SOVIET ATOMIC ENERGY VOL. 49, NO. 2

• Document Type: CREST
• Collection: General CIA Records
• Document Number (FOIA) /ESDN (CREST): CIA-RDP10-02196R000800040002-1
• Release Decision: RIFPUB
• Original Classification: K
• Document Page Count: 103
• Document Creation Date: December 23, 2016
• Document Release Date: February 14, 2013
• Sequence Number: 2
• Publication Date: August 1, 1980
• Content Type: REPORT

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Russian Original Vol. 49, No. 2, August, 1980
February, 1981
SATEAZ 49(2) 505-602 (1980)
SOVIET
? ATOMIC
ENERGY
rc
ATOMHAfl 3HEP1-14f1
(ATOMNAYA ENERGIYA)
TRANSLATED FROM RUSSIAN
CONSULTANTS BUREAU, NEW YORK
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- ,
SOVIET , Soviet Atomic Energy is a translation of Atomnaya Energiya, a
publication of the Academy of Sciences of the USSR.
,
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ATOMICf
tmakes available both advance copies of the Russian journal and
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the necessary time, lag between publication of the original and
ENERGY publication of the translation and helps to improve the quality
of the latter. The translation, began with the first issue of the
, 1 , ,
ROssian journal. '
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Soviet Atomic Energy is abstracted or in-
dexed in Chemical Abstracts, Chemical
Tit/s, Pollution Abstracts, Science Re-
search' , Abstracts, Parts A and B, 'Safety
Science Abstracts Journal, Current Con-
tents, Energy Research Abstracts, and
Engineering Index,
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' Editorial Board of Atomnaya Energiya:
Editor: 0. D. Kazachkovskii
Associate Editors: N. A. Vlasov and N. N. Ponomarev-Stepnoi
Secretary: A. I. Artemov ?
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V. F: Kalinin A. S. Nikiforov
? P. L. Kirillov A. S.Shtan'
. Yu. I. Koryakin , B. A. Sidorenko
- A. K. Krasin M. F. Troyanov
? E. V. Kulov E. I. Vorob'ev
B. N. Laskorin
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SOVIET ATOMIC ENERGY
A translation of Atomnaya energiya
February, 1981
Volume 49, Number 2 August, 1980
CONTENTS
Engl./Russ.
Nuclear Power Installation and Main Lines of Scientific and Technical
Progress ? M. Drahny and J. Svetlik 505 75
Sensitivity of Characteristics of Hybrid Reactor to Spectra
of Secondary Neutrons ? D. V. Markovskii and G. E. Shatalov 509 79
Characteristics of Flow Rate-Limiting Inserts in Modeling Emergency
Loss of Integrity of a Reactor Loop ? L. K. Tikhonenko, E. K. Karasev,
S. Z. Lutovinov, B. A. Gabarev, and E. I. Trubkin 516 83
Determination of Some Characteristics of Spent Fuel of Boiling-Water
Reactors Using a and y Spectrometry ? A. G. Zalenkov,
S. V. Pirozhkov, Yu. F. Rodionov, and I. K. Shvetsov ,520 86
Determination of Low Contents of Elements from Vanadium to Molybdenum
by an X-Ray Fluorescent Method Using a New Variant of Standardization
? A. G. Belov, V. Ya. Vyropaev, N. Sodnom, B. Dalkhsuren,
Sh. Gerbish, P. Zuzaan, and S. Davaa 525 91
Spectrophotometric Study of the Equilibrium of the Reaction
Pu4+ + Cl- Pu3+ + 1/2C12 in Molten NaCl-2CsC1 ? S. K. Vavilov,
G. N. Kazantsev, and V. V. Gushchin 530 94
Determination of the Coefficients of Separation of Boron Isotopes
in the Distillation of BC13 in the Temperature Range 278-438?K
? A. S. Aloev, V. A. Kaminskii, A. G. Kudziev, and R. Sh. Metreveli 536 98
Possibilities of Proton-Activation Analysis for Determining the Content
of Elements from Short-Lived Radionuclides ? V. A. Muminov,
S. Mukhammedov, and A. Vasidov 540 101
Spatial Distribution and Balance of 3H and 137Cs in the Black Sea in 1977
? S. M. Vakulovskii, I. Yu. Katrich, Yu. V. Krasnopevtsev,
A. I. Nikitin, V. B. Chumichev, and V. N. Shkuro 545 105
Use of Personnel Neutron Film Monitoring to Determine Equivalent Radiation
Dose behind Proton Accelerator Shielding E. K. Gel'fand,
M. M. Komochkov, B. V. Mantko, M. M. Salatskaya,
and B. S. Sychev 550 108
Experimental Simulation of Recuperator for Negative-Ion Injectors
? S. K. Dimitrov, A. V. Makhin, S. V. Turkulets 556 113
Measurement of Total Neutron Cross sections of 163Yb and 169Yb
? V. A. Anufriev, S. I. Babich, A. G. Kolesov, V. N. Nefedov,
and V. A. Poruchikov 560 116
LETTERS
Choice of Optimal Conditions of Experiment to Find Stopping Power
of a Substance by Streaming of Radiation through Absorbers
of Any Arbitrary Thickness ? G. N. Potetyunko 564 119
Criterion of Ignition and Reserve at Ignition for Thermonuclear Targets
? Yu. S. Bakhrameev, V. N. Mokhov, and N. A. Popov 567 121
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CONTENTS
(continued)
Engl./Russ.
Nondestructive Method for the Control of Nonirradiated Nuclear Reactor
Fuel Using a Pulsed Neutron Source -- S. B. ShikhOv, V. L. Romodanov,
V. G. Nikolaev, V. A. Luppov, and D. F. Rau 570 122
Study of the Field of Secondary Radiation beyond Lead Absorbers
Irradiated by 640-MeV Protons ? A. Ya. Serov, B. S. Sychev,
S. I. Ushakov, and E. P. Cherevatenko 572 123
Field Emission Microscope Study of Radiation Damage in Tungsten
Caused by 252Cf Fission Fragments ? V. M. Aleksandrov,
I. A. Baranov, R. I. Garber, Zh. I. Dranova, A. S. Krivokhvatskii,
I. M. Mikhailovskii, and. V. V. Obnorskii 574 124
Calculation of the Pertubation of Functionals of the Flow of Neutrons
by a Direct Monte Carlo Method Using Correlated Samples
? V. D. Kazaritskii 578 126
Influence of a Small Chang,e. of the Form of a Reactor on Its Criticality
? Yu. V. Petrov, and E. G. Sakhnovskii 580 127
Electrical Conductivity of Binary Alloys of Thorium Tetrafluoride
with Lithium and Sodium Fluorides ? V. N. Desyatnik,
A. P. Koverda, N. N. Kurbatov, and V. V. Bystrov 583 129
Effect of Heat Treatment on Blistering of Ts1-6 Molybdenum Alloy
? D. M. Skorov, M. I. Guseva, B. A. Kahn, and V. L. Yakushin 585 130
Blistering of Materials under Cyclical Bombardment with Ions
in a Wide Spectrum of Angles of Incidence ? B. A. Kahn,
? S. N. Korshunov, D. M. Skorov, and V. L. Yakhushin 587 132
Experience in the Operation of the Kola Nuclear Power Station
at Increased Power ? A. P. Volkov, B. A. Trofimov,
Yu. I. Savchuk, V. V. Zverkov, E. I. Ignatenko,
and A. N. Litvinov 590 134
Colorimetric y-Ray Dosimeter ? I. Kh. AbdukddyroVa 593 135
Effect of Heat-Conducting Properties of Spacers on Current?Voltage
Characteristics and Temperature Fields of Thermionic
Fuel Cells ? N. M. Rozhkova and V. V. Sinyavskii 595 137
Allowance for Induced Activity of Structural Materials of Borehole
Neutron Generators to Ensure Radiation Safety ? D. F. Bespalov,
A. A. Dylyuk, and Yu. V. Seredin 598 139
The Russian press date (podpisano k pechati) of this issue was 7/21/1980.
Publication therefore did not occur prior to this date, but must be assumed
to have taken place reasonably soon thereafter.
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NUCLEAR POWER INSTALLATION AND MAIN LINES OF SCIENTIFIC AND TECHNICAL PROGRESS
M. Drahniand J. Svetlik* UDC 621.039.003.2
A national nuclear power installation (NPI) is a complex entity of an inerindustry
nature, which incorporates, inaddition to nuclear power engineering itself, an array of
facilities which ensure and directly affect the development and operation of nuclear power.
The structure of the nuclear power installation has the following subsystems [1].
1. Atomic power, plant subsystem (APPS) ? a set of nuclear power plants and nuclear
facilities that is a component part of the electric power system (EPS) and of systems of
centralized heat supply (SCHS).
2. Nuclear fuel subsystem (NFS) ? a set of units for extraction, processing, and en-
richment of nuclear fuel, production of fuel elements, processing of these elements after
irradiation, and transportation and storage of radioactive waste. The APPS and NFS are inti-
mately linked and comprise the nuclear power engineering system (NPES) [2].
3. Nuclear power machinery subsystem (NPMS), incorporating the metallurgical, machine-
building, and instrument-manufacture base of nuclear power.
4. Nuclear power construction subsystem (NPCS), incorporating facilities for con-
struction of APPS and NFS.
5. A management system for ensuring proportional development and operation of NPI as
a whole and coordinating its internal and external and interbranch and international link-
ages. It is intended for the development of nuclear power policy as a component of the en-
ergy, technological, and economic policy of a country, including international relations;
for internal control of nuclear materials, nuclear safety, and protection of the environment
and for creating rules for legal norms and information in the nuclear power field.
Figure 1 shows the system of material linkages of NPI, while Fig. 2 shows the system
of information linkages.
Integrated Nuclear Power Installation
The nuclear power installation of a given country can be regarded as a subsystem of
the integrated nuclear power installation (INPI) of the COMECON countries [3]. International
cooperation, division of labor, specialization, joint construction or collaboration in cap-
ital investment within the framework of INPI facilitates effective solution of problems
whose solution by one country would be difficult or impossible.
The aim of the INPI is to provide the COMECON member with power from nuclear resources
(disregarding export to third countries). The material linkages are complex and interde-
pendent in this case. Therefore, it is necessary to coordinate them effectively so as to
manage the entire system with a view to long-term and short-term predictions.
The tasks of the nuclear power installation in the production and eocnomic sphere
can be divided into two groups: material (technological) and socio-economic.
The first group includes construction and operation of nuclear power facilities, nu-
clear machinery and nuclear construction facilities (plants); construction, production; and
delivery, including assembly; and import and export of nuclear power equipment, as well as
construction of research facilities, laboratories, and experimental test sites.
The second group encompasses managerial activity, aimed primarily at the fulfillment
of economic plans, and also bilaterial and multilateral collaboration. Multilateral collab-
oration in the production and economic sphere within the framework of COMECON is based on
long-term programs and plans for the individival agencies of COMECON ? the Committee on
*Deceased.
Czechoslovak Commission on Atomic Energy. Translated from Atomnaya inergiya, Vol. 49,
No. 2, pp. 75-78, August, 1980. Original article submitted November 27, 1978; revision sub-
mitted November 12, 1979.
0038-531X/80/4902- 0505$07.50 ? 1981 Plenum Publishing Corporation
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Power infra-
structure
EPS and SCHS
Export of
nuclear fuel
Export of nuclear
power equipment
APPS
NPI
Active and inactive waste
Effluent
Transport
Work force
Acquisition of property for ,
construction
Raw materials and semifinished
products for manufacture of nuclear
Extraction
Import of
Import of
power equipment
of nuclear fuel
nuclear fuel
nuclear power
equipment
Fig. 1. External material linkages of NPI.
Agencies of
m emational
collaboration
Higher govern-
mental
agencies
Czechoslovakl
Atomic enery
Commission
pranch
ministries
NPI
Territorial
governmental
agencies
Fig. 2. External information linkages
of NPI (using the Czechoslovak NPI as an
example).
Collaboration in Planning, the Committee on Scientific and Technical Collaboration, the
Permanent Commission on the Peaceful Use of Atomic Energy, the Permanent Commission on Elec-
tric Power, the Permanent Commission on Machine Building, and others. International agencies
(Interatomdhergo, Interatominstrument) have been created in some branches of industry for
industrial and economic collaboration.
The problems of NPI in the fields of science and engineering include the conducting of
research and preparation of design data for use in the production and economic sphere,
specifically:
? basic data for the development of long-term and ordinary plants;
? data for design, construction, and operation of nuclear power facilities;
? information for construction of metallurgical, machine-building, and construction
of metallurgical, machine-building, and construction capabilities, and also experimental
and research installations.
506
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Other problems
6 Work force/ personnel
5 Environmental protection
4 Nuclear safety
3 Development of control systems
2 Economics
1 Technology
0 Ge neral problems
General problems
APPS
of NPI
NFS
General
NPMS
problems
NPCS
Construction of
nuclear power plants
(NPP)
Operation of NFS
industries
Construction of
NPMS industries
Creation NPCS
facilities
Operation of nuclear
power plants
Operation of NFS
industries
Manufacture, delivery
and assembly of NPP
equipment
Construction of
NPES elements
Fig. 3. Division of system of MLR into problems and tasks.
It is best to generate the spectrum of research topics by constructing a system of
major lines of research (MLR). This system makes it possible to create and assure the fol-
lowing:
? coordination with respect to activities and time of scientific problems with problems
with problems in the production and economic sector;
? similar coordination among scientific and technical problems on the national and
international levels;
? the entire array of problems which,must be solved in accordance with their degree
of urgency or priority (elimination of so-calledblank spots or "holes");
? coordinated use of all available capabilities, interaction among all concerned
parties, and elimination of undesirable duplication;
? monitoring and evaluation of progress;
? effective utilization of achieved results.
It is best to divide the system of MLR into subsystems and hierarchical levels of NPI
and into certain functional structures corresponding to the following specific areas (Fig.
3): general problems; technology; economics; development of control systems;. nuclear safety;
environmental protection; personnel; other problems. Of course, this division is not def-
initive, and can be supplemented or normalized as needed for appropriate control or orienta-
tion. It is necessary to point out that not all MLR have the same importance or scale.
With regard to problems of nuclear power installations and their subsystems, the aim
of the main research lines is to develop a project for the program of development and opera-
tion of NPI. The project is the basis for the preparation of the five-year development plan
for NPI in the production and economic sphere and in science and engineering, and also for
preparation of a program of collaboration among COMECON member nations in the area of NPI for
507
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for the development of a five-year plan for the agencies of COMECON and international eco-
nomic entities.
This concerns primarily the development of predictions and structural and optimization
solutions for the developmemt and operation of NPI, on the basis of the requirements of EPS
and SCHs for power and energy production through nuclear sources. Naturally, these require-
ments are keyed to the capabilities of the national economies of the individual countries
and to the capabilities and requirements of international collaboration, with appropriate
observance of the conditions and restrictions on the part of the environment (territory,
effluent water, transport, personnel, demographics, etc.).
The input information and data for free processing within the framework of the MLR
can be obtained from the production and economic sphere of NPI, and also through solution of
other specific problems, e.g., the part played by particular types of power reactors, eco-
nomic impact and mathematical modeling, control systems (including ACS), systems issues of
nuclear safety and protection of the environment, personnel problems, the expansion of the
reseaLch and development base, etc.
Tne specific problems of MLR also include (to the appropriate extent in all subsystems),
e.g., problems of choosing technical and economic parameters ana operating figures for equip-
ment fornuclear power plants which reactors of given types, problems of economics control
systems, nuclear safety, protection of the environment, and personnel for power-generating
and other nuclear installations.
Conclusions
Nuclear power installations in both their national and COMECON-integrated forms al-
ready exist and will develop rapidly in conformity with the energy requirements for the
COMECON member-nations. The process of development and operation of the nuclear power in-
stallation is complex and intractable. It requires heretofore unimagined expenditures of
material and intellectual effort and resources, and yet the capabilities for increasing
these is limited. The problem is to better utilize them and to manage all processes with
maximum efficiency. This requires that scientifically well-grounded and comprehensive data
be systematically developed and made available.
In this paper we have stressed the general (systems) concept of an aggregate nuclear-
power economy. The systems and organizational approach that we have described, however,
makes it possible to take account of specific features and interrelationships by means of
functional structures that can be defined where needed. The concept of nuclear power instal-
lation, with its subsystems, hierarchical levels, and functional structures, is sometimes
regarded as inconsistent with the concept of so-called programmed-goal structures, whose
effectiveness has been confirmed by practice.
A nuclear power installation is "all-encompassing," incorporating both the production
and economic and the scientific and technical spheres, and, by means of the MLR system, it
can be treated as a systems entity. Programmed-goal structures include only problems that
must be solved to attain a certain goal. A nuclear power installation is "unique" but it
passes through various phases of development. Programmed-goal structures are of a one-shot
nature; there can be many of them (e.g., development of the VVER-l000 reactor, creation of
atomic thermal power centers, the breeder reactor development program, creation of a train-
ing center for nuclear power plant personnel), and they differ quantitatively and qualita-
tively.
As a result of its complexity and large resource consumption, a nuclear power installa-
tion is inflexible and slow to respond. Programmed-goal structures do not contain "excesses"
and lead to the goal in the shortest possible way. However, the simplest approach (i.e.,
programmed-goal structure) can be found only if there is a clear conception of the linkages
and structure of the entire nuclear-power installation. Programmed-goal structures can be
defined as some functional structure of NPI which makes it possible to evaluate how realistic
the goal is, its interrelationship with other programmed-goal structures, and also to intro-
duce order, preference., and proportionality.
Specific activity is carried out and local effects attained within the framework of
programmed-goal structures. Within the framework of a nuclear power installation, the cap-
ability is created for implementing individual programmed-goal structures. Nuclear power
508
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installations and programmed-goal structures are not mutually exclusive alternatives; they
complement one another and form a coexisting unity.
LITERATURE CITED
1.
M.
DrahnY, Yad.
Energ., 24, No. 9, 327 (1978).
2.
M.
DrahnY, Yad.
Energ., 23, No. 11, 403 (1977).
3.
M.
Drahn3C and J.
Svetlik, "Nuclear power engineering and the nuclear power installation
of
the COMECON member-nations," Conference of Specialists of COMECON Member-Nations
on Criteria and Initial Data for Predicting the Development of Nuclear Power and
Allowance for Heat Supply, Interaction with the Environment, and the Use of Math-
ematical Models, Moscow, Dec. 5-8, 1977.
SENSITIVITY OF CHARACTERISTICS OF HYBRID REACTOR TO SPECTRA
OF SECONDARY NEUTRONS
D. V. Markovskii and G. E. Shatalov UDC 621.039.51:539.125.52
The study of the relation between the errors of nuclear data and the results of calcu-
lations of the neutron-physical characteristics of various models is of considerable inter-
est from the point of view of estimating the indeterminacy of the parameters of systems being
designed and the strategy of nuclear data refinement. This problem was worked on intensively
for fast reactors [1-3].
In order to estimate the error due to the nuclear data it is necessary to have the
coefficients of the sensitivity of the functionals under consideration to the varied data
as well as the matrix of the errors of those data. Information about the errors comes into
being at the stage of estimation of the nuclear data. In order to obtain the sensitivity
coefficients special calculations must be performed with a view to determining the types of
systems, materials, and data.
The greatest error of neutron data in reactor blanket calculations correspond to the
range 0.1-15 MeV, which has been investigated less than has the low-energy range so impor-
tant for fission reactors. Not only a detailed description of the cross sections but also
data on the scattering anisotropy, spectra, and yields of secondary neutrons from inelastic
processes are essential here. In sensitivity calculations all of these parameters can, in
principle, vary. The largest number of papers has been devoted to the study of sensitivity
to cross sections [4-6].
The sensitivity, to the spectra of secondary neutrons for the model of a "pure" thermo-
nuclear reactor (without fissionable material) was considered in [6-8]. In the present paper
we study the sensitivity of the fission rate, the fission source, and the tritium yield in
the blanket of a hybrid reactor to the perturbations of the spectra of secondary neutrons
from the reactions 238U(n, 2n), 236U(n, 3n), and Fe(n,.2n) as well as the spectra of inelas-
tically scattered neutrons with excitation of a continuum of levels of 236U(n, n') cont and
Fe(n, n') cont. In the calculations we used estimated neutron data from the ENDL library
[9] in the range 0.1-14.1 MeV and a 21-group system of constants 110] below 0.1 MeV.
Method of Calculation
Neutron Transport Equation. The space-energy distribution of the neutron flux in the
problem with an external source satisfies the equation
t (x)== IN (x) S (x),
where fi is the transport operator; Ip(x), neutron flux at the phase coordinate x = (r, E);
and S(x), flux of unscattered neutrons from the external source. Writing the solution as a
series expansion in the generations of neutrons
(1)
Translated from Atomnaya Energiya, Vol. 49, No. 2, pp. 79-83, August, 1980. Original
article submitted June 4, 1979.
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(2)
and writing H as the sum of the operators 11 .(describing the neutron transport) and f (de-
scribing the source of fission neutrons), we get
(x) = ip (x) i=2 (x), (3)
where
11),(x) =4 (x) s (x);
ijj (x) (x), i >1.
Equation (5) for fission neutrons can be solved quite exactly by the method of spherical har-
monics in the P1 approximation with 21-group constants [10]. In order to tind the neutron
flux tp2 from an external source in the high-energy range it is necessary to employ more
exact approximations. In the present paper we use the Monte Carlo method with a detailed
system of constants at high energies and the P1 approximation below some limiting energy
(Eli, = 0.1 MeV). Then
(4)
(5)
11?i (x) = (x) -1- 11);2) (x);
(x) =-1111,11) (X) S (x);
1V12) (X) = 1;211)1" (X) +1i1211)1 (x),
where h1 and h2 are operators describing the neutron transport in the energy intervals (14.1
MeV, Eli?) and (Elim, Et) and h12 specifies the source of neutrons slowed down below and
energy of Elim.
For convenience we write
(PI (x)=1);1' (x);
(P2 (X) = 1)(12) .(x),
i
and recast Eq. (1) in the form
(P, (x)=122(P2(x)+ fiTi (x)+ i2T2 (x) + hi2T1 (x),
where the neutron fluxes c22(x) and q2(x) can be calculated in various approximations by us-
ing different libararies of nuclear data.
To find (pi in the energy range above Eli, we solved the exact equation of neutron
transport by the Monte Carlo method. The constants for this energy range were prepared with
the aid of the NEDAM program [11] from constants contained in the files of estimated data.
Nuclei of scattering on elements are continuous functions of the scattering angle and the
neutron energy before and after scattering while the probabilities of the processes are
piecewise-continuous with respect to neutron energy up to collision. The neutron flux com-
ponent (P2 in Eq. (7) was found from the solution of the transport equation by the method of
spherical harmonics in the P1 approximation.
Calculation of the Sensitivity Coefficients. The neutron-physical characteristics of
the model under study are usually linear functionals of the type of the reaction rates which,
for integrals or sums over the entire phase space, can be written in the form of a scalar
product R(ER,c0). The relative change in R corresponding to the relative change in some nu-
_
clear data ai,
SRA=-(cri/I)(6AYOG),
is called the sensitivity of R to the data
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TABLE 1. Composition of Blanket
,
o 0
? o
o N
Z
Zone
thick-
ness,
cm ?
Nuclear concns, 10-24
"Li
7Li
(1
' 0
iii,!
23s1J
1
900
--
-
2
0,5
--
--
0,0848
--
.3
1,1
0,0077
4
20
0,0163
0,0072
0,0I1(
5
1,3
--
0,0182
--
6
15
0,0188
0,0188
--
0,0141
0,0168
--
7
0,7
--
--
--
0,0121
8
35
--
--
0,0642
--
--
--
9
0,4
--
--
0,0212
--
10
10
0,0163
0,0163
--
0,0123
0,0165
11
0,8
--
0,0106
--
TABLE 2. Principal Functionals of Model
.-.
44
Ener
range,
MeV.
g
c,
P
f.t
PE
Fission 1
source
Ii
0
4-,
w
too
1
0
.
uoTssIJ
Jo .OI
IiIiurn I
yield
(1,1
- W2
q),-Hp.2
), 1-14,1-
0-10,5
0-14,1
0,267
-
0,267
0,092
--
0,092
1,296
0,3692,33
1,665
0,701
3,091
0,014 0,325
(1,011 0,138
0,0250,463
1,27C
1,122
1,398
The value of OR was calculated by the correlated sampling method [121. The calcu-
lations of the initial and perturbed systems were carried out according to one and the same
set of neutron trajectories while the change in the properties of the scattering nucleus in
the perturbed system was taken into account by introducing a weight.
The operator 111 In Eq. (6) is of the form
ii-.K (x' , x)dx';
K C (E', E, r) T (r, r, E),
where C describes the change in the energy, angle, and number of particles during collisions
and T describes the displacement of neutrons between collisions.
The solution of Eq. (6) can be written in the form of a Neumann series in collisions:
? i
(II== 11- (x') K (x, x') (lx' =
S -(xi) K (x1,372) . . . K (xi_i, x)dx . dxi_i.
The solution for the perturbed system is of the form
(I); = S (xi) K' 37,0
(x1_1, x)dxt ? ? ? dxi-t?
Introducing the weight of the i-th collision
coi xi)1K xi),
we can represent the perturbed flux by
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(8)
511.
Declassified and Approved For Release 2013/02/14: CIA-RDP10-02196R000800040002-1
(1); S (x (,),K (x1, ,T2) . . .
"
. . . x) dri ... (17'1_1.
Comparison of Eqs, (8) and (9) reveals that the estimate (pi' can be made on the same series
of trajectories as cpl, but at each collision the estimator should be multiplied by
(9)
11 (oh?
h -I
Since the estimates wi and (PI in this case are highly correlated, the error in the calcula-
tion of the deviation 6121 of the functional may be appreciably smaller than the statistical
error of R.
Along with an estimate 6R we can find the perturbation of the source, which is used to
calculatew2:
6S12 7/10 I Iv; (x) ? (pi (x) I.
The variation of R can finally be written as
- 6 (El(' T) - 0541, TO (ER p OTO
--I- (6E1(2, W2)-1 (42, 6T2)?
The first and second terms of this equation are determined in the correlation calculation,
the third is zero, and the last is calculated in the PI approximation with the source pertur-
bation 6S12.
Inclusion of Perturbations. The calculations were carried out according to a modified
BLANK program [13] which realizes the above methods of solving the neutron transport equa-
tion and correlated estimation. The constants for calculations in the range 0.1-14.1 MeV
were prepared according to the NEDAM program [11] from the estimated data files of the ENDL
library. In the working constants we used library spectra of secondary neutrons, converted
to the argument x = E/Ej'. and referred to ranges bounded by neighboring values El, where E!
are discrete values of the initial energy. The perturbed neutron spectrum p'(x) was ob-
tained by compressing the initial spectrum p(x) according to the relation
CI) (cx),
p' 0,
x a/c,
where a is the upper limit of the initial spectrum and c is the compression coefficient.
