Collected Experimental Papers of P. W. Bridgman, Volume VII: Papers 169-199

Table of contents :
Contents
169. Effect of hydrostatic pressure on plasticity and strength
170. Volume changes in the plastic stages of simple compression
171. Physics above 20,000 kg/cm2
172. The effect of pressure on the electrical resistance of certain semi-conductors
173. The electric resistance to 30,000 kg/cm2 of twenty nine metals and intermetallic compounds
174. The effect of pressure on the melting of several methyl siloxanes
175. Some implications for geophysics of high-pressure phenomena
176. Properties of materials under superindustrial stresses
177. Some results in the field of high-pressure physics
178. The resistance of 72 elements, alloys and compounds to 100,000 kg/cm2
179. Acceptance of the Bingham Medal
180. Further measurements of the effect of pressure on the electrical resistance of germanium
181. Miscellaneous measurements of the effect of pressure on electrical resistance
182. The effect of pressure on several properties of the alloys of bismuth-tin and of bismuth-cadmium
183. High-pressure instrumentation
184. Effects of very high pressure on glass (with I. Šimon)
185. The effect of pressure on the tensile properties of several metals and other materials
186. The use of electrical resistance in high pressure calibration
187. The effect of pressure on the bismuth-tin system
188. Certain effects of pressure on seven rare earth metals
189. Effects of pressure on binary alloys, II. Thirteen alloy systems of low melting monotropic metals
190. Certain aspects of plastic flow under high stress
191. Effects of pressure on binary alloys, III. Five alloys of thallium, including thallium-bismuth
192. Effects of pressure on binary alloys, IV. Six alloys of bismuth
193. Miscellaneous effects of pressure on miscellaneous substances
194. Synthetic diamonds
195. High pressure polymorphism of iron
196. Effects of pressure on binary alloys, V. Fifteen alloys of metals of moderately high melting point
197. Effects of pressure on binary alloys, VI. Systems for the most part of dilute alloys of high melting metals
198. Compression and the α-β phase transition of plutonium
199. General outlook on the field of high-pressure research
Index of Substances
Index of Apparatus

Citation preview

Collected Experimental Papers of P. W. Bridgman

Volume VII

P. W. BRIDGMAN

Collected Experimental Papers

Volume VII Papers 169-199

Harvard University Press Cambridge, Massachusetts 1964

® Copyright 1964 by the President and Fellows of Harvard College All rights reserved

Distributed in Great Britain by Oxford University Press, London

Library of Congress Catalog Card Number 64-16060 Printed in the United States of America

CONTENTS Volume VII 169-3980.

"Effect of hydrostatic pressure on plasticity and strength," Research {London) 2, 550-555 (1949).

170-3987.

"Volume changes in the plastic stages of simple compression," J. Appl. Phys. 20, 1241-1251 (1949).

171-3999.

"Physics above 20,000 kg/cm 2 " (Bakerian Lecture of the Royal Society), Proc. Roy. Soc. {London) [A] 203, 1-17 (1950).

172-4019.

"The effect of pressure on the electrical resistance of certain semi-conductors," Proc. Am. Acad. Arts Sei. 79, 127-148 (1951). "The electric resistance to 30,000 kg/cm 2 of twenty nine metals and intermetallic compounds," Proc. Am. Acad. Arts Sei. 79, 149-179 (1951).

173-4041.

174-4073.

"The effect of pressure on the melting of several methyl siloxanes," J. Chem. Phys. 19, 203-207 (1951).

175-4079.

"Some implications for geophysics of high-pressure phenomena," Bull. Geol. Soc. Am. 62, 533-535 (1951).

176-4083.

"Properties of materials under superindustrial stresses" (Charles M. Schwab Memorial Lecture, given at the General Meeting of the American Iron and Steel Institute, New York, 23-24 May 1951).

177-4105.

"Some results in the field of high-pressure physics," Endeavour 10, 63-69 (1951).

178-4113.

"The resistance of 72 elements, alloys and compounds to 100,000 kg/cm 2 ," Proc. Am. Acad. Arts Sei. 81, 167-251 (1952). "Acceptance of the Bingham Medal," J. Colloid Sei. 7, 202203 (1952).

179-4198.

CONTENTS

180-4201.

"Further measurements of the effect of pressure on the electrical resistance of germanium," Proc. Am. Acad. Arts Sei. 82, 71-82 (1953).

181 -4213.

"Miscellaneous measurements of the effect of pressure on electrical resistance," Proc. Am. Acad. Arts Sei. 82, 83-100 (1953).

182-4231.

"The effect of pressure on several properties of the alloys of bismuth-tin and of bismuth-cadmium," Proc. Am. Acad. Arts Sei. 82, 101-156 (1953).

183-4287.

"High-pressure instrumentation," Mech. Eng., February 1953, pp. 111-113.

184-4291.

"Effects of very high pressure on glass" (with I. Simon), J. Appl. Phys. 24, 405-413 (1953).

185-4300.

"The effect of pressure on the tensile properties of several metals and other materials," J. Appl. Phys. 24, 560-570 (1953).

186-4312.

"The use of electrical resistance in high pressure calibration," Rev. Sei. Instr. 24, 400-401 (1953).

187-4314.

"The effect of pressure on the bismuth-tin system," Bull. Soc. Chim. Beiges 62, 26-33 (1953).

188-4323.

"Certain effects of pressure on seven rare earth metals," Proc. Am. Acad. Arts Sei. 83, 3-21 (1954).

189-4343.

"Effects of pressure on binary alloys, II. Thirteen alloy systems of low melting monotropic metals," Proc. Am. Acad. Arts Sei. 88, 151-190 (1954).

190-4383.

"Certain aspects of plastic flow under high stress," in Studies in mathematics and mechanics presented to Richard von Mises (New York: Academic Press, 1954), pp. 227-231.

191-4389.

"Effects of pressure on binary alloys, III. Five alloys of thallium, including thallium-bismuth," Proc. Am. Acad. Arts Sei. 84, 1-42 (1955).

192-4431.

"Effects of pressure on binary alloys, IV. Six alloys of bismuth," Proc. Am. Acad. Arts Sei. 84, 43-109 (1955).

193-4499.

"Miscellaneous effects of pressure on miscellaneous substances," Proc. Am. Acad. Arts Sei. 84, 111-129 (1955).

194-4519.

"Synthetic diamonds," Scientific American 198, 42-46 [1-11] (November 1955). Reprinted with permission. Copy-

CONTENTS

right ® 1955 by Scientific American, Inc. reserved.

vii

All rights

195-4531.

"High pressure polymorphism of iron," J. Appl. Phys. 27, 659 (1956).

196-4533.

"Effects of pressure on binary alloys, V. Fifteen alloys of metals of moderately high melting point," Proc. Am. Acad. Arts Sei. 84, 131-177 (1957).

197-4581.

"Effects of pressure on binary alloys, VI. Systems for the most part of dilute alloys of high melting metals," Proc. Am. Acad. Arts Sä. 84, 179-216 (1957).

198-4620.

"Compression and the a - ß phase transition of plutonium," J. Appl. Phys. 30, 214-217 (1959).

199-4625.

"General outlook on the field of high-pressure research," in Solids under pressure, ed. W. Paul and D. M. Warschauer (New York: McGraw-Hill, 1963), pp. 1-13.

4639.

Index of Substances

4677.

Index of Apparatus

Collected Experimental Papers of P. W. Bridgman

Volume VII

Effect of Hydrostatic Pressure on Plasticity and Strength P. W. B R I D G M A N , Nobel Laureate, S.D., Ph.D. Physics Laboratories, Harvard University, Cambridge, Massachusetts IN this article various experiments are described which I have made during the last ten years concerning the effect of hydrostatic pressure on the phenomena of plasticity and strength as exhibited by various materials 1 . More specifically the question which these experiments were designed to answer was the nature of the results which we should obtain if we could transport our engineering testing laboratories to the bottom of an ocean of any arbitrary depth, so that the entire laboratory would be a region of any hydrostatic pressure that we cared to apply, and then repeated in this pressurized laboratory the conventional tensile, compression and fracturing tests of ordinary engineering practice. An answer of sorts to this question is already available, since the elementary theories of plastic flow postulate that in the range of stresses met with in ordinary engineering practice any pressure effects are going to be small. A special case of this is the assumption ordinarily made that the shearing stress at which plastic yield begins is not affected by the perpendicular stress across the plane of shear. But the point of interest here is what must be expected when the pressures are increased beyond the range of ordinary engineering practice until they become comparable with the intramolecular forces themselves. It is possible to ask this question because such pressures can now be produced in the laboratory and controlled sufficiently well to make simple experiments with them. I think that our untutored physical intuition would lead us to expect that when the pressure is raised to the intramolecular region appreciable effects will be produced ; this does indeed turn out to be so. PRESSURIZED

TESTING

LABORATORY

Obviously it is not easy to pressurize a testing laboratory and work has to be conducted under very definite restrictions. The most obvious restriction is on size, because the walls of the laboratory must be heavy enough to withstand the pressure. The ' pressurized laboratory ' in which I have done most of my work occupies a cylindrical space only J i n (1-27 cm) in diameter and 3 in (7-62 cm) long. In this small space it is possible to set up arrangements for a number of the easier kinds of testing : in particular, tests have been made on simple tension, simple compression, bending,

169 — 3980

punching and Brinell hardness. It would be more difficult to arrange tests on twisting, and such have not been attempted. There is not space here to describe in detail the experimental arrangements, which have been fully covered in technical papers 1 . The pressures reached range up to 450,000 lb/sq in (1,000 lb/sq in = 70-31 kg/sq cm), about fifteen times the pressure used in modern high calibre ordnance. Seven electrically insulated leads connect the interior of the ' laboratory ' to the outside world. These leads are connected to ' instruments ' inside the chamber for measuring the hydrostatic pressure, the force on the specimen under test, and the deformation of the specimen ; measurements of these three quantities are usually all that is required. The dimensions of the specimen vary according to the particular needs of the experiment and the material. The tension specimens, for example, were usually about 1 in (2-54 cm) long and could be up to 0 1 5 in (3 8 cm) in diameter. The force on the specimen was produced by the same piston which created the pressure in the miniature laboratory ; matters were so arranged that when a predetermined pressure was reached the piston came into contact with a member attached to the specimen, and from here the advancing piston served two functions i.e. to maintain or increase the pressure, and to apply load to the specimen. TENSILE

TESTS

More tensile tests were made than any others, the largest number of tests being on various grades of steel. Under ordinary conditions a tensile specimen, when loaded beyond the elastic limit into the plastic range, at first stretches uniformly over its entire length until an elongation of 10 or 20 per cent is reached. At this point the elongation begins to localize itself, a neck forms, and the load decreases as necking proceeds until fracture occurs when the cross section at the neck has been reduced from 50 to 40 per Figure i. Usual type cent of its initial value. of stress/strain curve

p. w. BRIDGMAN : Effect of Hydrostatic Pressure on Plasticity and Strength T h e state of affairs is thus far from homogeneous or uniform in the later stages of flow. T h e conditions at the neck are most important : these include stress and strain. T h e stress at the neck itself, which is often called the ' true ' stress, is the total load divided by the cross section of the neck, denoted by A, the original section being A„. T h e strain at the neck m a y for many purposes be defined as logfAc/A ; this is usually referred to as the ' n a t u r a l ' strain. I f we assume that the plastically strained metal a t the neck suffers no change of volume, which is approximately true, then logcA„/A = \ogj/l0, where I is the stretched length of a longitudinal fibre in the neck and l a the initial length of the same fibre. This relationship is obvious because Al = AJ0 from the conservation of volume. T h e elongation at the neck is l/la ; it is obviously not the same as the average elongation over the entire specimen, but it is the elongation of most significance and is w h a t w e shall understand when speaking of ' elongation '. If we plot natural strain against true stress for a tensile test at atmospheric pressure w e obtain a curve similar to that shown in Figure 1. The curve rises steeply and linearly in the elastic range, then turns over at the elastic limit a n d becomes concave to the strain axis u p to the point where necking starts and where the curvature nearly ceases ; finally the curve continues nearly straight to the fracture point, which occurs for ordinary mild steels at a natural strain of the order of magnitude of unity. I f a similar experiment is conducted in a pressurized laboratory and the corresponding curve is plotted, w e find that to a first approximation the curve is retraced u p to the former fracture point, then continues its linear course and is not terminated by fracture until a strain is reached in excess of that formerly supported. T h a t is, the steel has been m a d e more ductile by the pressure, so that it will support a greater strain (or elongation) than before. The amount by which the ductility is increased is of course dependent on the pressure. For ordinary mild steels under pressures in the upper ranges of these experiments, that is in the neighbourhood of 400,000 lb/sq in, the increase of ductility is almost unlimited ; reductions of area to 1 /300th of the original cross section, that is elongations at the neck of 300-fold, have been observed. T h e physical reason for this increase of ductility is easy to see. T h e external pressure will not permit the metal to fracture, because if the atoms attempt to separate the pressure pushes them together again and any incipient fracture heals itself. T h i s picture

551

presupposes that fracture starts somewhere in the interior of the metal, which is indeed true in ordinary tension tests, where the fracture usually starts on the axis.

EFFECT

OF

PRESSURE STRAIN

ON

DUCTILITY

AND

HARDENING

W e m a y study in detail how the ductility is affected by plotting the natural strain at fracture as a function of the hydrostatic pressure, see Figure s. T h i s curve is linear for all the varieties of steel tested, and has been followed up to strains of nearly 5 or elongations of the order of 50-fold. Ductility continues to increase beyond this, as indicated by the example above, but measurement of it lacks precision because at such high strains the specimen loses its circular section, individual grains dominate the cross section, and the formulae are no longer applicable. W e have just seen that ductility is a linear function of hydrostatic pressure. T h e r e is also another linear relationship, not necessarily connected with the ductility. This has already been indicated in Figure 1, a plot of stress against strain, which m a y be called the ' strain h a r d e n i n g ' curve. This curve is linear to a first approximation u p to strains of 3 or 4, or as far as one is permitted to follow the curve by geometrical indefiniteness due to the smallness of the section and experimental difficulties in measuring the rapidly diminishing loads. Actually, in working out the curves over such a wide range, certain corrections have to be applied because the stress is no longer uniform across the section owing to very great necking. These corrections cannot be described here, but they introduce no essential modification in the simple state of affairs described. Also, to a second degree of approximation, pressure introduces deviations from linearity and other kinds of deviation w h i c h need not concern this rough picture. By combining the linear ductility curve with the linear strain hardening curve we m a y obtain another linear curve in which the stress at fracture is plotted as a function of the strain at fracture. T h e character of these various curves is a strong function of the condition of the steel, that is, of its condition of hardness as fixed b y heat treatment. In general the curves rise more steeply the harder Si the steel. This means, a m o n g other things, that even the hardest steels Hydrostatic Pressure assume measurable ducFigure 1. Effect of tility under sufficiently pressure on ductility

169 — 3981

552

p. w . BRIDGMAN : Effect of Hydrostatic Pressure on Plasticity and Strength

high pressure. It has been found, for example, that a normally glass-brittle steel with R o c k w e l l C hardness of 63 will support an elongation of 10 per cent before fracture under a pressure of 350,000 lb/sq in. GEOMETRY

OF

FRACTURE

Hydrostatic pressure has an important effect on the geometrical character of the fracture. At atmospheric pressure we start with the conventional ' c u p - c o n e ' fracture, in which the fracture is a combination of tensile separation on the bottom of the ' cup ' with shearing slip on the sides. As fracture occurs under increasingly higher pressures the tensile part of the fracture becomes less extensive, and the bottom of the cup eventually disappears, leaving a single shearing crater which at still higher pressures undergoes various modifications, such as sometimes splitting into multiple craters, until at the highest pressure fracture has degenerated into slip on a single shear plane all the w a y across the specimen at approximately 45° to the axis. EFFECT

OF

PRESSURE

ON

FRACTURE

Let us now consider w h a t happens if a tensile specimen is pulled under pressure to a strain well below its breaking point, pressure and tension are released, a n d pulling is then resumed at atmospheric pressure. L e t us suppose, for example, that the specimen is one which under normal atmospheric pressure would fracture at a natural strain of 1, and that we pull it to a strain of 2 under a pressure sufficiently high to raise the strain required to fracture at that pressure to 4. W e now release pressure and tensile load and continue pulling at atmospheric pressure. It might be argued that the specimen ought to break at once with no further stretch when the load becomes high enough, because it is now supporting a strain of 2 whereas the strain for fracture is only 1. In fact the specimen will now tolerate further strain before fracture, which will occur at a strain of perhaps 2-5. T h e force required to stretch the specimen under these conditions is given by the strain hardening curve. T h e extra strain which the specimen will tolerate when re-stretched at atmospheric pressure is a function of the pressure at which it was previously pulled. Suppose, for example, that instead of pulling the specimen under the above conditions w e had pulled it to a strain of 2 under a pressure such that a strain just in excess of 2 would fracture, and then re-pulled at atmospheric pressure, we should have found that the specimen would fracture immediately with no further stretch. Here is a most surprising effect ; consider the two specimens each with a strain of 2 when w e start to

169 — 3982

re-pull them at atmospheric pressure. T h e shapes of the specimens are identical, the strains are identical, and the forces required to stretch them are identical, yet one will support a n additional strain of 0^5 before it fractures whereas the other fractures immediately. This means that strain and stress together are not sufficient to determine w h e n fracture occurs, but that past history must also be considered. The conventional conditions of fracture are usually formulated in terms of stress only or of strain only.

APPLICATION

TO

WIRE

DRAWING

W e have said that the specimen re-pulled at atmospheric pressure follows along the same strain hardening curve (to a first approximation) as w h e n pulled under pressure. T h i s has interesting consequences, since in view of the linear rise of the strain hardening curve it would mean that by pulling a tensile specimen under pressure and releasing to atmospheric pressure, material with strength greatly in excess of that normally possible a t atmospheric pressure could be produced. T h i s is indeed so, and tensile specimens of steel have been produced which at atmospheric pressure have supported at the neck tensions of 600,000 or even 700,000 lb/sq in before fracture. If wires could be produced with such strength, instead of merely necked tension specimens, important applications might be expected. T h i s suggests that if w e could d r a w wire in the pressurized laboratory to much greater elongations than are now possible without annealing, w e might expect increases of strength. I have made the beginning of such an attempt. It proved too difficult to set up a wire drawing shop in the J in laboratory, which could be pressurized to 450,000 lb/sq in, and I had to content myself with working with other apparatus in which the pressure ceiling was 180,000 lb/sq in. In this the entire wire d r a w i n g process was carried out. T h e expected effects were found, including enhancements of strength above those obtained in the ordinary wire drawing process, but the effects were not large. T h e reason is not difficult to see, because in the throat of the die during ordinary wire drawing there are already pressures of the order of 180,000 lb/sq in generated by the drawing process. If one could find how to d r a w wire in a medium at 400,000 lb/sq in, important enhancements in the properties of steel might be expected.

TENSILE

TESTS

ON

THAN

MATERIALS

OTHER

STEEL

Tensile tests like those just described for steel have been performed for a number of other substances. Copper and aluminium increase greatly in ductility

553

p. w . BRIDGMAN : E f f e c t of Hydrostatic Pressure on Plasticity a n d Strength under pressure ; their strain hardening curves have not been examined in detail as have those of steel, but it is probable that the hardening flattens off at high pressures, instead of rising linearly, so that such great enhancements of strength would not be possible as with steel. The experimental determination of the strain hardening curves for copper and aluminium is complicated by the fact that the grain structure begins to dominate, and the cross section departs from circularity much earlier in the drawing process than for steel. This is particularly true for aluminium, the cross section of which becomes square instead of circular when pulled to comparatively moderate elongations under pressure. Apparently the stretching process produces grain growth or recrystallization. Other normally brittle materials acquire marked ductility. A phosphor bronze, which normally is completely brittle, under a pressure of 450,000 lb/sq in permits 80 per cent reduction of area before fracture. Pure beryllium breaks at atmospheric pressure in a completely brittle manner at a tensile load of 28,000 lb/sq in or less ; under 400,000 lb/sq in hydrostatic pressure it exhibits a reduction of area of nearly 50 per cent at fracture, and the breaking load increases to 110,000 lb/sq in. Cast iron breaks under a supporting pressure of 450,000 lb/sq in with 83 per cent reduction of area, and under a tensile load of 480,000 lb/sq in. That is, the weight which would have to be hung on a rod of cast iron in order to pull it apart in a laboratory pressurized to 450,000 lb/sq in is equivalent to 480,000 pounds on one square inch of section at the neck. Single crystals of sodium chloride tolerate elongations up to 20 per cent and probably more with no loss of optical homogeneity. Perhaps the most surprising results were found for sapphire, which may now be obtained in the form of synthetic single crystal rods of different orientations. Normally, at atmospheric pressure, this is one of the most brittle of materials, and has to be heated to within 50° of the melting point at 2,ooo°C to exhibit appreciable plasticity. Yet when pulled in tension at room temperature at a pressure of 400,000 lb/sq in it will tolerate plastic slip on certain of its crystallographic planes without fracture. Some substances have not yet been made ductile in tension, but retain full brittleness up to 450,000 lb/sq in. Quartz crystal is one such material; ordinary glass another. Although glass does not lose its brittleness its strength may be enormously increased by pressure. The phenomena in glass are complicated because tensile fracture apparently begins at the surface instead of in the interior, and is accordingly very sensitive to surface conditions. If

the surface is wet, tensile fracture will occur at very low values of the load even when surrounded by the highest hydrostatic pressures, but if the surface is kept dry with a protecting coating of thin copper or lead, much higher tensile loads will be supported. The highest figure found for Pyrex glass was a tensile strength of 350,000 lb/sq in when subjected to 385,000 lb/sq in hydrostatic pressure. The normal tensile strength is of the order of 10,000 lb/sq in. It should be noticed that in the example just described the tensile load is 35,000 lb/sq in less than the hydrostatic pressure, which means that tensile fracture took place against a compressive stress of 35,000 lb/sq in, a paradoxical result difficult to explain according to some of the conventional theories of fracture. Another substance which does not lose its brittleness in tension under hydrostatic pressure is Carboloy, the cemented carbide of tungsten which is used for tool bits. Carboloy does, however, increase greatly in tensile strength under pressure ; under a supporting pressure of 400,000 lb/sq in tensile strengths of more than 800,000 lb/sq in have been found, which is an increase of twofold or threefold over the normal value of tensile strength. CONTRADICTION OF

OF

ORDINARY

THEORIES

FRACTURE

It is natural to inquire how all these results fit into the ordinary theories of fracture. The confirmation, unfortunately, is not very good, because it is possible to set up examples which violate all the ordinary simple criteria which have been proposed for fracture. In particular, the fact that tensile fracture may occur against a net compressive stress is difficult to reconcile with some of the points of view which are profitable in a more restricted range of conditions. It is probable that in general, as already suggested, fracture is determined by a combination of nearly all the variables known, including past history as well as stress and strain. HISTORICAL TENSION

BACKGROUND

OF

EXPERIMENTS

It may be of interest to mention the historical background of some of these tension experiments. Many of the experiments on steel were made during the 1939-45 war, on a government contract; the immediate interest was in connection with the penetration of armour by projectiles. It was known by direct measurement that the compressive stress in front of the nose of a penetrating projectile reaches values in the vicinity of 450,000 lb/sq in. We have seen that under these pressures ductility is enormously increased. It is evident therefore that a proper discussion of the penetrating projectile must take

169 — 3983

554

p. w.

BRIDGMAN

: Effect of Hydrostatic Pressure on Plasticity and Strength

a c c o u n t of the c h a n g e in the properties of the steel a c c o m p a n y i n g the stresses generated b y the act of penetration. M y experiments were undertaken w i t h the object of shedding light on this problem. A s it turned out, however, no practical use was m a d e of these results. T h e p r o b l e m of penetration is obviously one of extreme complexity, and d u r i n g the u r g e n c y of w a r it w a s better to obtain the results empirically. I think the p r o b l e m will never be really understood, h o w e v e r , until these effects are taken into account. Perhaps some b u r e a u of ordnance will now be able to return to it in the c o m p a r a t i v e leisure of p e a c e a n d w i t h the help of the n e w calculating machines.

COMPRESSION

TESTS

W e n o w turn f r o m this rather extensive description of tensile tests u n d e r pressure to other sorts of test. It is obviously not difficult to reverse the direction of the force a c t i n g on the specimen, so that w h a t w a s a tension becomes a compression. Tests in simple compression h a v e been m a d e mostly on brittle materials. T h e r e is less interest in the ductile materials, because under simple compression these permit almost indefinite distortion without fracture. A few such tests h a v e been m a d e on steel, h o w e v e r , a n d it has been f o u n d that strain h a r d e n i n g does not progress as rapidly in simple compression as in tension. O f the substances w h i c h retained complete brittleness in tension, some exhibit measurable plasticity in simple compression. Carboloy, for example, will support u p to 10 per cent shortening w i t h o u t fracture in simple compression. Single crystal sapphire in simple compression will support very m u c h greater plastic slip on the crystallographic planes than in tension, so that under compression a rod originally straight m a y be deformed into the shape of a stove pipe w i t h right angled elbows without fracture. Glass does not b e c o m e m e a s u r a b l y plastic in simple compression, b u t its strength m a y be greatly enhanced, m u c h more than in simple tension. A rod of Pyrex supported b y a hydrostatic pressure of 400,000 lb/sq in tolerated an additional compressive load of 670,000 lb/sq in against a n o r m a l strength at atmospheric pressure of the order of 10,000 lb/sq in.

EFFECT

OF

PRESSURE OF

ON E L A S T I C

LIMIT

STEEL

W e h a v e been considering h o w plastic flow fracture are affected b y hydrostatic pressure.

169 — 3984

and Let

us n o w ask h o w the elastic limit is affected. The effects here turn out to be m u c h less d r a m a t i c , at least for various grades of steel, w h i c h is the only substance for w h i c h measurements h a v e been made. I t is f o u n d that pressure raises the elastic limit in both simple compression a n d tension, w h i c h is w h a t might be expected, b u t the increase is c o m p a r a t i v e l y small, a v e r a g i n g perhaps 5 or 10 per cent for a pressure increase of 150,000 lb/sq in. Closely related to the increase of yield point in simple compression is the Brinell hardness. It is not difficult to a r r a n g e to press a hardened steel ball w i t h a k n o w n force into the specimen while it is surrounded b y h y d r o static pressure and to measure the diameter of the impression after release of pressure. T h e Brinell hardness of m i l d steel does indeed increase u n d e r pressure, f r o m 5 to 10 per cent for 150,000 lb/sq in, as w o u l d be suggested b y the experiments on simple compression.

EFFECT

OF

PRESSURE OF

ON

SHEAR

STEEL

T h e tests on shearing types of deformation w h i c h are easiest to p e r f o r m in ordinary laboratories are torsion tests. U n f o r t u n a t e l y it has not been possible to devise a n y simple w a y of m a k i n g such tests in the J in pressurized laboratory. S o m e t h i n g closely equivalent, h o w e v e r , is not difficult to realize. W h e n a p u n c h is forced through a plate the distortion at the edge of the p u n c h is p r e d o m i n a n t l y shearing distortion. It is not h a r d to drive a p u n c h through a plate in our apparatus, a n d to measure the force on it and the a m o u n t of penetration. A n u m b e r of experiments of this sort h a v e been m a d e on steel. T h e p h e n o m e n a of shearing show the same g r e a t increase of ductility w h i c h w e h a v e already f o u n d for simple tension a n d compression p h e n o m e n a . O r d i n arily, w h e n a flat ended cylindrical p u n c h is driven through a plate of steel at atmospheric pressure the p u n c h i n g breaks a w a y f r o m the plate w h e n the p u n c h has penetrated one quarter or one third of the w a y through the plate. If the p u n c h is driven t h r o u g h in the pressurized l a b o r a t o r y , the p u n c h i n g never breaks a w a y a b o v e a certain critical pressure, b u t the metal retains its perfect coherence, even for complete penetration, just as if one w e r e p u n c h i n g a sheet of butter. I n fact the coherence of the m e t a l a r o u n d the p u n c h i n g m a y be several times greater than that o f the virgin metal, as m a y be p r o v e d b y m a c h i n i n g a virgin piece to the same geometrical f o r m as the partially p u n c h e d plated a n d determining the force required to start the p u n c h . T h i s experi-

555

p. w . BRIDGMAN : Effect of Hydrostatic Pressure on Plasticity and Strength ment was carried out for a plate penetrated by the p u n c h under pressure through ninety five per cent of its thickness. SIMPLE

APPARATUS

FOR

TORSION

EXPERIMENTS

A l t h o u g h it was not feasible to make torsion experiments in our apparatus, it has been found possible with other much simpler apparatus to experiment on shearing deformations u p to pressures considerably higher than above, 750,000 lb/sq in instead of 450,000 lb/sq in, and with deformations m u c h greater than can be obtained in any torsion experiment. T h e apparatus used is shown schematically in Figure 3. T h e blocks β are two hardened steel cylindrical blocks bearing short cylindrical bosses C. A is a rectangular block of hardened steel. The material to be examined, D, is in the form of thin disks a few thousandths of an inch thick placed between C and A. T h e blocks ß are pushed together into A with a hydraulic press ; the mean pressure on the area of contact m a y be built up to as m u c h as 750,000 lb/sq in. U n d e r this pressure the material of the disks D extrudes laterally until some equilibrium thickness is reached, determined by the strength a n d Β coefficient of friction. C T h e block A is then rotated about the axis through the bosses C. T h e experiment consists in measuring the force Β required to rotate as a function of pressure. Figure 3. Schematic diagram A t first, a t low presof apparatus used to produce sures, rotation is pershear deformations under mitted by slipping on pressure the surfaces of D, but at higher pressure the surfaces of D are frozen fast to C and A by friction, and rotation is accompanied by internal shearing slip in the material of D. A b o v e the pressure where friction freezes the surfaces the experiment gives, therefore, the internal plastic shearing strength as a function of pressure. Since the rotation m a y be continued indefinitely and the disks are thin, very high shearing distortions may be realized, u p to hundreds or thousands of radians.

X /

RESULTS

OF

TORSION

EXPERIMENTS

W i t h this apparatus some hundred of materials of all kinds have been examined. T h e distortions are

so high that m a n y materials lose all trace of crystal structure e.g. the x-ray lines of copper disappear. I n fact the distortions a n d stresses are so high that in some instances chemical rearrangements are produced, the molecules being torn apart. T h e first result of the measurements was to show that plastic flow strength increases under pressure. T h e increase under 750,000 lb/sq in m a y v a r y from 50 per cent to two- or threefold for metals to thousands for complicated organic substances, like paraffin. Most metals, particularly those crystallizing in the cubic system, tolerate these high distortions smoothly, but with other materials indefinite distortion is punctuated by continual internal fracture, followed by self healing and repetition of the cycle. APPLICATIONS

OF

RESULTS

T h e application of these results to geological problems of the conditions deep in the earth's crust, particularly to deep seated earthquakes, suggests itself. Another result of these shearing experiments is to show the striking physical difference between a viscous liquid and a plastic solid. For a true liquid, velocity of shearing flow is proportional to shearing force, but for these solids the force varies little with the speed of shear, the precise variation depending on the material. T h e metals which approached most nearly to viscous liquids were lead and tin ; for these a tenfold increase of force produced a thousandfold increase of speed. With mica, however, a thousandfold increase of speed was produced by an increase of force too small to measure. T h i s sort of thing lends itself to instabilities. A g a i n a geological application suggests itself. Most discussions of the yielding of the earth assume that it acts like a viscous liquid ; it would be interesting to know w h a t would be the result of assuming that the deforming force is independent of the speed of yielding a n d determined solely by the conditions at the boundaries of the yielding mass. REFERENCES 1

BRIDGMAN, P. W . Effects of High Hydrostatic Pressure on the Plastic Properties of Metals Rev. mod. Phys. 17 (1945) 3 — The Tensile Properties of Several Special Steels and Certain Other Materials under Pressure J. appl. Phys. 17 (1946) 201 — Studies of Plastic Flow of Steel, Especially in Two Dimensional Compression ibid 17 (1946) 225 — The Effects of Hydrostatic Pressure on Plastic Flow under Shearing Stress ibid 17(1946)692 — The Effect of Hydrostatic Pressure on the Fracture ofBrittle Substances ibid 18 (1947) 246

169 — 3985

Volume Changes in the Plastic Stages of Simple Compression P. W .

