SOVIET ATOMIC ENERGY VOL. 54, NO. 6

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• Document Number (FOIA) /ESDN (CREST): CIA-RDP10-02196R000300020006-4
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• Original Classification: K
• Document Page Count: 58
• Document Creation Date: December 27, 2016
• Document Release Date: February 6, 2013
• Sequence Number: 6
• Publication Date: June 1, 1983
• Content Type: REPORT

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? f ^ ,
Russian OFiginal Vol. 54, No. 6, June, 1983
December, 1983
^~'
~ ~e
SATEAZ ,54(6) 389-440 (1.983)
SOVIET
.ENERGY
? ~ ~ ATOMHAfl 3HEP~VIA
-(ATOMNAYA ENERGIYA)
~ ~ ~ ~ . ~ ~~ ~ 'TRANSLATED FROM RUSSIAN ,
..
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 Declassified and Approved For Release 2013/02/06 :CIA-RDP10-021968000300020006-4
A translation of Atomnaya Energiya
December, 1983
Volume 54, Number 6 June, 1983
CONTENTS
Engi:/Russ.
ARTICLES
Iterative Algorithm for Optimization of the Energy Distribution
in High-Powered Water-Cooled Channel Reactors (RBMK)
with the Help of Measurement of: the Insertion Depth of the Safety
and Control Rods (SCR) - A. A. Shkurpelov, V. V. Postnikov,
N. V. Isaev, V. G. Nazaryan, Yu. V. Shmonin, A. S. Nemirow,
and G. V. Yurkin.
Control of the Neutron Distribution in a Reactor - V, N. Konev
and B. Z. Torlin.
Calculation of Critical Heat Flux?in Rod Bundles with .Local Turbulators
- V. K. Ivanov and L. L. Kobzar' .
Boiling of Coolant with Depressurization of High-Pressure Vessel
- A. A. Avdeev and V. K. Shanin .
Determination of the Yield Figures of the?Products.Resulting
from the 242Pu and 241Am Fission by Fast Neutrons'-with the Aid
of Semiconductor Spectrometry - A. N.. Gudkov, V. M..Zhivun.,
A. V. Zvonarev, A. F. Zoiotov, A. B. Koldobskii, Yu. F. Koleganov,
V. M. Kolobashkin, S. V: Krivasheev, and N. S. Piven' . .
Effects of Neutron Irradiation on the Failure Viscosity of Graphite
- L. L. Lyshov, V. N. Barabanov, Yu. S. Virgil'ev, 0. K. Chugunov,
and A. I. Plavskii.
Separation of Hydrogen Isotopes Hz~iT and DZ-DT by Adsorption on NaA
Synthetic Zeolites - I. A. Alekseev, I. A. Baranov,
V. A. Novozhilov, G. A. Sukhorukova, and V. D. Trenin .
Possibilities and Conditions for Vitrification of Medium-Level Wastes
- V. A. Bel'tyukov, E, V. Brovkova, V. N. Zakharenko,
A. A. Konstantinovich, N. V. Krylova, V. V. Kulichenko, N. D. Musatov,
I. A. Sobolev, and L. M. Khomchik .
LETTERS TO THE EDITOR
Calculation of a Complex Grid with Clusters in the Single-Group P3
Approximation - V. E. Raevskaya and B. Z. Torlin:: .
Determination of the Cross Section of the Reaction Z'Al(n, p)27Mg
with Neutrons of Energy 14.8 MeV - V. T. Shchebolev, N. N. Moiseev,
and Z. A. Ramendik.
Estimate of the Intercrystalline Adsorption of Helium in 1~?ickel
- E. U. Grinik and V. S. Karasev.
389
387
394
390
400
395
406
399
.
414
404
418
406
423
409
425
411
429
415
434
417
437
419
The Russian press date (podpisano k pechati) of this issue was 6/1/1983.
Publication therefore did not occur prior to this date, but must be assumed
to have taken place- reasonably soon thereafter.
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ARTICLES
ITERATIVE ALGORITHM FOR OPTIMIZATION OF THE ENERGY DISTRIBUTION
IN HIGH-POWERED WATER-COOLED CHANNEL REACTORS (RBMK) WITH THE HELP
OF MEASUREMENT OF THE INSERTION DEPTH OF THE SAFETY AND CONTROL
RODS (SCR)
A. A. Shkurpelov, V. V. Postnikov,
N. V. Isaev, V. G. Nazaryan, Yu. V. Shmonn,
A. S. Nemirow, and G. V. Yurkin
The problem of profiling the energy distribution arises in the solution of problems of
the ongoing operation of a reactor and is associated with providing the initial computational
information for the centralized control system (CCS) of the reactor, which is based on the
use of a computer. The power Wj of all the heat-generating assemblies (HGA) in a reactor
is determined in the- system from the readings WZ (Z = 1, 2, ..., Nd) of the energy distribu-
tion control detectors (EDCD) and from a priori information about the power of the HGA R.
(j = 1, 2, ..., NHGA) obtained by computational means [l, 2]. Calculations are performed
using the two-group two-dimensional diffusion program BOKR [1], in which a quasisteady model
of the reactor is employed. In view of the inadequateness of this model for an actual unstable
RBMK-1000 reactor, some difficulties associated both with the analysis of the objectivity
of the results obtained and with the need for additional correction of the computational data
arise in the description of the energy distribution for in-channel control of the power.
Taking additional account in the computational model of the dynamic factors has evidently
permitted obtaining the macrodistributions reflecting the actual state for an RBMK-1000 in
the best case at time intervals up to several minutes However, calculations using the ap-
propriate programs should take an order of magnitude more time, and therefore the question
of performing them in real time can evidently still not be posed.
The approach proposed in this article permits raising the objectivity of the a priori
information within the framework of the quasisteady reactor model as a result of .taking into
account the actions of the nuclear power plant personnel in the extremal regulation of the
'energy distribution [3]. The use of this information in the plant control system permits
limiting the error of determining the power of the channels within permissible limits.
A method for extremal regulation is proposed in the calculations in which the commands
for shifting the SCR rods are issued immediately during the iterative process for the nuclear
fission soruces in the solution of the diffusion equations. This results in a significant
reduction of the computational time (by approximately.a factor of 8-10) in comparison with
the case in which a program of physical calculation is used as a separate procedure for
determination of the system .response to shifting of the rods [3].
We shall indicate some distinctive features of the algorithm for recovery of the energy
distribution from EDCD readings realized in the PRIZMA program [1, 4] in the "Skala" CCS to
explain the method of preparing the a priori information. The assumption that the micro-
structure of the energy distribution realized in the reactor - the ratio of the power of
adjacent channels - is iaeil described by the quasisteady computational model of an RBMK of
the BOKR ^rogram serves as the basis of the program; this property of the computational model
has been confirmed by repeated experiments. Therefore, the recovered power distribution Wj
is represented in the form
Translated from Atomnaya Energiya, Vol. 54, No. 6, pp. 387-390, June, 1983. Original
article submitted April 26, 1982.
0038-531X/83/5406-0389$07.50 ? 1983 Plenum Publishing Corporation 389
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where F? is a reference distribution calculated from data of the physical computation of Rj
and the entire set of readings of the EDCD with the use of the expansion '
88tt ~,I'
(here ~kj are test functions evenly specified for the entire reactor; the
are determined by the least squares method)
Nd a
~~ g
LI (~_~ Ch"~hi, =min,
i=i ~ h-i ch
coefficients Ck
where the index d denotes a channel with EDCD, and Nd is the number of EDCD.
The reference distribution Fj is an estimate of the mathematical expectation of the
desired energy distribution Wj without taking into account plant estimates of the dispersion
of the calibration error of the EDCD. In relationship (1), Vj is the local correction with
corrects the estimate Fj with account taken of the four EDCD nearest to the channel under
discussion. Its use is justified only in the case in which estimates are known for the.
dispersion of the calibration error of the EDCD o~~Z. An estimate of"Vj is determined by
means of a smooth statistical interpolation .[4] of the approximate values VZ = W~/FZ - 1, so
that
Vi ? ~i bid lac ~~) Va?
The coefficients bjZ (oc~Z) are calculated from a .priori data input into the PRZZMA program
which takes into account .the results of experiments and computational modeling; the dependence
of bjZ on o~~Z is such that bjZ (oc Z)-30 as ac Z}??,and then W?-~F?, and. as az Z~0 in channels
with EDCD, bZZ~ (o~,Z)~sZZ' (SZZ~ is the Kronecker symbol, and~lZ'= 1, 2,c..., Nd), and
then WZ->W~. The choice of continuous test functions ~kj and the use of smooth interpolation
of-the correction Vj permits producing a microstructure of the recovered distribution which
is similar to the microstructure of the calculated energy distribution Rj:
On can judge the objectiveness of the :control from the deviations of FZ from WZ, in
particular, from the quantity
N
t_i i=! 1
Upon deterioration of-the quality of the a priori information, SZ increases, and in accordance
with the relationship (1) the role of the local correction V~, which is dependent on the
selected interpolation method, the estimates of the values of o~ Z, and possible individual
"spikes" in the EDCD readings, increases. When 8Z starts to exceed some specified value
BSp, it is necessary to introduced new data of the physical computation into the control
system.
During the initial period of operation of an RBMK the calculated energy distribution
RJ?_ obtained using the BOKR program i5 in good agreement in the channels having EDCD with
the measurement data of Wd, which permits maintaining S2 at a level ti(2-4) x 10-3. However,
as the fuel depletion in ~he active zone increases, the energy distribution in the reactor
becomes unstable, which does not correspond to the quasisteady computational model of the
reactor. This leads to a significant increase in 82 to values ti5 x10-s-and greater, the role
of a local correction in the expression (4) increases significantly, and the error in control
of the channel power increases-,
In practice and in reactor models operating in real time, the energy distribution is
stabilized in time intervals significantly less than the characteristic time of development
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of time-dependent processes [4]. Therefore, taking account of dynamic effects in the models
can be simplified, and as a result it proves to be possible to combine the "usual" two-
dimensional quasistatic neutron physics calculation with the optimization calculation.
In order to produce the specified energy distribution or one close to it, the reactor
operator with the help of the monitoring and control system performs in essence extremal
regulation of the energy distribution in the active zone with a goal function of the type
where Kr is the nonuniformity coefficient of the energy distribution over the reactor radius
and Ksf. is the safety factor to the maximally permissible or the specified value of the
distribution Wsp. In practice the goal functions (6) or (7) are realized by maintaining some
specified distribution. In this connection it is advisable to take into account the analogous
actions of the reactor operator in the calculations with this model in order to reduce un-
justified distortions in the calculated macrodistribution obtained with the help of the
quasisteady model.
