SOVIET ATOMIC ENERGY - VOL. 38, NO. 4

• Document Type: CREST
• Collection: General CIA Records
• Document Number (FOIA) /ESDN (CREST): CIA-RDP10-02196R000400050002-4
• Release Decision: RIFPUB
• Original Classification: K
• Document Page Count: 104
• Document Creation Date: January 4, 2017
• Document Release Date: September 25, 2013
• Sequence Number: 2
• Publication Date: October 1, 1975
• Content Type: REPORT

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Russian Original Vol. 38, No. 4, April, 1975 4
October, '1975
SATEAZ 38(4) 263-360 (1675)
?
SOVIET
TiMIC
ENERGY
ATOMHAil, 3HEPrI1fl
,(ATOMNAYA iNERGIYA)
TRANSLATED FROM, RUSSIAN
CONSULTANTS BUREAU, NEW VORK,
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SOVIET
ATOMIC
ENERGY
c
?
Soviet Atomic Energy is ?abstrabted or in-
dexed in Applied Mechanics Review's, Chem-
ical Abstracts, Engineering Index, INSPEC?
Physics Abstracts and Electrical 'and Elec-
tronics Abstracts, Current Contents, and
Nuclear Science Abstracts.
Soviet Atomic Energy is a cover-to-cover translation of Atomnaya
Energiya, a publication of,the Abademy of Sciences of the USSR.
An agreement with the Copyright Agency of the USSR ,(VAA.1/4P) -
Makes available both advance copies of the Russian journal and
original glossy photographs and artwork. This serves to decrease
the necessary time lag between publication of the original and,
publication of the,translation and helps to improve the quality
of the latter. The translation began. with the first, issue of the,
? Russian journal.
Editorial Board of Atomnaya Energiyi:
Editor: M. D. Millionshchikov
Deputy Director
I. V. Kurchatov Institute of Atomic Energy
Academy of Sciences of the USSR
Moscow, USSR
Associate Editor: N. A. Vlasov?
A. A. Bochvar
N. A. Dollezhal'
" V. S. Fursov
I. N. Golovin
V. F. Kalinin
A. K. Krasin
A. P. Zefirov
V.-V. Matveev
M. G. Meshcheryakov
P. N. Palei
V. B. Silevchenko
V. 1.-Smi-r7nov ?
A. P. Vinogradov
Copyright C 19'
75 Plenum Publishing Corporation, 227 West 17th Street, New York,
_N.Y. 19011. All rights' reserved. No article contained herein may be reproduced,
stored in a retrieval system', or transmitted, in any form or by any means, electronic,
mechanical, photocopying, microfilming, recording or otherwise, Without written
permission of the publisher.
?
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Published monthly. Second-class postage paid it Jamaica, New \York 11431.
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SOVIET ATOMIC ENERGY
A translation of Atomnaya Energiya
October, 1975
Volume 38, Number 4
April, 1975
ARTICLES
CONTENTS
Engl./Russ.
Czechoslovakian Heavy-water Reactor of Zero Power ? M. Gron and M. Voggek. . . .
263
203
Thermal and Resonance Neutron Spectra in a Graphite Cube ? Yu. M. Odintsov,
A. S. Koshelev, and A. A. Malinkin
270
209
Use of Few-Group Methods for Calculating the Physical Characteristics of Fast
Reactors ? V. A. Karpov, V. I. Matveev. N. E. Gorbatov, L. V. Averin,
V. A. Chernyi, and V. G. Samsonov
274
213
Removal of Tritium from the Gaseous Wastes from Nuclear Power Stations
? L. F. Belovodskii, V. K. Gaevoi, V. I. Grishmanovskii, V.V. Andramanov,
V. N. Demenyuk, and V. V. Migunov
279
217
Purification of Liquid Radioactive Effluents by Continuous Ion Exchange
? B. E. Ryabchikov, D. I. Trofimov, E I. Zakharov, A. S. Dudin,
and L. K. Mikheev
284.,
222
Calculation of Dose Composition outside Shielding of High-Energy Accelerators
by the Monte-Carlo Method ? N. V. Mokhov and V. V. Frolov . . . . . . .
288
226
Wave Absorption during Magnetoacoustic Heating in the TO-1 Tokamak
? N. V. Ivanov and I. A. Kovan
291
229
Quasi-Continuously Operating Inductive Accelerators ? V. N. Kanunnikov,
A. A. Kolomenskii, P. S. Mikhalev, and A. P. Fateev
296
234
RE VIEWS
Advances in Metrology of Neutron Radiation in Reactors and Accelerators
? R. D. Vasillev
302
240
ABSTRACTS
Experimental Investigation of Resonance Absorption of Neutrons in a Uranium
?Graphite Lattice ? L. N. Yurova, A. V. Bushuev. V. I. Naumov,
V. M. Duvanov, and V. N. Zubarev
307
245
The Hydrodynamics of Fissionable Materials. II. Nonlinear Solutions of the Simple
Wave Type ? V. M. Novikov
308
246
Electron Spectra behind Barriers Having:a Thickness Comparable to the Extrapolated
Range of the Electrons ? V. V. Evstigneev and V. I. Boiko
309
246
Transport Equation for Gamma Radiation in the Small-Angle Scattering Approximation
? L. D. Pleshakov
310
247
Spatial Distribution of Scattered Energy from a Unidirectional Point Source of
High-Energy Electrons in an Infinite Tissue-Equivalent Medium
? A. K. Savinskii and 0. N. Chernova
310
248
LETTERS TO THE EDITOR
The Discharge of Gaseous Fission Products from Fuel Elements of Nonhermetic
Construction ? V. M. Gryazev, V. V. Konyashov, V. N. !Polyakov?
andYu. V. Chechetkin. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
313
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CONTENTS
Quantitative Estimate of the Effect of Chloride Concentration on the Stability of the
Austenitic Stainless Steels under the Operating Conditions of a Boiling Reactor
- V. V. Gerasimov and G. V. Andreeva
Scale Effect in the Explosive Destruction of Water-Filled Vessels - V. I. Tsypkin,
0. A. Kleshchevnikov, A. T. Shitov, V. N. Mineev, and A. G. Ivanov
(continued)
Engl./Russ.
315 250
317 251
Setup for Testing and the Certification of Chemical Dosimeters Operating on the
Principle of Absorbed Photon Radiation Dose of 60Co and 137Cs
- V. A. Berlyand, V. V. Generalova, and M. N. Gurskii
319
253
238PU and 238PU Concentrations in the Air Layer Close to Ground of the Podmoskovve
Region in 1969-1971 - K. P. Makhontko, Ts. I. Bobovnikova, A. A. Volokitin,
and V. P. Martynenko
322
254
Evaluation of Surface Atmosphere Contamination by Discharges from Nuclear Power
Stations - V. P. Illin
324
255
Simulation of Electron Back-Scatteringby a Monte-Carlo Method - P. L. Gruzin
and A. M. Rodin
326
256
Grouping of Neutron Widths of 232Th p Levels - P. E. Vorotnikov
329
258
Determination of the Penetration of Decay Products of Radon into the Respiratory
Organs by a Direct Method - L. S. Ruzer
331
260
Neutron Activation Determination of Hafnium in Zirconium in the Case of Interference
from Fluorine - V. V. Ovechkin, A. Z. Panshin, and V. S. Rudenko
334
261
Neutron Activation Measurement of the Fluorine Content in Uranium and Plutonium
- V. I. Melenttev and V. V. Ovechkin
337
263
INFORMATION: CONFERENCES AND CONGRESSES
Seminar of the International Institute of Applied Systems Analysis in Relation to the
Energy Problem - V. I. Mastbaum
339 1/
265
International Seminar on Reactor Noise - D. M. Shvetsov
341
266
The Fifth All-Union Conference on Heat Exchange and Hydraulic Resistance in the
Motion of a Two-Phase Stream in the Elements of Power Machinery and
Equipment - M. Ya. Belentkii and V. A. Shleifer
343 /267
Soviet-French Seminar on Physics, Hydraulics, and Heat Transfer in Water-Cooled,
Water-Moderated Reactors - S. A. Skvortsov
345
268
G/Winter Session of the American Nuclear Society 1974
- F. G. Reshetnikov and I. S. Golovnin
346v
268
/Second International School on the Technology of Thermonuclear Reactors
- L. I. Rudakov
348,,
269
Fifth IAEA Conference on Plasma Physics and Controlled Nuclear Fusion Research
- V. A. Chuyanov
351,1
271
Conference on the Specialization in the Production of Accelerators - L. G. Zolinova
354-,
273
BOOK REVIEWS
M. N. Zizin, B. A. Zagatskii, T. A. Temnoeva, and L. N. Yaroslavtseva
- Automation of Reactor Calculations. Reviewed by V. P. Kovtunenko. . .
356
277
A. A. Luktyanov - Moderation and Absorption of Resonance Neutrons. Reviewed by
V. M. Mikhailov
357
277
E. F. Cherkasov and V. F. Kirilov - Radiation Hygiene. Reviewed by 0. M. Zaraev. .
359
278
The Russian press date (podpisano k pechati) of this issue was 3/25/1975.
Publication therefore did not occur prior to this date, but must be assumed
to have taken place reasonably soon thereafter.
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CZECHOSLOVAKIAN HEAVY-WATER REACTOR
OF ZERO POWER
M. Gron and M. Vo'fi'aek UDC 621.039.55:621.039.524.46
The TR-0 reactor may be regarded as the first nuclear reactor constructed principally by Czechos-
lovakian undertakings. Great help was received from the Soviet Union, which supplied the necessary
amount of heavy-water and various special items of equipment as well as the corresponding expertise.
The supply of modern experimental equipment for the reactor and automatio'n of its control offered
extensive prospects for a variety of physical measurements. The large size of the active zone and the
negligible influence of the side and end reflectors enabled us to carry out precision critical experiments.
These qualities of the TR-0 reactor make it unique not only in the Comecon countries but also on a world
wide scale, as has already been indicated by experts from a number of other countries.
The starting of the TR-0 reactor offered the possibility of making a careful check on the validity of
the computing methods commonly used in reactor design and obtaining valuable information as to the physi-
cal properties of reactors (chiefly heavy-water reactors) of the A-1 type (the reactor of the first Czechos-
lovakian Nuclear power Station in Yaslovski Bogunici [1-31). The basic program of the experimental work
designed to be carried out on the TR-0 reactor [3-5] up to 1975 was one of providing assistance in the start-
ing, optimization, and perfection of the A-1 reactor, and in also estimating the practical potentialities of
reactors of this type.
Fundamental Parameters of the TR-0 Reactor
The TR-0 operates with rod-type fuel elements of the A-1 class; it is intended for the rapid realiza-
tion of accurate physical experiments. The following are the main characteristics of the system.
Maximum reactor power
Maximum thermal-neutron flux in the
center of the active zone
Moderator
Fuel
Diameter of active zone
Maximum height of active zone
Maximum amount of D20
Maximum charge of natural uranium
Reactor tank
Taper of tank bottom
Outer coating of wall and tank base
Type of fuel
Diameter of rod (uranium part)
Coating of rod (thickness)
Material of fuel-element screen tube
(wall thickness) Aluminum 99.99% (3mm)
1 kW (briefly 3 kW)
109 neutrons /cm2. sec
D20 (99.87%)
Natural uranium
350 cm ,
400 cm
42 tons
39 tons
Made of aluminum, wall thickness
16 mm, bottom thickness 25 mm,
max. excess pressure 100 mm water
15 mm
Cadmium sheet 1 mm thick
Rod, A-1 type, withhermetically
closed bushing
6.5 mm
Magnesium (1 mm)
Institute of Nuclear Research, Rzez, Czechoslovakia. Translated from Atomnaya Energiya, Vol. 38,
No. 4, pp. 203-208, April, 1975. Original article submitted October 2, 1973; revision submitted Decem-
ber 28,1974.
0 1975 Plenum Publishing Corporation, 227 West 17th Street, New York, N.Y. 10011. No part of this publication may be reproduced,
stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming,
recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $15.00.
263
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8
Ea'
25
25 25
24
112
2391 2391
0422
s;2
10
t
1 I II,----11F,1
I 1 I i
111 12 11 ' 13 ' I 1 i 14 I I
A I
D4
21
21
6
D4
18
Fig. 1. Arrangement of the technological circuits of the TR-0 reactor. 1) Reactor
tank; 2) carrying lattice; 3) rotating cover with hydraulic sealing; 4) dry-air reser-
voir; 5) silica gel drying apparatus; 6) compressor; 7) electric heater; 8) measur-
ing tanks; 9) shut-off valves; 10) fan; 11) air cooler; 12) fan of freezing circuit;13)
heat exchanger; 14) freezing-out tanks; 15) mechanical filters; 16) ionic-exchange
columns; 17) collecting tank; 18), 19) pumps with deliveries of 100 and 600 liter
/min respectively; 20) heat exchanger with an intermediate layer; 21) store tanks;
22) control valves; 23) emergency valves; 24) mobile automatic-control detectors;
25) level gages; 26) drives of control and emergency rods; 27) neutron-source .con-
tamer; 28) hydraulic shutter.
Internal diameter of fuel-element screen
tubes (uranium occupation factor)
Length of active part of fuel element
Basic geometry of the lattice
Range of automatic adjustment of the
lattice step (in both perpendicular
directions)
Reflectors
side
lower
264
110 mm (0.264); 123 mm (0.246);
156 mm (0.196); 183 mm (0.179)
Max. 400 (comprising sections of
300 and 100 cm), 300 cm, or 200
cm (two sections of 100 cm)
Square
180-275 mm; 204-316 mm;
230-320 mm; 320-520 mm;
408-632 mm; 460-640 mm;
A D20 reflector may be provided
inside the tank, with a correspond-
ing reduction in the diameter of the
active zone; outside the tank any
reflector may be provided up to a
thickness of about 100 cm
Thickness referred to D20 0-50
cm (either without cavities or con-
taining cavities having the same
diameter as the screen tubes of
the fuel elements)
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Temperature of moderator
while cooling
while heating
Thermal insulation of tank
Maximum rate of filling with D20 (two
pumps)
Reactor cooling
Protective atmosphere over D20
Main access to active zone
Upper shielding of reactor
Side shielding of reactor
Reactor control
Automatic control sensors
Regulating organs (control devices)
of the automatic control system
Roughly 15?C
Roughly 90?C
Glass wool 20 cm thick
600 and 100 liters /min
None
Dry air, dew point ?40?C (excess
pressure up to 35 mm water)
Rotating circular top and experi-
mental openings therein
Movable shielding slabs, total
thickness ?60 cm, including ,-,50
cm of concrete (2.5 tons/m3), 6
cm mixture of polyethylene with
B203
Concrete bunker 2.3 tons/m3
with wall thickness 100 cm,
roughly 3 m from the reactor rank
Automatic-control device working
on two-out-of-three principle
Three tracking fission chambers,
three stationary neutron ionization
chambers, three coarse level gages
Cadmium control rod or control
valves
Three cadmium rods, two valves
Roughly 15 mm/sec for a D20
level of ?300 cm; 30 tons of D20
may be discharged in 350 sec
Ra?Be, 1 Ci
Emergency executive organs
Rate of emergency discharge of D20
Neutron source
Monitoring and measurement
of the D20 level
Three working level gages connected
to the emergency circuit of the auto-
matic control; measuring accuracy
mm in the range 0.5-430 cm
Brief Characteristics of the Basic Equipment
The technological equipment of the TR-0 reactor was described in detail in [5]. Here we shall pre-
sent some basic data relating to the technological circuits. The simplified scheme and general view of the
reactor are illustrated in Figs. 1 and 2.
