SOVIET ATOMIC ENERGY VOL. 48, NO. 1

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• Publication Date: January 1, 1980
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ISSN 0038-531X
Russian Original Vol. 48, No. 1, January, 1980
July, 1980
SATEAZ 48(1) 1-70 (1980)
SOVIET
ATOMIC
ENERGY
ATOMHAH 3HEPrVIA
(ATOMNAYA ENERGIYA)
TRANSLATED FROM RUSSIAN
CONSULTANTS BUREAU, NEW YORK
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SOVIET
ATOMIC
ENERGY
Soviet Atomic Energy is abstracted or in-,
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Editorial Board of Atomnaya Energiya:
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E. I. Vorob'ev
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SOVIET ATOMIC ENERGY
A translation of Atomnaya Energiya
July, 1980
Volume 48, Number 1 January, 1980
CONTENTS
Engl./Russ.
ARTICLES
Chemical Systems for Obtaining Tritium in Thermonuclear Power Generation
- V. G. Vasil' ev . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
3
Direct-Flow Scheme of Reactor with Smooth Tubular Fuel Elements
for Maneuverable Atomic Power Plant - V. N. Smolin, V. I. Esikov,
Yu. I. Mityaev, and S. A. Vasil' ev . . . . . . . . . . . . . . . . . . .
8
9
Regulating Reaction Neutron Field Using Inverse Models - I. Ya. Emel'yanov,
E. V. Filipchuk, P. T. PDtapenko, and V.. G. Dunaev. . . . . . . . . . .
12
12
Statistical Estimation of Fast-Reactor Fuel-Element Lifetime
- A. A. Proshkin, Yu. I. Likhachev, A. N. Tuzov, and L. M. Zabud'ko .
17
16
Effect of Cold Working on the Radiation Swelling of Metals - N. A. Demin
and Yu. V. Konobeev ... . . . . . . . . . . . . . . . . . . . . . . .
22
20
Determination of the Adiabatic Compressibility, Isentropy Index, and Other
Properties of Two-Phase Media - V. S. Aleshin . . . . . . . . . . . . .
28
24
Neutron Resonances of Osmium Isotopes in the 1-550 eV Range
- T. S. Belanova, S. I. Babich, A. G. Kolesov, and V. A. Poruchikov .
33
28
LETTERS TO THE EDITOR
Coice of Some Characteristics of Fast Breeder Reactor at Various Stages
of Nuclear Power Development - M. F. Troyanov, V. G. Ilyonin,
V. M. Murogov, V. Ya. Rudneva, and A. N. Shmelev. . . . . . . . . .
39
33
Calculation of Reactor Water Flow Rate for Purification of Coolant
in Boiling-Water Single-Loop Atomic Power Plants - V. V. Gerasimov,
0. I. Martynova, 0. T. Konovalova, and T. I. Kosheleva. . . . . . . . .
41
34
Reactivity Coefficients of Materials in Fertile Media with K. ~z-,1
- V. A. Dulin, Yu. A. Kazanskii, and V. F. Mamontov . . . . . . .
43
35
Comparison of Cross Sections for the Production of 115Cd and 14OBa
in the Photofission of 235U, 238U, 23'Np, and 2.39Pu - P. P. Ganich,
V. I. Lomonosov, and D. I. Sikora . . . . . . . . . . . . . . . . . .
45
36
Behavior of Boiling Reactor during Withdrawal of Shim Rods - R. E. Fedyakin
and E. V. Kozin . . . . . . . . . . . . . . . . . . . . . . . . . . . .
48
38
Gamma Dose Buildup Factors in Air - I. N. Butueva and I. N. Trofimov . . . .
49
39
Precision Method of Measuring Heat Release in Critical Assemblies
- A. T. Bakov, V. A. Volkov, and R. A. Musaev . . . . . . . . . . . . .
50
39
Effect of Hydrogen on the Error in Measuring the Content of Fissionable
Nuclides by Neutron Methods - V. I. Bulanenko and V. V. Charychanskii
53
41
Dependence of the Intensity of X-Ray Radiation Excited by Protons (Ions)
on the Ion Energy and the Target Thickenss - V. F. Volkov,
A. N. Eritenko, and Yu. A. Malykhin . . . . . . . . . . . . . . . . . .
55
43
Experimental Determination of Tritium Conversion Ratios - D. I. Efgrafova,
Z. V. Ershova, V. K. Kapyshev, and V. I. Sakharov . . . . . . . . . . .
59
44
Possible Use of 145Sm Source for Isotope-Excited X-Ray Fluorescence
Assaying of Tin Ores - V. V. Smirnov, A. P. Ochkur, N. G. Bolotova,
A. D. Gedeonov, E. P. Leman, V. N. Mitov, and B. N. Shuvalov.... . . .
62
46
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CONTENTS
(continued)
Engl./Russ.
Gamna.Rays and Neutrons from 23?Pu Fluorides - V. V. Ovechkin. . . . . 65 48
Effect of Additive Simulating Fission Products on the Elasticity Character-
ist'ics of UC - S. A. Balankin, V. S. Belevantsev, A. S. Bubnov,
V. A. Zelyanin, R. B. Kotel'nikov, and D. M. Skorov . . . . . . . . . . 68 49
The Russian press date (podpisano k pechati) of this issue was 12/25/1979.
Publication therefore did not occur prior to this date, but must be assumed
to have taken place reasonably soon thereafter.
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ARTICLES
CHEMICAL SYSTEMS FOR OBTAINING TRITIUM
IN THERMONUCLEAR POWER GENERATION
V. G. Vasil'ev UDC 539.17:541.121.124
In order to obtain tritium - the main component of the deuterium-tritium fuel in a
thermonuclear reactor (TNR) lithium material can be used by two methods, the optimization
of which is the subject of considerable study nowadays [1-3]. In the first method the TNR
serves as the source of neutrons which are used for the reproduction of tritium, and in the
lithium zone-of the blanket (the shield of the reactor the conditions necessary for the pro-
duction and separation of tritium are created. In the second method the TNR is used for
obtaining energy and nuclear fuel in a hybrid variant; this method uses tritium produced in
fission reactors. This production can be carried out by the use of a symbiotic system [3]
using molten salts, or by irradiating solid lithium materials [4-6].
There are two variants of the utilization of lithium materials: prolonged radiation
for the accumulation of tritium, and short-term radiation for the production of tritium in
the reactor itself [7]. Consequently, in order to obtain tritium from lithium materials, two
chemical systems can be considered - a closed system and an open system.
In the closed system there is no mass exchange with other systems, but the system
receives and gives off energy. The lithium material is situated in a hermetically sealed
vessel and receives energy which is removed by heat transfer. The thermodynamic potential
tends.to a minimum value, and tG is negative.
In the open system there is both matter and energy exchange with other systems, i.e.,
both the mass and the energy can change. The system does not reach equilibrium; the process
continues until the system changes its mass or energy (or both). In the open system, pro-
ducts o.f the nuclear reaction and radiolysis are taken out of the system.
