SOVIET ATOMIC ENERGY VOL. 32, NO. 1

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• Document Page Count: 127
• Document Creation Date: December 27, 2016
• Document Release Date: March 1, 2013
• Sequence Number: 1
• Publication Date: January 1, 1972
• Content Type: REPORT

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Russian Original Vol. 32, No. 1, January, 1972
Translation published July, 1972
SOVIET
ATOMIC
ENERGY
ATOMHAFI 3HEPINFI
? (ATOMNAYA ENERGIYA)
TRANSLATED FROM RUSSIAN
lc-
CONSULTANTS BUREAU, NEW YORK
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;
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SOVIET
ATOMIC
ENERGY
,
Soviet Atomic Energy is 'a cover-to-cover translation of Atomnaya
Energiya, a publication of the Academi of Sciences sof the USSR.
An arrangement with Mezhdunarodnaya Kniga, the Soviet book
export agency, makes available both advance copies of. the Rus-
sian journal and original glossy photographs and artwork. This
serves to decrease the necessary time lag between publication
of the original and publication of the translation and helps to im-
prove the quality of the latter. The translation began with the first
issue of the Russian joulenal.
Editorial Board of Atomnaya Energiya:
,. 'Editor: M. D. Millionshchikov
DeputY Director
V. KurchEitov Institute of Atomic Energy
Academy of Sciences of the USSR
Moscow, USSR
,
Associate Editors:'N. A. Kolokortdov
N. A. Vlesov. ,
#4 ?
A. I. Alikhanov V. V. Matveev
,
,A. A. Bophvar M. o. Meshcheryakov
N. A. Dollezhal' P. N. Palei '
V. S. Fursov, l " V. B. Shevchenko
I. N. Golovin' / D. L. ?SirtionerlkO-
,
V. F. Kalinin V. I. Smirnov ,
A. K. Krasin / ? ,' A: P. Vinogradov
? ,
A. I. Leipunikii, A. P: Zefirov
4 l ,
I 1
(Copyright 1972 Consultants Bureau, New `lark, a division of Plenum Publishing
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SOVIET ATOMIC ENERGY
A translation of Atomnaya Energiya
Translation published July, 1972
Volume 32,'Number 1 January, 1972
CONTENTS
Engl./Russ.
On the Stability of the Cans of Cylindrical Fuel Elements with an Initial Ellipticity
? Yu. I. Likhachev and V. V. Popov
1
3
Diffusional and Thermodynamic Properties of the 7-Phase of the System Uranium
?Niobium ? G. B. Fedorov, E. A. Smirnov, and V. N. Gusev
8
11
Deposition of Corrosion Products on the Surface. of Zirconium Alloys ? V. V. Gerasimov,
A. I. Gromova, I. K. Morozova, V. N. Belous, A. S. Ilyukhin, C. A. Shchapov,
L. G. Varnacheva, and G. P. Saenko
12
15
Mechanism of Reduction of Uranium Hexafluoride by Hydrogen ? Yu. N. Tumanov
and N. P. Galkin
17
21
Calculation of Regular Systems of Neutron Absorbers ? Ya. V. Shevelev
and I. L. Chikhladze
23
27
Thermalization of Neutrons in H20 at 318 and 77?K ? S. N. Ishmaev, I. P. Sadikov,
and A. A. Chernyshov
29
33
Determination of Lithium in Solid Materials from the Reaction Li6(n, cx)H3
? B. P. Zverev, Yu. F. Simakhin, and A. G. Dutov
35
39
Thermonuclear Combustion in a Bounded Region ? A. F. Nastoyashchii
39
43
Radiative Widths of U238 Neutron Resonances ? Kh. Maletski, L. B. Pikel'ner,
I. M. Salamatin, and E. I. Sharapov
45
49
ABSTRACTS
Variational Composite Methods of Calculating Neutron Distribution in Nuclear Reactors
? I. S. Slesarev, A. M. Sirotkin, and V. V. Khromov
48
53
Radioactivity of Metamict Zircons ? I. M. Lipova and G. A. Kuznetsova
49
53
Monte Carlo Calculations of Characteristics of Secondary Electrons Knocked Out from
Various Materials by 7-Radiation ? V. V. Smirnov and A. V. Malyshenkov
50
54
The Kaon Factory ? a Two-Stage GeV) Isochronous Cyclotron ? L. A. Sarkisyan
50
55
Thermal Stability of Anhydrous Uranium Trichloride ? V. V. Rachev, L. A. Tarasova,
and A. I. Pavlova-Verevkina
52
56
LETTERS TO THE EDITOR
Adjoint Reactor Kinetics Equations: Delayed Neutrons Case ? V. V. Orlov
53
57
A New Procedure for Measuring Thermal Coefficient of Reactivity and Worth of Control
Shim Rods in the IGR Reactor ? V. D. Lavrenikov
56
58
Redesign of the IRT-TM Reactor Dry Experimental Channels ? 0. F. Gusarov,
V. V. Karnaukhov, and V. K. Leus
59
60
Critical Thermal Fluxes in the Boiling of a Eutectic Sodium?Potassium Alloy under
Conditions of Free Convection ? V. I. Subbotin, D. N. Sorokin,
A. P. Kudryavtsev, V. I. Brigutsa, and R. I. Zhirova
61
62
Measurement of Integrated Characteristics of Slow-Neutron Spectrum of VVR-M Critical
Assembly? A. V. Nikonov and V. B. Klimentov
64
64,
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CONTENTS
(continued)
Engl./Russ.
Possibility of Measuring the Spectral Characteristics of a Neutron Flux using Direct-
Charge Detectors ? V. S. Kirsanov, M. G. Mitel'man, N. D. Rozenblyum,
E. N. Babulevich, V. A. Zagadkin, and Yu. M. Shipovskikh
66
65
Spectrometry of Low-Energy Ions by Surface-Barrier Silicon Detectors ? G. F. Bogdanov
and B. P. Maksimenko
68
66
Measurement of Neutron Spectra with Threshold Detectors ? K. K. Koshaeva,
S. N. Kraitor, and L. B. Pikel'ner
70
68
The Effect of Neutron Irradiation on the Operation of Surface Barrier Fission Fragment
Detectors ? E. A. Seregina, N. N. Semenova, and B. D. Kuz'minov
73
70
The Effect of the Angular Dimensions of a Detector on the Error in the Determination of
Certain Kinematic Characteristics ? G. N. Potetyunko
76
72
Visualization of Spatial Dose Distribution in a Fast Electron Beam? Yu. P. Vagin,
G. L. Kabanov, Yu. A. Medvedev, and B. M. Stepanov
78
73
Spectra of Electrons Ejected in the Passage of Co60 Gamma Rays through a Two-
Component Medium? L. V. Popova and L. B. Chegodaeva
80
75
Angular Distributions of Bremsstrahlung from 12-22 MeV Electrons as a Function of
Target Thickness ? V. P. Kovalev, V. P. Kharin, and V. V. Gordeev
83
77
Matching of Accelerating Channels in a High Energy Proton Linear Accelerator
? B. I. Bondarev and L. Yu. Soloviev
86
79
Effect on Nonlinear Resonances on Beam Dimensions in the 70-GeV Accelerator
?V. I. Gridasov, K. P. Myznikov, and V. N. Chepegin
89
81
Value of from Energy Balance in U233 and Pu239 Fission? N. P. Kolosov,
B. D. Kuziminov, A. I. Sergachev, and V. M. Surin
92
83
Absolute Measurements of the Quantity a for U235 and PU239 in the Neutron Energy Region
of 10 keV-1 MeV? V. N. Kononov, E. D. Poletaev, Yu. S. Prokopets,
A. A. Metlev, and Yu. Ya. Stavisskii
95
85
Chill-Casting Method of Bituminizing Natural Sorbents for Ir192? Kh. Daiev, G. Delchev,
G. Gradev, S. Simov, and V. Zhelyazkov
98
87
INFORMATION
All-Union Izotop Agency Serving the National Economy Exhibit at Exposition of
Achievements of the National Economy ? V. A. Dolinin
101
91
Seminars and Conferences at V/0 Izotop
104
93
CONFERENCES
Sixth All-Union Conference on Synthesis, Production, and Applications of Scintillators
? L. Ya. Zhil'tsova, E. N. Matveeva, and I. M. Stoletova
106
94
Fourth Conference of the International Nuclear Data Committee ? M. F. Troyanov
108
95
International Conference on Elementary Particles ? I. A. Savin
110
96
Fourth International Conference on Plasma Physics and Controlled Nuclear Fusion
? B. B. Kadomtsev and V. D. Shafranov
113
98
BRIEF COMMUNICATIONS
118
101
The Russian press date (podpisano k pechati) of this issue was 12/17/1971.
Publication therefore did not occur prior to this date, but must be assumed
to have taken place reasonably soon thereafter.
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ON THE STABILITY OF THE CANS OF CYLINDRICAL FUEL
ELEMENTS WITH AN INITIAL ELLIPTICITY
Yu. I. Likhachev and V. V. Popov UDC 621.039.54
The fuel-element cans of gas-cooled and water-cooled reactors are subjected to a fairly high external
pressure due to the coolant (sometimes exceeding 100 atm). The cans are thus in danger of losing stability,
possibly leading to the collapse of the compensation volume or to the formation of a longitudinal corruga-
tion in the parts of the can resting on the heat-emitting core.
The stability of the cans of cylindrical fuel elements was studied earlier [1-4]; however, no allowance
was made for either the initial ellipticity of the can or the creep of the material of which it was composed.
The creep of cylindrical cans with an initial ellipticity was considered (with various simplifying as-
sumptions) in [5-7], but without allowing for the influence' of the thermal flux, the swelling of the steel, and
the changes taking place in the temperature and pressure during deformation, which are important factors
in the cans of fuel elements.
Let us consider the creep of a cylindrical fuel-element can having an initial ellipticity w1 = Ivo cos 20
subjected to a time-varying excess external pressure q(t) and a thermal (temperature) field T(t, z), where
w0(0) is the radial deviation of the middle of the surface of the can from the ideal circular form and z is
the distance from the middle of the surface.
The process of can deformation develops as time progresses in a series of short stages [8]. Let us
suppose that at the n-th stage of deformation Ant = tn? tn_i the stresses, strains, and displacements have
received increments Ancr, Ane, Anw, Anv. ?The increments in the stresses should satisfy the following
equilibrium equations
n/2 6/2
TERAng= ?4
Anax dz de;
(1)
.c
0
?6/2
6/2
RAnq =
?
6,?cro dz;
(2)
?6/2
8/2
=
?
Ancrozdz,
(3)
?6/2
where AnM = AnMe Rwn-tAncl + RqnAnw is the increment in the bending moment; Anq = qn? cin...1 is the
increment in the constant component of the bending moment; qn_land qn are the pressures at the beginning
and end of the deformation stage.
In accordance with the "rigid-normal" hypothesis (Levi?Kirchhoff) and the assumption of plane de-
formation, we have [9] the following for the strain increments
A?ce = zA?x;
Anc?=Ane = const,
where Anc(10, An) are the increments in the circumferential deformation and the curvature of the middle of
the surface:
(4)
A . r_d ono Aniv ;
do
Ax 7Ccr
(12,-(A?w)-F (A?w).
(5)
Translated from Atomnaya Energiya, Vol. 32, No. 1, pp. 3-9, January, 1972. Original article sub-
mitted December 8, 1970.
C 1972 Consultants Bureau, a division of Plenum Publishing Corporation, 227 West 17th Street, New York,
N. Y. 10011. All rights reserved. This article cannot be reproduced for any purpose whatsoever without
permission of the publisher. A copy of this article is available from the publisher for $15.00.
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Let us write down the physical relationships between the stresses and strains in the form [8];
A?co = 4_A?(50_1 Ana. + T3-I AnS aAnT ? (4(n)) Ant;
Ane. = T A?crx - Ancro AnS f. aAnT ((n)) Ant.
(6)
The elastic modulus E, the Poisson coefficient II, and the thermal expansion coefficient a are taken as con-
stants (defined for a certain mean temperature); this may be justified from the following considerations.
During the operation of the reactor at normal load the can temperature usually varies little, so that the
average values of the characteristics in question may be used for practical calculations. In considering
transient processes (when the reactor is just coming up to power) the deformation of the fuel-element can
is calculated in short time stages, starting from a temperature Tn (characteristic of the particular can ma-
terial) at which creep deformation becomes appreciable (for example, in 1Kh18N9T steel, from Tn 500?C).
In the temperature range Tn - Tmax it is permissible to average the quantities E, 12, and a (for 1Kh18N9T
steel the working temperature Tmax 650?C). The quantity ,AnS determines the swelling of the can mate-
rial during the n-th stage of loading:
AS=Sn (z)-S_1 (z).
The swelling of the steel is determined [10-12] by the integrated neutron flux it (neutron energy E> 0.1 MeV)
and the temperature level:
the temperature dependence may be written
S=AncI)'L (T),
_ Qs Q:
L (T) e RT ? B se RT?
The creep deformations are determined by the expressions
(2ao oc;
For the theory of strengthening [13]
where
Q9
(PC (c1, T, ej). .43e- 7ere?H(e?Vi,13( 7?)?
ec
{.t.? H (7') for the stage of transient creep,
[I (e7) =
H (7') for the stage of steady creep;
- A4e "2. Gy- ) is the deformation at the beginning of the stage of steady creep; A3 and A4 are experimen-
tal coefficients; Q3 and Q4 are the activation energies of the creep process; m3(T), m4(11, H(T) are certain
functions of temperature, sci- dt is the accumulated creep deformation; def = (f2 /3) ji (deco - dex)2
7,
d4)2 (d4- d4)2 is the intensity of the differentials of creep deformation; ai=l/a-- - axao is the
intensity of the stresses. From the condition of the elastic change in volume
dc= - d6- decx. (9)
The increment in temperature in the range tn to tn_i may be found from the expression
A, T (z) = 7' (tn, z) -7 (tn-1, z); (10)
(7)
(8)
( c(n)) is a certain mean value, of the function c(ri) in the temperature range in question, refined by the meth-
od of successive approximations. In the first approximation, the function c(ri.) is determined from the
stresses in the previous (n - 1)-th stage of loading (en) )=
Thena_i the stress increments and the value of
the function [)
e ] at the end of the stage of deformation are determined.
(n
In the second and subsequent approximations we take
(11)
2
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the calculation being continued until the values of the function (e(n)) obtained in the previous and following
stages are sufficiently close.
The symmetry conditions should also be satisfied:
dAnu: = ; d4nw
0 = 0;
dO 0-0 dO
Any lo=o ---- 0; Any = 0
and also the initial conditions for the stresses:
aj (0, z) o-jo (0, z) (j x, 0),
(12)
(12a)
where o-jo(O z) are the stresses in the can at the onset of the deformation process. Solving the system of
Eqs. (1)-(12):
A?o-, 1 .Ett, [OA p.A?.xz Anel ? (1
A ?.S
A?uo [ e(6 ! RA?d + xz ? (1 -1- p.) aA?T - (1 1.t) 3 A?e6 ,
where Anec , An< are the increments in the creep deformations:
(e(n)) Ant; AnEfs'?= (n)) A?t;
A/2 6/2 6/2 6/2
2 1
A---- -- .-T .0 C AX,d0 dz 1-2p, .7? ,_i_ An ceo r
2E b .1 I. A?T dz -f -F36. C A?S dz;
6/2 6/2 n/2 6/2 6/2 6/2
A
,, . E a
dz+ t? f AX, dz ? --L2 .0 C A?e,:cv dO dz 2-11
A, ti T f A?T dz-'r-- C AnS dz;
2E 6, ' . 36
-.6/2 -.6, 0 -7.6/2 -.672 -.6/2
6/2 6/2 6/2 6/2
12 12u
63
C A?Tz dz ; 4 (16;1 ? C A?Sz.dz 3A?)II .
Anx --- --- C ,6,?6z d.z -1- --,-- C A?e..z dz ; ? 63 12a (1+11)
63 yeto '
?.6/2 ?.6/9 . ?.6/2 ?.6/2
. 6/2 5/2
Anill, ? e I- bo/2. _i C0RA 632 , 4 (1-17 0 H2 12a (1.,1- it) R2 C A?Tz dz 1 ;
1 2 , 63 J
00
con
A,,w==E b.; cos 2/0 ;
A/2
12/n ,c
bi = 4 jA2 F(0) cos 2j0 d0;
2
0
n/2 a/2
C0=--Ano; b? F(0)dO;
A2 =- (1-1- 3qn ) ; F (0) = A?q
e ge
6/2
'
? 4 R2 C A ?E'6z dz [1, A?e!.;:z dz
(13)
(17a)
Relations (13)-(17) enable us to calculate the increments in the stresses at each n-th step in time if
we know the stresses at the end of the (n? 1)-th step, the functions V (n) being refined by the method of suc-
cessive approximations. In considering the process in which the reactor is coming up to power, the
stresses in the can are determined from the following relationships for the initial stage of deformation (t = to):
(Teo (0, z) ? q (to) 12611:0 Z
[T7,? T (t, z)];
' --
lig (10) 12Mo
(Tx? (0, 26 tt ea Z
IT,,--(1, z)I.
t
(18)
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69, kg/cm2
120
100
80
60
?40
20
0
-20
-40
-60
-80
-100
-1200
-1400
-1600
-1800
Fig. 2. Stress distribution over the cir-
cumference for various periods of opera-
tion of the fuel element: 1) t = 0; 2)t=60
h; 3) t = 120 h; 4) t = 180 h; 5) t = 240 h;
6) t = 300 h.
I42
45
fir
d/
rr
0,3
42
,
f
,
-1600
l
-8
0 -6
0 -400
- 200
200
400
500
800
1000
1200
59,
140Q
kg/cm`
0,1
0,2
43
44
15
Fig. 1. Stress distribution over the thickness of the can for various
periods of operation of the fuel element: 1) t = 0; 2) t = 60 h; 3) t = 120
h; 4) t = 180 h; 5) t = 240 h; 6) t = 300 h.
7
6
7
7
7
7
7
41 42 0,3 44 0,5
,
48 49 100
4
i
FAN
44
MORINO
lik
riper
where M0(0) = q(to)R (w2 + wi) is the bending moment in the
cross sections of the can with an initial ellipticity w1 (0):
which, as a result of the application of the pressure q(to),
acquires the additional curvatures [14]:
w2 (0) -- w? cos 20,
ge.q ltol ?1
(19)
where qe =[E(T11)/4(1 ? iA2)](6/11)3 is the critical pressure
for an ideally circular tube; to is the time within which the
average temperature of the can becomes equal to the charac-
teristic temperature corresponding to the appearance of
creep T. A dangerous state of the can may occur for the
following reasons.
1. For ductile material, the creep-engendered in-
crease in the sag and the bending moments has the effect
that the intensity of the stresses in most stressed cross sec-
tion of the can reaches the yield stress:
a, (1, 0, -i- 6/2) = o (T, (20)
which may be regarded as the onset of the loss of stability
(owing to the small thickness of the can). Here we allow for
the change in the yield stress of the can material arising
from changes in temperature and the effects of irradiation,
the quantity n (t) determining the radiation damage accumu-
lated during the operation of the can (for example, this quan-
tity may be given by the dose of radiation or by the num-
ber of displaced atoms in the can material [15]).
2. For an ideally elastic material, at a certain critical time tk the sagging of the can increases
sharply and a loss of stability sets in.
3. The can material accumulates damage arising from the prolonged action of stresses at high tem-
peratures, which may cause the appearance of cracks and break the air-tightness of the fuel element before
the can loses stability. In this case the working efficiency is determined by the criteria of long-term
strength or long-term ductility.
4
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3000
2500
2000
1800
1500
1000
50
wI8
72
10-I
10-2

/ ii1
? /
1
I
/
A
I
2 3
/
.
1
/
/12
I
4
/8
/
lc-
/
GT
I
10-4
1
/tia
,
.
i
10
, 10-6
--.
..--"-...
'
/
.1/
/

/
/
.
? -
7
wa....._..z_.--__
....
___ --- .-:-_.
??????? ??????
....? ....
.....
_.- ...-?
...." /
????? ..????
??????
.....- ??????
..... ..-
."-
??????
.....- ...,
..-- .?-? ????
?
/
/
60
48
35
12,t
0,12
50 120 180 .240 SOO 350 'fr20 480 t, h
Fig. 3. Time changes in the intensity of the stresses (curves 1-4), the
maximum sags (curves 5-8), and the total damage to the can material
(curves 9-12) in the most-stressed parts of the can for different values
of the original ellipticity: 1, 5, 9) wo = 0.01; 2, 6, 10) woA5 = 0.007; 3,
7,11) wo/O = 0.005; 4,8,12) w01/45 = 0.002.
4. If, as a result of the increase in ellipticity, the can closes the gap and rests on the fuel core, there
may be an irreversible increase in the length of the can in the course of heat exchange (thermomechanical
rachet) [16]. The time tx required for the onset of this mechanism may be determined from the condition
where r(t) is the change in the radius of the core due to swelling.
We used the foregoing theory in conjunction with an electronic computer (the M-20) in order to cal-
culate the stability of austenitic steel fuel-element cans for a gas-cooled fast reactor.
Figures 1 and 2 show the thickness and circumferential stress distributions in a can with dimensions
of (5/It = 0.14 and an initial ellipticity of NA = 0.01 for various periods of operation of the fuel elements, the can
being subjected to a pressure of q = 130 atm at 670?C (the temperature drop along the wall is taken as zero).
The changes in the maximum sags, the damage to the can material, and the stress intensities at the most
stressed points are shown in Fig. 3 as functions of time for the same temperature and pressure and for
various values of the initial ellipticity (w0/5 = 0.01? 0.002). The dangerous state of the can for all w01/45
was determined by the appearance of plastic deformations (ci = CT); on reducing w0/6 (from 0.01 to 0.002)
the time to the onset of the loss of stability tk increased (from 323 to 535 h).
For all values of the initial ellipticity considered, the maximum sag at the instant of reaching the
dangerous state equals wo/O 0.36, while the damage factor a 1.4 ? 10-2. Curve la in Fig. 3 shows the
time variation in the stress intensity for the case in which the temperature drop along the wall equals
A = 30?C. The initial fall in the curve is due to the relaxation of the thermal stresses arising from the
drop A. The time of operation of the can before reaching the dangerous state was greater in the presence
of a temperature drop than in the A = 0 case. Figure 4 shows the effect of a reduction in the excess exter-
nal pressure, resulting from the accumulation of gaseous fission products under the can, on the loss of
can stability (NA = 0.01, T = 670?C). The time to the onset of can stability loss increases from 323 h (for
5
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Declassified and Approved For Release 2013/03/01 : CIA-RDP10-02196R000300100001-0
, kg/cm2
2000
1800
1500
1000
6
I?
7'
I
14
500 --c
0,1 02 3 4 5 10 20 30 40 50 60 708090100 200 300 400 5006007008001000
t,h
Fig. 4. Effect of changes in temperature (curves 2, 3) and pressure (cruves 4, 5) on
the loss of can stability: 1) q = const, T = const; 2) temperature increases by 0.3?C
in 1 h; 3) temperature increases by 0.2?C in 1 h; 4) pressure falls from 130 to 0 atm
in 104 h; 5) pressure falls from 130 to 0 atm in 103 h; 6, 7) system passes to nominal
power in 0.2 and 5 h respectively.
a constant pressure of q = 130 atm) to 356 h if the pressure falls linearly from 130 to 0 atm in 104 h. The
can does not lose stability at all lithe pressure falls from 130 atm to zero in 103 h. The same figure illus-
trates the effect of a change in the temperature of the can (w0/05 = 0.01, q = 130 atm) while the reactor is
working at nominal power on the loss of stability. If the temperature rises linearly by 20?C in 100 h, the
time to the onset of stability loss falls from 323 to 132 h; for a temperature rise of 30?C in 100 h the time
falls to 107 h.
The change in the stress intensity for two transient modes (reactor passing to nominal power in 0.2
and 5 h with a constant external pressure of q = 130 atm and wo/O = 0.01) is illustrated in Fig. 4. In the
case of the rapid transient mode, creep is unable to develop, the sagging is slight, and the can fails to reach
the dangerous state. For the slow passage to nominal power creep does occur, leading to substantial sag-
ging, and the dangerous state correspondingly arises (cri =
We may thus draw the following conclusions.