The reactor tank is placed in a concrete shielding bunker. The lower cylindrical part of the tank,
with an internal diameter of 350 cm, constitutes the active zone, 400 cm high; above this is a space, also
roughly 400 cm high. Through this space pass the fuel channels and also the control and emergency rods.
The upper part of the reactor tank is made in the form of a square housing, which accommodates the lattice
carrying the fuel elements and a beam for the channels of the control and emergency rods. In the demount-
able square top of the tank is a rotating round cover with hydraulic sealing. In the cover are four eccen-
trically-placed round holes 50 cm in diameter and two reactangular holes 40 cm wide and 240 and 100 cm
long. Fuel elements and experimental equipment may be passed in and out through these holes (without
removing the cover) to any part of the active zone. The wall and conical base of the tank (15 mm on the
axis of the reactor) are covered with cadmium sheets 1 mm thick.
The fuel assembly of the TR-0 reactor (Fig. 3) is a model of the fuel assembly of the A-1 reactor,
which consists mainly of rod-type fuel elements and a screen tube. The fuel rods, made of natural metal-
lic uranium, 6.3 mm in diameter and 300 and 100 cm long, are coated with 1 mm of magnesium. By means
of the spacing lattices the rods are assembled into two fuel sections, which are arranged in the aluminum
screen tube, hermetically closed with a lid.
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Fig. 2 Fig. 3
Fig. 2. General view of the TR-0 reactor; 1) Cylindrical part of the tank; 2)
working level gages; 3) thermal column with mobile fission chambers (auto-
matic-control sensors); 4) emergency valves; 5) fuel element; 6) control and
emergency rods; 7) neutron-source channel; 8) square part of tank; 9) rod
drives; 10) neutron-source container; 11) rotating cover with hydraulic seal-
ing; 12) mobile shielding slabs; 13) fuel element store; 14) part of carrying
lattice; a) beams; b) vertical hinged lever mechanism; c) suspension hook; ,
d) mobile mouting plate.
Fig. 3. Fuel element. 1) Cross section of a fuel element of the central type
11 = 1000 mm; /2 = 5 mm; /3 = 3000 mm; internal diameter 0 = 120 mm; 951
= 19.6 mm; 02 = 39.2 mm; 03 = 59.7 mm; 04 = 78.9 mm; 05 = 99.6 mm; 2)
one three-meter section; 3) two one-meter sections; 4) one three-meter and
one one-meter section; a) internal supporting rod; b) external supporting rod.
NumLer of rods on the circles 5, 10, 15, 20, and 25.
The special construction of the fuel-section couplings enables us to suspend a one-meter section from
a three-meter (or another one-meter) section. For siting the three-meter (or two one-meter) sections in
the screen tube, (supporting) rods are provided; these enable us to simulate a lower reflector (with cavi-
ties) 0-48 cm thick arranged in steps of 2 cm.
The external supporting rods fixed in the caps of the fuel assembly enable us to arrange the fuel ele-
ments at various heights above the bottom of the reactor tank and to create a reflector (without cavities)
0-52 cm thick arranged in steps of 2 cm. The fuel assemblies are set up automatically in both directions
in the carrying lattice, with a square step of 180-640 mm (positioning accuracy *0.2 mm).
266
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The control rod and the three emergency rods have an analogous construction. The absorbing ma-
terial is cadmium of cruciform profile, covered with aluminum. The length of the active part of the rod is
200 cm, the width 6 cm, and the thickness of the cadmium sheet 1 mm. The rods are placed in perforated
aluminum channels furnished with shock absorbers in the lower part. The channels are sited in a special
structure under the carrying lattice.
The heavy-water circuits are designed for filling and emptying the reactor tank, storing the D20 in
the storage (reserve) tanks, heating, cooling, and purifying the moderator, and so forth.
In order to carry out experiments at high temperatures, provision is made for the electrical heating
of the D20 (to 90?C). For cooling the moderator there is a heat exchanger with an intermediate layer (inlet
temperature of the D20 20-90?C, cooling water15?C). The circulation of the D20 is achieved by means of
three glandless stainless-steel pumps; two of these (delivery 600 and 100 liters /min) are used in the main
D20 circuit and one (100 liters /min) in the purification circuit. Rapid filling of the reactor with D20 (1-100
liters in less than 0.1 sec) is achieved by means of exactly calibrated measuring tanks.
In order to purify the D20 from soluble and insoluble impurities, two parallel circuits with mech-
anical filters and ion-exchange columns filled with deuterized resin are provided. In order to prevent con-
tact with light water vapor, a slight excess pressure of dry air is automatically maintained in the heavy-
water circuit. In order to avoid the loss of D20 as a result of the evaporation of the remaining traces of
moderator after emptying the reactor tank, the remaining D20 is passed into a special freezing apparatus
by means of a stream of heated dry air. Dry air is also used for heating the reactor before filling the tank
with the heated moderator.
A novel automatic control device is used for controlling the reactor power and providing emergency
protection; it is designed to carry out the following operations;
1) automatic verification of the state of readiness for operation;
2) automatic (or manual) achievement and stabilization of the critical state; this process consists of
three stages; a) raising the level of D20 to a specified minimum height; b) increasing the neutron
flux in accordance with a spedified program by changing the level of heavy-water while automati-
cally regulating the reactor period until the specified neutron flux is attained; c) achieving and
stabilizing the critical state while automatically regulating the steady neutron flux and automati-
cally extracting the neutron source;
3) automatic maintenance of a specified neutron flux by means of the control rod or the D20 level;
4) automatic (or manual) variation of the neutron flux in accordance with a specific program;
5) automatic continuous monitoring of the reactor in the steady and transient states, i.e., a deter-
mination of the actual state of the reactor and comparison with the specified state;
6) emission of warning signals;
7) emission of emergency signals for the rapid shutting down of the reactor.
The basic concept of the automatic-control device is the generally-accepted logical principle of two-
out-of-three. Three independent systems fulfil the function of tracking devices. For low neutron fluxes
these operate without moving the fission chambers, while for high fluxes the automatic control sensors
are moved within the water-filled thermal column. All three automatic-control systems operate in the
tracking mode. One of the two systems may be used as regulator. If one system becomes faulty the second
automatically assumes the function of regulator.
The working equipment includes (and these are extremely vital features) a set of level gages; three
working ("coarse") gages and one of much higher accuracy (experimental). These are placed in special
perforated channels on the periphery of the active zone. The working level gages, which have an error of
+1 mm in the range 0.5-430 cm, are connected to the automatic control device. These monitor the D20
level and emit a signal when the moderator has reached a specified height. The main function of the work-
ing gages is to prevent the level of D20 from exceeded the specified position; this is ensured by connecting
the gages to the emergency circuit of the automatic control device, using the two-out-of-three principle.
The accurate level gage is intended for experimental purposes; its error is *0.05 mm over a few centi-
meters and +0.2 mm over the range 30-400 cm.
267
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Experimental Equipment
In addition to instruments for activation, spectrometric, and time measurements, neutron detectors,
and so forth, the TR-0 reactor also contains an experimental device for measuring the neutron distribution
in the active zone of the reactor; this is placed on the reactor cover and is intended for the smooth or
stepped movement (in 2 mm steps) of the detector in the vertical and horizontal directions. The position
of the detector is measured to an accuracy of +1 mm. The motion of the detector may be controlled manu-
ally or by means of a specialized controlling computer (the ^ESTIMATOR") in accordance with a preselected
program. This computer is designed for controlling various pieces of experimental equipment (for ex-
ample. it is used in varying the level of the moderator) periodically, measuring the reactor period, analyz-
ing experimental data, and so on.
By using the equipment for varying the D20 level we may study the influence of periodic changes of
reactivity due to changes in the height of the D20 level close to the critical state. In order to vary the
level, the filling and emptying valves are periodically opened and closed; this is effected by means of the
"HETRO" system controlled by the ESTIMATOR computer or by a time converter.
The HETRO system gives a D20 level fluctuation period of 4-400 sec; we may specify 1-10 fluctu-
ations, or anyunlimited number. The change in level over one period may reach as much as 2 cm (the
corresponding change in reactivity is about 2? 10-3).
The main aim of the experiments carried out with the cadmium fluctuator is to determine the in-
fluence of periodic perturbations on the state of the reactor. A change in reactivity is achieved by rotating
one of two cadmium plates of special form (a rotor and a stator); these reside in an aluminum shell in-
side the reactor. The number of revolutions of the interchangeable rotor may be varied over the range
20-1800 rpm; the maximum change in reactivity is 2 ?10-3.
The absorbing rods (24) serve to imitate the influence of the absorbing properties of the emergency,
control, and compensating rods of the A-1 reactor on the reactivity and neutron field.
The absorbing part is made of cadmium, and has the shape of a tube with an external diameter of 53
mm and a wall thickness of 1.5 mm. The tube is held in a hermetic can (internal diameter 56 mm, wall
thickness 2 mm). The rod drives situated on the carrying lattice execute the following functions; facilitat-
ing the free fall of one to four rods into the active zone; remote control of the position of the rods to an
error of 2 mm; manual variation of rod position.
For measuring those characteristics of the lattice which depend on the fuel temperature, four special
fuel assemblies are provided, with electric heating to 350?C.
A model of the experimental loop of the A-1 serves for studying the physical properties of this loop
in the TR-0 reactor. This consists of suspension equipment, an outer casing, and inner tubes filled with
3%-enriched metallic uranium. The suspension equipment and the outer casing are made of the same con-
struction elements as the fuel assemblies of the TR-0. The inner tubes of the model are made of steel,
their diameters are 115 and 79 mm, the wall thickness is 6.5 and 2 mm respectively. The model consists
of 31 fuel elements with a diameter of 6.3 mm (thickness of magnesium coating 1 mm).
The model is intended for carrying out the following experiments: measuring the reactivity of the
model at various points and for various configurations of the active zone, and measuring the neutron-flux
distribution around and inside the model.
In order to determine the efficiency of the absorbing rods, the dynamic characteristics of the lattice,
and so forth, the pulsed-source method is also employed in the TR-0 reactor. The neutron intensity in the
pulse is 1010 neutrons/sec for a mean value of 2.108 neutrons/sec. The pulse length may be smoothly
varied from 5 to 8 ?sec, the frequency being varied in the range 1-5 ?104pulses/sec.
Thus from the very onset of its experimental activities (which began in July 1972) the TR-0 reactor
has been undergoing a wide range of experiments, mainly associated with the program of realizing physi-
cal initiation of the A-1 reactor, the central feature in the first Czechoslovakian Nuclear Power Station.
Some of these experiments were actually carried out before the physical initiation of the A-1 began and
were continued during the whole period of physical and power initiation.
The results obtained in the TR-0 for a number of parameters [6, 7] supplement the information ob-
tained in the physical initiation of the A-1, provide a more accurate theoretical description of the reactor,
and help in effecting a reliable extrapolation of the resultant data in the range corresponding to the working
state of the reactor.
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Experiments with the neutron converter carried out in cooperation with Soviet specialists and ZWE
--KODA workers enabled us to calibrate the detectors of the A-1 reactor and to carry out unique measure-
ments of fast-neutron fluxes. Great attention was also paid to experiments with a pulsed neutron source,
carried out in cooperation with Nuclear Power Station workers. These experiments were carried out in
order to develop methods of measuring reactivities, breeding factors, and neutron-migration areas.
After carrying out the first part of the experimental program, measurements which had proved im-
possible to realize in the A-1 were continued in the TR-0 reactor. These measurements may have an im-
portant significance not only from the point of view of verifying theoretical methods and programs of cal-
culating the physical parameters of heavy-water reactors but also from that of the efficient use of the A-1
power station and the assessment of the practical potentialities of reactors of this type.
LITERATURE CITED
1. A. Sevcik, Second Geneva Conference, Paper No. R/2092, Czechoslovakia (1958).
2. J. Holubec et al., Third Geneva Conference, Paper No. R/523, Czechoslovakia (1964).
3., I. Pau1i6ka et al., ibid., Paper No. R/542.
4. J. BArdo6 et al., 6JV-2737/R (1971).
5. M. VoH6ek, UJV-2845/R (1972).
6. M. Vofigek, fLIV-2967-F/R (1973); M. VoMek, F. Hudec, and Z. Turzik, tJJV 2968-F (1973);
Z. Turzik, 15,IV-2969-F (1973); Svoboda, 1.1JV-2970-F/R (1973); a Svoboda, OV-2971-F/R
(1973); J. Mikus and F. Kryl, UJV-3067/R (1973).
7. I. Pau1i6ka, A. Zbytovsk3C, and M. Voi-16ek, Jaderna Energie, 19, 291 (1973).
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THERMAL AND RESONANCE NEUTRON SPECTRA
IN A GRAPHITE CUBE
Yu. M. Odintsov, A. S. Koshelev, UDC 539.125.5:162.2.3
and A. A. Malinkin
In view of the ever-increasing demands for greater accuracy in the measurement of neutron spectra
in nuclear reactors, a great deal of attention has lately been paid to the metrological problems involved in
this process [1].
The creation of standard sources of resonance neutrons is an extremely important problem at the
present time, yet the development of such sources is still in its infancy. In referring to resonance neu-
trons, most papers [3, 4] only indicate the ratio of the resonance neutrons to those of the thermal type.
In actual practice it is often essential to study the characteristics of resonance neutrons in media in which
their spectra differ from the simple 1/E form. Clearly the study of neutron characteristics in these
media would be greatly simplified if we had a standard source with a set of known spectra not obeying the
1/E law. The spectral characteristics of resonance neutrons in graphite prisms were studied in [6, 7]; it
was shown that, depending on the distance from the primary neutron source, the resonance neutron spec-
trum could be expressed in the form E-(1 +13), where 1131 ? 1.
In order to create a calibrated source of thermal and resonance neutrons in the present investigation,
we studied the characteristics of thermal and resonance neutrons in a graphite cube with a side of 1 m,
which showed that there were a number of regions in the graphite cube in which the resonance neutron
spectra differed considerably from the 1/E form and could better be expressed in the form 1/E a(here 0.8
< a < 1). The neutron characteristics studied in the graphite tube subsequently justified us in using the
latter as a calibrated source of thermal and resonance neutrons with different spectral characteristics.
Construction of the Cube
The cube was made up of reactor graphite blocks with a density of 1.6 g/cm3 and placed on a scaffold
so that the center of the cube lay at a height of 2 m from the floor, on a level with the center of a 28-cm-
diameter sphere of 90%-enriched metallic uranium. The front face of the cube lay at 3 m from the center
of the uranium assembly. The cube was placed in a room 6.5 x 7.5 x 4.5 m in size with concrete walls.
Along the central axis of the cube in the direction of the assembly, an open channel 10 x 10 cm in section
was provided; this was filled with graphite blocks containing cells for indicating instruments. The cells
were placed along one face of the blocks in steps of 3 cm, and took the form of cylinders 20 mm in diam-
eter and 5 mm deep.
No protective screens (cadmium or boron) were placed on the faces of the cube.
Characteristics of the Detectors
In order to reconstruct the spectra we used the reactions indicated in Table 1. The range of mea-
surable neutron energies for the system chosen was 1.46 eV to 8.7 keV. All the materials of the indicators
had a natural isotopic composition. The indium, tungsten, and copper indicators were metal foil disks
5-15 cm in diameter. The indicators for the reactions 139La(n, y) and ledDy(n, y) were prepared from films
made of a mixture of powdered lanthanum or dysprosium oxides with saponlac (cellulose nitrate). The
indicators for the reactions 23Na(n, y) and 37C1(n, y) were made by pressing 15 mm diameter tablets of
Na2CO3 and C6C16 respectively.
