SCIENTIFIC ABSTRACT MEN, A. N. - MEN, A. N.

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

126-3-25/34
Influence of the changes in the equilibrium degree of
inversion with temperature on the thermal capacity of a
spinel. (Coat.)
ZnFe 0 since it is known that for k > 0 this ferrite
becoiet'ferromagnetic and in this case the characteristic
of the heat capacity is affected basically by the change in
the magnetic energy. King (6) gives data on the heat
capacity of CaFe 204 and CaFe2 05 for which heat capacity
anomalies were observed in the temperature ranGe 150-390 K
but no data are available on the structures of these crystals.
Acknowledgments are made to A. N. Orlov for his comments and
useful advice.
(Note: This is a full translation except that eq.(2), p.545,
has not been copied; in this equation 0 and m are elasticity
Card 5/5 coefficients).
There are 6 references, 3 of which are Slavic.
SUBMITTED: February 28, 195?.
ASSOCIATION: Sverdlovsk Agricultural Institute.
(Sverdlovskiy Sellskokhozyaystvennyy Institut).
AVAILABLE: Library of Congress

M', A.R. ; ORLOT, A.R.
Binding energy theor7 of transition metal oxides. Isal. po zharopr.
splav. 3:364-371 158. (MIRA 11:11)
(Cr7atal lattices) (Metallic oxides)

AUTHOR: Men' A N SOV/120--6-5-3/43
TITLE: Dependence of the Equilibrium Value of the Lattice
Constant of a Mixed Spinellrom-Composition
(Zavisimost' ravnovesnogo znacheniya postoyannoy
reshetki smeshannoy shpineli ot sostava)
PERIODICAL: Fizika Metallov i Metallovedeniye, 1958, Vol 6, Nr 5,
PP 781-785 (USSR)
ABSTRACT: The author deals with a spinel-type lattice. Such a
lattice is typical for many ferromaEnetic semicor~ductors
(ferrites). The spinel lattice may be represented
as a face-centred lattice o'L oxygen atoms, wit'a varicus
metal atoms in the tetrahed--T-al and octahedral positions
between lattice sites. To calcula+-e the birding energy
of lattices of this type Orlov and lie-a' (Ref 2) used a
simplified spinel model which represents su'Lficiently
well its main properties. Ttis mod--! has the following
characteristics. (1) The negative and positive charges
due to the oxygen electrons ar-d nucle-i are regarded as
smeared out throughout the lattice. This means that
the total electrostatic potential of this lattice is
Cardl/4 equal to zero. (2) The excess electrons of oxygen ions

SOV/126-6-5-3/43
Dependence of the Equilibrium Value of the Lattice Constant of a
Mixed Spinel itch Composition
and the valence electrons of metal at3ms (3d, 4s and 4p
electrons in the case of iror.-like atoms) are re~~arded
as distributed with a consta-Tit density throughout the
lattice. The interactions of these el,~trons with
metal ions are allowed for, using the statistical method
of Gombash (Ref 3). (3) The phase spaces of electrcns
with left--handed and right-han-~ed spias are considered
separately. Calculations were carried out on th'.e
assumption that in the expreSE_J~,n for the lattice energy
it is sufficient to Lnclucla the following tvio te:7ms:
(i) electrostatic interaction 0 .-ons and electron gas;
(ii) repulsion energy due to -oenetration of the "external"
electron gas into ion frameworks (this 6as is considered
to be smeared out uniformly throughout the crystal). The
author calculated constants s. . each cf which
represents interaction of the electron gas with a
Card2/4 particular ion framework. The values of s A (Table 3)

SOV/126-6-5-8/43
Dependence of the Equilibrium Value of the Lattice 'onstant of a
Mixed SpinelFrcm Composition
were then used to find, from the lattice energies, the
structural lattice constants a for 11 mixed spinels
(Table 4). The experimental 0 (Table 4, cols. 2 and 5)
and calculated (cols. 3 and 6) values of the lattice
constants a 'ere found to agree to within 0.1-0.2
for a0 of th8 order of 8 R. The experimental
dependence of the lattice constant of a particular
spinel, e.g. ZncCdl-cFe2o4') on the concentration c
of one component (e.g. zinc) was found to be fully
reproduced (Table 5) when the values of s. listed in
Table 3 were used to calculate the lattice constant ao.
The paper is entirely theoretical. Acknowledgment
is made to A. N. Orlov for his advice.
There are 5 table and 6 references7 4 of which are
Soviet and 2 English.
Card3/4

SOV/126-6-5-3/43
Dependence of the Equilibrium Value of the Lattice Constant of a
Mixed SpinelFwm Composition
ASSOCIATION: Sverdlovskiy sel'skokhozyaystvennyy institut
(Sverdlovsk Asricultural Institute)
SUBMITTED: February 18, 1957
Card 4/4

SOV/58-59-5-10516
Translation from- Referativnyy Zhurmal Fizi-ka, 1959, Nr 5, P 98 (USSR)
AUTHORS- Orlov, A.N., Men', A.U.
TITLE: Statistical Theory of Bond Energies 1~ In Oxides of Cubic-Lattice
Transition Metals
PERIODICAL. Tr. In-ta fiz. metallov. Uraltskiy fil, AS USSR, 1958, Nr 20, pp 43-52
ABSTRACT: This article is a survey of the authorst studies based on a generalization
of the method of solving the Thomas-Fermi equation for a diatomic mole-
cule (RZhPiz, 1955, Nr 8, 16122) to the case of a crystal with allowance
for electrons with two senses of spin (the d-shell of the transition
metals). The bibliography contains 21 titles.
Card 1/1

ORWVO A.R.; K01, A.U.
Statistical theory of bond energy in spinel-type crystals.
Piz. tvar. tela I no.2:195-202 F '59. OGRA 12:5)
(Spinal group) (Crystal lattices)

