SCIENTIFIC ABSTRACT SMIRNOV, A.A. - SMIRNOV, A.A.

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• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

A. A..,--BTjJTYLAiIK0, A. K. , DANM 'MKO, V. M. ?,',ILNAN, YU. V. , NAYDIC-H, YU. V.
AIM-, BYBAK, S. A.
Theoz7 of Electric Resistance of Alloys in Prof-rossim- Order
Izv. Kivevsk,_poj~tel~hn- in-ta, 192, 1953, pp 18-24
'F"xperimental curves, expressing ratio of electric resistance of alloys in
Pro-ressinq ol,der to compound and distant order, differ from theoretical ones
b-y presence of rectilinear sections, sharp ma-Kinums and uneven variations.
These peculiarities are theoretieplly explained in examples of alloys -,.ith
cubic latticed. The axticle confirms A. A. Smirnov's theory Zhur Elks i Theor
ZI& 17, 743 (1947) of veculiarities observed in PIloys in proCressin-a order.
(RZhFiti, No 5, 1955)
9- Sen 55
SO: Surn No. 630.,

U:S 8 R

7 en. PIL. 2J.. or the
'
us pubstitritional;
i diffusion of tuarked atoms "I ni
tmary, body-celitered cul ticy Lnech-

nuism was ns5umvl,~Sn .:b Interactions
d
were considerpdi~ eq
l

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bo, ing
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final'),Ah(i ion' 6i~ ar a

?.Wideritd, and In ds4
activatioii~,,Cnoky-witb winpii~ or
m&.W would be
cube of,.jAjfj# illoy jim. actiikila~
-d to;~~!%~.tbrougli a rivix. it the alloy tendc4 to ord,~,
d -deccanp. into
-if
tuid thiouik a saiii tile- alloy tell cd to
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53
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Muslim of extrallem
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eory o
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lite prvcev;,,.of,,btdtdo9. 1.
alloys
~KRtvoGEAz-lANt)lA A. S~mtlttvov. ~zk ASXF vr_
24 NO, 4 41YJ
'
prQblcm... thc~ diffusion of atorris
I Diswsks: t~~
inkiled into thle fniersikes of lbe bodymc6tred crysla
,
)ys, e.j.. Aras~ dWng l1w ordcr~
ja(tk4t~ OfIl.11tlry OK
,
rations of thc all )y
p"ime con"go
ini proccss AI.
ounding tW diffusi or_lN_-
moms-_~urt ng.atows,
'
trarmus cienimi are:talcefi into considcridoft.-. A .:
dcri~;Ltion i3, prLsented 'of- theoretical dependence
ofthe cocffickar cfdiffukiaii on remperaturt; and con-,

t dowfor both tho ordered and disordcrcd tit,
c
ra
of tile MIO.
liv

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

6740
THEORY OF THF IDIFiJISION OF EXTHMEOUS ATOMS,
-
IN ALLOWDURIAG
TH4 PROCESS 60.011DERING. ll.:
Zhur.- Ekaptl'I
M. A. Krivoglaz a4 Bra Mov,
'
1"-
fcL F1z. 24
No,~
ea (in Russian)-
The problem of the diffusion of items (nee rted-Into the
Interstices of a face centered crystAl Intilco.of binary.
-
-o'
alloys, e.g-AuCup during the disorder rder tr- altion 13
an
..;Jlsquss~ed. The ternkraturei andcowntrallon dependence.
of the coefficient of diffusion I-4 jn4cattgated (o th U16
r be
efreot of the
ordered and disordered state of the alloy. lie-
n:on the~co~fflctpnt or diffusion is
disdrder-order ti-ittO
-or for the face-centirid than for the body
be greO
found to
,
t
centered alloy, lattices. (Science Abstrac 13)

1. Vi-MTOVI A. A,
2. USSR (600)
4. Alloys
7. Oxidation of alloys. Zhur. fiz. khim. 27, no. 1, 1953.
9. Month!X List of Russian Accessions, Library of Congress, Hay 1953. Unclassift -ed.

