SCIENTIFIC ABSTRACT KRIVOGLAZ, M.A. - KRIVOGLAZ, M.A.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R000826520020-6
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Sequence Number: 20
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

SOV/126-8-2-1/26
On the Elastic Moduli of a Solid Mixture
elastic continuum approximation. The results obtained
are in qualitative agreement with the experimental data
reported by Koster and Rauscher (Ref 4) for Ag-Cu, Cd-Zn,
Al-Sn and Pb-Sn.
There are 4 references, 3 of which are Soviet and I German.
ASSOCIATION: Institut metallofiziki AN UkrSSR (Institute of Metal
Physics, Ac. Sc. of the Ukrainian SSR)
SUBMITTED: July 17, 1958
Card 2/2

/00.9/00 67683
AUTHORs XrIvoglazj M.A.- SOV/126-8-4-4/22
TITLE: -if-f-e-o-t-o-f-G-oo-metrioal~pefects on the Backgrouqd Intensity
Distribution in X-ray,%nd Neutron DiffractionYPatterus
PERIODICAM Fizika metallov I metallovedeniye, Vol 81 Nr 4f 1959,
pp 514-530 (USSR)
ABSTRACT: The present paper is concerned with the study of the
background intensity distribution in the case of the
scattering of monochromatic radiation by a monocrystal.
Particular attention is paid to those properties of the
background which are associated with the presence in the
expression for the intensity of a term which tends to
infinity in the neighbourhood of the reciprocal lattice
sites. The analysis is based on the formulae for the
intensity of diffuse scattering of monochromatic
radiation by a monocrystal It. which were obtained by
the author in Ref 3. As in f 3, only scattering on
Irregularities due to differences in scattering factors
Card and atomic radii is taken into account, veneral
formulae are derived which may be used to determine the
1/3 intensity as a function of the direction of the
scattered ray, They may also be used, with the aid of

67683
SOV/126-8-If-V22
Effect of Geometrical Defects on the Background Intensity
Distribution in X-ray and Neutron Diffraction Patterns
purely geometrical constructions, to determine the
intensity distribution in the Laue pattern under various
possible conditions. A detailed discussion is given of
the scattering of monochromatic radiation by a mono-
crystal whose position is slightly displaced relative to
the position giving purely Bragg reflection. In this
case, although the Bragg reflection is absents the Ewald
construction shows that near the direct reflection there
should be intense diffuse scattering maxima. Formulae
are derived giving the intensity distribution at such
points as a function of the scattering angle. It is
suggested that it would be useful to have experimental
data on the background intensity distributiong
especially near critical points and phase transition
Points of the second kind, since the present theory
gives expressions for the anomalously large scattering
Card which takes place near a critical point.
2/3 There are 6 figures and 9 references, of which 3 are
English and 6 are Soviet.

67683
SOV/126-8-4-4/22
Effect of Geometrical Defects on the Background Intensity
Distribution in X-ray and Neutron Diffraction Patterns
ASSOCIATIONt Institut metallofiziki AN USSR
--Mstituto of Physics of Metals, Lcademy o
or th-e--URFa-inIAn--AHR I
SUEMITTED: January 7, 1959
CFrd 3/3

67750
/1P .9100 BOV/126-8-5-2/29
AUTHOR: Krivoglaz K A.
TITLE: On the-ttfe-et
of Fluctuations in Correlation Parameters
on the ScatteriVA of X-rays0and Thermal Neutrons Mby
Solid Solutions IT
PERIODICAL: Fizika metallov i metallovedeniye, Vol 8p 1959, Nr 5,
pp 648-666 (USSR)
ABSTRACT: A detailed discussion is given of the scattering of
X-rays and thermal neutrons by solid substitutional
solutions, which is due to differences in atomic
scattering functions and geometrical defects.
Irregularities In both the composition and the
correlation parameters are taken into account, The
paper is divided into the following sections:
1) Introduction; 2) Determination of the Fourier
components of the atomic displacements; 3) Diffuse
scattering by Ideal solutions; 4) Diffuse scattering
associated with fluctuations in the correlation
Card parameters in the region of the phase transition point
of the second kind; and 5) Determination of the
1/3 reduction in the intensity of regular reflections.
If fluctuations In the composition and the correlation

67750
BOV/126-8-5-2/29
On the Effect of Fluctuations in Correlation Parameters on the
Scattering of X-rays and Thermal Neutrons by Solid Solutions
of parameters are taken into account, one finds that the
correlation parameter fluctuations lead to a change in
the coefficient which connects lattice defeats with
fluctuations in the composition and to the appeartnam of
additional scattering. Isodiffusion curves for the
scattering by correlation parameter fluctuations do not
have a lemnisoate-like form but a form close to an oval.
Iffeats associated with correlation parameter fluotua-
tions play a relatively greater role if the lattice
constant Is very dependent on the correlation parameters
and deviations from Wegard's rule are large, In ideal
solutions the scattering by correlation)iarameter
fluctuations is proportional to o2(1-0 and becomes
negligible at small concentrations. In non-ideal
solutions the,role of thee# fluctuations may become
enhanced. In partioularg near the phase transition
Card point of the second kind, they may lead to the appearance
2/3 of a strong diffuse scattering in the neighbourhoods a
structural reflection# whose intensity tends to infinity
for T -*, To.

67750
-JOVI26-8-5-2/29
On the Effect of Fluctuations in Correlation Parameters on the
Scattering of X-rays and Thermal Neutrons by Solid Solutions
There are 1 figure and 11 refeTences,of which 2 are
English, 1 is Ukranian, 1 is a Russian translation
from English and 7 are Soviet.
ASSOCIATIONs Institut metallofiziki AN USSR
(Institute of Metal P!jY.9iC3 of the Academy of
SUBMITTED: January 8, 1959
Card 3/3

24(7) SOV/48-23-5-21/31
AUTHORS: Geychenko, V. V., Danilenko, V. M., Krivoglaz, M. A
Malysinat Ze Ast Smirnov, A. A.
TITLE: On the Theory of the Diffused Dispersion of an X-Ray and Slow
Neutrons in Multicomponent Alloys (K teorli diffuznogo ras-
seyaniya renigenovykh luchey i medlennykh neytronov mnogo-
komponentnymi splavami)
PERIODICAL: Izvestiya Akademil nauk SSSR. Seriya fizicheskaya, 1959,
Vol 23, Nr 5, pp 637-639 (USSR)
ABSTRACT: The study of the diffused dispersion of various types of waves
in the nrysial lattice of alloys offers the possibility of
investigating the arrangement of the various atoms in the
crystal lattice and the influence exerted by microinhomogenei-
ties upon alloy properties. A formula must be developed and
expanded , permitting the computation of dispersion for the
cases of X-rap and slow neutrons by the application of
"faoiors of atomio dispersion". Such a formula (1) is written
down in the form of a finite sum and the factors for the
computation of the dispersion of an X-ray and of slow neutrons
are desoribeds This finite sum may be decomposed into two
Card 1/2 partial sums which consist of the diagonal or non-diagonal

SOY/40-23-5-21/31
On the Theory of the Diffused Dispersion of an X-Ray and Slow Neutrons
in Multicomponent Alloys
members, respectively. Thene two partial eume are then computed,
namely, for the disordered state In the Brave type lattice.
For an exemplification, these two formulae are written down
for a binary alloy with the hexagon systems AB and AB 30 Final-
ly, a wide space is devoted to the correlation parameters
characterizing the state of the crystal. There are 4 ref-
erenceat 3 of which are Soviet.
ASSOCIATION: Institut metallofiziki Akademii nauk USSR
(institute of Metal Physics of the Academy of Sciencee, UkrSSR)
Card 2/2

24 (7)
AUTHORS: triy6glazq He A., Tikhonoyng To. A. SOV/48-23-5-27/31
TITLE: The Theory of Dispersion of X-rays and Thermal Neutrons in
Fluctuating Inhomogeneities of Solid Solutions (Teoriya
rassayaniya rentgenovykh luchey i teplovykh noytronov na
fluktuatsionnykh noodnorodnostyakh tverdykh rnetvoroy)
PERIODICAL: Isvestiya Akadomii nauk SSSR. Seriya fizicheakaya, 1959, Vol2%
. Nr 59 pp 652 - 654 (USSR)
ABSTRACT: The considerations made in the present paper lie within the
framework of the kinematic theoryo The inhomogeneity of the
material in caused by the various factors of dispersion of
different atoms and by the geometrical tensions, caused by
the different atom radii* Similar papers are then referred to
(Refs I and 2) and for inhomogeneous binary solutions a form-
ula (1) is given for the intensity of the diffused dispersion
of X-rays. This formula in verified for the case of the ideal
solution. Non-ideal inhomogeneous solutions are considered
next and the intensity expressed in formula (1) is developed
from the thermodynamic point of view. The result is formula
Card 1/2 (3) whioh is examindd in the final part of the pres6nt paper.

