SOVIET ATOMIC ENERGY VOL. 59, NO. 4

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• Document Creation Date: December 27, 2016
• Document Release Date: February 20, 2013
• Sequence Number: 4
• Publication Date: October 1, 1985
• Content Type: REPORT

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~~rv uuoa 1X
Russian Original Vol. -59, No. 4.. October, 1985,
April, 1986
SATEAZ 59(4) 789-876 (1985)
SOVIET.
ATOMIC
ENERGY
ATOMHAH 3HEPIVIR
(ATOMNAYA' ENERGIYA)
TRANSLATED FROM RUSSIAN
CONSULTANTS BUREAU, NEW YORK
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SOVI ET Soviet Atomic Energy is a translation of Atomnaya Energvya, a
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Editorial Board of Atomnaya Energiya:
Editor: 0. D. Kazachkovskii. -
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SOVIET ATOMIC
A translation of Atomnaya Energiya
Volume 59, Number 4 October, 1985
CONTENTS
Engl./Russ.
ARTICLES
An Asymptotic Estimate for Optimal Reactor Refuelling Strategy
V. D. Simonov ..o ............. ? ? . 789 243
'Unified Drive Means of the Controlling and Shielding System
of Research Reactors - I. Yd. Emel'yanov, A. N. Bakushin,
N. I. Galyshev, A. N. Zinkin, and A. F. Lineva ......................... 795 247
Influence of Burning-Out Graphite Impurities upon the Parameters
of the RBMK-1000 Reactor - N. V. Isaev, I. F. Moiseev,
E. M. Saprykin, V. E. Druzhinin, and Yu. V. Shmonin .................... 800 250
Local Distribution of the Coolant Flow Rate in Fuel Assemblies
with a Blocked Flow_Through Section - L. Sabotinov,
I. Iordanov, N. Antonov, K. Papesku, and A. Buzhor ..................... 804 253
Use of Sample Recognition Methods for Detecting Currents
in Steam Generators - V. V. Golushko,.V. S. Dunaev,
and A. B. Muralev ...................................................... 812 258
Dynamics of Heat-Transfer Degradation in Channels with the Bottom
Inlet Sealed - B.. F. Balun.ov,.E.. L.,Smirnov,
and Yu. N. Ilyukhin .................................................... 816 261
Dimensional Stability of Structural Materials under Large
Neutron Fluences - N. K. Vasina, I. P. Kursevich,
0. A. Kozhevnikov, V. K. Shamardin, and V. N. Golovanov ............... 822 265
Effect of Thermomechanical Treatment on the Swelling
of Steel OKh16N5M3B - V. I. Shcherbak, V. N. Bykov
and V. D. Dmitriev..................................................... 825 267
Hydrogen Permeability in Kh18N1OT Stainless Steel from Plasma
Glow-Discharge - V. M. Sharapov, A. I. Kanaev,
and A. P. Zakharov ..? ? ? ? ................... 828 269
Variation of the Dislocation Density Under the Conditions
of Radiation-Induced Swelling of Strongly Deformed
Crystals - Z. K. Saralidze ............................................. 833 273
Automatic Remote Monitoring of the Separation Processes
of Transplutonium Elements by Ion Exchange
- I. V. Tselishchev, N. S. Glushak, A. A. Elesia,
V. V. Krayukhina, V. M. Nikolaev, V. V. Pevtsov,
N. I. Pushkarskii, and V. I. Shipilov.................................. 838 277
Dependence of the Mean Value and Fluctuations of the Absorbed
Energy on the Scintillator Dimensions - F. M. Zav'yalkin
and S. P. Osipov ....................................................... 842 281
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(continued)
Engl./Russ.
Measurement of the Radio of the 236U and 235U Fission Cross
Sections in the Neutron-Energy Range 0.34-7.4 MeV
- B. I. Fursov, M. P. Klemyshev, B. F. Samylin,
G. N. Smirenkin, and Yu. M. Turchin .................................... 846 284
LETTERS TO THE EDITOR
High-Temperature Strength of the 1OKh18N19 Steel in the Medium
of Carbon-Containing Sodium at 500?C - 0. V. Starkov,
I. P. Mukhin, V. V. Chukanov, and V. D. Zhelnin ........................ 851 288
A Materials-Technology Investigation of the Control Rod Bushes
of Reactor Type BOR-60 - V. N. Golovanov, A. V. Povstyanko,
V. S. Neustroev, V. M. Kosenkov, E. P. Klochkov, .
and V. K. Shamardin .................................................... 853 289
Quantitative Estimates of the Energy of Pulsed X Rays
Backscattered by Air - V. D. Kosarev and V. P. Mukhin .................. 856 291
Comparison of the Experimental and Theoretical Values
of the Effective Attenuation Factors of Radiation
in Monodisperse Absorbers - V. M. Zhdanova, V. I. Kostenko,
I. V. Krivolutskaya, and G.-K. Potrebenikov ............................ 858 292
Possibility of Detecting Sodium Boiling in the BN-600 Reactor
by Means of Neutron Noise - V. N. Efimov, S. N. Eshchenko,
A. A. Minakov, and Yu. I. Leshchenko .................................. 861 293
Experimental Determination of a Universal Excitation Function
of Characteristic X Rays by a Beam of Protons in a Massive
Target - V. F. Volkov, V. N. Sinitsyn, and A. N. Eritenko .............. 863 295
A Data Bank on the Methods of Materials Testing in Reactors
- N. V. Markina, A. V. Rudkevich, and E. E. Lebedeva ................... 865 296
Influence of the Position of the Group of Elements of the Controlling
and Shielding System Upon'the Integral Neutron Flux
through the Side Surface of the Jacket of the VVER-440
(Water-Water Powder) Reactor - L. N. Bogachek,
K. A. Gazaryan, A. M. Luzhnov, V. V. Lysenko,
'A. S. Makhon'kov, V. V. Morozov, A. I. Musorin, V. I. Pavlov,
E. S. Saakov, V. D. Simonov, and S. G. Tsypin .......................... 867 297
Model of Crater Formation Under Ion Bombardment
- V. P. Zhukov and A. V. Demidov ....................................... 870 298
Analysis of the Effectiveness of-Monitoring of the Energy
Liberation Field in Reactors Based on Conditional
Distribution Laws - V. A. Vlasov, P. I. Popov,
and V. V. Postnikov .................................................... 871 299
Monte Carlo Calculation of the Field Gradient of y Rays
M. P. Panin ............................................................ 874 301
The Russian press date (podpisano k pechati) of this issue was 10/3/1985.
Publication therefore did not occur prior to this date, but must be assumed
to have taken place reasonably soon thereafter.
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V. D. Simonov UDC 621.039.003
Mass production and standardization do not rule out the possibility of improvement of
the technicoeconomic indicators of operating and projected generating units of. nuclear power
stations by improving the reactor internal fuel cycle (IFC). Even with standardized fuel
enrichment and unified reactor and fuel-element design, we have a certain freedom in choos-
ing the quantity and the composition of the fuel, which makes it possible to adapt the IFC to
specific operating conditions of the various units.
Various factors, such as capital investment in power-generating units with identical
reactors, the load coefficient and the load curve, or the down time associated with refuell-
ing and equipment maintenance, may vary not only for different nuclear power stations but
even within the same station. Systems with identical nuclear power stations may also be
characterized by different operating conditions. Therefore, the IFC must be designed for
each reactor separately, taking into considerations the specific operating features of the
generating unit. If unanticipated effects are observed during reactor operation or, alter-
natively, anticipated effects are not observed, the IFC strategy must be adjusted in
accordance with the actual situation.
In this context, it is difficult to overestimate the role of asymptotic estimates as a
starting point in the search for an economically optimal IFC strategy. These estimates en-
sure fast orientation under conditions when we have to allow for the impact of many inter-
dependent factors; the easiest couse is to chart a steady-state refuelling strategy and to
determine the initial charge composition which is best suited for this strategy.
Asymptotic estimates clearly do not exhaust the economic performance analysis of the
IFC. They are insufficient in order to arrive at a strictly optimal decision. Yet they
provide the most efficient technique for identifying a bounded region of variables where the
optimal strategy is located.
Let us consider the main aspects associated with the derivation of such estimates for
a shell-type heterogeneous reactor with an open fuel cycle.
THE IFC ECONOMIC CRITERION
The economic indicator which enables us to assess the IFC performance is-determined by
the structural features of the power system in which the particular generating unit is in-
cluded. For a basic-mode reactor, we can identify two cases which should rely on essentially
different criteria.
1. The power system includes a sufficient number of identical units, so that when a
particular unit is shut down for scheduled refuelling or maintenance, another generating
unit steps in, for which refuelling or maintenance has been completed by that time. In this
case, scheduled shutdown of any reactor has no effecton the contractual commitments to users
or on power-generation costs. A suitable economic criterion for coordinated scheduling of
generating capacity and generating conditions is therefore provided by the discounted specific
power-generation costs of the various units (DSC) [1].
2. The power system is designed in such a way that capacity shortfall following the
shutdown of any unit may be made up, but the cost of the alternative power is higher than
the power-generation cost of the original unit. It is determined by the so-called closing
power costs in the given system [2].
In this case we are actually considering the profitability of alternative ways to meet a
given load schedule. A suitable criterion is the sum of discounted generating unit costs
and closing costs charged for the alternative power during shutdown.
Translated from Atomnaya Energiya, Vo. 59, No. 4, pp. 243=247, October, 1985. Original
article submitted May 28, 1982.
0038-531X/85/5904-0789$09.50 C)1986 Plenum Publishing Corporation 789
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case above, but the closing costs are replaced with the penalties for failure to supply the
demand.
MODELING THE FUEL BURNUP PROCESS
IFC optimization requires a mathematical model of fuel burnup which should express the
economic indicators and the given constraints as functions of the unknown independent vari-
ables. Multidimensional programs simulating in detail the spatial processes in a reactor
will lead to an optimization algorithm of intractable complexity, thus requiring computers
of enormous power. Asymptotic solutions of optimization problems, on the other hand, can
be obtained ignoring the detailed spatial picture.
The simplest and most flexible fuel burnup model under steady-state refuelling (SSR) is
provided by the so-called model of the fuel energy potential, which is useful and efficient
for generating asymptotic solutions of IFC planning problems. The fuel energy potential
(FEP) is defined as the energy that can be generated by burning and given guel in a reactor
of actual dimensions and power output but assuming hypothetical fuel charging mode: this
hypothetical mode ensures uniform burning of all the fuel moving through the reactor, by
stipulating continuous refuelling with infinitesimal fuel charges while maintaining full
power output and infinitely fast mixing of the fuel in the reactor core.* A quantitative
measure of the FEP is provided by the fuel lifetime in a reactor with such a (reference) fuel
cycle, i.e., the time that the fuel stays in the reactor under nominal power output condi-
tions,
T:r (x) = WPr (x)? (1)
Here W, days (kg/ton)-1, is the operating time of the reactor under normal power output
needed to produce 1 kg of slag for each ton of fuel; x is a vector whose components are fuel
enrichment, fuel density, reactor power, and all other parameters which determine fuel re-
activity; Pr, kg/ton, is the maximum attainable slag concentration in the fuel consistent
with reactor criticality (assuming uniform fuel irradiation during the entire operating
time): it is given by the equation [3]
1 ()r
VT T , k- (p, x) dpkd(x), (2)
0
where ka, is the multiplication factor of the actual subscripts fuel lattice, whose depend-
ence on p may be represented in the zero-dimensional approximation; kd is the volume-average
multiplication factor required for the realization of the designed operating conditions.
If the FEP is known, we can use the fuel burnup loss factor compared with the reference
burnup mode in order to determine that part of the FEP which is realized under discrete
charging conditions. If the loss factor is K(n) for a strategy which calls for n refuelling
during the lifetime of each fuel portion in the reactor (equal to 1/n of the total reactor
charge), then buildup of poison in the unloaded fuel under these conditions is given by
pf (n, x) = K (x)
_ it (X) (4)
if (n, x) K (n)
and the reactor lifetime between two consecutive refuellings (in the linear approximation)
is
ir(X) (5)
r (n, x) nK (n)
Formulas for the loss factor of a number of fuel charging modes are given in [3]. Thus,
for a reactor in which radial mixing of the fuel is performed with the same periodicity as
fuel charging, we have
--?*This fuel burning mode was first introduced by Feinberg [3].
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and without mixing
K (n)=e (id- I ),
where 0 and Or are integral characteristics of spatial and radial energy distribution in
the reactor, respectively (see [3]).
Relationships (l)-(7) constitute a fuel burnup model under steady-state refuelling
which is known as the FEP model.
STATEMENT OF THE PROBLEM
The search for an optimal IFC strategy always involves minimizing some objective func-
tion of several constrained variables. Depending on the specific conditions for which the
objective function, the constraints, and the sought parameters (the controls) are chosen,
different solution methods have to be used for the problem. We will only consider asympto-
tice estimates of the optimal number of refuellings during a given fuel lifetime.*
We thus assume that the effect of the period preceding the attainment of SSR has a
negligible effect on the choise of the refuelling strategy. We also assume that the changes
in the initial reactor charge associated with'SSR variation make only a small contribution
to the optimization criterion and may also be ignored. Then, if z is the objective function
of the problem, we seek to find no such that
z (no, x, q) = min z (n, x, q) (8)
x = const, q = const. (9)
This no is the asymptotic estimate of the optimal number of refuelling under SSR, where
z stands for discounted specific costs or the sum of discounted and closing costs for a
generating unit with a vector which has reached the SSR mode and is fuelled by fuel with the
properties x; the components of q are Trf, the length of one reactor refuelling; cp the unit
load ratio (the ratio of the average power output between scheduled shutdowns to the rated
power output); n, the net unit efficiency; Q, the rated reactor power; Ta, the average
scheduled maintenance time of a shutdown unit per days of operation with load ratio cp; 0
and Or; p, the cost discounting factor; capital investment and operating outlays; the cost of
-fuel and closing energy-.
OBJECTIVE FUNCTIONS
In order to solve problem (8)-(9), we have to express z ,as an explicit function of n,
x and q . This can be done in the following way. We divide the discounted specific costs
into two components,
3=3,'+'32,.
where 3, is the part of the discounted specific costs associated with the flow of payments
for fuel charges, and a2 is the part attributable to all other expenditures.
In the classical framework, assuming continuous fuel charging and constant power output
of the generating unit, for given fuel charges, fixed capital outlays (including the initial
charge cost), and fixed operating costs (depreciation charges, maintenance costs, wages,
etc.), 31 depends only on the efficiency of fuel utilization and 3, only on the rated output
utilization factor of the generating unit, Ku:
3, - K (n);
32 - [Ku (n)]-1-
The appropriate criterion for the second case may be written in the form
3=3g+3c.
*The proposed approach may be applied to other similar problems.
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where 3g 3Hw(1-I' are the discounted power generating costs of the unit;
3.c=3c((P- K.u' Q"
are the closing power costs; 3c is the price of closing power. We assume that the efficiency
is independent of (p.
Now consider a generating unit with a reactor which is equally capable of operating of
the reference mode and in the discrete mode; the reactor operating costs are assumed to be
independent of n and the initial charge cost is given. The generating unit equipment is such
that the unit may operate under the load cpfQ for (365 - Tm) days each year. On average,
Tm consecutive days each year are spent on scheduled equipment maintenance, so that
TM T
Ta= 365 rm' Ku -W (1 - 365
If in the reference mode with fuel enrichment x, the DSC are
3r (x) 3i (x) + 3z,
then in the discrete mode with the same fuel and n refuellings during the fuel lifetime,
assuming that Ta and T remain unchanged, the cost will increase to
K
3 (n, x)=31 (x) K (n)+sr Ku'
nt (n, x) T (n, x) 365.+ Trf
Ifu 365 m (n, x) = 1
Rr T(n, x)+Trf
U
is the annual number of reactor refuellings, when one of the refuellings coincides with
scheduled maintenance (Trf 0.35-0.40.
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1. R. Moeller, H. Tschoeke, and M. Kolodjiej, Experimentelle Betimmung von Temperaturfur-
feldern in natriumdurehstroemten Bundelm nit hexagonaler Stabanordung and gitterfoermin-
gen Abstandhaltern," KFK 2356, January, 1977.
2. G. Straub, "Berechnung der Temperatur and Geschwindigkeitsfeler in parallel angestroem-
ten Brennstabbuendeln Schneller natriumgekuehlter Brutreaktoren (ARTIS-Code)," Disserta-
tion an der TU-Stuttgart (1976).