SMIRNOV, A.A.
Iffect of vacancies In crystal lattice units on electric resistance
of an alloy. Dop. AN URSR no.4:250-2.55 '54, (MIRL 8:4)
1. Chlon-korrespondent Akademii nauk USSR. 2. Kiivafkiv politakh-
nichniy institut.
(Metallography) (Electric resistance)
/-I-

7~
Ov
USSR
,"Elf ect~i interstitial atoms an the self-Musion of a metal.
M. A. Krivoglaz and A. A.' SmImov. DuAlady .4 kzd.
Mauk S.S.S.R- 90, dependence of
self-difruiiou of -f-Fe on C content is explained theoretically.
'The equil. no. of vacaucies with 0 1; 2 3 '4~ 5, and 6
jjelghborine latenititia) atonis Ivas ~alcd.'by a statistical
method. Art expression for the diffusion coeff. D ofinarked
matrix ittonia was then obtained in terms of the setf-dif-
filsion coeff. Dj in pure tuatrix rn~tal A,~the conca. c of the
IntcvititiA atom C, the interaction cnergy V of alorns A
:and C at M diaEance ag/2, and the difference of interaction
erjergi,~ !i for distances (Ar,9141)oo and ri,/2, where a. is the;
latrice- cim5l. D. - DiIII(I - c))Il + 44HAV - 1)A4
(I -L -01AT
1 011. ~ Thim, D did not vary expant'
tizally -~% ith I/ T. HowLvtr, approx., the rbiervtd. expt],
valut~l Qf activatian energy and fiequeucy fath)r were ob-'.
tained for B - OAS c.v, R - 6 o, ane. c - 2 to 5 at.
The fR-quency factor decrea:,&d by a factor of 100 with
iocrc-4se in c from 0 to ".5 at. A. C~.Guy

J, It-i

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V ,

Ra,
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m
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~~
tifi.-Z77j4 cffcaO hatef the 6*7. re a
cf. C.A.'49,131
elm. reghtgri y
With cub(c,aysw littice stiaic, li itin oelm.
this rcs46uicle, WCS dft cOn-cnd as tkto-s of addat , COzKt, i
,
Tho mutlom tho Obtalaw OffLow, golumce Off
r4ticuil.
-
,
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-
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at Amf COUCO', swd lo #Wyo 6vable.of dJ4*t&,r suchi
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USSR/Physics Diffusion in alloys FD-1072
Card 1/1 Pub. 153 - 8/24
Author : Smirnov, A. A.
Title : Diffusion into penetrated alloys
Periodical : Zhur. tekh. fiz., 24, No 10, 18o2-1811, Oct 1954
Abstract : The author calculates the diffusion coefficient of atoms penetrating
into intermediate nodes of the body-centered cubic lattice of a binary
alloy which may be in the ordered state.
Institution : -
Submitted May 3, 1952

SMIRhOV, A. A., KRIVOGLAZ, M. A.
"The Effect of Admixtures of Implanted Atoms on Alloy Dissociation"
an article in the book "Questions of the Physics of Metals and Metal
Science", AS Ukr. SSR Kiev, 1955, 151 PP-
So: Sum. No. 1102, 19 Oct 56

USSR/Physical Chemistry. Thermodynamics, Thermochemistry, B-08
Equilibria, Physical-Chemical Analysis, Phase Transitions.
Abs Jour: Ref Zhur-Khimiya, No 5, 1957, 14683
Author M. A.
Krivoglaz. A. A. Smirnov
Inst
Title On the Theory of Disintegration of Alloys Accompanied by
A Separation of Chemical Compound.
Orig Pub: Fiz. metallov i metallovedeniye, 1955, 1, No 2, 311-1-315
Abstract: The paper contains the thermodynamic computation of the
general case of disintagration of an alloy of two metals,
4n the crystal lattice of which atoms of a third element
have been introduced; thia diaintergration consists in
the formation of a chemical compound of this third ele-
ment T,,jith the metals and a solid solution of an altered
composition. The computation of the first phase repre-
~sentin_- the so!--;d solution is carried out statistical.Ly
i-.aking into consideration only the configuration part cf
the free energy. It is assumed that the disintegrating
Card 1/2
emistry, B-8
USSR/Physical Chemistry. Thermodynamics, Thermoch Phase Transitions.
Equilibria, Physical-Chemical Analysis,
Abs jour: Ref Zhur-Yhimiya, No 5, 1957, 14683.
b
Abstract: alloy has a face-centered cubic lattice and that t-e
interaction energy of atoms does not, depend on the temper-
ature and composition of the alloy.
Card 2/2
-1 , 1) All) /' Ii - A)