The Theory of Dispersion of X-rays and Thermal Neutrons SOY/48-23-5-27/31
In Fluctuating Inhomogeneities of Solid Solutions
The influenoesexerted by the quantities occurring in the form-
ula are studiod in this connection. The parameters of order
and correlation, the superlattice reflection and the intensity
of regular reflection are also taken into account, There are
4 references, 2 of which are Soviet.
ASSOCIATION; Institut metallofisiki Akademii nauk USSR (Institute of Metal
Physics of the Academy of Soiencest UkrSSR)
Card 2/2

81639
S/181/60/002/06/27/050
B006/BO56
LUTHORt Krivoglas, M. A.
TITLEi The Theory of Phononic Thermal Conductivit of Non-perfect
CrystalslNear the Critical Point on the Curve of the Decay
or Phase Transition of the Second Type
PERIODICAL: Fizika tverdogo tela, 1960, Vol. 2, vo. 6, pp. 1200-1210
TEXTj It was the aim of the present paper to investigate the phononic
thermal conductivity of non-perfect crystals in which the defects are
not statistically distributedl the 4efsot concentration is not low, and
the distortion extends to all calls of the crystalf such crystals
are, e.g., concentrated solid solutions or asignottoolectries. The
author here theoretically investigates the low-temperature phononic
thormal conductivity of solid solutions which are cooled from the
critical point on the decay curve. At low temperatures which are
considerably below the Debys temperature the thermal conductivity of
such a solution is lower than that of a perfect solution, and with a
temperature drop it decreases proportionally to the latter. In the case
Card 1/3

81639
The Theory of Phononio Thermal Conductivity of S/lei/60/OOLI/06/27/050
Non-perfect Crystals Near the Critical Point on B006JB056
the Curve of the Decay or Phase Transition of
the Second Type
of a solution which is cooled from the range of the critical point, the
low-temperature thermal conductivity decreases with decreasing temperature,
passes through a minimum, after which it again rises. If the solution
approaches the critical state, the minimum is shifted toward lower
temperatures, and the minimum value of thermal conductivity decreases.
An analogous effect may be observed also at the critical point, whore
the curve of phase transitions of the second type goes over into the
decay curve (of. the phase diagram on p. 1206). For solutiors of
atoichiometric composition, transition from the unordered to a nearly
completely ordered solution must lead to a sudden increase of thermal
conductivity. In the last part of the paper, the processes occurring
near the critical point on the curve of phase transitions of the second
type are finally investigated for the case of one-component crystals.
The anomalies of low-temperature thermal conductivity occurring within
the range of the critical point (in which the curves of phase trans-
itions of the second type go over Into those of the first type) are
investigated for crystals having a symmetry center and whose critical
Card 2/3 V

81639
The Theory of Phononio Thermal Conductivity of S/181/60/002/06/27/050
Non-perfect Crystals Near the Critical Point on Boo6/BO56
the Curve of the Decay or Pha'be Transition of
the Second Type
point is in the low-temperature range. A. F. Ioffe and Ye. D.
Devyatkova are mentioned. There are I figure and 10 references:
7 Soviet, I German, 1 British, and I Dutch.
ASSOCIATIONt Inatitut metallofisiki AV USSR, Kiyev CLnstitute o
Metal Physics of the AS UkrSSR, Kiyev)
SUBMITTEDs June 26, 1959
Card

")11.1 ("00
AUTHOR:
TITLE:
PER1.01)1CAL:
ABSTRACT:
WY P,
1;0V17 0 0
M. A.
ConcevnItil, the X-Ray Seattet.-Iiij,, by Sti-ongly DI-Aorted
Uniform st"'Ild 30tuttono
0
196U. Vol '), Nv I 'I
COntInUlng tits otudles on the difftioe ocatterIng- of
X-rayB and thermal neutrono (Zli. e-kopet-Im. I teor.
flz-, -54, 204, 1958; et al.), the authov L'ound that the
scattlet-1tig Lnterwl.ty dinti,Lbutlon In otronglY dtototcd
of)!Ld soluttons is asymmetric; ao 1-to deterriLnutton ve-
(JUIPeO the grentev number of' temm, of' the exoauded ex-
pi-eosLon of' ~icattcrttig '-nt.cn:31ty, the ML;her tlie dervee
of' d1fitortions and the ave the Indl.Cell Of' re-
Nections. In a u1nary ~,~ollcl oolutlon, whooc scattering
In teno I t,,v Is 71 functlon of the ocattevln~,, power ol' the
con3l.1tuent atow A and B. and of' oti-uctm-e ~Ilstortl-on,
the licLevogenelty that scatti2vini-, ca:i he defl-ned

the X-HaY 5cattovlng by
11.,)tz-ongly Distoi,ted Uniform Solid Solutions
by osotimptIon that the Content C of' A AOm at :3-th
node equals I ov 0 when the node to occupted by A or, B,
and the vector of static displacemento fis13 a
ven va I ue nion, Lhe Fouvier, oct-tes of' tile vallies are
till, C,
all, tilt.
where c denotes the content of' A atom; ck Is Fourier
component of c; R 13 VadiLIJ VCCtOl' III 1n Ideal atructure;
N Is number of atoms In the crystal; C C_K
Rk R_k ; ItkIs fluctuation:3 In the corvelation of
parameters; summation over k Is carried out- In terms
of wave vector k/27T- In the first cell of the reci-
procal lattice. For an Ideal solid solution, whooe
lattice constant 13 prDportlonai to thQ conl-ent of
L
comoonenta, the scatt~ertng Intensity 1.3 cx-.)-cssed by
2/5
............
Note

all OC LTI I IM,
Tl lit I oil.
sc.,kt,Q I-Irif, r)
"IrK q, to dill'ovetwe
wavo ve~:tov'.',; K to i'lle
-'.trt , /' ~~ V
1:1U11ce pollit Ile -~;A tiv! eril or , '
I t I
!;o;IlA1!1.ltIj', power of' t) 1k'! I Vu I I 1--wo I i
o-~ 'lorilde-ti
-10 1 'o c1, ~O'Offl.'
p
Z\J' C k ((I,Ak)7
A B k
o Ic a n d d c f 1. 11 e oy
1 -4- JA
Ak - a a = -~- C 1)
k3 tr .