We consider the connection between the amount of tritium accumulated in 1 cm3 of lithium
material and the irradiation time for the neutron flux density of 1013 neutrons/cm'-sec and
an effectiveness coefficient of 0.1 (Table 1). The first days of operation of.a thermonu-
clear reactor are characterized by a tritium concentration of %l0-2-10-4 mg/cm3 in the lithium
materials. The optimum amount of tritium in lithium materials irradiated in fission reactors
can be accumulated in a few months [3].
When the tritium content of the lithium material is ti10 2=10-1 mg/cm3, for the closed
system we can speak of the existance of an independent lithium tritide phase (when metallic
lithium or its alloys with other metals are irradiated) or solutions of tritium water in the
original oxygen compounds of lithium. Consequently, the closed system must be analyzed from
TABLE 1. Lithium Irradiation Time for
Obtaining the Necessary Concentration of
Tritium
Amount of tritium
in 1 cm3
Amount of lithium
burned up for a
density of 0.5 g/
cm3, mass of
Irradiatiori
time, days
10-4
2.1010
4.10-?
0,23
10-s
2.1017
4.10-4
2,3
10-2
2.1018
4.10-3
23
10-1
2.1019
4.10-2
230
1
2.1020
4.10-1
2300
10
2.1021
4
Translated from Atomnaya Energiya, Vol. 48, No. 1, pp. 3-8, January, 1980. Original
article submitted December 25, 1978.
0038-531X/80/4801-0001$07.50 ? 1980 Plenum Publishing Corporation 1
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TABLE 2. Products of Thermal Dissociation and Radiochemical Processes in Lithium
Compounds
Chemical
compound
Radiolysis products
Lill
Lili-. Li-; 0,5 It,
500 'C
Colloidal lithium
hydrogen
[12,131t
LiA1114
LiA1114--. LiA1112-112
180-210?C
,
LiA1112-.1.iH-I-Al-,1 0.5i ll_
230--280 `C
Colloidal lithium
hydrogen
114-.171*, [181t
Lill-. Li 0.5 it,
370--480 ?C
,
LiNO3
LINO2
LiN03-+ LiNO.,-{-0.5 U,
LiNO2-.0,5 Li2O 1175 NO u,5 NO2
Oxide of Li2, LiNO22, N2, 02
[19-211 *, 122-241t
Li2C2
,
Li2C2--.2Li -2C
600 `C
Lithium, graphite
1251 *
Lil'
Lii" Vaporization
800 ?C
Colloidal lithium
fluorine
[26,271*, 128,2911
Lil,' ~ Li-L0,5I ., _
1300 ?C
,
Li2O
Li20 Vaporization
1000 ?C
Li, 02 $
[30-331 *
1.120-. LiO, Li. 02
140n ''C
.Li AlO2
LiAlO2-Lix 0.5A-1,O. -(1,25(1,
1400`C
Li, 02$
134-361 *
Li2SO4
Li2SiO3
Li2SO4 -- Vaporization
Li2SO4-. Li2O'.-SU2..~_0,502
Li2SiU3 -+ Vaporization
6(N) -C
Sot, ti(21 ()2
137-391*, 140-4311
Li4SiO4
L12S103 L1201- S'(),
Li, Si, 02$
*By thermal dissociation.
tBy radiolysis.
$ Hypothesis.
the viewpoint of the equilibrium state with respect to phases containing lithium in one or
another chemical form.
For an equilibrium chemical system we use the well-known phase rule C= K - 4) +n (C is
the number of thermodynamic degrees of freedom of the system, which. defines the largest num-
ber of factors that can vary independently of one another, i.e., the number of independent
parameters which completely define the state of the system in equilibrium; K is the number
of independent components of the system that take part in the formation of the chemical com-
pound; 1 is the number of phases; n is the number of external factors affecting the state of
equilibrium in the given system. The component parts of the system are determined by K,
which can be taken equal to the number of chemical elements making up the compound, plus the
tritium formed'in the system. The number of phases can be predicted if we determine the
value of'n. The systems'underconsideration are acted upon by pressure, temperature, and
radiation (y radiation, neutrons, and "hot" particles - helium and tritium).
The temperature. regime of the irradiation of lithium materials, taking account of the
construction of the ampule, the distribution of neutrons through the material as a function
of the 6Li concentration in it, and the thermophysical properties and composition of the
gaseous phase, is the subject of an independent investigation. If we compare the results
of the action of various types of radiation and high temperatures on the chemical compounds
of lithium, we note that the products formed are identical (Table 2). The mechanism of
formation of the products of dissociation of chemical compounds under heating and under the
influence of hot particles is probably the same, since a high temperature is observed in the
tracks of heavy particles of helium and tritium [8]. For metallic systems the action of
radiation does not lead to the formation of chemical products of radiolysis except for the
products of the nuclear reaction of helium and tritium. Consequently, the number n can be
taken equal to 2, and for closed systems with lithium materials. acted upon by neutron irradi-
ation, the phase rule is written in the form C- K - 4)+ 2. The equilibrium in the system
is affected by only two external factors - temperature and pressure.
The results of calculations of the number of phases and the composition of lithium
systems for two-component, three-component, and multicomponent systems for different values
of C are shown in Table 3. Metallic lithium and systems based on it are characterized by the
formation of lithium tritide, which is considered in a lithium-lithium-tritide system in
[44-46]; for lithium alloys with aluminium the formation of a three-phase system is most
probable [47]. -
In three-component systems formed upon the irradiation of LiF, Li20, and Li2C2, the
formation of systems with three or four phases is probable. For LiF the most probably result
is the formation of a system with colloidal lithium; thus, the compound LiF?HF dissociates
at a temperature of ''200?C [48].
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TABLE 3. Number and Composition of Phases for Closed Systems with Lithium and
Lithium Compounds
Li-Al (alloy
-Al (oy
with all
0-
b
lithium by
mass)-T
System
o
~
oo o
"
o y
Composition of phases
System
0
E
0
"c3 6
Composition of phases
dQ0
0
-t!
0
d
a
(assumed)
0)
o~
'
6
31
W
(3 co
(assumed)
z 0
a.
0
zv
z
M
-
za
0
4
Gaseous phase
O
5
Gaseous phase
Solid phase;lithium,
Solid phase: Li2O, MOT,
lithium tritide
LiO
Liquid phase
Liquid phase
Li-T
2
1
3
Gaseous phase
Li2O-1
3
1
4
Gaseous phase
Solid phase; lithium.
