SOVIET ATOMIC ENERGY VOL. 58, NO. 1

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• Document Release Date: March 11, 2013
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• Publication Date: January 1, 1985
• Content Type: REPORT

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' July, 1985
i
SATEAZ 58(1) 1J 84 (1985)
Russian Original-Vol. 58, lVo. 1, January, 1985
_ ,
SOVIET
TOMIC
ENERGY:
ATOMHAfl 3HEP~NA
fATOMNAYA -ENERGIYA)
,~ s -TRANSLATED FROM RUSSIAN
CONSULTANTS BUREAU,, NEW YORK
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 Declassified and Approved For Release 2013/03/11 :CIA-RDP10-021968000300060001-5
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50VIET
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ENERGY
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 Declassified and Approved For Release 2013/03/11 :CIA-RDP10-021968000300060001-5
SOVIET ATOMIC ENERGY
A translation of Atomnaya Energiya
Volume 58, Number 1
January, 1985
COI~iTERIT~
Engl./Buss.
ARTICLES
Region of Controlability of an Unstable Nuclear Reactor
- N. S. Postnikov.. .......................... ..........
1
3
Features of the Operation of Local Automatic Regulator Systems
with Lateral Ionization Chambers for Weighted Summation of
Signals from the Lateral Ionization Chambers
- I, Ya. Emel'yanov, A. N. Aleksakov, E. V. Nikolaev,
V. M, Panin, and L. N. Podlazov ............................. ........
7
11
Cesium Migration in Fuel Elements-with Vibrocompacted Oxide
Fuel with Getter Additives.- V. A, Tsykanov;
Yu. M, Golovchenko, I. G. Lebedev, A, V. Sukhikh,
and A. A. Maershin... .................. ..,.
.. ... .,. .,.....,...........
Allowing for the Effects of Residual Stresses on Creep in
Channel Tubes - Yu. N. Knizhnikov, P. A, Platonov,
and A. I. U1'yanov.,
?
?
?
?
.?.???.????.?
13
15
12
13
Effect of Diffusion on the
Selective
Sputtering
of
Composite
Materials on a Carbon Base with Hydrogen Ions
- M. I. Guseva, A. M, Izmailov, V. V, Kuchinskii,
Yu. V. Nikol'skii, and V. A. Stepanchikov............~ .................
20
18 -
An Apparatus for.Measuring.Bending-Stress Relaxation in
Reactors - G. F. Lepin, N. P, Losev, A. Ya. Rogozyanov,
and B. V. Samsonov.. ............
?
?
?
24
21
Structure of Molybdenum Bombarded
with
Low-Energy?Hydrogen
and
Helium Ions during Creep Tests - V. N. Chernikov,
I. B. Savvatimova, A. A. Babad-Zakhryapin,
and. A. P. Zakharov,. ,,,,,,,,,,,,,
?
?
?
?
?
?
28
24
Study of the Diffusion of
Hydrogen
.in
Materials
by
the
Method
of Elastic Scattering of Fast Neutrons - A. N. Valiev,
V. N. Kadushkin, Z. P. Kiseleva, V. N, Serebryakov,
B. G. Skorodumov, A. P. Sokolov, V. A. Shpiner,
P, K. Khabibullaev, and I, 0. Yatsevich ...............................
32
27
Possibilities of Reducing Radiation Erosion by the Use of
Protective Coatings - B. A. Kalin, I. I. Chernov,
D. M, Skorov, P. I. Kartsev, and E. P, Fomina .........................
O
i
38
32
pt
mizing Extractant Molecular Structure for Reprocessing
Spent Nuclear Power Station Fuel - A. M. ?cozen,
A. S. Nikiforov, V. S. Shmidt, Z. I. Nikolotova,
N. A. Kartasheva, and B. S. Zakharkin .................................
45
38
Determination of the Efficiency of a Detector in Gamma
Spectrometry of Large-Volume Samples - E. G. Tertyshnik
and A. T. Korsakov.. ...............
I
i
,
.
?
?
52
44
somer
c Ratios of the Yields
of
Photonuclear
Reactions
for
Gamma-Activation Analysis - M, G,.Davydov, V. G. Magera,
A. V. Trukhov, .and ~. M. Shomurodov ...................................
56
47
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 Declassified and Approved For Release 2013/03/11 :CIA-RDP10-021968000300060001-5
CONTENTS
cco~rin~ed)
Engl./Russ.
Possibility of Decreasing the Energy Dependence of Detectors
Based on the Thermal Luminophor LiF in the X-Ray Region
- L. Z. Kalmykov, T. G. Kandel', S. M. Grinberg,
and I. L. Kruglikov ......................................'............. 60 50
LETTERS TO THE EDITOR ~
Effect of Intragrain Pores on the Swelling of U0z - A. S. Gontar',
R. Ya. Kucherov, and M. V. Nelidov ......................... ......... 64 54
Study of the Conditions of Activation with a Radionuclide Neutron.
Source Based on 2szCf - V. N. Kustov and V. V. Ivanenko ............... 66 55
Determination of the Quantity of Tritium Formed in the Coolant
of Water-Cooled--LJater-Moderated Reactors - S. V. Popov,
A. G. Babenko, B. N. Mekhedov, V. M. Ilyasov,
I. G. Golubchikova, and L. E. Podporinova ............................. 69 57
New Formula for the Spectrum of Prompt Neutrons from Fission
- A. F. Grashin and M. V. Lepeshkin.... .... ....................... 72 59
Spectrometry of the Multiplicity of Gamma Quanta on a Stationary
Research Reactor - Yu. V. Adamchuk, A. L. Kovtun, G. V. Muradyan,
Yu. G. Shchepkin, G. Georgiev, N. Kalinkova, E. Moravska,
N. Stanclieva, N. Chikov, and N. Yaneva............ ..................... 75 61
Neutron Sources Based on a Booster - N. I. Alekseev ........................ 79 64
Use of Metallic Lithium for Detecting Solar Neutrinos
- E. P. Veretenkin, V. N. Gavrin, and E. A. Yanovich ................... - 82 65
The Russian press date (podpisano k pechati) of this issue was 12/28/1984.
Publication therefore did not occur prior to this date, but must be assumed
to have taken place reasonably soon thereafter.
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 ARTI~-Declassified and Approved For Release 2013/03/11 :CIA-RDP10-021968000300060001-5
REGION OF CONTROLABILITY OF AN UNSTABLE NUCLEAR REACTOR
N. S. Postnikov UDC 621.039.515
Many modern reactors suffer from an unstable energy distribution throughout the core.
We are only able to operate such reactors by using special systems of regulation, which must
be capable of stabilizing the neutron flux [1, 2]. Many articles have discussed the stabili-
zation of neutron flux ([1-5],,for example). A feature of the regulation of unstable reac-
tors is that the natural limitations on the effectiveness of the reactor control rods make it
impossible to cope in the steady state with all disturbances of the steady-state conditions
[6]. Consequently, the problem of finding the set of permissible initial disturbances of
steady state conditions is urgent.
The present article proposes a way of plotting the region of controlability and studies
in qualitative terms the set of deviations in the parameters of the reactor from their steady-
state values which can be compensated by such a system of regulation.
Mathematical Model. A Statement of the Problem
We use equations for a single-group diffusion approximation to describe the changes in
neutron flux, linearized in the region of the steady-state condition [7]:
~M ~ T
~- m (fib a -{- F) -E- ~ ~,ici -~ ~~
---i
a~;
cpfd(pcp,n)=0, rEI'
where ~ _ (~ - ~~)/~ is the relative deviation of neutron flux from its steady-state value
~*; ~ _ ~ I ~*dw)l f dw is the mean value of. neutron flux in the core 52, bounded by surface
s sa
P; r is the radius vector; r E ~ -I-I'; ci is the deviation from steady state of the concentra-
tion of nuclei radiators of delayed neutrons for the i-th group; Z is the life of the instan-
taneous neutrons; ai is the decay constant of the .source of delayed neutrons in the i-th
group; ~i is the contribution of the i-th group to the neutron multiplication coefficient;
~ _ }~ ~;; MZ is the square of the migration distance of the neutrons; n is the normal to
~__~
surface P;
~ is the steady-state neutron multiplication coefficient for an infinite medium;
a is a constant; t is time; F is the variation in the multiplication coefficient k~ caused by
the controls; the components of vector b(r) determine the reactivity coefficients; bTu is the
variation in reactivity due to internal feedback, which can be described by linear equations
of the form
8u .- Pu -~ a~P+
~t
where P(r) is an n x n matrix; a(r) and u(r, t') are vector functions.
(2)
Let us assume that the reactor is stabilized by an interconnected system of regulation
whose contribution to the multiplication coefficient can b
f
d f
e
oun
rom the expression
k
F- ~1 ~i (r) 6t?
Here ~yi(r) is a weighting function; of is the relative setting of the controls, which are'
Translated from Atomnaya ~nergiya, Vol. 58, No. 1, pp. 3-7, January, 1985. Original
article submitted March 11, 1984.
0038-531X/85/5801-0001$09.50 ? 1985 Plenum Publishing Corporation 1
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 gene Declassified and Approved For Release 2013/03/11 :CIA-RDP10-021968000300060001-5 ma-
terial ror neutron capture ~liquias, gases). 'i'ne rottowing limitation is imposed on movements
where points ?8i represent the extreme positions of the controls.
If we postulate that,
W _ I M20z-]-(k~-1) -~J/l; ~,i/l; cl~~bT/l
fit; ---? ~i; 0 ;
a; 0; P l (S)
i-1,....k
we can rewrite system (1)-(3) in the form
h
v= Wv+S h~Qi; l6i(t)I ~si? (6)
i=1
Let us assume that the reactor is unstable without a system of regulation, i.e., that part of .
the intrinsic value of operator W (the last term) lies to the right of the imaginary axis of
the complex plane. The problem consists in determining-the region of controllability Q of
system (6), i.e., the set of initial conditions v(0) for which a permissible (4) exists that
translates system (6) from v(0) to the point v = 0. Let us assume that the translation of sys-
tem (6) from v(0) to point 0 is permitted both at the end and also up to infinity in time, i.e.,
we shall endeavor to find a region of e controllability [8].
Method of Investigation
Space E of system (6) can be represented in the form of the sum of two half-spaces E _
Rn + Eo, where Rn and Eo a.re the unstable and stable invariant forms of operator W. We can
assume that the unstable half-space is finite. System (6) is usually divided into two sub-
systems [9]:
k
Y=W+Y 1-v hi 6i; YE~"; IQi(t)I~fiii (7)
i=1
z=tit'-z -f- ,~~ hoi; ZEE'o; 16i(t)I~si?
i=1
Subsystems (7), (8) describe the behavior of the initial system (6) and its unstable and sta-
ble forms Rn and Eo. In this case, W+ and W- are the constrictions of operator W in half-
spaces Rn and Eo; hi and hi are the projections of vector hi on Rn and Eo. The region of s
controllability Q cf system (6) takes the form [8, 10]:
Q=Q++Eo={v=3'~-z:yEQ+; zEEo}>
i.e., the set of those .values of v whose projection on the stable manifold is artibrary,
whereas their projection onto unstable half-spaces Rn belongs to a limited convex set Q+,
fully determined by its hyperplane of reference [10]:
Q+={Y: I~tTYI 4L -
0
i+
S: I siu :~i~j ~
~_i
2
S~T ~~~~>ZH2 +Q_l
The value of ~ characterizes the contribution made.by the control system to the i-th un-
stable harmonic. We can see from (18).that the size of the controllability region greatly
depends upon the. parameters of the reactor and the system of regulation. If the effectiveness
of the rods (di) is increased, the region of controllability will.itself increase. By choosing
an adequate degree of effectiveness, we are able to include any predetermined set of devia-
tions of the reactor parameters in-the region of controllability. However, the effectiveness
of the rods is not infinite., so we have to look to.other resources for increasing the permissi-
ble disturbances of the steady-state conditions. We can see from expression (18) that 4i = 0
and the reactor is not able to stabilize *n the i-th harmonic if. all the rods are in the posi-
tions belonging to this harmonic (sin ~ri~~ 0). We can increase the region of controllability
without changing the effectiveness of~the rods. by planting the rods at points corresponding to
the maximum for the harmonic (sin ~ri~~ = 1). We can see from expression (18) that 4i is in-
versely proportional to the positive intrinsic value of si. Therefore, the size of the region
of controllability falls to zero (or increases) with an increase (or decrease) in the degree
of reactor instability.
If it is only the fundamental harmonic that is unstable, then 41 (18) entirely determines
the regi:on'of instability, which is subject only to the u(~) for which I2x1I = ~yl~ < ~i? If
all the harmonics are unstable, then set Q+ in the plane.yl, yz is determined by taking into
account the interactions between-the fundamental and second harmonic. The set Q+ in Fig. 1 is
drawn for parameters (13) and b = 3.58. Curve 1 bounds Q+' when-only one control rod is in use
at the point l;i = 1/4, with an effectiveness S1 = f3/2. We can see that a reactor that is un-
stable in two harmonics can be stabilized by means of a singly linked system of regulation.
Curve 2 bounds Q+ in the presence of two control rods at points ~* = 1/4 and ~Z = 3/4, with an
effectiveness of dl = R/4, SZ = R/4. We can see from Fig. 1 that the controllability region
for one rod is little different from that for two-rods with the same summated effectiveness.
Let us assume that the reactor has a closed, system of control in addition to its open sys-
tem of regulations (17), which at-any given moment in time maintains the given value constant.
The contribution of these systems to the multiplication coefficient of .the neutrons can be found
from the expression F = F1 + FZ, where F1 has the form (17) and F2 is found from the following
expression:
Fig. 1. Regions of controllability
of systems (11), (17).
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 Declassified and Approved For Release 2013/03/11 :CIA-RDP10-021968000300060001-5
=1 (19)
1
0
In this expression, Yi signifies-the relative position of the control rod in the reactor, as
did 6i; gi(g), fi(b) are weighting functions: Equation (1.9) defines the law governing the
displacement of the rods. The operator, or an automatic system, moves the rods to a position
Yi such that Eq: (19) is satisfied at any instant in time. The system of 'regulation (19), by
maintaining m given values constant, is able_to stabilize the reactor. However, as with
the initial system, unstabilized high harmonics can remain in the reactor. We also introduce
an open system of regulation (17) to stabilize these.
To build up the region of controllability of system (17) in the presence of system (19),
we need to know the positive intrinsic values of si and ttie intrinsic functions ui, ui of
operators Wand W*, which are determined taking closed system (19) into consideration. Func-
tions ui, ui are solutions of the boundary problems
He dFe 1 Tat ~-1 J ~Pt -f"
m
j=1
I f j (~) ~Pt (g) d~ = D;
i=1, ... n
H? ag$t~+ ~ Tst-F1 - tl) tPi ~' I
m
j=1
0
i=1, ... n
~t (~) _ ~t (1) _ ~~
j=1, ... m
i
By postulating that yt = ~ ui (~) u (~, t) d~ and differentiating yi, we obtain subsystem (7) in
0
accordance with expressions (11), (17), and (19) in the form
k
Ts ? -~-1
yt = Styt -f- hT ~j ut (~i) 6i, i = 1, ... iz.
j=1
The region of controllability now has anew form:.(15).
I,et us assume that system (19) consists of one rod (m = 1), located at point 3/4 [g1 =
d(~- 3/a)] and maintaining the power [fl(y) =sin ~r~] constant. The solution to systems (20),
(21) takes the form
st - b z _ 11 i7';
- ~ (nt)z H ~-a
3
_ sin 4 ni
ui = Sin ~i~ - 3 sin ~~ , i - ~, 3 ... .
sin 4 n
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2,4
Fig. 2. Relationship of size of region
of controllability to arrangement of
control rods.
3
_ sin-rzi
a z
Yi = 3 f b- ("~M -}- a) (Tsl -I- 1)~ ; yi = 0?
sin4n L
Let us also assume that b = 3.55, while the remaining parameters correspond to expression (13).
As a consequence, a reactor equipped with a mean-power regulator will only remain unstable in
the second harmonic u2 = sin 2~ri;. A second regulator (17) (k = 1, S1 = 5/2) is introduced,
bringing in reactivity at point ~i', which has to be included among the parameters.
A region of controllability is assinged in half-space
` u (~) sin nid~=0 $nd comprises
0
only those values of u(~) for which
1
uz (~) u (~) di I < A,, (~i) = 0.631 sin 2a~1 -{-1.41 sin ~~i
0
By employing. an expression of u(~) in functions of sin ~ri~, we obtain a region of controlla-
If we consider a deviation of u(~) in the form of a second harmonic u(~) = x2sin 2~r~,
then the rod at point ~i can .compensate. for a deviation.of amplitude Ixz~ < 2~z(~i). The
relationship between the size of the region of controllability at the second harmonic and
the position of the second control rod is shown in Fig. 2 (curve 1). This same relationship
2~Z(~i) of form (18) is determined. in curve 2 for the case where there is no mean-power regu-
lator. By comparing. these curves, we can see that the interaction of the regulators has a
powerful influence on the size of the region of controllability.. In fact, Fig. 2 shows that
if the rod belonging to the open system of regulation is located in .the interval ~i E L0; 0.62],
then its interaction with the mean-power regulator facilitates third-harmonic stabilization,
to increase the region of controllability. When the rod is at point 3/4, the region of con-
trollab*lity does not reach zero,. even. if the second rod *s located at the harmonic "node":
point ~i = 1/2. If regulator (17) lies in the interval ~1E[0.62;11, however, the interaction
of the .regulators obstructs third-harmonic stabilization,-.reducing the size of the region of
controllability to zero when-both regulators are at the same point ~i = 3/4.
LITERATURE CITED
1. I. Ya. Emel'yanov, E. V. Filipchuk, P. T: Potapenko, and V. T. Neboyan, "Engineering
problems concerned with the regulation of an unstable distribution of power in:a nuclear
reactor," At. Energ., 37, No. 2, 118-122 (1974).
2. I. Ya. Emel'yanov, P. A. Gavrilov, and B. N. Seliverstov, The Control and Safety of Nu-
clear Power .Reactors [in Russian], Atomizdat, Moscow (1975):
3. I. Ya. Emel'yanov et al., "The development and testing of systems of local regulation
of reactor type RBMK-1000," Vopr. At. Nauki Tekh., Ser. Fiz. Tekh. Ya.d. Reaktorov, No.
1(5), 3-16 (1979).
4. E. V. Filipchuk, P. T. Potapenko, and V. V. Postnikov, Controlling the Neutron Field of
a Nuclear Reactor [in Russian], Energoizdat, Moscow (1981).
5. V. N. Konev and .B. Z. Torlin, "The validity of the problem of neutron distribution in
a reactor," At. Energ., 54, No. 6, 390-395 (1983).
6. N. S. Postnikov and E. F. Sabaev, "The stability of reactors with regulating systems
having positive coefficients of reactivity," Vop. At. Nauki Tekh.,-Ser. Dinamika Yad.
Energ. Ustanovok, No. 2(8), 79-89 (1975).
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 7' Declassified and Approved For Release 2013/03/11 :CIA-RDP10-021968000300060001-5
~i7v~~.
8. A. G. Butkovskii, Theory of Optimum Control of Systems with Distributed Parameters [in
Russian], Nauka, Moscow (1965).
9. S. G. Krein, Linear Differential Equations in Banach Space [in Russian], Nauka, Moscow
(1967).
10. A. M. Formal'skii, Controllability and Stability of Systems with Limited Margins [in
Russian], Nauka, Moscow (1974)..
11. V. G. Boltyanskii, r4athematical Piethods of Optimum Control [in Russian]., Nauka, Moscow
(1969).
FEATURES OF THE OPERATION OF LOCAL AUTOMATIC REGULATOR SYSTEMS WITH LATERAL
IONIZATION CHAMBERS FOR idEIGHTED SUMf4ATI0N OF SIGNALS FROM THE LATERAL
. IONIZATION CHAMBERS
I. Ya, Emel'yanov, A. N: Aleksakov, E. V. Nikolaev, UDC 621.039.56
V. M. Panin, and L. N. Podlazov
At the present time, high-powered water=cooled channel(RBP~) reactors with traditional.
neutron-power automatic regulators, using lateral ionization chambers (LIC), for the most
part employ local automatic regulators`(LAf~LIC), which were themselves developed from LIC.
Since LAR-LIC have.a.number of important advantages over a straight automatic regulator (AR)
[1], a. trend towards replacing these by ZAR--LIC has arisen. The AR rods in the RBMK reactor
are already-set at.distances that-are close to the optimum spacing for LAl~-LIC [1, 2]. Con-
sequently, the conversion-from AR to LAR--LIC can be considered as equivalent to replacing ,the
synchronous control of all control rods according to the average unbalance over all the mea-
sured channels by control of each rod separately according to the unbalance between the sig-
nal of the LIC and the setting for each measurement channel.
This can be written formally as
n
4i fit) = ~1 aijOJ j [t), (1)
where qi(t) is the unbalance of-the i-th control channel, aij is the weighting coefficient at
which the j=th LIC is taken into account in the i-th channel; ~Jj(t) is the deviation of the
signal of the j-th LIC from setting; n is the number of control channels.
For an AR system, all values of aij = 1; for the LAR~IC system, aij =. dij, where
Vij -
pp ~ ~' L ~,
1, (. = j.
We can see from Eq. (1) that AR and:LAR-LIC'are the extreme limiting cases of averaging
unbalances for forming the rod-control signal. Intermediate cases would seem to be possible
in which the i-th rod of the LAR-LIC system takes account of other (j-th) chambers, subject
to some weighting factor aij, in addition to the signal from the i-th channel.
,The introduction of weighted summation opens up wide possibilities for varying the prop-
erties of an LAR--LIC system,. by choosing one or other. method of weighting. Investigations
of these new possibilities are of undoubted interest, both scientific and practical. A major
role here appears to 'be played by the weighting coefficient itself.. If we assume that the
processes in .reactors characterizing the interacCions of the separate points-are of a relaxa-
tion type,. then the natural choice of weighting factors will be subject to an exponential re-
lationship, i.e., they will take the form
eaP ~-*I I ei-9j I )
aij _ n f
exp(-~ I si-ek I)
k=1
Translated from Atomnaya Energiya, Vol. 58, No. 1, pp. 7-11, January, 1985. Original
article submitted June 15, 1984.
0038-531X/85/5801-0007$09.50 ? 1985 Plenum Publishing Corporation
Declassified and Approved For Release 2013/03/11 :CIA-RDP10-021968000300060001-5
 Declassified and Approved For Release 2013/03/11 :CIA-RDP10-021968000300060001-5
Fig. 1. Relationships of dispersion
D (l, 2) and rod displacement R (3,
4),? that arise when processing a
polyharmonic disturbance, to coef-
f icient r~ .
where 8i and 6j .are the azimuth i-th and j-th LICs, respectively.