w, '1:atAev1n(_; by 0 1;
f, 0 r r-, I S 0 i t t~ f S o I u t' I o I 111 SOVI,
0- 13 Pul:;."~On f'actov; I.-, :0.0MIC The
mean ol' the Fourier component c 1:~
__ i ~.
wheue K 1,~, Bolt-man constant; V is volume; 4)
0 1 C_ (-
Is thet,modynamle potentlai of !i unit volume;
T/d . Both the low anJ hICher orde, teviris of'
the expansions of ac)ove 3erleB, varlatlon~; of the
terma depending on the vaiuez of various factor3 In
zpectal ~asez, the effect of tecm varlatIons on the
scattering Intensity of Ideal and nonideal solid
solutions are analy-zed by means of over 20 more equations,
parti,ally derived and ex-plained In the ~wthorls pre-
cedtng papers.. The scatteving Intensity d1stribution
in the vicinity of reclprocaL lattice, points and the Iso-
diffujlon curvej for nonl~laail soild ~iolutions a,,e found
otTl a fo-j- *'o '~Ajcy a,re
to cievlate 0
(31-C) ill the c-oc of' .30ilt.i ~30' ut, 1 on:3 Por In3tance,
h,2 1~,tckL7
Cu j

Crot)~,!(-' v!) I tl:L t, It t2 X-- It S~-:lt,tov 1by 3!, t oro.~l 6,
Disto.-ted Uniform Solid Sol,,!.lon~~', sov/,~ (i - /;7 0
ASSOCIATION:
SUBMITTED:
lli~;hc,r order termu iticreaze app~-ectauljr ".11th grouping
of lmpurltle3 and will-h the at,omic di";Placements due to
a immbardillient by Y-lgh-spee,ll pat,tl~,loj. Tiiere are
refevences, 5 Sovlet~ 2 'U.S. I U.K. Tl~ (.- U.S. and U.K,
are: C. W. Tucker, P. Sento, 11hy3. Rev., ~K)~ 17`-~, 1955;
Ti. Kan~:akl, J. Phys. Cher. Solllo.:3,
"'; K.
Huang A, 190, 1 GL~
g, Proc. Poy. SO(,'
Institute ot' 'Meta lp~iy;; I c~-i of ti-,'L, A,~----iJei%y ot,' S~~lences or
the Ukt,ainian SSR llnstit~it AN Ul~- SSR)
may 1~)51)
Card 5/5

DANILENKO, V.1,. [Danylenko, V.M.1 KRIVOGLAZv M.O.[Kryvoblaz, M.O.]
LARIKOV, L.N.; SMIRNOVj A. #
Ukrainian Republic Conference on the Theory of Metals and Alloys.
Ukr. fiz. shur. 5 no.ltl3O-l3,9 Ja-F 160. (MIRA 14:6)
Hatalo-Congreeaes
Alloys-Congresses~
~
vIk

00
AUTHORS:
TITLE:
PERIODICAL:
AD
S/185/60/005/002/004/022
D274/D304
Kryvoglaz, M.O. and Tykhonova, 0.0.
------------
Theory of X-ray scattering by multi-component
ordered solutions
Ukrayinalkyy fizychnyy zhurnal, v. 5, no. 2, 1960,
158-171
TEXT: X-ray scattering by partially-ordered multicomponent solid
solutions is considered; the solutions have unit cells of arbitrary
type, but only the case of each atom being the center of ay=.etry
of the crystal is considered. Formulas are derived for the inten-
sity of diffuse scattering. Solutions with lattice of P -brass type
are considered in more detail, as well as solutions in which one
sublattice is occupied by similar atoms and the other sublattice
contains atoms of two different types. First, the formula for the
intensity of the Bragg reflection is derived. Further, the formula
for the intensity of diffuse acattering is derived:
C ard 1/5

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Theory of X-ray scattering... D274/D304
n
IF N2 c Ow. B B (9)
0 q ya 'q" y CP a Y qcKO(I -Y'
a cot
Bqao(ty e2niKthW' (f V 0 Al, (A qY'XOL - Aq, 'yo(l)
(10)
The Fourier coefficients cqy, Oc* qX of can be expressed in terms
of the concentration c of components at various types of lattice
points and in terms of the correlation parameters. B is expressed
in terms of the difference between atomic-scattering Factors and
in terms of the factor of proportionality between the q-th Fourier
coefficients of concentration-fluctuations and of displacements.
(q characterises the distance to the reciprocal lattice points).
For a binary solution A-B, and ignoring the correlation, the formu-
la for the intensity reduces to
IF Ne No cl AcIBB2
t qAB'( (13)
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Theory of X-ray scattering...
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D274/D304
The expression for the intensity becomes very simple for solutions
in which the lattice points of all the sublattices, except one, are
occupied by a single type of atoms. In the neighborhood of reci-
procal lattice points, the intensity can be expressed -*n terms of
the second derivative of the thermodynamic potential with respect
to the concentration c. Formulas are derived by means of which B,q
can be expressed in terms of the interatomic coupling constanto.
If the interaction between nearest neighbors only is considered,
these constants can be expressed in terms of the derivative of the
lattice parameters with respect to concentration, and in terms of
the modulus of elasticity. In the case of certain actual crystal
structures, simpler formulas were obtained; (this for hex onal,
rhombic, tetragonalt and cubic crystals by the authors inafRef. 2:
IUZhF, 39 2979 1958). In the proximity of the reciprocal lattice
points which correspond to lattice, as well as superlattice reflec-
tion, the intensity of diffuse scattering varies in inverse propor-
tion with the square of the distance from the lattice point; in
that case the factor of proportionality cootains the aquare of a
structure factor which, 'for superlattice reflection, becomes zero
C ard 3/5

S118 60/005/002/004/022
Theory of X-ray scattering... D274%304
in case of a disordered solution. The obtained formulas permit cal-
culating the intensity by means of independent experimental data on
thermodynamic activity of components, elasticity modulus, and conc-
entration. On solutions with crystalline lattice of P -brass type,
formulas are derived (in the nearest neighbor approximation) which
express the intensity of scattering at any point of the reciprocal
lattice in terms of the concentration at different lattice-points
and of the correlation parameters; these formulas make it possible
(in several cases) to determine the correlation parameters experi-
mentally. Using a statistical theory of ordering, the correlation
parameters can be determined as functions of temperature and energy
of ordering. By means of the thermodynamic theory of fluctuations,
the intensity can be expressed directly in terms of energy of order-
ing. A formula is derived which makes it possible (in-principle)
to determine experimentally the energy of ordering. On solutions
with two sublattices, the second sublattice having atoms of two
different types, the results obtained can be uned for studying vac-
ancies in lattices of type NaC1 and CsCl. A formula is obtained
which permits determining (by numerical integration) the quantity
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D274/D305
L which characterizes the weakening in intensity of scattering.
The two sublattices have different L- in crystals of type NaCl and
CaCl, Ll exceeds L2 by a factor of 11 approximately. There are 5
references: 3 Soviet-bloc and 2 non-Soviet-bloc. The reference to
the English-language publication reads as follows: K. Huang, Proc.
Roy. Soc., 190, 1029 1947.
ASSOCIATION: Instytut metalofi ky AN USSR (Institute of Metal-
physics, AS UkrSSR7
SUB14ITTED: July 111 1959
Card 515