This approach makes it possible to deform the distribution of any form. In this case x'
(l/c) R or, for a spectrum of temperature T, we have T' = (1/c) T and the relative change in
the data, i.e., the "hardness" of the spectrum is
Cr ST1?c
,= =
In all the calculations we set c = 1.2, which corresponds to a "softening" of the spectrum.
To study the dependence of the sensitivity on the neutron energy up to collision the weight
of the neutrons was varied only in the range from the given threshold Elmin to 14.1 MeV.
The sensitivity S(E'. ) to such a change in the spectra will henceforth be described as
integrated. The diliarential sensitivity s(E') is related to the integrated sensitivity by
s(E')=?OS(E;,in)/OE'rnin.
Results of Calculations
For our calculations we chose the variant of hybrid blanket [14] in which the 23811
carbide is used as fissionable material and lithium oxide is employed to produce tritium
(Table 1). In the working system of constants for Monte Carlo calculations the range 0.1-
14.1 MeV was divided into 18 groups for the probability of processes and 8 groups in the de-
scription of the anisotropy of elastic scattering. The secondary neutron spectra of each
reaction were described by assigning 36 equiprobable values of the secondary energy for each
range of primary energies indicated in the estimated data files.
512
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s(0),
1/MeV
0,015
0,010
0
6
0,002
0
6,5
1,5
1,0
0,5
7 4 6 8 W E',MeV
Fig. 1. Differential sensitivity to
neutron spectra of reactions: a)
238U(n,
2n), b) 238U(n, n') cont, c)
Fe(n, n') cont.
All of the calculations were carried out for 10,000 histories. The principal func-
tionals of the unperturbed model with normalization to one source neutron in the plasma are
given in Table 2. The integrated sensitivity coefficients for the fission rate nf, the
fission neutron source Qf, and the tritium yield kT are given in Tables 3 and 4 as a func-
tion of EL n. The statistical errors of the functionals and the deviations of their corre-
lated values were estimated directly during calculations by the Monte Carlo method and
amounted to '1,1% for and, depending on the effect, from 10 to 60% for the deviations.
As follows from Tables 3 and 4 the greatest influence on the principal functionals of
the hybrid reactor is 'exerted by the spectra of secondary neutrons from the reactions 236U(n,
2n), 238u(n,
ne)cont, and Fe(n, n') cont, for which the contribution to the rate of fission
in 228U may
be considerable. The total sensitivity with respect to these reactions is 0.22
for the fission rate, 0.19 for the source, and 0.13 for the tritium yield, with a spread of
15-20% in the mean energy of the secondary neutron electrons in various estimated data files
[8] this corresponds to an indeterminacy of 3-4.5% for the fission rate and the source and
2-2.5% for the tritium yield. The sensitivity of the functional to the spectra of the re-
actions 238U(n, 3n) and Fe(n, 2n) is substantially lower because of the smaller cross sec-
tions for these reactions and lower secondary neutron energy.
Figure 1 gives the curves of the differential sensitivity to the spectra of the re-
238u(, ,
n 238u(n
actions 2n), ) cont, and Fe(n, n') cont in the range from the threshold to
14.0 MeV, obtained by differentiating smooth curves drawn according to the data of Tables
3 and 4.
The differential sensitivity of the fission rate and the source to the neutron spec-
trum of the reaction 238U(n, 2n) rises sharply above 11 MeV, which corresponds to the shape
of the neutron spectrum in the uranium zone, shown in Fig. 2. As follows from Table 3,
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TABLE 3. Integrated Sensitivities to 238U Spectra
Paam-P
2,81.1 (n, 2n) 1 238U 0,. 71/) cont
238U (n,
3n)
- MeV
11-111P
eter
6,51101121131(4111213 I I 6 j 8 I 14
14
- iv
0,1098
0,1086
0,1028
0,9962
0,0817
0,0581
0,0578
0,0438
0,0148
0,0122
0,0073
0,0066
0,0118
Qf
0,092
0,0910
0,087
0,0816
0,0694
0,0458
0,0457
0,0359
0,0142
0,0121
0,0080
0,0079
0,0084
kT
0,051
0,0445
0,0404
0,0361
0,0311
0,0142
0,0155
0,00523
0,00376
0,00176
--0,00524
-0,0060
0,0258
Y(EY't
101
10
10
TABLE 4. Integrated Sensitivities to Fe
Spectra
Param-
eter
re (a, n') coat
Pc (a, 2a)
Pmin, MeV
2 4 8
12 14
14
ni
(),.
kT
0,0504
0,0474
0,0558
0,0413
0,0408
0,0438
0,0217
(3,0255
0,0251
0,0162
0,0209
0,021
0,0174
0,0205
0,0145
0,00162
0,00103
0,0127
__,
HUJ
it
8 10 12 E, MeV
Fig. 2. Spectra of neutrons in blanket:
first wall; ) uranium zone.
neutrons with an energy above 14 MeV account for 75% of the integrated sensitivity of the
fission rate and 'b607. of the sensitivity of the tritium yield.
Neutrons from inelastic scattering with excitation of a continuum of levels in 238U
make the greatest contribution to the functionals at an energy in the range 2-6 MeV prior
to collision while only 15-20% of the contribution corresponds to an energy above 14 MeV.
This is in accord with the position of the maximum of the cross section of the reaction and
the increase in the neutron flux at an energy below 6 MeV (see Fig. 2).
Approximately one-third of the sensitivity to the spectra of neutrons from the reaction
Fe(n, n') cont is accounted for by the interaction between source neutrons with an energy of
14.1 MeV and the first wall. At a lower energy the sensitivity increases with a decrease
in the energy, judging by the spectrum of neutrons in the uranium zone.
Conclusion. In cases when the neutron transport equation is solved by the Monte Carlo
method, the application of the correlation sampling technique to the calculation of the
sensitivity coefficients makes it possible by means of a straightforward change in the algor-
ithm to attain an accuracy of calculation of differential effects that is sufficient for
estimations. This method is most convenient when the difference in the kernels of the inte-
gral equations corresponding to the ground-state and perturbed problem can be taken into ac-
count by introducing a weight function and the region of definition of the kernels. This
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corresponds to the cases of perturbation of the secondary neutrons, their spectra, or absorp-
tion cross section.
The calculated sensitivity coefficients show that in a hybrid reactor the greatest
influence on the principal functionals is exerted by the secondary neutron spectra of the
)
, nIN
reactions 238U(n, 2n), 238u(n cont, and Fe(n, n') cont, for which the contribution to
the fission rate in 238U and, therefore, in neutron multiplication per source neutron, may
be considerable. The indeterminacy of the functionals, owing to the 15-20% inaccuracy of
the spectra, is estimated for the hybrid reactor model studied to be 3-4.5% for the fission
rate and 2-2.5% for the tritium yield.
LITERATURE CITED
1. L. Usachev, J. Nucl. Eng., A/B, 18, 371 (1964).
2. L. N. Usachev and Yu. G. Bobkov, in: Proc. Conf. "Neutron Physics" [in Russian],
Part I, Naukova Dumka, Kiev (1972), p. 47.
3. Yu. G. Bobkov et al., in: Proc. Conf. "Neutron Physics" in Russian], Part I, Izd.
TsNIIatominform, Moscow (1976), p. 76.
4. R. Conn and W. Stacey, Nucl. Fusion, 13, 185 (1973).
5. S. Gerstl, D. Dudziak, and D. Muir, Nucl. Sci. Eng., 62(1), 137 (1977).
6. ID. Steiner and M. Tobias, Nucl. Fusion, 14, 153 (1974).
7. S. Gerstl, in: Proc. Fifth Int. Conf. on Reactor Shielding, Knoxville, Tenn.,
April 18-22 (1976).
8. V. V. Kotov et al., Preprint IAE-2817, Moscow (1977).
9. R. Howerton et al., UCRL-50400 (1971), Vol. 4.
10. S. M. Zakharova, B. N. Sivak, and G. N. Toshinskii, Information Bulletin of Nuclear
Data Center. No. 3. Appendix 1. Nuclear-physical Constants for Reactor Calculations
[in Russian], Atomizdat, Moscow (19,67).
11. L. N. Zakharov et al., Preprint IAE-2994, Moscow (1978).
12. V. G. Zolotukhin and D. A. Usikov, Estimation of Reactor Parameters by the Monte
Carlo Method [in Russian], Atomizdat, Moscow (1979).
13. S. V. Marin, D. V. Markovskii, and G. E. Shatalov, Preprint IA-2832, Moscow (1977).
14. V. Kotov and G. Shatalov, in: Proc. of US-USSR Symp. on Fusion-Fission Reactors,
Livermore, July 13-16 (1976), p. 129.
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Declassified and Approved For Release 2013/02/14: CIA-RDP10-02196R000800040002-1
CHARACTERISTICS OF FLOW RATE-LIMITING INSERTS IN MODELING
EMERGENCY LOSS OF INTEGRITY OF A REACTOR LOOP
L. K. Tikhonenko, E. K. Karasev,
S. Z. Lutovinov, B. A. Gabarev,
and E. I. Trubkin
UDC 621.039.587
The problem of limiting the flow of heat-transfer agent under conditions of emergency
loss of integrity is an extremely pressing one. The patent literature proposes several so-
lutions for this problem [1, 2]. As a rule, these solutions involve either safety devices
which automatically seal off a section of piping at the instant that emergency loss of inte-
grity occurs, or Venturi-type nozzles that do not seal off but only restrict the flow of
heat-transfer agent. The latter are more promising from the standpoint of realiability,
since they do not contain moving parts. At the same time, it should always be borne in mind
that, under rated operating conditions, such nozzles are "parasitic" resistances, and there-
fore in choosing the geometry of the flow part of the nozzle it is necessary not only to en-
sure efficient limiting the flowrate of heat-transfer agent under emergency conditions, but
also to guarantee low hydraulic resistance under normal operating conditions.
The design of limiting nozzles requires appropriate data on the flow of heat-transfer
agent under emergency and normal reactor operating conditions. The large number of factors
that determine the flow in these cases makes theoretical investigation difficult, so that
such investigations have chiefly employed approximate models [3, 4]: equilibrium homogenous
flow; flow with phase slippage; flow of a metastable fluid, and so forth. Such models are
in agreement with experiments only in narrow parameter ranges. The available information on
experimental studies (see Table 1) indicates that the ranges of operating and geometrical
parameters have been studied are diverse. None of the studies mentioned in the table offers
a systematic account of the relationship between the critical flowrate and the geometrical
parameters. Paper [6] is something of an exception; this paper considered a nozzle with a
cylindrical section 120 mm in diameter and a minimum cross-sectional diameter of 19.0 mm.
This study was conducted, however, only for saturated water (Atno = 0). At the same time,
for channel reactors of type RBNK the parameter range of practical interest is Atm = 0-30?C,
Po = 0.1-9 MPa and dtn- 150 mm. As Table 1 indicates, this range has hardly been studied
at all. Extrapolation of the available empirical data to this region is evidently not legit-
imate.
In this paper we offer some experimental results relating to the critical flowrate char-
acteristics of Venturi-type nozzles as a function of geometrical factors (diameter and length
of the cylindrical throat of the nozzle, aperture angle of conical diffuser) and of the op-
erating parameters (pressure and underheating of water at nozzle inlet). The experiments
were conducted using axisymmetric nozzles consisting of three elements: a narrowing input
section with rounding in the form of a quarter-arc of a circumference (R = 30 mm), a cylin-
drical section (dth = 10-30 mm,
-th = 0-160 mm, and an expanding diffuser a = 30, 6? and
180?). The nozzle geometry is given in Fig. 1 and Table 2. Experiments were conducted under
conditions of steady-state outflow for Po = 0.1-9 MPa and Atno = 0-100?C. The measurement
error did not exceed ?2% for the pressure, ?1.4?C for the temperature, and +4% for the mass
flow rate. The experimental setup and procedure were borrowed from [11].
The measurement results indicate that Po and Atm exert a substantial influence on the
critical mass velocity, referred to the minimum cross section of the flow part of the nozzle.
It follows from Figs. ,2 and 3 that the critical mass velocity increases with po and tno.
It should be pointed out that the results corresponding to Atm = 0, were obtained by inter-
polation of the graphs plotted in sPw( )cr ? (Ai/r)0 coordinates. In the case under considera-
tion, this step results from the technical difficulties associated with obtaining exact val-
ues of the saturation parameters at the inlet to the nozzle.
Translated from Atomnaya inergiya, Vol. 49, No. 2, pp. 83-86, August, 1980. Original
article submitted October 22, 1979.
516 0038-531X/80/4902- 0516$07.50 ? 1981 Plenum Publishing Corporation
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TABLE 1. Data of Experimental Studies
Initial parameters
Inlet section
- Throat
Diffuser
1
Liter-
ature
po,bar
A trio, ?C
profile
iin,min
dth, mm
/th, mil)
profile
F /1,0
cr
5
20-100
8-90
5-20
1,1-20
5-20
5-5
0
0-140
1-70
0-10
0-60
Lemniscate
Arc with R__.
-10 mm
Cone with ./i=
-180mm
Cone
Cone
Planenozzl
The same
40
10
I 114
? 103
93
I
3
3,84
19,0
6,4
10,0
5,0
1
18
05-120
0
0
7
Cone 3-7?
Cone 3.
Cone 3-6?
Cone 24.
Cone 3,6?
Cone 3,90
12-45
3,8
2,17-2,50
21,6-49,9
12,0
13,0
151
161
171
181
191
1101
TABLE 2. Geometry of Nozzles Investigated
Nozzle
No.
Inlet section
Throat
Diffuser
R'thm
a ' m 1r
in
dth,
' mm
itlITII,
n
'
deg
/clif,
mm
deo,
mm ?
1
30
30,5
20,04
0
6
180,3
38,95
2
30
30,5
90,04
41.3
6
180,3
38,95
3
30
30,5
90,04
81,1
6
180,3
38,95
4
30
30,5
20,04
160,7
6
180,3
38,95
5
30
30,5
20,04
161,3
Without diffuser
6
30
30,5
20,04
160,7
3
180,4
29,45
7
30
29,0
30,0
165,5
6?35
90
40,4
8
30
31,03
19,98
26,0
5-42
193
38,85
9
30
34,4
10,03
156,4
Without diffuser
Of the geometrical factors investigated, it is the length lth of the cylindrical
throat that exerts the greatest influence on(POcr. Obviously, the critical mass velocity
depends not on the length of the cylindrical section but on a somewhat larger effective
value that represents the sum of the length of the cylindrical section and of the length of
part of the input section. The latter is reckoned from the cross-section where the fluid
begins to boil. It can be seen from Fig. 4 that, over the entire range of Po investigated,
an increase in Zth leads to a decrease in the critical mass velocity of the outflow of both
saturated and underheated water. The effect of Zth on (pw)cr attenuates more rapidly, the
greater the unjerheating of water at the nozzle inlet. For example, for Atno = 10?C in-
creasing lth from 0 to 160 mm results in a 47% drop in (pw)cr, whereas for Atno = 30?C vari-
ation of Zth within the same limits reduces (pw)cr by only around 13% in all.
Of considerable practical interest is the probable effect of the diameter of the nozzle
throat on the critical mass velocity of outflow of underheated and saturated water. In the
present study, experiments were conducted using nozzles with throat diameters of 10, 20, and
30 mm. Figure 5 indicates that there is some stratification with respect to dth of the curves
that describe (pw)cr as a function of the relative underheating (1i/r)0 for various values
of the water pressure at the nozzle inlet. It follows from the figure that for dth = 30 mm
the values of (pw)cr are 5-8% higher than for dth = 10 mm. Of course, the problem of the
effect of throat diameter requires further experimental study, since the observed stratifica-
tion of the (Ai/r)0 curves with respect to dth is commensurable with the possible
error in measurement of (pw)cr (which amounts to +4%).
In this study we also investigated the effect of the aperture angle a of the conical
diffuser in the range from 3 to 1800. As the experimental data show (Fig. 6), the effect
of a on (pw)cr is negligible, at least in the range under consideration and for nozzles of
sufficient extension.
Conclusions
We have experimentally investigated the relationship between the critical mass velocity
of hot water on a number of operating and geometrical parameters. The greatest effect on
517
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5,
411 1_ L 1 LI 1
ZO 40 80 80 100 120 1411 1b0 1810
8t 00C
zIt00100.
//
VO4?5,/
4,5
'(-.; 4,6
a4,4
4,2
4,0
40 80 120 160 200 40 80 120 160 200
20
10
8 2 4 6
MPa
518
Fig. 1. Typical working section.
Fig. 2. Effect of intake under heating
on critical mass velocity (nozzle No. 9)
for Po = 9.0 (0); 7.0 (4); 4.0 (e);
2.0 (11); 1.0 00 MPa.
Fig. 3. Effect of pressure at inlet to
nozzle on critical mass velocity (nozzle
No. 9).
Fig. 4. Effect of length on critical mass
velocity (nozzle with throat 20 mm in
diameter): a) saturated water, Po = 9.0
(1); 7..0 (2); 4.0 (3); 2.0 (4); 1.0 MPa
(5); b) underheated water, Atno = 100 (1)
60 (2); 30 (3); 20 (4); 10 (5); 00 (6).
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8
4,5
4,0
'112 -410 -006 -404 -402
(01/r) t,
-gag -406 -404
(AL /r)0
-0,02
0
Fig. 5. Effect of throat diameter on critical mass velocity (nozzles Nos. 4-7,
9 with throat length 160 mm) for Po = 9.0 (1), 4.0 (2), 2.0 (3), 1.0 MPa (4) and
dth = 10.03 (D), 20.04 (11) and 30.0 (C)) mm.
Fig. 6. Critical mass velocity as a function of underheating at inlet for vari-
ous aperture angles of the output section (nozzles Nos. 4-6 with cylindrical
throat 160 mm long and 20 mm in diameter) for Po = 9.0 (1), 7.0 (2), 4.0 (3),
2.0 (4), 1.0 MPa (5) and a = 180 (?), 6 (4), 3? (0).
(pw)cr is exerted by the pressure and underheating of the water at the nozzle inlet. For
example, increasing Po from 2 to 9 MPa for Atno = 20?C results in an increase in (pw)cr
from 30 to 55.103 kg/(m2-sec), whilea change in Atno from 0 to 60?C for Po = 7 MPa increases
(pw)cr from 35 to 74.103 kg/(m2-sec).
The critical mass velocity of outflow of underheated or saturated water also depends
on the length of the cylindrical throat of the nozzle. It has been established that (Pw)cr
decreases as lth increases. However, this effect gradually attenuates as Zth increases.
The greater the underheating of the water at the nozzle inlet, the sooner the effect of Zth
attenuates. Investigation of the effect of throat diameter revealed that increasing dth
from 10 to 30 mm resulted in roughly a 5-8% increase in (pw)cr. The effect of the aperture
angle of the diffuser turned out to be negligible, at least for 3 5 a :5 180? and Zth/dth
1.5.
Notation
Po, water pressure at the nozzle inlet, MPa, Atm, underheating of the water at the
nozzle inlet, ?C; (pw)cr, criticalmassvelocity,referred to the narrow cross section, kg/
(m2?sec), (Ai/00,dimension1ess value of the underheating at the nozzle inlet, Zth and dth,
length and diameter of the cylindrical throat of the nozzle, mm, a, aperture angle of the
conical diffuser, deg.
LITERATURE CITED
1. R. Stroehlen, FRG patent No. 1155649, class 47g 49/02 (1964).
2. J. Piston, US patent No. 3172819, class 176-31 (1965).
3. V. A. Zysin et al., Boiling Adiabatic Flows [in Russian], Atomizdat, Moscow (1976).
519
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Declassified and Approved For Release 2013/02/14: CIA-RDP10-02196R000800040002-1
4. G. V. Tsiklauri, V. S. Danilin, and L. I. Seleznev, Two-Phase Adiabatic Flows [in
Russian], Atomizdat, Moscow (1973).
5. T. N. Parfenova, Candidate's Dissertation, Leningrad (1971).
p. E. K. Karasev et al., At. Energ., 42, No. 6,478 (1977).
7. W. Schrock, E. Starkman, and R. Braun, Teploperedacha, 99, No. 2, 113 (1977).
8. M. A. Koronkevich, Preprint, Institute of Technical Physics, Siberian Branch,
Academy of Sciences of the USSR, Novosibirsk (1977), pp. 55-77.
9. G. A. Mukhachev, B. M. Pavlov, and V. G. Tonkonog, in: Proceedings of Kazan
Aviation Institute, No. 158 (1973).
10. V. G. Tonkonog, Author's Abstract of Candidate's Dissertation, Kazan Aviation
Inst. (1975).
11. L. R. Kevorkov, S. Z. Lutovinov, and L. K. Tikhonenko, Teploenergitika, No. 7,
72 (1977).
DETERMINATION OF SOME CHARACTERISTICS OF SPENT FUEL OF BOILING-WATER
REACTORS USING a AND y SPECTROMETRY
A. G. Zelenkov, S. V. Pirozhkov, UDC 621.09.54:539.128.4.144:539.166.3
Yu. F. Rodionov, and I. K. Shvetsov
The international system of guarantees regarding the nonproliferation of nuclear
weaponry places considerable emphasis on supervision of special nuclear materials (SNM),
using methods of physical protection (protective measures) and nondestructive methods of re-
cording nuclear emissions.
An important element in supervision at spent-fuel reprocessing plants is the identifi-
cation of SNM in all phases of the technological process, from delivery to the plant until
storage of the product and localization of radioactive waste. The problem reduces to check-
ing the correspondence between the product and the certification data for fuel assemblies:
initial enrichment, average burn depth (B), and unloading time from reactor (holding time)
[1]. The solution of this problem is one of the tasks of the "Minimum Isotope Inventory
Safeguard Technique" (MIST),whoseauthors, however, confined themselves to only linear iso-
tope correlations and mass-spectrometric measurement techniques [2].
We will confine ourselves to the problem of identifying SNM for the purpose of detect-
ing their possible illegal inclusion into the technological process. For this it is ex-
tremely useful to determine the relative content of the maximum number of nuclides of the
actinoid elements, including nuclides of the transplutonium elements. The relative spectral
line intensities resulting from emission of not one but several nuclides can also be employed.
It is desirable to employ nonlinear isotope correlations because of the possibility of
predicting the relative content of nuclides for a batch of reprocessed fuel, primarily for
assemblies with known B, and also because of the achievable accuracy in determining the
above certification data. To solve the problem, it is desirable to employ relatively simple
methods, characterized by moderate equipment costs and speed and ease of analysis. Current
mass-spectrometric techniques can meet these requirements only with difficulty.
It appears promising to employ a-spectrometry (with semiconductor detectors) in combi-
nation withy spectrometry for this purpose: both types of measurements can be made using one
device equipped with two kinds of detectors, the methods are easily accessible, relatively
simple, fast, and insensitive to chemical admixtures. Alpha spectrometry is relatively in-
sensitive to the presence of radioactive fission products as well, but requires the prepara-
tion of uniform thin-layer targets (around 10 pg/cm2).
Translated from Atomnaya Energiya, Vol. 49, No. 2, pp. 86-91, August, 1980. Original
article submitted August 6, 1979.
520 0038-531X/80/4902-0520$07,50 ? 1981 Plenum Publishing Corporation
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Declassified and Approved For Release 2013/02/14: CIA-RDP10-02196R000800040002-1
a b 1,5.103
pulses
2.103
0
>
a)
3000
.310
2.10
1?10
0
a
>
0
cor.
500
Ji 0
=
1500 1500 2000 2200 2600
Channel number
Fig. 1. Alpha spectrum of spent fuel of VVER-440 reactor (a) and of
Pu (b) and U (c) extracted from it.
As an example, Fig. 1 shows the a spectra of a sample of solution of VVER-440 fuel
(from the Novovoronezh nuclear power plant) with a burn-up of 32 kg/ton, initial enrichment
of 3.6%, and holding time of 2.6 years, and also for plutonium and uranium extracted from the
same fuel sample. Measurements were made using a semiconductor silicon detector.
For purposes of considering the degree of informativeness of the measured relationships,
we give the absolute (Fig. 2a) and relative (Fig. 2b-d) group intensities in the a spectrum
of VVER fuel as a function of the burn depth. The figure also gives the ratios of the a
decay rates of238pu, 2391311, and 24IPU, and also of 235U and 235U, as measured by y spec-
trometry. Figures 2b and c show that the a spectrum of the fuel sample can be used to check
the extent to which the relative intensity of 244cm[244cm/(239pu 240Pu)] corresponds to
the burn-depth data, and the extent to which the relative intensity of 242cm [ 2 4 2cmi ( 2 3 9pu
240Pu)] (for given 1) corresponds to the known holding time. In view of the fact that the
dependence of the yield of these isotopes on the burn-up is very steep, and in view of the
rapid decay of 242Cm (T1/2 = 163 days), there is no need for a high degree of precision in
determining their relative content.
For large holding times, we can also employ the relative intensity of the 5.5 MeV line
[(238pu 241Am)/(239pu 240pol,
which reflects the accumulation of 241Am from 24"1.1
r (see
Fig. 2c). We can also employ y-spectrum data, which enable us to determine the relative con-
tent of '"Ru, 154Cs, 157Cs, 144Ce, 1%4Eu and 95Zr. As we know, they make it possible to
evaluate the burn-up (on the basis of 194Cs, /57Cs, 154Eu), the contribution of plutonium
fission products (on the basis of "Ru), and the holding time (on the basis of 144Ce, 95Zr).
Information on spent-fuel composition can be greatly expanded through a- and y-spectro-
metric analysis of the plutonium and uranium it contains. The chromatographic method can be
employed to separate small amounts of uranium from plutonium and to achieve the purification
depth required for y spectrometry (sorption of uranium and plutonium from hydrochloric acid
solution on an anionite and subsequent washing with hydrochloric and hydrobromic acid [6]).
521
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WOO
800 a
600
400
MO- 242liM n ._
00
ntM
bC1 100
u? 80
0.)
? 60
,
40
20
10
8
6
"8Pu
8
6
4
2
1
0,6
0,4
0,2
0,1
0,08
0,06
0,04
0,02
-b
239N+240pu
2117PU
rngPUM)
//
/11,/, /fJ/V: WO
1,39N+240pu
8 d
6
z
1,0
0,8
0,4
0,2
0,7
0,08
0,06
0,04
0,02
23'U
/ 13e
?