Translated from Atornnaya Energiya, Vol. 38, No. 4, pp. 209-212, April, 1975. Original article
submitted March 19, 1974.
? 1975 Plenum Publishing Corporation, 227 West 17th Street, New York, N.Y. 10011. No part of this publication may be reproduced,
stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming,
recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $15.00.
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TABLE 1. Characteristics of the Reactions and Indicators Used
Reaction
Thickness of indi-
oator referred to
the isotope, nuclei
/mg
v, T
o( 2200 m/sec), G
Eo,eV
Recorded energy of
y quanta, MeV
usIn (n? 1,)
1,01.1020
54,0 min
160?2
1,46
1,3
197Au(n, y)
2,86.10is
2,7 days
98,8+0,3
4,9
0,412
286W (n, ,y)
8,354019
24h
38?2
18,8
0,687
139La (n, y)
2,39.10i8
40,2h
8,2?08
72,4
1,597
63Cu (n, 7)
4,97.1020
12,88h
4,51?0,23
577
0,511
? 23Na (n, y)
2,464021
15,05h
0,531?0,008
2900
1,37
Cl (n y)
4,60-1021
37,12 min
0,56?0,12
8700
1,65
'Dy (n, y)
1,90.1018
2,36h
800+100
1/v- detector
0,412-0,511
Fig. 1. Thermal and resonance neutron
spectra in a graphite cube at the follow-
ing distances from the front face:1) 65
cm, Pr = 1/E (taken); 2) 41 cm, 'Pr
= 1/E0.88; 3) 28 cm, cot. =1 /0.83; 4) 16
cm, car = 1/E8?88; 5) 4 cm, (pr =11E084.
The indicators were employed in conjunction with a
scintillation gamma spectrometer containing an NaI(T1)
crystal 80 x 80 mm in size, calibrated with standard
y sources; the error in the activity was 3% (for a 95%
confidence interval). The absolute activity of gold was
determined in a p coincidence installation, which was
calibrated by comparison with the 4703?y and p?y systems
of the All-Union Scientific-Research Institute of Metrology.
The error in the determination of the absolute activity of
gold in our apparatus was +1.5% for a 95% confidence
range.
Determination of Neutron
Temperature
The effective neutron temperature was determined
using a "double sandwich" of gadolinium and dysprosium
(method described in [81). The filters were prepared by
spraying gadolinium oxide on a polyethylene substrate 0.05
mm thick. The thickness of the filters varied: from 6.8
? 1018 to 3.8 ? 1018 nuclei/cm2, referred to the 188Ga isotope.
The thickness of the indicator for the reaction 184Dy(n, y)
was 1 mg/cm2. The error in determining the temperature
(?6%) was mainly due to the inaccuracy of the 188Ga(n, y)
cross section and the thickness of the filters.
Determination of the Absolute
Flux of the Thermal and
Resonance Neutrons
In measuring the density of the reactions we found that the neutron spectrum was thermalized to the
greatest extent at 65 cm from the front face of the cube.
The energy distribution of the neutron flux at this distance may be expressed in the form [9]
(E),Oth (1,)2E (EEIkT)
e- EMT + (Devi
(1)
where k is 13oltzmannvs constant, T is the absolute temperature, A (E/kT) is a transitional function between
the Maxwell and Fermi distributions, t epi is the flux density of the resonance neutrons,tth is the flux den-
sity of the thermal neutrons It
N-tn =nV = 2nvt/Vir, , n is the neutron density, is average neutron velocity,
vt is the most probable velocity of the neutrons at temperature T).
It should be noted that the form of the intermediate neutron spectrum ? see Eq. (1) ? may differ
from the generally-accepted one in the range 1-10 keV. Thus it was indicated in [7] that the resonance
neutron spectrum in a graphite cube with a side of 70 cm obeyed the 1 /E law up to 1 keV but fell more
sharply than 1/E at higher energies.
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TABLE 2. Characteristics of Thermal and
Resonance Neutrons in a Graphite Cube
R,* cm
V ? 108 neut
?
(cm 2sec)
_.
nv/cDepi
Teff, K
a
4
3,40+0,14
54+3
378+22
0,84
16
4,70+0,19
68?3
352+21
0,86
28
5,25+0,21
92+4
324+19
0,93
41
5,22+0,15
135+6
315+18
0,96
65
3,06+0,09
195+10
309+18
1,0
rtalie.M
*Distance from the front face of the cube.
The absolute thermal neutron flux was determined
from the activation of gold in a cadmium filter, and also
in the absence of a filter. The value of fbth was found
from the equation
(Dth--=NthinAnuu?Crtu? (2)
Here n_Au is the number of 197Au nuclei in 1 mg of indica-
tor; Nth = N?FedNed; N and Ncd are the saturation
activities referred to the end of the gold-irradiation
period in the absence of the cadmium filter and after
the inclusion of the latter, respectively; Fed is the cad-
mium correction, equal to 1.07 for cadmium 0.6 mm
h N
thick, calculated in accordance with [9. 10];Vu = r71-
1(T)1/293.6/Tatr (2200m/sec) is the gold activation
cross section averaged over a thermal neutron spectrum with a Maxwell distribution; g(T) is a factor
allowing for the deviation of the gold activation cross section from the law a r-z--11/v; ut (2200 m/sec) is the
activation cross section for a velocity of 2200 m/sec.
The absolute value of the resonance neutron flux was determined from the reactions 197Au(n, y) and
e4Dy(h3
y) both in a cadmium filter and in the absence of the filter. For a thin resonance indicator we
may write
(Dih 0th(RCd?
dE
Fc res? 00
i:Dept
cract (E)
ECd
Here ECd is the cadmium boundary, equal to 0.58 eV for cadmium 0.6 mm thick [9]; Red is the cadmium
CO
ratio; aact(E)dE /E is the resonance integral. The resonance integral for gold is taken as 1534 ? 40 b
ECd
[9]. A correction was introduced into the measured value of the cadmium ratio, since the gold indicator
was insufficiently thin with respect to the resonance neutrons. The extent of this correction was deter-
mined from the tabulated values of [10].
For a thin 1/v detector we may write
L-? ah ECd
(RCd 1./v="- n, 4
wepi kT
(3)
(4)
The unknown quantity tbepi was determined from Eqs. (3) and (4). The values obtained from these relation-
ships agreed closely.
For known values of .1)th, tepi, A (E/kr), T [9] we used Eq. (1) to determine the absolute value and
spectral distribution of the thermal and resonance neutron fluxes.
Calibration of Resonance Detectors and Determination
of the Resonance Neutron Spectra along the Central
Axis of the Cube
The calibration of the indicators was carried out at a distance of 65 cm from the front face of the
cube, at which the spectrum was taken in the form of the 1 /E relationship, while the absolute neutron flux
was determined in the manner already indicated.
For the irradiation of indicator i and the gold indicator in a thermal neutron flux, the saturation
activities referred to the end of the irradiation period Nth and Ne were
?-,
Nith ?nnunv8vcA3thwth = kiCrinOth; (5)
NtAhu nki4.8yAuccA,r-orasth kAucr-phuoth.
(6Y
Here "au is the number of nuclei in the indicator my is the number of 'y quanta per decay E), is the recording
efficiencyia is the isotopic composition.
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From Eqs. (5) and (6) we have
Ni TrAu
i tit th ICAu.
ArtUjIth
(7)
During the calibration of the indicators we determined the values of ki for each of these. The measured
and calculated values of ki agreed closely.
In the relative measurements we compared the numbers of reactions (the indicators being irradiated
in a cadmium filter) due to resonance in the cross section of the indicator. The contribution from the 1/v
part of the cross section for each resonance indicator was determined from the 164Dy(n, y) reaction in the
cadmium filter and was subtracted from the total number of reactions, i.e., for all the resonance indicators
we obtained the quantities
Ai i Dy tit
21(65 cmyhr
= Cd iu Cd D ?D ?
The unknown spectra at a distance x from the front face of the cube were determined from the equa-
tion
px
(E i) = (P(65 cmgi) A, (X) ?
'''(65 Cm)
When measuring the 1/Eck spectrum by reference to resonance indicators calibrated in a 1/E spectrum,in
order to calculate the corrections for the side resonances we only have to allow for the changes in the
values of these corrections in the 1/Ea spectrum as compared with the 1/E distribution, since by calibra-
tion in the 1/E spectrum these corrections will already have been automatically introduced. The con-
tributions of the side resonances in the 1/E spectrum were calculated in [11] for thin indicators. The
form of the unknown spectral distributions was finally determined by introducing these corrections on the
successive-approximation principle. In reconstructing the spectra no corrections were introduced for the
side resonances associated with the 23Na(n, y) and 37C1(n, y) reactions, since the contribution of side reso-
nances was unknown.
The measured resonance neutron spectra (Fig. 1) have the form 1/Ea for energies between 1 eV and
1 keV. For energies above 1 keV the form of the spectrum may differ from that indicated in Fig. 1, since
no allowance was made for the contribution of side resonances in the reactions involving the 23Na and 37C1
isotopes (Table 2).
The neutron characteristics here studied justify us in using the graphite cube in question as a calib-
rated source of thermal and resonance neutrons with different spectral characteristics.
LITERATURE CITED
1. R. D. Vasillev, At. Energ., 34, No. 4, 277 (1973).
2. I. A. Yaritsyna et al., Neutron measurements [in Russian], Standarty, Moscow (1973).
3. B. G. Arabei et al., in: Nuclear Instrument-Making [in Russian], Vol. 17, Atomizdat, Moscow (1972),
13?
3.
4. E. Axton, React. Sci. and Technol., 17, No. 17, 125 (1963).
5. C. Hargrove and K. Geiger, Canad. J. Phys., 42, 1593 (1964).
6. T. Ryves and E . Paul, J. Nucl. Energy, 22, No. 12, 759 (1968).
7. V. I. Golubev et al., At. Energ., 23, No. 2, 138 (1967).
8. T. S. Mordovskaya and V. I. Petrov, in: Nuclear Instrument-Making [in Russian], Vol. 13, Atomiz-
dat, Moscow (1970), 13. 59.
9. K. Bekurz and K. Wirtz, Neutron Physics [Russian translation], Atomizdat, Moscow (1968).
10. Neutron Fluence Measurements, Technical Reports, Series No. 107, IAEA, Vienna (1970)?
11. V. N. Avaev and Yu. A. Egorov, in: Problems of Dosimetry and Radiation Shielding [in Russian],
Vol. 4, Atomizdat, Moscow (1965), p. 15.
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USE OF FEW-GROUP METHODS FOR CALCULATING
THE PHYSICAL CHARACTERISTICS OF
FAST REACTORS
V. A. Karpov, V. I. Matveev,
N. E. Gorbatov, L. V. Averin,
V. A. Chernyi, and V. G. Samsonov
UDC 621.039.526
One leading characteristic of fast reactors is the wide range of energies (1 keV-10 MeV) within which
the basic nuclear-physical processes take place. In order to calculate these reactions many-group (multi-
group) approximations are usually employed. To this end it is important to have a detailed knowledge of
both the upper part of the neutron energy spectrum (involving 238U fission and inelastic scattering) and also
the lower part (Doppler effect).
A fast power reactor is a fairly complicated system with a large number of inhomogeneities. In the
active zone some 10% of the cells are occupied by control and emergency devices (rods). In order to
equalize the heat-evolution field over the reactor radius, zones of different degrees of enrichment are pro-
vided. In the axial direction asymmetry occurs because of the gas phase.
For a correct description of a reactor with these characteristics we require a three-dimensional
model with a fairly large number of computing zones and also a detailed energy analysis. The computing
model is too cumbersome even for a computer of the BESM-6 type. The creation of approximate but fairly
accurate methods is therefore an important and pressing problem.
In its initial stages, the development of computing methods followed the principle of adopting a geo-
metrical idealization of the reactor, since the accuracy of calculating the principal reactor functionals (the
critical mass and the conversion ratio) is determined more by the accuracy of calculating the neutron spec-
trum than by a detailed analysis of the geometry.
The development of fast high-powered reactors required a detailed study of the heat-evolution
field; the accuracy with which this may be calculated depends very considerably on the reactor geometry.
For calculating the heat-evolution field and the quantities associated therewith (such as the interference
corrections encountered when determining the efficiency of the control and emergency rods), few-group
methods have proved very efficient. Problems arising in this connection include that of deciding upon an
adequate number of groups and choosing the manner in which energy ranges should be divided up, as well
as that of the method to be used in averaging the few-group cross sections. Another important point is the
accuracy of calculating the integrated reactor characteristics (the critical mass and conversion ratio), and
also the efficiency of the control and emergency rods.
In this paper we shall consider experience which has been gained in the use of few-group methods for
calculating reactors of the BN-600 type and the corresponding model assemblies [1, 2]. For these calcula-
tions we used programs based on the diffusion approximation with two-dimensional hexagonal geometry,
as developed in the Physical Power Institute and the I. V. Kurchatov Institute of Atomic Energy.
Computing Methods and Programs
Few-group methods are already used for calculating systems involving fast neutrons, especially as-
semblies simulating the BN-350 reactor. A one group approximation in two-dimensional (r, (p) geometry
gave satisfactory results in describing the heat-evolution fields for assemblies incorporating absorbing
rods [3].
Translated from Atomnaya Energiya, Vol. 38, No. 4, pp. 213-216, April, 1975. Original article
submitted August 9, 1974.
@ 1975 Plenum Publishing Corporation, 227 West 17th Street, New York, N.Y. 10011. No part of this publication may be reproduced,
stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming,
recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $15.00.
274
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TABLE 1. Principal Physical Characteristics of the Reactor Obtained by Means of
the Programs Devised for the BESM-6 Computer
,
Stateofthereactor
Tqunther of
groups
K 4.,
e"
Radial nonunifor-
mity coefficient
ofheatevolution
ntheactive zone
Conversion ratio
Efficiency of the rod
spmern,okAk/k
active zone
lateral
screen t
connpensat-
ing rods
emergency
rods
After fuel recharg-
ing
Beforefuel
recharging
2*
2
4
6
9
2
2*
6
9
1,0024
1,0048
1,0053
1,0019
1,0029
1,0028
1,0050
1,0040
0,9992
1,25
1,25
1,24
1,26
1,25
1,25
1,25
1,24
1,26
0,320
0,320
0,317
0,322
0,321
0,374
0,375
0,374
0,373
0,222
0,223
0,221
0,225
0,224
0,222
0,222
0,223
0,226
5,83
5,85
5,83
5,78
5,78
6,29
6,40
6,13
.6,20
3,40
3,42
3,49
3,47
3,55
4,22
4,32
4,36
4,28
* The boundary between the groups is equal to 0 . 2 MeV; in the other two-group calculations it equals 0. 8 MeV.
t Without allowing for the end sections.
Subsequently few-group methods were developed for a hexagonal geometry, in view of the fact that
this gave a better description of reactors comprising hexahedral cassettes. The first hopeful result of -
using a two-group diffusion approximation in hexagonal geometry for calculating the model of the BN-600
reactor was obtained on using the program developed by I. S. Akimov in the Physical Power Institute for
calculating thermal reactors [2].