The LAR-LIC system in use at the present time incorporates eight measurement channels, in
which signals representing the deviation of the LIC indications from:the settings are formed,
together with eight rods that can be moved individually in accordance with each signal. The
rods are controlled according to a relay law, i.e., the excursion of the unbalance outside the
limits of the set dead zone moves the rods at constant speeds in a direction designed to elimi-
nate the deviation. When weighted summation is introduced into the commands governing move-
ment of the rods, then not only-does the unbalance in. the measurement channel of the LIC ap-
propriate to the rod concerned contribute to the signal, but also the unbalances in the other
measurement channels.'
When studying the properties of LAR-LIC systems with weighting coefficients (2), we use
a polyharmonic radial-azimuthal dynamic model of the RBMI: [3]. This model makes use of the
equation for the dynamics of the neutron field, linearized about the rated condition of opera-
tion, and includes a description of the action of the LAR-LIC system itself. -The solution
appears in the form of a finite series of low harmonics (16 terms in the expansion)..
The quality of a "fast" reaction of the system is estimated by processing momentary dis-
turbances of the neutron-multiplication coefficient of equal amplitude to each other for the
whole set of harmonics participating in -the solution. The criterion of quality is the residu-
al deformation of_the neutron-field after processing the disturbance and the summated displace-
ment of the rods during this processing. The measure of the residual field deformation is the
dispersion
s
wherecp(r, tk) is the dimensionless deviation of the neutron flux from its steady-state value
at instant tk at the end of the disturbance-processing operation and the transition of the re-
lay-action LAI.-LIC into-the sliding state. The displacement of the rods is measured by the
sum of the squares of the linear displacements at that particular moment:
s
R (tk) _ ~i 41f ~tk)?
a~i
In addition to this high-reactivity criterion, an important characteristic of the system
is its stabilizing properties when there is a nonuniform distribution of energy. The rela-
tionship of dispersion D and the displacement of the rod system R to coefficient n is shown
in Fig. 1. When r~ = 0, the signals of all the chambers are summated for each channel of LAR-
LIC regulation and the system turns into an eight-rod AR. When n -} ??, the system turns into
an LAR-LIC system in which each rod operates in accordance with the signal from its individual
chamber.
Up to a point, the dispersion will rise above the asymptote corresponding to n = ~? when
the slope of the decay of the weighting coefficients falls. However, a marked reduction in
the rod displacement R begins even earlier. This shows that when weighted summation is intro-
duced, the quality of the processing achieves a level equal to that of an LAR-LIC system at
far smaller rod displacements. The nature of this effect is determined by the width of the_
dead zone d of the LAR-LIC relay system. The results set out in Fig. 1 were obtained for S =
1.0 (2, 4) and 0.5 (l, 3). It is clear that deviations in D and R from:'-.the asymptotes cor-
responding to n -} ~ start at lower values of n for d = 0.5% than is the case for S = 1.0%.
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 1r 1~ ~
Declassified and Approved For Release 2013/03/11 :CIA-RDP10-021968000300060001-5
'u,P7 -
J6 -'"
~ 09 v ~
~?
a
-0?
-0,78 O
.Vj~ ~6
?-0,0 -0,04 _02y O
? Q04
O'{ ?h :2 004
i ~
'
-021
O p
-0,01
-001
`0,0! ? -0,0
-0,29 ? ?
-0
21? ?-0,21
.003 ?~
O p
t~.2 ~q12 - ~. A
reduction in S leads to arise in the asymptote of D at relatively low values of S (8 ~ 1.5%),
since the greater the accuracy in processing the disturbance, the larger will be rod displace-
ment that is entailed. And insignificant increase in the accuracy with which the low har-
monics are regulated means that a reduction in d is swamped by an excess of high-harmonic ex-
citation, leading to an excessive reaction. of the rods: the R asymptote lies higher at n ->
for smaller values of d.I~~!pAn excessive extension of the dead zone results in loss of accuracy
in regulating the lower harmonics, and the D asymptote starts to grow at some value of.8 (3-
4%) . I~ ~~
Figure 2 gives the 'results of calculations at S = 1.0%, illustrating the changes in the
nature of the system reac~t~on due to disturbances close to the chamber, when weighted summa-
tion at various values of~~p is introduced. In the calculations, the disturbance is created
by manually withdrawing ~h~ control rod adjacent to the chamber at radius of 5.3 m. The rod
is extracted by 1 m:
When n -} ~, the motion of the rod operating in the channel in which the dis
turbance
arose is 1.46 m. The rods~~~n:the neighboring channels travel in the opposite direction by
0.21 m. The rod movement,in the remaining channels is insignificant (0.02-0.06 m). A rela-
tively large movement (O.i09~m)is observed in the rod diametrically opposite to the point of disturb-
ance.
When n = 1.0, the motion of the rod in the channel subject to the disturbance is 1.03 m
under the same conditions~,ga~s before. The rods in the neighboring channels move by 0.04 m in
the same direction. The remaining LAR-LIC rods move in a direction coinciding with the dis-
!. ,
turbance by 0.01-0.04 m, whale the diametrically opposed rod moves by 0.18 m.
When n = 0.5, the su~~pllus attenuation of the high azimuthal harmonics introduced by
weighted summation leads to a "blurring" of the .reaction to the disturbance. The processing
of the disturbance involves all the rods in the half of the reactor lying adjacent to the "dis-
turbed" LAR-LIC channel; The rod of the disturbed channel is moved by 0.53 m (disturbance =
1 m), while the diametricsl~y opposite rod moves by 0.24 m. Consequently, the case where n =
1.0 for 6 = 1.0% roughly corresponds to the state in which the reaction to a disturbance near
to a chamber is concentra.t``e~ mainly in the disturbed channel itself.
We will now turn ourlattention.to the behavior of the unbalance signals in the measure-
ment channels of the LAI~LIG. When n -} ?~, the signals remain within the dead zone. The in-
troduction~of weighted sum~~tion means that the unbalances after processing differ signifi-
cantly from zero. The greatest deviation is seen in the disturbed channel. As n decreases,
the distortion in the form~~o~f the neutron field caused by the disturbance becomes worse: When
rl = 1.0, the "residual" deviation in the disturbed channel is ti8.4% relative to the mean.?de-
viation in the two neighboring channels. This is increased to 16% when n = 0.5.
?
The introduction of wel~ighted summation leads to some freedom in variation of the unbal-
ance signal compared with the existing LAR--LIC system. This feature can be put to use when
there is a possibility.of iir~ft in the sensitivity of the measurement channels. The drift
can lead to a mistaken increase in power in the region of the rod of the drifting channel if
the sensitivity falls, andl~it is impossible to detect such a situation from the chamber sig-
nals in the existing LAR-LIC system.
~~
i`~
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 Declassified and Approved For Release 2013/03/11 :CIA-RDP10-021968000300060001-5
where Q is the matrix column's of the "operational" unbalances, A is the weighting factor ma-
trix, and ~ is .the matrix columns of the deviation of the LIC-from setting. This expression.
also relates to the case without .weighted summation, A in this case being a unit matrix. Since
the introduction of weighted summation changes only matrix A, .the changes in the stabilizing
properties of the system can be analyzed from the variation in the properties of-this matrix.
If the dead zone S = 0, then A~ = 0 with the system operating in the stabilization mode.
Since A is a unit matrix without weighting summation, then ~ = 0. If the determinant of the
matrix does not fall to zero when weighted summation is introduced, A~ = 0 only when ~ = 0.
This signifies that when S = 0-and det(9) ,1- 0, the introduction of weighted summation. does
not affect the stabilizing properties of the system. ----
Let us consider the properties of matrix A when weighted summation is used. Let us as-
sume that the weighting coefficients summated in the LIC signal when the unbalance is formed
vary symmetrically to the same ,extent for all channels with distance in azimuth from the basic
chamber. In this case, matrix A is cyclic and symmetrical. As a result, we find that
det (A) _ (ao ~- 2a1-{- 2az ~- 2as ~- aa) ~ao -f- j12a1- Y 2as - a4}z (ao - 2az + a4)z X
X (,ao-~2a~-~~~as-ay}z (ao-2a1-{-2az-2as-I-a4)
for an eight-zone LAC TIC system, where ao is the weighting coefficient of the basic chamber;
al, a~, a3 , and a4 are the weighting coefficients of chambers displaced by 45?, 90?, 135?,
and lII0? respectively,. relative to the basic LIC. The weighting coefficients are standardized
so that ao + 2a1 + 2az + 2as + a4 = 1. The determinant of :matrix A equals zero if one of the fol-
lowing conditions is satisfied:
ao - 2az .t a4 - 0; (4 )
a -j/2a, -f 2as-a4--0; (5)
ao - 2a1-}- 2az - 2as -{- a.y =-: 0. (6 )
10
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 Declassified and Approved For Release 2013/03/11 :CIA-RDP10_02196R000300060001~-5~ 1ics,
which permute the monitored system of rods for a given set of weighting coefficients. The in-
ability to monitor any azimuthal. harmonic shows that the unbalances in all regulation channels
are zero, regardless of the amplitude of the harmonic. For. example, condition (3) is equiva-
lent to a first azimuthal harmonic that is unmonitorable. To show this, we find the unbal-
ances of the LAR-LIC system due to deformation of the radial-azimuthal neutron field of the .
first azimuthal harmonic::type, aligned in such a way that the zero line passes through the
horizontal diameter of the reactor. The deviation in the lower half is positive, while that
in the upper half is negative. The transducers are numbered clockwise, starting with the
transducer on the lower end of the vertical diameter. The unbalance in the i-th regulation
channel, expressed through amplitude [Ao~(t)] and the spatial form [i~ol(r)cos6] of the first
azimuthal harmonic, equals
4t (t) _ !-~ ati~o~ (t) ~~oi (ri) cos At =C ~ a+t cos A~,
~=1 ~_.-~
where C = Aol(t)tJ~ol(r~).
Taking condition (3) into consideration, we find that
9f = ~' (ao -I- 2Z a1-F- Oaz ._ YZ d3 - a, - ~Z a3 -~ Oa2 -f- ~2 a =. C a
2 2 2 i) ~ 0-}-~2a+-Y2n3-a,)=0;
4z=C ~ jz2ao~-Qas- ~22aZ-a3 - ti22a4-1-Oas -I- ~ZZaz-I-a~) -C 22(ao-j12a3-a~-I-V2at~=0.
The symmetry condition apparently means that all other unbalances also equal zero. In
the same way, we can show-that satisfaction of condition (4') signifies that the eight-zone LAIC
LIC system does not monitor the second azimuthal harmonic.. Satisfaction of condition (5)
signifies that the third harmonic is not monitored, while satisfaction of condition (6) sig-
nifies that the fourth harmonic is not monitored.
Consequently, the determinant of matrix A is inverted to zero-only when specially se-
lected weighting coefficients are chosen to satisfy conditions (3)-(6). Specifically, within
the framework of the "harmonic" regulator idea [4], it is proposed to segregate one or two low
azimuthal harmonics, and having suppressed them, ignore the higher harmonics. When applied to
an LAR-LIC system, this idea is also realized in the form of weighted summation, the so-called
"harmonic" method of weighting, apparently leading to .coefficients that .correspond .to condi-
tions (5), (6).
Let us consider the case in which the weighting coefficients vary in accordance with ex-
ponential.law (2). Figure 4 expresses the relationship of the determinant of matrix A and
coefficient n. The determinant obviously varies in the range 0-1, equalling zero only when
r1 = 0. This signifies that the mathematical problem of determining stability when weighted
summation is introduced is equivalent to this same problem for an LAR-LIC system without
weighting coefficients, i.e., the conditions for stability with exponential. weighting and with-
out weighting are identical.
We should distinguish between the practical and formal-mathematical aspects of those re-
sults. For example, when n is very small but not equal to zero, A~ = 0 only when ~ = 0, even
though the weighting coefficients are virtually identical under these conditions. In fact, Q
also equals zero with a finite degree of accuracy (when a dead zone exists), and for small
values of n the system behaves in exactly the same way as .for p = 0; i.e., when there is a
Fig. 4. Relationship of determinant of matrix
A to`n.
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 dea Declassified and Approved For Release 20.13/03/11 :CIA-RDP10-021968000300.060001-5 an
analysis carried out on the supposition of no dead zone at all.
A system possessing the required practical effectiveness, both in its plan for process-
ing disturbances and from the viewpoint of stabilizing unstabilized field motions, can be ob-
tained for specific combinations of n and S. With regard to the condition of achieving ac-
curacy of regulation while maintaining a permissible frequency of operation of the control-
rod drives, a value of S equal to about l% is usually chosen. As we have seen already, the .
quality of processing disturbances.at such a value of S demands a value of r~ ~ 1.0, since
the dispersion virtually coincides with the asymptote corresponding to no weighted summation
for this combination of n and S. This also signifies that the. ability to monitor the high
harmonics and, consequently, the effectiveness of the field stabilization are virtually,un-
affected by the presence of the weighted summation process.. '
Consequently, our analysis confirms that the introduction of weighted summation effec-
tively enhances the operational properties of an LAR-LIC, provided certain conditions are
satisfied. Specifically, it allows us to:
.improve the reaction of an LAR-LIC to disturbances close to the chambers and simplifies
dialog between the operator and the LAR.=LIC system during manual regulation of energy distri-
bution;
monitor any possible drift in the sensitivities of the measurement channels and reduce
mistaken increases in reactor power during falls in channel sensitivity;
achieve these advantages and maintain a high level of system effectiveness in a plan for
stabilizing unstable energy. distributions, by selecting.a specific .combination of dead-zone
width (S = 1%) and decay constant (r1 ~ 1 rad-1) of weighting coefficient.
1. I. Ya. Emel'yanov, L. N. Podlazov, A. N. Aleksakov, et al., "Synthesizing a system for
stabilizing energy distribution and controlling. reactor power, based on lateral ioniza-
tion chambers," At. Energ:, 56, No. 1, 11-15 (1984):
2. I. Ya. Emel'yanov,.L. N. Podlazov, A. N. Aleksakov, and V. M. Panin, "Synthesizing. zonal-
asymmetrical systems of automatic energy-distribution regulation for a reactor," At.
Energ., 47, No. 6, 370-373 (1979).
3. I. Ya. Emel'yanov, L. N. Podlazov, A. N. Aleksakov, et al., "Synthesizing a system of
local automatic regulation for power reactors," At. Energ., 53, No. 5, 301-305 (1982).
4. P. T. Potapenko,."Harmonic regulation of the power of a power reactor," At. Energ., 50,
No. 1, 8-13 (1981).
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 Declassified and Approved For Release 2013/03/11 :CIA-RDP10-021968000300060001-5
CESIUM MIGRATION .TN FUEL ELEMENTS WITH VIBROCOMPACTED OXIDE FUEL
WITH GETTER ADDITIVES
V.
A.
Tsykanov,
Yu. M. Golovchenko,
I.
A.
G.
A.
Lebedev,
Maershin
A. V. Sukhikh, and
It has been established that fission products affect the efficiency of the fuel elements
of nuclear reactors. In the first place this applies to chemically active products, among
which cesium plays an important-role. Numerous domestic and foreign studies point to the
participation of this element in corrosion. damage of fuel-element cans in reactions between
uranium and plutonium oxides.
Model experiments have indicated that at a certain oxygen potential cesium causes corro-
sion damage to stainless steels, similar to the damage observed in the fuel elements o.f fast.
reactors (1, 2J. Studies with the aid of an x-ray microanalyzer confirmed the presence of an
increased concentration of this product on the outer surface. of the fuel core, in layered zones
of the interaction of the-fuel with the steel, and at grain boundaries during intercrystalline
corrosion of the can of spent fuel elements [3, 4].
The experimental results [5, 6] indicate considerable deformation of the can in the re-
gion of spikes of cesium concentration along; the length of the fuel element. Extrareactor
experiments confirmed the possibility. of cesium uranate-plutonates, of a density lower than
that of the initial fuel, being formed under certain conditions [7]. -The formation of these
compounds may lead to the deformation of fuel-element cans. All of this has aroused scien-
tific and technical: interest in the study of the physicochemical-state and behavior of cesium
in-oxide fuel. The cesium migration increases upon the introduction of metallic getters into
the oxide fuel.
The test fuel elements consisted of OKh16N15M3B austenit.ic steel tubes filled with pow-
dered uranium oxide with the ratio 0/U =-2.00-2.01. Enriched.U02 was used in the active part
and natural U02 was used in the reflectors. The getter, in the form of .a powder with a par-
ticle size of less than 50 um, was introduced at the rate of ti5% in relation to the heavy
atoms by means of prior mixing with one of the fractions of the U02 powder. The fuel elements
were irradiated in a BOR-60 reactor at an average thermal load of 40 kW/m to a burn-up of 5%
Fig. 1. Distribution of the concen-
tration of fission products over. .the
length of fuel elements with a.uran-
ium getter (a) and without a getter (b).
Bottom
,many .vl
Translated from Atomnaya Energiya, Vol. 58, N
Original article submitted April 19, 1984.
? 1, pp. 12-13, January, 1985.
0038-531X/85/5801-0013$09.50 ? 1985 Plenum Publishing Corporation
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 Declassified and Approved For Release 2013/03/11 :CIA-RDP10-021968000300060001-5
PartLinto1theuZonevof the Reflectors up-
on the Introduction of Getters (in %)
No 1-element I
Getter material I
Cesium yield
1
--
11
2
Cr
5-111
3
Nb
1~~--1fi
4
V
1U-1~i
5
'fi
~ 411
6
!, r
... 511
7
lJ
~ 50
of the heavy atoms. The concentration of fission products was measured on a semiconductor
gamma-spectrometer.
Figure 1 shows how 137Cs and 95Zr are. distributed over the height of the fuel column.
Data about the influence of the getter material on the yield of 137Cs from the active part
of the fuel elements into the zone of-the lower and upper reflectors are given in Table 1.
The experiments indicate self-purification of the fuel-core from cesium when active metals
are added to it. It was established that the placement of the getter in the upper and lower
reflectors (in the absence of getter in the active part of the fuel column) does not affect
-the cesium distribution.
When the relative yield of cesium from the fuel core into the reflector (see Table l), is
compared with the .values of the oxygen potential of the oxides [8], formed by the metal-getters,
a distinct correlation is noted: the lower the oxygen potential of the oxides, the higher the
cesium yield. It may be assumed that the introduction of the indicated getters leads to the
establishment, in the oxide fuel, of an oxygen potential that corresponds to dynamic equilib-
rium in the metal-oxide system. This potential determines the chemical state and behavior of
the cesium.
Thus, the introduction of metallic getters into the active part of the fuel core is an
effective means of acting on the thermodynamic state and behavior of the chemically active -
fission product cesium.
LITERATURE CITED
1. P. Hoffman and 0. Gotzmann, in: Behavior and Chemical State of .Irradiated Ceramical
Fuels,, IAEA, Vienna (1974), p. 237.
2. E. Aitken et al., Trans. Am. Nucl. Soc., 14, No,._l, 176 (1971).
3. K. Perry and C.. Craig,.Trans. Am. Nucl. Soc., 12, No. 2, 564 (1969).
4. V. A..Tsykanov., E. F. Davydov, E. P. Klochkov,.et al., "Study of the physicochemical
interaction of oxide fuel with .the cans of the fuel elements of a fast reactor," At.
Energ., 56, No. 4, 195 (1984).
5. U. Nayak et al., Trans. Am. Nucl. Soc.,. 19, 113 (1974).
6.. V. G. Dvoretskii and A. V.Sukhikh, :'Influence of the initial inhomogeneity of the den-
sity of vibrocompacted fuel on the state of the cans of test fuel elements irradiated
in a fast reactor," Vopr, At. Nauki Tekh. Ser. At. Mater., No. 1(12), 25 (1982)..
7. E. Aitken et al., Thermodynamics of Nuclear Materials ,. Vol. 1, IAEA, Vienna (1975), p.
187.
8. K. Weeks and F. E. Bloch, Thermodynamic Properties of 65 Elements and Their Oxides,
Halides, Carbides, and Nitrides [Russian translation], Metallurgiya, Moscow (1965).
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 Declassified and Approved For Release 2013/03/11 :CIA-RDP10-021968000300060001-5
ALLOWING FOR THE EFFECTS OF RESIDUAL STRESSES ON CREEP IN CHANNEL TUBES
Yu: N. Knizhnikov, P. A. Platonov, UDC 621.039.531
and A. I. U1'yanov
Introduction. The walls of channel tubes made of zirconium alloys show residual stresses
of the first kind [1] due to the manufacturing technology. It is of interest to consider-how
these stresses influence the creep, which in some cases determines the working life of the
channel tubes or fuel sheaths.. Here one expects the stresses to be distributed only over the
wall thickness, which is due to the symmetry of the working processes along the length and
in azimuth. The residual stress (axial oZ(r), circumferential o~(r), and radial 6R(r)) should
satisfy the conditions for self-balancing in the bulk as well as the boundary conditions at
the: walls:
Rz
R1
R,
Qe (r~) dr' = 0, oR (Rs) = dR (Rz) = 0,
R,
where R1 and R2 are the internal and external radii.
The integral self-balancing conditions should also be obeyed in various mechanical oper-
ations on the items, where there -will be the corresponding stress redistribution. Methods
of measuring the residual-stress distributions in tubular specimens are based on this, for
example, the ring and band deformation. method. [2]. It is also:possible to use x-ray methods.
As.an example, Figs. 1 and 2 show the measured distributions of o0? and a~ in the walls
of two high-powered water-cooled channel re-actor (RBMK) channel tubes, which are character=
ized by concentration of the tensile stresses at the outer wall. Conditions (1) are obeyed
in both cases. The dashed lines show the stepped distributions approximating the positive
and negative parts of the distribution curves 1 and 2, respectively.
Methods of Calculating Creep with .Allowance for Residual-Stress Relaxation The creep
strain is considered for the working conditions for RBMK channel tubes [3]. The creep rate
of the zirconium alloy [4] in the absence of infernal stresses is described by a superposi-
tion of thermal and radiation components:
eo [h-1) = 7.2.10-zt-o?sash 9.85x6 eXp - 4575 ,+, g.7.101~ sh 21.4a eR 26000 21 ( 6000
T ) ~ T ) ( T ~ p~- T ~+1.135.10- cp6exp l- T ~
-- (2)
where t is time in h, o is stress in Pg'a, T is temperature. in ?K, and ~ is neutron flux den-
sity,. m 2?sec-1.
Formula (2) has been derived by processing experimental data on the thermal and radia-
tion creed in the tube material under uniaxial load. The factor s in the transient thermal
creep component reflects the additional retardation of mobile dislocations by the damage,.
cascades.- The important point is that s decreases as the neutron fluence Wt increases from
s = 1 to the minimum value s~ =.0.385 at ~t = 3'lOZ`' m z.
In calculating the creep in an anisotropie material such as a zirconium alloy, one uses
the associated flow law for plastic deformation: The creep anisotropy is specified by the
coefficients F,, G, and H, which are analogous to the plastic-strain anisotropy coefficients
Translated from Atomnaya Energiya, Vol.. 58, No. 1, pp. 13-17, January, 1985. Original
article submitted February 2, 1984.
