SOVIET ATOMIC ENERGY VOL. 41, NO. 1

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• Publication Date: January 1, 1977
• Content Type: REPORT

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Russian Original
January, 1977 ,
SATEAZ 41(1) 605\--686 (1976)
SOVIET
:OMIC
ATOMHAFI 3HEP1141,
(ATOMNAYA iNERGIYA)
? TRANSLATED FROM RUSSIAN
CONSULTANTS BUREAU, NEW YORK ,
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1
IS
tOVIET
ATOMIC
ENERGY
Soviet Atomic Energy is abstracted or in-
dexed in Applied Mechanics Reviews, Chem-
ical Abstracts, Engineering Index, INSPEC-
1 Physics 'Abstracts and Electrical and Elec-
tronics Abstracts, Current Contents, and
Nuclear Science Abstracts.
Soviet Atomic Energy is a cover-to-cover translation of 'Atomnaya,
Energiya, a publication of the Academy of Sciences of the USSR.
An agreement with the Copyright Agency, of the USSR (VAAP)
makes available both advance copies of the Russian journal and
original glossy photographs and artwork. This serves to decreaie
the necessary time lag between publication of the original and
publication of.the translation ,and helps to improve the quality
of the latter. The translation began with the first issue of the
Russian journal.
Editorial Board of Atomnay- a Energiya:
Editor: M. D. Mi,Ilionshchikov ?
Deputy Director
I. V. Kurchatov Institute of Atomic Energy
Academy of Sciences of the USSR
Moscow, USSR
Associate Editor: N. A. VlesoV
r
A. A. Bochvar I V. V. Matveev
\ N., A. Dollezhal' M. G: Meshcheryakov
-
V. S. Ftirsov V. B. Shevchenko
. I. N.,Golovin ' V. I. Smirnov, ,
V. F. Kalinin , - , A. P. Zefirov
1
'
A. K. Krasin
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SOVIET ATOMIC ENERGY
A translation of Atomnaya energiya
January, 1977
Volume 41, Number 1 July, 1976
ARTICLES
Natural Nuclear Reactor in Oklo (Gabon) ? A. K. Kruglov, V. A. Pchelkin,
M. F. Sviderskii, N. G. Moshchanskaya, 0. K. Chernetsov, and
CONTENTS
Engl./Russ.
Yu. M. Dymkov
605
Studying the Interaction of Molten Fuel with Sodium in the Active Zone of a Fast
Reactor ? Yu. K. Buksha, Yu, E. Bagdasarov, and I. A. Kuznetsov
612
9
Estimate of the Corrosion of Zirconium Alloys under Operating Conditions
? V. V. Gerasimov, A. I. Gromova, and V. G. Denisov
617
14
Effect of the Presence of Kh18N1OT Steel on the Corrosion Stability of Zirconium
Alloys ? V. F. Kon'kov, A. N. Sinev, and A. A. Khaikovskii .
621
17
Determination of the Content of Tritium and Krypton in VVER Fuel Elements and a Study
of Their Distribution in the Preparatory Operations of Fuel Elements for
Reprocessing ? A. T. Ageenkov, A. A. Buravtsov, E. M. Valuev, L. I. Golubev,
Z. V. Ershova, V. V. Kravtsev and A. F. Shvoev 0000000000 ? . ? ? . ?
627
23
Mathematical Models of the Neutron Distribution in a Reactor
? P. T. Potapenko
630
25
DEPOSITED ARTICLES
The Distribution of Moving Holes in a Material with Sources of Gas Atoms
? V. V. Slezov and V. I. Ryabukhin
636
31
Effect of the Distribution of Neutron Flux in the Active Zone on Irradiation
Intensity of Uranium Radiation Contour ? A. V. Putilov, M. A. Markina,
N. A. Robakidze, V. A. Rudoi, E. S. Stariznyi, and N. P. Syrkus . . . .......
637
31
Deactivation of Weakly Active Discharge Waters by Fibrous Ionites
? G. L. Popova, R. I. Radyuk, A. S. Syltanov, and B. E. Geller
638
32
Errors of a Fluctuation-Type Reactor Power and Period Meter ? A. I. Sapozhnikov
and V. I. Kazachkov
638
33
Thermodynamic Properties of Liquid Alloys of Actinides and Lanthanides
? V. A. Lebedev
639
33
LETTERS
Numerical Buildup Factors and Average y-Spectrum Energy behind Scattering
Media ? A. A. Gusev
641
35
Quantitative Relationships of Tantalum, Radioactive Elements, and Zirconium
in Rare-Metal Ores ? G. N. Kotel'nikov .