mecra foreign Wing cm thb r
.11,y-. Al. A. Kriwaglaz and A. A. Saiknov-

all
1955, No. 6, loi-l Tcc~ of sul,
qllcutitle- Cf .1 3rd- elment; C ca tjj of an A~-Y
N-li thc demnun., phzv~irof IvIlIc"i ritai~l the lat-
eubic) ei-thc, ;Hoy alld IvIlt-11 ng 71 .1m
-io;tot Ownlically 1; ii imalvzol bv
ow,
raluced byzilum'.-
The divory It--tds to the conclL,'oa t t sniall quantitic, (it C
E when th-~ AE

;Cotlca. of ~c appro=C4 em I'l rL
t
'
A -fiv tim
ur 0
obtained, (vibm x; 7 ~tid x, , the coomi. 2
~phases), Le. fcr
the dt
Una Z, cmiapa. curvc is
rdfL-cti to the line- 711;-3 is ill
~agik-blcnt With the~mlition derived- by
W76
~)w!Ehoat. am =u~cm-

'USSR/Physics Diffusion in metals
10ard 1/2 Pub. 118 - 4/8
Authors I Krivoglas, M. A., and Smirnov, A. A.
Title A theory of atomic diffusion inalloys
Periodical t Uep. fiz. nauk 5513, 391-442, Mar 1955
Abstract I An explanation of the diffusion.plienomena is prIesented. Two theoriM 0ut,
of three mentioned) on the atomic diffusion are discusse& One theory
explains the diffusion phenomena as the atom movements along the lattice
intzr-sites. The theory considers two types of cubical structure crystal 8:
1. f the -brass crystals with regularly and irregularly arranged atoms;
Institution:
'Submitted

0

I . .

;author Srdrnov A A Stoyrnov, LA.
Inst Eev iolytc nic In'stitute, USSR
Title Influence of Injected Atous on the Ordpring of the Llloy
Orig Yub Fiz. metallov i iret,~11ovedcniye, 1956, 2, 11Jo 3, 524-55o
Lbstrv.ct The influence of edmixturo of injected atoms on the ordering
of on alloy, having a volime-centered cubic lattice, was in-
vestizated periodicelly. It vas shovm that the presence of
an admixture of injected atons increases the degree of order-
ina of the alloy anJ increases the ordering temperature. The
possibility of ordering the disordered alloy by injecting
admixture ntous into the interstices of its crystalline
lattice is clarified. The distribution of the injected Ptcm-s
of the adinixture over tho interstices of E different kind
in the ordering of the c1loy is investigeted.
Card 1/1

A4 i k /V 0 V'/
USSR/Electricity - C;nductors G-4
Abs Jour : Ref Zhur - Fizika, No 1, 1958, 1390
Author : Krivoglaz, M.A., Smirnov, A.A.
Inst : -
Title : Concerning the Dependence of the Residual Electric
Resistivity of an Alloy on the Composition and on the
Degree of Ordering.
Orig Pub : 3b. nauch. rabot In-ta metallofiz. AN USSR, 1956, No 7,
115-117
Abstract : Without employing the concept of the Tnesin free path and
without assuming the energy of the electron to be inde-
pendent of the direction of the wave vector, 'but within
the framework of the single-electron approximation, the
known relations for the resistance of an alloy were de-
rived for the following two cases: (1) for a Uinary
ordered alloy without allawance for the correlation --
the dependence on the concentration of the component
Card 1/2

