Physica status solidi / A.: Volume 52, Number 2 April 16 [Reprint 2021 ed.] 9783112501023, 9783112501016

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plrysica status solidi (a)

ISSN 0031-8965 * VOL. 52 • NO. 2 • APRIL 1979

Classification Scheme 1. Structure of Crystalline Solids 1.1 Perfectly Periodic Structure 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 State 3. 4. 5. 6. 7.

Crystal Growth Bonding Properties Mössbauer Spectroscopy Lattice Dynamics. Phonons 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 Band Structure 13.2 Fermi Surfaces 13.3 Surface and Interface States 13.4 Impurity and Defect States 13.5 Elementary Excitations (Phonons See 6) 13.5.1 Excitons 13.5.2 Plasmons 13.5.3 Polarons 13.5.4 Magnons 14. Eleetrical 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 and 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; Junctions 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 Paramagnetic Properties 18.2 Ferromagnetic Properties 18.2.1 Ferromagnetic Films 18.3 Ferrimagnetic Properties 18.4 Antiferromagnetic Properties (Continued

on cover three)

physica status solidi (a) applied research

B o a r d of E d i t o r s

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. H I L S U M , 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. VAN V L I ET, 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. SIZMANN, 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 2 • Pages 371 to 718, K 1 0 5 to K 2 2 0 , and A 9 to A 1 6 April 1 6 , 1 9 7 9 P S S A 52(2) 3 7 1 — 7 1 8 , K 1 0 5 — K 2 2 0 , A 9 — A 1 6 (1979) ISSN 0031-8965

AKADEMIE-VEKLAG .

BERLIN

Subscriptions and orders for single copies should be directed in the D D R : t o t h e Postzeitungsvertrieb, t o a book-shop, or to t h e Akademie-Verlag, DDR-108 Berlin, Leipziger Straße 3 —4; in the other socialist countries: to a book-shop for foreign language literature or t o t h e competent news-distributing agency; i n t h e B R D and B E R L I N ( W E S T ) : to a book-shop or to t h e wholesale distributing agency K u n s t u n d Wissen, Erich Bieber, D-7000 S t u t t g a r t 1, Wilhelmstr. 4 - 6 ; in ÖSTERREICH: to t h e Globus-Buchvertrieb, A-1201 Wien, H ö c h s t ä d t p l a t z 3 ; in the other Western E u r o p e a n countries: to K u n s t u n d Wissen, Erich Bieber G m b H , CH-8008 Zürich, Dufourstr. 51; i n USA and C A N A D A : to Verlag Chemie I n t e r n a t i o n a l , Inc., 175 F i f t h Avenue, New York, N . Y. 10010, U S A ; in other countries: to t h e international book- and journal-selling t r a d e , t o Buchexport, Volkseigener Außenhandelsbetrieb der Deutschen Demokratischen R e p u b l i k , DDR-701 Leipzig, P o s t f a c h 160, or to t h e Akademie-Verlag, DDR-108 Berlin, Leipziger Straße 3 - 4 .

Editorial Note: " physica status solidi (a)" u n d e r t a k e s t h a t an original paper accepted for publication before the 23rd of any m o n t h will be published within 50 days of this d a t e unless t h e a u t h o r requests a postponement. In special cases there m a y be some delay between receipt and acceptance of a p a p e r due to the review and, if necessary, revision of t h e paper.

Schriftleiter u n d verantwortlich f ü r den I n h a l t : P r o f e s s o r D r . D r . h.c. P . G ö r l i c h , D D R - 1 0 2 B e r l i n , N e u e S c h ö n h a u s e r S t r . 20 b z w . D D R - 6 9 J e n a , S c h i l l b a c h s t r . 2 4 . Verlag: A k a d e m i e - V e r l a g , D D R - 1 0 8 B e r l i n , L e i p z i g e r S t r . 3 - 4 ; F e r n r u f 2236221 u n d 2 2 3 6 2 2 9 ; T e l e x - N r . : 1 1 4 4 2 0 ; B a n k : S t a a t s b a n k d e r D D R , B e r l i n , K t o . - N r . : 6836-26-20 712. Chefredakteur: Dr. H.-J. Hänsch. Redaktionskollegium: P r o f . D r . E . G u t s c h e , D r . H . - J . H ä n s c h , D r . H . L a n g e , D r . S. O b e r l ä n d e r . Anschrift der R e d a k t i o n : D D R - 1 0 2 B e r l i n , N e u e S c h ö n h a u s e r S t r . 2 0 ; F e r n r u f : 2 82 33 80. V e r ö f f e n t l i c h t u n t e r d e r L i z e n z n u m m e r 1620 des P r e s s e a m t e s b e i m V o r s i t z e n d e n des M i n i s t e r r a t e s der D e u t s c h e n Demokratischen Republik. Gesamtherstellung: V E B Druckerei „Thomas Müntzer", DDR-582 Bad Langensalza. Erscheinungsweise: D i e Z e i t s c h r i f t „ p h y s i c a s t a t u s solidi ( a ) " e r s c h e i n t j e w e i l s a m 16. eines j e d e n MonatB. J ä h r l i c h e r s c h e i n e n 6 B ä n d e zu j e 2 H e f t e n . Bezugspreis: j e B a n d 165,— M z u z ü g l i c h V e r s a n d s p e s e n ( P r e i s f ü r die D D R : 130,— M ) . B e s t e l l n u m m e r dieses B a n d e s : 1085/52. © 1979 b y A k a d e m i e - V e r l a g B e r l i n . Printed in the German Democratic Republic. A N ( E D V ) 20 735