1. We have found a solution to the problem of the stability of a cylindrical fuel-element can in the
creep stage, allowing for the initial ellipticity and also accounting for changes in the pressure (due to gas-
eous fission products) and temperature during service.
2. The use of the theory of strengthening and the solution of the problem in terms of increments en-
able us to discuss the stability of the can in the transient modes of reactor operation.
3. In the solution we allow for the effect of the nonuniform swelling of the steel, such as may occur
for large integrated fluxes in fast reactors, on the loss of stability of the can.
4. The results of our calculations show that the time to the onset of can stability loss is considerably
affected by the initial ellipticity of the can, by any fall in excess external pressure, and by any change of
temperature.
LITERATURE CITED
1. E. Clukler and E. Passig, Nucl. Eng. and Design, 7, No. 3, 236 (1969).
2. D. Howl, J. Brit. Nucl. Energy Soc., 4, No. 4, 337?(1965).
6
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Declassified and Approved For Release 2013/03/01 : CIA-RDP10-02196R000300100001-0
3. K. Ward, J. Brit. Nucl. Energy Soc., 4, No. 4, 354 (1965).
4. D. Howl, J. Brit. Nucl. Energy Soc., No. 2, 103 (1969).
5. N. Hoff, IASS, No. 26, 663 (1959).
6. B. Sandstrom, Trans. Roy. Inst. Technol., Stockholm, No. 115 (1957).
7. T. Wam, J. Franklin Inst., 272, No. 1, 138 (1961).
8. I. A. Birger, Izv. Akad. Nauk SSSR, Mekhanika, No. 2, 113 (1965).
9. I. A. Birger, Circular Plates and Shells of Rotation [in Russian], Oborongiz, Moscow (1961).
10. S. D. Harkness and Che-Yu-Li, Symposium on Radiation Damage in Reactor Materials, Vienna Tuns
(1969), Sm-120/F-4.
11. S. Oldberg and D. Sandusky, Trans. ANS, 12, 588 (1969).
12. U. Wolf and A. Withop, Trans. ANS, 12, 114 (1969).
13. B. F. Shopp, in: Strength and Deformation in Nonuniform Temperature Fields [Russian translation],
Gosatomizdat, Moscow (1962).
14. S. P. Timoshenko, Stability of Elastic Systems [Russian translation], Gostekhteorizdat, Moscow
(1955).
15. W. Sheely, Nucl. Sci. and Engn., 29, No. 2, 174 (1967).
16. E. Duncombe and I. Goldberg, Nucl. Applications and Technol., 9, No. 1 (1970).
7
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Declassified and Approved For Release 2013/03/01 : CIA-RDP10-02196R000300100001-0
DIFFUSIONAL AND THERMODYNAMIC PROPERTIES OF THE y-PHASE
OF THE SYSTEM URANIUM ? NIOBIUM
G. B. Fedorov, E. A. Smirnov, UDC 539.219.3:669.822
and V. N. Gusev
Alloying of uranium with refractory metals having a bcc lattice improves the mechanical and core-
rosion resistance properties of the uranium, and is one of the principal ways of coping with radiation swel-
ling.
The effect of the alloying elements on resistance to swelling can be estimated with the aid of data on
self-diffusion of the components in alloys of uranium with refractory bcc metals. A decrease in the
self-diffusion coefficients of Y-uranium as molybdenum, zirconium, and niobium are added had been re-
ported earlier [1]. But later on it was demonstrated that alloying with zirconium actually increases the
self-diffusion coefficients of uranium, and only combined alloying of uranium with both zirconium and nio-
bium (in a ratio of 1: 1 at. %) results in an appreciable loss of mobility on the part of the uranium atoms.
Bulk diffusion coefficients of uranium and niobium in uranium alloys with niobium contents of 5, 10,
20, 35, 50, 65, 80, and 90 at. %were determined in this work. These investigations were carried out over
Ig
9
-10
11
-12
-13
-10
-11
12
-13
1900
1600 1400
1200
1000 ?C
1
??,."'',,,/
,
a
,
\
i
?\&0
9
8
7
6
-...?
b
4 3 2
--.:?....1
\NZ.Z*i
\
\
\
\
9
8
765
4050 60 ,0 8010"
Fig. 1. Temperature dependences Of the
diffusion coefficients of Nb 99 (a) and U235
(b) in uranium?niobium alloys: 1) Pure
uranium; 2) 5 at. % Nb; 3) 10 at. Nb; 4)
20 at. % Nb; 5) 35 at. % Nb; 6) 50 at. % Nb; 7)
65 at. % Nb; 8) 80 at.% Nb; 9) 90 at. % Nb; 10)
pure niobium.
the temperature range from 930? to 1900? C, using the ra-
dioactive isotopes U239 and Nb95 and the method of stripping
off layers and measuring the integrated radioactivity of the
remainder of the specimens. The alloys were prepared
by arc remelting from electron-beam niobium and electro-
lytic uranium.
The specimens, as remelted, were subjected to phase
recrystallization followed by a homogenization anneal, with
the purpose of eliminating the cast structure.
The procedure followed in measuring the bulk diffusion
coefficients of uranium and niobium has been described in
an earlier article [2]. The temperature dependences of the
diffusion coefficients of uranium and niobium are cited in
Fig. 1, and the values of the diffusion parameters of the
components appear in Table 1. Alloying of uranium with
niobium brings about a considerable fall-off in the self-
diffusion coefficients of the components. For example,
when uranium is alloyed with niobium in amounts from 5 to
20 at. %, a decline in the self-diffusion coefficients of uranium
is observed in the range of investigated temperatures, to the
extent of 15 times and 50 times respectively, and this is found
to be in excellent agreement with the earlier reported findings
[1] . Alloying of the uranium has practically no effect on the en-
ergy of activation of self-diffusion when the niobium content is
as high as 20 at.%. But any further increase in the alloying ele-
ment (to 35 at. % Nb, say, or higher) brings about a significant
rise in the energy of activation of diffusion on the uranium and
the niobium.
Translated from Atomnaya Energiya, Vol. 32, No. 1, pp. 11-14, January, 1972. Original article
submitted November 23, '1970; final revision submitted April 12, 1971.
_8
C 1972 Consultants Bureau, a division of Plenum Publishing Corporation, 227 West 17th Street, New York,
N. Y. 10011. All rights reserved. This article cannot be reproduced for any purpose whatsoever without
permission of the publisher. A copy of this article is available from the publisher for $15.00.
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TABLE 1. Diffusion Parameters of Components in 'y-Phase of System Uranium?Niobium
Diffusion
Niobium content, at.%
I
parameters 0
5 10 20 j 65
80
90 100
Q. kcal/g
36,0
34
35,2
39,6
53,2
57,2
65,6
?67,0
73,0
76,7
atom
[5]
[6]
U236
D0, cm2/sec
1,1.10-4
3,2.10-5
3,5.10-6
10-5
1,25.10-4
2,5.10-4
4,0.10-3
6,3.10-4
2,5.10-3
6,5-10-6
151
[6]
Q. kcal/g
28,5
--
--
68,8
72,7
77,5
91,5
100,6
100,6
atom
[21
171
rib95
D10 ,cm2/sec
1,2.10-5
--
--
--
3,1.10-2
3,1.10-2
7,6.10-2
1,1
5,2
0,91
[2]
[7]
IT
Ig Du
Nb
A-14
Av -13
?i
Al2
Ai!
A 10
Agif.4:1dAYIA
t44 9
ATATATAT-irV
11
Nb
Zr
Zr
Nb
Nb
Nb
80
7
t2,.t2,.0
.Z AIL
AVM.
A N. IS0
AVATA %AV
AVATAvAill 50
A74 Vkk
"*A742%, Af A
%Ta WO 0140
u itSltzrirv.747,2fik Zr
Fig. 2. Isolines of coefficients and of energies of activation of diffusion of compo-
nents in the system U?Nb?Zr at 1100?C.
A familiar procedure [4] was enlisted to provide a comparison in studying the effect of niobium alloy-
ing on self-diffusion of uranium in the a-phase at temperatures in the range 550-630?C. Introduction of as
little as 2 at.% niobium lowers the bulk self-diffusion coefficient of a-uranium by about three times.
It must be borne in mind that self-diffusion in pure uranium takes place in the supersaturated vacan-
cies of the matrix [5, 8, 9]. This makes it perfectly clear that the self-diffusion parameters of uranium
and the diffusion parameters of the vacancies are closely similar. The decline in the self-diffusion coeffi-
cients of the components as uranium is alloyed with niobium unquestionably improves resistance to swelling,
inasmuch as the basic transport process at work in the volume-diffusion mechanism of the motion of voids
is the movement of vacancies from one position on the surface of the void to another through the surrounding
host matrix [10].
On the basis of the results obtained and findings published earlier [2-4, 11], isolines of the diffusion
coefficients and energies of activation were constructed at 1100?C in the case of the system uranium?nio-
bium?zirconium (Fig. 2). The concentration dependences of the diffusion characteristics in the uranium
?niobium part of the ternary diagram show satisfactory agreement with diagrams of the solidus tempera-
ture [12] and with hardness and creep diagrams [13] of alloys belonging to the system uranium?niobium
? zirconium in the y-state, which provides experimental proof of the existence of some correlation between
the diffusion characteristics of the components and refractory behavior.
This lends added interest to investigations of interdiffusion in the system uranium?niobium, since
the interdiffusion parameters characterize to an even greater extent the refractory properties of the alloys
[4]. The interdiffusion coefficients were calculated on the basis of Darken's formula [14]:
-15=(DT.T2+ Mxi)(1-1- algti
aigxi '
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(1)
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0,8
44
0,2
0
\
\
\
1 \
\
\
//
/
/
2
N
lt\
A/..,
A
3
/
/
\MMIWppp
\
\
\
\
\
Li
20
40
60
?
80 Nb
at. 04,
4
where D:1` is the diffusion coefficient of the i-th component,
measured with the aid of radioactive isotopes; xi is the
concentration of the i-th component; fi is the coefficient
of thermodynamic activity coefficient.
The thermodynamic properties of the system were
3? studied by the method of measuring the electromotive
forces (emf) of the concentration cells [3] over the tem-
perature range from 750? to 900?C using, as one of the
electrodes, uranium alloys with contents of 5, 11.7, 20,
32, 47, 72, and 87 at.%Nb. Temperature dependences of
the emf of a concentration cell of the type
U (solid) U+3-,- (KC1? NaC1)1U? Nb (alloy).
were obtained. The potential-building process in the cell
is uranium transport. The thermodynamic activities of
uranium were found from the formula
2
1
Fig. 3. Thernodynamic properties ofr the
system U? Nb at 1000?C; 1) uranium ac-
tivity; 2) niobium activity; 3) thermody-
namic multiplicative factor.
Ig LJ
-8
-10
-12
-14
16
-18
\
\
-1
\
\\I
11111111
\
r
El.ffl
Kg
\
1
11 20 40 60
at. efo Nb
Fig. 4. Concentration dependences 'of coef-
ficients and of energies of activation of inter-
diffusion in the system U? Nb at 1000?C: 1)
D [15]; 2) to [present article]; 3) Q [15]; 4)
Q [present article].
80
Nb
Qin ,
kcal/g-
atom
120
ZuEF
Ig a== 2.3/1? 15,120?E
7' T '
(2)
where Zu is the valence of the uranium; F is the Faraday
number; E is the cell emf.
As earlier [3], the valence of uranium was assigned
the value three. The activity of the niobium was calcula-
ted by graphical integration of the Gibbs? Duhem equation:
XU
1g au
1g aNb ? dxu ? ? ig au.
Nb a-Nb
(3)
Results of the calculations are plotted in Fig. 3.
Recalling that fu = au/xu, we calculated the values
100 of the thermodynamic multiplicative factor in Eq. (1)
from the concentration dependence of the emf:
a ig fu 15,120 BE
fl
=i ig d1g alj
(4)
xU
The concentration dependence of the thermodynamic
60 multiplicative factor is also plotted in Fig. 3, for 1000?C.
The negative deviations of the thermodynamic ac-
tivity of the components from ideal behavior is evidence,
40 as an examination of the thermodynamic properties of
the system uranium?niobium clearly argues, for strength-
ening of the interatomic bond in they-solid solution.
20 On the basis of Darken's equation (1), the interdif-
fusion coefficients D were determined for 1000?C (Fig.
4). The concentration dependence of the energy of ac-
tivation of interdiffusion Q was calculated under the as-
sumption that the temperature dependence of D is of the
form
(5)
The interdiffusion coefficients in the system uranium?niobium were determined by other authors [15]
using the Matano method. Concentration dependences of the energies of activation Q and of the interdiffu-
sion coefficients D converted to 1000?C values are plotted in Fig. 4. The predicted and experimentally
determined interdiffusion coefficients in the range of niobium concentrations 50-100 at.% Nb are clearly
10
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Declassified and Approved For Release 2013/03/01 : CIA-RDP10-02196R000300100001-0
satisfactory agreement in Fig. 4. A slight discrepancy in the interdiffusion coefficients in the uranium-rich
region might be due to anomalies in the uranium diffusion characteristics stemming, in our opinion, from
supersaturation of the matrix with vacancies [5, 8, 9].
The resulting concentration dependences of the energy of activation of interdiffusion are in satisfac-
tory agreement with published data [15], except for the 80-100 at.% Nb region, where the published values of
the energies of activation are seen to be much higher.
Consequently, the rise in the energy of activation and the lowering of the interdiffusion coefficients
accompanying alloying of uranium with niobium provide evidence on increased refractory strength which,
as stated earlier, must have the effect of also enhancing the resistance of the alloys to gas swelling.
LITERATURE CITED
?
1. Y. Adda and A. Kirianenko, J. Nucl. Materials, 6, 135 (1962).
2. G. B. Fedorov, E. A. Smirnov, and V. N. Gusev?, At. Energ., 27, 149 (1969).
3. G. B. Fedorov and E. A. Smirnov, At. Energ., 21, 189 (1966).-
4. G. B. Fedorov, E. A. Smirnov, and F. I. Zhomov, in: Physical Metallurgy and General Metallurgy
of Pure Metals, No. 7 [in Russian], Atomizdat, Moscow (1968), p. 166.
5. G. B. Fedorov and E. A. Smirnov, in: Physical Metallurgy and General Metallurgy of Pure Metals,
No. 6 [in Russian], Atomizdat, Moscow (1967). p. 181.
6. G. B. Fedorov et al., At. Energ., 31, 516 (1971).
7. G. B. Fedorov, F. I. Zhomov, and E. A. Smirnov, in: Physical Metallurgy and General Metallurgy
of Pure Metals, No. 8 [in Russian], Atomizdat, Moscow (1969), p. 145.
8. G. B. Fedorov, E. A. Smirnov, and F. I. Zhomov, in: Physical Metallurgy and General Metallurgy
of Pure Metals, No. 5 [in Russian], Atomizdat, Moscow (1966), p. 92.
9. G. B. Fedorov, E. A. Smirnov, and S. S. Moiseenko, in: Physical Metallurgy and General Metallur-
gy of Pure Metals, No. 7 [in Russian], Atomizdat, Moscow (1968), p. 124.
.10. P. Shewmon, Trans. Met. Soc. AIME, 230, 1134 (1964).
11. G. B. Fedorov, E. A. Smirnov, and S. M. Novikov, in: Physical Metallurgy and General Metallurgy
of Pure Metals, No. 8 [in Russian], Atomizdat, Moscow (1969), p. 41.
12. E. M. Tararaeva et al., Theoretical and Experimental Methods for Investigating Phase Diagrams of
Metallic Systems [in Russian], Nauka, Moscow (1968), p. 266.
13. V. A. Bugrov and 0. S. Ivanov, Physical Chemistry of Thorium?Uranium Alloys and Refractory
Compounds [in Russian], Nauka, Moscow (1968), p. 86 and 92.
14. L. Darken, Trans. AIME, 175, 184 (1948).
15. N. Peterson and R. Ogilvie, Trans. AIME, 227, 1083 (1963).
11
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Declassified and Approved For Release 2013/03/01 : CIA-RDP10-02196R000300100001-0
DEPOSITION OF CORROSION PRODUCTS ON THE SURFACE OF
ZIRCONIUM ALLOYS
V. V. Gerasimov, A. I. Gromova,
I. K. Morozova, V. N. Belous,
A. S. Ilyukhin, G. A. Shchapov,
L. G. Varnacheva, and G. P. Saenko
UDC 620.197.1
The purpose of this work was to obtain experimental results and to generalize the literature data on
the amount of deposits on the surface of zirconium alloys as a function of the composition of the medium,
time of exposure, and temperature of irradiation.
For the investigation we used plate samples of zirconium alloys [1) with 1% niobium; 2) with 2.5% nio-
bium; 3) system Zr?Sn? Fe; 4) system Zr?Ni? Fe; 5) system Zr?Nb? Cu] with dimensions 50 X 20 X 1
mm. For each time exposure we tested three to five parallel samples. The tests were conducted under
static and dynamic conditions. After the experiments iron was washed off the samples with a hot solution
of hydrochloric acid (1:1) and analyzed by a chemicoanalytical method. The details of the method of con-
ducting the tests were described earlier [1].
The experimental data in the literature on the deposition of corrosion products on the surface of con-
struction materials are extremely scanty. The available indications pertain to general considerations of
K, g/m2. day
0,10
0,08
go5
0,04,
go2
3 2
01
0 02 g4 06 08 40
[F81 mg/kg
Fig. 1
0 5 lp 2
?A/cm
1 1 4 6 810112 4 6 8104 2 4
K, g/m2. day
Fig. 2
Fig. 1. Rate of deposition of corrosion products K of steels on con-
struction materials under static conditions in water at 300?C (in 100h
of tests): 1) on a zirconium alloy with 2.5% niobium; 2) on a nickel al-
loy (N-1); 3) on a titanium alloy (VT-1-2).
Fig. 2. Rate of deposition of corrosion products of steels on construc-
tion materials in water at 300?C: 1) on zirconium alloy; 2) on titanium
alloy; 3) anodic polarization on alloy of zirconium with 2.5% niobium.
Translated from Atomnaya Energiya, Vol. 32, No. 1, pp. 15-19, January, 1972. Original article
submitted December 14, 1970; revision submitted February 14, 1971.
12
C 1972 Consultants Bureau, a division of Plenum Publishing Corporation, 227 West 17th Street, New York,
N. Y. 10011. All rights reserved. This article cannot be reproduced for any purpose whatsoever without
permission of the publisher. A copy of this article is available from the publisher for $15.00.
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the possible pathways of accumulation of corrosion products in the system and their subsequent deposition
on the surface of the materials. In [2, 3], in particular, a predominant deposition of corrosion products
on stainless steel in comparison with zirconium alloys is mentioned. The authors of [4] note that the cor-
rosion products of the circuit are more firmly retained on stainless steel than on zirconium alloys, attrib-
uting this phenomenon to different models of growth of the oxide film? inward and outward.
It was shown in [1] that the absolute value of the deposition of corrosion products on a zirconium al-
loy (under static conditions in water at 300?C in the absence of a heat flow) is lower than on alloys of tita-
nium and nickel. It was reported in the same work that the value of the deposits on the surface of the ma-
terials was 0.01-0.1 g/m2 day, depending on the concentration of the corrosion products in the system. The
rate of deposition of corrosion products of iron on a zirconium alloy with 2.5% niobium has a concentration
dependence similar to that of the corrosion products in water (pH = 7) under static conditions (Fig. 1). In
water with an iron concentration of 0.1-0.3 mg/kg, the rate of deposition on a zirconium alloy does not ex-
ceed 5 .10-3-7 .10-3 g/cm2. day (see Fig. 1). In-
creasing the iron concentration in the water from
0.3 to 0.7 mg/liter leads to a substantial increase in
the rate of deposition on all three materials.
TABLE 1. Rate of Deposition of Corrosion
Products of Steels on Alloys of Zirconium,
Titanium, and Nickel
Medium
on con-
tent in
solution,
mg/liter
Rate of deposition
? 103 g/m2. day
alloy of
zirconi-
iml yit1.1
',1121111-
6
3,6
32,4
32,0
on
nickel
alloy
8,4
8,48
116
?
on ti-
tanium
alloy
6,0
6,0
42,2
102
Distilled water pH
?,--:,6,6,[02] 5 0,025
mg/liter
0,12
0,27
0,72
1,0
Distilled water,
pH =10 (NH4OH),
[02] 5 0,025
mg/liter ,
0,5
7,8
16
14
Distilled water, pH
= 3 (HNO3), [02]
5 0,025 mg/liter
0,12
0,24
8
23,5
25
11,3
29
12,8
Distilled water, pH
.?-?.6,6, [02]A.-, 2-3
me /liter
0,12
6,32
9,74
6,57
The change in the composition of water may be
the cause of the change in the rate of deposition. It
is known [5, 6] that the oxygen concentration in wa-
ter and the pH value may influence not only the con-
centration of the corrosion products in the system,
but also their dispersed composition [1], and, con-
sequently, the amount of deposits of the corrosion
products on the surface of the materials. When the
pH value is increased from 6.6 to 10 (at comparatively
close values of the concentration of corrosion prod-
ucts under static conditions), the rate of deposition
on the zirconium alloy with 2.5% niobium decreases,
while it increases with increasing pH up to 3 (Table
1). Increasing the oxygen concentration in the me-
dium from 0.02 to 3 mg/kg practically does not in-
fluence the rate of deposition of corrosion products
on the zirconium alloy at the same concentration of
corrosion products in water (see Table 1). The rate
of deposition on the zirconium alloy depends substan-
tially on the time: with increasing time of exposure
the rate of deposition drops, both under static conditions
TABLE 2. Dependence of the Rate of Deposition of Corrosion Products on a Zirconium
Alloy with 2.5% Niobium on the Time
Static conditions
Dynamic conditions
medium
time of
testing, h
rate of depo
sition? 10-3
g/m2. day
Desalted deaerated water,
pH= 10 (NH4OH),
t= 300C
100
300
25,1
1,58
Desalted deaerated water,
pH t= 300?C
100
300
500
7,8
1,6
0,6
medium
time of
testing,h
rate of depo-
gs mi o2n. day
10 3,
Steam?water mixture. pH
[0d= 0,02 mg/liter (in water),
[Fe=0,02 mg/liter, *t = 285?C, rate
of flow v p.-?,?61 m/sec ?
2600
9300
1.3
1.8
Moist steam, pH rate of
flow v = 20 m/sec
1500
3000
6700
1,7
0,46
0,13
The iron concentration in the water of the circuit increased to ?2 mg/kg during the testing.
13
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TABLE 3. Influence of Irradiation on the Rate of Deposition of Corrosion Products of Iron
on Zirconium Alloys
Alloy
No.
Medium
Rate of
movement
of coolant,
m/sec
Time of
t t
esing, h
Intensity of
neutnonflux,deposition
neutrons'
/sec
Rate of
.1073
g/rnz
? day
Color of film
1, ?C
pH
[021,
mg/kg
[Fel,
mg/kg
2
220--240
-- 6.5
0,1--0,5
-- 0,1
up tol
3500
?1013
- 0,33
Black
3
280
-- 6,5
?0,5
up to0,1
--
3450 I
--
0,139
.
3.1013
0,765
Dark gray
4
280
--6,5
--0,5
up to0,1
__
3450 {
--
0,486
Black
3.1013
1,25
Light gray
330
9-10
0,02
0,05
4
5500 {--
0,56
Black
1013
0,52
.
TABLE 4. Deposition of Corrosion Prod-
ucts on Zircalloy Jackets of Fuel Cells in the
Loop of the NRX Reactor, Cooled with a Steam
?Water Mixture 6] (t = 285?C)
Concentra-
tion of cor-
rosion.prod-
uctsin cool-
ant, nig/kg
Thermal
flux on
surface,
1A//crn2
Temper-
ature o,f
jacket '
oc
Time. Deposi-,
ofizs-z
?
days /cm2
RAte ?!
A'
g/rn
clay
0,035
0,006
0.005
.0,005
0,003
0.003
100
70
68
66
62
58
295
295
550
295
' 290
400
16
65
5
5
32
32
200
150
4
5
5
4
125
23
8
10 ?