Li-Al(alloy with 3'
lithium
lithium by mass)-T
.2
2
Gaseous phase
2
3
(Gaseous phase
Solid phase: solid solution
Solid phase: Li2O, LiOT,
of lithium tritide in
lithium
0
6
Gaseous phase
Solid phase: Li2SO4 solid
0
5
Gaseous phase
s
olution of T20 inLi2SO4
Solid phase: LiA 1 in alpha
solid solution of SOS in
phase, LiA 1 in beta phase
Li2SO4
Liquid
hase
lithium tritide
p
Liquid phase
1
5
Gaseous phase
3
1
4
Gaseous phase
Solid phase: Solid solution
Solid phase: LiAI in alpha
L'2SO4T
4
of T20 in Li2SO4 solid
solution of SO
SO4
in Li
phase, LiAl in beta phase
lithium tritide
S
2
Li2SO4, solid solution of
T20 and SO3 in Li2SO4
2
3
Gaseous phase
Solid phase:LiAl in alpha
2
4
Gaseous phase
phase, lithium tritide
Solid phase: L12SO4r solid
solution of T20 in Li2SO4
solid solution of SOS in
Li2SO4
For systems with more than three components (irradiation of Li2SO4, LiA102, etc.) the
most probable number of degrees of freedom is. two, since here it is possible that solid
solutions of water with the original substance will be formed. For Li2SO4 the number of
phases is equal to four, which is ' confirmed by the results of investigations of the systems
Li2SO4 - SO3 and Li2SO4 - H2O - SO3 [49-51].
Increasing the number of components in the system is reflected in the redistribution
of tritium among the phases formed, whose number also increases. For hydrogen compounds
of lithium containing Li20, A1203, Si02 and other oxides, tritium oxide will be distributed
among these components.
The above reasoning gives us some idea of the formation of new phases and of the chemi-
cal state of tritium in closed systems acted upon by radiation. The quantitative relations
can be found by means of thermodynamics, taking account of specific systems and the condi-
tions of their irradiation, which vary with time.
The displacement of equilibrium (the removal of some of the products of the system) is
carried out by vacuuming, using a carrier gas, and as a result of chemical reactions with
the walls of the ampule or various types of absorbers. Under these conditions the system
is regarded as open. We can regard as open systems the lithium materials. irradiated during
the first hours and days of operation of"a thermonuclear reactor and a fission reactor.
Published experimental data [52] on the properties of irradiated inorganic compounds of
lithium (the kinetics of the generation of tritium and helium, the chemical forms of tri-
tium in irradiated lithium compounds, radiolysis products) relate to the initial stages of
irradiation. These data, in combination with data on the thermal properties of compounds,
are necessary for a description of open systems.
The chemical forms of tritium formed in the lithium material as a result of the nuclear
reaction can be predicted on the basis of the nuclear chemistry of hot particles. The slow-
ing-down of hot atoms in the energy region in which they do not react is subject to laws
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TABLE 4. Variation of log Psat = f(T) and Average Values of Heat of Vaporization
M
d
f
h
seat of vaporization, kcal/mole
Compound and
Temperature,
?
et
o
o
is E' sat _ ! ~Tl Hg
published
composition, mole
K
measurement
-
expt.
data
LiF
833--1133
Langmuir
Ig p - 11,8 1(>1 1.8,34
54,3?4,0
58,271261
Knudsen
Ig 1, 13,4T 103' 1.10,65
GI,0?4,0
(17,6 [261
BeF2
833-1033
Langmuir
9 60.10
Ig P .:.- - -'
-{-7,02
44?3,0
47-55 j64-65]
T
Knudsen
1W P___ 8,8.103
--
-{-8;17
40,5+3,o
T
LiF-NaK--KF
833-1133
Langmuir
IgP=. --- 11'
2T1(13 -+6,65
42,4?4,0
,
46,5-11,5-42
Knudsen
Ig P -- --- 10,6-105 _}-9,25
48,6?4,0
Lff-Bel:z
833--1033
Knudsen
9 ,62?.103'
I g -
g
{ 7,.16
44,0+3,0
..
T
50-50
Langmuir
lg P- 8'7.103 -{-6;40
40?4,0
LiF-BeF2
833-1033
Knudsen
9,6.
103 x
8,3'7
1g P=-
44,0?3,0
-
T
66,7-:-33,3,
Langmuir
8,2-103-
lg P
I- 5,1~i
37,5+2,0
T
which follow from the assumptions on the collision of elastic particles. In this case, the
slowing-down spectrum is calculated on the basis of equations' which describe the process of
thermalization of, the neutrons [53]. The reactions of tritium recoil atoms take place
through the direct single-stage interaction of the recoil atom with individual atoms, or
more precisely, with chemical bonds. To calculate the yield of an individual tagged com-
pound from a two-component system, the following expression has been proposed [54, 55]:
Rti (fla) I - (f2/~2) K,
where f is the geometric probability of collision; is the average logarithmic decrement
of energy. The results of calculations performed for lithium halides, using experimental
data on the tritium yield R from these compounds [18), are shown in Fig. 1. It can be seen
R('/f)
2,4
Fig. 1. Variation'of R as a
function of f/t for various
compounds: ---) Li2BeF4; o)
experiment.
aW
0,4 9,8 1,2 f/g
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TABLE 5. Phase Composition afterVaporization of Fluoride Systems in a Vacuum
System and composition
Specimen
iporiza-
Loss of
Composition
mass
1o
mole
tiontemp, C
mass, %
?
.
Li
Be
LiF-BeF2
Original composition
9,6
12,32
50 50
Solid residue
560.
5.72
11.0
12,4
LiF-Bel
priginal composition
14,15
9,09
66,6 33,4 (
Solid residue
660
6;35
14,64
9,15
Same
660
7,28
15,94
9,09
? ?
760
20,2
12,2
7,54
760
27,9
18,82
6,67
LiF-NaF-KF
Li
Na
K
46,5 11,5 42
Original composition
7,91
6,41
39,7
Solid residue
660
11,3
8,4
7,5
40,7
Same
660
25,0
i),3
8,1
33,6
Condensate
660
3,16
1,6
53,5
that we do not have a rigorous linear dependence of R(E/f) on f/c. However, for Li2BeF4
we can determine R by calculating f and 1. Calculations show that 70-80% of the tritium
will be produced in the form of T2, and the rest in the form of TF.
The thermal stability of lithium materials can be considered by using the example of
nitric acid, sulfuric acid, and fluorine compounds, some-of"which form the basis of melts
proposed for use in reactors. Here we should emphasize the connection between thermal. and
radiochemical stability. At a certain temperature, the rate-of thermal dissociation will
be greater than the rate of radiolysis, since the recombination processes for radiolysis
products play an important role in the result of the annealing of defects. The rate of
generation of dissociation products by the thermal method will be greater than the rate of
their radiation generation, i.e., Got < (N/M) Ko exp (-E/RT). Using the example of LiNO3, we
can show that for E =15.8 kcal/mole, Ko =1.25.10-', Go= 5.5 ion/100 eV, and power I = 1018
eV/(g?sec) at which the material is not heated above (100?C, T 0.1 MeV corres-
ponded to a. dose of 5.8 displacements/atom).
B. Cold-worked material with an initial dislocation density of 3-10", CM 2, irradia-
ted under the same conditions as material A.
