Physica status solidi / A.: Volume 52, Number 1 March 16 [Reprint 2021 ed.] 9783112493120, 9783112493113

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pliysica status solidi (a)

00.11.8%.-, * VOL. 52

NO. 1

MAIÌCH 1979

Classification Schemc 1. Structure oi Crystalline Solids 1.1 Perfectly Periodic S t r u c t u r e 1.2 Solid-State Phase Transformations 1.3 Alloys. Metallurgy 1.4 Microstructure (Magnetic Domains See 18; Ferroelectric Domains See 14.4.1) 1.5 Films 1.6 Surfaces 2. Non-Crystalline S t a t e 3. Crystal Growth 4. Bonding Properties 5. Mössbauer Spectroscopy 6. Lattice Dynamics. Phonons 7. Acoustic Properties 8. Thermal Properties 9. Diffusion 10. Defect Properties (Irradiation Defects See 11) 10.1 Metals 10.2 Non-Metals 11. Irradiation Effects (X-Ray Diffraction Investigations See 1 and 10) 12. Mechanical Properties (Plastic Deformations See 10) 12.1 Metals 12.2 Non-Metals 13. Electron States 13.1 B a n d S t r u c t u r e 13.2 F e r m i Surfaces 13.3 Surface a n d Interface States 13.4 I m p u r i t y a n d Defect States 13.5 E l e m e n t a r y Excitations (Phonons See 6) 13.5.1 Excitons 13.5.2 Plasmons 13.5.3 Polarons 13.5.4 Magnons 14. Electrical Properties. Transport Phenomena 14.1 Metals. Semi-Metals 14.2 Superconductivity. Superconducting Materials and Devices 14.3 Semiconductors 14.3.1 Films 14.3.2 Surfaces a n d Interfaces 14.3.3 Devices. Junctions (Contact Problems See 14.3.4) 14.3.4 High-Field Phenomena, Space-Charge Effects, Inhomogeneities, Injected Carriers (Electroluminescence See 20.3; J u n c t i o n s See 14.3.3) 14.4 Dielectrics 14.4.1 Ferroelectrics 15. Thermoelectric and Thermomagnetic Properties 16. Photoconductivity. Photovoltaic Effects 17. Emission of Electrons and Ions 17.1 Field Emission Microscope Investigations 18. Magnetic Properties 18.1 P a r a m a g n e t i c Properties 18.2 Ferromagnetic Properties 18.2.1 Ferromagnetic Films 18.3 Ferrimagnetic Properties 18.4 Antiferromagnetic Properties (Continued

on cover

three)

Important Information to Authors Beginning from 1.1. 1980 it is intended to use exclusively units of the Système International d'Unités (SI units) in physica status solidi. To assist authors in changing over to the new system, below we give a compilation of units most frequently appearing in physica status solidi, which have to be replaced by the corresponding SI units (in brackets) in future: length

A

(1 Â = 10" 1 nm)

force

kp dyn

(1 kp = 9.80665 N) (1 dyn = 10~5 N)

pressure

bar Torr at atm

(1 bar = 10B Pa) (1 Torr = 133.3 Pa) (1 at = 9.80665 X 104 Pa) (1 atm = 10.1325 X 104 Pa)

work, energy

cal erg

(1 cal = 4.1868 J ) (1 erg = 10~7 J )

magnetic field density (induction) G

(1 G = IO - 4 T)

magnetic field strength

Oe

(1 Oe = 79.6 A/m)

ion dose

R

(1 R = 2.58 X IO"4 C/kg)

activity

Ci

(1 Ci = 3.7 X IO10 Bq)

I t is recommended to use SI units already now when submitting manuscripts to physica status solidi.

physica status solidi (a) applied research Board of Editors S. A M E L I N C K X , Mol-Donk, J . A U T H , Berlin, H. B E T H G E , Halle, K. W. B Ö E R , Newark, P. G Ö R L I C H , Jena, G. M. H A T O Y A M A , Tokyo, C. HILSUM, Malvern, B. T. K O L O M I E T S , Leningrad, W. J . M E R Z , Zürich, A. S E E G E R , Stuttgart, G. S Z I G E T I f , Budapest, K. M. V A N V L I E T , Montréal Editor-in-Chief P. G Ö R L I C H Advisory Board L. N. A L E K S A N D R O V , Novosibirsk, W. A N D R Ä , Jena, E. B A U E R , Clausthal-Zellerfeld, G. C H I A R O T T I , Rom, H. C U R I E N , Paris, R. G R I G O R O V I C I , Bucharest, F. B. H U M P H R E Y , Pasadena, E. K L I E R , Praha, Z. M Ä L E K , Praha, G. O. M Ü L L E R , Berlin, Y. N A K A M U R A , Kyoto, T. N. R H O D I N , Ithaca, New York, R. S I Z M A N N , München, J . S T U K E , Marburg, J . T. W A L L M A R K , Göteborg, E. P. W O H L F A R T H , London

Volume 52 • Number 1 • Pages 1 to 370, K1 to K104, and Al to A8 March 16,1979 PSSA 52(1) 1—370, Kl—K104, AI—A8 (1979) ISSN 0031-8965

AKADEMIE-VERLAG • BERLIN

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Contents Review Article R.

CISZEWSKI

New Effects of Magnetic Critical Phenomena in Iron

11

Original Papers D . Y . CHUNG a n d V . K O N E C N Y

The Determination of the Orientation of Cubic Crystals f r o m Measured Sound Velocities

29

G. KADEN a n d H . REIMER

Impulsstromverhalten von MOS-Strukturen mit zum Substrat kurzgeschlossenem externem pn-Übergang bei linearer Gate-Spannungsansteuerung .

