Soviet Atomic Energy Vol. 32, No. 4
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Russian Original Vol. 32, No. 4, April, 1972
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rc
Translation published November, 1972
SATEAZ 32(4) 303-434 (1972)
SOVIET
ATOMIC
ENERGY
ATOMHAFI 3HEP114F1
(ATOMNAYA ENERGIYA)
TRANSLATED FROM RUSSIAN
CONSULTANTS BUREAU, NEW YORK
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Dvot
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SOVIET:
ATOMIC ?
ENERGY
,
(
So yie t Atomic Energy is a dover-to-cover translation of Atomnaya
Energiya, a publication of-the Academy of Sciences of the USSR.
An arrangement with Mezhdunarodnaya Kniga, the Sciviet book
export agency, makes available both advance copies of the Rus-
sian journal and original gloss,photographs and artwork. This
serves to decrease the necessary time lag between publication
of thee original and publication of the translation and helps to im-
prove the quality of .the latter. The translation began with the'firat
issue of the Russian journal.
Editorial Board Atomnayl Energiya:
Editor: M. D. Millionshchikov
, . Deputy Director
I. V. Kurchakay.?Institute of Atomic Energy
. Academy Of Sciences of the USSR
Moscow, USSR
Associate Editors: N. A. Kolokol'tsov
N. A. Vlatov
A. A. tochvar
N. A. Doliezhar
? Fursov
I.N. Golovin
V. F. Kalinin
' Krasin
,A. I. Leipunskii
A. P. Zefirov
V. V. Matveev
M. G. Meshcheiyakov
P. N. Palei
,V. B. Shevchenko
D. L. Simorienko
V. I. Smir'nov
A. P. Vinogra'dov
?
Copyright ?1972 Consultants Bureau, New York, a division of Plenum Publishing
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SOVIET ATOMIC ENERGY
A translation of Atomnaya Energiya
Translation published November, 1972
Volume 32, Number 4 April, 1972
CONTENTS
Engl./Russ.
On the Occasion of the Seventieth Birthday of Academician Viktor Ivanovich Spitsyn ? ? ?
303
267
RE VIEWS
Problems if Safety of Nuclear Power Plants? V. A. Sidorenko
304
269
Peaceful Use of Atomic Energy and the Environment ? U. A. Israel
308
273
BOOK REVIEWS
New Books
313
278
ARTICLES
Antimony, Bismuth, Arsenic, and Other Elements in Ore Bodies and Haloes of a
Uranium? Molybdenum Deposit ? G. I. Rossman, N. A. Stepanova,
I. V. Sychev, and G. A. Tarkhanova
317
279
Radiation-Induced Growth of Polycrystalline a-Uranium ? M. A. Vorob'ev
V. F. Zelenskii, E. A. Reznichenko, and A. S. Davidenko
323
287
Calibration of Gamma ? Gamma Densitometers ? K. Umiastowski
328
293
Neutron Diffusion in a Polarized Proton Medium ? Yu. N. Kazachenkov
and V. V. Orlov
333
297
The Energy Lifetime and Diffusion of Particles in "Tokamak" Systems
? Yu. N. Dnestrovskii, D. P. Kostomarov, and N. L. Pavlova
337
301
ABSTRACTS
Neutron Slowing-Down Theory in P2-Approximation of the Method of Spherical
Harmonics ? I. A. Kozachok and V. V. Kulik
343
307
Multiparameter Optimization of Nuclear Power Station with Flash Desalination
Facilities ? Yu. D. Arsen'ev, Yu. S. Bereza, S. V. Radchenko,
and V. A. Chernyaev
344
308
Pseudoblind Startup of Nuclear Reactor ? B. G. Volik, T. A. Gladkova,
and G. L. Polyak
345
308
Redistribution of Fuel in Irradiated Dispersion Type Fuel Elements ? L. M. Tuchnin
and E. F. Davydov
346
309
The Neutron Radiation of Pu23802 Containing Different Amounts of 018 ? V. A. Arkhipov,
G. V. Gorshkov, B. S. Grebenskii, B. A. Mikhailov, V. V. Fedorov,
S. P. Khormushko, and A. A. Chaikhorskii
347
310
Magnetic Systems for the Transport and Accumulation of Slow Neutrons ? I. M. Matora
and 0. A. Strelina
348
310
Thermodynamics of Formation of Plutonium Trichloride in a Fused Potassium Chloride
Medium ? M. V. Smirnov, V. I. Silin, and 0. S. Skiba
349
311
Effect of Oxidation on Strength Characteristics of Graphite ? E. I. Kurolenkin,
N. S. Burdakov, Yu. S. Virgil'ev, V. S. Ostrovskii, V. N. Turdakov,
and Yu. S. Churilov
350
312
The Equation of State of Uranium Hexafluoride over a Wide Range of Parameters
? V. V. Malyshev
351
313
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CONTENTS
(continued)
Engl./Russ.
LETTERS TO THE EDITOR
Experimental Study of the Performance of the RG-1M Geological Research Reactor
- V. I. Alekseev, A. M. Benevolenskii, V. V. Kovalenko, 0. E. Kolyaskin,
L. V. Konstantinov, V. A. Nikolaev, V F Sachkov, and A M Shchetinin ?,`
. . M. A. , F. V. , ,
,6 rface Contamination of VVR-M Fuel Elements by Fissionable Material and its
Contribution to the Fragment Activity of the Coolant - N. G. Badanina,
K. A. Konoplev, and Yu. P. Saikov
Equipment for Study of Migration of Radioactive Products Along the Cross Section of
353
355
315
316
Fuel Element - A. V. Sukhikh, V. K. Shashurin, E. F. Davydov,
and M. I. Krapivin
358
318
Vacuum-Cathode Etching of Uranium in VUP-2K Equipment - D. M. Skorov,
A. I. Dashkovskii, V. V. Volkov, and B. A. Kahn
360
319
Change in the Structure and Properties of Titanium Carbide under the Action of
Irradiation - M. S. Kovaltchenko, Yu. I. Rogovoi, and V. D. Kelim
362
321
Change in the Density of Single-Crystal Tungsten durineNeut'ron Irradiation
- V. N. Bykov, G. A. Birzhevoi, and M. I. Zakharova
365
323
Some Principles of the Oxidation of Reactive Graphite - N. S. Burdakov
and V. N. Turdakov
367
324
How Inorganic Electrical Insulating Materials are Used in Reactors - N. A. Aseev . . .
370
326
Neutron Diffusion in a Medium with Channels - N. I. Laletin
373
328
Recording of Acoustic-Emission Signals in Construction Elements
- Yu. V. Miloserdin, V. M. Baranov, and K. I. Molodtsov
376
330
Determination of the Individual Fluxes of -y-Quanta and Neutrons by Means of a
Thermoluminescent LiF Crystal - K. M. Kudelin
378
331
Experimental Determination of Sensitivity of Direct Charge Detectors in Thermal and
Epithermal Region - N. D. Rozenbly-um, E. N. Babulevich, A. E. Alekseev,
V. A. Zagadkin, V. S. Kirsanov, E. M. Kuznetsov, A. A. Kononovich,
and M. G. Mitel'man
381
333
Gamma-Ray Detectors from i-Conductivity Germanium - V. S. Vavilov,
L. A. Goncharov, T. I. Pavlova, Ya. Khurin, and M. V. Chukichev ...... . .
384
335
Germanium Radiation Counters as Charged-Particle Spectrometers - S. M. Ryvkin,
V. V. Peller, N. B. Strokan, V. P. Subashieva, N. I. Tisnek,
and V. K. Eremin
386
336
Neutron Radiation Standardization - V. G. Zolotukhin, I. B. Keirim-Markus,
0. A. Kochetkov, V. I. Tsvetkov, and V. Cherkashina
388
338
Calculation of the Concentration of fl-Active Gases Radiometrically Measured with a
Cylindrical Counter - A. A. Gusev
391
340
Backscattering Coefficients for 12-25 MeV Electrons Incident Obliquely on Metallic
Surfaces - V. P. Kovalev, V. P. Kharin, V. V. Gordeev, and V. I. Isaev . . .
395
342
Searches for Tracks of Fragments from the Spontaneous Fission of Far Transuranium
Elements in Natural Minerals - 0. Otgonsuren, V. P. Perelygin,
S. P. Tret'yakova, and Yu. A. Vinogradov
398
344
,ve. sium Distribution in the Surface Layer of the Pacific Ocean - 0. S. Zudin,
B. A. Nelepo, A. N. Spiring, and A. G. Trusov
402
347
Seasonal Extremes of Concentration of Nuclear Fission Products in the Atmosphere
- A. E. Shem'i-zade
406
350
COMECON NEWS
Agreement on Setting up the Interatominstrument Society - Yu. Yurasov
409
353
Collaboration Logbook
412
354
INFORMATION: CONFERENCES AND SYMPOSIA
The Moscow Engineering and Physics Institute Scientific Conference - V. Frolov . . . .
414
357
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CONTENTS
Seventh All-Union Conference of Representatives of Four Nuclear Data Centers
(continued)
Engl./Russ.
? A. Abramov and V. Popov
417
359
The All-Union Conference on Plasma Theory ? I. P. Yakimenko
419
360
The Tenth International Conference on Phenomena in Ionized Gases ? P. P. Kulik
422
362
Dresden Conference on Mossbauer Spectroscopy ? A. M. Afanasiev
426
364
Warsaw September 1971 Symposium on Nuclear Electronics ? G. P. Zhukov,
V. G. Zinov, I. F. Kolpakov, and A. N. Sinaev
429
365
IAEA Draft Regulations for Safe Transportation of Radioactive Materials ? S. Martynov.
431
367
V/O Izotop Agency Seminars and Exhibits
432
367
The Russian press date (podpisano k pechati) of this issue was 3/ 29/ 1972.
Publication therefore did not occur prior to this date, but must be assumed,
to have taken place reasonably soon thereafter.
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ON THE OCCASION OF THE SEVENTIETH BIRTHDAY
OF ACADEMICIAN VIKTOR IVANOVICH SPITSYN
The editorial staff of Atomnaya t nergiya warmly greets Academician Viktor Ivanovich Spitsyn on the
occasion of his 70th birthday, and wishes him excellent health, long years of life, and creative successes.
Translated from Atomnaya Energiya, Vol. 32, No. 4, p. 267, April, 1972.
0 1972 Consultants Bureau, a division of Plenum Publishing Corporation, 227 West 17th Street, New York,
N. Y. 10011. All rights reserved. This article cannot be reproduced for any purpose whatsoever without
permission of the publisher. A copy of this article is available from the publisher for $15.00.
303
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REVIEWS
PROBLEMS OF SAFETY OF NUCLEAR POWER PLANTS*
V. A. Sidorenko
UDC 621.039.51
Problems of safety of nuclear power plants occupied one of the most prominent places among the sub-
jects discussed at the IV Geneva Conference.
Of 505 reports read at the Conference, 78 dealt with safety. In accordance with the topics they dis-
cussed, these reports can be arbitrarily divided into five groups:
1. Discussion of the general scientific and engineering aspects of nuclear power plant safety including
a study of the fundamental approach to safety control (so-called "philosophy of safety") (24 reports).
2. Legislation concerning safety, norms, standards, and legal problems associated with the division
of responsibilities, etc., (nine reports).
3. Effect of nuclear power on the environment including a discussion of the actual conditions prevail-
ing at nuclear power plant sites (23 reports).
4. Scientific and engineering problems associated with the removal of radioactive waste and its burial
(eight reports).
5. Effects of radiation on living organisms, radiation protection and shielding (14 reports).
Approximately the same attention has been devoted to two aspects of nuclear safety: the effect on en-
vironment and handling of nuclear waste (3rd and 4th groups, 31 reports) and the scientific and engineering
principles of nuclear plant safety and setting up norms for safety control (1st and 2nd groups, 33 reports).
The materials presented at the Conference reflect considerable advances in nuclear safety control:
the problem is now much better understood, technical and organizational measures of safety control have
improved, and a reliable basis has been provided for nuclear safety taking into account the expected growth
of nuclear energy.
The expected growth of nuclear power focussed attention on the effect on the environment of nuclear
?engineering in general and of specific power plants whose operation proved the adequacy of the safety mea-
sures provided. One conclusion that follows from the discussion is that the radioactivity level in the vicinity
of nuclear power plants and fuel processing plants is very low and that the amount of radioactive waste is
considerably less than allowed by national supervisory and legislative organs for every specific plant. De-
tailed information on the environmental effects of atomic installations was presented in the American Report
No. 087t, English Report No. 512, West German Report No. 399, etc. For example, the annual waste of
radioactive materials of commercial nuclear power plants in 1970 in the USA amounted to 0.14-25% and
0.002-6.5% of the allowed level of liquid and gaseous waste (Report No. 087). Even now it is possible to
design nuclear reactors with a radioactive waste level as low as desired. British experience indicates that
fuel processing plants produce the greatest amount of radioactive waste. Many countries have undertaken
special studies whose aim is the reduction of radioactive discharge from future high-output fuel processing
plants.
*Review of papers presented at the IV International Conference on Peaceful Uses of Atomic Energy, Geneva,
1971.
t Lists of reports presented at the Geneva Conference were published in the October issues of Atomnaya
Energiya (Soviet Reports) and Atomnaya Tekhnika za Rubezhom (foreign reports) in 1971.
Translated from Atomnaya Energiya, Vol. 32, No. 4, pp. 269-272, April, 1972. Original article
submitted January 13, 1972.
304
? 1972 Consultants Bureau, a division of Plenum Publishing Corporation, 227 West 17th Street, New York,
N. Y. 10011. All rights reserved. This article cannot be reproduced for any purpose whatsoever without
permission of the publisher. A copy of this article is available from the publisher for $15.00.
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By considering the possible ways of penetration of radioactive products into the surroundings, and by
comparing environmental pollution due to nuclear and fossil fuels, the authors of the Soviet Report No. 684
arrived at the conclusion that nuclear energy allows the conservation of a reasonably clean environment;
what is more, replacement of fossile-fuel power by nuclear power should lead to a considerably lower level
of contamination of the surroundings by toxic materials and so improve the environment.