BRIDGMAN

The Physics laboratories, Harvard University, Cambridge, Massachusetts (Received July 13, 1949) Λ method has been devised by which the volume changes occurring during plastic flow in simple compression are directly measured in a dilatometer during the flow process. The great superiority of such a direct determination over an indirect determination from the alteration of dimensions is pointed out. Results are obtained for three rocks, quartz crystal, and a number of metals, including several grades of steel and iron. The volume change during plastic flow is not equal to the product of mean hydrostatic stress into the ordinary compressibility in the elastic range, but may vary in a much more complicated way. There are in the first place permanent changes of volume retained after release of stress; these have long been known and may be of either sign. In addition to the permanently retained changes there INTRODUCTION

F

OR most practical purposes it is a good enough approximation to assume that volume changes in the plastic range are unimportant. In the actual solution of specific problems in plastic flow this assumption about volume change may be treated in different ways. In the majority of cases it is sufficient to neglect the volume change altogether by imposing such a condition on the strains that the associated volume change vanishes. A second stage of approximation, which neglects strain hardening, treats the volume change as constant during plastic flow and equal to the elastic change under the yield point stresses. The third stage of approximation, which I think represents the most advanced stage at present, takes account of strain hardening and recognizes that the volume may vary during plastic flow because of the variation in stress associated with hardening. The simplest assumption here is that the volume change is proportional to the mean of the three principal stresses, with the same constant of proportionality which holds in the elastic range. This assumption would not be inconsistent with the assumption of isotropy in the strain hardening range, but this assumption is known not to be a good approximation, except for small strains. Although the factor of volume change is not important in the majority of cases, there are cases where it is important. An example would be the problem of finding the surface separating the plastic from the elastic regions in a massive block of material exposed to stresses above the yield point over parts only of its surface. Another conceivable application would be to the interpretation of seismic waves in the earth. If the effective volume compressibility were different during the process of plastic flow than during static conditions, or if there were anisotropics in the velocity of propagation associated with the direction of plastic flow, conclusions drawn from seismic records might be modified. Very little has been done in the way of experimental

may be changes of volume during the action of stress which may be notably larger than the permanently retained part and which also may be of either sign. The most striking of these is a component of volume increase under increasing compressive stress which in the upper range of stress near the fracture point may be larger than the normal component of volume decrease, so that the total volume change is retrograde. This component is recoverable and reversible on release of stress. It would appear, therefore, that in at least some cases the irreversible phenomenon of fracture is prepared for in the region immediately below the stress of fracture by the appearance of a reversible change of volume of sign the opposite of that due to the elastic action of the stresses.

attack on this problem. There is work at the Bureau of Standards by Stang, Greenspan, and Newman 1 on two aluminum alloys and two grades of steel strained in simple tensions up to elongations of 18 percent. The principal strains were measured directly and the results expressed in terms of an effective Poisson's ratio. Most of the measurements were made on thin specimens cut from sheets, so that only two of the three principal strains were measured and the volume changes could not be obtained. The specimens of one grade of steel were circular in section, however, and the volume change was computed from the measured change of length and diameter, on the assumption of isotropy and unaltered Young's modulus on release. In these particular measurements the longitudinal strains were carried only to 1 percent. A large part of the volume change in the plastic range was found to be permanent up to nearly 0.1 percent decrease of density. The enormous superiority of a direct measurement of the volume change as compared with its indirect determination from measurements of the change of longitudinal and lateral dimensions, as at the Bureau of Standards, is apparent from a simple example. Consider a cylinder of mild steel plastically shortened to 0.85 its initial length by an axial load of 7000 kg/cm 2 . The change of radius under these conditions, assuming no change of volume, differs by only 0.07 percent from that which would be calculated assuming the full elastic change of volume corresponding to this stress. This means that any significant deviations of the change of volume from that expected must be described in terms of measurements within a 0.07 percent range. This is such a difficult problem as to be well nigh hopeless, and the direct attack seems the only one worth considering. EXPERIMENTAL METHOD

In the following a direct experimental attack was made on this problem by immersing the specimen 1 Stang, Greenspan, and Newman, J. Research Nat. Bur. Stand. 37, 211-221 (1946).

170 — 3987

1242 undergoing plastic deformation in a dilatometer, which is filled with a liquid and provided with a capillary open to the atmosphere in which the liquid meniscus moves in response to changes of volume of the contents of the dilatometer. Simplicity of construction suggested simple linear compression as the type of plastic deformation that could be most easily handled. The apparatus is shown in Fig. 1. The specimen S, surrounded by a liquid in the chamber C, is compressed by the piston Pi against the bed plate B. In order to compensate for the volume swept out by the piston as it descends compressing 5, Pi is coupled to another piston P i of exactly the same cross section, so that as Pi enters the liquid filled space Ρa is withdrawn by the same amount, and together there is no change of volume and no motion of the meniscus. The adequacy of the apparatus in this respect can be simply checked by displacing the coupled pistons in the absence of a specimen. The motion of the liquid in the capillary is determined by the volume change of the specimen plus a contribution arising from the distortion of the end of the piston and of the chamber C arising from the action of the stresses in the supporting members. The effect of these distortions can be eliminated by using the differential displacement of the meniscus between that given by the plastically deformed specimen and that of a dummy specimen of hardened steel which undergoes only elastic deformation. The compressive force was applied to the piston Pi in one of my standard hydraulic pressures, with 3.5

inch piston, actuated by a hand pump having a maximum capacity of 15,000 p.s.i. The pressure was altered in controlled steps by coupling the press to a free piston gauge, the weights of which were varied in appropriate steps. The specimens were almost always 2.5 long and from 1 to 1.5 inches in diameter, depending on the strength of the material. The load was increased in equal steps, usually about 15 in number, until a plastic shortening of the order of 16 percent was reached. Pressure increments were applied on a uniform time schedule, usually one step every 30 seconds. Every increment of load is of course accompanied by temperature effects. In the elastic range these temperature effects were beyond the sensitivity of the apparatus, but in the plastic range, where it is to be expected from the work of Taylor and Quinney2 that practically all the work of permanent deformation will be converted into heat, the temperature effects in the last and largest stages of plastic deformation become so large as to seriously disturb the course of the readings. In order to eliminate this effect, the maximum load was maintained constant for a long enough interval, usually about 15 or 20 minutes, for the heat of compression to dissipate itself by conduction to other parts of the apparatus, as shown by the cessation of drift in the readings. The load was then released in the same equal steps and on the same time schedule as during the increasing part of the cycle. The possibility of making readings during unloading is an advantage of this method. Temperature equalization was hastened by stuffing the space between specimen and chamber walls with narrow copper ribbon, such as is sold for scouring dishes in hardware stores. The apparatus was not thermostatted, but the room seldom varied as much as 0.2° during a run. A thermometer was mounted in close thermal contact with the outside of the dilatometer chamber and readings made of temperature drift before and after the run. During the maximum part of the plastic deformation this thermometer indicated a pulse of temperature rise of sometimes as much as 0.5°, but this rapidly dropped back to a permanent temperature rise of not more than 0.1 or 0.2°. Blank runs indicated that uniform temperature changes of as much as this introduced no appreciable error. The liquid filling the chamber and capillary was a mixture of water with a rust inhibitor sold by Sears Roebuck for use in automobile radiators. Water was chosen as the base because of its low thermal expansion. In much of the preliminary work the capillary thread was mercury, separated by appropriate means from the solution in the chamber. The purpose of the mercury was to avoid error from the aqueous solution dragging out on the walls of the capillary, but the error was found to be inappreciable, and since considerable complication was introduced by the use of two liquids, particularly in getting rid of air, the use of mercury was 1 G. I. Taylor and H. Quinney, Proc. Roy. Soc. A134, 307 (1934).

170 — 3988

abandoned in the later experiments. Complete absence of air bubbles in any part of the apparatus is essential. To this end the solution was freed from dissolved air by fresh evacuation before each filling, and the filling itself was conducted with the aid of a vacuum pump. The position of the meniscus in the capillary was adjusted after the apparatus was in place in the press by sucking out excess liquid with the air pump through a fine steel capillary thrust down inside the glass capillary. If there is air in any part of the apparatus the meniscus jumps on applying vacuum to the steel capillary; in this way satisfactory filling could be checked. In order to function satisfactorily the apparatus must be well made; for this reason the chamber and its supporting rim were turned from the solid piece. The pistons were hardened and ground all over and polished on their cylindrical surfaces. The ends of the specimens were ground to parallelism in the surface grinder. The rubber washers where the pistons enter the chamber are a crucial matter; they must be thin to avoid excessive friction and close fitting enough to avoid perceptible leak. Excessive friction at the packing reveals itself as an initial abnormal motion of the meniscus in the "wrong" direction on reversing the direction of motion of the piston. Part of this is due to elastic stretch in the tie rods coupling the two pistons, which can be minimized by making the rods large enough in diameter, and part is due to a frictional dragging of the rubber packing with the piston, which can be minimized by making the steel washers which confine the rubber a good fit for the piston. By proper attention to details this abnormal reverse motion of the meniscus was practically eliminated, but at first it proved troublesome. In the elastic range elementary elasticity theory indicates that the volume change, as given by the motion of the meniscus, should be simply proportional to the load and the length of the specimen and independent of the cross section. For an isotropic material the volume change under a principal stress system which has only a single component Zt along the axis of the cylinder is: AV/V0= (κ/3)Ζ1, where κ is the ordinary coefficient of cubic compressibility. Substituting the relations V0=rrH and load =irrtZ, gives at once AF=(k/3)-/-load.

(1)

As already mentioned, the experiment has to be performed differentially in order to eliminate distortion in the apparatus. In the apparatus as constructed this distortion was comparatively large. When the dummy of hardened steel was used only about 25 percent of the total motion of the meniscus was due to pure volume compression, the balance being due to distortion. This distortion arises almost entirely from change of length of P i under the compressive load. The capillary, which was calibrated for uniformity, had a cross section of 0.01 cm2. This, with a specimen of hardened

1243 steel 2.5 inches long, gave a total motion of the meniscus of approximately 20 cm under the maximum load of 40,000 kg. Of this 20 cm, 5 cm arose from pure volume compression. The position of the meniscus could be read to 0.1 mm, thus making possible, as far as sensitivity of reading goes, a determination of the effective compressibility to a few tenths of a percent. Actually, other irregularities made an accuracy as high as this illusory. In addition to measurements of the volume from the position of the meniscus the change of length of the specimen was read with an Ames 0.0001-inch dial gauge attached to the piston of the press. With this gauge the beginning of plastic flow could be determined. The fundamental question at issue was how the plot of AV against load continues beyond the plastic yield point; does it experience at once a change of character or does it suffer only slow change? One broad feature in the eventual behavior of the curve can be anticipated because it is known that many substances experience permanent alterations of density after exposure to plastic yield and release of the deforming stresses. The permanent alterations of density were given directly by the difference of position of the meniscus before and after the run. In a number of instances the permanent change of density so determined was checked by direct determination of the density before and after by weighings in air and water. The simplest anticipation of what to expect is that on the first application of load the curve of Δ V versus load beyond the first yield point departs from the linear relation below the yield point by a gradually increasing amount which at the maximum is equal to the permanent change of volume found on release of stress, and that on release of stress the whole curve, except for a correction to be described presently, is displaced by an amount equal to the permanent change of volume, and that it is straight with the same slope as in the initial elastic range. On the second application and release of stress the simplest anticipation is that the curve, corrected as will be indicated, will be straight and have the same slope as in the elastic range. The correction indicated arises from the permanent change of length, since according to formula (1) the change of volume is proportional to load and length. After the first maximum load the length is shortened by about 16 percent, so that on first release and second reapplication the changes of volume to be expected are 16 percent less than at the same load in the initial elastic range. Correction was made for this by multiplying the observed volume changes, after subtracting off the correction for the distortion of the dilatometer obtained from the dummy run, by the ratio of initial to final length. The simplest anticipation just outlined did not, as a matter of fact, turn out to be realized, but there were departures depending on the individual material. In all cases, and superposed on other complexities, there

170 — 3989

1244 was hysteresis, and therefore failure of the complete isotropy assumed in deriving Eq. (1). This means, even for those parts of the curve which are approximately linear, that the constant of proportionality between load and &V is no longer simply connected with the coefficient of cubic compressibility, that is, with the volume change under hydrostatic pressure. This coefficient would, under the circumstances, have to be determined by direct experiment in which a hydrostatic pressure is actually applied to the specimen. However one may, if desired, retain the same equation and speak formally of an "effective compressibility" defined by the equation *etf=3Δ VI {I · load).

(2)

What the further significance of this effective compressibility is out of its immediate context would have to be found by other sorts of experiment for obviously the present experiments cannot give a complete description of the behavior under all stress systems of material rendered anisotropic by simple compression. The actual stress system to which the specimens were subjected was not the simple one component Ζ, assumed so far in the discussion, but was complicated, after plastic yield had started, by the addition of frictional components on the ends, which manifested themselves as barrelling of the specimen. The magnitude of the barrelling was a function of the material; it was a maximum for copper, for which the plastic increase of di-

ameter was 35 percent less at the ends than at the center, and a minimum for iron, for which it was 21 percent less. Since in the elastic range shearing stresses are accompanied by no change of volume, it is probably safe to assume that under these conditions the frictional stresses on the ends introduced no appreciable change of volume. Some 40 experiments were made in all, of which 12 should be regarded as preliminary. The largest number of measurements were made on iron or steel from various sources, including cast iron, various low carbon steels of commerce, Norway iron, a high carbon steel, and an 18-8 stainless steel. The other metals were copper, brass, and duralumin. In addition, three rocks were tried: soapstone, marble, and diabase. Measurements were also made on two single quartz crystals. The results obtained with the rocks were unexpected and significant, opening up a new point of view with regard to what might be expected in general. Since the unexpected features shown by the rocks seem to be presented to a much less but still appreciable degree by some of the metals, it will probably conduce to clearness to describe the results for the rocks first. I owe all the specimens of rocks to the kindness of Professor Francis Birch, who has had much experience in the preparation of cylindrical specimens of various materials for his geophysical experiments. EXPERIMENTAL RESULTS

Soapstone

Fig. 2. The changes of length and of volume, both on an arbitrary scale, of soapstone as a function of stress during simple compression.

170 — 3990

Preliminary experiments with other specimens indicated the very narrow range within which this brittle material may be expected to support permanent deformation without fracture. The final specimen was exposed to two cycles of loading up to a maximum of 650 kg/cm 2 . The first application of load resulted in a permanent shortening of 0.07 percent. On the second application there was further permanent shortening of 0.015 percent, combined with a hysteresis of 0.07 percent. After the first cycle of loading there was a permanent increase of volume of 0.0069 percent, or one tenth the fractional change of length, and after the second cycle an additional permanent volume increase of one-half as much. The specimen had received no externally visible permanent damage at the end of the two cycles. In Fig. 2 the volume change during the first cycle is plotted as a function of compressive stress; the plot for the second cycle is essentially similar. The volume change during increase of load appears as the sum of two effects. The first of these is the normal volume decrease, linear in the load, contributed by the volume compressibility as analyzed in Eq. (1). Superposed on this there is an effect in the opposite direction, that is, a volume increase, which becomes larger so rapidly at the higher loads that it dominates the situation and at the two highest loads the volume increases with increase of compressive load. This increase of

1245

volume can naturally be ascribed to an opening of interstices in the structure as a premonition of the fracture that would occur at a load only slightly beyond the maximum reached. However, the unexpected feature is that this opening of interstices in preparation for fracture has a very large recoverable component, so that in the initial stages of release of load the volume decreases instead of increasing as it would in the elastic range. This recovery proceeds further during release of load so that only a small fraction of the abnormal volume increase at the maximum load is permanently retained on total release of load. This recoverable volume increase under compressive stress, probably associated with the opening of interstices, is the new feature disclosed by these measurements. Evidences of the same effect are to be looked for in other materials. I think it is natural to expect the effect to be largest in brittle crystalline materials. Marble Three specimens of superficially flawless marble from Darby, Vermont, were used. The recoverable volume effects are larger for marble than for soapstone, but on the other hand the balance between permanent plastic deformation and complete fracture is much more delicate and three specimens were used before satisfactory readings were obtained in the region of recoverable volume increase. The relation between volume and load for the third specimen is shown in Fig. 3. The maximum load reached was 510 kg/cm2. Application of this load was immediately followed by such rapid creep of the volume readings that the load was at once decreased as rapidly as possible to the next lower step, 500 kg/cm2, in order to avoid fracture. Although good readings could not be made in the region of rapid motion, the meniscus was momentarily observed several centimeters beyond the maximum recorded in Fig. 2, corresponding to a recoverable volume increase of perhaps 0.1 percent. An even more extreme case of recoverable volume change was observed in one of the preliminary specimens in which a volume recovery of 20 centimeters of the capillary, or 0.3 percent of the total volume, was observed during the rapid manipulations incident to saving the specimen from catastrophic fracture. Returning now to the third specimen, Fig. 3 shows a permanent volume increase after release of load of 0.04 percent. The specimen was so badly flawed and disintegrated in parts that a second application of load was not attempted. Marble differs from soapstone in that the recoverable volume change during release of load is not spread so uniformly over the entire range of load, but is confined practically entirely to the first 20 percent of release from the maximum. Over the mid60 percent on releasing load the curve is parallel to the same part of the curve for increasing load, unlike soapstone. The volume compressibility, to be calculated according to Eq. (1), does not agree with the volume

compressibility given directly by measurements with hydrostatic pressure. The compressibility so calculated is abnormally high in the first 10 percent of the range, being about 38X10 -7 (kg/cm2 unit), and in the midrange, where the relation is approximately linear, is abnormally low, being 7.6X10"', whereas the measurements of Adams and myself3 suggest a value in the neighborhood of 13.5X10-7. The change of length as a function of load is also shown in Fig. 3. The permanent fractional decrease of length was 0.25 percent, 6 times as great as the permanent fractional increase of volume. Diabase This proved to be an extremely brittle material, much more brittle than soapstone or marble. Measurements were made on two specimens. The first specimen fractured at a maximum load of 2490 kg/cm2, after practically no warning of impending catastrophe from the length measurements, the last length measurement before fracture differing from a Hooke's law linear rela13 14 13 0« as a function of pressure and temperature.

Mn 3 0 4 gave none of the creep effects of ZnO but resistance measurements were always clean cut. At the two higher temperatures, resistance is essentially single valued, but at room temperature there is marked hysteresis. It will be noticed that the pressure effects are the exact opposite of those for ZnO, for here resistance increases with pressure at the lower temperatures and decreases at the higher. It is true that the effect at the higher temperature appears small in the

172 — 4025

134

BRIDGMAN

diagram, but this is on a logarithmic scale, and the actual readings left no room for uncertainty. Nickel oxide (NiO). This was prepared by the Bell Telephone Laboratories by heating the carbonate to 1000° C. for fifteen hours in the air. The specific resistance stated by them was 108 to 10®, but as set up in my apparatus it was much less, close to 10δ. This was checked by emptying the apparatus and refilling four times, in the thought that there might have been an accidental contamination with conducting dirt, but always with the same result. In the endeavor to get a higher resistance the material was baked out again in quartz at 1000°. There would seem no doubt that 106 represents the correct resistance of the material actually used.

Ο

0

8

ο w

5.0

25° Ο

*

9

4.5

a:

ο cF ο

100° •—

- ö —

3.5

3.0

2.5

\

si 0 —

10,000

tf

20,000

g_200*

30,000

PRESSURE, kg/cm FIGUHE 4.

40,000

50,000

2

The logarithm of the measured resistance of NiO as a function of pressure and temperature.

EFFECT OF PRESSURE ON ELECTRICAL RESISTANCE

135

The experimental results are shown in Figure 4. The measurements were definite, with little hysteresis. Resistance tends to decrease with pressure at all temperatures, the effect becoming greater at the higher temperatures. At 100° and 200° the relation is definitely not linear, and the manner of deviation from linearity is different at the two temperatures. Titanium, Oxide (TiOi). This was supplied by the Bell Laboratories who obtained it from the Titanium Pigment Corporation, their "Titanox AMO no. 3552." The specific resistance was stated to be 1012 at 25° C., but this is much higher than the value found in the present apparatus, which was only 108·6. The experimental results are shown in Figure 5. At 25° and 100° resistance decreases with increasing pressure, but with marked hysteresis. At 200° there are marked seasoning effects, the behavior settling down into a small increase of resistance with pressure. At this temperature there were marked polarization effects on closing the circuit; the readings shown were the steady state readings after initial drift had ceased. The very large drop of resistance between 100° and 200° would suggest that this substance at 200° is near its intrinsic range. If so, experience with other semi-conductors such as tellurium or silver sulfide would suggest a large decrease of resistance with pressure. On the other hand, the polarization effects would suggest conduction by an electrolytic mechanism, which is consistent with the positive pressure coefficient. Vanadium Oxide (VzOs). This was prepared by the Bell Laboratories by recrystallization from the melt by cooling slowly from 700° C. to room temperature (from ammonium metavanadate). As received it was in the form of large dark red plates, and the specific resistance was stated to be 104 to 106. For the present experiments it was ground to powder in an agate mortar and baked out at 400° C. My measurements gave consistently, whether the powder was or was not baked out, a lower specific resistance, in the neighborhood of 10®. Measurements on the massive crystals also gave the same resistance. It is to be considered whether the resistance of this material undergoes a slow change with time, my measurements having been made six months after receiving it. The experimental results are shown in Figure 6. Resistance drops with increasing pressure at all temperatures, less at the higher temperatures. At 25° there is marked hysteresis, which becomes negligibly small at the higher temperatures. At no temperature was there drift or polarization effects.

172 — 4027

BRIDGMAN

136 8.5

qC

8.0

25°

* •

0

ο ^100°

•

7.5

•

·—

70

6.5

0C 9 σ> ο 6.0

5.5

5.0

υ

·*

4.5

0

d—= 4.0

—

200°

10,000

20,000

30,000

PRESSURE, kg/cm

40,000

50,000

2

FIGURE 5. The logarithm of the measured resistance of TiOi as a function of pressure and temperature.

172 — 4028

EFFECT OF PRESSURE ON ELECTRICAL RESISTANCE

137

3.0

2.5

a: ο

1.5

1.0 10,000

20,000

30,000

40,000

50,000

PRESSURE, k g / c m 2 FIGURE 6.

The logarithm of the measured resistance of V 2 0 6 as a function

of pressure and temperature.

Uranium Oxide (ί/ 3 0 8 ). This was supplied by the Bell Laboratories who in turn obtained it from Dupont Company. The resistance stated by the Bell Laboratores at 25° C. was 104. M y value, for the packed powder "as received" was lower by approximately a factor of ten. The resistance proved to be unusually sensitive to the degree of packing. The experimental results are shown in Figure 7. Resistance decreases at all temperatures with pressure, the coefficient being larger at the lower temperatures. There is also very marked hysteresis which is larger at the lower temperatures. The resistance did not drift after change of pressure nor show polarization effects. Feme Oxide (Fe^Oi). This was prepared by the Bell Telephone Laboratories by heating to 1100° C. for sixteen hours in oxygen. I t was provided in the form of a massive bar. For the present measurements the massive material was ground in an agate mortar and baked out at 400°. Satisfactory results were not obtained for the effect of pressure on this substance. At none of the three temperatures was it possible to

172 — 4029

138

BBIDGMAN

3.0

ö ο ^R/Π

2.5

r


139

• T O T A L NET CHANGE AFTER 3 0 , 0 0 0 , 2 W E E K S IN DRY ICE,12 HOURS AT 100° C 0 CHANGE IMMEDIATELY AFTER 3 0 , 0 0 0

«

-30

-40

1

>

20

40

60

1

COMPOSITION, ATOMIC PER CENT

80

>

°

100

Bi

Figure 18. Secular changes of specific resistance in the bismuth-tin system after exposure to pressure.

referred to of the changes of resistance at o ° C after holding at dry ice temperature for t w o weeks and then at ioo° for 12 hours. These results are shown in Figure 18. It will be seen that over most of the composition range exposure to ioo° is followed b y partial return to the resistance of the virgin specimen, but there are several notable exceptions, particularly at the tin rich end of the series. T h e most extensive observations of secular change after 30,000 were made on the composition 70.05 Bi — 29.95 Sn. T h e resistance of this after the first exposure to pressure increased b y 29 per cent, an unusually large amount, and quite out of line with the values shown in Figure 18. A second exposure to the 30,000 cycle was then made with negligible further change of resistance at atmospheric pressure. A f t e r the second pressure exposure the resistance at room temperature (fluctuations through 2 0 ) was followed at atmospheric pressure for 450 hours. T h e drop of resistance was at first rapid, half the total observed change occurring in the first 20 hours. A b o v e 150 hours the rate became practically constant, with no measurable difference in the rates at 150 and 450 hours. T h e total drop of resistance over the 450 hours was such as to

140

BRIDGMAN

carry the specific resistance back to a figure 8.3 per cent greater than that of the virgin material. Less extensive observations were made on eight other compositions. These will now be described, ordered according to composition. 97.98 At per cent Bi. Observed over 2.5 hours. After exposure to 30,000 resistance at atmospheric decreased by 27.48 per cent to 0.7252 virgin. In the first hour resistance dropped slightly further to 0.7251 virgin, after which the direction of motion reversed, leaving the resistance after 2.5 hours at 0.7255 virgin. T h e creep was almost within the errors of observation. 89.68 At per cent Bi. Observed for 17.5 hours. Atmospheric resistance after 30,000 was 4.3 per cent below virgin. With the lapse of time resistance continued moving in the same direction, and at the end of 17.5 hours was 6.0 per cent below virgin. T h e initial rate of decrease was 39 times faster than the final rate. 19.89 At per cent Bi. Observed for 20 hours. Atmospheric resistance after 30,000 was 26.6 per cent greater than virgin; after 20 hours this had decreased to 18.6 per cent greater. T h e initial rate of decrease was ten to twenty times greater than the final. 63.2η At per cent Bi. Observed for 3.8 hours. T h e atmospheric resistance after 30,000 was 18.7 per cent greater than virgin. After 3.8 hours this had decreased to 13.2 per cent greater. T h e rate was approximately constant over the entire time. 19.99 Per cent Β*· Observed for 8 hours. Atmospheric resistance after 30,000 was 10.0 per cent greater than virgin. A f t e r 8 hours it had dropped to 8.0 per cent greater. T h e initial rate was approximately twice the average over the entire time, with an intermediate episode between 2 and 3 hours when the rate decreased below average followed by a rise to above average. 10.08 per cent Bi. Observed for 8.6 hours. Atmospheric resistance after 30,000 was 3.6 per cent greater than virgin. A f t e r 8.6 hours this had dropped to 2.6 per cent greater. T h e rate of drop was constant after 0.7 hour; the initial rate was approximately twice the average rate. j.07 per cent Bi. Observed over 7.67 hours. Atmospheric resistance after 30,000 was 1.15 per cent greater than virgin. A f t e r 7.67 hours this had dropped to 0.74 per cent greater. T h e rate of drop was approximately constant over the entire time.

182 — 4270

EFFECT OF PRESSURE ON TWO ALLOYS OF BISMUTH

141

2.0J At per cent Bi. There was no change in atmospheric resistance after 30,000 and no creep during 3.5 hours, both to one part in 13,000, the limit of sensitiveness of the readings. There is thus a wide variation in the character of these creep phenomena, with great variations in the absolute value of velocity, with inversions in the rate of fall and even reversals in the direction of creep (in two cases). It would therefore seem probable that no one simple type of mechanism would be adequate to explain the results. In particular, the rate of nucleus formation to the stable phase is not proportional to the amount of unstable phase from which the nuclei form. E. Electrical resistance to 100,000 kg/cm2. T h e experimental accuracy in measuring resistances to r 00,000 is of a lower order than that in measuring to 30,000, as a consequence of the necessity of transmitting pressure with a plastic rather than a true liquid. There is a further special source of error with bismuth alloys in that correction cannot be applied so as to secure agreement with previous measurements in the interval 20,000 to 30,000 because of the occurrence of bismuth transitions in this interval. T h e chief interest in making the present measurements to 100,000 was to find whether there are further internal changes in addition to the formation of the compound BiSn or whether any of the high pressure bismuth transitions above 40,000 kg/cm 2 are accompanied in the alloys by measurable changes of resistance. It is known that the volume discontinuities of the pure bismuth transitions above 30,000 are not accompanied by measurable discontinuities of resistance. T h e technique of the measurements was the same as in the former published measurements and the same apparatus was used. A t first the specimens were prepared by rolling the extruded wire flat. This method of preparation produced visible imperfections and cracks and gave irregular measurements of resistance. These difficulties were avoided by squeezing the extruded wire flat between polished carboloy platens in an arbor press. T h e final thickness was of the order of 0.002 inch, squeezed from wire 0.020 inch in diameter. In Figure 19 is shown the ratio of the resistance at 65,000 kg/cm 2 to that at 30,000, and also the ratio of resistance at 100,000 to that at 30,000. T h e ratios shown were given directly by the

182 — 4271

I42

BRIDGMAN

Figure 19. Summary of the resistance measurements on the bismuth-tin system to 100,000 k g / c m 2 . T h e upper curve shows the ratio of resistance at 65,000 k g / c m 2 to the resistance at 30,000, and the lower curve the corresponding ratio for a pressure of 100,000, both as a function of composition.

readings without correction of any sort. There is considerable scatter, but no more than is characteristic of the method. In previous work four specimens of each material were measured to minimize the effect of scatter. Here, measurements were repeated only occasionally. The large number of specimens varying through a range of compositions permits an equivalent smoothing of results. It would seem that there are no new episodes in the region above 30,000 large enough to be reflected in the behavior of resistance within the error of the method. The behavior of resistance of all compositions is normal in that it decreases with diminishing slope with increasing pressure. The arithmetical values of the pressure coefficients seem to tend to be smaller in the middle of the composition range, and the curvature of the relation between resistance and pressure greatest at the two ends of the range. Comparison with previous results for the pure metals makes it probable that both the curves of Figure 19 are somewhat too high over their entire course.

E F F E C T OF PRESSURE ON TWO ALLOYS OF B I S M U T H

143

SHEARING U N D E R P R E S S U R E

The measurements were made with a new carboloy apparatus to be described in another place. In principle it is similar to the apparatus of steel with which extensive measurements have been made.6 With this new carboloy apparatus pressures of 100,000 kg/cm 3 are attainable as against 50,000 with the steel apparatus. In the present investigation pressure was pushed to the full 100,000 only a few times, and was usually restricted to 80,000 in the interest of longer life of the apparatus, the refiguring after use being much more exacting with carboloy than with steel. Since the principal interest of these shearing measurements is qualitative, measurements were made on only a few compositions, namely: 100, 97.97, 79.89, 63.27, 43.4, 19.99, 10.08 At per cent Bi and 100 per cent Sn. All of the curves of shearing stress against pressure, except that for pure tin, showed a low pressure episode in the general neighborhood of 25,000 kg/cm 2 , corresponding to the known bismuth transition here and to the irreversible formation of BiSn II near 20,000. The episode in all cases consists of a point of inflection followed by an upturn of the curve with eventual more rapid rise above 25,000 than at lower pressure. On the bismuth rich end the episode is more accentuated, consisting of a rise to a maximum, drop to a minimum, followed by accelerated rise. With diminishing bismuth content the maximum and minimum smear into each other and disappear, at the same time that the mean pressure of the episode drops approximately 5,000 kg/cm 2 . All the curves except that of pure tin show a second episode in the general neighborhood of 65,000 kg/cm 2 . Above this pressure shearing strength universally rises with pressure more rapidly than below. The episode is usually approached from below 65,000 by a decrease in the rate of rise and a point of inflection, although in one or two cases the preliminary decrease tends to disappear and the episode takes on more the character of a cusp. Over the middle of the composition range there is not much change in the episode, whether the composition is on the bismuth side, or whether the bismuth is entirely contained in the BiSn II phase. Bismuth is known to have a transition at 65,000; it would appear therefore that BiSn II also has a transition near the same point. The transition in pure bismuth is not accompanied by a

182 — 4273

144

BRIDGMAN

change in specific resistance; it would appear that the change of resistance at the BiSn transition is also small. With regard to the absolute values of flow strength, they are small through the series, and rise from approximately equal values for pure tin and pure bismuth to a flat maximum at intermediate compositions. T h e value under 100,000 kg/cm 2 pressure is approximately 3,300 kg/cm 2 for the pure components, rising to 4,200 at intermediate compositions. X - R A Y ANALYSIS

Professor Clifford Frondel of the Mineralogical Department of Harvard University most kindly undertook an X-ray examination in the effort to find the nature of the permanent change produced after exposure to high pressure, that is, to find the nature of C I. For this purpose material of 43.4 A t per cent Bi — 56.6 A t per cent Sn was rolled to a thickness of 0.0015 inch. One piece was exposed to 30,000 kg/cm 2 for approximately 15 minutes, then held at 18,500 for 20 minutes, and then pressure released to atmospheric in 5 minutes, the specimen immediately cooled to dry ice temperature and within another 5 minutes mounted in the X-ray camera where it was maintained below o ° C during the exposure of several hours. Professor Frondel describes the results as follows. T h e " treated " foils were those exposed to pressure as above, the " untreated " foils the controls from the same rolling. " The treated foils appear to differ structurally from the untreated foils. I do not feel, however, that the available evidence establishes this fact conclusively. T h e evidence so far as it goes would be in line with a theory that the untreated foil had a disordered structure and that your treatment brought about an ordering. " The X-ray photographs were taken in filtered copper radiation by transmission perpendicular to the surface of the foil, using the flat film method. The foils were bathed during the exposure in a stream of C 0 2 from dry ice held in a funnel immediately above the sample; the sample temperature was below o ° C as shown by the development of ice at the edges of the foil (no ice was present on the area being X-rayed). Five photographs were taken: two of the untreated foils, two of the treated foils, and one of a treated foil that had been warmed almost to melting.

EFFECT OF PRESSURE ON TWO ALLOYS OF BISMUTH

145

" The treated foils gave grainy patterns that indicated a considerable coarsening of the crystal size of the metal. T h e warmed foil gave a very grainy pattern, indicating a further recrystallization. T h e patterns of the treated and of the warmed material were identical, and they differed from that of the untreated foil in the presence of extra lines. I have not been able to determine the lattice type, symmetry or unit cell dimensions from the patterns. There were marked absorption effects on all the films." The general conclusion would seem to be that there is not much difference between the lattices of C I and of bismuth, a conclusion in line with the volume relations. A n extension of the same argument would suggest that the lattices of Bi II and C II are also similar. This means that some of the bismuth sites in the bismuth lattice can be occupied by tin without destroying the capacity of the lattice to undergo its polymorphic transitions. Under normal conditions the average atomic radius of bismuth is 9.3 per cent greater than that of tin. One would anticipate that pressure would favor the formation of a lattice of atoms of such different size.