251,70
S/185/60/00.5/602/005/022
D274/D304
AUTHORS: Kryvoglaz, M.O. and Tykhonova, 0.0.
TITLE: Theory of X-ray scattering by interstitial solid
solutions
PERIODICJ*.L: Ukrayins1kyy fizychnyy zhurnal, v. 5, no. 2, 1960,
174-188
TEXT: General formulas are derived for the intensity of diffuse
scattering for both ideal and non-ideal solutions. (Ideal solutions
are those with correlation parameters equal to zero). Solutions in
which the interstitial atoms are in the octahedral interstices of
face-centered and body-centered cubic lattices were considered in
more detail, as well as martensite-type crystals. The general form_
ulas obtained by the authors in the preceding article (of the same
issue) can be also used for interstitial solid solutions, provided
the interstices are considered as sublattices filled by interstitial
atoms with zero scattering factor). The problem is treated from a
macroscopic viewpoint, hence the intensity-distribution in the
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25570
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Theory of X-ray scattering... D274/D304
neighborhood of the lattice points of the reciprocal lattice can be
considered in detail irrespective of the atomic-interaction forces.
Formulas are derived in the nearest-neighbor approximation, which
permit determining the intensity distribution in the entire recipro-
cal-lattice space for any crystals to which this approximation
applies. Further simplifying assumptions are made. For small a
(q characterizas the distance to the reciprocal lattice oints),'
the correlation parameters (which are frequently unknown.3 can be
ignored, and the intensity Ip expressed in terms of the*second deri-
vative of the thermodynamic potential with respect to the concentra-
tion of the interstitial atoms; the quantity A,.(whicK is a propor-
tionality factor between the q-th Fourier coefficient of atomic dis-
placement from the lattice points and the q-th Fourier coefficient
of the concentration of interstitial atoms) for hexagonal, rhombic,
tetragonal and cubic crystals, can be expressed in terms of the
modulus of elasticity and the derivative of the lattice parameters
with respect to concentration. For an ideal solution, the intensity
of diffuse scattering is IF a Nf2c U - c)(ql,Al )2 (5)
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2
S/185/60/005/002/005/022
Theory of X-ray scattering... D274/D304
N is the number of interstices; c - the concentration of atoms in
these interstices, f - an atomic-scattering factor of the pure metal,
multiplied by a factor due to lattice defects; (q and A. were alread-
y defined). As the interstitial atoms can be found in various types
of interstices, the intensity of diffuse scattering in ideal solu-
tions can be obtained as the sum of the tems corresponding to the
various types of interstices. On interstitial solid solutions with
face-centered lattices, the interstitial atoms are found in the cen-
ter of the cubic lattices and in the middle of their faces, the
interstices having cubic symmetry. Just as in the case of substan-
tial solid solutions, the intensity of diffuse scattering is inver-
sely proportional to q2 in the nnighborhood of the reciprocal lat-
tice point. For small q, the isodiffusive surfaces are in the form
of two spheres which touch at the reciprocal lattice point, (in case
of elastic isotropy). For large q, the isodiffusive curves greatly
differ from a bispherical shape. On martensite-type interstitial
solutions, the formulas for A, are derivcd. Ths isodiffusive sur-
faces have a shape far from spherical; this is especially the case
for strongly anisotropic crystals. The intensity of diffuse scatter-
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25570
S118516olOO5100210051022
Theory of X-ray scattering... D274/D304
ing in the neighborhood of the two lattice points (hOO) and (00h)
differs greatly. On interstitial solid solutions with aody-centered
cubic lattices, the interstitial atoms can be found with same proba-
bility in any octahedral interstice (belonging to certain types).
The intensity can be found by the same formulas as for zhe Martensite
type. The interstices have tetragonal, and not cubic symmetry. The
isodiffusive surfaces do not pass through the reciprocal lattice
poirrt. As the type of isodiffusive surface varies according to the
type of solid solution, the study of diffuse scattering can be used
as yet another method of investigating the structure of solid solu-
tions. Thus it can be determined whether an interstitial atom is
to be found at the lattice point or in the interstice of a body-
centered lattice, or whether such an atom is found in the octahedral
or tetrahedral interstice of a face-centered lattice. Ille formulas
ob tained for A. can be used not only for studying the intensity of
diffuse scatter ng, but also.for ascertaining the displacements
about the interstitial atom, and for calculating the intensity re-
duction factor in the Bragg reflection. An example is given, where
the displacements of Fe-atoms about the interstitial carbon-atom in
Card 4/6

25570
S/185/60/005/002/005/022
Theory of X-ray scattering... D274/1)304
(X-Fe are calculated. The obtained displacements are wre accurate
than those of J.C. Fisher, (Acta Hetal., 6, 13, 1956). It Is noted
that the obtained distribution of defects about the interstitial
atom can be used for many other problems, e.g. for determining the
energy of interaction of carbon atoms in a Fe-solution, for studying
the ordering of carbon-atoms in martensite, for determining the in-
fluence of interstitial atoms on the electrical conductivity of Fe,
etc. The mean square displacement of atoms in the solid solutions
is found from formulas given. Experimental and calculated values
were compared, and it was found thatthough there is qualitative
agreement, considerable quantitative discrepancies occur, especially
for displacements alongthe x-axis. These could be narrowed by tak-
ing into account additional factors. There are 4 figures, 2 tables
and 12 references: 6 Soviet-bloc and 6 non-Soviet-bloc. The refer-
ences to the 4 most recent English language publications read as
follows: W. Cochran, G. Kartha, Acta Cryst., 9, 944, 1956; H. Kanz
aki, J. Phys. Chem. Solids, 2, 107, 1957; J.C. Fisher, Acta Metal.,
6, 13, 1953; D.D. Betts, A.B. Bhatia, G.K. Horton, Phys. Rev., 104,
43, 1956.
Card 5/6

25511 1002/005/022
$/185 60j
Theory of X-ray scattering., D274YD304
ASSOCIATION: Instytut metalofizyky AN USSR (Institute of Metal-
physics AS UkrSSR)
SUBMITTED: July 2, 1959
I
-_ r, -
Card 6/6

80134
s/i26/60/009/05/001/025
Z/ E032/E514
AUTHOR: Krivoglaz, M.A.
0= i~
TITLE: The Theory-of-Scattering of X-rays~by Distorted
Nonuniform Solid Solutions
PERIODICAL: Fizika metallov i metallovedeniye, 1960, Vbl 9,
No 5, pp A41-656 (USSR)
ABSTRACT: In previous papers (Refs 1-3) a development Was giVell 01~
the theory of scattering by uniform solutions, the
scattering being due to differences In the atomic
atattering factors and the atomic radii of the components.
The nonuniformities in the electron density are due to
thermodynamic fluctuations in the composition and the
order parameteraq Such fluctuations can be coilculated
without the use of simplified models so that- the theory
can be used to study the qualitative properties of the
intensity distribution pattern, to determino the numerical
values of the intensities and to carry out a quantitative
comparison between theory and experiment. Nonuniform
Card 1/6 solid solutions, i.e. solutions in which there are swall
.xt

80524
S/126/60/009/05/001/025
E032/E514
The Theory of Scattering of' X-rays by Distorted Nonuniform Solid
Solutions
segregations of particles of a new phase, which differs
from the parent phase in composition and/or structure
frequently have a high mechanical strength.
In this case, however, the study of the intensity
distribution is considerably complicated, since usually
the structure of the segregations, their form, the time
dependence of their dimensions and other characteristics
cannot be determined by independent experiments and
cannot be calculated with the aid of present theories
of solid solutions. Hence, in distinztion to the uniform
solutions, it is not possible to predict the intensity
distribution for.any given solution subjected to a given
heat treatment. It Is, however, possible to calculate
the intensity distribution for a number of simplified
models of the segregations. These intensity distributions
can then be used in a qualitative comparison with
Card 2/6 experiment and the beat model will then provide an

80524
S/126/60/009/05/001/025
E032/E514
The Theory of Scattering of X-rays by Distorted Nonuniform Solid
Solutions
estimate of the dimensions and properties of the
segregations. Such intensity calculations for a number
of models of the segregations have been carried out by
Yelistratov (Ref 4) and Bagaryatakiy (Ref 5) who did
not, however, take into account crystal distortions.
Some authors have obtained intensity distributions
with distortions taken into account with the aid of
one-dimensional models. However, the distributions in
one and three-dimensional cases are considerably
different. The results obtained for one-dimensional
crystals cannot in general be generalized to three-
dimensional crystals. The present paper gives a
calculation of the scattering of monochromatic X-rays
by a monocrystal containing segregations. The effect
of the segregations on extinction is not taken into
account, although there are cases in which this is
Card 3/6 important. It is assumed that the segregations are LK

