided by H. C. Froehlich and F. J. Studer of Large Lamp Engineering of General Electric. t J. Tregellas-Williama, J. Blectrochem. Soc. 1015, 173 (1958).

plot E; vs. " but rather the latter occurs at slightly smaller wave number jio

= I/(Xo

+ £lX)

where £lX = 1.44h 2XI. The parameters jio and h for each band were determined, in accordance with Eq. (9i-2), by minimizing the sum of squared deviations in fitting the logarithm of E'i to a quadratic function of v. For multiple-band emission arising from a single activator, a third parameter R is also given in Tables 9i-3 and 9i-4.

9-163

LUMINESCENCE TABLE

9i-4.

~I

EMISSION SPECTRA AND AFTERGLOW OF CATHODOLUMINESCENT SCREENS

,

PO X 10-4 cm "!

h X 10- 4

Pl ...... Zn1Si04: Mn(rhbhd.>t P2 ...... ZnS: C u,Ag (hex.) t

1.89 1.85 2.22

0.09 0.14 0.15

P3 ...... (Zn,BehSiO.: Mn

1.84 1.64

0.09 0.11

P4 .••••. ZnS: Ag (hex.)t (Zn,Cd)S:Ag (hex.)t

2.22 1. 76

0.15 0.16

Medium short, hyperbolic

P5 ...... CaW04 P6 •••.•• ZnS: Ag (hex.) (Zn,Cd)S:Ag (hex.)

2.21 2.22 1. 76

0.29 0.15 0.16

1.1 X 10-1 Short hyperbolic

P7 ...... ZnS: Ag (hex.) (Zn,Cd)S: Cu

2.26 1. 78

0.17 0.15

Blue flash followed by slow yellow hyperbolic afterglow

P11t.... ~Z!"B:Ag,Ni (eub.)

2.11

0.19

Short hyperbolic, current dependent 8.5 X 10-1

Phosphor

cm- 1

Afterglow

T,

sec

Comments

1.1 X 10-1 Medium, intensitydependent hyperbolic 6 X lO- a

P12 ..... (Zn,Mg) FI: Mn

1.68

0.11

P13 ..... MgSiO.:Mn P14 ..... ZnS: Ag (hex.) (Zn,Cd)S: Cu (hex.>t

1.54 2.26 1.65

0.10 0.17 0.16

1. 7 X 10-1 Blue flash followed by yellow-orange afterglow

PIli..... ZnO

3.15

0.12

2.42

0.24

P16..... (Ca,Mg)BiOa: Ce P17 ..... ZnO (Zn,Cd)S:Cu

2.60 2.21 1. 78

0.20 0.15 0.15

Ultraviolet 2 X 10-' Visible 4 X 10-' 4 X 10-' 10-1 Medium hyperbolic

PIS..... (Ca,Mg)SiO.:Ti (Zn,Be)SiO.:Mn P19..... KMgF.:Mn

2.34 1.84 1.64 1.68

0.40 0.09 0.11 0.09

P20 ..... (Zn,Cd)S:Ag

1. 76

0.16

P21. .... MgFI:Mn

1.66

0.08

Medium short, .hyperbolic 8 X 10-1

F22§.... ZnS:Ag ZOISi04:Mn Zn.(P04) : Mn P23 ..... ZnS:Ag (Zn,Cd)S:Ag P24 ...•. ZnO

2.22 1.89 1.56 2.22 1. 73 1.93

0.15 0.09 0.09 0.15 0.16 0.21

Short hyperbolic 1.1 X 10-1 1.2 X 10-1 Medium short, hyperbolic afterglow 1.4 X 10-7

P2li •••.. CaSiO.: Pb,Mn

2.80 1. 74 1.60

0.33 0.10 0.10

1.6 X 10-a

*

Ag blue only about olu of Cu green band Slightly concave upward exponential afterglowj R ... 0.30 White screen composed of two phosphors Same as P4, except more (ZnCd)S/ZnS for less blue white Two-layer screen: electrons excite ZnS: Ag, whose emission excitea (ZnCd)S:Cu Tends to burn at high currents Same 88 P7, except that higher Cd content in (Zn,Cd)S:Cu yields orange afterglow

Similar to P7, except ZnO substituted for ZnS:Ag

2 X 10-1 6 X lO- a 7.5 X 10-1

P26 ..... ZnF.:Mn

1.67

0.09

8.3 X 10-1

P27 ..... Zn.(P0 4}t : Mn P28..... (Zn,Cd)S: CU,Ag

1.56

0.09

....

. ...

1.2 X 10-1 Long hyperbolic

R - 0.71 Tends to burn at higher currents Also weak blue band present; tends to burn at high currents Three-color screen Similar to P4 No ultraviolet emiasion 88 in P15

R - 0.42 for Mn bands Tends to burn at high currents MUltiple emission bands in yellow green, two-phosphor screen

I

9-164

SOLID-STATE PHYSICS

TABLE 9i-4. EMISSION SPECTRA AND AFTERGLOW OF CATHODOLUMINESCENT SCREENS' (Continued)

vo

Phosphor

Screen

X

10-,1

cm- 1

....

PO>•.• "1 ZnS, Cu.A.

10-'

h X cm
" ........ Y aAloOl2: Hos+ ............

&I7-+ 582-+ 5h -+ 5b -+

Glass: Hos+ ............... Ca(NbOs) 2: Er s+........... CaW04: 1 % Er s+.......... YaAloOl2: Er s+ ............

517 -+ 5Is 4I¥ -+ 4I¥ 4J¥ -+ 41¥ 4f¥--+ 4I¥

CaF2:0.01 % Tm3+ ........