35

V . A . GRITSENKO, E . E . M E E R S O N , K . P . MOGILNIKOV, a n d S . P . SINITSA

High-Field Conductivity of Amorphous Insulator Films

47

S. K . BERA a n d S. K . GHOSH

Studies of Magnetic Damping Due to Pinned Domain Wall Motion (I) . .

59

T H . KARAKOSTAS, G . N O C E T , a n d P . DELAVIGNETTE

Grain Boundary Analysis in T E M (II)

65

R . BIRSOY a n d L . E . MURR

Coloring of Natural Fluorites

77

0 . A . T R O I T S K U , V . I . S P I T S Y N , N . V . SOKOLOV, a n d V . G . R Y Z H K O V

Application of High-Density Current in Plastic Working of Metals . . .

85

R . J . G A B O R I A U D e t J . CADOZ

E t u d e p a r microscopie électronique à haute tension de la configuration des dislocations, dans l'oxyde d ' y t t r i u m (Y 2 0 3 ) monocristallin déformé plastiquement

95

1. BALTOG, I . P I T I C U , M . CONSTANTINESCU, G . GHITA, a n d L . GHITA

Optical Investigations of P b l 2 Single Crystals after Thermal T r e a t m e n t . .

103

T . A . ABRAMOVSKAYA a n d M . D . ZVIADADZE

On Effects of the Dipole Reservoir in Radiofrequency Discrete Saturation .

Ill

C . JOUANIN, B . YANGUI, C. CESARI, C. BOULESTEIX, a n d G . NIHOUL-BOUTANG

Semi-Quantitative Study of Contrast near Bend Contours of Upper Laue Areas with t h e Incident Electron Beam Nearly Parallel to a Crystallographic Axis 1

121

4 A. KIENDL

Contents Kondensation der supraleitenden Phase in massivem Blei

131

J . GASTALDI a n d C. JOUKDAN

Observation of t h e Annealing Twin Growth b y Synchrotron Radiation X - R a y Topography

139

K . H . KRAATZ, G . FROHBERG, a n d H . W E V E R

Thermo- and Electromigration in High P u r i t y Cobalt

149

H . HOFFMANN, A . J . OWEN, a n d F . SCHROPF

Electron Microscopy of E v a p o r a t e d and Sputtered Gd/Co and Ho/Co Films

161

and M . Couzi R a m a n Spectra and Structural Phase Transitions in Chain Compounds (CH 3 ) 4 NMnCl 3 and (CH 3 ) 4 NCdCl 3

175

A Simple Model for Photo-Induced Polarization

189

Y . MLIK, A . DAOUD,

F.FISCHER

H . J . SCHENK, H . J . BAUER, a n d B . BARANOWSKI

Formation a n d Decomposition of the Hydride Phase in Ni-Mn Alloys in High-Pressure Gaseous Hydrogen Followed by Magnetic Measurements .

195

R . C. ECOB, J . V . B E E , a n d B . R A L P H

The Structure of t h e ß-Phase in Dilute Copper-Titanium Alloys

201

V . S . L Y S E N K O a n d A . N . NAZAROV

Formation a n d Annealing of Radiation Damage in Boron Ion Implanted MOS Structures

211

G . D L U B E K , 0 . BRUMMER, a n d ASHRAFUL ALAM

A S t u d y of Recovery and Recrystallization of Plastically Deformed a -j- ß Brass b y Positron Annihilation

217

Defect Electron Centres in Lead Molybdate Crystals

223

H J . BERNHARDT

G . FRANK, H . KÖSTLIN, a n d A . RABENAU

X - R a y a n d Optical Measurements in the I n 2 0 3 - S n 0 2 System

231

W . DECKER, J . D I E H L , A . DUNLOP, W . FRANK, H . KRONMÜLLER, W . MENSCH, H . E . SCHAEFER, B . SCHWENDEMANN, A . SEEGER, H . P . STARK, F . WALZ, a n d M . W E L L E R

Interstitial Migration in Iron a t 220 K

239

S . MAGER, E . W I E S E R , T . ZEMCIK, O . SCHNEEWEISS, P . N . STETSENKO, a n d V . V . SURIKOV

Investigations of the Magnetic Moments in (Fej-^Mn^JaAl Alloys . . . .

249

Contents

5

K . KURUMADA, T . MIZUTANI, a n d M . FUJIMOTO

F . VAVRA

Stationary Domains in Planar Gunn Elements

259

Influence of Metallic Impurities on Defect Production and Recovery in Niobium Neutron-Irradiated a t 4.6 K

269

M . E . VAN H U L L E a n d W . M A E N H O U T - V A N D E B V O R S T

D . VAN D Y C K

Influence of P b 2 + Ions on the Ionic Conductivity and the Space Charge Characteristics of Cubic Silver Halide Microcrystals

277

Improved Methods for the High Speed Calculation of Electron Microscopic Structure Images

283

J . C . BOURGOHN*, J . K R Y N I C K I , a n d B . B L A N C H A R D

Boron Concentration and Impurity-to-Band Activation Energy in Diamond

293

A . CAPLAIN e t W . CHAMBRON

E t u d e de l'interaction lacune-carbone dans l'alliage N i - 2 0 % at. F e par la méthode de l'anisotropie magnétique induite