This program was then considerably modified from the point of view of increasing the number of com-
puting points (2560) and automating the calculation of a number of functionals; it was then used for calculat-
ing fast reactors. The program was designed for the M-220 computer. In addition to this, analogous pro-
grams were developed for the BESM-6 computer in the Kurchatov Institute of Atomic Energy; these had a
larger number of computing points (1200-2000) and two to nine energy groups. The programs for the
SM-6 and M-220 computers are based on an adequate finite-difference approximation to the differential
diffusion equation, but differ in their methods of solving the systems of linear algebraic equations. The
finite-difference approximation is based on representing the reactor in the form of a model consisting of
hexagonal cells with computing points at the corners. The methods of obtaining the system of finite-dif-
ference equations and the iteration methods for their solution are set out in [4-6].
For solving the finite-difference problem a double iteration process is employed in the M-220 com-
puter program. The outer (source) iterations are followed by inner iterations, as required for calculating
fluxes with a specified distribution of neutron sources. The inner iterations are accelerated by the Yang
-Frankel method, with preliminary calculation of the group-relaxation coefficients. The number of inner
iterations depends directly on the accuracy of the outer iterations. The total number of iterations is deter-
mined by the accuracy specified both for Keff(ei) and for the source distribution over the reactor volume
(El).
In the program for the BSM-6 computer the interaction procedure for calculating many-group neu-
tron fluxes and sources no longer comprises the 'traditional combination of outer and inner iterations. The
calculation comprises a sequence of calculations relating to the neutron source and flux distributions, with-
out any internal iterations.
These programs calculate Keff, the group fluxes, the heat-evolution field, the heat-evolution non-
uniformity factor, and the power. The program for the M-220 also determines the position (nodal point
number) of maximum heat evolution in the cassette, while the BESM-6 programs calculate the isotopic
composition, the conversion ratio, and the doubling time.
The computing time for a reactor of the BN-600 type (with the complete printing of the results) using
the M-220 program is -50 min for Ei = 5.10-3 and Et = 5-10-3. ?An analogous calculation using theBESM-6
computer program requires -10 min for a Keff accuracy of 10-7 and a neutron-flux accuracy of 10-4. The
calculation of the same reactor in nine groups requires -45 min.
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TABLE 2. Characteristics of the One-Zone Fe w-G roup Cross Sect ions
Model of the BN-600 Reactor
No. of groups
Boundary,
MeV
Kerr
"
Rod efficiency,
0/0 Ak/k
0,4
0,9939
0,2
0,1
0,9933
0,9940
1,67
1
0,0465
0,9955
0,01
0,9967
1,64
96
0.9877
1,66
The determination of the few-group cross sections
has a considerable effect on the accuracy of the calcula-
tion. Experience shows that it is impossible to find a sin-
gle system of few-group cross sections for reactors of dif-
ferent sizes and compositions giving an adequate accuracy
for the calculations. Few-group cross sections, like those
of the many-group type, have to be found with due allowance
for the resonance blockings and for the special charac-
teristics of the neutron spectrum in the reactor under
consideration. We may realize this approach by using the
programs of [7, 8] in the following way:
Preparation of the
blocked many-group
cross sections
Two-( or three-) di-
mensional few-grou
calculation
Many-group calculation of
the reactor in idealized
geometry
Preparation of the few-grou
cross sections (averaging
over the neutron spectrum o
the previous calculation)
The reactor is thus calculated twice; first in the many-group approximation (in idealized geometry) and
then in the few-group approximation, with detailed allowance for the geometrical singularities. This ap-
proach is extremely effective when calculating practically all the main reactor characteristics.
For the few-group programs the following macroscopic constants are averaged; the diffusion coeffi-
cient (D); the total cross section for the passage of neutrons out of the group (including absorption) (lo); the
neutron breeding factor (Vg); the cross section for the transition of neutrons from group to group by vir-
tue of elastic and inelastic neutron scattering (l)i?j.
The original system of many-group constants is the BNAB-70 twenty-six-group system [9].
Averaging introduces a certain error, associated with the assumption that the few-group cross sec-
tions remain constant over the averaging zones. Since the neutron spectrum in the active zone of a fast
reactor varies little from point to point it may well be expected that this error will only be slight.
Another important aspect is that of obtaining the few-group cross sections for heterogeneous zones
(for example, absorbing rods) forming part of the reactor. In this case the few-group cross sections may
be calculated for the regions under consideration by arbitrarily placing them in the center of the one-dimen-
sional model.
Results of the Calculations
For purposes of calculation we chose the BN-600 reactor, the composition of which was described in
[1]. In order to equalize the heat-evolution zone, the reactor is provided with a central zone of low enrich-
ment and another zone of high enrichment. The low-enrichment zone contains nineteen compensating rods
incorporating natural boron carbide, six emergency rods containing enriched boron carbide, and two auto-
matic control rods containing natural boron carbide. The active zone is surrounded by the five rows of
cassettes of the lateral screen, containing uranium oxide.
The calculations were carried out for two characteristic states of the reactor; that immediately after
fuel recharging, when the packs which have achieved maximum burn-up are replaced by fresh ones and all
the compensating rods have been introduced into the active zone, and that immediately before fuel recharg-
ing when all the compensating rods have been withdrawn from the active zone.
For these calculations we prepared two-, four-, six-, and nine-group cross sections, respectively
having the following boundaries between the energy groups: 0.8 and 0.2 MeV; 0.2 MeV, 46.5 and 10 kev; 0.8 and
0.2 MeV 46.5, 10 and 2.15 keV; 0.8, 0.4, 0.2 and 0.1 MeV, 46.5, 21.5, 10 and 2.15 keV. In choosing the
boundaries we remembered the following points. In reactors of the BN-600 type the proportion of 238U
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TABLE 3. Efficiency of Boron Compensat- fissions is very considerable (-15% of the total number
ing Rods for the BFS-24-16Assembly, % K of fissions); hence one of the boundaries was taken as
/k 0.8 MeV. The greater proportion of the neutrons in the
active zone of reactors of this kind lies in the energy
range 0.01-1 MeV. This region was described in as much
Position of compen-
sating rod
Calculation
Experiment,
[2]
2 group
4 group
Inner ring
Outer ring
0,75
0,34
0,72
0,32
0,748?0,007
0,283+0,004
detail as possible in the system of few-group constants.
In the system of two-group constants, apart from the 0.8
MeV boundary we also made use of the 0.2 MeV bound-
ary, corresponding to approximately equal numbers of
fissions in both groups. A more detailed investigation
into the choice of boundaries in the two-group constants
will be presented below.
Table 1 shows the results of the calculations; these indicate that the principal physical characteris-
tics of a fast power reactor of the BN-600 type do not depend on changes in the number of energy groups
between two and nine, at any rate to an accuracy sufficient for design purposes (the changes in Keff are no
greater than 0.5%, in the conversion ratio and the heat-evolution nonuniformity factor 2%, and in the effi-
ciency of the compensating and emergency rod systems 5%).
Since we would not be absolutely sure that the group constants satisfied these accuracy requirements
(on the basis of experience with the use of the twenty-six-group constants), we made some additional cal-
culations using the M-220 program. We studied the accuracy of our determination of Keff, the heat-evolu-
tion field, and the efficiency of the boron rods in the two-group calculation by comparison with the one-di-
mensional twenty-six-group calculation in the same pi approximation. At the same time we studied the
influence of the choice of boundary for the two-group constants on the same characteristics.
The calculations leading to the results indicated in Table 2 were carried out for a one zone model (low-
enrichment-zone composition) of the BN-600 reactor with a compensating rod in the center.
The comparison between the twenty-six-group and two-group calculations showed that the values of
Keff differed by less than 1%, while the difference in the heat-evolution field (even close to the boron rod)
was no greater than 5%; the same applied to the efficiency of the compensating rod. The results depended
very little on the choice of boundary in the case of the two-group constants. However, a two-group-con-
stant boundary of 0.2 MeV appeared to be the best for determining these characteristics of the BN-600 type
of fast reactor (after comparing with the twenty-six-group calculation).
Thus our calculations for the BN-600 reactor have confirmed the permissibility of using few-group
approximations in determining the main characteristics of fast power reactors of this type.
Comparison with Experiment
The validity of the use of the few-group pi approximation for hexagonal geometry was also verified
when calculating the critical assemblies of the B FS-2 test-bed simulating the BN-600 reactor. Calcula-
tions carried out on the M-220 computer using a two-group program agreed closely with the calculated and
experimental efficiencies of the boron rods and heat-evolution fields indicated in [2].
In addition to this, we also carried out some calculations for one of the critical assemblies simulating
the BN-600 reactor (assembly B FS-24-16) by means of the two- and four-group programs designed for the
BE SM-fl computer (Table 3). We see from Table 3 that the calculated efficiencies of the boron rods inside
the low-enrichment zone agree satisfactorily with experimental data (the difference is 5%). The calculated
efficiencies of the boron rods close to the boundary between the zones of low and high enrichment are 15-20%
higher than the experimental values; this is evidently due to errors in calculating the neutron fluxes by the
diffusion approximation close to the boundaries of zones with different diffusion properties, and also pos-
sible inaccuracies in the many- and few-group constants. It should be noted that the results of the calcula-
tions agree satisfactorily with the results of many-group diffusion calculations.
Thus few-group diffusion methods in two-dimensional hexagonal geometry yield satisfactorily accu-
rate results in calculating the main physical characteristics of fast power reactors. The efficiency of such
methods is achieved by combining them with the many-group, one-dimensional calculations used for aver-.
aging the few-group cross sections. A comparative analysis of the methods employed (in which the num-
bers of energy groups varied from two to nine) has shown that even the two-group approximation is adequate
for calculating the physical characteristics of a fast reactor.
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LITERATURE CITED
1. A. I. Leipunski et al., The BN-600 Fast Reactor, Nuclex-69, Basel, Switzerland (1969).
2. V. V. Orlov et al., Symposium on the Physics of Fast Reactors, October 16-19, 1973, Tokyo, Paper
A-25.
3. V. V. Bondarenko et al., Proc. IAEA Symp. on Fast Reactor Physics, October 30-November 3,
1967, Karlsruhe, Vol. 2, p. 305.
4. W. Wasow and J. Forsyte, Difference Methods of Solving Differential Equations in Partial Deriva-
tives [Russian translation], IL, Moscow (1963).
5. R. Richtmeyer, Difference Methods of Solving Boundary Problems [Russian translation], IL, Moscow
(1960).
6. A. Hassit, in:ComputingMethods in Reactor Physics [Russian translation], Atomizdat, Moscow
(1972), p. 50.
7. Sh. S.Nikolaishvili et al., in: Transactions of the Tripartite Soviet?Belgian?Dutch Symposiumon
Certain Problems of Fast-Reactor Physics [in Russian], Vol. 1, Izd. TsNIIAtominform, Moscow
(1970),.
8. V. V. Khromov et al., in: Physics of Nuclear Reactors [in Russian], Vol. 1, Atomizdat, Moscow
(1968), p. 159.
9. L. P. Abagyan et al., Group Constants for Calculating Nuclear Reactors [in Russian], Atomizdat,
Moscow (1964).
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REMOVAL OF TRITIUM FROM THE GASEOUS
WASTES FROM NUCLEAR POWER STATIONS
L. F. Belovodskii, V. K. Gaevoi,
' V. I. Grishmanovskii, V. V. Andramanov,
V. N. Demenyuk, and V. V. Migunov
UDC 66.074.7:546.11.02.3
The expanding network of nuclear power stations and fuel element reprocessing plants is causing an
increase in the global environmental distribution of the radioactive isotopes of Ar, Kr, Xe, and I, as well
as 14C and T due to emission of these gases into the atmosphere. This results in additional irradiation of
the population [1, 21. The main contribution to this global irradiation of the population is from 85Kr and T
[2; 3]. It has been conjectured that by the year 2000 there will have been up to 5 .108 curies of tritium re-
leased to the environment [2]. Electric power production by thermonuclear reactors may also lead to a
significant buildup of tritium in the biosphere, since it is assumed that a thermonuclear reactor will re-
lease 104-105 times more tritium than a nuclear power station of equivalent power [4-5].
At present, methods and equipment for collecting Kr, Xe, and I have been developed [6-8]. Reducing
the emission of tritium, whose potential danger is associated with its possible absorption into genetic
material, is a serious problem which is practically unsolved at this time [9-11].
T is formed in nuclear reactors directly in the fuel elements, and in the coolant (H2O, D20), modera-
tor (graphite, D20), and boron control rods. The average emission of tritium depends on the type of nu-
clear power plant and ranges from 2 curies/year to 10 curies/day, with a maximum of more than 100
curies/day [5, 11]. The principal source of atmospheric T is fuel reprocessing plants which release 50-
432 curies/day 15, 12]. During accidents up to 2.9.1 05 curies/hour may be released [13]. Up to 25%
gaseous tritium and 75% HTO reaches the atmosphere [9]. The tritium at effluent stacks comes with waste
gases (air, inert gases) from the active zone or the primary loop of reactors, or from the processing
rooms (canyons) of fuel reprocessing plants. The concentration of T in the gases entering the ventilation
stacks varies from 10-5 to 20 curies/liter [11, 13].
Thus, the problem of cutting down emissions reduces to removal of T and HTO from the gases which
enter the ventilation system from relatively small localized volumes, i.e., to removal of hydrogen and
water vapor from air and inert gases. Highly effective adsorption gas drying methods are extensively
used in industry; hence, removal of HTO is comparatively easy by means of adsorption columns [14, 15].
It is more difficult to trap tritium since it constitutes 4 *10-7 to 8 .10-1% by volume of the effluent gases.
In practice, it is necessary to obtain gases of high purity (with respect to T) from the cleaned gases [16].
Of the known means of removing hydrogen from gaseous mixtures (sorption by certain metals and activated
carbon, deep freezing, chemical transformation, selective diffusion through palladium), the most widely
used in laboratory and industrial practice is chemical transformation. In this scheme oxidation of hydro-
gen on solid heterogeneous catalysts is most often used in continuously operating systems [14, 16]. Cataly-
tic oxidation permits reduction of the amount of hydrogen in inert gases from 1 or 2 to 10-4% with strict
conservation of the stoichiometric ratio of H2 and 02 [17]. The efficiency of catalytic removal of hydrogen
impurities (10-7-10-2%) from inert gases and multicomponent mixtures (air) is not sufficiently known and
does not yield to theoretical estimates. This is because the kinetics of the reaction H2 + 02 are compli-
cated due to the dependence of the properties of the catalyst on the composition of the gas mixture and
cannot be expressed in terms of a single equation over a wide range of concentrations of the components.
Thus, industrial installations are based on experimental devices with analogous catalysts and gaseous
mixtures [14, 18]. ?
Translated from Atornnaya Energiya, Vol. 38, No. 4, pp. 217-221, April, 1975. Original article
submitted August 9, 1974.
? 1975 Plenum Publishing Corporation, 227 West 17th Street, New York, N.Y. 10011. No part of this publication may be reproduced,
stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming,
recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $15.00.
279
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LL
FT
813 814
HTO
GB
042
812
Fig. 1
1,0
42
1,0
/,o
0,1
402
20 30 40 50
V. liter/min
Fig. 2
60
Fig. I. Diagram of the apparatus for testing the efficiency of removal of 3H
from gases: C) converter; A) adsorber; CF) electric crucible furnace, type
TG-lm; H) heat exchanger; AB) air blower, type VL-1; R) rotameter, type
RS-5; ICi, IC2) ionization chambers; DCAI, DCA2) direct current ampli-
fiers, type SP-1m; RP) recording potentiometer, type PS-1-10; V) vacuum-
tight volume; G) tritium container; FT) freezing trap; GT) gas bottle; Mi,
M2) vacuum manometers; 131?B16) valves.