T H E B I S M U T H - C A D M I U M SERIES

Bismuth and cadmium are listed in works on metallurgy 7 as being completely immiscible in all relative concentrations, so that the pressure phenomena may be expected to be especially simple. In order to check the immiscibility, an alloy was made of approximately 2 A t per cent of cadmium in bismuth and the resistance measured to 30,000 kg/cm 2 . T h e resistance of this alloy was not far from that of pure bismuth, and the effect of pressure on resistance not dissimilar to the effect of pressure on the resistance of pure bismuth. There was no suggestion of the anomalous behavior shown by dilute tin in bismuth. There seemed no reason therefore to question the immiscibility of the two components, and further investigation was confined to three alloys, of approximately 25, 50, and 75 A t per cent. T h e same sort of measurements were made on these as on the bismuth-tin series, except that since no new phases were formed, many of the former phenomena did not occur, such as permanent changes after application of pressure or creep back toward virgin values. The alloys were prepared in the same manner as before. T h e

182 — 4275

146

BRIDGMAN

same bismuth was used, and " spectroscopically pure " cadmium from the N e w Jersey Zinc Company. Density. The density at room temperature, approximately 25°C, is shown in Table V and Figure 20. T h e variation with composition gives no suggestion of solution or compound formation, and is the sort of thing to be expected. T h e density at the mid point is what would be calculated assuming additive volumes. T A B L E

V

D E N S I T Y OF B I - C D S E R I E S Composition At % Bi 100.00 75.58 49.95 24.90 0.00

Density 9.788 9.616 9.361 9.038 8.648

T h e density of this series has also been measured b y Gabe and Evans. 8 Their densities are consistently somewhat higher than mine; the discrepancy rises to a maximum of 0.04 on the density at the middle of the composition range.

COMPOSITION, ATOMIC

PER CENT

BI

Figure 20. T h e density at atmospheric pressure and room temperature of the bismuth-cadmium system as a function of composition.

182 — 4276

E F F E C T OF P R E S S U R E ON T W O A L L O Y S OF B I S M U T H

147

Compressions to 40,000 kg/cm2. Measurements were made by the same method as for the Bi-Sn series. Again the alloys were sufficiently soft so that it was not necessary to use an indium sheath. Because there were no other transitions to complicate the picture it was possible to resolve the I-II and II-III transitions. In Table V I are given the relative volume compressions as a funcTABLE VI AV/V

0

TO 4 0 , 0 0 0

kg/cm 2

OF B I - C D S E R I E S

Composition, At % Pressure kg/cm 2

100.00 C d

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

0.0100 .0194 .0283 .0368 .0449

28,000 30,000 35,000 40,000

7 5 1 0 Cd 24.90 B i

50.05 C d 49.95 B i

0.0124 .0234

0.0132 .0250

•0337 .0430 i.0523 I.0693 i.0748 [.0902 .0934 .1005 .1067

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99 L i I Sn •55*

10«

Temperature Coefficient

9.17

9.02

.00445

.00437

98 L i 2 Sn

95 L i 5 Sn .940

•555 10.68

15.83

.00430

Pressure kg/cm»

.00431

QO L i 10 S n

80 L i 20 Sn

1.50

2.62

20.66

37-5*

60 Li 40 Sn

20.9*

.00428

Rp/Ro

0

I.OOO

I.OOO

I.OOO

I.OOO

I.OOO

I.OOO*

I .OOO*

5,000

1.036

1.045

1.036

1.043

1.044

10,000

1.074

1.087

1.075

1.09 I

1.089

•945 .900

•957 .921 .890

15,000

1.115

I.I 30

1.114

1.139

1.137

.861

20,000

1.158

1.173

1.176

1.188

1.185

.829

.864

25,000

1.198

1.217

1.236

1.233

.800

.840

30,000

1.237

1.260

1.199 I.241

1.287

1.278

•773

.818

* Ufford's specimens.

Specific resistance a t room temperature.

very small solubility in pure lithium. On the average, the temperature coefficients of the alloys are slightly less than that of pure lithium, and the pressure coefficients, which are positive, somewhat higher. This is consistent with previous experience. The various minor irregularities in the progression of temperature and pressure coefficients may well be due to imperfect homogeneity in the material. Ufford measured in this range of composition only 9 and 10 per cent tin. His fractional changes of resistance at 10,000 were 0.088 and 0.084 respectively, to be compared with 0.089 found here. It would appear that up to 10 per cent tin the system is almost entirely a mechanical mixture; if Hansen's diagram is right this

189 — 4368

EFFECTS OF PRESSURE ON BINARY ALLOYS

177

would be a mechanical mixture of pure lithium with the compound LijSn. From the approximate constancy of the temperature and pressure coefficients the conclusion is to be drawn that the compound has nearly the same temperature and pressure coefficient as the pure metal. But this is completely inconsistent with present measurements on Ufford's specimen of the compound, which has a rather large negative pressure coefficient. T h e conclusion would seem to be forced that there is still another phase not known to Hansen between 10 and 20 per cent tin. This is also strongly suggested by Ufford's Figure 1, which demands a drastic break in the temperature and pressure coefficients in this range. Incidentally it is to be remarked that Ufford's value for the temperature coefficient of the 9 per cent composition, 0.00989, appears impossibly high. His temperature coefficients were not checked by a return reading, and he remarks that they were the least satisfactory of his measurements. The composition 60 Li-40 Sn corresponds to the compound Li 3 Sn 2 shown by Hansen. The behavior of the resistance of this under pressure is not noteworthy, there being a fairly large negative pressure coefficient of resistance with curvature in the normal direction. M y change of resistance of this composition at 10,000 is 0.079, against 0.068 by Ufford. This is far beyond either experimental error; it is to be noted that the specimens were not identical. Lead-Antimony. According to Hansen and Metals Handbook this system at room temperature consists of a simple eutectic mixture of nearly pure components, the mutual solubilities being one per cent or less. Five compositions were investigated in the following: 20, 40, 60, 80, and 99 atomic per cent antimony. Because of the large difference of melting point of the components the conditions were not specially favorable to homogeneity in the castings, and indeed appreciable differences of density were found between different parts of the same casting, rising in the extreme case to one unit in the first decimal place. The mean densities of the alloys were almost exactly a linear function of the composition, as would be expected of a eutectic. All compositions were too brittle to form into wire by extruding and all resistance measurements, except on the 1 per cent lead composition, were made on specimens squeezed at 230°, the eutectic temperature being 252°. T h e 1 per cent lead was squeezed at 450°.

i78

BRIDGMAN

As a consequence of the unfavorable shape of the specimens the specific resistances are not accurate, but nevertheless should be significant. Specific resistance plotted against composition is far from smooth. With increasing lead content the specific resistance drops to an intermediate minimum at 40 Pb, rises to a secondary maximum at 60 Pb, and then drops sharply, being nearly the same at 80 and 100 Pb. This is definitely not the behavior to be expected of a eutectic. This behavior is confirmed by the temperature coefficient, which is not affected by error due to unfavorable shape of the specimen. T h e temperature coefficients of the first three compositions are lower than for pure metals, as would be expected of solutions of intermetallic compounds rather than of a eutectic mixture. T h e behavior of specific resistance may be complicated b y lack of isotropy in the grains of pure antimony, but this can hardly be a factor in the behavior of temperature coefficient. Furthermore, there is a definite parallelism between the details of the variations of the specific resistance and the temperature coefficient, suggesting that the absolute error in the specific resistances is not important. T h e resistances as a function of pressure are shown in Table X . Consider first the dilute composition 99 Sb-i Pb. Resistance measurements to 30,000 only were made on two different specimens of this composition. Furthermore, only resistance measurements were made on this composition. T h e first specimen was prepared without special precaution, the weighed components being melted together in an evacuated quartz tube which was then quenched into water. T h e second specimen, after preparation as just described, was annealed in the quartz tube for 4 days at 6000 and then quenched. During the annealing there was appreciable distillation of antimony to the upper part of the tube, so that the lead content of this specimen was doubtless somewhat in excess of one per cent. T h e effect of pressure on the resistance of both specimens was highly anomalous, with much hysteresis and permanent alteration of zero. T h e resistance of the first specimen decreased slightly on the initial application of pressure up to 10,000, from where it increased nearly linearly to about 10 per cent more than initial resistance at 30,000. On release of pressure, resistance was nearly stationary down to 15,000, where an accelerated increase began, ending at atmospheric pressure with a 25 per cent increase above

189 — 4370

EFFECTS

OF

PRESSURE ON

T A B L E

BINARY

80 Pb 20 Sb

Density

11.33

10.43

poo X 10·

19.13

'9

Temperature Coefficient

.0042 I

.00368

60 Pb 40 Sb 9-39 48 .00224

SYSTEM

40 Pb 60 Sb

J,000 10,000

I J,OOO

7·5

.00296

I J,OOO 20,000 25,000 30,000 35,000 40,000

61.3

j .00328*

6 6

/ .00398

Rp/Ro

I.OOO

I.OOO

1.000*

i.000

•93 «5 .8746 .8245

•937 .885

.941 .888

1.060

.839

.960 .910 .860 .814

•977 .964

.839 .798

.938 .882 .828 .782

•959 .964

1.104

•771 •731 .662 .601

•977 1.000

.484

•544 •504 .469

•737 .697 .628 .569 .521 .480 .446

•452 .422

•433 .398

•417 .388

•444 •415 av/vo

.0123 .0230

.0119 .0228

•0333 .0427 .0512 .0586 .0660 .0730

•0330 .0422 .0511

.0120 .0229 .0329 .0420 .0503

•0593 .0670 .0740

•0579 .0651 .0716

•573 .546

10,000

(65.2

I.OOO

60,000 70,000 80,000 90,000

J,OOO

U7.8*

I.OOO

.7817

100,000

.00241

loo Sb 6.96

2

52

34

99 Pb ι Sb

ι .0000

20,000 25,000 30,000 40,000

JO,OOO

20 Pb 80 Sb

8.46

Pressure kg /cm'

0

7 9

X

LEAD-ANTIMONY 100 Pb

I

ALLOYS

•743· •7079 .65. .606

•524 .505 •490

•759 •7*3 .663 .609 .561 .520

•793 •749 •7'4 .647 .591

•551 .511 .478

-

.0118 .0224 .0323 .0414 •0499 .0579 .0650 .0718

1.103 1.078

1.021 .938 .837 .756 .674 .605

.0116 .0221 .0319 .0410

.0123 .0235

.0494 .0572

•0533 .0620 .0698 .0768

.0646 .0714

•0343 .0441

* See text.

initial. O n the first application of pressure to the second specimen there was an increase of resistance of 21 per cent in the first 5,000 kg/cm 2 , followed by a further nearly linear increase to 1.54 times initial at 30,000. On first release, resistance decreased to a flat minimum near 12,000, followed b y a small increase to 49 per cent more than initial. A second application of pressure was made to this specimen. T h e hysteresis was now much less and there was an approach to consistent behavior. With rising pressure there is a minimum of resistance near 12,000, followed by a rise to 30,000.

189 — 4371

ι8ο

BRIDGMAN

On second release the same minimum occurs, but with an exaggerated rise to a zero 10 per cent higher. The mean of second increase and decrease is a nearly symmetrical parabolic curve of resistance against pressure, with minimum at 15,000 at a resistance 4 per cent less than initial. This also is not far from the curve obtained with release of pressure on the first specimen. To a very rough approximation this may be assumed to be the probable final result for thoroughly seasoned material. The large initial changes are possibly an effect of shifting internal equilibrium. Metals Handbook remarks that at the lead rich end of the series equilibrium is attained at room temperature only over the course of years. The rough agreement of specific resistances and temperature coefficient for the two specimens of 1 per cent composition also suggests that the final values after exposure to pressure are perhaps not far from equilibrium values. Taking these results on the 1 per cent Pb composition at their face value, an appreciable solubility of lead in antimony is indicated, the specific resistance of both specimens being higher than that of pure antimony, and the temperature coefficient of both lower. The effect of solute in dilute quantity on pressure effect on resistance is anomalous, however, the resistance of pure antimony at first increasing with increasing pressure and passing through a maximum, whereas that of the dilute solution at first decreases, passing through a minimum. It is to be kept in mind, however, that the complicating effects of non-isotropy, which is very marked in the resistance and the pressure coefficient of resistance of pure antimony, obscures the straightforward interpretation of the results. The values of specific resistance and temperature coefficient listed in Table X for " 100 Sb " require special comment. These are the values obtained on the MacKay antimony actually used in making these alloys, it being thought that this would be more significant than to give results for antimony of higher purity. The specific resistance and temperature coefficient were obtained on a specimen of this antimony squeezed at 4000 C and measured by the four razor blade technique. The specific resistance and temperature coefficient differ notably from values which I have previously obtained 13 on single crystal material of presumptively much higher purity. The specific resistance of that pure material was 33.6 X io"e against 61.3 now, and the temperature coefficient 0.00510

EFFECTS OF PRESSURE ON BINARY ALLOYS

181

against 0.00466 now. T h e resistance as a function of pressure given in Table X is from a recent publication 1 4 on the pure single crystal stock. T h e compressibility to 40,000 of the M a c K a y material was also freshly determined and is given in the table; the difference compared with previous 1 5 accurate values to 30,000 on single crystal stock is of the order of 1 per cent. Consider next the effect of pressure on the 20, 40, 60, 80 compositions. T h e resistance of these decreases from the start, with increasing pressure. T h e r e is no hysteresis or permanent change of resistance after release of pressure. T w o of the compositions, 20 and 60 lead, show an initial episode in the first 5,000 kg/cm 2 of slight abnormal downward curvature, but in general, curvature is normal over the entire range. A t the antimony rich end of the series the addition of 20 per cent lead results in an algebraic decrease of the pressure coefficient of resistance, an exception to the general rule shown also b y the 99 Sb-i Pb alloy. A t the lead rich end the addition of antimony has the normal effect of increasing algebraically the pressure coefficient, that is, diminishing the proportional decrease of resistance produced b y pressure. T h e correction for making the readings to 100,000 agree with those to 30,000 is larger than usual and more consistent, varying from plus 40 to plus 55 per cent. It may be that the effects of shearing stress, which are an unavoidable accompaniment of the measurements to 100,000, are unusually large here and not adequately dealt with b y a simple multiplicative correction. T h e r e is internal evidence of this from the resistance measurements themselves, because up to 30,000 the effect of pressure on resistance at the lead rich end of the series is greater on the alloys than on pure lead, whereas the relation reverses between 30,000 and 100,000. Further evidence in the same direction will appear from the shearing measurements. T h e compressions are shown also in Table X . T h e compressions of pure antimony and pure lead differ only slightly. O n passing f r o m antimony to lead in the series there is at first a small increase of compressibility, then a slight drop, and finally a slight increase again to pure lead. T h e shearing curves of all compositions show unusually large episodes. Pure antimony is k n o w n f r o m compression measurements 16 to have a transition in the neighborhood of 80,000 kg/cm 2 .

189 — 4373

ι8ζ

BRIDGMAN

There is no reflection of this in the shearing curve, which rises smoothly with upward curvature in this vicinity, but there is a definite episode in a point of inflection near 50,000. This point of inflection becomes much accentuated in the 80 Sb composition, the pressure of inflection now being 45,000. With the 60 Sb composition this inflection has developed into a well marked maximum and minimum, maximum at 40,000 and minimum at 53,000. With the 40 Sb composition the maximum and minimum with increasing pressure are smeared together into a point of inflection with horizontal tangent, but with decreasing pressure a small maximum and minimum appear at 40,000 and 50,000. With the 20 Sb composition the well marked maximum and minimum reappear, with very little hysteresis between increasing and decreasing pressure, at pressures of 40,000 and 55,000. The maximum shearing strengths at 80,000 of the six compositions, from pure antimony, through the four alloys, ending with pure lead are, respectively: 4,300, 3,000, 1,700, 3,200, 1,000, and 1,200. It would appear probable that we have here another example of some sort of a shearing transition, analogous to the shearing transition of lithium. Furthermore, since the progression of numerical values in the series is not regular, it would seem that the relations are not simple, with perhaps not continuous miscibility of the phases formed under shearing stress. Lead-Tin. According to Hansen and also Metals Handbook the system at room temperature is a simple eutectic mixture of the practically pure components. There have been various claims of a transition at 150° in the solid phase on cooling and for a compound; neither of these claims seems well founded. The solubility of lead in tin is practically nil. Metals Handbook indicates a solubility of tin in lead of between one and two per cent. Pressure measurements were made here on four compositions, 25, 50, 75 atomic per cent lead and the dilute tin composition 99 Pb-i Sn. In addition to. the compositions measured under pressure, four other compositions, of 20, 40, 60, and 80 per cent were prepared and the densities determined at atmospheric pressure. These densities were 8.09, 9.07, 9.80 and 10.58 respectively with increasing lead content. The densities of these and the other compositions lie closely on a line joining the components, as would be expected of a mixture. The resistance specimens for 30,000 were prepared by extrusion at room temperature. The data for compression and change of

189 — 4374

EFFECTS OF PRESSURE ON BINARY ALLOYS

183

T A B L E XI LEAD-TIN SYSTEM loo Pb Density poo X 10· Temperature Coefficient Pressure kg/cm*

11.33 19.13 .00421

99 Pb ι Sn

II.29 19.2 .00414

50 Pb 50 Sn

75 Pb 25 Sn

IO.36

9-43

14.6

17.Ο

.00405

.00412

25 Pb 75 Sn

8.40 I 2.2

.ΟΟ427

1.0000

1.000

1.000

1.000

I.OOO

- 9 3 "5

•939

•944

•947

10,000 15,000 20,000

.8746 .8245 .7817 •7431 .7079 .651 .606

•933

•733

•751

30,000 40,000 JO,OOO

60,000 70,000 80,000 90,000 100,000

•573

.546 .524 .505 .490

.876 .826 .783 •745

.710

.888 .842 .802 .766

10,000 I 5,000 20,000 25,000 30,000 35,000 40,000

.0118 .0224 .0323 .0414 .0499 .0579 .0650 .0718

.896 .854 .816 .783 .702 .659 .624 .596 .570

.681 .638 .601 •57' •544

.522 .501 -

J,OOO

.00438

Rp/Ro

Ο J,OOO

2 J,OOO

100 Sn

7.29 11.89

•ΟΙ IO

.0209 .0303 .0391 .0478 .0560 .0633 .0698

•547 •5^3

.902 .863 .828 .796 .766 -717

.677 .643 .612 .586 .562 .540

Ι .0000 .9505 .9077 .8695 .8344 .8031 •7749 •724

.683 .647 .618 .592 .569 .548

ΔΥ/Vo

.0108 .0202 .0294 .0378 .0456 .0519 .0589 .0646

.0097 .0188 .0275 •0359 ,

.0436 .0512 .0580 .0644

.0099 .0184 .0265 .0342 .0417 .0488 .0548 .0610

resistance are given in Table X I . Both are approximately smooth in pressure and lie between the values for the components, as would be expected of a mixture. T h e electrical parameters of the 99 P b - i Sn composition differ from those of pure lead in the direction to be expected of a solid solution (specific resistance higher, temperature coefficient lower, decrease of resistance under pressure numerically less), but the differences are v e r y small and, except for specific resistance, about what might be expected in a mechanical mixture. T h e effect of any solution forces in this system would appear to be unusually small.

184

BRIDGMAN

Although resistance and compression show no high pressure episodes, the shearing curves show a marked episode, varying consistently with composition. The composition 75 Pb-2 5 Sn shows a marked maximum shearing strength of 920 kg/cm2 at a pressure of 50,000, followed by an equally sharp minimum of 710 at 75,000, followed by rise to 820 at 100,000. This curve was almost exactly retraced with decreasing pressure, which is somewhat unusual. The value 820 at 100,000 is probably a low record for shearing strength at this pressure. The composition 50-50 shows a horizontal point of inflection at 75,000 with increasing pressure, and with decreasing pressure a definite minimum of 920 at 70,000 and maximum of 980 at 55,000. The shearing strength at 100,000 of this composition was 1,300. The 25 Pb-75 Sn composition shows the same phenomenon in less degree, a horizontal point of inflection at 60,000 with shearing strength of 1,140 with increasing pressure, and with decreasing pressure at point of inflection, but without a horizontal tangent, in the same general vicinity. The shearing strength of this composition at 100,000 was 2,000, which lies on a regular progression with the two others. It would seem highly probable that this system experiences some sort of transition under shearing stress at high pressures which is not reflected in the behavior of resistance or of volume. Lead-Zinc. According to Hansen and Metals Handbook the liquids in this system show only very partial solubility at both ends of the range and the solids are practically immiscible. The principal interest in a study of the pressure effects is to find whether any new phases or compounds are produced under pressure, and for this a single composition, 50-50, is sufficient. It would be expected that it would be difficult to prepare a homogeneous casting, and this indeed was the case. The mean density of the whole slug was 10.09 against 9.93 expected for a simple mechanical mixture, but extreme figures for the density of 9.53 and 11.16 were obtained from pieces from the top and bottom parts. This failure of homogeneity is not of importance considering that no new phases were found. The resistance specimen for 30,000 was prepared by extrusion at room temperature. The numerical results for change of resistance and for compression are shown in Table XII. In general the alterations produced by pressure are between those for the components,

EFFECTS OF PRESSURE ON BINARY ALLOYS

TABLE

185

XII

LEAD-ZINC SYSTEM 100 Pb Density

11.33

pa> X 1 0 · Temperature Coefficient Pressure kg/cm 5

'9'3

so Pb so Zn j 10.09 16 17.8

.00421

.00410

ιοο Zn 7.08 5-5 .00408

Rp/Ro

0

1.0000

1.000

1.000

J,OOO 10,000

•93'5 .8746

•934 .880

15,000

.8245

•937 .887

2 Ο,ΟΟΟ

.7817

.83. .790

2 5,000 30,000

•743' .7079

•753 .719

40,000 50,000

.651 .606

.665 .622

60,000

.587 .558

•7J6

70,000

•573 .546

80,000 90,000

•524 .505

•532 .509

100,000

.490

•7'3 .695 .679

.487 -

.847 .812 .783 •733

ΔΥ/Υο

J,OOO

.0118

.0I03

.0079

10,000

.0224

15,000

.0323

•ο'99 .0289

.0157 .0229

20,000 2 J,OOO

.0414

.0372

.0297

.0499

•04J2

3 j,000

•0579 .0650

.0529 .οόοο

.0362 .0424

40,000

.0718

.0664

30,000

.0484 .0541

which is about all that could be anticipated. In both cases the alterations are nearer to that for pure lead than would be expected from the nominal volume concentrations, but this probably is without significance. The shearing curve, like the resistance and compression curves, is smooth and indicates no episode under pressure. The shearing curve is unusual in that it rises approximately linearly over the entire range, reaching a value of 1,600 kg/cm 2 at a pressure of 80,000.

BRIDGMAN

Tin-Zinc. Hansen describes this system as a simple eutectic, with complete immiscibility of the two components in the solid phase. Metals Handbook leaves open the possibility of small solubility of zinc in tin. Measurements were made here on five compositions: 20, 40, 50, 60, and 80 atomic per cent tin. The castings were probably not as homogeneous as they should have been, the curve of density against composition departing from smoothness. In particular, the 50-50 slug would seem to have been more inhomogeneous than the others, as shown by a variation of density from 7.06 (top) to 7.16 (whole). Probably imperfect evacuation of the tubes in which the castings were made was partly responsible, there being definite evidence of oxidation. Contrasted with the density, the curve of specific resistance against composition is smooth, except for a slight deviation at the 50-50 point. The difference in behavior of density and resistance is in part due to the greater difference in specific resistance of the two components, one of which is more than twice that of the other, whereas the densities of the components differ by only 3 per cent, so that any irregularities are magnified. The changes of resistance and compressions are given in Table XIII. The resistance specimens for 30,000 were made by extrusion at probably 150°. In general the changes of resistance and the compressions of the alloys are intermediate between those of the components, but the curves, when plotted against composition at a fixed pressure, are not particularly smooth. This is partly due to experimental error, the two components not differing greatly, and partly perhaps from uncertainty in the composition. It is also to be considered that neither of the pure components is isotropic; in particular the compressibility of zinc may vary eight fold with orientation and its pressure coefficient of resistance by a factor of two.17 Any preferential orientation of the grains of different compositions might obviously play an important part in lack of smoothness of the curves. The general result is that there is no evidence of any new phase at high pressure from the volume and resistance measurements. Neither is there any evidence for appreciable solubility at room temperature. The shearing measurements also give no evidence for any new high pressure phase, although there are changes in the direction of curvature with pressure. The compositions 20, 40 and 60 Sn, and

EFFECTS OF PRESSURE ON BINARY ALLOYS

TABLE

187

XIII

T I N - Z I N C SYSTEM 100 Sn Density poo X 1 0 · Temperature Coefficient Pressure kg/cm 2 Ο J,OOO

10,000 ι j,000 20,000 2 J.OOO

30,000 40,000 50,000 60,000 7o,ooo 80,000 90,000 100,000

80 Sn 20 Zn

60 Sn 40 Zn

So Sn So Zn

40 Sn 60 Zn

7.29

7-*7

7.16

7.II

7.18

11.89

10.59

9·Ι3

8.68

7·72

.00438

.00420

.00418

.00416

.00414

20 Sn 80 Zn

7.II 6.66 .00406

100 Zn

7.08 5-5

.00408

Rp/Ro

1.0000 •9505 .9077 .8695 .8344 .8031

I.OOO

•7749

•794 •748

•7H

.683 .647 .618

.592 .569 .548

.956 .916 .881 .849 .820

.708 .673 .645 .618 •594 •57*

1.000 •95'

.924 .893 .865 .839 .816 .776 •74' •713

.687 .666 .649 .632

1.000 .961 .928 .897 .871 .845 .824 .788 .758

ι.ooo .964

ι .000 .968

1.000

•932

•941

•937

•894

.887

•735 •7 = const.,

demands that the shearing stress shall not exceed anywhere a critical value given by the equation. When the critical value is reached the body enters the plastic condition, in which attempts to further increase the shearing stress will be followed by yielding so rapid as to defeat the attempt. Or stated inversely, the speed with which a body in the plastic state flows has nothing to do with the force: twice the speed requires only the same force. Under ordinary conditions the idealized plastic body is never approximated very closely, and is most closely approximated in a narrow range in the immediate neighborhood of the first yield point. The failure of ideality is due to the strain hardening always accompanying deformation to a greater or less degree. Under the conditions of the present experiments, however, when the final steady state has been reached and strain hardening has therefore ceased, the force is independent of the speed of deformation to a spectacular degree of approximation. Behavior such as this is in no way a consequence of the attainment of a steady state, which might conceivably be steady only for a constant velocity of deformation, and was hardly to be anticipated. In very general terms it would seem to mean that the kinetic

190 — 4385

230

BRIDGMAN

component in the mechanism of transmission of shearing stress, which is almost solely operative in an ordinary liquid, has under these conditions been almost entirely suppressed, and replaced by something purely geometrical on a microscopic scale. This appears perhaps not unnatural to reflection after the event. Although in the respect just discussed the plastic behavior of bodies becomes ideal at high stresses and deformations, there are other respects in which the highly disorganized material is in a far from ideal state of plasticity. In the first place, although the material is highly disorganized, it is not completely amorphous, but has structure with respect to the direction (not velocity) of deformation. If the direction of rotation is reversed, the previous absolute value of the shearing force is not at once reached, but is attained only after appreciable reverse distortion. The amount of reverse rotation necessary to reach again the former steady state varies with the material, but for most substances is of the order of magnitude of 10°. This means a shearing distortion of the order of 25 radians. There is a second respect in which plasticity is not ideal under these extreme conditions. In the equation above expressing the von Mises plasticity condition, the right hand side does not contain the stresses. Or expressed otherwise, in this sort of idealized body the tangential force required to produce shearing slip of one plane on another is independent of the normal stress. This condition appears to be satisfied to a useful approximation for many ordinary materials in the stress range of engineering practice, but under our extreme conditions it is far from satisfied, and in fact the principal interest of these experiments it to find how the shearing strength varies with normal stress. Already in the range up to 50,000 kg/cm2 the former experiments had shown marked variations of shearing strength with pressure for most materials. In general, unless the material experiences a polymorphic transition under pressure, the curve of shearing strength versus pressure rises with pressure, but at a diminishing rate at the higher pressures, so that the curve is concave toward the pressure axis. Measurements with the new carboloy apparatus have been made up to 100,000 kg/cm2 on some 30 simple substances and some 25 alloys, mostly of the softer metals. Even carboloy is not strong enough to afford the stresses necessary to put such materials as mild steel into the steady state of limiting work hardening and flow. In the lower range, the new measurements check gratifyingly with the former numerical results. In the new higher range, between 50,000 and 100,000 kg/cm2, there is, with few exceptions, a reversal of the trend at lower pressures, so

190 — 4386

CERTAIN ASPECTS OF PLASTIC FLOW UNDER HIGH STRESSES

231

that toward the upper end of the range the shearing strength rises at an accelerated rate with increasing pressure, and the curve of shearing strength versus pressure becomes convex toward the pressure axis. In other words, the deviation from idealized plasticity with respect to the independence of shearing strength of normal pressure becomes accentuated. The surprising independence of shearing strength of velocity continues, however. The absolute value of the shearing strength of copper under 100,000 kg/cm2 is about 16,000 kg/cm2, and that of NaCl 3,200 kg/cm2. These figures are getting within sight of the so-called "theoretical" values of shearing strength calculated on the assumption of the displacement of perfect rigid lattice planes with respect to each other. Ordinarily, the shear strength fails by a factor of the order of a hundred or a thousand to attain its "theoretical" value. It seems to be the present opinion that this failure is due to defects in the crystal lattice, primarily the so-called dislocations. Under pressure it is not unnatural to suppose that the number and mobility of these dislocations becomes less, with a consequent increase in shear strength. Another eventual factor in an increase of shear strength is the increase in the mean interatomic forces arising from the decreased interatomic distance produced by the pressure. This factor is, however, not yet important for pressures up to 100,000 kg/cm2, judging by the comparatively small decrease in cubic compressibility under this pressure. HARVARD

UNIVERSITY

190 — 4387

Effects of Pressure on Binary Alloys III FIVE ALLOYS

OF T H A L L I U M , By

P. W .

INCLUDING

THALLIUM-BISMUTH

BRIDGMAN

C O N T E N T S

Introduction Detailed Presentation of Data Thallium Thallium — Cadmium Thallium — Indium Thallium — Lead Thallium — Tin Thallium — Bismuth Summary and Discussion

ι ι ι 3 5 11 17 23 39

INTRODUCTION

In this third paper of the series1 several alloys are described for which the phase diagrams are complicated by the presence of a high pressure transition of one of the components, thallium. In the fourth paper the alloys of bismuth will be described, which have a similar complication, only more elaborate, because bismuth has several pressure transitions instead of the one of thallium. The alloys containing bismuth therefore have a greater wealth of detail than those with thallium, and accordingly the experimental material is more extensive. The alloys of thallium with bismuth, containing both complications, are being described in this paper instead of the following one in order to more evenly distribute the length of the two papers. In this paper new data are given for the pure component, thallium, as well as for the alloys. D E T A I L E D P R E S E N T A T I O N OF D A T A

Thallium. Various data for the effects of pressure on the pure metal have been obtained in the past,2 but in order that the results should be on the same material as that from which the alloys were made some of the former measurements have been repeated.

191 —4389

2

BRIDGMAN

The material used in the present work was obtaind from MacKay, described as " 99.9 plus pure." The measurements now made on this MacKay material were, specific resistance and temperature coefficient of resistance at atmospheric pressure, compression to 40,000 kg/cm 2 , shearing to 80,000 kg/cm 2 , and resistance to 100,000 kg/cm 2 . Among my previous measurements were specific resistance and temperature coefficient of resistance, and resistance to 30,000 and 100,000 kg/cm 2 . These measurements were made on material given to me by the Harvard Chemical Laboratory, being stock found in the laboratory of Professor T . W . Richards after his death. I was told that this was material which he had used in his atomic weight determinations. The implication, understood by both the Chemical Laboratory and by me, was that this was highly purified material. M y suspicions were aroused, however, by the discovery that the temperature coefficient of this was not materially different from that of my MacKay material and very materially lower than the temperature coefficient of the material on which I had made measurements in 1917. This latter had been subjected to a number of chemical transformations for my measurements of the effect of pressure on polymorphic transitions. It was received as pure metal, then successively converted to nitrate, iodide, and sulfate, and finally electrolyzed back to the pure metal. These various transformations would be expected to result in metal of high purity. This is confirmed by the temperature coefficient, which was 0.00517 between o ° C and room temperature, against 0.00436 for the material from T . W . Richards and 0.00434 f ° r the present material from MacKay. Another specimen of thallium was also investigated: this I owe to the courtesy of Professor N . Bloembergen, who obtained it from the Research Laboratories of the Thallium Corporation. The exact analysis was not given, but the impurities were stated to be in the hundredths of a per cent. The temperature coefficient of this was 0.00446 and specific resistance at o° 16.87 Χ ΙΟ_β· The specific resistance of the MacKay material was 16.94 a n d that of Professor Richards 17.4 X io~6. It seems probable that the three materials are much alike, with the specimen of Professor Bloembergen somewhat the best of the three, but that none of them approached in purity my own electrolytic material of 1917. Unfortunately the specific resistance of this was not determined.