[ 1 I 0,01 I [ J I w 1 1 f 1 0,01 IJ
I I
8 10 20 30 40 8 10 20 30 40 8 10 20 JO 40 8 10 20 JO 40
Bo, kg/ton
Fig. 2. Absolute a-emission intensity (Na) and ratio of a-decay rates of nu-
clides, obtained from a or y spectra (q) as a function of the burn depth B;
solid line: experimental data for Yankee nuclear power plant [3]; dashed
line and dot-dash line: data for first [4] and second [5] units of Novovoro-
nezh nuclear power plant, initial 235U enrichment 3.4, 2, and 3% respectively
(A is the radioactivity of 241Am corresponding to the content of
241pu).
The a spectrum of plutonium (see Fig. lb) can be used to determine the relative content
of 238Pu, and hence of 24IAm, and to additionally check the burn-up and holding time. Here
we can also isolate the weak 4.9 MeV emission line of 24IPu and 242pu.
The y spectrum of
plutonium can be used to determine the relative content of 238pu, 239pu, 240pu and 241pu.
These data can be used (see Fig. 2b) to additionally check the burn-up and, possibly, the
initial enrichment. The lines of 24IAm will also be present in the y spectra of stored
purified plutonium taken from storage. The mass ratio of Am 241 and 24IPu makes it possible
to determine the time elapsed from the moment of plutonium extraction.
The isotope composition of uranium is unambiguously related to its origin. In the
a spectrum, the relationship between the emission lines of 234,u,, 238U
and the combined emis-
sion line of (232u + 236..
u) and 235U (see Fig. lc) can be used to determine the initial uran-
ium enrichment and the burn depth (see Fig. 2d). Measurements of the y spectrum make it
possible to determine the ratio of 235U and 235Ue
The accompanying table gives the principal lines of the a and x spectra of spent boil-
ing-water reactor fuel, their origin, and information on fuel characteristics obtained via
a and y spectroscopy. Thus, measurements of the a and y spectra of a sample of spent fuel
makes it possible to estimate the burn depth and the holding time [1]. The nature of the
plutonium spectra is determined by the burn-up and storage time of the fuel. By analyzing
uranium emission, it is possible to determine the initial and final enrichments and the
burn-up.
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TABLE 1. Principal Lines in a and y Spectra of Spent Boiling-Water Reactor Fuel
and of Uranium and Plutonium Extracted from It
Source of
emission
a-emission
remission
- nuclide
E,_>
MeV
characteristic
determined
nuclide
I, *
-v,
MeV
characteristic
determined
Initial fuel ?
mixture
230pu + 2401,,,,
23gpt, + 241A,,,,
5,16 aseline
5,5 urn-up and holding
m7cs
"'ICS
0,662
0,604
Baseline
urn-up
time
(1,796
244cm
5,8 urn-up
n4Eu
1,004
?
24,2cm
6,1 olding time
1,274
1-44W"PO
0,696
olding time
1,489
"Zr("N 6)
0,724
? 0
0,766
106R,(109/10
0,629
,ontribution of
lutonium fission
o fission products
'Uranium
23811
4,2 baseline
2301v:14mPa)
1,001
Baseline
235u+ 236U
4,5 I 1 Burn-up and
initial enrichment
235 ij
0,186
Final enrichment
234U
4,8
239P, + 240pw,
5,16 Bseline
2391),,
0,129
Baseline
0,414
Plutonium
234M-1-241-Am
5 , 5 uaytearnedxsttroarcatl_e_
24,,i)ii
0,1 GO
Burn-up
iumme-
OU
,,"
0 153
0
2411,,q237( 0
0.,149
24113u + 2421,,
4,0 urn-up
0,208
2.41A iii
0,060
Storage time after
extraction
*Most intense lines.
It should be pointed out that the curves in Fig. 2 correspond to local burn-up and
cannot be employed directly to determine the content of nuclides in fuel assemblies. To
solve this problem we need to know how the burn-depth values are distributed over the mass
of the fuel; this can be determined from the burn-up distribution over the cross section of
the assembly and the length of the elements [7-9]. Figure 3 shows the distribution of the
burn depth over the fuel mass computed in this fashion, for the assemblies of the VVER re-
actor. The abscissa axis gives the relative burn depth (B/N), while the ordinate axis gives
the relative content of fuel with the given burn-up. The "tail" of the distribution in the
direction of low burn-up results from the lower burn-up at the ends of the elements (down to
0.3 T3), while the drop-off in the region of relatively large burn-ups results from increased
burn-up of peripheral elements of the assemblies. Analysis of the data indicates that the
histogram (see Fig. 3) gives a fairly good account of the distribution of burn-up for most
assemblies of boiling-water reactors with differing average burn-up and initial enrichment,
and can be used for estimating the production of nuclides of transuranium elements.
The curves in Figs. 2 and 3 were used to compute the intensity of some lines in the
a spectra of a sample of initial fuel mixture from the assemblies of the VVER-2 reactor and
of uranium and plutonium extracted from the sample for average burn-ups of 15, 20, and 30
kg/ton; it turned out that the expected differences in the relative line intensities in the
alpha spectra of samples taken from the assembly mixture and of samples corresponding to
local burn-up result in errors in determining the burn depth not greater than 10%, i.e., they
are within the limits of accuracy in determining the calculated burn-up.
The accuracy in estimating the burn-up can be improved, of course, if we employ experi-
mental data obtained in measuring the nuclide content in dissolved fuel assemblies of a given
type with differing burn-up. Here we can also take account of the effect of distortion of
the neutron spectrum at the edges of the assemblies. The achievevable accuracy in estimating
the average burn-up will be determined by the variations in the measured ratios of the nu-
clide content in response to the conditions of irradiation of the assemblies in the reactor.
In using the proposed procedure it is desirable that fuel with the same initial enrichment
and maximally similar burn-up be combined into one batch in the radiochemical plant [9].
Evidently there are also economic reasons for doing this. Consequently, a and y spectrometry
of fuel at the radiochemical plant enables us to determine with the necessary degree of pre-
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20
10
0,5 1:0
5/8
Fig. 3. Distribution of degree of
burn-up over fuel mass.
cision the extent to which the nuclide composition of the product (both the initial mixture
and the purified uranium and plutonium) corresponds to the certification data. As for the
basic problem of meeting the guarantees (monitoring illegal incorporation of extraneous SNM
into the technological process), it is natural to assume that this fuel has a different
origin and different initial composition, and was irradiated in a reactor of a different
type. The nuclide composition of transuranium elements in spent fuel differs greatly for
reactors of different types [10]. In view of the fact that the relative content of 18 nu-
clides can be determined using a and y spectrometry (see Table 1), we can anticipate that
our method will be highly sensitive to illegal incorporation of appreciable amounts of for-
eign products.
Yet another interesting possibility should be pointed out. In view of the high degree
of sensitivity of the yield of heavy nuclides formed as a result of multiple neutron capture
to the irradiation conditions for the assemblies in the reactor, we can assert that each
batch of SNM obtained as a result of reprocessing of a batch of assemblies will have an in-
dividual nonduplicable nuclide composition, or "dactyloscopic signature." Indeed, a and y
spectrometry can be used to measure the ratio of four isotopes of uranium and five isotopes
of plutonium. The necessary accuracy in measuring the relative spectral intensity is evi-
dently around 1%, a figure that is quite achievable experimentally.
Thus, it becomes possible to employ "dactyloscopy" of a batch of SNM over the entire
course of fuel reprocessing until it is used in new fuel elements. The problem can be sim-
plified by artificial tagging of nuclear materials by small amounts or 233U.
In our opinion, a combination of a and y spectrometry provides a good method for this kind
of "dactyloscopy" of SNM.
In concluding, we wish to thank V. A. Pchelin, V. P. Tarasevich, and V. S. Shiryaev
for their assistance with the paper, and A. N. Novikov, 0. A. Miller, and V. D. Sidorenko
for discussion of the results.
LITERATURE CITED
1. W. Miele and D. Nentwich, in: Proc. IAEA Symp. Safeguards Techniques, Karlsruhe,
6-10 July 1970, p. 1.
2. D. Christiansen. ibid., p. 563.
3. R. Matsen, Nucl. Technol., 15,343 (1972).
4. V. Ya. Gabeskiriya et al., Preprint, NIIAR, No. 88, Dmitrovgrad (1976).
5. V. Ya. Gabeskiriya et al., At. Energ., 44, No. 5, 446 (1978).
6. 0. A. Miller, S. V. Pirozhkov, and Yu. F. Rodionov, in: Proc. IAEA Symp. Nuclear
Safefuards Technology 1978. IAEA-SM-231/142. Vienna, 2 797 (1979).
7. D. I. Kamyshin and A. I. Novikov, in: Proc. IAEA Symp. Reactor Burn-Up Physics,
Vienna (1973), p. 125.
8. G. Ya. Andrianov et al., Kernenergie, 20,- No. 10, 309 (1977).
9. L. V. Kochanovskaja, ibid., p. 307.
10. A. K. Kruglov and A. P. Rudik, Artificial Isotopes and Methods of Calculating Their
'Formation in Nuclear Reactors [in Russian], Atomizdat, Moscow (1977).
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DETERMINATIN OF LOW CONTENTS OF ELEMENTS FROM VANADIUM TO
MOLYBDENUM BY AN X-RAY FLUORESCENT METHOD USING A NEW
VARIANT OF STANDARDIZATION
A. G. Belov, V. Ya. Vyropaev
N. Sodnom, B. Dalkhsuren,
Sh. Gerbish, P. Zuzaan,
and S. Davaa
UDC 543.422.8
X-ray spectral analysis is widely used in the determination of the content of elements
in ores, soils, materials of biological orgin, and in samples collected for environmental
monitoring [1-2]. A peculiarity of the analysis of such objects is the monitoring of low
contents of a group of elements, whereas in most cases there are no standards available. As
a result of this, the development and investigation of methods of x-ray spectral analysis
based on the use of a minimum of standards are promising. In this work we present the re-
sults of the development of a new method of x-ray spectral fluorescent analysis, based on the
use of one reference element as the standard for a group of elements from vanadium to molyb-
denum. It is expedient to use this method in the determination chiefly of low concentrations
of the elements, (:50.5%).
Theoretical Substantiation of the Method
Quantitative x-ray spectral analysis is a variant of the internal standard method [3],
based on the use of the relative specific intensity RJ of the analytical lines of the ele-
ments to be determined. The value of Ri is determined calculated for 1%:
/11-=(/j//0(C/X,), (1)
where I, Ii
and Cz, C. are the intensities of the analytical lines and the concentrations
of the elements Z and j, respectively, for the sample under consideration (in this case the
element is the reference element - internal standard).
Let us assume that in the sample under consideration the content of the group of ele-
ments does not exceed %0.5%. Let this be, e.g., elements from 23V to 42Mo. Using 1?9Cd to
excite the x-ray fluorescence, we can simultaneously investigate the K-spectra of these ele-
ments. In a calculation of the fluorescence intensity excited in the sample under considera-
tion by a 109Cd source, the primary spectrum can be considered monochromatic with acceptable
accuracy, since the contribution of the hard component with energy 88 keV will be negligible.
In view of the fact that the entire absorption edge of elements with 23 'IS Z 42 lies on the
long-wave side of AgK - the spectrum of the source - All the calculations can be made for the
AgKaline [4]. In this case we can neglect the contribution of the effect of selective ex-
citation to the fluorescence intensities. Then the following formula will be correct,
711
Si ?I ?I CI (2)
Ii kW
P. kr" lAtnI
samP 4- nu. sarnP
rmt
where k is a coefficient of proportionality; n = sin 'p/sin angles of incidence of the
primary fluorescent radiation on the sample and of collection of fluorescent radiation; Wk,
Z
fluorescenceyieldoftheelementl;P,probability of transition of the atom Z with emis-
Z 1
samp
sion of the line i; Sic;. jump in the absorption of the k-level. pZ psamp
' mI' mI ' and pmi ' mass
coefficients of absorption of the primary radiation by element l and the sample, as well as
the fluorescent radiation of the element land the sample.
1980.
USSR. Mongolia. Translated from Atomnaya Energiya, Vol. 49, No. 2, pp. 91-94, August,
0038-531X/80/4902- 0525$07.50 ? 1981 Plenum Publishing Corporation
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If now we
introduce the notation
Fig. 1. Dependence of the relative specific
intensity on the atomic number: o) calcu-
lation; o) experiment.
(3)
then for 0 we obtain the following expression
- IzE
s% 41P
L (4)
1-nPrnii
i
Figure 1 shows the dependence of the relative specific intensity R for elements from
23V
to 42Mb on the atomic number Z. The curve was constructed according to the results of
a theoretical estimate. We selected 40Zr (11r = 1) As the reference standard. All the
necessary parameters were taken from the tables of [5, 61. The mass coefficients of absorp-
tion were calculated according to the formula
(5)
where A is the wavelength of the radiation, while the parameters Cj and ai were calculated
for each element. A value of n equal to 0.707 corresponds to angles cp, = 45? and lp = 900.
It is not difficult to show that the dependence shown in Fig. 1 is constant when the
chemical composition is varied within broad limits, if there are no absorption edges of the
elements with a larger concentration (> 0.4-1.0%) in the range of wavelengths between X (pri-
mary radiation) and Xi max (maximum wavelength of radiation of the analytical line, inthe
case under consideration VKa). Actually, in the case the mass coefficient of absorption of
the sample will be a continuous function within the wavelength (AI ?Ai max). Then, in
accordance with formula (5)
samP tXr\m.samp
and the expression for Rj can be transformed into:
/-1-n(Xiil1)a
1 lit (kii/X1)a?
(6)
(7)
From this it is evident that the parameter 0 does not depend on the chemical composition of
the samples. Thus, the mutual influences of the elements are considered with the aid of the
relative specific intensity for the type of samples under consideration.
According to formula (3) we find that at small n, the value of R) is entirely deter-
mined by the ratio nj/fli. For large n, when um' can be neglected, formula (3) takes the form
Sa mp
Ri 11 ['ma
[trp
In this case the mass coefficient of absorption of the radiation of the analytical line
of an element with atomic number Z is always greater than for an element with (Z + 1), etc.
(8)
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Al
Pb
Fig. 2 Fig. 3
Fig. 2. Sample holder for a point source. 1)
Detector; 2) source; 3) shield.
Fig. 3. Sample holder for a ring-shaped source:
1) source; 2) aluminator collimator; 3) sample;
4) mylar; 5) detector.
As of a result of this, when n is increased, the value of Ri will always increase for elements
with large Z. Analysis according to the proposed method is performed as follows.
1. For a group of elements the dependence of the relative specific intensity on Z is
determined.
2. For samples one finds an element that can serve as a standard. Such an element
should not be present in the samples, or its concentration should be less than a definite
level.
3. A definite amount of material containing the standard element is added to the
sample to be analyzed. Such material may be, for example, boric acid, since strong tablets
are produced when it is introduced into the sample.
4. The intensity of the analytical lines is measured for the samples to be analyzed
under set conditions of analysis.
5. The results of the measurements are treated (finding the areas of the peaks, in-
tensities of the background, intensities of the analytical lines of Ii).
6. The concentration of the elements to be determined is calculated according to the
formula
C ij I CI
,
11 RI' /?Cb'
where Cb is the boric acid concentration in the emitter.
Experimental Verification of the Method
(9)
The effectiveness of the proposed variant of the internal standard method was verified
on an ORTEC x-ray spectrometer. In the investigation we used an ORTEC Mode 7016 Si(Li) de-
tector (4)10 mm, resolution 200 eV for the emission of the MnK, line, beryllium window
25 pm thick) and a ring-shaped radioactive 109Cd source from Amersham with activity 20 mCi
(inner diameter of source 26.5 mm, outer diameter 34.25 mm). Figures 2 and 3 present the
scheme of arrangement of the sample holder, exciting source, collimator, and detector. The
instrument is supplemented by a set of mixed collimators of aluminum 13 mm high with diam-
eter of opening 4, 6, 8, 10, and 14 mm. The possibility of varying the source-sample dis-
tance is also provided.
A ring-shaped excitation source has divergent beams. For example, at a distance from
the source to the sample of 15 mm and a diameter of the collimator 6 mm, the minimum value
of cp is equal to 340, the maximum 83?, while the angle tp varies in this case from 65 to 90?.
The value of n correspondingly increases from 0.62 to 1.09. In an estimate of the influence
of variation of this parameter on the shape of the curve (Fig. 1), it was found that the
relative specific intensity RNi decreases from 0.04 to 0.05. Since ,the maximum contribution
Zr
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TABLE 1. Theoretical and Experimental
Values
Ele-
ment
Rj
Zr
theor.
Rj exp.
Zr
Rj exp. /
4Zr
RJ theor, cio
Zr
23
V
0,0058
0,00695+0,0003
+2,6
25
M n
0,0144
0,0130+0,0003
-5,6
26
Fe
0,0219
0,0220+0,0002
+0,5
28
Ni
0,0469
0,0460-1,0,0010
0,0
29
Cu
0,0664
0,0685+0,0010
+3,2
30
Zn
0,0894
0,0803+0,0010
-3,5
32
Cc
0,159
0,142+0,0020
-10,7
40
Zr
1,0
1,0
-
41
Nb
1,185
1,207+0,007
+1,9
42
Mo
1,395
1,36+0,003
-1,5
TABLE 2. Results of X-Ray Fluorescent
Determination of the Content of Elements in
Standard and Copper-Molybdenum Ore Samples
Z
Element
TS
TI3
GM
0
-,
4-
--.
u
a)
certified
L2
-.
&-.
6..
26
Fe
5,21?
-
1,41?
1,24
4,84+
5,59
0,07
0,02
0,028
29
Cu
493+
473
12,8+
-
51?
-
102
1,4
5,5
30
Zn
-
-
39,1+
-
93+
82,0
8,4
8,5
37
111)
222+
226
253+
263
177?
193,0
22,8
20
15
38
Sr
93,3+
114
133+
129
150+
166,0
27
It
13
39
Y
-
174
20,3+
33
39,3+
52,0
5,3
3,1
40
Zr
279+
Stan-
148+
Stan-
178?
Stan-
28 , 9
dard
17
dard
15
dard
41
Nb
-
-
17+7
22
-
-
42
Mo
132?
155
-
-
-
-
29,3
to the intensity recorded by the detector is made by the central part of the sample, the
following values of the angles were selected for further calculations: cp = 450 and 11) = 90?,
which corresponds to n = 0.707.
Table 1 compares the values of the relative specific intensities Ri for the theoretical
estimates and the experimental measurements. The experimental data for vanadium were cor-
rected considering differences in detector efficiency. Evidently, the discrepancy of the
theoretical and experimental data does not exceed 11% (see 0 for Ge). The coefficient.of
variation, characterizing the discrepancy of the theoretical and experimental values, RJ
was 4.4%.
The correctness of function (7) was verified on samples with a content of the elements
to be determined, Ni, Zn, Zr, and Nb, equal to 0.4% each, a filler of Si02 (78.4%) and boric
acid (20%). It was found that replacement of the Si02 filler by Fe203 did not lead to any
significant change in the relative specific intensities of the Ka lines of the elements under
consideration. The experimental values RZn and RNb proved equal to 0.089, 0.090, and 1.20,
1.212 for fillers of Si02 and Fe203, respKEtivelyr The rate of count of the analytical lines
ZnKa, ZrKa, and NbKa changed approximately five fold when the filler was replaced. Analogous
results were obtained when 20% of the Si02 was replaced in the sample by Sn02.
When the concentration of any element from the range under consideration (from 23V to
42)
is increased substantially, the values of RJ for certain elements also are changed.
528
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'FJ
1,5
=
g 1,0
2
=
I: 0,5
8
0 0,5 1,0 1,5 Co?,%
According to x-ray fluorescent analysis
Fig. 4. Comparison of the results of x-ray
fluorescent and chemical analyses.
For example, when the nickel content is increased from 0.1 to 10%, the value of RNiZr increases
by 30%. The quantities RCu ' RCo ' Re, etc. change analogously (for elements from vanadium
Zr Zr
to copper, )NiR lies within the range from Al and Ai). The value ofrfor elements with
z
Z a 30 is practically unchanged in this case, since function (6) is undisturbed. Conse-
quently, when samples containing increased concentrations of individual elements 0.5%)
are analyzed according to the proposed method, it is necessary to consider the change in
RI (the level of concentration of such elements is determined by the accuracy of the analysis).
An x-ray spectral analysis of a number of artificial samples was made according to the
proposed procedure. The calculated values were used as the parameters RI. The error of the
analysis did not exceed the discrepancies between the thoeretical and experimental R. Thus,
for these elements it was not necessary to perform any measurements at the preliminary stage
of the experiment.
For a verification of the method, we detected the content of
standard samples TS, TB, and GM. Zirconium, present in sufficient
standards, was selected as the reference elements, and Fe, Cu, Zn,
also determined. The superposition of Ko, lines of Rb, Sr, Y, and
a number of elements in
amounts in all three
Rb, Sr, Y, Nb, and Mb were
Zr upon the analytical Ka
lines of Y, Zr, Nb, and Mo, respectively, was taken into consideration. For the copper Ka
line, a correction was introduced for the background content of copper in the collimator in
front of the detector (sample TS). As a result of the fact that this correction proved com-
paratively large (l, 500 g/ton), the copper content in sample TB was not determined. For a
determination of iron we considered the change in RYe with increasing Fe concentration (CFea'
0.5%). From the results obtained, cited in Table 2, we can see the satisfactory coincidence
of the certified values of the content and the data of x-ray spectral analysis. Samples of
copper and molybdenum ore were also analyzed. The results were compared with chemical an-
alysis of more than 300 samples in the determination of copper according to the proposed
procedure (Fig. 4). The reliability of this method was estimated by the method of variation
statistics. The method of analysis developed is used in finding a number of elements in sam-
ples of plant materials and soils.
The authors would like to express sincere gratidude to Academician G. N. Flerov for
constant support and interest in the work, as well as to Candidate of Physicomathematical
Sciences of Zhdanov Irkutsk State University, A. G. Revenko, for participation in the experi-
ment and in the discussion of the results of the work.
LITERATURE CITED
1. I. F. Losev, A. I. Smagunova, A. G. Revenko, et al., Zavod. Lab., 43, No. 2, 160
(1977
) .
2. L. Birks and J. Gilfrich, Anal. Chem., Aa, No. 48, 273R (1976).
3. I. I. Losev, QUantitative X-Ray Spectral Fluorescent Analysis [in Russian],
Nauka, Moscow (1969), p. 336.
529
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4.
Yu. I. Velichko and A. G. Revenko, in: Investigations in the Field of Solid-
State Physics [in Russian], No. 2, Irkutsk State Univ.
(1974),
p. 204.
5.
M. A. Blokhin, Physics of
X-Rays [in Russian], Gostekhizdat, Moscow (1957), p. 518.
6.
R. Fink et al., Rev. Mod.
Phys., 38, No. 3, 513 (1966).
SPECTROPHOTOMETRIC STUDY OF THE EQUILIBRIUM OF THE REACTION
Pu4+ + Cl-.. Pu3+ + 1/2C12 IN MOLTEN NaCl-2CsC1
S. K. Vavilov, G. N. Kazantsev UDC 546.799.4:143.543.42
and V. V. Gushchin
The equilibrium of the reaction
Pit4+-1-C1--130++112C12
in molten NaCl-2CsC1 was studied by a spectrophotometric method in the near IR region for
the temperature interval 550-750?C.
The arbitrary equilibrium constant of the reaction studied is described by the empir-
ical equation:
257,70
Ig K* == 2.52? + 0.05.
The values of the thermodynamic reaction parameters are equal to:
41-1*=(49?-.2)W/mo1e;
AS*---(48=1,17.2),VOTIo1e.degiO.
The temperature dependence of the arbitrary formal redox potential of the couple Pu41-/
Pu3+ relative to a chloride reference electrode takes the form
Epo-vp,,31-= ? 0.51 -I- 5.0 .10-4T -I- 0.01 .
The results of an investigation of the equilibrium of the reaction
Pu'l- -I-- Ci ? PIO+ + 1/2C12
(1)
by a spectrophotometric method in molten LiCI-KC1 [1] and LiCl-CsCL [2] are evidence of the
low stability of tetravalent plutonium in chloride melts, which can be judged according to
the closeness to zero of the arbitrary formal redox potential of the couple Pu44-/Pu3+ rel-
ative to a chloride reference electrode.
It is interesting to continue an investigation of the equilibrium of reaction (1) ac-
cording to a whole series of molten chlorides of the alkaline metals and their mixtures, for
a more complete idea of the chemical behavior of oxygen-free reduced forms of plutonium in
salt systems. We might expect an increase in the stability of the tetravalent state of plu-
tonium in the series from lithium chloride to cesium chloride, as has been established for
other metals [3]. This work presents the results of a study of the thermal dynamics of re-
action (1) in,molten NaCl-2CsC1 by the method of spectrophotometric measurements of the
equilibrium concentrations of tri- and tetravalent plutonium at various values of the partial
pressure of chlorine in the gas phase.
Experimental
The equilibrium concentrations of tri- and tetravalent plutonium at various values of
the partial pressure of chlorine were measured on an IKS-14A spectrophotometer, equipped for
work with molten salts [4]. The solvent was a NaCl-2CsC1 eutectic (Tm = 495?C), prepared by
fusing the individual cp grade salts and freed of traces of moisture and oxygen by treating
the melt with hydrogen chloride and chlorine. The density of the melt was calculated accord-
ing to the equation [5]
Translated from Atomnaya Energiya, Vol. 49, No. 2, pp. 94-98, August, 1980. Original
article submitted July 3, 1979.
530
0038-531X/80/4902-0530$07.50 ?1981 Plenum Publishing Corporation
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Fig. 1. Spectrum of molten NaCI-2CsC1,
containing equilibrium concentrations of
tri- and tetravalent plutonium at Cpu =
0.130 M; T = 650?C: 1) PC12 = 0, 2) PC12 =
0.08 x 105 Pa; 3) PC12 = 0.16 x 105 Pa;
4) PC12 = 1.0105 Pa; 5) spectrum of Pu(IV)
calculated according to Eq. (19).
d= 3,175-10,0140'47'
.
(2)
Plutonium was introduced into the melt in the form of the trichloride, which was synthesized
according to the reaction between plutonium dioxide with a purity of 99.5-99.7% by mass and
vapors of carbon tetrachloride at 600?C.
The reaction vessel was a spectrophotometric quartz cuvette (1 = 1 cm), equipped with
a hermetic teflon plug with a loading device and central inlet for the gas pipe. The temp-
erature of the melt in the cuvette was maintained with +2?C. The gas mixtures of chlorine
and hydrogen chloride was produced in a steel gas holder. The partial pressure of chlorine'
in them was varied from 2-105 to 1-105 Pa with an accuracy no lower than ?3%.
The experimental procedure consisted of the following. Plutonium trichloride, in an I
amount such that the summary plutonium concentration was (1.0-1.4).10" M, was introduced
into the melt through the loading device. Then a gas mixture of chlorine and hydrogen chlo-
ride of a definite composition was bubbled through the melt along the gas pipe. The absorp-
tion spectrum of the melt was periodically recorded in the range from 12,000 to 4000 cm-1.
treatment of the melt with the gas mixture was continued until a stable spectrum was ob-
tained, which was evidence of the reaching of equilibrium in the system.