Fig. 2. Dependence of the conversion coefficient of the catalyst for tritium
on the flow rate for various catalyst volumes and gas compositions: (a) 2.2
liters; (b) 1.4 liters; (c) 0.7 liters; 0) air; 0) argon.
In order to obtain initial data for calculations on industrial apparatus, in the present paper we des-
cribe a study of the efficiency of catalytic removal of slight additions of tritium (10-7-10-29) from gases
(air, argon, and their combination) followed by adsorption of the resulting tritium oxide.
This method also permits collection of HTO present in the gases being cleaned.
This cleanup system consists of two main parts: catalytic (converter) and adsorption (adsorber). The
decontamination coefficient (K) is defined by the efficiency of these parts. In general, K over the time
period (t2?t1) is given by the ratio
t2
S Coffdt
An
K_. (1)
(1)
AR
S CoRdt
t,
where CH, CH, and AH, AK are the concentration and activity of tritium at the input and output of the sys-
tem, respectively; vH and vK are the gas flow rates (in systems without suction and dilution, v11 = vic = v).
At nuclear power stations and fuel reprocessing plants AH is composed of the activity of T (AG .H) and of
HTO (A0.H) at the inlet, i.e., AH .AG.H + A011. Analogously, at the outlet, AK = AG.K. + Ao.K. The
degree of decontamination is determined by the conversion coefficient of tritium into the oxide (KK) and by
the coefficient of adsorption of HTO (Ka), i.e., K = f(KK, Ka). Expressing AK in terms of AG.H, Ao.H,
KH, and Ka, we obtain
AG H=AG. H1KII; Ao. A_Q.H?KAp.H/Kn AAoin
GM
Substituting the expressions for AH and AK in Eq. KKaa+
. (1).andwring Ao.H/AG.H , we find
K
Ka+KR(1-1-O ?1
The number 1 in the denominator may be neglected if Ka and Ick >> 1. From Eq. (2) it is clear that for con-
stants KHandKa, K increases with Z, i.e., as Ao.H increases. For A,D.H = = 0),
K=KaKKI(K Ic+ Ka). (3)
(2)
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70-1 10-2
C Ci/liter
Fig. 3
20 44
V, liter/min
Fig. 4
60
Fig. 3. Tritium conversion coefficient of the catalyst as a func-
tion of the tritium concentration in the mixture being decontami-
nated.
Fig. 4. Dependence of the tritium conversion coefficient of the
catalyst on the flow velocity in the second series of experiments.
Ka depends on the type of adsorbent, the humidity of the gas being cleaned, and other factors. If syn-
thetic zeolites are used as an adsorbent (drying to the dew point, 85?C), then, for a moisture content in the
gas of about 0.1 g/m3, Ka > 102 may be obtained [19]. KK depends on the type of catalyst, the volume rate
of gas flow, the presence of contaminants that poison the catalyst, the composition of the gas being cleaned,
etc. For these reasons, it is impossible to estimate the order of magnitude of KK for the conditions under
consideration., Thus it is determined experimentally.
Metals of group VIII serve as catalysts for the 112 + 02 reaction, with Pt and Pd being the most
active. In order to increase the working surface and the stability, adsorption catalysts were used in this
work. These consist of a thin layer of metal (0.1-3.0 wt.%) on a substrate (silicagel, alumogel, etc.).
A preliminary estimate of the necessary amount of adsorption catalyst may be made using the relation
given in [18]; the volume of catalyst, VK, increases with the amount of separated component and the decon-
tamination coefficient. Thus, VK was estimated for a maximum concentration of tritium of 20 curies/liter
(emergency case). The required decontamination coefficient was taken to be 1000, based on a comparison
of the emergency (2.9.105 curies /hour) and maximum allowed (8 -102 curies /hour from a stack of height
80 m [20]) emission including a factor of three reserve [11]. For these parameters, the estimated amount
of catalyst is 0.7 liters for v =100 liters/min and a catalyst working temperature of 200?C.
This cleanup system was experimentally tested during an apparatus (Fig. 1) consisting of a converter
and an adsorber. The converter is heated in a temperature regulated crucible furnace. A heat exchanger
is used to cool the gaseous mixture which passes from the converter to the adsorber. The gas mixture is
pumped through by an air blower, whose flow rate is controlled by a rotameter. The concentration of tri-
tium is measured using flow-through ionization chambers of volume 0.5 and 5.0 liters with two de ampli-
fiers. The readouts are recorded on a recording potentiometer. The gas mixture which is to be decon-
taminated is prepared in a vacuumtight volume of 1.3 m3. The required amount of T is fed into this volume
by passing tritium through a liquid air trap to remove HTO. The gas (argon, dry air) is fed into the volume
from a bottle. The vacuum manometers control the pressure in the container. The elements of the sys-
tem are interconnected by 20 mm diameter stainless steel tubing through type Du-15 valves.
The converter and adsorber were made of Kh18N10T steel in the shape of a cylinder 117 mm in
diameter and 280 mm high (volume 2.2 liters). The inlet and outlet of these components are separated
by a coaxial inner cylinder, whose cross sectional area (38 cm2) is equal to the area of the annulus between
the outer and inner cylinders. The converter was filled with a platinum catalyst in silicagel (KK brand)
to 1.3 wt.% Pt. The catalyst was prepared by impregnating silicagel (grain size 4 mm) with a solution of
platinum in hydrochloric acid and then recovering the platinum in a flow of hydrogen [21]. The adsorber
was filled with the zeolite NaA (MRTU 6-01-906-60). The zeolite could be reactivated by heating in a
vacuum of about 10-3 torr at 500?C for 4 hours.
In the experiments we studied the activity of the catalyst as a function of the flow rate and the con-
centration of T for various volumes of catalyst (from 0.7, the calculated volume, to 2.2 liters). The effi-
ciency of the adsorber was also determined. Two series of experiments were conducted. In the first, the
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concentration of T in the mixture to be cleaned was varied from 10-5 to 10-3 curies/liter while the concen-
tration of HTO did not exceed 0.1%. The moisture content was up to 0.05 and 0.3 g/mm3 in argon and air
with oxygen contents of 0.03 and 20% respectively.
, ?
In the second series of experiments, the T concentration was 10-4 to 2.6.10-1 curies/liter with an
HTO content of 1 to 90%. In this case actual conditions were being simulated, i.e., the presence of HTO in
the effluent gases. HTO was fed into the volume by evaporation of tritiated water of known specific activity.
The moisture content was 0.1-0.4%, and the oxygen content 0.2-2% in argon and 20% in air. The humidity
of the gases was measured by the dew point and the oxygen in argon was measured using an Orsat appara-
tus. The gas flow rate was varied from 10 to 60 liters /min.
K was calculated using Eq. (1) by means of graphical integration of CH and CH over time. In the first
series of experiments, KK was found using Eq. (3), since 4 = 0; in the second, by using Eq. (2) including
the HTO.
The amount of HT 0 was periodically monitored by sampling the gas at three points: the volume V,
and before and after A (Fig. 1). The gas was sampled with evacuated glass samplers (volume 0.1-0.2
liters). The HTO in them was isolated by distilled water placed in the sampler. The activity of the HTO
was determined by a liquid scintillation counter (type URB-1).
The efficiency of the adsorber was estimated by the coefficient Ka which was determined from the
ratio of the concentrations of HTO at the inlet and outlet of A (Fig. 1). Ka was found to be 102-2 '103,
where Ka increases as the humidity and T concentration in the mixture increase.
Curves showing the dependence of KK on the flow rate v for various catalyst volumes, based on the
data from the first series of experiments, are shown in Fig. 2. The value of KK at v r-=??? 15 liters /min is
taken as unity, since in this case KK is independent of VK and the gas composition (air, argon). The ab-
solute value of KH was 100 50, which corresponds to at least 98% conversion of tritium into oxide.
Evidently (Fig. 2), K decreases as v increases, with a much smaller drop in argon than in air. As
VK is increased, the dependence of KK on v is less noticeable. Thus, for Vic = 0.7 liters KK decreases
by a factor of 30 in air when v is increased from 15 to 60 liters/min, while for VK = 2.2 liters, KK falls by
only a factor of 3. In argon, the decrease in KK as v increases for various values of VK is insignificant
(20-30%). These data indicate a complicated dependence of KH on v, VK, and the composition of the gas.
KH also depends on the T concentration. This dependence was investigated in the second series of experi-
ments, where VK .2.2 liters. The curve KH = f(CH) is shown in Fig. 3, where the mean values of KK
from 3-7 measurements at a given concentration of T (in the gaseous phase) are given as well as the maxi-
mum deviation from the mean value.
KH as a function of CH was obtained at v = 15-20 liters/min. When v is increased to 60 liters /min,
the nature of this dependence is conserved, with a decrease in the absolute values. This is clear from
Fig. 4, where the function KH f(v) is shown for the second series of experiments for similar values of
CH. As opposed to the first series (Fig. 2), the function KK = f(v) was general for argon, air, and their
mixtures, since no significant difference in the conversion coefficient for air and argon was recorded. It
is possible that this was due to an increased oxygen content in the argon compared to the first series.
During the tests 98.6 m3 of gaseous mixture with a total tritium content of -1540 curies were sent
through the system; 6.5 curies were measured at the output, i.e., the integrated decontamination coeffi-
cient was 240. The maximum and minimum values of K were 2.3 .103 and 20 for v =19 and 60 liters /min
and CH = 2.6.10-1 and 3 ?10-3 curies/liter, respectively; i.e., 95.0-99.9% of the tritium was collected.
After the tests the zeolite from A (Fig. 1) underwent desorption in vacuum with freezing out of the
water released: 200 cm3 of water were released with a tritium concentration of 7.5 .103 curies/liter, cor-
responding to 1500 curies of tritium.
A good agreement in the amount of T measured by two different methods (ionization in the gaseous
phase and scintillation in water) indicates that these results are fairly reliable. Some divergence (5-7
times) is observed between the amount of moisture desorbed from the zeolite and that entering A during
operation. This is explained by periodic decontamination of the apparatus (Fig. 1) by blowing atmospheric
air, which has a much higher moisture content than the gaseous mixtures used in the experiments, through
it.
Thus, it is possible in principle to effectively remove tritium from the gaseous wastes in nuclear
power generation by catalytic oxidation and later desorption of the resulting HTO. Based on our data it is
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possible to estimate the amount of catalyst needed for real gas flow rates, tritium concentrations, and de-
contamination coefficients.
The tritium which is collected may be buried along with the zeolite in a sealed container, for ex-
ample, in the adsorber [22]. It is also possible to remove the HTO from the zeolites and to use it in scien-
tific research or to decompose the HTO to obtain gaseous tritium [23].
LITERATURE CITED
1. Yu. A. lzrael, Atomnaya nergiya, 32, No. 4, 273 (1972)
2. A. M. Kuzin, Atomnaya Energiya, 33, No. 4, 870 (1972).
3. L. I. Gedeonov and A. G. Trusov, Atomnaya Tekhnika za Rubezhom, No. 12, 22 (1973).
4. F. Parker, Science, 159, No. 3810, 83 (1968).
5. H. Peterson, et al., iTanvironmental Contamination by Radioactive Materials, IAEA, Vienna,
(1969), p. 35.
7. A. S. Oveshkov, Atomnaya Tekhnika za Rubezhom, No. 7, 3 (1972).
7. E K. Yakshin, et al., Atomnaya nergiya, 34, No. 4, 285 (1973).
L.8. I. E. Nakhutin, et al., Atomnaya Energiya, 35, No. 4, 245 (1973).
9. V. S. Yuzgin and B. E. Yavelov, Atomnaya Tekhnika za Rubezhom, No. 10, 24 (1973).
10. N. V. Krylova and A. N. Kondrattev, Atomnaya Energiya, 34, No. 4, 316 (1973).
11. A. D. Turkin, Dosimetry of Radioactive Gases [in Russian], Atomizdat, Moscow (1973).
12. N. Sax, J. Daly, and J. Gabay, Nucl. Appl. Technol., 7, No. 1, 106 (1969).
13. I. Nikolich, Express-Information [in Russian], No. 38 (817), lzd. TsNII-atominform (1972), p. 14.
14. A. L. Koulf and F. S. Rizenfeltd, Cleaning of Gases [in Russian] Gosoptekhizdat, Moscow (1962).
15. Cleaning of Ventilated Effluents in Foreign Industrial Plants [in Russian], No. 18 (318), lzd. TsNII-
61ektronika, Moscow (1971).
16. G. Muller and G. Gnauk, High Purity Gases [Russian translation], Mir, Moscow (1968).
17. V. G. Fastovskii, A. E. Rovinskii, and Yu. V. Petrovskii, Inert Gases [in Russian], Atomizdat,
Moscow (1972).
18. G. K. Boreskov and M. G. Slintko, Khim. Prom-stl, No. 2, 69 (1956).
19. Z. A. Zhukova, et al., ibid., No. 2, 24 (1962).
20. Maximum Allowable Release of Gas from Reactor Stacks [in Russian], Atomnaya Tekhnika za Rube-
zhom, No. 4, 32 (1966)?
21. V. S. Chesalovaand G. K. Boreskov, Dokl. AN SSSR, 85, No. 2, 377 (1952).
22. E. Evans, Tritium and RS Compounds [Russian translation], Atomizdat, Moscow (1970).
23. D. Jacobs, TID-24635, USAEC (1968).
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Declassified and Approved For Release 2013/09/25: CIA-RDP10-02196R000400050002-4
PURIFICATION OF LIQUID RADIOACTIVE
EFFLUENTS BY CONTINUOUS
ION EXCHANGE
B. E. Ryabchikov, D. I. Trofimov,*
E. I. Zakharov, A. S. Dudin,
and L. K. Mikheev
UDC 621.039.73
Experience of the use of pulsation sorption columns (PSC) to purify liquid radioactive effluents with a
low level of activity has revealed [1] that this type of apparatus has a number of advantages over the tradi-
tional type of sorption filters (higher relative productivity, small amount of sorbent loaded at a time, low
pressure loss, etc.). However, the volume of a PSC operating with free sorbent settlement is larger than
that of filters. The volume can be reduced by using fluidization conditions and slightly increasing the load
of resin. As a result of later investigations, it became possible to use the principles described in [2, 3]
to design an improved column specially for processing low-concentration solutions ? a column with trans-
port pulsation (PSC-T) [4].
*Deceased.
Starting
solution
C.8900
The column casing (Fig. 1), in which there are grid plates with small clear cross section, has a pulse
chamber, and is fitted with top and bottom settling zones. When the column is operating, solution is fed in
continuously from below, and sorbent is fed from above and falls to the top plate. Since the clear cross
section of the latter is small (Fci = 5-15%), the velocity of the solution in the holes in the plate is much
higher than the drift velocity of the resin particles, and as a result they cannot get through the holes and
accumulate above the plate. During the operational period (sorption), air is fed slowly through a valve in-
to the pulse chamber. The sorbent moves downward when air is suddenly released through an electro-
magnetic valve. Then the solution moves upward in the pulse chamber, and correspondingly downward in
the column, carrying resin from one plate to the next. By varying the frequency and amplitude of these
transport pulses, we can regulate the flow of resin and its residence time in the apparatus, i.e., we can set
up optimal conditions for purification of the solution and saturation of the resin.
Hydraulic and technological tests of these columns in a number of systems have enabled us to devise
a method of design calculation, and have shown that they are highly efficient in the treatment of effluent
water. It was found that if other conditions are equal, pSc-T columns give a sorbent residence time 10-20
times longer than that of PSC columns, and consequently that they can be shorter and smaller in approxi-
mately the same ratio.