2Ft -+ 2FI

0.8960

0

CaW04:Tm s+.............

sH4-+ 4H6

0.5232

325

SH4 -+ sH 6 sH4 -+ sH 6

0.5219 0.5170 0.5309

325

Er20S: Tm s+.............. Y sA150n: Tm s+............

0.4967 0.9712 0.9900 0.9823 0.3982 0.3827 0.4154

582 623 400

5Is 5Ia 5[a 51a

YsAloO,2:Yb s+............ 2Ft -+ Wi Glass (1): Yb s+............ 2Fi -+ W~ Glass (2): Yb s+............ 2Ft -+ 2F} CaF2:0.05% Us+ .......... 4I¥--+ 4f~ SrF2:Us+ .................

4f¥-+

4J~

375 525 .......

240

505 609 334

Excitation, v X 10- 4 cm'"!

2.38-3.12 1.66-2.00

1. 81-2.27 1.33-1.66 2.08-2.63 1.01-1.47 0.64-0.91 2.04-2.33 2.08-2.33 1.67-1.75 1.32-1.35

2.22-2.50 1.47-1. 72 3.57-5.00 2.13-2.17 1.85-1.92 2.17-2.27 2.17-2.27 0.85-0.88 0.51-0.53 3.57-5.00 3.57-5.00 2.12-2.17 1.85-1. 92 2.94-3.57 2.17-2.56 1.59-1.89 2.08-2.17 0.82-0.86 0.55-0.59 2.08-2.17 0.82-0.86 0.55-0.59 1.00-1.11 0.77-0.83

* Modified from Z. .1. Kiss and R. J. Pressley, Proc, IEEE, 154., 1238 (1966), and L. G. Van Uitert, "Luminescence of Inorganic Solids," Goldberg, ed., pro 520-523, Academic Press, Inc., New York, 1966.

9-167

LUMINESCENCE TABLE

9i-8.

SENSITIZED LASER MATERIALS AND TRANSITIONS·

Materialt

Transition

Y.Ah012:Yb S+, Er s+, Tm 3+, H03+......

5[7-+ fiI8

EraYaAho024: Er 3+ -+ H03+............ Y.Ah012: Cr 3+, H03+ .................

5[7-+ 5[8 517 -+ 518

Glass: Yb 3+, Host .................... CaMo0 4: Er 3+, H03+ .................

fi17 -+ 5[8 fi17 -+ 518

.-..-_.... _--

EraY.Aho024:Er 3+ -+ Tm 3+ ...........

SH4 -+ 3Ha

Y.Ah012:Yb s+, Tm 3+................

sH,-+ sHs

Y.Ah012: Cr 3+, Tm 3+.................

3H4 -+ 3Ha

En03: Er 3+ -+ Tm 3+.................. CaMoO,:Er 3+, Tm 3+ .................

3H,-+ 3Ha 3H, -+ 4Ha

Glass:Yb 3+ -+ Er 3+.................. Glass (silicate):U022+, Nd 3+ .......... Phosphate glass: Mn2+, N d 3+.......... Y.AI5012: Cr 3+, Nd s+ ................. Glass: Nd 3+, Yb 3+ . . . . . . . . . . . . . . . . . . . . Silicate glass: U022+, Yb 3+ ............

4JN- -+ 41¥ 4Ft -+ '1¥ 4Ft -+ 4J¥ 4Ft -+ 41¥ 2Ft -+ 2Fl 2Ft -+ 2fJ

Emission, iio X 10- 4 em"?

Terminal state, cm- 1

0.4697 0.4710 0.4765 0.4766 0.4767 0.4711 0.481 0.4821 0.4829 0.4864 0.4965 0.5307 0.5319 0.4966 0.5308 0.4967 0.4952 0.5170 0.5231 0.5246 0.6482 0.94 0.94 0.9423 0.982 0.985

530 520 460 462 462 510 ""300 ""250 582 240 228 580 582 ""600 ""325 ""2,000 ",,2,000 2,001 ""400

• Modified from L. G. Van Uitert, "Luminescence of Inorganic Solids," Goldberg, ed., pp. 520-523, Academic Press, Inc., New York, 1966. The excitation is in the characteristic bands of sensitizer or laaer dopant. t The last dopant in the formula is the activator with the lasing transition.

TABLE

9i-9.

Emission,

SEMICONDUCTOR LASERS·

Emission,

Material

VO X 10- 4 cm- 1

Excitationt

Material

VO X 10- 4 cm- 1

Excitationt

Pbo. aSno.27Te ..... Pbo.sSn0.2Te ...... PbSe ............. PbTe ............ InSb ............. PbS .............. Cdo.aHg0.7Te ...... Te ............... InAs ............. GaSb ............ InP ..............

0.036 0.038 0.118 0.154 0.19 0.233 0.25 0.27 0.31 0.62 1.11

PL PL EL, CR EL, CR, PL EL, CR, PL EL, CR PL CR EL, CR, PL EL,CR EL

In(P,As) ......... GaAs ............ GaAszPI_:r ........ CdTe ............ CdSe ............ GaSe ............ CdS .......... '" ZnSe ............. ZnO ............. ZnS ..............