Results and Discussion
Figure 1 presents the absorption spectra of molten NaCI-2CsCl, containing equilibrium
concentrations of tri- and tetravalent plutonium, obtained at various values of the partial
pressure of chlorine in the gas mixture. When the partial pressure of chlorine is lowered
the intensity of the absorption band with maximum at 7200 cm", belonging to trivalent plu-
tonium [6, 7], increases, while the intensity of the absorption band with maximum at 5300
cm-1, assigned to the spectrum of tetravalent plutonium [6, 71, decreases, i.e., there is a
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TABLE 1. Values of the Molar Extinction
Coefficients of Trivalent E3 and Tetra-
valent 64 Plutonium in Molten NaC1-2CsC1
? liters/
(mole. sec)
?C
550
000
650 700 750
e? (v
= 7200 cm")
(v =--
- 5300 cm")
4,7?0,3
4,4+0,1
4, 0?0,3
4,5+0,2
5,2+0,4
4,0?0,1
4,8?0,1
5,7?0,5
Fig. 2. Graphical verification of Eq.
(8) for 550 (1), 600 (2), 650 (3),
700 (4), 750?C (5).
reduction of tetravalent plutonium to the trivalent state. The presence of isobestic points
at 6000 and 7700 cm-1 is evidence of the presence in the melt of only two spectrally dif-
ferent forms of plutonium. It is evident that the absorption band at 5300 cm" is practi-
cally free of the interference of other bands and can be used for analytical purposes. How-
ever, it does not seem possible to determine the molar extinction coefficient for it di-
rectly, since melts containing only tetravalent plutonium cannot be obtained on account of
its insufficient stability.
We established that in melts containing only trivalent plutonium, for the absorption
band at 7200 cm-1 the Beer-Lambert law is fulfilled at optical densities from 0 to 1.2. The
dependence of the change in the molar extinction coefficient on the temperature for the ab-
sorption band of trivalent plutonium at 7200 cm-1 (62) is cited in Table 1. For melts con-
taining equilibrium.mixtures of tri- and tetravalent plutonium, the contribution of the
latter to the absorption at 7200 cm-1 is unknown.
The indices of absorption of a melt containing equilibrium concentrations of tri- and
tetravalent plutonium at 7200 and 5300 cm-1, respectively, are equal to
63Cpuo1n e4Tp11(I v);
k5.3=84CPuov),
(3)
(4)
where k7?2 and k5.3 are the indices of absorption of the melt at 7200 and 5300 cm-1, re-
spectively, cm-1, CPu(III) and Cpu (IV), equilibrium concentration of tri- and tetravalent
plutonium, M, es and e'4, molar extinction coefficients of tri- and tetravalent plutonium at
7200 cm-1, liters/(mole.cm), ?4, molarextinction coefficient of tetravalent plutonium at
5300 cm-1, liters/(mole?sec).
Dividing Eq. (3) by Eq. (4), we obtain
532
k7?21k5?3 =g"il 64+ 63Cp1mulE4CPil(Iv)? (5)
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TABLE 2. Dependence of the Ratio of the Equilibrium Concentrations of Tri- and
Tetravalent Plutonium on the Relative Partial Pressure of Chlorine at Various
Temperatures in Molten NaCl-2CsC1
Ig Cc' 2
550? (..
IMO? C
G5v c
ion" c
750- c
Ca
C3
i,4. _
Ca
c''
-
c,
, C1
' '-'
C.
C4
. Ci
CA
C.
C 1
C.1
C4
C4
C1
C
--1,698
3
1,74
0,24
2
2,46
0,39
3
3,88
0,59
2
5,25
0,72
3
7,58
0,88
--1,397
4
1,07
0,03
3
1,55
0,19
4
2,46
0,39
3
3,31
0,52
4
5,09
0.70
--1,096
4
0,72
-0,14
3
1,15
0,06
4
1,78
0,25
3
9,51
0,40
4
3,47
0,54
--0,795
3
0,54
--0,27
2
0,81
--0,09
3
1,26
0,10
2
1,70
0,23
3
2,57
0,41
--0,602
2
0,49
--0,31
--
--
2
0,95
-0,02
2
2,00
0,30
--0,444
2
0,36
-0,45
2
0,54
-0,27
2
0,79
-0,10
2
1,20
0,08
2
1,70
0,23
--0,310
2
0,34
--0,47
2
0,45
--0,35
2
0,76
-.0,12
2
0,94
--0,0/u
2
1,41
0,15
0,000
2
0,25
--0M)
2
'0,35
--0,45
2
0,56
-0,25
2
0,74
-0,13
2
1,10
0,04
Note. C3= C
-PU(III)' C4 = Cal(IV), n is the number of experimental points.
TABLE 3. Values of the Arbitrary Equili-
brium Constant and the Arbitrary Standard
Gibbs Energy of the Reaction Pu4 + Cl-
Pu3+ + 1/2 C12 in Molten NaCl-2CsC1
7% "C
Exponent
of Po,
1,4 IC.
I .
L1G * , kJ/
mole
550
22
0,50+0,02
-0,64?0,06
1,23+0,03
1-10,0+09
600
16
0,52+0,02
-0,39+0,06
),412:0,01"
+6,5+1,0
650
22
0,51+0,01
-0,244-0,05
),58
d 4,2+0,9
700
16
0,51=E0,01
-0,12+0,05
1,79+0,09
2.21?0,11
750
29
0,50+0,01
0,00?0,05
1,00+0,12
*n is the number of experimental points.
From the function for the arbitrary equilibrium constant of reaction (1)
1,11(111) n1/2
I Cl,
Cl'ii( IV)
we find the ratio of the equilibrium concentrations of tri- and tetravalent plutonium:
(6)
Crum]) K*13,112, (7)
CPu(IV)
where K* is the arbitrary equilibrium constant of reaction (1); PC12 rdpresents the relative
partial pressure of chlorine in the gas phase (related to standard pressure 1.01.105 Pa).
Substituting function
(7)
into Eq. (5), we arrive at the expression
e "2/k5 3 -- 04 d- / 80V*11 , (8)
which permits a determination of the ratio of the molar extinction coefficients of tetra-
valent plutonium at 7200 and 5300 cm-I as the segment intercepted on the y axis by a straight
line constructed in a plot of k7.2/0.5 versus P-11/2.
C2
Graphical verification of Eq. (8) showed (Fig. 2) that the ratio k7'2/k5" is propor-
tional to the quantity P-I/2, while the ratio e'4/E4 is equal to zero. Consequently, the
C12
contribution of tetravalent plutonium to the absorption of the melt at 7200 cm-I can be
neglected.
The summary plutonium concentration in the melt Cpu as a sum of the equilibrium con-
centrations of tri- and tetravalent plutonium can be expressed by the equation
cpu=k7.2/63+k5'3/E4,
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TABLE 4. Values of the Arbitrary Formal
Redox Potential of the Couple Pu4+/Pu3+
(relative to a chloride reference electrode)
from which
Solvent
- ,/m-)?
1.51 FC
GOWC
G111? C
700? C
770? C
LiC1- *
0,023
0,046
0,072
0,090
0,120
(40 mole /0)
LAU. CsC1
?0,090
--0,060
?0,024
0,010
0,042'
(55 mole ?Pt
NaC1-04C1
?0,110
?0,084
?0,056
?0.028
0,000
(66 mole t
*Calculation according to the data of [1].
tCalculation according to the data of [2].
'The present work.
F4 == I WN,--lc 7-210.
The values of c4 (see Table 1), calculated according to Eq. (10), as well as the values
of e3, were used to find the equilibrium concentrations of tri- and tetravalent plutonium in
the study of the equilibrium of reaction (1).
(10)
The arbitrary equilibrium constant of reaction (1) was calculated from the expression
obtained after taking the logarithm of Eq. (7):
Cpuum
la lgK* ?1/21g Pcie
b CPu( 1V)
Table 2 presents the experimental values of Cpu (III) /CPu(IV) as a function of the relative
partial pressure of chlorine and the temperature, while Table 3 presents the values of the
exponent of Pc12 and the arbitrary equilibrium constant of reaction (1), calculated by the
method of least squares according to Eq. (11) and the data of Table 2. From Table 3 it is
evident that the relative partial pressure of chlorine in the gas phase enters into the ex-
pression for the arbitrary equilibrium constant of reaction (1) to the exponent 0.5.
The temperature dependence of the arbitrary equilibrium constant of reaction (1) is
satisfactorily described by the equation
1glf*--2,52--2570T-1+-0.05. (12)
Using Eq. (12) we calculated the arbitrary formal redox potential of the couple Pu417
Pu3+ relative to a chloride reference electrode:
nui,/pu3+ 2.11?! ig
? ?0.51 --5.0.10-'?T 0,01v
and the change in the arbitrary standard Gibbs energy (AG*1) for reaction (1) in molten
NaC1-2CsCl:
AGT ?2,3RT lg K*
? ? 4,8 ?10-2T -1- 1, kJ/mole.
(13)
(14)
From Eq. (14) we found the changes in the entropy and thermal effect of reaction (1)
AS*--48?2 J/rmle.clegK:
Aii*--49?2,1q/mole.
Earlier [8] the emf method was used to find AG* in the-formation of dilute solutions
of trivalent plutonium, which for molten NaCl-2CsC1 is equal to
AG*pitch? ? 1.09+ 3,11 ?10-4T, MJ/mole.
Therefore we can calculate AG* in the formation of dilute solutions of tetravalent plutonium.
It is made up of AGpuci, and AG/: of reaction (1), taken with the opposite sign, i.e.,
AGPuci, = AGci,d- (_AG*)
= ?1,14 -F 3,6.10-4T, MJ/mole.
(15)
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Using the expression cited in the work of Benz [9] for the change in the standard Gibbs
energy in the formation of liquid plutonium tetrachloride from the elements
= - 0,89 -1- 2.1-10-'7', MJ/mole, (17)
and Eq. (16), we calculated the energy of mixing of liquid plutonium tetrachloride with
molten NaC1-2CsC1:
AGmix Aquci,
? ?0.25 + 1.5 ?10-"T MJ/mole.
(18)
From the results cited it follows that the stability of the tetravalent state of plu-
tonium in molten NaCl-2CsCl, just as in molten LiCl-KCI [1] and LiC1-CsC1 [2], decreases
with increasing temperature, since the equilibrium constant of reaction (1) increases. In
the series of solvents LiC - KC1, LiC1 - CsC1 and NaCl - 2CsC1, the arbitrary formal redox
potential of the couple Pu4-17Pu3 in the interval 550-750?C is displaced in the negative di-
rection (Table 4), which is evidence of an increase in the stability of tetravalent plutonium
in this solvent series.
The mixing of liquid plutonium tetrachloride with molten NaCI-2CsC1 is an exothermic
process, evidently due to the formation of chloride complexes of tetravalent plutonium of the
PuC1:- type in the melt [10].
APPENDIX
The contour of the spectrum of tetravalent plutonium was calculated according to the
equation
kvi ?/c7'2Fv1F71
" CPu
cru k 7,28;1
which was obtained in simultaneous solution of the ? following functions:
lc =83iCpuo11) +84 CPti(Ev)
=Cpuctil)-1-- CPu(1V);
(II)" k7'2c1;
if1,11(1V) = 84 L'Pu,
(19)
(20)
(21)
(22)
(23)
where kvi is the index of absorption of a melt containing equilibrium concentrations of tri-
and tetravalent plutonium at a set partial pressure of chlorine in the gas phase at the i-th
wave number, cm", 03)1, EY,1, molar extinction coefficients of tri- and tetravalent plutonium
at the i-th wave number, liters/(molecm), Cpu, Cpu(III), C Pu(IV), .summary and equilibrium
Pu
concentrations of tri and tetravalent plutonium in the melt, M' kyl(IV)'index of absorption
of a melt containing only tetravalent plutonium with concentration Cpu.
LITERATURE CITED
1. G. Landresse and G. Duyckaerts, Inorg. Nucl. Chem. Lett., 10, No. 8, 675 (1974).
2. G. Landresse and G. Duyckaerts, ibid., No. 11, 1051.
3. M. V. Smirnov, Electrode Potentials in Molten Chlorides [in Russian], Nauka, Moscow
(1973
) .
4. V. V. Gushchin and V. M. Barinov, Prib. Tekh. Eksp., 3, 279 (1972).
5. M. V. Smirnov, V. P. Stepanov, and T. Mukatov, in: Transactions of the Institute
of Electrochemistry [in Russian], Vol. 16, Izd. UNTs Akad. Nauk SSSR, Sverdlovsk
(1972), p. 16.
6. Y. Swanson, J. Phys. Chem., 68, 438 (1964).
7. S. K. Vavilov et al., in: Summaries of Reports at the Fifth All-Union Conference on
Physical Chemistry and Electrochemistry of Molten Salts [in Russian], Part 1, Izd.
UNTs Akad. Nauk SSSR, Sverdlovsk (1973), p. 67.
8. V. M. Silin and 0. V. Skiba, Preprint of the V. I. Lenin Scientific-Research Institute
of Atomic Reactors P-118 (1971).
535
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9. R. Benz, J. Inorg. Nucl. Chem., 24, 1191 (1962).
10. Yu. A. Barbanel' and V. R. Klokman, Radiokhimiya, 18, No. 5, 699 (1976).
DETERMINATION OF THE COEFFICIENTS OF SEPARATION OF BORON ISOTOPES
IN THE DISTILLATION OF BC13 IN THE TEMPERATURE RANGE 278-438?K
A. S. Aloev, V. A. Kaminskii, UDC 621.039.33
A. G. Kudziev, and R. Sh. Metreveli
The production of boron isotopes is an important scientific and technical problem,
therefore, it is necessary to select the most economically efficient method of separation
of these isotopes. Among the methods suitable for this purpose, researchers have always
been attracted by the distillation of BC13, thanks to the cheap and readily available initial
raw material and the simple technological formulation of the process. The deciding factor
in the question of the use of the above-mentioned method is the value of the coefficient of
separation and its temperature dependence. Despite a number of investigations [1-4], this
problem has not received a final resolution, especially for the region of increased temper-
ature. In view of this, in the present work an investigation was made of the temperature de-
pendence of the coefficient of enrichment of two mutually supplementing and controlling
methods. One of them permitted direct measurement of the difference of the saturated vapor
pressures of isotopically substituted varieties of BC13, while the other permitted direct
estimation of the separation achieved on the column in the process of fractionation of BC13,
all the way up to a temperature close to the critical point.
Determination of the Coefficient of Enrichment by a Differential Method. For a mea-
surement of the coefficient of enrichment we used the setup whose scheme is presented in
Fig. 1. A copper block 60 mm in diameter and 70 mm high with two working chambers with
volumes of 10 cm3 each was placed in a vessel with a boiling temperature-controlling liquid,
the vapors of which were condensed in a condenser. The boiling 'point of the temperature-
controlling liquid was determined by the air pressure in the cylinder. On account of the
rather large volume of the cylinder and the constant conditions of boiling, the pressure in
the thermostat system and the boiling point of the temperature controlling liqiud were pre-
served with high accuracy in the process of the experiment. The pressure difference was
measured with the aid of a brass mercury differential manometer and a KM-6 cathetometer. The
use of mercury, despite its great density, was due to the necessity of minimizing the sol-
ubility of the gas in the manometric liquid, especially in the high-pressure region.
The differential manometer was placed in a warming jacket together with the tubes in
order to exclude condensation of BC13 vapors in them. Up to 300?K the absolute pressure
was measured with mercury manometers, above it, the pressure was determined according to the
curve of the dependence of the saturated vapor pressure of BC13 on the temperature, consider-
ing the temperature of the copper block of the thermostat. The accuracy of the measurement
of the latter was ensured by the duplicate measurements of the temperature and pressure of
the boiling temperature-controlling liquid.
The boron trichloride used in this work (both enriched with 10B to 86.57 and of the
natural isotopic composition) was produced from BF3 according to the reaction
BF3+A1C13-13C13-HAIF3.
Its purification was achieved by several vacuum redistillations at 190 and 210?C, followed
by distillation of BC13 on a packed glass column 15 mm in diameter and 1 mm long at the
normal boiling point. The temperature dependence of the saturated vapor pressure of purified
BC13 of the natural isotopic composition coincided highly accurately with the published data,
which was a criterion of the absence of impurities that might have influenced the results of
the measurements.
Translated from Atomnaya finergiya, Vol. 49, No. 2, pp. 98-101, August, 1980. Original
article submitted June 26, 1979, revision submitted January 24, 1980.
536 0038-531X/80/4902-0536$07.50 ?1981 Plenum Publishing Corporation
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Declassified and Approved For Release 2013/02/14: CIA-RDP10-02196R000800040002-1
Fig. 1. Scheme of thermostat: 1) thermal
insulation; 2) casing with heater) 3) work-
ing chambers; 4) copper block; 5) condenser;
6) viewing window; 7) cylinder of manostat;
8) differential manometer.
TABLE 1. Values of the Coefficient of
Enrichment at Various Temperatures, Deter-
mined by a Differential Method
Temp.,
?K
P2.
11)-5 Pa
Am Pa
Rel. error,
/0
278
0,758
18,9
0,0030
4,3
285
0,971
203,5
0,0030
4,0
100
1,714
255,4
0,0021
3,3
03
2-, 527
208,2
0,0014
4,8
138
4,852
2053,
0,0008.
3,7
350
0,409
305,9
0,0000
? 3,4
393
10,072
325,8
-0,0002
2,11
To ascertain equality of the temperatures of the two working chambers, control experi-
ments were conducted at 285 and 393?K, in which both chambers were loaded with boron tri-
chloride of the natural isotopic composition. In this case, with an accuracy within 0.01
mm, no difference was noted in the levels of mercury in the differential manometer.
The results of the experiments are presented in Table 1. The pressure difference Ap
was determined according to a large number of measurements, in the process of which the sam-
ples in the chambers changed places. The standard deviation in the values of Ap was 3.1 Pa.
When nonmonoisotopic samples are used, according to [5, 6], the coefficient of enrich-
ment is expressed by the formula
Ap ( + Bp?
E \ ?
P1.1 (Cenr-Cn\
(1)
obtained with the assumption of ideality of the liquid phase and equality of the second
virial coefficients of isotopically substituted molecules, which is fulfilled in practice for
all the isotopes, with the exception of hydrogen and helium isotopes. Here pl and 131 are the
saturated vapor pressures of the pure components, Cenr and Cn are the concentrations of en-
riched and normal samples, B is the second virial coefficient. The unknown quantities pl and
P2 entering into this formula for BC13 can be replaced by the corresponding values of the ab-
solute pressure of samples of the enriched and natural compositions with an accuracy within
0.06%, after which the formula for calculation of c takes the following final form:
Ap
?1+ Bpi
P2 (Cenr-Cn` RT)
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537
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0,003
0,002
0,001
0
300
350
400
T,K
Fig. 2. Dependence of the coefficient of
enrichment on the temperature: 0) differ-
ential method,. method of fractionation;
N7,0, 0, ? ) data of [1-4], respectively.
In the calculation of the second virial coefficient we used the force constants of
interaction for the Lennard-Jones potential, cited in [7]. Within the investigated temper-
ature region the value of B remains negative, so that the correction for nonideality of the
gas phase led to a decrease in the coefficients of enrichment. Within the entire investi-
gated temperature region, the compound "BC13 proved more volatile. As can be seen from
Table 1, the coefficient of separation decreases separation with increasing temperature. It
should be noted that the increase in the relative error in the transition to the temperature
313?K is caused by a change in the method of determining the absolute pressure.
Determination of the Coefficient of Enrichment on a Column. For the determination of
the coefficient of separation of boron isotopes in the fractionation of BC13 at 300-438?K,
we used a column with inner diameter 15 mm and length of the packed portion 1.5 in, filled
with packing of segments of a triangular wire spiral 2.2 x 2 mm. The column had an evapora-
tor with a 500-cm2 capacity with an inner electric heater. Together with the evaporator, it
was surrounded by a vacuum jacket with a compensating electric heating element situated above
it. The condenser was cooled with flowing water, its upper part was connected to a cylinder
in which a set pressure of argon, determining the temperature of the process, was maintained.
On the column there was a device for measuring the irrigation flux. The column was made of
stainless steel, while the tubes of the level gauge and flow meter were made of thick-walled
glass, which permitted work up to the critical pressure 3.87.106 Pa.
The small values of the separation factor and their substantial decrease with increas-
ing temperature excluded the possibility of use of methods of determination of e according
to an analysis of the dependence of the concentration on the collection and according to the
kinetics of the change in the composition in the period of a nonsteady-state process. There-
fore, all the experiments were conducted with complete irrigation and a fixed evaporator
power of 33 W.
For a determination of the temperature dependence of the coefficient of enrichment ac-
cording to the values of the equilibrium separation factor obtained as a result of the ex-
periments, we used the values of the height of an equivalent theoretical plate (HETT), cal-
culated by the method of [8, 9]. In view of the small column diameter and the large values
of the irrigation density, the number of zones of complete statis A can be assumed equal to
zero, and the following formula can be used for the determination of the HETT:
1
EinD 1 l'`I ) i_ 11 I'm 1 (3)
HETT - i q c
R2 n g 1 2 R2 40 Di _ '
which in the region of the loads used leads to an error of no more than 10%. For packing
of segments of a triangular spiral 2.2 x 2.0 mm, the number of elements in a unit volume
N = 100, equivalent radius of the channel R = 0.7 mm, and the averagevalue of the sine of
the angle of inclination of the elements of the packing i = 0.9. The remaining quantities
in this formula are: the volume flows of gas in the ring and central regions of the channel
qr and qc, the radius of the central region ro, the liquid flow rate F, and the film thick-
ness m, depend on the load and the working conditions (temperature and pressure in the column)
[10]. The formulas for their calculation and the sequence of operations were described in
detail in [8], the diffusion coefficients Dg and D1 were calculated according to the formulas
of [11].
The results of a calculation of the HETT and the experimental values of the equilibrium
separation factor are presented in Table 2. It should be noted that work at a fixed power of
the evaporator led to an increase in the load with increasing temperature on account of a
538
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Declassified and Approved For Release 2013/02/14: CIA-RDP10-02196R000800040002-1
TABLE 2. Experimental Values of the
Equilibrium Separation Factor and Calcu-
lated Values of the HETT for Various
Temperatures
Temp.,
?K
Pressure
in colt).
1.0-5 Pa
Irriga-
tion
density,
(koolls.
Calc.
value of
HETT,
cm
No. of
stages in
column
Equilibrium
separation
factor, go
sec)
300
1,71
0,94
1,90
79
1,215
340
5,05
1,00
1,94 .
77
, 1,105
370
10,10
1,13
2,0
75
1,065
410
20,77
1,46
2,2
68
1,032
430
28,3
1,88
2,3
00
1,019
438
31,8
_1,96
2,7
56
1,013
p.
decrease in the heat of vaporization. In this case, the increase in irrigation density de-
termined a more rapid increase in the HETT than the competing influence of the actual temp-
erature of the process on the HETT.
The dependence of the coefficient of enrichment on the temperature obtained on the
column is presented in Fig. 2. Since E is determined by the expression e is determined by
the expression s = h ln q0/H (where h = HETT, while H is the height of the column), the ab-
solute error of AC was calculated according to the formula
Ac=Ili go Ah /1'1;12" AH+7170- Ago.
11
In the entire region of measurements, A8 did not exceed ?0.0005.
DISCUSSION OF RESULTS
(4)
As can be seen from Fig. 2, the results of the two methods are in rather good agree-
ment. Moreover, in the region of the normal boiling point of BC13, the two methods gave
results close to the data of other authors, which also indicates correctness of the methods
used, including the new method of estimation of e according to the calculated value of the
HETT. However, even if we refrain from estimating c, the dependence of the equilibrium sep-
aration factor obtained on the column unambiguously indicates a deterioration of the separa-
tion with increasing temperature and a virtual disappearance of the separating effect at a
temperature close to the critical value. This conclusion is correct despite the large neg-
ative error in the region close to the critical temperature.
The temperature dependence of the coefficient of enrichment obtained is evidence of
the inadvisability of using the method of fraction of BC13 for the production of boron iso-
topes.
LITERATURE CITED
1. M. Green and G. Martin, Trans. Faraday Soc., 48, No. 353, 416 (1952).
2. F. Muhlenpfordt et al., in: Proc. Int. Symp. Isotope Separation, Amsterdam
(1958), p. 408.
3. M. Ya. Kats, G. M. Kukavadze, and R. L. Serdyuk, Zh. Teor. Fiz., 26, No. 12,
2744 (1956).
4. N. N. Sevryugova, 0. V. Uvarov, and N. M. Zhavoronkov, At. Energ., No. 4,
113 (1956).
5. A. M. Rozen, Theory of the Separation of Isotopes in Columns
Moscow (1960).
6. A. V. Borisov, Candidate's Dissertation, Moscow State Univ.,
7. I. F. Golubev and N. E. Gnezdilov, Viscosity of Gas Mixtures
Goskomiteta Standartov, Moscow (1971).
8. V. A. Kaminskii and N. A. Giorgadze, Isotopenpraxis, 2, No. 1, 1 (1973)
9. V. A. Kaminskii and N. A. Giorgadze, ibid., 1A, No. 9, 321 (1978).
10. V. A. Kaminskii and N. A. Giorgadze, Zh. Prikl. Khim., L., No. 10, 2266 (1978).
11. J. 0. Hirschfelder et al., Molecular Theory of Gases and Liquids, Wiley (1964).
[in Russian], Atomizdat,
Moscow (1966).
[in Russian],
539
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Declassified and Approved For Release 2013/02/14: CIA-RDP10-02196R000800040002-1
POSSIBILITIES OF PROTON-ACTIVATION ANALYSIS FOR DETERMINING
THE CONTENT OF ELEMENTS FROM SHORT-LIVED RADIONUCLIDES
V. A. Muminov, S. Mukhammedov, UDC 543.53
and A. Vasidov
The proton-activation method of analysis used when determining trace elements in ma-
terials from their nuclear properties is not suitable for instrumental neutron-activation
analysis [1-3] or for investigating the elementary composition of the various parts of sam-
ples [4]. For multielement analysis, we mainly use relatively long-lived radionuclides [5-
7]. We can develop highly sensitive and rapid methods of activation analysis using charged
particles on the basis of nuclear reactions that form radionuclides with halflives TI/2
1000 sec. However, few articles have so far been published on methods of determining ele-
ments from short-lived radionuclides.