Calculation Results and Discussion. The calculations- of the pore characteristics for
material A were performed in order to check the soundness of the model used and the chosen
parameters. It is evident from Fig. 2 that the experimentally determined temperature depen-
dence of swelling of stainless steel 316, irradiated in the annealed state 72 displacements/
atom in an EBR-II reactor [13, 14], can be reproduced satisfactorily if the coefficient A
in expression (10) is equal to 8.10-8, while bo =2000 A (Eq. (8)) and rj= 1.033. Attempts
at describing the experimental data in the case of diffusion-controlled growth of pores
were unsuccessful. Therefore, the calculations for annealed and cold-worked materials were
performed under the assumption of the surface-controlled kinetics of pore growth.
As was to be expected, the observed drop in dislocation density in the cold-worked
material after irradiation to 10 displacements/atom and the temperature dependence of swell-
ing cannot be explained by assuming, as before, that the density of the dislocations pro-
duced.remains constant during irradiation (pdo =3-10" cm 2; pdo = 0). Calculations show
that. this conclusion also holds in the case where the. intensity of screw dislocations as
neutral sinks remains at a moderate'(pda = 101.? cm-2) and constant level, while the density
of edge dislocations varies under irradiation in accordance with Eq. (12).' The observed
behavior of the dislocation density can*be described if the values, of Pde and pds are ini-
tially,equal and then vary according to Eqs. (12). In Fig'. 2, the dashed curve illustrates
the temperature dependence of swelling for material B,'calculated fora dose of 81 displace-
ments/atom and ae =as =1100- It is evident that cold.working shifts the temperature curve
by approximately 15?C toward higher temperatures and toward higher values of maximum swel-
ling. This phenomenon becomes more pronounced as ae and'as increase. The predicted behavior
of swelling is in qualitative agreement with reactor test: data for stainless steel 304 in
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the cold-worked state [8] and for stainless steel 316 [13]. Calculations show that the
temperature behavior as well as the maximum value of swelling can be varied considerably
by changing the ratio of the densities of edge and screw dislocations in the initial micro-
structure of the metal.
The calculated relationship for the swelling of annealed and cold-worked materials in
the dose range 0-50 displacements/atom is close to a power relationship, i.e., S ti (Kt)n,
where nsi1.4 at 400?C, after which it increases, reaching 3.6 and ti5 at 650?C for annealed
and cold-worked materials, respectively. Calculations show that cold-working leads to an
increase in the "incubation period" of swelling: In the 0.1% swelling range, the "incuba-
tion" doses at 600?C amount to 8 and 20 displacements/atom for materials A and B, respec-
tively. The steeper rise in the swelling of the cold-worked material indicates that the
beneficial effect of cold working diminishes as the radiation.dose increases.
Figure 3 shows the theoretical dependences (for ae = as = 100) of the concentration and
the mean diameter of pores on the irradiation temperature as well as the electron-microscope
data [14] for stainless Steel 316, irradiated in the annealed and cold-worked (20%) states
in an EBR-II reactor to*neutron fluence values of 1.25.1023 and 1.4.1023 neutrons/cm2 (E >
0.1 MeV), respectively. It is evident from Fig. 3 that, apart from the range of low tem-
peratures, agreement with experimental data is fairly satisfactory for annealed stainless
steel. For cold-worked stainless stell, such agreement is observed only in the 500-600?C
range. At 650?C, with a dose of 72 displacements/atom, the calculated pore concentrations
and mean diameter were larger in the.case of material B (NV = 4.2.1011 cm 3; =5450 A),
rather than in the case of material A (NV = 3.4.1011 cm 3, = 4320 A). Analysis shows
that this increase is connected with the stimulating effect of moderate values of the edge
dislocation density on the rate of pore generation at the start of irradiation. However,
the measured NV values exceed considerably those found by calculation for the cold-worked
material. Moreover, the observed pore concentrations in cold-worked stainless steel 316
proved to be higher than in annealed steel. The abnormally small mean diameter of pores in
cold-worked stainless steel 316, irradiated at 650?C with a dose of 81 displacements/atom,
apparently indicates that evolving helium affects the generation and growth of pores at
high temperature, which has not been taken into account in the model discussed here..
1. J. Laidler, B. Mastel, and F. Garner, in: Properties of Reactor Structural Alloys
after Neutron or Particle Irradiation, ASTM STP 570. American Society for Testing and
Materials (1975), p. 415.
2. G. Kulcinski, in: Proc. of IAEA Workshop on Fusion Reactor Design Problems, Vienna,
IAEA (1974), p. 479. `
3. S. Harkness, J. Grappel, and S. McDonald, Nucl..Technol., 16, 25 (1972).
4. S. Harkness, J. Tesk, and Che-Yu-Li, Nucl. Appl. Technol., 9, 24 (1970).
5. R. Bullough and R. Perrin, in: Proc. Reading Conf. on Voids Formed by Irradiation of
Reactor Materials, Harwell, BNES (1971), p. 79.
6. II. Brager and J. Straalsund, J. Nucl. Mater., 47, 105 (1973).
7. W. Johnston et al., J. Nucl. Mater., 48, 330 (1974).
8. T. Kenfield, W. Appleby, and H. Busboom, Am. Nucl. Soc. Trans., 24, 146 (1977).
9. S. Harkness and Che-Yu-Li, Met. Trans., 2, 1457 (1971).
10. H. Brager and J. Straalsund, J. Nucl. Mater., 46, 134 (1972).
11. P. Barton, B. Eyre, and D. Stow, in: Proc. European Conf. on Irradiation Behavior of
Fuel Cladding and Core Component Materials, Karlsruhe, Dec. 3-5, 1974, p. 65.
12. D. Michel and H. Smith, in: Properties of Reactor Structural Alloys after Neutron or
Particle Irradiation, ASTM STP 570. American Society for Testing and Materials (1975),
p. 156.
13. T. Kenfield, W. Appleby, and H. Busboom, Am. Nuel. Soc. Trans., 26, 210 (1979).
14. T. Kenfield et al., J. Nuci. Mater., 75, 85 11978).
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 - Declassified and Approved For Release 2013/02/01 : CIA-RDP10-02196R000800030001-3
DETERMINATION OF THE ADIABATIC
COMPRESSIBILITY, ISENTROPY INDEX,,AND
OTHER PROPERTIES OF TWO-PHASE MEDIA
V. S. Aleshin UDC 621.1.013
Investigation of the proper-ties of two-phase media, and in particular steam-water mix-
tures, presents specific difficulties which are caused by the complexity of producing these
mixtures with a sufficiently uniform finely dispersed structure over a wide range of varia-
tion in them of the relative mass content of the.steam. In addition actual processes with
two-phase media are.usually nonequilibrium to a greater or lesser extent. The flow structure
also differs significantly for different flow modes of two-phase media. Therefore in study-
ing them it is advisable in the interests of_obtaining these or the other dependences to
dwell first on a discussion of some idealized two-phase medium and then to-evaluate the
degree of approximation of different actual processes to these conditions.