MMHO A.N
. ~_j ORWV. A.R.
Vibrational frequency spectrum of a gimPIS Model of an ordering
allay. Isal.po zharopr.splav. 4:96-101 159.
(MIRA 13:5)
(Crystal lattices) (Spectrum. Atomic)

AUTHORS:
Men', A411, and Orlov, A.11 c3OV/3.26-7-3-3/44
TIT M" to The j1pectLM of Vibrationn4Frequencies on the Simplest
Modef of an Ordering"iAlloy. II.
PERIODICAL: Fizika metallov i metallovedeniye, 1959, Vol 7, Nr 3,
pp 335-340 (USSR)
ABSTRACT: In Ref 1 the present authors have considered the
vibrations of a chain consisting of atoms of two types
having almost equal masses and located over the chain
sites with an arbitary degree of long-range order -9,
an arbitrary relative concentration c. and interacting
elasticaliy in such a way that the elastic coupling
coefficients between any two neighbouring atoms are the
saae. In the present paper the treatment is generalized
to the case Lu which the elastic coupling coefficients
are different but not very different. An approximate
calculation of the frequency spectrum shows that such
a chain may be replaced by a completely ordered chain
made up of effective atoms whose properties depend on
c and n accoi-ulng to BqS (2) and (3). It is shown
that the maximum (Debye) :~recjuency, as a function of
Card 1/2 the ratio of masses and coupling coefficients, may V/1"

O"OV/126--7-3--3/44
The Spectrum of Vibrational Frequencies on the Simplest Ulode! of
an ordering Alloy. Ii.
either increase or decrease as the degree of long-range
order in the chain increases. The theory is in
general agreement with the reduction in the Debye
temperature which was observed by Iveronova et al. (Ref 4)
in ordering Cu A:And Ni Fellalloys.
Z) =3L
There are 1 figure and 4 Soviet references.
ASSOCIATION: Institut fiziki metallov AN SSSR (Instit-ute of Physics
- of bletals, Ac.Sc., USSR)
SUBMITMED: November 2,2,, 1957
Card 2/2

AUI:hUR: Lie W. A - 11 SUV/126-7-3-27/44
-II2L-,: The Fieauenc7 ~-Pectrum ol a Chain of Atoms9OLtaine-d by
Taking into Account Interactions between Neighbours o~
any Older (Spektr chastot tsepochki atomov pri uchete
vzaimodeys'L-Iviya sosedey lyubogo poryadka)
PEi~IODD- L: F--zika inetallov i metallovedeniye, 1959, Vol ~, Nr 3,
Pp 4550-L03 (USSR)
The present note discusses the vibrations of a linear
chain made u-o of DI-atoms of one type. It is assumed that
the chain is closed and the equation of motion for the nth
atom is given by Eq (1), where X is the displacement
of the atom and cL(j) is the coupl~nE; constant. 'Solutions
of Eq (1) a-c-P, souS~-ru in the form of -L~q (2). Express.ons
are derived for tae freuuencies w and are Given by
." qS (8), (9) and (10). These equations are 'Lound to
reduce to all the special cases considered previousli,
u
(Refs 2-4). There are 4 references, 3 of which are
~3oviet and 1
A,~b-W'lk~iGN: O"verdlovskiy sel'skokhozyaystvennyy institut
(Sverdlovsk Agricultural Institute)
Z-1
SUB!,-,iIT' D: June 12, 1957
Card 1/1

5OV/126-7-4-22/26
AUTHOR: Men', A.N.
TITLE: On tile Determination of tile Number of Long-Range Order
Parameters for Multi-Component Alloys
PERIODICAL: Fizika metallov i metallovedeniye, 1959, Vol 7, Nr 4,
pp 633-635 (USSR)
ABSTRACT: It is shown that if the number of types of atoms is m
and the number of types of sub-lattice sites is ml,
then the number of arbitrary long-range parameters is
given by p = mml -(m + ml - 1). There are 4 references,
2 of which are Soviet, 1 Japanese and 1 Polish.
ASSOCIATION:Sverdlovskiy sellskokhozyaystvennyy institut
(Sverdlovsk Agricultural Institute)
SUBMITTED: February 10, 1958
Card 1/1

~.2 ~. 6 d-00 66905
AUTHORS. Men'. A.N. and Orlov, A,N. SOV/126-8-1-23/25
---------------- - I
TITLE: On the Theory of Vibrational Spectral'of Solid Solutions
PERIODICAL: Fizika metallov i metallovedeniye, 1959, Vol 8, Nr 1,
PP 154-156 (USSR)
ABSTRACTz The authors have calculated (Refs I and 2) the
frequency spectrum of elastic vibrations on a one-
dimensional model of an ordering binary solid solution,
using the method of "effective atoms",, Lifshits and
Stepanova (Ref 3) have also introduced this idea in their
work on the vibrational spectrum of the three-dimensional
binary solid solution of isotopes. The method of
fleffective atoms" may be used when the mass difference
between atoms of different kind M - NIP and the
difference between the elastic coupling coefficients
Ajj: - Ajtfjfl' are small, as a result of which the change
qq qq,
in the vibrational spectrum of an ideal monoatomic
crystal of given symmetry, due to the fact that the atoms
Card 1/2 are not identical and their distribution over the sites
is different from the ordered distribution, may be

66905
S0V/126-8_j_2-,/25
on the Theory of Vibrational Spectra of Solid Solutions
considered as a small perturbation, In the present
note it is pointed out that the method of "effective
atoms" is applicable both to the one-dimensional and
the three-dimensional case even if the coupling
coefficients are different and the number of atoms
per elementary cell is arbitrary,
There are 8 Soviet references., one of which is a
translation from German.
ASSOCIATIONS: Institut flzlki metallov AN SSSR (Institute of
Aetal Physics, Ac.Sc_ USSR) and
Sverdlovskiy sellskokhozyaystvennyy institut
(Sverdlovsk Agricultqral 14s_t;Lt_ute_)
SUBMITTED: August 25, 1958
Card 2/2