3. J. Creer, J. Bates, and A. Sutey, Turbulent.flow in a model nuclear fuel rod bundle con-
taining partial flow blockages," Nucl. Eng. Design, 52, 15-33 (1979).
4. M. Kazimi, "Heat transfer correlation for analysis of CRBP assemblies," LRA-74-114
(1974).
5. F. Mantlic et al., "Obzor teplofiziceskih isledovanii sborkov tvelov s ceasticunoi
blokirovoi prohodnih secenii," UJV 6057-T, KE9 (1982).
USE OF SAMPLE RECOGNITION METHODS FOR DETECTING CURRENTS
IN STEAM GENERATORS
V. V. Golushko, V. S. Dunaev, UDC 62-506:621.391.193
and A. B. Muralev
The operational detection of currents in steam generators working with sodium, the
water of fast reactors, is an important problem. Acoustic detection is one of the promising
and almost inertialess methods. When acoustic sensors are employed, the signals are usually
nonstationary, random signals at. the moment of flow initiation and are almost stationary sig-
nals when the background is recorded. Investigations of these processes make it possible to
develop an algorithm for the detection of flow signals (which below will be termed "the
effect") on the background of acoustic noise generated by the steam generator in its opera-
tion. The final goal of the investigations is to create a rather simple and reliable instru-
ment, a flow detector. Therefore, when methods for the initial data evaluation are selected,
the complexity of the actual technical embodiment is taken into consideration by the develop-
ment of a'-decision rule.
The present work reports on an attempt of employing the techniques of the theory of
sample recognition [1-3] in the analysis of signals obtained in an experiment in which cur-
rents were simulated by argon in a working module of a steam generator; the signals were
recorded. on magnetic tape. Experiments were made in a 24, MW PG-2 steam generator which was
mounted in a BOR-60 reactor and which is a model of the steam generator of a BN-600 unit.
The experiment and itsmain results have been described in [4]. The experimental data, for
which a processing algorithm is described in the present paper, were obtained from an acoustic
waveguide-type sensor.mounted in the upper part of the overheater. The distance from the
sensor to.the point of argon injection into sodium was 1.2 m; the argon consumption was 0.3
g/sec. The sensor was mounted so that the developing gas bubbles did not shield it.
The magnetic tape recordings of the signals obtained from the acoustic sensor were pro-
cessed with a special unit [5, 6] which allows the operational calculation of energy spectra.
Sixty samples were evaluated for the background and for the sum of effect + background with
20,000 values of the initial process in each of the samples. The samples formed an instruct-
ing sequence. The spectra were analyzed in an 80 kHz frequency band. Further, the spectra
were processed on a computer with especially developed programs.
REQUIREMENTS TO THE PROCESSING ALGORITHMS
The selection of the processing algorithms . is associated with the requirements of flow
detection. The main requirements are as follows:
- high stability against noise.,?i.e.,'a low'probability of spurious response (spurious
alarm);
Translated from Atomnaya nergiya, Vol. 59, . No. 4, pp. 258-261, October, 1985.. Original
article submitted August 6, 1984.
812 0038-531X/85/5904-0812$09.50 ? 1986 Plenum Publishing Corporation
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 Declassified and Approved For Release 2013/02/20: CIA-RDP10-02196R000300070004-1
^ 7U rl
2 ao y I~'~ n rl
u n d II
n
90'
I I I , I I
n
C I II
o y ~ 11 I I Z-Ir i II
n ., f 4~ 1 n ( I I I !JIL~ rl L, rn~
A id~o r
U 1,
I I i I ice? Y i i ".-
10 20 J0 90 SO 60 Frequency, kHz
0 2 9 6 6 10 12 Number of the band
Fig. 1. Energy spectra and ratio effect + background to
background: 1) background noise; 2) effect + background;
3) ratio of effect + background to background.
- technical simplicity and a sufficiently high probability of flow detection (low pro-
bability of missing acurrent); and
- the time of detecting a current of 0.3 g/sec must not exceed a few seconds.
We derived on the basis of..these conditions the technical conditions under which the
number of frequency bands to be analyzed in the instrument to be built was reduced to two;
it was assumed that the width of the filter resonance curves is 5 kHz. The probability of a
spurious alarm was preset as 10-6 and that of omitting acurrent as 10-9. The possible spread
of the resonance frequency of the sensors was ?5 kHz.
Algorithms for evaluating the data in the instrument must be as simple as possible for
reducing the required memory space and for increasing the response rate. Therefore, one
must study first of all the applicability of the algorithms of linear and piecewise linear
classifiers. The problem therefore implies the recognition of objects of a given number
of classes (background and sum of effect + background), i:e., separating lines must be drawn
on the plane of the parameters selected (the two frequency bands providing most of the infor-
mation).
The algorithms of recognition must provide, as far as possible, an objective classifica-
tion. One must employ also that a priori information which is at the disposition of the
researcher, namely the form of the frequency spectra of effect + background, information on
the physical processes which are associated with the generation and development of a current,
etc.
Figure 1 illustrates the form of the spectra of effect + background and of background
noise (spectra resulting from averaging over 15 samples); Figure 1 also illustrates the
ratio in dependence upon the frequency. Peaks which are typical for a resonance sensor appear
in the spectra. One also observes a tendency to an increase in the ratio with increasing fre-
quency. The background noise of the.steam generator develops from the interaction of turbu-
lent flow of liquid (sodium, water) and steam with the elements of the unit. This noise hasp
a broad frequency spectrum with a maximum which is usually situated at a few kilohertz. In
the simulation of the current, the outflow velocity of the gas stream is much greater (hun-
dreds of m/sec) than the flow velocity of the liquid and the steam in the steam generator.
Therefore, a relative increase in the spectral density must be observed at high frequencies
in the spectrum of the background + effect signal.
When two frequency bands are selected, one must recall that owing to their shifting in
the case of deviations of the resonance frequencies of the sensors (because the sensors are
not identical or are unstable) and in changes in the signal spectra generated by the current,
the positions of the classes will be shifted in parameter space. It is therefore necessary
to study the influence of the shift upon the quality of the classification (recognition);
the quality was in the present work assessed through the ratio of the minimum distance between
the limits of the separating lines along the straight line connecting the centers of gravity
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 Declassified and Approved For Release 2013/02/20: CIA-RDP10-02196R000300070004-1
9
background
x7o
2
J
102
9673
10
AFB
9
9
2
.B
2
2
/
10 2
/
10
0 Effect+
background
9
9
/ 1
2
6O /
.
2
10
101
~
9
6
660~.
I b
2
63
1
back
ground
,` 165
Jgr and
2 9 10' 2 9 1022 9 10''x13
Fig. 2. Distribution of the objects (a) for a
divison without shifting; b) for a division with
shifiting; X13) average energy infrequency band
13; X9) average energy in frequency band 9; and
X10) average energy in frequency band 10.
of the classes to the standard deviation of the two-dimensional distributions for the objects
of the background.
The form of the spectra and their ratio point to at least two strongly different states
(classes) in the system. Frequency bands which provide information must be looked for in the
high-frequency range.
ALGORITHMS OF THE INSTRUCTING MODE
Taking into account the given width of the frequency characteristics of the filters, the
spectra were split into 16 neighboring bands of equal width (5 kHz); in each of these bands
the data were integrated and averaged over the number of components summed. The second ver-
sion of splitting served to verify the influence of the shift upon the quality of the classi-
fication. The splitting was performed with a 1-kHz shift to the right for part of the spec-
tra of the effect + background signals. The data obtained were again centered and normalized
in both cases. These procedures were performed for each frequency band on all available ob-
jects (60 spectra). Furthermore, the correlation matrix lip (Xi, Xj)J!, was calculated where
Xi and Xj denote the normalized and centered values of the i-th and j-th parameters. A sub-
matrix with the numbers from 9 to 16 was separated from the matrix in accordance with a priori
data on the effect + background/background ratio.
The method of correlation groups of [7] was employed to single out two groups of parame-
ters which were divided by the smallest correlation coefficient. The following groups were
obtained for the unshifted frequency separation (the half-dark figures represent the parame-
ters numbers, i.e., the frequency bands):
14 16 15 13 12 11 first group;
9 10 second group.
For the Separation with Shifting of the Spectra:
12 16 15 11 9 14 first group;
10 second group.
The parameter groups determined can be treated further for calculations factors and for con-
structing classifiers in the newly obtained factor space [7]. But this approach would com-
plicate the calculation procedure. Therefore, the correlation matrix was used to construct
a simple criterion for the determination of a pair of bands with the greatest information
content; after that, a piecewise-linear classification was made. The selection criteria for
the parameter pair with the greatest information content was based upon the following con-
cepts:
- the higher the (effect + background)/background ratio the greater the probability
of obtaining a classification of good quality;
- the probability of a spurious alarm and of missing a current increases with increas-
ing dispersion of the background, i.e., the quality of the classification becomes worse;
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 Declassified and Approved For Release 2013/02/20: CIA-RDP10-02196R000300070004-1
- the quality or the classification will increase with increasing ratio of the average
value of the background; and
- the weaker the relation between the parameters (the smaller the correlation coeffic-
ient), the more objective properties of the system will be reflected.
Thus, the following criterion can be suggested:
K(Xi, Xj)=[1-p(Xi, X])1
SiSi (Xe.bi )2 (Xe.b)2
Qe.biabi(i.b ('bi
Si = Xe.b;/Xb i; Si = Xe.b,/Xb,; Xe..bi = n X ik
k=1
denotes the average Value of the i-th parameter over n objects of the sum of effect and back-
ground; Xbi denotes the average value of the i-th parameter for n objects of the background;
and oe.bi and obi denotes the corresponding standard deviations of the i-th parameter. A
similar notation was introduced for the j-th parameter. The maximum of the K(Xi, Xj) value
must correspond to the selection of the parameter pair (i, j) providing a maximum of informa-
tion.
Calculations made with the criterion selected rendered the following results: in the
case of an unshifted division according to frequency bands: i = 13 and j = 9; in the case
of a shifted division: i = 13 and j = 10. The numbers i and j obtained for the parameters
are in both cases in different groups which were determined by the method of correlation
groups. This detail partly confirms that the parameter selection is correct.
Figure 2 illustrates the possible classification of objects for various forms of divi-
sion. It follows from the.figure that as a results of the shifting, the effect + background
class is divided into two subclasses A and B and the quality index of the classification is
reduced, mainly because of the sharp increase in the dispersion of the parameter Xlo. At'the
same time, a change in the position of the objects of the effect + background class on the
parameter plane can be caused by changes in the operational conditions of the steam genera-
tor, the characteristics of the current or the parameters of the instrument. Information on
these changes can be used for improving the. diagnostic capacity of . the. instrument. But it
should be recalled that all this is associated with complications and an enhancement of the
time analysis. The dashed line of Fig. 2 indicates the position of the dividing straight
lines) the position was determined from the preset probabilities of a spurious alarm and of
missing a current. Such lines can be easily produced on a display screen without signifi-
cant time losses when simple programming is used.
The results of the processing of the recordings of the experiments have shown that a
classification of objects in the form of effect + background and background is possible in
accordance with the suggested criterion.
LITERATURE CITED
1. I. A. Birger, Technical Diagnostics [.in Russian], Mashinostroenie, Moscow (1978).
2. A. L. Gorelik and V. A. Skripnik, Recognition Methods [in Russian], Vysshaya Shkola,
Moscow (1977).
3. V. N. Vapnik and A. Ya. Chervonenkis, The Theory of Sample Recognition [in Russian],
Nauka, Moscow (1974).
4. V. M. Sokolov, Yu. P. Grebenkin, V. V. Golushko, and A. B. Muralev, Experimental
Foundation of the Possible Detection of Currents in a Steam Generator through Acoustic
Noise [in Russian], Preprint NIIAR-35 (550), Dimitrovgrad (1982).
5. V. V. Golushko and A. B. Muralev, A System for the Digital Processing of Random Pro-
cesses. Principles of its Construction [in Russian], Preprint NIIAR, P-3 (337), Dimitrov-
grad (1978).
6. A. N Bulanov, V. V. Golushko, and A. B. Muralev, A System for the Digital Processing
of Random Processes. Circuit Solutions [in Russian], Preprint NIIAR,P-8 (342),-Dimitrov-
grad (1978).
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 7. Declassified and Approved For Release 2013/02/20: CIA-RDP10-02196R000300070004-1 n of
Objects in Russian], Nauka, Moscow (1971).
B. F. Balunov, E. L. Smirnov, UDC 621.039.536
and Yu. N. Ilyukhin
In different operational statesiof power-generating equipment it is possible that in
a vertical heat-liberating channel water can stop flowing into the bottom of the channel.
At the same time, the water level can be located above the top of the channel. After some
finite time interval, required for heating all water present in the channel up to the satura-
tion temperature, the channel can be regarded as a steam-generating channel with the bottom
inlet sealed off. In such channels heat transfer is degraded when the balance between the
flow rates of the countermoving flows (rising steam flow G2 and descending water flow G1) is
destroyed [1]. This breakdown of the equality G1 = G2 (toward increasing G2 and decreasing
G1) can be viewed as a particular case of the hydrodynamic critical state of countermoving
gas-liquid flows (known in the literature as the phenomenon of"flooding" [2, 3]), determining
the maximum possible flow rate G1 for a fixed flow rate G2.
The hydrodynamical critical state appears in the section with maximum steam flow velo-
city w2 = G2/p2Fft, i.e., in the top section of the channel. When fluid enters the channel
from above (G1 > 0) the sections with the hydrodynamic critical state and the state of de-
gradiation of heat transfer may not coincide and the time between these characteristic states
can be equal to tens of minutes.
We shall study.a vertical cylindrical steam-generating channel with a constant flow-
through cross section (Fft) and a sealed inlet at the bottom (Fig. 1). At the moment that
the hydrodynamic critical state appears (T = 0), a steam-water mixture is present in the
channel. The:distribution of the true volume steam content over the height of the channel
is found from the well-known working dependences for bubbling:
To = f (P. wz),
w2 rp2Fft J ( z,) dz.
L
The maximum value of w2 occurs in the heated section of the channel at the top (z = 0); it'is
this section that must be regarded as being critical in the hydrodynamic sense.
For countermoving steam-water flows with steam-water flows with steam velocities ex-
ceeding the values corresponding to the condition of "free-fall" of water drops [4]
KW 2151 =0.7=1.4,
Z Q
only an annular flow state (descending water films at the wall and ascending steam core) is
possible. Experiments have shown that the particular case of the hydrodynamic critical
state (G2 > G1) in the top section of the channel studied here is characterized by the values
K2 = 0.8-2.2. Therefore, an annular flow state exists in this section. The film motion of
practically all water entering at the top along the channel walls also extends into the
lower part of the channel. At the same time the heat-liberating surface of the channel is
cooled in the normal manner by the evaporation of the descending film of fluid up to the
formation of stable discontinuities in it, whose appearance is characterized by a definite
-,trickling density:
Translated from Atomnaya Energiya, Vol. 59, No. 4, pp. 261-264, October, 1985. Original
article submitted November 5, 1984.
816 0038-531X/85/5904-0816$09.50 ? 1986 Plenum Publishing Corporation
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 Declassified and Approved For Release 2013/02/20: CIA-RDP10-02196R000300070004-1
oa
0 0
N chan
(S O o ,
~
u0~`7
z1
Fig. 1. Diagram of a vertical steam-generating channel
with a sealed inlet at the bottom.
rd Gd
I -- ad
The distance between the hydrodynamically critical section and the section with degraded heat
transfer (zd) can be found from the condition
zd/r
G,=Gd+ r J 1 dN ) dz. (3)
0
For a channel which is heated uniformly over its height (dN/dz) = N/L and the formula.(3)
assumes the form
Gj=Ga-I- N (4)
(if Gd > G1, then the. degradation of heat transfer occurs in the heated section at the top of
the channel). The mass of water between the sections z = 0 and z = zd in the film of des-
cending liquid
zd z d
,film 11P, ` dz = Fft Pi J (1- (pfilm) dz
0 0
is much lower than the mass of water in the same section of the channel at the moment that
the hydrodynamic critical state appears (T = 0):
zd
mo=Fft Pi 1 (1-yo)dz.
0
Thus, under the conditions of unbalance between the flow rate of the generated steam
and the water entering the channel at the top (G2 > G1 > Gd), a definite degradation time
Tdeg is required for evaporation of the water located in the channel between the sections
z = 0 and z = zd outside the film on the wall:
AncW=Fft pi I [(1-~Po)-.(1-film)) dz _Fft Pizd[(1-(Po)-(1-9~
0 fihri
The value of Tdeg can be determined from the equation of mass balance
(5 ).