1.13 1.18 1.14-1. 69: 1.25 1.45 1.67 2.02 2.17 2.67 3.06

EL EL, CR, PL EL CR CR CR CR, PL CR CR CR

• Modified from R. Rediker, Proc, 1966 Intern. Con], Luminescence, edited by G. Szigeti (Hungarian Academy of Sciences, Budapest, 1968) p. 1756; M. R. Lorenz and M. H. Pilkuhn, IEEE Spectrum 4.. 87 (1967); D. C. Reynolds, Trans. Met. Soc. AIME, SS9. 300 (1967). t CR = cathode ray, EL = electric injection, PL = photoexcitation. ! Depends on x in formula G"AszP 1 _ z.

9-168

SOLID-STATE PHYSICS

cadmium sulfide for part of the zinc sulfide shifts the emission band to smaller ii in accordance with the reduction in band gap of the material. The zinc sulfide phosphors activated with phosphorus, arsenic, and antimony are not included, since their emission spectra are not unambiguously described in the literature. The photoluminescence described in Table 9i-2 is efficiently excited by 3650-A ultraviolet radiation. The fluorescent-lamp phosphors described in Table 9i-3 have probably had their emission spectra most accurately measured. In some cases the parameters ii and hare derived from data taken on experimental lamps; in other cases, on the phosphors directly. In either case, the excitation is predominantly by 2537-A ultraviolet radiation. The calcium halophosphate phosphors merit additional comment. The emission spectrum consists of two broad and structureless bands. The intensity of the blue band depends on the antimony activator concentration; that of the orange band on the manganese activator concentration. In addition, Po for the manganese emission shifts to smaller ji with increasing chloro- to fluorophosphate content, with a maximum shift of approximately 2 percent of Po. The antimony emission shifts only 1 percent of Po with complete chloride substitution. In contrast to most phosphors activated with divalent manganese, there is evidence for a second, less intense manganese band at smaller ji (ref. 8). The quantum efficiencies shown in Table 9i-3 are based on the analysis by Tregellas-Williams (ref. 17). Another class of photoluminescent phosphors are those activated by tetravalent manganese. Their emission is characterized by a fine structure consisting of bands approximately 100 cm- I in width separated by approximately 200 cm :'. This material and the magnesium arsenate maintain high photoluminescent (ref. 9) efficiencies to 650 K. The high-temperature stability combined with their red emission leads to their use for color correction in the medium-pressure mercury lamp. Rare-earth phosphors related to those in Tables 9i-7 and 9i-8 are becoming important in discharge lamps. In principle, the cathodoluminescent screens described in Table 9i-4 are not confined to particular phosphors; however, the screen specifications are set up so that in practice only a particular phosphor or combination of phosphors meets the specifications. For screens composed of two or more phosphors, either as a mixture or as two distinct layers, the contribution of each phosphor to the emission spectrum may be slightly altered because of absorption by the other components. This accounts for some of the small discrepancies between the parameters given in Table 9i-4 which are based on the screen performance characteristics and the parameters based on data obtained on the separate phosphors. A single time constant does not describe the afterglow of the sulfide phosphors, because the afterglow is hyperbolic, rather than exponential, and is markedly dependent on current density. This arises from a broad distribution in energy of trapping states whose occupational probabilities depend on density of excitation. Both organic and inorganic phosphors are used in scintillation counters. The emission spectra of the organic phosphors consist of a series of narrow bands compared with the broad, structureless emission bands of the inorganic phosphors. The persistences of the organic phosphors are shorter, whereas the efficiencies of the inorganic phosphors are greater for particles which produce large ionization densities. The characteristics of the phosphors commonly used in scintillation counters are given in Table 9i-5. Electroluminescent materials are of two classes: those which operate by the collisionexcitation mechanism, and those which operate by minority-charge carrier injection. Zinc sulfide is the principal representative of the first class; silicon carbide and gallium phosphide are the most important members of the second class. The first are used as particles in a dielectric matrix with an applied a-c field; the second, as single crystals with either a-c or d-c fields. The parameters describing the emission of these materials are given in Table 9i-6.

9-169

LUMINESCENCE

9i-4. Formulas for Some Luminescent Characteristics. In addition to Eqs. (Di-I) and (9i-2), which are the theoretical and empirical formulas, respectively, for the optical spectra of activator systems, there are a number of other simple formulas for interpreting or describing luminescent phenomena. There are, of course, the formulas for the afterglow. The simplest is the exponential decay of the emission intensity, 1 = 1 0 exp (-At) (9i-3) where A is the spontaneous transition probability or the reciprocal of the lifetime T shown in Tables 9i-4 and 9i-5. At high temperatures the lifetime of the emitting state decreases because of nonradiative deexcitation, and under these conditions the afterglow is of the form (ref. 18): 1

=

1 0 exp { - [

A+ s exp ( -

k~) ] t}

(9i-4)

where s is the frequency factor, and E is the activation energy for the nonradiative process. Concurrently, under these conditions the luminescent efficiency decreases with increasing temperature (ref. 19): 1

11

(9i-5)

= "I + (s/ A) exp (-E/kT)

The luminescent efficiency is also dependent on activator concentration, and for activators distributed at random lattice sites and capable of efficient luminescence if no other activators occupy the z nearest-neighbor sites, the efficiency is of the form (ref. 20): e(1 - e)' (9i-6) 11 = e

+ K(1

- e)

where e is the atomic fraction of activator impurity, and K is the ratio of capture cross sections for nonradiative and radiative processes. The afterglow observed for zinc sulfide phosphor is fundamentally quite complex, since a distribution of electron traps and retrappings are apparently involved. Empirically, the following hyperbolic form has been extensively used: 1 = 1 0 (1

+ at)-n

(9i-7)