Contents Original Papers E . DYNOWSKA a n d J . STANKOWSKI

X - R a y Study of the Structural Phase Transition in Nickel Hexammine Perchlorate

381

J . KREMPASKY, J . VAJDA, A . ZENTKO, a n d P . D U H A J

Peculiarities in the Temperature Dependence of Electrical Resistivity of Metallic Glasses

387

K . BARTKOWSKI, D . WLOSEWICZ, a n d J . RAEALOWICZ

Lorenz Function and Horizontal and Vertical Component of Thermal Resistivity of Tin Monocrystals

397

L . F . VERESHCHAGIN, L . G . KHVOSTANTSEV, a n d V . F . SKOK

Thermoelectric Properties of Indium Antimonide under High Pressure u p to 35 kbar

401

S . GUHA, P . K . SEN, a n d S . GHOSH

Parametric Instability of Acoustic Waves in Transversely Magnetised Piezoelectric Semiconductors

407

M . F . V E R E S H C H A K , A . K . Z H E T B A E V , a n d S H . S H . IBRAGIMOV

A Mössbauer Study of the Effect of y-Rays and Neutron Irradiation on Iron Oxalates

415

R . T I D E C K S a n d G . VON M I N N I G E R O D E

The Influence of High-Frequency Radiation on the JJ-1 Characteristics of Superconducting Tin Whiskers

421

H . B E R G E R , B . K U H R I G , G . OELGART, U . P I E T S C H , a n d D . SCHIKORA

Investigation of Chemical Micro-Inhomogeneities Crystals

in Bijoo— .-tSb^ Single 427

R . S . POPOVIÖ a n d N . D . S T O J A D I N O V I C

Dependence of Dislocations on Emitter Phosphorus Diffusion Conditions and Their Effects on Electrical Characteristics of Silicon Planar N P N Transistors

433

V . L . VINETSKII, G. N . ERITSYAN, a n d R . A . MELKONYAN

On the Nature of the "Limiting" Position of the Fermi Level in Irradiated Silicon

441

R . Z . VALIEV, 0 . A . KAIBYSHEV, a n d SH. K H . KHANNANOV

Grain Boundaries during Superplastic Deformation

447

E . V . ZAROCHENTSEV, S. M . O R E L , a n d V . N . V A R Y U K H I N

Elastic Constants of a Stressed Crystal (I)

455

H . F . K A P P E R T , G . SIXT, a n d G . H . SCHWUTTKE

Minority Carrier Lifetime in Silicon after Ar + and Si + Implantation . . . .

25«

463

374

Contents

R . MOSSERI, C . S E L L A , a n d J . D I X M I E R

X - R a y Diffraction Study of the Effect of Hydrogen Atoms on the Si-Si Atomic Short-Range Order in Amorphous Silicon

H . J . E I C H L E R , J . E I C H L E R , J . K N O F , a n d CH. NOACK

Lifetimes of Laser-Induced Population Density Gratings in Ruby . . . .

475

481

W . R . THORPE a n d I . O . SMITH

A Model for High-Temperature Creep Incorporating Both Recovery and Thermally Activated Glide

487

A . J . DREHMAN a n d W . L . JOHNSON

Effects of Thermal Relaxation on an Amorphous Superconducting Zr-Rh Alloy

A . BOSE, G . FROHBERG, a n d H . W E V E R

Self-Diffusion of

60

M . PEYRARD a n d R . PERRET

Co and , 2 Ga in the Ordered Electronic Compound CoGa

F I R Spectroscopy (CH3CH2NH3)2CdCl4

Study

of

the

First-Order

Phase

Transition

of

J . G . E R L I N G S a n d F . W . SCHAPINK

K.

HUBNER

499

509

521

Electron Diffraction from Periodic Twist Grain Boundary Structures

529

Chemical Bond and Related Properties of Si0 2 (VI)

541

D . H A F N E R a n d H . HOFFMANN

Microscopic and Macroscopic Inhomogeneity of Magnetization and Anisotropy in Amorphous Rare Earth/Transition Metal Films

H . NEUMANN, D . P E T E R S , B . SCHUMANN, a n d G . K U H N

H. KRAUSE

549

Electrical Properties of CuGaTe2 Epitaxial Layers

559

Tunnel Hopping Current and Trap Filling in Insulating Layers

565

R . H . J . F A S T E N A U , C . M . VAN B A A L , P . PENNING, a n d A . VAN V E E N

On the Sink Concentration Dependence of Reaction Constants for Point Defect Trapping

R . G E M P E R L E , P . NOVOTNY, a n d A . M E N O V S K Y

Bitter Figure Observations on U 3 As 4 at Low Temperatures

A . MONTANER, M . G A L T I E R , C . B E N O I T , a n d H . B I L L

Optical Constants of Sodium Sulphide

J . NOVOTNY a n d Z . S P U R N Y

Absorption Shift in Aluminophosphate Glasses

577

587

597

603

Contents

375

J . H . BASSON a n d C . A . B . B A L L

Threading Dislocations in Single-Layer Heteroepitaxial Structures . . .