299

T . SAKATA a n d A . ENOMURA

Studies of the Rare E a r t h - I r o n Interactions in t h e Orthoferrites G d F e 0 3 and HoFe03

311

H . BARTHOLIN a n d 0 . VOGT

Magnetic Phase Diagrams of CejfLao.ieYo.24)1-iBi Compounds

315

J . P E R E Z , C . M A I , J . TATIBOUET e t R . VASSOILLE

E t u d e des joints de grains dans la glace I h par mesure du f r o t t e m e n t intérieur

321

I . G . R I T C H I E , J . F . D U F R E S N E , a n d P . MOSER

I n t e r n a l Friction in Deformed Hydrogen-Doped I r o n

331

L . A . D E M B E R E L , A . S . POPOV, D . B . K U S H E V , a n d N . N . ZHELEVA

R.

A.

VARIN

Deep Levels in Fe-Doped I n P

341

Spreading of Extrinsic Grain Boundary Dislocations in Austenitic Steel .

347

P . R . HERCZFELD a n d M . J . FISHER

Utilization of Noise Theory and Measurements in Modelling Electronic Processes and Transport Phenomena in Photoconductors

357

P . L . L I a n d N . C. HALDER

Frequency Response Characteristics of Amorphous Germanium Thin Films

365

6

Contents Short Notes

F . FOUQUET, P . MERLE, a n d J . MERLIN

Characterization of Stages during the Precipitation of the 0 Phase in an Al-4 w t % Cu Alloy

K1

S . S . BOLGOV, A . G . K O L L U K H , V . K . M A L Y U T E N K O , a n d 1 . 1 . B O I K O

The Influence of an External Magneti c Field on the Recombination Radiation and Current-Voltage Characteristics of Indium Antimonide under Impact Ionization Conditions

K7

A . V . A N D R E E V , A . V . D E R Y A G I N , L . Z . L E V I T I N , A . S . MARKOS Y AN, a n d M . Z E L E N Y

Magnetic Anisotropy of the Intermetallic Compound UFe 2

K13

F . DETTMANN a n d P . PERTSCH

N b - N b O ^ - P b l n Tunnel Junctions with Ultra-Thin Niobium Electrodes K17 M . OHTA, M . YAMADA, T . KANADANI, a n d A . SAKAKIBARA

Effects of the Fluctuation of Solute Concentration in Al-10 w t % Zn Alloy on Aging a t Low Temperature K21 J . S C H N E I D E R , B . S P R I N G M A N N , K . ZAVETA, G . W E N Z E L , a n d E . K O H L E R

Magnetic After-Effect in Amorphous Fe-Co Based Alloys

K25

M . V A N ROSSTJM, J . D E B R U Y N , I . D E Z S I , G . LANGOUOHF., a n d R . COXISSEMEKT

On the Quadrupole Interaction of Xe Implanted in Diamond

K31

A . J . TWAROWSKI a n d A . C . ALBRECHT

Thermoelectric Films

Absorption

Spectroscopy of Polycrystalline

Tetracene K35

Z . J IRAK, S . VRATISLAV, a n d J . ZAJICEIC

The Magnetic Structure of Pr 0 .flCa0.iMnO 3

K39

A . K R E L L a n d D . SCHULZE

-Zone Fracture Anisotropy of Sapphire

K45

C. PARACCHINI a n d G . SCHIANCHI

Electroluminescence in Pure CdF 2 CH. SCHNITTLER

K49

The Influence of a Spatial Trap Distribution on the SCLC Characteristic of Insulating Films and Related Problems of Trap Analysis K53

W . ZAHN a n d F . DETTMANN

Critical Currents of N b - N b O ^ - P b Tunnel Junctions with High Normal Resistance K57 L . M . C A S P E R S , A . VAN V E E N , M . R . Y P M A , a n d R . F A S T E N A U

Interaction of Helium with Small Self-Interstitial Platelets in a-Fe . . . K61

Contents

7

W . R Ü H L E , K . LÖSCH, a n d J . U . FISCHBACH

A New Optical Method to Investigate Deep Traps in GaAs and I n P . . . K65 J . ¡SWIJ^TEK

Thermally Stimulated Currents in Thin Polycrystalline Layers

p-Polyphenyl K69

A . V E H A N E N , J . Y L I - K A U P P I L A , P . HAUTOJÄRVI, a n d V . S . MIKHALENKO

A Positron Study of Deformed NiGe Alloy

K73

A . S T ^ P N I A K a n d J . SKWARCZ

Optical and Magnetic-Optical Properties of Smo.55Tbo.45Fe0 3

K77

A . V . G A I S A N Y U K , K . I . K U G E L , a n d V . A . PETROV

Some Peculiarities of t h e Hall Constant in Disordered Materials: t h e ZrC-C System as an Example K81 P . V . YUKOVSKII, V . P . STELMAKH, a n d V . D . TKACHEV

Dependence of Si Amorphisation on Low- Energy Irradiation Conditions . K85 A . S . SIDORENKO, E . V . MINENKO, N . Y A . FOGEL, R . I . SHEKHTER, a n d I . 0 . K U L I K

Critical Field Anisotropy in Inhomogeneous Superconducting Films . . . K89

S . P . SINGH a n d H . K U Z M A N Y

Amplification of Bleustein-Gulyaev Waves in a Piezoelectric Coated with a Semiconducting Film H . KIRIHATA

K93

Effects of Gas Pressure and Sample Temperature during Slow Electron Excitation on Exoelectron Emission K97

