Physica status solidi: Volume 23, Number 2 October 1 [Reprint 2021 ed.] 9783112494509, 9783112494493

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physica status solidi

V O L U M E 23 • N U M B E R

2 -1967

Classification Scheme 1. Structure of Solids 1.1 Alloys. Metallurgy 1.2 Solid-State Phase Transformations 1.3 Surfaces 1.4 Films 2. Non-Crystalline State 3. Crystallography 3.1 Crystal Growth 3.2 Interatomic Forces 4. Microstructure of Solids 5. Perfectly Periodic Structures 6. Lattice Mechanics. Phonons 6.1 Mossbauer Investigations 7. Acoustic Properties of Solids 8. Thermal Properties of Solids 9. Diffusion in Solids 10. Defect Properties of Solids (Irradiation Defects see 11) 10.1 Defect Properties of Metals 10.2 Photochemical Reactions. Colour Centres 11. Irradiation Effects in Solids 12. Mechanical Properties of Solids (Plastic Deformations see 10)see 10.1) 12.1 Mechanical Properties of Metals (Plastic Deformations 13. Electron States in Solids 13.1 Band Structure. Fermi Surfaces 13.2 Exoitons 13.3 Surface States 13.4 Impurity and Defeot States 14. Electrical Properties of Solids. Transport Phenomena 14.1 Metals. Conductors 14.2 Superconductivity. Superconducting Materials and Devices 14.3 Semiconductors 14.3.1 Semiconducting Films 14.3.2 Semiconducting Devices. Junctions (Contact Problems see 14.4.1) 14.4 Dielectrics 14.4.1 High Field Phenomena, Space Charge Effects, Inhomogeneities, Injected Carriers (Electroluminescence see 20.3; Junctions see 14.3.2) 14.4.2 Ferroelectric Materials and Phenomena 15. Thermoelectric and Thermomagnetio Properties of Solids 16. Photoconductivity. Photovoltaic Effects 17. Emission of Electrons and Ions from Solids 18. Magnetic Properties of Solids 18.1 Paramagnetic Properties 18.2 Ferromagnetic Properties 18.3 Ferrimagnetic Properties. Ferrites 18.4 Antiferromagnetic Properties ( Continued on cover three)

physica status solidi B o a r d of E d i t o r s P. A I G R A I N , Paris, S. A M E L I N C K X , Mol-Donk, V. L. B O N C H - B R U E V I C H , Moskva, W. D E K E Y S E R , Gent, W. F R A N Z , Münster, P. GÖRLICH, Jena, E. G R I L L O T , Paris, R. K A I S C H E W , Sofia, P.T. L A N D S B E R G , Cardiff, L. N É E L , Grenoble, A. P I E K A R A , Warszawa, A. S E E G E R , Stuttgart, F. S E I T Z, Urbana, 0 . S T A S I W , Berlin, M. S T E E N B E C K , Jena, F. STÖCKMANN, Karlsruhe, G. SZIGETI, Budapest, J . TAUC, Praha Editor-in-Chief P. GÖRLICH Advisory Board M. B A L K A N S K I , Paris, P. C. B A N B U R Y , Reading, M. B E R N A R D , Paris, W. B R A U E R , Berlin, W. COCHRAN, Edinburgh, R. COELHO, Fontenay-aux-Roses, H.-D. DIE TZ E, Saarbrücken, J.D. E S H E L B Y, Cambridge, P. P. F E O F I L O V, Leningrad, J. H O P F I E L D , Princeton, G. J A C O B S, Gent, J. J A U M A N N , Köln, E. K L I E R , Praha, E. KRO E NE R, Clausthal-Zellerfeld, R. KUBO, Tokyo, M. M A T Y A S , Praha, H. D. MEGAW, Cambridge, T. S. MOSS, Camberley, E. NAGY, Budapest, E. A. N I E K I S C H , Jülich, L. P A L , Budapest, M. RODOT, Bellevue/Seine, B. V. R O L L I N , Oxford, H. M. ROSENBERG, Oxford, R. Y A U T I E R , Bellevue/Seine

Volume 23 • Number 2 • Pages 439 to 766, K105 to K166, and A33 to A62 October 1, 1967

AKADEMIE-VERLAG•BERLIN

Subscriptions and Orders for single copies should be addressed to AKADEMIE-VERLAG GmbH, 108 Berlin, Leipziger Straße 3 - 4 or to Buchhandlung K U N S T U N D WISSEN, Erich Bieber, 7 Stuttgart 1, Wilhelmstr. 4 - 6 or to Deutsche Buch-Export und-Import GmbH, 701 Leipzig, Postschließfach 160

Editorial Note: "physica status solidi" undertakes that an original paper accepted for publication before the of any month will be published within 50 days of this date unless the author requests a postponement. In special cases there may be some delay between receipt and acceptance of a paper due to the review and, if necessary, revision of the paper.

