# SCIENTIFIC ABSTRACT KHACHATURYAN, A.G. - KHACHATURYAN, M.KH.

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Collection:

Document Number (FOIA) /ESDN (CREST):

CIA-RDP86-00513R000721620019-3

Release Decision:

RIF

Original Classification:

S

Document Page Count:

100

Document Creation Date:

November 2, 2016

Sequence Number:

19

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Publication Date:

December 31, 1967

Content Type:

SCIENTIFIC ABSTRACT

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CIA-RDP86-00513R000721620019-3.pdf | 3.02 MB |

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2 ID73
S/1 8V611003100910051039
Interxiction between carriers and lattice ... B102/B104
Here, A (,A) is the tensor of the def ormation potential, a(@ ) (x, s) 'is the
ij
Fermi operator of second quantization corresponding to an electron with
the spin e which lies in the,,*,-th energy minimum, of the Brillouin zone,
in the crystal density,.(,-- is the frequency of the v -th branch of the
kv
( . ) is the
acoustic spectrum, (k.@ is the unit vector of polarization,",,
Bose operator of second quantization, and E(-* ) is the dispersion law of
the electron in the/-th minimum. It is further assumed that no transitions
take place between the various minima. In contrast to Ref. I (where the
perturbation theory had been applied), the author uses the advanced and
retarded Green's two-time temperature functions for his calculations.,
By way of
(18)
I k,j=1-)k,j_ .2pFj,(jk,) 147')j
and
Card 3/ 6
2Pj073 S/181/61/003/009/005/039
Interaction between carriers and lattice ... B102/B104
%TNIF12 e-lx (H,
Ok M, 2 Cv (19)
and using thu symmetry properties of the tensor he obtains the
ji
following system of equations for a germanium-type cubic crystal (with
its minima in the [11 1j' --direction) and considering three directions of
the phonon wave vec@tor Tet
@.@Jyk Vj-p 8 (k' k r2-, (h k)t
ell-f-C124. C22
@ci i -I- cii I- 2cn' Vc, I -+- cit -4- 2c22 -+- 4A,
[1101 2 0 0 P
(h - k)2 12
3 k VP_ 16X,'k-VF, cif-CIS __.C22 -#-- 263
Vc"
-T I F'12 N (,.*)3 0-21t
A )kit
-PRB (k, AfA)
Card 4/6
21073
S/161/61/003/009/005/039
Interaction between carriers and lattice ... B102/B104
and A, are independent components of the tensor of the deformation
-4 _*
potential, 0- is the intensity of diffuse scattering in the point H+k of
k
the inverse space, H(hkl) is the lattice node vector in the inverse space,
N is the number of atoms in the scattering volume, m is the atomic mass,
cV is the observed velocity of the P-th branch, F is a structural factor,
and e- 2 Y1 is a temperature factor. 6-@- is given in A-units. is
k
simplified for non-degenerate electrons to become
13n f (,11@ 1 2
V 2fz _k for the sound velocity, the following holdss
,@2 C(O)2 + 2 Unlike the case of isotropic electron-phonon inter-
V Y "V.
action, the correction to the phonon spectrum due to anisotropic inter-
action can be determined also if the carrier concentration is constant.
The correction for sound velocity is, in a semiconductor with an electron
concentration of 1017cm,-3. of the order of 10'A. and the same aDDlies to
Card 5/6
"!,073
SIIBV611003100910051039
Interaction between carriers and lattice ... B102/B104
metals. V. L. Bonch-Bruyevich is thanked for having formulated the problem
and for discussions. There are 1 table and 5 references: 2 Soviet and 3
non-Soviet. The latter read as followsi J. Bardeen, W. Shockley. Phys.
Rev. , 80, 72, 1950; C. Herring a. E. Vogt. Phys. Rev. , 101 , 3, 944, 1956;
R. James. The optical Principles of The Diffraction of X-Rays. London,