J . M . ALBERDI, J . M . BARANDIABAN, a n d J . ILARRAZ

Temperature Dependence of Coercivity in Some R a r e - E a r t h - F e 2 Intermetallic Compounds K101

Pre-Printed Titles of papers to be published in the next issues of physica status solidi (a) a n d physica status solidi (b)

Al

9

Contents Systematic List Subject classification: 1 1.1

1.2 1.3 1.4 1.5 2 5 6 7 9 10.1 10.2 11 12.1 12.2 13 13.3 13.4 13.5.3 14 14.1 14.2 14.3 14.3.1 14.3.3 14.3.4 14.4 16 17 18

18.1 18.2 18.2.1

Corresponding papers begin on the following pages (pages given in italics refer to the principle subject classification): 11,29 65, 121, 283 175, 201, K81 231, Kl, K21 65, 121, 139, 201, 347 161 47, 161, 365, K25, K85 K31 175 K93 149, 195 139, 217, 239, 269, 299, 331, 347, K l K61, K73 77,95, 189, 223, 277, 321, K45 211, 239, 269, K31, K85 331, K l 321, K45 Ill, 283 35, K97 103, 189, 293, 341, K53, K65, K69 223 K81 85, 239, 269, K21 131, K17, K57, K89 293, K93 47,365 35, 211, 259 47, 341, K7, K53, K69 189, 277 189, 357 K97 Ill, 249 311 11, 59, 195, 299, 311, K13, K25, K101 161

18.3 18.4 19 20.1

K39, K77, K101 315 Ill 77, 175, 223, 231, 341, K35, K65, K77

20.3

103, 223, 341, K7, K49

Contents

21-1 21-1.1 21.4 21.5 22 22.1 22.1.1

85, 139, 217, 269, 347, K l , K17, K21, K57, K 8 9 149, 161, 195, 201, 249, 299, K l , K21, K 7 3 11, 239, 249, 299, 331, K13, K25, K61, K97, K101 161, 315, K101 K13 35, 47, 321, K 5 3 293, K 3 1 365, K 7 3

2 2 . 1 .2

211, K 8 5

21

22.2.1

259, K 6 5

22.2.2

341, K 6 5

22.2. 3

K7

22.3 22.4.1

K81 357

22.4.2

357

22.5

103, K 4 9

22.5.1

277

22.5. 2

189

22.5. 3

77

22.6

95, 121, K 4 5

22.6.1

231

22.8.1

223, K 3 9

22.8. 2

311, K77

22.9 23

175, K35, K 6 9 29

Contents of Volume 52 Continued on Page 373

Review

Article

phys. stat. sol. (a) 52, 11 (1979) Subject classification: 1 and 18.2; 21.1.1 Technical

University,

Sadorn1)

New Effects of Magnetic Critical Phenomena in Iron By R . ClSZEWSKI

Contents 1.

Introduction

2. Lateral maxima

in the intensity

of neutron

magnetic

critical scattering

in iron

2.1 Small-angle neutron magnetic critical scattering for different temperatures and different wavelengths 2.2 Discussion 3. The temperature dependence in neutron magnetic critical

of the "Curie scattering

point"

for iron

observed

3.1 Temperature shift of the maximum of magnetic critical scattering of neutrons in an iron monocrystal 3.2 Temperature shift of the maximum of magnetic critical scattering of neutrons in an iron polycrystal 3.3 Discussion 4. Anisotropy

of neutron

magnetic

critical scattering

in iron

monocrystals

4.1 Experimental results for different temperatures above Tc and around different reciprocal lattice points 4.2 The influence of the resolution function on the experimental data 4.3 Discussion 5.

Conclusions

References

1. Introduction Contemporary investigations of critical phenomena, such as critical opalescence, orderdisorder transitions in binary alloys, phenomena near the critical point in ferroelectrics or near the Curie temperature in ferromagnets, etc., show similarities which indicate that these effects are of a general nature for many-body systems. Because all critical phenomena may be described by the so-called correlation function, investigations of their space and time dependence are fundamental. The correlation function may be measured by diffraction experiments of different types of radiation, such as light, X-rays, or neutrons. The neutron as a nucleus having a magnetic moment will strongly interact with the magnetic system. The neutron scattering technique is unique for Malezewskiego 29, 26-600 Radom, Poland.