S c h r i f t l e i t e r u n d v e r a n t w o r t l i c h f ü r d e n 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 , 102 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 . 69 J e n a , H u m b o l d t s t r . 26. R e d a k t i o n s k o l l e g i u m : D r . S. O b e r l ä n d e r , D r . £ . G u t s c h e , D r . W . B o r c h a r d t . A n s c h r i f t d e r S c h r i f t l e i t u n g : 102 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. F e r n r u f : 4 2 6 7 8 8 . V e r l a g : A k a d e m i e - V e r l a g G m b H , 108 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 : 2 2 0 4 4 1 , T e l e x - N r . 1 1 2 0 2 0 , P o s t s c h e c k k o n t o : B e r l i n 3 5 0 2 1 . — 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 s o l i d i " e r s c h e i n t jeweils a m 1. d e s M o n a t s . B e z u g s p r e i s e i n e s B a n d e s M D N 7 2 , — ( S o n d e r p r e i s f ü r die D D R M D N 60,—). B e s t e l l n u m m e r dieses B a n d e s 1068/23. J e d e r B a n d e n t h ä l t z w e i H e f t e . G e s a m t h e r s t e l l u n g : V E B D r u c k e r e i „ T h o m a s M ü n t z e r 4 4 B a d L a n g e n s a l z a . — 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 1310 d e s Presseamtes beim Vorsitzenden des Ministerrates der Deutschen Demokratischen Republik.

Contents

Original Papers

Page

V . K . SUBASHIEV a n d A . A . KUKHARSKII

R. D.

GRETZ

The Reflection Coefficient of Optically Inhomogeneous Solids . . . Nucleation of Zinc Crystals in Multilayer Adsorption

G . D . GUSEINOV a n d A . M . RAMAZANZADE

Visualization of Dislocations on Basal Planes of GaSe Single Crystals

447 453 461

I . P . IPATOVA, A . A . K L O C H I C H I N , a n d A . V . S U B A S H I E V

The Influence of Localized and Resonance Modes of Lattice Vibration son the Radiative Recombination in Semiconductors

467

W . BRUCKNER, K . KLEINSTUCK. a n d G . E . R . SCHULZE

Atomic Arrangement in the Homogeneity Range of the Laves Phases ZrFe 2 and TiFe2

475

G . DUESING, H . HEMMERICH, D . MEISSNER, a n d W . SCHILLING

The Influence of Vacancies and Impurities on the Damage Production in Platinum Electron-Irradiated at 90 °K

481

P . S. H o a n d A. L . RUOFF

A Quasi-Harmonic Calculation of Lattice Dynamics for Na

. . . .

489

B . H E I N R I C H , D . FRAITOVÂ, a n d V . K A M B E R S K Y

The Influence of s-d Exchange on Relaxation of Magnons in Metals .

501

L . DOBROSAVLJEVIC e t C . D U P U T S

Etude d'eutectiques supraconducteurs plomp-étain à lamelles orientées

509

A . E . LORD J R .

Coupling of Magnons and Phonons at High Frequencies

521

D. J .

A Method for Describing a Flexible Dislocation

527

BACON

I . M . BERNSTEIN a n d J . C. M . L i

Thermally activated Deformation of Potassium

539

R . G E V E R S , J . VAN L A N D U Y T , a n d S . A M E L I N C K X

Fine Structure of Weak Kinematical Electron Diffraction Beams for a Foil Containing Stacking Fault or Anti-Phase Boundaries — TwoBeam Case

549

M . P I C A R D a n d M . HTTLIN

A Pseudopotential Approach to the Electron Band Structure of Tellurium

563

E . Y u . GUTMANAS a n d E . M . NADGORNYI

Estimation of the Peierls Stress in Alkali Halides

571

Z . P . CHANG, G . R . BARSCH, a n d D . L . M I L L E R

Pressure Dependence of Elastic Constants of Cesium Halides . . .

577

P . G . ELISEEV, A . I . KRASILNIKOV, M . A . MANKO, a n d I . Z . P I N S K E R

Band-Filling Model for Injection Luminescence at Higher Temperatures

587

STUART

Electrode-Limited to Bulk-Limited Conduction in Silicon Oxide Films

595

H . - P . HENNIG

Contribution to the Determination of Gold Centre Cross Sections in Single -Crystal Germanium by Double Injection Experiments . . .

599

M.

29»

Contents

442

Page

F.