An extremal regulation algorithm is implemented in the program BOKRUS [3], in which
the response of the system to displacements of the SCR rods is determined by calculations
using the BOKR program. As experience in the operation of RBMK has shown, the energy dis-
tributions calculated using the BOKRUS program prove to be close to the actual distributions
at very large time intervals. However, one should note that the position of the rods obtained
in the calculations may not correspond to those implemented by the operator. Due to this
microstructure of the calculated distribution may differ from the microstructure of the energy
distribution realized in the reactor, which, as has been noted above, is well predicted by
the calculations using the BOKR program with the initial position of the rods. In order to
overcome this difficulty, functions calculated in advance of the influence of a shift of.
the rods on the energy distribution are used. Such corrections to the results of the BOKRUS
program are determined from these functions, which bring its microstructure closer to that
predicted by the BOKR program without significantly altering the macrodistribution.* The
expounded method for preparation of the a priori information permits maintaining the value
of d2 from the expression (5) within a rather narrow interval which does not exceed 6 x 10-3.
The method has been implemented in a complex of programs which provide for the operation of
an RBMK. In order to reduce the computation time, a new algorithm has been developed in
which, in contrast to the BOKRUS.program, a step-by-step method of regulation of the SCR
control rods is used for correction of the iterations in the nuclear fission so~~rces in soly-
ing the diffusion equations. Units of the fast BOKR BIS programs [5] which permit determining
immediately after 3-5 internal iterations the direction of variation of the distribution as
a.function of the insertion depth of the SCR rods, are used to calculate the energy distribu-
tion at each iteration. Shifting of the rods is accomplished as follows.
n
The iteration Q(j) (h(m)) is. calculated for the position of the rods h(m) with a fission
source Q(~-1) 3-5 internal iterations by the scheme of Buleev and Ginkin [6]). The average
powers wk -') and W(n) (h(m)) in the k-th multicells, which are a set of 3 X 3 cells having a
central cell with an SCR rod, are determieed in these iterations. The ordered sequence of
numbers
W~"~ (1~(ml)
~7L, t") _ k
a~ W~n_i) _1, k-q, 2, ..., rod
k
a~1t' m) ~ CL~n? m) ~ a(n, an) ~ ... ~ ann. nil
2 3 Nrod
*The described method of preparation of the computational data - optimization of the energy
distribution by the BOKRUS program and the introduction of corrections to the microstructure
- is equivalent to the correction of the breeding properties of multicells with centers in
the SCR rods, which leads to a change in the macrodistribution [2].
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is constructed, where Nrod is the number of rods taking part in the regulation. We choose
n+ and n- rods, which correspond to the first n+ and the last n- terms of the sequence. For
these rods commands are issued for extraction to a dep*_h hkm+1) = h(~) - Oh, k = 1, 2, ...,n+
and for insertion to h(k+l) = h(k) +~h, k= Nrod Nrod-l~ ? ? ? Nrod-n-, where ~h is the shift
step of the rods (it varies from 0.4 to 0.1 m). One can take n~ = n- in the calculations;
for best compensation of the reactivity in the regulation process one can alter the relation-
ship between the number of withdrawn and inserted rods, using the estimate kef of the n-th
NHGA NiiGA
iteration (kef x ~ Qi"'(hc'">)/~! Qi"-") . The number n+' is specified within the limits from
i=t i=i
10 to 20 in the calculations. For each regulation operation the mean square deviation
Nrod
Nrod k-~
is calculated. In the case in which on,m < on,m_i, regulation is continued with a specified
source 0(n-1). When 6n~m becomes larger than (or equal to) on~m_1, a replacement of the
source occurs: 0{~)(h(n?) is substituted in place of O~n-1) the reference power distribution
W(k-1) is replaced by W~k), and the process is repeated with a reduced shift step ~h. The
distribution corresponding to the specified energy distribution Wip, for which the result
of the physical calculation being profiled, is selected as the initial distribution of the
fission sources. It is assumed in the BOKR program that the energy distribution Wj follows
the distribution of the fission sources:
tip; -- c~ o- ,
~ Q,
,_,
where Gth is the total thermal power of the reactor. Therefore, under these conditions the
algorithm under discussion reduces the discrepancy between successive external iterations,
which is equivalent to an acceleration of the iterative process. The algorithm permits reac-
ting to incipient distortions of the energy distribution caused by the effect of interference
of the rods shifted, and with a small shift step one can achieve the maximum approach of the
result of the iterative process to the specified energy distribution (according to the crite-
rion of the average power of the channels surrounding each rod).
The computational results show that for the RBMK computational model the contribution
to optimization of .the regulation in the-first 4-6 external iterations, when the solution
acquires practically all the regularities of the computational model, is the most important.
The results of the optimization depend little on whether or not the external iterations which
r-emained are performed with regulation or without it.
The algorithm discussed has been implemented in the program OPTIMA written in the
FORTRAN-4 language for series ES computers. The computation time of one version of the
program is about 20 min of machine time on an ES-1033 computer. The input of initial data
from punched tape output from -the "Skala" CCS is implemented in the program, and output of
the computational results onto punched tape in the form required for input into the control
system is also provided for. The OPTIMA program has been subjected for an extended time to
experimental checking by means of calculations of specific states of an RBMK-1000 for
the first and second units of the Kurskaya and Chernobyl'skaya nuclear power plants.
The possibility of .the application of the results obtained to 'the control system was
checked with the help of calculations using the PRIZMA program (see Table 1). It is
evident that the OPTIMA program significantly improves the quality of the physical calcula-
tion in comparision with the usual calculations by the BOKR program. When the results are
used for control of the channel power in channels with EDCD, the deviations between the ob-
jective estimate of the energy distribution FZ and the measured power W? are reduced. A
comparison is made for the following parameters: Kr; Gth, recovered by the PRIZMA program
(or by the PRIZMA-ANALOG program, which simulates on a computer the operation of the plant
PRIZMA program); Wmax; the minimum safety factor until a heat exchange crisis Ksfn; the
thermal. engineering reliability of the reactor H; and the dispersion of the energy distribu-
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TABLE 1. Computational Results Using the OPTIMA Program
xr
+
_
d
Plant PRIZMA
Nuclear power
Date
o 22
(/
)
?max~
Qmax~
v~,
~
plant unit
BOKR (
OPTIMA
?
%
%
(%)~
err I
Gth' Iv1W~
w~,
MW
Kurskaya I
Of,.03.79
1,602
1,346
fi,7
17,6
13
,9
6,2
1,30(1
3115
'1,52
II
27.03.80
1,604
1,279
4,5
20,8
1.4
,3
4,8
1,276
3201
2;6(i
C hernobyl'skaya 1
8
'
7
'
I
23.01..81
1,
38
1,404
5,3
.11 ,
L
1
,4
4,6
1,382
3216
1,69
Plant PRIZMA
PRIZMA-A
NALOG with calc, by OPTIMA
pro
gram
Nuclear power
plant unit
Kmin (
Dn I
x
Kr
I
Gth~ MWl
I
~'m
n I
s
Dn' I
H
MW
f
y I
Kurska a
1,1.2
18,8
0,998367
1,300
3117
2,50
1,12
13,0
0,998378
I[
1,04
55,0
0,996050
1,27
7
3198
2,65
1,04
28,2
0,996337
hernobyl'skaya I
~
I
1,14
39,0
0,998279
1,380
3221
.2,70
1,
4
25,0
0,998294
tion D,,. = 8g - Na. ~' ~a 1. The energy distribution obtained at nuclear power plants
r_ ~
by the PRIZMA program with use of the data of the physical calculation by the BOKRUS program
was used in the calculations as the specified W~p. The mean-square deviations o2 of the
results of calculating 'the power W?pt by the OPTIMA program and the data of the plant PRIZMA
program are indicated in Table 1, along with the maximum relative excess omax - max (W~Pt/
W~p - 1) and understatement omax - max (1 - W~Pt/W~p), and the mean-square .deviation oa cal-
l
culated for the channels with EDCD.
'The. results of calculations using the OPTIMA program show that-one can achieve and ap-
preciable reduction of Kr in comparison with the result's of the physical calculation using
the BOKR program in the regulation of the insertion, depth of the SCR rods. The. introduction
of such an energy distribution in the "Skala" CCS permits improving the values of Dn and
maintaining the remaining parameters practically constant. OPTIMA is a newfast program which
provides for equalization of the energy distribution in an RBMK by means of changing the
insertion depth of the SCR rods, and it i.s completely.suitable for use in the complex of
programs which provide for. operation of an RBMK.
In order to increase the informativeness of the estimate of the mathematical expecta-
tion of the energy distribution for reactors with an unstable distribution, it is necessary
not only to detail the model of the reactor and to refine the description of the dynamic ef-
fects in it, but also to introduce, mainly into the physical calculation, a unit for the
automatic optimization of the distribution with the goal control function adopted for' a given
reactor.
LITERATURE CITED
1. N. A. Dollezhal' and I. Ya. Emel'yanov, A Channel Power Reactor [in Russian], Atomizdat,
Moscow (1980).
2. A. A. Shkurpelov, N. V. Isaev, and A. S. Nemirow, At. Energ., 50, No. 1, 6 (1981).
3. I. Ya. Emel'yanov, V. V. Postnikov, and G. V. Yurkin, At. Energ., 47, No. 1, 8 (1979):
4. E. V. .Filipchuk, P. T. Potapenko, and V. V. Postnikov, Control of the Neutron Field of
a Nuclear Reactor [in Russian], Energoizdat, Moscow (1981).
5. A. A. Shkurpelov et al., At. Energ., 50, No. 5, 352 (1981).
6. G. I. Marchuk, Methods of Numerical Mathematics, Springer-Verlag (1975).
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CONTROL OF THE NEUTRON DISTRIBUTION IN A REACTOR
V. N. Konev
and B. Z. Torlin
The stability of the neutron distribution in a reactor having special systems of local
automatic control (LAC) has.been studied in a number of papers [1-3]. As a rule, the systems
considered had a small number of control rods (CR), and to each LAC was conventionally as-
signed the part of the core controlled by it with intrareactor control sensors and/or ex-
ternal chambers, producing jointly a control signal for "its own" rod located in this same
region of the reactor. In determining the stability of such systems certain characteristic
computational difficulties sometimes arose if the regions controlled by the various LAC were
not clearly delimited. Such difficulties arose in the analysis of the stability of the optimum
solution when many CR were used [4-6].