Reference [8] indicates the possibilities of determining eight elements with Z 34 in
13 matrices by the active products of reactions with 1 -5.;T1/2 5. 60 sec. To determine ele-
ments with concentrations 10-7 ? 10-1? gig, we must often use radionuclides with TI/2 > 1
min [9]. Rapid methods of determining nitrogen [10-12], carbon, magnesium, silicon [13],
and sulfur [14-15] have been developed. Nevertheless, there have been very few articles
published up to the present that investigate the possibilities of determining elements by
the use of radionuclides with TI/2 = 10-1000 sec that arise out of reactions based on pro-
tons. In a previous article [16], we estimated the sensitivity of determining sulfur, chrom-
ium, nickel, copper, zinc, and molybdenum by the proton-activation method, which proved to
be comparable with the sensitivity of other nuclear-physical methods. In the present article,
we assess the possibilities of determining 20 elements by measuring the emission of y quanta
after activation by protons with energies Ep = 12 MeV, and we also give the results of in-
vestigations of nondestructive, rapid, and selective methods of analysis.
In the nuclide that is most widely distributed in nature, the reaction has a large sec-
tion, and in this instance a radionuclide with TI/2 > 1000 sec is induced. In this case, we
are not considering nuclides with a natural occurrence of less than 1%, radionuclides with
relative intensities of y quanta of less than 1%, or elements which in their reactions with
protons do not form radionuclides with TI/2 = 10-1000 sec. Determining these elements by
proton-activation methods of analysis is of particular interest, since it is especially dif-
ficult to determine them by any other means, in view of the unsuitable activation character-
istics of the reaction. We therefore, in the present article, compare the analytical param-
eters of the various nuclear methods of analysis.
Experimental Technique. In our experiment, we used a 150-cm cyclotron of the Institute
of Nuclear Physics of the Academy of Sciences of the Uzbek SSR accelerating protons up to an
energy of 18 MeV. The samples were irradiated with the aid of a semiautomatic installation
equipped with a pneumatic rabbit (Fig. 1). The sample, held in a Duralumin target holder, is
fed to the position of irradiation along a polyethylene tube by the action of compressed air.
The target holder is stopped in a small chamber partitioned off from the main chamber by a
thin nickel roil (", 20 pm). The center of the cylindrical target holder coincides with
that of a 10-mm collimator. The former is pushed against a rubber seal and limit switch by
the action of the compressed air. The limit switch then cuts off the supply of compressed
air. The beam is first conducted to a refrigerated "Shutter" which, after receiving the
target holder, is opened by an electromagnet on the command of the limit switch to start the
irradiation of the sample. The exposure time is set with the aid of a relay. The small
chamber is insulated from the large chamber by Teflon. The target holder is served by a
Faraday cylinder. After irradiation of the samples, the shutter closes and the target holder
is transported by compressed air to the position at which the radioactivity is measured. The
Translated from Atomnaya Anergiya, Vol. 49, No. 2, pp. 101-105, August, 1980. Orig-
inal article submitted September 28, 1979.
540 0038-531X/80/4902-0540$07.50 0 1981 Plenum Publishing Corporation
Declassified and Approved For Release 2013/02/14: CIA-RDP10-02196R000800040002-1
Declassified and Approved For Release 2013/02/14: CIA-RDP10-02196R000800040002-1
TABLE 1. Emissions of y Quanta Yy [106 quanta (sec. pA)] and Sensitivity in Deter-
mining Elements at Ep = 10 MeV [10-9 g/(g.11A-1)]
Determined element
and product of re-
action
Energy and in-
tensity of quanta
Y
Sensi-
tivity of
analysis *
MeV
8
11)
1 I
1 2
1013, loc
(1,718(100)
9 9
?1,0
9,8
15,2
200
13c , 13N
0,510(200)
150
27o
340
400
430
470
500
3,70
lic,
14N -,,. 140
ilio __... 13N
0,510(20())
2,312(99)
0,510(200)
480
72o
480
1700
197
9110
25(10
410
1100
3ioo
650
1800
41.lio
951)
2'00
5000
1144
21;0)1
0,5
?,)
0,9
2.3Na _,.. ''Mg
0,439(9,1)
11
42
61
100 '
130
174
"Cr _, "Mn
1,434(98)
910
2100
:1480
5200
7120
0,5
"Ni --.- "Cu
1,332(88)
42
92
183
125
570
935
5,1
"Ca
0,991(43)
21
40
65
79
80s, ,. "Br
0,012(7)
91
136
170
214
250
280
308
6,6
7913? _, 797)1K r
0,127(30)
5,5
15
28
44
111;
97
134
251)
"lir -)- ''"Kr
89y , "Zr
0,190(05)
0,57800(1)
21
80
41;
180
78
300
110
440
147
595
200
r r
0,0
'Zr ->- "0"1Nb
).41-0 _, 11,2,T,
0,1225(71)
0,773(97)
IF
(8
08
30
68
420
71.0
)12cd _? .0.21,1
0,6171(27,(F)
39,6
88
1:1!)
198
200
12
10)!..;? _, 10.sb
1,293(88)
4,))
9,5
16,8
25
:i5
41
59
47
118s? _, 118Sb
1,n0om
9,8
14
18,1;
-A
29,0
89
120$,, _, '"80
1.)41la , '''La
1,171(2)
0,6049(1011)
0,1
10,8
0,3
14,4
0,6
17,4
1,2
21,5
2,1
110
2G00
-",f.,a
0,8185(2,5)
0,3
0,5
1,1
2,1
3200
139L? _, 1:wince
0,75403)
9,2
43
78
128
370
1411),. ,. 146)1Nd
0,755(92)
0,2
18
25
75
89
''Nil -. 1421'16
1,575(3,3)
(1,1
0,3
0,6
1,2
2,0
2600
isow _, 18,11/,
0,902(99,4)
2,0
4,8
2670
*The sensitivity is expressed as the quantity of the element being determined per
1 g of the material at which irradiation forms a radionuclide with an activity of
1000 y quanta/min (T2/2 5- 1 min) and 100 y quanta/min (T2/2 > 1 min).
time needed to transport the samples to the measurement station, a distance of 15 mm, is 1-5
sec. Behind the shutter on the same side as the sample there is a drum with twelve holes
for selecting absorbers. The drum can be rotated by a motor. The energy of the protons is
reduced with the aid of aluminum absorbers. In view of the fact that at proton energies
> 12 MeV a large number of interfering reactions of the (p, 2n), (p, 3n), (p, pn), (p, d),
etc. types take place, this energy was chosen as optimum. The charge on the Faraday cylinder
was measured by a current integrator.
Various compounds of the experimental elements type CLDA served as target, being glued
to the surface of the foil by a sticky suspension of polystyrene dissolved in dichlorethane
[9]. This film was subjected to irradiation by a 0.01-0.3 9A beam of protons for 5-20 sec.
The activity of the radionuclides was measured with the aid of a semiconductor Ge(Li)
detector with a working volume of 90 cm3 connected to a multichannel AI-4096 analyzer. The
energy resolution of the detector was not lower than 9 keV for the 1330 keV "Co line. The
memory of the analyzer was divided into 16 groups of 256 channels, the information in the
last group being aCcumulated to the extent that the first group is filled. We were thus able
to measure the activity of 16 targets which facilitated our work with short-lived radionu-
clides. The detector was energy calibrated and the relative efficiency was measured with the
aid of precision sources of y quanta.
Discussing the Results. Depending upon the halflife of the nuclide, the films were
irradiated either separately as one sample or as several samples by combining them in a stack.
The emission of quanta from the thin targets can be found by employing the expression
Y., 1E1,1 =-Stradej mfAtnifel/Ax(1--e-mrad) X
(1)
X (1-- em [y quanta. cm2/(sec ?A
where S is the area of the photopeak in pulses, trad, tm, tref, irradiation, measurement of
radioactivity, and sample refrigeration times, respectivel, sec, e, efficiency of the de-
tector, f, proportion of the element being studied present in the target by weight, Ax, thick-
ness of the target, mg/cm2, q, accumulated charge, pC, A, decay constant, sec-1, the emis-
sions of the thin targets are summated over an interval of thickness, the differences of the
541
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Declassified and Approved For Release 2013/02/14: CIA-RDP10-02196R000800040002-1
Fig. 1. Diagram of equipment with pneumatic
rabbit for irradiating samples in a cyclotron:
1) beam of protons, 2, 7) graphite collinators;
3) refrigerated shutter; 4) drum with absorbers;
5) motor; 6) insulating ring; 8) nickel foil; 9)
flange; 10) tube for feeding compressed air; 11)
polyethylene tube and penumatic rabbit; 12) tar-
get holder; 13) limit switch; 14) monitor; 15)
sample.
0
Fig. 2. Emissions from thin targets of certain
radionuclides formed by the reactions (p, n): a)
1(x4): "Be loc, 2 (x 0.2): 124Ba
b) 1: 14N 4 0 , 2: 25Cr 52MMn, 0 1 1 25N034'
23Ng, 2: 112cd 4. 1121n.
ranges corresponding to the initial energy of the protons and the range of the reaction,
gives us the emission of y quanta for a thick target:
Yv = Y., EJ] Ax quantagsec?
where R is the range of the particle, mg/cm2. The relationship of Yy to proton energy is
built up by using a "range?energy" table [17].
Figure 2 shows the emissions of y quanta from the thin targets. Table 1 gives the
emission of the more intense y quanta from thick targets for the proton energy range 6-12
MeV. Table 1 also shows the sensitivity in determining elements at Ep = 10 MeV.
542
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Declassified and Approved For Release 2013/02/14: CIA-RDP10-02196R000800040002-1
TABLE 2. Comparison of the Emissions of Radionuclides Formed by Activation of Ele-
ments by Various Nuclear Particles
Activation by protons*
Activatonbyfaa
neutroml
Activation by slow neu-
trons $
Activation by ycluantai.
nuclide
Y, 106
decays. ?
sec' %W
nuclide
Y, 106
decays.
ecI _t ? --1
g
nuclide
[ Y, 106
decays.
ec1g 1 -. -
nuclide
Y, 106
decays. ?
sec-l-gl
NB --)- "C
14N , 140
22Na -,- 22Mg
"Cr -4- "n)'Mn
"Ni -4- "Cu
"Zn -->- "Ga
"Sc -s- "Br
793r -s- "'Kr
"Br , simKr
soy , 89M zr
"Zr -)- "?m?Nb
"Tc
ii2c,d ,312.1?
illiSn _>. nos')
u8Sn -s- 118Sb
12"Sn -).- '20Sb .
12413a ._.? 134La
looBa , "'La
looLa , 139mCe
],o-pr _,.. 1.417nN d
"2Nd -4-1?42Pm
low ,Isoile
57,3
0074,7
8450,1
7102
2300.2
287
1310
1158
030,5
1579
281,0
3,21
2451,4
180,4
80,8
3130,4
2,8
88,3
200,9
84,8
70,2
3,4
1113 ?->- "Be
14N _, 1.3N
"Na ?->.- "No
"Cr --0- '2V
''Ni -s- ''Co
"Zr, _? "Cu
"Sc --)- "in80
"Br -4- "Br
8"Y -4-8'''''Y ?
"Zr -4- "Y
"Mo -)- "Mo
111Cd ->- """Cd
124s, ? ins,
,3813a ->- I:""113a
141 Pr 14019.
186w , 185mw
44,0
0,3
1099
50,1
0,007
0,5
150,7
134,8
270,0
0,18
4,98
0,79
2,4
280,2
574,1
43,0
"Na -4-24Na
"Cr ->s 'OCT..
"Ni -)- "Ni
"Zn ->- ""1"Zn
"Sc -->- 8'5e
"Br -,- "Br
bby , by
"Zr ->- "Zr
'"Mo -->- "'Me
'''Cd -)- ?'Cd
124Sn -)- 12'Sn
"813a ->- ?0'lfl,
'"La ? 1401-?,
"'Pr -4- "21'r
""Nd -s "'Nil
Isow _.1s7vy
0040
82,4
428
75,4
16000
293000
932
3,7
11,3
3,81
0,037
42,0
6450
15100
3200
9790
"N ->- "N
22Na -4- Na
"Cr --4- "Cr
''Ni -).- "Ni
"Zn --s- "Zn
"fir - "Br
by ? 88 y
"Zr -,- '')Zr
"2Mo -0-91Mo
04cd _, '''Ag
1125n -4- "1Sn
1411)1) ?lop,.
H2Nd ->- "'Nil
lsovv _, vow
70
0,0009
2
0,3
50
500
0,04
0,7
20
0,1
3
1000
20
0,05
*Proton current 1 pA/cm2.
tNeutron current density 109 cm-2'sec-1, energy 14 MeV, trad = 5 min [18].
tNeutron current density 1015 cm-2sec-1, trad = 1 h [18].
+Electron current 100 pA, energy Ey = 25 MeV, trad = 10 min [19].
The quanta were emitted from various nuclides at a level of 107-101? quanta/(sec.1JA).
A sensitivity of determination of (2670-0.5).10-9 g/(g. 0A-1) is achieved with the samples
irradiated up to saturation by a 1-pA proton beam current in cases where the protons of the
matrix (Li, Be, B, Al, Mn, Co, Eu, Ta, Bi, etc.) are not activated or where radionuclides
with short halflives are not formed and where the concentration of other traces is below
10-7 g/g (which means that they do not have any marked influence on the analysis). In all
other cases, the sensitivity of nondestructive testing by activation analysis varies over the
range 10-5-10-7 g/(g.pA-1) depending on the emission of radionuclides from the base and trace
impurities. The sensitivity in determining chromium, nitrogen, nickel, selenium, yttrium,
cadmium, and promethium is 5-10-1? to 4.10-7 g/(g.pA-1), while that for other elements is no
worse than 2-10-5 g/(g?pA-1).
As regards the specific use of various nuclear methods in elementary analysis, it is
of interest to compare the emissions of radionuclides arising during activation of the ele-
ments by protons, thermal and fast neutrons, and high-energy y quanta. Table 2 lists the
radionuclides that have the highest emission when activated by penetrating radiation. As
we can see from Table 1 the emissions of radionuclides arising following activation of the
sample by protons is always 10-108 times the emission of active products of reactions based
on fast neutrons. Furthermore, it is mainly long-lived radionuclides that are formed when
elements are activated by slow neutrons, and the emissions of these are close to the emission
by protons. Sodium, selenium, bromide, barium, neodymium, and tungsten all have high emis-
sions. If we use y quanta during the activation, then the emissions of the products of
photonuclear reactions with Mo, Br, and Pr are 2-10 times as great, and in all the remaining
cases lower by factors of 10-1000 than the emission of the radionuclides formed by nuclear
reactions with protons.
We can see from what has been said so far that irradiation of samples for short periods
with high intensity beams of protons is a way of determining the majority of the groups of
elements studied, with a limit of observation of 10-5-10-8 %.
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We have, therefore, shown that proton activation analysis by means of short-lived
products of nuclear reaction has the following advantages over other methods of analysis:
The sensitivity of determining elements is (2670-0.5).10-9 g/(g.TIA-1), which in the
majority of instances is 10-1000 times the sensitivity of other methods. When large proton
fluxes are used (> 1 11A), this limit will be lower.
The methods are nondestructive and rapid in use and the cost of determining one ele-
ment is less than the cost of analysis by means of long-lived radionuclides, since the time
needed to irradiate the sample is markedly lower.
The nondestructive analysis of matrices having large activation sections for thermal
and fast neutrons and y quanta is possible.
The content of elements can be determined, which would be impossible using other
methods, due to interference.
The method can be used for multicyclic and automated analysis.
The method has certain drawbacks, however, connected with difficulties in suppressing
the background due to the more long-lived radionuclides (particularly when the number of
these is large) and the Compton distribution arising out of annihilated quanta with constant,
high levels of intensity, since almost all the radionuclides decay by radiating 8+ particles.
LITERATURE CITED
1. P. Benaben, I. Barrandon, and J. Debrun, Anal. Chim. Acta., 78, 129 (1975).
2. J. Debrun et al., Anal. Chem., 47, 637 (1975).
3. N Krasnov, Ju. Sevasthyanov, I. Konstantinov, J. Radioanal. Chem., 16, 395 (1973).
4. V. A. Muminov, C. Mukhammedov, and R. A. Khaidarov, Zavod. Lab., 1, 40 (1977).
5. B. V. Zatolokin, I. 0. Konstantinov, and N. N. Krasnov, At. Energ., 42, No. 4, 311
(1977
) .
6. J. Barrandon et al., Nucl. Instrum. Methods, 127, 269 (1975).
7. J. Debrun, J. Barrandon, and P. Beneben, Anal. Chem., 48, 167 (1976).
8. J. Debrun, D. Riddle, and E. Schweikert, Anal. Chem., 44, 1386 (1977).
9. V. A. Muminov et al., Nuclear Methods of Analysis and Checking Manufacturing Processes,
[in Russian], Fan, Tashkent (1976), p. 50.
10. B. Sultanov, Authors Abstract of Candidate's Dissertation, Institute of Nuclear
Physics, Academy of Sciences of the Uzbek SSR, Tashkent (1977).
11. S. Bankert, S. Bloom, and G. Sauter, Anal. Chem., 45, 692 (1973).
12. I. V. Kozachevskii, V. D. Knozorov, and V. V. Sokol'skii, in: Applied Nuclear
Physics, Book 2 [in Russian], Fan, Tashkent (1973), p. 123.
13. I. McGinly and E. Schweikert, Anal. Chem., 47, 2403 (1975).
14. T. Burton, D. Swindle, and E. Schweikert, Radiochem. Radioanal. Lett., 9, 155 (1972).
15. I. Thomas and E. Schweikert, Nucl. Instrum. Methods., 9, 461 (1972).
16. V. A. Muminov, S. Mukhammedov, and R. A. Khaidarov, Izotopy SSSR, 49, 11 (1977).
17. C. Williamson, I. Boujot, and I. Picard, Rep. CEA-3042 (1966).
18. I. A. Maslov and V. A. Lukinitskii, Handbook of Neutron Activation Analysis
[in Russian], Nauka, Lenningrad (1971).
19. G. Lutz, Anal. Chem., 41, 424 (1969).
544
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SPATIAL DISTRIBUTION AND BALANCE OF 3H and 137Cs IN THE BLACK
SEA IN 1977
S. M. Vakulovskii, I. Yu. Katrich,
Yu. V. Krasnopevtsev, A. I. Nikitin,
V. B. Chumichev, and V. N. Shkuro
UDC 551.464.6.02
Studies of the behavior of radioactive impurities in the sea are aimed primarily at
human radiation safety and at preservation of the natural resources of the ocean. Particular
attention should be paid to radioactive contamination of seas with restricted water exchange,
including, in particular, the Black Sea, since this type is the most sensitive to contamina-
tion of technological origin.
At present the "Sr content of the Black Sea has been fairly well studied [1-5]. The
reserve of 137Cs, however, has been estimated on the basis of limited experimental data
[2, 3]. There is no published information on the content of 137Cs in bottom sediments of
the Black Sea or on the reserve and constituents of the tritium balance.
To obtain more detailed data on radioactive contamination of the Black Sea, samples
of seawater and bottom sediments were taken on board the research ship Mgla during September
and October 1977. Water samples were taken by a stainless-steel bathometer, while bottom
sediments were sampled using a Okean-0.25 bottom scoop. The sample volume was 2 liters for
determining 3H, and 100 liters for 137Cs. The 3H radiometry in the water samples was con-
ducted using the liquid of Mark-II and SL-30 scintillation spectrometers after preliminary
enrichment by the method of electrolysis [6]. The error in measuring the minimum activity
did not exceed 35%. In determining the 137Cs, water samples were passed through a column
with selective sorbent [7] on board the ship. The degree of cesium extraction was 80%.
Samples were measured using a low-background y-ray spectrometer (detector with well). The
minimum detectable 137Cs content for a 100-liter sample was 0.05 pCi/liter (1 Ci
dis/sec) for a measurement time of 10 h and a relative error of 50%. The 137Cs content in
bottom sediments was determined from measurements of dried samples of the bottom using a
DGDK-80 detector.
The mean 3H concentration for surface water (Fig. 1) in the eastern part (the boundary
between the parts being the 36? meridian) was (60 ? 6) tu, in the western and northwestern
part it was (48 ? 10) tu. In the western part there is a distinct shore region (from the
Bosphorus to the mouth of the Danube) with a mean 3H concentration of (35 ? 3) tu.
One possible reason for this distribution of 3H over the water area is differences in
its intake with atmospheric precipitation. The mean annual precipitation increases from
400-600 mm/y in the west to 1700-5000 mm/y in the east in the Sukhumi-Batumi region [8].
The concentration of 3H in atmospheric precipitation over the entire water area is the same,
while the amount of precipitation in the various regions of the sea and the adjacent shore
areas is similar. The tritium concentration in surface water in 1977, as averaged over the
entire water area, was (51 ? 3) tu, while in the layer from 0 to 100 in it was 36 tu, or
around 40% lower than in 1973 [9].
The distribution of 137Cs in surface water is more uniform than that of 3H. The aver-
age concentration for the entire water area is 0.53 ? 0.03 pCi/liter, except for the north-
western part, where the mean 137Cs concentration is lower than in the remaining area, by
approximately a factor of 1.3. This is evidently to be explained by the influx into this
region of river water with a low 137Cs concentration [10].
Measurements of 3H and 137Cs concentration at various levels revealed that the distri-
bution depth of these radionuclides is the same as in the eastern and central parts. This
made it possible to obtain averaged concentration profiles for these regions (Fig. 2), which
Translated from Atomnaya Energiya, Vol. 49, No. 2, pp. 105-108, August, 1980,
Original article submitted September 28, 1979.
0038-531X/80/4902-0545$07.50 1981 Plenum Publishing Corporation
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0
rn
500
1000
1500
2000
Danubej, 46
Z;11513
0/1 0
o9
57
,5()
vi
Novorossiik
01 2
A 0
74?
6 04
031
5
o
190
54
23
n 22
1Z3-.?
mo
Fig. 1. Concentration of tritium at
various sampling points on voyage of re-
search ship Mgla in September-October
1977 (the numerator represents the number
of the points, the denominator the tri-
tium concentration in tu).
csy tel. units
44 46 0,8 ZO
(5)
(16)
Fig. 2. Averaged vertical profile of
concentration of 3H (open circles) and
137Cs (solid circles). The number of
averaged values is given in parentheses
(for convenience in reading the figure,
the experimental points are somewhat
shifted vertically).
were normalized to the surface concentration and can be satisfactorily approximated by an
exponential relationship:
Ch == 0.96 exp (-0.693 h/h,/,) + 0.04,
where Ch is the 3H or 137Cs concentration at depth h, relative units, h, sampling depth, m;
and h1/2, depth (82 m) at which the concentration of the radionuclide decreases by a factor
of 2.
- It should be pointed out, however, that the depth distribution of 3H in the region
adjacent to the Bosphorus differs from that in the central and eastern portions of the
sea. This is clearly manifest in the depth distribution of 3H on the Bosphorus-Sevastopol
section (Fig. 3). The differences at points 5, 4, 3, and 2 may be explained by penetration
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Sampling points
Bosphorus
5
100
300
500
1000
? Sevastopol
2
9
58?9
47?7
J8!
?13
:C25?4
S%1360/t
vpvia
5,5?1,7
28?48
35?0,5
Fig. 3. Isolines of tritium concentration
(tu) on the Bosphorus-Sevastopol section
in September-October 1977.
TABLE 1. Reserve of 3H and 137Cs in Black Sea in September-October 1977
Layer, m
Volume of
water in layer
103 km3 [11]
Mean conc.*
Reserve, Ci
Fraction of
reserve, lo
311
total
137C8
"ll, tu
137cs, pCi/
liter
31r, foli
",Cs, UP
0-100
37
35,5+3,7
0,45+0,04
4,3+0,5
10,0+1,5
35
45
100-30(1
- 02
12,8+3,2
0,18+0,04
2,6+0,7
11,2+2,5
21
30
300-500
60
5,0+2,5
0,05+0,02
1,0:F-0,5
3,0+1,2
8 .
.15
8
500-1000
141
4,2+2,0
0,02+0,000
1,9+0,7
2,8+0,8
7,5
1000-4500
127
3,5+1,0
0,015+0,007
1,4+0,7
1,0:0,9
12
5
1500-2000
114
2,7+0,7
0,015?0,007
1,0+0,3
1,7+0,8
9
4,5
Total
541
?
12+3
37+8
100
100
?
*The mean concentration in the layer was taken to be equal to the half-sum of the
mean concentrations on the boundaries of the layer.
of the denser surface water of the Sea of Marmora into the deep layers of the Black Sea. The
data obtained on the distribution of 3H and 137Cs in surface and deep water enabled us to
calculate the reserve of these radionuclides in the sea (see Table 1).
The layer-by-layer reserve of 3H and 137Cs was determined by multiplying the (layer-
average) concentration by the volume of water in the layer. The mean 137Cs ccincentration in
the layer at a depth of 1-2 km was obtained by combining four samples taken in this layer on
different sections, and by subsequent measurement of the combined sample. The reserves as
thus computed in the water of the Black Sea amounted to (12 ? 3) MCi of 3H and (37 ? 8) kCi
of 137Cs. Around 65% of the 3H reserve, and more than 80% of the 137Cs reserve, is found in
a layer 500 m. The ratio of the 3H and 137Cs reserves is around 330.
To obtain the total 137Cs reserve it is also necessary to determine the reserve in
bottom sediments, which are good absorbers of cesium [12]. The I37Cs content in samples
taken at depths to 150 m varied from 80 to 30 mCi/km2 with a mean value of 47 mCi/km2. The
content of 137Cs in deep-water bottoms is much less than that in shallow water bottoms. For
example, the value 0.4 mCi/km2 was obtained for a sample from a depth of 660 m. Assuming
the 137Cs content to be 47 mCi/km2 for depths to 150 m and 0.4 mCi/km2 for the remaining
part of the sea, we can determine the 137Cs reserve in bottom sediments to be 5.2.103 Ci, or
around 14% of the seawater reserve. Thus, the total reserve of 137Cs in the sea is (42 ? 8)
kCi, or 98 mCi/km2, this agreeing with the 137Cs reserve in soils for the given latitude band
(100 mCi/km2 [13]).
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It is of interest to estimate the 3H and '37Cs reserve in the Black Sea on the basis
of individual constituents of the balance. Such an estimate was first made for '37Cs in
[4]. In the present study, we computed the 3H and 137Cs reserve under the following assump-
tions:
there are no local sources of 3H and 137Cs input into the sea;
input of 3H as a result of molecular exchange with the surface of the sea is equal to
twice the input with atmospheric precipitation, by analogy with [14, 15];
H concentration in river water is equal to its concentration in precipitation of the
given region [9].
Loss of 3H through evaporation from the water area was not taken into account for the
following reason. If we assume that the 3H concentrations in evaporating moisture and in
the surface water are the same, and assume that all the incoming 3H is concentrated in a
layer :5- 50 m, then the annual evaporation loss will not exceed 1.7% ? on the basis of the
ratio of the volume of water evaporated per year to the volume of water in a layer :5 50 m.