609

M . B O G D A N , A . NICTJLA, a n d D . LTTPU

Spin-Lattice Relaxation Time and Q.uadrupole Coupling of Deuterium in PdDo.7o

615

V . G . ZHDANOV, B . T . KOLOMIETS, V . M . L Y U B I N , a n d V . K . MALINOVSKII

Photoinduced Optical Anisotropy in Chalcogenide Vitreous Semiconducting Films

621

0 . V . PRESNYAKOVA, V . I . ZAITSEV, a n d N . A . DOROSHENKO

Aluminum Polygonization under High Pressure

627

J . D E GROOT, P . M . B R O N S V E L D , a n d J . T H . M . D E H O S S O N

Superlattice Dislocations in Cu £ NiZn

635

H . B A R T H O L I N , D . F L O R E N C E , a n d O . VOGT

Magnetic Phase Diagrams of Cex(Lao.7eYo.24)i - * S b Compounds

647

L . A . D E M B E R E L , A . S . P O P O V , a n d D . B . KTJSHEV

Deep Levels in Fe-Doped GaP

653

S. E . HORAN a n d L . M . SLIFKIN

Stress-Induced Anomalies in t h e Internal Friction of Strontium-Doped Silver Bromide

657

K . JAGANNADHAM a n d M . J . MARCINKOWSKI

Discrete Dislocation Analysis of Cracks

663

J . SHANKER a n d V . C. J A I N

Analysis of t h e Crystal Binding of Alkali Hydrides

675

S . B . P A T I L , H . V . K E E R , a n d D . K . CHAKRABARTY

C.

S.

PANDE

Structural, Electrical, and Magnetic Properties in t h e System Ba^Lai - z C o O j

681

Transmission Electron Microscopy of Radiation Damage in Nb 3 Sn

. . .

687

. . .

697

H . B . TRIPATHI, H . C . K A N D P A L , a n d A . K . AGARWAL

Non-Radiative Energy Transfer f r o m D y 3 + -> H o 3 + in Calibo Glass

V . E . ANTONOV, I . T . B E L A S H , B . K . PONOMAREV, E . G . P O N Y A T O V S K I I , a n d V . G . T H I E S S E N

Magnetic Properties of Hydrogen Solid Solutions in F e - N i - M n Alloys . .

703

V . TEODORESCU, L . C . NISTOR, a n d S . V . NISTOR

Electron Microscopy Study of Pure and Doped Synthetically Grown CaF 2 Crystals

711

Contents

376

Short Notes I . H . ISMAILZADE, A . Y U . K U D Z I N , a n d L . Y A . SADOVSKAYA

X - R a y Diffractional and Optical Investigations of Ferroelectric S r T e 0 3 K105 J . A R S E N E , J . LOPTTAUX, M . D R I F E O R D e t M . L E N G L E T

Mise en évidence de la coordination tétraédrique de l'ion Cr 3+ dans un chromigallate de lithium p a r analyse du spectre électronique Kill

G . A . ANDREEV a n d Y . A . KLIMOV

C.

BANSAL

Precipitation in K C l : P b 2 + Crystals

K115

Local Environment Effects in Ni-Cu and N i - A u Alloys

Kl

G . D . SOOTHA, G . K . P A D A M , a n d S . K . G U P T A

E S R Study of Oxygen Radicals Formed in Cadmium Sulphide

S. D.

RISTIC

19

K125

An Approximation of the Einstein Relation for Heavily Doped Silicon . . . K129

A . A . URTJSOVSKAYA a n d G . G . K M A B

Thermal Activation Analysis of Plastic Deformation of PbS Single Crystals K133 G . RUDLOF, J . BECHERER, a n d H . GLAEFEKE

A R e m a r k on Determining Activation Energies b y Fractional Glow Technique (FGT) in Case of Complex Glow Spectra — A Procedure of Improving This Method K137 R . BATJBINAS, F . S E N U M S , a n d J . V A I T K U S

Temperature Dependence of the Optical Ionization Energy of Deep Local Levels in CdSe Single Crystals K143 A . SUBRAHMAHYAM a n d K . V . RAO

F - B a n d Absorption and Thermoluminescence of KC1 Single Crystals under DC Field a n d X - R a y Irradiation K147 N . M . RAVTNDRA, S U S H I L A U L U C K , a n d V . K . SRIVASTAVA

Temperature Dependence of the Energy Gap in PbS, PbSe, and P b T e . . K151 H . FIEDLER a n d H . - R . BEILICH

Influence of t h e Substrate Temperature on t h e Dielectrie Relaxation of Amorphous Selenium Layers in t h e Glass Transition Range K157 F.

DETTMANN

E n h a n c e m e n t of Magnetic Field in "Window"-Type Tunnel Junctions . . . K161

W . SCHROTER, H . G . BRION, a n d H . SIETHOFF

Self-Diffusion and Dynamical Recovery in Silicon a t High Temperatures K165

Contents

377

M . PoPEScxr a n d C. GHIZDEANU

Cation Distribution in Cobalt Ferrite-Aluminates

K169

F . ADDTTCI, L . B A L D A S S A R R E , G . M A G G I P I N T O , A . M I N A F K A , a n d F . L E V Y

Defect Levels in P b l 2 by TSC Measurements H . PYKACZ

K173

Notes on the First-Order Ferroelectric Phase Transitions in an Electric Field

K179

R . M U C C I L L O a n d L . L . CAMPOS

Thermally Stimulated Depolarization Currents in Ceramic T h 0 2 I. M.

CHAPKIK

. . . .

Penetration of Electromagnetic Fields through Thin Layers of Tin.

. . . K189

J . ISOYA a n d J . A . W E I L

A.

TONEVA

K183

Uncompensated Titanium (3 + ) Center in a-Quartz Effective Mass of Holes in P b 1 _ x S n x T e

K193 K197

R . BINDEMANN, E . HEMPEL, a n d K . KREHER

Determination of the Dielectric Constant of GaP from S-C Donor-Acceptor Pair Spectra K201 G.