Amw=(Gz-Gi) ~ .
eg
(6)
G2=N/r,
(7)
and Gd in Eqs. (3) and (4) is obtained from the recommendations of [5]. The results of the
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 Declassified and Approved For Release 2013/02/20: CIA-RDP10-02196R000300070004-1
0 f0 B,0 p,MPa
Fig. 2. Minimum (without breaks in the film) trickling density
on the surface of a vertical channel for a descending film of
water: 1) unheated surface; 2) heated surface, q= (12-180)
kW/m2; 3) same, q = 250 kW /M2.
calculations of r = Gp/ird, confirmed by experiments in the range p = 0.2-12 MPa, q = 12-250
kW/m2, d = 30-53 mm; are presented in Fig. 2.
The value of G, is determined from the relation between the flow rate of the water
and steam in the presence of "flooding" in vertical heated tubes in terms of the criteria
of [6]:
V_K2 + a Y = b th (c Boo,25),
K G, Bo=d g(P16 P2)
1 Fft a P2i0g (PI_N)
'
In the range of state parameters studied p = 0.2-6 MPa; d = (30-53) 10-3 m; q = 50-250 kW/
2
m , this relation can be approximated by the dependence
11K,+0.94j T== 1.07 Bo-.125. (8)
It is recommended in [7] that the well-known formulas of Nusselt and Find be used to
calculate the thickness of the liquid film in the presence of flooding. These formulas do
not take into account the effect of the counterflowing gas (steam) flow and are therefore
universal for the entire region O 20 mm) gave the values 1 - cp film <
0.03. - Therefore the term (1 - Tfilm) in Eq. (5) can be neglected compared with the term
(1 - (p.o), which is not less than 0.3.
Thus Eqs. (5) and (6) can be put into the form
=d
Fft Pl J (1-(po)lo (9)
0
Tdeg G2-G1
To check the correctness of using in the proposed method the indicated dependences, we
performed experiments in tubes with d = (30-53)?l0-3 in, uniformly heated electrically over
the entire length, with the bottom inlet sealed. A vessel with an inner diameter of 79.10-3
M, filled with boiling water, was placed above the working section. Its level was more than
3 m higher than the top face of the electrically heated tube. In order to record the degra-
dation of heat transfer, 13 thermocouples, arranged uniformly along the height of the tube,
were fastened to the outer surface of the tube. We carried out the experiments under pres-
sures of 0.2-6.0 mPa with a virtually instantaneous (T < 0.5 sec) increase in the electrical
power up to values corresponding to G2 > G1.*
Using the dependences presented above (l)-(9) as well as the experimental results, we
compared the numerical values
*The power N > Ncr, where Ncr is defined according to the recommendations of [8], corresponds
conditionally to this value.
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 Declassified and Approved For Release 2013/02/20: CIA-RDP10-02196R000300070004-1
0 2 4 (GI) exp .102. kg /sec
Fig. 3. Comparison of the experimental and computed values
of G1. Electrically heated tube with an inner diameter
[mm] of 0 30; ? 40; ? 47; t 53; Glcalc was obtained
from Eq. (8).
I I I
0 2, r2 23 T,
Fig. 4. Change in the parameters accompanying a drop in the
pressure in the steam-generating channel: 1) effective
power; 2) critical power; 3) capacity of the steam-generating
channel: 4) pressure in the channel.
Pi ft (1-(po)dz
(GI) exp--.G2 - (~4 exp (10)
calculated using the formulas (1) and (7) based on the quantities p, N, and Tdeg measured in
the experiments and the values of G1 determined from the dependence (8) for the same values of
p and N. The results of this comparison are presented in Fig. 3.
In determining (Tdeg)exp, the time required for heating the tube wall up to the tempera-
ture characteristic for heat outflow accompanying bubble boiling (Tw) and for establishing
a stationary distribution of the steam content over the height of the channel (T,,) was taken
into account. In other words, the time required for steam bubbles forming at the bottom of
the channel to flow to the top was taken into account:
L
(1-cp)dz
U
T~0 4w
The time Tw + Tmo? is required to achieve the conditions for the onset of the hydrody-
namic critical state in the countermoving steam-water flows in the top section. The value
of Tw + TQo did not exceed 2-3 sec in the experiments.
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 Declassified and Approved For Release 2013/02/20: CIA-RDP10-02196R000300070004-1
(G2 > G1 > 0.5 G2), which gave a maximum error in (OL)exp of ?15%.
In this analysis the coordinates (zd)exp and (TyX)exp could be data from any thermo-
couple recording the degradation of heat transfer. The results of the comparison (see Fig.
3) indicate the correctness of the calculations performed.
It is therefore recommended that Eq. (9) be used to determine the time interval from
the moment the hydrodynamic critical state appears in the countermoving steam-water flows
up to the onset of the growth of the temperature of the heat-liberating surface. In order
to obtain the values of the quantities appearing in this formula, the expressions (1)-(3),
(7), and (8) are required.
We recall that if in the calculation using Eqs. (4) and (9) Gd > G1, then it is neces-
sary to set TYX = 0; this corresponds to the onset of the hydrodynamic critical state and
degradation of heat transfer in the heated top section of the channel.
In the computational procedure described above, it was assumed that the pressure and
power (of the thermal load) remained constant throughout the entire process. During real
accidents, however, these parameters changes as:a function of time, which complicates the
solution of the problem. Thus a drop in the pressure in the channel with the boiling
water causes additional generation of steam as a result of the heat (accumulated in the
water) present in the channel and in the metal structures over which the water flows. The
additional heat flux (Nadd) forms when the pressure (saturation temperature) in the channel
changes. In this case, Eq. (7) assumes the form
G2 = (Nchan + Nadd)/r = Neff A.
In the case when the duration of the accident T > 3 sec, when the pressure in the
channel drops, the process can be regarded as an equilibrium process and the expression for
Nadd can be written in the form
di, dp
(Nadd)T= (-mldpp d,r + Qmet '
Here Qmet is the heat flux from the metal structure of the steam-generating channel; over
which boiling water flows (it is determined from the formulas of nonstationary heat conduc-
tion); m1 and it are the mass and heat content of the boiling water in the channel, respec-
tively.
We shall describe the procedure for calculating the time interval from the moment that
the hydrodynamic critical state appears up to the moment that heat transfer is degraded under
nonstationary conditions for the process whose parameters change in the manner shown in Fig.
4. At the time Ti a hydrodynamic critical state (G2 > G1, i.e., Neff > Ncr) appears in the
channel with the bottom inlet sealed. Further growth of Neff and drop in pressure give rise
to an increase in the steam content as a function of time in the channel (under the condi-
tions of bubbling) and to continued ejection of the steam-water mixture from it (under the
condition that the volume of the channel remains constant). The termination of this process
is characterized by the time T2 corresponding to the maximum of the dependence
L
cpL = I cpdz = f (T),
0
where cp (z) is determined from the formulas for bubbling (1),and (2).
In the interval T1 < T < T2 water does not flow into the channel at the top and a criti-
cal state can (but is unlikely to) appear in heat transfer accompanying the ascending motion
of the steam-water mixture.
At the time T2 (with K2 < 3.2) the water once again begins to enter the channel at the
top, and in order to determine the time interval from T2 up to the moment of degradation of
heat transfer the procedure used above must be used.
In this case, the system of equations (3) and (5)
L ideg
Fft [PI (1 _ o) dz] -- \ (G2-G1) dT = l
o Sz 2
L
[P, ~ (1-q(,) dz]
zd deg
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 Declassified and Approved For Release 2013/02/20: CIA-RDP10-02196R000300070004-1
=d
(GE)T-(Gd-F 1 ( az ) dzI',
where the values of the quantities entering into these equations are obtained from formulas
(l)-(3), (8), (9), (11), and (12).
L
Terms of the form F
ftPl j (1 - cp) dz (with zi 0 and zi = zd) in the case of the assump-
tions made represent the mass of the water (mo)T and (mdeg)T present in the channel at the
times Ta and Tdeg, and can be used to calculate Nadd from Eq. (12).
The determination of the value of Tdeg is regarded as final when one of the following
conditions is satisfied: the left side of Eq. (13) becomes less than the right side or the
value of (G1)T becomes less than.that of (Gp)T.
When T > T3 the condition G2 > G1 is violated, and the mass of water in the channel
begins to increase and the degradation of heat transfer being studied here becomes impossible.
The calculations based on the foregoing method were compared with the results of experi-
ments performed with decreasing pressure (dp/pdT < 1.2.10-2 sec-1) and N = const. The dis-
agreement between the calculated and measured values of Tdeg (with T2 < 3 sec)_ does not ex-
ceed ?20%, which, under the assumptions made, must be regarded as satisfactory.
1. B. F. Balunov and E. L. Smirnov, "Critical thermal flows in the absence of coolant flow
in vertical steam-generating channels," At. Energ., 51, No. 4, 222-224 (1981).
2. G. Wallis, One-Dimensional Two-Phase Flow, McGraw-Hill (1969).
3. S. S. Kutateladze and Yu. L. Sorokin, "Hydrodynamic stability of some flow states of
gas-liquid systems," in: Problems in the Heat Transfer and the Hydraulics of Two-Phase
Systems [in Russian], Gosdnergoizdat, Moscow (1961), pp. 315-324.
4. D. A. Frank-Kamenetskii, Diffusion and Heat Transfer in Chemical Kinetics, Plenum Press
(1966).
5. N. Zuber and F. Staub., "Stability of dry patches forming in liquid film flowing over
heated surfaces," Int. J. Heat Mass Transfer, 9, No. 9, 897-905 (1966).
6. K. Chung, C. Liu, and C. Tien, "Flooding in two-pase countercurrent flows. 2. Experi-
mental Investigation," Phys. Chem. Hydrodynamics, 1, No. 2-3, 208-220 (1980).
7. H. Imura, H. Kusuda, and S. Funatsu, "Flooding velocity in a counter current two-phase
flow," Chem. Eng. Sci., 32, 79-87 (1977).
8. Yu. N. Ilyukhin, E. L. Smirnov, and B. F. Balunov, Energomashinostroenie, No. 1, 5-8
(1985).
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 Declassified and Approved For Release 2013/02/20: CIA-RDP10-02196R000300070004-1
N. K. Vasina, I. P. Kursevich,
0. A. Kozhevnikov, V. K. Shamardin,
and V. N. Golovanov
The dependence of swelling of the steels and alloys having fcc, bcc, and hcp crystal
structures on the temperature and the dose plays an important role in the choice of mater-
ials for nuclear and thermonuclear reactors. As applied to the field of large neutron
fluences, for a number of structural materials such data are obtained by carrying out
simulation experiments using charged particle accelerators [1-3]. In view of the well -
known shortcomings of such experiments and their uncoordinated nature, we carried
out direct determination of the radiation-induced swelling of a number of austenitic, fer-
ritic, refractory, and titanium-based materials in the 400-650?C range at a neutron fluence
of ,1.1023 cm 2 (E > 0.1 MeV). A comparative study of the obtained data and the results of
the simulation experiments conducted previously on these materials is expected to help in
establishing a possible correlation between the values of swelling found in both modes of in-
ducing radiational damages.
Table 1 shows the chemical composition and the regime of prior treatment of the experi-
mental materials.
The test specimens were in the form of cylindrical rods (wires) measuring 3 mm in dia-
meter and 27 mm in length with plane parallel polished end faces. The specimens were ir-
radiated in the core of a BOR-60 reactor using a special assembly for material studies.
The neutron fluence was maintained at (7.4-11.7).1022 CM -2 (E > 0.1 MeV) corresponding to
42-65 displacements per atom according to the TRN-standard. Along the height of the assem-
bly, the temperature was varied from 400 up to 650?C by creating a predetermined gap between
the external case and the internal ampul containing the specimen cassettes.
v 9
2
I I . . 1091
.00 500 500 T, G
6
Fig. 1 Fig. 2
Fig. 1. Temperature dependence of swelling of Kh15N35M2 steel
(in all the figures the numbers adjacent to the points indicate
neutron fluence x 1022 cm2; E > 0.1 MeV).
Fig. 2. Temperature dependence of swelling of the alloys of
the base composition Fe-20% Cr-45 Ni and pure nickel: 0) nickel
(99.99%); ?) Kh20N45M4BRTs (austenitizing at 1200?C, water
quenching + austenitizing at 1050?C for a period of 1 h, water
quenching), grain size number 3-4; ^) Kh20N45M4BRTs (austenitiz-
ing at 1050?C for a period of 1 h, water quenching), grain size
number 6-8; A) Kh20N45B (austenitizing at 1050?C for 1 h, water
quenching).
Translated from Atomnaya fnergiya, Vol. 59, No. 4, pp. 265-267, October, 1985. Origi-
nal article submitted August 23, 1984.
0038-531X/85/5904-0822$09.50 ? 1986 Plenum Publishing Corporation
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 Declassified and Approved For Release 2013/02/20: CIA-RDP10-02196R000300070004-1
TABLE 1. Chemical Composition and the Regimes of Prior Treatment of the Experimental
Materials
Material designation
Weight content of elements, 1o
and condition
C
Si
Mn
Cr
Ni
M.
Ti
Nb
Al
S
P
other
element
Fc
Kh16N11M3:
austenitizing at 1050?C
0,06
0,58
1,3
16,25
10,71
2,28
0,1
-
-
0,015
0,015
-
remain-
for 1 h, air cooling
der
austenitizing+1510
0,06
0,58
1,3
16,25
10,71
2,28
0,1
-
-
0,015
0,015
-
Same
cold deformation
austenitizing+5010
0,06
0,58
1,3
16,25
10,71
2,28
0,1
0,015
0,015
-
?
?
cold deformation
,
Kh15N35M2:
austenitizing at 1050?C
0,05
0,28
1,18
14,6
37,3
2,7
-
-
-
0,005
0,1
-
for 1 h+air cooling
Kh20N45B:
austenitizing at 1050?C
0,03
for 1 h + air cooling
0,23
0,36
18,89
44,55
-
0,01
1,25
0,12
0,009
0,006
-
-
Kh20N45M4BRTs:
austenitizing at 1200?C
0,022
0,18
0,51
19,5
44,6
3,92
-
0,79
-
0,004
0,007
0,02 Zr
for 5 h, water quech-
-
ing+austenitizing at
1050?C for l h, water
quenching (grain size
numbers 3-4)
Kh20N45M4BRTs:
austenitizing at 1050?C
0,022
0,18
0,51
19,5
44,6
3,92
-
0,79
--
0,004
0,007
0,02 Zr
remain-
for 1 h, water quench-
der
ing rain size number
6-8
Nickel, annealing at800?
-
0,02
0,0002
0,006
99,9
0,001
0,01
-
-
-
-
0,02
C for 1 h, air cooling
O1Kh13MCh, annealing
0,035
0,45
0,53
14,53
0,05
1,08
-
-
0,04
0,01
0,01
0,005Y
remain-
at 800?C for 1 h, air
der
cooling
Molybdenum alloy
annealing at 125b?C for
-
-
-
-
-
99,5
-
-
-
-
-
-
-
1 h, air cooling
Niobium alloy, annealing
-
-
-
-
-
-
-
99,8
-
-
-
-
-
at 1250?C for 1 h, air
cooling
Titanium, annealing at
?
0,04
0,02
-
-
-
-
99,2
-
0,53
-
-
0,080 H2
780
C for 1 h, air cool-
0,055 H2
ing
0,02 N2
TABLE 2. Swelling of the Steel Kh16N11M3
Under Different Structural Conditions
Condition
rradiation parameters
neutron
fluenFe _2 temp.,
X 10 cm C
(E >;.I Me
Length
change
4i/i. %
Volume
change
AV/V, %.
Austenitizing
11,2
500
2,0
6,0
?
I
11,7
550
4,15
12,5
ustnitizingg+
15
d
10,5
450
1,2
3,6
10 col
de-
formation
ame
11,7
550
3,0
9,0
? ?
8,9
650
2,0
6,0
ustemtizingg+
10,5
450
0,85
2,6
501o cold de-
formation
ame
11,7
550
2,4
7,2
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 Declassified and Approved For Release 2013/02/20: CIA-RDP10-02196R000300070004-1
2
400 S00 600 T, C
Fig. 3. Temperature dependence of swelling
of the bcc and hcp materials: O) titanium
(commercial purity); ?) OlKhl3MCh steel;
^) No alloy; A) Nb alloy.
The magnitude of swelling was determined by precisely measuring the length of the speci-
mens before and after irradiation within an error of ?0.01% using a special remote device
designed incorporating an IZV-3 length measuring machine.