80524
S/126/6o/oo9/05./001/02.5
E032/E514
The Theory of Scattering of X-rays by Distorted Nonun3.form Solid
Solutions
spherical in form and that scattering by dislocations
and other defects can be neglected. The distortions
are estimated on the elastic isotropic continuum
approximation and the difference between the elastic
constants of the segregations and the parent continuum
is neglected. The concentration of the segregations
and the volume occupied by them are assumed to be small
and the overlapping of segregations is neglected.
It in further assumed that the segregations are randomly
distributed, The concentration and order distribution
along the radius of a segregation can be very complicated.
Since these distributions are unknown at present, certain
simplifying assumptions have to be made, Three models
are considered. In model A a segregation which is
uniform in structure and composition occupies a sphere of
radius r inside a solid solution with constant
Card 4/6 concentrafion. Such segregation could appear in the case
e

80524
S/126/60/009/05/001/025
E032/E514
The Theory of Scattering of X-rays by Distorted Nonuniform Solid
Solutions
of allotropic phase tranrformations taking place without
changes in concentration and also in transformations in
which concentration does change but the effective
diffusion length exceeds the distance between the
egregations. The dependence of v (the "effective
tomic volumell which is equal to the mean atomic volume
:
of the t1 toms of the phase under consideration multipliedby the
ratJDcfqSmbor of atoms of this phase to the number of
atoms in tin equal volume of the parent phase before the
deformation of the lattice) on the radius for segregations
of type A is shown in Fig Ia. If the atomic volumes
v1 and v 3 of the segregation (phase I) and the parent
phase (phase III) are different, distortions will appear
in the crystal. If during a phase transformation the
concentration does not remain constant, then in the
initial stage of the process the segregation should be
Card 5/6 surrounded by a region impoverished in one of the LK

80524
s/i26/60/009/05/001/025
E032/E5i4
The Theory of Scattering of X-rays by Distorted Nonuniform Solid
Solutions
components. In order to take this effect into account
the model B (Fig lb) can be used or the model C
(Fig 1c). These models are used to calculate the scatter-
ing of X-rays by crystals. In the first section a
genoral formula is derived for the scattering intensity
on the basis of the kinematic theory. This is then
specialized to weakly distorted crystals (Section 2) and
strongly distorted crystals (Section 3). It is shown
that distortions,lead to much stronger attenuation in the
intensity of direct reflections than in the case of
uniform solutions and to the appearance of certain
characteristic features in the distribution of diffusely
acattered X-rays.
Card 6/6 There are 2 figures and 12 references, 6 of which are
Soviet, 1 Czechoslovak and 5 English.
ASSOCIATIONt Inatitut metallofiziki AN UkrSSR (Institute of Metal
Physics, Ac. Sc., VkrSSR)
SUBMITTED$ November 30, 1959 ~ /1

S/126/60/010/002/021/028/XX
E201/E491
AUTHOR; Krivoglaz, M A
TITLE-~ Static DIftortions and Weakeni of Line Intensiti*s
In IL:_ ~a6r Neutron DiffractioRfPatterns of Solid
Solutions With Face-Cen+,re~d _C%ibic Lattices
PERIODICAL; Fizika metallov i metallovedeniye, 1960, Vol.10, No,2,
pp.169-182
TEXT- Static displacements of crystal atoms around an impurity
affect quite strongly many properties of crystals. These
displacements govern weakening of intensities of "correct"
reflections (lines or spots) in X-ray or neutron diffraction
patterns and they cause diffuse scattering. Knowledge of such
displacements is essential in theories of the electrical resistance
of solutions and of their other properties. In the present paper V,
displacements of atoms at various distances from an impurity and
root-mean-square displacements in substitutional and interstitial
solid solutions with face-centred cubic lattices are calculated
with allowance for crystal structure. The displacements are
found in terms of a derivative of the atomic volume with respect
to Impurity concentration and Young's modulus. A quantity 1,0
Card 1/2

S/126/60/010/002/021/028/XX
E201/E491
Statiz; Distortions and Weakening of Line Intensities in X-Ray or
Neutron Diffraction Patterns of Solid Solutions With Face-C4n-tred
Cubic Lattices
is found it occurs in the exponent of an exponential function in
the attenuation factor which describes weakening of intensities of
fl, displacements.
.;orreztl* reflections9roduced by static The
numerical values of L and atomic displacements are calculated
for alloys based on Ag,. Al, ~u,.Cu, K1, Pb (Tables 1 and 4). j
Al!-~,wing for anisotropy, the displacements are found also at
large diatances from an impurity. The effect of establishment of
short-range order on LO is studied and shown to be considerable in
sortie ca5es, The paper is entirely theoretical. There are
5 tables and 19 references: 7 Soviet,'8 English, I German and
3 International,
ASSOCIATION,- Institut metallofiziki AN USSR
(Institute of Physics of Metals AS UkrSSR)
SUBMITTED. February 29,_1960
Card 2/2

rig'! -1w8fue I
It b~ I D4 r0-1-3
AUTHORt -,-Krivoglaz. M.A.
TITLE: Theory of Damping of
Mixtures
85035
S/126/6o/olo/oO/ool/023
E032/E314
Elastic Waves in Two-phase
PERIODICAL: Fizika metallov i metallovedeniye, 1960, Vol. 10,
No. 4, pp. 497 - 512
TEXT: 'The author discusses elastic waves in a two-pbase
mixture in thermodynamic equilibrium. Changes in the elastic
stress (pressure) and temperature which are associated with
the waves upset the conditions of phase equilibrium and produce
phase transformations. In addition to elastic deformations
other types of deformation will appear, for example, volume
changes associated with differences in the molecular volumes
of tho two phases, so that'the velocity of propagation of the
wave is not a function of the elnstic moduli only. and may
differ very considerably from the velocity in a singlc-phase
System. At large frequencies transformations do not iucceed
in taking place and the velocity is determ-Lned by the elastic
moduli only. It follows that the velocity of propagation
depends on the frequency and the phase-transformation relaxation
Card 1/2

6.1035
s/iL,6/6o/olO/0041001/023
E032/E314
Theory of Damping of Elastic Waves In Two-phase Mixtures
time. Expressions are derived in the present paper for the
velocity and absorption coefficient as functions of frequency
for various relaxation times, temperatures and relative
concentrations of the two phases. Single-component two-phase
systems and two-phase mixtures of solid solutions are discussed.
There are 10 references: 6 Soviet, 2 English and '_' internat-ional.
ASSOCIATION% Institut metallofiziki AN UkrSSR
(Institute of Metal Physics of the AS Ukrainian SSR)
SUBMI'fTED: May 23, 1960
Card 2/2

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-XI

Congress of the Ukrainian Republic on the Theory 3/053J60/070/01/006/007
of Metals and Alloys B006/BO17
daut 1. Me Lifshits and V. 0. Peachanskiy on the galvanomagne-
tic oharaoteriatiorlof metals with 6-pe-n-YorLi surf-aa-e-s-TH
strong magnetic f141491 in this connection a paper by LifshItel
-9. Yes Asbeliq and Us I. Kaenov on the relations between
the asymptotic behavior or these characteristics and the topo-
logy of the 7orml.surfaos were analyzed, the resistance change
in the magnstio field was (depending on the direction) found
to increase quadratioally or to approach a saturation valusj
according to the law by Pe L. Kapitsap howeverl the increase
should be linear* Us Yee Asbell reported on results of the
quantum theory of the electric high-frequenoy resistance which
he met upi Ya * A b 11 d Be A. Kaner investigated the
cyclotron ro;onanos ~ metals In the reilon of the anomalous
--skin efflo" magn*tio fields by the aid of the aforemention-
ed theoryl Me 1. laaanov investigated the o&se of a non-quadra-
tio dependence of the electron energy on the impulsol Yu. A,
Bvchkov. L, 3# Gureviohp and 0. Me Nedlin reported on the
the-r-m-om-agnatio OffsoWn strong magnetic fieldel A. A. Smirnov
and Me As Krivo I a ~ - determination of the ofiapo of th
las
Card 2b FOLNEFAI-osivEL _met:ls via a determination of the total ~7_