The influence functions of the CR play an important role in control problems. We use
the definition of the influence function ~j of the j-th CR given in .[7]. We call the value
of this function in the zone of the i-th sensor the influence coefficient V~ij of the j-th
~CR on the i-th sensor. If pi is a sufficiently small change of the effectiveness of the j-th
CR, its influence on the i-th sensor is ~ijPi? Let Xi be the change in response of the i-th
sensor as the result of :a small perturbation of the properties of the reactor not related to
the change 'in effectiveness of its CR, and ~Pi the change in response of the i-th sensor as
a result of -the simultaneous action of these effects. Then*
where N is the number of CR and M is the number of sensors. In matrix form
W = ~P .~ x. (1b )
Of the possible algorithms for the comtrolt of the neutron distribution, the simplest is
~=0 foc. M=1V. (2)
In practice, if .each sensor is located close enough to "its own" CR, and there are the
same number of CR and sensors, the matrix q"r will be diagonally dominant and well-conditioned.
It was shown in [3] that if the sensors are too near the rods, the neutron distribution be-
comes unstable.
Let us consider the neutron distribution stabilization system discussed in [3], which
employs six symmetrically placed-chambers and six CR located along the radial lines drawn from
the center of the reactor to the chambers. When the CR are located near the chambers, the
system has a very low stabilizing capability. As the CR are moved away from the chambers,
*For simplicity we assume that the reactor has a fast power reactivity effect (see note in
[7]?
tFrom now on we assume that the control system is sufficiently quick-acting in the sense
indicated in [8, 9].
~ In this case the influence matrix ~.is not only square, but also plays the role of the
control matrix.
Translated from Atomnaya Energiya, Vol. 54, No. 6, pp. 390-395, June, 1983. Original
article submitted July 8, 1982.
394 0038-531X/83/5406-0394$07.50 ? 1983 Plenum Publishing Corporation
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the stabilization is improved, but when the CR are near the center of the reactor, all the
elements of the matrix i~r approach the same value, and the condition of ty is sharply worsened.
If the CR are located at the same radius on the bisectors of the angle formed. by the lines
drawn from the center to the chambers, the matrix iY'becomes singular - its determinant is
zero. This is true for the CR at any radius, and for any?even N = M.
The operating algorithm for the LAC system of the RBMK reactor at the Leningrad nuclear
power plant [10, 11] is rather simple, but more complicated than the system discussed above:
4
where the components of rpr are the total signal E cpi of the deviation of the responses
k=1 k
of four snesors surrounding the i-th rod of the LAC. The elements of the control matrix are
4
E ~ikj. Obviously, as long as the limits of the region controlled by the sensors of each
k=~
CR are clearly enough delineated, the control matrix will be diagonally dominant and well-
conditioned. In the case under consideration there are many more sensors than CR in the
automatic control system, and therefore there are many possible ways of using this redundancy.
For example, the stability of control systems with least-square deviation (LSD) from the
specified neutron distribution was investigated in [3, 7, 12]. It was shown in [7] that when
there is a fast power reactivity effect the control algorithm has the form
where T denotes the transpose.
The control signal for the CR is now formed by all the sensors in the system, and not
just by the nearest one. Therefore, there are no "own" and "other" sensors. The control
matrix is formed by substituting Eq. (1) into (4) in the form Y'TtY. In general it is dif-
ficult to draw a conclusion about its condition. It can be shown that such a control matrix
-will be strongly diagonally dominant if the CR and sensors form a regular lattice and there
are many more sensors than CR.
In the RBMK there are more CR than sensors. in the radial-power distribution control
system [10, 11]. Therefore, e.g., including all the CR and sensors in the automatic control
system raises the problem of the redundant CR, which can be solved in various ways, in par-
- N
ticular, by the principle of least action of the rods min D = E p?. In this case the operat-
ing algorithm of the control system has the form p3 3-1 J
~ _ ~;
p -j-'YTS, = 0. .
The components of the M-dimensional vector .a are Lagrange multipliers which have a clear
physical meaning. This is easy to understand after substituting Eq. (lb) into (Sa), and
then (5b) into the result. The control matrix takes-the form ~YrT. Control is accomplished,
as it were, by group motions of the CR, and the ai play the role of the effective displace-
ment of the group. According to Eq. (Sb), the displacements of the CR in the group must be
proportional to their influence coefficients. By replacing the CR by sensors and the sensors
by CR and using the reciprocity property [13], it is easy to establish the "conjugacy" of
the control by the principle of least action with LDS. Therefore, the above statement about
the condition of the control matrix remains valid.
We have considered the simplest neutron distribution control algorithms based directly
on sensor responses. Optimal control algorithms are more sophisticated. For control by slow
processes using a system of quick-acting controls, the optimal solution can be obtained by
linear programming methods [5, 6]. In this case the number of operative CR determines the
number of channels reaching their maximum restricted temperature. We call these hot chan-
nels. For sufficiently small perturbations the optimal process will preserve the hot-chan-
nel parameters, i.e., it will follow algorithm (2). Now cp combines the power deviations
of the hot channels and not the sensor responses. This may have an unfavorable effect on the
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0 2 4 tg a-z
Fig. 1. Dependence of Re w on d-2. 1, 2)
for Figs. 2c, 2a; 3, 4) for Figs. 2f, 2e;
dashed-curve indicates the region of poor
numerical stability.
condition of the matrix ~ for the influence of the CR on the hot channels. This is related
to the fact that in contrast with sensors, whose disposition can be planned beforehand, the.
location of the channels is determined after solving the optimization problem, and may turn
out to be anywhere. Some of the variations of the location of hot channels may be unfortunate
'from the point of view of the condition of the matrix Y~. Let us analyze the conditions of
.its degeneracy. Suppose N hot channels are located in such a way that one of the rows ~i
of the matrix ~y is a linear combination of the others. We number the hot channels in such
a way that this row and .the channel associated with it have the number N, i.e.,
.N- t
Considering ~,N as a function of the displacement of .the N-th channel, we can obtain the equa=
tion .of the singular line, motion along.which will leave the matrixlp degenerate:
N-~ T T -
}J ,p~ dli= apN dz-l- a~N dy?
Obviously, the line or lines can pass through any of the remaining hot channels. Thus, when
x and y coincide with the coordinates of the k-th hot channel, at least N - 1 choices of
initial conditions of the form Zi = dik and ~N = ~k for any k < N, where Sik is the Kronecker
symbol, are determined for system (7). With these initial conditions the singular lines
passing through a'll the hot channels from the first to the (N - 1)-th can be determined* from
system (7). If the control matrix is well-conditioned, the N-th hot channel must not turn
out to be too close to one of these lines. Since it is impossible to guarantee that this
condition will be satisfied, we examine the dangers accompanying its violation and how to
avoid them. If the control matrix is ill-conditioned (in the present case this is the error
in the determination of p, the displacement of the CR, by algorithm (2) ytp + x = 0), gross
errors will appear in the solution, even at a .low noise level, e.g., in the responses of ,the
sensors or in the determination of the power distribution deviation vector in hot channels.
This is a typical case of low noise stability, when a small random error in measurement is
transformed into large-scale .random fluctuations of the whole state vector of the system,
or part of it. In the present case the conditionscp = 0 can be satisfied rather accurately
*Because of the Binet-Cauchy formula [14], the control matrix W''~v with .LSD for M > N may become
singular if all (!) M sensors turn out to be on the intersections of the singular lines of
all combinations of them N - l~at a time. If-there are considerably more sensors than rods,
this is extremely improbable. By the principle of least action, the same considerations
for the control matrix ~YVJ~ are valid for M < N.
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and p undergoes appreciable random fluctuations. If the matrix `Y were singular,'' this con-
dition could not be satisfied exactly for a~,y displacements p, and it would have to be satis-
fied approximately. It is advisable to do this even when ~Y is ill-conditioned, since it im-
proves the correctness of the control problem considerably.
If the concept of admissible straggling parameters S~ and Sp is introduced, the control
algorithm based on a combination of minimization of the deviation of the power distribution
in hot channels and the action of the CR
min (~ St
Ps ~ ~
will have the form
where
or in matrix form
After substituting Eq. (lb) into (8b), we obtain the control matrix in the form 'YTYr+ d2 E,
where E is the unit matrix. Now the control matrix is positive definite, and its condition
may be affected by 8, a single regularizing parameter determined solely by the ratio sW~aa?
The control matrix was found to be ill-conditioned in studies with the BASIRA program of the
stability of the solution close to that derived in [6] for two-dimensional power dis-
tribution. The spacings of the hot channels- and CR were taken from [6] and trans-
ferred approximately to the RBMK loading diagram. Feedbacks and the reactivity coefficients
characteristic of this reactor with 1.8% enriched fuel were used.f In the absence of a
spatial stabilization system, the unstable mode with the shortest period for a single auto-
matic control - the first azimuthal - develops in Toles 2 min.
The incorrectness of the problem before the introduction of regularization appears
in the form of instability of the calculation of the principal eigenvalue. In these cases
the spectral condition number [17] of the control matrix (the measured ratio of its maximum
and minimum singular numbers [18]) turned out to be greater than 10?. This kind of trouble
never arose if the CR and sensors, e.g.,formed a regular lattice and were near one
another. In using the control algorithm in the form (8), the principal eigenvalue can
be determined reliably without fear of a numerical instability of the solution. However,
the inroduction of d into the control algorithm worsened the dynamical stability of the
The simplex method [15] for solving the linear programing problem and modifications of it
cannot lead to a singular matrix ~Y, but it cannot guarantee that the control matrix will
be well-conditioned. This appears, e.g., in a weak sensitivity of the optimum coefficient
of nonuniformity of the power distribution to different variations of pops obtained with
different versions of the programs.
t?The power reactivity coefficient is 0.005, the temperature reactivity coefficient of graphite
is 0.013 with a time constant of 1 h, and the xenon reactivity coefficient is 0.0298 [16].
~To analyze the stability the BASIRA program determines the eigenvalue w of the system of
transient equations with the maximum real part [16].