Table 2 gives the results of studies on the steel Khl6NllM3 under various structural
conditions. The maximum swelling (1-l2.5%) was observed for the steel in the austenitized
conditon at an irradiation temperature of 550?C. Cold working the steel by 15% and, in
particular, by 50% effectively decreases swelling.
The temperature dependence of swelling of the Kh15N35M2 steel (Fig. 1) is characterized
by a clearly defined maximum at 550?C amounting to 8% which is close to the swelling of the
Kh16N11M3 steel in cold worked condition. Such a high swelling of the Kh15N35M2 steel does
not agree with the conclusion of Johnson et al. [4] based on simulation experiments that the
steels containing 35% Ni have a low swelling tendency.
Figure 2 shows the data on the swelling of pure nickel and the solid-solution strengh-
ened high-nickel alloys Kh20N45B and Kh20N45M4BRTs in the austenitized condition; here, the
alloy Kh20N45M4BRTs was austenitized at 1050 and 1200?C in order to obtain grain sizes cor-
responding to the numbers 6-8 and 3-4, respectively, The swelling curve of pure nickel has
nonmonotonic nature and exhibits a maximum at 550?C. Taking the temperature shift into
account, it agrees well with the previously published data [5] on the effect of ion bombard-
ment.
Swelling of high-nickel alloys of the composition Fe-20 Cr-45 Ni does not exceed 1-2%
independent of alloying and the heat treatment regime. This agrees well with the data of
the simulation experiments [1]. Furthermore, it is seen that the maximum resistance to
swelling is exhibited by the alloy Kh20N45M4BRTs after austenitizing at 1200?C whereby the
maximum amount of alloying elements is taken into the solid solution.
Based on an analysis of the obtained results, we can conclude that a satisfactory resis-,
tance to-swelling of the solid-solution strengthened austenitic alloys can be achieved at a
sufficiently high content of nickel (1-45%) and the other alloying elements (Al, Ti, Nb, etc.)
having a size incompatibility with the elements of the matrix.
The reduced radiation swelling of the Fe-Cr-Ni alloys at high nickel contents is attri-
buted to short-range ordering of the solid solution [6]. The absence of a correlation be-
tween the swelling of the steels of the composition Fe-15 Cr-35 Ni under neutron and ion ir-
radiation is apparently because of the difference in the duration of irradiation and in view
of the fact that in both cases radiation-induced segregation of various elements (including
nickel) occurs [7]. During prolonged neutron irradiation considerable depletion of nickel
from the austenite matrix takes place because of its migration to sinks and, therefore, the
nickel content in the solid solution becomes insufficient for reducing the magnitude of
swelling, for example, by the mechanism of short-range ordering. During ion irradiation,
where bombardment with charged particles lasts only for a few hours, the process of deple-
tion of nickel from the solid solution does not occur to a significant extent.
The data on the swelling of the ferritic stainless steel O1Kh13MCh (Fig. 3) confirms'
the well-known high resistance of this class of steels to swelling. Similar results were
obtained in the simulation experiments also [2].
Swelling of the molybdenum and niobium alloys (see Fig. 3) increases with increasing
irradiation temperature, but does not exceed 3% at 650?C. These results as well as the
data of Norris [8] show that the maximum swelling of the refractory metals having bcc lattice
occurs in the region of higher temperatures than in the case of the fcc metals. A study of
commercial purity titanium (hcp lattice) showed (see Fig. 3) that irradiation right up to a
824
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 hig- Declassified and Approved For Release 2013/02/20: CIA-RDP10-02196R000300070004-1
.. I .,.... -- w o -6LI -6i Vi awctttug to L11C Lemp-
erature range 500-650?C (OV/V _< 1.2%). This agrees with the data of the simulation experi-
ments [3].
LITERATURE CITED
1. V. F. Zelenskii et al., Vopr. At. Nauk. Tekh. Ser. Fiz. Rad. Povrezh. Rad. Materialoved.,
Issue 2 (13), 18-22 (1980).
2. A. M. Parshin et al., ibid., Issue 2 (13), 13-17 (1980).
3. V. F. Zelenskii et al., ibid., Issue 2 (16), 57-61 (1981).
4. W. Johnson et al., "An experimental survey of swelling in commercial Fe-Cr-Ni alloys
bombarded with 5 MeV Ni-ions," J. Nucl. Mater., 54, No. 1, 24-40 (1974).
5. V. I. Bendikov et al., Vopr. At. Nauk. Tekh. Ser. Fiz. Rad. Povrezh. Rad. Materialoved.,
Issue 4 (23), 9-11 (1982).
6. I. P. Kursevich, V. A. Nikolaev, et al., ibid., Issue 4 (32), 57-64 (1984).
7. P. Okamoto, J. Nucl. Mater., 53, 336 (1974).
8. D. Norris, Rad. Effects, 15, 1 (1972).
EFFECT OF THERMOMECHANICAL TREATMENT ON THE SWELLING OF STEEL OKh16N15M3B
V. I. Shcherbak, V. N. Bykov, UDC 621.039:553.3:669.15
and V. D. Dmitriev
Our earlier studies [1, 2] showed that thermomechanical treatment can significantly
affect the mechanical properties and swelling of steels irradiated with fast neutrons. In
view of this, it is interesting to carry out a more detailed study of the effect of such a
treatment on the microstructure of the'fuel element jackets of a BOR-60.reactor made from
the austenitized steel OKh16N15M3B (holding at 1100?C for a period of 20 min) and the jac-
kets made from the same steel, but subjected to thermomechanical treatment (15% cold defor-
mation and annealing for 1 h at 800?C). For the present investigation we selected two
centrally located adjacent fuel elements of a BN-6 experimental packet that was irradiated
up to a neutron fluence of 6.6.1022 CM -2 (En > 0.1 MeV) in the temperature range 340-640?C.
Electron-microscopic studies were carried out on 12 different sections along the height of
the jacket. The length of the fuel column in the fuel elements amounted to 500 mm.
The microstructure of the reference specimens showed that the austenitized steel
OKh16N15M3B had a dislocation density of 5.10' CM-2 . The thermomechanical treatment of
this steel led to the deposition of finely dispersed niobium carbonitride particles decorat-
ing the dislocations and the precipitates . of the Laves phase; in this case, the dislocation
density within the grains varied from 6.1010 up to 2.1011 cm2. An analysis of the electron
micrographs of the steel showed that the precipitate particles deposit only on the edge dis-
locations or 'tripod' faults originating from the dissociation (splitting) of dislocation
lines retained in the structure of the steel after cold working and annealing. The twin and
grain boundaries were also decorated significantly with niobium carbide particles; here, the
grain boundaries had precipitate-free zones measuring 700 A in width.
When studying the specimens cut out from different sections of the fuel. elements jackets
made from the austenitic steel, we obtained the characteristic microstructure of the neutron
irradiated OK16N15M3B steel (Fig. la, b, c). Dislocation loops and precipitate particles
were observed in the lower sections. The size of the dislocation loops increases with in-
creasing irradiation temperature. In this case, at the maximum fluence the dislocation den-
sity reached 7.1010 CM-2 , and in the segments irradiated at 600?C, it was equal to 1010
cm 2. Furthermore, Fig. 1 shows that the precipitate particles size increases with increas-
ing irradiation temperature. Particularly intense growth of the precipitate particles of
the other phases takes place at a temperature exceeding 550?C.
It was found that niobium carbonitride particles and the Laves phase are the main pre-
cipitates in the irradiated steel OKh16N15M3B. In the segments subjected to high tempera-
Translated from Atomnaya nergiya, Vol. 59, No. 4, pp..267-269, October, 1985. Origi-
nal article submitted August 6, 1984.
0038-531X/85/5904-0825$09.50 01986 Plenum Publishing Corporation
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 Declassified and Approved For Release 2013/02/20: CIA-RDP10-02196R000300070004-1
Fig. 1. Microstructure of the steel
OKh16N15M3B after irradiating up to a neu-
tron fluence (EU > 0.1 MeV) of 5.0.1022
cm-' at 430?C (a), 6.3.1022 CM-2,
460?C
(b), and 4.3.1022 cm a, 610?C (c). Mag.
x 50,000.
Fig. 2. Microstructure of the steel
OKh16N15M3B after thermomechanical treat-
ment and irradiation up to a neutron
fluence of 0.5.1022
CM -2
at 350?C (a),
5.8.1022 cm-2, 430?C
(b),
6.3.1032 cm-2,
460?C (c), and 4.9.10' Cm-2 , 610?C (d).
Mag. x 50,000.
Irradiation temp. ?C
350 405 W. 51S S70 525
j 2
-200 -100 0 900 200
Distance from the core
center
Fig. 3. Concentration Nv, average diameter , and
relative volume OV/V of pores in the steel OKh16N15M3B
subjected to austenitizing (0) or thermomechanical
treatment (?); the dashed line shows the fluence varia-
tion along the length of the fuel element.
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 Declassified and Approved For Release 2013/02/20: CIA-RDP10-02196R000300070004-1
ture, Lne r123L6 precipitate particles are observed on the grain boundaries as well as within
the grains.
After thermomechanical treatment, the steel OKh16N15M3B shows a more nonuniform struc-
ture (Fig. 2a, b, c). Irradiation of this steel led to a decrease in the dislocation density
up to 1011 CM -2 and up to 5.1010 CM -2 (in the upper sections); in this case, the concentra-
tion of the precipitates decreased from 2.1016 CM -3 up to 1016 CM-3 . The finely dispersed
niobium carbide precipitates decorating the dislocations are mostly retained even at high
irradiation temperatures. At a temperature exceeding 550?C, besides the finely dispersed
precipitates, the microstructure of this steel shows coarser particles of other phases
(Fig. 2d).
We note that the high dislocation density observed in the steel subjected to such a
treatment restrains the coalescence process of the finely dispersed niobium carbonitride
particles during irradiation up to a neutron fluence of 6.6.1022 cm 2.
Figure 3a shows the values of the average diameter and the concentration of pores
along the height of the steel jacket under different structural conditions. A comparison
of the results shows that after irradiating at a temperature below 500?C, the steel exist-
ing in the thermomechanically treated condition has higher concentration of pores of smaller
size as compared to the austenitized steel. Figure 3b shows that when irradiated at a
temperature below 460?C the relative pore volumes are closeto each other, and their maxi-
mum values amount to 3.2 and 2.6% for the steel subjected to austenitizing and to thermo-
mechanical treatment, respectively. When irradiation is carried out at a temperature above
520?C, thermomechanical treatment completely suppresses the process of vacancy related poro-
sity development at the given neutron fluence.
This type of porosity development in the fuel elements made from the steel existing in
the thermomechanically treated condition may be explained in the following manner. During
irradiation at a temperature below 460?C, blocking of the vast majority of edge dislocations
by the depositing precipitate particles occurs. These particles hinder the process of dis-
location climb and, thereby, sharply decrease the ability of dislocations to trap the point
defects. Owing to this, the dislocation structure formed during such a treatment affects
the supersaturation of the matrix with point defects to a considerably less extent. There-
fore, in the temperature range under consideration, close values of swelling are observed
after thermomechanical treatment and austenitizing. At a temperature above 460?C, where the
density of niobium carbonitride precipitates formed during such a treatment begins to de-
crease, the dislocations can become free from the precipitates more easily, owing to which
their effectiveness as sinks for point defects increases. In view of this, when irradiation
is carried out at a high temperature up to a neutron fluence of 6.6.1022 cm 2, the effect of
thermomechanical treatment is found to be similar to the effect of 10% cold deformation [3].
LITERATURE CITED
1. A. N. Vorobyev, V. N. Bykov, V. D. Dmitriev, and V. I. Shcherbak, "Radiation effects on
the mechanical properties and microstructure of solution-treated and cold worked
1Kh18N1OT and OKh16N15M3B stainless steels," J. Brit. Nucl. Energy Soc., 14,.No. 2,.
149-155 (1975).
2. V. N. Bykov, A. M. Dvoryashin, V. D. Dmitriev, and V. I. Shcherbak, "Stability of vac-
ancy pores, dislocation structure, and precipitate particles during annealing of neutron
irradiated OKh16N15M3B after austenitizing and thermomechanical treatment," Vopr. At.
Nauk. Tekh., Ser. Fiz. Rad. Povrezhd. Rad. Materialoved.. Issue 4 (27), 29-32 (1983).
3. N. P. Agapova, V. S. Ageev, M. I. Antipina, et al., "Structural study on the fuel-
element jackets made from the steel OKh16Nl5M3B in cold worked (15%) condition and ir-
radiated in a BOR-60 reactor-up to 12.5% depletion," Vopr. At. Nauk. Tekh., Ser.. At.
Materialoved., Issue 4 (15), 19-26 (1982).
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 Declassified and Approved For Release 2013/02/20: CIA-RDP10-02196R000300070004-1
V. M. Sharapov, A. I. Kanaev, UDC 533.15
and A. P. Zakharov
In recent years numerous studies have been made on the hydrogen permeability of stain-
less steels and on determining the parameters (constants) of the surface processes under ion
irradiation conditions [1-4]. Such studies are useful not only to understand the role of
different stages of the penetration (permeation) process, but also to predict the possibility
of using austenitic steels in thermonuclear installations. In this paper, we examine the
specific features of hydrogen penetration through the Kh18N1OT stainless steel from a glow-
discharge plasma.
The experimental setup and the procedure for measuring the hydrogen permeability of the
metals in contact with a glow-discharge plasma were described elsewhere [5]. The ion flux
density from the plasma on the specimen amounted to 3.1016 CM-2 -sec-' at an ion energy < 350
eV corresponding to the voltage applied across the specimen (cathode) and the anode, and the
temperature range was 520-1000?K.
Figure 1 shows the temperature dependence of hydrogen permeability in the case of two
Kh18N10T stainless steel specimens measuring 0.5 (1) and 1 mm (2) in thickness. In the en-
tire temperature range under study, hydrogen flux P is inversely proportional to the speci-
men thickness. In the high temperature region (670-1000?K) we observe an exponential depen-
dence of the flux on the reciprocal of temperature that is characterized by an activation
energy of 14.5 kcal/mole (60.3 kJ/mole); at lower temperatures ( St is valid up to 1000?K and that the reemission rate constant of hydrogen on the
irradiated side S1 is determined only by the radiation-induced desorption, i.e., S1 = S.
The rate of hydrogen reemission from the stainless steel within the pulse duration in
the TM-4 discharge chamber measured [11] at 300 and 600?K was found to be equal to 3.10-'
and 4.10-2 cm/sec, and the variation, may be described by the following equation (cm/sec)
(Fig. 41 line 4):
S1= 60 exp (- 8700 cal /RT ). (10)
Waelbroeck et al. [1] also measured the reemission rate at 300-700?K in the experiments
based on the so-called 'Langmuir effect':where the change of hydrogen pressure in the stain-
less steel chamber was recorded during the glow-discharge period. In order to explain the
results of these experiments, the authors [1] used a diffusion equation with the boundary
conditions showing quadratic dependence (square-law variation) on the concentration C. The
reemission rate constant kr, cma?sec-1, and the ratio of the actual surface area to the geo-
metric area o were found out according to this.
In order to obtain the relationship between S1 and akr, let us compare the equations
-.D C1 C2-aQ-SC
d 'j
-D Ca =aQ-2akrCi
(12)
assuming that the penetration is restricted (controlled) by diffusion, i.e., S1 >> D/d. and
2 /k >> D2/4d2Q. Equating the values of C1 obtained for Eqs. (11) and (12) (under the:con-
dition that C1 >> C2) we obtain the following relationship
Si = 26krQ, (13)
which is used for comparing the published data with the results of the present work. Recal-
culation of the published data [1] gives the following expression for S1 (Fig. 4, line 2)
S1 =16 exp (-1000.ca1/R7'), (14)
which coincides with that obtained in this work.
Apparently, Eqs. (7) and (14) may be considered to be more accurate than Eq. (10) that
was obtained from the experiments conducted on such a complex apparatus as TM-4. Evidently,
it may be confidently stated that under ion irradiation conditions at relatively low temper-
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 Declassified and Approved For Release 2013/02/20: CIA-RDP10-02196R000300070004-1
atures c 700?K) the reemission rate of hydrogen from the stainless steel has an exponential
dependence on temperature in that the activation energy amounts to til0 kcal/mole (41.9 kJ/
mole), whereas, at T > 700?K this rate does not depend on temperature.
We can propose two possible explanations for this phenomenon.