Simple bimolecular recombination leads to an equation of his form with n = 2; however, experimentally n ~ 1 is usually found. The distribution of trapping states is more clearly evident from thermoluminescent measurements. For traps which empty by first-order kinetics without retrapping and in accord with the activation energy E' and frequency factor s', the thermoluminescent intensity at temperature T is (refs. 21 and 22): E

1 = nos' exp ( - k ;

)

exp [ -

d;~dtJT~ exp

E

( - k;

)

dTJ

(9i-8)

where no is the initial concentration of occupied trapping states, To is the initial temperature, and dT /dt is the rate of temperature increase. Equations which include retrapping have also been formulated. As noted earlier, radiative recombination of electrons and positive holes at donoracceptor pairs is an important luminescent process in semiconductors. The transition energy for this emission at the ith pair with interimpurity distance R, is as follows, neglecting overlap of the effective mass functions for donor electron and acceptor hole (ref. 16): e2 (m-g) heii, =.E.g - (EA + ED) + KR,

9-170

SOLID-STATE PHYSICS

where E g is the band gap; EA and ED are the absolute values of the ionization energies of separated acceptor and donor, respectively; and K is the dielectric constant. Various formulas have been proposed to describe the voltage dependence of the brightness of phosphors which electroluminesce by the collision-excitation mechanism. The most successful for present electroluminescent cells are of the following form (refs. 23 and 24): (9i-10) where m = 0, 2 have been used; V is the applied voltage; and d is a constant. For injection electroluminescence involving a p-n junction the dependence of current J on applied voltage is eV J = J o exp {:JkT (9i-ll) where {:J is found to be of the order of 1 or 2. The solid-state laser acts as a resonance cavity with an amplifying medium. threshold power for oscillation is (ref. 12):

p

= 3h 2c2(12 -

R)A'P

The

(9i-12)

87r TM l

where R is the product of reflectivities of the end mirrors, T is the lifetime of the excited state, M is the dipole matrix element of the transition, and l is the length of the cavity. As noted earlier, the threshold power is less for emission bands of narrower width A'P. In Elq. 9i-12, hand c are respectively Planck's constant and the velocity of light. References Sources Referred to in Text 1. Pringsheim, P.: "Fluorescence and Phosphorescence," pp. 2-5, 290-297, Interscience Publishers, Inc., New York, 1949. 2. Kroger, F. A.: "Some Aspects of the Luminescence of Solids," p. 36, American Elsevier Publishing Company, Inc., New York, 1948. 3. Curie, D.: "Luminescence of Crystals," pp. 2-5, translated by G. F. J. Garlick, Methuen & Co., Ltd., London; John Wiley & Sons, Ine., New York, 1963. 4. Garlick, G. F. J.: In "Handbuch der Physik," vol. XXVI (2), Springer-Verlag OHG. Berlin, 1958. 5. Williams, F. E., and M. H. Hebb: Phys. Rev. 84, 1181 (1951). 6. Henderson, S. T.: Proc. Roy. Soc. (London), ser, A, 173, 323 (1939). 7. Lord, Rees, and Wise: Proc. Phys. Soc. (London) 59, 473 (1947). 8. Butler, K. H.: J. Electrochem, Soc. 93, 143 (1948); 97, 265 (1950). 9. Brinkman, H., and C. C. Vlam: Physica 14, 650 (1948). 10. Schawlow, A. L., and C. J. Townes: Phys. Rev. 111, 1940 (1958). 11. Maiman, T. H.: Nature 187, 493 (1960). 12. Kiss, Z. J .• and R. J. Pressley: Proc. IEEE, 54, 1236 (1966). 13. Mak, A. A., Y. A. Anan'ev, and B. A. Ermakov: Soviet Phys. 91, 419 (1968). 14. Bowers, R., and N. T. Melamed: Phys. Rev. 99, 1781 (1955). 15. Prener, J. S., and F. Williams: Phys. Rev. 103, 342 (1956). 16. Williams, F.: Phys. Stat. Solidi 15, 493 (1968). 17. Tregellas-Williams, J.: J. Electrochem. Soc. 105, 173 (1958). 18. Kroger, Hoogenstraaten, Bottema, and Botden: Physica 14, 81 (1948). 19. Gurney, R. W., and N. F. Mott: Trans. Faraday Soc. 35, 71 (1939). 20. Johnson, P. D., and F. Williams: J. Chem, Phys. 18, 1477 (1950). 21. Urbach, F.: Wien. Ber. 139(IIA), 363 (1930). 22. Randall, J. T., and M. H. F. Wilkins: Proc. Roy. Soc. (London), ser. A, 184,367 (1945). 23. Destriau, G.: Phil. Mao. 38, 700 (1947). 24. Curie, D.: J. Phys. Radium 13, 317 (1952). Monographs and Textbooks Adirowitsch, E. I.: "Einige Fragen zur Theorie der Lumineszenz der Kristalle," AkademieVerlag GmbH, Berlin, .1953. Originally published in Russian in 1950, this textbook