We will assume that the two-phase medium has a sufficiently finely dispersed structure,
is uniform, and is in an equilibrium state (the pressure, temperature, and chemical poten-
tials of the phases are equal to each other). The state of this medium is uniquely deter-
mined by two independent parameters - the pressure (or saturation temperature at a given
pressure) and the mass content of steam in the mixture. We will discuss the possibilities
of determining certain properties for a two-phase medium as x varies from zero to unity.
The speed of sound* am is, according to Laplace's equation, equal to
am===)~-vm (8p18v):m, (1)
where (ap/av)S is a quantity which is the inverse of the adiabatic compressibility and vm
is the specific volume of the mixture, which is determined by the expression
vm=v"x+v'(1-x). (2)
One can write with Eq. (2) taken into account
(8v18p)m- (8v"18p).. x-I-(8v'l5p)s (1-x) ?(8x18p)s (v"-v') (3)
for the adiabatic compressibility of a two-phase medium.
It has been shown in a number of papers [1, 2, and others]-that the propagation of
small disturbances (sound vibrations) in two-phase media is not accompanied by any kind of
appreciable heat exchange between the liquid and vapor phases in the zone of rarefaction
and compression of a sound wave. Thus assuming x = const, we have
(avlap)m= (8v"l8p). x+(8v'l8p)_ (1-x). (4)
It follows from Eq. (4) that the adiabatic compressibility of a two-phase medium in
the case under discussion varies, similarly to the specific volume, according to a linear
law from (av'/ap)s at x= 0 to 3v"/3p at x =1.
For steam-water media the-determination of the adiabatic compressibility, and conse-
quently the speed of sound, causes no difficulties, since there are tables of thermodynamic
derivatives for water and water vapor"[3] in which are given the values of'the adiabatic com-
pressibility (dv"/dp)s and (av'/ap)s for the upper (x= i) and lower (x =0) boundary curves.
The calculation of (.av/ap)S -is difficult, for other two-phase media; therefore-an approximate
dependence is proposed below which is 'convenient for calculation.
The isentropy index km is defined by the well-known expression:
*The dependence of the speed of sound on frequency is not taken into account.
Translated from Atomnaya Energiya, Vol. 48, No. 1, pp. 24-28, January, 1980. Original
article submitted January 15, 1979.
28 0038-531X/80/4801-0028$07.50 ? 1980 Plenum Publishing Corporation
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U y
r f ~ (a;/dp)S 10 X
CX - d to
~o o I .n I I ..,v I...... I'. U d A onI le- /ap~slll
60[ 10E12 ' ]0,6140018 we Y
i
R5
40[ 1 81~ 1~ ]44IJ0fl 4 3
2 0,10
E
I 4ua
44 g6 40 d 1 2
Fig. 1 Fig. 2
-Fig. 1. Dependences of 0, (8v/ap)S, (ap/8v)S, am, km, and gm on the mass concentra-
tion of steam -x in the mixture.
Fig. 2. Dependence of gm, x, and (3v/3p)' S on the pressure P2 in the exit cross sec-
t-ion: -) (2v/3p)' S calculated from Eq. (16); ---) (av/ap)S calculated from Eq. (4).
kM_ -vlp(opldv),,
as the ratio of the element of work expended in changing the kinetic energy of an element
of the medium.to the work of expanding this element. Eq. (5) is valid for gases, liquids,
and two-phase media.
Substituting the values vm and (av/2.p)S from Eqs. (2) and (4) into Eq. (5), we obtain
D*.r+y' i-?)
For a saturated vapor (with x = 1)
(dv"l8p),, - -(v lk"p),
and for water (with x =
(dv"ldp)_,= -(L' lk"p)?
Therefore after substitution of Eqs. (7) and (8) into Eq. (6) with account taken of the
fact that the mass vapor content x in the mixture is related to its volume content S by the
dependence
1
1 1 )J
V )7 T (T
r
The values of k" and k' are given in [3] for steam-water media. As the calculations
show, one can neglect the term 1/k' (1/a - 1) (i.e., the. liquid in the mixture is incom-
pressible) as x varies from 1 to 0.01, and then we obtain with a sufficient degree of accu-
racy a simple expression for km:
km=k"/(1. (11).
In the case of a variation of the pressure for a steam-water mixture from 0.1 to 10
MPa the calculation based on the approximate Eq. (11) gives a maximum error "4% at x =0.01
in comparison with the calculation based on Eq. (10), which decreases to zero at x =1. Cal-
culations of km from Eq. (11) were compared with calculations according to the procedure
outlined in [4] with Pz= 2 MPa and a variation of x from 1 to 0.1. The discrepancy did not
exceed 2.4% (at x =0.1).
Similarly, we determine the speed of sound:
29
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280
260
220
200
180
160
140
120
100
80
601! __1 :__-~_ ?1 - = ._.... = --j
.0 0,2 0,f Q6 ~8
Fig. 3. Dependence of the speed.of.sound in the critical cross section on (3
with (1) p =5.5 and (2) p -1.43 MPa: A flow velocity calculated from the
mass flow rate of the mixture; 0 - speed of sound calculated from P2 and x -
in the exit cross section.
Fig. 4. Variation of P2, MPa, Wm, m/sec, x, (av/ap)5, 1010 in 3 /kg-Pa
?C, gm, kg/cm2?sec, and km as a function,of the ratio Z/d (0 - experimental
points).
Neglecting the term 1/k' (1/0 - 1) in Eq. (12), we obtain an approximate dependence for
the speed of sound which is similar to the one given in [5]:
am= J/ Sa k"p . (13)
After substitution of Eqs. (7) and (8) into Eq. (4) we obtain for the adiabatic compres-
sibility
I8? m v x d{1-xj
T 1 1 - 5. k"p k'p
and the approximate dependence has the form
/ 8v\m_-/ n_x
t 8p s k11
The accuracy of the calculation based on Eqs. (13) and (15) in comparison with Eqs.
(12) and (14) is the same as for km according to Eq. (11).
The calculated dependences of the variation of the specific volume vm, the volume
content 0 of steam in the mixture, (av/ap)S, (ap/av)S, am, and km on the mass content of
steam in a steam-water mixture at p=3 MPa a-are given in Fig. 1.
The variation of the speed of sound is determined by the nature of the variation of
(ap/av)S and vm. Since (ap/av)S remains practically constant and close to (ap/3v")5 upon
a decrease of x from 1 to 0.3, the variation of am is determined by the decrease of the
specific volume of the mixture. Upon a further decrease of x from 0.3.to 0-the variation
of am depends mainly on (ap/av)S. A similar calculation of the speed of sound at p =0.1
MPa shows that the minimum value is am =24 m/sec at.x = 0.001.
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The limiting values of the specific mass flow rate of the mixture in the case of
critical flow conditions, when the flow speed in the exit cross section is equal to the
local speed of sound, are also given in Fig. 1, but p = 3 MPa and is constant for all values
of x from 1 to 0. Thus one can determine the characteristics listed, above for two-phase
steam-water media from the derived dependences for any specified parameters (p and x),
and it is possible to find km, (3v/ap)S, and am for any two=phase media from the approxi-
mate Eqs. (11), (13), and (15).