The Orientation Dependence of the Spin Wave Damping in Ferromagnetic Insulators with Spinel-Structure

VOIGT

607

R . G . J . GRISAR, K . P . R E I N E R S , K . F . R E N K , a n d L . GENZEL

Impurity-Induced Far-Infrared Absorption in the Phonon Gap Regions of K I and KBr

613

R . GKEGOROVICI, N . CROITORU, a n d A . D É V É N Y I

Thermoelectric Power in Amorphous Silicon

621

R . GRIGOROVICI, N . CROITORU, a n d A . D É V É N Y I

Photoconductivity in Amorphous Germanium

627

D . HAARER, D . SCHMID u n d H . C. W O L F

Elektronenspin-Resonanz von Triplett-Exzitonen in Anthracen . .

633

W . H Ö R S T E L u n d G . KRETZSCHMAR

M. L.

SWANSON

Akzeptorbildende Gitterdefekte im Tellur

639

The Effects of Defect Doping on Low Temperature Neutron-Irradiation Damage and Recovery in Aluminium and Platinum

649

CHR. N A N E V a n d D . IWANOV

Growth of Zinc and Cadmium Whiskers from the Vapour Phase on a Single Crystal Substrate of the Same Material

663

M . D . S T A F L E U a n d A . R . D E VROOMEN

De Haas-van Alphen Effect in White Tin

675

M . D . STAFLEU a n d A . R . DE VROOMEN

Fermi Surface and Pseudopotential Coefficients in White Tin . . . A . STELLA, A . D . BROTHERS, R . H . HOPKINS, a n d D . W .

LYNCH

Pressure Coefficient of the Band Gap in Mg2Si, Mg2Ge, and Mg2Sn . V . D . EGOROV, G . O . M Ü L L E R , a n d H . H .

683 697

WEBER

Cathodoluminescence Yields in Highly Excited CdS

703

A . L E TRAON, F . L E TRAON e t S . L E MONTAGNER

Influence de l'organisation en domaines du titanate de baryum sur sa température de transition

709

H . W . DEN HARTOG a n d J . A B E N D S

Electronic Structure of F-Centers in Alkaline Earth Fluorides . . .

713

J . Loos

The Nonlinear Excitation of Strongly Coupled Spin Waves . . . .

721

H.

On the r-Approximation Tensor

in the Quantum Theory of the Conductivity

729

A New Type of X-Ray and Electron Diffuse Scattering and Corresponding Strain Contrast on Electron Microscopic Images . . . .

745

STOLZ

A . G . KHACHATURYAN a n d M . P . USIKOV

G . G . K O V A L E V S K A Y A , D . N . N A S L E D O V , a n d S . V . SLOBODCHIKOV

Photoconductivity Oscillations in I n P V. L.

755

BONCH-BRUEVICH

On the Problem of Static Domains in Hot Electron Semiconductors

761

Contents

443

Page

Short Notes P.

PETRESCU

L-Bands Detected in Photoemission Spectra of NaCl, LiCl, and RbBr K105

P . REGISTER e t J . M . DUPOXJY

Glissement prismatique de monocristaux de béryllium

K109

I . D I M A a n d D . BORSAN

N. R E Z L E S C U F. VAVRA

The Polymorphism of CdTe Thin Films Zum Procopiu-Effekt bei Perriten A Note on Etching of Dislocations in AgCl Crystals

K l 13 K l 17 K121

R . TROÖ, A . M U R A S I K , A . Z Y G M U N T , a n d J . L E C I E J E W I C Z

The Magnetic Ordering in Uranium Monoarsenide

K123

GH. MAXIM u n d V . PETRESCU

Die Magnetische Diffusionsnachwirkung der Ni-Mg-Fe-Ferrite . . K125 R . M . EASSON a n d P . HLAWICZKA

Effect of Hei on ac Losses in Niobium

K129

A . A . MARYAKHIN a n d I . V . SVECHKAREV

H.

BÄURICH

On the Pseudopotential Coefficients and Spin-Orbit Coupling in Metallic Cadmium K133 Berechnung der Energie, Magnetisierungsverteilung und Ausdehnung einer Kreuzblochlinie Kl37

J . L . DAVIDSON a n d J . M . GALLIGAN

F.

KROUPA

Kinetics of Vacancy Annihilation in Quenched Copper A Note on Work Hardening in B.C.C. Metals

Kl39 K143

B . W . BATTERMAN a n d G . HILDEBRANDT

0. HENKEL

Observation of X-Ray Pendellösung Fringes in Darwin Reflection. . K147 Positive and Negative Interaction of Fine Particle Assemblies in Correlation with Other Magnetic Properties K151

M . BITTER, W . GISSLER, a n d T . SPRINGER

Lattice Dynamics of Solid Helium at 2.9 °K and 125 atm by Neutron Scattering K155 J . STANKOWSKI, S. W A P L A K , B . SCZANIECKI, a n d A . DEZOR

L.