191 — 4 3 9 0

EFFECTS OF PRESSURE ON BINARY ALLOYS

3

T h e various data for MacKay's thallium are given in the tables with the several alloys. T h e present values for the effect of pressure on resistance differ somewhat from those previously published on presumably the same material. In this connection it is to be remembered that precise reproducibility in resistances under pressure is not to be expected because thallium does not crystallize in the cubic system. Properly, the measurements on thallium should have been made on a single crystal and the variation with orientation determined. I did not, however, prepare any single crystal material. A difficulty encountered in ail exploratory attempt was the fact that molten thallium attacks glass on prolonged contact. Thallium-Cadmium. This system, according to Hansen 3 , is a simple eutectic between practically pure cadmium and thallium, with at most a very small percentage of dissolved cadmium. Four compositions were investigated: 20, 40, 60, and 80 atomic per cent. T h e homogeneity of the castings is vouched for by the fact that the observed densities agree with the calculated densities to the second decimal place, and in the two cases investigated there was no significant difference of density between different parts of the same casting. T h e specimens for the resistance measurements to 30,000 were extruded at 170°. T h e specific resistance against composition lies on a smooth curve. T h e values for specific resistance and temperature coefficient give no reason to think that there is appreciable mutual solubility at either end of the series at room temperature. T h e observed changes of resistance under pressure, compressions, specific resistances, temperature coeificients of resistance, and densities are given in Table I. In general the plot against composition is a more or less smooth curve joining the points for the pure components, with no intermediate episodes, as would be expected from the eutectic composition. T h e transition of pure thallium occurs between 40,000 and 45,000 kg/cm 2 , too high to appear on the compressions, which were measured to only 40,000. T h e transition does appear in the resistance data, however. T h e break in resistance which marks the transition occurs at progressively higher pressures with increasing cadmium content, reaching 60,000 kg/cm 2 at the 80 — 20 composition. T h e explanation of this may well be merely a super-

BRIDGMAN

4

TABLE I THALLIUM — CADMIUM SYSTEM 100 T1 DENSITY 11.86 POO X IO" 16.9 TEMPERATURE .00434 COEFFICIENT PRESSURE KG/CM' ο I .OOO 5,OOO .936 ι ο,οοο .882 15,000 .832 20,000 •795 25,000 .760 30,000 •727 40,000 I.665 JO,OOO

I.487 .436

80 T1 20 CD II.35 15.0 .00421

60 T1 40 CD 10.78 11.9

40 T1 60 CD 10.13 9-4

.00409

.0040

I.OOO .942 .892 .848 .811 •777 •748 .699

I.OOO .946 .901 .860 .826 •795 .768 •719

I.OOO .952 .911 .875 .844 .817 .792 -.747

I .000 •955 .917 .884 .855 .830 .807 •767

I.OOO .961 .927 •897 .872 •849 .828 .792

J-679 1-588 •553

F.710 I.646 .6.3

•733

.762

F.702 I.680 .654 .632 .612 .601

.736

60,000

.391

70,000 80,000 90,000 100,000

•352 .319 .290 .265

.489 .463 .438 .416

.524 .498 •474 •45 3

.0137 .0263 .0379 .0484 .0587 .0684 •0775 .0859

.0132 .0253 .0364 .0469 .0566 .0655 .0740 .0814

.0123 .0237 •0 343 .0443 •0534 .0622 .0704 .0780

-

191 —4392

.00407

100 CD 8.62 6.4

RP/RO

(•657 1-549 •517

J,OOO 10,000 15,000 20,000 25,000 30,000 35,000 40,000

.00408

20 TL 80 CD 9.41 8.0

.582 •555 •532 .511 AV/VO .0125 .0235 .0336 .0434 .0521 .0606 .0682 .0759

.0113 .0214 .0311 .0401 .0487 .0565 .0640 .0711

•713 .693 .675 .658 .0108 .0201 .0290 .0372 .0449 .0518 .0584 .0640

E F F E C T S OF PRESSURE ON B I N A R Y ALLOYS

5

cooling effect, the amount of which increases with the dilution of the thallium; this is perhaps not unnatural. The ratio of the resistances at the transition, before to after, rises continuously with composition, and except for the value for Cd 20 — T1 80, linearly within a small error. The exceptional point would not appear to be off the line by a significant amount. The shearing curves are not particularly sensitive to the transition of thallium. The curve for pure thallium has a cusp at 20,000 kg/cm2 at which the tangent of the shearing curve breaks upward (this is not the known transition) followed by another cusp at 45,000 (the previously known transition), at which the tangent breaks downward, but by a small amount. From here the shearing strength rises to 1,140 kg/cm2 at a pressure of 80,000 kg/cm2. The two cusps, in approximately the same locations, become somewhat accentuated in the alloys, the shearing strengths of which are in general greater than for pure thallium. The shearing strengths at 80,000 of the 80, 60, 40, and 20 thallium compositions are respectively: 2,600, 1,820, 1,720 and 1,680 kg/cm2. The shearing curve for pure cadmium, on the other hand, rises approximately linearly over the entire range, but with a slight upward break in the tangent at 30,000, to 2,480 kg/cm2 at a pressure of 80,000. Neither the resistance nor the shearing measurements indicate any radical difference above 45,000 between the cadmium alloys of the high pressure modification of thallium as compared with the alloys of the low pressure modification. Thallium-Indium. According to Hansen4 the system comprises, at room temperature, a solution of thallium in indium up to about 40 atomic per cent thallium, and a solution of indium in thallium between 60 and 100 per cent thallium, with a mixture of the two limiting solutions between 40 and 60 per cent. The two solubility limits, 40 and 60 per cent, are exceedingly tentative, and in fact no equilibrium points were actually determined below 150°. In any event, the system would appear to be an example of one with unusually wide solubility limits. In this investigation 15 compositions were measured: 0.2, 1, 2, 5, 10, 20, 40, 50, 60, 70, 77, 83.53, 92> 9^1 a n ( i 99 atomic per cent thallium. Only resistance measurements were made on the 0.2, i, 2, 98, and 99 per cent compositions, and of these only the first

191 —4393

6

BRIDGMAN

was carried to 100,000, the pressure range of the four others being 30,000. T h e resistance specimens for the measurements at atmospheric pressure and to 30,000 were wires formed by cold extrusion. T h e specific resistances and the temperature coefficients at atmospheric pressure are shown against composition in Figure 1. A t either end of the range the specific resistance rises smoothly, within experimental error, from that of the pure corn-

Figure i. Specific resistance and temperature coefficient of resistance at atmospheric pressure of the thallium — indium system as a function of composition in atomic per cent.

ponents, and the temperature coefficient drops smoothly, as is to be expected of solutions. T h e intermediate range, between 60 and 20 per cent indium, is not smooth, however, but there is one reversal of trend at 40 per cent shown by both curves. Figure 1 is consistent with Hansen's diagnosis of wide solubility in the two pure components, but the state of affairs at intermediate compositions is probably more complicated than the simple mechanical mixture of limiting solutions suggested by Hansen. Since the effect of pressure on the phase transitions is in certain respects opposite in the present thallium — indium system from that in the thallium — cadmium system, it will

EFFECTS OF PRESSURE ON BINARY ALLOYS

7

pay to briefly review the characteristics of the transitions of thallium. Thallium has a transition between 40,000 and 45,000 kg/cm 2 at room temperature at which there is a large drop of resistance. It also has a transition at atmospheric pressure at 230° to a modification with smaller volume. That is, the transition at 230° is of the ice type, temperature falling with rising pressure. This transition has been followed to a triple point at about 1500 with the 40,000 room temperature modification5. In Hansen's diagram of the thallium — indium system the transition at 230° is shown. The temperature of this transition drops rapidly with increasing indium content. Hansen's diagram would indicate that this transition fades out above ioo°, and that even above this the boundaries of the domains of the two phases are somewhat nebulous, being shown by dotted lines. In the present work four of the compositions richest in thallium, 70, 77, 83.5, and 92 per cent Tl, all in the range of solution of indium in thallium, show a high pressure phase change in the measurements of both resistance and compression. These measurements incidentally place the limits of the homogeneous phase at room temperature at the thallium rich end of the series in the neighborhood of 70 per cent thallium. The phase change indicated by the resistance takes place with considerable hysteresis. The mean pressure of the transition decreases with increasing indium content. This is the exact opposite of the behavior in the thallium — cadmium system, where the pressure of the transition increases with increasing cadmium content. The magnitude of the discontinuity of resistance increases with decreasing indium content in the present system. A very rough extrapolation of the mean pressures of transition gives a transition pressure for pure thallium of 35,000 kg/cm 2 . This is close enough to 40,000 to identify the transition as being to the high pressure room temperature modification of thallium (thallium III), as distinguished from the high temperature atmospheric pressure modification (thallium I). The two most dilute solutions, containing 2 and ι per cent indium, did not show a discontinuity of resistance up to 30,000 kg/cm 2 . Presumably the discontinuity occurs at a somewhat higher pressure. The volume discontinuities indicate the same thing as the discontinuities of resistance; in particular the pressure of the discon-

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191 — 4 3 9 7

ΙΟ

BRIDGMAN

tinuity decreases with increasing indium content. The somewhat irregular values of volume discontinuity extrapolate within experimental error to the value previously found for pure thallium, namely AV/V0 = 0.0062. A t 70 per cent thallium AV/V0 is roughly two thirds of its value at 100 per cent. The corners of the transition curves, for both compression and resistance, are rounded for both directions of the transition, indicating that indium is soluble in both phases, but to different extents. This, and diffusion phenomena, would account for the hysteresis. The data for resistance under pressure are given in Table II. Except for the hysteresis in the transition range just discussed the results for these alloys were unusually clean cut: the curves were smooth, single valued with increasing and decreasing pressure, and with no permanent change of resistance after the initial application of pressure, that is, with no seasoning effects. Furthermore, the agreement between the resistance measurements to 30,000 and to 100,000 was unusually good, the correction for reducing the 100,000 results to agreement with those to 30,000 varying between —6.2 and +6.5 per cent, average numerical value, 4.7. In general, the effects of pressure on resistance have no unusual feature; in the middle of the composition range and at the higher pressures the decrease of resistance brought about by pressure is less than for the pure metals. The immediate interest in the four compositions 1, 2, 98, and 99 per cent thallium was to check the previous generalization that the pressure coefficient of dilute solutions of one metal in another is greater algebraically than that of the pure metal. This rule is satisfied by the one per cent solution of indium in thallium, and also by the two per cent solution, but with less definiteness. The effects of the dissolved indium are in any event very small. A t the indium rich end, on the other hand, the rule is definitely broken, the pressure coefficients of the solutions being greater numerically, not algebraically, than that of indium. The maximum effect of dissolved thallium is shown already at 0.2 per cent Tl, beyond which the trend reverses, but the coefficient of pure indium is not regained until between 5 and 10 per cent thallium. The effect of small dissolved impurity would thus seem to be far from linear. This would underline the importance of procuring as pure metals as possible for determination of pressure coefficients.

191 —4398

EFFECTS OF PRESSURE ON BINARY ALLOYS

Consider next the compressions as given in Table II. T h e compressibilities of pure indium and pure thallium are unusually close together, and except for the influence of the transition, the compressions of the alloys are close to those of the pure metals. T h e progression of values as a function of composition deviates somewhat from smoothness, but it is not certain that this is beyond experimental error. T h e transition was affected with capricious hysteresis and supercooling, so that it is not possible to give a unified treatment of the data. For the 23 and 8 per cent indium compositions the hysteresis limits were sufficiently narrow to justify giving a mean pressure for the transition; the figures in the table apply to one modification at lower pressures and the other modification at higher pressures. T h e 30 and 16.47 per cent compositions, however, showed so wide a loop that it was necessary to indicate the compressions of the t w o phases over a range of pressure, which in the case of 16.47 composition extended from 10,000 to 25,000 kg/cm 2 . T h e magnitude of the change of volume at the transition increases in general with increasing thallium content. T h e increase is somewhat irregular, but an extrapolation which is as good as any other is consistent with the value 0.007 f ° r P u r e thallium found in previous measurements of compression to 100,000. Again, as in the case of resistance, there would seem to be no doubt that the transition encountered here is to the room temperature, high pressure phase, and not to the high temperature atmospheric phase. None of the shearing curves show any episode suggesting a transition, and the curves for all compositions are very closely similar, consisting of a nearly linear rise over the entire range to 80,000, with unusually small hysteresis between increasing and decreasing pressure. T h e absolute values of shearing strength at 80,000 for the respective compositions 80, 60, 50, 40, 30 and 16.47 indium were: 1,170, 1,240, 1,240, 1,320, 1,420 and 1,250 kg/cm 3 . Thallium — Lead. According to Hansen 6 the system at room temperature, between ο and 80 atomic per cent thallium, consists of solid solutions. Extrapolation of the melting phenomena would suggest that these solutions exist in two phases, but the actual phenomena at room temperature and lower exhibit nothing suggesting anything else than a single homegeneous solution range up to 80 per cent thallium. Beginning in the nebulous neighbor-

l y — 4399

12

BRIDGMAN

hood of 80 per cent, Hansen's diagram indicates that there is a domain of mechanical mixture extending up to within a few per cent of pure thallium, beyond which the solution is a dilute solution in thallium. Tang and Pauling7, from X-ray measurements on eleven compositions, conclude that there is strong evidence that the ordered structures PbTl 3 and PbTl 7 exist at room temperature, and that in intermediate ranges solid solutions exist. In this present work eleven compositions were studied: 2.5, 5, 10, 15, 20, 40, 60, 80, 95, 98, and 99 atomic per cent lead. There was no evidence of inhomogeneity in the castings, as indeed would not be expected because of the character of the melting curve. The densities are a linear function of composition within two units in the second decimal place. The alloys are all soft and were extruded into wire for the resistance measurements to 30,000 at temperatures varying from ι io° to 150°. The specific resistances should be good. In the range 15 to 100 per cent lead both specific resistance and temperature coefficient of resistance show the smooth catenary shape to be expected of a continuous series of solutions. Below 15 per cent lead, however, the regularity of the results is disturbed by the values for 2.5 per cent lead, the specific resistance of which lies high and the temperature coefficient low. There is evidently some complication in the system at low lead concentrations: one is reminded of the compound PbTl 7 of Tang and Pauling. Under pressure the resistance at the thallium rich end of the series shows transition phenomena, of quite a different character from the indium — thallium series. In interpreting Table III it is to be kept in mind that the double columns of resistances for some of the compositions refer to the measurements in the 30,000 apparatus, in which a pressure cycle was described from atmospheric pressure to maximum at 30,000 and back to atmospheric again. The fact that two columns are not given for the data above 30,000 does not mean that hysteresis would not have been shown in this range also, but is merely a reflection of the fact that in the 100,000 apparatus readings could be made only with increasing pressure. The 2.5 lead composition has a drop of resistance beginning, with increasing pressure, in the neighborhood of 20,000, accelerating strongly up to 28,000, beyond which it flattens out to 30,000. On release of pressure the corresponding

191 —4400

EFFECTS OF PRESSURE ON BINARY ALLOYS

13

rapid down-drop begins in the neighborhood of 17,000, is nearly completed at 10,000, but the original resistance is not exactly recovered so that there is a slight permanent change of zero. A t 5 per cent lead an accelerated drop begins in the neighborhood of 25,000, which has not progressed far by 30,000. On release of pressure from 30,000 there is no abrupt drop at any pressure, but the curve is smooth over its entire length, with continually decreasing pressure, down to zero pressure. This composition shows a major drop of resistance at 40,000 in the 100,000 apparatus. A t 10 and 15 per cent lead the same tendency continues, now manifested by increasingly slight hysteresis between increasing and decreasing curves over their entire length up to 30,000. Since here the pressure at the initiation of the break decreases with decreasing lead content, there can be no question of the new modification being the previously known modification of pure thallium at 40,000, but some new phase or phases seems indicated. It does not seem possible that the previously known transition at atmospheric pressure at 232° can be involved here, and it would seem necessary to invoke the compound PbTl 7 of Tang and Pauling and ascribe to it its own pressure transition. As far as the measurements with the 30,000 apparatus go it might be expected that the transition which apparently had been only partially initiated at 30,000 for the 5 per cent lead composition would be pushed to completion at higher pressures, where the transition should also occur for higher lead contents. This, however, did not prove to be the case except for the 5 per cent composition, but the measurements to 100,000 showed no transition for lead contents of 20 per cent or higher, although showing it for the t w o lower contents. That is, the transition simply fades out of the picture. This is not inconsistent with the existence of the compound PbTl 3 of Tang and Pauling. Reduction of the readings with the 100,000 apparatus to secure agreement with the 30,000 readings is affected with considerable uncertainty for the 2.5 and 5 per cent lead compositions because of the hysteresis in the 30,000 readings. The 100,000 readings were adjusted in a not altogether simple manner according to methods suggested b y my previous experience, and the details will not be elaborated. For the 2.5 composition the maximum correction was + 3 8 per cent, shading off at higher pressures,

BRIDGMAN

'4

TABLE

III

T H A L L I U M — LEAD SYSTEM

100 T1 Density 11.86 16.9 poo X 10* Temperature .00434 Coefficient Pressure 2 kg/cm ο 1.000 j,ooo .936 .882 10,000 i5,ooo .832 20,000 •795 2 J,000 .760 30,000 •727 i.665 40,000 1-487 JO,000 .436 60,000 •391 70,000 •352 80,000 •319 90,000 .290 100,000 .265

191

—4402

5,00ό ΙΟ,ΟΟΟ 15,000 20,000 25,000

.0137 .0263

30,000 35,000 40,000

.0684

•°379 .0484 .0587

•0775 .0859

97·5 T1 1.5 Pb 11.83 20.3 .00359 ι .000 .997 .941 .938 .892 .878 .848 .741 .805 .602 .615 .560 .526 •471 •427 •392 .367 •348 •334 .3.8 .0137 .0260 .0372 .0423 .0476 .0528 .0623 .0713 .0798 .0868

95 Ti 5Pb 11.86 18.3

90 Tl ro Pb 11.80 18.8

.00353 1.000

.003 14

Rp/Ro .995 i.000

•939 -934 .888 .879 .843 .831 .803 .787 •767 -749 •714 /•642 I.526 •479 •443 .411 •384 .361 •341

- ΔΥ/Vo

.0138 .0259 •£>373 .0472 .0567 i.0646 (.0670 •0759 .0842

.996

•943 -938 .894 .888 .860 .853 .816 .807 •783 -775 •745 .681 .626 .582 •551 •522 •495 •472 .0135 .0257 .0369 .0474 .0568 i.0654 \.o666 •0745 .0815

8S Tl is Pb II.79 19.7 .00274 1.000

80 Tl 20 Pb II.74 22.8 .0023;

.998

1.000

•949 -947 .905 .903 .868 .866 .836 .834 .808 .806 .780

•957 .921 .889 .861 .836 .814 .776

•737 .701 .669 .644 .622 .602 .585

•744 .720 .697 .679 .662 .650

.0133 .0252 .0364 .0443 .0556

.0135 .0255 .0366 .0469 .0565

.0639 .0722 .0796

.0655 .0738 .0824

EFFECTS OF PRESSURE ON BINARY ALLOYS

T A B L E III -

r

5

Continued

T H A L L I U M — LEAD SYSTEM 60 T1 40 Pb

1.62 IJ.8

.00168

40 T1 60 Pb

II.J2 35-9

.00190

20 T1 80 Pb

11.44 29.7

.00249

sTl

95 Pb "•35

22.7

.00350 Rp/Ro

s ΤΙ 98 Pb

II.34 20.6

.00383

1.000

I.OOO

I.OOO

I.OOO

I .OOO

•958

•949

•945

•935

•935

.922 .888 •859

.832 .808 .762 .728 .697 .673 .6JI .635 .622 .0122 .0236 •0347

.0451

•0547

.0637 .0724 .0807

.907 .870 .836 .810 •779 •73*

.898 .856 .820 .787 •759

.690 .656 .627 .602

.709 .669 .635 .607 .581

-581

.558

.560 .0129

.0242 .0348 .0448 .OJ42 .0631 .0716 .0797

•539

.0118 .0223 .0326 .0423 .0518 .0606 .0687 .0764

.882 .837 •797

.760 .728 .671 .624 •584 •552 •5*3 J -499 1 - 4 9 3 (?) •47 2 - AV/Vo

ι T1 99 Pb

II.34 20.4

-00394 1.000 -936

.878 .830 .789

.878 .829 .785

•7 5 2 •718

-747

.713

100 Pb

II.35 19.I

Density poo X 10» Temperature .0042 I Coefficient Pressure1 kg/cm I.OOO 0 •9 3 2

.875 .825 .782

5,000

10,000

.546 .524

15,000 20,000 25,000 30,000 40,000 50,000 60,000 70,000 80,000

.505 .490

90,000 100,000

•743

.708 .65. .606

•573

.0118 .0224 .0323 .0414 .0499 •0579

.0650 .0718

5,000 10,000 15,000 20,000 25,000 30,000 3 5,000 40,000

191

—4403

ιό

BRIDGMAN

and for the 5 per cent composition also +38, again shading off. The corrections for the other compositions were, in order: +38, + 31, + 1 2 , + 1 8 , +28, -(-19, and +30, all constant over the pressure range. A t the lead rich end of the series the variation of the pressure coefficient is in accordance with expectations for a solution, the coefficient becoming algebraically greater with increasing thallium content. A t the thallium end the phase transition with accompanying hysteresis obscures the answer to the question. A t the lead rich end of the series attention is to be called to a not entirely certain small jump in resistance at 90,000 kg/cm 2 for the 95 Pb — 5 T1 composition. Next consider the compressions as given in Table III. The evidence of a new phase at low lead content is confirmed by the volumes, the volume discontinuity shifting to higher pressures with increasing lead content and becoming less in magnitude. That is, again the transition fades out. A t the lead rich end the compressions of the alloys are greater than that of pure lead, and increase with thallium content. With one exception the shearing curves are all very much alike and with no episode certainly beyond experimental error. The shearing strengths of pure lead and pure thallium are nearly the same, being respectively 1,150 and 1,180 kg/cm 2 at 80,000 kg/cm 2 . There is a slight episode, an accelerated rise, for pure thallium corresponding to the known transition at 40,000, but it is very minor, not at all like the discontinuity of resistance or volume. The other compositions do not show this episode at all. The curves are nearly linear, with little hysteresis, sometimes with slight upward and sometimes with slight downward curvature, and with shearing strengths at 80,000 varying from 1,080 to 1,480 (the latter at 20 per cent lead). The shearing curve for 95 Pb — 5 Tl, which was carried to 100,000, has a small rise in the neighborhood of 80,000, confirming the possibility of a new phase shown by the resistance. The shearing curve for 40 per cent lead is markedly exceptional. This has a maximum at 40,000 and minimum at 50,000, confirmed on release of pressure, with an extreme shearing strength at 80,000 of only 720 kg/cm 2 , the lowest value observed at this pressure for any substance. Since the composition 20 per cent lead did not show this anomoly it is probable that the com-

191 —4404

E F F E C T S OF PRESSURE ON B I N A R Y ALLOYS

17

pound PbTl 3 of Tang and Pauling is not involved in this phenomenon, and again the hypothesis of a polymorphic modification produced by shearing stress as distinguished from hydrostatic pressure seems necessary to account for the effect. Thallium — Tin. According to Hansen" the system consists at room temperature of a solution of tin in thallium in the range from ο per cent to something in the general neighborhood of 20 atomic per cent tin, and for the rest of the range to pure tin a mechanical mixture of pure tin and the limiting solid solution, there being no detectible solubility of thallium in tin. In the present work eleven compositions were studied: 0.99, 2.5, 3.7, 5, 7.5, 10, 15, 20, 40, 60, and 80 atomic per cent tin, the majority of the compositions thus being in the range of supposed solid solution. The densities are nearly a linear function of composition over the entire range, the maximum deviation from linearity being about plus 1 per cent at mid range. This linearity is of special significance in view of the large difference of density between the pure components. There is no evidence of difference of density between different parts of the same casting, so that the homogeneity is doubtless adequate, as would be expected from the shape of the melting curve. The alloys are all soft and the resistance measurements to 30,000 were made on wires extruded at temperatures from 1 io° to 130°. Specific resistance, shown in Figure 2, in the domain ο to 20 per cent tin increases by a large amount, as would be expected of a solution, but the increase is not smooth, the first small additions of tin being accompanied by a disproportionally large increase of resistance, after which there is a slight dropping off to 10 per cent tin, where there is a sharp upturn to a sharp maximum at 20 per cent tin. It would seem highly probable that the interval out to 20 per cent tin is more complex than a simple solution, with perhaps a compound in the neighborhood of 10 per cent. From 20 to 100 per cent tin resistance falls off, approximately, but definitely not, linearly, in a way roughly consistent with a mechanical mixture in this domain. The temperature coefficient of resistance drops steeply with composition in the ο to 20 per cent tin range, with some irregularities, which, however, are much smaller than those of the specific resistance in the same range. Beyond 20 per cent tin the temperature coeffi-

191 —4405

18

BRIDGMAN

cient rises in a way not inconsistent with the diagram of Hansen. The transition phenomena in this series are entirely confined to the thallium rich end, there being no evidence for a transition from either resistance or compression from the composition 10 per cent tin and higher. In the range up to 10 per cent tin the transition phenomena are not sharp. There is much rounding of the corners of the transition, the appearance of which is irregular and not always the same as shown by the resistance and compression data. One generalization can be made from both the I

1

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ι COMPOSITION

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Figure z. Specific resistance and temperature coefficient of resistance at atmospheric pressure of the thallium — tin system as a function of composition in atomic per cent.

resistance and the volume measurements, namely that the addition of small amounts of tin smears out the thallium transition in the direction of lower pressures. The resistance of the 0.99 tin composition shows no premonition of the transition up to 30,000, the readings in the 30,000 apparatus being without creep and single valued. With this composition a discontinuity of resistance shows up in the 100,000 apparatus in the neighborhood of 40,000, and is so shown in Table IV. The transition of this

191 — 4 4 0 6

EFFECTS OF PRESSURE ON BINARY ALLOYS

19

composition shown in the volume apparatus occurs between 25,000 and 35,000, and is apparently complete at 40,000. T h e next three compositions, 2.5, 3.7 and 5 tin, show the initiation and partial running of the transition in the 30,000 apparatus, there being definite hysteresis between the readings with increasing and decreasing pressure with some permanent change of zero. A t none of these compositions, however, is 30,000 sufficient to complete the transition, but the major jump down in resistance shows up in the 100,000 apparatus, smeared over a region centering somewhere between 30,000 and 40,000. T h e amount of hysteresis in the 30,000 apparatus is not regular, being greatest for the 2.5 Sn composition. T h e measurements of compression in general show the transition confined within somewhat narrower limits than the resistance measurements, the center of gravity of the region of transition shifting to lower pressures with increasing tin content. T h e volume discontinuity at the transition becomes smaller with increasing tin content, but not with regularity, and apparently would vanish not far above 7.5 per cent tin. This latter composition shows no hysteresis of resistance in the 30,000 apparatus, the transition in the resistance appearing only in the 100,000 apparatus. Consistently with this the transition in the compression appeared with increasing pressure only above 30,000, but with decreasing pressure was smeared out down to nearly 10,000. Although the resistance of the 7.5 per cent tin composition is shown single valued in the table, there was, immediately after release of pressure, a depression of the zero of resistance by 0.38 per cent. There was practically complete recovery of the initial zero after 14 hours at room temperature. Effects of this sort remained perceptible up to 40 per cent tin, but were too small to show in the table. T h e resistance measurements in the 100,000 apparatus and the compression measurements on the compositions 0.99 and 3.7 per cent tin were made several months after the others and after the casting of the samples. These two specimens therefore had opportunity to approach internal equilibrium more closely than the others. T h e table does indeed show departures from the regular sequence of values which possibly are due to this effect. Above and including 10 per cent tin all trace of any transition

20

B R I D G M A N

TABLE

IV

THALLIUM — T I N

100

T1

Density 11.86 16.9 p o o X 10· Temperature .00434 Coefficient Pressure ! kg/cm 0 1.000 5,000 .936 10,000 .882 15,000 .832 20,000 •795 25,000 .760 30,000

•727 /-66 s

99.01 T ! .99 Sn

" • 7 9 20.0

97 5 T 1

2.5 Sn

11.75 19.6

.00395

95 T1

92.5 T l 7 - S Sn 11.56 19.5

5 Sn

11.66 '9-3

.00355

.00343

.003 18

Rp/Ro 1.000 •939 .888

1.000 .940 .889

.987 .925 .871

•844 .805 .770

•844 .804 .756

-799 .690 .612

•739 f.695 1-583 •548 •S15 .488

.938 .888 .842 .803 .766

. . . . .

9 8 8 7 7

3 8 3 9 4

2 0 5 2 1

.704

ι .000

.989

T.OOO

•937 .886 .841 .802

-924 .871 .822 .774

•937 .885 .839 .803 .766

•765 -735 /•735 I.606

(.660

80,000 90,000 100,000

-319 .290 .265

•445 .427

•453 •431 •4· 3

5,000 10,000 15,000

.0137 .0263 .0379

.0132 .0255 .0368

20,000 25,000 30,000 35,000 40,000

.0484 .0587 .0684

.0474 .0575 .0634 .0668 .0735 .0754 .0825 .0911

.466

I.OOO . 9 9 3

j-739 I.605

I.487 .436 .391 •352

( a ) T r a n s i t i o n a t 27.250. V o l u m e s .0634 a n d .0672.

191 —4408

T1 3 - 7 Sn 11.70 20.6 96.3

.00364

40,000 50,000 60,000 70,000

•0775 .0859

SYSTEM

.567 •532 .502 .476

I.627 •597 •571 .550 (-533 1-5*9 .511

.570 .538 .508 .481

.736 i.692 I.640 .612 .587 .564

.460

•494

•445 .419

•544 .528 .512

.0137 .0262 .0376

.0133 .0259 .0367

.0162 .0284 .0397

.0133 .0252 .0361 .0377

/· 0483 I.0520 .0620 .0710 .0794 .0872

.0471 .0512 .0569 .0609 .0662 .0701 .0774 .0807 .0902

.0501 .0595 .07i8 .0798 .0871

.0464 .0562 .0650

AV/Vo

u )

.0481 .0579 .0669

•0755 •0837

21

EFFECTS OF PRESSURE ON BINARY ALLOYS

T A B L E

IV -

Continued

THALLIUM — T I N

90 T1 10 Sn 1.48

85 T1 IS Sn 11.23

80 T1 20 Sn 10.98

60 T1 40 Sn 10.14

9-3

23-5

27·4

23.8

.00296

.00225

.00178

.00232

SYSTEM

40 T1 60 Sn 9.17 16.9 .00330

20 T1 80 Sn 8.24 14.2 .00383

Rp/Ro I.OOO •937 .88; .840 .803 .769 •74· .696 .660 .632 .608 .588 .570 •554 .0134 .0257 .0363 .0463 .0558 .0642 .0718 .0789

I.OOO .948 .905 .868 .836 .808 .783 •74' .709 .680 .657 .637 .618 .600 •0135 .0253 .0361 .0462 •0557 .0643 .0723 •0795

i.ooo

1.000

1.000

•954 •9'3 .879 .848 .822 .798 .756 .722 .694 .670 .648 .628 .609

•955 .914 .878 .846 .817

•950 .908 .87. .839 .810 .782 .738 .701

.0130 .0249 •0354 .0456 •0553 .0643 .0726 .0804

•79' •745 .708 .676 .652 .627 .607 .586 - AV/Vo .0112 .0219 .0321 .0418 .0J09 .0596 .0679 •0754

100 Sn Density poo X io· Temperature .00438 Coefficient Pressure kg/cm'

7·*9 11·9

1.000 .950 .908 .870 .836 .805

1.000

•775 •724 .683 .647 .618

.598 .578

•777 •7*8 .689 .656 .629 .605 .582 .562

.0114 .02 1 4 .O3IO .0402 .0486 .0564 .0641 .07 I 2

.0101 .0198 .0281 .0366 .0450 .0528 .0598 .0657

.0099 .0184 .0265 .0342

.669 .642 .619

•951 .908 .870 .834 .803

•592 .569 .548

.0417 .0488 .0548 .0610

0 5,000 10,000 I J,000 20,000 25,000 30,000 40,000 50,000 60,000 70,000 80,000 90,000 100,000 5,000 10,000 15,000 20,000 25,000 30,000 35,000 40,000

191

— 4 4 0 9

22

BRIDGMAN

has disappeared from both resistance and volume phenomena. T h e sequence of numerical values is not monotonic between 10 and ioo per cent tin, however, but both resistance and compression show some sort of turning point at 20 per cent tin. This composition is also the composition of maximum specific resistance, and doubtless marks some sort of landmark in the structure. Unlike the system thallium — lead the transition out to 10 per cent tin is doubtless the regular high pressure thallium transition, smeared out and depressed to lower pressures by the addition of tin. T h e failure of exact parallelism between resistance and volume phenomena may well be a result of the different geometry in the two cases, it being much easier for the transition to run only partially in isolated parts of the long slender resistance specimen than in the chunky compression specimen. T h e disappearance of the transition beyond 10 per cent tin suggests, as does also the turning point in the specific resistance, that 10 per cent approximately marks a new phase, and that below 10 per cent the system is a solution of pure thallium and the new phase. One is reminded of the phase PbTl 7 found by Tang and Pauling, but this cannot be exactly it. Furthermore, the new phase in the tin — thallium system does not have an independent high pressure transition, as it did in the lead — thallium system. Beyond 10 per cent tin and up to the general neighborhood of 20 per cent, both the pressure phenomena and the specific resistance suggest a mixture with still another new phase, perhaps analogous to the PbTl 3 of Tang and Pauling, but probably not exactly it. T h e shearing phenomena are very similar to those for the series lead — thallium. With a single exception the curves are nearly linear, with little hysteresis, and only slight curvature in either direction. T h e exception occurs at the composition 40 per cent tin, where there is a well marked point of inflection, an episode not so well marked as the maximum and minimum at the same composition in the lead — thallium series, but unmistakable, and also setting this composition off apart from the others as regards shearing phenomena. T h e shearing strengths at 80,000 for the compositions 2.5, 5, 10, 15, 20, 40, 60 and 80 tin were respectively: i,ioo, 1,040, 1,050, 1,120, 1,500, 1,150, 1,580 and 1,470 kg/cm 3 . Again the exceptional composition has a shearing strength, 1,150,

191 —4410

EFFECTS OF PRESSURE ON BINARY ALLOYS

23

well below those on either side, and again a polymorphic transition under shearing stress seems indicated. Thallium —Bismuth. Hansen's melting diagram 9 shows three eutectic cusps and two maxima, and therefore presumably at least two homogeneous ranges between the pure components. However, except in the neighborhood of pure thallium, no equilibrium points have been determined below 188°. The indications are that the attainment of equilibrium at low temperatures is very sluggish and therefore the material ill defined. Hansen's diagram suggests at room temperature a domain of mixed bismuth and delta reaching to 35 per cent Tl, a homogeneous domain of delta from 35 to 45 per cent Tl, a region of mixed delta and gamma from 45 to 65 per cent Tl, a homogeneous domain of gamma from 70 to 92 per cent Tl, and from 92 to 100 T l domains, not well established, of the beta and alpha (high and low temperature) lattices of pure T l and a mixture of beta and gamma. In this work attention was concentrated on the bismuth rich and the thallium rich ends of the series, only seven intermediate compositions being investigated. In all, 16. compositions were studied: 0.5, 1.0, 1.25, 1.5, 1.75, 2, 5, 10, 20, 50, 60, 70, 80, 90, 98, and 99 atomic per cent bismuth. The principal interest was in the behavior of dilute solutions of thallium in bismuth, and of dilute solutions of bismuth in thallium. Hansen's diagram indicates no solubility of thallium in bismuth, but solubility of bismuth in alpha (low temperature) thallium up to perhaps 10 per cent. A t the bismuth rich end the questions of interest were whether dilution of bismuth with thallium would produce the enormous effects found for tin and lead (the latter to be published in the fourth paper of this series), and whether new compounds are formed. A t the thallium rich end it was of particular interest to find whether the effect of dissolved bismuth on the thallium transition is the same as the effect of dissolved tin or lead. A t intermediate compositions it was of interest to find whether the new phases show any of the transitions of pure bismuth or thallium. It is to be remarked that the atomic radii of bismuth and thallium in the solid state are unusually close, being 1.52 and 1.55 A respectively, so that for this reason simple effects are to be expected on mixing the two metals. If, however, compounds

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193 — 4511

BRIDGMAN

124

The particular point of interest in making these measurements was to find whether this material exhibits a quasi-polymorphic transition under pressure in the same way that " teflon " does.13 A volume discontinuity was indeed found for fluorothene, but at a lower pressure and somewhat less in amount than for teflon. The occurrence of volume discontinuities in material of this constitution is somewhat unexpected, and must indicate an approach to at least some aspects of a crystalline arrangement. Lead. It was recently called to my attention by Mr. S. J. Jacobs of the U. S. Naval Ordnance Laboratory that I had published no values for the compression of lead, although I had referred in print in 194614 to unpublished data for the compressions of copper, aluminum, and lead. Compressions of copper and aluminum to 30,000 by the improved lever piezometer were subsequently published,4 but by inadvertence the values for lead were never published. These are now given in Table V I copied directly from my TABLE

VI

COMPRESSION OF L E A D

Pressure kg/cm 2 5,000 10,000 15,000 20,000 25,000 30,000

AV/V 0 .01118 .02186 .03213 .04192 .05125 .06005

7J° .01150 .02238 .03273 .04262 .05210 .0621 2

note book of 1939. The measurements were made with an older form of lever piezometer. However, the absolute compressibility of lead is so high that the accuracy should be as good as that for less compressible metals in the improved apparatus. The lead was of 99.9999 purity, the same material as used in many of my other measurements. Compression oj Hen's Egg Yolk and White. The following measurements were made in 1948 at the request of Professor Douglas Marsland of New York University, who said that they would be of some biological interest and that apparently no such measurements were in the literature.