0 0 1) /13 66220
AUTHORS: Men', A. N. and Orlov, A.N. SOV/126-8-3-3/33
TITLE., On Binary Solid Solutions with Interatomic Bonding of
Two Types
PERIODICAL: Fizika metallov i metallovedeniye, 1959, voi 8, Nr 3,
PP 337-341 (USSR)
ABSTRACT: In the theory of binary alloys the energy of the crystal
is often represented in the form of a sum of the energies
of interactions between pairs of atoms. It is assumed
that the interaction energy for a given pair is determined
only by the type of the two atoms. However, in general
this energy depends on the nature and the disposition of
all the atoms surrounding the given pair X-Y. Moreover,
even if one limits ones attention to the interaction of
the pair XY with the nearest neighbours, then th? il nergy
of the pair VXY can take on a number of valffes V XY
where i denotes the number of the configuration
surrounding the pair XY. One could try to take this
into account by expressing the energy of the crystal not
as a sum of all the possible XY and i but as the sum of
Card 1/3 energies of complexes formed by each atom, with its

66220
SOV/126-8-3-3/33
on Binary Solid Solutions with Interatomic Bonding of Two Types
nearest neighbours. In that case the energy of eqc4
complex is taken as equal to the sum of energies Vkay
XY
correspondIng to a given pair of atoms of given type XY
in the complex of type a. If the energy levels of
electrons in the atoms of a complex are close (almost
degenerate), then the formation of resonating orbits
becomes possible. This case is realised in pure metals,
If the levels are very distant, then the resonance is
less probable but, under certain conditions, localized
covalent bonds may be formed. If the atoms of a complex
do not have a sufficient number of electrons in order
to ensure the saturation of all the localized covalent
bonds, then some of them will become unsaturated. One
might expect that this would lead to a relatively stable
local distortion of valence angles and interatomic
distances in a complex. The distance between atoms
which take part in covalent bonding will be smaller and
the interaction energy greater between neighbouring atoms
of the same type but not coupled in this way. This
leads to the appearance of interatomic bonding of two
Card 2/3 types which can conventionally be designated as weak and.

66220
sov/126-8-3-3/33
On Binary Solid Solutions with Interatomic Bonding of Two Types
strong. An expression is derived for the free energy of
a binary solid solution with these two types of bondin,;.
From the condition for a minimum in this energy the
authors obtained at a given temperature the number of
strongly and weakly bonded pairs of neighbouring atoms
of different types. It is found that the number of pairs
of different types does not depend monotonically on
temperature. It is suggested that this effect may lead
to an anomalous temperature behaviour of resistivity in
certain alloys of transition metals,
There are I figure, I table and 6 references, 3 of which
are Soviet, I German and 2 English.
ASSOCIATIOM: Institut fiziki metallov AN SSSR and Sverdlovskiy
sellskokhozyaystvennyy institut (Institute of Physics
of Metals, Ac.Sc., USSR and Sverdlovsk Agricultural
Institute)
SUBMITTED: September 4, 1958
Card 3/3

/000 66235
AUTHOR: Men', A.N. SOV/126-8-3-19/33
TITLE: On the Determination of the Number of Arbitrary Short-
range Order Parameters for Multicomponent Alloys
PERIODICAL: Fizika metallov i metallovedeniye, 1959, Vol 8, Nr 3,
PP 449-452 (USSR)
ABSTRACT: The problem considered is that of a n-component alloy
containing X sublattices. It is shown that the
number of independent short-range order parameters is
given by
N (n - 1) (mzn - 2m1)
a 2
where n is the number of types of atoms, mzis
the number of elements in the matrix
Z = fZ1111 , (1)
zILV is the number of nearest sites in sublattice'l to
a given site in sublattice IL and ji,V = 1,2 ... X,
Card 1/2 MI is the number of elements in the matrix Z fo

66235
SOV/126-8-3-19/33
On the Determination of the Number of Arbitrary Short-range Order
Parameters for Multicomponent Alloys
which V> j&. A. N. Orlov is thanked for his valuable
suggestions.
There are 2 figures and 3 references, I of which is
Soviet, I Polish and I English.
ASSOCIATION: Sverdlovskiy sel'skokhozyaystvennyy institut
(Sverdlovsk Agricultural Institute)
SUBMITTED: January 2, 1959 kr~
Card 2/2

S/139/60/000/005/019/031
X032/9114
AUTHORs Men'9 L.N.
TITLE: Derivation of the Thomas- and the Thomas-Formi-
Dirac Equations Taking into Account Partly Filled
Electron Shells 4
PERIODICAL: Izvestiya vysshikh uchebnykh zavedeniy~ Fizika,
196o, No. 5, PP 112-117
TEXT: in using the Thomas-Fermi method to calculate the
charge density in systems containing ions of transition metals, it
is necessary to take into account the experimentally established
fact that the inner electron shells of these ions have non-zero
resultant spins. Moreover, in accordance with the so-called
maximum multiplicity rule (Hund's rule) the spins in the d-shell
are oriented so that the resultant spin has the maximum possible
value. The statistical theory which does not take into account the
spin-orbit interaction is unable to explain this fact. It can,
however, be taken into account by assuming that electrons with left
and right spin directions are located_in different effective fields
with potentials 11 and V2 where Vl - V2 is chosen so as to
Card l/ 7

B/139/60/000/005/019/031
E032/Ell'+
Derivation of the Thomas-Fermi and the Thomas-Fermi-Dirac
Equations Taking into Account Partly Filled Electron Shells
obtain the required relative number of left and right oriented
spins.. The present author gives a derivation of the Thomas-Fermi
and Thomas-Fermi-Dirac equations for these cases. The system is
assumed to be described by the Hamiltonian
n
H = a2 Z gzh + ~ d- - e 2 Vei + 1.2 (1-3)
2 r 1 2 m 2 rij
g1j, gh i=1 ij
where z is the atomic number of the nucleus g, V 9 is the
potential due'to the nuclei, and I is the additional potential.
The sum of these potentials is denoted by Vgi so that
V91 = V9 + 1. (1.3a)
The ground state energy of the system is then calculated from
E d q (1.10
where
Card 2/ 7