In real processes a two-phase medium in the exit cross section of a sufficiently long
cylindrical channel (Z/d >6-8) corresponds most completely under critical flow conditions to
the idealized conditions under discussion. Thus according to the experimental data'[6 and
others] in the case of the outflow of saturated water through cylindrical channels with
sharp entrance edges phase transformations are completed, the state of the flow is close to
the equilibrium state, and the flow structure is finely dispersed and sufficiently uniform.
The velocities of the liquid and vapor phases in the critical cross section are equal to
each other, and the flow velocity is equal to the local speed of sound.
Assuming that the process is isentropic, one can determine (av/ap)S, the flow velocity
Wm, and the isentropy index km for the exit critical cross section from experimental data of
the mass flow rates of the mixture gm and the pressure p, and pz and the temperature t, and
t2 in the entrance and exit cross sections, respectively, and one can compare the results
obtained with .calculations based on the. dependences given above.
For the determination of the adiabatic compressibility from the mass flow rate measured
in experiments we use the relation
(8v18P)?n= -(t/gm),
which can be obtained from Eq. (1) with account taken of the fact that the flow velocity in
the critical cross section is equal to.the local speed of sound:
Wm =am=gmvm.. (17)
We will determine the specific volume from Eq. (2) and the mass steam content from the
expression
S2-z - (18)
where Sj' is the isentropy of the liquid at the entrance to the outflow channel and S2' and
S2" are the entropy of the liquid and the saturated vapor at the exit cross section.
The value of (dv/ap)S calculated from the known flow rate of the mixture, i.e.., from
Eq. (16), and calculated from Eq. (4) in the case-of the outflow of saturated water (Atsat =
0?C) through a cylindrical channel (Z/d = 18.4) and variation of the initial pressure from
2.45 to 14.7 MPa are given in Fig. 2, and the flow rate of the mixture and the mass steam
content are also shown. Similar calculations were performed for the same pressure range
in the case of underheating of-the water to saturation temperature by Atsat = 10, 20, and
50?C. In all cases the discrepancy in the values of (av/ap)S does not exceed 1-15-17%.
The flow velocities calculated from the mass flow rates for some experimental points
are given in Fig..3, along with the local speeds of sound for these same points obtained
by calculation-from the adiabatic compressibility with p2 and x in the exit cross section.
The discrepancy does not exceed 10-12%. A similar error is obtained in connection with
the determination of the isentropy index.
The completely satisfactory agreement of the values (av/ap)S, am, and km calculated
from the experimental data and the computational dependences -confirms that in the first
place one can neglect phase transitions in connection with the propagation of small distur-
bances in two-phase media and assume Eq. (4) to be valid; secondly, the adiabatic velocity
defined by Eqs. (12) or (13) is realized in the critical cross section; thirdly, one can
use the derived dependences with an accuracy'sufficient for practical purposes in solving
different engineering problems, including for calculations of the flow rates of the mixture
in the flows of the reactor loops of an atomic electric power plant with a VVR reactor.
The derived Eqs. (11), (13), and (15) can also be applied to the calculation of two-
phase two-component mixtures. The effect of nitrogen dissolved in the coolant on the
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properties under discussion was estimated. Thus at a pressure o.f 14.7 MPa in the first
.loop, t= 300?C, and a nitrogen content of ti3000 nml/kg in the loop, the adiabatic compres-
sibility increases by 30%, and the speed of sound and the isentropy index decrease by
^:20%, which cannot be neglected in a discussion of the hydrodynamics and heat exchange in
the active zone of a nuclear reactor.
We note that the discrepancies obtained (up to 15=20%) are evidently the result of
errors in the measurements (especially the pressure) at the exit edge and also evidently
of some incompleteness of phase transitions and nonuniformity in the flow structure.
Upon outflow through short channels (Z/d , 0), (2)
whence p Vwy. The identical values of w for the steady-state and transient regimes of
operation of a given plant allow Eq. (1) to be analyzed further. The left member of the
equation for a given regime remains constant. The term CSDsu2 in the right member of the
equation depends on the operating parameters and, to some degree, on the separation devices.
The term CrwVclyw is not affected by the operating regime of the plant since the value of
w remains constant. Consequently, it is not possible to act on this term. What remains is
the term pCrwp1 which determines the amount of iron CP in the volume of the loop. The flow
rate of reactor water to establish loop purification can be increased, which will entail
higher capital and operating costs, or the concentration of iron CP in the water used for
purification can be increased. The latter can be accomplished by changing the inlet and
outlet for the water. In steady-state operating regimes these places are stagnant zones
with a comparatively low rate of circulation and it is possible to make systematic "rounds"
of these places.
There is a very substantial (up to 50-fold) increase in the concentration of iron CP
during transient periods of operation, which should be exploited to the maximum to eliminate
these products from the loop. In the given case, evidently, it is necessary to also incre-
ase the flow rate of water for coolant purification since the increase CP concentration
in the loop is not maintained for a long ti:-.ie (ti2-2.5 h). Moreover, during these periods
it is desirable to artificially stir up the CP, e.g., by changing the circulation rate by
switching pumps.
The proposed recommendations have already been taken into.accouritin the RBMK-1500 reac-
t-or project. During the transient periods, a larger volume of water used for purification
should pass only through mechanical filters whereas the volume of water entering the ion-
exchange filters can remain the same as in the steady-state regime. It must be emphasized
that the considerable quantity of suspended iron CP in the stagnant zones of the loop is
explained by their arrival with the feedwater since condensate purification takes place
directly after the turbine. One remedial measure is to purify the feedwater in rinsable
ion-exchange filters which are distinguished by a high efficiency and are capable of func-
tioning at elevated temperatures.
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REACTIVITY COEFFICIENTS OF MATERIALS
IN FERTILE MEDIA WITH K. 1
V. A. Dulin, Yu. A. Kazanskii,
and'V. F. Mamontov =
UDC 621.039.51
The use of integral characteristics, measured in critical assemblies, to verify and
correct nuclear data is meaningful only if the conditions of the experiment are adequately
described by a computational model.
Integral experiments on BFS critical assemblies showed [1] that calculation using the
BNAB-70 system of constants [2, 3] unsatisfactorily describes the reactivity coefficients
(RC) of typical.absorbing, scatteringfsand fissionable elements. It was of interest to study
RC in assemblies for which calculations can be made with minimal errors due to idealization
of the three-dimensional calculations. Such conditions were.met by the BFS-31-4, 33-2, and
35-1 assemblies whose central parts had compositions ensuring KwsYl [4], quite large dimen-
sions and a structure that displays little heterogeneity. The observed divergences between
experiment and calculation in this case'aie due to the constant component of the'computa-
tional error.