0038-531X/-85/5801-0015$09.50 ?1985 Plenum Publishing Corporation 15
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 , Declassified and Approved For Release 2013/03/11 :CIA-RDP10-021968000300060001-5
x=0,25; dG~~234;
day=?56,5
u
dZ,: MPa
~
'~
200
dz ,MPa
---
! I
i
-
150
?
~
900
-96'
-025'd
x- cs-
,
dna ' -25, 2
100
- Distance from outside
~ radius, mm
~ 1 2 . .~
XeD,JJ; 6c?=9fs;
0',~ ?-3Z
Fig? 1, Patterns of the circumferential
and axial residual stresses (type 1
distribution).
Fig. 2. Patterns of the circumferen-
tial and axial-residual stresses
(type 2 distribution).
introduced by Hill [5] for tube deformation.
The deviator expressions for the creep rates in the principal directions are
ee=EO(Qf)/Qf [(F-I-G)6e-GoZ-FaRI;
Ez - EO (Qt)l~t [ (G -{- H) oZ - Goe - HaR] ,
where of = F(oR - Qg)2 + G(oe - aZ)2 + H(oZ - oR)Z is the effective stress, which defines
the creep rate for a combined state. of strain.. The strain rates for all the principal direc-
tions will be defined by the observed creep rate go(of) as measured in uniaxial loading (for
example, by (2), where one substitutes the corresponding value of of for the uniaxial stress).
The creep anisotropy coefficients were calculated from the texture model TEXTUR. For a
typical texture in a channel tube [4], F 0.10, G 0.49,.H = 0.51; these values were used
in the calculations. It is usually assumed that. these characteristics are constant over the
wall thickness-for a given material.
Our task was to devise a method of calculating the strain on the basis of the residual-
stress relaxation. The residual stresses add to the stresses from the external pressure in
each layer, and so the strains could be appreciably different in uncoupled layers. However,
the tube is coupled and .continuous, so the strain is consistent in all layers. The correspond-
ing stress relaxation occurs over the section.
One can calculate the strain with detailed incorporation of the relaxing stresses from
a model implemented in the RELAXU program. However, the processes involving relaxation. can
be elucidated qualitatively by considering first a simpler two-layer model implemented in the
RELAX2 program. In this model, the real residual-stress distributions are approximated as
stepped functions in the layers H~ and HA (HA + HG = H):
oeC Rz~r>RZ--HC (layei C);
oe(r)- t QeA Rz-HC~r~Ri (layer A);
oiC Rz~r> Rz-Hc (layer C);
Q*(r)= ~ oZa RZ-Hc~r~R1 (layer A}.
h introduced the parameters x = H~/HA, the ratio of the layer. thicknesses, .and
Here we ave
y = RG/RA, the ratio of the median radii of the corresponding layers. Then x = 0.25 and y =
1.035 for distribution 1.
On the basis of the balancing conditions (1), we get relationships for the residual
stresses in the layers:
0 0 0 0
QeA = - xQec; vsA = - ~yazc; 5
0 0 0 0
QRA = y6RC; QRC = QQ9C>
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 when- ., , . ,. ? . _ ,
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To calculate the strain increments in the circumferential and axial directions (Deg, fez)
.occurring in a time interval 4t, we adopt the planar-.section hypothesis:
~Ez = C = consL (over the cross section) ( 6 )
and the condition for volume conservation during creep:
To obey (6) and (]), we introduce the residual-stress relaxation in a step 0t, with the
stress changes in the layers related by (5). The actual: principal stresses in the layers with
the additive ,increments are used. to. calculate the effective stresses in..the layers 6fC and ofA
of (3), together with the corresponding deviators. Then from (3) we calculate the increments
in the. strain for the free layers, namely: egC = EgC~t, EzC = ~zC~t, etc.
From the conservation of the planar section for the tube of (6) we get that the.axial
strains in both layers are consistent, and therefore it is necessary to include fictitious
elastic strains in order to allow for the residual-stress relaxation [2]. We have from (6)
that
0
4EZ = G= Ezc -L. DE cc - E (A6eC -r AQRC) = EzA
Another expression is obtained for, the circumferential strain from the volume conserva-
tion of (]). Then we use (8) and introduce the stress relaxation to express the circumfer-
ential creep strain for the -outer radius of the tube R2 in terms of the strains for the median
radii of the layers RC( and RA:
e ( z) _- 2 ec -f 0v
4E R Rz l_ E ~E c - E ( ?c -f ~o?RC) ] - R 2R Rc rEzc -i- ~Ec - E (OcreC -I- Donc)) _
2 ~
-- Rz [EeA + 4 EA - E (06zA'}- OQRA) J - Rz2RRA [EzA + 4 EA - ~ (AoaA ~- 06RA)] .
z
We solve (8) and (9) with (5) to express the stress relaxation in terms of the differences of
the calculated strai
i
h
f
ns
n t
e
ree layers:
~aec P1 Pt
E - ~ Ott ~ ~z;RR
~1 - EBA - yZEBC - N_4EzA +'NCEzC+
4a?C P9 Pa
E' - ~ ~1+ 4 ~2e ~z-E1A-EzCv
i RZ 1
~'A=2 (RA-1) ~c=2yz(Rc-1J'
where P1 = z + xy; Pz = uY(x + Y) + gC + xYSA~ P3 = ull + x + Q(1 - Y)~; Pa = x + Y + u(RC +
xR~,) + uQ(Y Y + RC - ysA); 4 = P1P4 - PZP3,
We see that the relation in all eases tends to reduce the disequilibrium produced by the
residual stresses, while the relaxation rate at any instant is determined by the difference in
the calculated strains for the contacting layers.
On substituting (10) into (8) and (9), we get expressions for the creep deformations:
4Eg (~z) _ ( RZ ) 2 {Eec - ~s E=c -I- Ol (- P1 (1 ~- Sy ?- ~Q ( 1 - Sa ~ ) ~ p3 ( ~ + ya ) ]
-~ e Cpz11+ ysc-?Q (q- yz ~)- p4(?+ y2 )JI' (lla)
DEz=EzC' Ol [ps-?(1-1-Q)I'il-I- ~2 [p4-?(1-I-Q)I'zl? (llb)
For a thin-walled tube, y = 1 (SC, SA, IQI ? 1); then (lla) and (llb) simplify to
DE8 (R2) - 1+i -1- i+~ ~ ~Ey = i+~ _~ 1EzA
-{- z .
06cA - ? (OQyA ~- 06RA)
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 a?, Declassified and Approved For Release 2013/03/11 :CIA-RDP10-021968000300060001-5
a?. MPa
200
Residual-
stress relaxa-
tion (type 1)
6e 1100?K, almost no rearrangement of the surface or enrichment of the near-surface layers with
metal atoms occurs,
LITERATURE CITED
1. M. I. Guseva, A. P. Zakharov, E. S. Ionova, et al., "Graphite and metal carbides as mater=
ials for the limiter, shield, and injector plates of a thermonuclear reactor," At. Energ.,
51, No. 4, 247 (1981).
2. V. V. Kuchinskii, Poverkhnost'. Fiz. Khim. Mekh., No. 4, 93 (1982).
3. V. M. Gusev, N. P. Busharov, S. M. Naftulin, and A. M. Propichev, Prib. Tekh. Eksp., 4,
19 (1968).
4. A. G. Zhiglinskii, A. M. Izmailov, and V. V. Kuchinskii, in: Sixth All-Union Conference
on the Physics of a-Low-Temperature Plasma (Collection of Theses) [in Russian], Vol. 1,
Leningrad (198.3), p. 204.
5. Handbook on Special Functions [in Russian], Nauka, Moscow (1979), p. 120.
6. F. Behrish, in: Sputtering by Particle Bombardment. I: Physical Sputtering of Single-
Element Solids, Berlin~lew York (.1980).
7. M. I. Guseva and Yu. V. Martynenko, Fiz. Plazmy, 2, 593 (1976).
8. K. Nielsen, in: Electromagnetically Enriched Isotopes and Mass Spectrometry, London
(1956), p. 68.
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 Declassified and Approved For Release 2013/03/11 :CIA-RDP10-021968000300060001-5
G. F. Lepin, N. P. Losev, UDC 621.039
A. Ya. Rogozyanov, and B. V. Samsonov
It is of interest to measure-the stress relaxation at the low strains usually char-
acteristic of fuel-pin sheaths in order to describe the stress train state in them and to
determine the viability.. Such measurements can be combined with other tests to give a more
reliable description of the stress-strain state.
It thus is necessary to have an apparatus for relaxation tests on structural materials
under irradiation, particularly for the SM-2 and RBT-6 reactors. Some additional specifica-
tions had to be met. The transverse dimension of the irradiation device should not exceed
45 mm, while the length of the loading ties should be a few meters. All the operations dur-
ing the measurements have to be made by remote control and do not allow halts in the tests.
It is impossible to place any complex measuring system near the irradiated specimen.. The
permissible temperature fluctuations are ?5-7?C for the specimen, while those in the compo-
nents of the irradiation device. are t20-30?C. The radiation resistance of the structural
materials should allow one to perform tests at fast-neutron fluxes.(E > 0.1 MeV) of 1010-101`'
cm Z?sec 1, temperatures of 300-700?C, and times up to 5000 h. No existing stress-relaxa-
tion test method for uniaxial stretching meets these requirements [l, 2].
.The method based on specimens in the form of Oding rings [3] is the most suitable for
reactor tests. It is then not necessary to place complicated measurement systems in the
irradiation zone, since the strain is not neasured but instead is set by the thickness of
-the loading wedge inserted in the slot in the specimen. Also, the effects of specimen tem-
perature fluctuation are eliminated. It is necessary to reduce all dimensions of the stan-
dard Oding ring (about 65 mm) by about a factor 2, but this does not affect the character
of the stress-strain state (Fig. 1).
A shortcoming of this method is that in fact one. derives the relaxation curve for the
bending moment, not the stresses. This required additional development in the method of
determining the relaxation-characteristics from tests on ring specimens in uniaxial stretch-
ing [4, 5]. A balance method of determining the stress was used to ensure continuity in
the reactor tests and remote measurement. A monotonically increasing force is applied at
the time of measurement. to the ends of the specimen from the wedge along the tangent to the
average circle, and one determine s. its value Q at the instant of failure of the electrical
contact between the specimen and the wedge. The wedge is made of two metallic parts sep-
arated by a thin section of radiation-resistant insulation (Fig. 2). Knowing the force Q [N],
which is equal to the reaction of the wedge on the specimen, one can [6] determine the nomi-
nal stress o (in MPa):
6 _ 2r Q = 122 Q - 1.029.10aQ, (1)
Wo bho
where Wo is the resistance moment of the radial section diametrically. opposite the slot, and
b and ho are the width and thickness of the ring in that section (Fig. 1), which are 2.5?
10-3 m. The improved method of [7] enables one to eliminate halts in the tests and to auto-
mate the measurements.
The structural scheme for the reactor relaxation tests (Fig. 3) includes the specimen
and wedge, the loading device, the electric heater, the load transducer, the thermal measure-
ment transducers, and systems for pneumatic loading, electrical control, and measurement.
These systems are located outside the reactor channel., while the other components form the
irradiation device. The specimen (F.ig. l) is made with-high accuracy in order to provide
stress determination with an error of not more than ?2%. The working (thinner) part of the
specimen is fitted with three thermal measurement transducers by electrospark wilding.
Translated from Atomnaya ~nergiya, Vol. 58, No. 1, pp. 21-23, January, 1985. Original
article submitted January 13, 1984.
24 0038-531X/85/5801-0024$09.50 O 1985 Plenum Publishing Corporation
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 ~ ~_ 2e, os
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~ I o o~-
i
~\~f
~_ ~ r
__ ..
- -._ I
Fig. 1
Fig. 1. Ring specimen for reactor tests.
Fig. 2. Wedge for loading ring specimens: 1) insulating layer.
The wedge design (Fig. 2) provides identical attachment of the lower metal part to the
specimen by welding, as well as reliable insulation between the metal parts and monolithic
structure after coating with KO-12 organosilicon paint. The electrical connection between
the two-metal parts of the wedge and the control system is provided by leads welded to it.
The separating force is applied to the specimen at the time of measurement by means of
the loading tie, which is connected to the bellows unit in the loading device. Compressed
gas is supplied to the bellows. from the pneumatic loading system. A reduction valve re-
stricts the pressure to 0.5 MPa. The system provides the required rate of pressure increase
(by the use of a throttle and additional vessel in front of the bellows), and the pressure
ceases to increase when the contact between the specimen and the upper metal part of the
wedge is broken, while the pressure is reduced when the force Q has been measured. The
electrical control-system provides for loading and unloading the specimen and indicates the
execution of the operations, and it also protects the specimen from overload and plastic
strain.
To measure the force, the upper part of the tie contains a load transducer near the load-
ing device in the form of a dynamometric transformer transducer of diameter. 14 mm and leng"th
177 mm (Fig. 4), which consists of the body 1, differential transformer winding 2, plunger 3,
.elastic component 6, and additional elastic components 7 to define the zero position of the
plunger. The lower end of the tie 4 is connected to the plunger 3, while the upper end 5 is
connected to the body 1 of the transducer. When the force is applied to the specimen, the
deformation of the elastic element 6 displaces the plunger, which produces a signal in coil
2, which defines the force by means of the standard instrument KSD-2 forming part of the mea-
surement system.
The measurement system also includes an EPP-09 multipoint automatic potentiome-ter to
measure the temperature in the specimen by means of the sensors. A VRT-3 regulator controls
the electric heater to maintain a given temperature in the specimen.
The system as in Fig. 3 was installed on the SM-2 and RBT-6 reactors in 1982.
Technical Specifications of the Measurement System
Specimen type Oding ring of
reduced dimen-
sions
Number of specimens tested simultaneously 1
Specimen test temperature, ?C 300-700
` Reduced temperature measurement error,
Nominal force, N 40
Force measurement range, N 0-50
Reduced force measurement error, % ?2.0
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 Declassified and Approved For Release 2013/03/11 :CIA-RDP10-021968000300060001-5
Fig. 3. Structural diagram of the apparatus for reactor
tests on stress relaxation: 1) irradiation device; 2)
loading device; 3) pneumatic loading system; 4) load trans-
ducer; 5) tie; 6) electrical control system; 7) wedge;. 8)
specimen; 9) heater; 10) thermal measurement transducer;
11) measurement system.
Fig. 4. Load transducer.
Fig. 5. Relaxation curve for steel OKh16N15M3B.
Fig. 6. Relaxation curve recorded for OKh16N15M3B
.steel without irradiation (1) and under irradia-
tion (2).
Fast neutron flux, cm 2?sec-1 1010'101`'
Test. duration, h Up to 5000
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 Declassified and Approved For Release 2013/03/11 :CIA-RDP10-021968000300060001_5 made
of OKh16N15M3B steel. The first relaxation curve (Fig. 5) was recorded at a fast-neutron flux
of 3.1013 cm Z?sec-1. This is typical of the stress-relaxation tests.
-Also, the calculated initial stress at a given temperature oo~T was equal to the stress
o1,T derived from the first measurement of Q when the reactor had been run up to power and the
specimen had acquired the required temperature (oo~T = o1~T = 1.22 MPa). The value of oo,T
was defined by
ET
60~ T - Ea Q0+
where oo is the actual value of the initial stress at 20?C, which was: determined before the
specimen was loaded-into the reactor and was 165 MPa, while Eo and ET are Young's modulus at
20?C and at the test temperature,: which are 2.04.105 and 1.51.105 MPa, respectively.
The effects of irradiation on the stress-relaxation rate are illustrated by the second
relaxation curve for the-same specimen (Fig. 6), first-part of which characterizes the relaxa-
tion outside the reactor., while the second characterizes that in the reactor at the relative-
ly low fast_neutron flux density of 2.1012 cm 2'sec-1. The irradiation increased the relaxa-
tion rate appreciably. This result agrees with the observed [8, 9] increase in the creep rate
for OKh16N15M3B steel specimens at 650?C under irradiation. The stress relaxation. and. creep
are coupled, and the .above agreement confirms the qualitative reliability of the test results.
The Oding rings were made from rod supplied by the industry, and when the results are
transferred to-fuel-pin sheaths (thin-walled tubes), it is necessary to allow for the possible
differences in the metal structure.
LITERATURE CITED
1. A. M. Borzdyka, Hot Mechanical Test Methods [in Russian], Metallurgizdat, Moscow .(1962).
2. A. M. Borzdyka and L. B. Gertsov, Stress Relaxation in Metals and Alloys [in Russian],, ..
Metallurgiya, Moscow (1972).
3. I. A. Oding, "A study of relaxation and creep in metals by means of a ring specimen," in:
A New Method of Testing Metals for Relaxation and Creep [in Russian], Mashgiz, Moscow
(1949), pp. 5-22.
4. G. F. Lepin and Yu. D. Bondarenko, "Constructing stress-relaxation curves from test re-
sults for ring specimens," Probl. Prochn., No. 5, 81-84 (1971).
5. V. N. Rozenblyum, "Relaxation tests on metals," Probl. Prochn., No. 10, 16-19 (1954).
6. I. A. Oding, V. S. Ivanova, V. V..Burdukskii,.-and V. S. Geminov, The Theory of Creep and
Long-Term Strength in Metals [in Russian], Metallurgiya, Moscow (1956).
7. G. F. Lepin,. V. F. Gorpinich, B. V. Samsonov, et al., "A method of streBS-relaxation
testing in bending," Inventor's Certificate.No. 896489, Byull. Izobret., No. 1, 196
(1982).
8. G. S. Pisarenko, B. V. Tsykanov, V. N. Kiselevskii, et al., "An experimental study of
the effects of reactor radiation on the creep resistance and .long-term strength of heat-
resisting steels," in: Radiation Effects orn the Mechanical Properties of Structural
Materials and Methods of Examining. Them [in Russian], Naukova Dumka,.Kiev (1977); pp.
3-11.
9. N. P. Losev, A. Ya. Rogozyanov, B. V. Samsonov, and A. G. Fin'ko, "Comparative studies
on the effects of reactor irradiation on the heat-resistance characteristics of planar,
cylindrical, and tubular specimens of 9Kh16N15M3B steel," Fiz. Khim. Obrab. Mater., No.
4, 3-8 (1979).
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 Declassified and Approved For Release 2013/03/11 :CIA-RDP10-021968000300060001-5
V. N. Chernikov, I. B. Sawatimova, UDC 669.28:620.187.192:620.172.251.2
A. A. Babad-Zakhryapin, and A. P. Zakharov
High-temperature bombardment with light ions accelerated in the region of the cathode
drop of a glow discharge changes .the dislocation structure of a metal [1] and affects its
behavior during creep tests under uniaxial tension [2]. Specimens of standard shape (diam-
eter of the test section 4 mm) were made from rods of single-crystal molybdenum, oriented
along the [111] direction. Below we give the parameters of the creep tests and the condi-
tions of bombardment from a plasma-forming medium (Hz or an He + H~ mixture in a 4:1 ratio):
T = 1500-1650?C, o = 0.5-0.8 kg/mmz, u = 350-500 V, j = 100-150 mA/cm2. It turned out that
the creep resistance in molybdenum specimens, tested under bombardment, is considerably
higher than in specimens tested without bombardment (in a vacuum). Under the conditions of
the bombardment in this case the curves of the stationary creep rate E _ ~(o) in the range of
stresses o studied were steeper than those obtained during tests in a vacuum. The intersec-
tion of the two curves corresponds too = 0.75-0.80 kg/mm2, i.e., at stresses o < oo ion
bombardment leads to hardening of the metal.
To find the causes of the increase in the creep resistance as a result of ion bombard-
ment, methods of high-voltage and analytic transmission electron microscopy were used to make
a detailed study of the three-dimensional dislocation structure of specimens of single-crystal
molybdenum, deformed. without irradiation and under bombardment with low-energy ions from a
glow discharge. Foils for transmission electron microscopy (TEM) were prepared from the axial
test sections of the molybdenum specimens, which-had been earlier subjected to creep tests [2].
Since bombardment with ions from a glow discharge causes bulk changes in the structure of
the metal by acting on its surface, it seemed natural to expect the most significant and in-
formative (in relation to an understanding of the phenomenon as a whole) structural changes
near the surface. Accordingly, we first made a detailed study of the defect structure of the
surface layers in the specimens subjected to bombardment without a mechanical load. For this
purpose a series of disk-shaped (diameter 3 mm) single-crystal specimens of molybdenum were
prepared [3] and were bombarded with helium and hydrogen ions from a glow discharge (T = 1500?C,
T = l h), after which the well-known methods of [4, 5] were used to prepare-foils for TEM and
their surface structure was studied with the aid of tomography. Most of the foils were ex-
amined in JEM=1000 and Et4-301 G microscopes at an accelerating voltage of 1 MV and 100 kV, re-
spectively. The three-dimensional dislocation structures of the specimens bombarded in a.dis-
charge of HZ or a mixture of He + HZ under strain differ considerately from the structures of
specimens tested in a vacuum. Figure 1 presents photomicrographs of low-angle boundaries in
molybdenum specimens after creep testing without (a, b) and with (c, d) irradiation from a
medium .of pure hydrogen. Even though the average size (ti100 um) and shape of the blocks in
both specimens are roughly the same, the dislocation structures of the interblock boundaries
and the-form of the dislocations themselves differ markedly, as can be seen well from the
photomicrographs. In the specimen tested under bombardment the dislocations are highly
curved, while in block boundaries they are intertwined, often forming pileups that cannot be.
resolved by TEM. Near block boundaries are dislocation loops of a size of 30-80 nm, whose
density varies within wide limits.
Extremely diverse dislocation configurations are formed in specimens that have been bom-
barded under strain with ions from a glow discharge in an He + Hs mixture (Fig. 2). The photo-
micrographs in Fig. 2a, b show a large-cell hexagonal dislocation wall and a wall with elements
of tetragonal cells formed in the bombarded specimen under strain. In practically all of the
dislocation lines of such walls, including purely screw dislocation lines, a fine serrated
structure was detected at higher magnifications. Even larger-celled dislocation walls with a
less regular structure are encountered (Fig. 2c) and so are individual phase precipitates of
Translated from Atomnaya Energiya, Vol. 58, No. 1, pp. 24-27, January, 1985. Original
article submitted January. 26, 1984.
28 0038-531X/85/5801-0028$09.50 ? 1985 Plenum Publishing Corporation
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 Declassified and Approved For Release 2013/03/11 :CIA-RDP10-021968000300060001-5
radiation from a glow discharge in hydrogen (c, d).
The scale is the same in all the photomicrographs.
Fig. 1 .Low-angle boundaries in the bulk of a molyb-
denum single crystal after creep testing (T = 1500?C,
o = 5.7 MPa) without bombardment (a, b) and under ir-
i ._ ' _r.
Fig. 2. Dislocation structures in molybdenum single
crystals subjected to creep tests (T = 1500?C, o =
5.7 MPa) under ion bombardment from a glow discharge
in a helium-fiydrogen mixture. '
a size of til um with dislocations pinned on them, and they are easily identifiable from their
characteristic system of thickness contours (Fig. 2d). It is important to point out that
large-celled dislocation walls, characterized by a different degree of perfection, were also
found in the central part of cylindrical molybdenum specimens that had been subjected only to
high-temperature ion bombardment, without tension (Fig. 3).