1,56
1,25 ?
and under dynamic conditions (Table 2). The increase
in the rate of deposition of corrosion products on the zir-
conium alloy in 9300 h of testing (in comparison with the
rate of deposition in 2600 h) is explained by an increased
concentration of iron in the system during the testing pe-
riod (up to ?2 mg/kg).
Irradiation in the reactor spectrum with intensity
1012-1013 neutrons/cm2? sec in the absence of a thermal
flux practically does not intensify the rate of deposition
of corrosion products on a zirconium alloy possessing a
dense black oxide film (Table 3, alloy 1). Irradiation in-
creases the rate of deposition of corrosion products on
the zirconium alloy only in the case when the color of the
film formed on the alloy changes from black to a lighter
color, and, consequently, its density changes (see Table
3, alloys 3 and 4). As is evidenced by the literature data, the rate of deposition of corrosion products on
the jackets of fuel cells, made of zircalloy, is somewhat higher under conditions of irradiation (Table 4)
than the results obtained on samples in the absence of a thermal flux (see Table 3). Regardless of the du-
ration of the testing, despite the fact that the concentration of corrosion products in the coolant in experi-
ments with fuel cells was significantly lower (0.006-0.04 mg/kg, see Table 4), in comparison with the iron
concentration in the system (0.05-0.1 mg/kg, see Table 3), the rate of deposition on the fuel cells proved
higher than on samples without a thermal flux. As is evidenced by the results of Table 4, as well as [7],
the rate of deposition of corrosion products on the zirconium alloy depends on the values of the thermal flux
(the authors do not characterize the oxide film formed on the jackets). In [8] it was indicated that although
ionizing irradiation somewhat increases the rate of deposition, it is a function of the amount of dissolved
and colloidal iron in the system. In the opinion of the authors of this work, the influence of irradiation on
the rate of deposition of corrosion products of iron on zirconium alloys must be related to the oxide films
formed on the alloy itself. Thus, thin dense oxide films can adsorb substantially less iron oxides and other
corrosion products than thick loose and more porous oxide films. If this assumption is correct, then the
amount of deposited iron should depend on the color of the oxide film and its thickness, i.e., ultimately on
the weight gain. Data on the dependence of the rate of deposition on the color of the film on alloy 1 under
conditions of irradiation with a thermal neutron flux with intensity 3.0 ?1013 neutrons/cm' ? sec (t = 280?C,
time of testing 3450 h), are presented below:
Rate of deposition ? 10-3,
Color of film g/m2. day
Black
Dark gray
Light gray
14
1.04
2.16
3.48
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TABLE 5. Dependence of the Rate of Depo- As is evidenced by the data cited, the rate of depo-
sition on the Weight Gain of Samples with sition depends on the color of the film (the lighter the film,
Oxide Films of the Same Color and, consequently, the looser it is, the higher the rate of
Color of film
Alloy
No
Rate of .
deposition Weight
10-4 g/m2 gain, mg
? day /cm2
Black (obtained with ir-
3
1,39 8
radiation)
1,39 30
2,78 20
1,39
17
2,08
95
2,78
12
2,78
17
2.78
24
4,86
11
4,86
13
Dark gray (obtained with
irradiation)
3
1
2 7,65
7,8
165
176
9
21,6
53
Light gray (obtained with
27,8
610
irradiation)
12,5
530
deposition of corrosion products). Under conditions of
irradiation on samples of a zirconium alloy possessing
black, dark gray, and gray films, the amounts of deposits
increase correspondingly. Thus, the amount of deposits
on the surface is a function of the properties of the oxide
films formed on zirconium alloys. Under conditions of
irradiation without a thermal flux, when, as a rule, a
lighter oxide film is formed on the samples, there is two
to six times as much deposition as without irradiation.
A change in the weight gain that is not accompanied
by a change in the color of the film does not lead to any
significant change in the value of the deposition (Table 5).
It may be assumed that the deposition of corrosion products
on the surface of construction materials is of an electro-
chemical nature. The rate of deposition should depend
on the potential of the zirconium alloy and the presence
of contact of the alloy with other materials.
However, experiments conducted in an electrochem-
ical autoclave on an alloy of zirconium with 2.5% niobium and on an alloy of titanium at the temperature
300?C did not confirm this hypothesis.
A sample of a zirconium or titanium alloy with area 50 cm2, to which a definite potential, maintained
potentiostatically for 100 h, was communicated, was placed in an electrochemical autoclave.
In the range of potentials from ?4 to +4 V (normal hydrogen electrode), the rate of deposition of cor-
rosion products of steel varied lathe range 0.005-0.02 g/m2. day (Fig. 2). The observable fluctuations, as
can be seen from Fig. 2, are not a function of the potential communicated to the electrode, but are explained
by a difference in the concentrations of the corrosion products in the medium (0.02-0.15 mg/kg).
Thus, on a titanium alloy in the potential interval from ?4 to +4 V (normal hydrogen electrode)* and a
stress in water at the temperature 300?C, a uniform dark phase film is formed. An analogous dependence
is observed on the zirconium alloy in the potential interval from ?1 to +1.9 V (i.e., in the case of formation
of a dark oxide film on the surface, corresponding to the passive region of the anodic polarization curve),
but then, as the potential is increased to +2 to 2.5 V, a white oxide film is formed (corresponding to the
region of superpassivation of the anodic polarization curve), and the rate of deposition of corrosion products
at the potentials in this region increases significantly (curve 1, Fig. 2).
Probably the increased rate of deposition of corrosion products on the zirconium alloy in this case
should be explained by a change in the sorption properties of the film formed on the surface of the alloy,
and not by the value of the set potential. The process of deposition of corrosion products on the surface of
construction materials is not of an electrochemical nature.
Thus, evidently the rate of deposition of corrosion products (iron oxides) on zirconium alloys is a
function chiefly of three components: the iron concentration in the coolant, the thermal flux, and the prop-
erties of the films formed on the alloy. Thus, the dependence of the rate of deposition of corrosion prod-
ucts of iron on an alloy of zirconium with 2.5% niobium on the concentration of corrosion products in the
medium found in this work convincingly shows that the iron concentration in the water of operating nuclear
installations, from the standpoint of the formation of possible deposits on the surface of construction ma-
terials, should be less than 0.5 mg/kg.
The results obtained permit us to assume that the deposits of corrosion products should be negligible
when the water system is observed. The authors of [9], who investigated the deposition on fuel cells, ar-
rived at an analogous conclusion.
*A potential of ?4 V was communicated to one of the samples in the autoclave, and a potential of +4V to the
other.
15
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Thus, the rate of deposition of corrosion products of iron on zirconium alloys under static and dy-
namic conditions in water at 300?C, including conditions of irradiation, was evaluated.
On the basis of the aforementioned we can draw the following conclusions.
1. If the zirconium alloy is corrosion-resistant and a uniform black oxide film is formed on its sur-
face, then:
1) with increasing iron concentration in the system (more than 0.5 mg/kg) the rate of deposition of
corrosion products of iron on the alloy increases significantly;
2) the rate of deposition of corrosion products of iron on zirconium alloys decreases with time and
when the pH is raised from 7 to 10;
3) increasing the oxygen concentration in the medium and irradiation in the reactor spectrum with in-
tensity up to 103 neutrons/cm' ? sec practically does not increase the rate of deposition of corrosion products
of iron on a zirconium alloy in the absence of a thermal flux;
4) the rate of deposition of corrosion products of iron on the zirconium alloys does not depend on the
potential in the passive region.
2. The rate of deposition of corrosion products of iron depends substantially on the quality of the ox-
ide film formed on the zirconium alloy. Thus, the rate of deposition of corrosion products on samples with
a dense black oxide film is lower than on samples possessing a lose light colored oxide film.
LITERATURE CITED
1. A. I. Gromova et al., Teploenergetika, No. 6, 54 (1970).
2. H. Hami et al., NSI-Tr-61 (1966).
3. W. Pearl, M. Fitzsimmons, and M. Siegler, Trans. Amer. Nucl. Soc., 4, No. 2, 349 (1961).
4. J. Wanklyn and P. Fones, J. Nucl. Mater., 6, No. 3, 291 (1962).
5. I. K. Morozova et al., Teploenergetika, No.-10, 72 (1970).
6. Garigliano Nuclear Power Plant Operation Report for 2nd Quarter of 1967 (TID-24131).
7. A. B. Andreeva et al., in: Transactions of the Symposium of the Council of Economic Mutual Aid,
"State and prospects of the development of atomic electric power plants with water-moderated water-
cooled reactors" (Moscow, 1968) [in Russian], Vol. 2, IAE, Moscow (1968), p. 357.
8. J. Simon et al., WAPD-CDA(AD)-446 (1959).
9. L. Joseph, Nucleonics, 24, No. 3, 51 (1966).
16
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Declassified and Approved For Release 2013/03/01 : CIA-RDP10-02196R000300100001-0
MECHANISM OF REDUCTION OF URANIUM HEXAFLUORIDE
BY HYDROGEN
Yu. N. Tumanov and N. P. Galkin UDC 546.6:541.121
The reduction of uranium hexafluoride by hydrogen is usually represented [1-5] by the equation of the
exothermic reaction
(UF6)gm+(112)gas(UF4), 2(I-IFlgas- 69.8 kcal.
(1)
Although the thermodynamic characteristics of this reaction indicate that the thermodynamics do not
limit the reduction of uranium hexafluoride by hydrogen [6], in practice this process begins only at 498-
523?K, and is slow and incomplete even at 873?K [7].
The difficulty of reducing 1SF6 by hydrogen is usually attributed [1-7] to the high activation energy; to
reduce this, one usually employs atomic hydrogen, generated by a gas-plasma reactionrof hydrogen with
fluorine, by an electric discharge [8], or by dissociation of ammonia [1].
The experimental activation energy of reaction (1) is 8.15 kcal/mole [5]. Since the activation energies
of the elementary stages may differ markedly from that of the overall reaction, the relatively low activation
energy of reaction (1) indicates a complex and stagewise re-
duction mechanism and the presence of a limiting state. Our
paper deals with these aspects.
Reaction (1) may be represented to a first approxima-
48 tion as consisting of two stages:
0
0
r21
1,0
X 1
0,6
0,4
300
500 700
Temperature, ?K
900
Fig. 1. Degree of hydrogen reduction of
UF6 versus absolute temperature: 1) cal-
culated curve at a molar ratio 1SF6 : 112
= 1:1; 2) calculated curve at a molar ra-
tio UF6: 112 = 1: 5; 3) experimental curve
[2] at a molar ratio 1SF6: 112 = 1:5, con-
tact time 30 min.
(tiFe)gas-1- (II2)gas..= (UF4)gas ? 2(H.F) g as+ 7'4 * kcal, (2)
(UF4)gas= (UF4)s ? 73.1 t kcal.
Although the first stage (2) is endothermic, it is not
limited by thermodynamics (Table 1).
The high exoeffect of condensation of 1SF4 is responsible
for the overall exothermic effect of reaction (1).
The fact that when 1SF6 is reduced by hydrogen under
fairly mild conditions both the tetrafluoride and pentafluoride
are present, may be some indication$ of the stagewise reduc-
tion mechanism of 1SF6, according to which reaction (2) takes
place in two stages:
(3)
*We took the following value of the heats of formation of gas-
eous fluorides at T =298?K and p =1 atm: AllijF6 = -510, 77
? 0.45 kcal/mole [9], AHijF5=? 449 ? 5 kcal/mole [7, 10], AllijF4
=- 374.9 ? 5 kcal /mole [11, 12], AT-T
--HF 64.2 ? 0.3 kcal/mole
[13].
tThe heat of sublimation of UF4 was assessed from data of
Akishin et al. [12].
$UF5 may be obtained by the reaction 1SF4 + 1SF6-' 2 UF6.
Translated from Atomnaya Energiya, Vol. 32, No. 1, pp. 21-25, January, 1972. Original article
submitted January 6, 1971.
0 1972 Consultants Bureau, a division of Plenum Publishing Corporation, 227 West 17th Street, New York,
N. Y. 10011. All rights reserved. This article cannot be reproduced for any purpose whatsoever without
permission of the publisher. A copy of this article is available from the publisher for $15.00.
17
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Declassified and Approved For Release 2013/03/01 : CIA-RDP10-02196R000300100001-0
TABLE 1. Results of Calculation of the Equilibrium of Reaction (2)
Temperature, ?K
298
400
600
1000
1400
1800
2200
2000
Equilibrium constant
Ke , atm
1,26.104
2,95.105
6,46.106
7,17.107
7,24.107
7,41.107
7,58.107
7,76.107
Degree of conversion
nf TIF-
0,988
0,998
? 1
? 1
? 1
? 1
?.? 1
? 1
*.Thethermodynamic properiies of uranium fluorides are given in /14/.
TABLE 2. Results of Calculation of the
Equilibrium of Stagewise Reaction of Re-
duction of UF6 by Hydrogen
T, ?K
Reaction (4)
Reaction (5)
!x ? degree
Ke' atml of conver-
sion of UF?
Ix
Ke' atmi
? degree
of conver-
ion of UF5
298
4.17.106
? 1
3,02.10-3
0,05
400
1,26.06
? 1
2.:14? 10-1
0,345
500
5,80?105
? ? 1
3,98.100
0,745
600
3, 82.105
? 1
1,95.101
0,893
1000
9,i2.l0
i
4,58.102
0,08
1400
6.46.104
? 1
1,02.100
0,99
1800
2.89.104
? 1
2.63.103
0,095
2200
2.0.104
? 1
3.8.103
0,999
2600
3000
1,55.104
1,26.104
? 1
? 1
5.103
6,46.100
? 1
? 1
(UFO)gas+ .(H2)gas= (UF5)gas-j,- (11F)gas? 2.4 kcal (4)
(UF5)gas+ (H2)gas = (UF4)gas+ (HF) g as+ 9.8 kcal (5)
The reduction of UF6 to the pentafluoride is not
limited by thermodynamics, but if we disregard conden-
sation of UF4, reduction of the pentafluoride to the tetra-
fluoride takes place quantitatively only above 1000?K
(Table 2). Therefore if condensation of UF4 in the reac-
tion zone is retarded in some way, we cannot assert that
the equilibrium of the reduction of UF6 by hydrogen to
UF4 is wholly displaced to the right.
Although the assumption of stagewise reduction Of
UF6 agrees qualitatively with the experimental data, Eqs.
(4) and (5) do not reveal enough about the mechanism of
(1). Furthermore, the experimental curve of the reduction of UF6 to UF4 versus temperature [6] lies far
below the calculated data (Fig. 1), which is hardly possible under the conditions of continuous displacement
of equilibrium of UF4 condensation.
Since all practical methods of hydrogen reduction of UF6 involve the appearance of atomic hydrogen in
some way or another, we mus, examine the ways in which hydrogen atoms are generated in the system UF6
?H2. The role of atomic hydrogen is usually reduced [1-4] to evolution of the heat of recombination in the
reaction zone by the reaction
-= H2-104.2 kcal.
However, markedly exothermic reactions of direct reduction of UF6 are just as possible:
(lHogas-H (I-1)gas? (UF5)gas (11F)g2,s ? 54,5 kcal,
(UF5)gas (H)gas=- (UF)gas -I- (HF) gas? 42,2 kcal.
(6)
(7)
(8)
How can hydrogen atoms be generated during reduction of UF6 in a reactor with a "hot wall"? Three
schemes of hydrogen atom generation in the system UF6?H2 may be visualized.
Scheme 1 ? via dissociation of H2 molecules:
= 21-1 -[ 104.2 kcal. (9)
Scheme 2? via dissociation of UF6 molecules:
(Mgas= (UFs)gas -I- (F)gas-I 80.77 kcal ,
(F)gas-1- (H2) gas-- (IIF)gas; - (II)gas? 31.1 kcal (11)
Scheme 3 ? via formation of monoradicals during bimolecular collision by the Semenov scheme [15]:
(10)
(U I"5 ? F)gas-:- (II H II) gas (UFs)gas+ (II ?)gas- (II)gas+ 49.67 kcal , (12)
where UF5, fluorine, and hydrogen are monoraclicals.
All the schemes include markedly endOthermic stages, but scheme 3 is thermodynamically more ad-
vantageous than schemes (1) and (2) (Table 3).
18
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TABLE 3. Thermodynamic Characteristics of Reactions Leading to the Appearance of
Hydrogen Atoms in the System UF6-H2
T, ?K
Scheme
Scheme
Scheme
K atm x-degree of
K, dissociation
of H2
Ke , atm
to
x-degree of
dissociation Ke atm
of IJFE?
x-degree of
conversion
of Hz
Ke atm
x-degree of
, ,
conversion
12 of UF6
298 5,92,10-72 1,22.10-36 ? 10-52
600 2,12-10-33 2,3.10-17 10-23
1000 5,1.10-18 1,13-10-9 3,02.10-"
1100 2,34.10-11 2,42-10-6 3,16.10-6
1800 1,27.10-7 1,78.10-4 1.855.10-
2200 3,14.10-5 2,8-10-3 1,01.101
2600 1,46.10-3 1,91.10-2 1,596
3000 2,47-10-2 7,83-10-2. 1.23-101
10-20
3,17.10-12
5,62-10-6
1,78.10-3
5.10-2
3,1-10-1
7.7.10-1
9,6.10-1
8,52.1m1
2,34.106
2,57.104 ?
2,09.103
4,28-102
1,37.102-
6,02.101
7,98.10-30 2,95-10-10
8,92.10-12 2,6.10-4
1,92.10-4 6,5.10-2
1,44..10-1 4,4.10-1
4.82.10 7,9-10'1
5.2.101
2,69-102 9,77.10-1
8,92.102 9,87.10-1
Therefore the following mechanism of reduction of UF6 by hydrogen may be presented
F5 --- 1")gas (H--H)gas (UF5)gas 1,- - F)gas+ (H) gas ,
F6) gas+ (1I)gas -> (UF4) gas+ (1-1F) gas ,
(UF6)gas+ (H)gas (11F6) gas+ (HF) gas ,
2(II)gas --> (IlOgas,
(UF4) gas -? (UF4)0
Furthermore, a certain part is also played by the reactions:
1"4)gas-1- (UF6)gas = 2(UF6)gas - 12. 43 kcal, (13)
(UF4) s (UF6)gas ii (-02F9)s (14)
3(liF4).s (UFO gas (1.14F17) s (15)
etc.
An attempt must be made to assess the kinetic constants of the elementary stages included in schemes
1-3.
Let us first assess the rates of establishment of dissociation equilibria of UF6 and H2, because they
are the limiting values in schemes 1 and 2. If we take as the rate the value 1/T (sec-1), where T is the time
required for the partial pressures of hydrogen and fluorine to reach half the equilibrial values [1], then for
bimolecular reaction (9), which must be written as
at a pressure p
116
M iE 2H+ M, (16)
106
p?
LTF6 = 0.5 atm, we get
2.23.1012
?1 = I1PmkG Ke9P112 1,2 Ke 1/7
(17)
To assess the value of 1/TF we must find the velocity constant of reaction (10). This was calculated
from the two independent equations:
-1
1
k 10 f exp - ?1Ein E Eo ?
-1
k7' AS*
kio exp R ) exp E,-RT
R7' '
(18)
(19)
where X0 is the velocity constant of monomolecular decomposition of excited UF6 molecules; f is the number
of oscillators involved in the reaction; E0 is the activation energy of the elementary stage; R, k, and h are
respectively the gas constant, the Boltzmann constant, and the Planck constant; and AS* is the change in
entropy.
The results of calculations by Eqs. (18) and (19) agree closely (Fig. 2) if we put f = 3, AS* = S
-UF5
-=
SLTF6' E0 EUF5-F = 80.72 kcal [14],
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6
4
2
-2
z 4
n 6
0
8
o 10
-18 0 0,2 44 0,6 0,8 40 1,2 1,4
Reciprocals of temperature /0 2/ 711(
Fig. 2. Logarithm of velocity constant of the reaction UF6-.? UF5
+ F versus the reciprocals of temperature. 0) 18; X) 19.
1,6
For the value of liTF we obtained the expression
? = 2k' (K. )112
10 eio ?
(20)
The results of the calculation (Table 4) show that dissociation equilibrium of UF6 is reached in the
range 1800-600?K more rapidly than for H2 by a factor of 0.5-4. The velocity constant of reaction (11)
in the range 1000-4000?K may be assessed by the equation [16]
?'7 76 .10"T? 2500-69exp RT ) .
(21)
Beginning at T 1800?K the role of dissociation of UF6 during its conversion to the tetrafluoride be-
comes appreciable and, with a further increase in temperature, scheme 2 becomes predominant. However,
at temperatures in the range 1000-1500?K, reduction of UF6 apparently Proceeds via scheme 3.
The activation energy of reaction (12) may be assessed by the equation [15]
Eact= EuFt, + En?H? EH? ;
(22)
it is 49.67 kcal. For reactions of saturated molecules of type (12), the preexponential factor is equal (with
high probability) to the value 1013 cm3 ? mo1e-1 ? sec-1 [15], so that
-1 -1
ki2 10,3 exp 49 600 ) 3.
RT cm mole . sec (23)
To calculate the velocity constants of reactions (7) and (8), we may propose the equation
0.28E ?F
RT ? - -1
1
k7_8 10'3 exp ) cm3 mole (24)
. sec
An equation of this type was used for calculating the kinetic constants of the analogous reduction of
sulfur hexafluoride:
Calculations by the equations
20
4'6+ SF, ?HF. (25)
k ( 30 000 4- 5000 )
? ==- 2.10" exp , [16]
RT
1c25= 1013 exp 27;7,00 )
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Declassified and Approved For Release 2013/03/01 : CIA-RDP10-02196R000300100001-0
TABLE 4. Rate of Establishment of Dissociation Equilibria of Hydro-
gen and Uranium Hexafluoride
T, ?K
I-12 218
UF6 U F 6 F
Ke atm
-1
1/ r , sec
K atm T F, sec -1
600
2;12.10-33
2,85.10-19
10-23
1,18.10-9
1000
5,1.10-19
5,04-10-3
3,02.10-11
1,43.10-1
1400
2,34.10-11
5,51.109
3,16.10-9
2,4.101
1800
1,27.10-7
2,54.102
1,855.10-3
4,0.102
give results displaying satisfactory mutual agreement. Therefore
/c8= 10" exp ( 22600) cm3 ? mo1e-1 ? sec-1, (26)
RT
26100 \ cm3 ,
k7 ,- 1013 exp ( mole-1 ? sec-1. (27)
RT I
The value of k6 for the reaction 2H +H2 '-'" 112 + 112 in the range 290-7000?K may be calculated by the
equation [16]
k6 = 6.03 .1018T-1. ? 9 cn.16' mole-2 ? sec-l? (28)
In accordance with the Frenkel' equation [17], the rate of removal of supersaturation of uranium te-
trafluoride by formation of nuclei of the condensed phase in UF4 vapor has the form:
?7,2.103o, T5/ (1g P/
1.13- 10,o2p g* sec
(29)
T3 (1g
uF4 exp ( m )1/2 i ,
pl:a 2 -
where u' is the surface tension; p and pc? are respectively the vapor pressure and the equilibrium pressure;
and g* and m are respectively the critical size of the nucleus and its mass.
For the velocity constant of k13, by analogy with k7 and k8 we may write the equation
0.28Eup _F
ki3 = 10" exp 2, 6
RT ) ? 10" exp ..00) cm3.
mo1e-1 ? sec-1. (30)
RT
The role of reactions (14) and (15) cannot be determined, but it is apparently fairly great after the
appearance of condensed uranium tetrafluoride in the system.
The results may be summarized as follows.
1. Reduction of uranium hexafluoride by hydrogen to the tetrafluoride is an endothermic reaction;
the exothermic effect of overall reaction (1) is due to condensation of UF4 and it cannot always be used for
activation of UF6 reduction.
2. The appearance of hydrogen atoms in the system UF6-112 activates reduction not only by recom-
bination of hydrogen molecules, but also as a result of markedly endothermic reduction of UF6 and UF5
molecules by atomic hydrogen.