The BFS-35-1 assembly consisted of metallic uranium with 5.61% enrichment and was a'
copy of the SNEAK-8 assembly [5]. The BFS-33-2 consisted of uranium oxide with.8.35% enrich-
ment while in,the BFS-31-4 the oxide of 235U was replaced by metallic 239Pu. The RC measure-
ments were made in the center of the assemblies with specimens of various sizes. The results
of the measurements are averaged over the heterogeneous structure. of the. assemblies within
the limits of the central cell (4-6 cm). Figure 1 gives the measured CR for specimensyof
239Pu, 1?B, and 12C of various sizes; the;RC are given as ratios to the CR of 235U of zero
size. Analysis of the RC ratios permit the errors of the three-dimensional calculations to
be eliminated and to emphasise the`constant- component of the-errors of calculation. The
size of the specimens in Fig. 1 are characterized by the value co = 1/nl, where n is the
nuclear density of the specimen, Z =4 V/S is its mean geometric size, V-is the volume, and
S is the surface of the specimen. '
The calculations were performed according to the M-26 program [6] in the P1 approxima-
tion using the BNAB-70 system of constants and its modification,OSKAR-76 [7]. Allowance
was made for the effect of the heterogeneous, structure of the assemblies on the RC ratio
[8, 9]. The finite size of the specimens was taken into account by methods described in
[1, 10]. Figure 1 gives the results of these calculations for the real structure of an
assembly (BFS-31-4) and its homogeneous model., For other assemblies the computational dif-
ference between the homogeneous and heterogeneous models is an order of magnitude smaller.
For 12C the dependence of the RC on the size of the specimens is due primarily to the un-
blocking the surrounding medium, which was taken into account in [11]. As seen from Fig. 1,
TABLE 1. Comparison of the Results of
Measurements and Calculations of RC Ratio
BFS
assem RC ratio
bly
2391/u/235U
10B/235 U
12C/235U
239 Pu/U235
/013/235 U
12C/235U
23911u/235U
10B/235 U
12C/235U
1,192?0,015
-0,74?0,02
-0,0114?0,0005
1,260?0,015
-0,895?0,015
--0,0042?0,0003
1,49+0,02
0,52?0,03
-0,0226?0,0010
BNAB- S R-
70 ( 76
1,133
-0,590
-0,0134
1,220
-(),733
-0,0082
1,413
-0,409
-0,0218
1,197
-0,725
-0,0112
1,257
-0,890
-0,0045
1,475
-0,452
-0,0238
Translated from Atomnaya Energiya, Vol. 48, No. 1, pp. 35-36, January, 1980. Original
article submitted January 30, 1978. -
0038-531X/80/4801-0043$07.50 ? 1980 Plenum Publishing Corporation 43
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 Declassified and Approved For Release 2013/02/01 : CIA-RDP10-02196R000800030001-3
Fig. 1. Ratio of reactivity coefficients of 239Pu, 12C, and 10B to reactivity
coefficient of 235U in BFS-31-4-assembly: 1, 2) calculation according to
OSKAR-76 for homogeneous and heterogeneous models; 3, 4) calculation accord-
ing to BNAB-70 for homogeneous and heterogeneous models; 0) experiment.
the dependent of the RC ratio on the specimen size is described well by calculations, as
noted earlier in 11].
Table i gives the results of calculations of the RC ratio, obtained by first-order
perturbation theory (in Fig. 1 this value of the RC ratio atao = o). Corrections for the
heterogeneous structure of the assemblies were introduced into the calculations. Calcula-
tions with OSKAR-76 are in much better agreement with the results of experiment. This is
not surprising since the results of experiments with BFS-31 and BFS-33 assemblies were used
in constructing this version [7]. Thus, the divergences between the calculated and measured
RC ratios for typical fissionable, absorbing, and scattering element-s are explained by the
existence of the constant component of the errors of calculation.
LITERATURE CITED
1. V. A..Dulin et al., At. Energ., 40, No. 5, 377.(1976).
2. L. P. Abagyan et al., Group Constants for the Calculation of Nuclear Reactors [in
Russian], Atomiz-dat, Moscow (1964).
3. L. P. Abagyan et al., Preprint FEI-325, Obninsk (1974).
4. E. N. Kuzin et al.,,Preprint FEI-698, Obninsk .(1976).
5. M. Darrouzet, J. Chandat, and E. Fisher, in: Proc: Int. Symp. on Physics of Fast
Reactors, Tokyo, Oct.-16-19 -(1973)-, Vol. 1, p.. 537. ' -
6. Sh. S. Nikoalaishvili et al., in: Proc. Trilateral Soviet-Belgian-Dutch Symp. on
Some Problems of Physics of Fast Reactors [in Russian]-, TsNllatominform, Moscow (1970),
Vol. 1, p. 192.
7. L. N. Usachev et al., in: Proc. Conf. "Neutron Physics" [in Russian], TsNllatominform,
Moscow (1977), Part IV, p. 27.
8. V. A. Dulin et al., in: Nuclear Constants [in Russian], Atomizdat, Moscow (1976), No.
21, p. 126.
9. V. A. Dulin, At. Energ., 45, No. 2, 107 (1978).
10. V. A. Dulin and V. F. Mamontov, Preprint FEI-392', Obninsk (1973).
11. N. E. Gorbatov et al., in: Proc. Conf. "Neutron Physics" [in Russian], TsNllatominform,
Moscow (1977), Vol. 2, Paper D36.
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 Declassified and Approved For Release 2013/02/01 : CIA-RDP10-02196R000800030001-3
COMPARISON OF CROSS SECTIONS FOR THE
PRODUCTION OF 1 5Cd AND 14OBa IN THE
PHOTOFISSION.OF 235U, 238U, 237Np, AND 239Pu
P. P. Ganich, V. I. Lomonosov, UDC 539..172.3
and D. I. Sikora
In the investigation of photofission processes in transuranium 'elements it is, of'inter-
est to know the yields and the cross sections for the photoproduction of fragments in'sym-
metric and asymmetric fission as a function of they energy. Data have recently been
published [1-4] on the yields of photofission products in the maximum and minimum of the
mass distribution of fragments (or their ratio) as a function of the'maximum photon energy
for 235U, ,238U, 237Np, and 239Pu nuclei. The photofission cross sections'for these nuclides
in the giant resonance region are given.'in.[1].
The existence of such data permits the calculation o'f.the total fission-fragment yield,
the yields of the 14OBa' and 11.'Cd fragments (normalized to'.one electron incident on the
bremsstrahlung?target) as functions of the maximum photon'.energy Eo, and from-the '40Ba and
Cd yield curves the integral and differential cross sections as functions of the photon
energy. The calculation was performed in the following way.. .The total fragment yield per
electron Yf (E0) asa function of the maximum photon energy Eo'is
Eo
Yf (Eo) _ avf (E) P (Eo, E) dE. '
En
The values of the photofission cross section oyf(E) were taken from [1], and the tabulated
numbers of photons P (E0, E) dE in' the bremsstrahlufig spectrum from [5] (En is the photofis-
sion energy threshold).
The yield of an individual photofission fragment.Yo(Eo) '
Yo (Eo)= Y (E
200 % Yf (Eo)-
The values of the percentage yield of fragments were first smoothed out by the least-squares
method.