SMIRNOV, A.A.
Theory of the electrical resistance of alloys. Ukr.fiz.zhur. 2
no-3:211-225 Jl-S '57. (MIRA 10:10)
l.Institut metalofiziki AN URSR.
(Alloys--Electrical properties)

DANILENKO, V.m.: iMIVOGLAZ, M&TYSINi., Z.k-, SHIR110Y. A.A.
I la
Theor7 of wave 01spersion by the crystal ttIce of solid so-
1vtions. Fiz, met, i metalloved. 4 no.1:28-35 157. (MLRA 10:6)
L. inatitut "tallofisiki Akademii nai~c USSR.
(Wave mechanics) (Crystal lattices)

AUTHORS: Smirnov, A. A. and Stoyanov, I. A. 126-2-V30
TITLE: Theory of the residual electric resistance of interstitial
alloys. (Teoriya ostatochnogo elektrosoprotivleniya
Bplavov vnedreniya).
PERIODICAL: "Fizika Metallov i MetallovedeniYe" (Physics of Metals
and Metallurgy), Vol.IV, No.2, 1957, pp.228-231 (U.S.S.R.)
ABSTRACT: Up to now authors have dealt mainly with the theory of
the residual electric resistance of substitution type
alloys (1-6). The aim of this paper is to investigate
the relations governing the residual electric resistance
of interstitial alloys as a function of the composition,
the distant order parameters and the correlation
parameters (which characterise the near order relations)
between the substituted atoms of various types of nodes
and interstices. The calculation was effected on the
basis of the multi-electron theory, using a method which
was described by this author and his team in other work
(3-5). The following simplifying assumptions were made:
the potential energies of the conductivity electrons
differ little in the field of the ions of the differing
Card 1/3 type which substitute the nodes of the lattice. and that
the putential energies in the field of the ions which

126-2-4/35
AUTHORS: Dykhne, A.M., Matysina, Z.A,.,and Smirnov, A.A.
TITLE: Theory of residual electric resistance of multi-
component ordering alloys. (Teoriya ostatochnogo
elektrosoprotivleniya mnogokomponentnykh uporyadochivayu-
shchikhsya splavov).
PERIODICAL: Fizika Metallov i lAetallovedeniye, 1957, Vol.5, No.2,
pp. 220-229 (USSR)
ABSTRACT: The theory of residual electric resistance of alloys has
so far been developed only for certain particular cases.
Nordheim. (Ref.1) evolved such a theory vrith single
electron approximation, without taking into consideration
correlations for disordered multi-component alloys and
Smirnov, A.A. (Ref.2) evolved such a theory for ordering
alloys with any lattice of the Bravais type in the
disordered state. Ryzhanov, S. (Ref.3) has taken into
consideration correlation for ordering alloys with a
simple cubic lattice. In all the here mentioned viork the
usLiaL assumptions of the single electron apDroximation
have been made which are unjustified and ere as3ocii-ated with
introducing the length of free travel, the character of
the energy spectrum of the conductivity electrons, etuc.,
Card 1/4 which are not really required for deriving relations

126-2-4/35
Theory of residual electric resistance of multi-component
ordering alloys.
expressing the dependence of the residual electric
resistance on the composition, the mrameter of tbe long range
order and the correlation parameters (see Krivoglaz and
Smirnov (Ref.4)). Within the framework of the multi-
electron theory of metals, the residual electric
resistance was calculated in earlier work (Ref.5) for
binary ordering alloys, taking into consideration the
correlation in the first coordinate sphere and in other
work (Ref,G) for ternary disordered alloys, taking into
consideration the correlation along all the coordinate
CD
spheres. The aim of this paper is to evolve a more
general multi-electron theory of the residual electric
resistance of multi-component ordering substitution
alloys with any Bravais type crystal lattice in the
disordered state,which.in the ordered state, have any
number of types of nodes, taking into consideration
correlations in all the coordinate spheres. The authors
did not aim to determine the numerical values of the
electric resistance and they limited themselves to
Card 2/4 deriving relations expressing the dependence of the