~:~~~ + Szp f = 0 for j =1, 2, ... , N,
i
s2 = (s~/sv)2
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Fig. 2. a, b, c, d, e, f: ^) hot channels.; O) CR.
reactor,. This change of the control algorithm is equivalent to a change from an astatic to
a static control law with a large amplification factor (tid-2). For a reliable guarantee of
the numerical stability of the problem i;t is sufficient to have 42..,10-4 of the maximum eigen-
value of the control matrix. Of course, this does not affect the stability of a system whose
control matrix is well-conditioned. However, 6 has an apprecialbe effect on the stability
of systems with ill-conditioned control matrices. Figure 1 shows the dependence on S of the
real of the principal eigenvalue w of systems with CR and hot channels in the positions shown
in Figs. 2a, b, e, and f. As d-~ 0 it should be possible to determine the asymptotic value
of Re w corresponding .to an astatic control law. Unfortunately, in a number of -cases, as in
the present situation when the spectral condition number becomes larger than 10?, this fails because
of numerical instability.* Therefore, in subsequent calculations we chose a single value
d2= 2.5 X 10-`. The straggling Sp, which is one-third the travel of a RBMK-1000 control rod,
corresponded to 8~ ~ 0.5 % in the value of ~/~?.
A study of systems with CR and hot channels in various positions showed that stability
is determined largely by how extensively the whole core is covered by control. Figure 2 shows
the positions of RBMK-1000 CR and hot channels for some of the larger number of cases cal-
culated. The arrangement of CR and 35 hot channels shown in Fig. 2b is similar to that in
[6]. Figure 2a differs from Fig. 2b only in the positions of hot channels, which are now
more widely spaced in the c.oxe. Figure 2c differs from Fig. 2b primarily in having .only 26
CR and hot channels, but arranged so that the region they control is not too different from
the analogous region in Fig. 2b. Finally, Fig. 2d shows the locations of 28 CR arranged in
a .regular lattice covering the whole core. The sensors are also spaced reguarly at distances
of two lattice constants from the CR. Figures 2e,f show the positions of 52 CR and hot chan-
nels covering practically the whole controlled region of the reactor. In this case all the
rods of the plateau region take part in control, and therefore they form a regular lattice.
Figure 2e differs from Fig. 2f in using regularly spaced radial control sensors.
*The spectral analysis of the control matrices was performed with the KIM and QREIG programs
from the library of standard BESM-6 programs 18]. A test showed that the calculated small
eigenvalues (8, which for water approximately corresponds to a saturation
pressure of up to 13 MPa, Eq. (17) is approximated with sufficient accuracy by the dependence
cPtw= 1-exp(-D.SIIZe),
I11e = - 2 Lt (1 --- ~G twl .
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 Declassified and Approved For Release 2013/02/06 :CIA-RDP10-021968000300020006-4
\ I Transi- ~ -~~ Fluid
I- ~`~ tional I io..oi
Fig; 1. Distribution of the true volume steam
content as a function of height in the vessel:
a) model of complete separation of steam; b)
uniform mixing model; c) semiempirical RELAP model
[3]; d) VTI model [5]; e, f) experimental data
[8, 9].
Having calculated the value of HZe,from Eqs. (16) and (18), the reduced height of the
position of the flow orifice can be determined as
1TZ = (hllh~e) TTIe" (19)
where hZ, hZe are the dimensional height of the position of the flow orifice and of the
evaporation surface, respectively.
Using .relations (18) and (T9)., the quantities cpZ~ ~Ple~ sought can be determined from
Eqs. (1) and (2) at each .step of numerical integration.
To close the mathematical description of the problem, the system of equations obtained
must .be supplemented ,by a relation that relates the flow rate of boiling coolant through
the location of the break with .the pressure in the vessel, steam content at the inlet to -the
discharge pipe, and its geometrical dimensionso
At the present time, well-founded-methods for calculating the critical flow rate of -boil-
ing coolant have been developed only for a relatively narrow region of initial fluid param-
eters and geometrical dimensions of the channel [13]o For this reason, to check the proposed
model, we use the results of only those experiments in which the flow rate of the outflowing
coolant was measured while emptying the vessel [4, 8, 9, 14].
Available experimental data, e.g., [8, 9],-show that at the time the leak appears, the
pressure in the vessel drops sharply below the saturation curve. Then, within fractions of
a second, the pressure is restored to a value close to the saturation curve. Subsequently,
the boiling proceeds at equilibrium.
The initial stage of the decompression process (transition from unheated to metastable
fluid) determines the dynamic action of shock waves. on the elements of the .installations
within the housing. This phenomenon was analyzed .theoretically by Avdeev .et al. in [15].
In the present work the equilibrium stage of the process, during which most of the coolant
is removed, is being analyzed. For .this reason the initial conditions for Eq. (11) were given
in the form
It was noted in [8, 9], that the heat accumulated in the walls of the vessel had an ap-
preciable effect on the distribution of the steam content over the height of the vessel.
For this reason the inflow of heat from the walls and from the bottom of the vessel was in-
cluded in the model of the regular cooling regime. In so doing, it was assumed that the
temperature of the internal surface of the walls equals the saturation temperature, while
the outer surface is adiabatically insulated. It was assumed that the initial temperature
field is homogeneous. Comparison of the thermal flux computed in this manner with the results
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Fig. 2. Comparison of computed curves showing the pressure
drop (p) and the level of the-boiling coolant (h), as well as
the distribution of the true volume steam content, with the ex-
perimental-data of MEI (---) [8, 9]. Leak diameter: 10 (a),
25 (b), 35 (c), 45 mm (d); change in steam content at the mark:.
1830 (1); 975 (2), 612 (3), 1400 mm (4).
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MPa
6
Fig.. 3. Comparison of computed pressure
drop curves with experimental data of ROSA
(---). Diameter of upper orifice is 50 mm.
Fig. 4, Comparison of computer pressure
drop curves with experimental data (---),
obtained on the "Udar-1" stand; orifice diam-
eter: 1) 5 mm; 2) 15 mm.
of :the "exact" numerical solution of the one-dimensional nonstationary .equation of heat con-
duction, performed with the use of the two-layer implicit six-point difference scheme (Crank-
Nicholson scheme), gave good agreement for the conditions examined. We solved the system
of ordinary differential equations (7), (8), (10) with the initial conditions (20) using the
Runge-iCutta method with fourth-order accuracyo In performing the calculations, the thermo-
physical properties of phases, as well as their derivatives along the saturation curve, stand-
ing on the ?right side of Eqs. (7) , (8) , and (10) , were fixed according to the data in [16] .
The distribution of the true volume steam content over the height of the vessel when the
vessel is depressurized was measured by Dement'ev.et alo [8, 9J by the method of transillumina-
tion with rays. The change in mass of the two-phase coolant as a function of time was de-
termined by integrating the steam content curve. The dimensions of the experimental vessel,
as well as the location of the transilluminating setups, are shown in Fig. 2. The diameter
of the leak was varied by restrictive diaphragms in the discharge pipe. It follows from a
comparison with the experimental data in [8, 9] that there is satisfactory agreement not only
with respect to pressure, but also with the distribution of the true volume steam content.
Analogous results were also obtained for the other orifice diameters investigated (d = 5, 15,
and 22 mm). We note that the maximum ratios of the area of the flow-through cross section of
the flow orifice and the vessel volume used in the experiment in [8, 9] are severai times
larger than the corresponding values characteristic for modern reactor installations. The
nature of the change in the true level of the coolant is interesting (see Fig. 2.): When the
upper edge of the orifice is attained, in spite of the continuing outflow of mass from the
vessel, the fluid level remains constant for a long period of time. This .phenomenon is charac-
teristic for experimental vessels. with a relatively high position of the discharge pipe.
Good agreement was obtained between the results of the calculation and the ROSA experi-
ment [4], performed on a vessel with a large volume. In these experiments the flow rate was
measured according to the hydrostatic pressure drop between. the top and bottom of the vessel.
The good agreement between the computed and experimental pressure curves occurred both with
the upper and lower position of the flow orifice. The only exception was experiment No. 409
(upper orifice with diameter 70 mm, initial pressure 6.87 MPa). We note that a large disa-
greement between the measured flow rate curves and the results of theoretical estimates, made
by Sobajima based on the RELAP-J program (Fig. 3), occurred only in this experiment.
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In the experiments described in [14], the results of which are presented in Fig. 4, the
coolant flow rate was determined with the use of a low-inertia strain system by weighing
the volume studied during the course of the experiment. It is evident that the agreement
is good.
Thus, the computational method developed permits including the "swelling" of the coolant
level accompanying nonstationary boiling under pressure-drop conditions and gives good agree-
ment with experiment. In addition, the universal nature of the recommendations in [10, 11]
on-which the present work is based, and the absence of empirical "adjustment factors", makes
it possible to extend the analysis presented here to different coolants (organic fluids,
heavy water, etc.). The use of the proposed procedure in multielement models does not ap-
preciably complicate the numerical algorithm and does not appreciably increase the computer
time required.
LITERATURE CITED
1. F. Moody, Transactions of the American Society of Mechanical Engineers, Ser. C, Heat
Transfer; No. 1, 160 (1965).
2. V. P. Spasskov et al., Vopr. At. Nauki i Tekh. Sero, Dinamika Yad. Energet. Ustanovok, No.
1, 111 (1971).
3. C. Solbrig and D. Barnum, Nucl. Safety, 17, No. 2, 194 (1976).
4. M. Sobajima, Nucl. Sci. Eng., 60, 10 (1976).
5. A. M. Bukrinskii and R. L. Fuks, Teploenergetika, No. 9, 58 (1978).
6. D. A. Labuntsov, I. P. Kornyukhin, and E. A. Zakharova, ibid:, No. 4, 62 (1968).
7.. M. A. Styrikovich, 0. I. Martynova, and Zo L. Miropol'skii, Steam Generation ~.n Power
Generating Plants [in Russian], Energiya, Moscow (1969).
8. B. A. Dement'ev and ICh. M. A1'-Bakhili, Teploenergetika, Noo 12, 72 (1978).
9. B. A. Dement'ev, Author's Abstract of Doctoral Dissertation, Technical Sciences, MEI,
Moscow (1977).
10. - A.- A. Avdeev and A. A. Avdeeva, Teploenergetika, No. 8; 53 (1980).
11. A. A. Avdeev, ibid., No. 3, 23 (1982).
12. M. E. Deich and G. A. Filippov, Gas-Dynamics of Two-Phase Media [in Russian], Energoizdat,
Moscow (1981).
13. D. A. Labuntsov and A. A. Avdeev, Teploenergetika, Noo 9, 71 (1978).
14. V. N. Maidanik, et al., At. Energ., 47, No. 2, 117-(1979).
15. D. A. Labuntsov and A. A. Avdeev, Teplofiz. Vyso Tempo, 20, No. 2, 288 (1982).
16. S. L. Rivkin and A. A. Aleksandrov, Thermophysical Properties of Water. and Water Vapor
[in Russian], $nergiya, Moscow (1980).