Since 3H does in fact penetrate to layers more than 50 m in depth, the evaporation losses
are even smaller and can be disregarded. For the same reason, outflow of 3H to the Sea of
Marmora and Sea of Azov as well as intake via the Bosphorus, was not allowed for (the annual
volume of water exchanged amounts to 1.8, 0.3, and 0.9% respectively of the volume of water
in a layer 550 m). We also disregarded the intake of 137Cs with river drainage, because
of its low concentration in river water.
Data on 3H fallout with precipitation during 1953-1970 were taken from [16], while
for 1970-1977 we employed the averaged results of our measurements for Odessa, Rostov-on-Don,
and Tbilisi. Intake from the Sea of Azov was computed by multiplying the 3H reserve in the
Sea of Azov by the fraction of water entering the Black Sea via the Strait of Kerch. The
sH reserve in the Sea of Azov was estimated in the same way as for the Black Sea. Data on
137Cs fallout along with global atmospheric fallout were taken from [13], data on I37Cs and
90Sr concentration were taken from [3, 17-19] in computing the exchange with the Sea of
Marmora and Sea of Azov. The 3H margin in the Black Sea for 1977 as thus computed amounted
to around 13 MCi (around 50% coming from molecular exchange, around 25% from precipitation,
and 25% from continental drainage).
Estimates of the equilibrium reserve of 3H of natural orgin based on the data of [20,
21] regarding the concentration of tritium in precipitation, equal to 8-10 tu, amount to
0.5 MCi, or around 4% of the reserve as determined from the measurement results. This im-
plies that virtually all the 3H in the Black Sea is of artificial orgin. Thus, the data on
sH and 1"Cs reserves as obtained experimentally and as computed under the above assumptions
regarding the intake of radionuclides into the sea are in good agreement. The difference
is 10% for both radionuclides. This is evidence that contamination of Black Sea water by
3H and 137Cs stems from global sources.
LITERATURE CITED
1. V. P. Shvedov et al., Radioactive Contamination of Seas and Oceans [in Russian],
Nauka, Moscow (1964), p. 76.
2. L. I. Belyaev, L. I. Gedeonov, and G. V. Yakovleva, Okeanologiya, 6, No. 4, 641
(1966).
3. L. I. Gedeonov et al., in: Disposal of Radioactive Wastes into Seas, Oceans, and
Surface Waters, IAEA, Vienna (1966), p. 373.
4. V. P. Barannik et al., Okeanologiya, 14, No. 2, 274 (1974).
5. S. M. Vakulovskii et al., Trudy 161, No. 6(64), Gidrometeoizdat, Moscow (1977), p. 73.
6. H. Ostlund and E. Werner, in: Tritium in the Physical and Biological Sciences, IAEA,
Vienna, Vol. 1 (1965), p. 95.
7. N. V. Brevnova et al., Byull. Izobret., No. 34, 72 (1972).
8. World Water Balance and Water Resources of the Earth [in Russian], Gidrometeoizdat,
Leningrad (1974), p. 153.
9. S. M. Vakulovskii et al., At. Energ., 44, No. 5, 432 (1978).
10. V. B. Strodomskii, in: Problems of Radioecology of Water Organisms [in Russian],
Ural Science Center, Academy of Sciences of the USSR, Sverdlovsk (1971), p. 53.
548
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11. B. A. Skopintsev, Formation of Contemporary Chemical Composition of Black Sea Water
[in Russian], Gidrometeoizdat, Leningrad (1975).
12. D. D. Baranova and G. G. Polikarpov, Okeanologiya, 5, No. 4, 646 (1965).
13. A. A. Moiseev and P. V. Ramzaev, Cesium-137 in the Biosphere [in Russian], Atomizdat,
Moscow (1975).
14. R. Michel and H. Suess, J. Geophys. Res., 80, No. 30, 4139 (1975).
15. H. Dorsey and W. Peterson, Earth Planet. Lett., 32, No. 2, 342 (1976).
16. Environmental Isotope Data, IAEA, Vienna, Nos. 1-4 (1969-1973).
17. S. A. Patin and A. A. Petrov, Meteorol. Gidrol., No. 7, 105 (1976).
18. O. M. Aleksaniyan, in: Radioecology of Water Organisms [in Russian], Vol. 2, Zinatne,
Riga (1973), p. 225.
19. G. G. Polikarpov et al., Stontium-90 in Brackish- and Fresh-water Reservoirs [in
Russian], Atomizdat, Moscow (1966).
20. W. Schell, Q. Sayzay, and B. Payne, in: The Physical Behaviour of Radioactivie
Contaminants in the Atmosphere, IAEA, Vienna (1973), p. 1. '
21. S. garo and A. Duka-Zoluomi, Yad. Energi., 22, No. 9, 338 (1976).
549
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Declassified and Approved For Release 2013/02/14: CIA-RDP10-02196R000800040002-1
USE OF PERSONNEL NEUTRON FILM MONITORING TO DETERMINE EQUIVALENT RADIATION
DOSE BEHIND PROTON ACCELERATOR SHIELDING
E. K. Gel'fand, M. M. Komochkov, B. V. Mantic?, UDC 539.1.06.7:539.12.175
M. M. Salatskaya, and B. S. Sychev
Attempts have been made [1, 2] to increase the reliability with which the neutron
dose can be determined behind the shielding of high-energy accelerators by means of person-
nel neutron film monitoring (PNFM). To this end, it was proposed in [1] to take account of
either the density of stars or the fraction of tracks which begin or end in the emulsion.
In [2], besides type-K emulsion use was also made of N-3 emulsion with a lowered upper en-
ergy threshold of detection.
The results of studies of spectra in the rooms of accelerators and behind their shield-
ing [3-5] allow two main groups to be distinguished: spectra of neutrons which have experi-
enced multiple reflection from the inner wall surfaces of the room (spectra of slowing-down
neutrons) and spectra formed when high-energy neutrons pass through shielding without aper-
tures. In spectra of the first group high-energy neutrons are present in extremely small
numbers since their albedo is small [6]. In spectra of the second group slowing-down neu-
trons are present only in the form of "concomitant" to the leading group of high-energy neu-
trons. In a paper [7] on the experimental investigation of neutron spectra in the JINR
accelerators Aleinikov et al. call the spectra of the first group "soft" and those of the
second, "hard."
In the present paper it is shown how the total equivalent dose of radiation can be
determined more accurately than previously from the tracks formed in the emulsion of a per-
sonnel neutron film badge [1]. The basis for the solution of this problem was the circum-
stance that tracks in an emulsion have different grain densities, depending on the energy of
the protons which form them. In [8] it was proposed to visually divide tracks in a type-K
emulsion into "black" and "gray." We used the adjective black to describe tracks in which
the fraction of length occupied by grains is greater than the fraction occupied by gaps.
All other tracks were called gray. From the experimental data of [8], it can be conclded
that the boundary between gray and black tracks corresponds to a proton energy of 40 MeV.
The existence of gray tracks indicates the presence of high-energy protons. Fast neutrons
(E < 20 MeV) can form only dark tracks.
Calculations were carried out to find the number of black and gray tracks formed in
the emulsion of a PNFM bdge. The separation into gray and black concerned the projection of
tracks onto the plane of the emulsion. A study was made of the reaction of the badge in
radiation fields behind flat shields of ordinary concrete of varius thicknesses, irradiated
with a broad beam of neutrons of various energy spectra: neutrons of direct nuclear reac-
tions, emitted from targets bombarded with protons possessing an energy E < 10GeVatan angle
8 = 700 (I); neutrons with an energy spectrum uniformly distributed ores the range 3.68-480
MeV (II); neurons with an energy spectrum uniformly distributed over the range 3.68-660
MeV (III); neutrons with a 1/E spectrum uniformly distributed with respect to a logarithmic
variable in the energy range 3.68 MeV-10 GeV(IV). Besides the variation of the neutron spec-
trum and the shielding thickness we studied the reaction of the film badge as a function of
the upper sensitivity limit of the emulsion, which varied from 150 to 175 MeV. The boundary
between the gray and black tracks was varied within the limits 30-50 MeV. The calculation of
track formation by neutrons was carried out in accordance with [9]. The maximum value of
the values of the equivalent dose in the tissue-equivalent plate (TEP) was associated with
the density of the tracks produced. The energy spectra of neutrons and protons in the range
0.1 MeV < E < E0 are shown in Fig. 1.
Translated from Atomnaya Energiya, Vol. 49, No. 2, pp. 108-112, August, 1980.
Original article submitted July 23, 1979; revision submitted March 7, 1980.
550 0038-531X/80/4902- 0550$07.50 ? 1981 Plenum Publishing Corporation
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Declassified and Approved For Release 2013/02/14: CIA-RDP10-02196R000800040002-1
/0 102
P.73 LM eV
Fig. 1. Energy spectra of nucleons behind con-
crete layer with thickness of 500 g/cm2, whose
surface is bombarded by broad beam of neutrons
with initial spectra I, III, IV.
TABLE 1. Composition of Hadron Field behind 500-g/cm2 Concrete Layer with Various
Primary Neutron Spectra*
Spectrum
Neutrons Protons I T? mesons
E, MeV
I ? 1 -- , 1 , 1 - 11 ,3
(1,5-2 2-20 > > 3,7
>3,7
0,36
0,11
0,23
, 0,29
0,97
0,031
? 0,001
II
0,36
0,11
0,23
0,28
0,96
0,033
0,001
Calculation
III
0,34
0,11
0,23
0,29
0,95
0,048
0,003
IV
0,36
0,12
0,24
.0,35
0,82
0,125
0,051
350 MeVt
0,40
0,91
1,0
Experiment
480 MeVt
0,36
0,63
1,0
669 MeVt
0,16
0,39
1,0
*Normalization to one hadron of energy higher than 20 MeV.
tThe proton energy given is for synchrocyclotron operation with external target.
Calculated data characterizing the hadron field studied according to energy groups are
presented in Table 1. For all of the initial spectra the fraction of cascade neutrons in
the 2-20-MeV group is 10% of their number in the group above 20 MeV. Therefore, the 2-20-
MeV group is represented on average by 70% slowing-down neutrons and 30% cascade neutrons.
The calculated data are compared in Table 1 with experimental results [10] characterizing
the neutron field behind the 2-m shielding of the JINR synchrocylotron. It is seen that the
calculated composition of the neutron field corresponds to the experimental data, although
there are some appreciable differences which can be explained by the difference in the con-
ditions of the calculation and the experiment.
Table 2 gives the results of calculations of the density of track formation and the
maximum equivalent dose Hmax in TEP. The following notation is used here: x, thickness
of the concrete layer (g/cm2).; Fn.and Fp, fluences of the cascade neutrons and protons
(particles/cm2); Nn, Np and Nb, Nb, densities of all the tracks and the black tracks, re-
n p
spectively, formed by the neutrons and protons of the radiation field (tracks/cm2); and N,
total density of all tracks (tracks/cm2).
Analysis of Table 2 reveals a relatively weak dependence of the given functionals on
the form of the primary spectrum and the shielding thickness. The number of tracks formed in
PNFM badges by protons of the radiation field is roughly 7-20 times the number of tracks
which are caused by recoil protons formed under the action of neutrons of the radiation
field. At the same time, as is seen from Fig. 2, the maximum equivalent dose of fast neu-
trons (E < 20 MeV) is smaller than Hmax by a factor of roughly 3. It thus follows that if
the number of tracks is interpreted in terms of equivalent dose of fast neutrons, then it
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552
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g
10
10-
r
1
F
_
7:,
Ill\
2
Wft%
?.,i
404446404;44
j '002 4
6
xo
6
;41111
4
7
N
ilegumms
1..........
10 20 0 0 20 0 W
Depth (5 of plate, cm
102
10
P
10-1
20 30
Fig. 2. Depth distributions of dose and its compo-
nents in TEP behind 500-g/cm concrete layer (pri-
mary neutrons with spectra I, III, IV bombard the
concrete surface): ) equivalent dose (our
calculation for monodirectional irradiation of TEP);
1) sum; 2) neutrons (E > 20 MeV); 3) neutrons (E <
20 MeV); 4) rr? mesons; 5) protons; 6) 11-0 mesons; 7)
y rays; - - -) total equivalent dose (calculation
[15]); a, b) total equivalent dose and absorbed dose
(our calculation for "real" conditions of irradia-
tion of TEP); 411, 0) total absorbed dose in TEP and
without TEP (experiment [13]).
TABLE 2. Relation between Track Formation
and Equivalent Radiation Dose (range of
detection of gray tracks 40-150 MeV)
8
C4
x, g/cm2
4.1(x,
&
.
i?'
ii
z,?,
--,
.?Z?r,4g
z 5
.-
? ..
p

z 9,
....
j!,5111
1
200
29,4
8,5
5,1
0,72
8,1
4,7
500
33,5
7,8
4,9
0,75
8,6
4,9
1100
39,1
7,1
4,6
0,78
9,2
5,2
1550
41,9
6,8
4,4
0;80
9,5
5,3
2000
43,9
6,5
4,3
0,81
9,8
5,4
II
200
20,0
12,2
6,8
0,62
6,3
3,9
500
27,0
9,4
5,5
0,68
7,5
4.4
1100
33,4
7,9
4,9
0,74
8,5
4,9
1550
36,2
7,4
4,6
0,75
8,9
5,1
2000
38,4
7,1
4,5
0,77
9,0
5,1
III
200
14,9
14,7
7,9
0,58
6,0
3,8
500
21,1
10,8
6,2
0,65
7,0
4,2
1100
28,1
8,7
5,2
0,70
8,0
4,7
1500
31,6
8,0
4,9
0,73
.8,5
4,9
2000
35,0
7,6
4,7
0,75
8,8
5,0
IV
200
5,5
20,9
10,2
0,55
7,9
5,1
500
7,3
16,4
8;4
0,59
7,7.
4,9
1000
9,8
13,6
7,3
0,62
7,9
4,9
1550
11,1
12.6
6,9
0,63
7,9
4,9
2000
12,3
11,9
6,6
0,65
8,0
4,9
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Declassified and Approved For Release 2013/02/14: CIA-RDP10-02196R000800040002-1
is expected that the "true" value is overestimated by a factor of 20-60 and this was indeed
established experimentally in [1].
The depth distribution of the radiation dose was calculated for conditions of normal
incidence on the TEP surface. The data of [11] were taken as the initial data. We also
estimated how sensitive the depth distribution is to the angular distribution of the radi-
ation incident on the TEP surface. Figure 2 shows the depth distributions of the components
of the equivalent dose for conditions of normal incidence with allowance for the angular
distribution ("real" irradiation conditions). The indeterminacy in the results of the cal-
culations for irradiation of TEP with allowance for the angular distribution is due mainly
to the statistical fluctuations of the initial data which we used for the depth distribu-
tions of the dose [12]. In Fig. 2 the results of the calculations are compared with the
experimental data [13] obtained behind the side shielding of the IFV (Institute of High-
Energy Physics) proton synchrotron. The distributions under comparison were normalized ac-
cording to the adsorbed dose without a TEP; in the calculations this was the thickness of
the TEP (0.5 cm) for conditions of normal incidence of radiation.
As is seen from Table 2 in the radiation fields under consideration the ratio between
the track density and the maximum equivalent dose is quite stable. With this ratio, Hmax
for unknown fields with a "hard" spectrum can be determined from the track density. In real
situations irradiation behind the shielding of accelerators can occur under conditions char-
acterized by the superposition of "hard" and "soft" spectra. In this case as well Hmax can
be determined. Allowance must be made for the fact that only black tracks are formed in a
"soft" spectrum while the black and gray tracks in a "hard" spectrum are in a ratio which
is determined by coefficient R (see Table 2).
Taking the values of the numerical parameters into consideration, we get the following
expression for determining the equivalent dose of a mixed field of radiation:
Hmax ?(6,0 ? 0.9) N ? (9.8 ?1.8) N g rem,
where N and Ng pertain to scanning over a traverse of area 0.0225 cm2.
For a clearly "hard" spectrum Eq. (1) is of the form
Hmax= (0.27 ?0.07)N mrem.
In the experimental determination of the track density in the emulsion there may be
subjective errors owing to the indeterminacy of the grain density which in the scanning is
adopted as the boundary between black and gray tracks as well as the minimum grain density
when an ordered group of grains is perceived as a track. The latter is particularly impor-
tant for tracks which intersect the emulsion at large angles to its surface. Both sources
of error are taken into account partially when we vary the pertinent initial data. However,
this variation is relatively small and apparently reflects the least error which should be
expected when films are scanned by experienced laboratory assistants. As will be seen from
experimental data given below the spread in the results of scanning of one emulsion by dif-
ferent laboratory assistants is greater than follows from our estimates, although on average
we can speak of agreement between experiment and calculation within the limits of the ex-
pected error.
The experimental data are the results of scans of emulsions irradiated behind the
shielding of the JINR and CERN proton accelerators. The scanning was done by two experi-
enced laboratory assistants according to the proposed scheme of dividing tracks into black
and gray. Using the scan results and Eqs. (1) and (2), we found the equivalent radiation
dose H1 which we then compared with the value Ho obtained by the most reliable methods of
dose measurement. Table 3 presents the results of scans of 13 emulsions irradiated at six
points behind the shielding of the JINR synchrocyclotron and synchrophasotron [1] and in
the "hard" spectrum of the CERN synchrotron [14].
It must be borne in mind' that points 1 and 3 (Fig. 1 [1]) were behind shielding without
apertures and channels; therefore, the irradiation conditions at these points are close to
the conditions of the calculation of the dose behind blind shielding, the results of which
are given in the present paper. The radiation dose at points 1 and 2 (Fig. 2 [1]) is also
due mainly to "hard" spectra. At point 4 (Fig. 2 [1]) the dose is due to a super-
position of "hard" and "soft" spectra. At point 9 (Fig. 3 [1]) in the synchro-
(1)
(2)
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TABLE 3. Results of Scanning of Emulsions Irradiated in Different Accelerators
Device
Point
of
meas.
No. of tracks on transv.
N b
h = ?,
N6.
Equiv. doses mrern
HI
Ho
Nb
Ng
HI
Ho
JINR synchrocyclotron, Ep = 660
1
340+50
560+120
0,60+0,15
240+70
210+70
1,1+0,5
MeV, Fig. 1 [1]
1
270+40
400+40
0,66+0,08
180+50
210+70
0,8+0,3
3
420+50
740+90
0,56+0,15
310+80
310+110
1,0+0,5
3
210+50
250+40
0,85+0,22
120+40
100+40
1,2+0,5
JINR synchrocyclotron, Ep = 660
1
210+30
600+140
0,34+0,10
220+60
190+20
1,2+0,4
MeV, Fig. 2 [1]
1
270+60
670+170
0,41+0,20
250+70
190+20
1,3+0,4
2
210+20
470+100
0,45+0,11
190+50
140+10
1,3+0,4
2
180+20
450+160
0,40+0,20
170+60
140+10
1,2+0,4
4
16+2
38+7
0,41+0,10
15+4
28+4
0,5+0,2
4
20+6
64+9
0,31+0,15
23+4
28+4
0,8+0,2
JINR synchrophasotron, Ep = 10
9
350+40
820+180
0,43+0,15
320+90
420+50
0,8+0,2
GeV, Fig. 3 [1]
9
110+10
490+30
0,23+0,02
160+40
190+20
0,8+0,2
CERN proton synchrotron, E0 = 28
590+100
1550+340
0,38+0,16
580+160
600+90
1,0+0,3
GeV [14], "hard" spectrufti
TABLE 4. Results .of Scan of Emulsion Ir-
radiated in "Hard" Spectrum Behind Shield-
ing of JINR Synchrocyclotron
No. of
scan
No. of tracks on transverse
h
Nb
Ng
N
1
340+30
300+30
730+40
0,87+0,09
2
430+30
320+30
750+40
1,3+0,1
3
200+20
300+20
590+30
0.06+0,08
4
400+40
230+30
630+50
1,7+0,3
5
340+30
560+50
000+60
0,60+0,08
6
210+20
480+30
690+40
0,45+0,06
7
270+20
340+30
610+30
0,79+0,09
phasotron tracks in the emulsion could also have been formed by secondary protons arising
when the primary proton beam passed through a channel close to point 9. The mean value of
the ratio 111/H0 according to the results of Table 3 is 1.0 ? 0.2, which confirms that the
calculations are correct.
In order to evaluate the subjective errors, one of the emulsions irradiated in a "hard"
spectrum was scanned by seven laboratory assistants. As is seen from the data of Table 4,
the results obtained by different laboratory assistants differ substantially. Averaging the
data of Table 4, we get: Nb. 330 + 60 tracks/traverse, -g8 = 370 + 90 tracks/traverse,
k = _b/ _g = 0.89 ? 0.25, and N = 700 + 90 tracks/traverse. The mean deviation of the results
of the scans exceed the statistical errors given in Table 4.
The equivalent dose found in this case according to Eq. (2) is 191 mrem. The value of
theequivalent dosefoun, with themost reliablemeasuring methods, in 210mrem, is15-20%. This per-
mits the conclusion that the calculations are in agreement with the experiment. It must be
pointed out that the results given here were obtained by laboratory assistants without prior
training. The subjective error can be reduced significantly as the assistants master the new
scanning technique.
On the basis of the data obtained, we propose the following technique for determining
the equivalent dose. In scanning the emulsion count the number of black and gray tracks
and then find k = Nb/Ng. If 0.4 k 5- 1.1, then determine the dose from Eq. (2) (the values
0.4 and 1.1 correspond to the limiting values k = 0.71 ? 0.16 which was obtained by aver-
aging the data of Table 1 with allowance for the subjective errors in dividing the tracks
into black and gray). If k < 1.1, find the dose from Eq. (1). When k < 0.4, the irradiation
conditions differ markedly from those considered in the present paper (e.g., irradiation
inside the accelerator room), and further studies are called for.
Conclusions. Calculations have been made of the laws governing the formation of the
radiation dose behind the shielding of proton accelerators. Numerical data have been ob-
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tamed on the indications of a personnel neutron film badge in the radiation fields studied.
It has been demonstrated that it is possible in principle to determine the total equivalent
dose of the radiation field behind the shielding of a proton accelerator by the PNFM method
if division of tracks into black and gray is introduced into the emulsion scanning proce-
dure. The reliability of the measurements of the equivalent dose in fields with a "hard"
spectrum is higher in this case than when the method proposed in [1] is used; the relia-
bility of the two methods is apparently the same in the case of superposition of "soft" and
"ard" spectra. Comparison of the experimental and calculated values revealed that the com-
putational method employed is applicable to modeling the dose characteristic of radiation be-
hind the shielding of proton accelerators.
The authors express their gratitude to the workers of the personnel monitoring group
of the Radiation Safety Department at the Joint Institute for Nuclear Research ('JINR) for
scanning the emulsions.
LITERATURE CITED
1. M. M. Komochkov and M. I. Salatskay,a, JINR Preprint, R16-8175, Dubna (1974).
2. A. V. Antipov et al., Preprint IFVE LRI 77-10, Serpukhov (1977).
3. L. P. Kimel' et al., JINR Preprint R16-3409, Dubna (1967).
4. B. S. Sychev, JINR Preprint R16-4304, Dubna (1969).
5. M. M. Komochkov and B. S. Sychev, in: Proc. Meeting on Dosimetry and Physics of
Accelerator Shielding [in Russian], JINR 16-4888, Dubna (1970), p. 15.
6. L. R. Kimel' et al., JINR Preprint R16-3514, Dubna (1967).
7. V. E. Aleinikov, V. P. Gerdt, and M. M. Komochkov, JINR Preprint R16-9870, Dubna
(1976), At. Energ., 42, No. 4, 105 (1977).
8. M. M. Komochkov et al., JINR Preprint 13-10188, Dubna (1976).
9. B. V. ManIko, in: Strong-Current Accelerators and Storage Rings [in Russian],
Proc. Radio Engineering Institute, Academy of Sciences of the USSR, No. 30,
Moscow (1977), p. 86.
10. V. E. Aleinikov, M. M. Komochkov, and V. I. Tsovboon, in: Int. Congress on Protec-
tion Against Accelerator and Space Radiation, CERN 71-16, Geneva (1971), p. 282.
11. Atlas of Dose Characteristics of External Ionizing Radiation [in Russian], Atomizdat,
Moscow (1978).
12. C. Zerby and W. Kinney, Nucl. Instrum. Methods, 36, No. 1, 125 (1965).
13. A. N. Antipov et al., Preprint IFVE ORI 78-15, Serpukhov (1978).
14. M. M. Komochkov and M. I. Satatskaya, JINR Preprint R16-9780, Dubna (1976).
15. E. K. Gel'fand et al., in: Accelerator Technique [in Russian], Proc. Radio
Engineering Institute, Academy of Sciences of the USSR, No. 22, Moscow (1975),
p. 242.
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Declassified and Approved For Release 2013/02/14: CIA-RDP10-02196R000800040002-1
EXPERIMENTAL SIMULATION OF RECUPERATOR FOR NEGATIVE-ION INJECTORS
S. K. Dimitrov, A. V. Makhin, UDC 621.039.6
S. V. Turkulets
Injectors of fast atoms obtained from both positive and negative ions are employed to
produce and heat plasma in some thermonuclear devices [1, 2]. In both cases the coefficient
of ion conversion to fast atoms is appreciably smaller than unity and, therefore, in order
to raise the efficiency of the injector it is necessary to effect direct conversion (recup-
eration) of the kinetic energy of the unrecharged ions into electrical energy.
The objective of the present paper is to study a variant of a system for recuperation
of the energy of monoenergetic beams of negative ions. The experiments were conducted with
electron beams since electron sources are simpler as is also their operation and the evacu-
ation requirements are less stringent. With electron beams it is possible to experimentally
simulate the effect of some factors on the efficiency of energy recuperation [e.g., the
effect of the geometry of the system, the space charge, and other beam parameters).
The problems of beam slowing-down, in which
transformed into electric energy of the field and
arise in the construction of electron-beam tubes,
trokinetic electric transmission lines now in the
the kinetic energy of the electrons is
is returned to the external circuit, also
radio-frequency electron tubes, and elec-
research stage.
In our study, wemade an experimental investigation of the problem of slowing-down and
collection of particles in a recuperation system consisting of a collector with suppressor
and a set of diaphragms setting up a retarding electric field (Fig. la). A similar system
was described in [3]. The surface of the collector is a cone with an apex angle a. An
aperture in the collector along the axis of the system is necessary so that the recuperator
could be used in the injector channel without need to use any deflecting magnetic field
("right through") and so that pumping of gas out of the region of the collector could be
facilitated. In order to block the stream of ions passing through this aperture, a special
electrode producing an ion-scattering electric field is placed behind the collector.