126-2-4/35
Theory of residual electric resistance of multi-component
ordering alloys.
residual electric resistance on the composition and
also on the parameters characterizinG the distant order
and the :=relation in the alloy. Therefore, in the same
way as in the earlier work (Refs-5,6), the authors
succeeded in carrying out their calculations with a
minimum number of model conceptions. In addition to
taking into consideration the properties of the
translatory symmetry, it was assumed that the potential
energies of the conductivity electrons in the field of
ions of a different type differ little from each other
and that the potential of the electric field in the
metal is so small that the Ohm la'w applies. Thereby,
the calculation of the residual electric resistance
can be carried to finality only if the atom concentrations
of all the components except two are small. The
subject matter is dealt with under the following
headings: Calculation of the probability of transition
of the system of electrons from one state to the other;
determination of the dependence of the residual electric
resistance of an alloy on its composition, the distant
Card 3/Lp order parameters and the correlation parameters
ail~i-taking correlation into consideration).
There are 7 references, 6 of which are Slavic.
SUBMITTED: May 3, 1956.
ASSOCIATION: Institute of Metal Physics, Ac. Se. Ukral=ian SSR
(Institut Metallofiziki AN USSR)
AVAILABL~;: Library of Congress.
Card 4/4

21-5-11/26
AUTHORS: Geychenko, V.V,(Heychenko, V.V.) Corresponding~!ember of the
AN Ukrainian SSR and Smirnov, A.A. (Smyrnov, A.A.)
TITLE: Study of Interatomic Interaction in Interstitial Alloys by the
Wave Scattering Method (Izuchehiye mezhduatomnogo vzaimodeyst-
viya v splavakh vnedreniya metodom rasseyaniya voln)
PERIODICAL: Dopovidi Akademii Nauk Ukrainslkoi RSR, 1957, Nr 5, PP- 470-
473 (USSR)
ABSTRACT; The authors consider the application of the theory of X-ray
scattering by interstitial alloys for determination of some
constants of interatomic interaction. The data obtained make
it possible to find the correlation parameters in alloys with
two kinds of atoms at the lattice points and one kind in the
interstitial positions by the intensity of scattered radiation
and making use of Fourier calculus. The authors consider a
particular case of an alloy whose lattice points are occupied
by atoms A and B and form a face-centered cubic lattice and
interstices are partially occupied by C-atoms. The correlation
parameters enable one to estimate the micro-nonuniformities
Card 1/2 of the alloy. Formula 7 in the article can be applied to

137-58-6-13104
Translation from- Referativnyy zhurnal, Metallurgiya, 1958, Nr 6, p 274 (USSR)
AUTHORS: Krivoglaz, M.A., Smirnov, A.A.
TITLE: To the Termodynamic Theory of Second-order Phase Transi-
tions in Solid Solutions (K t9rmodinamicheskoy teorii fazovykh
perekhodov vtorogo roda v,fverdykh rastvorakh)
PERIODICAL. Sb. nauchn. rabot In-ta metallofiz. AN UkrSSR, 1957, Nr 8,
pp 65-69
ABSTRACT~ Relationships are obtained between the second derivatives of
the thermodynamic potential 15 relative to the temperature T,
the pressure P, and the concentration c which are generaliza-
tions of Ehrenfest's relationships for solid solutions. Within
the framework of the thermodynamic theory of second-order
phase transitions, relationships of the degree of the lower-
range order of Y1 were calculated relative to P and c close to
the transition point. With T and P constant., 17 's ~-c o,
while with T and c constant, ~rVTP--p, where c. and Po are
the values corresponding to the transition curves. To deter-
Card I/-- mine the slope coefficient of these relationships it is necessary

137-58-.6-13104
To the Thermodynamic Theory (cont.)
to know the coefficients of the expansion of ~ according to powers of I I
as performed in thermodynamic theory, and the derivatives 9TOIC)c or
r,I Tolc9P, where To is the transition temperature. M.K.
1- Metals--Phase studies 2. Metals--Thermodynamic properties
Card 2/2