Common to all the specimens, bombarded with ions in a discharge under a load as well as
without the application of strain, is an increased average dislocation density in comparison
with that in specimens that had not been bombarded; an important circumstance in this case is
that part of the dislocations are decorated with second-phase particles. The latter follows
from analysis of the contrast in such dislocations, which does not vanish in any of the three
nonequivalent virtual reflections g of the type, despite the fact that all the images
were recorded in the photomicrographs in the two-beam dynamic approximation. Decoration is
also indicated by the fine serrated structure of the screw dislocations [6], demonstrating a
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 strc Declassified and Approved For Release 2013/_03/11 :CIA-RDP10-021968000300060001-5 dis-
locations or separate parts of them have anomalously wide double images (see Fig. Za, b),
this probably being due to the action, around these dislocations, of additional fields of
elastic stresses generated by phase precipitates along the dislocation cores [7]. Direct
structural identification of the phase precipitates in the bulk is hindered, but we can as-
sume that this is fcc molybdenum carbide P4o2C since precisely this compound is often detected
on the surface of irradiated specimens by means of-the microdiffraction method [3]. When x-
ray microspectral probe analysis was carried out in an EM-400T transmission electron micro-
scope with a scanning attachment (which detects elements with Z ~ 10) no. elements apart from
molybdenum were detected in these phase precipitates, but this does not contradict the assump-
tion that they have a carbide nature. The total carbon content in the carbide precipitates
in terms of volume concentration is considerably lower than the limit of carbon solubility in
molybdenum at the temperature of the tests.
Since in none of the creep tests of molybdenum under tension in a vacuum did we detect
second-phase precipitates in the bulk of the specimens, we can assume that this effect is due
to saturation of the specimen with carbon as a result of the action of a glow discharge since
the 'vapor phase contained products of the decomposition of heavy hydrocarbon molecules from
diffused oil and greases.
As a result of a study of the surface structure (at a depth of up to 10 um) of molyb-
denum after high-intensity ion. bombardment from a glow discharge (1500?C for 1 h) [3] we es-
tablished that when a mixture of He + HZ (in contrast to pure hydrogen) is used as. the plasma-
forming medium pronounced gas (helium) swelling (OV/V = 5-10%) develops in the layer of thick-
ness ti300 nm closest to the surface, the average diameter of the bubbles being 20-50 nm, and
the density of dislocations associated with the bubbles increases sharply [to p ~ (1-5)?109
cm 2]. In the bulk of these .specimens, after ion bombardment from a hydrogen glow discharge
as well as from a glow discharge. in a mixture of He + H2 or pure helium we detected numerous,
very long screw dislocat-ions with Burgers vectors b of the type a/Z in the process of slip
and interaction (Fig. 4). It was established that these dislocations are capable of slipping
in intersecting {110} slip. planes and interacting, thus forming irregular dislocation networks,
especially in the layers closest to the surface..
Comparison of :the data about creep in specimens in a plasma-forming medium of pure hydro-
gen and an He + HZ mixture shows that the formation, in the last case, of a highly swelled.
surface layer with a high dislocation density is not the main reason why these specimens .have
a higher creep resistance than do those tested in a vacuum.
As is known, in the stage of steady-state creep during ordinary tensile testing the
structure of a single-crystal molybdenum specimen has a block structure, as was observed in
the experiments conducted. In some respects similar changes in the structure also arise when
the specimen is subjected to intense high-temperature bombardment with low-energy ions with-
out a mechanical load. Indeed, bombardment of molybdenum single crystals in a glow discharge,
as already indicated, leads to the generation of screw dislocations which most likely are
formed in the surface layer and penetrate into the bulk by means of slip. In the process
the dislocations actively interact with each other and with impurities, as a result of which
after 3-5 h of bombardment (ion fluence `L1O22 cm Z) a columnar large-block structure is formed
with the axes of the blocks oriented perpendicular to the bombarded surface [2]. The genera-
tion of dislocations under such bombardment is probably caused by shear stresses due to the
high degree of supersaturation of the lattice in the surface layer of the metal with atoms of
the implanted gas [3]. From this we can conclude that the overall stressed. state of a.speci-
men tested for creep under bombardment is the superposition of the uniform field of
stresses (in the cross section of the specimen) produced by an applied external field
and the nonuniform field of stresses generated by atoms of the implanted gas. The inter-
action of dislocations generated by the action of these fields probably plays a certain role
in changing the creep characteristics of such specimens in comparison with specimens tested
in a vacuum.
At the same time, the results of the experiments indicate one more, much more signifi-
cant, cause of the observed change in these characteristics. We should consider that this
cause is the process of formation of finely dispersed precipitates of .the carbide phase on.
elements of the dislocation structure, including block-boundary dislocations. Indeed, the
low solubility of carbon in metals of subgroup VIA creates favorable conditions for its seg-
regation on structural imperfections [8], and this, in turn., is capable of causing consider-
able hardening of these metals up to a temperature. above 0.5Tm, which has been demonstrated,
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 Declassified and Approved For Release 2013/03/11 :CIA-RDP10-021968000300060001-5
Fig. 3 Fig. 4
Fig. 3. Fragment of a dislocation wall in a single-crystal molybdenum rod of diameter
4 mm, bombarded for 28 h with ions from a glow discharge in hydrogen at 1500?C.
Fig. 4. Dislocation structure in a single-crystal molybdenum disk bombarded with ions
from a glow discharge in hydrogen, at a depth of 3.3 um from the bombarded surface
(the plane.of .the surface is (110); T = 1500?C, T = 1 h).
e.g., on tungsten [9]. As was shown in [10], in the stage of steady-state creep deforma-
tion is effected by the motion of dislocations from the block boundaries through the blocks,
the rate of this process being determined by the climbing of the dislocations over.barriers .
in the block boundaries. The formation of microprecipitates of the new phase on elements of
the dislocation structure of the boundaries clearly should substantially retard the climbing
over these barriers and this is the main cause of the increase in the creep. resistance. The
presence of a large number of dislocation loops near the block boundaries in this case is
treated as the result of the interaction of dislocations with phase precipitates and other dis-
locations. The proposed explanation is also supported by the fact that an increase in creep
resistance was observed [2] only in those specimens whose bombardment had begun no less than
0.5-1.5 h (ion fluence ti2?lOZl cm 2) before-the application of the load. Indeed, diffusion-
estimates show that after carbonization for 1 h at 1600?C the average carbon concentration in
the bulk of a cylindrical molybdenum specimen of diameter 4 mm is no less than 20% of its
maximum concentration in the thin surface layer.. It must be pointed out, however, that high-
temperature ion bombardment can cause both carbonization and decarbonization of a metal [11],
depending on the quasistationary concentration of carbon in-the thin surface layer, which is
determined by the conditions and parameters of the bombardment [12].
Thus, the most probable cause of the hardening of single-crystal molybdenum during creep
tests under ion bombardment is the formation of finely dispersed carbon precipitates on ele-
ments of the dislocation structure, primarily on dislocations of the block boundaries. These
precipitates .retard the mobility of the dislocations and decrease the creep rate. Since carbon
atoms enter into the bulk of the metal by means of diffusion from the ion-bombardment surface,
the hardening under consideration differs from that observed earlier, e.g., in steel because
of the blocking of dislocations by carbide precipitates formed as a result of aging [13]. In
accordance with the data obtained in this work and also taking into account the conclusions
of [2], we can conclude that intensive high-temperature bombardment with low-energy light ions
in the plasma of aglow discharge can be considered as an effective means of enhancing the
strength characteristics of single-crystal molybdenum over a wide range of temperatures. There
are reasons to believe that this conclusion will be valid for all metals of subgroup VIA.
LITERATURE CITED
1. A. A. Babad-Zakhryapin and. M. I. Lagutkin, Metalloved. Term. Obrab. Met., No. 7, 70
(1976).
2. A. A. Babad-Zakhryapin, I. B. Savvatimova, P. V. Zubarev, and N. C. Tachkova, Fiz. Khim.
Obrab. Mater., No. 6,.155 (1981).
3. - V. N. Chernikov and A. P. Zakharov, Poverkhnost'. Fiz., Khim., Mekh.,No. 2, 79 (1984).
4. V. I. Chernikov, in: Eleventh All-Union Conference on Electron Microscopy [in Russian],
Vol.. 1, Nauka, Moscow (1979), p. 175.
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 5.
Declassified and Approved_For Release_2013/0.3_/1.1__:_ C_ IA-RDP10-021968000300060001-5
~j
Zakopane (Poland), Eindhoven (1979), p. 20.
6.
J.
Friedel, Di'sloca.tions, Addison-Wesley, Reading, Mass. (1964).
7.
F.
Montheillet, J. Haudin, and G. Frade, Phys. Status Solidi (a), 17., 593 (1973).
8.
V.
I. Trefilov, Yu. V. Mil'man, and S. A. Firstov, Physical Foundations of the Strength
of Refractory Metals [in Russian], Naukova Dumka, Kiev (1975), p. 26.
9. R. Schitzel, Trans. Am. Soc. Met., 58, 687 (1965).
10. V. G. Glebovskii, Ch. V. Kopetskii, M. M. Myshlyaev, and Yu. A. Romanov. Fiz. Met. Metal-
loved., 41, No. .3, 621 (1976).
11. A. A. Babad-Zakhryapin and G. D. Kuznetsov, Chemical-Heat Treatment in a Glow Discharge
[in Russian], Atomizdat, Moscow (1975), p. 175.
12. V. N. Chernikov, "Structural and .phase changes in molybdenum under low-energy bombard-
ment with hydrogen and deuterium ions," Candidate's Dissertation, Institute of Metal
Physics, Academy of Sciences of the Ukrainian SSR, Kiev (1980).
13. S. Keown, in: Electron Microscopy, 1968, Vol. 1, Tipografia Poliglotta Vaticana, Rome
(1968), p. 497.
A. N. Valiev, V. N. Kadushkin, Z. P. Kiseleva, UDC 533.15:532.546:539.171.016
V. N. Serebryakov, B. G. Skorodumov, A. P. Sokolov,
V. A. Shpiner, P. K. Khabibullaev, and I. 0. Yatsevich
Interest in the behavior of hydrogen in different materials has increased especially in
connection with problems of nuclear, thermonuclear, and hydrogen power. Nondestructive
methods, based on the interaction of accelerated ions with dissolved hydrogen [1], have been
used in recent years to study the diffusion of hydrogen in materials.
In this paper we examine a method for studying. the concentration profile .and, based on
it, the diffusion of hydrogen in materials with the use of elastic scattering of fast neu-
trons by hydrogen isotopes:: In this case, the calculation of the concentration profile sim-
plifies and the possibilities for. performing experiments increase in connection with the
higher penetrability of neutrons and the absence of any need for placing the sample into the
vacuum system of the accelerator; it is possible to study the diffusion of any isotope or
mixture of isotopes of hydrogen; there is practically no limit on the total thickness of the
samples; the range of measured coefficients of diffusion is extended; and, finally, the par-
ticles under study do not affect the process of hydrogen diffusion as a result of heating of
the material and formation of. defects.
The experimental setup (Fig. 1) consists of a source of 14.5-MeV neutrons (neutron gen-
erator), a vacuum chamber with a diffusion cell, a telescope of detectors, a gas-vacuum stand,
and electronic apparatus with a two-dimensional pulse-height analyzer.
The vacuum chamber contains three silicon detectors 1, which together with the disphragms
2 form the telescope 3. The target disk 4, aside from a diffusion cell 5, containing a mem-
brane 6 consisting of the material studied, also contains a target for alignment, energy cali-
bration, and providing a reference for the measurements. The targets are changed and fixed
in the working position through the vacuum input 7 with the help of a power unit and terminal
switches 8. The chamber cover 9 contains connectors 10, which, with the. help of flexible
..hoses ll, connect the injection chamber l2 and the collection chamber 13 of the diffusion cell
-with the gas-vacuum stand.
The chamber is evacuated through an outlet l4. Signals from the detectors are fed into
the electronics system through the vacuum inputs on the cover 15. The housing of the diffu-
sion cell is surrounded by the electrical heater 16 and is thermally insulated by a.Teflon
holder 17. The temperature of the membrane is measured with a Chromel-Alumel thermocouple.
The injection chamber of the cell has two channels for pumping gas. The collection chamber
Translated from Atomnaya Energiya, Vol. 58, No: 1, pp. 27-32, January, 1985. Original
article submitted December 23, 1984.
32 0038-531X/85/5801-0032$09.50 ?-1985 Plenum Publishing Corporation
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 Declassified and Approved For Release 2013/03/11 :CIA-RDP10-021968000300060001-5
Togas-vacuum
stand
F~
Electronics
system
9B0 0
X, ?m
Fig. 1. Diagram of the experimental setup.
is separated from the vacuum chamber by a 7-um-thick Lavsan window 18 for outflow of the prod-
ucts of nuclear reactions in the direction of the telescope.
The purpose of the gas-vacuum stand is to evacuate and fill the diffusion cell with .any
gaseous isotope of hydrogen or its mixture with other gases, as well as to measure-the gas
flow through the membrane. Liquid mixtures can be injected into the injection chamber.
The vacuum chamber, preamplifiers of the signals from the detectors, and the gas-vacuum
stand are mounted on a special table, positioned in front of the neutron source. The control
panel is located in a separate location, where- information enters from detectors and also
-from pressure and temperature sensors.
When any target placed between the neutron source and the telescope is irradiated, the
particles -.reaction products - are recorded by the detectors with the help of the electronic
apparatus, which includes a two-dimensional pulse-height analyzer and enables the identifica=
tion of the type of particles and the determination of its energy [2, 3]. The particle loses
part of its energy DE in the first two detectors and all of the remaining energy Erem in the :-
third detector. Information is accumulated in the analyzer, fed into the computer, and plotted
on a graphical display in the form of a spectrum in-the plane with coordinates ~E and E _
4E + Erem, Since DE x E ~ const, in this two-dimensional field the events fall on hyperbolas,
corresponding to protons (p), deuterons (d), and tritons (t). The hyperbolas are "traced"
and projected on the total-energy axis, forming the energy spectra for each hydrogen isotope.
Figure 2 shows a photograph of the graphical display after accumulation of information
with irradiation of a reference sample - a complex target consisting of five films of deutero-
polyethylene (tit mg/cmZ), interlaid with four aluminum films (90 um). The channels of the
analyzer, proportional to E, are plotted along the horizontal axis. In the two-dimensional
spectrum, channels proportional to DE are plotted along the vertical axis. at the bottom, and.
the number of counts in the spectrum-projection channel are plotted at the top. The points
in the two-dimensional spectrum reflect the program of drawing the deuteron hyperbola.
The thickness of the first. two detectors of the telescope {100 um each) determines energy
threshold of detection, corresponding to the energy of the given type of particles, whose
ratige is equal to the total thickness of the .detectors. The thickness of the- detectors is
chosen taking into account the fact that when the thickness is increased, the identification
of-the particles is improved, but the depth of the analysis simultaneously decreases. The
thickness of the third. detector (500 um) corresponds to the range of deuterons with maximum
Pd atom i ~ {
70 ~
~:. Backer. .I i
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 Declassified and Approved For Release 2013/03/11 :CIA-RDP10-021968000300060001-5
Fig. 2. Photography of the screen of
a graphical display, displaying .the
spectrum of a complex target. The
two-dimensional spectrum is shown at
the bottom and the projection of the
deuteron locus on the energy axis is
shown at the top:
possible energy of 12.9 MeV and the flight path of .protons with energy not exceeding lO.MeV.
'For this reason,.the proton hyperbola has a "turned up" form, which improves the discrimina-
tion of the deuteron spectrum. We note. that an increase in the thickness of the detectors.
increases the intensity of the entering phonon pulses, due to the reactions of neutrons with.
the silicon.
It is evident from Fig. 2 that the energy spectrum of recoil deuterons contains informa-
tion on the distribution of the concentration of the given hydrogen isotope'in the sample.
Indeed, at any depth of the sample the neutrons are scattered elastically by the nucleus of.
the hydrogen isotope with mass m with the same energy En, forming recoil particles with energy
E0 - (?L,-f-1)z E? cost 9,
where e = e1' + e2 can differ from zero due to the finite angular aperture of the systems neu-
tron-source-sample (81) and sample--detector (92).
Under the conditions of the experiment the .maximum values were equal to 81 = 6? and 6z =
8?, which leads to the appearance of an energy spread DE due to the spread over angles D8
where 0 = 6? is the average value of the scattering angle at the maximum of .the angular
resolution function of the setup, while D8 = 7? is the half-width of this function [4]:
After passing through a thickness x of the material, the particle reaches the telescope
with an energy E, which is related to the depth at which the hydrogen is located in the sample
by the relation
~o
x/cos 8,= R (E?) -R (E) _ `dE/S (E) ~0-~
E S.
where R(E) and S(E) = dE/dx(E) are the range and the stopping power of ttie sample material
for particles with energy E; S is the stopping ,power averaged over the interval .from Eo to E.
It is useful to insert the stopping power into~:expression (3).when analyzing thick samples, and
the range when analyzing thick samples. Since-cos 62 = 1 to within less than 1%, the express
sion (3) can be additionally simplified. ,
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 Declassified and Approved For Release 2013/03/11 :CIA-RDP10-021968000300060001-5
Fig,. 3. Photograph of the two-dimen-
sional spectrum obtained with the
interaction of neutrons with a lith-
ium target; p, d, and t are the lo-
calization of protons, deuterons,
and tritons, respectively.
The number of events in channel k of the spectrum=projection constitutes
dN/dk = J (dv/dw) C (x) dx4w, (4)
where J is the number of neutrons hitting the sample; do/dw is the differential elastic-
scattering cross section of neutrons scattered by the given hydrogen isotope; E(x) is the con-
centration of hydrogen in the layer dx at a depth x of the sample, related to the energy of
the detected particle E = yk by expression (3); Y = dE/dk is the energy value of the spec-
trometer channel; arid.~w is its solid angle. .Applying Eq. (4) when analyzing the-.sample and
the reference, we obtain the relations for finding from the measured instrumental spectrum
either the concentration profile of the isotope
C (x) = Jr~"'r dN dk dE
NrJnM dk dE dx '
or the total content of this isotope
(5)
C-NJ nr/NrJnMI. (6)
Here N and Nr are the total number of counts in the spectrum for measurements of the sample
studied and of the reference, respectively; ne is the number of hydrogen atoms per cubic cen-
timeter of the reference, multiplied by the .thickness of the reference; nlgZ is the number of
atoms of the material per cubic centimeter of sample volume, multiplied.by the thickness of
the sample. The concentration is measured as the ratio of the number of hydrogen atoms to the
number of metal atoms (H/M)at?
The selectivity of the spectrometer relative to the particle type is illustrated by the
photograph (Fig. 3) of the two-dimensional spectrum of the products of interaction of neutrons
with the target from a mixture of lithium isotopes based on the reactions (n, p), (n, d), and
(n, t). It is evident that all three hyperbolas are well separated.
The limit of detection of a given hydrogen isotope is determined by.tY~e intensity of the
background pulses, which; based on relation (5),-can be resealed to the equivalent hydrogen
concentration. The main source of the background is the nuclear reactions with the forma-
tion of charged particles in the membrane material and the material of the first detector.
The cross section of these reactions is 10-100 times lower than the elastic-scattering cross
section of hydrogen..
The reactions (n, d) and (n, t) have a lower yield than the reaction (n, p) and, in addi-
tion, their energy threshold exceeds 5 MeV, which shifts the background in analyzing deuter-
ium and tritium into the low-energy range, i.e., large depth. The background level for diffu-
sion of deuterium in.paladium is shown in Fig. l together with the distribution of the deu-
terium concentration over the thickness of the membrane. The background is minimum [ 0.2 um) by a factor of 100.
At T = 300?K (Tables 2 and 3), the density of the blisters on the samples with coatings
is significantly higher and-their average sizes are .lower than on the control samples. How-
ever, together with the fine and medium blisters, individual very coarse blisters are en-
countered on these. samples, the sizes of which attain 5-10 um. An increase of the coating
thickness leads to an increase of dmax of the blisters from 1-5 Um for h = 80 nm to 10-12 um
for h = 320 nm. At the same time, an increase of the fraction of the finest blisters (d <
0.5 Um) on the surface of the samples is characteristic with increase of the coating thick-
ness, which are formed even on the- cupolas of coarse blisters of several micrometers.(see
Fig.- 3b). This leads to two maxima in the distribution of the blisters by sizes. A similar
distribution of the blisters was observed earlier in the case of molybdenum and complexly
alloyed nickel alloy irradiated with 20 keV He+ ions [4, 12J.
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 Declassified and Approved For Release 2013/03/11 :CIA-RDP10-021968000300060001-5
Fig. 3. Blistering of steel 18-10 without coating
(a) and with aluminum coatings of thickness 160 (c
and 320 nm (b, d) as a result of irradiation by He~
ions with energy 20 keV at T = 300?K (a, b) and 470?K
(c, d) up to a dose of 5.1021 (a) and 1'1022 m-1 (b,
d) .
Fig. 4. Surface topography of aluminized alloy 20-45
(conditions 970?K, 5 h): a) before irradiation; b)
after irradiation with He+ at E = 40 keV, D = 1.1022
m 2, T = 470?K (the peeled sections are indicated by
the arrow).
With increase of the irradiation temperature to 470?K, the erosion coefficients of the
control samples and of the samples with coatings increase (see Table 2), but the erosion of
the latter nevertheless is considerably lower. At 470?K, the nature of the erosion of sam-
ples with a coating of thickness 80 nm is similar to the nature of the surface damage of the
control samples, i.e., peeling of the surface takes place by means of peripheral rupture of
the blister cupolas and their detachment. However, with increase of thickness of the coat-
ings, erosion is reduced and suppressed (see Fig. 3c, d). At T = 470?K and h = 360 nm, the
coarse blisters vanish (see Table 2 and Fig. 3d). Even the fine blisters (d ~ 0.2 um) also
disappear, and their distribution with respect to sizes has only one.maximum.
Coatings Obtained by Aluminization. By aluminization in a melt of 10% Al + 90% Li,
coatings are obtained for which the thickness attains several micrometers (see Table 1),
i.e., significantly higher than the projective range of He+ ions with energy 20 and 40 keV
in metals. For all the coatings obtained by aluminization, a surface microrelief is char-
acteristic (Fig. 4a), which has a cellular structure. At the same time, a reduction of the
aluminization temperature from 970 to 870?K leads to a significant reduction of the cell sizes.
As it can be seen from Table 3, at a higher aluminization temperature the surface layer is
markedly depleted in chromium and titanium, but enriched in aluminum.
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 T Declassified and Approved For Release 2013/03/11 :CIA-RDP1O-021968000300060001-5 -
of the Coatings Obtained by Aluminization, ings Obtained by Aluminization, Irradi-
mass % ated with He+ Ions with Energy 40 keV
Backin
Condi
mater121 I
t1on5
Al I
Fe
Nl I
Cr I
Tl
Rem.