1. The temperature dependence of S1 indicates the activated nature of the process
with an activation energy close to that of thermal desorption (8700 cal/mole or 36.45 kJ/
mole), whereas, the radiation-induced desorption rate is clearly independent of temperature
[15]. It is possible that accelerated thermal desorption occurs in this case as a result
of ion bombardment. From Fig. 4 it follows that such an accelerated thermal desorption is
as if it were equivalent to a temperature increase in the surface layer by 300?K.
2. The constant S1 characterizes the radiation-induced desorption rate and, may be
expressed [11] in the following form:
S,=Sn_a'R (aQ),
where Rp is the jump depth of the ions of a given energy in the metal, cm (at an ion energy
of 350 eV, RP 20-30 A); and a' is the transverse section of radiation-induced desorption,
cm2. In this case, we may assume that a' is a function of temperature (at T < 700?K). The
values of a' calculated according to Eq. (15) were found to be 4.10-16, 3.10-13, 2.10-12,
3.10-12, 3.10-12 cm2 at T = 300, 500, 600, 800, and 900?K, respectively (Fig. 5). The vari-
ation of a' with temperature in the range below 700?K may be expressed in the following way:
a' =10-8 exp (-10400 cal /RT). (16)
Nonavailability of data on the a' measurements at temperatures above the room tempera-
ture did. not make it possible to compare the obtained results. The experimentally determined
[12, 13] a' value for the stainless steel at 300?K using 350 eV bombarding ions was equal to
(2-3).10-16 cm2;.on,the other hand, according to the data of McCracken [14], in the case of
unannealed stainless steels a' > 10-16 cm2. The derived values are very close to the value
calculated from Eq. (16): at 300?K, a' = 4.10-16 cm2. This apparently indicates the opera-
tion of the radiation-induced desorption process. However, in this case, it is difficult to
explain the increase in a' with increasing temperature: up to as high value as 3.10-12 cm2
at 700?K. The aforementioned effect may be related to the capture of hydrogem atoms by the
defects created at the moment of irradiation whose probability of liberation from these de-
fects increases with increasing. temperature. However, additional experiments are required
for verifying this hypothesis. In any case, the value S1 = 7'10-9 cm/sec., that is obtained
at T ? 700?K and is independent of temperature, forms the ultimate (limiting) value of the
hydrogen reemission rate at the bombarding hydrogen ion fluxes amounting to 3'1016 cm 2.
sec-'.
Table 1 shows that right up to low temperatures, hydrogen penetration through the stain-
less steel is diffusion controlled (d/D >> l/S1, l/St) in contrast to, for example, molyb-
denum [15] in which at low temperatures, the penetration is governed by the surface proces-
ses. The rate of the surfaces processes (S1, St) becomes comparable to the diffusional dis-
charge rate (D/d) only at T > 1000?K. Using Eq. (5) and the Si., St, and D values given in
Table 1, we can evaluate P at high temperatures (see Fig. 1, cross symbols). The observed
bend point in the temperature dependence of hydrogen permeability in the high temperature
region indicates that in this case, the superficial (surface) stage of penetration begins
to play a decisive role. From Eq. (5) it follows that the maximum obtainable permability
Pmax = aQ provided that l/S1 >> l/St, d/D. However, in the case of the stainless steel,
the valuesof 1/Si, l/St, and d/D are fairly close to each other in the entire range up to
Tmelt and, therefore, Pmax always remains less than aQ. Thus, at T = 1600?K, the flux
P 3'1016 cm-2'sec 1 which is approximately 4 times less than aQ = 1.2.1016 cm2'sec-1.
CONCLUSIONS
In the entire temperature range under consideration (520-1000?K), the radiation-induced
desorption rate is higher than the thermal desorption rate.
In the temperature range below 700?K, the magnitude of hydrogen permeability is deter-
mined by the radiation-induced desorption rate that depends on temperature according, to the
equation
S, =18exp (-10000:cal IRT).
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 Declassified and Approved For Release 2013/02/20: CIA-RDP10-02196 R000300070004-1
7.10-3 cm/sec.
Above 1000?K, the rates of the radiation-induced desorption, thermal desorption, and
diffusional discharge are comparable, and the exponential temperature dependence of flux
would be disrupted.
LITERATURE CITED
1. F. Waelbroeck, J. Winter, and P. Weinhold, J. Nucl. Mater., 103-104, 471-475 (1981).
2. M. Brown, B. Emmoth, F. Waelbroeck, and P. Weinhold, J. Nucl.. Mater., 93-94, 861-865
(1980).
3. V. M. Sharapov, A. I. Pavlov, and A. P. Zakharov, "Hydrogen permeability of some struc-
tural materials under the conditions of low-energy ion bombardment," Zh. Fiz. Khim.,
56, No. 5, 1202-1206 (1982).
4. M. Baskes, J. Nucl. Mater., 92, 318 (1980).
5. V. M. Sharapov, A. P. Zahkarov, and V. V. Matveev, "Effect of the glow-discharge para-
meters on the hydrogen permeability in molybdenum," Zh. Tekh. Fiz., 45, 2002-2004
(1975).
6.' K. Wilson and M. Baskes, J. Nucl. Mater., 76-77, 291-297 (1978).
7. V. M. Sharapov, A. I. Pavlov, and A. P. Zakharov, "Hydrogen permeability in nickel
from plasma glow-discharge," Zh. Fiz. Khim., 54, No. 11, 2887-2890 (1980).
8. D. I. Slovetskii and R. D. Todesaite, "A study of the mechanism of disintegration of
nitrogen molecules in glow-discharge," Khim. Vys. Energ., 7, No. 4, 291-296 (1973).
9. V. M. Sharapov and A. P. Zakharov, "Peculiarities of hydrogen permeation in molybdenum
under glow-discharge conditions," Zh. Tekh. Fiz., 46, 611-614 (1976).
10. K. Wilson, J. Nucl. Mater., 103-104, 453-463 (1981).
11. S. A. Grashin, Yu. A. Sokolov, A. E. Gorodetskii, et al., Interaction of Hydrogen with
the Material of the TM-4 Discharge Chamber [in Russian], Preprint IAE-3622/7, Moscow
(1982).
12. G. Farrell and S. Donnelly, J.Nucl. Mater., 76-77, 322-327 (1978).
13. E. Thomas, J. Appl. Phys., 51 (2), 1176-1183 (1980).
14. G. McCracken, Vacuum, 24, No. 10, 463-467 (1974).
15. A. P. Zakharov and V. M. Sharapov, "Effect of surface processes on the hydrogen permea-
bility of molybdenum," Fiz. Khim. Mekh. Mater., No. 6, 54-58 (1971).
VARIATION OF THE DISLOCATION DENSITY UNDER THE CONDITIONS OF RADIATION-
INDUCED SWELLING OF STRONGLY DEFORMED CRYSTALS
The dislocation structure of crystals undergoes considerable changes under irradiation
and the dislocation density can either increase or decrease, depending on'its initial value.
An interesting feature of the evolution. of the dislocation structure during irradiation is
a tendency toward the attainment of a certain steady-state dislocation density. It?is known,
e.g., that when annealed (initial dislocation density po < 10' cm-2) and colds-worked (po
1012 CM-2 ) austenitic stainless steels are bombarded with fast neutrons, the dislocation
density attains the same constant value ps = 6.1010 cm-2 at a neutron fluence ,.1022 cm2 [1].
Since the stresses necessary for dislocation glide do not arise in the crystals, during
irradiation, it must be assumed that the rearrangement of the dislocation structure of the
crystal is caused solely by the climbing of the dislocations, by the annihilation of the
dislocations during collision, and the formation of new dislocation loops from the solid
solution that is supersaturated with point defects. It is thus of interest not only to
elucidate the mechanism responsible for the tendency toward a constant dislocation density
and to estimate the steady-state concentration ps, but also to establish what, during the
irradiation of the crystals in the free state, causes an uncompensated steady-state flow of
Translated from Atomnaya Energiya, Vol. 59, No. 4, pp. 273-277, October, 1985. Origi-
nal article submitted July 16, 1984.
0038-531X/85/5904-0833$09.50 ? 1986 Plenum Publishing Corporation 833
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 Declassified and Approved For Release 2013/02/20: CIA-RDP10-02196R000300070004-1
a r?--~~~~~a~ err= ~L FU~LLL UCLCI:LA LU LIIC uLSLUCaLlons, wnicn is necessary tor steady-
state climb by dislocations.
Edge dislocations have a capability for preferential absorption of interstitial atoms
[2-4]. However, this is insufficient for the existence of a steady-state flow of uncompen-
sated interstitials to such dislocations. Such flows can exist only.if the crystal contains
different sinks with an unlike tendency toward preferential absorption of point defects. It
is usually assumed that besides dislocations the crystal contains vacancy pores, which most
often are considered as neutral sinks without a tendency toward preferential absorption. In
highly deformed crystals, however, pore formation is suppressed until sufficiently high flu-
ences, which lead to a very substantial change in the dislocation density, are attained.
Therefore, when explaining the comparatively rapid decrease in the dislocation desntiy in the
case of crystals with a high initial density, Bondarenko and Konobeev [5] considered neutral
sinks in the form of mixed helical dislocations introduced into the material during deforma-
tion. Since this assumption was not sufficiently substantiated, it was considered as a pos-
tulate [5].
It should be emphasized that in the case of steady-state spearation of flows of vacan-
cies and interstitials to sinks of unlike types one of the sinks need not be considered to be_
neutral or capable of preferential absorption of vacancies. All of the sinks can have a
tendency toward preferential absorption of any one type of point defect (e.g., intersti-
tials). Nevertheless, if the different sinks have a different tendency toward such preferen-
tial absorption, then under steady-state conditions of irradiation one type of sink will ab-
sorb predominantly interstitials and the other type predominantly absorbs vacancies.
The stronger elastic interaction of edge dislocations with interstitial atoms than with
vacancies is one of the principal causes of preferential absorption of interstitials by edge
dislocations. The elastic field of an edge dislocation depends on the orientation of its
Burgers vector relative to the crystallograhic axes. Therefore, dislocations with Burgers
vectors of different orientation should interact in different ways with different point de-
fects. Accordingly, they should also have different tendencies toward preferential absorp-
tion of interstitials. This, as mentioned above, is completely sufficient for the steady-
state separation of flows of interstitials and vacancies to dislocations with Burgers vectors
of different orientations and as a result conditions are created for steady-state climb of
these dislocations during irradiation. The factor nD of the tendency of dislocations toward
preferential absorption of interstitials is usually assumed to be of the order of several
per cent. In principle, however, its relative change can be calculated as a function of the
orientation of the Burgers vector and the dislocation line and for qualitative analysis we
can take An ,:; 10-2, assuming that this value is not grossly overestimated.
We also note that the presence of preferential sinks of only interstitial atoms produces
an excess supersaturation of the crystal with vacancies and, consequently, should be condu-
cive to the nucleation of vacancy pores but not of interstitial dislocation loops. The cri-
tical size of interstitial dislocation loops. The critical size of interstitial dislocation
loops (if only the small loops do not have an anomalously strong tendency toward preferential
absorption of interstitial atoms) under such conditions should be too large and, therefore,
the observed loops should have a subcritical size and cannot make any significant contribu-
tion to the formation or evolution of the dislocation structure of the crystal. It should be
added here that the conditions for the nucleation of interstitial loops do not improve appre-
ciably even when neutral sinks or sinks with a small tendency toward preferential absorption
of vacancies are present in the crystal. We shall henceforth assume that the evolution of
the dislocation structure of the. crystal during irradiation occurs mainly as a result of the
climbing of the edge segments of the dislocation network that exists in the crystal and the
climbing of helical dislocations that can form from screw segments of dislocations of the
probability of this process is sufficiently large.
Two parallel processes can occur during the climb of dislocations: multiplication of
dislocations through the formation of new dislocation loops by the Bardeen-Herring mechanism
from climbing edge segments [6] and the annihilation of dislocations of opposite sign when
they enter into the region of "spontaneous mutual. recombination," i.e., when they approach
to a distance at which the force of the mutual attraction becomes equal to the force that
starts the slip of dislocations. Naturally, when the initial dislocation density is low,
the multiplication process will predominate and the dislocation network will become denser
under irradiation. Conversely, when the initial density is high, the process of dislocation
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 annihi,--'-- --"" --- ------- - .L_ -~ s- --s? - l -
Declassified and Approved For Release 2013/02/20: CIA-RDP10-02196R000300070004-1 y
state ..~~~.. uc{._7 {{.,- .,c GO{ 6U110{ISU W11CLS L1{= LaLC.7 Ut L.11= LWU jJL UCtbbCb UdLe
equal. An exact mathematical description of the process of change in the dislocation struc-
ture is extremely complicated. The phenomenological equations presented in [5] for the de-
scription of the behavior of the dislocation density contain indeterminate parameters and
the applicability of these equations is limited. It is thus desirable to.attempt a quali-
tative description of the time dependence (fluence dependence) of the dislocation density on
the basis of fairly simple but physically substantiated assumptions.
Suppose that P(t) is the dislocation density and Z _p-1/2 is the average length of
the segments in the dislocation network. Then the bulk density of dislocation segments n =
(p'/Z) = p3/2. A segment, as a source, can generate a dislocation loop whose radius is com-
mensurate with its length. If v is the velocity of climbing by dislocations, then T1 = Z/v
is-the creation time and v1 = v/Z is the rate of creation of loops of size Z per unit time by
one segment-source. In this case the rate of increase of the dislocation density because of
all such sources is (apart from a factor of severalfold) equal to
(dpldt), x nlv1 = p3/2v.
If z is the number of different possible orientations of the Burgers vector in the crystal,
then with an isotropic distribution for the orientation of the dislocations the bulk density
of dislocation segments that climb in parallel planes is n1 = n/z = p3/2/z. By Go we denote
the starting stress for dislocation slip. Then the distance h at which climbing dislocation
segments can annihilate is found from the formula h= b(G/ao), where G is the shear modulus
of the crystal. The average distance between segments that climb in parallel planes and are
separated by a distance < h can be expressed as:
(n,h) -1/2 = (p3/2h/z) -1/2.
The lifetime T2 of a climbing dislocation to annihilation will be determined from the
condition A = vT2. In this case the rate of change of the. dislocation density as a conse-
quency of annihilation (to within a numerical factor) is
(dpl dt) an ^-' (p/T2) = (pv/),) = p7/4 (h1z)1/2.
Thus, for the rate of change of dislocation density we get the equation
(dpldt) = p3/2v- p'/4v (h/z)1/2. (1)
The climbing velocity v in the general.case can depend on the dislocation density.
The stationary solution of Eq.. (1) (dp/dt = 0), which corresponds to a long irradiation
time (large fluence), has the form
P$ _ (zoo/bG)2 (2)
and does not depend on either the initial plane of the dislocations or their climbing--velo-
city since it is determined only by the structure of the crystal (z) and its mechanical-
characteristics (ao, G)'. If for a rough estimate we use the values b = 3.10-8 cm And -Go/-G,=
8.10-4, then for cubic crystals (z = 9, three orientations and six orientations)
we get ps = 5.7.1010 cm-2, which is close to the value established during the irradiationrof
stainless steels.
V -_ - 2a b In (l/ro) D( )c(-)QTI,
where b is the Burgers vector, ro is the radius of the dislocation core, D(-) is the vacancy
diffusion coefficient, c(-) is the steady-state vacancy concentration during irradiation,
and On is the orientational difference of the factors of the tendency toward absorption of
interstitials by dislocations.
The quasi-steady-state vacancy concentration c(-) can be determined from the condition
for the balance of point defects
C(-) (q) 4 + 4reQ n2 (l/ro) 1/2_ 1 ~ (4)
4r1. In (l/ro) { [ 7tp2D(-) I
where r is the radius of spontaneous recombination of point defects and Q is the number of
separated Frenkel pairs that form in a unit volume of the crystal per unit time (K = wQ is
the rate of formation of displacements). For simplicity, Eq. (4) does not make allowance
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 fo_ Declassified and Approved For Release 2013/02/20 : CIA-RDP10-02196R000300070004_1
in a unit volume is smaller than the dislocation density.
Substitution Eq. (4) into formula (3) and then into Eq. (1), we get the. following
equation for the time dependence of the dislocation density during irradiation:
;4 w 4r K in2 (1/1-6) 1/2 1 l 1 _ r LC 1/2 ~1/4 ~5/2
dt 2brc 10 (1/r,) j 1 + nc)p2D(-.) - ) C \ zoo ( J (
(5)
The solution of Eq. (5) in the general form reduces to integration of a fiarly compli-
cated function and, therefore, we shall confine ourselves to consideration of the limiting
cases when Eq. (5) assumes a form that is more accessible to integration.