WOJTCZAK

Temperature Anomaly of EPR Spectra of Paramagnetic Ions in Ferroelectrics K159 The Melting Point of Thin Films K163

Pre-printee Titels and Abstracts of papers to be published in this or in the Soviet journal ,,H3HKa TBepnoro T e j i a " (Fizika Tverdogo Tela) A33

444

Contents

Systematic List Subject classification: 1.4

Corresponding papers begin on the following pages (pages given in italics refer to the principal subject classification): K113

2

621, 627

3.1

453, 663

4

549, 745

5

475, K147

6

467, 489, 613, 755, K155

8

K163

10

461, 527, 571, 639, K121

10.1

481, 539, 549, 649, K107, K139, K143

10.2

713, K105

11

481, 649

12

577

13

501, 521, 721, 761

13.1

489, 563, 621, 675, 683, 697, 755, K133

13.2

633, 703

13.4

467, 587, 599, 713

14

729

14.1

481, 489, 649

14.2

509, K129

14.3

697, 639, 761

14.3.1

595, 621

14.4.1

595, 599, 761

14.4.2

709, K\59

15

621

16

627, 755

17

K105

18

509, 675

18.2

521, K137, K151

18.3

607, K117, K125

18.4

K123

19

501, 607, 633, 713, 721, K159

20.1

447, 613, 697

20.2

703

20.3

587, 467, 703

21

501, 509, 649, 663, 675, 683, IC129, K133, K163

Contents 21.1

453, 663, K139, K163

21.1.1

475, 549, K151

21.2

489, 539, 577

21.3

K109

21.6

481, 649, K163

22

461

22.1.1

599, 627, 761

22.1.2

447, 467, 621, K147

22.1.3

563, 639

22.2.1

587

22.2.2

755

22.4.1

703

22.4. 3

K113

22.5. 1

K121

22.5.2

571, 613, K105

22.5. 3

713

22.6

595, 745

22.7

697

22.9

633

23

K155

The Author Index o! Volume 22 Begins on Page 767 (It will be delivered together with Volume 24, Number 1.)

445

Original

Papers

phys. stat. sol. 28, 447 (1967) Subject classification: 20.1; 22.1.2 Institute of Semiconductors, Academy of Sciences of the USSR,

Leningrad

The Reflection Coefficient of Optically Inhomogeneous Solids By V . K . SUBASHIEV a n d A . A . KUKHARSKII

The optical reflectivity of some optically inhomogeneous solids is considered and the appropriate general reflectivity formulae are determined. Some particular cases of these formulae are also discussed. The infrared reflectivity spectra of epitaxial and diffused semiconductor layers are calculated as examples.

PaccMaTpHBaeTCH OTpajKemie cseTa OT ormmecKH HeojxHopoaHHX TBepaux Teji oCrnaH $opMyjia. 06cy>K«aiOTCH HeKOTopbie HacTHbie cjiyiaw. B KaqecTBe npHMepa «aeTCH pacieT HH$paKpacHoro CHeKTpa OTpaweHMH nH 1 equations (11) to (12) reduce1) to 6 N I. c /dlnK\ . c /dlntfU

(11a)

, ,

This expression differs from (1) by the term

> which is equal to

zero in homogeneous solids. In the case e = const (11) and (12) transform into 1 - e

i

i^-r**

AG-iV

1 V ed %*—

\ie + lf

where R is defined by (1). I t is equivalent to Barnes-Czerny's [3] formula, which takes into consideration the interference and multiple reflections of light from the front and back surfaces of the sample. Some words are to be said about Eg. One can show with the help of (5) to (5 c) that it is exactly equal to Eq when e(x) = e0 2Md*/o. °L But, as will be seen hereafter, in some practical problems it is quite possible to assume Ei ¡v E$ that corresponds to the so-called geometric optical approximation. Then, inserting (6a) into (11a), separating the real and imaginary parts and taking the square of the module one gets K + An~ if + (*0 + Axy K + An + 1)2 + (*0 + Axf

where

c "»Wo 2 co

and

(lib)

(13)

(14)

2m

According to (13) and (14) equation ( l i b ) contains values which are defined

(

de\

de

— J but not by the integrals of e(x) and — . The reason lies in the /0 U = £ „ ,

(7)

where (uf (t) Ui'(0)')m is the Fourier-component of the atomic displacement correlator, which is connected with the retarded Green's function of the lattice vibration in the following way [9]:

with l'-,(0)= f d/e'-') the equation [7] = D) = *L Z D°*(l,

l';m)

. + (Si)2 z

k; ©) «i.

h; a»)

I'; a>) +

; «>) A ^ f e r ;