R. ClSZEWSKI

12

investigating magnetic bodies also in the vicinity of the critical point. Scattering near the Curie temperature has been investigated for more than twenty years. Although experimental results doubtlessly contribute to better understanding of the reality of magnetic critical phenomena, there are still discrepancies between theory and experiment. The situation in magnetic critical phenomena is rather complicated. There is still no uniform theory explaining all peculiarities of experimental data. Measured results can be interpreted only partially and in different approaches. Some new effects of critical scattering are predicted by the latest approaches, but the agreement between the experimental data and the theoretical predictions is still open to discussion. First experiments on neutron critical scattering performed by Palevsky and Hughes [1] and Squires [2], gave rise to the pioneer theory of magnetic critical phenomena given by Van Hove [3]; however, measurements of the inelastic critical scattering performed afterwards by Passel et al. [4] remained in contradiction with Van Hove's theory. Fisher [5] modified the Lorentzian shape of the Van Hove's cross-section. Halperin and Hohenberg [6] extended the static scaling hypothesis proposed by Widom [7] and Kadanoff [8] in the area of the dynamics of critical phenomena. Marshall developed a new kind of notation in the theory of magnetic critical phenomena [9]. Kocinski's and Wojtczak and Kocinski's theories [10 to 16] are based on original ideas of Smoluchowski [17], treating fluctuations as a subsystem in a reservoir. Such an approach allows to predict the appearance of new effects of critical phenomena in various systems, which cannot be explained by the remaining theories. These new effects are: 1. the anisotropy of critical scattering, 2. the lateral maxima in the intensity of critical scattering, 3. the temperature shift of the main maximum of critical scattering. As predicted by the theory, these effects can be detected using only large scattering vectors q (in comparison with the inverse of correlation length q 25; xx), therefore in this paper many experiments performed for small q's will not be discussed, which are already satisfactorily interpreted by classical scattering theories. One of the new static correlation functions given by Kocinski [10 to 16] has oscillating character, i- e - A T = = CqW. I n 1969, Stump and Maier [25] found out that the temperature shift depends also on the density of dislocations in the investigated sample. The theoretical approaches based on the assumption of elastic critical scattering cannot explain the observed dependence of the temperature shift on the wavelength Xi of incident neutrons [24], The only theory which seems to be able to deal with this newly observed effect, is the dynamic scaling theory [6]. This approach was used by Als-Nielsen [26], however, only for one value of Xi and for a narrow range of q values. I n order to explain experimental results obtained by a double-axis spectrometer one should analyze the shape of the intensity of scattered neutrons I{d) as a function of temperature for a given scattering angle 0 and a wavelength /.¡. This intensity can be calculated from the standard formula

(2 m n )

where /„ is the intensity of the beam of incident neutrons. I n the first Born approximation, the differential cross-section for neutron critical scattering is proportional to a S s - i s ^ r

(2l

where kf is the wave vector of scattered neutrons, ¡i = \jkB T. and scattering vector q are defined as 2m,

(kf — kf) ;

q = k

I

— k

l

.

>

The energy transfer e

(22)

The generalized static susceptibility %(q) and the relaxation function F(q, e) are defined in terms of the generalized linear susceptibility. Their forms depend on the models and approximations used to describe the system. F o r temperatures T 2 ; T c , the static susceptibility y\q) is proportional to the longitudinal correlation function and has the classical Ornstein-Zernicke form (23)

xf + q 2

where x1 is the inverse of correlation length, the amplitude R not depending on temperature. The relaxation function F(q, e) given by the dynamic scaling theory has the form F(q,e)=

r 2(q,

2

Ki) + E2

(24)

with the half-width r(q, xj defined by the dynamic scaling function f{x1 lq) [27, 6] : r(q,*i)

=

(26)

20

R. ClSZEWSKI 3.1 Temperature shift of the maximum of neutrons in an iron monocrystal

of the magnetic

critical

scattering

As mentioned above, many measurements of the temperature shift of the maximum of the critical scattering were performed for different scattering vectors, as well in mono- as in polycrystalline samples. But till now, there has been no experiment in ferromagnets indicating the dependence of the temperature shift on the crystal orientation with respect to the scattering vector. As predicted by Kocinski, such a dependence was found for a ferroelectric B a T i 0 3 monocrystal using X-ray radiation [28]. In order to investigate this dependence on the orientation of the scattering vector with respect to the three main crystallographic directions, most convenient would be a crystal in the shape of a cylinder with its vertical axis parallel to the [110] direction. Such a crystal was used in the experiment but it had a very small diameter — only 4 mm, so for this crystal the temperature shift was measured only for one case, i.e. q parallel to [111]. The remaining measurements, i.e. for q parallel to [110] and [100] directions were performed for a much larger monocrystal, but with 4 % Si. As previously reported in a short communication [24], the sample was cut in the shape of a cylinder with its vertical axis parallel to the [100] direction; the diameter of the crystal was equal to 14 mm and the height to 40 mm. I n spite of the fact that the Curie temperatures for both crystals have different values, the measured temperature shifts are the same for the same absolute value of q and for the same orientation of q with respect to the crystal axes, which has been checked for some experimental points. This leads to the additional conclusion that the admixture has no influence on the value of the temperature shift, at least in the case of pure iron and iron with 4 % of Si. The samples were heated in a high-temperature vacuum furnace. The temperature inside the furnace was automatically stabilized within + 0 . 1 K and its gradient along the vertical axis of the sample did not exceed + 0 . 1 K . For temperature measurements two chromel-alumel thermocouples were mounted at the basis and the top of the sample. The Curie temperatures were determined from neutron critical scattering measurements for very small scattering vector q (q iS 0.03 A - 1 ) . The measurements were performed on the DN-501 double-axis neutron spectrometer, located at the reactor " E w a " at Swierk. A monochromatic neutron beam of wavelength 1.53 A was extracted from the reactor beam by Bragg diffraction in the focusing Zn monochromator crystal. Soller collimators with 10 and 13 min of arc horinzontal divergence were placed in front of the sample and B F 3 counter, respectively (Fig. 6). In Fig. 7 the results obtained for three different crystal orientations are presented in a double-logarithmic scale. For comparison, there are also shown the results obtained for a polycrystalline sample for the same incoming neutron wavelength. In the measured g-range, i.e. (0.035 to 0.215) A - 1 for the temperature shift A T = Cqx, the following parameters

Fig. 6. Schematic outline of a double-axis spectrometer

21

New Effects of Magnetic Critical Phenomena in Iron

Fig. 7. Measured temperature shift of the maximum of neutron critical scattering in an iron monocrystal versus scattering vector q for three different crystal orientations. Results obtained for an iron polycrystal are also shown. • q || T ( no], A q || T[ioo], • T[inj, o polycrystalline iron; A = 1.53 A

15

-05V -12

III

-1Q

— -Iqlqi/i'll

i

-08

,

[

-OS

were found for each curve, by use of the mean-square method: for

q || [110]

a; = 3.64 ± 0.31,

lg C = 3.82 ± 0.28;

q || [100]

x = 4.29 ± 0.07,

lg C = 4.22 ± 0.06;

q || [111]

iron polycrystal

a; = 5.43 ± 0.15, z = 4.65 ± 0.26,

lg C = 4.94 + 0.11; lg C = 4.45 + 0.21.