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 Declassified and Approved For Release 2013/02/06 :CIA-RDP1O-021968000300020006-4
DETERMINATION OF THE YIELD FIGURES OF THE PRODUCTS RESULTING
FROM THE 242Pu AND 2.41Am FISSION BY FAST NEUTRONS WITH THE AID
OF SEMICONDUCTOR SPECTROMETRY
A.
N.
Gudkov, V. M. Zhivun,
A.
V.
Zvonarev, A. F. Zolotov,
A.
B.
Koldobskii, Yu. F. Koleganov,
V.
Mo
Kolobashkin, S. V. Krivasheev,
and
'N.
So Piven'
Since the yield figures of the products resulting from the fission of transuranium nuclei,
among them 242Pu and 241Am, by fast neutrons are increasingly used as nuclear constants in basic and
applied work in nuclear physics and technology, the requirements to the accuracy and reliabil-
ity of the yield figures become ever more stringent. To date, the results of measurements
of the yield figures of the products resulting from the fission of 242Pu by fast neutrons
have been listed only in [1] for the heavy peak of the mass distribution. Furthermore, one
of the two sets of yield figures of 242Pu listed in [2] is a preliminary set without error
estimates. This set does not allow specific conclusions on the experimental technique em-
ployed to obtain the data. The yield figures of the products resulting from the fission of 241Am
by fast neutrons were experimentally determined only in [2], but, as far as the method is
concerned, that work is practically outdated. All this implies limitations in regard to the
accuracy and reliability of the yield figures in view of the limited applicability of the
experimental techniques used in {1, 2] and the large probability of systematic experimental
errors influencing the final results. Furthermore, the list of the fission products consid-
ered in the cited papers is very limited.
In our work the yield figures of the fragment nucleides of 242Pu and z41Am were deter-
mined for the first time by semiconductor y-spectrometry of an undivided mixture of fission
products in an irradiated sample. This technique; which we used for the first time in in-
vestigations of the yield of the products of neutron-induced fission of other heavy nuclei
[3-6], helps to substantially overcome the above-indicated.difficuities in the evaluation of
the research work.
The samples of the material to undergo fission were irradiated in the center of the BR-1
reactor core (FEI). The neutron flux density at the point of irradiation was 6 ?1010-neutrons/
(cm2 sec). The samples were 242Pu and 241Am dioxides compacted and hermetically sealed in
4-mm-high cylindrical steel shells with a diameter of 6 mm. -The wall thickness was about,
0.15 mm (Table i). The mass concentration of the impurities in the samples did not exceed
0.1%.
Measurements on the irradiated samples were made with a semiconductor y-spectrometer
of standard design with a DGDK-32A Ge(Li) detector having a resolution of 3.5 keV for the
1333 keV 6OCo radiation. The spectrometer was calibrated with the aid of an OSGI set and,
TABLE 1. .Characteristics of the Samples
of the Materials Undergoing Fission
(Pure mass of the
Sample material under- '
Irradiation time, h
going fission
='=Pu (first)
84,1
7,23
=a"1'u (second)
72,6
1,00
='41Ani
54,5
4,00
Translated from Atomnaya ~nergiya, Vol. 54, No. 6, pp. 404-406, June, 1983. Original
article. submitted August 2, 1982.
414 0038-531X/83/5406- 0414$07.50 ? 1983 Plenum Publishing Corporation
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 Declassified and Approved For Release 2013/02/06 :CIA-RDP10-021968000300020006-4
TABLE 2. Yield of the Products Resulting
from the Fission of 242Pu and Z41Am by Fast
Neutrons
Fission ~ qa^-Pu
galpm
products our work
~1]
our work
~2~
Ns~~~lir
U,~37?U,O:t
~
0,87?0,18
s71Cr
1,47?U,`L3
U, 91?0,23
K~Kr
(1,77?U, 111
1,80?0,41
xASr
1 ,LO?p, lU
AtSr
1, i i?D, 14
2, 13?0, 21
1,9U?U,U5
A"Sr
1,93+0,11
2,89_?(1,18
A4Y
2 15 11,25
A:fY
3,32?0,(ill
3,-0QtO,'LU
AaY ~
'L, 71?U,28
9JZr .
3,`L4?0,38
2, 7U?0, 10
A7""/..r
4,18?0,32
5,47?0,27
AAMu
6, 3?U, 3
l~~:lltu
7,710,2
(Iw~?~
5, 5`LtU, 55
5, 35?U, 83
losliu
(i,92?11,43
6,6?0,2*
toST:h
7, 48?0.47
111/16
0, 22tU, i i
S45SI,
n,95vtn,009
125Sb
0,050
S4RS11
11, 1i3t-11,41
G,fi7?9, U8
12ASb
?,;;3+11,74
1,70?11,42
1:uimcii
11, i1?U,Ui
1,fit0,118
Sa1Sb
i, 97?U, 3U
1s1mTi
Il.~il?0,11(.
1,25f0,29
lalI
3, 19?U.21
3, SfU, 1
SsiSn
3, 11if11, 19
1st\c
3,32
1s4Tc
4.46?U, 6U
1a4I
4.114?(!, 38
Ssszl?
4,59?U,'l8
1;t4~1!
4, 52
Sssl
7,U4-~U,42
7,iG?U.5G
4,Ot0,`L
1:1:I,Cs
6,!17fU,~i2
tsaCs
6,49
13x1'c
li, i5?(1,78
5,44tU,fiU
tsaI
6, 83?U, 38
5, 311fU. 36
134 ;CC
_7,59tG,~i G'
Ssa~,.
7, 36
lsST
U,83-rU.;'.8
5,30?(1,30
4,810,3
tsSntSu
~
2 21i~U-, 55
SasSc
G,!I!)i-U,41
G,G1t0.4(I
1:15\c'~'
ll, 20?U, 02
t~t>Cs
'r, 1.3?U, 43
laSTS
laa(;s $
ii, 89
0, 1610. 08
lili(;~
(i, 5(i
'
Sa7Cs
-
6,46?U,39
5,6f`L,8 '
ts7Cs
6,31
SaaCs
4, 4'LtQ,48
_6,4t1r,4
lax(-s 'r
U, 19?U. 1U
Ss~13a
G,'LS-?--0.38
taA11~
8'i?U,3i
5
G, 72?1,14
1sAI,;,
,
5,99tU, 36
SxU~;I
6,711?-0, GO
4,82?U, 45
5.2?U,1
SauLa
Sa,Lat
6.49+U,78
5,62?0,59
U,02U?U,UU6
1auCc
4, 95tU, 3U
7tU, 2
4
tal to pa ?sec
42
-
58
8 ? f if-~~
1 ? 10-~~
02
-
38
O Itl-a
2?f0-5
Fluorite
45
s
sz
a,s?SO-~
l,5?uf-5
itoa?c;
5, i Pa ?sec
Fig. 1. Arrangement of the furnace for
electrical melting: 1) molydenum elec-
trodes; 2) gas condilit; 3) barrier prevent-
. ing dust entrainment; 4) connecting pipe
for load; 5, fi) melting and working zones;
7) unloading chamber; 8) Silit heaters.
estimated from the sodium ion (Table 2). As is evident from Table 2, the rate of leaching
from specimens obtained with the use of loam and quartz sand as fusing agents is quite low.
However, their melting temperature (> 1200?G)and the viscosity of the melt.(> 10 Pa -secs
makes it difficult to obtain these materials in commercial furnaces and to unload.them.
In this case it is necessary to introduce additional compounds that contain boron anhydride
or calcium fluoride.t
It is most advantageous to nse datolite concentrate and fluorite together with quartz
sand. As the laboratory investigations demonstrated, when using datolite concentrate, it is
possible to obtain a preparation with a very low rate of leaching (see Table 2). For an
oxide content in wastes equal to 30 mass %, 25 mass % of quartz sand, and 45 mass % of da-
tolite concentrate at a temperature of 1100?C, the dynamic viscosity of the melt does not
exceed 2.2 Pa ?sec (22 P). An oxide content in wastes equal to 35-40 mass % and 35-40 mass
Si02 in the melt does not greatly change the viscosity: 2.5-3.2 Pa ?sec at 1100?C. When
*In melting and clarification of the glass mass in the glass-making industry, the allowable
values of viscosity do not exceed 10 Pa?sec (100 P).
tFor liquid wastes from nuclear power plants with VVER, which include boric acid, this may
not be necessary.
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 Declassified and Approved For Release 2013/02/06 :CIA-RDP10-021968000300020006-4
using a fusing agent consisting of fluorite and quartz sand to fix the wastes, the following
glass composition is recommended (in mass %): oxides of wastes 45; SiOz, 50-52; CaF2, 3-4.
The viscosity of the glass melt with this composition at 1100?C is 5.7 Pa? sec.
The amount of fluorine remaining in the glass when using fluorite as the fusing additive
is (95 ? 5) mass % (with total fluorine content in the glass equal to 1.6 mass %). When hold-
ing the melt obtained with datolite concentrate and quartz sand added as fusing agents and
containing 11 g of fluorine per 1 kg of glass mass for 20 h at 1200?C, the fluorine content
in the glass did not change.
The low acidity of medium-level wastes makes it difficult to remove the chloride ion
in the process of vitrification in the form of volatile hydrogen chloride. In laboratory
experiments, up to 80-90 mass % of chlorine (from the starting quantity) is included in the
glass mass, while 10-20 mass % is fixed in the vapor-was phase.
Up to 1 mass % of the sulfate ion relative to its content in the wastes was observed
in the vapor-gas flow; the remaining sulfate was included in the glass. However, its dis-
tribution in the glass mass is nonuniform, which is indicated by the considerable spread
in the results of analysis of the glass in different parts of the glass: The spread increases
with increasing sulfate content in the wastes. Apparently, when wastes with the composition
studied are vitrified, sulfate is not completely included in the melt and the excess amount
of sulfate is mechanically distributed in the glass mass. When wastes containing the sulfate
ion in quantities exceeding 10 kg/m3 are vitrified, a sulfate layer is separated on the surface
of the melt.