Despite the optimistic prospects of the present and future states of nuclear safety, all reports call
for still more stringent measures to ensure the safety of nuclear power plants with respect to both "actual"
and "potential" radiation dangers (reduction of allowed radioactive-discharge levels and improvement of
the reliability of safety devices and radioactivity containment devices). This trend is associated with the
ever increasing number of nuclear power plants and their location in densely populated areas.
Perfection of safety systems, including containment devices, proceeds in the direction of higher de-
vice efficiency and reduced size and cost. This is quite pressing as the rise in the cost of nuclear power
plants is due largely to the additional safety measures necessary to meet the more stringent requirements.
Another feature characteristic of modern trends is the increasingly important role of equipment re-
liability in securing actual plant safety and in reducing the probability of accidents. Although these aspects
of the problem of safety are not entirely new, they have become recently of primary importance together
with safety measures that can be termed "obvious." Of independent significance is the supervision of plant
equipment at all stages, from its manufacture to utilization. The accumulated operational experience helped
to improve methods of continuous supervision and periodic inspection of nuclear plants (ultrasonic flaw de-
tection, noise monitoring, etc.).
As follows from the reports, particular attention is now devoted to specific solutions to key technolo-
gical safety problems that are revealed in studies of the possible developments of dangerous processes in
nuclear plants especially under emergency conditions.
The basic trends in nuclear plant safety were discussed in USA reports (Nos. 038, 040) from the point
of view of "protection in depth" which includes the following steps in the provision of nuclear safety: secur-
ing equipment reliability, provision of technological and circuit impossibility of dangerous consequences of
any single failure or damage, limitation of the consequences of any possible emergency case.
The fact that problems of nuclear plants safety are complex and many-sided and have no single uni-
versal solution has been stressed in many reports. In particular, one cannot expect that security can be
provided only by high-quality equipment (much better than used in conventional power plants) or only by en-
suring containment of the effects of possible emergencies (such as isolation of the plant). The problem
must be considered from all its aspects.
The implementation of the safety-in-depth principle can be seen in the different approaches to nuclear
plant safety.
In one of the possible variants all systems and equipment of the plant are divided into three functional
parts: the reactor proper, equipment and systems that ensure its normal operation; "external" protection
systems that reduce the possibility of hazardous deviation of plant parameters from their design values and
protect the plant in case of failure of normal operating devices; systems whose task is to reduce as much
as possible the consequences of any potential accident. The safety of nuclear power plants is ensured by
independent and reliable performance of all these three functional parts.
In a different approach, safety-in-depth is ensured by different independent and reliable "barriers',
that prevent penetration of fission fragments to inhabited areas: from the fuel to coolant, from the coolant
to the reactor location, from the power plant location to the surroundings, and finally from the surround-
ings by various means to the population.
The development of specific concepts and criteria of safety in several countries merits special atten-
tion.
The desirability of a numerical and probabilistic approach to the evaluation and standardization of
nuclear safety has been recently frequently stressed together with the fact that the amount of statistical data
on the performance of nuclear power plant equipment is still insufficient. The expensiveness of putting this
approach into practice and the importance of international cooperation for the solution of this problem has
been pointed out in the French Report No. 579. The Conference proved beyond doubt that the necessity of a
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numerical approach to safety analysis is now generally accepted, but that, at the same time, the feasibility
of a probabilistic approach to safety standardization is still treated with reserve. Numerical methods of
estimating equipment reliability and accident probability are quite advanced and should be widely used in
design practice of nuclear power plants. These methods make it possible to compare various approaches
and to select optimum solutions in the design of safety equipment and devices. However, there is apparent-
ly no sufficient basis for a numerical treatment of the standardization of nuclear plant safety in the immedi-
ate future. In the West German Report No. 364 attention is called to the fact that throughout a normal life
span all existing nuclear power plants are unable to provide sufficient statistical data for very grave acci-
dents whose probability is estimated as 10-7 per year; in such cases the numerical approach becomes mean-
ingless.
The most frequently used concept in safety control is still the concept of the "basic design accident."
Perfection of this concept is partially evident in the fact that attempts are made to apply probabilistic meth-
ods in selecting the basic design accident. One of the most important advances in this field is the use of
not only "the maximum probable accident" but of a full spectrum of possible accidents of which the basic
design accident is one. This is done in order to protect the plant not only against major but little probable
potential dangers but also against real dangers presented by much more probable equipment failures. An
effective and systematic approach to the analysis of the spectrum of emergency situations is the so-called
"failure tree." This method reveals all situations that are liable to result from any specific failure or
damage. The failure tree makes it possible to demonstrate and evaluate numerically various combinations
of serious damages that can lead to an emergency situation.
In aqueous reactors the basic design accident is still assumed to be the total disruption of the main
pipeline of the circulating loop. The possibility of reactor vessel rupture is also considered. Some designs
(e.g., in West Germany) even consider the probability of an accident involving vessel damage. The most
probable location of vessel damage is considered to be the region where the circulating loop pipes are con-
nected to the vessel. An analysis of the probability of crack development in the vessel makes it possible
to take into account in the design defects in the vessel that can cause leakages much smaller than resulting
from a burst in the main pipeline (West German Report No. 364).
A modification of the basic design accident concept was described in the Canadian Report No. 150. The
plant safety is evaluated by quantitatively analyzing the frequency of occurrence of probable hazardous pro-
cesses in the system, but the use of specific maximum radiation exposure of the population is based on two
principal schemes of accident occurrence: a single failure in standard technological equipment with the pre-
servation of full capability of accident prevention and containment devices or the coincidence of failure of
both the standard operating system and the accident prevention system. In the first case maximum radiation
exposure is that acceptable for normal operation; the second case involves the use of special maximum radi-
ation exposure rates.
The available design and operational experience made it possible to find many specific solutions in
various safety control systems (USA Report No. 040). For example, methods have been developed for the
construction of equipment and buildings resistant to earthquakes (Japanese Report No. 226, Swiss Report
No. 672), hurricanes, floods, and other natural disasters. There is also the experience of building a nu-
clear power plant near an airfield where the danger of collision or fire caused by an airplane accident must
be taken into account. Instruments and a program have been developed for monitoring the spread of radio-
activity in the locality surrounding nuclear power plants.
Devices have been developed for aqueous reactors which monitor and if necessary suppress effects
associated with xenon power fluctuations (such as, for example, absorbing rods of partial length); fixed in-
termitent absorbers are used for canceling the positive temperature coefficient of the moderator reactivity.
Comprehensive programs have been developed for analyzing the vibrations of intravessel devices in the
course of start-up tests for the detection and elimination of weak points. Specific solutions aimed at im-
proving the construction reliability, provision of continuous and periodic supervision, and ensurance of
operating efficiency under emergency conditions are incorporated in the design of reactor cooling systems,
of buildings and containment installations, of safety control systems, monitoring and measuring apparatus,
and other systems.
Among problems that require further research are:
development of flaws in steel structures of circulation loops;
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thermal interaction of fuel and coolant, in particular the heat exchange crisis (British Report No.
477);
embrittlement of thick steel samples (including thermal shock in case of emergency cooling of the re-
actor core);
performance of safety systems under emergency conditions;
critical parameters and power (this can be said to be a "perennial" problem);
the probability of natural phenomena which must be allowed for in the design of nuclear power plants;
improvement of the safety systems of core cooling (USA Reports Nos. 040 and 039);
conditions of heat removal in time of and after emergencies involving the loss of coolant;
hydrodynamic effects in the reactor vessel and in the cooling loop in case of large leakages;
improvement of remote monitoring methods of the equipment state in the course of reactor operation
and perfection of ultrasonic methods;
melting of the reactor core (West German Reports Nos. 365 and 364).
Special attention has been devoted to the safety of fast-neutron reactors. In sodium-cooled fast reac-
tors characteristic hazardous events in which a single failure or damage is liable to cause grave conse-
quences are damages in the primary loop, sodium ignition, chain damage of fuel elements, the passage of
large gas bubbles through the core, etc. Accordingly, in the analysis of various design accidents (fast re-
activity buildup, stoppage of coolant circulation, etc.), and in the development of protective measures parti-
cular attention was given to the study of such phenomena as the formation of voids in sodium, interaction of
the coolant with molten fuel, the mechanism of the spread of fuel element damage, the Doppler effect, the
formation and spread of aerosols in connection with sodium ignition (USA Report No. 041).
In conclusion, one should stress once more the generally accepted importance of the creation of a
system of norms and rules for all stages of the design, equipment manufacture, construction, operation,
and maintenance of nuclear power plants. The reaction of such a system of norms and rules is a continuous
process. Besides this work, which is conducted by the Atomic Energy Commission for the development of
general rules, criteria, specifications, procedures, etc., with the participation of 1200 representatives of
400 organizations, work is going on in the USA on the creation of a system of 78 most important nuclear
standards. The development is now being concluded of the first ten standards to which belong:
secondary criteria for pressurized-water reactors;
secondary criteria for boiling water reactors;
criteria for taking into account seismic effects in the location and design of power reactors;
qualification and training of nuclear power plant personnel;
specifications of periodic test in nuclear power plants;
specifications on prestart and startup tests of nuclear power plants;
criteria and practical measures for securing quality performance of nuclear power plants, etc.
One thousand and five hundred nuclear standards are to be developed in the next decade. Experience
indicates that nuclear power plants can be and are designed to operate reliably and safely. The development
and introduction into practical use of a system of norms and standards should consolidate the present level
of technology and extend it successfully to other fields.
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PEACEFUL USE OF ATOMIC ENERGY AND THE ENVIRONMENT*
U. A. Izrael' UDC 621.039.77
With the rapid development of nuclear power engineering and a large-scale introduction of atomic
energy in industry and daily life it is inevitable that mankind would be affected by nuclear radiation and
radioactive products would get into natural media. These problems appear in the production of nuclear
fuel and atomic power, in reprocessing fuel, and in handling wastes and isotopes.
Numerous estimates show that by the year 2000 the generation of electrical power from atomic power
plants (APP) will exceed 3 mill. MW and will comprise -50% of the entire electric power generation.
At present the number of APP is increasing in many countries.
One of the most important conditions for extending the network of APP consists in ensuring the safety
of operation of these power plants from the point of view of the effect on the environment.
Estimates show that the main source of radiation effect on man (at present and in future) is the con-
tamination due to the production of atomic energy [1]. Besides, it is necessary to consider specific thermal
contamination of the natural media in the operation of APP.
A large attention is being devoted to these problems. The effect of radioactive contaminants on the
environment is tieing investigated extensively and the problems appearing in these investigations are dis-
cussed in international meetings and symposia [2, 3]. At the IV Geneva conference on the peaceful use of
atomic energy many papers were devoted to this problem. In two meetings of the special section on "The
effect on the environment and the reaction of the population" 12 papers (of which three were from Soviet
authors) were read and in addition six papers (two by Soviet authors) were presented in abstract form. A
number of papers, presented in other sections, were also related to this problem (for example, papers on
working out the principle for locating APP and the choice of safe areas for APP).
It was noted at the conference that the problems of the effect of radioacitve substances on man and the
biosphere as a whole are focal in the peaceful use of atomic energy.
It is clear from the papers presented at the conference that extensive investigations are being carried
out in different countries on the possible ways of incidence of radioactive products into the environment and
their interaction with the biosphere and the migration of isotopes to human body through different biological
chains. On one hand careful measurements and study of the behavior of radioactive products penetrating
into the environment from reactors and plants are being made; on the other hand the interaction of the radio
nuclides with the natural media are being studied in a general way.
The Soviet papers discussed in detail the results of the study of biological effect and behavior of radio-
active products in agricultural cycles [4] and in forest plantations [5]. Extra-root entry of radio nuclides
into plants and also their assimilation by plants from the soil and passage to livestocks is discussed.
During global fall-outs of long-life radioactive products the maximum amount of radio nuclides is
retained in agricultural plants. It is found that the maximum content of radio nuclides in harvest is ob-
served after the period of formation of the productive organs (for example, the radio nuclide content in
wheat is maximum when the wheat attains milk ripeness).
*Review of papers presented at the IV International Conference on Peaceful Uses of Atomic Energy, Geneva,
1971.
Translated from Atomnaya Energiya, Vol. 32, No. 4, pp. 273-277, April, 1972. Original article
submitted January 31, 1972.
? 1972 Consultants Bureau, a division of Plenum Publishing Corporation, 227 West 17th Street, New York,
N. Y. 10011. All rights reserved. This article cannot be reproduced for any purpose whatsoever without
permission of the publisher. A copy of this article is available from the publisher for $15.00.
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The assimilation of radio nuclides by agricultural plants from soil is characterized by the following
figures: the contaminated area froni which the radioisotope is assimilated (per kg of the product) is hundreds
of cm2 for Zr95, tens of cm2 for W185, a few cm2 for Cs137, Sr90, and Fe59, a few tenths or hundredths of cm2
for Ce144, Ru106, Zr95, and varies between a few tenths to a few thousandths of cm2 for PU239, 1J235, PM147
Y91.
For extra-root incidence the radio nuclide content in a wheat grain is ten times higher than in the case
of their assimilation from soil. In respect of the concentration in milk and meat radio nuclides form a
descending series I"1 > Mo99 > Sr89 > Bat?.
The limiting fall-out intensities of radio isotopes and their content in soil, at which the annual inci-
dence of nuclides into human organism along with food does not exceed the limiting admissible value, are
estimated as: for Sr" ?1.5 mCi /month ? km2 (content 2 Ci/km2), for 1131 ?0.5 mCi /day ? km2. It is shown
that the main degree of radiational affliction of grain cereals is caused in the forming ears.
The problems of migration of radio nuclides in forests, radiation decrease in forests and the effect
of radioactive fall-outs on bio-organisms under the forest cover are discussed in [5]. The results of the
investigations show that the forest, as a part of the landscape, is among one of the most sensitive biological
systems to radioactive fall-out.