Congress of the Ukrainian Republic on the S/0,53/60/070/01/006/007
Theory of Metals and Alloys B006/lBO17
moment& of the photon pairs which are formed in the annihila-
tion of positrons and conduction electron a; I* M. Kosevioh on
a theory of the influence exercised by elastic deformation on
the energy spectrum of the electrons in the metal and on
the oscillation of magnetic susceptibility; B. I. Borkin and
1. M. Dmitronko on the results of an experimental invie-sligation
of the influ-snoo ofa compression from 11 vides~cn the aniso-
tropy and the do Haas-Van Alfor, ~r n crystals jqf weakly
I offeo
magnetic motalal V. L. Gureviah on sound absorptioigIn the
magnetic field in the case of an arbitrary law of dispersionj
0. L~ Kotkin on sound absorption in metals for arbitrary Fermi
surfacoal A. A. Ga2kin and I. P. Korolyuk on Ihe experimental
determination of fluctuations of the ultrasonic absorption co-
efficient in the magnetic field for tin and zinc; It. A. Krivo-
glaz and Ye, A.,.Tikhonova on the theory of X-ray- and slow
neutron soatteriawn solid solutions; V. 1. Iveronova and A.A.
Natenellson on the theory of the intensity diatxihution of dif-
fused scattering; V. A. Krivoglaz on the scattering of X-rays
and of thermal neuirons; A. A. Smirnov and Ye. A. Tikhonova
Card 3/9 on the concentration dependence of the intensity of regulair

Congress of the Ukrainian R*publio on the 3/053/6)/070/01/006/007
Theory of Metals and Alloys B006/BO17
I
reflection and of the background of scattered X-ray 1 V. M.
Danilenko on dislooa tions in orders ; * o enl.and
A. No Orlov on the computation of the maximum oscillation
frequency of the atoms of a binary solid solution with cubic
body-centered lattioel A, P. Zvyagina and V. 1. Iveronova on
the dependence of the characteristic Debys temperature of an
alloy on the form of the spectrum of the thermal vibrations
of the atomal.Ke Bs Vlasov on the rotation of the polarization
plane of elastic transversal waves which propaEate in a metal
along the direction of the magnetic field; A. A. Berdyshe and
B. V. Karpenko on the interaction of the inner electrons by
means of conduction electronel B. V. Karpenko and A. A. Berdy-
shev on the interaction of conduction electr6ne and spin waves
in an antiferromagnotiqt- L. M. Petrova and Yu. 1. Irkhin on
the computation of Hall's constant f a feiromagnetic tal
within the framewoik of the s-d e hange model by Vonsovskiy;
P. so Zyrzanov, To Go Izyumova, and 0. V. Skrotakiy on the
electric resTsiance o ferromagnstio meGla in radiofr quen-
Card 4/9 by range near the ferromagnetio resonance; Yuo A*_Izyumov :nd
~I

Congress of the Ukrainian Republic on the 5/053/60/070/01/006/007
Theory of Metals and Alloys B006/B017
0, V, Skrotakiy on the magnetic spin resonance of conduction
aleatronel I* . Gubanov on ferromagnetism in azorphous ferro-
magnotioal Us Yes Azbellp V. 1. Geranimenko, and I* M. Lifshits'
on a resonanos it the skin depth is very
garamaj!eti ikn met-ale
small compared Io Ihe Wiple dimensional V. P. Silin on a
maoromoopio theory of the optical effects ia metals in the
range of the normal and of the anomalous skin affeat. S. V.
Konstantinov and V. I; Perell on tho conductivity and the
magnetic sus''ceptiRlity of Z metal in the variable alectro-
magnetic field in taking into account three-dizensional dis-
Psrsionj_P., As Grinberg and,A. ff. Orlov on the resistance
change in the magnesia field and the Hall effeat in a pure
metoll As As Smirnov and A. 1. Nocarl on a theory of the 41so-
trio reei&tance of alloys with dietwited lattice within the
framework of the manyelsotron model of metall G,,V&.S%msonnv
and V, Ot Weshpor on the conductivity of Mo3Bf , ind"MoSid.1 'k%
0. V. �amsonoy and Tu. B. PadUM on the investigations of the
physical properties and the electron configuration of rare
Card 5/ 9 earth hexaborideal V, Yes Mikryukov on the experimenta=results

Con,gress of the Ukrainian Republic on the 8/053J60/070/0/006/007
Thoor.r of Metal# and Alloys B000017
concerning the Wiedemann-Frans law in metals and alloyel
a, o. Man and 1, 1# 71k on the elsotrotochnioal effects
in-liguid-Not It Bf SoroylMX and X, 1. Gu v on the
$0410441-6 igiffiis-on the p4sloal properties of Irgnsi-
---- lion me a : 90 loreunokiy and Ot Ps Borovikova on the in-
ri W-0 I purihim on the X-ray spectra volidol 1. Ms.
Moshits an 4 nil type of phase tranoitio in metals at high
"'Provs,4fo-11 It M, Ufshits To on 0 method of
_e 4g1roduotion of correlation tuna
4qq;r$%In# so;!qOons by t4
lIaqq far ,the WA fragm LAPInkellebteyA on the thermo-
4poOao of
at AS 4 1 -of---
0 4' 14'.
- mirnov a;; 11 ,
Stara4ubay, *44 14 19 Dolk#Vlob on tht-ISIS11,~
--#1~1 omorphlo - W&A or wxgllFn-s of 4 series
of 4OWN 3 Iq Me Lifshill and V, ve 81450T
OR too cossul 1 04 or all# In the late stage of doo
Aollos of par* formation In rook all,
Q4:F4 6/ qVyqjsjaj Vt y1golmiray an the theory of coagulatIOA of

Congress of the Ukrainian Republic on the S/053/60/070/01/006/007
Theory of Metals and Alloys B006/BO17
urplum vacancies in a solldl B, Tas Lubov and A. L. Rovtb d
:
n the theory,of.the growth ofjmartensits orysta sjjL. N.
Larikov on the kinetics of thoolrooryatallization in deformed
metals and alloyal 1. V. Salli on the problem of the lines
of the metastable equilibrium in the diagrams of binary eye-
temal M. 1. Zakharova apd r. N. Stateenko on phase transform&-
tions inAiron-va`n__&_Wum;1&lloye; K. P. Gi V on t relation
between A79-lot-N-a-i-ion energy of self -AlrKpionxith the
characteristic temperature of pure metalej I. X. Yedarohouko
and A. 1. RUohonko-on the volume increase in heating mixed
~4 powderal Too A. Tikhonova, on the diffusion theory of inter-
Ot-i-t-i-a-1 aioms In alloys of the CuAu typ*l V. 1. Pike on the
mobility mechanism of the impurity ions in metals in an oleo-
trio fieldI.P. P. iNualmenko and Ye. I. 'Kharlkov on experimen-
tal investigations of charge transfer in pure metals by means
of tracer atomal I. N. Frantsevich, D. P. Kalinovich, 1. 1.
Kovenakiyg go D, Smolin, and M. D. Glinahuk on investigations
Card 7/9 of the mutual charge transfer of both components In binary solid