EFFECTS OF PRESSURE ON MISCELLANEOUS SUBSTANCES

125

The possible pressure range of such a measurement is not much more than 5,000 kg/cm 2 because of the onset of coagulation at higher pressures. The measurements were accordingly made with a recent form of apparatus15 which permits rapid determinations of the compression of liquids to 5,000 kg/cm 2 by a modified free piston technique. The material was two fresh unfertilized hen's eggs obtained from a local dealer. The whites were separated from the yolks by my wife by a well known feminine technique. The whites were homogenized by stirring and rubbing with the finger. Both whites and yolks were exhausted to a moderate vacuum to remove the bulk of the air without removing an appreciable amount of water. T A B L E VII COMPRESSION OF W A T E R , H E N ' S E G G Y O L K AND H E N ' S E G G W H I T E

AT 22.5°C. Pressure kg/cm'

-AV/V0

Water

Yolk

White

500

.0210

.0203

.0184

1,000

.0387

.0371

I,JOO 2,000

.0J44

•0347 .0493

.0086

.0519 .0650

2,JOO

.0814

.0769

.0623 .0742

3,000

.0930

.0877

.08 JI

3,joo 4,000

.1036

.0975

.0951

.1132

.1063

.1044

4,joo

.1222

.1143

.1130

J,000

.1308

.1215

.1210

The results are shown in Table VII. Water is included in the same table, since the chief interest in the results was the comparison with water. It is not to be assumed that the values thus given for water are the absolutely best values which are to replace values previously obtained with other and better apparatus. It is merely that the values here given for water were determined in the same apparatus and at the same time as those for the egg material, and thus offer the best comparison. It will be seen from the table that both white and yolk are some-

193—4513

126

BRIDGMAN

what less compressible than pure water, that up to 2,500 kg/cm 2 the white is less compressible than the yolk, and above 2,500 more compressible. A slight degree of coagulation was produced by 5,000, but not enough to affect the compressibility, the measurements with decreasing pressure being indistinguishable from those with increasing pressure. T h e yolk was stiffened so much that it would not pour out of the pressure vessel on inverting; the coagulation of the white was less, inasmuch as it did pour. Electrical Resistance during Plastic Extension under Pressure. It is not uncommon to compare the resistance of a wire in the virgin condition and after it has been permanently stretched; there are a few measurements of the changing resistance of a wire during the process of plastic extension at atmospheric pressure, but as far as I know the change of resistance has never been studied during the process of plastic extension in a medium under hydrostatic pressure. This might be expected to be of some interest because the voids formed in the metal by the process of plastic extension should be materially altered by pressure. A n apparatus was constructed for this sort of measurement and a few measurements made on copper and iron. Tension is applied to the wire by a simple modification of the apparatus used in studying the tensile properties of metals under pressure.16 Measurements of resistance are made with a potentiometer technique, using four terminals attached to the specimen. T h e length of the tension specimens was of the order of 3.5 cm and the diameter 1.7 mm. T h e diameter had to be made small to bring the resistance to a high enough value to be within the sensitiveness of the electrical measurements. A small diameter means a comparatively small tensile load and therefore high sensitivity in the load measuring device. This was a " grid " of the same general construction as the grid formerly used, but made as thin as possible to give sensitivity. This means a grid of high fragility, difficult to handle. It was fracture of the grid that finally terminated these measurements, which were not resumed because other more important work was waiting. T h e method demands the use of seven electrically insulated leads into the pressure chamber: three to measure the resistance of the specimen, three to measure the resistance of the grid which gives the tensile load, and one to measure the pressure with the manganin

193 — 4514

EFFECTS OF PRESSURE ON MISCELLANEOUS SUBSTANCES

I 27

gauge. A common ground, the apparatus itself, is used for all three measurements. T h e seven terminal plug is the same as that used previously 17 in measurements of compression to 100,000 kg/cm 2 . As in the previous measurements the apparatus is so arranged that during the first part of the stroke of the piston only hydrostatic pressure is built up. W h e n a prearranged pressure is reached, which can be controlled by varying the amount of liquid in the apparatus or by the use of suitable stops, the piston makes contact with the tension member. Further advance of the piston stretches the tension member as well as increasing the pressure. By suitably varying the pressure at which contact is made, the change of resistance during the stretching process may be studied at different mean pressures. T h e only measurement of the length of the specimen during tension was afforded by measurements of the position of the piston. This includes the contribution of the distortions in various parts of the apparatus; these were large enough to mask the changes of length of the wire itself during the elastic part of the range. During the plastic part of the extension, when the displacements are much larger, the piston displacements give a rather good picture of the elongation of the specimen itself. Measurements were made at room temperature on commercial copper and Armco iron. In addition to control measurements at atmospheric pressure, two specimens of copper were measured, one at a mean pressure of 4,500 kg/cm 2 and the other at a mean pressure of 17,000 kg/cm 2 , and one specimen of iron at a mean pressure of 22,000 kg/cm 2 . Plastic extension was purposely kept in the initial range, reaching the necking point as nearly as possible. Perceptible necking had not started in the copper specimens — in the iron it was just perceptible. Several ranges are to be distinguished. In the first place there is the range of pure hydrostatic pressure; here the question of interest is the comparison of the pressure coefficient of the wire in the virgin condition and after it has been plastically stretched. In the range during which tensile load is acting there is to be considered the effect of stretching on resistance during the initial elastic part of the cycle, then the effect of stretch on resistance during plastic extension, and finally the change of resistance during tensile unloading after maximum plastic stretch. In general, these three effects are functions of mean pressure.

128

BRIDGMAN

For both copper and iron the resistance decreases under hydrostatic pressure and increases with increase of length under tension. The following results were obtained: For copper. The pure pressure coefficient of resistance of the specimen pulled at a mean pressure of 4,500 kg/cm2 was 3 3 per cent less numerically immediately after it had been elongated permanently up to approximately the necking point than it was in the virgin condition. The specimen pulled at a mean pressure of 17,000 kg/cm2, on the other hand, showed no certain difference of pressure coefficient between the permanently elongated and virgin condition. There is an abrupt increase of the slope of the curve of resistance versus length on passing from the elastic region to the region of permanent set. At atmospheric pressure the ratio of the two slopes may be as great as 7. When pulling under pressure, the ratio of the two slopes becomes less, dropping to something of the order of 2. There was no certain effect of pressure on this ratio. This is as one would expect, the cavities opened up in the structure during plastic flow being less important when the flow occurs under pressure, because the pressure pushes the cavities together again. During release of tensile load after pulling to maximum elongation, there were prominent non-linear effects in the relation between resistance and load. The data were not sufficient to establish the nature of the effect of pressure on the relative tension coefficients of virgin and permanently stretched material. For Armco Iron. The pure pressure coefficient of resistance of iron in the virgin condition and permanently stretched to the necking point under a mean pressure of 22,000 kg/cm2 was practically the same. At atmospheric pressure the slope of the curve of resistance versus length increases by a factor of 2.7 on passing from the elastic to the plastic range. At 18,000 kg/cm2, the pressure at which plastic extension first occurred, the slope increases by a factor of 3.8 on passing from the elastic to the plastic range. This direction of change is the opposite of that found in copper, and not expected. At 27,000 kg/cm2, the pressure of maximum extension and the pressure at which release of the tensile load began, the slope of the curve of resistance against length on the beginning of release of tensile load is 5.3 times greater than on the virgin specimen. This

193 — 4516

EFFECTS OF PRESSURE ON MISCELLANEOUS SUBSTANCES

129

again is not in the expected direction. It is to be remarked, however, that there are marked deviations from linearity during release of tensile load after stretching to the necking point. It is to be regretted that fracture of the grid terminated these measurements. T h e difference of the effect in iron and copper suggests that there is material here for further investigation. I am indebted to M r . L . H . A b b o t and M r . Charles E . Chase for assistance with many of the experiments of this paper. L y m a n Laboratory of Physics, Harvard University, Cambridge, Mass.

REFERENCES

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.

P. W . Bridgman, Proc. Amer. Acad. 83, 1-22, 1954. Reference 1, pages 4-5. P. W . Bridgman, Proc. Amer. Acad. 82, 92, 1953. P. W . Bridgman, Proc. Amer. Acad. 77, 187-234, 1949. Reference 4, page 198. P. W . Bridgman, Proc. Amer. Acad. 72, 186, 1937. P. W . Bridgman, Proc. Amer. Acad. 82, 71, 1953. P. W . Bridgman, Proc. Amer. Acad. 56, 96, 1921. P. W . Bridgman, Jour. App. Phys. 24, 560-570, 1953. P. W . Bridgman, Jour. App. Phys. 18, 247, 1947. P. W . Bridgman and I. Simon, Jour. App. Phys. 24, 405-413, 1953. P. W . Bridgman, Proc. Amer. Acad. 81, 165-251, 1953. P. W . Bridgman, Proc. Amer. Acad. 76, 74, 1948. P. W . Bridgman, Rev. Mod. Phys. 18, 23, 1946. P. W . Bridgman, Proc. Amer. Acad. 77, 133, 1949. P. W . Bridgman. Studies in Large Plastic Flow and Fracture, McGraw Hill Book Company, New York, 1952. 17. P. W . Bridgman, Proc. Amer. Acad. 76, 55, 1948.

193 — 4517

SYNTHETIC

DIAMONDS

Their Recent Production was the Culmination of a Hundred Years of Attempts, some of which were Claimed to be Successful. An Account of these Efforts and the Thermodynamic Laws Defining the Problem. B Y P . W . BRIDGMAN

Now that the problem of synthesizing diamond has at last been solved, it is perhaps of interest to survey some of the highlights of the history of this long endeavor. The attempts to solve this glittering problem have revealed the whole human spectrum: those engaged in it have ranged from first-rate scientists to downright muckers and charlatans. There has been no little wishful thinking and self-deception, not unmixed with avarice. The project has generated an extensive literature in technical journals and many accounts in the popular press, based on rumors later proved unsubstantial. Many amateurs have done their own unpublished thinking about the subject. I suppose that over the last 25 years an average of two or three people a year have come into my office, offering to share the secret and the profit of making diamonds in return for my constructing the apparatus and reducing the idea to practice. The problem has got into the thriller literature, and I have often encountered the belief that the successful solver of this problem would be in danger of his life from the Diamond Syndicate. The beginning of a foundation for scientific attack on the problem was laid in 1797 when the Englishman Smithson Tennant showed that diamond is a form of elementary carbon. This may be proved by burning a pure diamond in an atmosphere of pure oxygen: it burns to carbon dioxide without any residue. The common crystalline form of carbon, of course, is graphite. Diamond has a density of 3.51 against 2.25 for graphite. Modern X-ray analysis has disclosed the structural differences between them. Diamond crystallizes in a cubic system, with each atom symmetrically surrounded by four others, all at the same distance and arranged at the corners of a regular tetrahedron. Graphite crystallizes in the hexagonal system: the atoms are arranged in layers; within each layer the pattern is not greatly different from the arrangement in diamond, but the layers are separated by comparatively large intervals. It is to this that graphite owes its lubricating properties, for the layers can slip over one another under the action of weak mechanical forces. Paradoxically, although diamond is very dense and is the hardest substance known, its atoms are not packed in the closest possible geometrical arrangement. It would be much denser if each atom were surrounded by 12 other equidistant atoms instead of only four. 194 — 4519

P. W.

BRJDGMAN

D I A M O N D S made in the General Electric Research Laboratory are enlarged about seven diameters. They were grown by H. P. Bovenkerk in the press depicted on page 4.

Willard Gibbs's work in thermodynamics at the turn of the 19th century made it possible to say theoretically under what conditions carbon might take the form of diamond in preference to graphite. Gibbs's studies made clear that graphite could not turn into diamond unless the "thermodynamic potential" of diamond was less than that of graphite. The thermodynamic potential plays for chemical reactions a role closely analogous to the ordinary potential of mechanics. Just as a weight falls from a higher to a lower position because its potential is less near the earth, so a chemical reaction tends to run in the direction in which its thermodynamic potential becomes less — or, expressing the rule more rigorously, a chemical reaction can run only in the direction in which its thermodynamic potential decreases. Gibbs showed how to calculate the thermodynamic potential in terms of the specific heat, the thermal expansion and other measurable properties of materials. It appeared probable at the time, and later it became a certainty, that the ther— 4520

SYNTHETIC

DIAMONDS

3

modynamic potential of graphite is lower than that of diamond — which is another way of saying that under ordinary conditions graphite is thermodynamically the more stable form. It follows that if any transformation is to take place at all at ordinary temperatures and pressures, it is from diamond to graphite. But there is a catch when it comes to using these considerations to predict what will happen. For although we can tell when a transformation may run, we cannot tell when it will run. Although diamond has thermodynamic permission to transform itself into graphite under ordinary conditions, it has no mandate to do so. (Thermodynamic stability is not the same as mechanical stability.) Everyone knows that diamonds do not spontaneously change to graphite, and my wife has worn her engagement ring these many years with no solicitude on that score. The mathematical expression for the thermodynamic potential showed that if the pressure could be raised high enough, graphite would receive thermodynamic permission to transform, even at ordinary temperatures, to diamond. This pressure was calculated to be about 20,000 atmospheres. But here again permission does not mean that the reaction will inevitably run. Just as we cannot say that graphite will change to diamond if only it has thermodynamic permission, so also we cannot say that when a carbon compound decomposes, or when carbon is precipitated from a solution, the form of carbon that separates will be the form thermodynamically preferred. We know from the thermodynamic potential that graphite is ordinarily the preferred form, but this does not enable us to say that the actual precipitate will be graphite and not diamond. As a matter of fact, there are many known instances in which an element's unstable form, corresponding to diamond, separates from a solidifying liquid or solution in preference to the more stable form. The possibility that diamond may be formed as an unstable phase under conditions where "nascent" (uncombined) carbon is liberated makes it impossible to rule out the chance of an accidental success. Thus I could never say to the hopeful amateur who walked into my office: "Your process certainly will not work." I could only say this when he proposed to transform graphite directly into diamond under thermodynamically impossible conditions. The aforementioned possibility has been one of the bogeys in the whole situation. Many geologists and mineralogists have been of the opinion that diamond is formed in nature under unstable conditions, which would mean that it might be a matter of anybody's lucky guess to find the proper conditions. None of the sophistications we have considered entered into the early attempts to make diamonds. Many of those who made the attempt were guided simply by the fact that diamond is more dense than graphite, which naturally suggested the possibility that it might be formed by subjecting carbon to great pressure. There were then no means of producing anything like the 20,000 atmospheres later calculated to be necessary, but claims of success were numerous nonetheless. One of the earliest and still most discussed attempts was by a Scotsman, J. B. Hannay, in 1880. He mixed hydrocarbons, "bone oil" and lithium, sealed the mixture in a wrought-iron tube and heated it to redness in a forge. All but three of 80 tubes exploded. (The pressure in the tubes could not have been more than 194 — 4521

P. W.

BRIDGMAN

H Y D R A U L I C P R E S S in which the diamonds were grown is capable of exerting a force of 1,000 tons. The pressure chambers are located below the floor level (bottom).

194 — 4522

SYNTHETIC

DIAMONDS

5

one or two thousand atmospheres.) In the residue of the unexploded tubes it was said that diamonds of density 3.5 were found. The claim was accepted at its face value and reported in the London Times by N. Story-Maskelyne. Subsequent attempts by a number of experimenters failed, however, to reproduce Hannay's results. The matter was reopened in 1943 by the discovery in a forgotten corner of the British Museum of a small exhibit labeled "Hannay's Diamonds." These were analyzed with X-rays by F. A. Bannister and Kathleen Lonsdale, and found to be certainly diamonds, and of a somewhat rare type at that. On the theory that it was unlikely that diamonds fraudulently inserted would be of this rare type, Bannister and Mrs. Lonsdale argued that Hannay's claim was probably genuine. But there was also contrary evidence, in particular, as pointed out by Lord Rayleigh, some known instances of bad faith on Hannay's part. It seems to be the present consensus that Hannay was a fraud. Mrs. Lonsdale recently told me that she now also inclines to that view. Perhaps the best known experiments of all are those of the Frenchman Henri Moissan, made in the 1890s when he was perfecting the electric furnace. Cast iron is known to dissolve fairly large quantities of carbon. Moissan melted a mixture of iron and graphite in his electric furnace and plunged the white-hot crucible into water. The iron of course solidified first on the outside. The inner core, on solidifying later, was supposed to expand against the rigid outer shell, thus producing a tremendous internal pressure, and the pressure was further enhanced by the contraction of the external shell as it cooled. (It is now known that the pressure produced could not have been more than a few thousand atmospheres, because, in the first place, hot cast iron is not strong enough to withstand greater pressures, and, in the second place, cast iron actually contracts when it solidifies instead of expanding as was then erroneously supposed.) After the crucible was cooled to room temperature, its contents were dissolved in acids and given other appropriate chemical treatment. In the end there was a small residue which Moissan reported to be diamond. His experiments have been repeated a number of times, and a number of times with announced positive results. One attempt that seemed particularly convincing was by 0. Ruff of Germany. In 1917 he made an elaborate investigation, tiying all the methods of synthesis that had been reported successful. All gave negative results except the method of Moissan: according to Ruff's report this method did yield some diamonds. Later, however, he changed his opinion, and in a communication published as a footnote in a paper by other authors he stated that he believed his own supposed diamonds were not genuine. It must be remembered that it is an extraordinarily difficult matter to establish the true nature of material obtained in such small quantities as has been the case in most of the supposed synthetic diamonds. Another celebrated repetition of Moissan's work was by Sir Charles Parsons, the shipbuilder who invented the steam turbine. The problem of diamond synthesis was Parsons' hobby; on it he spent hundreds of thousands of pounds. He had at his command the enormous hydraulic presses of his shipbuilding establishment, and he tried nearly every conceivable method feasible at that time. He 194 — 4523

P. W.

BRIDGMAN

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EFFECTS OF PRESSURE ON BINARY ALLOYS

*37

is a falling off, not regular in fine detail. T h e shearing strengths vary considerably, but in general the shearing strength diminishes with the addition of silicon, not in the expected direction. Iron — Silicon. Measurements were made on six compositions, ranging from 0.39 to 5.75 A t per cent Si. The metallurgical phase diagram shows only a homogeneous solid solution in this range, although at higher concentrations the diagram becomes exceedingly complicated. As already mentioned, I owe the alloys to Dr. C. A . Domenicali who prepared them at the Franklin Institute. T h e y were melted in alundum crucibles in an induction furnace in a vacuum of less than 5 μ. T h e y were then homogenized six hours at 950° C in a vacuum varying from 3 to 5 μ. T h e y were then cold rolled and swaged to wires of approximately 0.040 inch diameter, in which form they were supplied to me. T h e iron from which these alloys were prepared was 99.93% pure iron from Vacuum Metals Corporation ( " Ferrovac-R "), and the silicon was from DuPont, as already described. For my measurements of resistance short lengths of the wire were rolled down to approximately 0.002 inch thickness, with several annealings at red heat. During this rolling several of the specimens broke up into longitudinal filaments, indicating seams in the wire as furnished. H o w ever, in all cases homogeneous appearing strips were obtainable large enough for the resistance specimens, and there is no reason to fear any lack of homogeneity in the measured material. Two only of the wires as received were sufficiently perfect geometrically to justify direct measurements of specific resistance; these were compositions 0.78 and 1.95 A t % . T h e specific resistances of these compositions given in Table II should be somewhat more accurate than the others, which were measured on strips of only 0.002 inch thickness, permitting appreciable error. T h e compression measurements were made on 0.75 inch lengths of wire selected as free from imperfections as possible; there were nevertheless sometimes obvious surface imperfections. A l l compression specimens were annealed and subjected to a preliminary pressure seasoning to 30,000. T h e resistance measurements on pure iron given in Table II were not made on the same material as that from which the alloys were prepared, but on material of presumptively very high purity, although no chemical analysis was available. This material I owe

196 — 4539

i38

BRIDGMAN

to the General Electric Company. It had been prepared by five zone melting treatments from iron originally obtained from the National Research Corporation, which showed an analysis of 0.004% C and 0.004% O· Resistance measurements under pressure on this iron agreed gratifyingly well with my previously published values for pure iron.4 The temperature coefficient between room temperature and o° C is slightly higher for this new G. E. iron, indicating presumptively higher purity. No attempt was made to redetermine the compression of this iron. Compression is not sensitive to impurity, and I had previously done a very elaborate job on the compression of iron, with hundreds of measurements, this being basic to all my other compressibilities. The compression of pure iron listed in Table II is taken directly from my previous work.5 The numerical results for resistance and compression are given in Table II. No shearing strengths are given, the material being too hard. The general behavior is similar to that in the coppersilicon series. There are no discontinuities or cusps — the regularity of the readings is about the same. The addition of silicon markedly decreases the effect of pressure on resistance. It is perhaps to be anticipated that with greater concentrations the sign of the pressure coefficient may reverse, resistance increasing with pressure instead of decreasing. The compression decreases with increasing silicon by much less than does the resistance, but still the decrease is well beyond the limits of error. Nickel — Silicon. The metallurgical phase diagrams indicate homogeneous solid solutions of silicon in nickel up to about 10 At per cent silicon, and beyond that, extreme complication. Measurements were made here on five concentrations, varying from 0.08 to 5.8 atomic per cent silicon. I am again indebted for my material to Dr. C. A. Domenicali, who prepared the alloys at the Franklin Institute. They were made in 100 gram ingots by melting in an induction furnace in zirconium oxide crucibles at a vacuum of less than 5 μ. They were then homogenized for 48 hours at 118o° C in a vacuum lower than 1 μ and then cold rolled and swaged to bars approximately 0.125 * nc h i*1 diameter, in which form they were supplied to me. For the compression measurements pieces 0.75 inch long were cut from these bars without reduction of diameter; they were subjected to a preliminary pressure seasoning

196 — 4540

EFFECTS OF PRESSURE ON BINARY ALLOYS

*39

to 30,000. The resistance specimens were rolled to a thickness of 0.002 inch with annealings during and after rolling. The nickel from which these alloys were made was 99.98% nickel from the International Nickel Company, and the measurements of the effect of pressure on resistance shown in Table III were made on this nickel. The compression measurements of Table III were, however, made on nickel from a different batch, that supplied by Professor Pugh as one of his copper-nickel series. The source of this nickel was also the International Nickel Com-

T A B L E III N I C K E L — SILICON SYSTEM 100 Ni 6.69 ο X 10-« Temperature .00611 Coefficient

09.92 Ni .08 Si

99.6 Ni 0.4 Si

7.38

8.30

.00600

5,000 10,000 15,000 20,000 25,000 30,000 (a) (b) (c) (d)

I 3.8

.00528

Pressure kg/cm* 0 J,000 10,000 15,000 20,000 2 j,000 30,000 40,000 50,000 60,000 70,000 80,000 90,000 100,000

98.0 Ni 2.0 Si

.00334

96.1 Ni 3.9 Si 17.7 .00276

94.2 Ni 5.8 Si 21.1 .ΟΟ256

Rp/Ro 1.0000 .9902 .9807 •971J .9626 •9J38 •945* .930 .917 .904 .893 .883 .873 .863 .00270 .00524 •00795(a) .01065 .01317 .01560

1.0000 .9903 .9811 .9721 .9632

•919 .907 .897 .888 .879 .870

.897 .887 .878 .870

1.0000 .9930 .9863 .9800 .9740 .9681 .9625 .952 .942 .932 .924 .916 .910 .903

.00256 •00515(b) .00786 .01054 .01299 .01535

- AV/Vo .00272 .00544 .00810(c) .01064 .01313 .01558

.00266 .00264 .00524 .00528 .00784(e) .00784 .01037 .01043 .01301 (d) .01300 .01566 .01550

•9549 .9466 .932

Cusp at 10,300 Cusp at 8,200; - AV/Vo =.00416 Cusp at is 000 Cusp at 21,700; — AV/Vo = .01120

1.0000 .9908 .9819 •9733 .9651 .9569 .9492 •934 .920 .908

1.0000

1 .OOOO

•9994 .9890 •9837 .9787 .9740 .9694 .962

•9947 .9898 .9850 .9804 .9760 .9718 .965

•955 .950

•957 .950

•944 •939 •935 .930

•944 .938 •933 .928 •00255(0 .00528 .00793 .01048(g) .01300 .01543

(e) Cusp at 12,000; - AV/Vo =.00625 (f) Cusp at 4,700; - AV/Vo =.00239 (g) Cusp at 16,500; - AV/Vo =.00872

196 —

454}

140

BRIDGMAN

pany, stated by them to be their purest. The presumption would be that it also was of 99.98% purity, but Professor Pugh stated in a letter that " apparently it is of no better than 99.9 purity." The results for resistance and compression are shown in Table III; the strength was too high for shearing measurements. Previous measurements on pure nickel have shown that its behavior is anomalous. The anomaly is most manifest on the compression, where it displays itself as a cusp, the compressibility being greater at pressures above the cusp, contrary to what might be expected. The occurrence of the anomaly is not clean cut; the pressure at which it occurs and the magnitude of the discontinuity in the slope may be altered by heating or by subjecting to pressure. In previous measurements on a single crystal of presumably high purity,® obtained from Dr. Bozorth of the Bell Telephone Laboratory, the location of the cusp finally settled down to 10,500 kg/cm 2 with an upward break in compressibility of 14.5 per cent. Professor Pugh's nickel, after a single preliminary pressure seasoning to 30,000, also showed a cusp in compression at 10,300, with an increase of compressibility of 6.7 per cent. The average compressibility over the 30,000 range of Professor Pugh's nickel was about 3 per cent greater than that of Dr. Bozorth's. In view of the similarity of the results obtained with these two specimens of nickel and the sensitiveness of the results to slight variations in the treatment of the material, compressibility measurements were not repeated on the present nickel of Dr. Domenicali. The compressions of pure nickel shown in Table III are for the material of Professor Pugh. N o anomaly was manifest in the resistance of the present material from Dr. Domenicali. However, another specimen7 has shown an abrupt numerical decrease of the slope of the curve of resistance versus pressure at 10,000 kg/cm 2 amounting to about 5 per cent of the slope. The present resistance measurements to 30,000 showed a slight hysteresis, amounting at the maximum to a difference between increasing and decreasing readings of one per cent of the change of resistance at 30,000. It would constitute a research in itself to reduce the results on " pure " nickel to complete consistency and reproducibility. The behavior of the silicon alloys was similar to that of the pure metal. All the compression measurements showed cusps, but

EFFECTS OF PRESSURE ON BINARY ALLOYS

141

with no consistency in the location of the cusp or in the magnitude of the discontinuity of slope. The behavior of two compositions, 0.08 and 5.8 Si, was best represented by two cusps. The capricious behavior of these anomalies is not surprising in view of the erratic behavior of a single specimen of pure nickel in response to repeated heat treatment and pressure seasoning. The resistances of the alloys, on the other hand, showed no evidence of any cusp. The resistances showed a rather consistent small hysteresis, the width of the hysteresis loop being of the general order of three or four per cent of the maximum change under 30,000. Except for the hysteresis, the resistances were as smooth as usual in the pressure. Because of the nature of the apparatus the hysteresis in resistance in the range above 30,000 could not be determined. Superposed on the anomalies contributed by the nickel, an inspection of Table III discloses the expected effect of the addition of silicon in that the arithmetical magnitude of the pressure coefficient of resistance diminishes with addition of silicon. The effect of silicon on compression is more difficult to disentangle and more obscure — perhaps on the whole the compression tends to diminish slightly with added silicon. Copper — Silver. This is the first of four series of alloys which I owe to Dr. T . J. Rowland, the others of the series being Al — Mg, A l — Zn, and Cu — Zn. These alloys were prepared in connection with the thesis work of Dr. Rowland under the direction of Professor N. Bloembergen at Harvard on the general subject of nuclear magnetic resonance in metals and alloys.8 The metallurgical phase diagram shows negligible solubility of silver in copper or of copper in silver at room temperature. It is to be expected, therefore, that at room temperature the alloys will be mechanical mixtures of practically pure copper and pure silver. The silver from which the alloys were prepared is described simply as " c.p.". The copper showed the following "typical analysis." A g 0.0008; As 0.0002; Bi Tr; Fe 0.001; Mg Nil; Ni 0.0006; Pb 0.0002; Sb 0.0002; Si 0.00025; Sn 0.0003; T e 0.0005; Zn Nil; and traces of A u and Cr. N o P, S or Se. The total purity is thus of the order of 99.99. Since I had available 99.999 material, the values for " pure " copper given in the table were obtained from this rather than from the material from which the alloys had been actually prepared.

142

BRIDGMAN

The material was furnished me in the form of slugs approximately ι cm in diameter and 2 cm long. From these slugs small pieces were cut for the various measurements. The resistance specimens were rolled to 0.002 inch thickness, with several annealings at red heat during rolling and a final annealing to red heat in a stream of helium followed by immediate exposure to room temperature. The resistance measurements were made without pressure seasoning. The compressibility specimens were swaged, with annealings at red heat, and subjected to a preliminary pressure seasoning at 30,000. The results are shown in Table I V . The resistance measurements to 30,000 on the 0.5 and 1.0 compositions showed no change of zero on the first application of pressure nor significant hysteresis. The 4.0 composition showed a permanent change of zero of about 2 per cent of the total change of resistance under 30,000, and a hysteresis loop of 4 per cent maximum width; both these effects are well beyond the limits of error. In the table the mean of the resistances with increasing and decreasing pressure are given for the 4 per cent composition. The compression measurements indicated nothing unusual, there being, if anything, less than the normal amount of scatter in the individual readings, with the exception of the ι per cent composition. Here it is not impossible that there is a cusp with very slight drop of compressibility in the neighborhood of 20,000. The effect is, however, very uncertain, and in the table the mean results with increasing and decreasing pressure have been smoothed over any possible cusp. The arithmetic magnitude of the pressure coefficient of resistance diminishes with increasing silver content, just as if we were dealing with a solution. A change in the opposite direction is to be expected by the simple rule of addition, since the pressure coefficient of pure silver is greater by a factor of 1.73 (at 30,000) than that of pure copper. The pressure coefficient of the 4 per cent silver composition is as much as 20 per cent less than that of pure copper. The compressibility increases significantly with increasing silver content. This is what would be expected from the additive rule of mixtures, silver being more compressible than copper by about 30 per cent. However, the increase of compressibility on passing from the 0.5 to the 4.0 composition is markedly greater than would be expected from such a rule of mixtures, being 4.5

196 — 4544

EFFECTS OF PRESSURE ON BINARY ALLOYS

I43

per cent. (In this comparison the values for pure copper are not strictly comparable, since they were obtained from different material.) The shearing strength shows no consistent nor certain variation with composition. Silver — Palladium. The phase diagram shows complete mutual solubility over the entire range of composition.