The results of a 15 year study of the behavior of radio nuclides, falling into water and earth ecosys-
tems during the operation of a reactor in model experiments at Oak Ridge laboratory in USA, are presented
in [6]. For water systems the isotopes Sr", C sl", Co", and T3 (sometimes Ru'", Sb125, and Zn") are typical;
for forest and field systems Co", Sr", Zn + Nb, Rolos, Cs137, and Ce144 are typical.
The results of studies of dilution and diffusion of radio nuclides in sea water, and also of the possi-
bility of incidence of these products in sea organisms (Co", Fe59, and Mn54) are presented in Indian [7] and
Japanese [8] papers.
The background radiation situation and also the dose from medicinal procedures in different countries
are discussed in some papers. For instance, it is shown that the natural background from the radiation
from mountain rocks and cosmic rays comprises 120 mrem/ yr [9]; the intake of radiation through medicine
gives an average genetic dose of 20-37 mrem/ yr [9, 10], while the global fall-outs from the past tests of
nuclear weapons give an average dose of 10 mrem/ yr [9].
The radioactive contamination of ocean waters and the behavior of some radio nuclides in sea water
are estimated in a Soviet paper [11]. In 1966-1967 on the whole there was a decrease in the contamination
of the surface waters of Pacific and Atlantic oceans. The amount of Sr", going deep into Pacific ocean,
exceeds the fall-out during this period. Technogenic radioactive regions have been detected (for instance,
near the west coast of North America, close to the mount of Columbia river). The results of the study of
physicochemical and biological processes, which control radioactivity, are interesting. It is found that
the accumulation of iron in suspended matter in oceans leads to the transformation of a number of radio
nuclides (Y91, Ce144, Nb95) in the suspended fraction. In the presence of iron the coefficient of accumulation
of these isotopes by plankton increases by an order of magnitude. This shows that the disposal of radioactive
wastes into oceans presents a definite hazard and can not be recommended (however, Japan, for example,
does not adhere to this practice) [8].
It is obvious that no branch of industry has such a control and measures of protection against the pos-
sibility of contamination of the environment as the nuclear power industry.
A careful control of exposure of the population to radiation, the study of contamination of the environ-
ment, and the measures of protection of the population are discussed in [8, 10, 12, 13] and other papers.
It is shown in [13, 14] that detailed investigations of the contamination of the environment are carried
out around APP: investigations of agricultural vegetations, drinking water, precipitations, water organisms,
and fishes, domestic and wild animals, and so forth. The problems of utilization of ground, the settlement
density, meteorology, geology, seismology, hydrography, hydrology of the region are also studied. It is
especially important to know what is the admissible limit of dilution of water and air basins near APP by
liquid and gaseous wastes. These investigations are necessary for the prognosis of possible contamination
of environment at present and in future.
The construction of APP almost excludes the possibility of ejection of fission products into the en-
vironment during their normal operation. Only the gaseous isotopes Ar41, Xel", Kr85, H [1] and very
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insignificant amount of 1131 can get into the atmosphere. Gaseous ejections of C14 and 1129 (latter with To
= 1.7 ? 107 yr is formed during the processing of nuclear fuel) are described in [13]. Liquid disposals con-
tain H3 and in very small quantities also Mn54, Co", Co", Sr", Sr", Ru106, Sb125, Cs134, Cs137, Ba140 [1,
13]
The number and amount of ejections varies in wide limits during the operation of reactors. The
average amount of liquid waste in reactors in USA and England in 1966-1969 was 6-11 Ci/yr (maximum up
to 27 Ci /yr), tritium up to 3700 Ci /yr, noble gases up to 3.8. 105 Ci/yr (mainly Ar41 up to 2- 105 Ci/yr), which
comprises about 24-28% of the admissible level for liquid wastes and 15% for gaseous wastes [1].
The largest yield of noble gases is observed in the operation of boiling water reactors (BWR) and in
gas cooled reactors (GCR); the smallest yield is observed in reactors cooled by pressurized water (PWR).
The pattern is reversed for the yield of tritium in the operation of these reactors.
Thus the ejections from the American BWR in 1968 comprised [13] 240 thousand Ci/yr, of which Xe133
was 9000 Ci,Kr85 3 Ci, H3, 0.2 Ci, and11310.02 Ci.The annual liquid disposal was 2 Ci H3, 0.6 CiCo", and 0.9
Ci Co". Gaseous ejections of the American PWR during the year was 14 Ci H3, 3 Ci Kr"; the total gaseous
ejection comprised 103-104 Ci, while the liquid disposals were estimated at 1000 Ci H3.
The fuel treatment plants discharge Kr" in appreciable quantities. In liquid discharges Ru106, ura-
nium, plutonium, americium, and curium have been detected [13]. The concentrations of radio nuclides
in liquid discharges comprise 1.4. 10-10-2.2 ? 10-6 mCi/cm3.
The ejection of noble gases into the atmosphere by Canadian reactors comprises an average of 6400
Ci/day from the first reactors and up to 440 Ci/day from the new reactors; the ejection of tritium is up to
30 Ci/day (ejection of 1131 is in all 10-5-10-3 Ci /day and about 10-2 Ci/day in the oldest reactor.
The amount of tritium in liquid discharges goes up to 15 Ci/clay. In old reactors the ejection of Sr90
(up to 7.5 mCi/day) is observed; Cs134, Cs132, and Co" (6 ? 10-6mCi/cm3onthe average) are also present.
At the beginning of 1971 the gas ejection at four APP of Japan comprised 8-10-4-11 mCi/sec (up to
1000 Ci/day. At "Mishana" APP the ejections in February 1971 comprised 0.1 Ci/day. Liquid discharges
were up to 7-1200 mCi /month [81.
Such ejections lead only to an insignificant concentration of radio nuclides in the environment. Thus
the concentrations in expendable surface waters of some APP in the USA reached 100-270 nCi/liter, , 2-6 nCill3/m1
in drinking water, up to0.6 nCi Co"/ g in fish, up to 120 nCi Mn54/g in precipitations, and up to 57 nCi Co"
/ml in vegetables [13]. A concentration of 1 nCi Co60/g was observed in the organisms of sea shells in the
vicinity of one Japanese APP [8].
From the ejections mentioned above the population living in the immediate vicinity of an APP can re-
ceive only a small dose of radiation. Thus the maximum doses of external radiation from ejections (mainly
Ar41) from the tubes of Canadian APP in 1968 was up to 0.26 rem/yr at a distance of 1 km, and 0.037 rem
/yr at 4.8 km. The total integral dose of radiation of the entire population at a distance up to 50 km is 16
man ? rem/yr [14]. Ata Japanese APP the dose at a distance of 1.5 km for constant wind and gaseous ejec-
tion of 7500 mCi/yr is 7 mrem/yr [8].
In 1968 at an Americal BWR the dose of external radiation at a distance of 2 km was 10 mrem/yr; the
maximum dose of internal radiation received by fishes in the region of fuel treatment plants was 4 mrem/yr
[13].
Specialists of different countries use the standards recommended by the International Commission on
protection from radioactivity (ICRP) in the design and construction of APP. However, there is a system
of licensing and additional requirements in the zone of construction of APP. They amount, for example, [9],
to the following: for the atomic industry in FRG a genetic dose of 2 ber in 30 years (instead of 5 ber accord-
ing to ICRP) is acceptable.
For long-range planning the dose from gaseous ejections for the population is restricted to 1 rem in 30
years or 30 mrem/yr. It is assumed that for different persons the dose must be approximately the same.
At new plants charcoal filters and delay lines for gaseous ejections are used for purification. For
liquid wastes also (in future planning) the acceptable dose is 1 rem in 30 years, uniformly distributed among
the external radiation, internal radiation in drinking water, and internal radiation in cereal requirements.
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Individual enterprises are allowed an ejection of liquid wastes not exceeding 5-20 Ci/yr (without con-
sidering tritium). The concentrations of radio nuclides in river water must not exceed 10-30 nCi /liter, and 3000
nCi /liter of triti urn (from all the sources excluding global fall-outs) . Drainage water with concentration larger
than 5 ? 10 -4 MCi /Ml must be cleaned before disposal [9] . In Canada it is stipulated that an additional conditions
that the genetic dose be no more than 104 man ? rem/yr, must be fulfilled for each reactor [14]. The concen-
tration of radioactivity in water, discharged into oceans, must be below 10-7 ?Ci/cm3 [8].
In some papers a desire is expressed that radioactive discharges from APP be as low as practically
possible [8, 15].
In [14] it is estimated that, if the ejections from APP cause 20% of the ICRP admissible dose, then
3.4 ? 104 man ? rem is received per million of population, or the maximum dose is 4.5-104 man ? rem per 2000
MW of electrical power per year taking into consideration the growth of power production in future.
The radiation doses of the entire world population from the radioactive products`of APP up to the year
2000 are estimated in [1, 16].
It is calculated that by 2000 up to 500 MCi of tritium will go into the environment per year (from which
the dose for each man will be up to 0.04 mrem/yr); the corresponding input of 1123 will be 6.3 .104 Ci (radia-
tion dose for one man 0.2 mrem/yr) and of Kr85 7 ? 103 MCi (dose 0.4 mrem/yr)at a level of power production
of 4260 GW/yr [1].
Thus, at present the radiation doses from radioactive materials produced in the process of peaceful
uses of atomic energy are small and appreciably below the admissible levels recommended by international
organizations.
However, a sharp increase in the power generation from nuclear sources (almost by a factor of 200)
by the year 2000 forces one to consider carefully the possibilities of contamination of the environment. Ac-
cording to some estimates the doses on global scale may comprise about 1% of the values of the natural
background, which is smaller than its variations. Different conditions over the globe, permeation of iso-
topes and their passage along biological chains may change the results of these estimates by a factor of ten
or more. This makes it necessary to watch the contamination of natural media carefully.
A comparative estimate of the consequences of operation of ordinary power plants and APP, presented
in a Soviet paper [16], is interesting. It is calculated that in the operation of ordinary enterprises even by
the year 2000, for the dilution of toxic substances to the admissible level several thousand times larger
amount of air is needed than in the operation of APP. The computations were done for large areas: for
short-lived substances (or rapidly washed out from the troposphere) up to 107 1cm7, for long-life isotopes
(Kr85 and H3) ? for the entire surface of the earth. The possibilities of accidents in APP (up to five cases
in a year over the globe) were also taken into consideration. For ordinary electric power plants the calcu-
lations were done for ,sulfur anhydride, ash, and other toxic substances. Furthermore, it was necessary
to consider that the total amount of dissipated heat (which may, in the final analysis, cause undesirable
climatic changes) per unit usable power of APP is appreciably less than in the operation of ordinary power
plants due to the high efficiency. The use of atomic energy does not involve consumption of oxygen and does
not lead to continuous increase of carbon dioxide in air. It is true that the amount of heat given off to water
in the operation of APP is about 1.5 times larger than in the operation of ordinary power plants (per unit
power) [15], which must be taken into consideration. This may cause undesirable heat contamination of
water. An American paper [17] was devoted to the thermal effects accompanying the operation of APP.
The growing reaction of the population and the society to the development of nuclear power was noted
at the Geneva conference. This problem undoubtedly requires the most careful attention and painstaking
analysis.
A meeting of experts on the ecological aspects and public recognition of atomic energy was held during
the conference. The representatives of the USSR, India, Spain, Italy, Great Britain, USA, France, Czec-
hoslovakia, Switzerland, Japan, and Argentina participated in the meeting. The experts produced a sum-
marized report of the conclusions in short statements (4-5 min) given by each of them on different problems.
The general problems of the effect of APP on the environment were discussed and APP and plants operating
with chemical fuel (the representative of the USSR reported on this) were compared; possible ejections from
APP into the environment, the problems of safety of the society, and also the possible ways of entrance of
isotopes into human organism, the safety standards, thermal effects of APP, possible accident situations
in atomic power plants, the reaction of the society to the use of atomic energy in daily life were discussed.
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Problems regarding the role of the scientist in the formation of correct public opinion at the epoch
of development of nuclear energetics, the fate of accumulating radioactive wastes, the basis of the existing
standards for ensuring safety, lowering of these standards, the possibilities of bringing a correspondence
between the obtained electrical power and the dose, etc were also touched upon.
The conference stressed that the task of the scientists consists in a careful investigation of the con-
tamination of the environment and an accurate prognosis of the contaminants considering all possible situa-
tions. The -role of the nuclear energetics in reducing the contamination of the environment by toxic sub-
stances from ordinary fuel was noted.
Thus, the development of nuclear energetics can ensure the conservation of adequately clean environ-
ment; the replacement of the energy produced from common fuel by atomic energy results in a decrease of
the contamination of the environment by toxic substances formed in the combustion of ordinary fuel.
LITERATURE CITED
1. IV Geneva Conference (1971), Paper No. 652 (Voz).
2. Environmental Contamination by Radioactive Materials, Proc. of a Seminar, Vienna (1969).
3. Environmental Aspects of Nuclear Power Stations, Proc. of a Symposium, New York (1970).
4. E. A. Fedorov et al., See [1], paper No. 686 (USSR).
5. F. A. Tikhomirov et al., See [1], Paper No. 685 (USSR).
6. S. Auerbach et al., See [1], Paper No. 085 (USA).
7. P. Kamath, See [1], Paper No. 536 (India).
8. T. Masatoshi et al., See [1], Paper No. 253 (Japan).
9. K. Aurand et al., See [1], Paper No. 399 (France).
10. E. Kunz et al., See [1], Paper No. 550 (Czechoslovakia).
11. V. M. Vdovenko et al., See [1], Paper No. 457 (USSR).
12. A. I. Burnazyan et al., See [1], Paper No. 429 (USSR).
13. B. Kahn et al., See [1], Paper No. 087 (USA).
14. A. Marko et al., See [1], Paper No. 160 (Canada).
15. E. Larson Clarence et al., See [1], Paper No. 723 (USA).
16. Yu. A. Izrael and E. N. Teverovskii, See [1], Paper No. 684 (USSR).
17. R. Foster, See [1], Paper No. 086 (USA).
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BOOK REVIEWS
NEW BOOKS
Modelirovanie i Optimizatsiya v Avtomatizirovannykh Sistemakh Upravleniya. [Simulation and optimi-
zation in automated control systems], G. N. Balasanov, Atomizdat, Moscow (1972).