In such a system secondary electrons are blocked by a suppressor whose potential is
lower than that of the collector [3]. In front of the diaphragms is a secondary-electron
collector (SEC), whosecurrent provides an approximation of the number of electrons which are
reflected by the electric field of the system and do not reach the collector as well as
secondary electrons not blocked by the suppressor. The SEC current is part of the loss of
recuperated power in the calculation of the efficiency of energy conversion in the given
system (the recuperation efficiency is the ratio of the electrical power taken from the col-
lector to the beam power at the entrance to the recuperator).
The apertures of the collector, suppressor, and diaphragms were chosen with allowance
for the angular divergence of the electron beam and the divergence due to the influence of
the space charge in the stream of particles. In order to take the beam to the region of
the collector with minimum losses, we employed beam focusing over the entire retardation
zone. To this end, some diaphragms were given a negative potential roughly equal to the
accelerating potential of the electron gun (see Fig. lb). Because of this, with this system
it is possible to recuperate beams with a large angular divergence (in our case, 0 = 8?).
The system was optimized in respect of the potential of the collector Uc, the suppressor Us,
and the auxiliary electrode Ua, as well as the apex angle a of the cone.
The dependence of the efficiency n on Uc with an optimal Us for each Uc is shown in
Fig. 2. The dependence was measured at a = 300 and optimal Ua. The dependence of n on Us
with the other parameters at optimal values and a = 30? is shown in Fig. 3. The maximum
efficiency of recuperation at an electron energy of 200 eV was n = 88 ? 2%. The decrease in
n as Us deviates from the optimal value can be explained as follows. Since the suppressor
Translated from Atomnaya Energiya, Vol. 49, No. 2, pp. 113-115, August, 1980.
Original article submitted September 28, 1979.
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0038-531X/80/4902-0556$07.50 ?1981 Plenum Publishing Corporation
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Declassified and Approved For Release 2013/02/14: CIA-RDP10-02196R000800040002-1
23
4
5 6
-200
U, V
a
7
Distance along axis, rd. units
Fig. 1. a) Diagram of recuperator, and b)
qualitative distribution of potential on
electrodes: 1) beam; Wo = 200 eV; 2)
collimating diaphragm; 3) secondary-electron
collector; 4) retarding-field electrodes; 5)
suppressor; 6) collector; 8) auxiliary elec-
trode of scattering field.
serves to form a potential well in the near-collector region, thus stopping secondary elec-
trons from reaching the collector, an increase in Us reduces the ability of the suppressor
to block electrons. When Us falls below Us opt the region of the potential well grows so
much that it covers the region in which the electron beam passes and prevents it from reach-
ing the collector, reflecting the electrons backwards.
The efficiency of the system with a solid collector (without an aperture and auxiliary
electrode, i.e., without beam scattering at the end of the retardation) proved to be lower
since the potential well set up by the suppressor does not cover the central regions of the
collector and does not stop secondary electrons, as indicated by the growth of the current
from the SEC.
The experiments allowed it to be shown that in order to have maximum conversion effi-
ciency, 90-95% of the beam should be retarded. The influence of the space charge in the
beam, according to [4], is characterized by the dimensional parameter d/rd, where d is the
beam diameter and rd is a parameter with the dimension of length and is calculated from the
current density and beam energy. It was shown experimentally that within the limits of
variation of d/rd from 0.06 to 0.11 the efficiency remains constant. This is explained by
the fact that the slight beam divergence owing to the space charge, which exerts an influ-
ence on the conversion efficiency, is compensated by the negative potential of the focusing
diaphragms (Fig. 4).
The conversion efficiency also depends on the angle which the collector surface makes
to the axis of the system. For maximum slowing-down of the particles this surface should be
orthogonal to the electron trajectories. From the curves obtained (Fig. 5) it is seen that
the efficiency of such a system reaches its maximum value of 89 ? 2% at a collector slope
of 50 (other parameters remaining optimal).
As was ascertained, an appreciable influence on the electron trajectory (and, hence, on
the efficiency) is exerted by the potential of the electrode forming the scattering field.
The optimal potential Ua at which maximum efficiency is observed also depends on the geom-
etry of that electrode. Figure 6 shows the dependence of the efficiency n on Ua for an
electrode in the form of a solid cone (see Fig. la). With operation according to the
557
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71,0/0
90
80 0
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( /M)
50
150 MU 170
Fig. 2.
optimal
Fig. 3.
optimal
Fig. 4.
(-7M)
(..770)
1180
Fig. 2
Dependence of efficiency n on Uc (the
values of Us).
Dependence of efficiency n on Us (the
values of Uc).
Dependence of efficiency on d/rd.
100 -u, v
Fig.
3.
Vio
90
88
86
84
82
-15
15 30 a
0,04
0,08
0,12 d/rd
Fig. 4
numbers in parentheses are the
numbers in parentheses are the
Fig. 5. Dependence of efficiency on
a/2.
Fig. 6. Dependence of efficiency on
potential Ua of scattering-field elec-
trode for a/2 = 30?.
straight-through scheme, the electrode should be made in the form of a ring. In this case
the potential applied to it must be twice that applied to the solid design studied.
The process of retardation of a 500-keV ion beam in the given system with d/rd = 0.08
was simulated by computer by the "large-particle" method. Figure 7 shows the position of
the beam in the region of retardation and the picture of the equipotential lines. The role
of the scattering electrode (made in the form of a ring) is illustrated. In the given case
there is no necessity to have periodic focusing of the field since the beam emerging from
the ion source has practically no angular spread. The length of the entire system is less
than the distance over which a virtual cathode is formed (of the order of rd).
The variant of the position of the recuperator in the injector system of a tokamak is
shown in Fig. 8. The recuperator for D+ ions formed as the result of the processes D? D+
and D- D+ may consist, e.g., of a system of skewed diaphragms [4] which, at D1--beam param-
eters of d/rd =0.08, has a 90% efficiency (for a monoenergetic beam).
558
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Declassified and Approved For Release 2013/02/14: CIA-RDP10-02196R000800040002-1
-5 kV
50 kV
0
100 kV
200 kV
300 kV
400 kV
500kV
500 kV
40kV
-25 kV
0
100.kV
200 kV
300 kV
400 kV
500 kV
Fig. 7. Position of beam in retardation region (a) and pic-
ture of equipotential lines at the same parameters (b) when
t = 0.6 psec, j = 55 A/m2, Wo = 500 keV.
Fig. 8. Variant of position of recuperators in
injector system of tokamak: 1) charge-exchange
chamber; 2) magnetic shield; 3) tokamak; 4)
atoms; 5) recuperator of DI--ion energy (system
of skewed diaphragms; 6) cryopanels; 7) recup-
erator of D--ion energy.
Thus, the recuperation efficiency in the system studied, with d/rd = 0.08-0.1, can be
'N., 90%, which is roughly 10% higher than in the system of skewed diaphragms for the same D-
beam parameters [5].
LITERATURE CITED
1. V. N. Pistunovich, Preprint IA-2209, Moscow (1972).
2. Yu. V. Gribov, V. A. Chuyanov, and G. E. Shatalov, in: Proc. Second Soviet-American
"Fusion-Fission" Seminar [in Russian], Atomizdat, MOSCOW (1978), p. 192.
3. E. A. Abramyan and A. N. Sharapa, Prib. Tekh. Eksp., No. 2, 30 (1971).
4. 0. A. Vinogradova et al., At. Energ., 35, No. 1, 15 (1973).
5. S. K. Dimitrov and A. V. Makhin, At. Energ., 46, No. 4, 245 (1979).
559
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Declassified and Approved For Release 2013/02/14: CIA-RDP10-02196R000800040002-1
MEASUREMENT OF TOTAL NEUTRON CROSS SECTIONS OF 168Yb and 169Yb
V. A. Anufriev, S. I. Babich,
A. G. Kolesov, V. N. Nefedov,
and V. A. Poruchikov
UDC 621.039.556
In this paper we present data on the total neutron cross sections and resonance param-
eters of 168,169-
Yb (T1/2- 31days). Measurements weremode usingthe transit-timemethod anda neu-
tron spectrometer mounted on the horizontal channel of an SM-2 reactor. The measurement
procedure was described in [1].
To determine the total neutron cross section and resonance parameters of 168Yb we
measured the transmission of two specimens enriched with (15.6%). The characteristics of
these specimens are given in Table 1.
Specimen No. I was made of Yb203 powder poured into a sealed aluminum ampule with an
inner diameter of 1.8 mm. Specimen No. 2 was prepared in order to make a more precise de-
termination of the resonance parameters of the "strong" level of 168Yb with Eo = 0.590 eV.
A target with 169Yb was obtained by exposure of a specimen analogous to specimen No. 1 in
the SM-2 reactor to a flux of 3.2.1020 neutrons/cm2. Several measurements of the transmis-
sion of the irradiated specimen were made over a 175-day period in order to identify the
levels and to determine the amount of 169Yb.
The amount of 169Yb was determined from the accumulation of 169Tm upon 3-1- decay of
169Yb from the following expression:
Ni"rnc-
it
1?P\ pl-kn,u?i, (ti+, -11)1 ' ti
where ti is the time of the i-th transmission measurement, days, N169Tm, number of 169Tm
nuclei for the i-th transmission measurement, A169yb rate of 169Yb decay, days". In com-
puting the amount of 169Tm we employed the resonance parameters of the E0 = 3.9 eV level,
recommended in [2]. Figure 1 shows the transmission of an irradiated specimen of ytterbium
in the region of the Eo = 3.9 eV level for two measurements with a time interval of 24 days.
It was determined that at the instant irradiation was terminated, there were 1.14.10-4
nuclei/b 169Yb, 1.9.10-4 nuclei/b 168Yb and 0.2210-4 nuclei/b 169Tm in the specimen.
In the energy range 0.014-46 eV we discovered four levels of 168Yb and 21 levels of
169Yb. The form method, using the Bright-Wigner formula, was employed to compute the
resonance parameters. Table 2 gives the neutron-resonance parameters of 16811b, which are
compared with the data published in [3-5]. The 3.925 and 8.17 eV energy levels given in
[4] were not observed by us.
The measured transmission was used to calculate the behavior of the total neutron
cross section of 168Yb in the range of neutron energies 0.014-1 eV (Fig. 2). The behavior
of the total neutron cross section of 168Yb in this range is described by the positive
level parameter.
The resultant value a220? = (2200 + 170)b (capture cross section of 168Yb at thermal
point) is much less than that recommended in [2]. This difference can be accounted for by
the fact that the value a22" = 3470 b of [2] is based on integral measurements employing
either the cadmium difference method or measurements in the thermal Maxwellian neutron spec-
trum. The presence of a "strong" neutron level with E0 = 0.590 eV near the cadmium boundary
causes the cross section at the thermal point as obtained by the integral method to be too
high.
The resultant parameter values were used to compute the resonance capture integral of
ideYb, equal to Iy = (24700 + 3000) b. The value of I is less than that recommended in
[2].
Translated from Atomnaya Energiya, Vol. 49, No. 2, pp. 116-118, August, 1980.
Original article submitted October 22, 1979.
560 0038-531X/80/4902-0560$07.50 C) 1981 Plenum Publishing Corporation
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0,2
J 1 1 1 1 1 1 1
4,0 4,? 444 446 E, eV
Fig. 1. Transmission of irradiated specimen
of ytterbium in energy range 3.4-4.6 eV, 30
days (solid circles) and 6 days (open circles)
after irradiation.
TABLE 1. Composition of Ytterbium Speci?
mens, Nuclei/b*
Specimen
number
Isotope of Vi,, I I(1:-
.11;8 1,70 f 271 172 17:1 174
175
2
30,0
0,74
* ] b -
17,5
0,30
0-2" m2.
44,3
0,90
46,9
0,91
27,2
0,55
43,7
13,2
0,27
TABLE 2. Neutron-Resonance Parameters of
16 eyb
Eo, eV
r, eV
r. MeV
this paper
,
published data
0,590+0,005
9,71+0,01
22,44+0,05
27,17+0,08
00+3
(90)
172+9
(90)
2,2+0,1
0,08+0,01
.24,0+1,0 -
2,45+0,20
3,1+0,3 13]
2,1+0,2 141
0,10+0,00 [4]
50+5 141
29+2 151
5,2+2,0 141
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4
5
-01
1
0
i I I
0014
002 0,04 0,06 01 02 E,
eV
Fig. 2. Total neutron cross section of
peaks are reduced by a factor of 50.
0,75
050
0,25
Au 0,145 0,1 05 F, eV
168Yb in energy range 0.014-1 eV. The
Fig. 3. Transmission of unirradiated specimen and two transmissions of irradi-
ated specimens in energy range 0.014-1 eV. Solid circles: prior to irradiation;
open circles: 6 days after irradiation; triangles: 80 days after irradiation.
\6?-?
2
0
Fig. 4. Total neutron cross section of
169Yb in energy range 0.014-1 eV. The
peaks are reduced by a factor of 5.
o02
40 0,1 E,eV
TABLE 3. Parameters of Neutron Resonances of 169Yb
E0, eV
r*, MeV
2gr?, MeV
eV
F*, MeV
2 gr MeV
1,807+0,005
(80)
0,42+0,03
23,3+0,1
(80)
2,9+0,5
1,32+0,01
(80)
0,046+0,08
24,1+0,1
(80)
1,0+0,5
2,10+0,02
72+0
0,42+0,04
25,1+0,1
(80)
2,0+0,5
6,90+0,04
(80)
0,35+0,05
28,3+0,1
(80)
10,2+1,5
8,57?0,06
(80)
0,55+0,08
33,5+0,2
(80)
? 14,7+7,0
9,20+0,06 ?
75+11
2,7+0,2
33,9+0,2
(80)
?9,3+5,0
12,31+0,07
93+12
2,4+0,2
37,4+0,2
(80) ?
2,6+1,6
12,53+0,07
(80)
1,6+0,2
41,6+0,2
(80)
11,2+2,6
13,46?0,08
(80)
.1,1+0,4
43,2+0,2 -
(80)
5,7+2,3
14,66+0,08
103+26
6,2?0,6
45,4+0,2
(80)
. 20+10
21,8+0,1
(80)
5,5+0,6
*F = 80 MeV was taken as the mean of the measured
values for levels with E0 = 2.19; 9.20; 12.30 and
14.66 eV..
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Table 3 gives the neutron resonance parameters of 169Yb, while Fig. 3 offers the re-
sults of two measurements of the transmission of an irradiated specimen and one measurement
of that of an unirradiated specimen in the thermal range of neutron energies. The measure-
ment interval or the irradiated specimen was 70 days. The differences in the transmission
for the irradiated specimen can be accounted for by changes in the amount of 169Yb and 169Tm.
The total neutron cross section of 169Yb in the thermal range of neutron energies is
shown in Figs. 4. The behavior of the total neutron cross section of 169Yb in the thermal
range cannot be described by the resonance parameters of the positive levels. For 169Yb
we have a22?? = (3600 + 300) b. The calculated value of Iy = (3800 + 500) b. The error in
the measurement results is determined primarily by the contribution of the error in deter-
mining the amount of 1681ib (5%) and 169Yb (8%).
Our results enabled us to estimate for 268Yb the mean distance between levels: D =
9 eV and the force function: So = 2.4.10-4. For 169Yb the calculated values are 17) = 2.2 ?
0.5 eV and So = (2.1 ? 0.7).10-4.
1. T. S. Belanova et al.,
2. Neutron Cross
3. V. Sailor et al., P
4. V. P. Vertebnyi et
Kiev (1972), p. 18
5. H. Liou, Phys. Rev.
Sections
LITERATURE CITED
Preprint NIIAR, P-6(272), Dmitrovgrad (1976).
(3rd ed.), Vol. 1, BNL-325 (1973).
hys. Rev., 96, 1014 (1954).
al., in: Neutron Physics [in Russian], Part 1, Naukova Dumka,
1.
, C7, No. 2, 823 (1973).
563
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LETTERS
CHOICE OF OPTIMAL CONDITIONS OF EXPERIMENT TO FIND STOPPING POWER OF A
SUBSTANCE BY STREAMING OF RADIATION THROUGH ABSORBERS OF ANY
ARBITRARY THICKNESS
G. N. Potetyunko UDC 539.12.04
In two earlier papers [1, 2] the present author proposed a new method of finding the
stopping power of a substance from the results of experiments on radiation streaming through
absorbers and developed the mathematics of the method. The application of the proposed [2]
method of processing the experimental data was not related to any limitations on the ab-
sorber thickness; this permitted use of thicker absorbers than employed hitherto, thus re-
ducing the error of determination of dE/dx introduced by the error in the value of the thick-
ness. This circumstance is especially important when finding dE/dx in the region of the
maximum of the dE/dx curve or before it where the standard method of finding dE/dx (AE/Ax)
gives overly large statistical and methodological errors [1]. Let us point out that appar-
ently this is precisely why in the region of the maximum the error of reproduciblity, caused
by the spread between the results of different authors, is substantially higher than at a
higher energy [3] and greatly exceeds the statistical error of the experiments.
With an increase in the thickness of the absorber, however, the energy straggling also
grows and, along with it, so do the attendant errors. Accordingly, there arises the ques-
tion of the necessity of choosing the optimal conditions for the experiment. This conclusion
is also confirmed by the results of numerical experiment [2] from which it follows that the
experimental conditions affect the accuracy of the determination of dE/dx.
The gist of the problem is: on the basis of the published data obtained under dif-
ferent experimental conditions find how these conditions affect the accuracy of determina-
tion of dE/dx and, to the extent possible, to make particular tentative conclusions as to
the optimal conditions.
The choice of experimental conditions boils down to the choice of the energy range in
which dE/dx is determined and to the choice of the initial values of the beam energy and
absorber thickness. The choice of the energy range is usually determined by the conditions
of the problem. On the other hand, the choice of the values of the initial beam energy and
absorber thickness can be made in various ways.
1. The initial beam energy is fixed and the abworber thickness is increased so that
at maximum thickness the beam energy after the absorber would correspond to the minimum en-
ergy of the chosen energy range.
2. The absorber thickness is fixed and the beam energy is varied within the limits of
the range chosen.
3. At several values of absorber thickness the beam energy is varied in more or less
small steps or, conversely, at several beam energies the absorber thickness is varied within
certain limits.
The results of experiments on streaming radiation through absorbers, allowing the
technique of [2] to be employed, were given in [4,5]. The conditions of the experiments in
these papers were different and it is therefore possible to reveal the effect of the experi-
mental conditions on the accuracy of dE/dx.
Al-Bedri et al. [4] presented the results for protons in the energy range 0.3-1.6 MeV
and the following media: melinex, aluminum, copper, and gold. The scheme of the experiment
in the main corresponded to variant 1 formulated above: the number of values of the initial
beam energy for each medium was two or three and for each value of beam energy the absorber
thickness was varied within quite wide limits. The energy loss in this case ranged from 5
to 95-100% of the energy range.
Translated from Atomnaya gnergiya, Vol. 49, No. 2, pp. 119-121, August, 1980.
Original article submitted January 24, 1979.
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Fig. 1. Values of cross sections for proton
stopping in aluminum, copper, and gold, ob-
tained by processing the experimental data of
[4] by the technique of [2]: 0) data of [6];
A) data of [7];411) data of [8].
Bourland et al. [5] gave the results for a particles in the energy range from 0.3 to
2.0 MeV. The medium was oxygen. The scheme of the experiment corresponded to variant 2:
the target thickness was practically constant while the energy of the beam was varied. The
energy loss was 5-20% of the energy range. The values of the initial beam energy and the
particle energy after the absorber were distributed quite uniformly over the range.
The results of the processing of the experimental data of [4] are given in Figs. 1
and 2. The numbers next to the curves in these figures denote the degree of the polynomial
in the energy used to approximate (dE/dx).
For gold, first and second-degree polynomials give results which practically coincide
and are in fair agreement with the experimental data (see Fig. 1). We should only note the
weakly expressed irregular bend in the curve in the low-energy range in the case of the
second-degree polynomial. The third-degree polynomial makes the dE/dx curve begin to
"wander" around the truve curve, deviating from it slightly only in the low-energy range.
The wandering of the curve is explained by the fact that the degree of the polynomial is
commensurate with the number of experimental points so that the statistical spread of the
experimental data is affected. For aluminum and copper, polynomials of all three degrees
yield results which are in poor agreement with
giving altogether absurd results.
For melinex (see Fig. 2), the first- and
Practically coincide with each other while the
sults.
the experimental data, with the third degree
second-degree polynomials yield results which
third degree gives appreciably different re-
Thus, if the experiment is in accord with variant I formulated above, the results for
dE/dx are unstable: along with correct results (gold) incorrect results are also obtained
(aluminum, copper). More over, there is no stability of results in relation to an increase
in the degree of the polynomial for (dE/dx)-1.
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460
200 I I
,4 0:
0 8 1,ZE,MeV
Fig. 2
140
2 JE,MeV
Fig. 3
Fig. 2. Values of mass stopping power of melinex for protons, ob-
tained by processing the experimental data of [4] by the technique
of [2].
Fig. 3. Values of mass stopping power of kovar for deuterons, taken
from [9] (0) and obtained in the present paper by the technique of
[2] with the use of the experimental data of [9] (----)
"corridor of error."
TABLE 1. Stopping Cross Section for a-
particles in Oxygen
e(E), 10-15
eV ? cm2/moi.
..s7'
e(E), 10-15
eV ? cm2/mol.
results of
[5], c1(E)
results of
present
paper, 62(E)
results of
[5], 61(E)
results of
present
paper, 62(E)
>
(1)
.-
-
>
a)
-
w
uS
uT
?,,,
300
81,8
81,9
0,1
1200
00,2
90,6
0,4
400
89,0
89,5
0,6
1300
87,8
87,9
0,1
500
93,4
94,3
1,0
1400
85,3
85,1
--0,2
- GOO
96,0
06,0
0,9
1500
82,8
82,4
--0,4
700
07,0
07,0
0,9
1600
80,4
70,8
--0,7
800
96,0
07,7
0,8
1700
78,2
77,6
--0,8
000
96,0
96,7
0,7
1800
76,2
75,7
--0,7
1000
04,4
95,1
0,7
1900
74,0
74,2
--0,2
1100
92,4
93,0
0,6
2000
72,0
72,7
0,0
When a-particles pass through oxygen the polynomials for (dE/dx) -1 up to the sixth
degree give results which are in good agreement with [5]. Table 1 gives values of the
stopping cross section taken from [5] and those which we obtained by using sixth-degree
polynomials for (dE/dx)'. A further increase in the degree leads to wandering of the
dE/dx curve.
Thus, experiments formulated in accordance with variant 2 give quite reliable results
which are stable under an increase in the degree of the polynomial for (dE/dx).
Therefore, the results of our paper along with the results of [2] permit the first
tentative conclusions to be drawn about the optimal conditions of experiments on determining
dE/dx by the method of [2]. It is desirable to conduct the experiment according to the
scheme in which, at several values of absorber thickness, the initial energy beam is changed
in quite small steps. The absorber thickness is preferably taken so that the energy loss in
it amounts to 5-20% of the energy range. The initial values of the beam energy must be
distributed approximately uniformly over the energy range.
Along with the choice of optimal conditions of the experiment to determine dE/dx it
is of interest to develop a technique for finding the corresponding variances. Comparative
566
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analysis of the various methods of finding the variances can be conducted according to the
results of [9]. That paper, in particular, gives the results of measurements of the mass
stopping power of Kovar for deuterons by the AE/Ax method (under conditions when this method
gives reliable results), the corresponding errors, and the experimental material necessary
for processing by the technique of [2]. The analysis showed that the method of finding the
errors [2], based on the classical theory of the transfer of the latter, gives
results which are underestimated by a factor of 1.5-2 in comparison with the results
of [9]. More exact results are obtained by using the following technique. Suppose
that yp is some experimental value of the ratio of the absorber thickness to the energy loss
in it and s(yp) is the variance of that value. We process the experimental material accord-
ing to the technique of [2] at values of the ratio of absorber thickness to energy loss in
it equal to yp and yp ?s(yp) and we take the difference of the corresponding values of
dE/dx to be their variance. Figure 3 gives the results of such processing of the experimen-
tal data of [9]. It is seen that our results are in good agreement with the results of that
paper.
1.
2.
3.
G.
G.
G.
LITERATURE CITED
N. Potetyunko, At. Energ., 41, No. 2, 134 (1976).
N. Potetyunko, At. Energ., 43, No. 2, 118 (1977).
N. Potetyunko, Izv. Vyssh. Uchebn. Zaved., Fiz., No. 9, 123 (1979).
4.
M.
Al-Bedri, S. Harris, and H. Parish, Rad. Effects, 27, No. 3-4, 183 (1976)
5.
P.
Bourland, W. Chu, and D. Powers, Phys. Rev. B, 2, No. 11, 3625 (1971).
6.
D.
Kahn, Phys. Rev., 90, No. 4, 503 (1953).
7.
D.
Green, J. Cooper, and J. Harris, Phys. Rev., 98, No.
2, 446 (1955).
8.
H.
H. Andersen et al., Phys. Rev. A, 16, No. 5, 1929 (19
77).
9.
C.
Shepard and L. Porter, Phys. Rev. B., 12, No. 5, 1649
(1975).
CRITERION OF IGNITION AND RESERVE AT IGNITION FOR THERMONUCLEAR TARGETS
Yu. S. Bakhrameev, V. N. Mokhov, UDC 533.92
and N. A. Popov
In comparing various types of thermonuclear targets compressed by the action of exter-
nal energy sources (lasers, electron beams, magnetic fields, etc.), the relation of the
thermonuclear energy obtained to that expended and to the demands placed on the energy source
to ignite the target (the energy delivered and the character of its growth in time), we
usually consider the quality of the target as the basic parameter. However, in order to ob-
tain a real thermonuclear flash in compressing systems, it is necessary to have a certain
reserve at the ignition in order to compensate for calculational inaccuracies and possible
variation of real parameters from their calculated values. Therefore, it may be incorrect
to compare targets without calculating their reserve at ignition.
At the present time sufficiently powerful external energy sources have not been created
and we are lacking the possibility of experimentally checking the thermonuclear combustion
of various types of targets. It is necessary to have an understanding of the reserve at
ignition in order to unambiguously define the target characteristics, which is especially
important, particularly for a more correct comparison of various targets. Below we will
present one of the possible criterion of ignition and the corresponding definition of the
reserve at ignition. This criterion is practically the generalized Lawson criterion [1] for
a dynamic system.
We will examine a target of volume S2, which has a mass M of thermonuclear fuel. In
the process of compression, the target volume Q(t) and the matter temperature e(t) change
with time t. The change of entrophy S(, 0) is defined by
Translated from Atomnaya Energiya, Vol. 49, No. 2, pp. 121-122, August, 1980.
Orginal article submitted April 23, 1979.
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where
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dS 1 1
71-=-17Qtn (52, 0) - Qui (52, 0, t)
Qtn is
the thermonuclear energy generated and Qth is the thermal loss.