643
36
Analysis of the Spectral Composition of X-Ray Signals Backscattered
from Various Surfaces ? F. L. Gerchikov
645
38
Estimating the Nuclear Safety of Systems of Subcritical Assemblies by the
Interaction-Parameter Method ? V. D. Laptsev and Yu. I. Chernukhin
647
39
Texture in Oxide Films on Zirconium and Binary Zirconium?Tin and
Zirconium?Titanium Alloy Single Crystals ? F. P. Butra and
A. A. Khaikovskii
650
42
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CONTENTS
Relative Yields of Xenon Isotopes in the Photofission of 237Np and 235U
? K. A. Petrzhak, E. V. Platygina, Yu. A. Solov'ev, and
(continued)
Engl./Rus.
V. F. Teplykh
654
44
Measurement of a (E) = o-c(E)/crf(E) of 233PU for 0.007-eV-12-keV Neutrons
? Yu. V. Ryabov
655
45
Yields of 73As and 74As in Nuclear Reactions with Protons, Deuterons, and a Particles
? p. P. Drnitriev and G. A. Molin
657
48
Nondestructive Analysis of Thin Surface Layers of Materials for Hydrogen Content
? I. P. Chernov, V. V. Kozyr', and V. A. Matusevich..
661
51
Anomalous Isotope Composition of Xenon and Krypton in Minerals of the Natural
Nuclear Reactor ? Yu. A. Shukolyukov, G. Sh. Ashkinadze, and
A. B. Verkhovskii ? ..
663
53
COME CON DIARY
Cooperation Notes
667
56
CONFERENCES AND SEMINARS
39th Session of the Scientific Council of the All-Union Institute of Nuclear Research
? V. A. Biryukov
671
59
Seminar on the Prospects for Development of Secondary Power Sources
in Nuclear Instrument Construction ? A. F. Belov
675
61
Conference of Experts of the International Atomic Energy Agency (IAEA) on
the Treatment of Radioactive Wastes ? M. K. Pimenov
677
64
The Second Session of the Soviet?American Coordination Commission on Fast
Reactors ? V. B. Lytkin and E. F. Arifmetchikov
679
65
Soviet?American Seminar on the Safety of Fast Reactors ? Yu. E. Bagdasarov,
682
67
Seminar on General Purpose and Special Accessories for Nuclear Power Stations
? G. V. Kiselev
685
69
The Russian press date (podpisano k pechati) of this issue was 6/23/1976.
Publication therefore did not occur prior to this date, but must be assumed
to have taken place reasonably soon thereafter.
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ARTICLES
NATURAL,NUCLEAR REACTOR IN OKLO (GABON)
A. K. Kruglov, V. A. Pchelkin,
M. F. Sviderskii, N. G. Moshchanskaya,
0. K. Chernetsov, and Yu. M. Dymkov
UDC 539.17:549.514.87
When in the middle of 1972 the workers of the French Atomic Energy Commission prepared an opera-
tional uranium reference, they observed an abnormally low concentration of the 235U isotope. Search work
and other investigations have established that the anomaly stems from ore of the Oklo site (Gabon). A careful
investigation of the ore-bearing region has shown that the 235U concentration in the ore of the site reaches only
0.621% and even only 0.440% [1-3]. Such substantial isotope anomalies were observed for the first time in nat-
ural beddings.
Investigations of the isotope shifts which occur in nature have been for a long time the object of intent
attention of Russian scientists. Various suggestions have been made to explain the small isotope shifts which
reach less than 20% of the Clarke ratios. The explanations were based on natural isotope fractionation, bio-
geochemical separation, radioactive release in a decay, etc. [4, 51.
However, in addition to the small shifts, a spread of the isotope concentration reaching 103-1010% was
established in the case of He, Xe, Ne, and Sm [6,7]. Even samples with a ratio 2391)11/U = 10-6 [8] were found;
244PU was found in natural samples in amounts exceeding the calculated amounts 106-108 times [6]; a 235U ex-
cess of the order of 0.3-0.02% was observed [1,2,6,7].