LUMINESCENCE

9-171

discusses the luminescence of crystals using thermodynamic, kinetic, and quantummechanical methods. Aven, M., and J. S. Prener, eds.: "Physics and Chemistry of II-IV Compounds," NorthHolland Publishing Company, Amsterdam: John Wiley & Sons, Inc., New York, 1967. Authoritative review of electrical and optical phenomena in II-VI semiconductors and luminescent materials. Curie, D.: "Luminescence Cristalline,' Dunod, Paris, 1960. Translated into English by G. F. J. Garlick, "Luminescence in Crystals," Methuen & Co., Ltd., London; John Wiley & Sons, Inc., New York, 1963. A compact textbook emphasizing theoretical work on luminescence in crystals. Forster, T.: "Fluoreszenz organischer Verbindungen," Vandenhoeck and Ruprecht, Gottingen, 1951. A textbook on the fundamentals of luminescence in organic materials. Garlick, G. F. J.: "Luminescent Materials," Oxford University Press, New York, 1949. An elementary textbook emphasizing the fundamental processes in phosphors. Goldberg, P., ed.: "Luminescence of Inorganic Solids," Academic Press, Lnc., New York, 1966. Comprehensive modern review with each chapter by different authority. Ivey, H. F.: "Electroluminescence and Related Effects," Academic Press, Inc., New York, 1963. Review of luminescence involving electric fields. Kroger, F. A.: "Some Aspects of the Luminescence of Solids," American Elsevier Publishing Company, Inc., New York, 1948. A monograph on inorganic phosphors classified by activators. Kroger, F. A.: "Chemistry of Imperfect Crystals," North-Holland Publishing Company, Amsterdam; John Wiley & Sons, Inc., New York, 1964. Comprehensive treatise on defects, and imperfections in luminescent materials and semiconductors. Pringsheirn, P.: "Fluorescence and Phosphorescence," Interscience Publishers, Inc., New York, 1949. A descriptive encyclopedic reference text on the luminescence of gases, liquids, and solids.

Review Articles Curie, D.: Theories of Electroluminescence, in "Progress in Semiconductors," vol. 2, p. 251, Heywood and Co., London, 1957. Destriau, G., and H. F. Ivey: Electroluminescence and Related Topics, Proc, IRE 43, 1911 (1955). Garlick, G. F. J.: Cathodoluminescence, Advan. Electron. 2, 151 (1950). Garlick, G. F. J.: Luminescence, in "Handbuch der Physik," vol. XXVI(2), SpringerVerlag OHG, Berlin, 1958. Klick, C. C., and J. H. Schulman: Luminescence in Solids, Solid State Phys. 5, 97 (1957). Piper, W. W., and F. Williams: Electroluminescence, Solid State Phys. 6, 95 (1958). Williams, F.: Solid State Luminescence, Advan. Electron. 6, 137 (1953). Williams, F.: Phys. Stat. Solidi, 26, 493 (1968).

Reports of Symposia Fonda, G. R., and F. Seitz, eds.: "Solid Luminescent Materials," John Wiley & Sons, Tnc., New York, 1948. Papers of the symposium at Cornell University in 1946. Kallmann, H. P., and G. M. Sprueh : "Luminescence of Inorganic and Organic Materials," John Wiley & Sons, Inc., New York, 1961. Papers and discussion of the symposium at New York University in 1961. Luminescence, Brit. J. Appl. Phys. 64 (1955). Papers and discussion of the symposium at Cambridge, England, in 1954. La Luminescence des corps cristallins anorganiques, J. Phys. Radium 17, 609 (1956). Papers and discussion of the symposium at Paris in 1956. Riehl, N., and Kallmann, H. P.: "International Symposium on Luminescence: The Physics and Chemistry of Scintillators," K. Thiemig, Munich 1966. Papers of symposium on luminescence emphasizing scintillators in Munich in 1965. Thomas, D. G., ed.: "II-VI Semiconducting Compounds," W. A. Benjamin, Inc., New York, 1967. Paper and discussion of symposium at Brown University in 1967 on II-VI semiconductors and luminescent crystals. Proceedings of 1966 Internaational Conference on Luminescence, edited by G. Szigeti (Hungarian Academy of Sciences, Budapest, 1968). Papers and discussion of conference in Budapest in 1966. Proceedings of 1969 International Conference on Luminescence, edited by F. Williams (North Holland Publishing Co., Amsterdam, 1970). Paper and discussion, with indices, of conference at the University of Delaware in 1969.

9j. Work Function and Secondary Emission GEORGE A. HAAS

u.s. Naval Research Laboratory 9j-1. Work Function Measurements. The work function cf> of a substance is given as the difference in energy between the Fermi level (or electrochemical potential) of a solid and the electrostatic surface potential just outside. This is what is generally measured in thermionic (Th) and contact potential (C.P.D.) measurements. The photoelectric "work function" (P.E.), however, is normally taken as the measure of the photoelectric threshold and represents the energy difference between the level of the highest-lying electron at room temperature and the electrostatic surface potential. Although the highest-energy electron of a metal at room temperature is very near the Fermi level, this is not necessarily true for semiconductors. (This fact must be kept in mind when one is comparing photoelectric work functions of semiconductors with those derived from thermionic or contact potential techniques.) Table 9j-1 lists the work functions of elements as determined by thermionic, photoelectric, and contact potential difference methods, while Table 9j-2 gives the thermionic work functions of various compounds used in electron emitter applications. The thermionic work function cP as a rule is obtained by analyzing the emitted current by means of the Richardson equation:

where J in the current density in amp Zorn", T is the absolute temperature, k is 8.62 . 10- 5 e V/deg, and cP is given in electron volts. cP is usually not constant in the temperature range of measurement but for most substances can be expressed in terms of a linear temperature dependence cP = cPo + «T, where cPo is the temperature-independent component of the work function, and a is the temperature coefficient. In many thermionic measurements, unfortunately, the work function quoted and subsequently recorded in review articles is the value obtained from the slope of a Richardson plot (log J IT2 vs. liT), which is just cPo. If there is an appreciable temperature dependence, this value can be highly erroneous since these measurements are obtained at fairly high temperatures (i.e., 1000 to 2000 K). Consequently, unless the temperature dependence can be determined from the published data by some other method (e.g., from the intercept of the Richardson plot or "Richardson A value") the results are not included in this review. Furthermore, since the linear approximation to the temperature dependence very likely does not hold for all temperatures, the temperature range in which the measurements were made is also included. Except where specifically noted, the photoelectric work function measurements are carried out at room temperature and therefore require no additional information regarding temperature, range. The same is also true of contact potential difference measurements which are normally obtained at room temperature by measuring the difference in electrostatic surface potential between a substance having a known work function value or "standard" (e.g., W, Hg, Ag, etc.), and the substance to be measured. 9-172

WORK FUNCTION ANb TABLE

Element Ag ...........