S/139/60/000/005/0i9/031
R032/9114
Derivation of the Thomas-Fermi and the Thomas-Fermi-Dirac
Squations Taking into Account Partly Filled Electron Shells
0 (1.1)
(112 .... n) = (n')4 d e t 4ul--,un~
and uj are. the spin orbit functions which are linearly
indepeAdent but are not necessarily orthogonal. The ground state
energy is then given by
B = 22 'zgzh Vgl e(11) d q, - 1- e Ve OU31) d q, +
29,h rgh 2
+ 2 Q2 ZL1 2
p (l 51) d q IL2~1~ d q d q,,, (1-7)
2 m 1 2 r12
where V d q2, (1.8)
Card 3/7

S/139/60/000/005/019/031
903 2/3111+
Derivation of the Thomas-Fermi and the Thomas-Fermi-Dirac
Equations Taking into Account Partly Filled Electron Shells
The kinetic energy Ek and the exchange energy EA are assumed
to be of the form
Ek X Ik ~ e5/3 d q, (1-9)
where X 3 h2 (1.10)
k 5
EA a d q
where 3
a 2 e
and when these are substituted into Eq, (1,7) the final expression
for the ground state energy as a function of the charge density
p is given by
Card V 7

B/139/60/000/005/019/031
E032/Ell)+
Derivation of the Thomas-Fermi and the Thomas-Fermi-Dirac
Equations Taking into Account Partly Filled Electron Shells
t~ Y , 1& - " Vg, p d q -- ;L 6SVaqdq +
2 g, h r gh 9 2 1 ~ p+/3 d q UJ3)
+ X k ~ '0 5/3 d q a
The expression for the total energy of a cryst-al consisting of a
mixture of two electron gases with densities V1 and e2
corresponding to the two spin orientations is then
E e V (qp 1 + p 2) d q V + e2) d q +
S 9 2
g, h rgh 4
+ 5/3 + 5 d q X1 .'/3 +P 2 /3 dq
k (el e2 a
It follows from these equations that the Poisson equation
connecting the potential with the charge density is of the form
Card 517

S/139/60/000/005/019/031
E032/Elll+
Derivation of the Thomas-Fermi and the Thomas-Fermi-Dirac
Equations Taking into Ac2ount Partly Filled Electron Shells
A V = 4. ')- e ( p 1 + , (1.23)
oo
tz I I~ 2), - 3
0 [(V - V, + "')f + -r
0
1,2)
where 9
2
((V V, + +
91 0 0 (1 1,2), (L,21)
and I f, )+x 12 -1
3 e ZA
T 0 A_ . (1~22)
0 k 15x' a
k
Thus the final Poisson equation de5cTibing the system and
Including the effer.,ts of partly filled shells is of the form
V = 2 n e a 0~F( V - V + + -i~()] 3 + 1_0 + Z103
1 L(V - V 2 +
V/
Ca-r-d' V 7
0

S/139/60/000/005/019/031
E032/E114,
Derivation of the Thomas-Fermi and the Thomas-Fermi-Dirac
Equations Taking into Account Partly Filled Electron Shells
The usual Thomas-Fermi-Dirac equation can be obtained from this
by putting V1 = V2 = VO and the Thomas-Fermi equation by putting
'Co= 0. The solution of Eq.(1.7) is subject to the boundary
conditions
lim i)V = zie~ lim V = 0. (1-31)
Fi r i -) co
This is an abridged translation. Acknowledgements are made to
A.N. Orlov for discussions and valuable advice.
There arT-8 referencess 6 Soviet, 1 German and 1 English.
ASSOCIATIONs Sverdlovskiy sellskokhozyays.tvennyy Institut
(Sverdlovsk Agricultural Institute)
SUEMITTED: November 16 1959, and after revision May 9 1960
Card 7/7

AUTHOR:
TITLE-
6ii26/6o/oo9/o6/ool/O25
Men', A.N. E032/E314
lre-E-ermination of the Number of Independent Long- and
Short-range Order Parameters in Multicomponent Solid Solutions
PERIODICAL-. Fizika metallov i metallovedeniye,
Nr 6, pp 8o1 - 8og (USSR)
l9bO, Vol 9,
ABSTRACT: The present work is concerned with the discussion of the
concept of long- and short-range order parameters in
multicomponent crystals having a complex structure, the
determination of the number of independent parameters and
the generalization of previous results obtained by the
present author in Refs 2 and 6. Surface, linear and point
defects are not considered, although the mathematical
apparatus developed can be used to allow for them. The
discussion is quite general. In the determination of the
long-range order, the distribution of atoms over both
equivalent and non-equivalent sites (these are defined in
Refs 2 and 6) is taken into account, while in the case of
the short-range order both the distance and the position
of the atoms in the intermediate spheres are accounted for.
Cardl/2 A method is given for finding the number of independent

S/126/6o/oog/o6/001/025
Determination of the Number of A-.,rdeE0eaX'nR4ong- and Short-range
Order Parameters in MulticompaL=tnt Solid Solutions
short-range order parameters which takes into account second-
order neighbours. The treatment is highly abstract, but
the results obtained can (and should) be taken into account
in the statistical theory of order in multicompaient. solid
solutions and, in particular, in the study (-.;f temperature
and concentration dependuras of short-range order parameters
in the first and second coordination sphere's. /I
Acknowledgment is made to A.N. Orlov for discussions and ,e
helpful advice. There are 10 references, 7 of which are
Soviet, 1 Japanese (in English) and 1 English.
ASSOCIATION: Sverdlovskiy sellskokhozyaystvennyy institut
(Sverdlovsk Agricultural Institute)
SUBMITTED: April 22, 1.959
Card 2/2