Various hypotheses, among them the hypothesis of an annihilating explosion [9], were made to explain
the Oklo effect and the above anomalies. The hypothesis of a natural nuclear reactor is the best explanation
of the isotope anomalies [3,10]. The hypothesis is corroborated by the fact that 2 billion years ago the 235U
TABLE 1. Minimal Critical Masses for
Enriched Uranium
235U concn
(%) in the ?
material
Critical mass (kg)
of 35Uof
Critical mass (kg)
u
heterog.
system
with
reflec.
homog.
systern
without
reflec.
heterog.
systemsystem
with
reflec.
homog.
without
reflect.
0,8
150
00
18750
oo
1,6
15
oo
1500.
on
2,0
3,8
6,0
190
300
3,0
2,31
4,0
78,7
133
4,0
2,0
3,3
50
82,5
5,0
1,8
2,8
36
56
6,0
1,75
2,6
20
43
7,0
1,5
2,5
21
36
8,0
1,4
2,3
18
29
9,0
1,3
2,2
14
24
10,0
1,2
2,1
12
21
20,0
1,05
1,9
5,25
9,5
30,0
1,0
1,8
3,33
6,0
40,0
0,95
1,75
2,4
4,4
50,0
0,9
1,7
1,8
3,4
60,0
0,87
1,65
1,45
2,75
70,0
0,86
1,60
1,23
2,29
80,0
0,85'
1,55
1,06
1,94
90,0
0,82
1,50
0,91
1,67
100,0
0,8
1,45
0,8
1,45
Translated from Atomnaya Energiya, Vol. 41, No. 1, pp. 3-9, July, 1976. Original article submitted
September 19, 1975.
This material is protected by copyright registered in the name of Plenum Publishing Corporation, 227 West 17th Street, New York, N.Y. 10011. No part
of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying,
microfilming, recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $7.50.
605
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TABLE 2. Long-Lived and Stable Isotopes Which Accumulated upon Neutron Irradiation of the
Uranium in the (n, 'y) Reaction
Z
Initial material
Reaction
Intermediate
isotope
Isotopes accumulating
upon irradiation
Isotopes forming after
reaction
Isotope
preserved to
now
half-life
(years)
quantity
(g)
reaction
type
cross sec-
tion, b
name
(0
a)
....
21 4
a.) 71
v ..c
quantity
.(g)
a)
...
...
-.
T'a
-d
quantity
(g)
decay type
name
half-life
(years)
quantity
(g)
type of
decay
name
quantity
(g)
288u
28573
mu
Plom
231pa
227Aa
282pu
240pu
242pu
236U
343Am
Remark.
4,51? 109
7,1 3. 108
2,5.105
7,52.104
3,45.104
22
24360
6580
3,74.105
2,39.107
7950
Uranium
972
28
0,052
0,013
0,003
6,5-10-5
2,65
0 , 8
0,086
2,82
1,73.10-5
quantity
n, y 2,75
n, y 101
n, y 105
n, y 23
n, y 200
n, y 800
n, y 300
n, 7270
n, y 20
n, y 6
n, y 100
1 kg;
239U
-
-
237Th
232Pa
228AC
-
241Pu
243Pu
2377.7
244Am
neutron
is 23,4min
_
_
p 25,64h
p 1,32 t
6,13
p 13,32 y
Id 4,98 fl
f3 6,75 d
{3 10,1 h
flux 1021
239Np 2,35 d
23813 2,39.10
Y
28503 7,13.103
Y
234Pa 3,45.104
23213 73)1,6 y
228Th 1,91
240Pu 65801
241Arn 458
_
243AM ,950y
2 37NP 2,14 ? 108
244cm 18)1,4 y
neutrons/cm2;
2,65
2,82
0,005
3,6.10-4
5,9.10-4
5,3.10-5
0,8
0,216
1,73.10-3
0,014
1,73.10-5
irradiation
fi 239P11
a 236U
a 23413
a 231Pa
cc 288Pb
a 208pb
a 232Th
a 237Np
a 239PU
a 2371IP
CC 236U
time
24360 0,154
2,32.107 2,81
7,13.108 0,005
3,45.104 2,9.10-4
Stable 6,2.10-4
Stable 4,8?10-5
1,39.1010 0,84
2,14.108 0,213
24360 1,7 ? 10-3
2,14 ? 108 0,014
2,39.107 1,67.10-4
105 years.