OELGART

Avalanche Multiplication of Electron-Beam Excited Carriers in G a P p - n Junction K205

W . P A U L a n d B . FROMM

Some Remarks on the AC Behaviour of Thin Sputtered Amorphous GeSe Films K209 R . A . B A R T E L S , J . C . K o o , a n d M . L . THOMAS

Temperature ad Pressure Dependence of the Dielectric Constants of CaO and SrO K213 A. A.

BAHGAT

A New Method for Quantitative Analysis of the Mossbauer Effect . . . .

K217

Prc-Printcd Titles of papers to be published in the next issues of physiea status solidi (a) and physica status soldii (b)

A9

Contents

379 Systematic List

Subject classification:

Corresponding papers begin on the following pages (pages given in italics refer to the principal subject classification) :

1.1

427, 681, K105, K i l l , K169

1.2

381, 521

1.3

635

1.4

427, 529, 627, 687, 711

1.5

475, 609

2

387, 475, 499, 549, 603, 621, K157, K209

4

541, 675

5

415, K217

6

521, 597

7

407

8

397

9 10

509, 615, K165 663

10.1

447, 487, 529, 577, 627, 635

10.2 11 12 12.1 12.2 13.1 13.4 14 14.1 14.2 14.3 14.3.1 14.3.3 14.3.4 14.4 14.4.1 15 16 17 18.1 18.2 18.2.1 18.3 18.4 19 20.1 20.2 20.3

433, 609, 657, 711, K115, K133, K165, K183 415, 441, 463, 687, K193 455 487 657, 675 541, K151, K197 441, 481, 559, 565, 603, 653, 697, K137, K143, K173, K201 681 387, 397 421, 499, 687, K161, K189 401, 441, K129, K173, K197 559, K209 433, 463, 565 407, 653, K205 541, K157, K183, K201, K213 K105, K179 401, K197 K143 K137 K119 587, 681, 703, K119 549 K169 647, 703 615, K125, K193 441, 521, 549, 597, 603, 621, 653, K i l l , K147 481 481, 653, 697, K147, K201

380 21 21.1 21.1.1 21.4 21.6 21.7 22 22.1.2 22.1. 3 22.2.1 22.2.2 22.2.3 22.2.4 22.4. 1 22.4. 2 22.5 22.5.1 22.5. 2 22.5. 3 22.6 22.7 22.8 22.8. 1 22.8. 2 22.9

Contents 447, 499, 509, 577, 615, 627, K161 509, 549, 635, 703, K119, K189 703, K217 549 529, K119 397, 421 587, 597, 621, 675, K133, K151, K197 433, 441, 463, 475, K129, K165 K157 609 653, K201, K205 401, 407 609 K125 K143 K173 657 K115, K147 711 481, 541, 565, K137, K183, K193, K213 427, 647, K209 381, 415, 559, 603, 681, 697 K105, K i l l , K179 K169 521

The Author Index of Volume 52 Begins on Page 719 (It will be delivered together with Volume 53, Number 1.)

Original

Papers

phys. stat. sol. (a) 52, 381 (1979) Subject classification: 1.2; 22.8 Institute of Physics, Polish Academy of Sciences, Warsaw (a) and Institute of Molecular Physics, Polish Academy of Sciences, Poznan

(b)

X-Ray Study of the Structural Phase Transition in Nickel Hexammine Perchlorate By E . DYNOWSKA (a) a n d J . STANKOWSKI (b)

An X-ray study is made of the high-temperature and low-temperature phases of Ni(NH 3 ) 6 (C10 4 ) 2 . At room temperature, the unit cell is regular, of the CaF2 type, with lattice constant ac = = 11.44 A. The monoclinic cell of the low-temperature phase has, at T = 100 K, the constants am = (8.19 ± 0.01) Ä, bm = (11.76 ± 0.01) Ä and c m = (15.08 ± 0.01) Ä with/J = (93.9 ± 0.2)°. The total change in volume amounts to 3.2%, that related with the change in structure amounting to 0.7%. The structural phase transition is found to be of a diffusional nature. Es wird eine Köntgenstrahlanalyse der Hochtemperatur- und der Niedertemperaturphasen von Ni(NH3),,(C104)2 durchgeführt. Bei Zimmertemperatur ist die Elementarzelle regulär vom CaF2Typ und die Gitterkonstante ac = 11,44 A. Die monokline Zelle der Niedertemperaturphase besitzt bei T = 100 K die Konstanten a m = (8,19 ± 0,01) Ä, bm = (11,76 ± 0,01) Ä und c m = (15,08 ± ± 0,01) Ä mit ß = (93,9 ± 0,2)°. Die Gesamtänderung des Volumens beträgt 3,2%, die mit der Strukturänderung verknüpfte 0,7%. Es wird gefunden, daß der strukturelle Phasenübergang vom Diffusionstyp ist.