; m

) = * 2 M N

¡«J ^ . eik(n-n') a>2 — a>lj + i d sign m

(ii)

where cofcJ- is the perfect crystal frequency of the branch j with the wave vector k, is the polarization vector of the phonon, M is the mass of the host lattice atom. Then, M — M' h

M h

where M' is the mass of the isotope defect We define as F the product of matrix elements in the numerator of (7): < c p " \c!\ cpy

F = l ,

rt) = 2 K

(14)

p

where for the hydrogen-like impurity °P~PA -

8 „1/2 £3/2 F1/2

tl +

{p_pa)2

R2]2

'

1">J

where R is the effective radius of the impurity. In (14) is the valence band Bloch's function. In the intermediate and initial states an electron is represented by the conduction band Bloch functions

470

I . P . IPATOVA, A . A . KLOCHICHIN, a n d A . V . SUBASHIEV

uC:Pi and u e p , correspondingly. Thus, we obtain 4 jr «2 h ABM 1, and the corresponding resonance frequency is equal to = e - 1 (ft)" 2 )" 1 , (25) where d o W ) (26) These resonance vibrations result in a maximum of the frequency distribution density for impurity atom vibrations. The relative width of the maximum is defined by the value for the perfect lattice distribution: r = 7i |e|ft)?e8Sr(ft&s) .

(27)

We can get the correct estimation of the resonance frequency with the Debye distribution function g = 3/2 (co/cof,), since to only the lowest frequencies contribute, ft)res=-^. y 3e

(28)

Expanding the denominator of (23) near the resonance frequency and assuming that the linewidth (27) is small, we obtain for the spectral density /res(v) = c d

— 3c.3w0 M (Oresn \e\ \ ZA VI ! £

i [»(aw) + 1 ]d(Ep-

yi K" "D (p" - p'h f l-p —PA ¡>P>-pa A E,~ Ep + hv 4 jj

Et-hv-h

x s [w(cores) 8 (Ep — E( — h V + h , 1 -—

f

(30)

where < c o > = dco2 g ( o j ) OJ . For ft)loc ^>re3) + 1] , X •{ \(hv + Ei-h twres)1/2 e - (» - + " * °>™>IT w(cores) , ,

,

tuv)

X

= Cd x

/A Z\2

A

E

N V(h vf

E L I 7 R T Y

e T3l2{hcoioe)

_ D

(32)

x

f(ft v - Ei. +. ;* Oioo)1'2 [«(co,oc) + 1] e - (» * - «I + » -I-)/' ,

{(fc v — Ei —

Here Ei is the energy of the impurity level and D is given by _ 16 3

he2 r) 1/2 i f c? mgv0 M

n* A f* . ^ Ei — EPA

(34)

The relations (32) and (33) show the temperature and frequency dependence on the effective charge of the impurity and on e. The recombination radiation density has been studied recently for Si at low temperatures [10]. There are several maxima in the spectrum due to conduction electron capturing by neutral acceptors in n-Si and hole capturing by neutral donors in p-Si with phonon creation. This radiation recombination spectrum for B i in Si differs from the spectrum of Ga in Si by the presence of the line corresponding to the strong direct transition. Usually this line is accounted for by the fact that the B i level in Si being deeper has large uncertainty in momentum. This makes the direct transition non-forbidden. This paper shows another possible explanation of the effect. B i in Si is a heavy defect. The corresponding value of e is —6.4. Therefore, the existence of a resonance mode in the lattice vibration spectrum seems to be very much probable. The resonance frequency estimated from (28) is as follows: h cores = = + 3 . 6 X 1 0 - 3 eV, h col being equal to 1.6 X 10~ 2 eV. As ojrea is small (cores ft>L) the radiation density (32) must have a maximum at the frequency that differs from the direct transition frequency by this small value core3. The measurements have been carried out at a temperature T ¡=a h coles. Therefore, within the experimental errors, this indirect transition with a resonance mode involved can be considered as a direct transition. In the case of Ga in Si there is no indirect transition with a resonance mode as corresponding to e fa 1, and there is no resonance maximum in (32).