AI............

Au ...........

As ............ Ba ...........

B ............ Be ...........

Bi ............ C ......•.....

Ca ........... Cd ...........

Ce ...........

9j-1.

S~CONbARY ~MtSSION

9-173

WORK FUNCTIONS OF THE ELEMENTS

Work function eV 4.31 + 0.1 X 1O-4T 1160-1200 K 4.32 1230 K 4.5 4.3 4.32 4.3 4.44 4.29 4.36 4.08 4.2 4.24 4.19 4.18 4.25 + 0.15 X 1O-4T 1160-1280 K 5.1 5.4 5.45 5.22 5.4 4.66 4.72 2.3 + 5 X 10- 4T 1000-1300 K 2.49 2.48 2.42 2.35 2.66 2.5 4.4-4.6 3.67 920-1180 K 3.3 3.92 3.89 4.31 4.46 4.34 4.39 + 1.7 X 10- 4T 1300-2200 K 4.6 + 0.6 X 10- 4T 1490-1670 K 4.81 3.2 2.7 3.21 4.07 4.099 4.0 4.22 2.48 + 1.8 X 10- 4T 1060-1450 K 2.84

Notes

Technique

Reference

Year

Th

1

1

1953

Th

2

2

1956

P.E. P.E. C.P.D. C.P.D. C.P.D.

.......

3 4 5 6 6 6 7 8 9 5 10 1

1950 1953 1951 1964 1964 1964 1936 1936 1944 1951 1957 1966 1953

12 13 14 15 13 16 17 18

1961 1966 1966 1966 1966 1949 1949 1965

19 20 21 22 23 24 25 26

1939 1940 1935 1941 1952 1963 1948 1966

27 28 29 30 31 17 32

1934 1937 1963 1936 1941 1949 1947

33

1952

13 4, 6 2, 4

34 35 36 37 38 9 39 40 41

1926 1932 1936 1937 1931 1944 1953 1955 1926

.......

35

1932

c.r.o.

P.E. P.E. P.E. C.P.D. C.P.D. C.P.D. Th

P.E. P.E. C.P.D. C.P.D. C.P.D. P.E. P.E. Th P.E. P.E. C.P.D. C.P.D.

c.r.n. c.r.n. P.E. Th P.E. P.E. C.P.D. P.E. P.E. P.E. Th Th P.E. P.E. P.E P.E P.E. P.E. C.P.D. C.P.D. Th P.E.

.... I,.

3, 4 4, 5 4,6 4, 7 ••••

0

•

•••••

•

0

•

•••••

0

•

3,4 4, 5 5,8 9

11

9 9 9, 10 5,9, 11 5,9, 10

. ......

....... 2 •••••

0

•

•••••

0

•

10

•

3 5 6 ••••

•••••

••

0

0

•

••••

•••••

••••

0

•

to'

12 •••••

0

•

••

0

•

0

••

••••

•

1

10.

•••

0.

1 .0

•••

0

•

•••••

0

•

....... ....... •••••

•••

0

0

•

•••

9-174

SOLID-STATE PHYSICS TABLE

9j-1.

Work function eV

Element

(Continued)

WORK FUNCTIONS OF THE ELEMENTS

+ 0.9 X 10- 4T K 4.41 + 0.6 X 10- 4T

Co ........... 4.4

Technique

Notes

Reference

Year

Th

..'I .......

42

1942

Th

1

43

1952

P.E. P.E. Th

14

15 1

44 44 43

1931 1931 1952

26

1966

12 45

1961 1966

46 6 1

1964 1964 1953

~1200-1450

1410-1590 K 4.12 4.25 Cr ............ 4.58 + 0.6 X 10- 4T 1450-1600 K ~3.9

1100-1400 K 4.4 Cs ............

Cu ...........

Er ............ Fe ............

Ga ........... Ge ...........

~1.86

"-'500 K 2.14 1.84 4.5 1160-1280 K 4.6 "-'1350 K 4.4 1100-1300 K 4.76 4.86(111) 5.61(110) 4.60 4.51 2.97 + 0.65 X 10- 4T 1150-1500 K 4>fJ = 4.48 + 1.3 X 1O-4T 4>-r = 4.21 + 3.75 X 1O-4T ~1200-1450 K 4.31 + 0.6 X 10- 4 1410-1610 K 4.5 1200-1500 K 4>fJ = 4.62 4>-r = 4.68 4.16 3.8 ~3.5

"-'900 K 4.11(111) Hf ........... 3.6 + 1.4 X 1O-4T 1250-1820 K 3.85 "-'1000-1700 K Hg ........... 4.52 4.5 Ir ............ 5.3 + 0.2 X 10- 4T 1700-2200 K 5.4 - 0.3 X 10- 4T 1590-2320 K ~5.28

1300-2000 K 4.57 K ............ 2.24 2.26

Th P.E. Th

.......

0.

............ .. ..........

P.E. C.P.D. Th

.............

Th

..........