3. Owing to the high thermodynamic stability of 112 and UF6 molecules, at least up to 1400?K, the
primary stage of reduction of UF6 is the endothermic reaction of formation of monoradicals of hydrogen and
UF5, accompanied by exothermic reduction of UF5 and UF6 by atomic hydrogen.
4. Above 1400?K an important part is played by dissociation of UF6 molecules, accompanied by the
exothermic reaction of atomic fluorine with hydrogen molecules to form atomic hydrogen.
5. The concentration of UF4 molecules in the gas phase decreases continuously to the equilibrial con-
centration owing to formation of nuclei of a condensed phase, which at a = 5 .103 erg ? cm-2 include from 4
to 67 UF4 molecules in the range 400-1200?K. Under these conditions the rate of condensation of UF4 is
104 sec-i. Condensation of UF4 molecules may be accompanied by decomposition of UF6 molecules, giving
two UF5 molecules.
6. The appearance of condensed tetrafluoride in the system UF6-112 may accelerate decomposition
of UF6 with formation of UF5 and "intermediate" uranium fluorides.
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7. The experimental activation energy of hydrogen reduction of UF6, 8.15 kcal/mole, is not the true
activation energy. The activation energy of the limiting stage of reduction of UF6 is ??? 49.67kcal/mole. The
appearance of condensed uranium pentafluoride, atomic hydrogen, and condensed tetrafluoride reduces the
activation energy of reduction of the hexafluoride.
LITERATURE CITED
1. C. Harrington and A. Ruele, Technology of Uranium Manufacture [Russian translation], Gosatomiz-
dat, Moscow (1961), p. 108.
2. Chemistry and Technology of Uranium Fluorides (N. P. Galkin, editor) [in Russian], Atomizdat,
Moscow (1961), p. 226.
3. Ya. M. Sterlin, Metallurgy of Uranium [in Russian], Gosatomizdat, Moscow (1962), p. 402.
4. Technology of Uranium (N. P. Galkin and B. N. Sudarikov, editors) [in Russian], Atomizdat, Mos-
cow (1964), p. 327.
5. N. B. Sudarikov and E. G. Rakov, Processes and Equipment of Uranium Manufacture [in Russian],
Mashinostroenie, Moscow (1969), p. 164.
6. J. Dawson, D. Ingram, and L. Bireumshaio, J. Chem. Soc., 1421 (1950).
7. J. Katz and E. Rabinovich, Chemistry of Uranium, Vol. 1 [Russian translation], IL, Moscow (1954),
p. 355.
8. W. Sham, R. Spenceley, and F. Feetzel, US Patent cl. 23-14.5, N 2, 898, 187 (1959).
9. J. Settle, H. Feder, and W. Hubbard, J. Phys. Chem., 67, 1892 (1963).
10. A. Wolf, J. Posey, and K. Rapp, Inorg. Chem., 4, 751 (1965).
11. Yu. V. Gagarinskii and L. A. Khripin, Uranium 'ITetrafluoride [in Russian], Atomizdat, Moscow
(1966), p. 90.
12. P. A. Akishin and Yu. S. Khodeev, Zh. Fiz. Khim., 35, 1169 (1961).
13. Thermodynamic Properties of Individual Substances (V. P. Glushko, editor) [in Russian], Izd-vo AN
SSSR, Moscow (1962).
14. N. P. Galkin, Yu. N. Tumanov, and Yu. P. Butylkin, Thermodynamic Properties of Inorganic Fluo-
rides [in Russian], Atomizdat, Moscow (1972).
15. V. N. Kondrat'ev, Kinetics of Chemical Gaseous Reactions [in Russian], Izd-vo AN SSSR, Moscow
(1958).
16. V. N. Kondrat'ev, Velocity Constants of Gas-Phase Reactions [hi Russian], Nauka, Moscow (1970).
17. Ya. I. Frenkel', Selected Works, Vol. 3 [in Russian], Izd-vo AN SSSR, Moscow- Leningrad (1959).
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CALCULATION OF REGULAR SYSTEMS OF NEUTRON ABSORBERS
Ya. V. Shevelev and I. L. Chikhladze UDC 621.039.51
The most frequently used method of calculating systems of absorbers is based on a solution of the
criticality equations [1-3]. It is not easy to calculate the effect of absorbers by this method, however, since
the neutron distribution must be investigated simultaneously both over the reactor as a whole and close to
each individual absorber. The difficulties are increased if several energy groups are taken into account.
We propose a two or three stage procedure for calculating systems of absorbers occupying a small
fraction of the reactor volume. First the actual reactor is replaced by an equivalent reactor in which the
neutron distribution over the region occupied by the absorbers is a smooth function of coordinates, possibly
having discontinuities in magnitude and slope at some boundary. At large distances from this region the
neutron distribution coincides with the true distribution. The equivalent reactor is critical when the actual
reactor is critical. The criticality condition for the equivalent reactor and the smooth neutron distribution
in it are then found. If necessary the true neutron distribution over the region occupied by the absorbers
is calculated. The calculation as a whole is greatly simplified, and the last stage is not always necessary.
Statement of the Problem. Let us consider the simplest problem of this class. Suppose a plane strip
of material which is a weak neutron absorber contains cylindrical rods which absorb thermal neutrons only
(an unessential restriction). The strip is placed in the reactor core or reflector and is periodic in the y
direction (Fig. 1). A cell contains n rods positioned arbitrarily at the points ri, where i = 1, 2.....n: the
rods are numbered in order of increasing xi. The coordinates of the remaining rods are given by
r,?,= rr+ ma, where m = ?o0. ..., ?1, 0, 1, ... 00. (1)
It is assumed that pi/L xn;
a
y) dy, x < xi.
0
The true flux 43 outside the absorbers is given by
(2)
(3)
where q is the density of thermal neutron sources. We assume the strip is so thin that q is the same on its
lower and upper surfaces. For .:13T (x) we obtain the equation
d.r2
(4)
Translated from Atomnaya Energiya, Vol. 32, No. 1, pp. 27-32, January, 1972. Original article
submitted February 16, 1971.
0 1972 Consultants Bureau, a division of Plenum Publishing Corporation, 227 West 17th Street, New York,
N. Y. 10011. All rights reserved. This article cannot be reproduced for any purpose whatsoever without
permission of the publisher. A copy of this article is available from the publisher for $15.00.
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---4-----.
Fig. 1. Cell with n rods spaced with pitch a
The problem can be solved by assuming that q varies or
that the properties of the media and the source strengths
inside the strip and on opposite sides of it are different, but
we limit ourselves to the simplest case when
D D_; g q_-= q+; L+=- L_.
At large distances from the strip clo coincides either
with 434. (above) or with (13_ (for x < 0). We extrapolate the
functions cl3+ and c13_ by Eq. (4) inside the strip to some ar-
bitrary boundary separating the regions, e.g., to the line
x = 0. We obtain the values of the functions &Ho and 4._o
and their derivatives dc13.4_0/dx and d(1)_0/dx on this boundary;
the values of 040 and 01)_0 may differ, and the values of the derivatives will also differ. The specific prop-
erties of the strip must appear in a definite relation among the four quantities mentioned and also possibly
q/Z which appears in Eq. (3). Since the equations are linear and Eq. (3) is second order, these relations can
be written in the form
m(+1)0+0 Ap2),I10_0 ,r?na N
iv ?4- dcpdx+? (1)a d&0+ K'> -f--- =
dx
m(42)0+0+ jp2)0_0 Na da'd;to N(2>a +.K12) =0.
By using Eqs. (4) and (5) the solution of Eq. (3) in the lower part can be related to the solution above
the strip. Thus the dimensionless coefficients M2, A2, and K1,2 completely determine those properties
of the strip which affect the thermal neutron flux far from it. In solving the criticality problem these equa-
tions are used instead of the standard joining equations for thermal neutrons. In a similar way equations
of the type of (5) are obtained for neutrons undergoing moderation. After the criticality condition has been
found it is possible to return to the equations determining the actual rather than the smoothed out fluxes,
and to construct them.
(5)
We determine the coefficients M, N, and K.
Solution of the Problem for Constant Neutron Flux at the Surface of the Absorber. The problem is
simpler to solve when the absorbers are rather widely separated (pi/a ?1).
We write the solution of Eq. (3) as the sum of a regular part cbreg and singular solutions symmetric
with respect to each rod
71 00
c1:0 (r) CD reg(x) + E ci E K, (1 r -1"11
1=1 ? co
The function (1) r e g(x) satisfies Eq. (3) over the whole volume. The singular terms satisfy Eq. (3)with-
out the right hand side. Since Eq. (3) does not hold close to the surface of an absorber, effective boundary
conditions are set [4]:
(6)
where
acl) =0(11V+Pii) ; yi 7 (Pj
Irr?ril=pi
By substituting (6) into (7) we obtain the equation for the coefficients
Civi+ civt; + oreg(x.,)+ 4 1C, -0,
k
[ 2 K0 ( I ?ri?ma ) ? v ri ? a )
a ' L a '
771=--- co
v (Lpi) (.2.L ' ? JI.)
pi L L, a L ?
The term 7L/A in Eqs. (8) and (9) is separated out because, as is shown in the Appendix, if a/L 0 the
quantities remain finite. The coefficients v1 are calculated in the Appendix. By using (8) the Ci can
be expressed in terms of cbreg which by Eq. (3) is given by
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(8)
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Fig. 2. Smoothed out extrapola-
ted neutron flux for vi < 0; absor-
bers are placed in the plane of sym-
metry. The shaded region is "dis-
placed."
It is known [5], that
and therefore
where
reg o (x) = 4)rego ch Tx + L d d.c
reg o sh ' Lx " (1 cliL-r-)
' l' L ' (11)
where ''reg o and d4'reg0/dx are the values of this function and its
derivative on the arbitrary boundary x = 0. Thus the values of the
Ci are expressed linearly in terms of q/Z and the two so far un-
determined constants (I, reg o and dl)reg okbc.
Let us calculate the functions (I)?(x). We first average the
sum in (6)
E Ko
1r ) 4 E Ko
.0 ?,=_00 0
ix+ ? ri ?Oa .,a) 1) . 4
? L
After the change of variable m + = t we obtain
E? ( )
dt =L , ?Or\
2
\
L2 1 dt.
711--,-0. ? la
?
K0 (Irp2+ q2) dq =
1 00 22?X,
C K0 (11.?ri?Za?a11)dE =" e L
0 1a=-00
Thus according to (3) and (13)
GDT = (Dreg 60,,
-so+ E ci e L ; = E aL
e
a
(12)
(13)
(14)
(15)
Each of the functions oI satisfies Eq. (14) without the right hand side and (Dreg satisfies it withzthe
right hand side. Therefore the extrapolations of the functions dIT are obvious.
(I)-0 ? ' ? (1) E ciexi/L' +0 ? (nreg o xa E Ce;
77.
, N-1 - /L da)-0 d(1) rego , xa -x-/L
(1)..0= (Drego -i - L Cie ; dx = dx a L ?
We rewrite Eq. (8) by using (11):
cid)reg0 x q Xi
CiVi E , E Oregoch L sh (1 ? Tr-) =0.
(16)
(17)
The unknowns C-,
-rego, and drego/th can be eliminated from (16) and (17) to yield two equations in (40,
dt. (Aix, and q/Z since the number of equations in these systems is n + 4 and the number of unknowns elim-
inated is n + 2. Therefore Eqs. (16) and (17) lead to relations of the type of (5), i.e., to explicit expres-
sions for the required coefficients.
Specific Types of Lattices and Analysis of Results. Arbitrary regular lattices can be analyzed by
using Eqs. (16) and (17) and formulas (A.6), (A.7), and (A.10). In the simples case when n = 1 it is con-
venient to set the arbitrary boundary along the line of centers of the absorbers. Then according to (16)
and from (17)
(D+o 0-0 --- (=Dreg o tL C,;
do+o d(I)reg o
dx dx
C,
d(Dreg o do+,
(18)
dx dx
+ (Dreg o = 0.
(19) '
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TABLE 1. Types of Absorber Lattices Considered and Results of Two-Group Calculations
of Reflector Savings. The Core and Reflector Parameters Correspond to the IGR Reactor
[6]
Lattice structure
?,0 ,'
d
----0,i4 .L1,'
ft It
v *
23,4
27,0
29.0
20,3
21,9
23,7
17,1
17,7
18.9
Vi
Y2
T3
i S-/
1
VA I
1.--
17,0
20,5
22,3
15,7
10,8
18,0
13,8
14,2
14,9
-,
.1
T2
ri
Y
15,0
17,1
18,7
13,3
14,1
15,0
11,9
12,9
13,9
Yi
72
T3
13,3
14,9
16,1
12,4
1.3,0
13,i; t
11,4
11,6
12,6
10
T2
l'3
? . .T
.
? 41114. el
X
" 72 =1.3; y3 = 1.616 corresponds to IGR rods. In all three cases a= 14 mm.
t Data for lattice used in IGR.
By eliminating the unknowns Ci,reg?, an and dcDrego/dx from (18) d (19) we obtain the two equations
'D
(I)+o = (D-o ;
a dcb+0 ,
CLia dx at
By comparing (20) and (5) we find
/1/(:" - /1/(1); Ar(l)_]r(i)K(i)0.
2V(2)-- Ar(2); /1;14)-- a 2174!")*
vi ?
(20)
m(2) Ar); K(2) _ 0.
Equations (20) are similar to the boundary conditions which describe absorption in a thin foil [4]. Thus
an array of cylinders can be regarded as equivalent to an absorbing layer for which the product of the thick-
ness A and the macroscopic absorption cross section Ec is
(A/c)equ- ''p phi a
a
3vla 3 ; 1.
2,t 2ap
(21)
However the analogy with a thin absorber does not completely represent the situation. The quantity
v1 can be negative for a/(2p) < ir as is confirmed by more accurate calculations. If a zero value of vi in
Eq. (20) can be interpreted as the blackness of the equivalent absorbing layer becoming infinite* then a
negative value of vi can only be interpreted as the result of the displacement of the medium by absorbers
of finite thickness (Fig. 2). It is clear that the width of the displacement region must not exceed the diam-
eter of the cylinders. Fortunately this physical requirement is satisfied even in the crude approximation
considered.
By using Eqs. (16) and (17) in the two-group approximation and taking the usual continuity conditions
at boundaries for neutrons undergoing moderation, reflector savings were calculated for various lattices of
absorbers placed close to the core in the reflector of the IGR reactor [6]. The results of the calculations
are shown in Table 1 and in the corresponding graphs of Figs. 3 and 4. These calculations permitted the
selection of a five-rod absorber lattice for the lower reflector of the IGR reactor. The calculated results
are in satisfactory agreement with experiment.
*Actually it is well known that the flux cl) is not zero even on the boundary of an absolutely black absorber.
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6, mm
28 ?
2 7 ?
25 ?
25 ?
24 ?
23-
22 ?
21 ?
20-
19 ?
18 ?
17 ?
16
15
14
13 ?
12-
11
10
? 20; 0,9843
I I 1 1 i
1 2 3
If 5
n
6, mm
28 ?
27 ?
26 ?
25 ?
24-
23-
22-
21 ?
20 ?
19 ?
18 ?
17 ?
f6 ?
15 ?
14-
13 ?
12
11
10
10 15 20 25
d, mm
Fig. 3 Fig. 4
Fig. 3. Reflector savings 6 as a function of the number of absorbing rods n in a
cell for rods of various diameters and various values of 7.
Fig. 4. Reflector savings 6 as a function of the diameter of an absorbing rod dfor
various numbers of adsorbing rods n in a cell and various values of y. Values of
are listed in Table 1.
APPENDIX
Calculation of coefficients v1vj, and v. According to (9)
(ri ?.r; a ?
L) ;
a ( a
)=
[ K0 ( Vx2 (j/, mar'
Following [4] the Poisson summation formula is used:
y (27(m) E
'111=-0c v .= co CO
Using (A.2) and (A.1) we obtain
ar,
a
(A.1)
(p (K) e-ivk dK. (A .2)
(
I \ x y +) 1 N Z?I C x2_4_ y_4221 2 ( 27t
2n 1
Making the change of variable t = (y + ak/27r)/L and using the formula [5]
p2+,
Ko(Vp2+t2)= e "
0
we obtain
where
dk.
21t
-i_STVt-t2 X2 oo
e"* _du e
u 4?udt, ?
00 Li
, L2
?i2av ?L t--t2
?s2?i2xtv ?L us ?4n2v- ? u
2 1,/ e ds = 2 V Tut e at ?
?oo ?co
(A.3)
(A.4)
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Thus
.0 v e2nu .0
:EL iv
E a .c e
a2 4/.20 du
a a a
or
iv2a 2- (1+4112,4 L-i2) -x-1
00
a L
al, L e r 41
j2
a a i L'2 2 17 r-c 1 e 2 dt
, 1+ 40,,2 b
a2
V=---00
and further
00 L q
i2.7tv IL- _If' -,1 Ili?(23-tv -1=-)2
?a -7 P = 7;.- E? a
v=-00 V1H-(2av --.a ) - e
Separating out the term with v = 0 we obtain
2vixi -V1+
? ivo:t1J-
03c-:-y ; a) ,..= 21L (e---E-Isi , Re e a 1
1) i
V a
( 9fr,vL')
Equation (A.6) is the working formula and has the obvious limit as a/I, 0:
2
2:tvL)
Ix ?
V (X")= 7('iax I ' Re Yi ie 2a' ?
-a = ni?
ax11 ?
a COS 2a =1-
a v e-2:r! a
(e-2.1-1s1 sh
a 2)2j=
1 2ax
, In 12 (ch ?a ?CoS ?2ay .
a
As v increases the terms of series (A.6) converge rapidly to the corresponding terms of the series
(A.7). In view of this the obvious relation
(A.5)
(A.6)
(A.7)
V r-rz V L.= co +.(5. v S v k=00),
(A .8)
can be used where the Sp are the partial sums of the corresponding series. In particular it follows from
(A.7) that if lix2 + y2 = p, then for p>kT, the
flux of monochromatic neutrons has a sharp maximum, and its extent is determined by the time of retarda-
tion to the specified energy. For neutrons with E kT, the thermal motion constitutes the factor prevent-
ing the achievement of the maximum possible flux value, since a considerable proportion of the neutrons
are scattered into a higher energy range, with the acquisition of energy. Furthermore, the length of the
pulse is very considerable in this case, being mainly determined by the lifetime of the neutrons in the equi-
librium spectrum. The intensive cooling of the moderator to a temperature at which the condition kT (nod)cr.
TABLE 1. The der Values (in centimeters)
s=1
s=2,
8=3
X =- X,
0,60
0,75
0,85
X -= Xi
0,25 0,30
0,35
x=0
0,17 0,17 I
0.,17
The a's lose energy primarily due to "cooling" in collisions with electrons. Here the a range depends
on the electron density n and temperature T:
T3/2
= a ?n ,
(5)
where we are to set a = 3.8 ? 1010 cm4/degil- 2.
At an electron density of n = 4 ? 1022 cm-3 and temperature of T = 108?K, the a range is /a = 0.95 cm.
We will assume that the shell has an infinite heat capacity, so we can assume zero temperature on the
surface bounding the plasma. At the center of the plasma layer symmetry requires that gradients vanish.
Accordingly, the boundary conditions on Eq. (1) can be written
(6)
Converting to the dimensionless variables = xd-1, 0 = TA-1 and assuming a power-law temperature
dependence for the thermal conductivity, 34 = PTk, we can convert Eq. (1) with boundary conditions (6) to
a Oh
=
ts--10 40 +1
q (no d, 0); (7)
0 It= = 0. (8)
Examination of the structure of Eqs. (1)-(3) shows that the right side of Eq. (7) will depend on the
electron density and the plasma dimensions only through the combination n0d:
(k +1) (nod)2
q IF (no d) F qT1
Ak+1
(q p' = Fn-2 QT = T11-2)1
(9)
where qF and qT are functions of the dimensionless temperature 0; n0 = /IA 0 is the plasma density at the
center of the layer; and d is the half-width of the layer.
This problem is apparently quite similar to the familiar problem of a "thermal explosion" in chemical
kinetics. In fact, there are significant differences, due to nonlinear thermal conductivity (4), which differs
from the Arrhenius conductivity by heat-evolution law (2) and the existence of volume energy loss due to
radiation. As a result of the combined effects of these factors, a thermal explosion in its usual sense [2]
does not occur during thermonuclear combustion.
The steady-state temperature distribution satisfying Eq. (7) and boundary conditions (8) must be of the
form
0 0 (a? nod),
i.e., it must depend on nod as a parameter. There are no other parameters in this ?problem.
In order for there to be a steady-state solution, certain conditions must be satisfied. These conditions
must take the form of some dependence of the parameter nod on the temperature 00 = = 0:
nod -= (01) ?
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nod ?10-22cm-2
10
9
8
7
5
4
3
? 2
1,0
9
2
8
7
65 6 7 8 9 108
10
9
8
7
5
10
;9
8
7
6
nod ?10-a.cm
2 3 4 5 6 7 8 9109
a T?1(
3 4 5 6 7 8 9109
TV(
dno 10-2 C111-2
10
9
8
7
5
5
4
2
1,0
.9
8
7
65 6 7 8 9108
2 3 4 55 7 8 9 109
r/K
Fig. 2. Temperature dependence of
nod found under the assumption of spa-
tial homogeneity for the heat sources.
a) s = 1; b) 2; c) 3.
It is shown below that the function f(00) reaches a minimum at some temperature 0,, corresponding to the
minimum possible value (nod)er; with nod < (nod)er a steady state is not possible.
The dimensions der calculated for the normal density of solid deuterium turn out to be comparable to
the a range. We will accordingly consider two limiting cases.
1. In the first case of d 108?K.
1) s = 1; 2) 3.
R 2s 71.
qx P k+1 (n0)2 ?
The quantity Qx = ntiqx represents the rate of heat loss per unit volume due to conduction. This loss
depends on the exponent k in the expression for x as well as on the configuration of the plasma volume (s).
Figure 1 shows a typical ob = (1)(00) dependence for a fixed nod value. The intersections of the 43(00)
curve with the line cl) = 1 correspond to steady states; if the curve maximum lies below the line, no steady
state is possible.
With nod > (nod)er there are two possible states of thermal equilibrium. Here the equilibrium corre-
sponding to the left-hand intersection is unstable. In fact, because of the positive derivative of the function
(1)(00), which represents the ratio of the volume heat evolution to energy loss from the plasma, the slightest
overheating of the plasma will result in self-heating. As a result the system should enter a new equilibrium
state, corresponding to the right-hand intersection.
The characteristic transition time is
FQ
Tr "-?
nT
(15)
At a plasma density of n = 4 ? 1022 cm-3 and a temperature of T = 108?K, this time is T f/ 5 ? 10-9 sec.
By way of comparison, we note that the total "burn-up" time of the mixture under these conditions is TF-10-8
sec.
A thermal equilibrium cannot be reached with nod < (nd)er, and the plasma quickly cools. The corre-
sponding cooling time* is TX ? d2 nix ?-? 10-8 sec with d 1 cm.
According to the theory for a thermal explosion [2] with d < der, on the other hand, a steady state is
reached, and with d> der the temperature of the reacting mixture increases without limit (a thermal ex-
plosion). This discrepancy arises because in the thermal-explosion problem the corresponding function
4,(00), if plotted on the basis of the Semenov diagram, would have a minimum at some point Omin (in con-
trast with the case under consideration here).
Figure 2 shows temperature dependences of nod found under the assumption of a spatially homogenous
heat source qk. The function F is assumed given by
F = 1?e
(16)
We consider three different cases corresponding to the different curve labels in Fig. 2: 1) the heat
is transferred by electrons, and we have 'A, = xe; 2) heat is transferred by ions (the electrons are mag-
netized), and we have x = xi; 3) the thermal conductivity if formally set equal to zero (there is no thermal
*Here and below, all the calculations correspond to the normal density of -solid deuterium, with n = 4 ? 1022
cm-3 and T = 108?K.
42
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contact between the plasma and walls), and we have x = 0. Here the second case corresponds to the ap-
plication of a magnetic field of 3 ? 105 G < B < 2 -106 G. The third case should be treated as purely hypo-
thetical.