Congress of the Ukrainian Republic on the 6/053J60/070/01/006/007
Theory of Metals and 11loys B006/BO17
.solutions of Cl Cr, Mo, and tungsten In iron by means of radio-
active isotopes; I. A. Oding and V. ff. Geminov on the destruo-
tion of metals In creeping at increased temperatureA"I.I.
Oding and L. X. Gorcf1-71W on the variation of the mechanical
properties of the metals with preceding creeping test; B.-Yao
Pines on characteristics of the diffusion mechanism in creep-
ingl 1. So Zhurkov and A. V. Savilp
.k1Z on the experimental
verification of.the diffusion theory in the mechanical destruc-
tion in pure silver and in an Ig + 5% Al alloy; N. S. Yastov
on the thermodynamics of irreversible processes in the deforma-
tion of metals; V. 1. Khotkq~ich obtained the s&me 'results in
this respectj A. 1. Gindin communicated data on the increase
of the plasticity of ~Lrmoo ironGt low. temperatures by pre-
ceding plastic deformation at hig4er'.temperatures. Yu. U.
Plishkin reported on the stable configurations of atomic layers
in expanding cylindrical orystalq into the direction of the
axis. K. P. Rodionov reported on the anomalous change of
physical properties of a solid in a'tempersture range which,
Card 8/9 in general# does not coincide with the melting temperature. ~/

Congress of the Ukrainian Republic on the S/053J60/070/01/006/007
Theory of Metals and Alloys B006/BO17
No 1. Barich on the rules governing the periodic change of
Ge interatom o binding forces as depending on the position
of the elements in the periodic system by Do 1. Mendeleyev.
Go M. Voroblyev on the measurement of the intensity of X-ray
interferences in the case oftexturated camples. A. S. Vigli
also spoke about problems of texture.
Card 919

23121
3/181/61/003/005/026/042
BIOS/320,9
AUTHORSt Kashoheyev, V..L and Krivoglazy M, A.
TITLEt. Effec-t-49-anharmonism upon-the 9
nergy distribution of in-
elastically scatUred neutrons. I. The case of a weak bond
PERIODICALt Fizika tverdog6 tela, v, 31 no. 5.# 1961, 1528-1540
TEXTs In studying the scattering of slow monochromatic neutronap the
authors oofifins themselves to single-phonon scattering from a perfect
crystal. Neutron absorAtion and magnetic scattering are neglected. The
expression for the differential scattering oross section of the above
neutrons is,divided into'two portione, carresponding'to coherent and in-'
coherent scattetinRi
k2 Q Q
(qt. CN. V ~ (5)
A-j
of (q,. 40)=Ck (k) (6)1
Card 1/7

23121
SIISIJ61100310051026104~
Effect of anharm6nism upon the 3108/B209
where
C=
Q MI
j. A,
(k) qlakh 4-7.71.
X an'd A -'A are the mean and the varying portions of the constant A
I I By. I
which characterizes the lattice nodes of kind 1. A By and B are the con-
stants in the exprespion for the interaction energy of slow neutrons with
a nucleus at the lattioeenode ay (a indicates the number of the respective
Idttice cell). .-II. it2- VI ; -4 - -41 -2 A-9nj itnis the vector of the re-
ciprooal latticel By is theradius vector of the respective nodes and
-0
ekj, ie the polarization.vector, The quantities 11 und y" entering Eqo.(5)
Card 2/7

233;1
8/161J61/003/005/026/042'
,Effect of anharmonism upon the .3108/3209
and,,(6) *re: then.0 Wainei fr'o'a the.relations
r dlf~4 So (ikj G+w (0) e-I (SP
T
0 ake (0) OP
Since thoee'quantities are chiefly determined by the dynamical properties
of the systems they are calculated -from the Hamiltonian as expresse ,d.by
.the creation an& annihilation oq~ratorss With the help of Green's funa-
tion according to Ref. -8 (Nf It, Bogolyulboyp S. V. Tyablikov. DAIT SSSR'p
126
53;. 19591 D. N. Zubar*v. Ung 71, .71.s 1960),v the authors obtained* 1.7
Card
3/7-

3/1811 611(001005/026/042
Effoot of'.anharmofiism upon th
BIOS)B209
(12)
-W Pkj (O)f 111
Pbjr (40) a(").
-4~ x
ki 4. - low
0 &Oki
Pkf Wr Itr (W)
(0) (A
x
x 0 cm OV).
Pw (,N)r r:, (0)
Card-4/7

lt?~$,,;~,-P,.~!T% it, VIVe MUA KM,~ (P k:N
23221--
S/18IJ61/003/005/026/042
Effect of anharmonism upon the B108/B209
where
r V
x -t- (14)
2
and
(W -WW,- Whil
4. nbj I -I- Rb pis 2 xbj. Rhi.
obj, - eve
Ph/ ES Pl./i (0).
n., n (w,,).
Card 5/7

23121
S/181/61/033/005/026/Q42
Effect of anharmonism ulon the B108/B209
The coefficients at the third-order term in the expansion of the pot
energy of the crystal aocordipg to the displaoement of the atoms, ential
vikl I off if t enter these, re~~*6ns through the expression
_49"
X
Vh A')
(10).
Y ekp (kRn -4- k2ef -I- L-Ror]),
The widening of the peaks in the energy distri?ution of the scattered
neutrons' .is fou;d to be proportional to kT4 at low temperatures
4 heom), and to kT at high temperaturbso both in necond. approxi6atione
&)m is the maximum frequenoy of acoustic phonons. Eqo.(14) and (15) show
Card 6/7

3/181j61/003/005/026/042
Effect of anharmonism upon the B108/B209
that for j - J1 for short-wave acoustic and optical phonons, the frequency
shift of the phonon vibrations, pri (w), is approximately equal to the
widening of the scattering peaks, Thus, in rough estimation, P-t
. (w) ed 0. 1&j
for low temperatures and (o)dlc 0.1 VTfor high temperatures. There are
pit i ii
16 referencest 10 Soviet-bloo and 6 non-Soviet-bloc. The two references
to English-language publications read as followas G. Placzek, L. van Hove.
Phys. Rev., 11, 1207, 19541 M. Cohen, R. P. Feynman. Phys. Rev.p 107# 13,
1957-
ASSOCIATION: Institut fiziki AN LSSR (Institute of Physics, AS Latviyakaya
SSR), Institut metallofiziki AN USSR Kiyev (Institute of
Physics of Metals, AS UkrSSR, Kiyev)
SUBMITTEDs November 19, 1960
Card 7/7

23122
S/181/61/003/OC5/027/042
R108/B209
AUTHORSt Kashcheyev, V, N. and Krivoglaz, M. A.
'TITLEt. Effect of spin-opin and spin-phonon 'interaction in a forro-
magnetic on the energy distribution of-scattered neutrons.
FZRIODICAtt Fizika'tvardogo tela, V, 31 no- 5s 1961, 1541-1552
TEXT: The authors studied the effect of elementary excitations on the en-
ergy distribution of neutrons scattered from a forromagnetic at tempora-
tures far below the Curie point. The differential scattering croas section
of unpolarized neutrons may be written in two components, one of rhich
accounts for magnetic dingle-magnon (opin3rave) scattering (a,), the other
for magnetic singl~-phonon soattiring (62
G(qj. w)=Ol(ql, w)-4-Qj(qt, (3~
(qj. ON k (w) (4)
q,
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M

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Effect of apin-spin and B108/B209
dif-W SO (b
-R (1) b, (0) e") (SP e"
IN H die-W Sp (6+ (1) b., (0) e-1m) (Sp e-18)
Wit
2 1-4 .k k vectors of the
In these expre'sai6ns, q, q
n 1 2 1 n
nodes of the reciprocal lattioe. -Expressing and by Green's function
one obtains
CJV k 'I, r. M N M
a. (qjO ) Nq - pq (a)),
2 (10)
CON - k r. (w) liv (w) -t- il
to - P, HP - 1" H
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Effect of spin-spin, and ... 3108YB209
for the cross sections :of single-magnon scattering (Ref. 21
.V. N. Kashcheyev,41. A. Krivoglazp FTT, v. 3, no- 5, 1961), where d; corro-
sponds.to the absorption and d"'to the emission of a magnon by a neutron.
1
The, attenuation of a phonon, r (ti), its frequency shift P M, and N(w)
are given by the following expressiOn3:
Card 318
N
(m) Vw.+.. Is (N., - N.W) 8 (w -f- w., W-41")
(to - 0
N-1 N-1)