We performed the experiments on vitrification of wastes using agents based on datolite
concentrate on an experimental setup with an electrically heated furnace. Liquid wastes with
different degree of dehydration were mixed with the fusing agent, consisting of datolite con-
centrate and quartz sand in a ratio ensuring that a melt containing 30 mass % of oxides in
wastes is obtained. The mixture obtained was inserted into the furnace with the help of a
screw conveyor setup (see Fig. 1). The furnace was separated into three zones: melting,
working, and unloading. The area of the melting zone was 0.09 mZ and the area of the work%ng
zone was 0.02 m2. The bottom of the furnace is made of the DVD-11 ceramic with high aluminum-
oxide content, the walls were made of ShA-3 fireclay, and the bottom and walls of the furnace
are water cooled. The charge is introduced into the furnace with the help of the screw con-
veryor setup through water-cooled connecting pipes. To prevent dust entrainment, the charge
loading zone is separated from the gas line by a barrier. Power is introduced by passing
alternating current through two horizontally positioned molybdenum electrodes with diameter
18 mm. The distance between the electrodes is 400 mm.
The glass mass is poured through the pouring connecting pipe into a special chamber.
To prevent cooling of the stream of glass mass, the temperature in the unloading zone was
maintained at 800-900?C with the help of Silit heaters. The vapor~as mixture enters from
the furnace through the gas conduit into a gas scrubbing system, consisting of a bubbler-
condenser, adsorber for trapping nitrogen oxides, and filters for coarse and fine cleaning.
We performed two series of experiments with liquid wastes on this setup. The solution
capacity was 6. 10_3 m3/h and was chosen taking into account the optimum ratio of the area of
the melting zone of the furnace and the volume of the solution, determined when developing
the vitrification process for high-level wastes [1]. In the second series of experiments
we introduced molasses into the solution. The interaction of molasses with the nitrate ions
during calcination of the solution leads to the formation of a loose foam on the surface of
the glass melt,. which excludes the formation of a dense crust of calcinated product in the
furnace and decreases the amount of radionuclides carried away with the vapor-gas phase [2].
We performed the experiments on wastes with the same composition used to check the process
of bituminization, included in the design of nuclear power plants.
The results of the experiments are presented below:
Salt concentration in wastes,
kg/m3 450 450* 930
Specific S activity of wastes,
Bq/m3 1.8 ' 109 1.8 ' 109 3.7 ' 109
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 Declassified and Approved For Release 2013/02/06 :CIA-RDP10-021968000300020006-4
Capacity:
with respect to liquid wastes,
10-3 m3/h
with respect to glass,
kg/ (m2 ? h)
6?0.6
34 ? 3
6?0.6
34 ? 3
10?1
85 ? 8
Temperature, ?C:
glass mass
1100-1150
1150-1200 .
1100-1150
outgoing gases
130
130
200-220
Consumption of electricity,
kW ? h
7.2
7.0
13.2
Matter carried out of the furnace,
%fi:
solid phase
1.0
0.4
0.9
JOSr
0.5
0.3
0.3
1 "Cs
4.6
2.7
2.8
sum of a emitters
0.6
0.6
0.6
boron anhydride
7.5
4.2
4.7
The higher removal of 137Cs and Bz03 from the furnace compared with the removal of 9OSr and
of the solid phase is explained by the high vapor pressure of compounds of these components.
Boron leaves the furnace mainly in the form of alkaline borates and metaboric acid, whose
evaporation increases in the presence of water [3]. The decrease in matter carried away
with introduction of molasses is related with the filtering action of the foamlike product
forming on the surface of the melt.
The glass-mass capacity of -the furnace can be increased by initially decreasing the water
content of the wastes. A concentrate obtained by concentrating liquid wastes in a drum dryer
up to a salt content of 930 kg/m2 was used in-these experiments. The rate at which the wastes
are introduced into the furnace was chosen according to the conditions for performing the
process when the surface of the melt is completely covered by a layer of calcinated product.
Removal of material was further reduced by reprocessing the additionally concentrated wastes
and the glass-mass capacity of the furnace increased.
The volume of solidified wastes obtained as a result of vitrifying 1 m3 of liquid wastes
is 0.2-0.3 m3, which is a factor of 3.7 smaller than the volume obtained by including the
wastes in bitumen and polymers and almost ten times smaller than the volume of the cement
block obtained with the same wastes. The rate of leaching out of the least strongly bound
radionuclide 137Cs is (2-3) ?10-e g/(cm2 day), which is two orders of magnitude lower than
the rate of leaching out of a block of bitumen and four orders of magnitude lower than the.
rate of leaching out of cement. Another advantage is the elimination of contamination of
water and soil by nitrates as a result of the absence of these ions in the glass block..
Because there is no danger of fire;-the transportation and burial processes are simplified,
although compared to bituminization and cementing, the apparatus for the solidification process
is more complicated, which is related with the necessity of using high temperatures.
In order to introduce the vitrification method at nuclear power plants, additional work
must be performed on improving the apparatus, and a number of problems involving repeated
.use of the condensate must be solved.
*Addition of molasses (100 kg/m3).
tAverage data from several experiments are presented.
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 Declassified and Approved For Release 2013/02/06 :CIA-RDP10-021968000300020006-4
LETTERS TO THE EDITOR
V. E. Raevskaya and B. Z. Torlin UDC 621.039.51
In the Galanin-Fainberg theory, the neutron field is described by the superposition of
the field of individual assemblies placed at grid points of a homogeneous reactor. The dif-
fusional approximation, in which the assemblies are replaced by individually calculated ef-
fective boundary conditions at their surface, is more developed [1]. In [2], the basic idea
of heterogeneous theory - the superposition principle - is extended to the P3 approximation.
In this case the neutron field is calculated simultaneously in the assemblies and in the
interchannel moderator. In the programs realized [2, 3], the grid was regarded as not being
tight and the "intrinsic" field of the assemblies as azimuthally isotropic (the monopole ap-
proximation). Subsequently, the numerical method was refined [4, 5] as a result of the use
of matrix fitting to calculate the neutron field inside the assemblies. This guaranteed
numerical stability of the method for any assemblies both with black and with transparent
layers, and provided a series of additional conveniences in calculations. As shown in [4],
this procedure reduces to calculation of the matrix Y and the vector D relating the three-
component "flux" W and the current j of neutrons at each concentric boundary bf the multilayer
assembly by the boundary condition
Using recurrence relations, the matrix Y and vector D are calculated successively from
the center to the external surface of the assembly. After determining y and D at the sur-.
faces of-the assemblies, the neutron fluxes there are calculated by the scheme outlined in
[4, 5], similar in general outline to the scheme of the analogous calculation of heteroge-
neous grids in the diffusional approximationo These principles of the construction of solu-
tions in grids with multiring assemblies are also valid for assemblies containing bundles
of cylindrical (and even multiring) fuel elements immersed in coolant, i.e., clusters.
The neutron field of the cluster is represented as the superposition of the fields of
the individual rods. Then, following [2, 4], the following expressions are obtained in the
monopole approximation at the surface of the k-th rod pk:
~ (Pk) _ ~Fn' (Pk) An -~ f~l> (Pk) B -)-C(1) (Pk):
rt
i (Pk)= (~r'ii' (Pk) An-)`f~2) {Pk) B-~C(~) (Pk)?
rz
Here A, B, and C are three-component vectors; F, f, 3X3 matrices; and C, source vectors
described in [4]; A are the amplitudes of the "intrinsic" fields of the rods and, for equiv-
alent r-ods (with identical "intrinsic" fields), may be taken outside the summation sign.
Then the summation is~taken not over all the rods but only over all the monequivalent ele=
menu . The rules for the formation of the matrices F and the calculation of their elements
were described in sufficient detail in [5].
The appearance of the second terms on the right-hand side of Eq. (2) is relatively new
here. These are associated with the finiteness of the cluster dimensions and are absent in
inf finite grids. For matrix f, the matrix elements tnv {pk) ~ cT~?I,,, ( a'Z ~) !~ ( "irk) Here rk is
the distance from the cluster axis to the axis of the k-th rod. The coefficients cn~ are
Translated from Atomnaya Energiya, Vol. 54, No. 6, pp. 415-417, June, 1983. Original
article submitted April 19, 1982.
0038-531X/83/5406- 0429$07.50 ? 1983 Plenum Publishing Corporation 429
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 Declassified and Approved For Release 2013/02/06 :CIA-RDP10-021968000300020006-4
C; 4
yv
J, 09?,
Fig. 1. Symmetry element (one sixth) of the RBMK-~
reactor channel: 1) zirconium rod; 2, 3) elements;
4) vapor~aater mixture; 5) zirconium tube; 6, 7)
graphite.
given in [2, 3]. The relation between the number of rows n and the index of the modified
Bessel function Im is established by means of the following relations: If 'n = 1, 2, and 3,
then m =S - 1 and S + 1, respectively, while
a~= 18 ,Q \ 1 ~ l~1_ 108e 1-Q-}-e? ~ for v =1 and 2, a3 = 7; e = Z/Za (where Z and Za are the total
interaction length and the absorption length of neutrons in the coolant, respectively); u
is the mean cosine of the angle of neutron scattering; a = i -~- e r ~ --35 ? (1 - e) J . ,
From symmetry considerations, equivalent elements must be at the same distance from the
cluster axis, be congruent, and have identical physical properties. Then the k-th group of
Mk equivalent elements may be any rod at a distance rk from the cluster axis with an external
radius pk, boundary matrix y(pk), and vector D(pk).
The vectors ~(pk) of these representations of all N equivalent groups are combined into
the vector ~ci = col (~P (pl), ..., ~ (pN)L the vectors j (pk) into the vector j cZ = col [j (p,), ..., j (pN)L
the vectors D(pk) into the vector DcZ =cot (D (p,), ? ? ?, D (PN)1, and the vectors Ak and Ck
into the vectors AcZ = col (Al, ..., AN) and ~cl = col [ C(~) (p,), ... C(P) (p?)1 These new vectors are of
dimensionality 3N.
A series of new matrices are also formed: diagonally cellular matrices YcZ = {y(pk)SN?}
and square matrices F(s) ={F;~)(p~,)}-{F(E)Z}kn (k = 1...., N; n. _ 1,..., N) of dimensionality 3N x 3N,
cZ
and also rectangular (vertical) matrices f~s)= {f(s)(pk)} of dimensionality 3N x3. In the new
notation, Eqs. (1) and (2) take the following form for all k:
jcl =ycl~cl-~Dcl;
~cl - Pcl?A cl-F f~hB + C~i:
j F,sip ~' fO
4
0,1438
0,1473
-2,3
0,1442
-0,3
Zr
4,4
0,2131
0,2140
-0,4
0,1965
8,4
C
G,4
0,2334
0,2343
-0,4
0,2167
7,7
C
9
0,2538
0,2512
1,1
0,2336
8,7
When pH.,o = 0, 2
Zr
0,75
0,0976
0,1066
-8,4
0,7,017
-4
U Oz
1,6
0,0944
0,0952
-0,8
0,0917
3,0
LT02
3,09
0,1256
0,1226
2,5
0,1241
1,2
I-I20
4
0,1341
0,1413
-5,1
0,1425
-5,9
Zr
4,4
0,1824
0,1879
-2,9
0,1946
-6,3
C
6,4
0,2180
0,2230
-2,2
0,2297
-5,1
C
9
0,'1532
0,2518
5,7
0,2585
-l,0
*Here and in Table 4, the normalisation
of the flux is arbitrary.