2. In the other limiting case of large plasma dimensions (la d), the heat evolution can be assumed
local and dependent on the local temperature. The corresponding problem is solved numerically; Fig. 3
shows temperature dependences obtained for nod.
In the transition region (d /a) the results of the numerical calculations are in satisfactory agreement
with results of the preceding model and with the results of [3], obtained by reducing to the problem to the
thermal-explosion model [2].
Figure 4 shows characteristic temperature distributions which arise in the stable plasma state. The
temperature is seen to change relatively slowly over most of the gap and to fall off rapidlyto zero as 1.
At a low-temperature thermal equilibrium we observe oscillations in the temperature distribution.
These oscillations are damped as the average plasma temperature is raised. The oscillations are expressed
most clearly in the spherical and cylindrical cases. The oscillations arise because in this temperature
range the heat-source function may change sign.
Table 1 shows der values for the normal density of solid deuterium: n = 4 .1022 cm-3. With 14. = xi
and x = 0, we can assume der Fy the main source
of information on Ey is the measurement of radiative capture, as was shown in [7]. When necessary a cor-
rection was introduced for the capture of neutrons after scattering.
Table 1 shows that the radiative widths are nearly the same for neutron energies up to 1200 eV. The
mean value fy = 24 MeV and the deviations from the mean barely exceed the experimental error which is
about 10% for most resonances. An increase in the accuracy of the measurements might possibly show
46
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TABLE 1. Parameters of U238 Neutron Resonances
EQ, eV
rrt, MeV
ry, MeV
Eo, eV
rn. MeV
rIP MeV
611t0,1
24+1,5
25?2
621?0,9
33+10
24+3
80,7j0,1
2,2 +0,2
629+0,9
7+1
102,4+0,1
70j3
26?2
662+1
150+20
22+2
1169?0.1
22?3
23?2
694+1
40+10
24+2
145,8+0,1
0,84+0,06
709+1
20+5
26+3
165,4+0,1
3?0,3
733+1,1
3,5+0,6
189,5+0,2
164+5
22?2
767+1,2
7+1
208,4+0,2
481-2
26+3
792+1,2
6+1
237,6_0,2
27?3
26+3
822+1,3
66+16
24+3
273.9+0.25 ?
. 22?3
25+3
853+1,4
26+3
291,2+0,25
16,4?2
23+2
857+1,4
25+3
311,7?0,3
0,9+0,1
869+1,4
5+2
? 348.1+0,35
78+10
22+2
907+1,5
40+10
25+3
377+0,4
0,9+0,15
939+1,6
120+20
24?3
398,1?0,45
4.7?0,5
960+1,6
130+20
22?3
410,7?0,45
20?3
25?4
994+1,7
27+3
434,6+0,5
8?1
1 026+2
8+2
464,1+0,55
5+0,5
1 057+2
90+30
22+3
479,4+0,6
3,5+0,5
1100?2
25+3
519+0,7
42?6
23+2
1142?2
26?3
536,2+0,7
55+15
23+2
1 170+2
23+3
580,7+0,8
36+6
23+2
1179?2
22+3
594,8+0,8
93+10
24+2
1197?2
26+4
small fluctuations in I', but in any case Fig. 1 shows that the fluctuations reported in [4] are clearly not
real. The mean value = 19 MeV obtained in [4] is also a considerable underestimate.
We previously reported the main results on the radiative widths of U238 [8], and the data of the Belgian
group [9] published at the same time are in good agreement with ours.
In conclusion the authors thank T. S. Afanas'evoi and N. T. Khot'ko for help in performing the mea-
surements.
LITERATURE CITED
1. L. Bollinger et al., Phys. Rev., 105, 661 (1957).
2. F. Firk, J. Lynn, and M. Moxon, Nucl. Phys., 41, 614 (1963).
3. J. Garg et al., Phys. Rev., 134, B985 (1964).
4. N. Glass et al., Proc. II Conf. on Neutron Cross Sections and Technology (D. Goldman, editor)
(1968), p. 573.
5. J. Rosen, Phys. Rev., 118, 687 (1960).
6. M. Asghar, C. Chaffey, and M. Moxon, Nucl. Phys., 85, 305 (1966).
7. Kh. Maletski et al., Yadernaya Fizika, 9, 1119 (1969).-
8. Kh. Maletski et al., Soviet? French Seminar on Nuclear Data [in Russian], Dubna (1970).
9. G. Rohr, H. Weigmann, and J. Winter, Proc. II Intern. Conf. on Nucl. Data for Reactors, Vol. 1,
CN 26/18, IAEA, Vienna (1970).
47
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ABSTRACTS
VARIATIONAL COMPOSITE METHODS OF CALCULATING NEUTRON
DISTRIBUTION IN NUCLEAR REACTORS
I. S. Slesarev, A. M. Sirotkin, UDC 621.039.5/6
and V. V. Khromov
The variational approach has broad possibilities for the creation of composite methods which, in cal-
culations of physical systems, allow the simultaneous use of approximations of different orders within the
scope of one method or the application of several different methods at once in an arbitrary combination of
their approximations.
The variational formulation of the problem usually consists of the construction of a functional for which
the equation under examination is a Euler? Lagrange equation.
A one-velocity kinetic equation in plane-parallel geometry was used in the study, and the functional
Fo, stationary for the solutions of the initial equation and equal to the quantity keff, was examined. The
fact that Fo allows the use of discontinuous trial functions is significant.
A sufficiently general approximate representation of the desired solution in the geometry examined is
N(z)
'jk(x, tt) E (ti) a;th (x), (1)
n=-0
where ik is the number of the phase space region for the variables x and /2; Qni is some known polynomial;
ik
an is the desired function; N is the number of members in the series, which depends on the number i of
the physical zone.
Many approximation methods may be obtained through the variational method, if trial functions are
used which are a particular case of (1) and satisfy the restriction that Fo be stationary.
It is shown that the functional examined is suitable for the derivation of the equations for DPn, Sn and
of other methods.
Since Fo allows the use of all kinds of trial functions, having the form of (1) in different zones of the
reactor or of another physical system, all "matching" conditions for equations for a broad class of approx-
imation methods are obtained from a single principle ? the need for the functional Fo to be stationary.
The extraction of matching conditions at the boundaries of zones where the change of method or num-
ber of approximations takes place is the important step in the derivation of the composite methods equations.
Matching conditions of a general type, which are suitable for combinations of many existing methods, were
formulated in the study.
Equations and matching conditions of certain variational composite methods ? DPn-DPrn, DPn-Srn,
Sn-Sm (the indices n and m indicate the possibility of using different approximations in neighboring zones
of the system) ? were presented as concrete examples.
The DPn-DPrn method was verified in calculated investigations of the quantity keff and of the neutron
distribution in a multiregion heterogeneous multiplying system. The results of the calculations, which are
presented, demonstrate the flexibility of the method and its high degree of accuracy, together with a sig-
nificant decrease in the extent of the computations. This decrease is due to the reduction in the order of
the approximations for the DPn method in those zones where this is warranted a priori from physical con-
siderations.
Translated from Atomnaya Pnergiya, Vol. 32, No. 1, p. 53, January, 1972. Original article sub-
mitted September 22, 1970.
0 1972 Consultants Bureau, a division of Plenum Publishing Corporation, 227 West 17th Street, New York,
N. Y. 10011. All rights reserved. This article cannot be reproduced for any purpose whatsoever without
permission of the publisher. A copy of this article is available from the publisher for $15.00.
48
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Declassified and Approved For Release 2013/03/01 : CIA-RDP10-02196R000300100001-0
RADIOACTIVITY OF METAMICT ZIRCONS
I. M. Lipova and G. A. Kuznetsova UDC 553.494:539.16
Interpretation of the nature of the metamict state in minerals is one of the urgent problems in current
mineralogy. The most popular relevant viewpoint on metamict minerals sees them as primary crystalline
substances coverted to an amorphous form under the influence of radioactive radiations emitted by uranium
and thorium incorporated in the minerals.
Zircon is a most abundent accessory mineral, and an important industrial source of zirconium, and
is known in nature in both crystalline and metamict states. The role played by radioactive radiation in met-
amict decay of a mineral was studied in tests run on a series of zircon specimens (incorporating zircon per
se, cyrtolite, malacon, alvite, naegite, etc., comprising a continuous series from crystalline to complete
x-ray amorphous differences). The way the uranium and thorium contents, the a-activity, the total a-ex-
posure dose vary, the forms of occurrence of uranium and thorium, and the distribution of uranium and
thorium in the minerals, were studied.
Specimens of zircons from various types of geological formations existing in the USSR and in foreign
countries were investigated. The entire series of zircons was arbitrarily broken down into three groups
on the basis of the number of reflections on the Debye powder diagrams: crystalline, semimetamict, and
metamict.
The uranium content was determined by the luminescent method, and the thorium content was deter-
mined colorimetrically, using arsenazo-III reagent. The a-activity was measured in a thin layer of the
specimen applied to the substrate, with a scintillation counter and a PS-10,000 scaler used in the measure-
ments. The total a-exposure dose was calculated by multiplication of the a-activity by the absolute age of
the mineral.
The uranium content and thorium content in the zircons increase from the crystalline differences (hun-
dreds of a percent of uranium and thorium) to metamict differences (whole percents of uranium and thorium).
But no exact quantitative relationship linking the degree of x-ray amorphousness of zircon and the content
of the radioactive elements (uranium and thorium separately, or their sum) was observed.
The thorium/uranium ratio is determined by the genesis of the rocks. As a rule, Th/U > 1 in zircons
from pegmatites of alkaline granites, alkaline syenites, nephelin syenites, greisens, albitites bound with
alkaline rocks, and hydrothermalites of alkaline composition, and usually the ratio Th/U < 1 in zircons
from granites, granitic pegmatites, and apogranites.
The degree of x-ray amorphousness of zircon tends to increase with increasing total dose of uranium
and thorium a-emission: in the case of crystalline zircons n 10" a/mg, in the case of semimetamict zir-
cons n 10" a/mg, and metamict zircons n 1016-17 a/mg.
Uranium and thorium are represented as both by the scattered or dispersed form and by microinclu-
sions of radioactive minerals. The latter are syngenetic in rare instances, but more often epigenetic with
respect to the zircon. When the content of inclusions of uranium and thorium minerals is high, the direct
relationship between the degree of x-ray amorphousness and the a-radiation dose breaks down.
Dispersed uranium is unevenly distributed throughout the volume of the mineral (microradiography).
Portions with a higher density of a-tracks correspond to the optically isotropic phase, and portions having
a lower track density correspond to the anisotropic phase of the mineral. These data are confirmed by the
microprobe method.
The maximum uranium content in the specimens investigated was detected in Japanese naegite (6.66%
U308 in the transparent fraction of the mineral containing no microinclusions when viewed in 497-fold mag-
nification). All of the uranium seems to be included isomorphically in the structure of ZrSiO4 (4'mole %
uranium). Naegite is the most deeply metamict of the whole series of zircons investigated.
Translated from Atomnaya Energiya, Vol. 32, No. 1, pp. 53-54, January, 1972. Original article
submitted March 23, 1971.
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MONTE CARLO CALCULATIONS OF CHARACTERISTICS OF
SECONDARY ELECTRONS KNOCKED OUT FROM VARIOUS
MATERIALS BY 1, RADIATION*-
V. V. Smirnov and A. V. Malyshenkov UDC 539.124.17
Energy spectra, angular distributions, and quantum yields of secondary electrons knocked out by )'-
radiation from aluminum and copper targets of different thicknesses were calculated by the Monte Carlo
method. In the region of energies of interest (0.4 to 1.3 MeV), production of electrons in the irradiated
material was due solely to Compton scattering and to photoelectric absorption of the Y-emission. Values
of the energies and directions of escape of the Compton electrons were calculated on the basis of the Klein
?Nishima formula. The pattern of angular distributions of the photoelectrons was obtained on the basis of
tabular data compiled by Hallberg. The target-depth distribution of the electrons formed was assumed uni-
form.
In dealing with the motion of an electron through the material, the entire path traversed by the elec-
tron from the point of origin to the target boundary was broken up into discrete segments within which the
electron energy losses were determined according to Bethe?Bloch theory, and the angular distributions
were estimated in conformity with Mollier theory.
As a result of these calculations, the energy spectra, angular distributions, and quantum yields of
secondary electrons knocked out by the 7-radiation of the radioisotope isotopes of Co?, Cs137, and Auln
from aluminum targets 0.1 Ro and 0.6 R0 in thickness were determined (R0 is the total range of the electron
having the highest energy). The quantum yields of the secondary electrons knocked out of an aluminum tar-
get of equilibrium thickness (0.6 Ro) by y-radiation emitted by Cog), Cs137, and Aulm, in the forward direc-
tion (0-90?), was, respectively, 8.0, 3.0, and 1.1 in units of 10-3 electron photon, and respectively 0.25,
0.20, and 0.06 in the same units in the backward direction (90-180?). Comparison of the calculated energy
spectra, angular distributions, and quantum yields of secondary electrons knocked out in the forward direc-
tion and available experimental data indicated agreement within 10%.
The calculations of quantum yields of secondary electrons for targets of various thicknesses (alumi-
num and copper targets) indicated that the relative yield of electrons for a given thickness expressed in
terms of a fraction of Ro, and the atomic number of the target, is independent of the energy of the incident
'7-photons. The relative yields of secondary electrons in the case of aluminum and copper targets of dif-
ferent thicknesses were approximated by empirical formulas which were in agreement with the experimen-
tal data to within 5%.
THE KAON FACTORY ? A TWO-STAGE (^J 3.7 GeV) ISOCHRONOUS
CYCLOTRONt
L. A. Sarkisyan UDC 621.384.633.5
Many research centers are carrying out investigations into the creation of "kaon factories," that is,
accelerators aimed at producing 3-7 GeV protons with an average beam current of the order of 100 ?A.
Tables 1 and 2 indicate possible parameters for three versions of a cascade-type isochronous cyclotron pro-
posed by the author in 1970 [1, 2].
*Translated from Atomnaya Energiya, Vol. 32, No. 1, p. 54, January, 1972. Original article sub-
mitted June 23, 1971.
tTranslated from Atomnaya Energiya, Vo . 32, No. 1, pp. 55-56, January, 1972. Original article
submitted May 3, 1971; revision submitted August 2, 1971.
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TABLE 1. Parameters of 2.7 GeV Three-Stage Cyclotron System
Stages of
cyclotron
Ho , Oe
N
71, cm
(4
roc, CM
r?. Cm
r, C111
F?
w
K'
eV,
MeV
Aystemp
GeV
/rev"
First
6000
8
8
0,2
--- 1 -,--,c.: Q r -.,.:,: 2
521
.-. 0
415
0,281
0.8
1
Second
3000
12
14,1 '
0,65
--- 1,86 < Or - 0.1 X0 the slope of the curve for as a function
of the electron energy increases with increasing Z.
4. The width tends to increase with a lowering of the threshold for recording bremsstrahlung. With
an increase in the angle the difference in the angular distributions measured by detectors with different
thresholds becomes more noticeable as predicted theoretically by Hisdal [4].
The dependence of the width of the angular distributions on electron energy, thickness, and atomic
number of the target in the range of target thicknesses and energies examined can be described by the semi-
empirical expression
_b(z)
200+ a (E , Z)e t deg,
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(1)
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where 0 = 57.28 m0c2/E; m0c2 = 0..511 MeV; E is the electron energy in MeV; t is the target thickness in
radiation lengths; and a (E, Z) and b(Z) are functions of the electron energy and the atomic number of the
target material.
The functions a (E, Z) and b(Z), determined from the experimental data, have the form:
a (E., Z) = (5.17 ?1,32 Ig E+ 2.28?10-2Z)
a (E, Z) = (4.72 ? 1.826 lg E+ 7.62.10-2Z)
b (Z)= (5.1-10-3+ 3.1?10-4Z).
The widths of the angular distributions of bremsstrahlung calculated by Eq. (1) do not differ from the ex-
perimental values by more than 10%.
A comparison of the experimental angular distributions of bremsstrahlung with theory confirms the
conclusion of Lanzl and Hanson [5] that the use of the Moliere formula [6] for the angular distribution of
electrons gives better agreement with experiment than does the Schiffer and Lawson [3, 7] theory in which
the Williams [8] and Rossi and Griesen [9] formulas are used for the angular distributions of electrons.
The calculations were compared with measurements made with a copper detector. The Lanzl and Hanson
calculations give good agreement with experiment for small angles (0 50) and target thicknesses less
than 0.1 Xo.
for the Cu 63 detector:
for the ionization chamber;
LITERATURE CITED
1. H. Koch and J. Motz, Rev. Mod. Phys., 31, 4(1959).
2. V. P. Kovalev et al., Atomnaya Energiya731, 289 (1971).
3. J. Lawson, Proc. Phys. Soc., A63, 653 (1950).
4. E. Hisdal, Phys. Rev., 105, 1821 (1957).
5. L. Lanzl and A. Hanson, Phys. Rev., 83, 959 (1951).
? 6. G. Moliere, Z. Naturforsch., 3a, 78 (1948).
7. L. Schiff, Phys. Rev., 83, 252 (1951); E. Muirhead et al., Proc. Phys. Soc., A65, 59 (1952).
8. J. Williams, Phys. Rev., 58, 292 (1940).
9. B. Rossi and K. Griesen, Rev. Mod. Phys., 13, 240 (1941).
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Declassified and Approved For Release 2013/03/01 : CIA-RDP10-02196R000300100001-0
MATCHING OF ACCELERATING CHANNELS IN A HIGH ENERGY
PROTON LINEAR ACCELERATOR
B. I. Bondarev and L. Yu. Solov'ev
UDC 621.384.64
To achieve particle energies of the order of 100-200 MeV in a linear proton accelerator, a transition
is made to an accelerating field of shorter wavelength. With a wavelength reduction by a factor n, the phase
width of a bunch becomes n times larger, as measured in the phase scale of the shortwave section, while
the phase capture area of the shortwave section remains the same as the capture areas of the longwave sec-
tion.
At the same time, the momentum width of a bunch remains practically unchanged during the transition
into the second section; it is less than the momentum capture area. Therefore the phase width of a bunch
can be decreased at the entrance to the shortwave section by virtue of an increase in the momentum spread
of the particles.
Known devices for matching accelerating channels* require the introduction of a third, intermediate
wave. The construction of such devices requires rf oscillators, accelerating systems, and other equip-
ment operating at the intermediate wavelength. The two matching devices described below operate at the
wavelength of the first, longwave section of an accelerator.
The first of the devices is a cavity installed between the two sections of the accelerator and operating
at the frequency of the longwave section. The frequency of the longitudinal oscillations in this cavity is
greater than the frequency of the longitudinal oscillations in the other cavities of the longwave section of
the accelerator. The cavity length is equal to an odd number of quarter wavelengths of the longitudinal os-
cillations.
Increases in the frequency of longitudinal oscillations in the matching cavity is achieved by an increase
in synchronous phase (to 60-70?) and amplitude of the rf field (to maximum permissible values). This cavity
also accelerates particles but with lower efficiency.
The operating principle of the matching device is shown in Fig. 1. We consider the phase plane (0, h),
where 0 = (p? (pc, h= (p ? pc)/pc, Q and p are
Longwave
section
'Shortwave section
Matching cavity
the phase momenta of the accelerated particles, and (pc and
Pc are the phase and momentum of the center of the bunch.
We assume that the particle coordinates in this plane at
the entrance to the matching cavity of the long-wave section
lie within the shaded ellipse A. In proportion to the accel-
eration in the matching cavity, the particle image points
in the phase plane are shifted into an ellipse which is more
elongated along the ordinate when compared with the ellipse
which is the envelope of the bunch because of the higher
frequency of longitudinal oscillations in the cavity. After
a quarter cycle of the longitudinal oscillations, i.e., at
the exit of the last cavity of the longwave section, the bunch
will have the shape of the shaded ellipse B. The phase
Fig. 1. Matching accelerating channels with *A. D. Vlasov, Theory of Linear Acceleration [in Russian],
a quarter-wave cavity.
Atomizdat, Moscow (1965), p. 75.
Translated from Atomnaya Energiya, Vol. 32, No. 1, pp. 79-81, January, 1972. Original article
submitted December 18, 1970.
86
0 /972 Consultants Bureau, a division of Plenum Publishing Corporation, 227 West 17th Street, New York,
N. Y. 10011. All rights reserved. This article cannot be reproduced for any purpose whatsoever without
permission of the publisher. A copy of this article is available from the publisher for $15.00.
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Declassified and Approved For Release 2013/03/01 : CIA-RDP10-02196R000300100001-0
IShortwave section
Longwave section
Drift
Ldr
Matching cavity
Resonator
L
res 27r
P? PC / PCc
Fig. 2. Matching of accelerator channels by using a drift space
and matching cavity.
dimension of the bunch is reduced and the momentum spread increased while the area of the image ellipse
is preserved. Such an ellipse better fits in the capture area of the shortwave section. Optimum matching
can be achieved by choosing the synchrotron phase and amplitude of the accelerating field in the matching
cavity.
The second device consists of a drift space and matching cavity at the end of the longwave section.
The wavelength, synchronous phase, and field intensity in the matching cavity are chosen to be the same
as in the other cavities of the longwave section, and the cavity length is selected such that the longitudinal
dimension of a bunch at the exit from this section of the accelerator is minimal.
Consider the operation of such a matching device. Let St be the frequency of the longitudinal oscilla-
tions at the exit of the next to last cavity and in the last, matching cavity of the longwave section (we neglect
adiabatic variation of parameters in it). As before, we assume the particle coordinates in the (0, h) plane
at the e5cit of the next to last cavity lie within the ellipse A (Fig. 2), which satisfies the equation
11)2 h2
=
(D2 H2
(1)
with (13 and H the semiaxes of the ellipse A, which are related by the expression H = (STY2/co)(13, where co is
the frequency of the accelerating rf field; Y = (1? P2)-1/2; g = v/e; v is the particle velocity; and c is the
velocity of light. After passing through a drift space of length Ldr, the particle representative points are
displaced parallel to the abscissa by an amount ?lch, where k = 2rLdrAY2 and X is the wavelength of the
accelerating field. The ellipse A transforms into the ellipse B, the equation for which is
(11)? hh)2 h2
(D2 -1- H2 ? (2)
After drifting, the particles arrive at the matching cavity and the ellipse B is rotated by an angle
7112 + a in proportion to the acceleration in the cavity, and is transformed into the ellipse C, the axes of
which coincide with the coordinate axes. The matrix M which describes the transformation of coordinates
at the cavity entrance into the coordinates at the exit is
M-=+- c21,2 )
. (3)
( Qyz
? sin a, cos cz
? cos a, ? sin a
(0
Subjecting the coordinates 1/) and h in Eq. (2) to the transformation (3), we obtain an equation for the
ellipse C at the exit of the longwave section. To make the axes of the ellipse C coincide with the coordinate
axes, we set the coefficient of the Oh term equal to zero in the equation for this ellipse. Then
1 2
arctg ,
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(4)
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where m = (S2Y2/co)k. Substituting the resultant value of a in the equation for the ellipse C, we find that its
phase spread is reduced by a factor x in comparison with ellipse A:
(5)
and the momentum spread of the particles is increased by the same factor.
By selecting Ldr, the shape of the ellipse can be optimally matched to the capture area of the short-
wave section.
It is easy to show that nonlinearity and nonconservation of longitudinal motion, as well as random per-
turbations of it, do not reduce the practical efficiency of the matching devices discussed.
In principle, the matching devices discussed above can be used where there is a need for linear trans-
formation of bunch phase space.
In high-energy and high-current linear proton accelerators (meson factories, neutron generators),
matching devices can be used for matching the accelerating channels of the longwave and shortwave sections
of the accelerator, making it possible to prevent particle loss and to increase operational reliability and
acceleration efficiency. In linear accelerators used as injectors for proton synchrotrons, matching of ac-
celerating channels helps to decrease particle momentum spread at the accelerator exit along with an in-
crease in acceleration efficiency.