18-10
A-1
21
53
12
7,5
.0,1
6,4
18-10
A-2
11
50
20
13
4
2
20-45
A-1
28
10
55
1
-
6
20-45
A-1
4
30
40
3
-
23
Irradiation
Samples with
I Control
conditions
coaring
samples
Material
T, H
D ? 10'2x,
Ie-
S,
atom ton
m z
gime
_ -.
Steel
300
0,5
A-1
~ 0
-
18-10
300
0,8
~ 0
-
300
2
0,04f0,01
0,19f0,05
470
2
0,0410,01
0,2110,05
470
4
0,0210,01
--
570
4
0,09?0,02
.0,2810,07
770
1
0,13f0,03
0,0510,01
300
2
A-2
~ 0
0,1910,05
470
2
0,0210,01
0,21?0,07
570
1
0,050,01
0,28f0,07
Nickel
470
1
A-1
0,100,02
1,580,39
steel
570
1
0,26f0,0(i
1,1410,28
20-45
The cellular structure of the coating obtained by aluminization on a nickel alloy of
the type 20-45 has a more contoured topography by comparison with steels, which .obviously
is due to the higher rate of dissolution of nickel (the principal, component of the alloy)
in lithium and to the .high diffusion mobility of the alloy components at 970?K.
The contouring of the cellular structure at a low (870?K) temperature for this reason
is expressed more weakly. The higher rate of interaction of the nickel in comparison with,
steel is confirmed also by the greater thickness of the coating (see Table 1).
A qualitative phase analysis showed (see Table 1) that. the coatings consist of a number
of intermetallides. In steel 18-10 aluminized at 870?K, by the method of secondary ion emis-
sion, lithium oxide LiZO is detected, which is absent at 970?K. In coatings on. alloy 20-45
obtained at 970?K, phases of the intermetallide FezAls are detected. The complex intermetal-
lide composition of aluminized alloy at a depth of 7-15 um determines the microhardness of
the coating, increasing with increase of thickness of the layer, which, in its turn, is pro-
portional to the aluminization temperature (see Table 1).
The results of an electron-microscopic investigation of the surface of irradiated sam-
ples are given in Table 4, and typical photomicrographs of-the surface are shown in Fig. 4.
Radiation damage of the stirfaee of the aluminized layers is effected by a peeling mechanism
without visible swelling (Fig. 4b), which, evidently, is due to the complex structure of the
coating and to the high bond energy of the intermetallide phase, causing large-scale damage.
As it can be seen from Table 4, the coefficients of erosion of the aluminized materials in-
crease with temperature right up to 770?K, while the erosion maximum of austenitic steels is
found in the range 570-670?K. In this case, erosion of the aluminized alloy 20-45 is some-
what higher than the erosion of aluminized steel 18-10 during irradiation in identical con-
ditions. A reduction of the cells of the surface microrelief (by a change of aluminizing con-
ditions from A-1 to A-2) causes a reduction of the coefficients of erosion (see Table 4). A
comparison of the coefficients of erosion of aluminized steel and alloy with the erosion
of the original materials indicates a significant reduction (by afactor of 10-100) of erosion
as a result of deposition of the coating (see Table 4, Fig.. 4b, and Fig. ld).
Discussion of Results.. The data obtained confirm the considerable suppression of blis-
ter formation and erosion of the. materials investigated, by the deposition on them of silicon
and aluminum coatings by means of thermal vaporization, or of intermetallide coatings
produced by aluminization. This effect is maintained for coatings in all ranges of
.thickness h investigated for both small and large values of Rp. With increase of h, the ef-
fect of erosion reduction is enhanced. If the reduction or suppression of blistering as a
result of the deposition of the coatings by aluminization is explained by the formation of
a rough cellular structure on the surface, which destroys the coplanarity of occurrence of
the implanted helium [9], then the silicon and aluminum coatings used had an improved uni-
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 Declassified and Approved For Release 2013/03/11 :CIA-RDP10-021968000300060001-5
~; 1 1 Y 1 1i V 'ISteel '~
Fig. 5. Distribution of helium with.energy.20 keV
and probable sites of origin of blister cracks in
steels with silicon (a) and aluminum coatings (b-
d): ---) helium profiles in pure silicon and alumi-
num, as if there were no backing; ,,,) helium profiles
in iron (backing) , as if there were no coating; -) actual
helium profiles in a two-layer system of coating-steel; X1)
origin of fine (d < 0.5 Um) blisters; X2) origin of
normal (typical for the given energy of He+ ions)
blisters; X3) origin of anomalously large (d ti 10
um) blisters at the coating-backing boundary.
form surface (see, for example, F.ig. la). Therefore, the development of blistering must have
proceeded just the same as in pure aluminum (if h > Rp) or in steel (for h < Rp); i.e., ac-
cording to [13, 14] in both cases peeling must have occurred.. As this was not observed,. then
it remains to be supposed that suppression of peeling must be due to destruction of the pro-
file of occurrence (deposition) of helium through the depth of the samples [14] and to the
properties of the coating~acking system. It is possible that with different ratios of h and
Rp, different suppression mechanisms of blistering act. Let us consider from these aspects
the results obtained.
In accordance with the calculated values of the range of He+ ions in Si, Al, and Fe
(steel) [15], a thickness of-the silicon coating of 20 nm amounts to ti10 and 6% of Rp for He+
ions with energy 20 keV and. 40 keV in silicon, i.e., the silicon film cannot significantly
deform the distribution of helium (and defects) in the backing (Fig. 5a), and the whole process
of the creation of blisters, including the formation of helium bubbles and primary cracks,
takes place in the depth of the steel backing. At the same time, the difference in thickness
of the blister caps on samples of steel without coating (275.? 40 nm) and with a silicon coat-
ing (305 ? 175 nm) mentioned above confirms that silicon, firstly, in practice does not re-
duce the range of He+ ions in steel (see Fig. 5a) and, secondly, somewhat shifts the site of
formation of a blister crack into the depth of the target.
This shift can be due to a number of causes, to which can. be related a change of mechanie-
al properties and, in particular, an increase of the strength and rigidity of the surface lay-
er of the steel as a result of the implantation of silicon atoms and an increase of the dis-
location density in consequence of the Rebinder effect. An electron-microscopic investigation.
of the dislocation structure of steel with and without coating confirms the higher dislocation
density in the near_surface layers of samples with a coating. An increase of strength of the
implanted layer promotes an increase of the level and gradient of the lateral compressive
stresses originating during the implantation of helium ions, which, evidently, causes a re-
distribution of helium into the depth of the target. Hardening of the material, moreover, in-
creases the resistance of the steel to blister formation. As a result of the combined effect
of the thin silicon coating, the effect of suppression of blistering is observed during ir-
radiation.with ions of energy 20 and 40 keV.
The characteristic feature of the effect on the blistering of aluminum coatings is the
dependence of the blister sizes on the thickness of the film. In order to refine this rela-
tion, we shall carry out an analysis of-the relation between the average ranges of helium ions
and the thickness of the coating in a two-layer system of aluminum-steel, shown in Fig. 5.
This system,-with h = Rp/2 and h = Rp, distorts the profiles of the helium distribution. With
h < Rp (for h = 80 and 160 nm), the helium distribution profile includes the coating~acking
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 bour . ,. ... - _ _ .,_ _ ~~? __~ _t_ L_, _.-_ ~~ ~.._~t-ttion
Declassified and Approved For Release 2013/03/11 :CIA-RDP10-021968000300060001-5
is WnUtty tuca~eu tit sue wa~liig \5CC rl~. ~u~. ruc vvciia~ vy ~..~ ..c~~~..~. .+~~~~~...~~~~.. Jf the
boundary of separation at a thickness of 80 and 160 nm, obviously, is the principal cause of
formation of the anomalously large convex blisters (see Fig. 3c). With h = 320 nm, the es-
cape of helium at the coating-backing boundary also is possible in principle, but in a much
smaller quantity by comparison with the thicker coatings, and therefore the number of such
blisters also is significantly less (see Fig. 3b). In all cases, the .aluminum-steel bound-
ary of separation is the site of the preferable accumulation of helium and the formation of
blisters. The correlation between the diameters of the coarse blisters and the thickness of
the coating testifies in favor of this supposition. In fact, if the diameter of the blisters
is related with the thickness of the cupola as d ti tk, where k is a constant, then in the case
of the formation of blisters at the coating-steel boundary,. the ratio log dl/log hl = log dZ/
log hZ = log d3/log h3 must be satisfied. If we take the maximum sizes of the coarse blis-
ters from Table 2 (dl = 5..2 um, d2 .= 9.0 um, and d3 = 12.0 um) on samples with coatings of
thickness hl = 80 nm, h2 = 160 nm, and h3 = 320 nm, respectively, then this equation is satis-
fied quite well, and taking account of the error in the measurement of the blister diameters
and the thickness of the coatings, the ratio log di/log hi amounts to 1.790 ? 0.154.
The relative increase. of the fraction of coarse blisters with increase of the irradia-
tion-temperature also testifies in favor of the supposition concerning the escape of helium
at the boundary and the role of the boundary in the formation of anomalously large blisters.
It should be emphasized that the coarse blisters are ruptured in the first place with increase
of the temperature of the samples. to 470?K. However, with increase of the coating thickness
to 180 and 320 nm, the effect of temperature on erosion is weakened (see Table 2), as the
blisters with a thick cap are in a position to.endure a greater plastic deformation than
blisters with h = 80 nm.
Thus, the results in this paper confirm the feasibility of reducing the erosion.of the
primary wall of thermonuclear facilities and reactors by the use of coatings deposited by
thermal sputtering in vacuo and coatings obtained by aluminization. At the same time, for
a'choice of the optimum coatings, in order to reduce radiation erosion, to refine the mecha-
nisms of suppression of blistering, and to study the behavior of helium in two-layer systems,
further investigations in this direction are necessary.
LITERATURE CITED
1. J. Davis and G. Kulcinski, "Major features of DT tokamak fusion reactor systems," Nucl.
Fusion, 16, No. .2,.355-373 (1976).
2. B. A. Kalin, N. M. Kirilin, D. M. Skorov, and V. G. Tel'kovskii, Problems of the Choice
of Materials for Thermonuclear Reactors, in: Reports of the All-Union Conference on
Engineering Problems of Thermonuclear Reactors [in Russian], Vol. 1, D. V. Efremov Sci-
entific Research Institute of Electrophysical Equipment, Leningrad (1977), pp. 114-119.
3. I. V. Gorynin, Sh. Sh. Ibragimov, 0. A. Kozhevnikov, et al., "Special features of struc-
tural transformations in high-nickel austenitic alloys and their effect on radiation dam-
age," in: Reactor Material 'Behavior [in RussianJ, Central Scientific-Research Institute
of Atomic Information, Moscow, Vol. 2 (1978), pp. 274-316.
4. E. E. Goncharov, M. I. Guseva, B. A. Kalin, et al., "Effect of thermal treatment and
alloying on the radiation erosion of austenitic-stainless steels and alloys," At. Energ.,
53, No. 4, 243-250 (1982).
5. R. Behrisch and B. Kadomtsev, "Plasma impurities and their significance in fusion re-
actors," in: Proc. Int. Conf. on Plasma Physics and Controlled Thermonuclear Fusion Re-
search, Vienna, Vol. 2.(1975), pp. 229-249.
6. G. Kulcinski, R. Conn, and G. Lang, "Reduction of plasma contamination effects and first-
.wall erosion in fusion devices," Nucl. Fusion, 15, 327-333 (1975).
7. K. Wilson, G. Thomas, and W.. Bauer, "Reduced-erosion in helium implanted aluminum coat-
ings," J. Nucl. Mater., 61, No. 1, 113-116 (1976).
8. M. I. Guseva, .E. S. Ionova, and Yu. V. Martynenko, "The problem of erosion of the first
wall of the tokamak facility," At. Energ., 48, No. 3, 162-166 (1980).
9. E. S. Ionova, B. A. Kalin, P. I. Kartsev, et al., "Investigation of the erosion resist-
ance of aluminized steel during irradiation with helium ions," Fiz. Khim. Obrab. Mater.,
No. 3, 8-11 (1983).
10. L. B. Begrambekov, 0. A. Malofeev, S. B. Skulanov, and V. G. Tel'kovskii, "Angular dis-
tribution of atoms, sputtered from a metallic surface by light ions, in: Interaction of
Atomic.Particles with a Solid Body [in Russian], Kharkov State Univ., Pt. 1 (1976), pp.
100-127.
Declassified and Approved For Release 2013/03/11 :CIA-RDP10-021968000300060001-5
 11. Declassified and Approved For Release 2013/03/11 :CIA-RDP10-021968000300060001-5 _on
accelerator with ion separation by mass," Prib. Tekh. Eksp.., 4, 19-25 (1969).
12. B. A. Kalin, S. N. Y.orshunov, D. M. Skorov, and V. L. Yakushin, "Blistering of materials
during cyclic irradiation over a wide spectrum of incidence of the ions," At. Energ.,
49, No. 2, 132=134 (1980).
13. W. Bauer and G. Thomas, "Helium implantation effects in SAP and aluminum," J. Nucl. Ma-
ter., 63, No. 1, 299-306 (1976).
14. V. V. Gann, I. M. Neklyudov, L. I. Pivovar, et al.., "Structure of the surface of stainless
steel after irradiation with a beam of helium ions, scanning with depth;" Problems of
Nuclear Science and Technology. Series Physics of Radiation Damage and Radiation Mater-
ial Behavior [in Russian], No. 1(12) (1980), pp. 79-82.
15. A.. F. Burenkov, T. I. Zhukova, F. F. Komarov, et ai., Distribution of Ranges of Accele-
rated Ions.- Isotopes of Helium and Lithium [in Russian], Preprint IAE-3468/6, Institute
of Atomic Energy, Ploscow, p. 60.
OPTIMIZING EXTRACTANT MOLECULAR STRUCTURE FOR REPROCESSING SPENT
NUCLEAR POWER STATION FUEL
A. M. Rozen, A. S. Nikiforov, V. S. Shmidt, UDC 621.039.59
Z. I. Nikolotova, N. A. Kartasheva, and B. S. Zakharkin
Researches in the USSR and elsewhere have been designed to improve solvent-extraction.
systems based on tributyl phosphate (TBP), which is widely used throughout the world in re-
processing spent nuclear power station fuel, particularly to eliminate the disadvantages of
TBP: it's relatively. high solubility in water and the formation of a third phase in the ex-
traction of high concentrations of actinoids(IV).
In the USSR, it has been suggested [1, 2] that tributyl phosphate should be replaced by
esters of phosphoric acid (trialkyl phosphates) having long-branched hydrocarbon chains:
total number of carbon atoms NC from 14 to Z1. In [3, 4], there is a discussion of improv-
ing extraction systems by replacing the diluents, and it is also stated that TBP can be re-
placed by trialkyl phosphates with long hydrocarbon chains (NC = 15.21) having isomeric
structures.
A review from the USA [5] states that trihexyl phosphate (N~ = 18) has advantages over
TBP, as does triisooctyl phosphate (NC = 24), but no data are given to confirm. this. Recom-
mendations supported by data are to be found iri [6]. The extraction agents that can replace
TBP are given as trihexyl phosphate, triisooctyl phosphate, triisoamyl phosphate (NC = 15),.
and triisohexyl phosphate (NC =.18). It was stated that successful tests have been per-
formed on solvent extraction with a cascade of mixers and settlers in hot cells.
Here we provide a scientific basis for optimizing the reagent structure and confirm the
conclusions of [1-4].
Advantages and Disadvantages 'of Tributyl Phosphate
Tributyl phosphate has been widely used in the last. 30 years because of its good ex-
traction features [7]. On the one hand, the. extraction capacity of TBP is sufficient to ex-
tract the valuable elements - uranium, plutonium, and neptunium - without the use of unex-
tracted salting-out agents; on the other, the etraction capacity of TBP is not too great,
which enables one to perform the necessary technological operation of reextraction without
the use of chemical reagents by reducing the acidity of .the solution and raising the tempera-
ture. The selectivity: of-TBP is also high [7]. Therefore, TBP continues to be the main re-
agent in radiochemical technology, although we now know of neutral compounds having incom-
parably higher extraction capacity, such as the phosphine oxides, but the reextraction of
metals from such media requires the additional use of. effective chemical reagents.
Translated from Atomnaya Energiya, Vol. 58, No. 1, pp .. 38-.43, January, 1985. Original
article submitted May 28, 1984:
0038-531X/85/5801-0045$09.50 m 1985 Plenum Publishing Corporation
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 Declassified and Approved For Release 2013/03/11 :CIA-RDP10-021968000300060001-5 .s of
quadrivalent metals (plutonium and thorium) are poorly compatible with hydrocarbon diluents
[8, 9]. For example, if one uses a 30% solution of TBP in n-dodecane, a second organic
phase is formed when the plutonium concentration in the extract is about 40 g/liter [10],
and the same occurs with n-tetradecane at 20 g/liter. It has previously been demonstrated
[8] that there is a deterioration in the compatibility as the hydrocarbon chain in the dilu-
ent lengthens by reference to systems containing U(VI) and Th(IV). This disadvantage is
particularly undesirable in reprocessing spent fuel from fast reactors.
Secondly., there is the comparatively high (about 0.4 g/liter) solubility of TBP in the
aqueous phase, which leads to losses of the agent and contamination of the extracted metals
with phosphorus, which is accentuated when the diluents are long-chain hydrocarbons.
Thirdly, rates of hydrolysis and radiolysis of TBP are comparatively high.
It is thus of practical interest to synthesize extraction agents having the extraction
capacity of TBP but with improved physicochemical characteristics and at least free from
the first of these two disadvantages.
A solution is available from-the following results on the physical chemistry of extrac-
tion and the relation between extraction capacity and. structure [8, 11-14]. An electron
donor-acceptor mechanism. is involved in the formation of complexes between metals and or-
ganophosphorus compounds R1R2RgP0 (the donor is the phosphoryl oxygen and the acceptor is
the metal atom). The strength of the complex is the higher, the larger the electron density
on the oxygen, and the latter is determined by the electronegativity of the substituents XR.
The larger XR., the lower the electron density and correspondingly-the extraction. The sub-
stituent electronegativities are dependent on the chemical natures of them, being ,lowest for
the alkyl radicals CnH2n+~ (XRa = 2.0 for n ? 4). For the alkoxy groups CRH2n+10, the elec-
tronegativities are much higher (XRO = 2.9), so replacing the RO group by R increases the
extraction, which increases in the series from phosphates (3 RO groups, EX = 8.7).-to the
phosphonates (EX = 7.8) and onward to the phosphine oxides (3 R groups, EX = 6). The ex-
traction capacity is very sensitive to the nature and electronegativity of the substituents:
.for example, replacing one RO group by`R raises the extraction constants for uranium and
.plutonium nitrates by factors of 50 [11-14]. On the other hand, the length of the hydrocar-
bon chain has little effect on the extraction capacity. The changes are appreciable only for
short radicals: n~ = 1 and 2 for methyl (X~N4 = 2.07) and ethyl (X~Zg4 = 2.02), while X = 2
on further extension, and the electron density on the oxygen remains virtually constant, and
there is Tittle change in extraction capacity. 471-ien allowance is made for the effects of
the steric factor on the Kextr = f(ns) curves, one finds a weak maximum at n~ = 8 [8, 12].
Therefore, there is virtually no change in the chemical parameters of the reagent or
the extraction. capacity when the hydrocarbon chain length alters, whereas the physicochemical
properties (solubility and capacity to form a second organic phase) are very much dependent
on the chain length and structure. Therefore, if one wishes to keep the extraction perform-
ance at the TBP level, one must keep substituents of the same chemical nature, i.e., one
must use trialkyl phosphates (R10)(Rs0)(R30)P0, where R = CnHzn+l. The necessary changes in
the physicochemical properties must be obtained by varying the length and structure of the
hydrocarbon chain.
The separation of organic solutions of the aetinoids into two phases is a consequence
of the high positivedeviation from ideal behavior (large values of the activity coefficients*
Y [8]), which is due to the large differences in the intermolecular force fields. and in
the solubility parameters d of the solvate Me(N03)4(TBP)z and the n-alkanes (we recall that
RTlny = V(Ssol - dalk)? To reduce the difference in the S (or rather in the dispersion com-
ponents) and thereby improve the compatibility of the solvates .and the long-chain n-alkanes,
it is necessary to make the hydrocarbon chains more nearly equal in length, i.e., to lengthen
the hydrocarbon chains in the ester, and also to use the iso structure. .The same measures
.will also tend to weaken the association between the complexes, which is a major reason (if
not the main one) for the large positive deviations from Raoult's law (positive nonideal be-
havior) in the system formed by the complex with the n-alkane. Lengthening the hydrocarbon
chain also reduces the solubility of the ester in the aqueous phase.
*For example, the activity coefficient of the solvate of thorium in hexane amounts to
ti60 [8].
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 Declassified and Approved For Release 2013/03/11 :CIA-RDP10-021968000300060001-5
U
N
~o2i- .;A ~i ~ ~oor ~3
,~ ?
:~ ~ ,-, Z' 4 - 3 2 y
~ ' goy Z~~ oo '
-0~4 -0,2
6R t 62*,
~~ ~75~ .5 n4
~Z,
~ r. ~ i
~ n. ~~ ~
-/~4 -0,2 ~"?
Fig. 1 Fig. 2
13 15 17 19 fns
Fig. 3
Fig. 1. Effects of structure of the esters (F.0)(R`)P(0)F on the rate constants
K for hydrolysis at 25?C constructed from the data of [15] for R/R': 1) CH3/CH3i
2) C2Hs/CH3j 3) n-C3H,/CH3; 4) iso-C3H,/CH3i 5) iso-C3H,/CzHs; 6) iso-C3H,/iso-C3H,.
Fig. 2. Effects of structure in the esters (.CnH2n+10)3P0 on the yields of di-
alkyl phosphoric acids on irradiation constructed from the data of [23], the
numbers by the points being the values of n.
Fig. 3. Dependence on the overall length of the hydrocarbon chains EnC for the
water solubilities of trialkyl phosphates: l) TBP; 2) DibiAP; 3) iBDiAP.; 4)
TiAP; 5) DiBiOP; 6) TiHP; 7) TiHepP.
There is the following basis for reducing the phosphate hydrolysis. The data of [15]
on hydrolysis rates for organophosphorus compounds (Fig, 1) can be described by the equation
lg Khyd. - 2 -~- 4E6* . 2 -{- 8E (X - 2.07),
where 6* is the Taft constant, o* ~ 2(X - 2.07) [12]. Therefore, to reduce the hydrolysis,
the electronegativity of the substituents should be reduced as much as possible, which can
be done by using long-chain iso structures (there is a positive effect on the hydrolysis from
going to the iso structure, namely from TBP to TiBP [16]). However, the scope for this is
very limited, since the changes in X and o* are small:. while o* = 0 for the methyl radical,
o* _ -0.13 for n-butyl and n-amyl, and o* _ --0.16 for isoamyl, i.e., 40* = 0.03, 4X = 0.015.