Localized and Resonance Modes of Lattice Vibrations

473

An example for a light defect in Si is the boron atom. It is established experimentally that it leads to a loxalized mode in the vibration spectrum at the frequency h 99.5%) and solid Armcoiron. ZrFe2 was molten in Zr0 2 crucibles and TiFe 2 in A1203 crucibles under argon atmosphere using inductive heating. The subsequent annealing was performed without variation of the experimental arrangement (ZrFe2: 1300 to 1400 °C, 8 h; TiFe 2 : «1300 °C, 8 h) thereby yielding homogeneous samples which are practically of single-phase in the homogeneity range (1 to 3% foreign phases or eutectic). All the samples were studied by metallographic and X-ray diffraction methods. Some of them were analysed additionally by chemical and X-ray fluorescent methods. In Fig. 1 the correlation between the lattice constant and the iron concentration of ZrFe2 is given. The lattice constants were determined from Straumanis patterns by lattice constant extrapolation to •& = 90°. Using the above preparation method, a max = (7.087 + 0.003) A and amin = (7.015 + 0.003) A were obtained for the largest and the smallest lattice constants, respectively. In Fig. 1 the results of Svechnikov and his coworkers are also given. If ZrFe2 was molten in an A1203 crucible, lattice constants up to a = 7.135 A were observed because of the formation of a Laves phase Zr(Fe, Al) 2 [4] as the aluminium is taken up from the crucible material (up to several percents by weight). In the Zr-Fe samples with a concentration of 30 wt% Zr (=20.8 at% Zr) the phases Zro.8iFe2.19 (MgNi2 type) and Zr6Fe23 (Th6Mn23 type) were partially

72 74 CgiatZfeJ-

_ 7b

Fig. 1. Lattice constant dependence on the iron concentration for ZrFe a (solid line — own measurements, dotted line — measurements made by Svechnikov, Pan, and Spektor [1])

Atomic Arrangement in the Homogeneity Range of ZrFe2 and TiFe 2

477

observed as reported in the literature [5,6]. In spite of the variation of the preparation conditions we were not successful in demarcating the production or the existence conditions of the two phases. The following can be stated: Zr0.8iFe2.i9 is preferentially formed by melting under rough vacuum, Zr6Fe23 by melting under argon atmosphere. Usually, these phase appear only in small portions beside ZrFe2 and Fe. From measurements on smaller pieces of the sample mainly containing the indicated phases the following lattice constants were obtained: for Zr0.8iFe2.19 a = (4.949 + 0.002) A, c = (16.13 + 0.002) A, and for Zr6Fe23 a = (11.705 ± 0.004) A. In the TiFe2 lattice aluminium was dissolved, too, as A1203 crucibles were used. The A1 content was determined by means of an electron probe X-ray microanalyser. The aluminium content in the samples is dependent on different factors (heat treatment, iron concentration, etc.) and, therefore, different in the individual samples. Consequently, it is not possible to establish in this paper a quantitative relation between the lattice constants and the iron concentration. For the ratio c/a no concentration dependence and thus no dependence on the aluminium concentration could be observed. The average value is 1.631 + 0.001. In TiFe2 samples being rich in titanium TiFe appears as the second phase. Because it is extremely difficult to establish by X-ray diffraction methods whether the intermetallic compound TiFe crystallizes in disorder in a W-type lattice or in order in a CsCl-type lattice this question was investigated by neutron diffraction in the course of our work. Details will be reported in a following paper [7], The result can be anticipated as follows: TiFe crystallizes in a CsCltype lattice. 3. Intensity Measurements and Evaluations 3.1

ZrFes

For the X-ray intensity measurement a ZrFe2 sample was used having the following properties: lattice constant a = (7.022 + 0.002) A; chemical analysis: (61.5 + 0.5) wt% Fe, (38.4 + 0.2) wt% Zr (this corresponds to 72.3 at% Fe); phase contaminations: a - F e « lvol%, Zr0.8iFe2.i9 or Zr 6 Fe 2 3 « 1 vol%. All the eight reflections in the pattern using cobalt Ka radiation were measured pointwise. The atomic scattering amplitudes were corrected by Honl values taking into account the anomalous dispersion. The evaluation of the pattern was done by a least square method using a computer. Beside a scale factor the iron concentration c-g in the ZrFe2 phase and a distribution parameter to were determined. This parameter to shows if single B-atoms or B-atom tetraeders were built in on the A-sites, or if both substitution cases are realized simultaneously, in which portion they are present. Statistical independence of the substitution cases was supposed. The parameter to means the average number of iron atoms on the A-sites which are occupied by iron atoms. In this calculation to is meaningful only in the range 1 sS m sS 4. The direct substitution (to = 1) and tetraeder substitution (to = 4) are the limiting cases. From the values 1 < to < 4 the proportion of direct and tetraeder substitutions can be calculated. For the ZrFe2 sample was obtained TO = 0.80 ± 0.24 ,

c B = (71.8 + 0.9) at% Fe , R = 1.3% .