The book outlines the basic methods of optimum process control based on computerization (linear and
dynamic programming, game theory and Monte Carlo techniques, operations research and queuing theory,
pattern recognition, theory of learning and adaptive systems, theory of optimum systems). The requisite
mathematical concepts are discussed.
The bulk of the examples cited refer to optimum control, and to mathematical description of technolo-
gical processes in hydrometallurgy and in chemistry. The methods described in the book are likewise ap-
plicable in the chemical, petroleum and petrochemical, metallurgical, and other diverse branches of in-
dustry.
The book is intended for students in technical colleges, for graduate students, and also for research
workers in planning institutes and industrial plants interested in production control problems.
Rukovodstvo po Vychisleniyu i Obrabotke Rezulitatov Kolichestvennogo Analiza. [Handbook on com-
putation and processing of quantitative analysis data], R. I. Alekseev and Yu. P. Korovin, Atomizdat,
Moscow (1972).
The book discusses the basic problems that workers in analytical laboratories have to confront in the
computation and statistical processing of the results of quantitative analysis of the composition of a sub-
stance.
The methods for computing and processing the analysis results are presented in "cookbook recipe"
format, with numerical examples, so that the techniques recommended can be utilized directly by analyti-
cal chemists regardless of their background, or lack of one, in mathematical statistics.
The book is written for analytical chemists working in all branches of the national economy.
Radiatsionnaya Biokhimiya Timusa. [Radiation biology of the thymus], E. F. Romantsev, V. D.
Blokhina, Z. I. Zhulanova, N. N. Kashchinko, and I. V. Filippovich, Atomizdat, Moscow (1972).
The book presents modern concepts on the physical and biochemical mechanisms operative in exposure
of the thymus, one of the most highly radiosensitive tissues found in the mammalian organism, to ionizing
radiations. This lymphoidal tissue is involved in immunological reactions which are of general biological
significance. The book goes into the mechanisms at work when the thymus is affected by ionizing radiations
and by antiradiation protectants. Information on the structure and function of the thymus is cited; distur-
bances in nucleic acid and protein metabolism and in the oxidative phosphorylation process in the thymus
in response to radiation exposure are described, as well as the way these processes are affected by the
presence of chemical radioprotectants.
The book is written for specialists in various lines of work interested in current problems in radio-
biology and radiation medicine, for health physicists and medical radiologists, and for senior biology ma-
jors in universities and medical institutes.
Svoistva Deformirovannykh Yader s K = 1/2. [Properties of deformed K = 1/2 nuclei], B. S. Dzhele-
pov, G. F. Dranitsyna, and V. M. Mikhailov, Nauka, Leningrad (1972).
The most frequently encountered deformed atomic nuclei are those whose ground states or excited
states have the quantum number K = 1/2. Several interesting features arise in the structure of the rotational
Translated from Atomnaya Energiya, Vol. 32, No. 4, pp. 278, 286, 292, April, 1972.
? 1972 Consultants Bureau, a division of Plenum Publishing Corporation, 227 West 17th Street, New York,
N. Y. 10011. All rights reserved. This article cannot be reproduced for any purpose whatsoever without
permission of the publisher. A copy of this article is available from the publisher for $15.00.
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bands, in the intensity ratios of the transitions, in the magnetic moments, etc., some to light. The mono-
graph reviews all of the available experimental material on the range of nuclides 150 < A < 190 and the
range A > 230, and discusses predictions of theory and inferences that can be drawn from the experimental
data. A generalized model and the results of a microscopic approach to the description of the properties
of deformed nuclei are utilized in the theoretical analysis.
The book is written for scientific-research workers and for graduate students working on the structure
of the nucleus.
Beta-Protsessy. Funktsii dlya Analiza Beta-Spektrov i Elektronnogo Zakhvata. [Beta-decay pro-
cesses. Functions for analysis of ,3-ray spectra and electron capture], B. S. Dzhelepov, L. N. Zyryanova,
and Yu. P. Suslov, Nauka, Leningrad (1972).
This book is devoted to the functions required for analysis and processing of experimental data on
nuclear )3-decay and capture of orbital electrons. The self-consistent potential of the atom is utilized in
the calculations, and the finite dimensions of the nucleus are taken into account at the same time. The
tabular data presented in the book make it possible to analyze the shape of allowed and forbidden /3-ray
spectra, to determine the value of the product ft, to find the relative probability of capture of electrons
from different shells and subshells of the atom.
The book is written for experimental physicists and theoretical physicists working with spectroscopy
of the atomic nucleus, and may also prove useful to graduate students specializing in nuclear physics.
Neitron-Neitronnyi i Neitronnyi y-Metody v Rudnoi Geofizike. [Neutron?neutron and neutron ? y
logging techniques in mining geophysics], E. M. Filippov, B. S. Vakhtin, and A. V. Novoselov, Nauka,
Novosibirsk (1972).
The book presents general information on neutrons, on neutron sources and neutron detectors, on
safety techniques, and provides a classification of relevant techniques, etc. Separate sections of the book
deal with laboratory, mine, and borehole modifications of those methods. Extensive material available on
these topics is reviewed and generalized systematically. Emphasis is placed on work done by the authors
in recent years.
The book will be of interest to staff members of scientific-research institutions, and to workers on the
staff of production planning organizations interested in applying nuclear physics techniques or interested in
learning about the potentialities of those methods.
Fiziko-Khimiya Redkikh Metallov. [Physical chemistry of rare metals], Nauka, Moscow (1972).
This collection of articles is devoted to the 60th birthday of the major Soviet metals scientist E. M.
Savitskii, Corresponding Member of the USSR Academy of Sciences, Disciples and colleagues of the scientist
generalize the results of their research in a series of articles and acquaint the reader with the latest achieve-
ments in the fields of the production technology of ultrahigh-purity single crystals of rhenium, vanadium,
tantalum, yttrium, scandium, gadolinium, ruthenium, and rhodium; production of pure metals and of alloys
of tungsten, molybdenum, niobium, etc. Results of the construction of over a hundred "composition vs.
property" phase diagrams for those materials are demonstrated. Results of determinations of new chemi-
cal compounds and of calculations of the Fermi surface, in order to ascertain the interrelation between the
structure and properties of the substances studied, are cited.
This publication is written for a broad range of research personnel; metals scientists, metallurgists,
machine designers and instrument designers engaged in the study, winning, processing, and utilization of
refractory metals and rare metals in industry, and also for students and instructors in chemical, metallur-
gical, and machinery design colleges.
Svobodnoradikal'noe Sostoyanie v Khimii. [The free-radical state in chemistry], Nauka, Novosibirsk
(1972).
This collection includes articles by leading Soviet scientists and foreign scientists devoted to the most
urgent topics in the physics and chemistry of free radicals. The vigorous development of this new branch
of chemical physics has made it possible to present convincing and unambiguous proof of the decisive role
played by free-radical processes in various radiation-chemical and photochemical reactions, in combustion
processes, and so forth. The collection of articles is dedicated to the memory of Academician V. V. Voe-
vodskii, whose work and activities played a decisive role in the development of various research trends
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in the physics and chemistry of free radicals. Some of the articles were written by disciples of V. V.
Voevodskii.
The book is written for a broad readership of research workers engaged in various branches of physi-
cal chemistry, and also for chemists, biologists, and physicists interested in the physics and chemistry of
free radicals.
Metallotermicheskie Metody Polucheniya Soedinenii i Splavov. [Metallothermic techniques in the pro-
duction of compounds and alloys], Nauka, Novosibirsk (1972).
Metallothermic methods for the production of intermetallic compounds and alloys prove to be more
convenient, technologically and economically, than methods based on direct fusion of the components, in
many instances of practical interest. This collection of articles reports the results and research findings
on metallothermic synthesis of intermetallic compounds and alloys in the reduction of oxides, halides, and
other substances. The optimum conditions for producing the compounds and alloys are ascertained, as well
as the physicochemical characteristics of the substances involved in the reactions; in some instances, at-
tempts are made to lay bare the underlying mechanism and the kinetics of the reduction process.
The book is written for theoretical chemists and for practising chemists.
Elektricheskoe Modelirovanie Yavlenii Teplo- i Massoperenosa. [Electrical simulation of heat-trans-
fer and mass-transfer phenomena], L. A. Kozdoba, Energiya, Moscow (1972).
This book deals with research on the heat-transfer conditions affecting machine parts, assemblies,
facilities, and rooms based on the use of such electrical simulators as resistor networks and combined
electrical simulating models. A procedure is presented for electrical simulation of linear and nonlinear
problems in nonstationary heat transfer and nonstationary mass transfer. Examples of solutions obtained
with electrical simulators are given for direct as well as inverse and inductive problems in heat condition.
The book is intended for engineers and research scientists, and may prove useful to technical college
students.
Uspekhi Fiziki Plazmy. Tom 1. Fizika Vysokotemperaturnoi Plazmy. [Translation of: Advances in
Plasma Physics. Vol. I. Physics of High-Temperature Plasma, edited by A. Simon and W. Thompson,
New York (1968)], Mir, Moscow (1972).
A team of leading American specialists on plasma physics (Dyson, Furth, Kroll, Fowler) decided to
undertake a complete review of the advances achieved in plasma physics and applications of plasma physics in
various fields. The book includes part of the material appearing in the first volume of the original Ameri-
can edition. Its contents cover a range of key problems in the physics of a high-temperature plasma re-
lated to emission, confinement, stability, and thermodynamics of an unstable plasma. The contents reflect
the current point of view on those topics, embodying generalizations of the contents of numercus papers
published up to 1968 only in the periodical literature.
The book is of considerable interest both to specialists in plasma physics and to research scientists
and technicians concerned with the topics discussed, and also to senior undergraduates majoring in related
branches of physics.
Magnitnye Poluprovodniki. [Magnetic Semiconductors, S. Methfessel and D. Mattis, translated
from the English original in: Handbuch der Physik, Bd. 18/1], Mir, Moscow (1972).
This is the first review to appear in the worldwide literature on the physics of magnetic semicon-
ductors, and sheds light on several topics of theoretical or experimental interest. The quantum mechanism
underlying the magnetic and electrical properties of magnetic semiconductor materials is discussed, and a
wealth of experimental data is presented.
The book will be useful to research physicists and engineers engaged in theoretical and experimental
studies of the properties and applications of magnetic materials, and also to readers interested in the phys-
ics of semiconductors, as well as to senior undergraduate students and graduate students in physics and en-
gineering physics technical colleges majoring in solid state physics.
Garmonicheskii Ostsillyator v Sovremennoi Fiziki: ot Atomov do Kvarkov. [Translation of: The Har-
monic Oscillator in Modern Physics from Atoms to Quarks, New York (1969)], M. Moshinsky, Mir, Mos-
cow (1972).
315
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M. Moshinskii, a professor at the University of Mexico, is a recognized authority in the field of ap-
plications of group-theoretical methods to quantum mechanics. The book, which is based on a lecture
course given by this author, is a unique monograph in which a single model is utilized in the investigation
of some crucial problems in theoretical physics. Some common vantage points are used to attack what
appear to be entirely dissimilar systems (molecules, atoms, molecules). The book is written in a clear
and lucid style, so that it is accessible and interesting not only to specialists but also to student physics
majors.
Metod Fazovykh Fu_nktsii v Teorii Potentsionaltnogo Rasseyaniya. [Translation of: Variable Phase
Approach to Potential Scattering], F. Calogero, Mir, Moscow (1972).
F. Calogero is one of the founders of a new and efficacious method for solving problems in quantum
mechanics, the method of phase functions. This method, developed in the past 10-15 years, enables scien-
tists to obtain many general results in quantum mechanics in a simple manner. The method is particularly
effective in dealing with scattering problems, and also in computer work.
Since this method has not yet filtered down to standard courses given on quantum mechanics, the book
will be useful to students specializing in the field of theoretical physics, and to instructors as well. It is
also needed by theoretical specialists, since the literature on this topic in the Russian language is meager.
Osnovy Kvantovoi Elektroniki. [Translation of: Fundamentals of Quantum Electronics, New York
(1969)], R. Pantell and H. Puthoff, Mir, Moscow (1972).
This is a monograph textbook on the fundamentals of quantum electronics. The book expounds a uni-
que approach to many of the relevant problems, including the latest achievements in the fields of nonlinear
optics, semiconductor lasers, and interaction of radiation with matter. The textbook contains problems
and exercises.
The book is written for senior undergraduates majoring in engineering physics, radio physics, and
electronics, and also for specialists in related areas who are interested in familiarizing themselves with
the fundamentals of quantum electronics.
Kataliticheskie Prevrashcheniya Uglevodorodov. [Translation of: Catalytic Conversion of Hydrocar-
bons, London (1969)], J. Germain, Mir, Moscow (1972).
The book discusses conversions of hydrocarbons belonging to different classes to heterogeneous cata-
lysts, and specifically discusses the oxidation of hydrocarbons, one of the most prominent processes in
modern photochemistry. Classification of catalysts (inorganic complexes, metals, acidic homogeneous
and heterogeneous catalysts, bifunctional catalysts) is presented, with analysis of the operating mechanisms
of the catalysts from the standpoint of modern concepts of physical chemistry and organic chemistry.
The book is of interest to physical chemists, organic chemists, and petroleum chemists working in
research institutes and in industrial plants.
Technika Radiacyjna. Podrecznik Akademicki. [Radiation engineering Academic textbook], Wydaw-
nictwa Naukowo-Techniczne, Warszawa (1971) [in Polish].
This text covers ionizing radiations used in radiation engineering, and describes isotope sources and
electrical sources of ionizing radiation, industrial radiation facilities, dosimetry, radiation polymerization
and irradiation of polymers, radiation conservation of foodstuffs, the use of radiation techniques in chemical
process technology, and also radiation effects in inorganic solids.