88
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EFFECT OF NONLINEAR RESONANCES ON BEAM DIMENSIONS
IN THE 70-GeV ACCELERATOR
V. I. Gridasov, K. P. Myznikov, 'UDC 621.384.6
and V. N. Chepegin
The emittance of an accelerated proton beam is one of the most important parameters determining
the operating efficiency of an accelerator extraction system. However, the very first measurements made
at the IHEP (Institute of High-Energy Physics) showed that beam emittance at the end of acceleration dif-
fered considerably from the calculated value [1]. Our present purpose is the clarification of the reasons
for this effect and an experimental study of the possibilities for suppressing it.
The dependence of horizontal and vertical dimensions of the beam on the magnitude of the magnetic
field in the accelerator is shown in Fig. 1. In this case, acceleration was produced at the central radius
beginning at 4000 Oe. The beam dimensions were determined by means of internal targets. A target was
introduced into the beam at a given time in the acceleration cycle. Its position could be changed both
,mm
r,z
25
20
15
10
5
4000 6000 8000
Fig. 1
--?
10000 H2Oe
97
?916
9,
N-,
30, =29
2
/
/
/

/ / __411.
V
-
41%0TIDANN
OPP
N?
yrAllrfill
.c .414
I
a*
N/
/
Fig. 2
2
6
Fig. 1. Dependence of horizontal (1) and vertical (2) beam dimensions in a ra-
dially focusing section on the magnetic field in the accelerator during accelera-
tion at the central radius. ----) The same dependence when a correction was
introduced into the magnetic field gradient in the accelerator.
Fig. 2. Operating region for the frequencies Qr, z with linear resonances to fourth
order. 1-6) Operating point trajectories for radial beam displacement at various
inductions; 1) 4000, 2) 9000, 3) 10,000, 4) 11,000, 5) 11,500, 6) 12,000; aa, bb, cc)
operating point trajectories corresponding to acceleration at radii equalling
?10, ?5, and 0 mm; AB) operating point trajectory with gradient correction.
Translated from Atomnaya Energiya, Vol. 32, No. 1, pp. 81-82, January, 1972. Original article
submitted January 6, 1971; revision submitted May 10, 1971.
C 1972 Consultants Bureau, a division of Plenum Publishing Corporation, 227 West 17th Street, New York,
N. Y. 10011. All rights reserved. This article cannot be reproduced for any purpose whatsoever without
permission of the publisher. A copy of this article is available from the publisher for $15.00.
89
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Or,z ,nun
25
20
15
10
-20 -15 -10 -5 0 5 10 15 20
00
500
1000
E ,keV
Fig. 2. Dependence of the quantity a for PU235 on neutron energy: co) FEL 1970, ,pres-
ent study; V) LASL, 1962, [1]; 0) ORNL, 1967, [3]; V) IAE , 1956, [5]; ) FEI, 1958,
[6]; x) FEI, 1965, [7]; --O--) UCRL, 1970, [9]; --0--) OIY,aI, 1970, [14]; --0--)ORNL
?RPI, 1970, [11]; --N---) Harw, 1970, [12]; OIYaI? FEL 1970, [13].
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[4] with coatings of U235 and PU239. In experiments with plutonium this quantity for our detector was Cpu239
= 0.2955 ? 0.0073, and in experiments with uranium, Cu235 = 0.2962 0.0053. Moreover, to control the
conditions of the experiment the quantity C was periodically determined in the process of the experiment
through the detection of spontaneous Pu240 and Cf252 fission events. During the analysis of the experimental
results for high neutron energies a small correction for the dependence of the probability C on the average
number of fission neutrons v was introduced.
The values of the quantity a obtained in the experiment for U235 and PU239 are presented in Figs. 1 and
2. They are the result of averaging live independent series of measurements for U235 and nine for PU239.
The error indicated in the figures is root-mean-square error obtained as a result of averaging and does
not include the indeterminancy of the constants of the experimental apparatus Elf/eye and C, characterizing
thereby the indeterminancy in the relative energy dependence of the quantity a. The total absolute error
of the quantity a, including the indeterminancy of all quantities in (1), is 10-15%. The majority of experi-
mental data available at present on the quantity a in the region of neutron energies 10 keV-1 MeV is also
presented in the figures.
It is possible to note a substantial agreement of all experimental data on PU239 obtained on van deGraaf
accelerators by the analagous method. For U235 our data in the region of neutron energies 20-100 keV lies
systematically lower by 15% than the results of [1-3]. However, it must be observed that in these studies
significantly thicker (^. 6 times) samples were used, and a detailed comparison evidently requires consid-
eration of the different effects of resonance blocking. The marked structure in the dependence of the quan-
tity a on the neutron energy obtained by us both for U235 and for PU239 is worthy of attention. This structure
may be the cause of significant discrepancies in the case of U235 in the results of measurements of a by the
transmission method in the spherical geometry on photoneutron sources Sb-Be [5-7]. The presence of such
a structure in the quantity a is not surprising and may be linked with the strong structure in the fission
cross section, which for U235 in this region of neutron energies was recently discovered [8].
In conclusion the authors express their gratitude to A. I. Leipunskii, L. N. Usachev, A. I. Abramov,
and V. A. Romanov for their constant attention and cooperation in the completion of the present study and
also to V. S. Shorin, M. V. Bokhovko, N. S. Kosulin, V. I. Volodin, and V. N. Kanaki for their participa-
tion in the preparation and conducting of the experiments.
LITERATURE CITED
1. J. Hopkins and B. Diven, Nucl. Sci. Eng., 12, 169 (1962).
2. L. Weston, G. de Saussure, and R. Gwin, Nucl. Sci, Eng., 20, 80 (1964).
3. G. de Saussure et al., Nucl. Data Reactors, Vol. II, Vienna, --IAEA (1967), p. 233.
4. V. N. Kononov et al., Pribory i Tekh. Eksperim., No. 6, 51 (1969).
5. P. E. Spivak et al., At. Energ., No. 3, 21 (1956).
6. V. N. Andreev, At. Energ., 4, 185 (1958).
7. A. A. Van'kov and Yu. Ya. SFavisskii, At. Energ., 19, 41 (1965).
8. B. Patrick et al., AERE-R 6350 (1970).
9. Y. Czirr and J. Lindsey, Nucl. Data Reactors, Vol. I, Vienna, IAEA (1970), p. 331.
10. Van-Shi-Di et al., Phys. Chem. Fission, Vol. I, Vienna, IAEA (1965), p. 287.
11. R. Gwin et al., Nucl. Sci. Eng., 40, 306 (1970).
12. M. Schomberg et al., Nucl. Data Reactors, Vol. I, Vienna, IAEA (1970), p. 315.
13. V. N. Kononov et al., Preprint P-3-5112, D-ubna (1970).
14. Yu. V. Ryabov et al., Preprint P-3-5113, Dubna (1970).
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CHILL-CASTING METHOD OF BITUMINIZING NATURAL
SORBENTS FOR Ir192*
Kh. Daiev, G. Delchev,
G. Gradev, S. Simov,
and V. Zhelyazkov
UDC 546.93
The chill-casting method of bituminizing the isotopes Cs137, Ag110,204, sr90, and Ca45 retained on
natural sorbents (zeolite with clinoptilolite and vermiculite) has been described in the literature [1-3]. This
article reports a study of Ir192 sorption by several naturally occurring sorbents, and the fixing of those sor-
bents in bitumen by a method which we developed.
In contrast to the above elements, iridium ions in aqueous solutions tend to form various complexes
[4, 5] which have the effect of complicating iridium sorption processes. Data are available on sorption of
iridium only on synthetic resins [6], none being available on sorption of iridium on naturally occurring sor-
bents. It seems that the complicated relationship between the different forms in which iridium occurs adds
difficulties to sorption of iridium on a specific cation or anion exchange resin. On the other hand, the lit-
erature contains descriptions [4, 7] of sparingly soluble iridium compounds with silver, mercury, lead,
thallium, etc., of the type M3IrA6, where M stands for silver, mercury, lead, or thallium, and the IrA6
denotes complexes of iridium in which A stands for Cl-, OH-, NO, and so on. Sorbents of that type ex-
hibit high sorption power with respect to silver, mercury, lead, and thallium. We therefore undertook an
investigation of the iridium sorption conditions via precipitation reactions, i.e., we converted an appropri-
ate sample of sorbent to the silver, mercury, lead, or thallium form suitable for precipitation reactions,
and passed a solution of iridium through the bed of sorbent. For example, in the case of the silver form
of the sorbent, a reaction of that type can be represented as follows:
3Ag4 ?? Ag,T)C1, .
(from sorbent) (from solution) (on sorbent)
Sorption of Ir192 on natural sorbents (zeolite and vermiculite) and bituminization of sorbents retaining
the isotope in question were investigated.
*This research was done at Vienna under IAEA contract.
TABLE 1. Chemical Composition of Sorbents (%)
Sorbent
Co
0
bI
c).?
0
E.
CO
Zeolite
with cli-
65,90
noptilolite
Vermicu- 41,92
lite
0,45
5,46
12,97
5,41
2,30
4,03
0,43
23,84
2,12
0,61
4,93
0,28
0,08
0,82
5,93
77,015,
70
60
50
40
30
20
10 -
1 2 3 4 5 6
7 8 9 10 11 pH
Fig. 1. Dependence of sorption co-
1,34 efficient ti of Ir192 on pH: 1) zeolite;
2) vermiculite.
Physics Institute of the Bulgarian Academy of Sciences, Sofia. Translated from Atomnaya
Ener-
giya, Vol. 32, No. 1, pp. 87-89, January, 1972. Original article submitted May 20, 1971.
98
C 1972 Consultants Bureau, a division of Plenum Publishing Corporation, 227 West 17th Street, New York,
N. Y. 10011. All rights reserved. This article cannot be reproduced for any purpose whatsoever without
permission of the publisher. A copy of this article is available from the publisher for $15.00.
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TABLE 2. Results of Experiments on Sor-
bents with Presorbed Cations
Cation
Zeolite with clino-
ptilolite
specific ac-
tivity, pulses
2min,m1
*nitial
olu-
tion
solu-
tion
passed
through
bed
Vermiculite
sorp-
tion
co-
effi-
cient,
To
pecific ac-
vity, pulses
initial solu-
tion
solu- passed
through
bed
tion
Silver
Mercury
Lead
Thallium
2040
2040
2040
2040
202
135
235
032
90,1
93,4
88,5
49,4
2040
2040
2040
2040
118
33
299
857
TABLE 3. Specific Activity of Natural Wa-
ters and of Waters Washing Bitumen Block
Specific radioactivity, nCi/liter
Water
1970
1971
analyzed
sorp-
tion
Octo-
ber
No-
vem-
ber
De-
em-
ber
Jan-
uary
Feb-
ru-
ary
March
co-
effi-Water washing
cient, bitumen block
with embedded
It 192
0,045
0,044
0,012
0,013
0,025
0,020
0,018
0,017
0,028
0,021
0,170
0,170
94,2
98,4 Radioactive
85,3
58,0 fallout
The chemical composition of the sorbents used in the
naturally occurring state appear in Table 1; the grain size
belongs to the class (-3.0; +0.3 mm).
The initial solution containing the iridium in the form of
ammonium chloroiridite (N114)3IrC16 has a specific activity of
2040 pulses/min?ml. A specified volume of a solution whose
pH is controlled by buffers was passed through a sample of
sorbent at a specified flowspeed. The specific activity of the
initial solution and of the solution passed through the sorbent
was measured, and the sorption coefficient of iridium was cal-
culated. The results, plotted in Fig. 1, lay bare the compli-
cated dependence of the iridium sorption on pH, and the pos-
sibility of retaining as much as 50% (roughly) of the iridium on
the sorbents referred to.
In the experiments staged with sorbents that had first
been converted to their silver, mercury, lead, or thallium
7 form, a solution of silver, mercury, lead, or thallium in ni-
trate form was passed through the sample. After washing with
distilled water till a negative reaction was obtained for the cor-
responding ion, a solution containing iridium was passed through
the sorbent. The results (Table 2) attest to the possibility of
sorption of Ir132 by natural sorbents in amounts of 98-99%, upon
prior sorption of silver, mercury, or lead.
Bituminization of sorbents retaining Ir132 was carried out
according to a procedure developed by the authors [1]. Stor-
age-battern bitumen was used to make the bitumen bowl, which
was cast in a special metal chill mold. Two layers of sorbent
were laid down in the bowl (Fig. 2): a lower layer of vermiculite and a top layer of zeolite. A solution of
silver nitrate was passed through the sorbents, and after washing with distilled water, a solution of Ir132
with total activity of 10-3 Ci was passed at a flowrate of 15 to 20 milmin. After that, the activity of the Ir132
solution did not differ from the activity of the naturally occurring sample due to radioactive fallout.
The sorbents were washed with distilled water (silver and iridium were not detected in the wash wa-
ter), and after drying in air the bowl was sealed with molten bitumen.
The bitumen block with sorbent "loaded" with the radioactive isotope was left to stand in the open.
Measurements were taken on a monthly basis to monitor the?radioactivity of the water (rain or snow) wash-
ing the block, and the status of the surface of the block was observed visually.* The results, listed in
Table 3, show that the eluted radioactivity is of the order of magnitude of the amount due to radioactive fall-
out.
Fig. 2. Layout of bitumen fixing unit:
1) bitumen bowl; 2) radioactive solu-
tion of Ir132; 3) sorbent treated with
silver nitrate; 4) fiber glass (glass
wool); 5) metallic gauze; 6) support
stand; 7) control valve; 8) discharge
tube.
*The method of retention and the results of monitoring observations checking on the state of the bituminous
block and on the radioactivity of the collected atmospheric precipitation washing the block are described in
detail in [1].
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The investigations of Ir192 on natural sorbents (zeolite with clinoptilolite and vermiculite) established
the favorable effect of the presorbed cations: silver, mercury, or lead, on sorption of iridium through
the formation of precipitated compounds on the sorbents. The sorbents retaining Ir192 were bituminized by
the chill-casting method.
The method proposed here expands the range of applications of the chill-casting method for processing
low-level and medium-level liquid radioactive wastes.
LITERATURE CITED
1. Kh. Daiev et al., in: Management of Low- and Intermediate-Level Radioactive Wastes, IAEA, Vienna
(1970), p. 739.
2. Kh. Daiev et al., Izv. Inst. Fiziki s ANEB Bolgar. Akad. Nauk, 22 (1971).
3. Kh. Daiev et al., Izv. Inst. Fiziki s ANEB Bolgar. Akad. Nauk (in press).
4. A. Werner and 0. Vzies, Ann. Chemie, 364, 87 (1909).
5. F. Bimish, Analytical Chemistry of Noble Metals, Part 1 [in Russian], Mir, Moscow (1969).
6. 0. Samuel'son, Ion Exchange Separations in Analytical Chemistry [in Russian], Khimiya, Moscow
(1966), p. 347.
7. M. Delepine, Comptes Rendus, 149, 1073 (1909).
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INFORMATION
ALL-UNION IZOTOP AGENCY SERVING THE NATIONAL ECONOMY
EXHIBIT AT EXPOSITION OF ACHIEVEMENTS OF THE
NATIONAL ECONOMY
V. A. Dolinin
A topical exhibit designated as "All-Union Izotop Agency Serving the National Economy" was inaugu-
rated in September, 1971 at the Atomic Energy pavilion of the Exposition of Achievements of the National
Economy. This is the first time that an exhibit of that type has been set up at the Exposition. It consti-
tutes a sort of report on the ten years of activities of the WO Izotop agency.
This agency, set up in 1961, has been called upon to serve various branches of industry, agriculture,
science, and medicine in providing them with sources of ionizing radiations, radioactive and stable isotopes,
labeled compounds and rare earths, radioisotope process monitoring instrumentation, radiation techniques
and equipment, personnel shielding equipment, equipment for handling radioactive materials, electron
physics equipment, dosimetric and radiometric equipment.
The problems highlighted by various sections of the exhibit are timely ones. The displays clearly
indicate how the problem of utilizing nuclear and radiation processes in science and in industrial practice,
posed in the resolutions of the XXIV Congress of the Communist Party of the Soviet Union, is being met.
There are seven sections in the exhibit.
The introductory section is devoted to the activities of the WO Izotop agency and of its subdivisions.
The beautifully conceived display stands graphically illustrate the increased volume of WO Izotop deliveries
in 1970 over the 1965 level, in percentages:
Isotope production 200
Radioisotope process monitoring
devices 180
Electron physics, dosimetric, and
radiometric equipment 350
Shielding and personnel protection 250
Radiation equipment 150
Total volume of deliveries 278
Volume of export deliveries 676
It is also clear that the production of isotope equipment in 1970 increased by 318 items over the 1965
level, while the production of electron physics equipment, and of dosimetric and radiometric equipment,
was increased by 175 items.
The "Personnel protection and equipment for handling radioactive materials" division of the exhibit
informs visitors of measures taken in the USSR to ensure labor safety in work with radioactive materials.
Specimens of special plastic laminate protective clothing, as well as equipment for handling radioactive
materials, such as: various types of glove boxes, hoods and dry boxes, remote-control manipulating equip-
ment, protective devices, and conveying equipment, are on display in that section.
Several types of gamma-ray nondestructive testing instruments were on display in the "Radiation
equipment" section. At the present time, gamma-ray inspection and nondestructive testing is one of the
Translated from Atomnaya Energiya, Vol. 32, No. 1, pp. 91-93, January, 1972.
1972 Consultants Bureau, a division of Plenum Publishing Corporation, 227 West 17th Street, New York,
N. Y. 10011. All rights reserved. This article cannot be reproduced for any purpose whatsoever without
permission of the publisher. A copy of this article is available from the publisher for $15.00.
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Fig. 1. In the exhibit halls.
Fig. 2. In the exhibit halls.
efficient methods available in quality control of materials, parts, and equipment (with no need to destroy
or dismantle the equipment inspected), laying the basis for great strides forward in improving the charac-
teristics of goods manufactured, improving the reliability of machine parts performance, and preventing
damage to equipment, mechanisms, and parts. Visitors have the opportunity to become familiarized with
the RID-11, 111D-21, Gazprom, andother gamma-ray nondestructive testing instruments, as well as acces-
sories for gamma-ray nondestructive testing instruments.
The radiation processing outfits designed for radiation research and radiation processes in biology,
medicine, chemistry, and agriculture, were presented at the exhibit in the form of diagrams, photographs,
and working mockups.
The neutron activation analysis section deals with one of the most sensitive and up-to-date methods
of ultimate analysis of the composition of materials, and displays a full-size K-1 neutron activation analysis
set for oxygen determinations and a diagram of the SO-1 neutron activation analysis system.
The "Radioisotope process monitoring instrumentation" section is the most representative one at the
exhibit. Automated measurements of forgings and automatic control of 2000-ton and 3000-ton hydraulic
drop forge presses with the aid of the RTP2-1S dual-channel radioisotope relay instrument have been in-
stituted at the V. I. Lenin Neva Machinery Factory, with improved forging precision, increases in the
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number of press strokes, better forging quality, and better working conditions resulting. Annual savings
of 59,000 rubles are reported.
Nine UR-8 radiosotope level gauges and 32 gamma relay units are in use at the Slavgorod chemical
plant, for monitoring flowrate and fill level of liquefied gases and corrosive fluids. Savings of 200,000
rubles annually are reported.
The installation of three radioisotope liquid density gauges at the Nikopol'marganets trust ore pro-
cessing mill in Grushevka has resulted in annual savings of 60,000 rubles.
Use of an ITShch-496 radioisotope thickness gauge on a coil cut-up line at the Novolipetsk metallur-
gical plant, with automatic sorting and grading of steel plate, made it possible to free 30 workers for other
assignments, and resulted in annual savings of 42,500 rubles.
The RRV-64 radioisotope gauges and weight controllers for paper and cardboard sheet, installed on
four machines at the Sloka paper and pulp combine, have constituted an efficient means of raising labor
productivity, achieving savings in raw materials and finished materials, and in improving product quality.
Savings resulting from the installation of RRV-64 devices on production lines have totalled 30-40 thousand
rubles per year per device.
The use of 120 radioisotope instruments on automatic process lines for interlocking in the event of
cutting tool breakage has yielded savings of 500 rubles annually per instrument, through curtailment of
scrap and turnover of tools.
The display stand of the Karaganda metallurgical plant, showing 172 radioisotope instruments in ef-
fective service for automated monitoring and control of the fill level of materials in tanks, for measuring
moisture content and weight of sinter burdens, ash content of coals, thicknesses of hot-rolled plate, and
analysis of raw materials and finished products, is of great interest. The use of 82 gamma relay units
in the sintering department of that plant, for automatic monitoring of the fill level of materials in hoppers,
has yielded 90,000 rubles yearly in savings. The display of the Krasnoe Sormovo plant gave an account of
automatic control of metals casting on a continuous steel casting machine. Savings have amounted to 160,000
rubles a year.
The "Electronic nuclear physics equipment" section presented full-size specimens of various types
of equipment, including: PP-9-2M, BP-100, and PP-15 scaling circuits, the Protoka proportional-flow
47r-counter, and many others.
Dosimetric and radiometric instrumentation for monitoring the radiation environment and ensuring
radiation safety of personnel in handling of radioactive materials is on display: a pocket set of direct-in-
dicating DK-02 dosimeters with the ZD-5 charging device, the KID-20 set of personnel dosimeters, the
IFK-2, 3 set of personnel film badges, the IZV-1 portable dosimeter for monitoring the dust load in the
local air and the content of radon daughters in dust, the 01'kha-1 aerosol radiometer, and the Araks dosi-
metering device.
The "Stable and radioactive isotopes" section is set up in an interesting and attractive way, informing
visitors that the V/O Isotop agency is the general delivery agent for all isotope products in the USSR.
Many of the display stands present accounts of the applications of stable isotopes in chemistry. biol-
ogy, biochemistry, physics, and also applications of radioactive isotopes as labeled atoms in scientific and
industrial research, as sources of ionizing radiations in automatic process control and monitoring instru-
mentation.
The exhibit came to constitute a large educational forum for hundreds of specialists in the national
economy. Seminars were held for the benefit of specialists from various regions of the country on special
passes issued by the Exposition of Achievements of the National Economy of the USSR. to promote more
widespread utilization of the atom for peaceful purposes.
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SEMINARS AND CONFERENCES AT V/O IZOTOP
While the topical exhibit "All-Union Izotop agency in the service of the national economy" was being
held at the "Atomic Energy" pavilion of the Exposition of Achievements of the National Economy of the USSR,
the All-Union Izotop agency was holding five seminars. The agenda of these seminars consisted of presen-
tation of reports on the agency's activities. The seminar participants were familiarized with the list of
devices, dosimetric and electron physics equipment, supplied to industry by the agency for research and
industrial use, and the new types of instruments planned for delivery in 1972. The seminars attracted a
total of 250-odd specialists: representatives of ministries, representatives of management boards, scien-
tific-research and planning institutes, grass-roots level isotope laboratories, organizations and industrial
plants in the various cities and districts of the country.
The seminars will contribute to more widespread acceptance and utilization of radioisotope techniques
and equipment in the various branches of industry, agriculture, and in scientific and medical institutions
throughout the nation.
The three day seminar on the topic "Isotopes and isotope instruments in the national economy" was
held at the Scientific-Research Institute for Nuclear Physics, Electronics, and Automatic Control attached
to the S. M. Kirov Tomsk Polytechnic Institute, in July, 1971. About 300 engineering and technical per-
sonnel from plants, scientific-research personnel, and party leaders took part in this seminar.
An "Isotopes in the service of humanity" exhibit was running concurrently with the seminar. This
exhibit displayed 250 items in isotope products, nuclear instrumentation, and personnel protection.
The seminar and the exhibit stimulated a good deal of interest on the part of specialists in the city and
nearby localities.
A conference on "Radiation techniques in the automation of mines and ore processing plants" was held
at Donetsk on September 22-24, 1971. Specialists from power and machinery management bodies of mining
and ore combines dealing with automation, mine automation mechanics, and technology, and other special-
ists, were attracted to the conference. The implementation and perspective applications of radioisotope
equipment in the coal industry were discussed at the conference. The conference participants heard reports
on experience in the introduction of radioisotope equipment and practice at the Donetskugol', Artemugol',
Makeevugol', Voroshilovgradugol', and Pavlogradugol' combines.
After hearing and discussing the papers and reports, the conference participants pointed out that a
lot of work has been done in recent years on applications of radioisotope equipment at plants and enterprises
in the coal industry.