18(7) PHASE I BOOK EXPLOITATION S011/2025
Krivoglaz., Mikhail. Aleksandrovich,, and Adrian Anatollyevich Smirnov
Teoriya uporyadoclaivayushchikhsysL splavov (Theory of Ordering in Alloys)
Moscow,, Fizzatgiz, 1958. 388 p. 5,000 copies printed.
I
Ed.: K.P. Gurov; Tech. Ed.: W.Ya. Murashava.
PURPOSE: This book is intended for solid-state physicists and advanced students
specializing in the physics of metals.
C01TERAGE: The book aims to give a systematic presentation of the more extensively
investigated aspects of the theory of ordering in alloys. The phenomenon is-
studied from two points of view: the actual ordering of atomejand the effect
thereof on the properties of the alloy. The author states that the theory of
ordering makes it possible to determine the short-and long-range order estab-
lished in alloyp of various compositions at different temperatures and to ex-
plain the effect of-composition and heat treatment on the properties of alloys.
Sufficient experimental data are included to illustrate the basic assumptions
of the theory. No personalities are mentioned. There are 337 references, of
which 153 are Soviet, 140 English, 31 German, 6 Japanese, 4 French, 1 Danish,
1 Dutch, and 1 Chinese.
Card 1/ 6

theory of Ordering in, Alloys
TABLE OF CONTENTS:
Preface
SOV/2025
5
Ch. I. General Informa;tion on the Phenomenon of Ordering in Alloys 7
1. The Ordering of atoms in alloys 7
2. Examples of the ci-jstal structure of ordered alloys 13
3. X-ray analysis of ordered alloys 19
4. Neutron diffraction study of ordering in alloys 34
5. Change in heat capacity and energy of alloys in ordering 41
6. Effect of the ordering of atoms on the electrical resistance
of alloys 43
7. Kinetics of ordering 51
a. Effect of bombardment with fast particles on the ordering
of alloys 58
9. Investigation of the relationship between ordering and the
mechanical, magnetic, magneto-resistive, and other properties
of ordered alloys 69
Ch. II. Thermodynamic Theory of Ordering
. 10. Classification of phase transformations
85
85
Card 216

Theory of Ordering in Alloys SOV/2025
11. Thermodynamic theory of phase transformations of the second type 90
12. Thermodynaziie theory of nearly completely ordered alloys 109
13* Fluctuations in the long-range order and.composition of alloys 117
Ch. III. Statistical Theory of Ordering 127
14. Method of approach 127
15. Matrix methods 131
16. Theory of ordering without regard to correlation in the alloy
(Theory of Gorskiy, Bragg, and Williams) 142
17. Method based on the expansion of the free energy in a power
series of v (Kirkvood's method) 153
T,
18. Quasichemical method 165
19. StatistIcal theory of almost fully ordered alloys 172
20. Effect of the pdmixture of a third element on the ordering of
alloys 181
21. Discussion of results of the statistical theory and comparison
with experimental data 195
Card 3/6

Theory of Ordering in Alloys SOV/2025
32. Investigation of frequent cases of X-ray scattering 291
33- Scattering of slow neutrons by ordered alloys 301
34. Application of the method of fluctuation to the problem
7
of scattering '08
Ch. VII. Theory of Residual Electrical Resistance of Alloys 335
j5. Determination of the lirobabillty of electron scattering
by the alloy crystal lattice 335
36. Derivation of formulas for determining residual electrical
resistance 343
37- Residual electrical resistance of binary alloys 345
38. Residual electrical resigtance of ternary alloys 352
Ch. VIII. Magnetic, Magneto-resistive, Optical, and Mechanical
Properties of Alloys 357
)9. Magnetic, magneto-resistive, and optical properties of ordered
alloys 365
Card 5/6

GEYCHRIKO, V.V.; KRIVOGLAZ, M.A.; SMIRNOV, A.A.
Studying atomic interac-t!6~~_in alloys by, means of wave scattering by
the crystal lattice of alloys. Isal. po zharopr. sPlav. 3:140-149
1 58- (MIRA 11:11)
(Alloys) (Crystal lattices) (Particles, Elementary--Scattering)