- MM', A.11-
Theory of the oxidation-reduction equilibrium in wfistite.
Fiz.met.i matalloved. 10 no.1:142-145 j1 160. (HIRA 13:8)
1. Institut metallurgiiUrallsko.--o filials AN SSSR.
(Wustite) (Oxidation-reduction reaction)

M&111, A.H.
Determining short-range order in a rmlticomponent disordered
solid solution. Fiz.met.i natalloved. 10 no.1:145-148 J1
16o. (MIRA 13:8)
1. Institut metallurgii Ural'skogo filiala All SSSR.
(Solutions, Solid) (Crystal lattices)

MI, A.M.
1%4
Configurational free energy of multico=onent so,114 solution consi-
dering the distribution of atoms J
&n. sublattice interstices. ?is. wt.
i metalloved. 10 no.4:63o-6.31 o 16o. (MIRA 13:11)
1. Institut metallurgUAN SSSR.
(Crystal lattices) (Solutions. Solid)

S/126/60/010/005/003/030
B032/E4i4
AUTHOR: Men
TITLE: Calculation of the Correlation Parameters for the
Second Coordination Sphere of an n-Component Solid
Solution
PERIODICAL: Fizika metallov i metallovedeniye, 1960, Vol.10, No-5,
pp.655-66o
TEXT: This is a mathematical paper and a continuation of the
previous work by the present author in Ref.1 to 4. A calculation
is given of the correlation parameters for the second
coordination sphere of a multi-component solid solution. The
disposition of the atoms on intermediate sites is taken into
account. The theory applies to an unordered solid solution with
equivalent sites containing Ni atoms of type i,
where i = 1, 2, 3,...,n, There are 6 references: 5 Soviet and
I Non.-Soviet.
ASSOCIATION: Institut metallurgii UFAN SSSR
(Institute of Metallurgy, UFAN USSR)
SUBMITTED: April 11, 1960
Card 1/1

21510
S/i3g/61/000/002/005/018
E032/E414
AUTHOR: Men'. A.N.
TITLE: Approximate,.Solutions of the Thomas-Fermi Equation for
U:
an Atom
PERIODICALt Izvestiya vysshikh uchebnykh zavedeniy, Fizika,
1961, No.2, pp.42-45
TEXT: Analytical expressions giving approximate solutions of
the Thomas-Fermi equation for an atom
3/2 1/2
/X
have been given by H.C.Brinkman (Ref
.5), T.Tietz (Ref.6) and
K.Umeda and S.Kobayashi (Ref.7). The approximate solutions of
(1)
are based on the fact that
Eq.
(2)
is a slowly varying function (assumed constant). The arbitrary
constants are then chosen so that y should agree with
tabulated values. The present author uses the method of
Card 1/8,,

21510
73/139/61/000/002/005/018
Approximate Solutions-of ...
approximate integration of differential equations put forward by
A;,ChAplygin (Ref,4) to obtain approximate solutions of Mq.ft),
in this method two functions z and u are chosen so that
> 0, a"-U""1X'/- < 0. (3)
The choice of the functions z and u can be made with the aid
of the following two lemmas.
-Lemma 1. If two functions f(x) and V(x) are differentiable
in the region Q and satisfy the conditions fl(x)*> TIW and
f(xo) = (p(xo) then for any XEG the.following inequality will
always hold: (X
f (X) > (P
Lemma 2. If two functions f(x) and (p(x) can be differentiated
n times and satis'Ay the conditions
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21510
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Approximate Solutions of E032/E414
then for any x(-G the following inequality will always hold;
f(x)> 9(x). Consider n6w the differential equation
y1n, = f(X, Y, Y" Y ".-YO-1), (5)
where
.H Y (X-) = Y., Y, (X.) = YY("-I) Gr.)
Let us now set up another differential equation of the form
z(n) = (P(Xsz,zl 'ZI, ... z(n-1) (6)
wher e Z(X,) = YO, ZI(XO) = Yol..., Z(n-1)(,o y,(n-1)
In Eq.(6) the function 9 is chosen so that V> f in t~e)> Y(,),
region G. It then follows from Eq.(5) and (6) that z n
i.e. using Lemma 2, we have z >y. Proceeding in a simila'r way
for ~p y > u
(7)
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s/i-,)/61/000/002/005/018
Approximate Solutions of ...
Consider now
Y11 Nxty) (8)
where
af > 0, Y(xo) yo, Y I (xo) Y 10
BY
Then, according to the above, one can find the function z
satisfying Eq.(7) from the differential equation
z" = (P(X,Z) (9)
Consider the equa-tion
zill = f(x,z) (10)
One can show that z> z].> y. In fact from Eq,(9) and (10) we
have
z" z1 11 (X, Z) - f (X, Z) > 0 (11)
Cqrd 4/8

Approximate Solutions of ...
s/139/61/000/002/005/ol8
E032/E414
It follows from Lemmx 2 that
z > ZI
(12)
Subtracting Eq.(8) from Eq.(10) we find that
Z111 - Y" = C(x,z) - f(X,Y) > 0 (13)
and since af > 0 and z > y, we have In accordance with
3Y
Lemma 2, ZIL > Y- Proceeding in a similar way with the function y
we are led to Eq.M. By continuing this process indefinitely,
we can establish the limiting functions zn and un which are as
near to y as required. In order to find the functions V and
(P for Eq. (1) let
max
from which it is clear that
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Approximate Solutions of ... E0712/E414
19=10 -a, (e 11 ~ ~ - II- " )J,
WO W, (15)
The solution of the equation
z1f = z (16)
x
subject to the condition Z(O) Z,(O) Y,(o)
gives z ql7c K , (2V~ x%),
(17)
where KI is the modified Bessel function of the second kind
and C 0.42. The solution of the equation
Ulf = !L2
subject to the condition u(o) 1, u,(0)
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S/139/61/000/002/005/018
Approximate Solutions of ... E032/E414
gives
61L
U_
+ Vgi-)2 (19)
The quantity IL can easily be found from the data reported by
P.Gombash (Ref.2) and is found to be.
0.70 (20)
Expressions similar to Eq.(17) and (19) have been obtained by
H*C.Brinkman (Ref.5) and P.Gombash (Ref.2) from the condition
const and are of the form
y cj/_XK, (2 1/!-L x'!-), I-t = 0,64, c = 1,73,
y = 61,. (x + 0,58.
There are 7 references: 4 Soviet and 3 non-Soviet.
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21510
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Approximate Solutions of ... EC-*.2/E414
ASSOCIATION: Sverdlovskiy selfskokhozyaystvonnyy inatitut
(Sverdlovsk Agricultural Institute)
SUBMITTED: November 16, 1959 (initially)
May 9, 1960 (after revision)
Card 8/8