The expression
(4rK In2 (1Jro)/31(Op2D(-)) (6)
which appears in formulas (4) and (5), depends on the rate of formation of displacements,
the dislocation density, and temperature. If from the condition E = 1 we determine the
critical values of these parameters [Tc(p, K), pc(T, K), and Kc(T,p)], which, naturally,
will depend on the true values of the other two parameters, then clearly when one of the
conditions Tirr >> Tc(p, K), p >> pc(Tirr, K), or K ? Kc(Tirr? p) is satisfied, the para-
meter C will be much smaller than unity and Eq. (5) takes on the form
dt -= OGK P1/2 [ 1- (P!PS)'/'l, ? 1, (7)
where ps is described by. formula (2). This limiting case corresponds to irradiation condi-
tions when the volume recombination can be neglected and the steady-state concentrations of
point defects are determined by the disappearance of the point defects in sinks (in disloca-
tions, in the given case). If one of the conditions Tirr 1011 cm 2 even when the rate of formation of displaced atoms is K = 10-3
sec I. If the crystal is irradiated at Tirr > Tc(po, ?K), the steady-state vacancy concen-
tration (4) has the form
C(_)_ In (1/ro) K (14)
2n pD(-)
and depends significantly on the dislocation density.
The exponential temperature dependence of the parameter nDc(-)/CO(-) in formula (13) is
responsible for the peculiar temperature dependence Rc(T). If we introduce the temperature
T*, which is determined from the condition
TIDc(-)/C,(,-) -1, (15)
then it is easily seen that for Tirr > T* the function Rc(T) begins to increase sharply
with rising temperature and this should correspond to a rapid decrease in the rate of pore
nucleation. This allows the temperature T* to be identified with the high-temperature limit
of pore formation (swelling of crystals). Substituting formula (14) into Eq. (15), we get
T*- Eo+Em
1-'/rIDK 1n(d/ro)]
k In [2npD0
where Eo and Em are energies of vacancy formation agd migration and Do is the preexponen-
tial factor of the diffusion coefficient. When DoJ = 10-1 cm2/sec, K = 109 sec-1, and
21r/ln (Z/ro) "'1 the dislocation density decreases from po = 1012 CM -2 to p = 1010 CM -2 can
shift T* downward by more than 10%.
Thus, if the initial dislocation density in the crystal is too high (po >> ps),and
Tirr > T*(po), then the crystal should not swell. However, if T*(p) becomes smaller than
Tirr as p decreases during irradiation, the crystal should begin to swell. The time`neces-
sary for the dislocation density to decrease to the value determined from the condition
T* [p (t)] =T irr (17)
will be called the swelling delay time. This time can be determined directly from Eq. (10)
if on the left-hand side of the equation p is replaced by the solution of (17) with formula
(16). It should be pointed out that the value obtained for the delay time cannot be consi-
dered to be quantitatively accurate. For a more accurate quantitative description of the
processes under consideration it is necessary to know the value of An and the detailed
mechanism of evolution of the dislocation structure; this permits an accurate description
of the change in the dislocation density with time.
1.
H. Brager et al., in: Proceedings of International Conference on Radiation Effects
Breeder Reactor Structural Materials, Scottsdale, June 19-23 (1977), p. 727.
in
2.
F. Ham, J. Appl. Phys., 30, No. 6, 915 (1959).
3.
I. G. Margvelashvili and Z. K. Saralidze, "Influence of the elastic field of a disloca-
tion on the steady-state diffusion flows of point defects," Fiz. Tverd. Tela (Leningrad),
15, No. 9, 2665 (1973).
4. W. Wolfer and M. Ashkin, J. Appl. Phys., 47, No. 3, 791 (1976).
Declassified and Approved For Release 2013/02/20: CIA-RDP10-02196R000300070004-1
 5. Declassified and Approved For Release 2013/02/20: CIA-RDP10-02196R000300070004-1__stals,"
At. fnerg., 50, No. 1, 17 (1981).
6. J. Bardeen and C. Herring, in: Imperfections in Nearly Perfect Crystals, Wiley, New York
(1952), p. 261.
AUTOMATIC REMOTE MONITORING OF THE SEPARATION PROCESSES OF TRANSPLUTONIUM
ELEMENTS BY ION EXCHANGE
I.
V.
Tselishchev, N. S. Glushak,
A.
A.
Elesin, V. V. Krayukhina,
V.
M.
Nikolaev, V. V. Pevtsov,
N.
I.
Pushkarskii, and V. I. Shipilov
Ion-exchange processes are used to produce pure samples of transplutonium elements with
a high atomic number from irradiated accumulative reactor targets. The behavior of the ele-
ments to be separated in a production line must be carefully monitored because the separation
coefficient of these elements in such processes is low, the volumes of the solution with the
valuable products are small, and the requirements with respect to purification and yield are
high. The monitoring cannot be fully effected by laboratory analyses after taking samples
because the analyses take a long time and are laborious and the relative losses of the valu-
able products are high. Laboratory analyses must be necessarily supplemented by a continu-
ous remote monitoring on the producing line so that information on the development of the
processes can be rapidly obtained, optimal fractionation of the products can be performed
during the processes, and the number of laboratory analyses can be minimized.
In order to increase the amount of information on the behavior of the elements to be
separated in a production line, one employs monitoring systems with a set of detectors cor-
responding to the specific conditions of the process. For example, the authors of [1] have
described the use,of BP3, y-Ge(Li), and NaI detectors for monitoring the separation of
Cm, Am, Cf, and Eu by ion exchange processes. The detectors were mounted near a loop with
output to a semiservicing station of the production line, and the information obtained from
the detectors was processed in a computer.
The present work concerns an investigation of the possible use of immersed alpha, neu-
tron, and y-NaI detectors and of an information retrieving and processing system as
described in [2] for monitoring ion exchange processes in the separation of 253Es and 252Cf.
In the-process to be monitored, first Es and thereafter Cf are washed out and the separation
coefficient amounts to %,1.4. The required purification and yield of Es are attained by a
three-step refining of the initial mixture. The remote monitoring system must reliably de-
termine. the limits of the Es fraction and the beginning of the Cf washing-out. When the Cf
concentration is relatively high in the mixture to be separated, one employs in the first
stages of the process immersed alpha and neutron detectors for the monitoring and immersed
a- and y-NaI detectors in the last stage. Certain characteristic features of the nuclides
to be monitored are listed in Table 1 in terms of nuclear physics; the table includes the
parameters of the detectors employed.
An immersed n-silicon surface-barrier detector is employed for measuring the 233Es and
252Cf concentrations from the a-activaty [3]. The a-spectrum obtained with the aid of such
a detector from a mixture of those nuclides in a nitric acid solution is illustrated in
Fig. 1. The specific overall a-bulk activity of the solution is determined with a formula
of [4]: -
V - TIN, (1)
where y denotes the specific a-bulk activity (Bq/ml); n denotes the detector calibration
coefficient (Bq?sec/(m1?pulse)) determined in measurements of the a-activity of standard
solutions) and N (pulses per sec) denotes the repetition frequency of the pulses on the 20%
discrimination level. The relative concentration of the a-emitters is obtained with formulas
of [5] : -
Translated from AtomnayaEnergiya, Vol. 59, No. 4, pp. 277-280, October, 1985. Origi-
nal article submitted October 22, 1984.
838 0038-531X/85/5904-0838$09.50 @1986 Plenum Publishing Corporation
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 Declassified and Approved For Release 2013/02/20: CIA-RDP10-02196R000300070004-1
meters .. .... ...... .,..~~~,..,~ ~o~a
Immersion detector for alpha particles, area 10 mm2,
resolution 1.5o
Gamma-NaI detector,
25Y 25 mm resolution
870 (660 keV)
Neutron detector,
area 25 mm2
Nuclide
Specific.
a-
aparticle
ener v
Sensitivity
thre hold
Specific
activity (Bq/
Sensitivity
threshold
(p
/ml) f
Er~eF y (key)
of ttt2 main
Sensitivity
threshold -
Specific
activit
Sensitivity
threshold
s
activity
(ke '
(Pg1ml) for
Pg) of spon-
g
or
fissionfrag-
gamma
pines and of
(Pg/ml)for
y
(neutron/
(Pg/
ml) for
(Bq /Pg)
particles
taneous
fission
ments -
the x-ray
gamma
(sec, P g))
neutrons
radiation
radiation
forneutrons
252C1
1,9.107
6118
0,5.10-4
6,2.105
0,8.10-3
41; 97
1.10-4
2,3.106
0,4.10_1
253Es
9,3.108
6632
0,1.10-5
-
-
42; 77; 112
-
-
-
E
z 2000
97
4'1A
Fig. 1. a-Spectrum obtained for the
2S2Cf and 253Es mixture with an immer-
sion detector.
; K2 ~i
120 /'i0 160
channel
el - h1-hl+i;
h, nh (Co+Cik)I (Co -I- Cik)
h h
0 40 00 120. 160 200 24-0
Channel
Fig. 2. y-Spectra obtained with an NaI
detector; a) 160Tb and 2?3Es; b) 160Th,
233Es, and 252Cf; c) 252Cf; the numbers
at the peaks denote the energy values
(keV).
where h Z denotes the relative concentration of the Z-th a-emitter; nk, contents of the k-th
channel of the a-spectrum; and Co and C1, parameters of the linear dependence which describes
the distribution function of the number of a-particle over the energy; this dependence is ob-
tained with the least-square method for the spectral section from k1 to k2 (see Fig. 1). The
concentration K1 of the Z-th a-emitter is (expressed in pg/ml)
K1= ye1/a, (4)
where a denotes the specific a-activity (Bq/pg) of the nuclide; y, total specific a-bulk
activity (Bq/ml); and cZ, relative concentration of the Z-th alpha emitter in the solution.
Es and Cf were separately determined through their a-activity in the interval 0.1 < e1 < 0.9
when the results of the laboratory analysis coincided within the error limits.
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 Declassified and Approved For Release 2013/02/20: CIA-RDP10-02196R000300070004-1
H OMB-O7
DDB -01 ExM
control connecting
unrt circuits
BKI -01
Konsul -2110
Fig. 3. Structure of the monitoring system: 1) receiving vessel; 2) flow cell with
immersed alpha detector; 3) neutron shield made of polyethylene; 4) detector of fast
neutrons; 5) column; 6) shield of the chamber or box; 7) box for gamma samples;
8) lead shield; 9) 6931-17 NaI detector; BUS2-96) preamplifiers; BUS2-95 and BUS2-97)
amplifiers; VS1-VS3) voltage supplies; BSA2-95) discriminator; C2-95) counter; AC2-
95) amplitude converter; SCU-8) switch control unit; OMB-01) operational memory
block; DDB-01) data display block; BKI-01) timer; ExM) external memory of the 1530-17
type.
Additional information on the 252Cf concentration in the solution is obtained by record-.
ing fragments of spontaneous fission with the aid of an immersed alpha detector. The ampli-
tude of the pulses resulting from 252Cf fission fragments substantially exceeds (by about
one order of magnitude) the amplitude of the pulses generated by the a-particles; therefore,
by recording the fission fragments, the Cf concentration can be precisely determined, and
this is particularly important at high loads in the a-measuring channel (more than 10?
pulses per sec) when the resolution of the a-spectra is significantly reduced.
A fast-neutron sensor is used to measure the neutron flux from the 252Cf. The sensor
is a silicon surface barrier detector with an area of 25 mm2. A thin layer of a hydrogen-
containing material (lucite) was applied to the sensitive surface of this detector. Though
the sensitivity of such a detector is relatively low, one can obtain with this detector
useful information on the 252Cf concentration at various points of an ion-exchange unit.
A spectrometric 6931-17 NaI detector (25 x 25 mm) with a resolution of 8% for the 660-
keV.line is employed for recording the y-radiation of the nuclides to be separated. The
main contribution to the y-radiation of the solutions to be monitored is provided by 16oTb
which is the chemical analog of Es and which is washed out together with the latter. This
detail makes it possible to determine the relative 253 Es concentration of the solution from
the area of the "oTb photopeaks. at 200-300 keV (Fig. 2). The 252Cf concentration is
assessed from the-repetition frequency of the pulses resulting from the remaining part of
the spectrum and generated. by the y-radiation and from the neutron flux from 252Cf; this
part of the spectrum is determined by subtracting the contribution produced by 16oTb and
253Es from the total spectrum.
The structure of the monitoring system is systematically illustrated in Fig. 3. The
immersed a-sensor is mounted in flow cell of the production line inside a hot chamber
or hot box. The neutron sensor records the neutron flux at the output of the production
line or at another point of the unit (the dashed lines indicate the position of the detector
in the scanning of a column). The y detector is mounted near a production line loop
which. was extended into the service area. The information supplied by the sensors is pro-
cessed with an information-retrieving and processing system. The system under consideration
is distinguished from the previously described system of [2] by equipment with channels for
measuring the y-radiation (6931-17 detector, supply block VN3, and BUS2-95 amplifier)
and the neutron flux (neutron detector, BUS2-96 preamplifier, BUS2-97 amplifier, BSA2-95
discriminator, and supply block VS1).
The program for the operation of the monitoring system is designed for testing indivi-
dual units, calibrating the measuring channels, periodic connection of the sensors during
process monitoring, processing of the information arriving from the sensors, and outputing
of the results of the measurements on a printer or the screen of the data display unit. The
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 Declassified and Approved For Release 2013/02/20: CIA-RDP10-02196R000300070004-1
9o sa as 7u au .ru
Volume, ml
Fig. 4. Results of the monitoring of the separation
of 253Es from 252Cf : a) with the aid of immersed
a- and neutron detectors; b) with the aid of im-
mersed a and y detectors.
program and the initial data are inputted from magnetic tape or from the computer keyboard.
The results of measurements made with the a-sensor are outputted as concentration of
the nuclide (Bq/ml or pg/ml) on a printer, whereas the recordings of the fission fragments,
of the neutron flux, and of the y-radiation are outputted as pulse repetition frequency
(pulses per sec), which corresponds to the relative concentration of the elements to be
separated. The periodicity of the measurements depends upon the dynamics of the process
and is 100-300 sec. Each measurement has its particular number and time which corresponds
to the solution volume passed through. The results of the monitoring of the entire process
are recorded in an external memory and can be displayed on a screen of the data display unit
as curves of washing out; these results can be additionally processed (calculation of the
purification, extraction).
Figure 4a illustrates an example of remote monitoring on a line for separating 253Es
and 252Cf via the a activity, fission fragments, and the neutron flux. The a -monitoring
(curve 2) facilitates the determination of the front edge, the position of the maximum, and
the beginning of the drop of the curve of Es washing-out. The front edge of the Cf washing-
out curve is determined mainly from fission fragments (curve 4) and the neutron flux (curve
5), because at a high load in the a-measuring channel, it is hard to separately determine
252Cf on the 253Es background. The gently sloping front edge of curve 5 of monitoring the
252Cf concentration through neutrons can be explained by insufficient shielding from the
spurious neutron flux and by the low sensitivity of the neutron detector. Curves 1 and 3
reflect the change of the 25 'Es and 262Cf concentrations according to the laboratory analy-
sis data of individual samples. The results obtained with y-monitoring are shown in Fig. 4b.
In the particular case, the a-activity in the solution monitored results mainly from 239Es
(curve 2), and the total y activity (curve 1) is composed of the activity of 16OTb (curve
3) and the activity of 262Cf (curve 4). Curve 5 indicates the change in the-252Cf concentra-
tion according to laboratory measurements on individual samples in a neutron unit. It fol-
lows from the examples that the results of remote monitoring on a production line rather pre-
cisely describe the behavior of the elements to be separated and are close to the results of
laboratory analyses in a wide variability range of the concentrations,?as well as in cases of
various Es and Cf ratios in the initial mixtures. a- and y-monitoring are the basic monitor-
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 Declassified and Approved For Release 2013/02/20: CIA-RDP10-02196R000300070004-1
inb LLVI GO~Gp, WIIGLGQJ 5LLLL1L1V iLQl LILULLLLUL.LLLb' LLLVU.LVe5 LLSSLULL LLdrLIICLLLS aL1u neuLrons. The
sensitivity of the neutron detector can be increased by increasing the sensitive surface
area, and the background in the neutron channel can be reduced by employing appropriate
neutron shields.