The cross section for the photoproduction of a fragment o1o(E) was found from succes-
sive solutions of the equation
Ero
Yo (Eo)= avo (E) P (Eo, E) dE
En
for various values of Eo.
Figures 1-3 show the results of the calculations of Yf(Eo) (curve 1) and the values of
Yo(Eo), aYoint (E), ayo(E) (curves 2 and 3) multiplied by the factors in parentheses. It
TABLE 1. Cross Sections for the Produc
tion of 14OBa and115Cd for E =10.5 MeV
avo (E)14? Ba,
a Vo (E)l15 Cd,
10-3 ayo E116( d
mB
ub
Qvf (E)
2,55?0,8
102?30
1,6
1,43?0,4
23+6
0,5
3?0,1
120+40
1,06
5,7?1,8
180+_60
0,95
Translated from Atomnaya Energiya, Vol. 48,:No. 1, pp. 36-38,.January, 1980. Original
article submitted November 27, 1978; revision submitted May 3, 1979.
? 1980 Plenum Publishing Corporation
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 Declassified and Approved For Release 2013/02/01 : CIA-RDP10-02196R000800030001-3
ate, mb?MeV
2)8PU
2J5
LU
'
20
12
/737(4
) 3(9)
238U
n7f, p
4 0
-
30
-
J(41) 0)2fl
2(41 1 3(410)
116
0
-
18 6 10
E0, MeV
Fig.l
2J9
Pu 1000
235U
1 2(37)
800
3(4 40)
600
-
400
-
200
ZJSU 1800
23 'N
1
1400
1000
/
600
241)
00
-
18 6 10 14 18
E0, MeV
Fig. 2
Fig. 1. 1) Photofission yield; 2) photoproduction of 14OBa; 3) photoproduction of
11,5Cd?The value of the ordinate must be multiplied by 3.9.10-25 to obtain the abso-
lute value.of the photofission yield.
Fig. 2. Integral cross sections for 1) photofission; 2) photoproduction of 14OBa;
3) photoproduction of 11$Cd.
is clear from the figures that, within the limits of error, curves 2 for the photoproduc-
tion of 14OBa coincide with the corresponding curves for the" photofission of 235.U, 238U,
and 237 Np.
6,
mb
2)9PU
2J5U
160
3(440)
3(9)
126
-
2(37)
80
40
Z38 u
217Np
3(770) 140
160
.3(410
2(41)
2(41)
80
Fig. 3. Differential cross sections
for 1) photofission [1]; 2) photopro-
duction of 14OBa; 3) photoproduction
of'115Cd. For 239PU curve 3 is in
relative units.
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 Declassified and Approved For Release 2013/02/01 : CIA-RDP10-02196R000800030001-3
The ratio of the yields
K (E0) = Yo (Eo)11scd/Yo (Eo)14OBa
for 239Pu is given in [4] as a function of the maximum photon energy.. Under the assumption
that the shapes of the curves for 239Pu characterizing the dependence of the integral and
differential cross sections for the photoproduction of 14OBa are the same as those for
photofission, it is possible to compare the relative yields Yo (Eo) and the relative cross
sections ay,,(E) for the photoproduction of 115Cd with the,correspondifig functions for the
photofission of 239Pu (Figs. 1-3 for 239Pu).
The relative yield of the photoproduction of 115Cd was determined from the relation
Yo (Eo) = K (Eo) Yf (E0),
and the relative values of the functions aY0(E) and 6Yoint (E) were determined in the same
way as oyo(E) and.oyoint (E)
The relative error in determining the fragment yield AYo (Eo)/Yo (Eo) was'assumed
equal to the relative error in measuring the percentage yield of fragments [1], and did not
exceed.10%. The maximum errors shown in Table land Fig. 3 were determined by the recipro-
cal matrix method [5]. '
A comparison of the data obtained shows:
1) The curves for Yo (Eo),,o1oint (E),'ayo (E),, Yo (Eo), oYoint (E), and coo (E) for
the photoproduction of 115Cd are shifted with respect to the analogous curves for the photo-
production of 14OBa or the photofission of 235U, 238U, 237Np, and 239Pu by 2-3 MeV toward
higher photon energies. Such a shift is observed for photon energies up to 12 MeV, and
cannot be accounted for by computational errors.
2. In the fission of 235U, 238U, 237Np,'and 239Pu by 10.5-MeV photons the cross sec-
tion for the production of 34OBa is larger than the cross section for the production of
115Cd. Tabled shows that the cross section for the production of 115Cd is of the same
order of magnitude as the cross section for the production of isomers in (y, n) reactions
in plutonium and americium nuclides [6].
This behavior of the yield curves and the cross sections for symmetric and asymmetric
photofission may be related to the fact that in the interaction of y rays with a nucleus
there is an octupole deformation as shown in [6, 7] in which the height of the second fis-
sion barrier i-s lowered by 2-3 MeV, and the probability of asymmetric fission is greater
than that for symmetric fission.
In conclusion, the authors thank V. M. Strutinsky and B. D. Kuz'minov for helpful
adviceand assistance with the work.
1. V. M. Gorbachev, Yu. S. Zamyatnin, and A. A. Lbov., Interaction of Radiation with Nuclei
of Heavy Elements, and Nuclear Fission (Handbook) [in Russian], Atomizdat, Moscow
(19,76).
2. M. Ya. Kondrat'ko, V. N. Korinets, and K. A. Petrzhak, At. Energ., 34, 52 (1973).
3. M. Ya. Kondrat'ko, V. N. Korinets, and K. A. Petrzhak, At. Energ., 35, 214 (1973).
4. M. Ya. Kondrat'ko, V. N. Korinets, and K. A. Petrzhak, At. Energ., 40, 72 (1976).
5. 0. V. Bogdankevich and F. A.-Nikolaev, Work with a Bremsstrahlung Beam [in Russian],
Atomizdat, Moscow (1964).
6. S. M. Polikanov, Isomerism of Atomic Nuclei [in Russian], Atomizdat, Moscow (1977).
7. V. Strutinsky, Nucl. Phys., A9.5, 420 (1967); Rev. Mod. Phys., 44, 320 (1972).
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 Declassified and Approved For Release 2013/02/01 : CIA-RDP10-02196R000800030001-3
WITHDRAWAL OF SHIM RODS
R. E. Fedyakin and E. V. Kozin UDC 621.039.58
An important aspect in thestudy of problems of reactor safety is that of reactor
behavior in various emergency situations. One dangerous situation can arise in the event
of an unforeseen withdrawal of shim rods, as a result of which excess reactivity is released,
causing a sharp rise in the neutron density and heat liberation and, in the final account,
this leads to the destruction of the fuel elements. To prevent such an emergency, control
and safety systems have provisions for limiting the rate of withdrawal of the absorber rods
and,. as a rule, they are moved in steps.
In the VK-50 boiling reactor in the critical state without boiling in the core as well
as in VVER (water-moderated-water-cooled power reactors) [1] the withdrawal of any group
of shim rods by 20-25 mm results in a rapid increase in the neutron density (with .a period