I
'I- IMENI 0 A.N.
Distribution of cations In a multicomponent stoichiome-tric spinel.
Fiz.tver.tela 3 no.4:1054-1060 Ap 161. (MERA 14:4)
le Urallskiy filial AN SSSR, Institut metallurgii., Sverdlovsk.
(Spinel group) (Cations)

I
A
......
Effect of cation diatrilution in a mullticonwonent sto:!~hiomtric spinal
on the equillbriun pressure of oxygen. Fiz-tver.tela 3 no.4:1.101-
U04 Ap 161. (KMA 14:41'
1. Uralfskiy filial AN SSSR, Institut metallurgii Sverdlovsk.
(cations) (Spinel groups

MIS A.11.
Deterdination of the configurational heat capacity of a
malticomponent spinal.' Fiz. tver. telaJ no.8:2466-2469
Ag 061. (MIRA 11*:8)
1. Urallskiy filial AN SSSRS Institut metallurgUt Sverdlovsk.
(Spinal group-Thermal properties)

'et -doe)
AUTHOR: Men' A.
30 3
S/141 1 004/0 4/020
E192/E382
TITLE r----VFn-_a_pp_rox1mat e method of analysis of non-stationary
fluctuation spectra
PERIODICAL: Izvestiya vysshikh uchebnykh za-edeniy,
Radiofizilca, v. 4, no. 3, 1961, pp. 521. - 533 + 1 plate
TEXT: Experimental investigation of the fluctuations
encountered in the propagation of u1trahigh-frequeney waves
in the troposphere by a number of authors (Refo 1. - A.P. Deam,
B.M. Tannin Proc. IRE, 43, 1402, 1955, Ref. 2 -,-,.the author
and his team DAN SSSR, 125, 1019, 1959- Ref..3-- - ditto -
this journal, 2, 848, 1959; Ref. 4 m,.6. Thompidn.% H.B.Yanes,.
~.Res. NBS, 63D, 45, 1959; Ref. 5 - the author '-'.Radiotekhnika
i elelctronika) showed that their aUtocorrelation: ,and spectral
characteristics were non-stationary~. ConsequentlyD in order
to determine the average spectral characteristiesq it is necessary
to employ the statistical method of analysis of'_44hole series
of independent measurements which should be r;arrl~e&_out under
identical conditions. This inethod is based on the *spectral analys:b
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30763
s/i4l/61/oO4/oo3/oi4/o2o
An approximate method .... E192/E382
of a given process by an analyser having a high resolving
power; this consists of a large n1amber N of narrow-band
filters and is a very complex equipment. Howevero in many cases,
it is sufficient to employ a more simpleanalyser.consisting of
several (e.g. 2) wide-band filters which cover the whole
fluctuation spectrum. In the simpleat two-filter,analyser
it is possible to determine approximately the relative bandwidth
of the spectrum by an integral coefficient y 0 which is equal
to the ratio of the fluctuation powers at the input of these
filters. The experimental application of this method for deter-
mining the phase-difference fluctuation spectra LE(investigated
'i easured
in this wor1r. The phase-difference spectra were M
at a wavelength of X = 10 cm overa distance of
L = 33 km The spectra were f o un d for various heights of
the receiving and transmitting antennae h and h 0 i
respectively, and distances d between the antennae. The
spectra could be determined from the coefficient y , which is
defined by:
Card 2/8

50 63
/~1/004/003/oi4/020
93 P
An approximate method .... J2
y(d) = &B/oH = (6(p 6T )2/(6T 6~p 2 (2)
1 d B I dTH
wh or e &B and (rH are the average square values of the
phase-difference fluctuations measured at
the output of the high- and low-frequency
filters, respe.:tlvely,., and
Y1 and Yd are phase flu%:.tuatians of the signals at the
points spaced by a distance d .
In general, y is a function of d., h. ho . L and time t
The parameter y is also dependent on the I.i.miting frequency
FC between the bandwidtb.~of the filters and this should be
chosen in such a way that y shoul.d be near to unity, The
coefficient y as a function of d can be expressed by;
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30763
s/i4l/6i/004/003/01.4/020
An approximate method E192/9382
2 r r
y(d) = 6YB B, __ =- Y B (4)
6Y2 r r
H H H
where rB and rH are the spatial correlation coefficients
for the high- and low-frequency fluctuations, respectively.
It is shown that these coefficients can approximately be
expressed by:
H d d
rH erf rB erf - (8)
2d CH 2d 1B
where erf X e,-t2dt is the probability Integral and
Card 4/8

