Soviet Atomic Energy Vol. 49, No. 2
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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
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ENERGY publication of the translation and helps to improve the quality
of the latter. The translation, began with the first issue of the
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ROssian journal. '
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Soviet Atomic Energy is abstracted or in-
dexed in Chemical Abstracts, Chemical
Tit/s, Pollution Abstracts, Science Re-
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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 ?
? I. N. Golovin V. V. Matveev
'V. I. ll'icheir I. D. Morokhov
V. E. Ivanov A. A. Naumov ?
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.
0038-531X/80/4902-0509$07.50 C) 1981 Plenum Publishing Corporation
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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
510
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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.
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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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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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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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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).
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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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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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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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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$07.50 0 1981 Plenum Publishing Corporation
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TABLE 1. Emissions of y Quanta Yy [106 quanta (sec. pA)] and Sensitivity in Deter-
mining Elements at Ep = 10 MeV [10-9 g/(g.11A-1)]
Determined element
and product of re-
action
Energy and in-
tensity of quanta
Y
Sensi-
tivity of
analysis *
MeV
8
11)
1 I
1 2
1013, loc
(1,718(100)
9 9
?1,0
9,8
15,2
200
13c , 13N
0,510(200)
150
27o
340
400
430
470
500
3,70
lic,
14N -,,. 140
ilio __... 13N
0,510(20())
2,312(99)
0,510(200)
480
72o
480
1700
197
9110
25(10
410
1100
3ioo
650
1800
41.lio
951)
2'00
5000
1144
21;0)1
0,5
?,)
0,9
2.3Na _,.. ''Mg
0,439(9,1)
11
42
61
100 '
130
174
"Cr _, "Mn
1,434(98)
910
2100
:1480
5200
7120
0,5
"Ni --.- "Cu
1,332(88)
42
92
183
125
570
935
5,1
"Ca
0,991(43)
21
40
65
79
80s, ,. "Br
0,012(7)
91
136
170
214
250
280
308
6,6
7913? _, 797)1K r
0,127(30)
5,5
15
28
44
111;
97
134
251)
"lir -)- ''"Kr
89y , "Zr
0,190(05)
0,57800(1)
21
80
41;
180
78
300
110
440
147
595
200
r r
0,0
'Zr ->- "0"1Nb
).41-0 _, 11,2,T,
0,1225(71)
0,773(97)
IF
(8
08
30
68
420
71.0
)12cd _? .0.21,1
0,6171(27,(F)
39,6
88
1:1!)
198
200
12
10)!..;? _, 10.sb
1,293(88)
4,))
9,5
16,8
25
:i5
41
59
47
118s? _, 118Sb
1,n0om
9,8
14
18,1;
-A
29,0
89
120$,, _, '"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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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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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
Place Published
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