The conference participants were afforded the opportunity of familiarizing themselves with the opera-
tion of automation instruments in the mines of the Krasnoarmeiskugoli mining and ore combine.
A seminar on "Applications of radioisotope methods and instruments in the chemical process industry"
was held in the "Atomic Energy" pavillion of the Exposition of Achievements of the National Economy of
the USSR in September, 1971. The seminar attracted 112 representatives of 40 chemical and petrochemical
plants, scientific-research institutes, organizations, and design agencies. The purpose-of the seminar was
to promote exchanges of experience and information on the development of new radioisotope hardware, and
on the implementation of radioisotope techniques and instruments in various branches of the chemical pro-
cess industry.
The reporters drew attention to the increased number of studies and projects in applications of radio-
isotope instruments in the design of automatic process control systems, as well as the development of
Translated from Atomnaya Energiya, Vol. 32, No. 1, pp. 93-94, January, 1972.
? 1972 Consultants Bureau, a division of Plenum Publishing Corporation, 227 West 17th Street, New York,
N. Y. 10011. All rights reserved. This article cannot be reproduced for any purpose whatsoever without
permission of the publisher. A copy of this article is available from the publisher for $15.00.
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nuclear physics techniques for monitoring the composition and properties of chemical products, and im-
plementation of full-scale industrial methods for monitoring chemical processes with the aid of radioactive
tracers. Several chemical process plants and combines are already making use of a hundred or more
radioisotope instruments each, with appreciable savings and improvements in working conditions as a re-
sult.
The seminar participants acknowledged the need for more widespread acceptance of radioisotope in-
struments in chemical production processes, in order to facilitate further expansion of the utilization of
the achievements of applied nuclear physics in the chemical process industry, with emphasis on their use
in the production of mineral fertilizers, in the plastics industry, in synthetic fiber production, in the pro-
duction of ore processing raw materials, and in chlorine industry, where they be used to maximum economic
effect.
On the initiative of the Ministry of Public Health of the USSR and the Moscow Scientific-Research In-
stitute for X-Radiology, a seminar on "Modern techniques and equipment for radiation therapy of malignant
neoplasms and clinical dosimetry" was held in September, 1971 at the "Atomic Energy" pavilion of the Ex-
position of Achievements of the National Economy of the USSR. Participating in this seminar were 130 ra-
diologist-physicians (radiation therapists). Of these, 80 were representatives of therapeutic?prophylactic
and scientific-research institutes in the republics of the Union.
The seminar participants heard reports in which the present state of the art and the developmental
outlook of radiation therapy and clinical dosimetry were examined.
The seminar participants recommended holding of future seminars on medical radiology. The feasi-
bility of scheduling a symposium on diagnostics and treatment of lymphogranulomatosis was pointed out.
A scientific-technical conference on "Applications of radioisotope instruments in the national economy"
in October, 1971, was held in the city of Dushanbe. There were four panel sessions at the conference. The
conference participants heard over 40 papers and reports discussing applications of radioisotope techniques
and instruments in the ore and mining industry, in the building materials industry, cotton growing, medicine,
and other fields.
The reporters noted that the Dushanbe reinforced concrete structures and structural parts plant is
making successful use of radioisotope equipment and techniques, with appreciable gains in the engineering
costs picture. Methods of nuclear geophysics are being used effectively in expeditions and laboratories of
the Geology Board of the Council of Ministers of the Tadzhik SSR. The Institute of Plant Physiology and Bio-
Physics of the Academy of Sciences of the Tadzhik SSR worked out a method for autoradiography of cotton
plants, and completed work on control of the transport of plant assimilants. Radioactive isotopes and sources
of ionizing radiations are being used effectively in some medical institutions in Central Asia for diagnostics
and treatment of various illnesses.
The conference contributed to exchange of experience on the applications of radioisotope equipment
in the national economy, and more widespread implementation of scientific-research developments in in-
dustry.
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CONFERENCES
SIXTH ALL-UNION CONFERENCE ON SYNTHESIS, PRODUCTION,
AND APPLICATIONS OF SCINTILLATORS
L. Ya. Zhil'tsova, E. N. Matveeva,
and I. M. Stoletova
The regular VI All-Union conference on the synthesis, production, and applications of scintillators
was held in May, 1971, in Khar'kov.
A large number of the papers submitted to the conference dealt with research and development work
in the physics of the scintillation process in alkali halide crystals. A paper by L. M. Shamovskii and col-
leagues dealt with the nature of light diffusion centers and the conditions governing their formation in the
process of growing ionic crystals from a melt. The nature of light-scattering inclusions was studied in
the case of melt-grown fluorite crystals produced under a variety of melt conditions. It was shown that
elimination of light-diffusing inclusions brings about improved scintillator quality.
A report by E. M. Arm et al. dealt with the outlook for utilization of scintillation detectors with a
base of CsI(Na) single crystals at elevated temperatures. They established the advantage of these scintil-
lators over CsI(T1) scintillators. The scintillators investigated display a plateau in their counting charac-
teristic at temperatures 140-150?C. A large number of papers were devoted to investigation of the proper-
ties of these crystals. In line with the expanding opportunities for applications of CsI(Na) crystals, we note
an interesting paper submitted by I. I. Kisel' and N. I. Krainikov on growing CsI(Na) single crystals in a
horizontally rotating ampule. It was demonstrated that the growth rate of the single crystals can be in-
creased above five times over the rates used in growing single crystals by the Stockbarger method. Single
crystals grown at a rate of 11 mm/h are not inferior in their scintillation characteristics to the best single
crystals grown by the Stockbarger method at a rate of 2 mm/h.
B. K. Damitov et al. proposed a new method for determining the intrinsic resolution of small-size
NaI(T1) crystals by using a photomultiplier with a large photocathode diameter.
A report on an improvement in the technological process in mass production of polystyrene scintilla-
tors was submitted by a team working at the VIIMonokristallov (All-Union Scientific-Research Institute of
Single-Crystals) (0. A. Gunder, A. L. Lifshits, others), covering investigations of the technological factors influ-
encing the polymerization process and the scintillation properties of plastic scintillators, and presenting recom-
mendations on how to best fabricate them.
G. P. Volosyuk et al. gave an account of the effect of such secondary solvents as naphthalene on the
optical and scintillation properties of element-containing (heteroorganic) plastic scintillators, which are
capable of raising the light yield of plastic scintillators by 30-35% when secondary solvents are used and
luminescence additives are selected.
0. A. Gunder and colleagues studied the effect of vinylxylene synthesis technology on the light yield
of plastic scintillators. It was demonstrated that an isomer of 2,4-dimethylstyrene exhibits the best scin-
tillation properties.
Research on polymethylmethacrylate base plastic scintillators has been continued (S. A. Malinovskaya
et al.). Shortening of the fluorescence decay time and simultaneous increase in the amplitude of the light
pulse with increasing concentration of luminescent additives have been detected.
Translated from Atomnaya Energiya, Vol. 32, No. 1, pp. 94-95, January, 1972.
o 1972 Consultants Bureau, a division of Plenum Publishing Corporation, 227 West 17th Street, New York,
N. Y. 10011. All rights reserved. This article cannot be reproduced for any purpose whatsoever without
permission of the publisher. A copy of this article is available from the publisher for 815.00.
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A. E. Buklei et al. developed and investigated a 1000 x 1000 x 20 mm counter based on such a plastic
scintillator of enhanced transparency. The counter efficiency was measured with a beam of relativistic
ir-mesons, and found to be close to 100% over its entire area.
Many of the reports presented were read at the panel on applications of scintillators and detectors
based on scintillator crystals.
A report by V. V. Chernikov (in the name of a team of colleagues at VNIIMonokristallov) was devoted
to a slow-neutron activation detector using plastic and liquid scintillators containing chlorine, bromine,
iodine, and zinc. Introduction of iodine into plastic scintillators proved most successful. Neutron record-
ing efficiency was 0.61 when plastic scintillators with a base of styrene and 10% diiodobenzene copolymer
was used. A liquid neutron detector with an efficiency 0.66 was obtained by the authors upon introducing
a tributylphosphate solution of InC13 into a-methylnaphthalene.
E. M. Burymov reported on applications of platelet type deuterated scintillators in fast-neutron spec-
trometry. Deuterated anthracene or naphthalene can be used as the platelet material. This scintillator,
in the form of a stack of alternately sandwiched deuterated (0.05 mm) and glass (0.1 mm) wafers, can pro-
vide an amplitude resolution of 1.3% and a peak-to-valley ratio of 30.
During the conference discussion, investigations of scintillators as detectors of long-wavelength x-
ray emission and of new scintillation detector units for x-ray equipment came under discussion (V. R. Al'per-
ovich et al.), as well as enhanced sensitivity in recording of ultraweak bioluminescence of living tissues
(E. V. Buyanov et al.), utilization of a low-background scintillation Y-ray spectrometer for investigating
radiation purity of several materials (V. D. Gorin), investigations of the characteristics of scintillation
detectors with the aid of light generators (Yu. N. Kuzin et al.), and so forth. Topics relating to the solu-
tions of those problems received a prominent place in the discussion. A report by E. I. Minsker on optical
adhesives with a polyorganosiloxane base was considered of great practical interest.
The conference proceedings will be published in the next collection of articles in the series "Single
Crystals, Scintillators, and Organic Phosphors" issued by VNIIMonokristallov, Khar'kov. The next confer-
ence, the seventh, is scheduled for 1974.
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FOURTH CONFERENCE OF THE INTERNATIONAL NUCLEAR
DATA COMMITTEE
M. F. Troyanov
The regularly scheduled IV conference of the IAEA International Nuclear Data Committee (INDC) was
held in July, 1971, at the Homi Bhabha Atomic Research Center in Trombay (India). The conference was
attended by 14 INDC members, 13 representatives of various countries plus one IAEA representative, in
addition to six scientific advisors and observers.
The conference was opened with welcoming remarks by the director of the Center, H. Setna, who
emphasized the importance of nuclear data in the development of atomic science, particularly for India.
An isochronous cyclotron is being built in India (at Calcutta) to aid nuclear physics research there, and a
pulsed fast reactor is also under construction (near Madras).
The INDC conference agenda began with communications from the representatives of the several coun-
tries, dealing with work on nuclear data measurements made and reported over the past year. The basic
findings on new measurements were reported at the conference on neutron cross sections held in the
USA (Knoxville, State of Tennessee, March, 1971), and at a neutron physics conference held in Kiev (May,
1971). Written reports of the activities on nuclear data studies in various countries are on file at the Ob-
ninsk nuclear data center.
Neutron standard data came under discussion at the INDC conference. Current "standards" for this
work are the nuclides H1, He3, Lis, Bio, C12, u235. The importance of working out a system of recommended
data on standards was stressed, and agreement was reached on the free exchange of estimated data on nu-
clear standards. This means that the estimated data on the nuclides mentioned, obtained in various labora-
tories throughout the world, will be made available for general use.
The committee reviewed the status of the most important nuclear data, and discussed the principal
discrepancies found in the fund of data. It was reported that recent measurements of fission spectra at
Argonne and Karlsruhe have confirmed the Los Alamos data. An opinion was expressed on the need to con-
duct additional integrated experiments to secure information on fission spectra. In that connection, IAEA
scheduled its August, 1971 conference of specialists to discuss the findings of fission spectrum measure-
ments.
Disparities in the determination of the number of secondary neutrons emitted in spontaneous fission
of Cf252, which still eludes explanation, were discussed. The measurements will have to be continued, using
a variety of methods.
A suggestion was advanced to measure the energy dependence of the ratio of the capture cross section
of gold to the fission cross section of plutonium, with the object of clearing up some discrepancies in the
fission cross sections of PU239 and U235.
A review paper authored by M. Sowerby (Britain) and V. Kon'shin (USSR) dealt with analysis of a set
of experimental values of the ratio of the radiative capture cross section to the fission cross section (a) of
the nuclide PU239. This review paper analyzes results reported by various authors, and suggests the rec-
ommended data.
A protracted discussion followed the presentation of reports on neutron data, particularly in the light
of the interaction between INDC and the Working Team on nuclear structures and reactions organized under
Translated from Atomnaya Energiya, Vol. 32, No. 1, pp. 95-96, January, 1972.
C 1972 Consultants Bureau, a division of Plenum Publishing Corporation, 227 West 17th Street, New York,
N. Y. 10011. All rights reserved. This article cannot be reproduced for any purpose whatsoever without
permission of the publisher. A copy of this article is available from the publisher for $15.00.
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IAEA sponsorship. The committee stressed the fact that neutron data retain unquestioned priority in any
nuclear data work, and that the entire activities of the team must be directed primarily toward the solution
of applied problems, with the team working under the supervision of INDC.
The conference heard reports on the work of nuclear data centers and on exchange of experimental
information between four such data centers. A conference of the four centers was held in October, 1971
at Brookhaven, facilitating thorough discussion of their activities.
The INDC IV conference discussed compiling a list of inquiries on nuclear data. At the present time
several inquiry formats, including some developed in the USSR, have been submitted to IAEA. In the com-
ing months all of these inquiries will be incorporated in a general list broken down by sections: reactors,
thermonuclear fusion reactors, system of guarantees. These lists will be revised on a basis of roughly
once every two years.
The INDC conference heard reports on nuclear data estimates activities. The agreement reached on
free exchange of estimated data based on "standards" is a first step on the path to free exchange of all es-
timated data based on "standards" is a first step on the path to free exchange of all estimated data. To
smooth the free exchange of these data and reach agreement on approaches to estimating techniques, IAEA
prepared and scheduled a conference of specialists on the subject for August-September, 1971. A seminar
on estimates of nuclear data was called in Rumania for the summer of 1972. In 1972, IAEA will be holding
a conference on neutron "standards," and in 1973 a symposium on the acquisition, compilation, estimates,
and dissemination of applied nuclear data, to be followed by the III general nuclear data conference sched-
uled for 1974.
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INTERNATIONAL CONFERENCE ON ELEMENTARY PARTICLES
I. A. Savin
The International Conference on Elementary Particles was held in Amsterdam (Holland) from June
30 to July 6, 1971 under the auspices of the Dutch Ministry of Education and Science and the University of
Amsterdam, with the support of the European and Dutch Physical Societies, and the active participation of
CERN.
The work of the Conference was centered on plenary meetings with raporteur's talks on broad topics
preceded by parallel section sessions where reports of original work ormini-rapporteur's talks on original
works were heard.
The Conference was attended by 590 scientists from many countries. About 440 original experimen-
tal and theoretical papers were discussed.
The plenary sessions were concerned with the following topics: high energy hadron physics (G. Gia-
comelli, H. Zats), medium energy hadron dynamics (R. Barluto, M. Deutchman, and R. Phillips), low
energy hadron physics (H. Dalitz, K. Shmid), weak interactions (K. Winter), electromagnetic interactions
(E. Drell), and hadron symmetry (K. KaHan). Two invited talks were heard: on the status of the CERN
proton?proton colliding beams (ISR) (K. Johnson) and on electron?muon universality (V. Telegdi).
The raporteur and invited talks will be published. The more interesting experimental results reported
at the conference are outlined below.
High energy hadron physics was represented, in the main, by work done at IFVE (Serpukhov) on the
70 BeV accelerator and by preliminary results from the ISR.
The results of measurement of the 7+, K+ and proton total cross sections on protons and deuterons
was at the center of attention of the conference, particularly the discovery at Serpukhov that the K-Fp total
cross sections grow at high energies. Much interest was aroused by the relatively slow decrease in the
rthp interaction cross section difference [Aut(71-Ip) 120-1?2]. According to other data from IFVE the total
charge-exchange cross section decreases with increasing energy at much faster rate (crex P-1.2) up to 50
BeV. It was pointed out in discussions that there must be a change in the energy dependence in the 200
BeV energy range or the well-known inequality 04702 const uex would be violated.
Thus, the results of measurement of positive particle total cross sections together with the previously
verified results on negative particles imply that the total cross section differences for r?p, KTp, and p?p
continue to decrease with increasing energy. It follows that speculations about the possible violation of the
Pomeranchuk theorem were premature.
Another direct method of verifying theories of the behavior of scattering amplitudes, and in particular
of measuring the behavior of the difference of total cross sections was used in an experiment performed at
IFVE by a group from Dubna in conjunction with groups from countries participating in OIYaI (HPR and
ChSSR). This consisted in measuring f, the amplitude for transmission regeneration of K1-1(95 on
hydrogen, whose imaginary part is proportional to ,Ao-t (14I?? lep), the difference of the K9p and K9p total
cross sections (or through isotopic spin invariance len and K-n). The results indicate that the modulus of
the regeneration amplitude 1111/K if" while its phase (41) is constant in agreement with Regge model
calculations and dispersion relations. It follows from these results that Aut (K9 ? R9p) decreases with
Translated from Atomnaya Energiya, Vol. 32, No. 1, pp. 96-97, January, 1972.
0 1972 Consultants Bureau, a division of Plenum Publishing Corporation, 227 West 17th Street, New York,
N. Y. 10011. All rights reserved. This article cannot be reproduced for any purpose whatsoever without
permission of the publisher. A copy of this article is available from the publisher for $15.00.
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increasing energy in agreement with requirements of the Pomeranchuk theorem. More accurate data
will be available in the near future on the energy behavior of If1 I and arg ((p?21) from American (3-10 BeV/C)
and Dubna (10-42 BeV/C) groups.
Much time was given at the conference to the presentation of preliminary results from the ISR. The
greatest interest was aroused by the announcement that the slope parameter (b) of the pp diffraction cone
has different values at a given center of mass energy S for different momentum transfer intervals (for in-
stance, for S = 2800 BeV2, b equals 12,8 ? 0.2 and 11.6 ? 0.15). This apparently reflects a decrease in
the growth of b as compared with extrapolations of the results of the Dubna group at the IFVE accelerator to
ISR energies. This fact implies that the effective proton radius ceases to grow at very high energies.
Many papers were devoted to medium energy hadron dynamics. First of all, we consider papers on
elastic scattering. The combined data shows that the pp and ep diffraction cones shrink with increasing
energy up to ?-? 25 BeV/C, 7r+p shrinks slowly, pp shrinks and then reaches a plateau, while K-p does not
shrink at all. At large momentum transfers the cross sections have a complex behavior with minimums
and maximums. Some of these were observed for the first time.
For backward scattering there are peaks for all reactions except pp. Elastic lrp scattering is iden-
tical to pp scattering up to momentum transfers of 6(BeV/C2). The polarization of p?, 7r?, and K? scatter-
ing on protons has been studied in detail.
Among papers on inelastic two-body scattering, we note the first results on pp ? EZ,E+1+, 27r, and
2K reactions. The first reaction exhibits a forward peak in the angular distribution, while the second has
a forward peak and a break in the angular distribution for t= ?1.2 (BeV/C)2 together with a break in the po-
larization in the same region.
Quasi two-body reactions were represented by papers on the angular distributions and exchange dy-
namics of definite strange and nonstrange states for processes of the type Ic-p A+K*-, PK*-, nK*? (890
MeV/C2), PK*-, nK*? (1420 MeV/C2), K-p Ap, Aw, p, E? K?p A++K?, ep A++ co, etc. for which
information was obtained regarding the angular distributions and dynamics of exchange through specific
singular and nonsingular states.
The study of many-particle reactions was represented by two methods: exclusive reactions, i.e.,
experiments where the parameters of all particles are fully determined, and inclusive reactions, where
the characteristics of one (or two) particles are studied and the parameters of the remaining finite system
are summed over (missing-mass type experiments).
Definite success has been achieved in the study of exclusive reactions due to the use of van Hove's
LPS procedure (decreasing the number of variables by summing over the perpendicular momenta). An ex-
change hierarchy o-(P) > o(M) > o(S) > a(E) has been established for both total and differential cross sections
were P, M, S, and E indicate vacuum, mesonic, strange, and exotic poles. All the cross sections except for
those proceeding through P exchange diminish with increasing energy.
Inclusive reactions were analyzed in terms of the hypothesis of scale invariance according to which
cross sections at high energies depend only on PI and the ratio X = /Pmax. This hypothesis was tested
in a large energy region including ISR energies. Scaling invariance holds for certain reactions (pp ? 7r+
; pp p + ...) while it is obviously broken for others (K?p K? + ? X +
or holds in a limited region of X (ep 1r + , r+p ? 7r+ . . . )
Low energy hadron physics was represented at the Conference by papers studying the characteristics
of resonances. ?Reports were heard on the systematic study of baryon resonances in K+N interactions.
Resonances have been observed in the Aar, 7r- , * (1385 MeV/0, 7r, and Er systems. There are indica-
tions of the existence of a strangeness +1 resonance in the reaction K?d K?pp with M = 1760 MeV/C2 and
= 300 MeV/C2. The existence of a AY resonance with a mass of 1327 MeV/C2. in the reaction ic-p 71-0Ay
has not been substantiated. Two groups, ITEF and CERN, have also reported observation of a resonance
in the per+ system (1700 MeV/C2).
New information on boson resonances has been found. One of the most important results is the ab-
sence of splitting in the A2 meson as determined by high-statistics experiments at CERN and Brookhaven.
Also of interest is the joint IFVE and CERN work on the energy dependence of boson production cross
sections. The A2 meson production cross section is constant over a wide momentum range (25-40 BeV/C)
while the R meson either disappears completely from 10 to 25 BeV/C or has a factor of ten decrease in its
production cross section.
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Weak interactions, which have been intensively studied by experimentalists and theorists since 1964,
when CP-invariance was found to be violated in KL? + 7r- decays, were again generating broad interest.
The effort of many years by physicists to measure the modulus and phase of the parameters 74_ and
noo, which are the branching ratios for the KL and 4 neutral and charged two pion decay, would seem to
have ended in 1970 when ITEF and OIYaI groups established reliably that koo I 174_1. This result was con-
firmed at the Conference by a CERN group whose results were In00/74_ I = 1.00 ? 0.06. Taken together with
the mean weighed values of the phases 900/9_, = 0.99 ? 0.25, this means that the superweak interaction the-
ory which explains the mechanism of CP-invariance violation is correct. It follows from this theory that
there should be no CP-violation effects except in KL decays. This has held true up to the present despite
the vigorous efforts of experimentalists to find other CP-violating decays.
An experiment recently performed at Berkeley which established the upper limit for KL 11+12-
(5 1.8 ? 10-9) decays was discussed at the Conference. This limit is several times lower than the possible
theoretical limit which is estimated using electromagnetic interactions on the basis of the previously shown
decay probability K ry confirmed at the Conference by an ITEF group.
If one assumes both results to be correct, then one can expect that the new result is tied to another
manifestation of CP-violation.
From the remaining data on the properties of weak interactions, the work of a CERN group concluding
the long effort to verify the AS = AQ rule in leptonic decays of le mesons should be noted. It has been shown
experimentally that this rule hold to an accuracy of a percent in 43 decays.
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FOURTH INTERNATIONAL CONFERENCE ON PLASMA PHYSICS AND
CONTROLLED NUCLEAR FUSION
B. B. Kadomtsev and V. D. Shafranov
The Fourth International Conference on Nuclear Fusion of the IAEA was held in June, 1971, at the
University of Wisconsin at Madison. About 600 scientists from about 30 countries participated in the con-
ference, and about 140 reports were heard. Most of the reports were delivered by the rapporteur system.
The conference dealt with the results of work in controlled thermonuclear fusion over the last three years.
As in previous conferences, most of the work has been experimental.
The conference opened with a session on studies of plasma behavior in toroidal traps having inner
conductors ? levitrons and multipoles; reports on an astron were also heard. At one time it appeared that
devices having internal conductors would significantly simplify studies of physical properties of plasmas in
a toroidal geometry, since a deep magnetic well, which should lead to a prolonged stable confinement of the
plasma, can be easily produced in such devices. Unfortunately, this turned out not to be so. The quite
complicated behavior of the plasma in multipoles has necessitated a prolonged and persistent study which
has not yet led to a common point of view regarding the mechanisms for plasma escape.