Effect of spin-spin and
23122
S/18 61/003/005/027/0112
Bl OBXB209
r., (0) 2% (1 N, 4- N,) - x
A-2
WO
x -4- 6" X
X 0 -4- N,, -+. No) -I- N.JV..a(10-0 W., W..) -4-31 x
(12)
r.., M V"W
Y.+* bi 11 (n., - Nk+.) b4~ bj)
ka
(13).
P.3 (-) -4- P.*4 P.1 W.
In the tollowing, the authors study the dependence of r and F on tempera-
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Effect of spin-spin and 3108/B209
ture ana on the wave vector. The' attenuation due'to spin-spin interaction
in cubic crystals iq found to be
C (S Z: r 3
V1 0. 1 (7*)%
Wj%3
320 vi-x tt 3F 7-r-
2 r I A. %2
VIWIX4 (16),
48n3
C_ -L. %117!
L( % )1( 2 %T
W
rhere (5/2) 1 .1~341 (Riemannian zeta function), 1 , To -Curie tem-'
perature, g - 9 1h 9 -.gyromagnetic factor, Bohr's mag-neton,
0114 0 0
[I - magnetic moment of the atom, =6 Boltzrann's constant, v - atomic
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Effect of epin-spin and ... BIOB/B209
valume. The temperature dependence of P is givenby
P. C Pb) I SIT 0.04 T
7 HY-) - - W.. (18)
12ax YN To
where I indicates the volume integral. In the case of spin-phonon inter-
action,
2
*I(.STyp XBT,3. (24)
Nj
holdn'for high temperatures (T hlgh~er,than the Debye temperature) and great
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3
Effect of apin-spin and ... B103 209
cl; M."2 1 c and c are the velocities of longitudinal
no w 2 nI w 2 1 2
and transverse phonons, respectively). For non-zero te.7,peratures, this
expression goes over into
~1 -+. Pjr n., (n.,
(25)
n., (n., _+_ X,
Upwls
v,hen -ae ~C V, and -hw,~t zetT; P, and are dimensionless constants of the
n P2
order of unity. For the same case, the frequency shift has the form
%r2- t ('11) r < o.1 71 (27)
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Effect of spin-spin and ... 3108/3209
I-, Nry Of -NY 2
(2z" ", 0. 1 '1,4 TT,, (28)
Ir
45 Ael
0
P-1 -girt 0, T > T'j, 0. 1 7~'j > L. (29)
PAW,*, Wil-,
the corresponding expressions for trhneverae phonons are obtained from.
2 1 2
Eq.(27) by the substitutions -), 7 , and c --- ~ c There are 15
('111 + 0 2 4 1 1 2-
references: 8 Soviet-bloc and 7 non-Soviet-bloa. The reference to an
English-language publication reads as follors: R. j. Elliott, R. D. Lords.
Proc. Ray. Soc., 230, 46,1955-
AS30CIATIONs Institut fiziki AN L-.).~H Onstitute of Physics, AS Latviyskaya
S&R), Institut matallofiziki All MR Kiyev (Institute of
Metal i1hysics, AS LlcrSSP, 4iyev)
SUBMITTEI)i November 19, 1960
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KRIVOGLAZ M A
Effect of conduction electrons on neutron scattering by
cr,yotale. Fiz. tver, tela 3 nd.9:2761-2773 S 161. (MMA 34:9)
1. Institut metallofiziki AN USSRO Kiyev, ~
(ELectrons) (Noutrona--Scattbring)

KalicHEM, V.N.;. FJ1IV0G11Z9 H.A. Cattering on impuritY centers in
Theory of inelastic nOutrOn 0
crystals* rizetvar.tala. 3 UO-10:2167-2180 0 '61- (KML 14:10)
1. inst,tut fisiki AN Latviyoly SSR, Rig& i InOtitut
metallofiziki AN USSR, Kiyev- latticOB)
(Neutrons-Scattering) (crystal

" ")
5 0,
J
AUTHORs Krivoglaz, 14. A.
3/181/61/003/012/018/028
B104/BI02
TITLF, Extension of singularities of the frequency dependences of
the damping of elementary excitations in crystals
PZRIODICALt Fizika tvardogo tela, v. 3, no. 12, 1961, 3678 - 3681
TEM The author studies the frequency dependence of the dnmping of ele-
mentary excitations near spectral aingularities such as minima, maxima or
saddle points. The author also studies the frequency dependence of damp-
ing near the threshold points of the elementary excitation with emission
of a long-wave phonon. Referring to L. P. Pitayevskiy (ZhETF, 36, 1168t
1959) and to a previous paper by himself the author studies the extension
of singularities for the case where the damping of phonons is duo to their
scattering from static inhomogenities of a solid solution. The Hamilton-
ian then has the form
hj kj~j'
(Vl,,.,,a a+
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Extension of singularities ... MOW
where a + and a are the phonon production and annihilation operators.
Using relation,
=- Zx R,,j M - Qkj (WY (2)
where I"
RW (W) Wk'J'Ay (.) w + tol,.j. + Rio, (-W) (3)
for the Green functions, correlation functions between a+ and ak-s for
damping and level shift are found. A successive approximation is made of
the inverse Green function with reopect to the phonon interaction para-
meter V wbich is of higher order than that made in the mentioned previous'
papers. If this higher approximation is taken Into the sineularities of
the frequency dependence of damping are extended. For T-70 the extension
2
interval decreases as T . At T - 0 the singularity does not seem extended.
The author thanks L. P. Pitayevskiy for discussions. There are 5 refer-
ences, 4 Soviet and 1 non-Soviet. The reference to the Enelish-language
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Extension of singularitie3 B104/B102
ica tion reads as f o1 Iowa iL. Van flove. Phyu. Rev., D1, 1189, 1953.
AS30CIATIONi Institut metallofiziki AN USSR Kiyov (Institute of Physics
of,getmls of the AS UkrSSH, Kiyov)
SUBMITTED: July 10, 1961
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0) B100102
AUT11ORj Krivoglaz, M. A.
TITLEs Theory of diffuse scattering of X-rays, neutron, and electzw
beams in ion crystals containing chnrged defects or impuri-
ties
PERIODICALt Fizika tverdogo tela, v- 3, no. 12, 1961, 3602 - 3690
TMTt In the first part the author studies the elastic scattering of*
X-rays and neutron beams from charged defects in non-piezo-olectric ion
crystals such as NaCl or CaClO in which positive and negative defects of
equal concentration are assumed to exist. The deformations and polariza-
tions of the lattice around these defects and the Debye shielding of the
defect fields are taken into account.
r2q' (13)
2
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Theory of diffuse scattering ... B104/B102
to obtained for the intensity of the diffuse scattering of X-rays. a is
the concentration of the defects, N in the number of cells, ft , ff
nc nPI fne
and fnp are scattering factors, q, is the difference botween the wave Vec-
tors of scattered and incident waves, q stands for the distance to the
lattice points, A-o and B--,~are determined experimentally. The singulari-
q q
ties of 1, due to Ooulomb shielding, are stu4ied. In piezoelectrics,
essential effects occur due to the fact that the atomic displacement is
inversely proportional to the first power of the distance from the defect.
In analogy to (13),
4. -L,,Nfl... J "q r (qlv~? 4- r191 (17)
2 92
i! obtained for the piezoolootriced Ifere a' and i~l are unit vectors. It
q q
is shown, that for the diffuse electron scattering from chareed defects,
on the condition rq>>l, and if the Coulomb shieleing is unimportant, the
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Theory of diffuse scattering B100102
differential elastic electron scattering cross section is proportional
to q'-4., For rq