TABLE IV COPPER — SILVER SYSTEM

IOO Cu Ρ X 10« Temperature Coefficient Pressure kg/cm»

I.69

Ο 5,000 ΙΟ,ΟΟΟ I J,000 20,000 2 J,OOO 30,000 40,000 JO,000 60,000 70,000 80,000 90,000 100,000

1.00000 .99054 .98195

.ΟΟ436

99.5

99.0 Cu 1.0 Ag

96.0 Cu 4.0 Ag

1.62

1.87

2.15

Cu 0.5 Ag

.00404

.00391

.00237

Rp/Ro

.9737 .9656 •9Ϊ79 .9506 •939 .928 .919 .911 •903 .896 .890

ι .0000 •9915 •9835 •9700 .9687 .9617 •9549 •943 •932 .922 .914 .905 .898 .891

1.0000 .9919 .9842 •9768 .9697 .9628 .9562 .946 •937 .930 .923 .917 .911 .906

ι .0000 •9927 .9859 .9792 .9729 .9669 .9612 •953 •945 •939 •933 .927 .923 •9'9

- AV/Vo J,OOO 10,000 I J,OOO 20,000 2J,000 30,000 20,000 40,000 60,000 80,000 100,000

.00387 .00759 .01117 .01465 .01800 .02119 1,600 3.420 5,090 6,410 7-Jio

.00366 .00727 .01079 .01420 .01757 .02092

.00373 .00735 .01090 .01440 .01778 .02113

Shearing Strength, kg/cm2 1,420 1,510 3.'4° 4,700 6,340

3.240 5,060 6,900

.00389 .00756 .01120 .01472 .01817 .02185 1,420 2,810 4,000 5,200

BRIDGMAN

144

TABLE

V

SILVER — PALLADIUM SYSTEM

ioo Ag ο χ i8 .9892 .9867 .9844 .980

•99J4 •9945 .9938 •993 .992

.835 .823 .8ij .806

•977 .976 •974 •973

•99' .991 .990 .990 .989

.00473 .00938 .01385 .01820 .02236 .02619

.00445 .00875 .01295 .01707 .02112 .02501

.0041 2 .00815 .01212 .01602 .01978 .02345

.985 .983 .981 .980 .978 •977 .976 - AV/Vo .00386 .00764 .01135 .01501 .01858 .02207

•975 .972 .969 .965 .963 .960 .00376 .00741 .01099 .01450 .01796 .02132

1.0000 .9967 .9940 .9913 .9886 , 9 8J8 .9832 •979 •975 .971 .968 .96J .963 .961

.0036 j .00716 .01069 .01443 .01744 .02071

ι .0000 •997 J .99 j ι .9927 .9906 .9884 .9863 .983 .981 .978 .976 •974 •973 .972 .00341 .0067.0100 .0132 .0164 .0195

Shearing Strength, kg/cm» 20,000 40,000 60,000 80,000 100,000

196 — 4546

1,120 2,050 2,810 3.7JO

1.530 2,960 4,300 5,810 7,33°

1.77° 3.240 4.490 5,900 7.320

1,980 3.520 4,960 6,700 8,270

1,890 3,380 5.310 7,800

i,6JO 3,300 4,620 6,690

1,840 3,500 4,800 J.980

EFFECTS OF PRESSURE ON BINARY ALLOYS

T A B L E

V —

145

Continued

SILVER — P A L L A D I U M S Y S T E M

44·2 Ag 55-8 Pd 38.5

39-3 Ag Pd

60.7

47.0

.00006

.00006

34-5 Ag Pd

65.5

48.4

29-5 Ag Pd

70.5

46.8

•OOOI7

.00033

I4-S Ag Pd

85.5

28.4 .00110

100

Pd

I 1.4J .00368

Pressure kg/cm2

Rp/Ro 1.0000

1.0000

1.0000

.9977

•9974 .9950

.9971

•99ΪΪ •9934 .9914 .9893 .9874 .984 .980 .978 •97J .972 .970 .968

•9926 .9903 .9880 •9859 .982 •979 •977 •97J •973 .971 •970

•9942 .9914 .9886 .9859 •9833 •979 •975 .972 .969 .966 .964 .962

ι .0000 .9964 .9931 .9898 .9866 .9835 .9806 .976 •973 .970 .968 .965 .963 .96·

pXio" Temperature Coefficient

1.0000 •9947 .9896 .9846 •9799 •97J2 .9709 .963 .956 .951

1.0000 .9894 •9793 .9697 .9604 •9517 •943' .926 .910

•935 .930

•895 .882 .870 .859 .848

.00293 .00583 .00866(a) .01129 .01384 .01637

.00267 .00517 .00761 (b) .01015 •01273 .01522

•945 •940

0 5,000 10,000 15,000 20,000 25,000 30,000 40,000 50,000 60,000 70,000 80,000 90,000 100,000

- AV/Vo .00343 .0067 J .01002 .01322 .01637 .01940

.00332 .00657 •00973 .01284 .01586

.00322

.01877

.01826

.00639 .00946 .01248 .01542

.00307 .00610 .00907 .01 201 .01487 .01769

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

Shearing Strength, kg/cm2 i,77o 3.400 4,670 j,900

(a) Cusp at 15,000 (b) Cusp at 16,500

2,240 3.900 4,900 6,250

2,240 4,020 5,200 6,670

2,200 4,000 5,000 6,410

1,980 3,760 4,990 6,350

1,650 3,110 4,3io 5,480

20,000 40,000 60,000 80,000 100,000

146

BRIDGMAN

In the following, measurements were made on eleven compositions distributed over the entire range, which I owe to Mr. Α. I. Schindler, who used them in the laboratory of Professor Ε. M. Pugh at Carnegie Institute of Technology for measurements of the Hall coefficient.® This work has not yet been published in detail. The alloys were originally prepared by Baker and Company of Newark to certain nominal compositions. The exact compositions were later determined at the Naval Research Laboratory, to which in the meantime Mr. Schindler had moved, and it is these compositions, changed from weight to atomic per cents, which are given in Table V. A spectroscopic analysis was made of the pure components and the various alloys at the Naval Research Laboratory. The principal impurities in the palladium (of the general order of 0.1 per cent each) were Si, Rh and Al, and the principal impurity in the silver was Cu. The total silver content of the pure silver, determined by wet analysis, was 99.75 per cent. The material was supplied in the form of small slabs, 1 cm square and ι mm thick. The resistance specimens were prepared by rolling to about 0.002 inch thickness, with annealing in the air at red heat. The compression specimens were rods approximately 0.75 inch long and 0.06 inch diameter, prepared by forging from pieces approximately 0.40 X 0.22 X 0.040 inch. The first few stages of the forging process were at a red heat, followed by cold hammering with frequent anneals at red heat. The rods were turned to final dimensions and subjected to preliminary pressure seasoning to 30,000. The resistance measurements went smoothly, with no permanent change of zero after the first application of pressure, and no hysteresis to nearly the sensitivity of the readings, although slight hysteresis was usually detectible. The general behavior is as to be expected; that is, the pressure effect on resistance is smaller in the middle of the concentration range, rising to the pure metals at either end. The effect is far from symmetrical in the composition, however, reaching its maximum at 20 per cent Pd. The sign of the pressure effect is negative throughout, as is normal. At the composition 20 Pd the decrease of resistance under 30,000 is only approximately 1 per cent. In the table the resistances given for the pure metals between 30,000 and 100,000 were not redetermined

E F F E C T S OF P R E S S U R E ON B I N A R Y ALLOYS

147

on this particular material. The measurements to 30,000 for the present material were in such close agreement with previous measurements10 on other material that it did not seem worth while to redetermine the resistance for the present material in the range 30,000 to 100,000, but previous measurements to 100,000 were used, applying a slight correction. This correction was plus 0.004 on the relative resistance of silver uniformly over the 30,000 — 100,000 range, and similarly plus 0.001 for palladium. The compressions, except for one composition, presented no incident, the readings being smooth with no more than the normal scatter and with slight hysteresis, which, however, was no more than found with other materials and may be due to the apparatus. The compressions given in Table V for the pure metals are values previously obtained on other material.2 The effect of impurity on compression being slight it was thought to be not worth while to redetermine the compressions. Previous measurements of the compression of palladium had disclosed a slight cusp at 16,500. The single exceptional composition referred to above was 14.5 Ag — 85.5 Pd, the composition nearest to pure palladium. This also showed a very slight cusp at 15,000; this cusp was independently found, I having forgotten that pure palladium had a cusp. There was no cusp at higher concentrations of silver, so that the probability is high that the effect is genuine. Both cusps are so small that this independent confirmation is welcome. In general the shearing strength is greater for intermediate compositions than for the pure metals, as seems natural. Like the resistance, the effect is not symmetrical in the composition, but the maximum shearing strength comes at 35 Pd, against 20 Pd for the maximum effect on resistance. Aluminum — Copper. The metallurgical phase diagram shows a range of homogeneous solubility of aluminum in copper up to about 20 At % Al. In the following, two compositions, 4.81 and 9.98 At % Al, were investigated. These I owe to Professor Charles S. Smith of the Case Institute of Technology. The alloys were prepared in connection with Professor Smith's program of determining the effect of dilute alloying on the elastic constants of single crystals.11 I have no specific information as to the materials from which these alloys were formed. The specimens were provided in the form of discs about 2.5 mm thick sliced from a cast

BRIDGMAN

TABLE

VI

Copper — A l u m i n u m

100 Cu Density 0 X 10«

95.19 Cu 4.81 AI

8.504 7.65

1.69

Temperature Coefficient

.00436

Pressure kg/cm ! ο J.OOO 10,000

15,000

20,000 2 J,OOO

30,000 40,000 JO,000 60,000

70,000 80,000 90,000

100,000

System

.001

90.02 Cu 9.98 Al

8.199 10.40 10

.OOO9 2

Rp/Ro

1.00000 .99054 .98195 •9737 .9656 •9579 .9506 •939 .928 .919 .911 .903 .896 .890

ι .0000

1.0000

•997S •9951 •992 7 .9905 .9885 .9866 .984 .982 .980 .978

.9985

•977 .976 •975

•997' .9958 •9947 .9936 •992 7 .991 .990 .989 .988 .987 .986 .986

- AV/Vo J,000

10,000 I J,000

20,000 25,000

30,000

.00387 .00759 .01 I I 7 .01465 .0 I 800

.00374 .00738

f.01769

.021 19

I.01794 .02 1 2 I

.01094

.01435

.00371 .00735 .01087 .01431 J .01767 \.oi8i4 .02138

Shearing Strength, kg/cm*

20,000 40,000 60,000 80,000

1,600 3.420 5,090 6,410

1,250 2,270 3.310 4,370

1,240 2,390 3,480 4.570

E F F E C T S OF PRESSURE ON B I N A R Y ALLOYS

I49

ingot 2 cm in diameter. The resistance specimens were formed as usual by rolling to a thickness of approximately 0.002 inch, and annealing. Resistance measurements made to 30,000 with no pressure seasoning showed no permanent change of zero and only insignificant hysteresis, the width of the loop being 2 or 3 per cent of the maximum pressure effect. No episode was shown by the resistance measurements. The compression specimens were formed by hammering, annealing, turning to a length of approximately 0.75 inch and diameter of 0.08 inch, and seasoning by a preliminary application of 30,000. The compression measurements on both compositions showed a reversible discontinuity, indicating a phase change, at about 25,000 kg/cm2. The magnitude of the discontinuity was about twice as great for the 9.98 composition as for 4.81. In speculating as to the probable nature of this phase change significance must be attached to the fact that doubling the amount of dissolved aluminum leaves the pressure of the discontinuity approximately unaltered, but doubles the magnitude of the discontinuity. At low pressures the effect of the addition of aluminum on compressibility as shown in Table VI is uncertain and in any event slight. At higher pressures and below the transition the compressibility of the alloys seems definitely less than that of pure copper. Professor Smith has inferred by calculations from his dynamically determined elastic constants that at atmospheric pressure the compressibility of the alloys would be greater than that of pure copper. The effect of aluminum in solution on the pressure effect on resistance is what we have come to regard as " normal," namely a decrease of numerical magnitude of the effect of pressure on resistance. The pressure coefficient of resistance is negative throughout; the effect of dissolved aluminum is only slight. Shearing strength probably on the whole decreases on addition of aluminum. Aluminum — Magnesium. The phase diagram indicates that at room temperature magnesium is soluble in aluminum up to something of the order of 2 At %, and that beyond this the system consists of a mechanical mixture with the intermetallic compound Al 3 Mg 2 . Six alloys were measured at the aluminum rich end of the series, ranging from 0.64 to 14.3 At % Mg. I owe these to Dr. T. J .

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EFFECTS OF PRESSURE ON BINARY ALLOYS

15 I

Rowland, w h o prepared them as part of the program already described under the silver-copper series. T h e alloys were made from commercial " pure " aluminum of 99.99 purity, and commercial " pure " magnesium, also of 99.99 purity. T h e y were cast into graphite molds, and several were given a forty-hour soak at 450 T h e resistance specimens were rolled as usual to a thickness of 0.002 inch, annealed at 440° to 450° and cooled in air. T h e compression specimens were cut and turned, without swaging or hammering, to a length of 0.50 inch and diameter of 0.136 inch and pressure seasoned b y a preliminary exposure to 30,000. T h e experimental results are shown in Table VII. T h e resistance parameters for pure aluminum were redetermined on this present aluminum, since its purity, 99.99, is somewhat higher than that of any aluminum on which I have previously published values.12 M y best previous aluminum had an analysis of 99.966. T h e higher purity of the present aluminum is attested by its higher temperature coefficient of resistance and numerically larger pressure coefficient of resistance. T h e fractional decrement of resistance under 30,000 of the present material was 0.1120 against 0.1080 found formerly. T h e compressions of " pure " aluminum given in the table are, however, for the former 99.966 material, compressions not being sensitive to impurity. T h e measurements both for resistance and compression on the alloys went unusually smoothly, without appreciable alterations of zero or hysteresis. Both these effects would be anticipated if pressure were effective in changing the solubility limits, something to be looked for particularly at the lower concentrations. T h e effect of adding magnesium to aluminum is to diminish the effect of pressure on resistance, as is to be expected. T h e diminution continues right through the range of concentration studied here. T h e compression, on the other hand, is at first diminished b y the addition of magnesium but there is a reversal between 1 and 3 per cent. T h e shearing strength is not greatly affected b y the addition of magnesium, with, however, a definite tendency to increase, as might be expected. Aluminum — Ζ inc. Eight compositions at the aluminum rich end of the series, ranging up to 15.4 A t % zinc, were investigated. For this range of compositions the phase diagram shows, at higher temperatures, a homogeneous solid solution in the lattice of pure

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1,720 2,740 3,920 5,690

1,530 2,830 4,090 6,060

1,790 3,180 4,400 5,75θ

1.730

3,260 4.940

6,500

EFFECTS OF PRESSURE ON BINARY ALLOYS

189

upward curvature of the curves for low concentrations and the downward curvature of the curves for high concentrations. The compressibility measurements of the three lower concentrations showed no certain feature greater than the experimental irregularity of the individual points, which was somewhat greater than usual, except for a definite hysteresis between increasing and decreasing pressure. This was greater than normal, rising to a maximum of ι per cent of the total change of length for the 13.01 comTABLE V GOLD — PALLADIUM S Y S T E M Au 100 fXio· Temperature Coefficient Pressure kg/cm2 0 J,000 10,000 I J.OOO 20,000 25,000 30,000 40,000 50,000 60,000 70,000 80,000 90,000 100,000

2.19 .00391

1.0000 0.9849 0.9707 0.9571 0.9441 0.9316 0.9194 0.896 0.874 0.855 0.840 0.829 0.821 0.816

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

.00281 .00558 .008 31 .01101 .01367

30,000

.01626

20,000 40,000 60,000 80,000

i.3J° 2,760 4.320 6,420

Au 9g.19 Pd 0.81

Au 98.18 Pd 1.82

Au 96.99 Pd 3.0t

Au 96.01 Pd 3-99

2.44

2.80

3-25

3-59

.00339

ι .0000 0.9871 0.9748 0.9631 0.9519 0.9412 0.9310 0.913 0.897 0.884 0.872 0.862 0.853 0.846 .00294 .00594 .00870 .01149 .01425I .01422 J .01693

.00291 Rp/Ro ι .0000 0.9885 Q-9775 0.9670 0.9569 0.9472 0.9378 0.923 0.910 0.899 0.888 0.879 0.871 0.864

.00245

ι .0000 0.9895 0.9794 0.9698 0.9606 0-9SI9 0.9435 0.930 0.918 0.907 0.898 0.891 0.885 0.879

- AV/Vo .00289 .00575 .00856 .01134 .01410

.00288 .00573 .00852 .01131 .01406

.01681

.01676

Shearing Strength, kg/cma 1,630 1,680 3,000 2,930 4,300 4,010 5,920 J.3IO

I,600 2,860 4,200 6,020

.00224

ι .0000 0.9900 0.9804 0.9713 0.9625 0.9542 0.9462 0.934 0.924 0.915 0.907 0.901 0.895 0.890 .00288 .00572 .00856 .01132 .01412 .01406 .01675 1,580 2,670 3,820 5.290

190

BRIDGMAN

position. T h e highest concentration, 18.64% Mn, showed a well defined reversible discontinuity of magnitude more than ten times the deviation of any single reading from a smooth curve, and more than three times the hysteresis between ascending and descending readings. This hysteresis was exhibited only at pressures below the transition, and doubtless corresponds to the hysteresis at the lower concentrations over the entire pressure range. It would seem that there is some connection between the transition found here and the possible ordering or phase change remarked by Otter for this composition at temperatures around 300° to 4000 at atmospheric pressure. T h e general effect of adding manganese to gold is to increase the compressibility. T h e shearing strength of the alloys is, at low pressures, greater than that of pure gold, and at the highest pressures not greatly different on the whole, although it is irregular. W i t h increasing concentration of manganese there is a progressive change of shape of the shearing curve, the upward curvature characteristic of pure gold becoming less and eventually vanishing for the highest concentration, for which the curve is sensibly linear over its entire length. Gold — Palladium. Four compositions were available from Otter, ranging up to 3.99 A t % Pd. Hansen and Metals Handbook agree in showing a homogeneous solid solution over the entire composition range. T h e results are shown in Table V . Resistance decreases smoothly with pressure, without episode, over the entire range of pressure and composition. The magnitude of the decrease decreases with increasing palladium content. T h e compressibility of two of the compositions, 0.81 and 3.99 Pd, showed disturbances at the higher pressures sufficiently definite to justify recording in the table, where a slight reversible increase of volume is shown at 25,000. T h e volume increase was, of course, not directly measured, but was calculated under the usual assumptions 'from an observed increase of length. Thermodynamically, a reversible increase of volume with increasing pressure is not possible, and the only significance to be ascribed to the entry in the table is a purely formal one, namely that a disturbance was found at this pressure, the exact nature of which is in doubt, but which

EFFECTS OF PRESSURE ON BINARY ALLOYS

191

certainly cannot be a disturbance corresponding to a uniform increase of volume in all directions. The two intermediate compositions, 1.82 and 3.01 Pd, showed no discontinuity, but were unusual in the larger than usual hysteresis, which furthermore was in the abnormal direction. There is doubtless some connection with the discontinuities shown by the other compositions. It would seem fairly certain that the system is not in a state of complete internal equilibrium, with the presumption that the phase diagram is more complicated than known up to the present. The shearing results are not particularly regular. On the whole, the shearing strength increases with addition of palladium at the low pressures and decreases at the higher pressures. The regular progression of curvature with composition shown by some of the other gold alloys is not shown here. Gold — Platinum. Four alloys were available from Otter, ranging up to 4.04 per cent platinum. Hansen and Metals Handbook agree in showing a range of homogeneous solid solution at each end of the composition range, with a very considerable intermediate heterogeneous mixed crystal range, which the Handbook remarks may extend up to 85 or 90 per cent gold at low temperatures. The presumption would seem to be that the compositions studied here are all in the homogeneous range. The internal evidence did not bear out this expectation, however. The results are shown in Table VI. Measurements were first made on the resistance of the four compositions up to 30,000 kg/cm2. These specimens were rolled to a thickness of 0.002 inch from the original wire and after rolling quenched from a temperature of 7000 C. For any one composition the resistance decreased smoothly with pressure, but the progression of pressure coefficient with composition was highly anomalous, the decrease of resistance for the 3.10 composition being notably larger than for compositions either smaller or larger. The normal sequence would be a continuously decreasing pressure coefficient with increasing concentration. As a check, the measurements were repeated for die first three compositions on new specimens prepared from the original wire by as nearly as possible the identical procedure. The abnormal increase of pressure coefficient at the composition 3.10 was again found, but there were numerical discrepancies between the two sets of runs on ostensibly identical material which were far beyond

192

BRIDGMAN

any possible experimental error. The values for the fractional decrease of resistance under 30,000 were respectively: for the 1.01 composition, 0.0173 and 0.0217; f ° r the 2.02 composition, 0.0147 and 0.0266; and for the 3.10 composition 0.0268 and 0.0324. The decrement for the first specimen of the composition 4.04 was 0.0146. The identical specimens of the first set of measurements were now subjected to an additional heat treatment by annealing in vacuum at 400° for an hour and cooling with the furnace over night. Runs made on the specimens thus seasoned now gave for the TABLE VI GOLD — P L A T I N U M S Y S T E M Au 100 pXioi Temperature Coefficient Pressure kg/cm» 0 J,000 10,000 15,000 20,000 25,000 30,000 40,000 50,000 60,000 70,000 80,000 90,000 100,000

2.19 .00391 1.0000 0.9849 0.9707 0.9571 0.9441 0.9316 0.9194 0.896 0.874 0.855 0.840 0.829 0.821 0.816

Au 98.99

Au 97.98 Pt 2.02

Au 96.90 Pt 3 1 0

Au 95.96 Pt 4.04

4.01

4-94

6.20

7.19

Pt

i.oi

.00250 1.0000 0.9965 0.9934 0.9905 0.9878 0.9852 0.9827 0.978 0.974 0.971 0.968 0.965 0.963 0.961

.00209 Rp/Ro 1.0000 0.9971 0.9944 0.9920 0.9892 0.9872 0.9853 0.982 0.980 0.978 0.976 0.975 0.974 0.973

.00165 1.0000 0.9949 0.9902 0.9856 0.9812 0.9771 0.9732 0.967 0.961 0.957 0.953 0.949 0.947 0.945

.00138 1.0000 0.9972 0.9945 0.9920 0.9897 0.9875 0.9854 0.982 0.979 0.976 0-974 0.972 0.971 0.970

- AV/Vo

5,000 10,000 15,000 20,000 25,000 JO,000

.00281 .00558 .00831 .01 ΙΟΙ .01367 .01626

.00296 .00586 .00873 .01156 .01434 .01708

.00296 .00588 .00874 .01158 .01437 .01711

.00294 .00583 .00868 .01147 .01426 .01697

.00293 .0058 I .00863 .01143 .01419 .01691

Shearing Strength, kg/cm2 20,000 40,000 60,000 80,000

197 — 4594

1,350 2,760 4.320 6,420

1.370 2,690 4,IOO 5,500

1.530 2,780 4,010 5.310

1,490 2,840 4,110 5,360

1,510 2.950 4,460 6,050

EFFECTS OF PRESSURE ON BINARY ALLOYS

193 ΟΙ

decrements of relative resistance at 30,000: 0.0184, °· 73ι 0.0322 and 0.0181 respectively for the four compositions. Again the results were perfectly smooth in pressure for a single composition. In general the results for the annealed material differ from those for the quenched material by an amount less than the differences between the two sets on ostensibly similar quenched material, except for the anomalous composition 3.10, for which the annealed and the second quenched specimen gave nearly equal values. It is to be noticed that, unlike the pressure coefficients, the values of specific resistance and temperature coefficient of resistance of the 3.10 composition fall in. the regular sequence with the other compositions. It was concluded from these three sets of resistance measurements that the alloys are not in internal equilibrium, and that the attainment of internal equilibrium with reproducible results would be a matter of some difficulty, and would demand a more elaborate investigation than I had time or material to make. The results are accordingly given as they were obtained, for what they may be worth, as an indication of possible behavior. The resistances given in Table V I as a function of pressure are those of the first set on material quenched from 700° C. The resistances above 30,000 in the table were measured on the identical specimens used for resistances below 30,000. The anomalously great decrease of resistance of the 3.10 composition is seen to persist over the pressure range to 100,000. The compressibility measurements gave no indication of anything unusual at the higher pressures, but all four compositions consistently indicated some sort of internal disturbance at pressures of 5,000 or lower. The disturbances are not of sufficient regularity to characterize either as a phase change or a discontinuity of tangent. In the extreme case this disturbance amounted to a change of length of less than one per cent of the maximum pressure effect. The irregularities are doubtless connected in some way with the irregularities shown by the resistance. It is to be noticed that the compression of the composition 3.10 is not significantly different from that of the others. The shearing strength shows no notable feature — on the whole the strength of the alloys tends to be greater than that of pure gold at the low pressures and less at the high — a tendency found before.

194

BRIDGMAN

Copper — Chromium. Hansen and the Metals Handbook agree in a phase diagram in which the range of solubility of chromium in copper is extremely narrow, most of the composition range being occupied by a mechanical mixture. Three compositions from Otter were available for these measurements: 0.061, 0.122, and 0.182 per cent Cr. Otter remarks that the composition 0.061 is probably approaching the solubility limit; the other two compositions therefore probably exceed it. The results are shown in Table VII. The resistance decreases T A B L E VII COPPER — C H R O M I U M Cu 100

ρ X io® Temperature Coefficient Pressure kg/cm» Ο Ϊ,ΟΟΟ 10,000 15,000 20,000 2 J,OOO 30,000 40,000 JO,OOO 60,000 70,000 80,000 90,000 100,000 J,OOO 10,000 I J,OOO 20,000 25,000 30,000 20,000 40,000 60,000 80,000

197 — 4596

1.69 .00436

SYSTEM

Cu 99-939 Cr 0.061

Cu 99.878 Cr 0.122

Cu 99.818 Cr 0.182

I.70

1.76

1.78

.00384

.00378

.00366

Rp/Ro I .OOOOO 0.99054 0.98195 0.9737 0.9656 0.9579 0.9506 0.939 0.928 0.919 0.911 0.903 0.896 0.890 .00353 .00696 .01039 .01370 .01695 .02010 1,600 3.420 5,090 6,410

t .0000 0.9925 0.9853 0.9782 0.9715 0.9649 0.9587 0.949 0.940 0.933 0.927 0.922 0.917 0.914 - AV/Vo .00356 .00707 .01054 .01396 .01734 .02068

1.0000 0.9919 0.9843 0.9767 0.9697 0.9630 0.9566 0.946 0.938 0.929 0.922 0.915 0.909 0.905 .00357 .00710 .01059 .01403 .01743 .02077

Shearing Strength, kg/cm2 1,920 1,910 3,360 3,440 5,020 4,800 6,850 6,730

1.0000 0.9926 0.9853 0.9783 0.9715 0.9650 0.9590 0.948 0.939 0.930 0.923 0.917 0.91 2 0.907 .ΟΟ359 .00713 .OI062 .OI4O7 .OI746 .02084 1,890 3.35Ο 4,720 6,450

EFFECTS OF PRESSURE ON BINARY ALLOYS

195

smoothly with increasing pressure for all three compositions. Particularly for the 0.061 composition there is no change of direction of the curve which might be associated with a shift of the solubility limit under pressure. It is to be remarked, however, that the progression with composition of the pressure effect is not normal. T h e decrease of resistance with pressure of the 0.122 composition is slightly greater than for the 0.061 composition instead of less as expected, and the decrease for the 0.182 composition is practically identical with that of the 0.061 composition, instead of materially less. These effects are consistent with 0.061 being very close to the solubility limit. T h e compressibilities of all three compositions are very nearly the same and materially less than that of pure copper. T h e volume is a smooth function of pressure, with no episode. Comment is required on the compression of pure copper given in the table. I have made determinations of the compression of two different specimens of 99.999 per cent copper, which differ in absolute magnitude by about 5 per cent, far beyond the error of measurement. In the fifth paper of this series the compressions given for pure copper were those most recently determined, which were the high values. T h e material of that paper offered no definite internal evidence as to which value was preferable, since the compositions of the alloys were not close enough to that of pure copper to give presumptive evidence. W i t h the dilute alloys of this paper, however, the presumption must be that the compression of the alloys should not be far from that of pure copper. It would thus appear that the more recent value for pure copper is distinctly too high, but that on the other hand the earlier value fits well in line. Accordingly in the table the earlier value for 99.999 copper is used.4 T h e difference between the two specimens of copper is doubtless an effect of mechanical flaws. It would have been desirable if the compression measurements could have been made on single crystal material, which was not the case for either set of measurements. T h e shearing strength shows no notable feature; at low pressure the strength of the alloys is somewhat greater than that of pure copper, but at high pressures roughly the same. Copper — Manganese. Eleven different compositions were available from Otter, ranging up to 9.14 per cent manganese. Of these,

197 — 4597

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f.c.c.) temperatures for each alloy, as determined by resistance measurements, are as follows: A t % Ni

Ms

1442 19.10 23.84

525° C 350 200

A„ 685° C 625 J70

The 33.1 and 37.0% alloys will not undergo f.c.c. b.c.c. transformations even when cooled to 4° Κ (liquid helium). The resistivity of the f.c.c. structure is about 90 X io -8 ohm-cm at 25° C, while the resistivity of the b.c.c. structure is about 40 X io _e ohm-cm at room temperature. The f.c.c. —> b.c.c. reaction can be induced in the 33.1% alloy by cooling a specimen in liquid nitrogen and bending it." The material as furnished me was in the form of wire approximately 1/16 inch in diameter. Measurements on the wire, as received, were made of specific resistance and temperature coefficient of resistance at atmospheric pressure and of compression up to 30,000 kg/cm 2 . For the resistance measurements under pressure short lengths of the wires were cold rolled to a thickness of approximately 0.002 inch (all the compositions were soft and the rolling was easy), and then subjected to an additional annealing treatment by me to remove any mechanical strains left by the rolling. For the three alloys with lower nickel content, which normally occur in the b.c.c. lattice, the annealing temperature was taken as 450° for the most dilute and 400° C for the other two so as to avoid any danger, according to Mr. Kaufman's table, of inducing the b.c.c. to f.c.c. transition by annealing. The two higher compositions, being normally in the f.c.c. arrangement, presented no such danger of a transition and the annealing temperatures for them were accordingly taken as a red heat. One alloy, composition 19.1% Ni, was studied in both the un-

197 — 4609

BRIDGMAN

2o8

annealed and annealed condition after rolling. The temperature coefficients were respectively 0.00230 and 0.00226 and the specific resistances at o° 31.7 and 30.6 X io~e. The latter certainly agree within experimental error, and the difference between the temperature coefficients is probably not significant either, so that the conclusion was drawn that the annealing after rolling was hardly necessary. Later measurements of specific resistance and temperature coefficient of the same composition in the form of wire "as received" gave 28.8 for specific resistance and 0.00240 for temperature coefficient. The specific resistance cannot be positively said to be TABLE

XII

FIVE IRON — N I C K E L ALLOYS

Fe 85.58 Ni 14.42 pXicf Temperature Coefficient Pressure! kg/cm 0 5,000 ΙΟ,ΟΟΟ I 5,000 20,000 25,000 30,000 40,000 50,000 60,000 70,000 80,000 90,000 100,000

28.6

Fe 8o.go Ni 19.10 28.8

.002 17

.00240

Fe 76.16 Ni 23.84 28.1 .00272

Fe 66.9 N> 33-1 79-4 .001 30

Fe 63.0 Ni 37.0 63.1 .00281

Rp/Ro 1.0000 1.0029 1.0054 1.0075 1.0092 1.0105 1.0116 1.012 1.012 1.0 I I 1.01 I I .Ο I 2 1.014 1.015

1.0000 1.0081 1.0 I 5 2 1.0217 1.0277 1.0335 1.0390 1.047 1.053 1.058 1.062 1.066 1.069 1.073

1.0000 ι .0128 1.0240 1.0356 1.0463 1.0566 1.0666 1.084 1.098 I.I 10 I.I 2 I 1.133 I.I46 I.158

ι .0000 ι .0116 ι .0161 1.0158 ι .0117 1.0055 0.9976 0.982 0.967 0.954 0.942 0.931 0.922 0.916

ι .0000 1.0483 1.0899 1.1259 1.1563 I.I 804 1.1978 1.221 i.231 I.235 I.236 I.237 I.237 I.24O

- AV/Vo 5,000 10,000 I 5,000 20,000 25,000 30,000

.00332(a)

.00296

.00300

.00634 .00924 .01207 .01488 .01767

.00591 .00879 .01161 .01445 .01720

.00602 .00899 .01 190 .01477 .01751

(a) Cusp at 6,000; — AV/Vo .00401 (b) Cusp at 11,200; - AV/Vo .00862

•00434I .00562 J .00956 .01360 .01756 .02154 .02544

.ΟΟ385 .OO77I .01176(b) .01577 .OI983 .02381

EFFECTS OF PRESSURE ON B I N A R Y ALLOYS

209

significantly different from that of the rolled material, because of the unfavorable geometrical dimensions of the rolled material, but the difference of temperature coefficients is certainly beyond the error of the individual measurements and probably significant. In spite of the fact that measurements of specific resistance and temperature coefficient had indicated that annealing after rolling produces little effect, measurements were made on the effect of pressure on the resistance of both annealed and unannealed material of the composition 19.1% Ni. It was a surprise to find a very material difference in the behavior of resistance under pressure, the annealed material showing an increase of relative resistance at 30,000 of 0.0390 and the unannealed an increase of 0.0504. This difference persists over the entire pressure range up to 100,000, the relative resistance at 100,000 of the annealed being 1.0729 and of the unannealed 1.1145. Previous experience had hardly prepared me to find the pressure coefficient of resistance more sensitive to internal condition than specific resistance or temperature coefficient. The resistances given in Table XII are all for the material annealed after rolling. In all cases resistance is smooth in the pressure, with no discontinuities or cusps, and with no appreciable hysteresis, except for the single composition 14.42% Ni, for which there is a slight hysteresis associated with a permanent decrease of resistance after release of pressure of approximately 0.05 per cent. At the lower pressures the resistance of all compositions increases with increasing pressure. Composition 33.1% passes through a well defined maximum, followed by an eventual decrease to approximately 9% less than the initial resistance. The curve for the composition 14.42% rises to a flat maximum, followed by a still flatter minimum with eventual rise again, the total variation of resistance over the entire pressure range being r.5 per cent. The resistance of the three other compositions rises over the entire pressure range by amounts varying from 7 to 24 per cent, in all cases with downward curvature, which is not the normal curvature for a material with positive pressure coefficient. The volume change, unlike the resistance, does show episodes, there being two cusps and one volume discontinuity. There is no detectible regularity in the progression of these episodes through the sequence of compositions. This is not surprising in view of the