a 23517
a 232Th
a 287Pb
a 207ph
tab,lesoRpb
table 222pb
a 232Th
a 208B1
a 28473
a' 289Bi
a 232Th
0,435
2,55
0,044
3,2.10-4
6,2.10-4
4,8.10-5
0,77
0,187
1,63.10-3
0,012
1,6.10-4
concentration reached 3.64% in place of the present 0.72%, because the half-lives of 235U and 28U are 0.707
and 4.5 billion years, respectively.
Table 1 lists the values of the minimal critical mass for an isotope mixture dependent on the
235U concentration [11] in heterogeneous and homogeneous systems. It was established in experiments that
for an at most 3% uranium enrichment, the critical mass decreases when the uranium is heterogeneously
distributed in a moderator. A self-sustaining chain reaction cannot occur when the enrichment is less than
0.7% in heterogeneous systems or less than 1% in homogeneous systems. It follows from Table 1 that the
critical mass amounts to 79 kg for 3% 235U concentration in the case of heterogeneous systems; the critical
mass is 133 kg in the case of homogeneous systems, which corresponds to 222 kg for ore with a 60% ura-
nium concentration in homogeneous systems.
, The geological structure of the site, the conditions of its formation, and the presence of water as a
moderator favored the development of the reactor in the crust and guaranteed critical reactor conditions
for large uranium quantities. The scientists of the entire world took interest in this unique phenomenon to
which the International Symposium of June, 1975, in Libreville was devoted. The Soviet Union participated
in the Symposium [121. In the last few years ample experimental data confirming the hypothesis of a natu-
ral nuclear reactor were accumulated.
We present in the present paper some results of isotopic, radiochemical, and mineralogical investi-
gations of the ores of the Oklo site. The samples which we have are distinguished by both uranium and
235U concentrations. The scheme of the sample picking is shown in Fig. 1.
Figure 1 shows that samples 1410, 1414,and 1418 are of the zone of the chain reaction and are char-
acterized by high uranium concentration (in excess of 40%) and low 235U concentration; the other samples
are from the zone of contamination. Based on data concerning the age of the site and the degree of 235U
burnup, the neutron flux of the natural nuclear reactor could be calculated; the flux proved to be 1021
.2150.
0.42-
0,46 -
1150 - 1410
454-
-
14081/
0,58 -
- - 1406
462 - 140412
456
470 -
1401
'-
130 140 150, 50
1414
14.15
1422
606
-70 .
- 60
-50
-40
-30
423
- ZO
: 10
170 180 190 200 210
Distance (cm)
220 230 240
Fig. 1. Scheme of sample pick-
ing: - - -) U, ) 235u.
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2354 %
44
45
46
47
45
0 2 4 6 8 10
Th ? 103 concentration, g /gU
Fig. 2
Fig. 2. 232Th amount per gram of
burnup.
Fig. 3
uranium in dependence upon the 235U
Fig. 3. Prismatic pseudomorphs and granular accumulations of uraninite (white)
and phyllite (gray). Polished section (x200).
neutrons/cm2. This value was used to calculate the accumulation of certain isotopes in the natural ura-
nium (Table 2).*
It follows from Table 2 that 232Th, 2 0 pb 2 09 pb 2 09B ? ,
and 235U can be the end products which reach
the present from (n,)/) reactions. We note that 208Pb can result from both 232Th and 232U decays. The 208Pb
quantity resulting from the 232U decay is negligibly small relative to the 208Pb from 232Th and cannot be
detected at the present time.
The 232Th quantity formed in the reaction 235U(n, 236u a 232Th 208Pb is about 0.3% of the ura-
nium quantity. The fact that the 235U quantity, which was formed again by 238PU decay, can reach several
per cent deserves particular attention.