The book is intended for students majoring in chemistry in technical colleges.
Fizyka dla Inzynierow. Fizyka Wspolczesna. Czesc 2. [Physics for engineers. Modern Physics.
Part 2], Wydawnictwa Naukowo-Techniczne, Warszawa (1971) [in Polish].
The book presents general information on atomic physics, solid state physics, and nuclear physics.
The material is presented in concise format, and is richly illustrated.
The book is intended for engineers of various specialities, and also for students enrolled in technical
colleges.
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ANTIMONY, BISMUTH, ARSENIC, AND OTHER
ELEMENTS IN ORE BODIES AND HALOES OF A
URANIUM ? MOLYBDENUM DEPOSIT
G. I. Rossman, N. A. Stepanova, UDC 550.8
I. V. Sychev, and G. A. Tarkhanova
A geochemical assessment of radiometric anomalies of a uranium mineralization involves determina-
tion of the group of indicator elements of this mineralization within the anomalies. Lead and molybdenum
are typical indicator elements of many uranium deposits; the sensitivity of their determination by standard
analytical methods is fairly high [1]. However, in regions containing lead and molybdenum mineralizations
as well as a uranium mineralization, the use of only lead and molybdenum for assessing radiometric anom-
alies may lead to errors. In such cases one must use other indicator elements of uranium mineralization,
such as arsenic, bismuth, antimony, and thallium. However, as the sensitivity of determination of these
metals by standard methods is usually inadequate, their value as a criterion for prospecting has never been
recognized.
Our paper gives the results of an investigation of the distribution of arsenic, antimony, bismuth, tin,
mercury, and thallium in ores and country rocks of a typical uranium-molybdenum deposit. With the ex-
ception of mercury, these elements were determined by highly sensitive chemical and chemical- spectral
analysis methods [1-5]; mercury was determined by the atomic absorption method.
The sensitivity of these analytical methods is sufficiently high and the errors fairly small (Table 1),
which enables one to detect and trace the distribution of the elements in ores and the country rocks. The
threshold sensitivity of the analytical methods for arsenic, antimony, bismuth, tin, mercury, and thallium
is one order of magnitude higher than that of simple spectral analysis by the "spill" method.
The ore bodies of this uranium-molybdenum deposit are localized in a band of alternating volcanic
and sedimentary rocks, in acid tuffs, and occur in blocks bounded by disjunctive dislocations (Fig. 1).
These ore bodies, lying in different structural blocks, have been oxidized and leached to different degrees.
Samples were taken from borehole cores and the walls of underground mine workings by the procedure
in [1, 61; replicas of trench samples were investigated within the limits of the ore bodies.
TABLE 1. Sensitivity of the Analytical Methods
Element
Mean content of elements in acid
rocks, wt. 0/,
Threshold sensitivity, wt ,
Accuracy of determina-
tion, rel. 07,
Threshold of sensitivity in local
geochemical backgrounds
according to A.
P. Vinogradov
(1962)
local geochemi-
cal background
(1969)
spectral analysis
highly sensitive
method
spectral analysis
highly
sensitive
method
spectral analysis
highly sensitive
method
As
Sb
Ti
Bi
Hg
Sn
1.5.10-i
2.6-10-5
1-10-6
3-10-4
8-10-6
1.5-10-4
4-10-4
2 - 10-4
1-10-5
8-10-4
5-10-6
2-10-5
3-10-3
5.1O-4
5-10-5
1-10-5
1-10-2
1'10-5
1-10-4
1-10-4
1-10-5
2-10-5
1'10-7
1.10-5
120
80
80
85
200
120
20
32
30
33
50
33
7.5
2.5
50
1.25
2-106
100
0.25
0.50
1.0
0.025
2
0.5
Translated from Atomnaya Energiya, Vol. 32, No. 4, pp. 279-285, April, 1972. Original article
submitted May 6, 1971.
03 1972 Consultants Bureau, a division of Plenum Publishing Corporation, 227 West 17th Street, New York,
N. Y. 10011. All rights reserved. This article cannot be reproduced for any purpose whatsoever without
permission of the publisher. A copy of this article is available from the publisher for $15.00.
317
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zA,
318
g.
0 Cl)
0 ....... q-1
. 4-1
Cq 0 in
0 ,....i
0 in +' C17
0
0 CD CI) 0
c; C). 75 N
0 ''''' 0
"--? V r-I ^-
N 1 o
..
;; cl
-4, 0 ;/).? P
0 0 Cll a)
CD?
- Cll
F-1 bp
0 ''''-'
r?-i fa,
---
0 r-I o?
E g
a) cii
71> d ''''' g
1 ?
o cc) Cil N
4-A
0 ....Y 0
Ci) 0 C.) 0
:14 C5 0 .1-1
r0
????? (1)
0 0
4.1
"4 0
0 ;4' O cC'Ti
..-1
Cri
a.
...
P A
0
4.4 C.)
,--' Cr'... 0? 0
at
cri
0 0 0 MI
(1) O) $.4 g
no ? Q.) 0
X)
0 0
..0'
E CD C.) at
0 03 rtj
E P X
0 0
GO Ci)
4-4
0
0 CD
(:) 4-1 0
CG N
0 CI)
o co CD CV
>1 C'
E f.,
TS c= w
0 C: ,c1) 0
4 0 ?,-.
?-o
.a)_-'1- 0
L..-- 0
CD ...-)ril CD
,17.
P
..,?5., 9c; g 0
4-I A ..1.. r..4
0 0
0 0 Cj C9
04-4 [E
?,--, ,g? 0
-4.- +4 0
o
0 co.,
U) N
I
U) In
C.) i
C3F-I C:'?. Lt C?;\)c 1
r-I G.) ?s'
A-,
..-4 Li.4. 0 .1:2 ._1,)
CD
> c; ?CG
A g E I
?1-1 0
r-I
CD 4
?,-,
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Ores
r = - 1
r = +1
U-Mog
U-Snx
U-TLx
U-Cur
U- 8ix
(J-Asx
ti-Cu
(I-As
U-Pb
U-Sb
r =
Ores
r=+1
Cu-Cux
Cu-As*
Si-Ask
Cux-Asx
Sbx-Bix
Pb - Cux
Ho-As
Pb-Sb
MO-Cu
Ho- Pb
Pb- Cu
MO -Snx
Cu -Se
As -Snx
Cd-Sn'
r=-
U-Snx
Haloes of country rocks
r=+1
U-Sbx
U-Cul
U-811
U-Asx
U-Cux
(1-As
U-Pb
r =
Fig. 2. Pairwise correlations of elements
in the ore bodies and haloes: x denotes ele-
ments determined by the highly sensitive
method; r denotes the correlations.
It was established that simultaneously with uranium, molybdenum, lead, and copper, arsenic (more
than 100), antimony (more than 10), bismuth (about 100), mercury (about 80), and thallium (about 100) are
concentrated in the ores of the deposit.* However, the ores have low tin contents (0.1).
The data (Fig. 2, Table 2) clearly indicate a close relation between these elements (with the exception
of tin) and molybdenum and uranium (their minerals and the minerals present in paragenesis with them).
Antimony, arsenic, and bismuth are not only concentrated as admixtures, but form their own minerals, of
which the most typical is fahlerz. A much smaller part of the arsenic is also combined with arsenopyrite.
Mercury is concentrated as an admixture in fahlerz and is found as occasional segregations of cinnabar. A
considerable amount of these elements is present in collomorphic pyrite as an admixture.
These minerals were segregated at about the same time as uraninite. Hence it follows that the bulk
of the antimony, arsenic, bismuth, thallium, and mercury is related to the productive stage of the ore-form-
ing process. These elements may be regarded as mineralization indicators which form aggregation haloes;
this is confirmed by the data of Fig. 2. On the other hand, tin forms an evacuation (negative) halo.
Haloes of indicator elements are contained mainly in the beds of tuffs adjoining the ores; they are
larger than the uranium haloes above the site where the ore bodies taper out (the boundary of the haloes is
drawn along the lower anomalous values of the element concentrations, which differ markedly from their
background concentrations at a unilateral significance level of 0.05).
Haloes of thallium and mercury are also observed around the ore bodies, but their effective dimen-
sions have not been established. Judging from the existing data, ?the mercury halo reaches beyond the limits
of the bed adjoining the ore and is larger than the uranium, antimony, bismuth, arsenic, molybdenum, lead,
and copper haloes. The thallium halo is apparently comparable in size with the bismuth halo.
*The figures in parentheses are the concentration coefficients with respect to the local geochemical back-
ground.
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TABLE 2. Form of Occurrence of Uranium in Indicator Elements in Ores, the Surround-
ing Geochemical Haloes, and the Unaltered Rocks
Indica-
tor ?
ele-
ment
In ores
In haloes
In zone of oxidation and leach-
ing (halo)
In unaltered rocks
A
B
A
B
A
B
A
B
U
Uraninite
Sooty uraninite
Secondary ura-
nium min-
erals
?
Sooty ura-
ninite
?
Sooty ura-
ninite
Secondary
uranium
minerals
(silicates,
arsenates,
phosphates)
Manganese hydro-
xides
Gypsum
Kaolinite
_
Orthite
Monazite
Zircon
Mo
Femolite
Molybdenite
Molybdenum
black
Uraninite
Skolite
Calcite
Hematite
Molybdenum
black
Calcite
Chlorite
Powellite
Wulfenite
In all secondary ?
uranium mineralst
Manganese and
iron hydroxides
Kaolinite
Pyrite
Ti
?
Femolite
Pyrite
Marcasite
?
Pyrite
Iron hydroxides
Manganese hydro-
xides
?
As
Arsenopyrite
(a little)
Fahlerz
(a little)
Chalcopyrit ?
Skolite I
CarbonateIof
Quartz I
Pyrite
?
Uranospinite
Torbenite _
In all secondary
uranium miner-
ala (a little in
uranium silicates
Powellite
Malachite
Pyrite
In minerals
the ?
electro -
magnetic
fractions
Sb
Fahlerz
Uraninite
Hematite
Pyrite
Femolite
?
#
Urani.um?molyb- _
denum black
Torbenite
Malachite
Manganese
hydroxides
Pyrite
Hg
Cinnabar
Fahlerz
?
D
?
?
?
Bi
Fahlerz
Uraninite
Hematite
Tennantite
Early pyrite
Tennantite
Hematite
Sooty urani-
nite
?
Secondary urani- ?
um phosphates
Malachite
In minerals
of the
electro -
magnetic
fractions
Note: A) Intrinsic mineral forms; B) as admixtures in the minerals; the principal form of the minerals is shown in
boldface. An asterisk denotes uranium in sorbed form; a dagger denotes an admixture of molybdenum, characteris-
tic of secondary uranium minerals of U?Mo ore bodies; a question mark denotes that the forms of occurrence
have not been revealed.
A characteristic feature of these haloes is the zonality of the structure,* which is expressed in a
regular variation of the dimensions of the haloes, the correlation coefficients of the indicator elements,
their mean contents, and the linear productivities characterizing the different hypsometric levels, which
replace one another to the dip of the ore-adjoining structure. The most objective expression of the zonal
distribution of the elements is given by the values of the linear productivities (Fig. 3, Table 3).
*It is not our intention to examine the nature of this zonality. A study of this very complex problem is the
subject of special investigations of the diitribution of a radiogenic admixture of Pb2" and uranium in cross
section of ore bodies and the surrounding haloes. According to the data of our comparative investigations
on isolated ore bodies of deposits with different degrees of oxidation, the primary zonal distribution of the
elements developed above the sites where the ore bodies taper out is very similar to that in the zones of
oxidation and leaching of ore bodies of similar primary composition [7].
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TABLE 3. Change in Values of Linear Productivities of Haloes of Uranium, Its Com-
panion Elements, and Their Ratios
Bore_
tole 'the
No.
Depth to
dip
of the
structure
Linear productivities. Mo b
Ra.tios of linear producti-
vities
Geological position of
sarnpling site
U
As
Sb Bi
Sn
As/U
Sb/U
Bi/U
Sn/U
2675
60
0,0375
0,0665
0,035
0,00290
0,0142
8,9
4,7
0,38
1,9
Surface beaching zone
2632
80
0,0117
0,0382
0,028
0,0006
0,0167
3,27
2,4
0,054
1,43
2656
140
0,0247
0,0393
0,0163
0,0004
0,0065
1,59
0,66
0,016
0,26
Zane of leaching and oxi-
dation of primary ores
(upper parts of the ore
bodies)
2578
160
0,0240
0,0296
0,0150
0,0010
0,0078
1,23
0,63
0,044
0,32
2634
180
0,0247
0,0355
0,0147
0,00062
0,0061
1,44
0,59
0,025
0,25
2533
320
0,0624
0,0236
0,0221
0,00091
0,0053
0,38
0,35
0,015
0,1
Zone of ore body with oc-
currence of regeneration
processes (lower parts of the
ore body)
2488
340
0,0103
0,0272
0,0146
0,00022
0,0109
2,64
1,46
0,022
1,0
2519
400
0,0027
0,0251
--
--
__
9,3
__
__
Zone of development of
haloes below the boundary
of tapering out of the ore
body
2517
420
0,0029
0,0079
0,0083
0,00051
0,0056
2,7
2,86
0,19
1,93
2625
460
0,0015
0,0224
0,0094
0,00106
0,0049
15,0
6,3
0,70
3,28
Zwie of influence of under-
lying ore body
2622
465
0,0048
0,0155
0,0118
0,00119
0,0071
3,23
2,5
0,25
1,5
2620
480
0,0019
0,0248
0,0530
0,0037
0,0058
13,6
23
1,9
3,2
It will be seen from the data that prefential deposition of arsenic, antimony, and bismuth is corre-
lated with the upper horizons of the haloes, located above the ore body.
In contrast with this, the linear productivity of uranium in the haloes is maximal for the level of the
middle and lower parts of the ore body. The tin content in the region of its "negative" halo is somewhat
higher above the upper parts of the ore body.