1950,,
ASSOCIATIONs Inatitut metallovedeniya i fiziki metallov Moskva (Institute
Of Metal Science and Physics of Metals, Moscow)
SUBY,ITTEDj January 27, 1961
Card 6/6
7 7--.77
S/18 YB 62/004/010/031/063
B108 104
AUTHOR; Khachaturyanp A. Q.
TITLE: ermination of the elastic energy of the pair interaction
of impurity atoms in a crystal lat.tice
PERIODICAL: Fizika tverdogo tela,. v- 4, no. 10, 1962, 2840-2844
TEXT: The energy of the purely elastic intdraction of two impurity atoms
in a crystal lattice is calculated in the atomistic approximation of the
dAscontinuous structure of the crystal. The final formula
V"' (k) _h (K(k, p'). ej(P.'(k, p1g.) (14)
xp 1 (k, h? Ami . MW"
W
obtained by expressing the functions in the energy of the system due to
impurity atoms by their Fourier components is applied to the calculation
of the diffusion ect%tterin of X-rays by face-centered interstitial
solutions. f, and oaa are the unit vector of polarization and the
Card 1/2
75/181/62/CO4/010/031/063
Determination of the elastic... B108/B104
frequency of the a-th brancht'of the phonon speotrup. is known from
experiments for many substances. If it is not known, w 2(k*) and _F (k'pp)
8 n
can be'_4xPrd67sdU 'ap@?6x_f`ffi-a_1_e_1y` Yy__th5-Wji@stTc-*m*6dujf -an'd -by' the depefideifc-e
of the linear expansion coefficient on the concentration (M. A. Krivoglaz,-
Ye. A. Tikhonova. UFZh, 4, 297, 1958; 174, 1960). F characterizes the
n
chemical interaction of the foreign atom with the solvent atoms.
ASSOCIATION: Instit t fiziki metallov.i metallovv4eniya,,Moskva
(Inst! @e of Physics Of Metals and Metal Science, Moscow)
SUBMITTED: May 29, 1962
CE:@rt 2/2
Determining the elastic energy of pair interaction of ir4wity
atoms in the crystal lattice. Fiz.tver.tela 4 no.10:2840-
2844 0 162-0 (MIRA l5d2)
1. Insitut fiziki metal-lov i metanovedeniya Moskva.
(X-ray crystallography@
KHACHATURYAN, A.G.
Using the method of two-timed Green's functions to the ordered
alloy problem. Fiz. met. i metalloved. 13 no.4:493-501 'Ap 162
(MIRA 16;5)
1. Inatitut metFillovedeniya fiziki motnllov TSentrallnogo nnuchno-
inaledovatellsk o instituta chernoy metallurgii.
lAlloya-Metallography) (Crystal lattices)
9/1 a V63/005/0011/002/064
B102/Bla6
AUTHOR Kivichaturyan, A. G.
TITT
UE: Application of the Green function method to the
thermodynamics of interstitial solutions
PERTODICAL: Fizika tverdogo tela, v- 5, no. 1, 1965, 15-20
TEXT: Jri a previ)us paper (P.!,-!,4,4)962), the author used the method of
retarded and advanced Green functions to study the equilibrium of a
two-component ordered .9olid solution. Here 'the thermodynamic equilibrium
of an interstitial solution is considered in a similar vay, viz., by
assuming that this solution can be regarded as a system of interacting
.-;olute ptrticles in the periodic field of the solvent 11toms. The model
Hamiltonian 1@2 ' V2(c(x)) forms the basis'of the theoretical inveptign-
tions; if the pluce,x in occupied by an interstitial atom, c(x) - 1;
otherwise C(X) = 0; U 2 is the total pair interaction of all interotitial
atoms. In second-quantization representation,
*2MM_11Va(x)a(x*-+-'-1 V(X, x)a(x)a(x,d( a(x,),
2 ) X) 3)
Card 1/4 A
3/1131/65/005/001/002/064
Application of the Green fiinction ... B102/B186
whare V(x,xl ) In the pair interaction energy oil two interstitial atoms
located at x and xI , while "a(x) and r,(x) are the. proluction and
annihilation operators in Heiaenberf, representation, oubject to the
Formi anticommutation rules. Introducing the two-time Green function
G(x) @(X'x a(x,x., );,4, using the approximation
0
.