1. Introduction At certain characteristic temperatures Tc, compounds of the type [Me(NH 3 ) 6 ]X 2 (where Me is a bivalent metal ion and X a monovalent anion) exhibit anomalies of their physical properties. I n particular, for the nickel compounds [Ni(NH 3 ) 6 ] (BF 4 ) 2 and [Ni(NH 3 ) 6 ] (C104)2 at certain temperatures T c a drastic broadening of the E P R lines [1, 2] and an anomaly of the specific heat [3, 4] have been reported. For [Ni(NH 3 ) 6 ] (C104)2 the Raman spectra also point to a phase transition at T c = 173 K [5], The earliest theoretical attempts at explaining the anomalies were based on considerations of the motions of the ammonia molecules in the Ni(NH 3 ) 6 complex [6], However, high pressure results for ammoniacates with simple anions, I - 1 , B r - 1 , CI - 1 [7], and composite anions NO3", C104 [8, 9] suggest a structural transition. According to the new approach, the transition involves a re-construction of the crystal structure with a change in mutual disposition of the anions and cations [10], whereas ths transition energy is related with a change in the crystal potential. This is best supported by the Tc(a„) diagram given in the present paper. I n search for a final proof, X-ray studies were performed throughout a wide range of temperatures, for [Ni(NH 3 ) 6 ] (BF4)2 in the first place. This work proved the transition to be of the structural type and to be diffuse with respect to temperature [11]. Next, an investigation was performed aimed at determining the structure of the lowtemperature phase of [Ni(NH 3 ) 6 ] (C104)2 [12] applying Chojnacki's method [13] for indexing the powder patterns. The latter method, however, because of the hardly avoidable subjective approach of those using it, can easily lead to erroneous results. I n the present work, we preferred to apply a numerical procedure of indexing [14] for the same purpose, and the results appear to provide a more plausible solution of the problem.

382

E . D Y N O W S K A a n d J . STANKOWSKI

2. Experimental I n the case of [Ni(NH 3 ) 6 ] (C104)2 and the majority of related compounds the choice of the apparatus for the structural studies has to take into account the fact that only polycrystalline material is available and that the work has to be done at low temperatures. This considerably complicates the problem, regarding both experiment and interpretation. We opted for an X-ray DRON-1 diffractometer and a low-temperature chamber KRN-190, the latter well adapted for polycrystalline materials and worked at 85 to 300 K. The sample was cooled by means of a cold tube connected with a reservoir of liquid nitrogen and heated by means of a heater built-in in the sample holder. By appropriately setting the current flow through the heater, the temperature of the sample could be maintained constant to within + 0 . 5 K for arbitrary periods of time, in the range from 85 to 300 K. A drawback arises from the fact that the thermocouple is fixed on the cold tube, so that a temperature gradient can arise between the point of measurement and the sample. The latter circumstance, however, was of little importance since the present work was not aimed at determining the absolute temperature of the transition but rather at establishing the transition itself and determining the structure of the low-temperature phase. 3. Results Diffraction patterns obtained at temperatures ranging from 85 to 300 K were analyzed.In agreement with earlier results, the compounds [Ni(NH 3 ) 6 ] (C104)2 was found to crystallize in a cubic structure of the type Fm3m (CaF2) at room temperature. The lattice constant, after Wyckoff [15], amounts to ac = 11.41 A whereas our measurements led to ac = 11.44 A. This value was derived from powder measurements, applying extrapolation with the function cos2 6 to the last ten diffraction lines and, next, a least-squares procedure to draw the straight line through the set of our experimental points. The value a given by us is that at 6 = 90°. Successive diffraction patterns taken at lower and lower temperatures showed no changes, except for some slight shifts of the diffraction maxima towards larger angles, due to the thermal dilativity of the material. Close to T — 158 K the diffraction spectrum undergoes a radical change, and an additional diffraction peak appears at about T = 128 K. The proceeding observations prove beyond doubt that a structural phase transition takes place in two steps: a considerable re-structuralization occurs near T = 158 K, followed by a (probably slight) modification of the structure at 128 K. I t should be noted that the temperature was measured on the sample holder and not on the sample, where it is surely higher. This temperature gradient, by the way, can be assessed as amounting to about 15 K from a comparison of our results with those of a c p -study by Rachwalska et al. [4] for the same compound reporting a strong anomaly of c p at T = 173 K related with a drastic re-structuralization and a slight anomaly at T = 143 K corresponding to a slight change in structure. None the less, all the temperatures given in this article concerning our X-ray studies were measured on the sample holder. The nature of the diffraction spectrum subsequent to the phase transition shows the low-temperature phase to have a structure of symmetry much lower t h a n t h a t of the cubic phase a. We denote the phase in the immediate neighbourhood T Tc as [i, whereas at 100 K the phase 8 exists. The structure of the phase S was determined from measurements made at T = 85 K . I n cases of unknown low-symmetry structures, the indexing of powder diffraction patterns is considerably difficult and requires complicated methods. Recently, to this

Study of the Structural Phase Transition in Nickel Hexammine Perchlorate

383

aim, recourse has been made to special numerical procedures, programmed to highgrade computers, and based on the method of trial and error. We used a method of this kind, proposed by Taupin [14], using as data the positions of the diffraction maxima [2]. The program, on successively testing all the crystallographical systems for the experimentally obtained set of data, selects the type of structure and yields the parameters of the unit cell. I n order to obtain a univocal solution, the angles 26 have to be determined with a high degree of accuracy. According to Taupin [2], the accuracy could not be worse than 0.03° in the 26 scale, which is very difficult to achieve in practice. I n our case, chiefly because the spectra obtained were not of the very best quality and with regard to difficulties in the adjustement of the low-temperature chamber, 29 could be determined with an accuracy of about 0.04°, i.e. less than that required, notwithstanding the fact that each 26 value was the average of ten independently performed measurements and that all possible corrections had been taken into account. I n this situation several solutions were obtained, all of them relating to a monoclinic structure, though differing as to the unit cell parameters. An analysis on the assumption of an unit cell volume decreasing at T = Tc enabled us to select one solution, characterized by the required variation in volume of the cell, and according to which the low-temperature phase of [Ni(NH 3 ) 6 ] (C104)2 at T — 100 K (on taking into consideration the correction for the temperature gradient) has a monoclinic structure of the type P, with the following parameters: a =

(8.19 + 0.01) A ,

b =

(11.76 ± 0.01) A ,

c =

(15.08 ± 0 . 0 1 ) A ,

FuBeell =

1449 A ,

ß = (93.9 ± 0.2)° ,

F/Fcub = 3.2% .