2

1956

Th

..........

26

1966

47 48 48 5 10 48a

1934 1935 1935 1951 1957 1967

3,4 1

P.E. P.E. P.E. C.P.D. C.P.D. Th

.......... 3, 4 4, 5 .. ..........

Th Th

............

42 42

1942 1942

Th

1

43

1952

Th

..........

26

1966

P.E. P.E. C.P.D. C.P.D. Th

.........

............

49 49 10 50 2

1953 1953 1957 1938 1956

P.E. Th

..

51 52

1959 1957

Th

2

53

1962

P.E. P.E. Th

. .......... ..

........

54 55 56

1931 1934 1951

Th

..........

57

1956

Th

..........

58

1966

16

50 59 60

1938 1932 1937

C.P.D. P.E. P.E.

.......

0

..

.........

0

..

..........

..

..............

4,5 16 ............

..........

"""

••

0

..

........

'I

...

........

'I

...

WORK FUNCTION AND SECONDARY EMISSION TABLE

9j-1.

9-175

WORK FUNCTIONS OF THE ELEMENTS (Continued)

I

Element La ............ Li ............ Mg ........... Mn ........... Mo ...........

Na ........... Nh ...........

Work function cV ~3.0

1200-1500 K 2.42 1.4 3.66 3.12 3.83 + 1. 1 X 1O-4T 1370-1520 K 3.76 4.38-0.25 X 10- 4T 1410-2110 K 4.33 + 0.1 X 1O-4T rv1300-1900 K 4.25 1600 K 4.33-1.52 X 10- 4T 1200-2000 K 4.41 4.20 2.06 2.29 2.28 4.0 1400-2100 K 4.3 2200 K ~4.19

1050-2100 K 4.33(110) 4.55(335) 4.66(111) 4.38 Nd ...........

~2.95

1150-1450 K Ni. ........... 5.24 + 0.75 X 10- 4T ~1100 K 4.5 1410-1610 K 4.41 1170-1250 K 6.27-1.0 X 1O-3T 1380-1500 K 5.05 T = 623 K 5.2 T = 1108 K 4.73 5.22 Os ......•..... 5.43-3.9 X 10- 4T 1413-1640 K ~5.17

rv1500 K(?) 5.93 Ph ........... 3.97 3.49 3.83 Pd ........... 4.64 Pro ........... 2.57 + 1.5 X 10- 4T 1120-1410 K

Technique Th P.E. C.P.D. P.E. C.P.D. Th P.E. Th Th Th Th P.E. C.P.D. P.E. P.E. P.E. Th Th Th

Notes 2 ••••

eO'

16

. ...... 13 1 ....• 0.

. ...... •••••

0

•

•••••

0

•

•••••

0

•

....• 0.

4 ........

....... ....... •••••

0

•

•••••

0

•

....

".

Reference

Year

41

1926

47 50 61 62 43

1934 1938 1964 1951 1952

47 52

1934 1957

63

1962

64

1966

58

1966

63 6 47 28 20 65

1962 1964 1934 1937 1940 1964

66

1964

58

1966 1963 1963 1963 1964 1926

P.E. P.E. P.E. C.P.D. Th

. ...... 2

67 67 67 68 41

Th

.......

69

1949

Th

1

43

1952

Th

"0 .0 ••

26

1966

26

1966 1949 1949 1957 1966 1966

Th

•••••

0

•

.0 .....

4

••

0

••••

P.E. P.E. C.P.D. C.P.D. Th

.......

. .... 0.

69 69 10 14 58

Th

.......

70

1967

71

1966 1928 1951 1956 1953 1926

P.E. P.E. C.P.D. C.P.D. C.P.D. Th

....... 4, 5 10

•••••

0

•

....... 13 4, 5 13 2

72 62 73 39 41

9-176

SOLID-STATE PHYSICS TABLE

Element

Pt ............

Rb ........... Re ...........

Rh ...........

Ru ........... Sb ............

Se ............ Se ............ Si ............

Sm .. ~ ........

9j-1.

Work function eV

5.3-5.5 "-'1600-1900 K(?) 5.03 + 4.2 X 10- 4T 1620-1946 K 4.82 2.09 4.85 + 0.6 X 10- 4T 1470-2150 K 4.7 + 0.75 X 10- 4T 1820-2860 K 4.8 1600-2200 K 4.96 1325-2250 K 4.8 + 1. 1 X 1O-4T "-'1500-1900 K(?) 4.9 + 0.2 X 10- 4T 1550-1950 K 4.92 4.52 4.01 4.6 4.14 4.1 3 . 13 + O.8 X 10- 4 T 1150-1500 K 5.11 4.42 3.59 + 2.3 X 10- 4T 1250-1700 K 4.02 + 2.6 X 10- 4T 1373-1623 K 5.4(111) 3.95 (n type) 4.2 (p type) 4.5 (n or p) ~3.15

1150-1600 K 3.62 4.21 liquid 4.38 a phase 4.50 {3 phase 4.21 4.42 Sr ............ 2.3 + 0.5 X 10- 4T 850-950 K 2.24 2.74 Ta ........... 4.35 300-1860 K 4.25 1100--2200 K 4.33 + 0.25 X 10- 4T 1700-2230 K 4.1 4.05 4.22 Sn ............

(Continued)

WORK FUNCTIONS OF THE ELEMENTS

Technique

Notes

Reference

Year

Th

.......

74

1950

Th

.......

26

1966

C.P.D. P.E. Th

13

.......

. ......

39 59 75

1953 1932 1963

Th

.......

76

1963

Th

.......

65

1964

Th

.......