Since PSC columns [4-7] give their greatest efficiency when working with concentrated solutions [5],
it is advisable to compose a continuous-action plant for processing liquid effluent from PSC-T columns act-
ing by sorption and PSC columns acting by regeneration and washing of resin. Using this scheme, at the
Moscow Purification Station (MPS) we built a plant with a throughput of 1 m3/h for purifying wastes with a
KU-2-8 cation exchanger. Sorption was effected in a pSc-T column 200 mm in diameter and 10 m long,
and regeneration and washing in PSC columns 76 mm in diameter and 9 m long. The columns occupy an
area of 0.5 m2, and the whole plant with its storage tanks occupies 5 m2. The load of resin is 30 kg.
The apparatus (Fig. 2) operates as follows. The solution to be purified is fed to the bottom of the
sorption column through a rotameter. In the column it comes into contact with a counterflow containing
separate layers of cation exchanger. The purified solution overflows from the column into the special
drains. Regenerated and washed resin is continuously fed from a separator to the upper zone of the sorp-
tion column. As it moves downward it becomes saturated and is pumped from the bottom zone of this col-
umn by an air-lift to the regenerator. The action of the air-lift is monitored by an air rotameter. Since
the air-lift pumps solution over together with the resin, over each column there is a separator consisting
of a stationary cylindrical grid containing a revolving worm screw. The filtered solution is returned to
the column from which it was pumped, while the worm screw feeds the resin to the top zone of the next
column. In the regeneration column the sorbent is regenerated by nitric acid, and in the washing column
it is washed free of traces of acid by mains water which is fed to the bottom of this column via a rotameter.
Emerging from the wash column, the wash solution contains up to 0.8 M HNO3. It flows by gravity through
the rotameter to a line connected to the regeneration column. Concentrated 12 M HNO3 is fed via a rota-
meter to the same line. The concentration of the resulting regeneration solution is calculated from the
ratio of the wash solution and acid flows and is checked by analyzing samples. The regenerate is passed
to the concentration unit.
Pulsation of the solution in columns 6 and 11 at 50-100 vibrations per minute with an amplitude of
5-10 mm is effected by special autopulsators.
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Declassified and Approved For Release 2013/09/25: CIA-RDP10-02196R000400050002-4
TABLE 2. Composition of Regenerated Nitric Acid
Concentration
Concentration ratio
Regenerate
, ll
regenerating
regenerat-
ing HNO3'
Na,
Ca + Mg,
8-Activity, Ci
flow, liters
HNO3 soln., M
solution. M
mg-eq
/liter
mg-eq
/liter
/liter
Na
Ca + Mg
MO
/11
Range
1,8-2,2
0,35-0,64
160-520
180-480
9,540-6-2,040-5
50-165
70-180
50-100
9-12
Mean
2,0
0,51
335
330
1,7.10-5
105
130
85
10
Range
4-5
0,54-0,92
400-860
430-680
(2,25-3,75)?10-5
125-270
175-265
110-180
4-6
Mean
4,5
0,72
540
535
3,0.10-5
170
215
150
5
The apparatus successfully passed hydraulic operational tests with a throughput of 1.0-1.2 m3/h (rela-
tive productivity 30-40 m3/m2-h) with a resin flow of 3-20 liters/h (the ratio of the resin to the solution
flow was 1 :50 to 1 :300) with wash water and regenerate flows of 5-20 liters/h. The residence time of the
resin in the sorption operation is 1-10 h, and that in washing and regeneration is 20-30 min.
Laboratory investigations of the purification of liquid radioactive effluent by the KU-2-8 cation exchanger
in the H+ form revealed that equilibrium of the resin?solution system is established in 30-60 min, and the
maximum purification factor with respect to the total beta activity for a given radioisotope composition
(Table 1) is 10-15.
In our technological experiments we purified liquid radioactive effluents (total beta activity 5.107
Ci/liter) processed by the MPS, after blending, coagulation, and conventional filtration. During our ex-
periments we processed over 100 m3 of solution. The throughput of solution was 0.9-1.0 m3/h, and the
current of resin through the system was 3-10 liters/h. The current of 2 M HNO3 to the regenerator was
10-12 liters/h, or 4-5 liters/h in the experiments with 4-5 M 11NO3. A residence time of 3 h of the resin
in the sorption process was effected by transport pulsations at 0.5 vibrations/min with an amplitude of
50 mm.
Table 1 lists the average compositions of the original solution and the waste filtrate, the purifica-
tion factors, and the mean permitted concentrations (MPC). The data on the microcomponents were ob-
tained by analyzing samples. From Table 1 we see that the solution is freed from radioisotopes in cation
form (Cs, Sr, Ru, Zr, Nb) down to the MPC. The purification factor for total beta activity was 10-15.
The residual activity is evidently due to the presence of radioisotopes present as anions, complexes, or
compounds (I, Co). Further purification of this solution on an anion exchanger in the laboratory reduced
its activity by another order of magnitude. These data agree with those obtained from ion-exchange filters.
It was also found that fluctuations of the Na content of the waste solution between 0.02 and 0.5 mg-eq
/liter (purification factor 10-100) had practically no effect on the purification factor for the total beta acti-
vity, because heavier elements, which are mainly responsible for the total activity, are nearly completely
removed. The content of macrocomponents in the waste solution is close to that in filtrates after passing
through the cation exchange filters of desalination plants.
Since the treatment of liquid radioactive effluents includes not only purification but also concentration
of the activity into the minimum possible volume, it is interesting to consider the results of regeneration
of the resin (Table 2).
The results show that when 2M HNO3 is used for regeneration (the same as in the basic MPS scheme),
the content of Na salts and hardness salts (Ca + Mg) in the regenerate averages 330 mg-eq/liter, which is
1.5 times greater than the mean results for the basic MPS scheme during the period of the tests [8]. The
use of a smaller amount of more concentrated acid (4-5 M HNO3) gave regenerates with concentrations of
these ions ranging from 400 to 850 mg-eq/liter (average 530 mg-eq/liter), i.e., 2.5 times greater than
that obtained at present at the MPS. Consequently, continuous ion exchange can increase the concentration
of the regenerates and reduce their volume. If these regenerates are additionally treated or buried, there
will be economic savings on the process as a whole.
286
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TABLE 3. Analysis of KU-2 Resin*
Item
Saturation of resin,
125,.eq/g
Na Ca + Mg total
8-Activity,
Ci /liter
Saturated resin
Regenerated resin
Coefficient of re-
generation
2,0
0,18
11
2,9
1,37
2,1
4,9
1,45
3,5
9,2.10-8
1,0-10-8
9,2
=The resin was analysed by regenerating it with excess
of 4 M HNO3 and detemining the components in the re-
generate.
periments with completely regenerated
no' influence on the purification factor.
These concentrated regenerates are obtained as a
result of increasing the ratio of the currents, the concen-
tration of the regenerated solution, and the saturation of
the resin. If the resin is in contact with the solution for
3 h during sorption, the saturation of the resin averages
4.9 mg-eq/g (Table 3), which is practically equal to
its total exchange capacity (rated value 4.8 mg-eq/g).
The degree of regeneration of the resin with respect
to the macrocomponents was 709; the Na ions were prac-
tically completely removed, but the heavier Ca and Mg
ions partly remained on the resin. For more complete
regeneration we can alter the conditions of operation of
the column, creating a fluidized bed, or increasing the
flow of regenerating solution. However, additional ex-
resin revealed that this residual content of cations has practically
Therefore it is expedient to work in the cheaper conditions with a
residual saturation of 1.0-1.5 mg-eq/g.
LITERATURE CITED
1. F. V. Rauzen et al,, At. nerg., 36, No. 1, 27 (1974).
2. F. Cloete and M. Streat, Nature, 200, No. 4912, 1199 (1963).
3. F. Cloete and M. Streat, British Patent No. 1,070,251 (1963).
4. B. E. Ryabchikov and E. I. Zakharov, Equipment for Ion Exchange [in Russian], lzd. NII Tsvet-
metinformatsiya, Moscow (1974).
5. S. M. Karpacheva, E. I. Zakharov, and V. N. Koshkin, in: Development and Use of Pulsation Appa-
ratus [in Russian], Atomizdat, Moscow (1974), p. 184.
6. E. I. Zakharov et al., ibid., p. 170.
7. S. M. Karpacheva et al., Chemical and Petroleum Refining Engineering: Pulsation Apparatus [in
Russian], lzd. Tsintikhimneftemash, Moscow (1971).
8. D. Trofimov et al., in: Proc. Symp. IAEA "Practices in the Treatment of Low and Intermediate
Level Radioactive Wastes," Vienna, 6-10 Dec. 1965, SM-71 /5 9.
287
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Declassified and Approved For Release 2013/09/25: CIA-RDP10-02196R000400050002-4
CALCULATION OF DOSE COMPOSITION OUTSIDE
SHIELDING OF HIGH-ENERGY ACCELERATORS
BY THE MONTE-CARLO METHOD
N. V. Mokhov and V. V. Frolov UDC 621.039.78
The hadron contribution to the dose outside homogeneous shielding of an accelerator has been investi-
gated [1]. The calculation was performed for a one-dimensional geometry using the HAMLET program [2,
3]. This paper describes the MARS program which was written for the Monte-Carlo calculation of the nu-
clear cascade in a heterogeneous accelerator shield. A method is presented for estimating particle fluxes
in an arbitrary geometry and results are presented for maximum dose and dose composition outside the
shielding of accelerators of energies E0 = 1-1000 GeV. The contribution of kaons, muons, and y rays to
the dose is taken into account. A knowledge of the radiation dose composition makes it possible to deter-
mine the magnitude of the total dose outside shielding from the magnitude of a partial dose obtained either
by calculation or from experiment.
The MARS program uses the Monte-Carlo method to determine the energies and scattering angles for
particles at selected points in a three-dimensional block of material irradiated by a beam of protons, neu-
trons, or pions having an arbitrary angular and spectral distribution. The shielding block may be hetero-
geneous and may have arbitrary cavities. The fluxes of protons, neutrons, and charged pions with E 15
MeV, and their energy spectra. are computed for four hundred given elementary regions in the block. The
primary hadron energies are 0.05-1500 GeV. The maximum transverse and longitudinal dimensions of the
shield block are 2500 g/cm2. The program employs both standard methods for the reduction of variance
and also modifications developed for this energy range which, together
with the use of a system of semi-empirical formulas for the descrip-
rs tion of inclusive distributions, make it possible to go beyond the
parameters of existing programs [4, 5].
The MARS program includes six basic subprograms written in
FORTRAN.
10-O
to-7
'I IP
to-9
A1040
1012
100 101 102
E0, GeV
Fig. 1. Dependence on primary
proton energy of maximum dose
equivalent (1, 3) and absorbed
dose (2, 4) outside a shield; 1, 2)
iron (1500 g/cm2); 3, 4) iron and
concrete (1500 and 115 g/cm2 re-
spectively).
los
BEGI ? preparation of input data; selection of energy, direction
cosines, and coordinates of incident primary particle.
TRACE ? calculation of mean free path including ionization loss
for charged particles; calculation of statistical weight for exponential
transformation.
GE OM ? calculation of coordinates of point of interaction; re-
cording of events involving escape of particles from the block of ma-
terial or the crossing of planes bounding cavities or assigned regions
for various materials. If a particle arrives in an assigned element of
the block, the preliminary analysis program FINI is initiated and the
result and its variance are stored.
TREE ? treatment of the "trajectory tree." The tree is scanned
in accordance with a lexico-graphical scheme [6]. Selection of the
energy E, scattering angle 0, and azimuthal angle cp occurs in the
program SELECT by means of sampling functions for each type of
particle (j = p, n, ir) and each energy range. Depending on the type of
Translated from Atomnaya Energiya, Vol. 38, No. 4, pp. 226-228, April, 1975. Original article
submitted July 10, 1974.
? 1975 Plenum Publishing Corporation, 227 West 17th Street, New York, N.Y. 10011. No part of this publication may be reproduced,
stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming,
recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $15.00.
Declassified and Approved For Release 2013/09/25: CIA-RDP10-02196R000400050002-4
Declassified and Approved For Release 2013/09/25: CIA-RDP10-02196R000400050002-4
TABLE 1. Dependence on Primary Proton
Energy of Contribution to Maximum Dose
Equivalent from Radiation Components out-
side Various Shields (%)
'
0
a
w
Shield
p-i-nd-ic
n
7
R
-Q.
bo
.
x
material
>
4
n
>
n
>
V
')
n
>
n
1500
Iron
0,01
0,19
97,3
2,5
--
1
1500
Iron
115
Concrete
0,7
7,8
56,3
35,2
--
1500
Iron
2,2
2,0
93,8
2,0
0,03
1500
Iron
115
Concrete
32,6
26,6
28,0
12,4
0,4
10
1440
Iron
60
Lead
2,3
2,2
95,2
0,2
0,1
1440
Iron
115
Concrete
34,0
32,3
31,5
1,5
0,7
60
Lead
1500
Iron
3,2
2,3
93,0
1,4
0,1
1500
Iron
115
Concrete
40,5
27,5
22,2
9,3
0,5
50
2500
Iron
1,5
1,6
93,8
2,1
1,0
2500
Iron
115
Concrete
20,5
22,3
26,5
15,0
15,7
2500
Iron
2,0
1,7
93,1
1,9
1,3
500
2500
Iron
115
Concrete
24,0
19,5
21,8
12,0
22,7
problem to be solved (deep penetration, lateral shielding,
calculation of energy deposition, etc.) biased sampling
of angle and energy is performed from the necessary func-
tions f.(E' 0) normalized to unity. For example, in a deep-
penetration problem, preference is given to high energies
and small angles, i.e., energy is selected from functions
such as AE or AE2 and angles from functions -exp (-BE2
'02), where A and B are certain constants. Bias is
eliminated by a statistical weight which is included in the
total statistical weight.
FANG - calculation of spectral and angular distribu-
tions of secondary particles from nuclear interactions.
The same system of semi-empirical formulas that is used
in the HAMLET program [2, 3] is used for the description
of inclusive spectra.
SERV - final analysis; calculation of functionals
and errors, printout of results, and plotting of curves.
At high primary energies, the "trajectory tree" be-
comes highly branched and the following procedure is em-
ployed in order to reduce computing time. For each par-
ticle type j, a maximum weight WInax(K) for the K-th in-
teraction is selected in preceding histories. A number
P ? 1 is chosen and events having a weight Wi(K)
< Wrax(K)a, where a ?1, are neglected with a probability
1-16. These events are included with a probability P but
with a weight W(K)/P. For values P = 0.01, a = 0.0001 and primary energies E0.5'30 GeV, the required
computing time is reduced by factors of 10-15. Significant sampling with respect to space and biased
sampling from well-chosen functions fi(E, 0) reduce the statistical error by an order of magnitude. The
time required for the calculation of particle fluxes having 10% error is 10-20 min on a BESM-6. Spectra
having the same statistical error are calculated in 30-45 min.
The program SYNHET, which synthesizes calculated results from the programs MARS and HAMLET,
was written to estimate fluxes of neutrons with E < 15 MeV and fluxes of rays, charged kaons, and muons
in an arbitrary geometry. Let there be known functions of flux density for particles of type j with energies
above some value ri which are calculated for identical initial conditions from the programs HAMLET
? ] and MARS [F.(r, F.)]. We use the fact that the flux density of the particles at some depth Z for a broad
r J)
j
beam is numerically the same as the flux from a point monodirectional source integrated over the trans-
verse plane at the same depth. Then the following relations will be approximately satisfied:
F? (z,r,)==F;(z, room (Z, ri)1(1)., (Z, ri) 1.