The above equation was used in the forecast, according to which 41ogKhyd = 8E~X, together
with the values of the I:abachnik constant 64~, which for C3H,, C4H9, and C,H11 are -1.18,
-1.22, and -1.21, while for the iso analogs they are -1.30 and -1.27 [17]. As X~ 2.4 + o~/3_for
alkyl :groups, the changes in electronegativity on going to the iso structure for C4H9 and CsHii
are x.027 and -fl.02 (DX = x.017 if we take -1.22 for CsHii)? As EDX = 34X, the reduction
in the hydrolysis.. rate predicted by the above equation for the n-C4H9/iso-CoHy pair is about
a factor 4.3, while for the pair n-C4H,/iso-CsHxi it is from -2.5 to 3. A relationship analo-
gous to this equation is also obeyed by the radiolysis rate (Fig. 2), but the dependence is
much weaker: the yield of radiolysis products should be reduced by about 7% as EnC goes from
12 to 15.
Experimental Check on the Theoretical Forecasts
To check these forecasts and to identify the optimum structures, we synthesized trialkyl
phosphates with hydrocarbon chains longer than in TBP and with the iso structures indicated
in Table 1, and we examined their physicochemical and extraction features.
We also synthesized acid phosphates, which enabled us to examine the. purification of the
reagents from acid impurities.
Physicochemical.Parameters of Trialkyl Phosphates Having Optimized Eydrocarbon Chains.
To establish the lower and upper bounds to the overall chain length, we examined the solu-
bilities of the esters in -water (which determines the lower limit to EnC)and the washing-
of the 'reagents free from acid impurities (which determines the upper limit to EnC), Figure
3 shows that the forecast is confirmed: an increase as End. reduces the solubility in waters to any
desired extent (s decreases exponentially as EnC increases, which corresponds to a known
regularity [18]). With EnC = 13-14, the solubility is still quite large, but increasing, the
number of carbon ator_is to 15-16 reduces the solubility by comparison with TBP by. more than
an order of magnitude, which is sufficient.-
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 Declassified and Approved For Release 2013/03/11 :CIA-RDP10-021968000300060001-5
Name I
A bbre-
viation I
Formula
~'ic
D ensity,
kg/ dms
Diisobutyl isoamyl
DiBiAP
(iC4Hs0)E(iC51i110)YO
f3
0,41(iL
phosphate
Isobutyl diisoamyl
iBDiAP
(iC4IiB0) (iC5II110)2P0
14
0,955
phosphate
Triisoamyl phos-
iAP
(iC5H110)9P0
15
0,950
phate
Dtisobutyl isooctyl
iBiOP
(iC4IIa0)a(iCAlI170)PO
16
0,944
phosphate
Triisohexyl phos-
iHP
(iCeII190)3P0
18
0,938
phate
Triisoheptyl phos-
TiHepP
(iC~II1~0)9P0
21
0,922
phate
Triisooctyl phos-
TiOP
(iCaIi170)91'O
24
0,918
phate
TABLE 2. Results from Soda Washing
istribution
coefficient
for
(KO)zY00Na
oi~~lue i
lion in
gone con-
tact for
O:W =
~
1
5.Oo1o
TBP
iBDiAP
(C,~HAO)zP001I
(iC4H80) (iC6H110) POOH
0,7.10-a
-
> 96
-
TiAP
(iC5H110)aP00H
2,3.10-a
90
DiBiOP
(iC4I[s0)zP00H
0,7.10-2
>.96
(1C4II90) (1CeH170) POOH
7.10-a
74
TiHP
(iCeH110)zP00H
10-1
f,7
THP
(CsHuO)aP00H
1,1.10-1
G6
TiHe~P
(iC7H1b0)zPOOII
3,4.10-1
40
TiOP
(iCeH170)ZPOOH
2,0
9
*In three washings with n = 10, the cones
centration of TiOP (D2EHPA) was reduced by
about 13%.
The upper limit to the chain length must be chosen on the basis that as End increases,
there is an increase in the_distribution coefficient for the sodium alkyl phosphates (RO)zP00Na
formed on soda: washing of the reagent to remove hydrolysis and radiolysis products (the di-
alkyl phosphoric acids (RO)zP00H), with a corresponding deterioration in the washing effect.
Experiments on soda washing (1.09 moles/liter solution in saturated hydrocarbons) were per-
-formed with a volume ratio O:W = 5:1, with especially synthesized acis impurities added to
the organic solution (Table 2).
The data show that heptyl and octyl compounds -(EnC = 21-24) result in the acid impuri-
ties not being well eluted. -This means that we should have EnC < 18, and the subsequent de-
velopment was based on esters having EnC = 15-18.
Checking Compatibility of the Esters with the Hydrocarbon Diluent. We tested the ex-
traction of Th(IV) nitrate from 3 moles./liter HN03 and solutions of certain phosphates of
concentration.1.09 moles/liter in' n-tetradecane. Table 3 and also Fig. 3 of [2] give the
results. The theoretical forecast is confirmed: extending the chain to EnC = 15-16 im-
proves the compatibility with.the normal hydrocarbon diluent to the necessary extent for the
trialkyl phosphate complexes of plutonium and thorium nitrates.*
Effects of the Iso Structure and Chain Length on the Hydrolytic and Radiation Stability
of Organophosphorus Extraction Agents. The yields of. hydrolysis products were measured by
.heating the compounds to 96 C with 2 moles/liter HN09 for 12 h. The results are given in
Table 4 (TBP is taken as 100%). The above suggestions are confirmed, but only qualitatively:
the hydrolysis rates decrease somewhat as the radicals .lengthen and are appreciably reduced
when the iso structure is employed, but the effects of both factors weaken as the chain
*It has been found [8, 9] that the solvates of Pu(1V) nitrate are more compatible with n-
alkanes than are.Th(IV) solvates.
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 TA Declassified and Approved For Release 2013/03/11 :CIA-RDP10-021968000300060001-5
~~ ~i ~`ic~ut r,1CIItenLS
Th(IV) at Which the Second Organic Phase between Equilibrium Phases
Is Formed
Phosphate I , I[Th] inorganic
z,~ ,
phase
[Th] in
aqueous
phase
Compound
Concen-
trati~n
Concentration in organic
phase
in aque-
(
ous phase
TBP
TiAP
DiBiOP
ITiHP
HNO;,, moles/liter
1
0,23
0,24
0,23
0
l3
HNOz, moles/liter
3
(1,61
0,61
0,62
,
0
61
UOz(NOz)z, molesJl.
0,7
0,35
0,36
0,3i
,
0
36
UOz(N03)z-f 31iN03,
0,3
0,46
0,47
0,46
,
0
48
moles/ liter
,
Th(N03),~, g Th/liter
15
19
20
19
20
Th(N0,),-{-3 moles]
60
Two
40
39
41
liter HNOs,
pha-
g Th/liter
ses
T BP
( 12
23
I
18
TiAP
15
65
265
DiBiOP
1(i
Not formed
TiHP
98
Not formed
TABLE
4. Hydrolytic Stability of
Esters
*Tri-n-amyl phosphate.
tTriisobutyl phosphate. Unfortunately,
the TiBP complexes formed. by. uranium and
plutonium produce a second organic phase
with the normal. hydrocarbon diluent even
at low concentrations, although the iso-
structural effect is larger for these
(the results of [16] are confirmed);
the solubility of TiBP in water is also
comparatively high.
TABLE 6. Distribution Coefficients for
Trace Amounts of Elements between the
Organic and Aqueous Phases a on Extrac-
tion from Nitric Acid Solution (3 moles/
liter HN03)
Compound I
TBP I
TiAP
IDiBiOP
I TiHP
Pu(NOs)a
11 I
12
11,5
12,5
Np(NOa)4
3,5
3,6
3,5
3
7
Zi?(NOg)4
0,19
0,19
0
18
,
0
20
Ru*
1,2
0,9
,
1,1
,
1,0
*Contact time 5 min, O:W = 0.1.
lengthens. Also, the effects are appreciably less than those predicted.
The changes in radiolytic resistance were small (the differences from TBP were within
the experimental accuracy). One assumes that using the iso structure and lengthening the
chain would enable one to reduce the hydrolysis rate somewhat and thereby increase the work-
ing life.
Phase Separation Rate. We compared the rates of phase separation in systems containing
TBP (volume fraction 30%) and DiBiOP (35%) in n-dodecane; the aqueous phases were 3 moles/
liter HN03 and 3 moles/liter HN03 + 300.g/liter U(VI), the mass proportion of Na2C03 was 5%.
Lde used the simplest method [19]: the two solutions were shaken together in a graduated cy-
linder (with O:W = l:l). ?
We found that the separation rates in systems containing TiAP were approximately as
with TBP, while they were somewhat lower: with DiBiOP (for example, 1.9 mm/sec for TBP with
3 moles/liter HN03, but 1.4 mm/sec with DiBiOP). Therefore, replacing TBP by esters with
longer chains has little effect on the phase separation time. The fire hazard naturally is
somewhat reduced as the hydrocarbon chain lengthens, since the flashpoint increases.
Extraction Parameters of Trialkyl Phosphates Having Optimized Hydrocarbon Chains.
Tables 5 and 5 and also [2 ]. give some data on the extraction parameters. of trialkyl phos-
phates having EnC = 15-18. We used solutions in n-tetradecane of concentration 1.09 moles/
liter.
The data show that the theoretical forecast is completely confirmed. The extraction
parameters for the proposed compounds are virtually the same as those for TBP, although, an
exception must be made for elements extracted.in the form of trisolvates (Am, Tc, and so on),
where steric hindrance (iso structure and elongated hydrocarbon chain) reduces a (Fig. 4).
Laboratory Check on Valuable-Element Extraction. The mathematical description and simu-
lation of the extraction [20, 21] indicate that the technological parameters are entirely de-
termined by the distribution coefficients for the target elements and fission products. We
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 Declassified and Approved For Release 2013/03/11 :CIA-RDP10-021968000300060001-5
Fig. 4. Dependence of the distribution
coefficients for Am (a, undiluted re-
agents) and Tc (b, volume proportion of
reagents in n-dodecane 30%) on the
equilibrium nitric acid concentration
in the aqueous,phase:0) TBP; 4) TiAP;
x) DiBiOP.
B 10 0 1 2 r3 ~
XnNU3 ~ mole/ liter
have shown that-the test esters and TBP .have virtually identical extraction performance,
which means that the technological parameters in the extraction and purification of the ele-
ments in multistage systems should be identical.
This conclusion. was additionally confirmed on the operations of solvent extraction, wash-
ing, and reextraction for uranium and plutonium. The experiments were performed by Alder's
method of countercurrent simulation [22]. The method was used in multistage extraction of
the uranyl and plutonium nitrates followed by washing. The acidities of the initial and-wash
aqueous solutions were 3 moles/liter. Five extraction stages and three wash stages were used.
The initial uranium concentration was:300 g/liter, and that of.pltitonium was 300 mg/liter,
with O:W = 3.3 in the flows of reagents, while O:W = l0 in the wash section (Table 7). We
also performed experiments on four-stage reextraction of uranium from -the organic phase with
acidified water (0.05 mole/liter HN03) with a flow volume ratio of 1:1 at 30?C (Table 8).
Tables 7 and 8 show that these reagents provide a high extraction of the valuable com-
ponents when used in place of TBP. The simulation data [20, 21] show that identical distribu-
tion coefficients for fission products (for example, Zr and Ru in Table 6) do not adversely
affect the purification coefficients Kp for the valuable elements relative to the fission pro-
ducts* (provided-that the technical reagents have the same purity as TBP, which can be.checked
by measuring the distribution coefficients given in Table 6). Another important point is
tkat the technical reagent and the hydrolysis products from it should not contain surface-
- active impurities capable of. increasing the phase unmixing time appreciably or of stabilizing
the emulsion (this can also be checked under cold conditions).
These studies completely confirm the theoretical forecasts and show that trialkyl phos-
phates with lengthened chains and the iso structure arse practically identical wit2i TBP as re-
gards extraction behavior, which applies whether they are symmetrical in radicals (TiAP and
TiHP) or have different radicals (DiBiOP), while-they have two major advantages: increased
compatibility. of the actinoid(IV) solvates with long-chain normal hydrocarbon diluents {the
undesirable formation of the second organic phase is virtually excluded), and lower solubil-
ity,in the aqueous phase. The hydrolytic stabilities are also increased somewhat. These
advantages are attained while retaining the parameters for the recovery and purification of
the valuable elements at the level of those for TBP.
*Kp = 1/(ain')(asn')...(ain') (a, n), where a is the distribution coefficient (al is the sup-
ply stage), n is the ratio of the phase flows, a prime denotes a quantity in the wash section,
and Z is the number of wash stages [20].
TABLE 7. Results from the Extraction- -TABLE 8. Results on Uranium Reextraction
Washing Stage (trialkyl phosphate con-
Uranium Residual ura- Degree off' ura-
centration 1.09 mole/liter)
nium in organ-
Uranium
Uranium
Degre
Plutoni-~
De ree
in out-
contents
of ura-
um con-
of Plu-
Reagent
N
t
oO1amc
of tail
solutions-
ium
extrac
tent of
tail solu-
tomum
extrac-
phase,
mg/liter
tion, .
tion,
tion,
g/liter
%
mg/liter
%
TBP
12
94
30
99,99
0,06
99,98
TiAP
15
91
2(1
99,99
0,05
99,98
DiBiOP
96
91
20
99,99
0,05
99,98
TiHP
78
91
20
99,99
0,05
99,98
ea ent
R
g
content in
is phase, mg/
nium extrac-
,
reexteact,
g/liter
liter
tion, %
T BP
91
3
99,996
TiA P
91
2
99,996
DiBiOP
91
2
99,996
TiHP
91
'l.
99,996
Declassified and Approved For Release 2013/03/11 :CIA-RDP10-021968000300060001-5
 Declassified and Approved For Release 2013/03/11 :CIA-RDP10-021968000300060001-5
1. A. M. Rozen, A. S. Nikiforov, V. S. Shmidt, et al., Inventor's Certificate No. 841140,
Byull. Izobret., No. 14,.319 (1982) (with priority from 7.2.80).
2. A. M. Rozen, Z. I. Nikolotova, N. A. Kartasheva, V. S. Shmidt, and A. S. Nikiforov, Dokl.
Akad. Nauk SSSR, 27, No. 5, 1139 (1984).
3. A. S. Nikiforov, V. S. Shmidt, and A. M. Rozen, Abstracts for the Twelfth Mendeleev Con-
gress [in Russian], Vol. 1, Nauka, Moscow (1981), p. 182.
4. A. S. Nikiforov,.V. S. Shmidt, A. M. Rozen, and A. P. Ilozhev, Radiokhimiya, 24, No. 5,
.631 (1982).
5. R. Shonn and R. McDowell, in: Proc. Symp. Actinide Separation, Am. Chem. Soc., Ser. 117,
Washington, D.C. (1980), p. 71.
6. D: Crouse, W. Arnold, and F. Hurst, in: Int. Proc. Conf. Solvent Extraction Chem. ISEC-
1983 (ORNL), pp. 90-91..
7. H. McKay, "TBP - meeting-point of science and technology," in: Proc. Conf. Solvent Ex-
traction Chemistry, Gothenburg, North-Holland, Amsterdam (1967), p. 185.
8. A. Rozen, in:"Proc. Conf. Solvent Extraction Chemistry, Gothenburg, North-Holland, Am-
sterdam (1967), p. 223; Radiokhimiya, 10, No. 3, Z73 (1968).
9. A. Mills and W.. Logan, in: -Int.. Proc. Conf. Solvent Extraction. Chem. ISEC-1983 (ORNL),
_ ~ ~ .,
10. V. E. Vereshchagin.and E.'V. Renard, At. Energ., 44, Issue 5, 422 (1978); 45, Issue 1,
45.
11. A. M. Rozen and Z. I. Nikolotova, Zh. Neorgan. Khim., 9, No. 7, 1725 .(1964).
12. A. M. Rozen et al., Proceedings of the Third Geneva Conference, 1964, USSR Paper No-. 364.
13. A. M. Rozen, Controlling the extraction capacities of organic compounds," in: Hydro-
metallurgy [in Russian], Nauka, Moscow (1976), p. 194.
14. A. M. Rozen, Z. I. Nkolotova, and N.A. Kartasheva, Zh. Neorg. Khim.., 24, No. 6, 1642.
(1979). -
15. R. D. O'Brien, Toxic Phosphorus Esters, Academic Press (1960).
16. V. V. Yakshin and E. A. Filippov, Radiokhimiya, I9, No. 6, 715 (1977).
17. T. A. Mastryukova and M. I. Kabachnik, Usp. Khim., 38, Issue 10, 1751 (1969).
18. G. Pierotti et al., Ind. Eng."Chem., 51, No. 1, 95 (1959).
19. V. G. Voden, N._E. Obukhov, and M. F. Pushlenkov, Radiokhimiya, 18, No. 5, 722 (1976).
20. A."Rozen, At. Energy Rev., 6, No. 2, 98 (1968).
21. A. M. Rozen and Yu. V. Reshet'ko, At. Energ., 37, No. 3, 187 (1974).
22. L. Alders, Liquid-Liquid Extraction, Am. Elsevier (1959).
23. G. F. Egorov, in: Proceedings of the Third COMECON Symposium on Research on Reprocessing
Irradiated Fuel [in Russian], Vol. 1, KAE Czechoslovakia, Prague (1975), p. 302.
Declassified and Approved For Release 2013/03/11 :CIA-RDP10-021968000300060001-5
 Declassified and Approved For Release 2013/03/11 :CIA-RDP10-021968000300060001-5
E. G. Tertyshnik and A. T. Korsakov UDC 539.1.074.55:539.166.06
Measurements on large-volume (up to 1000 ml) preparations in the analysis of environ-
mental samples and .samples of rocks is an important problem of applied gamma spectrometry.,
whose accuracy is in many ways determined by the technique used. The use of the method of
direct comparison with a standard presumes the existence of reference or standard prepara-
tions, containing a known amount of gamma-emitting nuclides, uniformly distributed in a non-
active inert filler. The standard preparation must exactly model the sample both with re-
spect to geometrical dimensions and with respect to the coefficient of attenuation of y radia-
tion in the filler material. The technique used to prepare standard preparations is quite
complicated, since it is necessary to ensure a uniform distribution of the introduced radio-
active substance by repeated mixing while avoiding uncontrollable losses of radionuclides [1].
In addition, the samples to be analyzed-have a different chemical composition and are distin-
guished by .their bulk density (samples of ion-exchange resin; soil samples, ashes from plants,
etc.). 'For this reason, the coefficients of attenuation of radiation in the sample and in
the sample preparation are practically never equal, and the reliability of the results ob-
tained by the method of direct comparison with a standard is lowered. In many laboratories
~y-spectrometric analyses are performed with the help of detectors whose efficiency is known.
The calibration. of detectors over a wide range of y-quanta energies is performed by
filling measuring containers of standard sizes with water and adding standard radioactive
solutions (SRS) to the water. Since .,the mass of the added SRS is determined on analytical
scales and an ideal distribution of radionuclides over the container volume is ensured in
the water, the detection efficiency is measured with'high accuracy. By detection efficiency
of Y quanta we mean the ratio of the number of'eounts recorded. under the total absorption
peak during a chosen interval of time to the number of Y quanta arising in the preparation
over :the same time. interval. The number of Y quanta arising in the preparation is calcu-
lated starting from the mass of-the sample solution introduced into-the:container and the
data on the certificate accompanying the?SRS.
The calibration curves obtained can be used to calculate the, content :of radionuclides
in the soil samples, bottom deposits, etc., if the. radionuclides being determined emit hard
~y rays (-for example, cesium 137), since it is known that for high Y-ray energies the self-
absorption of radiation is approximately the same in water and in the sample material.
In the general case, the efficiency e(E) of detection of Y radiation. from the sample,
placed in a standard container, differs from the values eo(E) which are obtained for the
container filled with water with known specific activity. This difference is all the more
noticeable the larger the difference between the attenuation coefficients of the sample
materials and the water.
In this paper we examine`a method which permits determining -the coefficient w(E) = e/eo
and, therefore, calculating the function e(E), if the dependence so(E) for water has been ob-
tained, for a sample with arbitrary density and unknown chemical composition.
Quantity w is a function of the geometrical dimensions of the preparation and of the
detector, their. mutual arrangement, and also the attenuation coefficients of the sample mate-
rial and the water. The flux density of .y rays for'volume.sources with different configura-
tion was calculated, taking into account self-absorption, in [2] by integrating the effects
produced by point sources taking into account the. attenuation kernels (the influence func-
tion of a point source). In [3] the results of such calculations were used to estimate the
influence of variations in the density of the measured .samples on the characteristics of the
y-spectrometric setup with a small number of channels. `
Translated from Atomnaya Energiya, Vol. 58, No. 1, pp. 44-47, January, 1985. Original
article submitted March 20, 1984.
0038-531X/85/5801-0052$09.50 ? 1985 Plenum Publishing Corporation
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 1 Declassified and Approved For Release 2013/03/11 :CIA-RDP10-02196800030006000_ _1-5_ j .~
rays ~ (cm `?sec-1) at the center of its base is equal to
where S is the specific yield of the volume source, i. e., the number of quanta emitted per
unit volume per unit time, cm-3?sec-1; u is the linear coefficient of attenuation of radia-
tion, cm 1; G is a special function whose values are found from the curves in [2, 4]. There-
fore, for a cylindrical container the coefficient w can be determined from .:the following for-
mula
m=l~nG(?l~, ?~)/?G (?o K, ?n R)?
A source in the form of a hemisphere with radius Z creates at the center of its base
a y-ray flux density of
(1)
=S~1-exp(-?l).l/2??
For this reason, if the measured preparation is shaped like a hemisphere, then the coef-
ficient w is calculated using formula (2). The same formula is valid for a preparation in the
form of a spherical layer with a thickness Z with a point detector placed at the geometric
center of the sphere. We note that in the latter case the value of w does not depend on the
radius of the sphere
~= ?u 1--exp(--?l)
u 1-exp(--?ol) ' (2)
A container with a complex shape, with whose help the "well in the sample" geometry is
realized (Fig. 1), can be viewed as a combination of two cylindrical sources, and the source
of height h and radius r should be viewed as a source with a negative intensity.' For such a
container the value of w is found from the formula
~ !4 G(?oH, ?oR)-G(?oJi, ?ot) .
The value of the coefficient of .linear attenuation of radiation, which is necessary in
calculating w, can be measured quite simply for any bulk material or liquid. It is known [5]
.that the flux density of unscattered y quanta behind the absorbing layer for a diverging beam
of radiation from a point source is determined from the formula
cis _ ~ob2 exp (- Est)/(b -~ t)2:
.where ~o is the flux density of y quanta on the surface of the absorber, ~ is the flux den-
sity of quanta of unscattered radiation after passage through an absorber of thickness t and
b is,the distance from the source to the surface of the absorber.