An approximate method ....
.,./J.4i/61/004/003/014/020
7192/E382
11 and B are the charactoristic scaling factors
characterising the size of the nonhoi-4ogeneities which produce
the fluctuations. In the case when the i-,rave propagates over
a sharp discontinuity the phase-difference fluctuations can be
e.-cpressed by (Rcf. 10 - the author and his team - DAN SSSR, 2,
740, 1959; Ref. 11 -ditto- this journal, 2, 388, 1959):
r,(z)
2 = 0, 2 5 r. 5, (2 J.:_)2 "" [_1 - I + r,(-,)
tg' (,p,/2)
L I - n, (Z) + r, (z)
tg' ~2) (13a)
i-,rh er e rH(z) and rB(z) are correlation coefficients of th e
fluctuations in the direct and reflected waves for the
discontinuity. These coefficients can be o.-:pressed by:
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3076.3,
s/141/61/0.04/003/014/020
An appro.-timat e method E192/E382
r,, (z) erfz r. (z) erfz (14)
2z I. 2z
Z= 2hh,, (14a)
h+h, ,
wh er e (p is the spatial delay angle between the direct and
reflecteA waves. The coefficient y can be express'ed by:
z 2i'ld
Td-canzt(h, L) erf ctg2 ( + 14- -V eff x
k 2z L& 2z
(15) :15)
Ctgj ( 2-m hh,+ z
x erf erf
2z I. LX 2z
-wh er e x is a constant given by:
erf erfd (15a)
2d 2d 1"
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An approximate method ....
Eq. (15) can be simplified for various s-)(-,cial cases, such
as z -\-) ~ Bor z '~~ / H Some of the results obtained
with this formula are illustrated in r'iL;. 56, where y is
plotted as a function of the distance L for various values
O.L H and B The calculated an,,. t1he experimental data
show that as thL I e n !7 th of the transmission route is
increased, it is possible to observe a relative broadening
of the fluctuation spectrui-a which is due Z.o t, e presence of
a boundary surface and the nonhomogeneity of the medium. The
time dependence of the spectral characteristics of the fluc-
tuations was also studied experiment ally; in particular, their
dependence on the velocity and the direction of wind was
measured. It was found that y was almost independent of the
direction and strength of the wind.
Tlhere are 8 figures and 13 references: 10 Soviet-bloc and
3 non-Soviet-bloc. The English-lan-cui3e riot iiontioned in
the text is- Ref. 6 - R.B. Muckutiore and A.D. Wheelon, Proc.
IRE, 43, 1437, 1955.
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An approximate method .... E192/E582
ASSOCIATION: Institut radiofizilzi i ele7,troniki AN UkrSSR
(Institute of Radiophysics and Electronics
of the AS UkrSSR)
SUBMITTED: December 1, 1960
g
kl~ Q% Q-
Card 8/8

qW I p A. N.
Frequency spectrum of a linear chain of a special form, IZVVYBG
uchob.zav.; fiz. ao.5:101-108 161. (MIU 14: 10)
1. Sverdlovskiy sellskokhozyaystvannyy institut.
(Spectrum, Atomic)

~,J~~I t~.A.N.
Determination of short-range order parameters for the first co-
ordination sphere of unordered solid solutions. Fiz. met. i
metalloved 11 no.3:347-352 Hr 161. (MM 14:3)
1. Institut metallurgii Urallskogo filials, Akademil nauk SSSR.
(crystal lattices)
(Solutions, Solid)

MEN', -A.N.
Heat capacity !if sYstrms vitb a sPecial additional t~aram-eter. Fiz.
met. i metalloved. 12 no.1:15F-16C U'l '61. (1",IRA 14:8)
1. Institut metallur ii Ural'skogo filiala iuN SSSR.
I
~Alloys--I'hermal propertips)

S/048/61/025/011/017/031
B104/B102
AUTHR: Men' , A. N.
TITLE;: Determination of parameters characterizing the cation di~:,tri-
bution in multicomponent spinels
PFRIODICAL: Akademiya nauk SSSR. Izvestiya. Seriya fizicheskaya, v. 25,
no. 11, 1961, 1385 - 1387
TFUT: The structure of spinels containing N i (i = 1,2 ...... n) cations of
kind i was studied. The cation distribution over tetrahedral and octahedral
lattice sites is described by one parameter 1. The dependence of,~ on the
composition c, is determined from a solution of the equation dF/dj = 0,
I
i,;hpre F = K(-1 , Ci , T) - kT 1n w(.1 , ci). The author bases on his own experi- V//
mental results (Fizika tverdogo tela; in print) regarding the relation
It =~(Ci), to represent the equation:
d 1n w 1 dK
d kT d It
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5/048/61/025/011/017/031
Determination of parameters... B104/B102
derived from the relations indicated above, in the form
(3c, + Xt + r) alt
(I - X, - r) (3cL - A.,)
%.I (I - 3c, + ).2 - r) (7)
(3c, - X3) (3c, + 3c: -1 -~3+0
where NA, -NI,' . N(
- ; X, - --- N I Cl =
N 'V
I h n (5)
r = -;V- Y, N A N,-- 3N.
i=3
(6)
at exp (kc, T)
kT
Card 214

Dpterminnfi-,n of parampters . . .
S/046/61/025/011/017/051
B104/B102
If, for thij ca,,;o lim 0, f is independent of A (low 'Lumperatures), it,
T-; 0
follows:
(a, + otbi
a, = 3c2 + r-1,
b, = 3c, + I - r,
d, = 3c, (I r),
(9)
a2 ~ I - 3c, - r;
bg = 6r, 4- 3c, - I + r;
d, = 3c, (3c, + 3c~ + r).
For the case of high temperatures,
C1, X2 - 3cl
i~3
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5/048/61/025/oil/017/0"1
Determinntion of parametern ... B104/B1G2
is obtained. The proposed function f~k) is well satisfied for the systenis
1, Mg, -)0 ; 14gFe Mn 0 kO.8 ~c~ 1.2), and
14e I -,I mg'~(Fe I +j--( 4 2-c c 4
Fel- Ti (Ni 1+C Fe 1-2c+.). Ti c-A)O 4' In case of magnesium ferrite, a good
agreement with experiment is attained if f is taken as a linear function of
1. Experimental results concerning the system N 1+0 Fe 2-2c Tic04 are in good
agreement with theoretical data if f i.-i taken as a linear function of ( and
of c. There are 1 table and 13 refererces: 9 Soviet and 4 non-Soviet.
The two most recent references to Englisb-language publications re~td as
follows; Kriessman C. J., Harrison S. F., Phys. Rev., 103, 857 (10~1-t);
Neel L., Ann. Phys., J, 137 (1948).~'
ASS-"CIATION: Institut metallurgii UPAN SSSR (Institute of bletallur;4y of
the Ural Bray1ch of the Academy of Sciences.USSR)
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33337
3/181/62/004/001/003/052
2L1. -1100 B102/B138
AUTHOR: Men', A. N.
TITLE: Cation distribution in multi-component spinel
PERIODICAL: Fizika tverdogo tela, v. 4, no. 1, 1962, 14 - 21
TEXTt Formulas are derived for the concentration and temperature
dependence of the parameter ?i - W'IN for a spinel-type lattice containing
j j
N cations in tetrahedral (A) and octahedral (B) sites. HILis the number
i B i
of i-atoms in.IL (tt - A,B) sites; I + N Ni (i = 1,2 ... n). The sub-
i
script j runs.from I to n-1. At T=O, 1 0. 'k i(T,ci) is sought,
0 1 NiIN. For (T,c,) a set of n-1 equations is obtainedt
aj=expl- I Jul,
Nkr dkj
Aj (d, 1j) =aj U=.1- n (6). d, = b,
(ey -)j) (dg -- Xj) ajc4-4-
Card 1/3
(I= 1, 2)