It was therefore shown in the example of the separation of 25 3Es from 252Cf that when
immersed a-, neutron, and y - NaI detectors and an information-retrieval- and process-
ing system are used in the automatic remote monitoring of ion-exchange processes for the
separation of transplutonium elements with high atomic numbers, the elements to be separated
can be operationally observed in the production line during the process and an additional
processing of the results of the monitoring after termination of the monitoring is possible.
The information obtained is a necessary supplement to the analysis data of samples and helps
to reach optimal fractionation of the products with a minimum number of laboratory analyses.
When the set of detectors used becomes greater, the detector parameters are improved, and
the information retrieving and processing system reaches a faster response, ion exchange,
and extraction processes in the separation of transplutonium elements can be successfully
monitored in the case of a complicated nuclide composition of the solution treated while
requirements in regard to fast execution of the measurements and their accuracy are being
met.
1. M. Wakat and S. Peterson, Nucl. Technol., 17, 49 (1973).
2. V. A. Bikineev, N. S. Glushak, and V. V. Pevtsov, "An automatic system for monitoring
the production process of separating transplutonium elements," At. knerg.,,55, No. 3,
179 (1983).
3. V. V. Pevtsov, "An immersed alpha-spectrometry detector," Prob. Tekh. Eksp., 4, 78
(1976).
4. M. I. Krapivin, M. P. Malafeev, et al., "Immersed semiconductor detectors for the de-
termination of the specific alpha-activity of solutions," in: Reports of the First Sym-
posium of the SEV "Research in the Processing of Irradiated Fuel," Vol. 3, Atomic Energy
Commission of Czechoslovakia, Prague(1977), pp. 188-201.
5. E. A. Vznuzdaev and V. I. Orlov, "An analysis of alpha spectra of transuranium radio-
nuclides obtained from thick uniform sources," Prib. Tekh. Eksp., 1, 57 (1982).
DEPENDENCE OF THE MEAN VALUE AND FLUCTUATIONS OF THE ABSORBED ENERGY
ON THE SCINTILLATOR DIMENSIONS
F. M. Zav'yalkin and S. P. Osipov UDC 539.16
In [1, 2], it was shown that the level of signal fluctuations at a detector output
depends on the number of y ,quanta and the spread of their absorbed energy; the dependence
of the mean absorbed energy Eab and accumulation coefficient of the fluctuations E on the
radius of a cylindrical NaI(Tl) scintillator (thickness 7 cm) for 1.25-MeV y quanta was
described; and it was established that Emax = 3-4. In [3], the dependence of the amplitude-
distribution coefficient n = f on the radius of the cylindrical scintillator was investi-
gated for large values of the recording efficiency (0.5-0.9). A method of estimating the
maximum value of r1 as a function of the energy spectrum of the radiation incident on the
crystal was proposed, and analytical expressions were obtained. It was shown that n does
not exceed 1.2-1.4 for scintillators of different materials and monoenergetic sources and
for sources with a continuous spectrum cannot be larger than 1.5.
The presence of such contradictory and partial data and the need to know the dependence
of the mean absorbed energy Eab and accumulation coefficient of the fluctuations C on the
scintillator dimensions for designing scintillator detectors of the ionizing radiation
operating in the current-recording mode means that the above-noted dependences must be in-
vestigated. This problem takes on special importance in designing multichannel systems,
Translated from Atomnaya Energiya, Vol. 59, No. 4, pp. 281-283, October, 1985. Origi-
nal article submitted November 5, 1984.
0038-531X/85/5904-0842$09.50 ? 1986 Plenum Publishing Corporation
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 Declassified and Approved For Release 2013/02/20: CIA-RDP10-02196R000300070004-1
Fig. 1. Dependence of Eab on the radius of the cylin-
drical CsI scintillator at an energy of 1000 keV; 1) Z =
2.5 cm; 2) 5; 3) 10.
Fig. 2. Dependence of Eab on the radius for various en-
ergies and crystal materials when Z = 5 cm; 1) Eo = 250
keV; 2) 1000; 3) 1750; 4) 2500; 5) 1000, CdWO4; 6) Eo =
1000 keV, plastic.
multilayer detectors [4] for tomographical apparatus, and spectrometers based on deriving
the radiation spectrum [5] from the experimental absorbed-energy distribution.
In the present work, the mean absorbed energy and accumulation coefficient of fluctua-
tions for cylindrical scintillators.made.from.materials_covering the density and atomic-
number ranges employed (CdW041 CsI,. plastics), of radius a and length Z for a narrow photon
beam of energy Eo incident on the crystal along the cylinder axis is calculated. The accumu-
lation coefficient of the fluctuations is determined by the mean square deviation So of the
energy absorbed by the detector material E = 1 + S. Using the dispersion property of the
random quantity a'x = x' - x', it was found that E = Eab/Eab. No account is taken of elec-
tron leakage in the calculations. The interaction coefficients of y quanta with materials
are taken from [6). The Monte Carlo method is used in the calculations, taking account of
the recommendations made in the present work.
Typical curves of Eab as a function of the radius a of the cylindrical CsI scintillator
for various crystal lengths and Eo = 1000 keV. As is evident, with increase in scintillator
radius, the function Eab increases with increase in saturation from minimal Emin (the approx-
imation of a needle-shaped scintillator, a 0) to maximal Emax value of the absorbed energy
(a = ~) This is explained in that, beginning at some radius, y-quantum lekage through the.
front and rear surfaces of the scintillator will predominate over leakage through the side
surface; this effect is increased as the photons leaving through the side surface lose,a
larger proportion of their energy in the crystal than those leaving through the rear surface.
It follows from Fig. 1 that, when Z = 2.5 cm, saturation sets in more rapidly than
when Z = 5 cm and Z = 10 cm. Thus, the rate of absorbed-energy accumulation decreases with
increase in crystal length. This is explained by increase in the proportion of energy leak-
age through the side surface.
The dependence of the mean absorbed energy on the radius is also determined by E0 and
the scintillator material (Fig. 2). Comparison of curves 1-4 shows that the rate of accumu-
lation of Eab with increase in Eo at first decreases since there is a sharp decrease in the
proportion of the photoeffect, and then increases because forward-scattered photons predomi-
nate in the quantum leakage. In analyzing curves 2, 5, 6,_increase in density of the scint+
illator material with increase in rate of accumulation of Eab is established; this is asso-
ciated with increase in the influence of the photoeffect.
On the basis of analysis of the results obtained, it is possible to describe the depen-
dence of the mean energy absorbed in a crystal of radius a
Eab = Emtn+ (En,ax -Eniin) (1 -e-ga), (1)
where g is a coefficient depending on Eo, Z, and the crystal material; Emax, Emin are ex-
pressed in terms of Eo. The error with which Eq. (1) approximates the theoretical data is
no more than 1%.
The value of Emin is found [3] using the Klein-Nishina-Tamm formula
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C
C)
0"S
Fig. 3. Dependence of Emin on Eo;
1) CsI; 2) CdWO4i 3) plastic.
Fig. 4. Dependence of n on a for
the CsI crystal: 1) Eo = 250 keV;
Z = 2.5 cm; 2) 1000, 2.5; 3) 1000,
10; 4) 1750, 2.5.
TABLE 1. Coefficients t, bl, b2 for Var-
ious Scintillator Materials
Coefficient
Plastic CsI
CdWO4
t
0,51
0,85
0,75
b,
1,51
2,01
2,33
ba
0,25
0,61
0,73
E - F!pb Er,-1,02 ?b C r -20a4 {--102a3+ 186a2 + 102a + 18 - 2a +3-a2
m1n- ? E, t 2? L 3a (1+2a)3 a2
In (1+2a)], (2)
where E0 is the energy, MeV; u, linear attenuation coefficient of y radiation of energy E0
by the scintillator material uph, attenuation coefficient of the radiation as a result of
the photoeffect; Pb, attenuation coefficient of the radiation due to pair creation; a =
Eo/511; C, a coefficient proportional to the number of electrons per cm3 of the scintillator
material.
The dependence of Emin on E0 calculated from Eq. (2) for various crystal materials is
shown in Fig. 3. The minimal energy at first falls sharply with increase in E0. This is
because'of the sharp decrease in influence of the photoeffect in the range E0 = 0-5 MeV.
Then-Emin>increases slowly, since the proportion of energy lost in the crystal from the re-
corded quantum increases. For CdWO4, Emin is larger when E0 < 1 MeV than for CsI, on ac-
count of the large contribution of the photoeffect to the.total linear attenuation coeffi-
cient of the radiation. Beginning at E0 = 1 McV,'Emin is practically the same for CsI and
CdWO4,(0.5-1%). For plastic, Emin is less than for CsI and CdWO4, and the minimum is reachedl
earlier, which is explained by the absence of a photoeffect for E0 > 0.2 MeV.
The function-Emax depends on Eo as well as the length and the material of the scintilla-
tor. With increase in Z from 0 to infinity, Emax increases monotonically from Emin to 1.
With increase in Eo, the behavior of Emax is the same as that of Emin.
The dependence of Emax on the crystal length may be approximated with an error of 1.5-
3% by the expression
Emax = Emin + (1-Erufn) (1 (3)
Here'f is a coefficient depending on Eo; f = tu(Eo), where t depends on the scintillator
material (Table 1).
The coefficient g,(Eo, L) determines the rate of increase in Eab, its dependence on Eo
is qualitatively described above. For Z = 0, the function g = -; when Z tends to infinity
g tends to a constant value. The function g(Eo, Z) may be described by the formula
g (E0, l) = b)?+ ?. (4)
l
The values of the coefficients bl, b2 for various types of crystals are given in Table
1. The minimum values of Eab calculated by the Monte Carlo method and from Eq. (2) are in
good agreement; the deviation is no more than 0.7-1%.
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 Declassified and Approved For Release 2013/02/20: CIA-RDP10-02196R000300070004-1 _
io ring the mean accumulation _coefficient of the fluctuations of. absorbed energy, Eab
is calculated. The dependence of Eab on a, Z. Eo, and the type of crystal is completely
analogous to the dependence of Eab on a, Z, Eo, and the type of crystal. The dependence
of the accumulation rate of Eab and Eab on a is the same for each set of Z, Eo, i.e., the
dependence of Eab on a may be described by the formula
Fab Emiu+(Emax-Emin) (1(5)
2 2
ax are expressed in units of Eo. The limiting minimal value of the mean
where qin, Em
square absorbed energy is [3]
A h (Eo-1.02)Z?ab C r-68a55-{-184a4.4 566a3+494a2?180a-~-24, 2a-{-4--a2
Emin- ? + EoN a2 L 3 (1-d-2a )4 - a In (1-+ -2a)1 . (6)
The dependence of Emax on Eo and Z is written analogously to Eq. (3)
Lm2 2 2
ax =Emi,, -I- (1-Emin)(1-e-tu(E(j)1).
The values ofnin calculated by the Monte Carlo method and from Eq. (5) coincide with an
error of 0.7-1%.
The accumulation coefficient of the fluctuations may be determined from Eqs. (1) and
Amin-(Emax-Emin) (1-C-9a)
IEmin-t-(Emax -Emin) (1-a-ea))2
It was noted in [3] that the dependence n = /I is approximated by a linear function if
the scintillator the thickness is sufficiently large. As shown by the results of machine
calculations, this is not true for small thickness. Theoretical curves of n as a function
of the radius a of a cylindrical scintillator for different Z and different values of the
energy are shown in Fig. 4. At small crystal thickness, n does not depend on the radius;
when ph = 0.2-2, this dependence is significant on both the thickness and the crystal dia-
meter. At large scintillator thickness,,:n.is approximately the same. Since n decreases to
some value with increase in diameter, it is possible to approximate the dependence of n on
a by a formula analogous-to Eqs. (1) and (5); the rate of decrease of n is analogous to the
rate of accumulation of Eab and Eab, that is
T1=Amax- (Tlo-Amax) a ,>a (8)
where the coefficients g, nmax depend on Z, Eo, and the type of scintillator;no depends on
Eo and the type of scintillator. Equation (8) is more convenient than Eq. (7). The value-
of no is determined from Emin__and min- The dependence of nmax on Z may be ob;tained.from.
the dependences E max(Z) and Emax(Z)?
The results obtained are only valid for monoenergetic sources. The specific feature
of the use of a nonmonoenergetic source for radiometric measurements in the mean-current
recording mode is that n 4 1 for a total-absorption crystal. The values of Eab and Eab may
be found from the formulas from [3] and from Eqs. (l)-(6).
The value of n may be calculated for total-absorption crystals and sources with a dis-
crete spectrum. It is found that n is no greater than 1.07 (BeRa). It is not difficult to
estimate n for total-absorption crystals and x-ray sources. The Kramers energy spectrum
[7], disregarding the high-energy component, is
f(E) = 2(E,_- )
Li"L
where Eo is the maximum energy in the spectrum and
E, E,,
I Ef (E) dE, E?- J Elf (E) dE.
0 0
Then n = 1.5. If the high-energy component is taken into account, then
1.5 (Eo?4B) (Eo+2B)
h1 - 1/- (Eon-3B)2 '
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 whe_gleclassified and Approved For Release 2013/02/20: CIA-RDP10-02196R000300070004-1 _hat
n < 1.5. The theoretical values of the limiting n for Shiff bremsstrahlung spectra with
maximum energy Ec = 10-15 MeV according to the experimental data of [8] are in good agree-
ment (discrepancy no more than 3%) with the values obtained from Eq. (9). This is because
the physical nature of the bremsstrahlung radiation does not depend on E0, i.e., the Shiff
and Kramers spectra are adequate from a physical viewpoint.
Any barrier between the bremsstrahlung source and the detector hardens the spectrum and
hence decreases the accumulation coefficient of the fluctuations. In this case Eab and Eab
are determined from the formulas of [3] and from Eqs. (l)-(5).
Theoretical investigations and Monte Carlo calculations allow the dependence of the
absorbed energy and the accumulation coefficient of the fluctuations on the dimensions, type
of crystal, and radiation spectrum incident on the crystal to be estimated. The results ob-
tained may be used to estimate the expected signal and signal/noise deviations or to select
the minimal dimensions of the cylindrical scintillator on the basis of the required signal/
noise ratio. The results may also be used to establish the radiation spectrum from a known
absorbed-energy distribution over the radius or length of the cylindrical scintillator.
1. A. A. Maiorov, S. V. Mamikonyan, L. I. Kosarev, and V. T. Firstov, Radioisotopic Defecto-
scopy (Methods and Apparatus) [in Russian], Atomizdat, Moscow (1976).
2. V. I. Gorbunov et al., Radiometric Radiation-Monitoring Systems [in Russian], Atomizdat,
Moscow (1976).
3. F. M. Zav'yalkin, Yu. G. Zubkov, and S. P. Osipov, "Dependence of the signal/noise devia-
tion on the radius of a cylindrical scintillator," Defektoskopiya, No. 11, 56-59 (1984).
4. R. Alvarez and A. Macovski, "Energy-selective reconstructions in x-ray computerized tomo-
graphy," Phys. Med. Biol., 21, 733-744 (1976).
5. A. S. Kek, "Machine tomography using x-rays, radioactive isotopes, and ultrasound," Tr.
Inst. Inzh. Electrotekh. Radioelektron., 67, No. 9, 79-110 (1979).
6. Handbook on Radiational Protection for Engineers [in Russian], Vol. 1, Atomizdat, Moscow
(1972).
7. X-Ray Engineering [in Russian], Vol. 1, Mashinostroenie, Moscow (1980).
8. V. A. Vorob'ev, V. I. Gorbunov, et al., Betatrons in Defectoscopy [in Russian], Atomiz-
dat, Moscow (1973).
MEASUREMENT OF THE RATIO OF THE 296U AND 23 5U FISSION CROSS SECTIONS
IN THE.NEUTRON-ENERGY RANGE 0.34-7.4 MeV
B. I. Fursov, M. P. Klemyshev,
B. F. Samylin, G. N. Smirenkin,
and Yu. M. Turchin
The present work continues a cycle of measurements of the fission cross sections of
nuclides [1, 2] in the neutron-energy range that is most important for fast-reactor calcula-
tions by the method described in [1]. Neutrons were generated in T(p, n) and D(d, n) reac-
tions in solid targets from titanium hydride on copper substrates (En < 1 MeV) or scandium
hydride on molybdenum substrates while tritons and deuterons were accelerated in the electro-
static accelerators of the Physics and Power Engineering Institute, Obninsk. The energy
resolution, which depends on the target thickness and the solid angle in which the fission-
able layer was located, was AEn = ?30-40 keV in the region of the 236U fission threshold and
increased to ?100-200 keV for En < 3.8 MeV. A fissionable triuranium octaoxide (U3O8) layer
of diameter 10-15 mm and thickness 0.3-0.5 mg/cm2 was deposited onto thin (5 0.1 mm) sub-
strates of polished aluminum (Table 1). The fission fragments were detected by a double
ionization chamber. The efficiency of fission chambers for 235U and 236U was 98.3 and 98.8%,
respectively. We used B/A layers for measurements of the energy dependence of the 236U/235U
Translated from Atomnaya Energiya, Vol. 59, No. 4, pp. 284-287, October, 1985. Origi-
nal article submitted January 25, 1985.