F,,(Z, (Z, I's) (z, roton (z, ri) '
Fm (r, TO/1,1=z
=F., (r, r (z,zri)/cD; (Z,
iri=
?
F (r, TO/iri=z0y, (Z, (Z, s)
Here, Fi(Z, Ti) = S dx dyFi(r, ri), rk 1< or >
0
1
1
0
2
1,00+0,02
0,886+0,017
0,928+0,005
.4
0,97+0,03
0,841+0,027
0,921+0,008
6
0,98+0,02
0,763+0,023
0,887+0,009
Translated from Atomnaya Energiya, Vol. 38, No. 4, pp. 245-248, April, 1975.
? 1975 Plenum Publishing Corporation, 227 West 17th Street, New York, N.Y. 10011. No part of this publication may be reproduced,
stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming,
recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $15.00.
307
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Declassified and Approved For Release 2013/09/25: CIA-RDP10-02196R000400050002-4
LITERATURE CITED
1. T. V. Golashvili, At. Energ., 13, No. 5, 435 (1962).
THE HYDRODYNAMICS OF FISSIONABLE MATERIALS
II. NONLINEAR SOLUTIONS OF THE SIMPLE WAVE TYPE
V. M. Novikov UDC 621.039.51
In a previous paper [1], the author showed that for sufficiently high neutron fluxes the dispersion of
the acoustical oscillations in fissionable materials can be changed substantially. This is manifested by a
change in the effective velocity of sound and the occurrence of acoustical instability, resulting in a pro-
nounced increase in the amplitude of the oscillations. Consideration of the subsequent evolution of such a
wave results in a nonlinear problem. In this paper, the nonlinear solution of the simple wave type (Rie-
mannian solution) is generalized for the case of the hydrodynamics of fissionable materials in constant
neutron fluxes. The solution is constructed on the assumption that the dissipation of the heat from the fis-
sion is completely determined by the thermodynamic quantities themselves and not by their derivatives.
This assumption is fulfilled well for a gas occupying a sufficiently long duct with heat removal through the
lateral surface.
Analyzing the solutions obtained, one can make the following conclusion regarding the difference of
the nonlinear solutions of the simple wave type in the hydrodynamics of an ideal liquid (gas) and in a fission-
able liquid (gas).
The simple wave adjusts to propagate in only one direction and a wave trail disturbance arises behind
it, moving in the opposite direction. With heat removal occurring according to Newton's law or by means
of radiant thermal conduction from an optically thick layer, the density of matter increases (decreases) in
the vicinity of the wave if the initial density is greater (lesser) than the equilibrium value. For an initial
disturbance of the "humpy' type, the density of matter in the vicinity of the trail is lower than the equilib-
rium value. Near the characteristic curve x = ?cot (Fig. 1), one can distinguish an "echo" region of the
wave, where the density is almost constant and different from equilibrium. In the vicinity of the wave,
the Cf-characteristic curves adjust to be straight lines, which results in a faster trarwition of the simple
wave into a shock wave. For initial disturbances of density Ap/po 10-2 and wave extent A 10 cm, the
time of this transition can be shortened by ten-fold for neutron fluxes N 1016cm-2.sec-1. The diagram
shown in the figure illustrates the evolution of an initial disturbance of the 'thump'? type in a fissionable gas
up to the formation of a dislocation.
*74111Ir'e
I;
li1111!
imommoloo 11111111111
Fig. 1. Evolution of the initial disturbance
of the "hump" type in a vissionable gas.
LITERATURE CITED
1. V. M. Novikov, At. Energ., 30, No. 4, 446 (1971); Preprint IAE-2007 (1970).
Original article submitted May 20, 1974.
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Declassified and Approved For Release 2013/09/25: CIA-RDP10-02196R000400050002-4
ELECTRON SPECTRA BEHIND BARRIERS HAVING
A THICKNESS COMPARABLE TO THE
EXTRAPOLATED RANGE OF THE ELECTRONS
V. V. Evstigneev and V. I. Boiko UDC 539.121.72
The article reports on investigations of the energies in a beam of electrons which passed through alu-
minum, copper or lead barriers having a thickness of (0.1-0.9)Re, where Re denotes the extrapolated range
of the electrons. The initial energies amounted to 3-8 MeV.
An ironless magnetic spectrometer with a homogeneous magnetic field was used as the analyzer of
the electron energy.
The basic characteristics of the spectra (most probable energy losses .6,Ep, the average energy loss,
and the half-width of the energy distributions) are listed in a table (see full text of the article). The results
were compared with the characteristics of spectra measured behind barriers having a thickness of up to
0.6Re; the spectra had been previously obtained by van Camp [1], Lonergan [2], and Gusev [3]. A selective
comparative calculation in the model of catastrophic collisions was made for several spectra with the aid
of the Monte-Carlo method using the program described in [4].
The dependencies of the basic spectral characteristics upon the initial energy, the atomic number,
and the thickness of the absorber were analyzed for great depths of penetration. It was shown that the
most probable energy losses are not sharp in these distributions and that the nonlinearity of the thickness
dependence of the characteristics is rather strong. The average energy loss exceeds the most likely
energy losses, but the difference decreases in proportion to the increase in barrier thickness. At sample
thicknesses of (0.8-0.9)Re, the spectra are smeared so that the half-width of the spectral distributions
cannot be considered an objective parameter of fluctuations of energy losses.
A detailed investigation of the experimental energy distributions behind thick ((0.6-0.9)Re) absorbers
led to the detection of a maximum in the low-energy parts of the energy distributions, with the maximum re-
sulting from the accumulation of electrons with energies of about 1 MeV. The accumulation of electrons is
more intense when the initial energy of the electrons and the atomic number of the absorber are increased.
The accumulation reaches its maximum at thicknesses of (0.7-0.8)Re. The additional maximum which was
recorded coincides to some extent with the experimental results of Bumiller et al., [5] and with the calcula-
tions of Baranov et al., [6]. The maximum at low energies in the electron spectra observed behind barriers
results from multiple processes and the strong dependence of the total energy losses of electrons upon their
initial energy.
LITERATURE CITED
1. K. I. van Camp and V. I. Vanhuyse, Z. Physik, 211, 152-164 (1968).
2. I. A. Lonergan, C. P. Jupiter, and G. Merkel, J. Appl. Phys., 41, 2(1970).
3. E. A. Gusev and B. A. Kononov, Izv. Vuzov, Ser. Fizika, 6, 12-16 (1969).
4. A. V. Plyasheshnikov et al., in; Monte-Carlo Methods in Computational Mathematics and Mathemati-
cal Physics [in Russian], Izd-vo Vychisliteltnogo Tsentra SOAN, Novosibirsk (1974), p. 285.
5. F. A. Burailler, E. R. Buskirk, and I. M. Dyer, Z. Physik, 224, 182-192 (1970).
6. V. F. Baranov et al., Atomnaya Energiya, 32, No. 2, 156 (1972).
Original article submitted July 1, 1974.
309
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Declassified and Approved For Release 2013/09/25: CIA-RDP10-02196R000400050002-4
TRANSPORT EQUATION FOR GAMMA RADIATION
IN THE SMALL-ANGLE SCATTERING APPROXIMATION
L. D. Pleshakov UDC 539.171.015
The propagation of gamma radiation in matter is described by the Boltzmann kinetic equation, whose
solutions are generally obtained by numerical methods. In the development of apparatus which uses gamma
radiation, shielding design problems occur for which it is desirable to have an analytic solution, thus elim-
inating the need for an electronic computer to do the calculation. An analytic solution of the kinetic equa-
tion has been given [1, 2] for the case of plane-parallel geometry, using the approximation of "direct for-
ward scattering." In this case, however, the distribution function of the gamma photons gives a satisfac-
tory description of their propagation for source energies of at least 5-6 MeV.
In this communication, we solve the kinetic equation in the small-angle scattering approximation in the
the case of plane-parallel geometry. For this case the equation contains an additional term which is neg-
lected in the "direct forward scattering" approximation. The spatial, energy, and angular distribution
functions of the gamma photons give a satisfactory description of their propagation for the case of both light
and heavy elements for source energies of at least 1 MeV.
The function describing the propagation of those photons which have traveled more than four mean
free path lengths must be calculated by an electronic computer because of the large increase in the amount
of calculation.
The distribution function is obtained under the assumption that the attenuation coefficient can be
approximated by linear and quadratic functions. When the attenuation coefficient is approximated by a
linear function, the distribution function for the flux of energy density has the form
/ (X, ko) e -110x { 6 (A. xo) F b 1 ? e (" ? ? 1 L (bx)2
X0) i(??) kh--A.0) ,
L 010+1-ti)(k?xo) J 2! (' 0) [1? 3 k 2 1417- 2 rr- 4.3
/ 13 11 11 \ 1 ox)3 r x (k? 21.0 X2 (A. ? )or / 15 35 35 ,
x k p?s+-3? Roi?Li+pil -i? ? ? ?J +., (,-4)21_1 4 (110 + 111)-F 5 8 .4 k ps+ ,4-14) ? ? ? ?]+ ? ? ?,
/ 12
where b = 27m0rg, no is the electronic density of the matter, and 1-0 is the classical radius of the electron.
The terms within the square brackets give the contribution of individual scatterings to the distribution func-
tion.
The present study shows that within the small-angle scattering approximation, the distribution func-
tion of the density of energy flux from a point isotropic source is accurately described to within a factor
1/4rr2 by the same expression as the distribution function of the density of energy flux for a plane per-
pendicular source.
These results have been compared with the experimental data and also with the results obtained by
the method of moments.
LITERATURE CITED
1. V. I. Ognevitskii, Zh. Eksperim. i Teor. Fiz., 29, 454 (1955)?
2. L. I. Foldy, Phys. Rev., 82, 927 (1951).
Original article submitted August 14, 1974.
SPATIAL DISTRIBUTION OF SCATTERED ENERGY FROM
A UNIDIRECTIONAL POINT SOURCE OF HIGH-ENERGY
ELECTRONS IN AN INFINITE TISSUE-EQUIVALENT MEDIUM
A. K. Savinskii and 0. N. Chernova UDC 539.12.08:539.124
Both theoretical and experimental data pertaining to the geometry of the source under consideration
are virtually nonexistent in the literature. An exception is the paper [1], in which the authors, solving the
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Fig. 1. Spatial distribution of scattered energy from
an isotropic; point source of electrons with energies
of 25 keV and 1 MeV in a tissue-equivalent medium:
1) results of the calculations of Narkevich and collabo-
rators [1]; 2) results of the calculations of Spenser [2];
3) experimental results of Bochkarev and collaborators
[3].
kinetic equation for electrons in the continuous deceleration approximation, obtained a series of spatial
distributions of the scattering energy, (dE/dv)(Eap, a), for a "narrow beam" of electrons in polystyrene over
the range from 25 keV to 10 MeV. Here, dE/dv is the energy, scattered into a volume element dv by a
"narrow beam" of electrons with energy E6; p is the distance from the source to the volume element under
consideration as a fraction of the mean free path of the electrons; a is the angle between the normal to the
surface of the scatterer and the orientation of their source in the volume element under consideration.
It is difficult to estimate the accuracy of the results obtained at the present time in view of the ab-
sence of experiments with sources of this type. In connection with this, an independent method of calculat-
ing the distribution dE/dv was developed, based on the method of statistical sampling, having a number of
advantages over the kinetic equation approach. In particular, the method allows one to investigate the fluc-
tuation in the energy loss of the electrons and to obtain information on the energy and angular distributions
of the electrons at an arbitrary point of the medium being studied.
The method was executed on an electronic computer for a uniform, infinite tissue-equivalent medium
over a range of initial energies for the source electrons from 25 keV-1 MeV. It was shown that, for p
0.2, one can describe the distribution of the scattered energy with an accuracy not worse than 10-15% by
a general (independent of the energy of the source electrons) function n (p, a), which one can represent as
a dosage function of a unidirectional, point source of electrons with unit initial energy and mean free path.
In order to estimate the accuracy of the results obtained, an indirect comparison of them was made
with the theoretical and experimental data on a source with a different geometry, i.e., for an isotropic
point source of monoenergetic electrons W(Ea, p); here
W (E6, p)IL (Eo) 221E6 p2 n (p, a) sin a da,
L (E6)?Rg 0
(1)
where Ea is the initial energy of the source electrons; Ito is the mean free path of the electrons with energy
Ea; W(E 6, p) is the energy scattered into a spherical layer of unit thickness at a distance p from the
source; L(E a) is the mean energy loss per unit length of the path of the electrons in the medium being
studied.
In Fig. 1, the values of WE a, p) from the present work are compared with the calculations in [1]
(curve 2) and [2] (curve 1) obtained in the continuous deceleration approximation (kinetic equation method)
and with the experimental data in [3] (curve 3).
From the figure, it is seen that the results of the calculations agree satisfactorily with the "experi-
mental" data in [3]. One can consider this? as a verification of the calculational algorithms obtained and of
the accuracy of the analysis of the experimental data, on the basis of which the values of W(E 6, p) are also
calculated. The disagreements with the theoretical data in [1, 2] are caused mainly by the approximation,
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which does not take into account the effect of a fluctuation in the ionization loss in energy by the electrons
during their deceleration in matter.
LITERATURE CITED
1. B. Ya. Narkevich, V. S. Endovtskii, and I. E. Konstantinov, At. Energ., 26, No. 5, 473 (1969);"
2. L. Spenser, NBS, Washington, GPO (1959).
3. V. V. Bochkarev et al., Int. J. Applied Radiation and Isotopes, 23, 493 (1972).
Original article submitted September 9, 1974.
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LETTERS TO THE EDITOR
THE DISCHARGE OF GASEOUS FISSION PRODUCTS
FROM FUEL ELEMENTS OF
NONHERMETIC CONSTRUCTION
V. M. Gryazev, V. V. Konyashov, UDC 621. 039. 548
V. N. Polyakov, and Yu. V. Chechetkin
The utilization of fuel elements with discharge of gaseous fission products from under the jacket
enables one to reduce the volume of the gas cavity, which results in the saving of neutrons in the active
zone, an increase in the specific heat release, and the improvement of the hydraulic characteristics of
the active zone. Moreover, the discharge of gases from fuel elements and the reduction of pressure in
them ought to prolong the period of nondefective operation and, consequently, to reduce contamination of
the loop by radioactive fission products.
In order to investigate the
of gaseous fission products
10?
efficiency of such fuel elements and to determine the fractional discharge
(GFP) in a BOR-60 reactor, tests were conducted on two assemblies of 37 fuel
elements with special, nonhermetic subassemblies. The
conditions for the irradiation of the fuel elements were
similar to the usual ones.
kr5
10-7
10-9
131'"Xe9re '339(e Kr 87(r 137Xe
. la a .
10-8 10-7 104 10-3 10-2
10-8 ? 10-5
Disintegration rate, sec-1
Fig. 1. Fractional discharge of GFPts
from nonhermetic and defective fuel ele-
ments: 0 and ? refer to the stationary
level and maximum emission of gases,
respectively, for an assembly of fuel
elements of nonhermetic construction; x
refers to a defective fuel element; - -)
refers to the theoretical values for an
assembly of fuel elements of nonhermetic
construction fib A refers to a fuel ele-
ment with a subassembly of the "bell jar"
type [2].