Since at the peak of total absorption the detector registers unscattered y quanta, and
the coefficient of linear attenuation for air .is small (for example, for 60-keV quanta u =
0.00022 cm 1 [6]), when determining the coefficient of linear attenuation of rad-iation of any
substance it is sufficient to: fix the source, emitting quanta with energy Elf relative to the
detector; measure the counting rate under the corresponding total-absorption peak with an
.empty container (a layer of air) and with the absorber placed into the container; calculate
the value of u(E1) from the relation
In (n/m)
where u(E1).is_the linear coefficient of attenuation of y rays with energy. El (cm 1), t is
the thickness of the layer of absorbing material in the container, n is the counting rate
with an empty container, and m is the counting rate with the absorber or sample placed. into
the container.
As sources of radiation,. it is convenient to use sources from the set of standard spec-
trometric y sources (SSGS). They are fixed with the help of a centering insert, placed on
the top of the measurement container, as shown in Fig. 1. If the coefficient of attenua-
tion is being measured for active samples, then m in formula (4) must be replaced by k =
m - f, where f is the counting rate under the total-absorption peak corresponding to Elf aris-
ing due to .the. radioactivity of the sample. When measuring f, the source 4 (see Fig. l) must
be removed.
Declassified and Approved For Release 2013/03/11 :CIA-RDP10-021968000300060001-5
 Declassified and Approved For Release 2013/03/11 :CIA-RDP10-021968000300060001-5
S00
E~., keV
Fig. 1 Fig. 2
Fig. 1. Measurement geometry: a) scheme for .determining the coefficient of lin-
ear attenuation of radiation by the sample material: 1) detector; 2) sample; 3)
stabilizing insert; 4) radiation. source; b) cylindrical container with a volume
of 500 cm3 (H = 53 mm, R = 55 mm); c) complex-shaped container with a volume
of 1000 cm3 (H = 87 mm, R = 71 mm, h = 52 mm, r = 47 mm, the inner dimensions
are indicated).-
Fig. 2. Energy dependence of the ratio e/so for materials with different den-
sity: A) ethanol; ?, o) solution with a density of 1.2 and 1.5 g/cm3, .respectively.
The suitability of the proposed method for calculating the efficiency was checked on
a y-spectrometric setup with a DGDK=80B Ge(Li) detector for two containers with volumes of
500 and 1000 cm3, The diameter of the cryostat of the detector was equal to 90 mm. The
values of u were found-with the help of the formula (4) for aqueous solutions of cadmium
sulfate with a density of 1.2 and 1.5 g/cm and ethanol with a density of 0.8 g/cm3, These
solutions simulated samples with different attenuation coefficients .. We used the numerical
values of u, characterizing solutions with different density, to.calculate-the coefficients
~ according to formulas (1)-(3). It turned out-that the .values of w obtained using formula
(2) for both types of containers differ to a lesser extent from the experimental data than
the values calculated using formula (1) or (3). In addition, formulas (1) and (3) a.re.in-
convenient for .practical applications, because the function G(uH, uR) is not tabulated and
determining the values of this function from graphs is a time-consuming process and introduces
additional errors. The function Z(uH, uR, R/H, a%H), which describes the radiation field of
a cylindrical volume source at a distance a from its end face, turned out to be unsuitable
for calculating w [4].
-The values of w for a complex-shaped container with a volume. of 1000 cm3, calculated
using formula (2), are presented in Table 1. The table also gives the values of e/.so ob-
tained experimentally. We performed the experiment as follows. We added several milliliters
of the solution of radionuclide .(for example, 241Am) into the container with the absorber
modeling the sample. After carefully mixing the contents of the container, we measured the
counting rate under the corresponding .total-absorption peak (60 keV) and scaled it to the
volume of_the solution introduced, finding the value of N,. pulses/(sec?ml). We then deter-
mined the counting rate No, normalized to the volume of the solution introduced, with a
container filled with water, tagged with the same radioactive solution, placed on thedetec-
tor. Since the normalized counting rate is proportional to the detection efficiency, S2 =
N/No.
Declassified and Approved For Release 2013/03/11 :CIA-RDP10-021968000300060001-5
 Declassified and Approved For Release 2013/03/11 :CIA-RDP10-021968000300060001-5
- ., ----------- .w.
Using Formula (2)-and Obtained Experiment-
ally (S2) for a Container with a Volume of
1000 cm3 (Z = H - h)
Density, g/cm3
Energy of y
rays, keV
i,5
!,2
n,8
tti .~
Q
~
I 4
m~
l ~
6i~
0,18
0,98
0,38
0,37
1,1
1,0 {
88
0,44
0,45
0,67
0,71
1,115
1,1
122
0,64
0,65
0,79
0,80
1,03
1,03
135
0,71
0,72
0,86
(1,85
1,U5
1,01
966
0,78
0,82
0,91
0,91
9,i12
1,02
320
0,93
0,98
0,94
1,02
1,05
9,09
392
i),92
0,97
0,96
1,06
1,02
9,05
662
0,95
0,92
0,98
0,98
1,03
~~,97
835
U,95
0,99
0,99
0,97
9,02
-
In experiments of this type, powdered materials are usually used to model the sample:
soda, quartz sand, chromium oxide, etc. [3]. The use of salt solutions in containers as
absorbing media .increases the accuracy with which e/eo is determined because of the uniform.
distribution of the radionuclides introduced over the volume of the container.
It follows from the table that for ethanol in the energy range 60-835 keV .the computed
and experimental values of m are close to one. For solutions of cadmium sulfate the rms.rela-
tive deviation of the. computed values from the data obtained by model experiments is equal to
5%. The maximum deviation ,does not exceed 10%. Analogous results were obtained for a cylin-
drical container-with a volume of 500 cm3 (Fig. 2). Taking into account the spread of the
experimental data and the error in the determination of the coefficients of linear attenua-
tion, it is evident that the computer and experimental values are in good agreement.
It has thus been shown .that in order to determine the efficiency of detection~of Y radia-
tion by a detector when measuring samples with a large volume, the following are necessary:
using standard radioactive solutions, the dependence eo(E) must be obtained with the
measuring container filled with water;
the coefficient of linear attenuation of the sample material (matrix) must be deter-
mined using formula (4); the value of uo(E) for water can be taken from the tables [C];
'the efficiency of the detector for radiation from the sample must be calculated using.
formula e(E) = weo(E), finding the value of the coefficient w for .the relation (2).
For a cylindrical container Z = H and for a complex-shaped container Z = H - h..
The activity of the radionuclide, emitting y rays with energy E1, is calculated from
the relation
A = FlT t1wFO ~Es)+
where A is the activity of the radionuclide in the sample in Bq; F is the area of the total
absorption peak in counts; T is the duration of the measurements in sec; and n is the quantum
yield of the radionuclide.
Compared with the method of calibration of the spectrometer based on the efficietcy,
which is proposed in [7] and recommended for wide application~[8], the method described here
is distinguished.by its universality and lower labor intensiveness.
LITERATURE CITED
1. Ts. I. Bobovnikova, S. ~. Iokhel'son, and V. N. Churkin, in: Apparatus and Methods for?
Studying Environmental Pollutants [in Russian], No. 2, Gidrometeoizdat, Leningrad .(1970),
p. 117..
2. Shielding of Nuclear Reactors [Russian translation], IL, Moscow (1958).
3. V. I. Parkhomenko, E. M. Krisyuk, and E. P. Lisaehenko, Prib. Tekh. Eksp., No. 4, 46
(1983).
4. Handbook on Radiation Shielding for Engineers [in Russian], Atomizdat, Moscow (1973).
Declassified and Approved For Release 2013/03/11 :CIA-RDP10-021968000300060001-5
 5. Declassified and Approved For Release 2013/03/11 :CIA-RDP10-021968000300060001-5 Lan] ,
Atomizdat, Moscow (1974). ,
6. V. P. Mashkovich, Shielding from Ionizing Radiation [in Russian], Energoatomizdat, Mos-
cow (1982).
7. G. G. Doroshenko et al., in: Problems o?f Ensuring Radiation Safety during Operation of
Nuclear Power Plants [in Russian], Vol, 2, Prague (1976), p. ?24.-
8. Methodological Recommendations on Public-Health Monitoring of the Content of Radioac-
tive Materials in Objects in the Environment [in Russian], Minzdrav SSSR, Moscow (1980).
ISOMERIC RATIOS OF THE YIELDS OF PHOTONUCLEAR REACTIONS FOR GAMMA-
ACTIVATION ANALYSIS
M. G. Davydov, V. G. Magera, UDC 543.0
A. V. Trukhov, and E. M. Shomurodov
The requirements for photonuclear data for Y-activation analysis are described in the
review [1]. In this paper, the question of the needs, requirements, and means for providing
data on the cross sections of photonuclear reactions with excitation of the isomeric states
of nuclei for Y-activation analysis is examined in greater detail. Such reactions constitute
ti4O% of all photonuclear reactions of interest for Y-activation analysis, including: (Y, n) -
14%, (Y~ P) - 6%~ (Y~ 2n) - 5%, (Y~ Pn) - 12%.
The cross sections of photonuclear reactions (crY~x) for Y-activation analysis are best
represented in the form of Lorentz curves with the following parameters: half-width r; posi-
tion of the maximum Em; and cross section at the maximum om. In addition, it is necessary
to give the value of the energy threshold of the reaction En [1]. In our case, this means
that it is necessary to obtain the values of the parameters of the cross sections for two
reaction channels, corresponding to the formation of the final nucleus in the ground and.meta-
stable states. The thresholds of. the reactions (Y, x) and (Y, xm) differ by the value of the
energy of the metstable state Em, i.e., En = Eg + Em.
It was previously established that with quite good accuracy-the cross sections of the
reaction channels studied in the region of-the giant dipole resonance have a similar form: Em =
Em and rm = rg. If 'the cross section of the reaction (Y ,. x), measured, for example, by the
methods of direct detection of the reaction products, is known, then it is sufficient to
determine the so=called isomeric ratio of the cross sections r(EY) = om/og. It can be shown
that this ratio for EY > Em + P, to within a constant a practically equal to one, is equal to
the isomeric ratio of 'the yields d(EYm) of the reaction (Y, x), corresponding to the forma-
tion of the final nucleus in the .metastable and ground states:
Evm
I am (Ey) W (Ev, Evm) dEv
"` = ar E
d (Evm) = yg - Eym ~ v)?
' a~ (F,y) W (Ey, F,y,n) dEy
En
Analogous-results were obtained in [2-5]. In [4, 5] d(EYm) is determined with-the help
of the isomeric ratio of the cross sections.r(EY), weighted by the bremmstrahlung radiation
.spectrum, and in [3] the average photon energy EY, with which the reaction occurs, is used
to obtain .the transition from r(EY) to d(EYm)?
The results of compilations, based on 40 works published before 1983, permit determining
the completeness and quality of the data on r(Ey) and d(Eym) and facilitate the planning of
the work for obtaining the missing data. The compilation did not include reactions as a re-
sult of which the number of nucleons in the nucleus changes by more than three. For Y-activa-
tion analysis, there is no particular reasorn for using the bremmstrahlung radiation with EYm >
25-30 MeV. Due to the possible contribution of the direct processes, the values of r(EY) and
Translated from Atomnaya Energiya,-Vol. 58, No. 1, pp. 47-50, January, 1985. Original
article submitted February 13, 1984.
56 0038-531X/85/5801-0056$09.50 ? 1985 Plenum Publishing Corporation
Declassified and Approved For Release 2013/03/11 :CIA-RDP10-021968000300060001-5
 d(Eym) Declassified and Approved For Release 2013/03/11 :CIA-RDP10-021968000300060001-5
- o-----
dipole resonance of interest to us. For this reason, we included, as a rule, in the com-
pilation the results of measurements of r(EY) and d(EYm), obtained with EYm < 30 MeV.
The available experimental data are presented in publications in the most diverse form:
r(EY), d(EYm), Ym/(Ym + Yg), Yh/YZ (Yh is the yield of the high-spin isomer; YZ is the yield
of the low-spin isomer). These primary data are resealed to r(EY) or d(EYm), which are used
as the basic representations of the isomeric ratios.'
Almost all of the first results, contained in publications in the 1950s and 1960s, were
obtained with the help of scintillation spectrometers, and to calculate the isomeric ratios
incomplete or inaccurate decay schemes of isomeric pairs were used. For this reason, the
accuracy of these data is low, and the results of some works agree poorly with other known
data. Kato [6], whose work was performed specially for y-activation analysis, presents the
isomeric ratios of the yields in the form Ym/(Ym + Yg)for 12 photonuclear reactions, which
in some cases not only do not agree with the results of other works but are clearly con-
tradictory - for two cases Ym/(Ym + Yg) > 1. In recent years, the isomeric ratios of the
cross sections of photonuclear reactions have been studied most actively by Bartsch's group
[4], which can perform measurements for the short-lived states also.-.The largest number of
measurements was performed for the isomers 58Co, `'`Sc, B9Zr (5-7 papers each, whose results,
in general,. agree within the limits of the measurement error. The remaining isomeric pairs
were studied significantly less (1-3 papers each). The reaction (Y, n) was primarily studied
(28 cases).
More or less reliable data on the isomeric ratios are available for a very small number
of cases of activation of nuclei of interest for Y-activation analysis (13%). The experi-
mental data were obtained for 21% of reactions (Y, n), for 13% of reactions (Y, 2n), 10% of
reactions (Y, p) and 3% of reactions (Y, pn).
Approximations cannot be introduced for the parameters of cross sections as a function
of N, Z, and A of nuclei in order to obtain r(EY) because r(EY) are to a large extent determined
by the quantum characteristics of the metastable, ground, and all intermediate excited states
of the nuclei, which do not have a systematic dependence on the number of nucleons in the
nucleus.
The methods for calculating r(EY), based on the statistical theory of nuclei, were first
developed by Huizenga and Vanderboch [7, 8]. Usually, information on the parameter of the
density of nuclear levels a and the parameter characterizing the spin-dependence of the den-
sity of states o is obtained by comparing the computed and measured values of ar(EY). In
later works the Huizenga-Vanderboch formalism was improved by taking into account the parity
of the levels, the pairing mechanism, and admixtures of quadrupole transitions in the Y cas-
cade. Different models were used to describe .the density of nuclear states: Fermi gas; in-
dependent pairing,.and superconductivity. In some works attempts were made to take into ac-
count the contribution of the direct or preequilibrium processes within the framework of the
preequilibrium statistical model.. In order to perform concrete calculations a series of
nuclear parameters, including primarily the parameters of the density of nuclear states, must
be selected.
The most reliable, correct, and in many cases least laborious method for obtaining data
on r(EY) and d(EYm) is to measure these parameters directly. The fact that in the region of
the giant dipole resonance r(EY) = d(EYm) = const makes it possible to restrict the measure-
ments at the f first stage to measurements of d (EYm) with the same value of the energy EYm. This energy
can be taken as E~ym= 22 MeV, because in this case for most photonuclear reactions -the condition
E~ym >_ Em + t holds and the contribution of direct processes cannot be especially important.
Of course, in some cases there will be no similarity between om(EY) and og(EY) (experimental
indications of this exist in the form of a nontrivial energy dependence of the isomeric ratios).
For this reason, the data obtained for EYm = 22 MeV must be used with care.
The techniques used to measure the isomeric ratios of the yields are described in great
.detail in the literature, including in_[9], and we shall consider only the methodological fea-
tures of our measurements. In the measurements we used the well=known technique of direct
pairing of measurements at the photo peaks of the Y lines, characteristic for the metastable
and ground states, obtained from one Y spectrum (GS) of an activated sample,.and the technique
of decomposing the curve of the decay or accumulation, measured based on one Y line (RS).
The accuracy of the measurements of d(EYm) by these methods (the error does not exceed 3-8%)
Declassified and Approved For Release 2013/03/11 :CIA-RDP10-021968000300060001-5
 Declassified and Approved For Release 2013/03/11 :CIA-RDP10-021968000300060001-5
Eym
De=
Meth-
Et,m
De-
Meth-
Source
Reaction
d or r
of
rector
od
Source-
Reaction
d pr r
of
rector
od
v
v
aSSc (~~ ~~) +~tic
Il 23?O,f$
'
2'L
SFD
GS
This
"5Nb(y.a) ";lib
0,31~O,f2
22
SS
GS
This
work
work
0,21
30
SFD
GS
[6J
0,37f0,01
45
SFD
RS
[5]
U,23?0,1?3
-
-
--
[121
0,1TL
30
SFD
GS
[sJ
0
`11?0
04
50
SS
--
[3J
,
,
0,16f0,02
0,19f0,02
22
36
SS
SS
RS
RS
(13J
[13]
BBSr (y, n) ASSr
0,14?0,02
22
SS
GS
This
0,19?0,1'2
48
SS
RS.
[13J
work
0,28f0,o8
0
18?11
03
-
23
-
-
-
-
[14J
[15J
1,780,25
31
SS
GS
[17j
,
,
0,2110,02
30
-
-
[15J
`L,0?0,4
--
SS
GS
[20J
0,19f0,02
36
-
--
(15J
1,46?0,15
14,5
SFD
RS
[29(
0,19f0,02
48
--
-
[15J
90Zr(y, n) BBZr
1,44?0,02
. 22
SFD
GS
This
work
68C~ (1, n,) 58('i0 ~
0,920,02
22
SFD
RS ~
'T'his
work
0,61
30
SFD
GS
[6]
1,58
> 17
-
-
[26]
0,8210,03
30
SS
RS-
[161
1,`L7~0,17
> 18
SS
GS
[27]
0,79f0,C4
30
SS
RS
[17]
1,0
> 1.8
SS
G S
(28]
1,33t0,f9
48
SFD
RS
[18J
2,00,6
30
SFD
GS
[17]
1,3310,05
35
SS
RS
[19J
0,66~O,i~2
14,5
SFD
RS
[2g[
1,330,05
54
SS
RS
[19]
0,810,1
-
SS
RS
[20]
1,63~O,C8
68
SS
RS
[21J
98Mo(y, p) g7Nb
0,71f0,02
22
SFD
GS
This
0,85f0,C4
150
SFD
RS
[22]
work
Base (y, n) 81Se
0,5410,03
22
SFD
GS
This
work
ucCd(Y,,l)u5~d
0,1'lt0,G2
22
SFD
GS
This
1,0?0,5
20
SS
RS
[23J
work
76 78
Se (y, n) So
0,100,02
22
SFD
GS
This
work
0,27
0,25
30
30
SFD
SS
GS
GS
[6]
[17[
0,13?0,02
14,5
'
SFD
-
RS
I [29J
SFD
GS
This
usgu(y P) 111TH
O,C44t0,001
22
B1gr (y, n) Boar
.0,4810,03
22
SFD
RS
This
work
work
0,4010,02
0,4910,01
25
16
-
SS
-~-
-
[241
[25]
ue 119In
Sn (Y' P)
9,53f2,68.
`L2
I
I SFD
I GS
I This
work
0,4710,03
30
-
-
[171
is much higher than with a separate measurement of the yields in the ground and isomeric
states of the final nucleus (error of 20-30%) [19].
We activated the samples, prepared from porous materials (in the elemental form, in the
form of oxides or porous salts) in the form of disks with a diameter of 35 mm and a mass of
10-15 g, in the beam of bremmstrahlung radiation of the B 25/30 betatron with EYm = 22 MeV
at a distance of 20 cm from the stopping target-. The error of the values of EYm presented
does not exceed 0.2 MeV taking into .account the possible drift of the energy scale of the
beatYon. We measured the Y spectra and the-decay curves on the scintillation spectrometer
with a-150 X 100 mm NaI(T1) crystal (SS) or on a Ge(Li) spectrometer with a sensitive area
of 13 cmZ and a thickness of 1.15 cm (SFD). We calibrated the spectrometers with respect
to the energy with the help of standard spectrometrical Y sources. The Ge(Li) spectrometer
had a resolution of 2.2 keV for the 12-keV line and 2.9 keV for the 1332-keV line. We
determined the areas of the photopeaks by the-well-known Wasson method. We determined the
ratio of the detection efficiencies of the Ge(Li) spectrometer e(EY) for Y lines with dif-
ferent energy with the help of the semiempirical Kane and Moriscatti relation In e = bx +
cx2 [x = ln(a/E)].j10], the coefficients for which are determined by the method of least
squares from the results of additional measurements with the set of standard spectrometric
Y sources. We interpreted the decay curves using a special program for the M-6000 computer
or graphically. We selected the time conditions for the measurements for each isomeric pair
taking into account its decay scheme. The data on the decay scheme, required for analysis
of the measurements, are taken from tables [11]. We estimated the measurement errors start-
ing from the statistics of the counts in the photopeaks, used for determining d(EYm). Sep-
arate measurements in a series of identical samples showed that the errors in the reproduci-
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 bilit Declassified and Approved For Release 2013/03/11 :CIA-RDP10-021968000300060001-5
~ .- . ~-.-~-v ~.. ~~.~io~i~.ni ciLVi~. li~c ulC l.llVLLil461 CLLVLS WCLC 11UL CSLlIIId LCU. In
required cases, we checked the contribution of interfering reactions to the isomer yield by
additional measurements. The values of d(E~,m) were obtained for 12 photonuclear reactions
(see Table 1) .
Within the limits of the measurement error our result for the reaction 45Sc(y, n)'`i4S.c
agrees with [3, 6, 12], is somewhat higher than the values Liven in [13, 15],and is lower
than the values in [14], though it does not contradict the works cited.
The measurements for the reaction 59Co(y, n)58Co, obtained with E~ < .30 MeV from [16,
17, 20], agree well with one another and are lower than our value, obtained at E~,m = 22 MeV.
The remaining values were determined for E~,m > 30 MeV and, as a rule, they are higher than
our .values. It should be noted that this reaction has not been adequately studied for E.1,m ~
30 MeV. The isomeric ratios for the reactions 82Se(y, n)81Se and 81Br(y, n)eOBr agree within
the limits of error of the measurements. Our result for the reaction BSRb(Y, n)B4Rb agrees
with the value .obtained in [5], but differs substantially from the data in [6].
The significant difference between our results for the reaction 86Sr(y; n).BSSr and the
results in [17 ,20, 29] requires a more detailed analysis and check, just as for the reaction
11eCd(y, n)115Cd. .With the exception of the low values 'in [6, 28, 29], the measurements. for
the,:reaction 90Zr(Y, n)B9Zr agree with one another to within the quite large measurement error.
We were the first to obtain the results for the reactions 98Mo(y, p)97Nb and 112Sn(y,
P)L11In' 1185.n(,Y' p)117Iri.
Thus, due to the existence of perfected Y spectrometers and quite accurate information"
on the decay schemes, it is now possible to obtain with comparatively less effort experi-
metally more reliable and accurate data on the isomeric ratios of the cross sections (yields)
of photonuclear reactions required for further progress in the-area of Y-activation analysis.
LITERATURE CITED
1. M. G. Davydov, V. I. Kuksa, and A. P, Naumov, "Nuclear data for gamma-activation analy-
sis," No, 2318-82, VINITI, Moscow (1982).
2. M: G. Davydov and V. A. Mantoptin, in: Abstracts of Reports at the 32nd Conference on
Nuclear Spectroscopy and Nuclear Structure [in Russian], Nauka, Leningrad (1977), p. 239.