The indexing results, contained in the print for the solution, are given in Table 1. Likewise to the compound [Ni(NH 3 ) 6 ] (BF 4 ) 2 [11], the transition does not occur at a well defined temperature but rather extends over a temperature interval AT. We determined the interval by measuring the intensity at the maximum of the [111] diffraction peak for the cubic phase as a function of temperature (Fig. 1). With regard to the sensitivity of the method of measurement, the interval was found from the graph to extend from 153 to 164 K . Diffraction patterns taken in this range of temperatures (shown in part in Fig. 2) point obviously to the coexistence of two phases in this transition region. Accurate studies led to the conclusion that, at a given temperature Ti from the interval 153 < Tt < 164 K , the ratio of the two phases is a constant, independent of time. The transition is reversible in that, on being brought to room temperature, the compound again goes over into the cubic structure Fm3ra, also, a change in temperature between 153 and 164 causes a shift in equilibrium of the two phases oc and ¡3.

Tig. 1. Temperature dependence of the intensity of the diffracted beam at the maximum of the [111] peak for the cubic phase oc of powdered [Ni(NH 3 ] 6 ) (CIO.),. T c = 164 K, AT » 11°

384

E .

777

m

777

IB'

S

150K

153

13' 156

K \13 158

13" 162

1

IB'

D y k o w s k a

J .

S t a n k o w s k i

Fig. 2. Diffraction patterns showing that the transition of [Ni(NH 3 ) t ] (C104)2 from the cubic phase a to the monoclinic phase is diffuse

h ¿H

163

a n d

173

Table 1 ¿exp

¿cal

hkl

10" 3 A(1 ¡d2)

6.677 6.321 5.822 5.537 5.141 4.999 4.076 4.012 3.766 3.585 3.507 3.426 3.340 3.286 3.165 3.068 2.912 2.767 2.705 2.497 2.457 2.338 2.225 2.145

6.709 6.337 5.882 5.478 5.154 5.015 4.084 4.012 3.761 3.582 3.509 3.419 3.345 3.279 3.163 3.065 2.915 2.767 2.710 2.500 2.452 2.342 2.229 2.149

110 012 020 021 112 003 200 201 004 014 10Ï 131 212 203 132 203 015 140 141 125 016 241 151 007 standard deviation :

-0.219 -0.130 -0.592 0.704 -0.190 -0.247 -0.243 0.00401 0.199 0.110 -0.113 0.396 —0.295 0.356 0.126 0.218 -0.227 -0.0155 -0.461 -0.386 0.613 -0.681 -0.756 -0.813 0.411

Study of the Structural Phase Transition in Nickel Hexaromine Perchlorate

385

4. Discussion and Conclusions The unit cell proposed above results from a computer analysis of the changes in powder X - r a y diffraction patterns as well as a crystallochemical analysis of the structure of [Ni(NH 3 ) 6 ] (C10 4 ) 2 . I n the transitions a —> [} and (3 ->• 8 the structural reorganization is but slight, showing that the disposition of the ions in the monoclinic cell is close t o that in the cubic cell. Fig. 3 shows the cells of [Ni(NH 3 ) 6 ] (C10 4 ) 2 for the two phases: the high-temperature phase a of the CaF 2 type, and the monoclinic lowtemperature phase a and 8 resembling the double tetragonal cell of Zr0 2 . Fig. 4 shows projections of the monoclinic cell on the axes bm, cm, and am. The cell shape obtained enables us to draw conclusions concerning the experimentally observed vibrations of the complex ion [Ni(NH 3 ) 6 ] 2+ and the perchloric ion C10f~. The decrease in dimensions of the crystal along the [110] direction of the cubic cell causes the c m -axis of the monoclinic system to be shorter than a|/2. The increase in dimensions of the cell in the plane perpendicular to this «-direction, i.e. in the directions of bm and am of the monoclinic system, permits the statement that the ion [Ni(NH 3 ) 6 ] 2+ which at high temperatures performs isotropic vibrations with a large amplitude, exhibits a change in motion: vibrations still occur in the planes am and bm, but the individual octahedra are strongly bonded along the c m -axis. This causes a deformation of the Ni(NH 3 ) 6 octahedra along the C 4 -axis, two NH 3 molecules being strongly bonded in the chain running in the c m -direction and far less strongly bonded to the anions surrounding them. Earlier, Pislewski et al. [16] suggested that two kinds of NH 3 groups exist in the Cd(NH 3 ) 6 ion in order to interpret the values of proton relaxation times in NMR. The recent results of Krupski [17] concerning the thermal dilativity permitted the determination of the changes in cell volume on cooling to the phase transition temperature. Taking, after Krupski [17], the volume dilativity coefficients as /?c =

Fig. 3. Outline of the unit cell in the phase a) a and b) phases ß and S of [Ni(NH 3 ) 6 ] (C10 4 ) 2

Pig. 4. Projections of the monoclinic unit cell a) along bm, b) along the axis a m , and c) along the axis c m . Thin lines denote the cell of cubic [Ni(NH 3 ) 6 ] (C104)2