Nor was a common point of view reached at this conference. For example, in studies carried out at
the University of Wisconsin with two octupoles ? a small one with supports and a larger levitating octupole,
it has been shown that the plasma is subject to an anomalously rapid escape at a rate of the order of the
Bohm rate. This anomalously rapid plasma escape may be associated with small perturbations from in-
homogeneous external fields. It was reported in other studies that the plasma confinement time in an oc-
tupole reaches 300 Bohm times; collisional diffusion approximately three times as rapid as classical dif-
fusion is observed at a high plasma density, and only at low densities do the additional losses associated
with the imperfections in the magnetic field and the plasma loss at the supports become apparent.
Preliminary data indicate that the imposition of a toroidal magnetic field does not reduce the collision-
al diffusion of the plasma as is expected on the basis of "neoclassical" theory; in other words, so-called
pseudoclassical diffusion is observed. This expression is now used for the semiempirical dependence of
the transport coefficients proposed first by L. A. Artsimovich (USSR)for the electronic thermal conductivity,
which is proportional to the collision frequency and the square of the Larmor radius corresponding to the
"poloidal" (azimuthal) magnetic field. S. Yoshikawa et al. (USA) have observed in a levitated spherator
that the plasma decays after emission at decay times approximately equal to the classical values, but they
observe increased diffusion during the plasma heating.
Other studies of traps having internal conductors have been concerned with such topics as the isola-
tion of supports by current flow within them, plasma stabilization by freezing of lines of force at the plasma
boundary, oscillations in the stable-confinement regions, the formation of convective cells associated with
inhomogeneities in the neutral-gas flow, etc.
Reports on the astron device dealt with electron accumulation in a E layer, the equilibrium of this
layer, and its stability along with that of the plasma. Theory shows that the flute instability cannot be
avoided in the ordinary astron, so the astron modification having an additional toroidal magnetic field is to
be preferred. The resulting system is actually similar to a tokomak operating in the escaping-electron
mode. One astron version having a toroidal magnetic field is an astron spherator, proposed in a report by
S. Yoshikawa and N. Christophilos (USA). It has been found possible to invert the magnetic field within a
ring formed by relativistic electrons in a small model at Cornell University.
Translated from Atomnaya Energiya, Vol. 32, No. 1, pp. 98-101, January, 1972.
0 1972 Consultants Bureau, a division of Plenum Publishing Corporation, 227 West 17th Street, New York,
N. Y. 10011. All rights reserved. This article cannot be reproduced for any purpose whatsoever without
permission of the publisher. A copy of this article is available from the publisher for $15.00.
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There was much interest in tokomaks (two complete sessions were devoted to these devices). Ex-
perimental results found in studies of plasma behavior at the new T-4 and T-6 tokomaks (I. V. Kurchatov
Institute of Atomic Energy) and the TS tokomak (Princeton University), were reported and there was a dis-
cussion of the theory of plasma properties in tokomaks.
The experimental results reported demonstrated progress in the study of plasma parameters and of
the mechanisms operating in plasmas. For example, the achievement of an electron temperature of 3 keV
and an ion temperature above 0.6 keV was reported by L. A. Artsimovich, V. S. Strelkov, et al. (USSR)
in studies with the T-4 device, which is based on the T-3. This became possible because of a significant
current increase achieved by overcoming the barrier at q = 3 (q = rBz/RB0 is the so-called stability re-
serve, where r and R are the minor and major axes of the torus, and 13, and Bo are the toroidal and azi-
muthal magnetic fields) and by converting to smaller q values, as low as q = 2 (according to preliminary
data, values as low as q = 1 have sometimes been achieved).
The physical bases of the possible change to lower q values were clarified in a report by S. V. Mir-
nov and I. B. Semenov (USSR), who reported correlation measurements of corkscrew instabilities in plas-
mas. It was shown that instabilities of mode m arise in a plasma when the q value at the plasma boundary
approaches integral values of m. Between these values there are wide stability regions, so that by rapidly
changing the current and going by the critical q values, one can reach stability regions having smaller q.
These results correspond well to theoretical ideas about the resistive nature of corkscrew instabilities of
modes having m> 1 (V. D. Shafranov). These results also show why it is possible to pass the critical q
values only at a high plasma conductivity. Interestingly, precisely these same results regarding the de-
velopment of the corkscrew instabilities at the edge of a plasma were found in studies with the Princeton
TS tokomak.
Identical results were obtained with these two devices on another subtle effect ? the kink or disruptive
instability: a series of sharp negative spikes in the time dependence of the loop voltage, accompanied by
plasma expansion. This instability, observed in all tokomaks, is initiated as the current channel is con-
tracted (e.g., due to corkscrew perturbations or neutral-gas cooling of the plasma periphery, and when
the plasma is displaced along the major radius). However, the nature of the instability has not yet been
resolved. H. Furth and P. Rutherford (USA), e.g., analyzed the natural assumption that the m = 1 mode
develops within the plasma, but it turns out that the negative voltage spikes cannot be explained in this
manner. It should be kept in mind, incidentally, that the quasilinear approximation was used in this study,
while according to the experimental data of Mirnov and Semenov (USSR) there is a random, turbulent spec-
trum of magnetic perturbations at the instant of the disruptive-instability outburst.
As was mentioned above, experimental results obtained with the T-3 and T-4 devices, on the one hand,
and the TS device, on the other, display an agreement which is rare in plasma studies. However, there
are some discrepancies. One concerns the radial dependence of the electron temperature: in the TS device
this temperature has a sharper maximum at the center of the plasma than in the T-3 and T-4 devices. Furth
reported that this discrepancy could be caused by a temperature instability: the radial temperature distri-
bution turns out to be extremely sensitive to slight perturbations, e.g., in the netural-gas flux from the
chamber walls. Another discrepancy is in the conclusions regarding the diffusive flux. In the T-3 and T-4
devices, the diffusive flux is reported to be much less than the thermal flux, while in the TS device these
fluxes are comparable. This discrepancy will probably require refinement of the calculation of the diffusive
flux in the T-3 and T-4.
In regard to the magnitude of the plasma escape we find for the ionic thermal conductivity a good
agreement with the neoclassical value (except perhaps for the "banana" region of very low collision fre-
quencies), while the electronic thermal conductivity (and, in the TS device, diffusion) is much greater than
neoclassical, while the thermal-conductivity coefficient is roughly proportional to the collision frequency
and independent of the toroidal magnetic field. A special term was even introduced for this dependence,
which was proposed previously by Artsimovich on the basis of an analysis of experimental data: "pseudo-
classical diffusion (or thermal conductivity)." Yoshikawa showed that a slight random inhomogeneity of the
plasma, due, e.g., to drift instabilities, can lead to pseudoclassical diffusion. He also reviewed many ex-
periments in toroidal devices, including some in stellarators, in which diffusion may be interpreted as
pseudoclassical.
The conference heard some results of studies carried out at the recently completed TO-1 and T-6
tokomaks in the Institute of Atomic Energy (USSR); these devices differ structurally from the "traditional"
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tokomaks. Instead of a conducting sheath to maintain the plasma at equilibrium in the TO-1, there is a
system which automatically regulates the transverse confining field. In the T-6 the conducting sheath is
within the evacuated chamber. The spectrum of neutral charge-exchange atoms escaping tangent to the
wall of the torus has been measured in this device, and it has thus been possible to prove the isotropy of
the ion temperature. Interferometric measurements have shown that the plasma density profile is accentu-
ated in the discharge, and the density increases at the axis. This new effect may be due to the pinching of
toroidally trapped particles discussed in a report by A. Ware (USA).
The conference heard theoretical reports on the equilibrium and stability of a toroidal plasma and the
recent developments in neoclassical theory. A. A. Galeev and R. Z. Sagdeev (USSR) carried out a detailed
study of the role of impurities in neoclassical theory. M. Rosenbluth (USA), L. M. Kovrizhnykh (USSR),
and T. Stringer et al. (Great Britain) have derived a systematic theory for plasma revolution in a toroidal
magnetic field and have studied its role in the diffusion. In particular, they have shown that revolution
along the minor, rather than the major, azimuth along the torus plays the more important role when longi-
tudinal viscosity is taken into account. The theoretical reports took up certain effects described by neo-
classical theory: the plasma pinching, the related additional heating, the temporal evolution of the plasma,
etc
Working on the basis of neoclassical theory, B. B. Kadomtsev and Shafranov (USSR) showed that the
diffusive expansion of a low-density plasma results in movement of a poloidal magnetic field toward the
periphery. As a result, when a sufficiently large ratio of the plasma pressure to the pressure of the poloi-
dal magnetic field is reached, it becomes possible to maintain a longitudinal current in a tokomak by a sin-
gle diffusive flux, without an external vortex electric field. In this manner a steady-state (instead of pulsed)
tokomak becomes possible, differing little in this regard from a stellarator. An analogous idea was ad-
vanced by R. Bickerton, J. Taylor, and 0. Connor (Great Britain).
Although the tokomak data found in various laboratories were found to be similar, the stellarator data
remained extremely contradictory. Several years back in conference discussions, one frequently heard the
expression "Munich mystery" for the sharp contradiction between classical plasma confinement at the Wan-
delstein stellarator at Munich and the anomalously rapid plasma decay with a Bohm time at stellarator S.
Today, not only has this "mystery" not been resolved: the number of contradictions has even increased.
One gets the impression that stellarators can be classified into a group in which classical confinement is
observed and into a group in which there is an anomalously rapid decay.
A very nearly classical confinement (within a factor of two to four) has been observed in the Proto-
Cleo device, in which the collisionality parameter, i.e., the ratio of the loop length to the mean free path,
was varied over five orders of magnitude. Classical confinement has also been observed in Saturn 1, in
which the dependence of the confinement time on the neutral-gas pressure has been measured. In a study
carried out under similar conditions and in the presence of a neutral gas, V. I. Volosov observed anoma-
lously rapid plasma leakage governed by the development of instabilities of the drift type. Japanese phys-
icists have also observed anomalously rapid decay of plasma accompanied by the excitation of drift-type
fluctuations. Diffusion an order of magnitude more rapid than classical has been observed in a heliotron.
These contradictory results on confinement have not yet been resolved. Presumably plasma confinement,
at least at a very low density, is very sensitive to small changes in the field geometry and the parameters
of the device, so that it can easily enter a region of unstable confinement. It is satisfying in this connection
to note that in the transition to higher densities and temperatures in the Uragan device the behavior being
observed has much in common with that of the plasma in tokomaks. Specifically, although the confinement
time is much less than classical, the results have been in qualitative correspondence with those found in
tokomaks: the energetic lifetime is governed by the anomalous electronic thermal conductivity (almost two
orders of magnitude greater than the classical thermal conductivity), while the diffusion time has been
much greater than the energetic time.
The lack of agreement on the basic question of mechanisms for plasma leakage has not stopped stel-
lerator studies of subtler physical phenomena. Soviet reports dealt in detail with the increase in the plasma
decay rate near values of the rotational-transformation angle corresponding to closing of the lines of force.
It was shown that the increased leakage is due to the development of convection in the plasma. An experi-
mental study has been made in the Liven-1 stellarator of the development of a quasistationary ion flow in
the plasma, apparently due to the formation of departure cones in the ion distribution function. A detailed
study of turbulent plasma heating in a stellarator was also reported.
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Thirteen reports were delivered to the session on open traps, covering the most recent and deeper
studies of leakage mechanisms and physical properties of the plasmas in adiabatic traps. Successful studies
have been made of plasma parameters [a temperature of up to 106 eV at a density of 1012 cm-3 in a hot-elec-
tron plasma (R. Dandl et al., USA) and an ion temperature of up to 8 keV at a density of 5 -101.3 crif-3 in a
hot-ion plasma in the 2X device] and the processes in plasmas.
Some studies were devoted to plasma instabilities. D. Sweetman et al. (Great Britain) showed that
the threshold for cyclotron instability in a hot-ion plasma is governed by Landau electron damping. They
have observed capture of an injected neutral beam in a confined plasma. The cyclotron instability of a low-
density plasma was also studied by M. K. Romanovskii, N. N. Brevnov et al. (USSR). M. S. Ioffe
(USSR) reported that the plasma in the PR-6 device, having a density of 1011 cm-3 and an ion energy of about
1 keV, decays anomalously rapidly because of an instability of the cone type, which turns out to be extremely
sensitive to the plasma potential (this instability is excited when the potential is increased). As yet no ade-
quate theoretical description of this effect has been reported.
Studies of z-pinches were discussed. Dutch and British physicists have succeeded in improving the
z-pinch stability with a longitudinal magnetic field. Theoretical stability studies by D. Robinson have shown
that magnetic field configurations exist in which the plasma is hydrodynamically stable at currents much
larger than those attainable in tokomaks. The essential question here is whether the conditions necessary
for stability can be arranged. According to the classification proposed by H. Bodin et al. (Culham, En-
gland), pinches stabilized by longitudinal magnetic fields can be divided into three groups according to sta-
bilization method: the screw pinch, in which the stabilizing longitudinal field increases at the same time
as the current in the plasma does; the "stabilized pinch," in which there is a paramagnetic distribution of
the longitudinal magnetic field; anad a pinch with an inverted (outside the plasma) longitudinal magnetic
field. Unfortunately, the experiments which have been carried out so far by Bodin and colleagues have
been devoted only to the stability itself, which sets in under the conditions predicted by theory. The maxi-
mum plasma temperature, of the order of 100 eV, according to data from experiments carried out both at
Culham and at Julich and Garching (West Germany), is found in the screw-pinch mode. The high tempera-
ture is retained for only a short time, however, because of the rapid decay (in 20 Asec) of the discharge
current. Van der Lane et al. discussed the reasons for this rapid current decay.
In recent years there has been much interest in 0-pinches, in which quite high plasma parameters
have been achieved. Numerous results found with linear 0-pinches were reported at the 1968 Novosibirsk
conference. However, these results were flawed because of the presence of end losses and the hydromag-
netic instability of a 0-pinch of finite length. The 0-pinch configuration has now been changed; the linear
systems have given way to toroidal systems, which are similar to stellarator or tokomak systems.
The first experimental results were reported on 0-pinches of toroidal geometry ? in a spatially peri-
odic magnetic field with protective annular conductors (Nagoya University, Japan), in a tokomak configura-
tion with an elongated elliptical cross section (Julich), and in a corkscrew configuration corresponding to
a single-turn stellarator (Garching). F. Ribe reported experimental heating and confinement of a plasma
in the 5-m toroidal sector of the Scyllac device at Los Alamos. The first experiments have shown the va-
lidity of the theoretical prediction of a possible counterbalancing of the toroidal extension of the plasma
through the combined use of a spatially periodic field and a single-turn corkscrew field. Freiberg showed
that the experimental absence of the second and higher perturbation modes predicted on the basis of MHD
theory was due to the finite size of the Larmor ion radius.
Definite progress in the study of plasma-focus physics was demonstrated at the conference. Rayleigh
?Taylor instability of the focus has been observed, the ion energy has been measured on the basis of light
scattering, the temporal dependence of the soft x-radiation has been studied, and the angular distribution of
the neutron radiation has been studied. Calculations by Potter and Haines have shown that the ion velocity
distribution at the focus axis may become highly anisotropic. This result is apparently a key to the ex-
planation for the observed anisotropy in the neutron emission from a plasma focus.
Several reports were devoted to the possible creation of a thermonuclear plasma by means of intense
electron beams (Babykin et al., USSR) and laser beams. Calculations and some first experimental results
on laser heating of a solid target were reported by others. J. Dawson et al. (USA) proposed a thermonu-
clear reactor with magnetic thermal insulation based on a long-wave N2- CO2 gas laser.
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A long session (22 reports) was devoted to theoretical and experimental studies of collective turbulent
phenomena in plasmas. A detailed review of turbulent plasma heating incorporating new results found from
noise measurement in plasmas was given by K. E. Zavoiskii et al. (USSR). Other reports dealt with the
results of a detailed study of turbulent plasma heating under various conditions. These results are gener-
ally in agreement and lead to the conclusion that ion-acoustic oscillations play the leading role in producing
the anomalously high plasma resistance. However, electron beams appear in the plasma, either simul-
taneously with the ion sound or at alternate times, and the beam-plasma interaction which arises compli-
cates the pattern of turbulent processes. The interaction of electron beams (including relativistic beams)
with plasmas have been studied at Khaekov, Prague, Oak Ridge, and Novosibirsk, where many interesting
results have been found on the physics of this beam-plasma interaction and on energy transfer from the
beam to the plasma. In particular, it has been shown that in the interaction of an intense beam with a plas-
ma the heating is achieved by a reverse current induced in the plasma. Several reports were devoted to
the theory of anomalous plasma resistivity [L. I. Rudakov and D. D. Ryutov (USSR) and W. Drummond
(USA)].
Some new experimental results were reported on rf heating of a plasma during propagation of electro-
magnetic waves in it, and new ideas regarding the use of rf fields in plasma heating were reported.
One aspect of the conference which reflected the clear progress in controlled-fusion research was
the session on reactor systems. In the corresponding reports, hypothetical reactors were discussed on the
basis of existing plasma-confinement systems: tokomaks, stellarators, open traps, etc. Analysis of the
engineering problems involved in thermonuclear reactors is already necessary, to furnish a basis for better
evaluation of the outlook for various research directions.
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BRIEF COMMUNICATIONS
The State Committee for Utilization of Atomic Energy of the USSR organized a "scientific familiariza-
tion visit" to the Soviet Union from August 5 to September 7, 1971 for groups of specialists from member
countries of the International Atomic Energy Agency with the theme, "Use of isotopes and irradiation in
agriculture." Representatives from Cuba, Rumania, Poland, Chile, the UAR, Cyprus, India, Ceylon,
Iran, Iraq, Ethopia, Burma, Uraguay, and other countries took part in the visit. This arrangement was
made through facilities granted voluntarily by the USSR from the technical aid funds of the International
Atomic Energy Agency.
One-day seminars were organized for the participants during the visit on the problem of use of iso-
tope tracers in studying the fertility of soil at different levels, use of stable N13 and radioactive P32 isotopes,
and the adoption of radiation technology in agriculture.
The specialists from abroad visited and learned about the research works of the V. I. Lenin All-Union
Academy of Agricultural Science, the V. V. Dokuchaev Soil Institute, the Timiryazev Agricultural Academy,
the All-Union Research Institute for Electrification in Agriculture, the All-Union Research Institute for
Fertilizers and Agronomic Soil Science, the Department of Soil Biology of the Moscow State University, the
Leningrad Agrophysical Research Institute, the Ukrainian Research Institute for Plant Physiology at Kiev,
and the Institute of Cytology and Genetics of the Ural Branch of the Academy of Sciences of the USSR at
Novosibirsk.
* * *
A return delegation of Canadian specialists on reactor materials, headed by Dr. Hart, was received
in September, 1971 in the Soviet Union.
The Canadian specialists visited the I. V. Kurchatov Institute of Atomic Energy, the Khar'kov Physical-
Power Institute at Obninsk, the Atomic Reactor Institute at Melekess, the Beloyarsk nuclear electric power
station and the "First Nuclear Power Station in the World." They became acquainted with the work of Soviet
scientists and specialists on vacuum extrusion of uranium, zirconium, niobium, and tantalum; with findings
on the properties of zirconium alloys working in boiling liquid conditions; with the technology for extrusion
of cladding materials from zirconium alloys and their inspection; with the particular features of the struc-
ture of zirconium alloy with 1% niobium; with problems on hydrogen absorption and corrosion in a neutron
field in a boiling medium. The Canadian delegation were interested in work on structural materials for fast
reactors and for low-power reactors for use in the far-North.
At the concluding meeting with the State Committee for Use of Atomic Energy in the USSR, opinions
were exchanged between the Soviet and Canadian specialists on the problems examined. A recommendation
was expressed regarding the provision of scientific seminars on a defined range of problems.
* * *
An International School on High Energy Physics for Experimental Workers was held from 13 to 27
June, 1971 and the Joint Institute for Nuclear Research together with the Bulgarian Academy of Sciences
and with participation from the European Organization for Nuclear Research (CERN), not far from Varna,
Bulgaria. The object was to acquaint young experimental physicists with the contemporary state of theo-
retical physics.
Translated from Atomnaya Energiya, Vol. 32, No. 1, pp. 101-102, January, 1972.
O 1972 Consultants Bureau, a division of Plenum Publishing Corporation, 227 West 17th Street, New York,
N. Y. 10011. All rights reserved. This article cannot be reproduced for any purpose whatsoever without
permission of the publisher. A copy of this article is available from the publisher for $15.00.
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? The scientific program was in three parts: 1) a basic course of lectures devoted to the theory of
strong interactions and multiple production and also problems of extreme nonelastic electron?proton in-
teractions; 2) specific problems in the theory of relativistic equations, duality and Venetsiano's model;
3) the scientific work of the Joint Institute for Nuclear Research, the high-energy laboratory of the Joint
Institute for Nuclear Research, the Institute for High-Energy Physics at Serpukhov, and work at CERN.
Seminar tasks were set on the basis of the lectures.
The main course of lectures was given by D. V. Shirkov (JINR), Zh. Prentki (CERN), V. S. Bara-
shenkov (JINR), A. Byalas (Poland), Nguen Van Quey (Vietnam) (in a lecture written jointly with A. A.
Logunov), 0. Kofed-Khansen (CERN), and V. A. Matveev (Dubna).
Prominent in the program of scientific research were: the Vice-Director of JINR, A. Mikhul and the
Director of the High-Energy Laboratory at JINR, A. M. Baldin; the Corresponding Secretary of Institute
of High-Energy Physics, V. A. Yabra (with a report written jointly with the Director of the Institute, A. A.
Logunov) and the Director of CERN, V. Entchke.
The total number of participants was 109 from 21 countries. Their training was not all alike ? more
than half those who took part had virtually no experience in research work and approximately 1/3 of the par-
ticipants had been occupied in research work for three years or more.
The school succeeded in the main task of acquainting young experimental physicists with contemporary
aspects of theoretical physics. In the opinion of Soviet participants the school was of great value. Mention
should be made of the excellent organization of the school and the warm welcome extended by our Bulgarian
friends to all those who attended.
The proceedings of the school are being published by the Joint Institute for Nuclear Research in two
volumes.
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(
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; I
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A New Bimonthly Journal
Covering Man-Made Fibers
FIBRE CHEMISTRY
A cover-to-cover translation of Khimicheskie voiokna,
a periodical,organ of the Ministry of the Chemical Process Industrybf the USSR
k
????.
Editor-ih-chief: G. I. Kudryavtsev
Editorial Board:
N. Ya. Alekhin, A. G. i3orshakov, A. L. .Borisov, A. G.
Borik, A. G. Grigoeyants, V. A. Gruzdev (Deputy Chief
Editor), S. 1... Dich, A: A. Konkin, A. P. Krainov, R V.
Kupinskii, B. A. Mukhin, N. V. Mikhailov, E. M. Mogil-
evskli, B. V. Petuichov, A. B. Pakshver, Z. A: Rogovin,
and A. T. Serkov (Deputy Chief Editor).
Translated from the Russian
This bimonthly journal, devoted to furthering
the growth of artificial ',fibre production, will
provide- access to Soviet and non-Soviet
advances in the science and technology of
fibre synthesis. The journal describe's the
present state Of the industry, and its future
prospects, discusses=theoretical and prac-,
tical progress in the production of all-types
of artificial fibres, and presents the most im-
portant advances in research on Macro-
molecular compounds suitable for the manu-
facture of fibres. It deals with the develop-
ment of new processes, the mechanization
and automation of individual operations, the
designs of new equipment, the planning "and
modernization of plants, the economics and
organization of production, and quality con-
trol. All those concerned with the science
and technology of man-made fibre produc-
tion will find this English language edition
a valuable reference source.
Selection of articles from issues 1-5, 1968
CONTENTS: Polymerization of acryloni'trile'in presende
of the potasdium persulphatesodium metabisulphite
'system, N. M. Seder and V. A. Meglitskii. Influence of
the molecular weight of polythene on fiber formation
and properties,' A. A. Aver'yanov, D. V. Fil'bert, and
A. A. Konkin. Supermolecular structure of graft-modi-
fied cellulose fiber& T. S. Sydykov, L. S. Antonyiik:
R. M. Lilishits, and Z. A. Rogovin. Prevention of foam-
. ,
\
ing in thse spinning,and finishing baths in manufacture
of high-strength viscose coed, V.1