The radioactivity of the GFPs in the gas cavities of
the assembly was measured daily in gas spectrometric
loops equipped with NaI(TI) crystal detectors. The mean
error in the relative measurements was ?10%, while the
mean error in the absolute measurements of the radio-
activity was ?25%.
The level of radioactivity of 133Xe and 735Xe in the gas
cavity of a reactor prior to the installation of an assembly
of fuel elements with nonhermetic subassemblies was
4.10_6 and 2.7 ?10-6 Ci/liter, respectively. A rapid in-
crease in the specific activities of 133Xe and 135Xe in the
gas cavities was observed with attainment of ?0.8-1.1%
burn-up in the assembly being studied. Subsequently, with
an increase in the burn-up to 3.7%, the radioactivity of the
GFPs was again increased 2-4 times and reached (1-2) ? 10-3
and (1-10) ? 105 Ci/liter for 133Xe and 135Xe, respectively.
The level of radioactivity of short-lived GFPS (86Kr, 88Kr,
87Kr) did not increase in comparison with that observed in
the case of a completely hermetic active zone.
Changes in the radioactivity of the GFPs are char-
acterized by the presence of stationary levels of (0.8-1)
? 10-3 and (0.8-2) ? 10-5 for 133Xe and 135Xe with emissions.
The ratio of the specific activities of the isotopes 133Xe and
135xe varies from 50-80 at the stationary level up to 10 at
the time of emission.
Translated from Atomnaya Energiya, Vol. 38, No. 4, pp. 249-250, April, 1975. Original article
submitted July 1, 1974.
0 1975 Plenum Publishing Corporation, 227 West 17th Street, New York, N.Y. 10011. No part of this publication may be reproduced,
stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming,
recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $15.00.
313.
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As subsequent measurements showed, the variation in the radioactivity is connected with the behavior
of an assembly of fuel elements of nonhermetic construction, and not with defects in the regular fuel ele-
ments. As regards this, the small amount of radioactivity,for a single emission (
Fig. 2. Integral distribution of reduced neutron widths of 232Th
p resonances for En < 1400 eV. Dashed curves show the divi-
sion into two Porter-Thomas distributions for v = 1.
Fig. 3. Distribution of distances D between *strong" p reso-
nances (g111-5_ 2.5 .10-8 eV-1/2). Dashed curve shows the
Wigner distribution for small D.
235U (n, f) reaction at E*1-.1 6.4 MeV, i.e., above the fission barrier. Obviously, not all these structures can
be associated with compound states in the intermediate minimum of the fission barrier and require a dif-
ferent explanation.
The results of measurements obtained with a good energy resolution indicate the presence of similar
resonance groups in other nuclei, for example in 238U at En 250 eV [9].
The presence of p resonance groups with a reduced neutron width grn1 >?' 10-7 eV-1/2 must be probably
accounted for in calculations and in the interpretation of experimental data. In certain cases, for example
at En Ps 100 keV, they can cause marked spectrum distortion in the passage of a neutron flux through a sam-
ple only several millimeters thin.
LITERATURE CITED
D. Paya et al., in: Proc. IAEA Symp. *Nuclear Data for Reactors, 1966," Paris, 17-21 October
1966, Vol. 2, p. 128.
2. E. Migneco and J. Theobald, Nucl. Phys., A-112, 603 (1968).
3. V. Strutinsky and S. Bjornholm. Proc. IAEA Sympos. Nuclear Structure, Dubna (1968), p. 431.
4. P. E. Borotnikov, Yadernaya Fiz., 9, 303 (1969).
5. L. Forman et al., Proc. III Conf. oil Neutron Cross Sections and Technology, Knoxville (1971),
p. 735.
6. Neutron Cross Sections, BNL-325, 2nd Edition, Suppl. No. 2 (1965).
7. C. Bowman et al., Proc. III Conf. on Neutron Cross Sections and Technology, Knoxville (1971),
p. 584.
8. Yu. V. Ryabov and N. Yaneva, in: The Program and Abstracts of the 19th Annual Conference on
Nuclear Spectroscopy and Structure [in Russian], Nauka, Leningrad (1969), p. 72.
9. F. Rahn et al., Proc. III Conf. on Neutron Cross Sections and Technology, Knoxville, (1971), p. 658.
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DETERMINATION OF THE PENETRATION OF DECAY
,PRODUCTS OF RADON INTO THE RESPIRATORY
ORGANS BY A DIRECT METHOD
L. S. Ruzer UDC 621. 039. 766
The determination of the absorbed doses of internal irradiation of the lungs of mine workers in the
case of inhalation of short-lived decay products of radon is an urgent problem. Up to the present time it
has been solved by measuring the concentrations of isotopes at the work sites and computing the absorbed
dose according to set rates of inhalation and the coefficients of retention of aerosols in the respiratory
organs. But the value of the retention coefficient depends on the physicochemical properties of the aerosols
and cannot be measured with sufficient accuracy. The value of the rate of inhalation also is rather indefi-
nite, since it depends on the physical load (the nature of the work) and varies within broad limits.
The question of the treatment of the value of the measured concentration is extremely important.
The concentration of isotopes in air at the same place is subject to substantial variations. For example,
a variation of the intensity of ventilation even for a short period of time leads to a change in the radon con-
centration of severalfold. Moreover, the content of isotopes directly in the zone of respiration of the
miners may differ substantially from the value measured by the usual instruments. Finally, the very con-
cepts of "work place" and "concentration at the work place" are indefinite, since miners are at several
work places during their work shift, with variable concentrations of decay products of radon in the mine
atmosphere.
Since a measurement of the concentrations at the work places in mines is performed once or twice a
month, there can be no precise correspondence between the actual and measured concentrations, and, con-
sequently, it is practically impossible to correctly calculate the individual values of the intake.
The summary error of the calculation of the absorbed doses according to the concentrations is esti-
mated at approximately 5-10-fold in comparison with the actual indices of internal irradiation [1].
In 12-5] a direct method of determining the intake of products of radon into the respiratory organs is
described. An analysis of the systematic and random errors of this method showed that the summary
error of the measurement in the case of constancy of the concentration of isotopes in the zone of respira-
tion, of the coefficient of retention and respiration rate, determining 0.3 of the value of the permissible
intake in a work shift, does not exceed 25% [4].
The systematic errors associated with contamination of the body, work clothes, as well as with the
influence of the radon accumulated in the adipose tissues of the abdominal cavity, are eliminated by the
introduction of the corresponding corrections. For example, it has been shown that the contribution of y
radiation from the region of the abdomen to the total value of the rate of count in measurement of the acti-
vity in the lungs 30 min after leaving an atmosphere contaminated with radon does not exceed 5%. The
error associated with contamination of work clothes and the body of the worker drops to 15 and 1% of the
measured value, respectively, after the work clothes have been taken off and a shower is taken. Random
errors associated with geometrical factors, the shift of the equilibrium of RaA, RaB, and RaC, and the
stability of the apparatus background, have been analyzed in detail.
We must consider the changes with time in the concentration q, the volume rate of inhalation vt, and
the coefficient retention x. The corresponding correction can be introduced experimentally and by calcula-
tion.
Translated from Atomnaya Energiya, Vol. 38, No. 4, pp. 260-261, April, 1975. Original article
submitted October 1, 1974.
? 1975 Plenum Publishing Corporation, 227 West 17th Street, New York, N.Y. 10011. No part of this publication may be reproduced,
stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming,
recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $15.00.
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Fig. 1. Forms of functions: I) Q =Qmax;
0 :s 0 01;Q = %min; 01 0; II) Q = Qm4.3.;
0 5_ 0 :5 ei; Q = Qmax; e a-- el; IX) Q =Q0
? sin2rt/T; X) Q =Q0 + Qebtsin2rt/T.
The expressions for It,
In the experimental method, the instrument for
measurement by the direct method is placed directly
underground close to the work site [4], as a result of
which the activity in the lungs of the miners can be
measured without any appreciable interruptions in the
work.
On the other hand, a consideration of the varia-
tions of q, vt, It, and the introduction of the corres-
ponding correction 6 can also be performed by calcula-
tion [6].
Let us denote as Q = qv tx the rate of penetration
of isotopes into the lungs per unit time. Let us consider
the case when Q changes with time. Let us break up
the entire time interval of filtration 0 into individual
portions .A0, during which Q can be considered con-
stant:
AO = 0/k,
where k is the multiplicity of division, determined
by the required value of the error with which the condi-
tion of constancy of Qi on the portion of the division
should be fulfilled.
Let us apply the formulas for the activity in the
case of constant Q successively to each interval of divi-
sion and for each short-lived daughter product of radon.
The final expressions for RaA, RaB, and RaC (RaCt)
will take the form:
AA= 2 Q.Ial (0, k), rite al (0)
= (1_ e -XAOM) e Xike (1 ).
A
AB= {QiAltit [0,l1c; 9 (1--- Tc)]
(43(0111 [0 / k; 0 (1 ? )]} ;
AC= QiA(Dt Pik; e (1? k )1
i=1
Q13018[0 k; 0 (1?Tei )]+ QL(1)2[0fic; 0 (1-7-ci )]1.
4,B 4,A 41,33
' ' , and ?C are cited in [7].
B C C C
The correction due to a change in the value of Q is conveniently represented in the form:
E (Qkt(Dt(0, k)-E(1) (0, k)] (213 [OE (0 , 4:018 (0, k)] *1:12 (0 , k
1,
Th (8) (D''d (0)] QB (0) +018 (8)I+ Cl:D2 (0)
where represents the average values of the rate of penetration of the isotopes into the respiratory system
in the time 0. The value of 6 depends on the type of the curve Q(0), the ratio Qmax/Qmin, the shift of
equilibrium, etc.
For the calculation we selected 10 variations of the function Q(0) (Fig. 1), as well as a number of
values of the parameters, which reflect the variety of situations arising under practical conditions.
The general values of the parameters for all variations are:
1. 0 = 30; 60; 90; 120; 180; 420 min.
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2. :Number Of divisions:. k-=. 2;.3.; .5; .7; 10;14;18; -42:
.3. QA:QB:Qc =1:1:1; 1:0.8:0.6; 1:0.6:0.4;1:0.5:0.5; 1:0.4 i0.2; 1:0.3:0.1; 1:0.5:0.05; 1:01
:-0.05; 1:0.1:0.01; 1:0:05:0.01;
1:0.01:0.01.
4. Qmax/Qmin =1'5; 2.0;
3.0;
5.0;
10;
15; 20; 30; 50;
100;-300;
1000.
:01/0k
=0.1; 0.2;
0.3;
0.4;
0.5;
0.6; 0.7; 0.8;
0.9.
5. (02-01)/Oic
6. Qmin = 50 disintegrations/min/min (q = 10-h1 Ci/liter; k =0.2; vt =10 liters/min).
The calculation was performed on a BESM-6 electronic computer [6].
The method of introduction of the correction associated with the change in Q with time presupposes the
selection of the function Q(0) closest to the real form (variations I-X, see Fig. 1) and a search according to
the set values of Qmax/Qmin, 01,
as well as the other necessary parameters of the correction 6.
The value of the activity (penetration) in the lungs sought, X, is expressed in terms of the measured
value of A as follows:
-A= 1
1+6 A.
The degree of error in the determination of 6 depends on the closeness of the selected variant of the
distribution to the variant under real conditions. It must be noted that since the correction 6 is largest inab-
solute magnitude, and that means also the largest difference of A 'from X, are given by variants I and II,
we can limit ourselves to the maximum value of 6 for these variants. This is also advisable because even
in these cases, for Qmax/Qmin 30, the summary error of measurement by a direct method does not ex-
ceed 40% at the level of the maximum permissible intakes, which is quite sufficient for practical purposes.
LITERATURE CITED
1. L. S. Ruzer, Dissertation [in Russian], VNIIITRI, Moscow (1970).
2. L. S. Ruzer, Byul. Izobret., No. 18 ,(1964).
3. L. S. Ruzer and S. A. Urusov, At. Energ., 26, No. 3, 301 (1969).
4. S. A. Urusov, Dissertation [in Russian], In-t Biofiziki. Minzdrav SSSR (1972).
5. A. D. Allterman, Dissertation [in Russian], Institut Gigieny Truda i Profzabolevardi AMN SSSR,
Moscow (1974).
6. Yu. S. Gerasimov and L. S. Ruzer, Methods of Determination of the Content of Radioactive Isotopes
in the Human Organism. Materials of the Symposium [in Russian], Izd. Leningr. NII Radiatsionnoi
Gigieny mz RSFSR, Leningrad (1973), p. 58.
7. L. S. Ruzer, Radioactive Aerosols [in Russian], Izd. Komiteta Standartov, Mer i Izmeritellnylch
Priborov Pri Sovete Ministrov SSSR, Moscow (1968).
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NEUTRON ACTIVATION DETERMINATION OF
HAFNIUM IN ZIRCONIUM IN THE CASE OF
INTERFERENCE FROM FLUORINE
V. V. Ovechkin, A. Z. Panshin, UDC 543.53
and V. S. Rudenko
A rapid neutron activation method of determination of hafnium, based on the recording of the activity
of the short-lived isomer 179mHf (T1/2 = 19 sec, Ey = 0.217 MeV), is used in analytical practice [1-3].
The large value of the cross section of the 178Hf(n, y) reaction (-75 b) on thermal nuetrons per-
mits the use of portable neutron sources: low-voltage generators [2] and isotopic sources [3], for activation
in addition to reactors. The induced activity is usually measured with a scintillation y spectrometer ac-
cording to the photopeak 0.217 MeV.
According to the data of [2], the use of a 14 MeV neutron generator and moderator permits an in-
crease in the activity of the isomer 179mHf, and in addition, a substantial lowering of the background of the
zirconium matrix, due to the y radiation of 88mZr and 88mY, formed from zirconium according to the reac-
tions 9tr(n, 2n) and "Zr(n, ntp). The sample for irradiation is placed in a moderator at a distance of
?4-5 cm from the neutron source, where the flux of thermal neutrons is a maximum [4]. However, at such
a distance in the moderator the fraction of neutrons with energy exceeding the threshold of the indicated
reactions is still large (12.53 and 8.79 MeV, respectively). On account of the large difference of the energy
spectra of neutrons determining the useful and background effects, it is advisable to find the optimum dis-
tance from the target, at which more profitable conditions of measurement of hafnium in zirconium are
realized.
? It should be kept in mind that in the presence of fluorine in zirconium a serious difficulty arises for
the measurement of a hafnium impurity on a scintillation y spectrometer according to the photopeak 0.217
MeV on account of the interference from the 0.197 MeV y radiation of the isotope 190 (T1/2 = 29.3 sec),
C, pg
4,70
300
200
100
0 5 10 15 20 /cm
Fig. 1. Dependence of the lower
limit of the measurement of hafnium
on the position of the sample in the
moderator relative to the source: 1
and 2) mean-square error 20 and
309, respectively.
0
4197
.4217
4511 4588
x10 ft It
4277
4588
100 200 300 400
Channels
4910
500
Fig. 2. y spectrum of irradiated samples.
Translated from Atomnaya Energiya, Vol. 38, No. 4. pp. 261-263, April, 1975. Original article
submitted July 15, 1974.
0 1975 Plenum Publishing Corporation, 227 West 17th Street, New York, N.Y. 10011. No part of this publication may be reproduced,
stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming,
recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $15.00.
334
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TABLE 1. Hafnium Content in Samples, %
by Weight
Materials
Activation Spectral
method method
Zirconium
Zirconium
Zirconium
Potassium fluorozirconate
Potassium fluorozirconate
0,8.10-2
4,2.10-2
3,0.10-2
4,6-10-2