An analysis of the change in the linear productivity ratios As/U, Sb/U, Bi/U, Sn/U to the dip of the
ore-adjoining bed reveals that these ratios regularly decrease as one approaches the ore body. The maxi-
mal gradient corresponds to the As/U ratio.
It should be noted that there is a slight change in the sign of the gradient of the values of the linear
productivities As/U, Sb/U, Bi/U, and Sn/U in the haloes located below the tapering out of the ore body.
Here we again observe an increase of the ratios of the linear productivities of arsenic, antimony, bismuth,
and tin to uranium. Such a change in gradient indicates the presence of another, deep ore body, the upper
parts of the haloes of which were superimposed on the lower parts of the haloes of the investigated ore body.
In fact, a hitherto-unknown blind U - Mo (uraninite -hematite) ore body was discovered 100 m below the point
at which the investigated ore body tapers out (see Fig. 1).
The data enable us to infer that arsenic, antimony, and bismuth are accumulated in the zones of oxida-
tion and leaching of the mineralization (see Fig. 3, Table 3). This is confirmed both by their absolute linear
productivities and by the ratios of the productivities to those of uranium.
Removal of uranium from the oxidation and leaching zones is proved by comparative investigations of
lead isotopes and uranium contents [7].
The place of mercury and thallium in the scheme of zonal structure of the haloes has not been finally
established. The existing data indicate that high concentrations of mercury and thallium are characteristic
of the upper parts of the haloes developed above the ore bodies. Another characteristic feature is the
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U n.10-4 As n.10-4
0 100 200 300 400 500 600 0 100 200 300 400 500 600
i1410 III ir
100
200
300
400
500
Sb n10"
0 100 200 300 400
11,??
100
200
300
400
500
Fig. 3.
and their
n.10-4
100 200300 400
0i n.10-5
0 100 200 300 400
I I I
?
100?...............:_o__
200'
300
300.
400
500
5,0
m
0 1 5 6 7 8 9
10 11
12 13
-
4
,FL,
11
->x .
/4
/
As a
?
1 3
%
300
400
500
?
:),,.?,-..&-0.,..,.
. --xii.42-x 44 -
U
1,5
Cn
Bi
GiEl 2 CI 3
Change in linear productivities of haloes of uranium, its companion elements (a)
ratios (b) to the dip of the U-Mo ore body (see Table 3): 1) ore zone exhibiting
oxidation and extraction processes; 2) ore zone exhibiting regeneration (cementation) pro-
cesses; 3) intersection of the central part of the ore zone by the exploratory drill-holes.
asymmetric structure of the haloes of these elements and their extensive occurrence in the strata above
the ore body.
Thus the ores and adjoining rocks of this U-Mo deposit, localized in volcanic rocks, contain anoma-
lous concentrations of antimony, arsenic, thallium, and mercury. With respect to uranium, these elements
are concentrated in haloes above the point at which the ore bodies taper out to the rise, and persist during
weathering of the country rocks.
LITERATURE CITED
1. 0. 0. Kablukov et al., Use of Dispersion Haloes of Uranium and Its Companion Elements in Prospect-
ing for Hydrothermal Uranium Deposits. Handbook [in Russian], Nedra, Moscow (1964).
2. Symposium: Chemical Analysis of Mineral Raw Material [in Russian], No. 8, Nedra, Moscow (1965),
p. 104.
3. Ibid., p. 165.
4. Symposium: Chemical Analysis of Mineral Raw Material [in Russian], No. 11, Nedra, Moscow (1968),
p. 43.
5. N. A. Stepanova, L. I. Zemtsova, and T. A. Butkina, Papers of the Seminar "Determination of
Microimpurities? [in Russian], Vol. 1, MDIPT im F. E. Dzerzhinskogo, Moscow (1968), p. 3.
6. D. A. Vigdorovich et al., Provisional Instructions for Geochemical Prospecting for Pyrites - Poly-
metallic Deposits in the Presence of Very Thick Unconsolidated Deposits [in Russian], Seriya Obmena
Opytom, No. 34, ONTI VITR (1960).
7. G. I. Rossman et al., Izv. Akad. Nauk SSSR, Seriya Geol., No. 1 (1971).
322
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RADIATION-INDUCED GROWTH OF
POLYCRYSTALLINE a-URANIUM
M. A. Vorob'ev, V. F. Zelenskii, UDC 621.039.548.3
E. A. Reznichenko, and A. S. Davidenko
Anisotropic growth of the components of polycrystalline a-uranium crystallites lies at the basis of
radiation-induced growth of that uranium phase. Consequently, the problem of what mechanism underlies
radiation-induced growth of polycrystalline uranium reduces to ferreting out the relationship between the
growth of single-crystal uranium and the growth of polycrystalline uranium, while ignoring the effect of the
grain boundaries and of the dislocation structure of the polycrystalline uranium on the growth rate.
This problem arose earlier in calculations of what is termed the growth index, characterizing the de-
pendence of radiation-induced growth of polycrystalline uranium on the degree of definition of the texture
[100] or [010] (see references [1, 2]), and also in the discussion of the possible effect impurities might have
on radiation-induced growth of uranium single crystals. The problem is that the investigation was carried
out on polycrystalline specimens, and the results had to be extrapolated to the case of single crystals in
order to reach definitive conclusions [3, 4].
Currently existing methods for calculating the growth index [1, 2] based on the assumed linear rela-
tionship between texture and growth rate, fail to take into account interactions between the crystallites, so
that they are not of much help in understanding the true relationship between the growth of single-crystal
uranium and the growth of polycrystalline uranium. A plausible mechanism underlying radiation growth of
polycrystalline uranium, with the interaction between variously oriented crystallites in the irradiated poly-
crystal taken into account, has been put forth in [5].
It was shown that the interaction between crystallites constituting a polycrystalline aggregate and ex-
posed to radiation is capable of bringing about changes in the initial orientation of the crystallites when
adaptive plastic deformation of the crystallites takes place by twinning. It is proposed that this will sub-
sequently bring about the same rate of deformation of all the crystallites in the direction of the overall ani-
sotropy of the material, while at the same time determining the observable rate of radiation-induced growth
of the polycrystal as a whole. The change in the initial orientation of the crystals is a necessary prere-
quisite for radiation-induced growth of polycrystalline uranium, in conformity with such a twinning mecha-
nism accompanying adaptive plastic deformation, and also as a consequence of it.
It is not clear, however, just how radiation-induced growth of uranium must come about in the case
where deformation by twinning is hampered, or is absent altogether, at elevated irradiation temperatures
and at a low rate of deformation. For example, it has been pointed out [5] that only 10% of the adaptive
plastic deformation takes place by twinning even at ?196?C, and that the bulk of the deformation occurring
does so by gliding. Without completely ruling out the possibility of some reorientation of the crystals in
response to irradiation, we can anticipate that this is not the sole cause of the common and identical rate
of deformation of all the crystals in the direction of growth of the polycrystal. An alternative mechanism
linking the radiation-induced growth of a-uranium single crystals and polycrystals is discussed in the pre-
sent article.
Mechanism Underlying Radiation-Induced Growth of Polycrystalline a-Uranium. We consider a poly-
crystalline specimen of uranium exhibiting a certain degree of anisotropy. Under irradiation, the interac-
tion between the growing crystals brings about a state of affairs where the crystals will deform, indepen-
dently of their orientation, and at the same rate in the direction of the overall anisotropy of the specimen.
Translated from Atomnaya Energiya, Vol. 32, No. 4, pp. 287-291, April, 1972. Original article
submitted April 19, 1971.
C 1972 Consultants Bureau, a division of Plenum Publishing Corporation, 227 West 17th Street, New York,
N. Y. 10011. All rights reserved. This article cannot be reproduced for any purpose whatsoever without
permission of the publisher. A copy of this article is available from the publisher for $15.00.
323
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Suppose that the external stresses have no effect on the radiation growth processes in the single crystal [5].
Then the rate of growth of the crystallites comprising the polycrystalline aggregate can be assumed equal
to the rate of growth of a free single crystal for those irradiation conditions. The effective rate of radia-
tion growth of the polycrystal in the direction of overall anisotropy will be determined by the relationship
between the rate of radiation-induced growth of the crystals with preferred orientation and the rate of com-
pensating plastic deformation. In order to determine the rate of the compensating plastic deformation, we
consider those factors contributing to that deformation. Clearly, the deformation is brought about by re-
straining stresses on the part of crystals with other than preferred orientation. These stresses can be
determined from the condition
(801+ (8p. d)i = (8 g)2 + (8p. d)2;
where the subscript 1 refers to crystals with preferred orientation, the subscript 2 refers to the remainder
of the crystals; g and ip.d are the rate of radiation-induced growth and the rate of plastic deformation, re-
spectively; 01, G2 are the stresses generated in the interaction between crystals 1 and crystals 2; f is the
ratio of the transverse cross section area of crystals 2 to the area of transverse cross sections of crystals
1.
If the expression for the dependence of the rate of plastic deformation of crystals 1 and 2 on the stress
is known, then we can find the effective rate of radiation-induced growth of the polycrystallite once we have
determined 01 and 02. Irradiation is known to generate appreciable internal stresses in polycrystalline
uranium through the interaction between crystals of different orientation. In a completely isotropic ma-
terial, these stresses bring the material to the familiar "superplasticity" state, when the rate of strain
can be described by the Cottrell formula [6]
8
where 0 is the applied stress, and GT is the yield limit of the material.
However, in the case of an arbitrary polycrystalline aggregate, the dependence of the rate of plastic
deformation of the crystals on stress must be a different one. The reason is that the interaction between
crystals 1 and 2 differs from the interaction of crystals in a completely isotropic material. Because of the
difficulties associated with attempts to take the interaction of crystallites in an arbitary polycrystal into
consideration, we deal here only with the simple case when the expression can be obtained for the rate of
plastic deformation, in order to illustrate the actual possibility of achieving radiation-induced growth of the
polycrystal in line with the scheme proposed here.
For that purpose, we consider a simplified model of a polycrystalline specimen exhibiting a certain
degree of anisotropy in one of the directions. Considering only a stack of identical crystals with three
principal orientations [100], [010], and [001], we represent the polycrystalline aggregate in the form of an
isotropic matrix with crystals of some one orientation, say [010], "disseminated" in it. In that case, if the
density of crystals having the orientation [010] in the selected direction is assigned the value n, then the
density of crystals having each of the remaining orientations will be (1 - n)/ 2. The area of the transverse
cross section of the isotropic matrix will therefore be 3(1 -n)S/2, and that of the "disseminated" crystals
will be (3n-1)S/2, where S is the transverse cross section area of the entire specimen.
Recalling that the isotropic matrix experiences no growth under irradiation, but does deform at a rate
= a ?g/ crT in response to the effect of growth stresses on the part of the "disseminated" crystals, the ef-
fective rate of radiation-induced growth experienced by the polycrystal can be found by solving the system:
? ? 02 ?
ei+Eg =
Cra F 3n 1 02-0; (1)
,g2 0. In that case the rate of deformation can
be represented as the difference between the rate of deformation iso of the crystal in an isotropic medium
and the rate of deformation due to restraint by two crystals having the orientations [100] and [001] (4estr):
8 = 8 iS0? 8restr,
(2)
grestr= estr feg.
We assume that the coefficient k' is independent of the stress. We find this coefficient from the con-
dition that irestr = g in the absence of external applied stress, since the crystal having the orientation
[010] is then acted upon by the stress crestr = crT:
Writing Eqs. (2) in expanded form, we get
and hence
?k'cr,+eg-= ?8g;
2 ?
k' = Ty; eg.
a ? 2 ?
? eg aeg
GT
3 ?
k = TriT eg.
In sum, the dependence of the rate of deformation of a crystal under irradiation and "disseminated"
in an isotropic matrix, has the form
3 ?
81 = crieg e-F g ?
Using this formula to solve system (1), we get
3 ? 41. 62 ?
? aieg. + 4,8g = ? Eg?
aT aT
Cr20.83.
s
It is interesting to note that if the Cottrell formula is used
in the case of rate of deformation of irradiated crystals
"disseminated" in an isotropic matrix, the solution of the
system of equations (1) for the radiation growth coeffi-
cient of the polycrystal will become
G. 3n -1
G.
poly 2 isg
A similar expression for Gipoiy can be derived, with this model of a polycrystalline specimen, when we
resort to the procedure of calculating the x-ray growth index [1] and the growth index based on combined
measurements of the linear expansion coefficient and the electrical resistivity [2]. By relying on a rough
approximation which leaves the complicated nature of the interaction of crystals in the polycrystalline spec-
imen out of account, we can derive expressions for the growth indices currently in use.
Figure 1 shows a predicted Gipoiy curve obtained by using Eq. (3) at Gisg = 1000. We make use of
measurements results at 80?C borrowed from [5] to afford a comparison between predicted and experimental
cripoly values. The texture of the specimens was brought about by different cold deformation of uranium
wire previously quenched from the 3-phase. In this case, it appears that we can anticipate formations of
the simplest texture, one analog of which is the model of a polycrystalline specimen used in the work de-
scribed here. Experimental values were plotted together with the predicted theoretical curve in Fig. 1.
The agreement between predicted and experimental values is reasonably satisfactory. In particular, the
predicted growth coefficient in the region of small textures increases to a slighter extent, and in the region
of large textures to a greater extent, than the linear dependence indicates. When n 0.83, the radiation
growth coefficient of the polycrystalline uranium attains values typical of a single crystal.
Consider some of the remarks relating to the proposed mechanism of radiation-induced growth of the
polycrystalline a-uranium. The expression for the rate of Cottrell creep was used for the quantitative cal-
culations of Gipoiy at the irradiation temperature 80?C; Anderson-Bishop analysis [7] can be used in the
case of higher temperatures. In both cases the polycrystalline aggregate is treated as an assemblage of
distinct crystals whose properties determine the properties of the polycrystal. This explains the need to
take that factor into account in the case of irradiation of polycrystalline uranium in the temperature range
where intercrystal effects begin to play a role.