For the same absolute value of q, the temperature shift is the largest for q along the [110] and the smallest for q along [111]. In the case of q parallel to the [100] direction intermediate values have been obtained. The magnitude of the temperature shift for the polycrystalline sample falls in between the two extreme values. 3.2 Temperature shift of the maximum of neutrons in an iron polycrystal

of magnetic

critical

scattering

In the experiment measurements of the temperature for which the maximum of small-angle magnetic critical scattering appears have been performed for four different wavelengths of incoming neutrons for the same range of the elastic scattering vector defined as q0 = kfi, where ki = 2nj/.i is the wave vector of incoming neutrons, 0 the scattering angle. The polycrystalline Fe sample was an Armco block of the dimensions 3 X 2 X X 0.5 cm3. The sample mounted on the ceramic holder, was heated by a coil wound on a ceramic tube 17 cm long. The temperature inside the high-temperature vacuum furnace was automatically stabilized within + 0 . 1 K, and its gradient along the vertical axis of the sample did not exceed the same value. For temperature measurements two chromel-alumel thermocouples were mounted at the base and at the top of the sample. The Curie temperature was determined from the peak of critical scattering for very small scattering vectors. It was found to be equal to Tc = (1043 + 0.25) K . Scattering measurements were performed on two spectrometers located at the reactor " E w a " at Swierk. Part of them were made on the double-crystal spectrometer presented in Fig. 5, and the remaining ones on the double-axis spectrometer presented in Fig. 6. Monochromatic neutron beams of wavelengths A, = 0.92, 1.14, 1.29, and 1.53 A were extracted from the reactor beam by Bragg diffraction in the Zn monochromator crystals. The statistical counting error did not exceed 3%. The accuracy of determining the value of the scattering vector q was higher than 1 %. The results obtained are presented in Fig. 8. The experimental curves plotted versus scattering angle d are nearly parallel to each other (Fig. 8 a), but plotted versus q0

22

R . ClSZEWSKI Fig. 8. Experimental data of the temperature shift A T = = Tm — Tc of the maximum of neutron critical scattering intensity for iron polycrystal versus a) scattering angle 0, b) elastic scattering vector q0 — fc,0 for different neutron wavelengths: o Ai = 0.92, • 1.14, A 1.29, + 1.53 A

exhibit a rapid change of their shape in the interval of A; between 1.14 and 1.29 A (Fig. 8b). As it has been already mentioned in the introductory part of this section, none of the existing theories based on the assumption of elastic critical scattering can explain the observed dependence of the temperature shift on the wave vector of incident neutrons. The only theory which seems to be able to deal with this newly observed effect, is the dynamic scaling theory. To calculate the intensity from the standard expression (20), one needs the formula for the scaling function. Such a formula was found on the basis of the data given in [26, 27, 30, 31]. The calculations were performed for two different values of the parameter C from formula (25), i.e. 130 and 150 meV A5/2 a n d for different values of parameters A and v appearing in the power law for x1 = A(AT/TC)V in the ranges (0.02 to 2) A" 1 and (0.2 to 0.8) for A and v, respectively. The calculated intensity for given scattering angle 6 and wavelength ?ii can be presented as a function of temperature T or inverse of correlation length x1 and the points Tm and xm for which the maximum of this function appears, can be found. The calculations performed showed that the variations of the parameters A and v within the intervals mentioned above do not affect the values of x m for given 6 and This allows to establish the dependence of xw on 6 and / j for the two values of C and the four values of used in the experiment. The comparison of these results with the experimental data leads to the estimation of r.m versus reduced temperature e m = These functions are presented in Fig. 9 for C = 130 and 150 meVA 6 / 2 . = (Tm—TC)ITC. The least-square fitting curves of the form given by the power law x1 = Aevm were found and the values of the critical index v were estimated (Table 1). I t means that the best fit would be achieved if one takes different values of the critical index v for each of the experimental curves. s

t 3

/ V

/ V / /

7

2

f r 1

]

/

h /

/

*

3/'/lì

!