478

W . BRUCKNER, K . KLEINSTUCK, a n d G . E . R . SCHULZE

The latter value is the discrepancy factor defined to 1/2

R =

S i— 0' n ^ - j F i ^ i La

(1 /a weights, j multiplicities, F structure amplitudes). Because TO < 1 is senseless the evaluation was repeated for the caseTO= 1 = const: m = 1 = const, c B = (72.4 + 0.8) a t % Fe , R = 1.5% . Fig. 2 illustrates the latter case. In the diagram the double ratio V(CB) = ' is given for different reflection combinations (every reflection was used in two combinations). Supposing that the measurement errors are zero and that the regarded model is correct, all the curves F(c B ) must intersect at the point V = 1, c B iron concentration in the investigated ZrFe 2 sample. For a correctly selected model the deviations are a measure for the experimental errors. For meaningful values of m the smallest intersection range was found for TO = 1 (Fig. 2a). In Fig. 2 b for the caseTO= 2 (i.e. from three substitution cases fall two on direct and one on tetraeder substitutions) it is not possible to refer to an "intersection range". The result of Fig. 2a is well in agreement with that given above. Based on the hitherto existing results the presence of tetraeder substitutions can be excluded practically for nonstoichiometric composition. There remains the proof if the homogeneity range is associated with the existence 0 4. 6 8 10 2 of vacancies. For this purpose it was Asta/XfèJ AMW studied in additional calculations the combination of vacancies and direct l" substitutions on A-sites. The best ^Amm agreement between the observed and the calculated values was found, as wabove, for the case of exclusive direct substitutions. -mm OS03

~~—•—mum kJattFe)—-

Fig. 2. Graphical intensity evaluation for ZrFe* for a) m = X and b) m = 2

Atomic Arrangement in the Homogeneity Range of ZrFe 2 and TiFe 2 3.2

479

TiFes

The problem stated in the introduction was solved by neutron diffraction measurements for TiFe 2 because the values of scattering amplitudes of Ti and Fe are highly different (&Ti = —0.34x 10" 12 cm, bVe = 0.96 X 10~12 cm). Therefore, iron atoms on titanium sites can be easily detected. Of particular interest was the investigation of the sample being richest in iron having the following properties: lattice constants a = (4.785 + 0.002) A, c = (7.799 ± 0.003) A, c/a = 1.630 + 0.002; X-ray fluorescent analysis: (74.7 + 0.5) wt% Fe = (71.7 ± 0.5) at% Fe; electron probe X-ray microanalysis: « 1 a t % A1 in the TiFe 2 phase; phase contaminations: fa 1 vol% TiO, « 1 . 5 vol% a-Fe. Using a powder sample thirteen reflections or reflection groups were measured by neutrons of wavelength 1.18 A. The evaluation was done in a similar way as for ZrFe 2 . Only for the hexagonal TiFe 2 phase (space group Dgh—C6/mmc) the values of the crystal structure parameters x for the position (6h) and z for the position (4f) were determined additionally. For the sample described above the results are as follows: m cB a; 2 R

= 0.93 + 0.16 , == (70.7 + 0.8) a t % Fe , = - 0 . 1 7 0 7 + 0.0006 , = 0.067 + 0.005 , =2.3%.

Taking m — 1 = const because of the reasons mentioned above for ZrFe 2 the result is m — 1 = const, c B = (70.9 + 0.7) a t % Fe , X = - 0 . 1 7 0 7 + 0.0006 , z = 0.067 + 0.005 , R = 2.5% .

i. Discussion For ZrFe 2 as well as for TiFe 2 results as the optimal case from the intensity measurements that the excess iron atoms directly substitute the absent A-atoms on their sites. On the other hand, the concentrations evaluated from the intensities are in good agreement with the analytical results with respect to the foreign phases. Tetraeder substitutions and vacancy formation can be excluded with an accuracy that only a small fraction of such substitutions in relation to the total number of substitution cases is allowed. It is still interesting to give the percentage of the substituted A-atoms in the samples investigated here: From 100 A-sites 17 are substituted by B-atoms in the ZrFe 2 sample and 13 in the TiFe a sample, respectively. It should be noted that the lattice constant variation is compatible with the substitution model found. In Fig. 1 the lattice constant variation with the concentration is presented for ZrFe 2 . It was found that in the homogeneity range for Ac B = 1 a t % the lattice constant decrease is about 0.15%. This result is comparable with that resulting from the following consideration: On the premises of Vegard's law the contraction of the B-sublattice is evaluated taken out off the A-sublattice. The B-sublattice influence can be roughly esti-

480

W. BRUCKNER et al. : Atomic Arrangement in the Homogeneity Range

mated subsequently by the investigation of the lattice constant dependence on the atomic radius r&tio in the cubic Laves phases AFe 2 . This gives