DANILENKO, V.M.;JYj,VOGLAZ, M.A.; MATTSINA, Z.A.; SMIIUIOV. A.A.
. I
-
_I-
-
'-"
Thmory of slow neutron scattering In a . Inal. po zharopr.
QPlav- 3:150-160 158. (IGRA 11:11)
(Neutrons--Scattering) (Alloys)

r
18(0)9 24(2) SOV/181-1-9-13/31
AUTHORS: Smirnov, A. A., Tikhonova, Ye. A.
TITLE: On the Theory of Scattering of X-Rays and Thermal Neutrons
by blulticomponent Substitution Alloys /?
PERIODICAL: Fizika tverdogo tela, 1959, Vol 1, Nr 9, PP 1393 - 1400 (USSR)
ABSTRACT: The authors investigated the influence exerted by geometrical
lattice disturbancesq caused by different atomic radii of the
components, on the X-ray- and neutron scattering in disordered
binary and multicomponent alloys. Special attention is devoted
to the concentration dependence of the scattered radiation
intensity. The investigations,were conducted after the model
of the Boris elastic continum for the special case of binary
alloys* ~Moreover, they were made on the assumption of the
displacements being superposable, without considering the
correlations between the substitutions of the various lattice
points by atoms. Calculations are made within the kinematic
scattering theory-. The authors considered the scattering of a
monochromatic radiation on a single crystal. First, the general
theory of X-ray scattering in multicomponent alloys is
Card 1/2 developed, and this is then applied to the special cases of a

On the Theory of Scattering of X-Rays and Thermal SOV/181-1-9-131'31
Neutrons by Multicomponent Substitution Alloys
binary and a ternary alloy. The formulas obtained can be used
for the calculation of scattering intensity in alloys with
disturbed lattice, and permit the investigation of the cor,
centration dependence of the regular reflection and the back-
ground intensity. There are 8 references, 5 of which are
Soviet.
ASSOCIATION: Institut metallofiziki AN USSR Kiyev (Institute of Metal
Physics of the AS UkrSSR Kiyev)
SUBMITTEDi December 30, 1958
Card 2/2

SWRNOV, A.A. [Smyrnov, A.A.]; TIKOZIOVA, Ye.A. [Tykhonova, 0.0.1
Contribution to the theory of X-ray and thermal neutron scattering
by multicomponent substitutional alloys. Ukr, fiz. zhur. 4 no.3:322-333
M,v-Jo '59. (MIRA 13:2)
I.Institut metallofiziki, AN USSR.
(I rays--Scattering)
(Neutrons--Scattering)
(Alloys)

AUTHORS: Yi-rivoglaz, M.A. and Smix-nov, A.,~L.
SOV/126-7-1-23/28
TITLi,.. On the Possibility of Determining the Form of the Fermi Surface
From the Angular Distribution of Y--Quanta Formed in the Trans-
formation of Electron-Positron Pairs into Photons
(0 vozmozhnosti opredeleniya formy poverkhnosti Fermi po
uglovomu raspredeler-kiyu -~-kvantov, obrazovavshikhsya
pri prevrashchenii elektronno-Dozitronnykh par v fotony)
PERIODICAL: Fizika Metallo-v i Metallovedenie, 1959, Vol 7, Nr 1,
pp 151-152 (USSR)
ABSTRACT: In units of h/2rr (h being Planck's constant) the character-
istic momentum vectors for the crystal lattice, electron,
positron and resultant photon are denoted by a, y,, KI and
p respectively. The transition probability for pair annhil-
ation with photon production in the lattice is then given by
the standard formula:
2
w u ull exp ( -2 -Tr i_~r) d7.' 2
Card 1/3