The fact that thorium is present in samples with high (>40%) uranium concentration suggests that the
thorium resulted from the reaction 235U (n, y)236u 232Th. Table 3 lists the results of uranium, thorium,
and lead determinations made on several samples. The dependence of the amount of thorium per gram
uranium upon the degree of the 235U burnup is linear (Fig. 2), which means that the thorium can accumulate
by the conversion 235U (n, T)236u a 232Th. This process can occur only in a high neutron flux. When the
straight line is extrapolated to the abscissa, the straight line does not pass through the coordinate origin,
and, this obviously means that there exists a small thorium concentration which is not associated with
uranium minerals.
The burnup of 238U, 235U, and 232Th during the activity of the natural nuclear reactor must reduce the
concentrations of 206Pb, 110 and 2?8Pb which are the end products of the decay of the mother isotopes.
The later the nuclear reaction began, the greater the amount of lead corresponding to the initial undis-
turbed amount of the mother isotopes. This process must be very clearly noticeable in the case of 207Pb,
because the burnup of the 235U isotope is most clearly noticeable in the ore of the Oklo site.
*Most of the investigations of the scientists of the French Atomic Energy Commission dealt with the ac-
cumulation and analysis of isotopes resulting from fission.
TABLE 3. Concentrations of Uranium, Thorium, and Lead in Sam-
ples of the Oklo Site.
Sam-
ple
No.
uranium
concen-
tration
(%)
235U
235u con-
centra-
tion
(g/g)
Thorium concentration
Lead concen-
tration
238u+23su
%
g/g
uranium
%
g/g
uranium
1410
51,25
0,539
2,77.10-3
(0,32?0,02)
6,25.10-3
6,17
0,12
1414
44,1
0,4166
1,83.10-3
(0,38?0,02)
8,64.10-s
5,05
0,115
1418
58,9
0,569
3,36.10-3
(0,32?0,02)
5,34?10-3
6,13
0,104
1402
2,87
0,657
1,89.10-4
(0,06)
?
?
?
1406
6,4
0,0126
3,9.10-4
(0,14)
?
1,23
0,192
1422
5,0
0,5098
2,55.10-4
(0,066)
?
1,33
0,266
607
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Fig. 4 Fig. 5
Fig. 4. Grains of uraninite (bright gray) and nasturan from coffinite (gray) and the argil-
laceous mass. Polished section, immersed (x2000).
Fig. 5. Coffinite (dark gray) replaces uraninite grains (bright gray and gray phase); the
bright dots are galenite grains. Polished section, immersed (x2000).
Unfortunately, radiogenic lead was several times removed while the site existed. Therefore only
about one third of the initially accumulated lead was preserved in the samples taken from the reaction
zone. The problem can be indirectly solved by comparing the isotope composition of the radiogenic lead
determined by mass spectrometry with the calculated composition. The data of the chemical analysis
listed in Table 3, the age of 1.7 billion years (accumulation time), and the formulas
207pb 230U (0.235t ?1); mph = 238tf(ex230 _1);
zospb = 232Th (0.232t ?1).
were used for the calculation.
A comparison of the results of an isotope analysis performed on three samples from the reaction
zone did not render a clear result. The average concentration of the 207Pb isotope in the samples exceeded
the calculated concentration by 5-10%. The excess was about 20% in the zone of contamination. Samples
taken from the contaminated zone are distinguished by a rather low 235U concentration (0.6%) and a rela-
tively high uranium concentration (5-10%) and an even higher lead concentration per gram of uranium.
All this may indicate that uranium isotopes migrated several times from the reaction zone into the
contaminated zone and in this migration a large deficit of 235U and of radiogenic lead existed. The migra-
tion took place to various degrees and in various amounts which cannot be accurately assessed. The
608
Fig. 6. Uraninite
crystals. Polished
section, immersed
(x 2000).
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Fig. 7. Block structure of uraninite crystal.
Clearly visible are two phases with different
reflection (which was enhanced on the print);
white corresponds to galenite. Polished sec-
tion (x1000).
intense migration can be explained by the activity of the natural nuclear reactor.
The results of mineragraphic investigations and x-ray diffraction studies agree with the above data.
Three types of ore can be distinguished on the site [13]: bituminous nasturan, uraninitic ore, and urani-
nitic nasturan ore. Rich uraninitic ore containing about 40-60% uranium (zone of the chain reaction) has
the lowest 235U concentration. According to the x-ray diffraction data and the diffractometric measure-
ments, the powders of uraninitic ore from the reaction zone (samples 141.0, 1414, and 1418) are com-
posed of uranium oxide with the crystal lattice parameter a0 = 5.43-5.44 A; this corresponds to the lattice
parameter of typical Oklo uraninite [14].