°> >

W'J

b '

Fig. 9. Calculated inverse correlation length y.m versus the experimentally determined reduced temperature e m = (Tm — TC)ITC. The straight lines are the leastsquare fitting with disposable parameters A and v. The calculations were performed a) for the parameter O = 130 meV As/2 and b) C = 150 meV As/2. Neutron

wavelengths are (1, o) Aj = 0 . 9 2 , (2, •) 1.14, (3, A)

1.29, (4, +) 1.53 A

23

New Effects of Magnetic Critical Phenomena in Iron Table 1 Best fit of v and A values (A)

0.92

1.14

1.29

1.53

C = 130 meV Â5/2

v A (A - 1 )

0.67 ± 0.07 0.93

0.70 + 0.6 1.11

0.29 + 0.06 0.19

0.47 + 0.17 0.44 "

C = 150 meV As/2

v A

0.64 ± 0.07 0.90

0.64 + 0.5 0.94

0.27 + 0.05 0.19

0.45 ± 0.16 0.45

If the explanation of the temperature shift proposed by the dynamic scaling theory were correct, this procedure should give only one value of v, independently of Aj. Because of differences in the estimated v values one may conclude that in the present form the dynamic scaling theory cannot account for differences in the observed behaviour of the A T(q0) dependence for different Ar 3.3

Discussion

As mentioned above the detected anisotropic character of the temperature shift for a monocrystal cannot be explained by a spherically symmetric cross-section of Van Hove type. The only theory which predicts the anisotropy of magnetic neutron critical scattering, is the theory based on the correlation exp [—«i//3 {\x\ + \y\ + |z|)]. But, unfortunately, this correlation is valid for crystals with simple cubic symmetry only. The dependence of the cross-section upon the crystal lattice symmetry was recently discussed by Kocinski and Marzec [29] for various symmetries. According to the cross-section for a b.c.c. lattice derived in that paper, the magnitude of the temperature shift, in the elastic approximation, should be larger for q along the [100] direction than for q along [111]. However, no shift should appear for q along the [110] direction. The experiments yield a proportionality of the shifts to powers of q higher than 2. Theoretically, in the elastic approximation the shifts should be proportional to q2. The determined temperature shifts give new evidence of the existence of the anisotropy of neutron critical scattering in iron monocrystals, but there is no quantitative agreement between experiment and theory which predicts the existence of this new effect. The results obtained for polycrystals indicate that the dynamic scaling theory, where the Ornstein-Zernicke form of the static susceptibility is used, cannot be reconciled with the experiment. The test used assumes the validity of the power law for x(T), which cannot be disproved in the investigated region of the reduced temperature, i.e. 10- 3 to 10" 1 . The reason for the discrepancy between the discussed theoretical approach and the experiment probably stems from the fact that the dynamic scaling theory concerns only the excitation with wavelengths smaller than the size of the single fluctuation, ignoring the effects of the collective excitations which can take place in the ensemble of such fluctuations. One evidence for such excitations comes from the observed magnetic Mandelstam-Brillouin doublet. The recent investigations of the effect of the temperature shift within dynamical secondBorn approximation [32], although they are able to deal with the Aj dependence of the shift, cannot account for the peculiarities of the phenomenon found in the experiment.

R. ClSZEWSKI

24

4. Anisotropy of Neutron Magnetic Critical Scattering in Iron Monocrystals The connection between crystal symmetry and anisotropy of critical scattering was discussed in [12, 13]. In contradition to the classical forms of the correlation function, which always have spherical symmetry, Wojtczak and Kocinski's one [16] shows anisotropy for small distances. For large distances it does not differ much from the Ornstein-Zernicke correlation. For a monocrystal for temperatures above T c the corresponding cross-section indicates the dependence on the directions of the scatterring vector q with respect to the crystal axes. According to the expression (5), the ratio of two cross-sections, for example, for the case when T [ 1 0 o ] II H and T [ 1 1 0 J | q, is not equal to unity and depends on q/x1:

(26)

E can be a measure of the anisotropy of critical scattering. For a given temperature (given Xj) the larger is the scattering vector q, the larger the anisotropy should be and for a given q the anisotropy should decrease with the increase of temperature. The anisotropy of the cross-section (or measured intensity) is also well seen on the isointensity curves presented in the reciprocal lattice space. I n the last few years ,X-ray and neutron critical scattering experiments were performed in ferroelectries, dielectrics, and binary alloys. An anisotropy was found in BaTiOg [28, 33], TGS [35], AuCu 3 [35], and NaNO s [34, 36]. B u t there was no experiment for magnetic materials. Thus it would be reasonable to investigate whether anisotropy of critical scattering also exists for ferromagnets. 4.1 Experimental results for different temperatures and around different reciprocal lattice points

above

Tq

To measure the anisotropy of neutron critical scattering for ferromagnets an iron monocrystal with 4 % Si was used. The [001] direction was parallel to its vertical axis. The diameter of the crystal was equal to 14 mm and the height to 40 mm. The temperature stability and the gradient along the vertical axis of the sample did not exceed + 0 . 1 K . Scattering measurements were performed on a double-axis neutron spectrometer (Fig. 6) around the (110) reciprocal lattice point. Changing the angle of the spectrometer arm a and independently the angle of the sample table ip, one can [1101 \

Fig. 10. Scattering diagram presented in the reciprocal lattice space for the measurements of the anisotropy of,critical scattering, ?[iio] and 7[iio] are given by equation (27)

25

New Effects of Magnetic Critical Phenomena in Iron

Fig. 11. Neutron critical scattering measured on an iron monocrystal presented in the reciprocal lattice space. The dashed line is calculated as a convolution of the isotropic Van Hove cross-section with the experimental resolution function. (T - Tc)/Tc = 39 x 1 0 ' 4 , Aj = 1.53 Ä

^ümA1)

irmi

change the components of the vector q so that a

!