3. W. Walters and J. Hummel, Phys. Rev., 150, No. 3, 867 (1966).
4. H. Bartsch et al., Z. Phys , A285, No. 1,'71 (1978).
5. U. Kneissl et al., Nuc1. Phys.., A135, No. 2, 395 (1969).
6. T. Kato, J. Radioanal. Chem:, 16, No. 1, 307 (1973).
7. J. Huizenga and R, Vandenboch, Phys. Rev.,. 120, 1305 (1960).
8. J. Huizenga and R. Vandenboch, Phys. Rev., 120,, 1313 (1960).
9. L. Ya. Arifov et al., Izv. Akad. Nauk SSSR, Ser. Fiz., 42, No. 4, 831 (1978).
10. W, Kane et a1,,,Nuc1. Instrum. Method., 56,-189 (1967).
11. Tables of Isotopes, C. Lederer and V. Shirley (eds.), Wiley, New York (1978).
12. R. Volpel, Nucl. Phys., A182, 411 (1972).
13. J. Tatarezuk and H.. Medicus, Phys. Rev., 143.; No. 3, 818 (1966).
14. M. Erikson and G. Jonsson, Nuc1. Phys , A242, 507 (1975).
15. S. Steinberg, in: B. S. Thesis, University of Illinois (1963).
16. P. Decowski et al., Nucl. Phys , A112, 513 (1968).
17. J. Carver,. G.. Coote, and T. Sherwood, Nucl. Phys., 37, 449 (1962),
18. C. Rhoades and H. Medicus, Phys. Rev., 167, No. 4, 1049 (1968).
19. H. Lichtblau and A. Goldman, Z. Phys , 205; 47 (1967).
20: L. Apers, P. Capron, and L. Gilly, J. Inorg. Nucl. Chem.., 5,: 23 (1957).
21. D. Christian and D. Martin, Iowa State College Report No. ISC-197 (1951).
22. E. A. Skakun et al., in: Abstracts of. Reports at the 32nd Conference on Nuclear Spectro-
scopy and Nuclear Structure [in Russian], Nauka, Leningrad (1982), p. 565.
23. E. Silva and J. Goldemberg, Ann. Acad. Brasil. Sci., 28, No. 3, 275 (1956).
24. A. King and A. Voigt, Phys. Rev., 105, 1310 (1957).
25. L. Katz, L. Pease, and H. P4oody, Can. J. Phys , 30, 476 (1952).
26. S. Costa et a1 .:, Nuc1. Phys , 72, 158 (1965).
27. L. Katz, R. Baker, and R. Montalbetti, Can. J. Phys., 31, 250 (1953):
28. .T, Fox, Ph. D. Thesis., University of Illinois (1960).
29. Fam Zui Khien,.Ngo Kuang Zui, and Nguen Tak An', Yad. Fiz., 35, No. 2, 257-263 (1982).
Declassified and Approved For Release 2013/03/11 :CIA-RDP10-021968000300060001-5
 Declassified and Approved For Release 2013/03/11 :CIA-RDP10-021968000300060001-5
POSSIBILITY OF DECREASING THE ENERGY DEPENDENCE OF DETECTORS BASED
ON THE THERMAL LUMINOPHOR LiF IN THE X-RAY REGION
L. Z. Kalmykov, T. G. Kandel', UDC 621.386.92(088.8)
S. M. Grinberg,-and I. L. Kruglikov
Lithium fluoride (LiF) plays a leading .role among luminophors used in thermoluminescent
dosimetry. This is a result of its many useful characteristics: high sensitivity and possi-
bility of detecting different forms of radiation, wide range of measurable doses,. good pres-
ervation of dosimetric information, possibility of its use in the single-crystalline and
powdered forms as well as introduction into :an organic matrix, etc. The effective atomic
number of.LiF is 8.14 and that of muscle tissue is 7.47. For this reason, based on the inter-
action with photon ionizing radiation, LiF is close to-soft biological tissues. In the re-
gion of photon energies Ftable (Ftable = 13.74). Therefore, the presented re-
gression equations adequately describe the experimental data. The correlation coefficient r
indicates that there is a determinate dependence of the thermoluminescence signal on the com-
position of the mixture.-When the presented regression equations are compared in pairs based
on the Student's t criterion with the equation obtained for the 6OCo radiation, a significant
difference is established- for all energy values with the exception of 17 keV (t = 2.969
-with p = 0.01). This gives a basis for calculating the value of the energy dependence for mix-
tures with different composition K (Table 3):
(ao ~-Q~ P)Ei
l;Z-1.,50 keV
Thus the use of materials with low Zeff decreases the energy dependence of dosimetric.
composite materials containing the thermoluminophor LiF; in addition, K decreases as the con -
tent of these substances in the .composite material increases.
An analysis of the values of K presented in Table 3 shows that they are somewhat higher
than the computed data (see- Table 1), Information on the experimentally obtained high values
of the energy dependence of LiF and other thermoluminophors has been published [3-5]. This
fact is explained by the influence of the scattered radiation from the material surrounding
the detector and the-fact that the real spectrum at the location of the detector was not taken
into account. In particular, there exist data indicating that the thermoluminescence accom-
TABLE 3. Effect of the Composition of
Mixtures of LiF and Li2C03 on the Ener-
gy Dependence of the Thermoluminescence
Mass fraction
K for Ei
in the mixture
(p)
S7
I 26
I 36
( 82
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 Declassified and Approv_e_d For Release 2_013_/03/_11 :CIA-RDP10-021968000300060001-5
of the Components on the Energy Dependence
of the Dosimetric Composite Material K
with Respect to Ei = 1.25 MeV
Particle I
size, ?m
i7 keV I
3s keV
I szkeV
1n2-25n
1,12?n,n9
1.,32?n,13
1,15?n,n9
4~~--88
1,27?n,1~~
1,39?n,n9
1,22?n,n9
G4~~
1,25?~~,n8
1,28?n,n9
1,11?n,n7

(1)
Translated from Atomnaya Energiya, Vol. 58, No. 1, pp. 57-59, January, 1985. Original
article submitted December 28, 1983.
0038-531X/85/5801-0069$09.50
? 1985 Plenum Publishing Corporation 69
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 Declassified and Approved For Release 2013/03/11 :CIA-RDP10-021968000300060001-5
._. a
3 000 .
~ 900
a~
a
b
I
c
~~
)
?~
4 ~~--- ?
d
0
o + +
+? T " pp
o Q F
40 BO 120 160 t, days
Fig. 1
u
I I i i i i
0 40 BO 920 t, days
Fig. 2
F.ig. 1. Change in the reactor power`(a), H3B03 concentration (b),
tritium concentration in the first loop (c) and in the tanks of
pure condensate (d) in B9 (+) and B10 (~), respectively,-for the
third operating period of the fifth block of NVAES as a function
of time.
Fig. 2. Change in the reactor power (a), H3B03 concentration (b),
tritium concentration in the first loop (c) and in the tanks of
pure condensate (d) in B9 (+) and :B10. (~) as a function of time,
respectively, for the fourth operating period of the fifth-block
of NVAES: v) experimental values; -) the least-squares curve
approximating the experimental dat~'a.
where PL is the mass fo the water in the first loop; vfm(t) is the rate of formation of
tritium in the coolant; Cm(t} is the concentration of tritium in the makeup water; vm(t)
and vl(t) are the flow rate of coolant for makeup of the first loop and leakage from it; and
a is the decay constant of tritium.
In view of the fact that the water level in the first loop is maintained constant,-the
equality vm(t) = v2(t) holds. Then the amount of tritium AT, formed over a time T, will be
equal to r' ~
AT- 1 ?fm (t)dt- r {PL dCat(t) -I- m(t) ICT (t)- ~,(t))-f-7~PLCT (t)} alt-Pl; [CT (ti)--CT(~)1-F-
0 0
r (2)
I Um(t)[C~, (t)-- m(t)1 ~t-f-~.PL C CT (t)dt.
0 0
Therefore, to calculate AT it is necessary to know the dependence of the tritium con-
centration in the water of the first loop and in the makeup water on time as well as the
consumption of water. for makeup in the first loop.
Periodic makeup in the first loop in-the nominal operational regime of the reactor~is
performed, as a rule, with pure condensate, introduced in order to maintain the required
70
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 conce Declassified and Approved For Release 2013/03/11 :CIA-RDP10-021968000300060001-5
~.~..,ub...
In addition, boron concentrate and solutions of chemical reagents (KOH, NH40H, N2H,,) are in-
troduced into the first loop. The latter are prepared in water taken from tanks containing
the pure condensate. The pure condensate and-the solutions of .chemical reagents are intro-
duced over a definite period of time ~ti by special pumps with a capacity of Qa. Thus the
makeup flow rate is equal to
aril:-.= ~ Qia,
u=_ ~
where n is the. number of simultaneously operating pumps in the i-th time interval.
The dependence of CT(t) and Cm(t) versus time is, as a rule, smooth [2]. For this rea-
son, a curve of the following form can be drawn through the experimental points:
C (t) _ , biPi (t),
~=o
where Pj(t) are the orthogonal Chebyshev polynomials; bj are independent expansion coeffi-
cients; and N is the maximum degree of the polynomial. The coefficients bj can be found by
the method of least squares [4]. Substituting expressions (3) and (4) into Eq. (2), we ob-
tain
s ~~ N N, N i
A7 _ PL ((%1' (ti) - (%?C (~~))-{- ~ ~ Qia4ti ~ ~ SiPi (t) - ~ G~ Yi (t) 1 dt-f-~,PI, ~ bg I Yj (t)dt.
O a=1 7=0 7=0 J J=0 0
The integrals in these expressions can now be easily found analytically.
Using formula (5) and the actual data,- we calculated the amount of tritium formed in the
coolant of the first loop of WER-1000 in the fifth block of NVP,ES (Novovoronezhk Nuclear
Power Plant) within the third and part of the fourth operating periods (from December 5, 1981
to December 20, 1982).
Figures 1 and 2 show: the change as a function of time in the concentration of tritium
in the water of the first loop and in the tanks of pure condensate used for makeup (B9, B10).
The figures also show the change as a. function of time in the reactor power and the concentra-
tion of boric acid in the coolant of the first loop. We determined. the tritium concentration
in the samples by a scintillation method using the SBS-2 setup. We first removed extraneous
radionuclides from each .sample by means of double distillation and performed no less than four
measurements.
It follows from Fig. 1 that there were two prolonged shutdowns of the reactor during the
third operating period. For this reason, the entire period was divided into three intervals,
for each of which experimental data on the concentration of tritium in the coolant of the first
loop and in the water in the tanks of pure condensate-were described by their own curve (see
Fig. lc and d). In the fourth operating period; all experimental points CT(t) were de-
scribed by a single curve - a parabola, and Cm(t) was described by a straight line (see Fig.
2c and d).
As a result of the calculations it was found. that AT is-equal to 2.7 ? 0.3 TBq and 4.3 ?
0.2 TBq for the third and fourth operating periods, respectively. To determine the computa-
tional error in AT, the following formula was used:
aAT z
i
=1
where xi denotes the independent coefficients bj, b~, and Qia. The calculation of the error
in AT was performed with a confidence probability of 0.95.
To clarify the contribution of the reaction 1OB(n, 2a)3H to the overall tritium activity
of the coolant, the amount of tritium formed was calculated-using the procedure in {3]. The.
values used for the. H3B03 concentration in the coolant of the first loop and the reactor
power were obtained by operational control (see Fig. la, b; Fig. 2a, b).
For the third and fourth operating periods, the contribution of the indicated reaction
according to the calculations is equal to 2.5 TBq and 5.O TBq, respectively. These values dif-
fer from AT by not more-than 15%. Therefore, during the operating periods studied, tritium
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 was -Declassified and Approved For Release 2013/03/11 :CIA-RDP10-021968000300060001-5 :ons
6Li(n, a~ n ana -non, YJ_ri ana the trltlum output trom the Yuel cells and control rods are
insignificant, which agrees with the results of [3]. The contribution of the reaction 6Li-
(n, a)3H turned out to be small due to the fact that in the third operating period KOH was
not introduced, i.e., the .lithium impurity also did not enter. The partial overloading of
the filter permitted introducing only 5 kg of KOH instead of the planned 40 kg during the
fourth operating period.
Thus in this work we proposed a mathematical model for calculating the amount of tritium
formed in the coolant of the first loop of WER. A comparison of the amounts of tritium cal-
culated for the first loop of the fifth block of NVAES based on the proposed model and based
on the procedure published in [3], taking into account only the reaction`1OB(n,.2a)3H, showed
that these values differ by not more than 15%.
In conclusion, we thank V. V. Tagirov and V. N. Kuklin for useful discussions.
LITERATURE CITED
1. K. Langeker and H. Graupe, Kernenergie, 15, No. 165 (1972).
2. L. I. Golubev, V. M. Ilyasov, A. I. Lure, et al., "Tritium content in the coolant of
water-cooled-water-modulated (WER) reactors," At. Energ., 46, No. 2, 79 (1979).
3. V. P. Kruglov, V. M. Ilyasov, I. G. Golubchikova, et al., "Tritium content in the water
systems of the reactor in the fifth block of the Novovoronezhsk nuclear power plant,"
At. Energ., 53, No. 4, 225 (1982).
4. V. N. Grishin, Statistical .Methods of Analysis and Planning of Experiments [in Russian],
Moscow State Univ. (1975).
-The Maxwellian or Watt distribution is still commonly used to describe the laboratory.
spectrum of prompt neutrons from fission. Experiments, however, have repeatedly indicated
deviations from these semiempirical formulas, the physical reasons for which were never clari-
fied. The-.most interesting study in this respect is [1], where it is pointed out that a super-
position of Maxwellian terms must be introduced to describe the energy spectrum n(e) in the
center of mass system of the fragments for spontaneous .fission of zszCf. Analogous effects
were observed in the study of fragmentation of heavy nuclei in high-energy collisions (see, .
for example, [2]), which indicates the existence of a single mechanism governing the emission
of particles with low and high excitation energy.
Ali of this served as a foundation for proposing a statistical-model with a continuous
temperature for describing the spectra [3.]: .
~ ~ const a exp [- ~a$+2aslti
n s)= ~ n~ (e, 8) exp [-0F (0)/0J d0= ~ ~a -~-2~xeli ~ (1)
0
Here the Maxwellian distribution nM(e, 8) for the temperature 8 is averaged with a weight-
ing-factor which depends on the change in-the free energy ~F(6) in the process of emission of
the observed particle. The integral in Eq. (1) was calculated analytically using .the two-term
expansion ~F(6) = c? + c26~ of the free energy in powers of the temperature. The coefficients
of this expansion .cannot be calculated in the general case, so that two parameters are re-
twined in formula (1): the average temperature T = 6 and the parameter a, whose inverse is
determined by the variance of the temperature. In the limit a -} ~, the weighting factor has
a S-function form, so that the function (1) transforms into a Maxwell distribution. The super-
position on an infinite time interval with finite values,of a has a simple physical meaning,
since it ultimately reflects the nonuniformity of nuclear processes. In other words, formula
(1) may be viewed as the result of the application of nonequilibrium thermodynamics to nuclear
Translated from Atomnaya.Energiya, Vol. 58, No. 1, pp. 59-61, January, 1985. Original
article submitted April 19, 1984.
72 0038-531X/85/5801-0072$09.50 ? 1985 Plenum Publishing Corporation
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~ i
70' E, MeV
_r ~ ~ ~ ~ ~ ~ ~i r i
ff 8 10 12 E, MeV
Fig. 2
Fig. 1.. Ratio of the spectrum (2) and neXp(Ei) [5] for zssU + n(0.53 MeV) to
the Maxwellian spectrum (8) with the parameter Tpg = 1.321 McV;.XZ/DF = 0.371.
Fig?232 Ratio .of the spectrum (2) and ne~p(Ei) [5] to the P4axwellian spectrum
for Cf (sf) [6] with TM = 1.424 MeV, X = 11:4 for E >_ 6 MeV.
processes.*
If the distribution (1) is transformed into the laboratory system of coordinates, a
simple analytic formula is obtained:
n'(E, Ei)-=N [osp (-- ll%--Y)--exp (-- llX~-Y)] ;
X =as-{-2a ~E-f-EI)lti; Y=4a EEf/ti,
where Ef is the average kinetic energy of the fission fragments per nucleon; the coefficient
N is found from the normalization condition of the energy spectrum. The limit a -; ~ corre-
sponds to the usual equilibrium thermodynamics, and Eq. (2) transforms into the Watt dis-
tribution
nw (E) = Nw exp (- E/ti) sh (2 ~/EE~/i), ( 3 )
The formula (2) was used to analyze the data on the fission of 233U by 0.53-MeV neutrons
[5] and the spontaneous fission of zssCf [6]. Here, we normalized the theoretical spectra as
follows: we calculated the sums '
J ? (E, EI) dE = stheo u, "exp (Ei) DEi=SeXp ,
i=mm
~mlrr
after which we minimized the weighted mean of the.sum of the deviations of the experimental
values nExp(Ei) from the values. -
h* (E z, EJ)::=(gexp/S'theo) r~ (E~, E1). (5)
Substituting the experimental. values of the average energy Ef 0.805 and 0.784 MeV for uran-
ium and californium, respectively, we obtainedt
*In [4] the neutron spectra were. also calculated taking into account-the temperature continuum,
but the superposition of the temperature on a finite interval 0 s 8 _< 0max was studied.. This
leads to a considerable difference in the high-energy region (see below).
-rWe point out the fact that in contrast to uranium we did not have reliable tabulated data for
californium, so that the values of the parameter (7) must be refined as experimental data is
accumulated.
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10'
102
10'~
>06
l0e
~ 1 p ,~ g 6 MeV 0 4 B 12 16 20 24 f, MeV
Fig.. 3 Fig.. 4
.Fig. 3. Comparison of the experimental spectrum for light and heavy fragments
in the cenfier of mass system of the fragments with the theoretical formula
(1)'for the parameters (?7) in the case sssCf (sf). The values of n(e)/? ex-
amined in [1].are shown.
Fig. 4. Comparison of the theoretical-spectrum (2) with the parameters (7)
and the Maxwellian spectrum with TM = 1.424 MeV (broken curve) with the ex-
perimental data for zszCf(sf): x) [6], ?) [7]. The normalization is arbi-
trary
i=0.777 ~ O,n07 MeV.. (6)
a=18.4 t 1,6 for a3~U-{-n (0.53 MeV),
ti=0.848 t 0:007 MeV,
a=13.50.8 for 25aCf(sf). (~)
Figures 1 and 2 show the theoretical spectra and the experimental points, divided for
convenience by the previously used Maxwellian function
nM (E, TM) = NM }~E exp (- F,/TM)> (8)
which was normalized analogously to the function (2). The agreement between Eq..(2) and the
laboratory spectra leads to the agreement between Eq. (1) and-the data in [1] in the cen-
ter of mass system (Fig. 3). A significant. difference between the distribution (2) and the
Maxwellian distribution and the spectrum presented in [4] is the increasing: excess in the
high-energy part, i.e., in the "tail" of the distribution. We observed this excess experi-
mentally [7] for 252Cf(sf) in the region 16.< E < 30 MeV (Fig. 4). We observed an analogous
difference from the Plaxwellian tails for different particles created in high-energy colli-
sions [3].
The thermodynamic theory of fission [8] gives a relationship between the changes in the
temperature T and. the. excitation energy E* of the fissioning nucleus
where aef is the effective parameter of the density of states; To = 1.15 MeV, which .permits
resealing the values of T obtained from the analysis of the spectra to -the case of other
values of the excitation energy-with constant a. Thus for 235U the relation (9) with the
parameter aef = AF/15 MeV can be written in the form
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by 7-MeV neutrons T = 0.89 MeV with a = 18.4, which agrees with the experiment .in.[9].
It should be noted that T obtained from neutron spectra for s3sU + n(th) agrees within
the limits of error with the nuclear temperature T = 0.75 MeV in the thermodynamic theory of
fission [8]. Thus, the parameters of the proposed model and the model itself have a clear
physical meaning. In addition, the Watt distribution (3) does not agree with experiment for
the physical values of Ef, so that it is used as a two-parameter formula, varying T and Ef
simultaneously. In this case, both the parameter and model become physically meaningless.
In conclusion, we note that more accurate experimental data should be analyzed by apply-
ing formulas (2) to the light and heavy fragments and summing the corresponding weighted con-
tributions. In this work, we restricted our attention to an analysis using the value of Ef
averaged over the light and heavy fragments.
LITERATURE CITED
1. H. Bowman et al., Phys. Rev., 126, 2120 (1962);.E. Khaid, I. Perlman, and G. Seabo:rg,
Nuclear Properties of the Heavy Elements .[in Russian], No. 5, Atomizdat, Moscow (1969).
2. G. Westfall et al., Phys. Rev., C17, 1368 (1978)..
3. A. F. Grashin and Ya. Ya. Shalamov, Yad. Fiz., 29, No. 3, 625 (1979).
4. D. t4adland and J. Nix, Nucl. Sci. Eng., 81, 213 (1982).
5. P. Johansson and B.. Holmquist, Nucl. Sci. Eng., 62, 695 (1977).
6. J. Boldeman, D. Gulley, and R. Cawley, Trans. Am. Nucl. Soc., 32, 733 (1979).
7. H. Marten, .D. Seeliger, and B. Stobinski, in: Proc. 12th Int. Symp. Nucl. Phys. Heavy-
Ion.Collisions and Nucl. Fission, Gaussig, Nov. 22-26, 1982, p. 122.
8. A. F. Grashin, A. D. Efimenko, and V. M. Kolobashkin, in: Methods of Experimental Nu-'
clear Physics in Studies of Fission Processes and products [in Russian], Energoatomiz-
dat, Moscow (1983), p. 43; A. F. Grashin, in: Current Problems in Fission Physics [in
Russian], Moscow (1983), p. 28.
9. J. Frehaut, A. Bertin, and R. Bois, Trans. Am. Nucl. Soc., 32, 732 (1979).
SPECTROMETRY OF THE MULTIPLICITY OF GAMMA QUANTA ON A STATIONARY RESEARCH REACTOR
Yu. V. Adamchuk, A. L. Kovtun, G. V. Muradyan, UDC 539.125.5.164.078:
Yu. G. Shchepkin,* G. Georgiev, N. Kalinkova, 621.039.55
E. Moravska, N. Stancheva, N. Chikov, and
N. Yaneva~`
A new technique has been developed at the I. V. Kurchatov Institute of Atomic Energy, for
measuring neutron cross sections and studying the channels of formation and decay of excited
nuclei: the spectrometry of .multiplicity of secondary radiation emitted by excited nuclei [l,
2]. In particular, spectrometric measurement of~the radiation of reaction products enables
the identification of radiation capture, fission, and neutron scattering events. The neutron
cross sections of nuclei of many elements have been measured with high accuracy with this
method in a wide. range of energies [3-6]. In this paper we describe the technique for mea-
Suring the neutron-cross sections based on the spectrometry of the multiplicity in the low- .
energy range (