SOV/126-7-1-23/28
On the Possibility of Determining the Form of the Fermi Surface From
the Angular Distribution of "--Quanta Formed in the Transformation
of Electron-Positron Pairs int._ Photons
U
Here the u's are the particle wave-functions and of course
involve the configuration vector r; eur is the unit of
volume In configuration space- t7he dq1ta-term insurgs the
conservation of momentum. The angular distribution of
quanta may be obtaLried explicitly from this formula by
writing r and its dprived functions in terms of polar
co-ordinaTea r. r!, / and integrating out the redundant
variables. The di3tribution is related to the Fermi energy
surface through the latti3e and particle ventors, and in
principle this surface could be determined for all values of
.E by absolute intensity measurements of the photon dis-
tribution at a large number of angles. In practie-,g it is
feasible to make only relative intensity measurements at a
few angles, and the note suggests how these angles be selected
to afford the maximum possible information about the general
form of the Fermi surfase. In particu.1ar, the theoretical
interpr9tation is considerably simplified for angles
correspondinS to the vanishing of one or other of the basic
Card 2/3 vectors.

SOV/126-7-1-23/28
on the Possibility of Determining the Form of the Fermi Surface From
the Angular Distribution -o7f 1( -(duanta Formed in the Transformation
of Electron-Positron Pairs into Photons
There are 7 references, of which 4 are Soviet and 3 English.
ASSOCIATION: Institut metallofiziki AN USSR (Institute of Metal
Physics, Ac.Sc. UkrSSR)
SUBMITTED: October 7, 1957
Card 3/3

AUTHORS: Nosar', A. I. and Smirnov A._&. SOV/126-7-6-2/24
TITLE: Theory of the Residual Electrical Resistivity of Binary
Disordered Alloys with Imperfect Crystalline Lattices
PERIODICAL: Fizika metallov i metallovedeniye, 1959, Vol 7, Nr 6,
pp 8o9-8211 (USSR)
ABSTRACT: The theory of the residual electrical resistivity of
disordered substitutional alloys of non-transition metals
was given by Nordheim (Ref 1) in terms of the one-electron
model, without any allowance for correlation and static
defects of the crystal lattice. For binary alloys A-B
this theory leads to a parabolic symmetrical curve which
gives the dependence of the residual electrical
resistivity e on the relative concentration C of the
A atoms in the alloy; this curve can be expressed as
e = kcA (1 - cA).
Further developments of the theory (Refs 2,3) allowed
for various factors which affect P. The many-electron
Card 1/3 theory of the residual resistivity was used by several
workers (Refs 4-10) for binary ordering alloys. These

SOV/126-7-6-2/24
Thecry of the Residual Electrical Resistivity of Binary Disordered
Alloys with Imperfect Crystalline Lattices
workers allowed for correlation but not for geometric
defects of the crystal lattice. The present paper deals
with the effect of lattice defects due to different
dimensions of the alloy atoms on the concentration
dependence if the residual resistivity of binary (A-B)
disordered substitutional alloys of non-transition metals.
The many-electron theory of metals is used but correlation
between lattice substitutions in the alloy is not allowed
for. Since the treatment is qualitative, in the sense that
a numerical value of the electrical resistivity is not
obtained, the defects are allowed for by means of a rough
"elastic-medium" model, used in discussion of X-ray
scattering in alloys (Ref 14). Dependence of the residual
electrical resistivity on the concentration c A is obtained
in the form
(0= AcA(l - CA ) + BcA U - c A (a0 + a1c A) (105)
Card 2/3 where a 0 and a 1 are functions-of A(cA ) and wB(cB ) and
W's are mean volumes of A (or B) atoms, which depend on the

SOV/126-7-6-2/24
'Theory of the Residual Electrl 100 A the edge of the.
optical absorption is weakly pronounced., but when a - 1-3 Py the absorption curve
is similar to that for bullqr single crystals., but is shifted in the-long-r e
re ion. The temperature coefficient determined from this ratio dEWdT
ev h
X 103 V/gM wit
'~deg, agrees with data for single crystals. An so field of 5
frequency 16 cps shifted the absorption range in the region of X 5100 A'by.an
CaM V2
io 7- o I-"),