846 0038-531X/85/5904-0846$09.50 C)1986 Plenum Publishing Corporation
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 Declassified and Approved For Release 2013/02/20: CIA-RDP10-02196R000300070004-1
1fUl,a: 1. 1JVLVp1\. VVIIIj)UOS L SV11 VL L'1JJ1V110V1G LY Yl.1G1, al.? 1.
Laver
Principal
isotope
234U
235U
236U
2381)
A
235U
0,0010
99,9955?0,0010
0,0035
0,0005
B
2i 6U
, Radm, where Radm is
the admissible value of the level of thermotechnical reliability. The functional J can be
taken, for example, as the average value Jo of the total power of the reactor.
At each time t the distributions p~(y1f .., ym, 01, ..., SZ) and pv(xl, ..., xm, N1,
..., OZ), are refined with the help of the observed vector n with the coordinates n1, ...,
nn, i.e., these distributions are conditional. Therefore-the conditional value t of the
level of thermotechnical reliability of Jy(t) and the conditional value of ~y(t) of the functional
J can be calculated at each time t. The problem of controlling the field lies in selecting
the values of the control parameters at each t such that Jy(t) assumes a maximum value, the
condition Ry(t) % Radm is satisfied, and other restrictions on S1, ..., OZ of a structural
or regulating character also hold. Thus the field is indirectly controlled from the vector
ob observations n correlated with it.
Variation of the control parameters involves a change in the observed values nl, ...,
nn, which affects Ry(t), Jy(t). Therefore, in order to make the correct choice of control
parameters the dependences of the observed values on R1, 01, obtained on the basis
of modeling of the physical properties of the reactor, must be known. Finding the condi-
tional distribution laws pC(yl, ..., ym, S1, ???, 01) pvy(xl, ???, xm, 01, ???, OZ) in the
general case is a laborious computational operation. For a normal joint distribution law
of all random quantities studied, the conditional distribution laws for V,t are also normal
[4]. The optimal linear estimates of the coordinates of the vectors V and t summarize all
information about these laws incorporated in n [5]. The optimal linear estimates of the
coordinates of the vectors V and ; are conditional mathematical expectations of these coor-
dinates, and the conditional covariational matrices of the vectors are independent of n [4].
Thus for the normal distribution law the most accurate monitoring of the field is an inter-
mediate operation for finding the conditional distribution laws of the vectors V and E and
correspondingly Ry(t) and Jy(t). The statistical interpolation, used for reconstructing the
energy-liberation field [2], is equivalent to searching for the conditional mathematical
expectation of random quantities.
Finding the optimal values of the control parameters, even under the conditions of a
normal distribution law is a laborious operation, because of the large dimensions of V and
. We shall therefore begin the analysis of the control efficiency with the analysis of
the admissible value of the observed energy liberation in one fuel channel of the reactor.
Let the control parameter at the beginning of the analysis be the mathematical expec-
tation u of energy liberation ET in the channel; in addition, CT and its critical value
ET?cr, are monitored with random errors ET and Ecr, respectively, so that the observed values
are equal to nT = ET + CT, nT?cr = ET?cr + Ecr. The observed values nT, nT.cr are assumed to
be arbitrary unbiased estimates of ~T' ~T?cr, obtained as a function of the vector of measure-
ments T. Under the assumption that the vector 0 with the coordinates ET, CT?cr, ET, Ecr is
distributed according to the normal law with a known covariation matrix k and known mathema-
tical expectations of the coordinates M[CT] = P, M[ET.cr] = Pcr, M[ET] = M[Ecr] = 0, the
vector 8 with the coordinates nT, nT.cr, VT = ~T?cr - ET, linearly related to AT , also has a
normal distribution law with known mathematical expectations M[nT] = u, M[nT.cr] = ucr,
M[VT] = Pcr - U and a known covariation matrix K, which can be calculated from the matrix K.
The conditional distribution law vT is the normal distribution with mathematical expec-
tation uvy and mean-square deviation avy, so that the level of thermotechnical reliability
for the channel is equal to
RT =4D(1vri/?vu), (1)
where ~D(u) is the distribution function of the normal distribution of a random quantity, hav-
ing unit variance and zero mathematical expectation. The unfolded form of the analytical
dependence of pvy, avy on the parameters of the distribution law of the vector 0 is pre-
sented, for example, in [6]:
2 _2 1_Pi-Pz-Ps {-2PlP2P3
6V V 1-P5
?vy - RCr - N'+aCr O1T,cr -ICr +XT(1T-P)'
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 Declassified and Approved For Release 2013/02/20: CIA-RDP10-02196R000300070004-1
v a - - "I "1
Pi=P[VT, flT.cr 1; P2-P[VT, rlTl; P3-_-P [1T.cr ,1T];
P[.,.1
is the symbol for the correlation coefficient; av, ccr? OT are the mean-square deviations
of the random quantities VT, nT?cr, nT?
The quantity Ay, by which pvy must be changed in order for the equality RAT = Radm,
to hold, is calculated according to the relation (1) from the equation
Radm = cn[(?vu+ Or)/wyl, (3)
where avy takes into account the possible change in the parameters of the distribution law
of the vector 0 accompanying a change in the control parameter p.
Under the assumption that when p varies the remaining parameters of the distribution
91
law of 0 remain unchanged and the quantity n
T = nT - p remains constant, from the expression
(2) we find that the change Ap in the parameter p, for which the condition (3) holds, is
equal to
A?=?cr-?-xavy+~cr (9T. cr -Ncr)+XT (21T-0,
where x = V1 (Radm) , and (D-1(u) is the function inverse to 4(u).
The constancy of nT is a model of the dependence of the observed value of nT on the
control parameter u, since nT = u + nT?
Using this model enables the calculation of the admissible observed value
"ict=?cr-xavy+7 cr ('lT.cr - ?cr)+ (1-1-21T) ;T-
Thus the admissible observed value of energy liberation depends on the observed values
nT.cr, nT.
Control consists of selecting a p at time t such that the observed value of energy
liberation would be equal to nadm' At the same time, as an analysis using a formula similar
to (2) shows, the equality M[~T1 = pcr - x cvy will be achieved. Thus the more accurately
VT, is monitored, the higher is the average value of energy liberation achieved with the
use of the observed values for generating the control actions. When the conditional mathe-
matical expectation of the quantity vT is used as the observed value, the admissible (lowest)
value is constant and equal to xay.
In practice the number Z of control parameters is less than the number m of fuel chan-
nels. For this reason, in the general case, it is impossible to satisfy the equality nT =
nadm for all channels simultaneously, and for an optimum choice S1, ..., SZ there exists an
admissible value nadmi. < nadmi for each channel with which the maximum of Jo is attained. If
it is impossible to calculate the optimal values of the control parameters, then they can
be determined by approximate methods, in particular, from operator experience. An approxi-
mate determination of 01j ..., OZ produces an additional lowering of the energy liberation
in each fuel channel by Si. The sum So = Yi6i determines the total power of the reactor and
i=1
serves as a characteristic of the method for selecting the control parameters (in particular,
operator experience), and lowering the mean-square monitoring error vi by navy enables in-
creasing Jo by a value close to
AJo=mxAcvy.
The critical values of the coordinates V are known exactly (they are equal to zero),
since the vector IF with the coordinates Ti = nadmi -nadmi -Si is actually thevector of regula-
tion errors [2]. The exact value of OJo can be obtained only by taking into account the
dependence of the errors in monitoring and regulation of V.
There is one other factor determining the desirability of using the procedure for re-
constructing the energy-liberation field. The parameters of the distribution law ET, for
example, the mathematical expectation p, may be unknown, but can be estimated from the col-
lection of observed values ni(i = 1, 2, ..., n) [2]. Focusing on the indications in each
fuel channel, it is possible to use the estimate uyi = ni of the conditional mathematical
expectation of p i; in addition the accuracy of uyi is characterized by the quantity coy =
where a' and
M((nT - py)2 ]. For example, for unknown ET, we have ~T, where co2 I2 y = a /c + C12'
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 a2 Declassified and Approved For Release 2013/02/20: CIA-RDP10-02196R000300070004-1
e -- -- --- --y ..- -,.., ate. Uu.?. w?en
1- A. ensuring the thermophysical reliability of the active zone of the reactor. The use of the
entire collection of observed values substantially increases the accuracy of estimates of
the unknown parameters of the distribution laws and correspondingly the accuracy of the
estimation of Ry.
LITERATURE CITED
1. I. Ya. Emel'yanov, A. I. Efanov, and L. V. Konstantinov, Scientific-Technical Founda-
tions of Nuclear-Reactor Control [in Russian], Energoizdat, Moscow (1981).
2. E. V. Filipchuk, P. T. Potapenko, and V. V. Postnikov, Control of the Neutron Field of
a Nuclear Reactor [in Russian], Energoizdt, Moscow (1981).
3. A. 0. Klemin, L. N. Polyanin, and M. M. Strigulin, Thermohydraulic Calculation and
Thermotechnical Reliability of Nuclear Reactors [in Russian], Atomizdat, Moscow (1980).
4. T. Anderson, Introduction to Multidimensional Statistical Analysis [Russian translation],
Fizmatgiz, Moscow (1963).
5. V. A. Vlasov and P. I. Popov, "Forecasting of the values of random quantities and esti-
mation of unknown parameters," in: Automation of the Control of Technological Processes
[in Russian], No. 2, Atomizdat, Moscow (1977), pp. 69-72.
6. V. A. Vlasov and P. I. Popov, "Peculiarities of estimation from dependent random values,"
ibid., pp. 72-76.
MONTE CARLO CALCULATION OF THE FIELD GRADIENT OF Y RAYS
M. P. Panin UDC 519.283
The radiation field behind a shield of complex geometric form is distinguished by con-
siderable spatial inhomogeneity. In connection with this, it is of interest, in investigat-
ing the field, to determine not only the functionals of the field but also their deriva-
tives. In the present work, an algorithm is proposed for the direct calculation of the
gradients of the photon flux density, the energy flux, and the photon radiation dose by the
Monte Carlo method.
To estimate the gradient of the y-ray flux density at the point of detection r*, use
is made of the well-known local estimate [1] for a point detector Fi(ri,r *, p) depending
on the point of-collis-ion ri and the corresponding cosine of the scattering angle ii. If
the flux density ' is the mathematical expectation of this estimate, its gradient will be
Differentiating the local estimate Fi with respect to the spatial variable r*, an explicit
expression for OFi in terms of the differential scattering cross section as(p) and the opti-
cal thickness T between the points ri and r* is obtained
I r"`-r[ vas (?)
~` `-F` L-2 Jr*-rile ? as (Ft)
For the second term in this formula, it is found that
t_a3 40 V t das D-?w (3)
as (?) (Y. (ii) d? ' ~? it*-ri l '
where 9 is the direction of photon motion before collision; to is the direction to the detec-
tor r* from point ri. Using the Compton model of scattering, it may be shown that
1 da, _ 3E'2+E2+2EE' (u-1)?2~tE' (4)
ds du E'-I-Ez(1-?)-I-E?2
Here and below, E and E' are the photon energies before and after scattering, expressed in
units of moc2.
Translated from Atomnaya Energiya, Vol. 59, No. 4, pp. 301-302, October, 1985. Original
article submitted February 1, 1985.
874 0038-531X/85/5904.-0874$09.50 ? 1986 Plenum Publishing Corporation
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 Declassified and Approved For Release 2013/02/20: CIA-RDP10-02196R000300070004-1
NI "I I wlalyi
Fig. 1. Diagram for determining the direction of
the vector Vpj.
2,0
a 1 2 3 4 Z' CM
Fig. 2. Dependence of the photon flux density (a)
and z projection of the gradient of the photon flux
density (b) on the distance to the barrier surface.
Displacement of the detector D along the X axis by
4 cm; source energy S = 0.1 MeV. The filled circles
correspond to results of calculation by the Monte
.Carlo method and the crosses to. estimates of the
derivative by the quadratic approximation; the line
segments show the value of Vz~P.
Now consider the calculation of VT. Suppose that the optical thickness is formed by
the sum of n zones, each of which has the length Zj and the cross section ai for energy E'.
Then
`
~i- a)Vli+~ ljVa)~. (5)
7=1 7=1
The first term in this formula is transformed to a form more expedient for calculationby
expressing the length Z. in terms of the distance pj from the point of collision ri to the
point of intersection of the zone boundaries of the photon trajectory Zj = pj - pj_1. The
result obtained is -
n n-1
' anm, (6)
i=1 i=1
where the summation is taken over the intersecting zone boundaries. To calculate this sum,
it is necessary to determine not only the distance pj for each point of intersection but
also the vector normal Ni of the zone boundary at these points in constructing the estimate
in the detector.
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 Declassified and Approved For Release 2013/02/20: CIA-RDP10-02196R000300070004-1
.,??.,.,..--?b -1 r- - ??ii--L .,i Luc LAULL1L J. LLUm Lue cvnulLlon nj = INj > U, the
orthonormalized triad of vectors o lalgi is constructed at the point of intersection of the
j-th boundary (Fig. 1)., as follows
a=[oNil/I [oNilI, gi=foal/I foal I. (7)
Since the vector a belongs to plane r, which is tangential to the zone boundary and perpen-
dicular to to, small displacements of the detector position along this vector do not change
the distance pj. Displacement along to also does not change pj. Then Vpj coincides in
direction with the vector
The expression within the summation sign in Eq. (6) may now be completely determined since
VPi=Pil/1-Xi/?iIr*-riI? (9)
To calculate Va' in Eq. (5), the following relation is used
Va 7- (E') D?
? (10)
together with Eq. (3) for the. gradient of the cosine of the scattering angle. The value of
da/du as a function of the energy is calculated in advance on the basis of the constants of
[2] and tabulated.
Analogously to the estimate in Eq. (2) for the gradient of the photon flux density, the
estimate is constructed for the gradient of the photon energy flux density VTi, and also
the gradient of the photon-radiation dose VDi, taking into account that
VI;, =E'VF1-FiE'2V[,
VDi= IiVlidcra/d? [ Ua~Ii? (11)
Here the calculation of the dose gradient requires tabulation of the derivatives of the
energy absorption cross section daa/dp.
Note, however, that the use of estimates in the form in Eqs. (2) and (11) is limited to
the case when the detector is outside the scatterer, on account of the singularity of type
In r of the first term in the square brackets in Eq. (2).
As an illustration of the use of this algorithm, the results of calculating the flux
density 0 of the scattered photon radiation and the corresponding gradient VQ+ beyond an
infinite plane two-layer barrier (aluminum and carbon; each layer is of thickness 0.5 d.s.p.
with respect_to..the.normal) are. shown in Fig. 2. The energy-of apoint semiisotropic source of unit power at the barrier surface is 0.1 MeV. In Fig. 2a, an inclined line segment shows
the projection of the gradient on the Z axis VZO calculated from the given algorithm for
each value of O(z). The quantitative reliability criterion of these results may be taken to
be coincidence of the theoretical values of VZO with H /3z, estimated from the set of points
of 4)(z). obtained. This comparison is shown in Fig. 2b, where the approximate values of the
derivative are obtained by plotting an approximating quadratic polynomial from three adjacent
points. It is evident that both results coincide satisfactorily within the limits of statis-
tical error of the calculation, and this confirms the effectiveness of the algorithm.
Including a calculation procedure for the gradient VO in the program increases the cal-
culation time by approximately 30-35%. The relative statistical errors for VO are higher
than for 0, as a rule, and this difference increases as the detection point approaches the
scatterer (barrier).
1. M. Kalos, "On the estimation of flux at a point by Monte Carlo," Nucl. Sci. Eng., 16,
111-117 (1963).
2.. E. Storm and H. Israel, "Photon cross sections from 1 keV to 100 MeV for elements Z =
1 to Z = 100," Nucl. Data Tables, A7, 565-681 (1970).
876
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CHANGING
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M
%j
eir
ap"
j
0 IN
0111 WIN
10, WN 1,
'40~011010 _~Ioll_ VMS-
P, g'
A"", rdl
i
asp
0 40p,
All
10
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