If we consider nuclear fuel consisting of only tritium and deuterium, then
(1)
, , X/VdNi
Qtn (?)(l(1-I- (12 VIVIdt
where (av)dd is the thermonuclear reaction rate for deuterium into two approximately equal
channels (producing 3He or T) [1, 2], Nd and Nt are the number of deuterium and tritium
atoms in the volume 0, and ql and q2 are energies which are released by the corresponding
thermonuclear reactions in the volume Q. In particular, if the neutrons remove their entire
energy from ,'ze, and the charged particles are completely retained in it, then qi Q 1.3 MeV
and q2 3.6 MeV. At the same time the possible reactions of neutrons and 3He are not cal-
culated.
We will assume that we know the solution to a complete system of equations describing
the compression and initial heating of a target without calculating the thermonuclear re-
actions. From this solution we know the temporal change in the volume V(t) and the temper-
ature T(t) of the above mass of matter M. These quantities conform to equation
dS (V, T) 1
Qth (V, T, t).
dt ?T
(2)
To determine the criterion of ignition, we will examine the very beginning of heating
when (and also long before this) OW r=,'T(t), the significant difference between T(t) and
0(t) comes later. Concerning this, it is possible to neglect the depletion of nuclear fuel,
i.e., suppose Nd = const and Nt = const, furthermore, we may consider that Q(t) = V(t), be-
cause the rate of change dWdt is weakly dependent on the temperature, and time is necessary
for the difference to develop.
Equation (1) determines the temperature 0(t) from the values of V(t), which we assume
to be well known. To obtain an approximate analytical expression for 0(0 we will isolate
the basic dependence of (av)dd and (av)dt on 0 in the range of temperatures where ignition
occurs (0 2-6 keV), as a power function:
coodd?o-qin and(au)d 0.0112
where in 4, and f1(0) and f2(0) in the selected interval 6 are weakly dependent on the
temperature.
Following this, in the weakly temperature-dependent functions, for 0 wewill substitute
T, i.e., we put f1(0) fl(T) and f2(0) f2(T). In the same manner, we will put Oth{Q,
0,t}/00th {v, T, t}/T, as the temperature dependence of the heat flow, in the cases of
interest, is moderate (bremstrahlung loses, electron thermal conductivity). By calculating
all that stated above from expressions (1) and (2), we obtain an equation for the tempera-
ture in the form
d
dt
--[S(1',0)?S(V,T)1,,G0)m
-1 Qtn(T,V)
T '
which, for the case of an ideal gas with an equation of state E = AMT, allows us to reach
the following solution:
0 (t)-T (t)11 1? (In --1) ? dtit.
m-
AMT
(3)
(4)
Let us call the moment of ignition that moment when OW, according to formula (4),
becomes infinite. In reality, at a high temperature its growth ends due to dispersal and
burnout of the target matter and weakening of the dependence of (av)dd and (av)dt on T.
However, for the characteristics of ignition (we are not interested, in this work, in fuel
energy release) this is irrelevant. Thus, ignition of a system is determined by the ex-
pression
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W (t)=(m-1) QtrLAI(T;, V) dt
-
(5)
If we find such a volume V in the target, which has, at the moment t W > 1, that
target will ignite. To characterize the reserve at ignition, we propose to use W(tm), the
value of W at the moment of maximum compression, tm of the region of the target considered.
A limitation at this time is connected with the fact that after the maximum compression dur-
ing the dispersal of the target matter, pertubations usually grow very quickly and turbulent
mixing occurs. Therefore if the system does not ignite at time tm then the probability of
ignition is generally small.
The criterion for whether or not ignition is obtained in a system which during time
has a constant density i and temperature T, is expressed by the well-known Lawson criterion
[1]:
AMT 4
nT>
IVq2(ctv)dt tn-1 '
(6)
where n = 2nd = 2nt is the density of the nuclei, and N is the total number of nuclei in the
D + T mixture. At the minimal value of the right-hand side of inequality (6) (at T 15-
20 keV), we get n T >1014 cm-3- sec.
The criterion of ignition found and the subsequent understanding of the reserve at
ignition W(tm) might be easily extended to more complex cases. For example, when the temp-
eratures at various points in the volume Q are unequal, or when the equation of state of
the matter is not that of an ideal gas, a more exact calculation of the dependence of Qth
on temperature is required. Also to be considered are systems with admixtures of various
chemical elements in the nuclear fuel or with other types of fuel. This article does not
make a recommendation on the selection of the volume V, as this is intimately connected with
the concrete construction of a target and the fulfillment of the approaches shown above.
For the majority of practically interesting systems the use of the proposed criterion
does not cause difficulties and gives satisfactory accuracy. The authors understand, how-
ever, that systems are possible for which criteria of another type might be more expedient.
LITERATURE CITED
1. S. Yu. Luktyanov, in: Hot Plasma and Controllable Nuclear Synthesis [in Russian],
Nauka, Moscow (1973), p. 17.
2. B. N. Kozlov, At. Energ., 12, No. 3, 238 (1962).
569
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NONDESTRUCTIVE METHOD FOR THE CONTROL OF NONIRRADIATED NUCLEAR REACTOR
FUEL USING A PULSED NEUTRON SOURCE
S. B. Shikhov, V. L. Romodanov,
V. G. Nikolaev, V. A. Luppov,
and D. F. Rau
UDC 621.039.516.22
Significant progress in the area of experimental methods of nuclear physics has re-
cently caused a wide circulation of nuclear-physical methods of analyzing the composition
of expensive prepared products without their destruction [1, 2]. This is related to the
definition of the contents of 235U in the fuel elements of nuclear reactors.
The physical basis of the proposed method of control of the fissionable matter con-
sists of the following. The pulsed neutron source irradiates the moderator block, after
slowing down, the thermal neutrons enter the sample studied where fission of 235U occurs.
The fast neutrons from fission, slowed in another moderator block surrounded by a neutron
absorbing screen, are recorded by thermal neutron counters. To calculate the shielding by
the internal layers of the fuel, thermal neutron counters are used. There are arranged in
such a way as to record the transmission of thermal neutrons through the sample (Fig. 1).
The temporal behavior of the neutron current in the detector of fission neutrons,
which consists of moderator 3 and thermal neutron counter 6, for times after the pulse of
the source, may be described by the following expression
(I) (t) ? A exp (?at) + B exp (-131) (1)0.
(1)
The first term characterizes the temporal decrease in moderator 3 of the thermal neu-
trons which are formed form the secondary neutrons arising as a result of the fission of
235U nuclei by thermal neutrons. Here a is the time constant of thermal neutrons in modera-
tor 1, as these neutrons, which cause fission of 235U, will have a rate of decrease which is
determined by the material and geometry of moderator 1. The coefficient A depends on the
concentration of 235U and is proportional to the power of the source. The second term re-
flects the temporal decrease of thermal neutrons which are formed as a result of the slowing
down of the source neutrons in moderator 3, 0 is the time constant of thermal neutrons in
moderator 3. The coefficient B is proportional only to the source power. The material and
sizes of the moderators are selected to satisfy the condition B > a, (Do is determined by the
delayed neutrons and is constant, if the repetition period of the pulsed source is much less
than the minimum half-life of the delayed neutrons, (Do is also proportional to the source
strength.
We will designate by NA, NB, and
the total neutron number flux recorded
the beginning and end of the analysis
We determined the functions:
N the portions of each component of the flux (D(t) of
in the interval of time (to, ti), where to and ti are
ti
interval (e.g., NA------ .f A exp (--at) d t )
to
F (P1'5) = AIN 13; (2)
11) (V5/T8) = NoiNn ? (3)
Here p is the fuel density, y5 and ye are the concentrations of 235U and 238U in the sample.
The functions F(py5) and cp('y3/y8) do not depend on the source strength, their value is mea-
sured in a single electronic channel and we thereby eliminate errors associated with in-
stabilities of the apparatus. One may determine the content of 235U in the sample if one
compares the values of the functions F(py5) and (I)(y5/y8) with their analogs on the calibra-
graph.
Translated from Atomnaya Energiya, Vol. 49, No. 2, pp. 122-123, August, 1980.
Original article submitted August 6, 1979.
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00-5
0
2
3
4
Fig. 1
Fig. 2
Fig. 1. The experimental arrangement: 1) Moderator block for
source neutrons, 2) pulsed neutron source, 3) moderator block for
fission neutrons, 4) sample studied, 5) thermal neutron counter
measuring transmission through the sample, 6) thermal neutron
counter, 7) cadmium shield.
Fig. 2. Dependence of the function F on the concentration of
2"U (p = 18.7 g/cm3).
A constructed and optimized arrangement was used for experimentally checking the
method. It seems that the accuracy of determining the concentration is essentially depen-
dent on the ratio of the time constants 0 and a. By optimally measuring the arrangement we
get the following values for the time constants: 13 = (31920 +100) sec-1,a = (5890 +5890 +56)
sec-1. Organic glass served asthematerialfor themoderators. Thecharacteristic dependenceof
function F on the concentration of 235U is shown in Fig. 2. The temporal range of analysis
of (D(t) was the followings to = 250 psec, ti = 2000 psec. The neutron source was a neutron
generator with a frequency of neutron pulses equal to 450 Hz and the mean strength was '1,103
neutrons/sec. The accuracy of determining the concentration here was equal to 5%. The
value is not limiting and can be improved in the future.
LITERATURE CITED
1. V. V. Frolov, Nuclear-Physical Methods of Controlling Fissionable Materials, [in
Russian], Atomizdat, Moscow (1976).
2. T. Dragnev, At. Energy Rev., 11, 341 (1973).
571
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STUDY OF THE FIELD OF SECONDARY RADIATION BEYOND LEAD ABSORBERS IRRADIATED
BY 640-MeV PROTONS
A. Ya. Serov, B. S. Sychev, UDC 539.12.175
S. I. Ushakov, and E. P. Cherevatenko
This work, an extension of [1], measures the space-energy and radial distribution of
secondary radiation which exits when a lead absorber is under bombardment by a beam of 640-
MeV protons. The thickness of the absorber along the beam direction is d = 60 cm (680 g/
cm2); the cross-section is 70 x 40 cm. The proton beam diameter at the forward end of the
absorber (from the beam side) is 2.5 cm (Fig. 1).
The beam is monitored with an ionization chamber calibrated by way of measuring the
absolute yield of products of the reactions 27A1(p, 3pn) 24Na, 27A1(p,
spall) I8F and I2C
(p, pn)IIC in aluminum foil and graphite plates. During this work, data from [2] concerning
the cross sections of these reactions were used. The estimated calibration error was '?,10%.
The energy spectra were measured by a spectrometer along with the time of flight with time
resolution 2 T = 1 nsec and with a proton detection threshold of 60 MeV. A more detailed de-
scription of the spectrometer is given in [3].
The spectra of protons were measured at a constant distance of 1 mfrom the absorber
end to the first counter and a distance L = 2.36 m between base counters (spectrometer base).
The angular resolution was 5.7.10-4 Sr. The cross section of the spot "viewed" by the
spectrometer on the end of the absorber was 9.8 x 9.8 cm2. The systematic error (" 12%) of
the measured spectra of protons was determined by the error of monitoring (10%), by the in-
accuracy of the alignment of the spectrometer (6%), and also by the portion in the spectra
of charged TrI mesons and protons which occur during the interaction of neutrons with the
material of the scintillator in the first counter (',4%). The background level, which is de-
termined with experimental samples, does not exceed 1%.
The measured distribution of the secondary yield is seen in Fig. 2. The cross-hatched
region of indeterminancy is caused by the statistical error, energy resolution of the spec-
trometer, and in the region of energy below 150 MeV, by the indeterminancy of the correction
for multiple coulomb scattering. The systematic error is not calculated.
This work will present a calculation of fields of secondary radiation which are formed
during the development of an internuclear cascade in the given lead absorber with the help
of program CASC-2 [4], which realized the method of successive collision, applied to calcu-
lating an internuclear cascade in the axisymmetric geometry [5]. The system of constants
D2N1 [4, 6] was used as the input information. This work also experimentally determined the
radial distribution of the fluence of secondary particles and absorbed doses. Carbon de-
tectors, nuclear emulsion of type K, and x-ray film were used for measurements. The absolute
yield of the reaction 12C(x, xn)IIC in the irradiated carbon detectors was measured using the
scintillation y spectrometer. The cross section of this reaction for secondary nucleons of
energy E > 20 MeV was equal to 21 mb (1 b = 10-28 m2) [2]. From the data in [7] it follows
that the effective region of the registration of protons in nuclear emulsion of type K corre-
sponds to the energy interval 0.5-150 MeV. X-ray films, intended for measuring the exposed
dose of y radiation, were used for measuring the absorbed dose in this work. The response
of the x-ray films was interpreted in terms of an absorbed dose, considering the data rela-
tive to its sensitivity to the protons [8]. Experimental and calculated data on the radial
distribution of detector readings are seen in Fig. 3.
The fraction of protons and TrI mesons in the fluence of hadrons beyond the lead ab-
sorber of such a thickness is 2-3%. Figure 4 shows the angle integrated energy spectra of
protons and neutrons for various distances r. The data from this diagram (originally for
Translated from Atomnaya Energiya, Vol. 49, No. 2, pp. 123-124, August, 1980.
Original article submitted September 28, 1979, revision submitted March 26, 1980.
572 0038-531X/80/4902- 0572$07.50 ? 1981 Plenum Publishing Corporation
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2
C1 C2
C3 C4
1
Fig. 1. Geometry of the experiment: 1)
incident protons; 2) "spot"; 3) lead.
100 200 300 c MeV
Fig. 2. Energy spectra of protons emitted
from the surface of the lead absorber at
various distances r from the beam axis at
angle 0 =,00: the cross-hatched section is
the experiment; calculation.
0
1100 2100 3100 E,MeV
Fig. 3 Fig. 4
Fig. 3. Experimental (0,0, A) and calculated (-) data on the radial
distribution of detector readings beyond the lead absorber, 0) F, fluence
of hadrons with energy E >20 MeV,O) N, density of tracks in nuclear
emulsion, A) D, absorbed dose (measured by the blackening of the x-ray
films), calculation of N: 1 and 2) Ethr = 150 and 50 MeV.
Fig. 4. Calculated energy spectra of protons and neutrons at the sur-
face of a lead absorber at various distances from the axis of the beam:
-----) protons, - - -) neutrons (the calculated data have been multiplied
by 0.01).
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calculating the fluence of hadrons) clearly illustrates the small fraction of protons in
the field of nucleons.
Since we cannot reliably determine the effective correct threshold of the response of
the emulsion K, the experimentally measured number of tracks will be compared with the cal-
culated data in Fig. 3, which corresponds to the values of the threshold 50 and 150 MeV. A
comparison of the experiment and the calculation show their fully satisfactory agreement.
In conclusion, the authors wish to express their thanks to V. P. Dzhelepov for support
of the work, Yu. M. Kazarinov and V. S. Kiselev for assistance in its execution. We are
grateful to M. M. Komochkom, M. I. Salatskoi, and G. N. Timoshenko for showing methodical
help. Throughout the entire work we were constantly helped by our colleagues E. K. Gellfand,
A. A. Dem'yanov, and Yu. A. Razumov, to whom we are deeply grateful.
LITERATURE CITED
1. A. Ya. Serov and B. S. Sychev, At. Energ., 45, No. 3, 235 (1978).
2. E. Bruninx, CERN-61-1, Geneva (1961).
3. A. Ya. Serov and B. S. Sychev, in: Methods of Controlling Accelerators [in Russian],
Proceedings of the Radiotechnical Institute, No. 25, Academy of Sciences of the USSR,
Moscow (1976), p. 176.
4. E. K. Geltfand et al., in: Questions of Dosimetry and Radiation Shielding, [in
Russian], No. 18, Atomizdat, Moscow (1979), p. 160.
5. A. Ya. Serov, E. K. Geltfand, and B. S. Sychev, in: Thesis. Second All-Union
Conference on the Shielding of Nuclear-Technical Arrangements from Ionizing Radiation,
MIFI, Moscow (1978), p. 28.
6. A. Ya. Serov and B. S. Sychev, in: Charged Particle Accelerators [in Russian],
Proceedings of the Radiotechnical Institute, No. 14, Academy of Sciences of the USSR
Moscow (1973), p. 173.
7. M. M. Komochkov, et al., Report of the Joint Institute for Nuclear Research 13-10188,
Dubna (1976).
8. A. Ya. Serov and B. S. Sychev, in: Proceedings of the Fifth All-Union Conference on
Charged Particle Accelerators, [in Russian], Vol. 1, Nauka, Moscow (1977), p. 210.
FIELD EMISSION MICROSCOPE STUDY OF RADIATION DAMAGE IN TUNGSTEN CAUSED BY
252Cf FISSION FRAGMENTS
V. M. Aleksandrov, I. A. Baranov,
R. I. Garber, Zh. I. Dranova,
A. S. Krivokhvatskii, I. M. Mikhailovskii,
and V. V. Obnorskii
UDC 537.534:539.16
The characteristics of radiation damage significantly depend on the type of material,
its structure [1, 2], the energy and nature of the particles of the penetrating radiation
[3], and also the radiation dose [4]. Radiation damage of tungsten by fission fragments was
studied [5, 6] with the help of the field emission microscope. Irradiation was carried out
in the core of a reactor using 335U as the fissionable material. However, the interpreta-
tion of the results obtained caused definite difficulties due to the continuous energy spec-
tra of fission fragments in the region up to 100 MeV, connected with the great thickness of
the 235U layer, which exceeded the range of the fission fragments. Therefore, this work
used a thin layer of 252Cf as the source of fission fragments, becasue the energy spectra of
252Cf has two maxima. Since the tungsten needles arrange the perpendicular flow of fission
fragments, we succeeded in exposing the deformation of the structure and other defects which
had not been detected in previous studies [5, 6].
Translated from Atomnaya Energiya, Vol. 49, No. 2, pp. 124-126, August, 1980.
Original article submitted October 4, 1979.
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Experimental Method. The irradiated samples presented their own point, which was
formed by electrochemical etching from a tungsten wire of 99.95% purity and exposed subse-
quently to low-temperature evaporation in an electric field of high intensity (,5.108
V/cm) for the purpose of forming an atom-smooth surface. The irradiation was conducted in
a vacuum chamber, here the point arranged the perpendicular flow of fission fragments at a
distance of 6 mm from the layer of 252Cf with thickness 10 pg/cm2. The intensity of the
current of fission fragments over 4i sr was 3.5-106 sec-1. The fission fragments were
collimated in angle by ?25?. The time of irradiation was chosen in order to provide the
incidence of several fission fragments onto the peak of the point. To cut-off nuclear recoils
of 248CM of energy 100 keV due to the a decay of 252Cf, and also to prevent contamination
of the vacuum chamber and samples, the layer of californium was covered by two thin films of
nickel of a combined thickness of 200 pg/cm2. The mean energy of heavy and light fission
fragments is, accordingly, 69 and 96 MeV (Fig. 1). Since 252Cf is simultaneously the source
of a-particles of energy 6.1 MeV, and also of fission neutrons of mean energy 2 MeV, it is
necessary to evaluate the additional fraction in the radiation damage of the tungsten needles.
Having information [5] about the role of fission neutrons and the low value of the fluence of
fast neutrons for the irradiated points (less than 1.1012 neutrons/cm2) allows us to neglect
the influence of such a factor. The dose of a-particles which hit the point is 2-1012 par-
ticles/cm2. The control experiment of irradiating tungsten needles with an equivalent cur-
rent of a-particles was carried out using a 255PU source. To cut-off the nuclear recoils
of 234U with energy 100 keV, which occur from the a-decay of 255PU, the layer of plutonium
was covered by a thin film of nickel.
The irradiated samples were studied in a helium field emission microscope with cooling
of the tungsten needles by liquid nitrogen. The image is registered using an electron-opt-
ical transformer with an amplification coefficient of 10,000. The microphotographs of the
surface of the irradiated samples were studied by the distribution of the field-emission
contrast and by its changes in the process of controlled evaporation of atomic layers (110)
with a field .
Results of the Experiment and Discussion. The control samples, irradiated by a-part-
icles from a plutonium source to a dose of 2.1012 cm-2, after the desorption by an electric
field of two-four atomic layers, showed practically atomic layers, showed practically an
atom-smooth surface. Evaporation of the material of the samples to a depth 102 nm did not
show extended damage to the lattice. The characteristic atom-smooth surface of a tungsten
point with a radius of curvature at the top of 21 nm irradiated by a-particles is seen in
Fig. 2.
In the samples irradiated with fission fragments, we see surface damage as depressions
with a mean diameter of up to 7 nm. Immediately after irradiation of samples with fission
fragments and the removal from their surface of absorbed atoms, we can observe two depres-
sions in the area of the faces (101) and (011) having a type of crater connected with
bright contrast bands (Fig. 3). An analysis of a series of microphotographs obtained during
laminar evaporation by the field shows that the craters are arranged on a line perpendicular
to the axis of the sample, and, evidently, correspond to the point of entrance and exit of
the fragment. Such a correlated arrangement of depressions is observed in all irradiated
samples. In individual cases over the area of the passage of the fragment we see the dam-
aged zones of width up to 9 nm (Fig. 4), indicating that the passage of the fission fragment
in the surface layer essentially changes the topography of this surface region. In Fig. 4a,
b the divergence of the axis of the fragment track from the surface reaches 12 nm, but sim-
ilar distortions are detected even after the passage of the fragment to a depth of 15 nm.
An analysis of a series of field emission microphotographs allows us to construct the de-
pendence of the width of the damage zone on the depth of the axis of the fragment track
(Fig. 5). During the increase of the intensity of the electric field (> 4.5.105 V/cm),
inside damage zones separate atoms appear; these zones are characterized by porous layers.
Similar damage was not detected earlier [5, 6], possibly due to the use of samples arranged
almost parallel to the current of fragments, many of which were slowed down inside the
source. The appearance of big craters is connected [5] with the action of a return pulse
which occurs in the case when the fragment does not exit the sample. It was also discovered
in [6] that at complete passage of the fission fragment across the point, the surface re-
mains almost undamaged, which is explained [6] by the absence of the return pulse. The ex-
periments conducted show that at the complete passage of fission fragments of energy greater
than 50 MeV through the tungsten needle, large craters form at the places of entrance and
575
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576
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1000
0 gip,
"
13
.L?
.)
cd 0
0
30 50 70 .90 110
Energy of fission frag-
ments, MeV
Fig. 1. Energy spectrum of fission'
fragments from 252Cf.
Fig. 2
Fig. 3
Fig. 2. Surface of a microcrystal of tungsten
irradiated by a particles.
Fig. 3. Field-emission image of a tungsten
sample irradiated by fission fragments. The
damaged parts of the surface are marked by
arrows.
Fig. 4. Erosion of part of the surface of
tungsten by the tracks of fission fragments of
252Cf immediately after irradiation (a) and
after evaporation to a depth of 2.3 nm (b).
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d,
Fig. 5. Dependence of the width of the
damage zone d on the distance from the
fragment track, A.
exit of the fragment that were not detected earlier [6] with the radiation by slowed fission
fragments. The size and form of the damage of tungsten needles by fragments of high energy
may, evidently, be described as a result of the formation of a thermal spike around the
track of the fragment.
A characteristic peculiarity of these experiments is a sufficiently close location of
the tracks near the atom-smooth surface of the sample. Therefore, the surface atoms succeed
in evaporating at the beginning of recrystallization. As a result, the formation of craters
occurs, as does a porous layer of a certain part of the surface over the track of the fission
fragment.
In conclusion, we should note that the presence of a band of contrast, analogous to
that described earlier [8], will confirm the former conclusion about the possibility of the
formation of a belt of contrast due to the formatio of saddle-shaped surfaces connected with
localized depressions (e.g., craters).
The authors wish to extend their thanks to V. P. Eismont for discussing the results.
LITERATURE CITED
1. K. Izni, J. Phys. Soc. Jpn., 20, No. 6, 915 (1965).
2. B. M. Aleksandrov et al., At. Energ., 41, No. 6, 417 (1976).
3. B. M. Aleksandrov et al., At. Energ., 38, No. 1, 47 (1975).
4. J. Biersack and D. Fink, J. Nucl. Mater., 36, 193 (1974).
5. K. Bowkett et al., Phil. Mag., 11, No. 111, 651 (1965).
6. K. Bowkett, ibid., 15, No. 134, 415 (1967).
7. Van Byuren, Defects in Crystals, Publ. Abroad, Moscow (1962).
8. I. M. Mikhailovskii et al., Fiz. Tverd. Tela, 19, No. 4, 1116 (1977).
577
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CALCULATION OF THE PERTUBATION OF FUNCTIONALS OF THE FLOW OF NEUTRONS
BY A DIRECT MONTE CARLO METHOD USING CORRELATED SAMPLES
V. D. Kazaritskii UDC 539.125.52:621.039.51.12
The definition of pertubations of reactivity by the direct method of diffusion of
neutrons correct to second-order terms is seen in [1]. An analogous approach may be ex-
tended to arbitrary linear functionals of the neutron flux.
The Boltzmann equation in the integral form in the context of the density of colli-
sions is
(x)'.= Ks (x x') (x')dx' (x Ix') 11.1 (x') dx'
(1)
Here x is the point of phase space X = tr, E,Q1,and Ks (x/x') and Kf(x'x') are accordingly
the kernels of scattering and fission. The search for a solution to Eq. (1) proceeds by
iteration. For this purpose, it may be split into the system of coupled equations
(x) = K (x x')11' (x') dx' - .S' (x);
S (x)= .C1 K1 (xIx')W (x') dx', 2, 3 ...,
(2)
(3)
Sl(x)=S(x). The system of equations (2), (3) is itself solved by the Monte Carlo method for
the successive generations of neutrons. Subscripts i-1 and i indicate the i-1 and i-th
generation of neutrons. We will introduce a linear functional of the flow of neutrons
R= (x) (x)dx S (x)
(4)
where (/) (x) is a bounded function, and Ri is normalized per fission neutron. In a physical
sense this is the reaction rate. The variation of the functional is equal to
(x) dx 4- (i) (x) 6T (x) dx
C
?R 6, (x) dx}/ c Si (x) dx
The
The function Ti(x) is the solution to Eq. (2) and is given by the Neumann series [2]:
tit (x) ? Si (x)d- K s(x1x0) S (x0) dxo C K (x Ix K s(xilxo) Si (xo)dxidx0+ ? ? ? .
?
(5)
(6)
The collision density in the perturbed systernipri'(x) is given analogously. We will now
introduce the function
111/1'i (x)=Si (x)? K (x1x0)S (x0) dxo (x xi) Kis' (xilxo) S (x0) dxidxo . . . .
Series (6), (7) converge and corresponding solutions exist; this follows from the
properties of the operator Ks(x/xf) and the function Si(x):
O