This estimation is rough. Therefore, it can be stated that the lattice constant variation is compatible with the direct substitution model. For tetraeder substitution a highly positive Aa/a Ac B can be expected. For TiFe 2 a lattice constant decrease with the iron concentration also results qualitatively. Quantitatively, the variation could not be investigated because the experimental values are masked by those of A1 contaminations. For TiFe 2 nearly the ideal value z = 1/16 was found for the crystal structure parameter, whereas the parameter x differs considerably from the ideal value x = —1/6. This difference can be understood taking into account that the observed c/a ratio is lower than the ideal value c/a = 1.633. This lattice compression in the c-direction leads to the phenomenon that the B-atoms lying in the corners of B-atom double tetraeders press apart the B-atoms lying in the basic plane. This again corresponds to a parameter variation in the observed direction. Within the limits of errors the same parameter values were obtained also for samples with iron concentrations being closer to the stoichiometric value. Thus, they are practically independent from the concentration, certainly owing to the concentration independence of c/a. With regard to the extent of the homogeneity range the results by Svechnikov and coworkers (66 to 72.5 a t % Fe) [1] can be confirmed: For our samples the maximum iron concentration in ZrFe2 is about 73 at%. There are no signs for a noticeable Zr solubility in ZrFe2. For TiFe 2 according to our results the iron solubility limit at 1300 °C is between 71 and 72 a t % Fe. Acknowledgements

We are indebted to Mrs. R. Buchalla for her efforts in the preparation of the polished sections, to Miss E. Richter for her assistance by the X-ray investigations of our samples, and to Mr. R. Schulze for the careful analytical investigations. References [1] [2] [3] [4]

V. Y. G. V.

N . SVECHNIKOV, V . M . PAN, a n d A . S . SPEKTOR, Z h . n e o r g . K h i m . 8 , 2 1 1 8 ( 1 9 6 3 ) . MURAKAMI, H . KIMURA, a n d Y . NISHIMURA, J . J a p a n I n s t . M e t a l s 2 1 , 6 6 5 ( 1 9 5 7 ) . E . R . SCHULZE, Z. K r i s t . Ill, 2 4 9 ( 1 9 5 9 ) . Y A . MARKIV a n d P . I . KRIPYAKEVICH, K r i s t a l l o g r a f i y a 1 1 , 8 5 9 ( 1 9 6 5 ) .

[5] H. J . WALLBAUM, Z. Krist. 103, 391 (1941).

[ 6 ] P . I . KRIPYAKEVICH, 288 (1965).

V . S . PROTASOV, a n d E . E . CHERKASHIN, Z h . n e o r g . K h i m .

[7] W. BRUCKNER, Kristall und Technik, to be published. (Received April 1, 1967)

10,

G. DTJESING et al.: Influence of Vacancies and Impurities on the Damage

481

phys. stat. sol. 23, 481 (1967) Subject classification: 11; 10.1; 14.1; 21.6 Institut für Festkörper- und Neutronenphysik,

Kernforschungsanlage

Jülich

The Influence of Vacancies and Impurities on the Damage Production in Platinum Electron-Irradiated at 90 °K By G . DTJESING, H . HEMMEBICH, D . MEISSNER, a n d W . SCHILLING

In platinum foils of 99.999 and 99.9% purity different vacancy concentrations are frozen in by quenching. The foils are then irradiated with 3 MeV electrons at 90 °K. The difference between the radiation damage build-up in these foils and the damage built-up in annealed foils which are irradiated simultaneously is investigated up to electron doses corresponding to induced resistivities of 3 X 10~7 ß c m . I t is found that 1. pre-quenching can reduce the initial damage rate by a factor of more than 20; 2. the initial damage rate of the annealed samples is independent of their purity; 3. with further irradiation, the rate of decrease of the damage rate for the annealed samples increases with the purity of the samples; 4. for large damages the dose dependence of the damage lies between A¡> ~ and Ag ~ 9P1/2. The results can easily be explained by interstitials which migrate freely at 90 °K and are either annihilated by vacancies or converted into another interstitial configuration at impurities. The direct production of immobile interstitials at 90 °K can be excluded. Platinfolien von 99,999 und 99,9% Reinheit erhielten durch Abschrecken verschiedene Leerstellenkonzentrationen. Anschließend wurden sie bei 90 °K mit 3 MeV-Elektronen bestrahlt. Der Unterschied im Schädigungsaufbau zwischen diesen Folien und gleichzeitig bestrahlten getemperten Proben wurde bis zu Schädigungen von 3 X 10~7 ß c m untersucht. Wir erhielten folgende Ergebnisse: 1. Durch vorheriges Abschrecken kann die Anfangsschädigungsrate um einen Faktor von mehr als 20 reduziert werden. 2. Die Anfangsschädigungsrate der getemperten Proben ist unabhängig von der Reinheit. 3. Mit fortschreitender Bestrahlung nimmt die Schädigungsrate der getemperten Proben um so stärker ab, je reiner die Proben sind. 4. Für große Schädigungen liegt die Dosisabhängigkeit der Schädigung zwischen Ap