Material I
`~tut~ cm'1 (
'n. ctn t (
9. cm"s
Zirconium-
0,3475
0,0075
0,00755
Graphite
0,4x)0
0,0003
0,0636
Water(Pi(z~ = i)
2,3900
0,0170
1,3660
Fuei
O,fi708
0,3133
0
TABLE 2. Initial Data
W~cl = Ecl ~ (Rcl)-]-acl..
~~u
D (Rcl):-[P(2) (Rcl)-V (Rcl)r?(') IRcl)] /-d-
-Y (Rcl) C(1> (]sell -~-C(~) (Rcl);
~ 8)
?cl _ [Fcl~ - Ecl1'(1) (Rcl1 J 1-'d--E?clC(~) (Rcl)-F C~i;
(9)
cl -fcl~_Fci rt;
f~? ~~,.
t-Vcl cl -fcl'
d-Ycl~cZ-Ccl-FDcI
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 Declassified and Approved For Release 2013/02/06 :CIA-RDP10-021968000300020006-4
TABLE 3. Use Coefficients of Thermal Neu-
trons in the Channel of an RBMK Reactor
o
a
~:
m
~"
m
v:
m
p
x
m
?'
m
m
I v
m
Y
m
! ~
m
p,
~
I v'
o? m
J
m
0
0,9114
0,9098
0,9150
0,18
-0,39
-0,57
0,6
x,9358
0,!1340
0,9370
0,98
-0,13
--0,31
O,Z
0,9110(1
11,9589
0,958(1
0,18
11, 2(i
U,O8
_
~
Op_o 2-Ou_1
O,U492
0,(ui99
0,(r43i1
-
-
-
0~,_~ s-0~_1
0,0244
0,0242
0,0220
-
-
-
TABLE 4. Neutron Fluxes in Zones of Polycell Assemblies
Assembly number
Zone
M
t ~ 2 ~ s
f ~ 2 ~ 3
t ~ 2 ~ s
b~
.
ate-
r1a).
UH2O
PH 2O
NHzO
1,0
I U;6
I 0,2
1,0
~ 0,6
I 0.6
0,2
I 0.0
I 0,11
1
'Lr
3,994
3,579
4,431
4,029
3,697
3,677-
4,291
3,501
3,527
'?
UU~
3,755
3,611
4,379
3,811
3;754
3,730
4,239
3,516
3,548
3
UO_
7,244
6,683
6,218
7,506
7,057
6,995
6,011
(1,436
6,5'LO
4.
H ~O
8,518
7,477
6,584
8,819
7,887
7,818
6,366
7,20G
7,298
5
Zr
14,658
12,477
9,459
15,332
13,267
13,136
9;137
11,954
12,131
O O
Fig. 2. Cartogram of-the polycell in the calculation.
O O
Thus, the cluster is characterized by the boundary conditions in Eqs. (5a), (6), and
(8) at its external boundary, and further calculation of the assembly and the whole grid may
be performed by the scheme described in [4], On the basis of the foregoing, the CLUST program
is written [6]; it is similar to programs already described, By its use, however, calcula-
tions may be made in the single-group P3 approximation for both quadratic and hexagonal poly-
cells containing not only multiring assemblies, but also assemblies including bundles of
multiring fuel elements.
The cross section of part of the channel of an RBMK reactor is shown in Fig. 1. The
results of calculating these channels in a homogeneous square grid by the CLUST program and
in cylindrical geometry by the PRAKTINEK program [7] on the basis of the GN method (where N
is the number of spherical harmonics used and p is the number of azimuthal harmonics used)
of surface pseudosources are given in Table 1. The initial data for this calculation are
given in Table 2, Table 3 gives values of the thermal-neutron use coefficients 0. It follows
from the given data that monopolar P3 and G3 approximation lead to very similar results.
The neutron fluxes calculated in the more accurate* G3 approximations differ markedly from
these results (the maximum discrepancy reaches almost 15% at the center of the cluster with
a water density pg2= 1); the difference in the value of 8 is small. Whereas the present
calculation has the aim of comparing new results with those already existing and being able
BAs shown in [7], the neutron fluxes calculated by the Monte Carlo and G3 methods coincide,
with a statistical error of < 2%.
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 Declassified and Approved For Release 2013/02/06 :CIA-RDP10-021968000300020006-4
to establish the efficiency of the program and sufficient accuracy of the approximation,
future investigations should demonstrate the programs in calculations of polycells.
A cartogram of the assembly positions (with equivalence numbers) in the polycell is shown
in Fig. 2, results of the calculation of which by the CLUST program are given in Table 4.
The assembly geometry is as in the preceding example. The grid step is 25 cm. As follows
from Table 4, the neutron flux increases in assemblies with an increased coolant density on
account of increase in the volume density of sources. This effect should facilitate an in-
crease in the vapor content in the polycell. The fuel elements are regarded as single-zone
only because the constants of the preceding calculation ,are used. The CLUST program allows
assemblies and rods with up to 30 annular zones to be calculated. The possible number of
nonequivalent rods is up to 10, and the maximum number of nonequivalent assemblies in the
polycell is 10. The calculation time for a double grid is 20-30 sec, depending on the number
of zones in the assembly. The maximum calculation time of a variant is ti4 min. The program
is written in FORTRAN for a BESM-6 computer.
It remains to thank A. D. Galanin and B. P. Kochurov for discussion of the work and
assistance in choosing examples:
1. A. D. Gaalnin, Theory of a Heterogeenous Reactor [in Russian], Atomizdat, Moscow (1971).
2. A. D. Galanin and B. Z. Torlin, At. Energ., 36, No. 2, 125 (1974.).
3. V. E. Raevskaya and B. Z. Torlin, Preprint ITEF, No. 60 (1977).
4. V. E. Raevskaya and B. Z. Torlin, At. Energy., 49, No. 5, 310 (1980).-
5. V. E. Raevskaya and B. Z. Torlin, Preprint ITEF No. 127 (1980).
6. V. E. Raevskaya, Preprint,ITEF No. 22, (1982).
7. N. V. Sultanov, Preprint IAE No. 3005 (1978).
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 Declassified and Approved For Release 2013/02/06 :CIA-RDP10-021968000300020006-4
DETERMINATION OF THE CROSS SECTION OF THE REACTION Z'Al(n, p)27Mg
WITH NEUTRONS OF ENERGY 14.8 MeV
V. T. Shchebolev, N. N. Moiseev, UDC 539.172.4
and Z. A. Ramendik
The value of the (n, p)-reaction cross section in aluminum is widely used in calcula-
tions of the structures of nuclear physics facilities as a reference value when measuring
the cross sections in other elements, and also when measuring the neutron flux density on
accelerators. in particular, in Great Britain foils of aluminum are certified, taking
account of the value of the activation cross section as a secondary standard of the unit of
neutron flux density [1]. However, as the published data differ strongly (up to 20%), the
problem of the exact measurement of the cross section 0 of the reaction 27A1("n,p)z7Mg is
urgent.
In the present paper, samples of specially pure aluminum are used in the form of disks
with diameter 30 mm adn with a thickness from 0.5 to 1.0 mm. The number of nuclei in the
specimene was determined from.the results of accurate weighing and chemical and mass-spectro-
metric analyses.
Irradiation was carried out in the field formed by a neutron generator as the result
of excitation of the reaction T(d, n)?He. The distance (6-12 cm)~between the sample and the
center of the tritium target was measured with an error of _< 0.02 mm, and it.s azimuthal posi-
tion relative to the direction of the deuteron beam was measured with an error of 0.0006 rad.
The neutron energy was 14.8?o~i MeV. The neutron flux density was determined by several-in-
dependent methods [2] with an error not exceeding 1% (with confidence coefficient of P = 0.99).
Irradiation was continued for 30 to 60 min, and 10 min after completerion the induced activity
was measured by the absolute S-Y-coincidence method and on a Y-scintillation spectrometer,
the efficiency of which was determined beforehand with respect to standard sources from the
OSGI collection. In the latter case, certain OSGI sources (in particular, 54Mn and 65Zn)
were certifie2 with an error of i.0-1.5% for P = 0.99. A standard program was used for
processing ti:e spectral distributions and for calculating the area under the photopeaks. A
UNO-4096 analyzer was used -for the measurements. The .effects of the neutron flux density
variation ever t'ie thickness of the sample with time, during prolonged irradiation, geometrical
factor, etc., were taken .into account.
The sources of the component errors-and estimates of their values, taking account of the
.weight factors, are given in Table 1 (So is the mean-square deviation, 6o is the unincluded
systematic error).
The results of the experimental determination of the cross section of 27A1(n, p) Z'Mg,
obatained in the present paper, are as follows (1 b = 10-ZS m2): 01 = 68.0 mb; 001.= 1.6% -
S-Y-coincidence method; 02= 68.5 mb; So2= 2.1% - y-spectrometer method. The mean-square.
value of 0(n, p) _ (68.2 + 0.9) mb is taken. as the final result.
Table 2 gives the data of some original papers on the experimental determination of the
cross section of the (n, p) reaction on aluminum, with errors not exceeding 10%, for a range
of neutron energies of 14.6-14.9 MeV.
According to the criteria of adequacy of the group of data and their membership to one
and the same general set, the value from [4] must be excluded from further consideration.
The average value of the cross section obtained without taking account of the measurement
errors is equal to X71.0 ? 1.1) mb, and in this case So, of the series of measurements (column
Translated from Atomaya Energiya, Vol. 54, No. 6, pp. 417-419, June, 1983. Original
article submitted June 2, 1982.
434 0038-531X/83/5406- 0434$07.50 ? 1983 Plenum Publishing Corporation
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 Declassified and Approved For Release 2013/02/06 :CIA-RDP10-021968000300020006-4
TABLE 1. Estimates of the Errors in the
Determinaton of the Cross Section
Method of measurement
Source of error
B- y coin- ~
cid
y spectrom-
ence
eter
etermination of neutron flux
density
-
0,6
-
0,6
etermination of number of
nuclei in sample
-
0,05
-
0,05
ecay constant
-
0,2
-
0,1
easurement of time intervals
-
0
1
--
1
0
ctivity measurement
2
0
,
8
0
-
,
-
etermination of area under
,
,
photopeaks
_
-
0,3
0,5
etermination of y-spectrom-
eter efficiency y.