386

E . DYNOWSKA

and

J . STANKOWSKI

: Study of the Structural Phase Transition

= 16.5 X 10- 5 K - 1 for the cubic phase, == 30.6 X 1CT6 K - 1 for the monoclinic phase, and AVjVTc = 1.56% for the volume change at Tc, the total change in volume when cooling the sample to 100 K from room temperature is A F / F = —5.5%. The change in volume of [Ni(NH 3 ) 6 ] (C104)2 at the structural phase transition previously calculated by us [18] from high-pressure measurements amounts to AV/VTC = —0.7%, i.e. twice smaller. The variation of A F / F = —5.5% from thermal expansion is in good agreement with the X-ray data, according to which the change in volume of the unit cell (F 290 — F 180 )/F 290 amounts to —3.2%. The results of the present study, as obtained for a powder, do not provide a final solution concerning the nature of the phase transition of [Ni(NH 3 ) 6 ] (C104)2. None the less, the transition is proved to be of a structural nature. Work aimed at obtaining single crystals is proceeding. The fact that the transition is diffuse, as observed in this laboratory by E P R [19, 20] by Dynowska [11] and subsequently by Hodorowicz et al. [12] applying X-rays, points to the complexity of the transition. This may be due to the strong dependence of the transition on hydrostatic pressure. On transition of some part of the crystal into the low-temperature phase, the internal pressure acting on the remaining part decreases. The positive pressure coefficient 8TJdp, lowers the transition temperature of the latter part, still awaiting the transition. As a result, an interval of about 10 to 20 K exists in which the two phases are at equilibrium. Detailed studies are now proceeding on monocrystals. Acknowledgements

The authors wish to thank Prof. Dr. habil. J . Auleytner for his kind advice, Doc. Dr. Z. Galdecki for his help in preparing the computer program, and Mr. J . Makowski for making the samples. References [ 1 ] J . STANKOWSKI, J . M . J A N I K ,

A.

DEZOR,

and

P . B . SCZANIECKI,

phys. stat. sol. (a)

16,

K167

(1973).

[2] P. B.

SCZANIECKI,

L.

LARYS,

and U.

GKUSZCZYNSKA,

Acta phys. Polon. 46, 761 (1974). and T . W A L U G A , phys.

[ 3 ] T . GRZYBEK, J . A . J A N I K , J . MAYER, G. PYTASZ, M . RACHWALSKA, [4]

stat. sol. (a) 1 6 , K 1 6 5 ( 1 9 7 3 ) . M. R A C H W A L S K A , J . M. J A N I K , 30, K 8 1

J.

A.

JANIK,

G.

PYTASZ,

and

T . WALUGA,

phys. stat. sol. (a)

(1975).

and J . SOKOLOWSKI, Report I F J No. 9 2 6 / P S ; J. Raman Spectr., in the press. A. R. B A T E S and K. W. H. S T E V E N S , J. Phys. C 2, 1573 (1969). M . P A G A N N O N E and M . G. DRICKAMER, J. chem. Phys. 43, 4064 (1965). L. L A R Y S , J. STANKOWSKI, and M. K R U P S K I , Acta phys. Polon. 50, 351 (1976). J . STANKOWSKI and M . K R U P S K I , Bull. Acad. Polon. Sci., in the "press. J. STANKOWSKI, Proc. Conf. RAMIS 75, Ed. Univ. A. Mickiewicz, Poznan, No. 19 (p. 243); Mater. Sci. II 3, 57 (1976). E . D Y N O W S K A , phys. stat. sol. (a) 3 1 , K 2 3 ( 1 9 7 5 ) . S . HODOROWICZ, M . CIECHANOWICZ-RUTKOWSKA, J . M . J A N I K , and J . A . J A N I K , phys. stat.

[ 5 ] J . A . J A N I K , J . M . J A N I K , G . P Y T A S Z , T . SARGA,

[6] [7] [8] [9]

[10] [11] [12]

sol. (a) 4 3 , 5 3 ( 1 9 7 7 ) .

[13] J. CHOJNACKI, Thesis, Jagiellonian University Cracow, 1945. [14] D. T A U P I N , J. appl. Cryst. 6, 380 (1973). [15] R. W. G. W Y C K O F F , Crystal Structure, Chap. X , Interscience, New York 1960. [ 1 6 ] N. P I S L E W S K I , J . STANKOWSKI, and L . L A R Y S , phys. stat. sol. (a) 3 1 , 4 1 5 ( 1 9 7 5 ) . [ 1 7 ] M . K R U P S K I , to be published. [18] M. K R U P S K I and J. STANKOWSKI, Acta phys. Polon. in the press. [19] P. B. SCZANIECKI and J. STANKOWSKI, Acta phys. Polon. 51, 117 (1977). [ 2 0 ] M . K R U P S K I and J . STANKOWSKI, Acta phys. Polon. 5 0 , 6 8 5 ( 1 9 7 6 ) . (Received

November

1,

1978)

J.