3 's.3 3 7
S/181/62/004/001/003/052
Cation distribution in ... B102/B138
For example, for the system Fel-Mgi (Fej+jMgj-j) 01
IUO
r
(10)
is found, and for Fel-ITix [Nij,,Fej-zj+xTI,-i) 0#
' I U,
Ill - 2C X) = e- T7.
For U IAT - 0.96, the results agree with experiment. For spinels of type
Xz 20 4 which may be normal or inverse at T-0, X i - -(1+2a)+ 1+8a
2(1-a)
(L. Neel, C. R. 230, 190, 1950); ?~norm. t ~Ba+a where a =exp(-U~d~
2(1-a)
At T-T 0 dX/dT has a maximum, To U 1/kx 0 , where
a [x0 (I -1- 2 (1 - x,,,% (b +3a"') 0. (16)
and-a 2 1 a
4+5a, b Ba + a ' 5+4a, b I+8U. Numerical
n. n. inv. inv.
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Cation distribution in- B102/B136
solution yields (X dinv. c12,75, (xo)n. ~~24,65- U, may be defined as the
activation energy of an elementary event of Cation diffusion, Tc:~L4400K,
(U Oinv,n~0,07 ev. For N(T) at T-T., (U On./Pi4nv = 1-8'
followin'g,
the system
Ninv, (T0) = m64, X n.(T0) = 0,008. In the
xcY1-c z204is treated analogously, the results are tabulated. There are
1 figure, 4 tables, and 19 referencess 11 Soviet-bloc and 8 non-Soviet-
bloc. The four most recent references to English-language publications
read as follows% A. Miller, J. Apple Phys. Sup. 30, No. 4, 249, 1959;
J. B. Goodenough, A. L. Loeb, Phys. Rev. 98, 391, 1955; C, J. Kriessman,
S. F. Hairison. Phys. Rev, 103, 857, 1956; K. Muramori, S. J. Miyahara,
J. Phys. Soc. Jap. 15, 2354, 1960.
ASSOCIATION: Inatitut metallurgii UFAN Sverdlovsk (Institute of
Metallurgy of UFAN, Sverdlovsk)
SUBMITTED: May 24, 1961 (initially~
June 13, 196, (after revision)
V,
Card 3/3

S/18 62/004/004/009/042
B108YBI02
AUTHOR; Men', A. N.
TITLE. Concentration and temperature dependences of the correlation
parameters of a three-component spinal
PERIODICAL: Fizika +.verdogo te).a, V. 4, no. 4, 1962, 889 - 895
TEXT: The author establishes the correlation Darameters of a three-
component spinal with the composition X cY1-Cz2 04for which the distribution
with respect to the sublattices is determined by the probability of
finding a certain cation at a definite lattice site. Extensive formulas
are derived, which ce
.nnot be presented in this abstract. There are
1 figure, 3 tables, and 10 references: 7 Soviet and 3 non-Soviet. The
three references to the i;n8lish-language publications read as followst
N. Yiyata. J. Phys. Soc. Jap., 16, 2o6, 1291, 1961; j. M. Hastings,
L. J". Corliss. Phys. Rev., 104_, 328, 1956.
ASSOCIATIONs Institut metallurgii UFAN SSSRSverdlovsk (Institute of
Metallurgy of the Ural Branch AS USSR Sverdlovsk)
SUBLIMED: November 9, 1961
Card 171

44174
8/18 2/004/012/023/052
!to B1 04YB'102
AUTHORS: Ment, A. N., and Na7sh, V. Ye.
TITLE: The term splitting in multicomponent disordered crystals
PERIODICAL: Fizika tverdogo tela, v- 4, no. 12, 1962, 3522-3525
TEXT: The theory of term splitting in crystalsp developed by Bethe (Ann.
de Phys-, 3, 133, 1929) is extended to multicomponent disordered crystals.
It is assumed that a multicomponent crystal comprises N sites. In the case
of n types of atoms, Nt (t . 1,2,.... n), 7- Nt - N holds. Each site is
t -
characterized by a set M of four symbols (ikla). i characterizes the color
(the type of atom) of the point, k the number of atoms of a given type,
1 the spatial distribution of the other points with respect to the one
considered and a gives the condition that among sites of equal color there
may be such as have different magnetic moments. I(R) characterizes an
island in space which is bounded by a sphere of radius R. M is the set of
all sites, whilat the set Mi(i,k,l) of all sitep of the same type is a
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S/181/62/004/012/023/052
The term splitting in multicomponent B104/B102
subset of M. A sequence R(j) < R(j) < R(j) is obtained if one point
min 1 max
is connected by rays with the remaining sites and if the distances apart of
two sites are ordered. 1(R ) '< 1(R12 holds for the symmetries l(Ri,)
il >
of the island if R ii