1 — sin 0 sin2 ^

îtiio] =

sin 3in — cos 10 [ t/ +-+•— —

?[iio] =

sin (7 sin

jtem.p nichtstationäre Elektronen- bzw. Löcheremissionsstromdichte der Oberflächenzustände; jtcap,n> Jtcap.p nichtstationäre Elektronen- bzw. Löchereinfangstromdichte der Oberflächenzustände Fig. 5. Verlauf der Stromdichtekomponenten bei tx < 0. Die P a r a m e t e r der M O S C - P N - S t r u k t u r entsprechen Fig. 3 3 ) I n [17], Fig. 7, 8, war infolge anderer Geometrieverhältnisse der MOSC-PN-Struktur Z / i ^ A s ) bedeutend kleiner als hier.

39

Impulsstromverhalten von MOS-Strukturen mit externem pn-Übergang 5

i -

2 0 - 2 - 1 - 6 -usm

-8

Fig. 7 Fig. 6. Verlauf der Stromdichtekomponenten bei • 0. Die Parameter der MOSC-PN-Struktur entsprechen Fig. 3 Fig. 7. Abhängigkeit des normierten Oberflächenpotentials von der Gatespannung. Die Parameter der MOSC-PN-Struktur entsprechen Fig. 3

Beispiel ist in Fig. 7 die Abhängigkeit des normierten Oberflächenpotentials us von TJQ bzw. t angegeben. Da die nichtstationäre Oberflächenzustandsladungsdichte g tns geringer (a. 0) oder größer (a. 0) als die Gleichgewichtsladungsdichte qt ist, weicht |ws| im Nichtgleichgewicht zu höheren ( 0) Werten hin a b . 4. Berechnung des nichtstationären Stromverlaufs im Verarmungsbereich I m Verarmungsbereich nimmt der Ausdruck für qs nach [17], Formel (3), die Form qs

=

qD

=

2qniLD[—(us

+

1)

e—

(8)

an, und für js ergibt sich .

_

.

* qn-,L i Dd • [ — K + 1) e + M F ] 1 / 2 '

_

(9)

Mit qY) und / D wurden dabei die Ladungs- und Stromdichte in der Verarmungszone bezeichnet, die anstelle von qs und j% in Gleichung (3) und (5) eingesetzt werden können. Ferner ist die Debye-Länge des Eigenhalbleiters, ni die Eigenleitungsdichte und wF das normierte Fermipotential. Mit (5) und (6) ergibt sich Cox 0)

Die nichtstationäre Umladung der Oberflächenzustände vollzieht sich vorwiegend durch Elektroneneinfang, der sich im Gatestromverlauf durch ein flaches Strommaximum äußert (siehe Fig. 3 und 6). Die nichtstationäre Elektroneneinfangstromdichte sowie u m (u s ) erhält man nach [17], Formel (19) und (21). I m äußeren Stromkreis gilt = 0 und jB — y'D + ?tcaP,n5. Berechnung des nichtstationären Stromverlauis im Inversionsbereich Der Inversionsbereich wird im Gleichgewicht durch us u¥ bzw. |i7 G | li/J festgelegt. Dabei ist Uj die für Eigenleitung an der Oberfläche notwendige Gatespannung, deren Wert aus der Bedingung u s = wF mit (3) und (4) bestimmt werden kann. 5.1 Hinlauf

(a

5 )

—

0

(21)

möglich.

fcwr? V

'

]

Wijifi

C It) jimax

1 1 i»

\

Fig. 8. Modell der Oberflächenraumladungszone MOSC-PN-Struktur bei schwacher Inversion

einer

42

G. K a d e n

and

H .

R e i m e r

Mit Z, As und Dp wurden dabei die Breite der Randzone, die Gatefläche und der Löcherdiffusionskoeffizient bezeichnet. 5.3.2 Schwache Inversion Bei schwacher Inversion erhält man mit (17) und (18) unter Berücksichtigung von wF us > 2uv für die Löcherladungsdichte in der Randzone gl,5MF— Us+f qv = q n i L J ) — = = (22) / - ( « . + 1) Nach [23] ist ein Diffusionsstrom von Minoritätsträgern, für den man mit (20) und (22) in Anlehnung an [24] den Ausdruck fi pl,5«F — «a h = J-r D ^ L » — (1 (23) LiAs (/-K+1) erhält, der sich bei | m a x ig —3 zu ei,5«p-MS

Z

z

K + !)

LiA*

1

s

vereinfacht. Unter Ausnutzung der nahezu linearen Abhängigkeit us(UG) kann man nach [25] folgende Näherungsformel für die stationäre Löcherladungsdichte am pn-Übergang g p l i/=0 erhalten: U$-Ui-xt 71 e 9W=0 = qn^yy . (25) 'Ut-Ui-OLt 5 1 ,5mf — 1 Dabei ist hT

n

=

— Cox + qkTNst + 9 '

qntLD

g

-mf/2

/—(1,5mf + 1 )

Wx

und U * = ^G|«Ì„ = 1,5WF •

Die ab U i in die Oberflächenraumladungszone eingeflossene Ladung erhält man durch Integration von (24) mit

-"l^S wobei

(26) "

\

«

/

t

B(t)

•J

( und - | -^jja-dz zl/2 " 0

z=

U* — U 1

— 1,5wf — 1 — —t 7t

ist.

Von großem Interesse, nicht zuletzt zur Bestimmung des Übergangspunktes UA (siehe Abschnitt 6), ist die Berechnung der Aufteilung von in /pns und /tcap.p- Um zu einer Lösung dieses Problèmes zu gelangen, soll die Umladung der Oberflächenzustände durch Elektronenemission bei |Î7G| U^ vernachlässigt werden. Dann gilt ?pns(