2 ΙΟ

BRIDGMAN

behavior of pure nickel, which may on occasion show a very pronounced cusp, the details of the appearance of which vary capriciously with the details of the past history of the particular specimen, and which I have never been able to reduce to reliable reproducibility. The table shows results for only five compositions, but Mr. Kaufman's original letter gives data for six compositions that were furnished me. The sixth composition, not quoted above, was stated to be 9.61% Ni. It would appear, however, that there must have been some slip-up with regard to this alloy, because most of its properties, both at atmospheric pressure and under higher pressure, were indistinguishable from those of 33.1 Ni content, which has a f.c.c. instead of a b.c.c. structure, and a specific resistance nearly three times that of the other. Furthermore, my own previous measurements® of the iron-nickel series agreed roughly with the expectation of properties suggested by Mr. Kaufman. I had no alternative, therefore, except to suppose that there had been some mix-up, and that two specimens of 33.1 Ni content had been sent me. The only respect in which the measurements under pressure of the ostensible 9.61 composition were distinguishable from those for composition 33.1 was in the compression. The former showed an obtuse cusp at 18,000 with volume decrement of 0.1633, whereas the latter showed a small volume discontinuity at 5,000, and no cusp at higher pressure. This failure of exact agreement has no significance, because it has been found before that these slight irregularities are capricious and not reproducible. In any event, the volume measurements agreed rather closely: the relative volume decrements at 15,000 of the two compositions were respectively, 0.1366 and 0.1360. The corresponding figures at 30,000 were 0.02510 and 0.02544. These alloys were too strong to permit measurements of shearing strength. I have previously® measured the effect of pressure on the resistance of a number of iron-nickel alloys, varying from 10 to 70 per cent Ni, and the compressibility to 12,000 of a single composition, "invar", of 37.5 Ni content. The former material had not been subjected to as elaborate heat treatment as that measured here, and the compositions do not exactly correspond. Exact comparison of the results is therefore difficult, particularly in view of the fact

197 — 4612

E F F E C T S OF P R E S S U R E ON B I N A R Y

211

ALLOYS

that there are ranges of composition where slight changes make very large changes in behavior, as shown, for example, by the relative behavior of the compositions 33.1 and 37.0 in Table XII. However, when all these factors are discounted, I remain with the impression that the agreement between the present and the former measurements is not as good as it should be. This only emphasizes the fact that the behavior of the iron-nickel series is sensitive to obscure disturbances, and that consistent results are difficult to get. In the large, it would seem that there is a rather definite difference of properties between the f.c.c. and b.c.c. arrangements, but a characterization in terms of the lattice can be only a very rough characterization and other factors must be taken into account. T A B L E XIII T w o

H E A T T R E A T M E N T S OF A 4 . 3 1

(AT

Fe 100 Ρ Χ ΙΟ»

% )

CARBON

Fe 95.69 — C 4.31 13.2

11.3 (1)

Temperature Coemcient

(5) .00475

.00585 .00395

Pressure kg/cm 2 Ο J,OOO ΙΟ,ΟΟΟ ι j,ooe 20,000 25,000 30,000 40,000 JO,OOO 60,000 70,000 80,000 90,000 100,000

.00448

Rp/Ro 1.0000 0.9904 0.9812

1.0000 0.9884 0.9773 0.9666 0.9562 0.9464 0.9368 0.920 0.906 0.893 0.881 0.870 0.861 0.852

1.0000 0.9906 0.9814 0.9725 0.9640 0.9556

0.9734 0.9639 0-9S57 0.9480

0.9477 0.936 0.925 0.915 0.906 0.897 0.891 0.885

0.936 0.926 0.918 0.911 0.904 0.898 0.894 - AV/Vo

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

STEEL

.00289 .00575 .00856 .01133 .01406 .01676

.00288 .00578 .00857 .01132 .01407 .01676

212

BRIDGMAN

Carbon Steel. Professor Cohen furnished me, through Mr. Lement, with a highly pure carbon steel to be investigated in different heat treatments. T h e analysis as furnished showed only 0.96 W t % C (4.31 A t % ) with no detected Mn, Si or Ni. T h e material was furnished in the annealed condition, in the form of wire 0.064 i n c h in diameter. In this condition measurements were made of specific resistance and temperature coefficient of resistance at atmospheric pressure and compression to 30,000. Specimens for the resistance measurements under pressure were rolled from the wire to a thickness of 0.002 inch, and returned to Mr. Lement for further heat treatment. This treatment consisted in the first place of a hardening treatment which consisted of maintaining at 845° C for l/2 hour, quenching in iced brine, cooling to -195 0 C for 1 hour, and returning to room temperature. T h e specimens were then divided into five groups, and subjected to the following further tempering treatments: 1, none; 2, 93 0 C for 1 hour; 3, 204° C for 1 hour; 4, 316° C for I hour; 5, 4270 C for 1 hour. Of these, the specimens with the tempering treatments 1 and 5 were measured to 30,000 and 100,000 in the regular way. T h e resistances of these two extreme treatments were so closely the same under pressure that it did not seem worth while to measure the intermediate treatments. T h e results are given in Table XIII. In this table the value for the specific resistance, one value of temperature coefficient (0.00475), a n d the compression are for the annealed material "as received". Values are also given for pure iron for comparison. T h e two heat treatments exhibit practically the same effect of pressure on resistance, but there is a definite difference in temperature coefficient, that of treatment 5 approaching closer that of the fully annealed material. T h e effect of added carbon on the pressure coefficient of resistance, namely a diminution in the decrease of resistance, is in the same direction as we have come to expect from other alloys with added metallic elements. T h e compression of the annealed material is indistinguishable from that of pure iron. I had previously found that the compression of pure martensite differs very little from that of pure iron.7 Three Invars. Professor Cohen suggested that it would be of interest to find the effect of varying carbon on the iron-nickel alloy known as invar, and the results are therefore included here, although these are not binary alloys. Three invars were supplied in

EFFECTS OF PRESSURE ON BINARY ALLOYS

the annealed condition with the following compositions (Wt per cents). No Ni Nj

N7

C 0.02 0.25 0.58

Mn 0.09 o.oj 0.07

Si 0.01 0.20 0.22

Ni 36.0 36.6 30.2

The specific resistance, temperature coefficient of resistance and compression were measured on the "as received" material in the form of wire 0.063 ' n c h in diameter. Pieces were cut from these wires, rolled to a thickness of 0.002 inch for the resistance measurements, and returned to Mr. Lement for further heat treatment. This consisted in the first place of heating to 1200° C for 1 hour, quenching in water, reheating to 200 0 C for 1 hour and quenching in water. Three specimens of the three compositions, designated as Ν ι — ι, N5 — i, and N7 — 1, were measured for resistance under pressure without further treatment. Three other specimens, designated as N i — 2, N5 — 2, and N7 — 2, were subjected to a further aging at 70° C for 500 hours, and then the resistance measured under pressure. The results are given in Table X I V . The differences between the different carbon contents and different heat treatments are small and not wholly consistent. In general, the properties do not vary monotonically with composition; both the pressure effect on resistance and the compression of the median carbon content are less than that on either side. Furthermore, the intermediate composition shows two volume discontinuities. These are small, however, and particularly the one at 5,000 must be regarded as somewhat in doubt. Compared with the binary iron-nickel alloys of Table XII the specific resistances, temperature coefficients, and pressure effect on resistance of these invars are all intermediate between the two compositions of greatest nickel content in Table XII. The compressions, however, are on the whole somewhat greater than for the binary alloys. DISCUSSION AND S U M M A R Y

The material of this paper exhibits no spectacular features in the way of interruptions of smoothness or continuity. The generalization previously found to hold almost without exception with regard

197 — 4615

214

BRIDGMAN

to pressure coefficient of resistance, namely that the addition of a small amount of an alloying element increases algebraically the pressure coefficient of resistance, continues to hold without further exception. There does not, however, seem to be any obvious connection between the numerical magnitude of the alteration of the pressure coefficient and the atomic fraction of added metal. Manganese, when added in sufficient quantity to copper, silver or gold, changes the sign of the pressure coefficient from negative to positive. T h e effect deviates markedly from linearity with the composition. Interpolation indicates that the sign of the pressure TABLE

XIV

THREE "INVARS" W I T H DIFFERENT CARBON CONTENTS Ni

ι ρ X 10» Temperature Coefficient

2

71.9

2

ι

71.7

.002 I 3 •002 20 .002 20

.Pressure kg/cm2 0 5,000 10,000 15,000 20,000 25,000 30,000 40,000 50,000 60,000 70,000 80,000 90,000 100,000

NS

ι

Ν7

2

73.8

.00212 .00204 .0020J

.00203 .00220 .00227

Rp/Ro 1.0000 1.0362 1.0643 1.0854 1. 1000 1.1088 1.1125 1.113 1.105 1.095 1.083 1.070 1.057 1.045

1.0000 1.0352 1.0698 1.0884 1.1059 '•"79 1.1244 1.120 '•"3 1.103 i.09 3 1.083 1.075 1.068

ι .0000 1.0326 1.0576 1.0761 1.0882 1.0945 1.0965 1.091 1.08 I 1.071 1.060 1.050 1.040 1.034

1.0000 1.0326 1.0579 1.0761 1.0882 1.0948(a) 1.0955 1.090 1.08 I 1.071 1.060 1.049 1.041 1.033

1.0000 1.0323 1.0609 1.0854 1.1053 1.1200 1.1297 1.140 1.144 ..138 I.I 36 1.129 1.122 1.117

1.0000 1.0331 1.0624 1.0886 1.1094 1.1261 1.1365 1.148 1.151 1.146 1.139 1.132 1.125 1.120

.00948 .01388

- AV/Wo •00394) •00J08 J .00798 .01278I

.00942 .01385

.01811 .02221 .02616

•01375/ .OI7J9 .02144 .02473

.01805 .02214 .02605

J.OOO

.00482

10,000 15,000 20,000 2 J,OOO 30,000

(a) Maximum, 1.0060 at 28,500

.00478

EFFECTS OF PRESSURE ON BINARY ALLOYS

coefficient reverses for the addition of about 0.5 A t per cent Mn to copper, 1.5 per cent to silver and 2.5 per cent to gold. Pure manganese decreases in resistance under pressure, with a comparatively large coefficient. A theoretical discussion of the reason for the abnormal effect in alloys would be of interest. T h e compressions of the dilute alloys in general differ little from the pure metals. In the majority of cases the dilute alloy is more compressible than the pure metal, even in some cases where the dissolved metal (platinum or palladium) is intrinsically less compressible than the solvent metal. Small scale irregularities abound. As in earlier papers of this series most of these irregularities are exhibited b y the compressions rather than b y the resistances, which might perhaps have been thought to be more sensitive. T h e gold-platinum series shows an abnormal sequence of pressure coefficients of resistance with composition. T h e copper-palladium and copper-platinum series give evidence of incomplete equilibrium in the resistance phenomena, as shown b y hysteresis and a permanent change of resistance after exposure to pressure of the most concentrated Cu-Pt alloy. The volume abnormalities may be summarized as follows. T h e gold-manganese series shows a small phase change at the highest concentration and hysteresis at lower concentrations. Gold-palladium shows a reversible increase of length for two compositions near 25,000, which thermodynamically cannot mean a volume increase, but must be due to some other obscure instability. Goldplatinum shows irregular compressions at pressures below 5,000 kg/cm 2 . Copper-manganese shows various irregularities, rising to the magnitude of definite volume discontinuities for two compositions. Copper-palladium shows small transitions at t w o composisions. Silver-magnesium and silver-zinc show definite volume discontinuities. T h e iron-nickel series shows several examples of cusps or volume discontinuities, which vary capriciously with composition, as might be expected from the capricious behavior of pure nickel. Similarly, one of the three "invars" shows t w o rather large volume discontinuities which do not appear in the two others. In general, the shearing curves show little episode; the more common tendency is for the shearing strength to increase with addition of alloying metal. A n exception is afforded by certain compositions of copper-manganese, copper-palladium, and cop-

197 — 4617

2 ΐό

BRIDGMAN

per-platinum at the highest pressures. These show a new type of shearing anomaly which consists of a catastrophic drop, during the shearing process, of the shearing strength from a poorly defined upper value to a well defined lower value. The possibility is to be considered of a transition to a modification stable only under shearing stress, or possibly some new two-dimensional surface structure. As in all this work I am indebted to Mr. Charles Chase for preparing the specimens and setting up the apparatus. Also, as in the previous paper of this series, I am much indebted for grants from the American Philosophical Society and from the Research Corporation with which out-of-pocket expenses to the University have been defrayed. Lyman Laboratory of Physics, Harvard University, Cambridge, Mass.

REFERENCES

1. P. W . Bridgman, Proc. Amer. Acad. 82, IOI-IJ6, 1953; 83, 149-190, 1954; 84, 1-42, 43-129, 1955 (fifth reference to paper now in press). 2. P. W . Bridgman, Proc. Amer. Acad. 74, 11-20, 1940. 3. P. W . Bridgman, Proc. Amer. Acad. 77, 191, 1949. 4. P. W . Bridgman, Proc. Amer. Acad. 77, 198, 1949. 5. Roger Bacon, T h e Elastic Constants of Silver Alloys, Technical Report No. 15, Office of Naval Research, Sept. 19JJ. Contract Ν ό ORI-27303, N R 017-611. 6. P. W . Bridgman, Proc. Amer. Acad. 63, 329-345, 1928; 77, 216, 1949; 81, 242, 1952. 7. Reference 3, p. 216.

COMPRESSION AND THE a-ß PHASE TRANSITION OF PLUTONIUM

Compression and the a-5 Phase Transition of Plutonium P. W. Bmdgman Harvard University, Cambridge, Massachusetts (Received July 30, 1958) Recent lifting of the security restrictions now permits publication of measurements of various effects of pressure on plutonium made during the war. Compressions on the alpha phase were measured at room temperature to 40 000 kg/cm 2 in one apparatus and to 100 000 in another. The total volume compression under 100 000 is very close to 10%. Compressibility decreases with increasing pressure as is normal. Exploration for other transitions was made to 20 000 kg/cm a at 100° and 200°—none were found. The pressure and the volume change of the alpha-beta transition was measured at 162.6° and 205°. The transition curve is "normal," the pressure rising with increasing temperature with downward curvature, and volume increment decreasing. The volume increment averages nearly 9%. The pressure of transition at 205° is very approximately 7000 kg/cm 3 . The calculated latent heat of transition at the mean pressure is roughly 4.5 cal/g. INTRODUCTION

T

HIS paper reports the results of various measurements of the effect of static hydrostatic pressures on plutonium made during the spring of 1945. The security restrictions have just been lifted, permitting publication in full detail now for the first time, although a partial publication in summary has been previously published. I am indebted to Dr. Henry L. Laquer of the Los Alamos laboratory for his active interest in this matter and for acquainting me with all the declassified work on plutonium published up to November, 1957.1 The measurements comprise: (a) volume measurements at room temperature with two different types of apparatus, the first with rather good accuracy to 40 000 kg/cm 2 , and the second with much inferior accuracy to 100 00 kg/cm 2 ; and (b) measurements of the effect of pressure up to a temperature of 205°C of the phase change which normally occurs at atmospheric pressure in the neighborhood of 115°C. The measurements were made in the Lyman Laboratory of Harvard University with apparatus and by methods already developed and described in detail, 2 except for unessential modifications to guard against probable effects of possible accidental explosions. The various piezometers were set up with their charges of plutonium at Los Alamos and transported to Cambridge by special messenger, who returned the material to Los Alamos after the measurements had been completed. At Los Alamos, Dr. Cyril S. Smith and Dr. Eric R. Jette were in immediate charge of the arrangements. The material was the best available at the time, with an impurity content of the general order of 0.1 wt %. It was not in a perfectly well defined condition, as shown by variations of the initial density between the 1 A. S. Coffinberry and Μ. B. Waldron, Progr. in Nuclear Energy, Ser. V 1, 354-410 (1956). This paper contains references to all the published work up to time of publication. There is a later paper: Μ. B. Waldron, Atomics, 383-386 (October, 1957). ' P. W. Bridgman, Proc. Am. Acad. 76, 71-87 (1948), for compressions to 40 000; 76, 55-70 (1948) for compressions to 100 000 74, 399-424 (1942) for transitions to 50 000.

198 — 4620

different samples. The total quantities of plutonium were approximately 3.5 g for the transition studies, 1.5 g for the compressibility measurements to 40 000, and 0.1 g for the compression measurements to 100 000. The actual measurements for the transition studies were made by Mr. L. H. Abbot; the other measurements and all the computations were made by me. DETAILED DATA

Compressions to 40 000 Two different pressure containers were used, giving measurements on two different specimens of plutonium. It was intended to make two complete sets of independent measurements with each pressure container, but various mishaps (breakage of a piston and inadvertent contamination during one filling) reduced the number of good measurements to one run to 40000 with one container, and two independent runs to 25 000 and 40 000, respectively, with the other. In these measurements to 40 000 the container is subjected to both external and internal pressure, thus minimizing the elastic expansion of the bore. The pressure is transmitted by indium. Because of the approximate equality of diameter and length of the charge, frictional and other hysteretic difference between measurements with increasing and decreasing pressure is less than 5% of the maximum effect. The total corrections for compression of the indium transmitting medium and distortion of the apparatus are of the order of only 40% of the total measured effect. All these factors are unusually favorable for measurements of compression. The deviation of any single reading from a smooth curve was seldom as much as 1 % of the total pressure effect. In Table I are shown the relative volumes to 40 000 kg/cm 2 as given by measurements with the two containers. The initial density of the material in container III, as determined at Los Alamos with a slight correction for initial compaction, was 19.47, and that in container II 19.66. If the readings with container

COMPRESSION

AND

a-p

I I I are taken a t their face value a reversible transition in the neighborhood of 900 k g / c m ' with fractional volume change of 0.0047 is indicated. However, no trace of such a transition was found with the other container, nor was it found during a repetition of the measurements with number I I I . The other measurements on this repetition were vitiated as far as calculations of exact compressions is concerned because of splitting of the carboloy piston, but they should be competent to indicate the presence or absence of the transition. This possible transition was therefore ignored in the calculations summarized in the table. A possible explanation of the apparent transition is a reversible buckling of a flat steel washer a t the lowest pressure of the range, but there was no opportunity to check this. The measurements to 25 000 maximum with container I I afford a valuable check on the reliability of the deviations from linearity of the change of volume with pressure. Other things being equal, the accuracy of a deviation from linearity increases with the square of the pressure range, and hence should be 2.5-fold greater for the 40 000 range than for the 25 000 range. The deviation from linearity of the proportional volume decrement a t the midpressure, 12 500, of the measurements to 25 000 was 0.0021, and the corresponding figure at the same pressure from the measurements over the 40 000 range was 0.0023. This agreement is as good as one has a right to expect, and should give confidence in extrapolating the volumes to considerably higher pressures. Only the measurements from the two 40 000 ranges have been incorporated into the table. The compressibilities to be deduced from the volumes in Table I agree reasonably well with determinations of compressibility made by Laquer by a pulse technique u p to 2000 kg/cm 2 as reported by Coffinberry and Waldron.

Compressions to 100 000 The material is confined in a carboloy piezometer jacketted with steel, which is enclosed in a second pressure vessel and exposed, for support, to a uniform hydrostatic pressure of between 25 000 and 30 000 kg/cm 2 over the entire external surface. The material TABLE

I. Volume compressions to 40 000.

Pressure kg/cm a

Container II

V/V, Container III

Average

0 5000 10 000 15 000 20 000 25 000 30 000 35 000 40 000

1.0000 0.9907 0.9822 0.9745 0.9675 0.9612 0.9555 0.9503 0.9455

1.0000 0.9909 0.9828 0.9756 0.9690 0.9629 0.9571 0.9514 0.9460

1.0000 0.9908 0.982S 0.9750 0.9682 0.9620 0.9563 0.9508 0.9457

TRANSITION TABLE

OF

215

Pu

II. Volume compressions to 100 000.

Pressure kg/cm 1

Average I I and I I I

0 5000 10000 15 000 20 000 25 000 30000 35 000 40 000 50 000 60 000 70 000 80 000 90 (XX) 100 000

1.0000 0.9908 0.9825 0.9750 0.9682 0.9620 0.9563 0.9508 0.9457

v/v.

Average 3 piezometers

0.9620 0.9561 0.9504 0.9448 0.9335 0.9242 0.9161 0.9092 0.9032 0.8981

is compressed by two pistons, driven into the piezometer from the two ends. The force driving the pistons is measured with an independent device also exposed to the supporting pressure. The speciman is enclosed in an indium sheath to transmit pressure approximately hydrostatically, but because the diameter is of the order of only one-quarter of the length, the frictional and hysteretic effects are much greater than with the 40 000 apparatus. This apparatus gives its best results only for materials of relatively high compressibility— plutonium is not one of them. Measurements were made with three different piezometers to maximum pressures, respectively, of 97 700, 92 300, and 100 900 kg/cm 2 . Five piezometers had been planned for, b u t there were mishaps with two. The density of this material was not determined at Los Alamos. Determinations by me, of quite inferior accuracy, from the dimensions and with subtractive corrections of over 50% for the value cccupied by the indium etc. gave for the respective initial densities 21.1, 19.5, and 20.0; the apparent variation is doubtless not real. The chief value of these measurements to 100 000 is in indicating whether there are any new important transitions. All three runs showed irregularities which are not inconsistent with a small reversible transition. If the transition is real it runs with increasing pressure between 73 000 and 84 000, between 57 000 and 68 000, and between 48 000 and 55 000 for the three fillings, respectively, and with decreasing pressure between 47 000 and 41 000, between 61 000 and 51 000, and between 38 000 and 31 000, respectively. The great variation in these figures could be explained b y stickiness of the transition and by overshooting. The figures are not inconsistent with the existence of a transition thermodynamically reversible somewhere between 51 000 and 55 000. The volume change of such a transition could not be more than 1%. However, it seems to me that the balance of probability is against it, and in the following I have smoothed the volume decrements right over any such possible transition.

198 — 4621

216

P.

W.

B R I D G M A N

The relative volume as a function of pressure, averaged for the three piezoemeters, is shown in Table II. The zero for these computations is the volume at 25 000 given by the other apparatus. The results for the individual piezometers varied considerably, from 0.0090 to 0.0106 for the total fractional volume decrement between 25 000 and 100 000. The two first fillings gave results within 2% of each other and 15% less than the third filling. The arithmetical average, therefore, as given in the table, probably errs in giving volume decrements which are too large. Taken at their face value, the figures of Table II indicate a drop of compressibility at 100 000 to between 0.25 and 0.30 of its initial value at atmospheric pressure. Plutonium thus appears as a substance of median over-all compressibility. Its volume at 100 000 of 0.898, may be compared with volumes of 0.884, 0.910, and 0.915 for arsenic, zirconium, and aluminum, respectively. The original exceptation was that the compression of plutonium would prove to be materially higher.

Effect of Pressure on the a-(5 Transition Measurements were made with a single filling of a single container in my regular apparatus for the study of compressions and transitions up to 50 000 kg/cm 2 and up to 250°. The plutonium was encased in a lead capsule, instead of indium as in the compression measurements. Before starting these measurements it was known that there is a transition at atmospheric pressure at approximately 117°, the density being said to drop with rising temperature from 19.8 to 17.5, that is, with a volume decrement of 13%. It was therefore to be expected that the transition would run at higher temperatures with increasing pressure, but without knowledge of the heat of transition the expected rate of rise with pressure was not calculable. The present measurements consisted in the first place of exploratory applications of pressure to 20 000 kg/cm 2 at 100° and 200°. This exploration was sensitive enough to detect volume changes of 0.0002 of the initial volume. I t was thus established that there was no new transition under these conditions between atmospheric pressure and 20 000 at 100°, and at 200° no transition except the expected one at comparatively low pressure. The transition parameters were determined at 205°, 163°, and again independently at 205° by the method of piston displacement at constant temperature, and at about 1600 kg/cm 2 by the method of lowering temperature at constant piston displacement. The latter was by way of check, the transition running catastrophically and irreversibly in the region of thermodynamic instability. The first method, however, gives the reversible parameters. Here the general idea is to so manipulate the pressure as to force the material to be approximately equally divided between the two phases. Small pressure displacements are then made in

198 — 4622

either direction until the transition can just be observed to be running in one direction or the other. The mean is taken as the pressure of thermodynamic equilibrium. After equilibrium pressure is thus determined pressure is pushed far enough beyond the equilibrium pressure to force the transition to run to presumptive completion in either direction, thus permitting a determination of the total volume change of the transition. The temperatures given in the following are the temperatures of the thermostatically controlled temperature bath. No correction was attempted for any self-heating due to radioactivity; under the conditions any such effect should be small. The same remarks apply to the measurements of compressibility. The results are shown in Table III. In general, this transition ranks high among the clean-cut transitions. It starts without much over shooting in either direction, apparently runs to completion within a moderate pressure range, and the equilibrium pressure can be enclosed within tolerably narrow limits. On the check run with decreasing temperature at constant volume, at a rate of approximately 0.5° per min, the transition ran catastrophically, apparently to completion, somewhere between 100° and 75°. The equilibrium temperature was thus over passed by somewhere between 40° and 65°. The indicated fractional change of volume under these conditions was 0.0818, much lower than the change to be expected according to the data of Table I I I at this pressure under equilibrium conditions. The value 0.0818 would suggest that the thermal expansion of the high-temperature phase is materially higher than that of the low-temperature phase, a result which does not agree with the general consensus of other observers as reported by Coffinberry and Waldron. The discrepancy can be explained by a small undetected running of the transition before the catastrophic drop, or incomplete running of the transition. Any reasonable extrapolation to atmospheric pressure of the volume changes measured under pressure would indicate a probable value distinctly less than the originally expected 13% already mentioned, and within the range 8.30 to 11.03% permitted by the values quoted by Coffinberry and Waldron. Comparison of the slopes of the isotherms above and below the transition indicates that the compressibility of the alpha phase is about 20% less than that of the TABU: I I I . Effect of pressure on the α—β transition.

Temperature

Pressure of beginning4 of transition, kg/cm from from above below mean

205.1°C 162.6 204.9

8250 5880 7060 4650 1550 3100 8250 5880 7060

Volume change on transition fractional, AV/Vt c m ' / g decreasing increasing pressure pressure mean

0.0879 0.0870

0.0951 0.0893

0.00437 0.00452 0.00439

COMPRESSION

AND

α-β

beta phase. A difference in this direction would be expected because of the large difference in density. Linear extrapolation to atmospheric pressure of the equilibrium pressures and temperatures indicated in Table I I I gives a transition temperature of 129.4°. This is distinctly higher than any of the transition temperatures indicated in the literature, showing that in all probability the transition line is concave toward the pressure axis, which is the normal direction of curvature. The transition data permit a calculation of the heat of the transition, a quantity apparently not yet

TRANSITION

OF

Pu

217

determined by direct experiment. The data of Table I I I give at the mean equilibrium pressure and temperature of 5080 kg/cm 2 and 183.8°C a latent heat of transition of 190 kg cm/g (approximately 4.45 cal/g), and by a rough extrapolation 130 kg cm/g at atmospheric pressure, assuming a transition temperature of 120.0°. Qualitatively the transition appears normal in the most important respects—transition temperature rising with increasing pressure with downward curvature, and a volume change decreasing with increasing temperature and pressure. Quantitatively, the volume change is high.

198 — 4623

1 General Outlook on the Field of High-pressure Research P.

W.

BRIDGMAN

Harvard University Cambridge, Massachusetts

1-1

1-2

1-3 1-4

The N e w Field of High Generalized Mechanical Stress 1 - l a Hydrostaticity 1 - l b Measurement of Transitions 1 - l c Challenges t o Technique New Physical Phenomena l-2a Phase Transitions in Solids l - 2 b Anomalous Behavior of Liquids l-2c Behavior of Alloys l-2d New Permanently Stable Forms l - 2 e Effect of Pressure on Electrical Resistance l-2f Pressure Calibration Using Resistance Discontinuities l - 2 g The Melting Curve Problems in the Lower Pressure Range Shock-wave Techniques

.

.

.

.

00 00 00 00 00 00 00 00 00 00 00 00 00 00

At the present time interest and activity in the field of high-pressure research are increasing with notable acceleration. No doubt a large part of this is due to the spectacular success of the General Electric Company in synthesizing industrial diamonds on an economically successful scale. A rapidly increasing number of laboratories are becoming equipped to deal with pressures in the low hundred-kilobar range and temperatures in the low thousands of degrees Centigrade. These pressures and temperatures can be sustained for times long enough to reach equilibrium conditions for many classes of phenomena. In addition to the new field of high static conditions thus recently opened, and of almost equal importance, is the somewhat prior discovery of methods of reaching much higher pressures and temperatures transiently by various detonation techniques. 1 De1

See Chap. 13.

[From Solids under pressure, ed. Paul and Warschauer, copyright © 1963, McGrawHill Book Company, Inc. Used by permission.]

199 — 462.5

2

P. W. BBIDGMAN

velopments here are the more or less direct outgrowth of the discovery of the effectiveness of shaped charges for military use during the last war. As in any rapidly growing field there is danger in this new field of high pressure that not all the activity will be directed to the best advantage, and that short-range considerations, arising perhaps from competitive conditions and the understandable desire to achieve tangible results quickly, will play too large a role, to the detriment of longer-range and less personal considerations. It would seem therefore that it may be well to stop for a preliminary breather and take a look at the whole field in order that the attack may be directed as intelligently as possible. In thus attempting to look over the entire field, I shall be mostly concerned with the purely experimental aspect of the subject, and I shall draw to a very large extent on my own personal experience. This experience for the most part has been confined to pressures considerably below those now accessible, although it has at times reached into the lower edge of the new pressure range. 1-1

The New Field of High Generalized Mechanical Stress

It is in the first place to be emphasized that the new field is in reality much more complicated than would be indicated by the words "high pressure." Technically, "pressure" means hydrostatic pressure, which of course is only a special case of generalized stress with its six independent stress components. "High-pressure" physics is only a special case of "high-stress" physics, and the ultimate task of the physicist here is to find the effects of varying all six components of stress through the widest possible range. Hydrostatic stresses par excellence occur in and are transmitted by fluids, and, in the lower stress ranges formerly exploited, the overwhelmingly preponderate part of scientific activity was confined to the study of various effects of the pressures produced in fluids, acting either on other fluids or on solids immersed in them. Thus in the lower range of earlier experimenting, the condition that the stress should be a hydrostatic pressure could be automatically realized. But in the new range this is no longer the case, for at ordinary temperatures fluids cease to exist as such in the ten-kilobar range, and they turn into solids. Because of this, it becomes a matter of great technical difficulty to attain a state of true hydrostatic pressure in a highly stressed system whose members are of necessity solids. Still more is it a matter of great technical difficulty to apply and control a generalized stress system with its six arbitrary components. Although the new field now open to us is the field of high generalized mechanical stress, I believe that most physicists would agree that the first, and perhaps most important, stage in conquering this field is

199 — 4626

GENERAL OUTLOOK ON HIGH-PRESSURE RESEARCH

3

mastering the effects of high hydrostatic pressure. It might be argued as to what extent this attitude is justified. It doubtless has partly a theoretical background and partly a practical background. It would appear plausible that it is only the hydrostatic component of stress that is capable of being raised to indefinitely high magnitude, for the other components of stress are limited by such phenomena as plastic flow and rupture. This could mean that in the ultimate domain of truly astronomical stresses the nonhydrostatic components degenerate to more or less irrelevant perturbations. Nevertheless, in the stress range below the astronomical, nonhydrostatic components can, in general, by no means be regarded as small perturbations; they are of the same order of magnitude as the hydrostatic components themselves. The presumptive importance of the nonhydrostatic components is enhanced when it is considered that the plastic-flow point and rupture strength may be enormously increased beyond their normal values by the action of the hydrostatic component. 2 I think it must not be too easily assumed that the only stress systems physically realizable at astronomical magnitudes are approximately hydrostatic. 1 - l a Hydrostaticity. In most conventional forms of apparatus in use hitherto in this field the frictional effects contributed by the nonhydrostatic shearing components may be integrated by the design of the apparatus in such a way that they give a total force of the same order of magnitude or even greater than the pure pressure itself. In fact this frictional force is usually deliberately exploited to make the seal. An extreme example is the optical window of Drickamer,3 which is retained against the thrust of the internal pressure by friction on the sides. It is nevertheless, I believe, the present consensus that the most important immediate problem of technique in this field is to find methods of producing stress systems which are truly hydrostatic. The technical problems are particularly challenging in the important field of combined high pressure and low temperature, a field which has no counterpart in nature. The importance of realizing a true hydrostatic pressure depends to a large extent on the sort of phenomenon concerned. If we are concerned merely with producing a qualitative effect, as in diamond synthesis, it is a matter of no importance at all. But the situation is different if it becomes a matter of measuring the physical parameters which control the phenomenon. Ideally, such a transformation as that of graphite into diamond is controlled by all six components of stress, not merely by the hydrostatic components, and the subject will not be mastered until the efforts of all six are determined. Such a high degree of mastery of the stress pattern 2

P. W. Bridgman, "Studies in Large Plastic Flow and Fracture," McGraw-Hill Book Company, Inc., New York, 1952. ' See Chap. 12.