KEEMPASKY

et al.: Electrical Resistivity of Metallic Glasses

387

phys. stat. sol. (a) 52, 387 (1979) Subject classification: 2 and 14.1 Department of Physics, Faculty of Electrotechnical Engineering, Slovakian Technical University, Bratislava1) fa), Institute of Experimental Physics, Slovakian Academy of Sciences, Kosice (b), and Institute of Physics, Slovakian Academy of Sciences, Bratislava (c)

Peculiarities in the Temperature Dependence of Electrical Resistivity of Metallic Glasses By J . K R E M P A S K Y ( a ) , J . V A J D A ( a ) , A . Z E N T K O ( b ) , a n d P . D U H A J (C)

A model of electrical resistivity of metallic glasses is suggested based on the theory of modified relaxation time. The analysis shows that the low value of the temperature coefficient of resistivity, its various signs, and the existence of a minimum can be explained by a proper combination of the parameters in the proposed model. A new kind of anomaly is also reported that is observed experimentally in the low-temperature region on an annealed sample. This anomaly can be interpreted within the suggested model as well. All reported pecularities are attributed to structural disorder of metallic glasses, nevertheless, combination with other scattering mechanism is not excluded. H a 0CH0Be TeopHH MOflmjHmHpoBaHHoro BpeMH pejuiaKcamiH npenjio;KeHa Moaejib 3jieKTpHHecKoro conpoTHBJiemiH MeTajiJiniecKiix cTeKOJi. AHaJiH3 Monejin noKa3biBaeT, HTO NOHXOUHMEFT KOM6nHauiieil napaMeTpoB BO3MOH?HO KaiecTBeHHoe OS-bHCHemie HH3KOro TeMnepaiypHoro K03 6.

for T

6, and

3. Results of Calculations The integrand in the expression (2) is too complicated for the temperature dependence q(T) = to be found analytically. Because of this the integral was computed numerically b y use of a computer. I t was found in the course of the computation t h a t 26*

390

J. Krempasky, J. Vajda, A. Zentko, and P. Duhaj Kg. 1. Calculated temperature dependence of electrical resistivity related to the value of resistivity at chosen temperature. (1) EF > W; (2) EF = W; (3) EF g W; (4) and (5) EF < W. The resistivity minimum occurs only in the case EF < W. If EF lies deeper below W, the negative temperature coefficient appears at all temperatures. It is obvious from curves 3, 4, and 5 how for decreasing EF the temperature of resistivity minimum is shifted to high values. Insert: b) basic curve 4; a) curve 4 affected by increasing the ratio l^/d (i.e. d is lowered). The increase of the barrier thickness has an analogous influence with the lowering of d. (In this case d lowered 4 times)

the integrand had a distinct maximum at E = EF. In case ET v, v being the electron collision frequency. The pump wave number k0 ~ k is taken to incorporate spatial non-uniformity of the pump. A large transverse magnetostatic field B0 is applied such that the crystal becomes a magnetoplasma (coc ~ cop). I t is shown that the threshold value of the oscillatory electric field for instability is reduced considerably in the presence of the finite wave number of the pump. The present analysis further reveals that the instability of the acoustic wave can be caused at smaller values of k and E0 in the presence of a large transverse magnetostatic field. The growth rate \QX\ as well as the phase velocity v v of the unstable mode have also been obtained analytically. Numeric estimates of the acoustic wave increment in the instability region are made for I n S b at 77 K . 2. Dispersion Relation W e use the hydrodynamic model of a homogeneous semiconductor plasma of infinite extent. A high frequency oscillatory electric field E0 exp [i (co0t — k0 • r ) ] is applied parallel to the wave vector k (along «-axis) and the dc magnetic field B0 is taken normal to k (along z-axis). W e have assumed a) 0 (s= cop) v. Our starting equations are 1 f+{v0 -S/)v0

8%

Vu

8E _ en 8x e 8n ~8i~ ~ r 8»)

at

+

= -(E0

(1)

QE

(2)

8 2u

ft

(3)

e 8x 2 ' 8n

(c

+ v0xB0)-vv0,

7)

8«

r

8t>, n—? = 0 ,

e =_(£• + „

m

X

B

0

(4)

hT mn0

) - ^ — y n - w .

(5)

The equations and the notations are explained by K a w [1] except the additional terms necessary to incorporate the effects of a transverse dc magnetic field B0 and the spatial dependence of the pump ; kB is the Boltzmann costant. We assume that the acoustic wave has an angular frequency Q and wave number k such that Q co0 and k ~ and the low-frequency perturbations are proportional

Parametric Instability of Acoustic Waves in Piezoelectric Semiconductors

409

to exp [i(Qt — lex)]. The transverse acoustic wave is propagating in such a direction of the crystal that it produces a longitudinal electric field ; for example, in n-InSb, if k is taken along (Oil) and u is along (100), the electric field induced by the wave is a longitudinal field. Using (2) and (3) we obtain =

(6)

£Q /

6

£Q

Differentiating (4) with respect to time and using (1) and (3) we get 82n , n0e8lt> , x /8n 8«A 2 + v k u W + ^ W + ^ - l{k + ko) • 0i + Txl + = i{k + k0) n (— E0 — a)cvoy + \m

ikQvLI, /

l k w

"

= (7)

where ojc = —eBJrn is the electron cyclotron frequency; a>| = Wp + k2(kBT/m) the frequency for dispersive electron-plasma waves, cop being the electron-plasma frequency given by cop = (w0e2/me)1/2, e = e0e1( E[ being the lattice dielectric constant, and e0 the absolute permittivity; w0 is the equilibrium electron concentration. I n the collision-dominated regime Q, k • v0, k0 • v0), vy can be obtained from (5) and when substituted in (7), we obtain v^

at*

ci

+ ^P,k*u me

= i(k + k0)nE,

(8)

where (Or = col (1 1+ i and

g E = —E0—

+C«2c ) cocv0y + ik0vlx .

Equation (8) can now be resolved into two components (fast and slow) by writing v = i-'fast + fsiow and n = wfast + nslow (subscripts fast and slow represent the fast and the slow component, respectively). Hence one gets 9 Vast . + 8