An idealized model of a polycrystalline aggregate was selected for quantitative calculations of the
radiation growth coefficient of polycrystalline uranium with a different degree of texture definition. Clearly,
in a real uranium polycrystal the distribution of the poles of the principal crystallographic directions will
differ from the one considered here. The radiation growth coefficient of polycrystalline uranium calculated
on the basis of Eq. (3) might consequently differ from the one measured experimentally in the case where a
different relationship prevails between the density of the poles [100] and [001]. The theoretical growth co-
efficient will be somewhat too high, if the density of the [100] poles is greater than the density of the [001]
poles, and will be somewhat too low if the density of the [100] poles is lower than the density of the [001]
poles. Nevertheless, the discussion of the simple model of a polycrystalline aggregate does prove useful
for throwing light on the overall regularities of radiation-induced growth in polycrystalline uranium.
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With those remarks in mind, we can draw the following inferences with the aid of the proposed mech-
anism, in analyzing the possibility fhat radiation-induced growth of polycrystalline uranium will occur.
1. Radiation-induced growth of polycrystalline uranium must be described without assuming mutual
reorientation of the component crystals, and while taking as point of departure the presence of internal
stresses generated by the interaction of differently oriented crystals subjected to irradiation. These con-
cepts can then be used subsequently in quantitative calculations of the effective radiation growth coefficient
of polycrystalline uranium specimens, in a manner similar to the procedure followed in the simplest case,
provided formulas describing deformation of the crystal under conditions where radiation-induced growth
is restrained to different extents are derived.
2. The radiation growth coefficient of polycrystalline a-uranium is a nonlinear function of the degree
of initial anisotropy of the material. Conclusions on the effect of alloying on radiation-induced growth of
uranium single crystals, obtained on the basis of linear extrapolation of the results obtained for weakly
textured specimens [3, 4] must not be accepted as sufficiently validated, for that reason.
3. Radiation-induced growth of polycrystalline uranium is associated with the generation of internal
stresses, which at the same time constitute the primary cause of accelerated creep in irradiated uranium.
Deformation of polycrystalline uranium due to the combined effect of texture and an external applied load
cannot be treated, consequently, as the result of a simple superposition of those phenomena.
LITERATURE CITED
1. E. Sturcken and W. McDonnell, J. Nucl. Mat., 7, 85 (1962).
2. J. Stobo and B. Pawelski, J. Nucl. Mat., 4, 109 (1961).
3. W. McDonnell et al., J. Inst. Metals, 97, 26 (1969).
4. J. Lehman et al., Radiation Damage in Reactor Materials, Vol. II, Vienna (1969), p. 413.
5. S. Buckley, Institute of Metals, Symposium on "Uranium and Graphite," Paper No. 6, London (1962).
6. A. Roberts and A. Cottrell, Phil. Mag., 8, 711 (1956).
7. R. Anderson and J. Bishop, Institute of Metals, Symposium on "Uranium and Graphite," Paper No.
3, London (1962).
8. A. S. Zaimovskii et al., 2nd Geneva International Conference on the Peaceful Uses of Atomic Energy,
1958, Report No. 2191 (USSR).
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CALIBRATION OF GAMMA ? GAMMA DENSITOMETERS
K. Umiastowski UDC 550.83
The gamma?gamma method, which is one of many geophysical methods of investigating the proper-
ties of rocks, is based on measuring the intensity of gamma radiation scattered in the medium. Depending
on the relative position of the radiation source, the detector, and the investigated medium, one distinguishes
between 27r geometry, 4r geometry, and 27r borehole geometry (Fig. 1). The results of gamma? gamma
measurements are used to determine the rock density, the effective atomic number (Zeff), and the content
of heavy elements. The gamma? gamma method should be used only for density studies even if the obtained
results are usable also for other cases.
Calibration Curve for Gamma?Gamma Densitometers. According to the principle of similitude [1,
2], the radiation intensity I, measured at a distance r from the source, can be written as
I (r, p,)=N f (%C) ,? (1)
where r is the distance between the source and detector, p is the rock density, x = pr, N is a parameter
depending on the source activity and detector efficiency, and is a parameter depending on other conditions
of measurement. If the probe length is ro and if other conditions of measurement remain unchanged, the
recorded radiation intensity depends solely on the density of the material:
/ (0= TCN I fro, P, =1\r'i (P),
(2)
where N' = N
The curve f(p) = N*r2I(x) is called the calibration curve. It reflects the dependence of the count rate
on the density of the material.
The shape of the calibration curve was calculated with the aid of the Monte Carlo method [3]. The
theoretical curves are shown in Fig. 2, where I denotes the number of quanta n through a unit surface S
per unit time:
I=
a
Fig. 1. Schematic representation of 27r geometry (a), 47r geo-
metry (b), and 2r borehole geometry (c).
(3)
Institute of Nuclear Physics of the Mining and Metallurgical Academy, Cracow, Poland. Translated
from Atomnaya Energiya, Vol. 32, No. 4, pp. 293-296, April, 1972. Original article submitted October
14, 1971.
328
C 1972 Consultants Bureau, a division of Plenum Publishing Corporation, 227 West 17th Street, New York,
N. Y. 10011. All rights reserved. This article cannot be reproduced for any purpose whatsoever without
permission of the publisher. A copy of this article is available from the publisher for $15.00.
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r21
5
4
3
2
10-
2
10-
I
ii
Nis
..z.
mI
1--
od
kill
_ili
p
-no
oss-
1p.
OIL
111
:a
r.,
= =
=WE=
Ia
inliti
70 20 30 40 50 60
x,q1cm2
Fig. 2
r2
40-3
14
i2
10
8
6
2
0
i
?
x
A
X
\
X
?
? ?,,,,,.
X
? ""ii
?
X
2 3 4 5
Fig. 3
6 7 x 10
Fig. 2. Theoretical calibration curve for different materials and source energies: 1)
0.66 MeV, water; 2) 0.66 MeV, aluminum; 3) 1.25 MeV, water; 4) 1.25 MeV alum-
inum; 5) 0.28 MeV aluminum.
Fig. 3. Theoretical calibration curves for Hg203 (s), Cs137 (A), and Co66 (x). x is ex-
pressed in quantum free path units (70).
The calculations were made for aluminum (Z = 13) and water (Zeff = 7.4).
By expressing the distance between the source and detector in free path units (A 0) of a quantum with
source energy E0, the shape of the calibration curve can be made practically independent of the source en-
ergy (Fig. 3).
Let us introduce the new quantity Ap = k0. The probe length is then expressed in dimensionless
units = rp/ ?T. Expression (1) then becomes
I = f (x, t),
where the function f()4,, t) is independent of the source energy.
N*r21,
410-5
12
10
8
4
2
0
A
0
2 3 4 5
7
A?
?0
'40
CUD
49
48
425
Fig. 4
Fig. 4. Universal calibration curve. x is given in 70 units.
to 1.0 for Hg203 (0), 0.87 for Cs137 (A), and 1.03 for Co60 (s).
Fig. 5. Energy dependence of A0, Ap, and k.
45 475 1,0 1,25
E, MeV
Fig. 5
The factor N* is equal
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(4)
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1.21
102
8
6
2
101
8
6
4
X X
IIII=
AMINE
11=1
NMI
NMI
MIMI
111111111111111111
?
? 2
4)4.. ?
.k 0
?
2 3 4 5 6 7 8 m==5-
4
Fig. 6. Universal calibration curve. Experimental data
adopted from different sources: Co60 (e), Cs137 (A), Hg203
(El), and Se75 (x).
By selecting proper normalization factors N, the curves for radiation sources of different energies
can be superposed so that the result is a single universal calibration curve independent of the source en-
ergy as shown in Fig. 4.
The dependences of the 2to, A p, and k values on the y-quantum energy is shown in Table 1 and in
Fig. 5.
Comparison with Experimental Data. The function f(x) can be found experimentally with models of
different densities p and constant probe length ro or with models of a fixed density po and probes of differ-
ent lengths r.
To check their validity the theoretical results were compared with experimental data. The results in
[4] were obtained with a graphite model in a 21r geometry. The density of the model material was 1.75 g
/cm3. The probe length varied from 20 to 60 cm. The measurements were conducted with a scintillation
counter. Cs137 and Co50 sources were employed. The results of [5-8] were also considered.
With properly selected normalization factors (x, expressed in A13 units), all experimental points lie
on practically the same curve (Fig. 6). The data of Fig. 4 are also plotted on this figure. It is seen that
the theoretical and experimental data are in close agreement. The experimental data were obtained in
27r and 27r borehole geometries. The radiation source energy ranged from ?200 keV (Se75) to 1.33 MeV
(Con. Both gas-discharge and scintillation counters were used. The chemical composition of the models
differed appreciably. A more detailed comparison of experimental data with expression (4) is given in [10].
Calibration of Gamma?Gamma Densitometers. The shape of the calibration curve depends on the
measurement geometry, the discriminator threshold, and on the chemical composition of the medium [9].
For provisional calculations in which an accuracy better than 15% is not required one can use the
theoretical calibration curve shown in Fig. 7. This curve was drawn through 80 points. To find the norma-
lization factor, measurements should be made on one model only with a density pa. The factor for the
given source energy (E0) and probe length r0 is then con-
verted into density in accordance with the expression
r2/
XpEo
10-2 (5)
8 ro
6 The use of theoretical calibration curves with probes
other than those for which the calculations were originally
2
io8
6
TABLE 1. Energy Dependence of A0,
A and k
13,
9
xo, g /ems
X g/cms
Fig. 7.
2 3 4 5 5 7 8-L
Universal calibration curve for
aluminum.
E, MeV
up
1,25
0,66
0,28
17,8
13,2
9,2
0,83
0,90
0,96
14,8
11,9
8,8
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made can introduce an error not exceeding 15%. This conclusion is based on the calculation of the relative
,imean deviation of experimental dat6.. from the theoretical ones. The theoretical curve was calculated for
the following conditions: 50 keV discrimination threshold, source and detector collimation angle equal to a
27r solid angle about the normal to the surface of the medium, detector efficiency equal to 100% and inde-
pendent of radiation energy.
If higher accuracy is required for probes of different construction, the calibration curve must be found
experimentally. This can be made with a small number of models provided gamma radiation sources of dif-
ferent energies are used. The calibration curve can be plotted for a wider range of densities than those of
the models available. The calibration procedure is explained below using a specific example. Let the probe
length be r = 20 cm, and let models have densities p = 1.5, 2.0, and 2.5 g/cm3. Using these models with a
Cs137 source (E0 = 0.66 MeV, Ap = 11.9 g/cm3) we obtain intensities at points corresponding to xi = 2.52,
X 2 = 3.36, and x3 = 4.2 calculated from
roP
x ?
Xp (E) ?
Then, using a Co60 source (E0 = 1.25 MeV, )p = 14.8 g/cm3) and a Hg203 source Op = 8.8 g/cm3), we ob-
tain I at the points 4.4 = 2.03, x5 = 2.70, x 6 = 3.38, x7 = 3.40, x8 = 4.54, and x9 = 5.68. The values of I
at the points x2, x 6, and 3t7 are used to normalize the results obtained with three different sources (since
it is practically impossible to find sources of the same activity). Converting then x into densities p for a
cesium source in accordance with
xXP 11.9 g/cm3
?
P 7.0 20cm '
we obtain finally p4 = 1.21, p5 = 1.61, p6 = 2.01, p7 = 2.02, p5= 2.7, and p5= 3.37 g/cm3.
Thus, using three models with densities between 1.5 and 2.5 g/cm3, we obtained seven points on the
calibration curve corresponding to densities between 1.21 and 3.37 g/cm3.
A second densitometer calibration technique follows from the expression [11]:
3,5
Ab (pr) sn ?aPr?biZeq
e
(6)
where Ab, n, a, 131 are factors that depend on the conditions of measurement. Substituting into this expres-
sion
pr =X
P X
we have
(AbXn) ?(cck yx?biZ3'5
xne P cq
Denoting (Ab Aril) = A, a Ap = B, and equating (8) with (1), we have
f(u) = xne?Bx?bi4e
(7)
(8)
(9)
The factors n and B do not depend on the source energy as the function f(x) is valid for any source energy.
Finally, the intensity of recorded radiation is expressed as
I e?B x? 61445 ? Axn (10)
r2
where the factors n and B depend only on the probe construction and do not depend on the radiation source
energy. The factors A and b1 depend on both the probe construction and the source energy.
Making measurements on Nm models and using Ni sources with different energies we should find 2Ni
+ 2 factors in (10) (the two factors B and n, and also the two factors A and b1 for each source). These fac-
tors are found from NinNi measurements. Hence follows the condition
or
NmNi >2Ni+ 2
2
Nin >2+ Ni ?
(11a)
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Thus, at least four models are required if only a single source is available for the unknown factors.
If the calibration is made with two sources, the number of models necessary is reduced to three.
Obviously, the use of several gamma radiation sources with different energies allows a significant
improvement of the calibration curve accuracy (provides a greater number of calibration points with the
same number of models), and makes it possible to plot the calibration curve for a wider range of densities
than that of the models employed.
LITERATURE CITED
1. Sh. A. Guberman, At. Energ., 10, 369 (1961).
2. J. Czubek, Report CEA-R 3099 (1966).
3. K. Umiastowski, Nukleonika, 15, No. 1, 37; No. 2, 215; No. 3, 259 (1970).
4. K. Umiastowski, Report CEA-R 4028 (1970).
5. J. Tittman and J. Wahl, Formation Density Logging (Proc. Conf. Nuclear Geophysicists), Cracow
(1962), p. 339.
6. F. G. Baembitov, I. A. Gulin, and I. G. Dyatchin, Prikl. Yadern. Geofiz., No. 17, 284 (1958).
7. V. A. Artsybashev, Izv. Vuzov; Geol. i Geofiz., No. 9, 102 (1964).
8. E. M. Filippov, Prikl. Geofiz., No. 17, 231 (1958).
9. K. Umiastowski, Nukleonika, 13, No. 4-5, 413 (1968).
10. S. Rychlicki and K. Umiastowski, Nukleonika, 15, No. 1, 47 (1970).
11. J. Czubek, Report INP No. 715/1.
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NEUTRON DIFFUSION IN A POLARIZED PROTON MEDIUM
Yu. N. Kazachenkov and V. V. Orlov UDC 621.039.512.4
Methods have been recently developed for preparation of highly polarized (up to 80%) proton targets.