58

1966

~h

. ......

77

1938

Th

••

56

1951

16 3,4

78 50 79 17 50 6

. ......

48a

1931 1938 1937 1949 1938 1964 1967

.......

47 50 32

1934 1938 1947

80

1953

81 82 82 83 41

1962 1947 1947 1949 1926

72 84 84 84 85 86 87

1928 1929 1929 1929 1952 1963 1955 1934 1938 1957

P.E. C.P.D. P.E. P.E. C.P.D. C.P.D. Th P.E. C.P.D. Th Th

•

••

0

•

.......

16

....... .......

16

. ...... ••

0

••••

P.E. C.P.D. C.P.D. C.P.D. Th

. ......

P.E. P.E. P.E. P.E. C.P.D. C.P.D. Th

....... ....... ....... .......

17 17 18 2

13 19 20

P.E. P.E. Th

....... 21

47 88 89

Th

.......

58

1966

90

1966

35 91 6

1932 1935 1964

Th P.E. P.E. C.P.D.

•••••

••••

0.

00.

....... •••

4

••

0

•

WORK FUNCTION AND SECONDARY EMISSION TABLE

9j-1.

(Continued)

WORK FUNCTIONS OF THE ELEMENTS

Work function

9-177

Technique

Notes

Reference

Year

Te ........... 5.0 4.7 Th ........... 3.38 + 0.45 X 10- 4T 1250-1800 K

P.E. C.P.D. Th

.......

92 50 93

1953 1938 1926

~3.4

P.E. P.E. C.P.D. C.P.D. C.P.D. Th

35 47 50 94 94 43

1932 1934 1938 1962 1962 1952

65

1964 1954 1938 1935 1938 1959

Element

eV

3.66 3.46 3.71 3.44 Ti ....... .... 3.95 + 0.85 X 10- 4T 1370-1520 K 4.0 1300-1600 K 4.45 4.14 Tl. ........... 3.68 3.84 U ............ 3.0 + 2.7 X 10- 4T 1250-1400 K 3.47 1250-1400 K 2.9 + 2.3 X 10- 4T 1020-2000 K ~3.55

Th

16 ••

0

••••

•••••

0

•

....... 16 7 3 1 •

1

•••

0.

.......

P.E. C.P.D. P.E. C.P.D. Th

.......

16 20

95 50 96 50 96

Th

22

96

1959

Th

20

76

1963

Th

22

97

1967

98 98 98 99 99 99 100 97 97 97 43

1962 1962 1962 1967 1967 1967 1962 1967 1967 1967 1952

47 50 101

1934 1938 1950

76

1963

90

1966

16

1000-1500 K 3.47 (a) 3.52 (f3)

3.39 (-y) 3.65 (a)

3.59 ({3) 3.45 (-y) 3.19 3.63 (a)

V•.•..•...•..

W ............

Y ............ Zn ...........

3.58 ({3) 3.53 (-y) 4.12 + 0.75 X 10- 4T 1410-1540 K 3.77 4.44 4.52 + 0.6 X 10- 4T 1350-2200 K 4.5 + 0.15 X 10- 4T 1820-2940 K 4.58 + 0.15 X 1O-4T 2100-2600 K 4.52 1150-2200 K 4.6 4.565 4.49 4.55 2.95 + 0.2 X 10- 4T 1150-1400 K 4.26 4.307 4.11 4.22

P.E. P.E. P.E. P.E. P.E. P.E. C.P.D. C.P.D. C.P.D. C.P.D. Th P.E. C.P.D. Th Th Th

•••••

0

•

....... .. 0.· .. ••

0

••

••

0

••••

•••••

0.

0

•

3, 4 4 4 4 1 .......

16 •••••

0

•

....... •••••

0

•

Th

.......

58

1966

P.E. P.E. P.E. C.P.D. Th

....... .......

35 102 103 10 48a

1932 1935 1948 1957 1967

104 9 105 85

1940 1944 1940 1952

P.E. P.E. C.P.D. C.P.D.

.......

4, 5 ....... ....... .......

4 13

9-178

SOLID-STATE PHYSICS TABLE

9j-1.

Work function eV

Element

Zr ....••......

WORK FUNCTIONS OF THE ELEMENTS

3.78 T = ? 3.73 4.33 3.60

Technique

Th

P.E. P.E. C.P.D.

Notes

••

e

••••

....... ....... 16

(Continued)

Reference

Year

106

1951

35 95 50

1932 1954 1938

However, since the resulting work function values depend on the accuracy with which the work function of the standard is known, the substance used for the standard and its assumed work function are also included. Some of the earlier work function measurements quoted in other reference works are omitted here, especially where an appreciable number of results on the same subject have been recently published employing more refined experimental techniques. That is not to say, however, that "recentness" is synonomous with "cleanliness"; rather, the most recent studies involving techniques such as low-energy electron diffraction and Auger spectrum analysis serve to show how contaminated "clean" surfaces really are. Consequently, the values listed here merely serve to indicate the measured values of the work functions as they are presently limited by experimental refinement of measuring methods. For some substances which can be easily cleaned they are quite accurate; for others they will most certainly be considered outdated by the next review.

Notes for Table 9j-l 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22.

Effusion method. Deduced from published results. Film on W substrate. Assuming q, for bulk W is 4.54. Film on glass substrate. Film on Ta substrate. Bulk. Assuming q, of Au is 5.22. No Hg contamination. Absolute work function value using fleld-emission-retarding potential method. Assuming q, of Al ~ 4.2. From breakdown voltage of metal insulator-metal junction, assuming