-
-
-
1,p
Total
~ 0,2
11,4
I U,3
11,8
Total relative error b0
1,G
I 2,1
TABLE 2. Cross Section of -the z'A1(n, p) -
27Mg Reaction
Proton
energy, MeV I
a (E>, trib
Literature I
!
1
Scaled cross
section, mb
14,60.
74,4714,2
[3], 1973
72,9514,2
14,6510,10
67,312,0
[4J, 1978
6F,16f2,0
14,6710,09
78,015,5
(5J, 1968
77,0115,5 ,
14,7010,15
66,012,0 ~
[6], 1964
fi5,24~2,0
14,7010,15
73,012,0
[7], 1~J70
72,2412,0
14,7510,25
68,015,0
[8], 1960
67,6215;0
14,7810,10
68,012,3
`[1], 1973
67,8512,3
14,810,9
54,015,0,
[9], 1959
54,gt5;0
14,8010,20
73,015,0
[10J, 1971)
73,015,0.
14,80
75,016,0
[11J, 1971
75,016,0
14,8
70,5813,4
[12], 1974
70,583,4
14,9
7115
[13J, 1978
71,7615,0
14,$?u. ;
fi8,2t0,9
Present
68,'1?0,9
paper
2, Table Z) amounts to 3.5 mb; the average value without taking our value into account is
equal to (71.3 ? 1.1) mb; Soz = 3.5 mb, and the estimate of So3 by difference amounts to 3.5 mb.
The estimates given above for the cross section values were obtained without taking
account of the difference in the neutron energies for the range 14.6-14.9 MeV. The values, scaled
to an energy of 14.8 MeV, are given in column 4 of Table 2, using the gradient of the excita-
tion curve of the reaction equal to -7.6 inb/MeV [14] for the stated energy range. In this
case the similar estimates of the value and errors amount to: arithmetic mean (70.6 ? l.i)
mb, So, = 3.6 mb; arithmetic mean without taking our result into account (70.8.? l.l) mb,
Saz = 3.6 mb; estimate of So3 by difference equal to 3.5 mb. The mean weighted value (column
4, Table 2) amounts to (68.6 ? 0?6) mb, and without taking our result into consideration it is
(68.9 ? 0.9) mb. Thus, the most reliable value from the data given should be assumed to be
the mean weighted value of a = (68.6 ? 0.6) mb.
When determining the (n, p) cross section by the y-spectrometry method, the area under
the 27Mg photopeak was obtained as the sum of the areas under the photopeaks of the 0.842
and 1.010 MeV lines, taking into account the variation of efficiency of the spectrometer in
this .energy range. The efficiency for the energies 0.835 and 1.115 r1eV was determined with
high accuracy by 54Mn and 65Zn 'y=quanta sources. Comparison of the photopeaks corresponding
to the 0.842 and 1.010 MeV lines of 27Mg allowed the quantum yield of this radionuclide to
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 Declassified and Approved For Release 2013/02/06 :CIA-RDP10-021968000300020006-4
be o~Lainea - equal to by.ti and 3U.Z% respectively. The error of the determination of the
relative quantum yield amounted to 2.3%. The values obtained for the probability of decay
of 27Mg by two channels coincides quite well with the data given in [15] - 71.5 and 28.5%;
however, they disagree with the data of [6] - 58 and 42%.
LITERATURE CITED
1. J, Robertson et al., J. Nucl. Energy, 27, No. 3, 139 (1973),
2, V. T, Shchebolev and Zo A. Ramendik, in: Neutron Physics. Data of the Fifth All-Union
Conference [in Russian], Central Scientific-Reasearch Institute-Atominform, Moscow,
Part 4 (1980), p, 270.
3. Report iER-1464, 12 (1973).
4. T. Ryves et al., J. Phys, G: Nucl. Phys., 4, No. 11, 1783 (1978).
5. J. Cazzocrea et ai, Nuovo Cimento, 54, 538 (1968). -
6. G. Bonazzola et al,, Nuc1. Phys., 51, 337 (1964).
7. W. Shante, Thesis Vienna. University, Vienna (1970).
8. C. Mani et alo, Nucl, Phys., 19, 535 (1960).
9. 9. Poularicas and R, .Fink, Phys. Rev., 115, 989 (1959).
10. L. Husain et al., Phys. Rev., C1, 1233 (1970).
11. G. Salaite, Nucl. Phys,, A170, 193 (1971).
12o T. Navoddot et al,, Inorg, Nucl. Chem., 36, No. 5, 953 (1974)0
13. V. I. Melent'ev and V. V. Ovechkin, At. ~nerg., 44, No. 2, 171 (1978).
14. E. A. Borisov et al., in: Metrology of Neutron Measurements on Nuclear-Physics Facilities
[in Russian], Central Scientific-Research Institute-Atominform, Moscow, Vol. 1 (1976.),
p. 1940
15. N. G. Gusev and P. P, Dmitriev, Quantum Emission of Radioactive Nuclides (Handbook)
[in RussianJ, Atomizdat, Moscow (1977)<
16. B. S. Dzhelepov et al., Decay Schemes of Radioactive Nuclei [in Russian], Nauka, Moscow
(1966).
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 Declassified and Approved For Release 2013/02/06 :CIA-RDP1O-021968000300020006-4
ESTIMATE OF THE INTERCRYSTALLINE ADSORPTION OF HELIUM IN NICKEL
E. U. Grinik and V. S. Karasev UDC 621.039.531:539.67
The buildup of helium at grain boundaries promotes high-temperature radiation embrittle-
ment of materials [1] and affects the grain-boundary relaxation [2]. For the experimental
determination of the very slight changes of concentration of impurities at the grain bound-
aries, it is advantageous to use- the method of internal friction. The height and temperature
of the grain-boundary maximum varies in proportion to the change of concentration of impurity
and these variations cease with the adsorption saturation of the grain boundaries by impuri-
ties without phase separation [3].
The binding energy of the impurity with the grain boundaries F is determined by the re-
lations
F= -kT? In (Cgr/C),
(1)
where k is Boltzmann's constant; Tn is the temperature corresponding to the grain-boundary
maximum of internal friction at the instant of attaining saturation; C and Cgr are the con-
centration of impurities in the material and in the adsorption zone of the grain boundaries.
The concentration of impurities in the adsorption zone is expressed by the degree of
filling, i.e., by the ratio of the number of impurity atoms to the number of adsorption
centers of the given impurity [3]. In the case of saturation, when all adsorption centers
are filled, Cgr = 1 [3], and relation (i) assumes the form
Relation (2) enables F to be determined on the basis of the experimental data concerning
the temperature Tn and the calculated values of the helium concentration C for a duration of
irradiation corresponding to the attainment of steady values of the temperature and height
of the internal friction peaks.
~ 600 _-~-_ - ~.-~.,e.+ 450 ~
~ ao 3.U0 440
~' ~ w
w ..~ 410
pd400
~ c 470 ~
~ ~ o
.
c ~ 100 - M
.~. F
no ~
o ~ 200 400
00
a 900- 190
0 2.9079 .7 4 5 6 7 8- IOZO 2
Fluence, neutrons~cm2(E ? U.1 MeV)
Fig. 1. Dependence of the variation of
height (~) and temperature (~) of the grain-
boundary internal-friction maximum of nickel
during reactor irradiation on the neutron
fluence; o) height of peak before irradiation. '
Translated from Atomnaya ~nergiya, Vol. 54, No. 6, pp. 419-420, June, 1983. Original
article submitted June 22, 1982.
0038-531X/83/5406- 0437$07.50 ? 1983 Plenum Publishing Corporation
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 Declassified and Approved For Release 2013/02/06 :CIA-RDP10-021968000300020006-4
YJUI --~
c ~ J60
~~
,$ a~ J20 -
c
?~ o ZBO
00
~ ~ ~ 240
~ r,
?~ ~ ~ 200
x~a
i6o
0 2~ ~d' J 4 5 G 7 B 9 X010 2 J .
Fluence, neutrons/ cmZ(E ~ 0.1 MeV)
Fig. 2. Dependence of the variation of
height of the principal (~) and impurity (~)
grain-boundary internal-friction maxima of
the alloy Ni-1OB during irradiation on the
neutron fluence.
Experiments were conducted on specimens of polycrystalline nickel (grain size ti50 um)
from electron-beam smelting, with purity 99.99%, by the procedure described previously in [4].
The diameter and length of the specimens was 0.8 and 70 mm. After annealing for 1 h at a
temperature of 700?C in a vacuum of til3 mPa, the initial temperature dependence of the in-
ternal friction was determined, representing the exponentially increasing background component,
on which is superimposed the grain-boundary maximum for a temperature of 450?C. The frequency
of the torsional vibrations amounted to 5-7 Hz, and the amplitude of the relative deformation
of the surface of the specimen was maintained equal to 3' 10-5. The measurement ampul, with
this specimen, was loaded into the material behavior channel of the WR-M reactor in the
Institute of Nuclear Research, Academy of Sciences of the Ukrainian SSR. The irradiation
temperature (350?C) was maintained constant but was raised briefly during the measurements to
650?C; the fast (E >_ 0.1 MeV) neutron flux density amounted to ti1014 neutrons/(cm2? sec), and
the thermal neutron flux density was ti5 1013 neutrons/(cm2? sec).
During irradiation the height of the grain-boundary internal-friction maximum decreased
in proportion with increase of the neutron fluence, but the temperature corresponding to this
maximum, on the contrary, increased (Fig. 1), and in both cases saturation was attained with
an identical fast neutron fluence (ti1.2 1020 neutrons/cm2? sec). This behavior of the param-
eters of internal friction is characteristic for the adsorption saturation of the grain
boundaries by impurities.
The effect revealed should be related to the saturation of the grain boundaries with
helium, formed as the result of the (n, a) reaction. For confirmation, experiments were
carried out to measure the internal friction in the case .of the irradiation of platinum
and specimens of nickel of the same batch but alloyed with 0.007 mass % of 1?B, which is
disposed mainly over the grain boundaries. For the samples of platinum, in which no (n,a)-
reactions occur, no changes of the grain-boundary internal-friction maximum were detected,
for a fast neutron fluence of