Because of the strong spin? spin dependence of neutron?proton interaction the diffusion of neutrons in such
media should differ from diffusion in nonpolarized targets. It suffices to say that the neutron?proton in-
teraction cross section is ?3 b for parallel spins and ?38 b for antiparallel spins, and is independent of en-
ergy for neutrons of up to ?60 key. This difference remains significant up to 4 MeV even if it diminishes
with increasing energies. When nonpolarized neutrons are scattered on polarized protons they become
partially polarized in the direction of the proton polarization vector thus reducing the scattering cross sec-
tion for subsequent interactions; this means that the transparency of polarized proton shields is higher than
that of similar nonpolarized shields.
Let us now derive equations describing neutron diffusion in a polarized proton medium. First let us
find expressions for the scattering cross section and for the neutron polarization after scattering. Before
scattering the neutron and proton are described by the density matrix pin:
P in = (1 ? Pioi) (1 + P2a2),
(1)
where p is the polarization vector, a is a vector whose components are the Pauli matrices; the subscripts
1 and 2 refer to the neutron and proton respectively.
It is known that the density matrix of particles after scattering can be expressed in terms of the den-
sity matrix before scattering and the interaction amplitude:
Pout = Pin f + ?
For energies up to -40 MeV the amplitude of neutron scattering on protons has the form [1]
i= (-4-3 A + t) + (A ? f s) clia21 (3)
where fs and ft is the scattering amplitude in the singlet and triplet states respectively. For neutron en-
ergies up to 10 MeV, the only contribution comes from the s wave, and the triplet and singlet scattering
amplitudes are written as
(2)
, 2i8 t
i" 2ik
where k is the wave vector.
The scattering phases obey the equation [2]
1 k2rs,t
kctg6?
as, t 2 '
(4)
(5)
where as, t is the scattering length, and rs, t is the effective interaction radius; their numerical values are
given in [3].
The mean value of any operator L acting in the spin space of the exit channel is given by
(L) Sp (LPout)
SPPout
(6)
Using the expressions (1)-(4), after simple but quite time-consuming manipulations, we obtain expres-
sions for the interaction cross section of polarized neutron and polarized protons, and for the polarization
vector of scattered neutrons pi:
Translated from Atomnaya Energiya, Vol. 32, No. 4, pp. 297-300, April, 1972. Original article
submitted May 6, 1971.
? 1972 Consultants Bureau, a division of Plenum Publishing Corporation, 227 West 17th Street, New York,
N. Y. 10011. All rights reserved. This article cannot be reproduced for any purpose whatsoever without
permission of the publisher. A copy of this article is available from the publisher for $15.00.
333
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da 3 1 1
= Iftr+Tlf,12+ ?4 ( I ft 12-1 isl2) (PIN); (7a)
da 1 2+ Reftfs)Pi+ 1 1
Regis) P2 ?T
PiTirc?r(lit1 Im f s [P1P21? (7b)
lithe neutrons were not polarized before, then in the course of diffusion they can only acquire a
polarization colinear with p2 (which can be easily verified considering successive collisions) and the last
term in (7b) turns identically to zero.
Let us divide all neutrons into those having spins parallel to p2 and antiparallel to p2. The probability
of scattering with and without the change of neutron polarization can be easily determined from (7):
where
w++?T+wl:
T w2; = I w2,
W2 =
I Reft fs+
311112+1 fs12?(.
I /112+ Ref tfs-
31 ft12+11812-1-(
f t12?Reftfs) P2
I f t12 ?I fs II) P2
t 12? Reit f s) P2
lit 12-1/.12) Pz ?
(8)
(9)
In (8), the first and second upper signs indicate the neutron polarization before and after scattering
respectively, p2 = 1P21.
In addition to protons, practical proton targets also contain nuclei of other elements whose polariza-
tion, however, is so negligible [4] that they can be said to be nonpolarized. On being scattered by these
nuclei neutrons are depolarized. If the neutron energy is such that the principal contribution Into scattering
comes from the s wave, the probability of spin reversal by scattering on nonoriented nuclei is [5]
2 ('+l) Ip (a+?a_)2
Q = 2 bi) 3 (2/p +1) RI p +1.) af,+? I pap '
where ap+ and ap_ are scattering lengths of neutrons on the p-th isotope along channels with total spins
Ip + 1/2 and Ip? 1/2 respectively, bp = Esp/Ese is the relative probability of neutron scattering on the
p-th isotope nuclei except hydrogen (Elap = 1); the sum is taken over all nonpolarized isotopes in the target,
Esp is the macroscopic scattering cross section on the p-th isotope, and Ese is the macroscopic scattering
cross section on all isotopes with nonoriented nuclei.
Let us divide all neutrons into two groups: neutrons with spins parallel to the veetor p2 (denoted by a
"+" sign) and with spins antiparallel to 132 (denotedby "-"). Taking the balance of both these groups of neu-
trons, and allowing for the possibility of neutrons passing from one group to the other as a result of scatter-
ing, we obtain the following system of equations (scattering on the nuclei of all isotopes except hydrogen is
assumed isotropic):
(10)
(QV) F+ (r, SZ, E) + I+ (r, E)F+ (r, g, E)= S (1W dE' (wn(E'?>
x (r, E') F+ (r, E') w++ + 1;,(r, E') F- (r, fr, E') w-+]
?Ese(r, E') (1 ? Q) F+ (r, Q' E') +Ise(r E') QF- (r, E'));
(5217)F- (r, E)+E- (r, E) F- (r, Q. E) = (152' dE' (E' ?? E Q' ft)
x [E, (r, E') F- (r, SY, E) w-- +Es+, (r, E) F+ (r, Sr, E') W] + Ese(r, E') (1?Q)
X F- (r, 52, E')+ Ese(r, E') QF (r, 51, E'))
(11a)
(1 lb)
where E+ and E- is the macroscopic interaction cross section of each neutron group respectively, En and
E-en is the macroscopic scattering cross section of each group of neutrons on oriented protons,
P ;
4= Esn (1-
Esti is the macroscopic neutron scattering cross section on nonpolarized protons, wn(E' E, f2' S2) is
the indicatrix of neutron scattering by protons.
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Generally speaking, in considering the diffusion of fission neutrons in the upper energy groups one
must take into account the change iri polarization resulting from spin? orbit interaction. However, as
shown in [6], the corresponding corrections are quadratic with respect to the spin? orbit interaction param-
eters which, in turn, are much smaller than the parameters of spin? spin neutron?proton interaction. It
can be thus assumed in the first approximation that spin? orbit interaction does not affect the neutron trans-
port in polarized neutron shields.
As already noted before, the albedo of a polarized proton shield should be lower than that of a similar
nonpolarized shield. As an example of calculating this effect we have determined the change in Keff of a
plutonium slab reactor caused by polarization of a water reflector (existing polarized proton targets con-
tain many crystallization molecules of water). Since the lifetime of one generation increases with reflector
thickness, and since the effect is small in thin reflectors, we have selected a reflector 6 cm thick. After
considering various concentrations of nuclei and different core dimensions, we have accepted the following
reactor dimensions and element concentrations:
1.715 cm,
dcore=
ppu,?= 0.5.1024 nuclei/cm3,
PBro = 0.149. 1024 nuclei/cm3,
d ref= 6 cm.
p016 = 0.0335 ? 1024 nuclei/cm3,
--= 0.067.1024 nuclei/cm3,
The first three lines refer to the core, the last three to the reflector. The calculations were made in a
26-group P2 approximation for a reactor with polarized and nonpolarized reflectors. The results indicate
that Keff of the reactor with a polarized reflector is 2.7% less than with a nonpolarized reflector. The life-
time of one generation / was found to be ?2 .10-8 sec.
If the reactor is used in a pulse mode, the minimum halfwidth of a neutron pulse At is 1 ?sec. The
numerical calculations were made by Yu. G. Kaufman.
The reactivity of a reactor with a polarized proton reflector can be rapidly increased by applying a
magnetic field normal to the direction of proton polarization. In such a case the spins of protons and neu-
trons will start to precess in opposite directions and the nucleons will "forget" their former polarization.
Let us estimate the dependence of this effect on the magnetic field. The change of the average particle
momentum in the beam, and thus of the polarization p in a domain of magnetic induction B, obeys the equa-
tion of motion (see, e.g., [7])
op
= iPB1'
(12)
where y is the gyromagnetic ratio of the particle. From (12) follows that the change of the scalar product
of neutron and proton polarization, pn and pp, in time is described by
d (11/41)p)
dt (7n ? 'VP) BiPnPpl,
where yn and yp are the gyromagnetic ratios of the neutron and proton.
As mentioned above, before the field is applied pn and pp are colinear; when the magnetic field is
applied their precession will take place in the same plane.
Thus
PnPp = Pn I pp cos 0;
B [pnpp] B I pnj I pp I sin 0
(13)
(14a)
(14b)
(the field is assumed to be normal to the plane of rotation of the polarization vectors).
Solving equation (13) under the conditions (14), for neutrons polarized at the instant t = 0 along Pp we
have the expression
PTIPP = I Pn IN COS (rn Vp) Bt.
(15)
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d
Fig. 1. Calculation of neutron polariza-
tion.
As before, let us divide all neutrons into two groups: those
that at the instant t = 0 were polarized along or against the
direction of polarization of protons. Expression (15) then
becomes
PnPp =I PP I RI -4- I Pn ) COS (y?- yp) Bt
- (1 -1 Pn ) COS (17? -1)p) MI.
(16)
The scalar product of neutron and proton polarization
of the beam at a given point of space can be represented as
the average scalar product of all neutrons arriving at this point and proceeding in the given direction. This
circumstance makes it possible to evaluate the change in the scalar product of polarizations due to the mag-
netic field.
Consider an infinite homogeneous polarized medium in which there acts a magnetic field normal to
the direction of polarization. Let neutrons diffuse along the x axis with a velocity v (see Fig. 1). The
scalar product of neutron and proton polarization can then be written as
PnPp -
00 x
tiPpi [1-1-(-1)7nIPnil S d cos xx exp [?E S dx' {1+ (-1)m a [Pp I COS Zen
Tn=-.0 0 0
E 0.+(-1]. pr, II S dt exp [? E S dx' {1+ (-1)m a cos ax' }1
m=0 0 0
(17)
where x = tv, ?yt = (yn- yp)B/v, 3 = Ipp I / (yn- yp)B, a = p,and Ep is the macroscopic polariza-
tion cross section.
Solving the integrals in (17) and considering strong magnetic fields only (0 ? 1), we have
PnPp
1 a
Y p )2 B2I Pn I I PP I ? 4(7? y)2B 2 i
I P ) I2'
k Y - ? p
1+
u22:2 v2E2
(18)
It should be noted that the scalar neutron and proton polarization product will decrease with increas-
ing magnetic fields faster than follows from Eq. (18) since the absolute value of neutron polarization IPI
also decreases. The reduction of polarization effects with an increasing magnetic field as given by Eq.
(18) can be thus regarded as an upper bound. This is particularly rapid in magnetic fields for which
(vn-- V p) B
vl
1.
In the case of a water reflector, for example, this quantity equals unity for a magnetic induction of
13,000 G and a neutron energy of -1 MeV.
The design of reactors with polarized proton reflectors will certainly meet with technical difficulties
(construction of large polarized targets (-1 liter), application of cryogenic techniques, use of very strong
pulsed magnets). These difficulties are however not fundamental, and the parameters of a pulsed reactor
should be considerably much more attractive than those of conventional reactors.
LITERATURE CITED
1. V. F. Turchin, Slow Neutrons [in Russian], Gosatomizdat, Moscow (1963).
2. L. D. Landau and Ya. A. Smorodinskii, Zh. Eksp. Teor. Fiz., 14, 269 (1944).
3. V. S. Barashenkov, Interaction Cross Sections of Elementary Particles [in Russian], Nauka, Moscow
(1966).
4. V. I. Lushikov, Yu. V. Taran, and F. L. Shapiro, Yadern. Fiz., 10, 1178 (1969).
5. 0. Halpern and M. Tohnson, Phys. Rev., 55, 898 (1939).
6. Yu. N. Kazachenkov, Yadern. Fiz., 1, 763 (1965).
7. Yu. G. Abov, A. D. Gul'ko, and P. A. Krupchitskii, Polarized Slow Neutrons [in Russian], Atomiz-
dat, Moscow (1966).
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THE ENERGY LIFETIME AND DIFFUSION OF PARTICLES
IN "TOKAMAK" SYSTEMS
Yu. N. Dnestrovskii, D. P. Kostomarov, UDC 621.039.643
and N. L. Pavlova
In our previous papers [1-3] we studied the energy balance in a plasma on the basis of the neoclassical
thermal conductivity for ions [4, 5] and a phenomenological description of the anomalous conductivity and
thermal conductivity of the electrons. The results of the calculations of the ion and electron temperatures
and the current-diffusion time in the plasma are found to be in good agreement with experiments. At the
same time the experimentally measured energy lifetime TE turns out to be several times smaller than the
calculated value. This means that an additional departure of energy from the plasma exists which was not
taken into account in [1-3].
The present paper considers two models which allow the results of the theory and experiment to be re-
conciled. According to the first model the additional departure of heat takes place due to the elevated ther-
mal conductivity of the electrons. Since in [2, 3] the thermal conductivity of the electrons was already
anomalous, such a still further elevated thermal conductivity is naturally called "superanomalous." The
calculations showed that for a fixed superabnormality factor (equal to 7) the experimental and calculated
values of TE coincide in a wide range of variation of plasma currents and density.
According to the second model the additional energy losses take place via the ions. Whereas in [1-3]
the hea
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