199 — 4627

4

P. W. BRIDGMAN

as is implied in this ideal is evidently a long way in the future. In the meantime we console ourselves as best we can with the hope that the nonhydrostatic components are comparatively unimportant and that such transformation phenomena are essentially controlled by the mean pressure (average of three principal stress components). Even so, it is at the present time difficult enough, particularly in the apparatus used by the General Electric Company and others of similar type, to know even what the mean hydrostatic stress is. 4 Our present experimental sights might well be set at determining acceptable values for this mean stress. I t would then be for experiment to decide whether the mean stress enters into the thermodynamic equations for the transformation (for example, Clapeyron's equation) in the same way that the true hydrostatic pressure does. I think it should not be assumed too easily that in all cases the nonhydrostatic components will prove to be unimportant. In fact there is experimental evidence of the existence of at least one transition which occurs only in the presence of shearing stress. { 1 - l b M e a s u r e m e n t of t r a n s i t i o n s . Up to now most of the extensive work which has been done on transformations or transitions under pressure has been directed toward finding the temperature at which a transition runs as a function of pressure. In this work, increasingly effective means are being found for making the stress system truly hydrostatic (by minimizing the effects of friction) and for obtaining good values for the mean stress. Much remains to be done, however, in finding methods capable of general application, instead of particular methods devised for particular situations. Perhaps the principal desideratum here is control of larger volumes. Full command of transitions will not be attained at high pressures, however, until we have methods for measuring the other independent thermodynamic parameters (in addition to temperature and pressure). This has been done in comparatively few cases; in these cases the parameter measured has been almost always the discontinuity of volume accompanying the transition. Latent heats are much more difficult to measure than volume discontinuities, because the latent heat of the reacting material is in general swamped by that of the massive containing apparatus. However, the use or investigation of all thermal phenomena is not thereby ruled out, as in the determination of temperature-arrest points on heating or cooling. * See F . P. Bundy, W. R . Hibbard, Jr., and Η. M. Strong (eds.), "Progress in Very High Pressure Research," J o h n Wiley & Sons, Inc., New York, 1961. For a discussion of calibration techniques, see F. P. Bundy, Calibration Techniques in Ultrahigh Pressure Apparatus, J. Eng. Ind., vol. 83, series 13, no. 2, pp. 207-214, 1961. t Professor Bridgman may here be referring to his observation of a sudden drop in shear stress at high pressure in his work on three copper alloys about 1955. l i e had privately speculated that the discontinuities might be explained by formation of a new modification stable only under shear stress. [Ed.]

199 — 4628

G E N E R A L OUTLOOK ON H I G H - P R E S S U R E

RESEARCH

5

In general, change of volume is one of the most significant parameters to determine in the high-stress domain, not only in connection with transitions, but also for cubic compressibilities, which are generally regarded as of great theoretical importance. Change of volume is in general insensitive to nonhydrostatic components of stress, which means in particular that it is not sensitive to geometrical distortions in the specimen under measurement. Such geometrical distortions are exceedingly difficult to avoid. The result should be that measurements of the change of volume under pressure are comparatively easy to make. Nevertheless, relatively few have been made up to now. Because geometrical distortions are so hard to avoid, a type of measurement which instrumentally is much easier to make than a volume measurement (namely a measurement of electrical resistance) has, up to the present, a more doubtful physical significance than volume measurements. Changes of resistance as measured under high stress involve at least two effects, one due to the intrinsic effect of pressure on specific resistance, and one due to the changes of configuration of the specimen. The latter is controlled by adventitious features in the design of the apparatus and the method of applying stress. Unfortunately up to the present the adventitious component is, even under the best of circumstances, of the same order of magnitude as the intrinsic effect. 1 - l c C h a l l e n g e s t o t e c h n i q u e . Here we have two immediate challenges to technique: first, to devise better methods of measuring volume changes, including both discontinuities and changes over a range, and second, to devise methods of applying pressure without distortion to specimens for resistivity or other sorts of measurement, or failing this, to devise satisfactory methods for correcting for the effects of distortion. In addition to the two immediate challenges to technique just mentioned, it is possible to visualize an almost limitless number of other challenges. It is not easy to imagine methods capable of giving good values for the effect of pressure on dielectric constant or magnetic permeability or such obscure electrical effects as the four transverse effects or the full complement of twenty-one elastic constants of the general crystal. 5 Imagination of a high order will be required, the same sort of imagination as shown by Drickamer with his optical windows. There is thus plenty to be done in the field of presently attainable pressures. When it comes to extending the pressure range, the most obvious problem is to find some way of extending the cascading method of supporting an inner vessel by nesting it in an outer vessel, beyond the single stage of cascading support to which we are at present limited. Present methods of exploiting frictional support so as to permit high stress concentrations in small regions are merely special and partial applications 6

See Bibliography.

[Ed.]

199 — 4629

6

P. W. BRIDGMAN

of the cascading principle. Whatever the ultimately successful method, it would seem that we must reconcile ourselves to the use of increasingly larger and more complex apparatus, with the increasing expense thereby implied, with perhaps, presently, instruments the size of cyclotrons, and all the unwelcome features of government support. 1-2

New Physical P h e n o m e n a

In speculating as to what sort of phenomena to anticipate when the pressure range is indefinitely increased, we may perhaps recognize two different ranges. In the first and lower range, to which we are at present almost exclusively confined, the atoms themselves are inviolate, and phenomena are determined in largest part by the interaction of atoms or molecules. The second, higher, range is one in which the atoms are subject to increasing deterioration, resulting ultimately in a "pressure squash" of protons and electrons. The first steps in atomic deterioration might be expected to be the rearrangement of electron orbits within the individual atoms and the sharing of orbits between atoms. Because there are many electrons in the majority of elements, and because there are a great many possible electron orbits, it would seem that we have the potentiality for an enormously richer variety of phenomena in the highpressure range of atomic deterioration than in the conventional lower range of atomic inviolability. One may anticipate discontinuous rearrangements of electron orbits, in which case there will be discontinuous effects on various physical parameters such as we find in a conventional transition, or the rearrangement averaged over a pressure range, in which case there will be points of inflection and ranges in which the change of the parameters is in an "abnormal" direction. I t is most unfortunate, and it offers another challenge to technique, that this region of increasing "fine structure" in the properties of matter should be precisely the region in which physical measurement becomes increasingly blurred because of technical difficulties. l - 2 a Phase transitions in solids. I t is not to be expected that the domain of electronic rearrangement within the atom is sharply separated from the domain of atomic inviolability. In fact a few instances are already known in which it would appear that electronic rearrangements provide the mechanism for observed effects. The most definite of these are the transitions of cesium and cerium, in which there are large volume discontinuities with no change in the type of lattice, which is the same type of close-packed structure on both sides of the transition. In these two cases theoretical calculations have indicated rather definitely what the precise electronic rearrangement must be. In general, the electronic rearrangement need not be as abrupt as in these two cases. There are in fact anomalies in the behavior of all the rare-

199 — 4630

GENERAL OUTLOOK ON HIGH-PRESSURE RESEARCH

7

earth metals, most of them spread over a pressure range, which one might plausibly anticipate to be due to electronic rearrangements. These invite further experimental and theoretical study. The rare-earth metals are particularly favorable candidates for this sort of thing because of the frequent occurrence of unoccupied inner electron shells. T h e probable existence of an indefinite number of abnormal ranges at high pressures due to interior electronic rearrangements makes any smooth extrapolation of results obtained at lower pressures increasingly hazardous. We can less and less be confident of the reality of any extrapolated phenomenon at high pressure; actual production and exhibition of t h e phenomenon becomes increasingly essential. The same remark applies, but much less forcibly, to interpolation. l - 2 b A n o m a l o u s behavior of liquids. Qualitatively the general behavior to be anticipated at very high pressures, that is, the occurrence of smooth normal behavior interspersed with ranges of the abnormal behavior which accompanies electronic rearrangement, is very much like the behavior which I have already found in almost all liquids at lower pressures. At pressures in the thousands or low tens of thousands of atmospheres it appears, as the accuracy of measurement is increased, that all liquids exhibit regions of "abnormal" behavior characteristic of the individual liquid, superposed on a rough generalized behavior which may be taken to characterize liquids as such. I have explained these effects as perhaps arising from the details of the interlocking to which the molecules of a liquid are forced by sufficiently high pressures, the details being different for each different sort of molecule. I had only started on the exploration of these effects when I abandoned work on them to take up the (to me) more enticing possibilities of extending the pressure range. But I am convinced that a great deal more remains to be done in finding how the fine structure of the temperature-pressure behavior of liquids depends on the individual molecule. Theoretically there is a wide field here for further exploitation, and experimentally there is the challenge of the high accuracy of measurement demanded and the difficulty of defining the conditions necessary to obtain reproducible results. 6 l - 2 c Behavior of alloys. Another area of investigation at comparatively low pressures not yet exhausted is that of the properties of alloys. There is an enormous amount of potential complexity here, and in the few studies which I have made, the field has barely been entered. There are a number of examples of new phases produced under pressure; in some cases the new high-pressure phase may be brought down to atmospheric pressure, where it is capable of permanent existence as a new alloy form. Here again there is a challenge to the theoretical physicist, • For a good review, see P. W. Bridgman, Recent Work in the Field of High Pressures, Revs. Mod. Phys., vol. 18, no. 1, 1946. [Ed.]

199 — 4631

8

Ρ. ΛΥ. BRIDGMAN

namely to find how to anticipate the possible stable existence at atmospheric pressure of hitherto unknown forms. This, of course, is merely a special case of the problem of predicting all possible transitions and t h e conditions of stable or metastable existence of the various forms. I t is probable that the limitations set by the necessity for a suitable spontaneous nucleation preceding the appearance of a new phase will prove t o be vitally important here, as has already proved the case in diamond synthesis. l - 2 d New p e r m a n e n t l y stable forms. I t is intriguing to speculate t h a t there may be a number of new hitherto unsuspected forms permanently stable under atmospheric pressure, which can be produced if only some critical stress can be exceeded. We already h a v e a couple of examples in black phosphorus^ and solid black carbon bisulfide. One may claim with some justification that diamond itself is almost an example, because considering the extreme rarity of diamond in nature, it would seem to have been to a large extent a matter of luck t h a t diamond was known before General Electric synthesized it. A number of possible candidates present themselves for such new irreversibly created forms. I have tried unsuccessfully to permanently transform sulfur, perhaps t h e most plausible candidate. One could imagine possibilities of fantastic physical properties if one could only produce a close-packed carbon lattice, of density severalfold greater than that of diamond. (The possibilities would be exciting enough if one could produce a sintered diamond aggregate, analogous to the cemented carbides.) Or even if a new form could not be permanently retained at atmospheric pressure, it might be possible to produce such forms with greatly enhanced physical properties within the interior of a cascaded nest of pressure vessels, thus permitting otherwise impossible extensions of the present pressure range. In principle, predicting the occurrence of such new forms is straightforward enough and involves the calculation of the stability of all conceivable lattices. But up to now it would have involved unsurmounted computational difficulties to carry out any such program. Now, perhaps, the accessibility of calculating machines offers some prospect of success. In default of this, if I were again active in reaching new high pressures, I could not resist the temptation of subjecting plausible substances to the action of hitherto unreached pressures to see whether some permanent change had been produced. t It is of interest that black phosphorus can be produced at essentially atmospheric pressure, using mercury as catalyst. (See H. Krebs, Η. Weitz, and Κ. H. Worms, Die katalytische Darstellung des schwarzen phosphors, Ζ. anorg. u. allgem. Chern., vol. 280, p. 119, 1955.) This presents the intriguing possibility that other metastable forms produced at high pressure may be obtained at atmospheric pressure. [Ed.]

199 — 4632

GENERAL OUTLOOK ON HIGH-PBESSURE RESEARCH

9

l - 2 e Effect of pressure o n electrical resistance. We pass now from this discussion of the possible effects of pressure on transitions of various sorts to consider the effects of pressure on electrical resistance. I t is in the first place to be remarked that there is at present no adequate theory of the effect of pressure on resistance, and in fact little has been done with this topic in the last thirty years. Experimentally there is a great wealth of undigested material waiting theoretical discussion and understanding. 7 This applies particularly to the range below 30 kilobars, where unambiguous results can be obtained. In the range above 30 kilobars it is at least now evident that the phenomena exhibit a greater qualitative richness and diversity than was at one time suspected. I t would seem that there is no simple type of behavior which can be called "normal" here. In the range of lower pressures it would have been plausible to anticipate that "normal" behavior of resistance under pressure would be a smooth decrease with decreasing curvature, perhaps asymptotically to zero or some finite resistance at infinite pressure. The broadest generalization that now appears justified is that the change of resistance with pressure is in general not smooth, but that there are more or less extended episodes of "abnormal" behavior. Whether these are usually associated with internal electronic rearrangements does not at present appear. There are a number of cases of minimum resistance at high pressure, one or two of maximum resistance, many cases of reversals of curvature with points of inflection, and several highly spectacular instances of an enormous cusplike increase of resistance with recovery to the initial order of magnitude at still higher pressures. In the semiconductors there are sometimes dramatically large effects. There is no obvious correlation between changes of resistance and changes of volume. There is no rule which connects the direction of resistance change at a transition with the direction of volume change, and instances are known of volume discontinuities with no detectable resistance change and, conversely, of resistance discontinuities with no detectable volume change. l - 2 f Pressure calibration u s i n g resistance discontinuities. I t has already been remarked that the technique problem of straightforwardly determining resistance as a function of hydrostatic pressure has not yet been satisfactorily solved. The great difficulty is to eliminate 7 For critical discussion of the present status of agreement between theory and experiment see, for example, A. W. Lawson, The Effect of Hydrostatic Pressure on the Electrical Resistivity of Metals, in Bruce Chalmers and R. King (eds.), "Progress in Metal Physics," vol. 6, chap. 1, Pergamon Press, New York, 1956; F. P. Bundy and Η. M. Strong, Behavior of Metals at High Temperatures and Pressures, in F. Seitz and P. Turnbull (eds.), "Solid State Physics," vol. 13, Academic Press, Inc., New York, 1962; and Chap. 8 of this volume. [Ed.]

199 — 4633

10

P. W. BRIDGMAN

the effect of irreversible plastic distortion. In my own work I had to make complicated adjustments for this (the details varying with each special case), leaning heavily on measurements in the truly hydrostatic range up to 30 kilobars. My ultimate objective was to get an idea of the most probable shape of the pressure-resistance curve as a whole, not to get best values for the resistance at any specified pressure. In the various adjustments, in particular in adjusting the slope at 30 kilobars to agree with the previously determined slope, some distortion of the pressure scale was inevitable. As a result of this distortion there was usually some displacement of the pressures of the discontinuities indicating polymorphic transitions. These displaced pressures of transition were allowed to stand without further correction in my final tabulation of the results, and I contented myself with as concise an account of the particular adjustment procedure as I could accomplish without going to the extreme of reproducing all the experimental data. The pressures of tabulated discontinuity thus obtained did not in general agree with the pressures of transition which I had previously obtained by the much more reliable method of change of volume. I t is to be remarked that in general it is not known to what extent agreement is to be expected because of the unknown effect of the large component of shearing stress known to be present in the resistance measurements. I t is in any event much to be regretted that some recent work in this field, particularly that at General Electric, has utilized the tabulated pressures of resistance discontinuities as calibration-fixed points, rather than the much more reliable pressures of volume discontinuities. However, the situation is in the process of being straightened out, and recent measurements, particularly by Kennedy and by Drickamer, are on the way to establishing the pressures of transition under true hydrostatic pressure in terms of resistance measurements. The solution of the more difficult problem of finding the true shape of the pressure-resistance curve in its entirety would appear, however, not to be so far advanced. l - 2 g T h e m e l t i n g curve. Another fruitful topic for investigation in the ranges now available is the character of the melting curve. So far, the probability seems to be that a "normal" melting curve will rise indefinitely with continually decreasing curvature. My own experimental examination of this question has been confined to comparatively low temperatures, but there is recent work by Clark at the Geophysical Laboratory 8 in which the same state of affairs has been found to hold up to 1200°C for a number of alkali halides. Up to date there appears to be only one possible exception to the rule: the melting curve of rubidium 8

S. P. Clark, Jr., Effect of Pressure on the Melting Points of Eight Alkali Halides, J. Chem. Phys., vol. 31, pp. 1526-1531, 1959.

199 — 4634

GENERAL OUTLOOK ON HIGH-PHESSURE RESEARCH

11

investigated by Bundy 9 of the General Electric Company. Bundy, using the method of change of resistance, followed the melting with increasing pressure, and presently found a maximum temperature, followed by decreasing temperatures at higher pressures. But Bundy himself stated that it was not certain that he was following the melting curve at higher pressures, and it seems to me by no means impossible that it was actually a transition between two solid forms, and that the melting curve had been lost in a triple point. There are several cases known of "abnormal" falling melting curves, which occur when the crystalline phase exceptionally has a greater volume than the liquid. I t is to be expected that such exceptional solid phases will presently become unstable and give way to a normal solid with smaller volume than the liquid (and in consequence a rising melting curve). This actually occurs for water, bismuth, and gallium, but apparently pressures have not yet been pushed high enough to produce this effect in antimony, although a transition is known in antimony near 80 kilobars at room temperature which might do the trick. Nor has the effect been found in germanium, which shows a falling melting curve that has been followed for hundreds of degrees into the hundred-kilobar range. The important question arises as to what is "normal" in a melting curve at astronomically high pressures. How would shifting electronic orbits be expected to affect it? It would seem that very few substances have been investigated hitherto for which the pressure has been carried high enough to force electronic rearrangements, and it is quite conceivable that our generalization with regard to the melting curve would have to be abandoned under drastically altered conditions, if indeed what one would be willing to call "melting" occurs at all under these conditions. 1-3

Problems in the Lower Pressure Range

Let us now return to a consideration of the domain of less than astronomical pressures. The experimental physicist will hardly be able to exhaust this lower domain in the foreseeable future. This is the domain in which, in the first instance, all six stress components are the experimental variables (in addition to temperature) or, ultimately, in the case of transient and dynamic nonequilibrium phenomena, there are nine stress components. The ultimate problem is a complete mapping out of the behavior of matter under nine arbitrary stress components. In the more usual range of six arbitrary components, large deviations from linearity in the relation between stress and strain are to be expected at 9 F . P. Bundy, Phase Diagram of Rubidium to 150,000 k g / c m 2 and 400°C, Phys. Rev., vol. 115, pp. 274-277, 1959.

199 — 4635

P. W. BRIDGMAN

12

high stresses. Under conventional conditions, not only is the relation between stress and strain linear, but it is also reversible. As the range of stress increases, there are increasing departures from this simple behavior; there are departures from linearity, the stress-strain relation is no longer reversible but there is hysteresis, and finally there are permanent alterations of configuration when stress returns to zero. These phenomena gradually extend themselves, first into the range dominated by fracturing and other phenomena of discontinuity, to be followed presently by the phenomena of indefinitely large plastic flow and the disappearance, over most of the range, of the phenomena of fracturing. Time effects become increasingly important, and parameters associated with the rate of flow obtrude themselves. The two domains of normally sharply distinguishable phenomena, that is, the domain of ordinary static phenomena and the domain of times (measured in microseconds) of the phenomena of detonation, become increasingly blurred and eventually merge together. Only the beginning of an attack has been made on this enormous field. Initial explorations have been presented in my book2 and in my studies of the behavior of a large number of substances under combined shearing and normal stress,6 but the conditions in all this work were highly specialized. It is clear that a great wealth of qualitative behavior, to say nothing of quantitative behavior, awaits more detailed study. In particular, the possibility of transitions which occur only with the cooperation of shearing stress demands further study. I should have liked to investigate further a phenomenon of rather unconventional character in this region. On a number of occasions, when studying the behavior of glass in a stress range in which there were still discontinuous fracturing effects, I found large and capricious electrical effects, manifested by spasmodic deflections in a ballistic galvanometer connected across the two platens of the shearing apparatus. It is natural to associate these with polarization effects arising from the fracturing of molecular dipoles. 1-4

Shock-wave Techniques

The very highest pressures will doubtless continue to be reached by some sort of shock-wave technique.10 It is conceivable that a way will be found of superposing shock-wave pressures on static pressures, although there are indications that the ordinary chemical type of detonation may be increasingly difficult to produce at higher pressures. Perhaps some fortunate experimenters may ultimately be able to command the use of atomic explosives in studying this field. It appears that there are still pressing questions in the ordinary range of detonation which must be solved before this powerful tool becomes capable of yielding results of 10

199 — 4636

See Chap. 13.

GENERAL OUTLOOK ON HIGH-PRESSURE RESEARCH

13

precision comparable with those of static methods. The calibration of the pressure scale still leans heavily on extrapolation of results obtained at lower pressures by static methods. Temperature control should be refined. Some way should be found of dealing more adequately with lack of isotropy, as in single crystals, which at present is almost always smothered in a general amorphousness. At the same time, any unique results which this technique is capable of giving because of the very short time intervals involved should be further exploited. An example is the possibility of carrying the solid large distances into the normal domain of stability of the liquid. Under static conditions it is not possible to superheat a solid, but in the very short times involved in detonations this becomes possible. In the case of bismuth, experiments at Los Alamos have realized a transition between two solid forms at a point 100° or more within the domain of normal melting. Here would appear to be a promising tool for studying the mechanism of transitions and of melting.

199 — 4637

INDEX OF SUBSTANCES In this index elements and inorganic chemical compounds are listed alphabetically by chemical formula. Minerals and organic compounds are listed alphabetically by their commonly accepted names. The number in brackets following the chemical formula of an organic compound is the number of that compound in the International Critical Tables. A + following a number indicates that the compound was not listed in the Tables but that Professor Bridgman felt it would have been listed at this place. References are to paper and page numbers; thus 167:141 means Paper 167, page 141. Pressures are in kilograms per square centimeter; temperatures in degrees centigrade; R.T. means room temperature. Melting and melting parameters, effect of pressure on, to 6000, 109:24 Scattered volumes as function of pressure down to -172°, 109:25 Volume between 2000 and 15,000 at 55°, 48:371; 52:194; 81:345 Acenaphthene, CI2HI0 [4218] Compression to 40,000 at R.T., 167:141 Acetamide, CH,CONH 2 [238] Phase diagram: to 11,000 and 180°, 21:515; 26:97, 167;—and transition parameters to 50,000 and 200°, 123:247 Velocity of polymorphic change under pressure, 25:72 Acetanilide, C e H,NO [2649] Shearing to 50,000, 123:266 Transition not found to 12,000 and 200°, 26:155 Acetic acid, CH,C0 2 H [212] Phase diagram: to 12,000 and 200°, 21:515; 81:354;—and transition parameters to 12,000 and 200°, 26:92, 163 Acetone, CH,COCH, [448] Thermal conductivity to 12,000 at 30° and 75°, 47:342; 51:158 Transition not found to 12,000 and 200°, 26:156 Viscosity to 12,000at30°and 75°, 61:604; 65:78 Volume to 12,000, 20° to 80°, together with various thermodynamic parameters, 11: 58; 81:347, 348 Acetophenone, CH,COC,H 6 [2571] Melting data, approximate, at 12,000 and 200°, 19:30 Polymorphism not found to 12,000 and 200°, 26:155

Acetyl toluidine (acetotoluide), CjHnNO, ο-, m-, and ρ- forms [3194] Compression to 40,000 at R.T., 161:84 Ag Compression: to 12,000 at 30° and 75°, 43: 362; 45:193; correction, 114:313;—to 30,000 at R.T., 168:199, 207 Ohm's law, departure from, at high current densities, 39:300; 42:165 Resistance: to 12,000, 0° to 100°, 27:599; 28:11;—to 20,000 at 30°, 110:80;—to 30,000 at 30° and 75°, 121:172; 124:15;— to 100,000 at R.T., 178:192;—to 7000 down to -183°, 97:326 Shearing to 50,000, 112:844; 115:665; 116: 333; 118:410, 442 Tension: coefficients of electrical conductivity, 60:435ff;—and resistance, 50:127;— and thermal conductivity, 50:127 Thermal conductivity to 12,000 at 30°, 41:110 Thermoelectric properties to 12,000, 0° to 100°, 31:316 Ag-Au alloys Compression: to 12,000 at 30° and 75°, 101:63-69;—to 30,000 at R.T., 197: 185 Resistance: to 12,000 at 30° and 75°, 101: 65-70;—to 30,000 and 100,000 at R.T., 197:185;—specific, at 0", and temperature coefficient, 0° to R.T., 197:185 Shearing to 80,000-100,000, 197:185 Ag-Bi alloy. See Bi-Ag alloy AgBr Compression: to 50,000 at - 7 9 ° and R.T., 130:238; 134:36, 49;—to 100,000 at R.T. and transition at 90,000, 147:4

4639

4640

INDEX

OF

Shearing to 50,000, 118:442 Transition: not found to 12,000 and 200°, 26:149;—and parameters to 50,000 and 146°, 117:202; 119:65 AgBrO, Compression: to 25,000 at R.T., 148:19;—to 100,000 at R.T., 147:4 Shearing to 50,000, 118:443 Transition uncertain to 50,000 and 200°, 119:128 AgCN Compression to 40,000 at R.T., 161:79 Shearing to 50,000, 118:443 Transition and parameters to 50,000 and 200°, 117:202; 119:81 AgCd Compression to 12,000 at 30° and 75°, 114:295 Resistance to 12,000 at 30° and 75°, 114:296 Shearing to 50,000, 118:442 Ag-Cd alloys Compressibility to 30,000, resistance to 30,000 and 100,000 at R.T., shearing to 80,000-100,000, specific resistance at 0°, temperature coefficient of resistance between 0° and R.T., 197:203 AgCl Compression: to 50,000 at - 7 9 ° and R.T., 130:238; 134:36, 49;—to 100,000 at R.T. and transition at 90,000, 147:4 Shearing to 50,000, 112:829; 118:442 Transition: not found to 12,000 and 200°, 26:149;—and parameters to 50,000 and 200°, 117:202; 119:64 AgClOa Shearing to 50,000, 118:443 Transition not found to 50,000 and 150°, 119:128 AgC10< Shearing to 50,000, 118:443 Transition and parameters to 50,000 and 200°, 117:203; 119:110 Ag-Cu alloys Compressibility to 30,000, resistance to 30,000 and 100,000 at R.T., shearing to 80,000-100,000, specific resistance at 0°, temperature coefficient of resistance between 0° and R.T., 196:141 Agl Compression: to 50,000 at - 7 9 ° and R.T., 130:238; 134:37;—to 100,000 at R.T., 147:4 Shearing to 50,000, 118:443 Transition and parameters to 12,000 and 200°, 20:97; 21:514; 26:166 AgIO» Shearing to 50,000, 118:443

SUBSTANCES Transition and parameters to 50,000 and 200°, 117:203; 119:108 AglO < Shearing to 50,000, 118:443 Transition improbable to 50,000 and 200°, 119:128 Ag-In alloys Compressibility to 30,000, resistance to 30,000 and 100,000 at R.T., shearing to 80,000-100,000, specific resistance at 0°, temperature coefficient of resistance between 0° and R.T., 197:203 Ag-Mg alloys Compressibility to 30,000, resistance to 30,000 and 100,000 at R.T., shearing to 80,000-100,000, specific resistance at 0°, temperature coefficient of resistance between 0° and R.T., 197:203 Ag-Mn alloys Compressibility to 30,000, resistance to 30,000 and 100,000 at R.T., shearing to 80,000-100,000, specific resistance at 0°, temperature coefficient of resistance between 0° and R.T., 197:182 AgN0 2 Shearing to 50,000, 118:443 Transition and parameters to 50,000 and 200°, 117:203; 119:85 AgNOs Compression: to 25,000 at R.T., 148:18;— to 100,000 at R.T., 147:4 Shearing to 50,000, 112:829; 118:443 Transition and parameters: to 12,000 and 200°, 21:514; 24:582; 26:166;—to 50,000, - 7 8 ° to 200°, 117:203; 119:87 Transition velocity at various pressures, 25:60, 68 Ag-Pd alloys Compressibility to 30,000, resistance to 30,000 and 100,000 at R.T., shearing to 80,000-100,000, specific resistance at 0°, temperature coefficient of resistance between 0° and R.T., 196:143 Ag-Pt alloys Compressibility to 30,000, resistance to 30,000 and 100,000 at R.T., shearing to 80,000-100,000, specific resistance at 0°, temperature coefficient of resistance between 0° and R.T., 197:185 AgZn Compression: to 12,000 at 30° and 75°, 114:297;—to 30,000 at R.T., 168:215, 217 Resistance: to 12,000 at 30° and 75°, 114: 297;—to 30,000 at R.T., 173:171; to 100,000 at R.T., 178:241 Shearing to 50,000, 118:442

INDEX

OF

Ag-Zn alloys Compressibility to 30,000, resistance to 30,000 and 100,000 at R.T., shearing to 80,000-100,000, specific resistance at 0°, temperature coefficient of resistance between 0° and R.T., 197:203 Ag,Al Compression: to 12,000 at 30° and 75°, 114:299;—to 30,000 at R.T., 168:215, 217 Resistance: to 12,000 at 30° and 75°, 114: 300;—to 30,000 at R.T., 173:174;—to 100,000 at R.T., 178:241 AgsO Shearing to 50,000, 112:829; 118:442 Transition phenomena, with parameters, and compressions to 12,000 and 200°, 96: 627-632; 106:20; 142:330 AgiS; see also Argentite Compression to 12,000 at 30° and 75°, 114:307 Resistance to 12,000 at 30°, 114:308;—to 100,000 at R.T., 178:244 Shearing to 50,000, 112:829; 118:443 Transition and parameters to 50,000 and 200°, 117:203; 119:66 AgjSO, Shearing to 50,000, 118:419, 443 Transition uncertain to 50,000, —79° to 150°, 119:128 AgjS0 4 -4NH s Compression to 12,000 at 30°, single crystal, one orientation, 114:310 AgiCde Compression to 12,000 at 30° and 75°, 114: 289 Resistance: to 12,000 at 30° and 75°, 114: 290;—to 30,000 and to 100,000, 178:240, 241 Shearing to 50,000, 118:442 AgjZnj Compression: to 12,000 at 30° and 75°, 114:290;—to 30,000 at R.T., 168:215, 218 Resistance: to 12,000 at 30° and 75°, 114: 291;—to 30,000 at R.T., 173:172;—to 100,000 at R.T., 178:241 Shearing to 50,000, 118:442 Al Compression: to 12,000 at 30° and 75°, 43:362; 45:194, 195; correction, 114:313; —to 100,000 at R.T., 160:63 Detonation under shearing stress with FejOj and K 2 C 2 0 4 , 112:829 Flow point, 22:222 Linear compression: to 6500 at R.T., 3:262; —to 30,000 at R.T., 168:199, 208

SUBSTANCES

4641

Resistance: to 12,000, 0° to 100°, 27:597; 28:11; 44:154;—to 30,000 at R.T., 173:153;—to 100,000 at R.T., 178:205;— to 7000 at 0° and 200°, 181:87;—down to -183°, 97:325 Shearing to 50,000,112:841; 118:431; 116:333 Tensile properties under pressure, 152:206; 169:553 Tension, effect of: on longitudinal and transverse resistance, 60:434;—on thermal and electrical conductivities, 50:127;— on thermoelectric quality, 31:377 Thermoelectromotive force, Peltier heat, and Thomson heat to 12,000 between 0° and 100°, 31:308 Al-Cu alloys Compressibility to 30,000, resistance to 30,000 and 100,000 at R.T., shearing to 80,000-100,000, specific resistance at 0°, temperature coefficient of resistance between 0° and R.T., 196:147 Al-Mg alloys Compressibility to 30,000, resistance to 30,000 and 100,000 at R.T., shearing to 80,000-100,000, specific resistance at 0°, temperature coefficient of resistance between 0° and R.T., 196:149 Al(NO,), Transition, polymorphic, not found to 12,000 and 200°, 24:618; 26:149 Al-Zn alloys Compressibility to 30,000, resistance to 30,000 and 100,000 at R.T., shearing to 80,000-100,000, specific resistance at 0°, temperature coefficient of resistance between 0° and R.T., 196:151 AlSb (intermetallic compound) Compression to 12,000 at 30° and 75°, 90:257 Al2Mg3 (intermetallic compound) Compression to 12,000 at 30° and 75°, 114:300 Resistance to 12,000 at 30° and 75°, 114:301 Specific resistance and volume contraction on formation, 114:315 A12OJ (synthetic sapphire) Compression to 12,000 at 30° and 75°, 101:56 Linear compression to 30,000 at R.T., 168:222, 228 Shearing to 50,000, 118:431 Tension and simple compression under supporting hydrostatic pressure, 158:251, 253 Al2Sa Shearing to 50,000, 118:431 A12(S04). Shearing to 50,000, 112:829

4642

INDEX

OF

Al„Mgx Compression to 12,000 at 30° and 75°, 114:301 Albumen (egg white) Coagulation phenomena to 12,000, 18:511 Compression to 5000 a t R.T., 193:125 Alizarin, CuHeOi [4626] Shearing to 35,000, 123:266 Alloy No. 193. See Fe-Ni-Cr alloy Amidol Shearing to 50,000, 123:266 Amino benzene sulfonic acid (anilinesulfonic acid), CjHtNOsS, ο-, τη-, and p-forms [1455] Compression and transitions to 40,000 at R.T., 161:84 Aminobenzoic acid, C7H7NO2, 0-, to-, and p- forms [2075] Compression: to 25,000 at R.T., 148:20;—to 40,000 at R.T., 161:83 o-Aminobutyric acid, C4H9NO2 [766] Volumes of several aqueous solutions to 8000 at 25° and 75°, 105:37 e-Aminocaproic acid (leucine), CeHi 3 0 2 N [1705] Compressions to 8000 at 25° and 75° of five aqueous solutions and atmospheric densities, 105:36 Aminophenol, C 8 H 7 NO, 0-, TO-, and p-forms [1446] Compression to 40,000 at R.T., 161:84 Ammonia alum Compression to 12,000 at 30° and 75°, single crystal, 87:62 Shearing to 50,000, 118:454 Ammonium phosphate Compression to 40,000 at R.T., 161:82 Shearing to 50,000, 118:454 Ammonium picrate, C«H«N