Mineragraphic investigations were made on nasturan? uraninite ore from the contaminated zone.
Monolithic pseudomorphs of uraninite proper to some nonidentified mineral and pseudomorphous aggre-
gates of granular uraninite, nasturan, and coffinite with the outlines of chlorite crystals were found in the
ore of the contaminated zone. Veins of separated uraninite crystals in phyllite are strongly developed
(Fig. 3); recent nasturan (Fig. 4), which under the electron microscope is determined as pseudomorph
of coffinite, and even more recent coffinite (Fig. 5), which, according to the diffraction measurements,
conserved its crystal lattice, are present along with uraninite in the veins.
Some small grains of uraninite from the veins or from aggregates of polymineral pseudomorphs
have regular crystallographic outlines (Fig. 6) which are close to cubic-octahedral structures. The larger
crystals have block structure and have a tendency to splitting and forming spherulites (Fig. 7). Certain
phases of different ages can be distinguished with high magnifications on certain complicated uraninite
grains which had been etched with acids. Signs of dendritic or spherolithic-crystalline growth were deter-
mined for the early phases; indicators pointing to intense recrystallization and to a more recent multiple
uraninite coffinite replacement were found (see Fig. 5). It was not clearly established whether the
ancient uraninite was the primary uranium mineral or whether the uraninite replaced the coffinite.
In x-ray diffraction work on single grains of uranium oxides from the contaminated zone, E. N.
Zav'yalov detected up to three cubic UO2+, phases having the following lattice parameters ao: 5.48-5.49,
5.43-5.45, and 5.39 A.
Uraninite from pegmatites usually has a greater lattice parameter because thorium is contained in
that uraninite. Thorium-free uraninite with the lattice parameter 5.48-5.49 A is known from a metasomat-
ic ferrouranium site which, like the Ooklo site, has an age of 1.8 .109 years [15]. One might assume that
the uranium oxide with ao = 5.48-5.49 A in the samples 1404/2 and 1408/2 belongs to relicts of ancient
thorium-free uraninite.
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TABLE 4. Results of Radiochemical Investigations
Sam-
ple
No.
u, %
2351J, g /g)
280Th, (dig)
226B a,(Ci/g)
223Ra,(Ci/g),
230Th/2881J
22135a/238U
228R 84235U
1402
1406
1410
1414
1418
1422
1425
2,87
6,4
51; 25
44,1
58,9
5,0
2,18
1,89.10-4
3,9-10-4
2,77.10-3
1,83.10-3
3,36.10-3
2,55-10-4
-
(1,70+0,05) 10-8
(2,23?0,08) 10-8
(2,05?0,07) 10-7
(1,77?0,09) 10-7
(2,1?0,1) 10-v
(1,76?0,06) 10-8
7,9.10-8
9,65-10-8
2,84-10-8
1,65.10-7
1,45.10-7
1,87.10-v
1,87-10-8
7,15.10-8
4,0.10-i8
8,6-10-10
5,35.10-8
3;60.10-8
6,1-10-8
5,15.10-18
-
1,74
1,03
1,18
1,18
1,05
1,04
1,06
0,99
1,31
0,95
0,97
0,94
1;10
0,97
0,98
1,05
0,89
0,92
0,84
0,94
-
Assuming that the lattice parameter of uranium oxide increases in proportion to the incorporation of
lead atoms at interstitial sites (with the lead atoms formed in the radioactive decay), uranium oxide with
the lattice parameter a0 = 5.43-5.44 A can be considered younger than the ancient uraninite by at least one
order of magnitude. Uranium oxide with the lattice parameter (20 = 5.39 A is usually created when coffinite
decays into the recent stages of mineralization [16].
The oxides are distinguished not only by the time of their formation but also by the mechanism of
their formation. The experiments made by A. I. Tugarinov et al. [15] have shown that a uranium oxide
with ao = 5.44 A is formed when lead is removed from the lattice of ancient uraninite with ao = 5.48 A,
provided that the uraninite is heated in solution to 600?C. It is possible that the ore of the Oklo site was
also liberated from radiogenic lead in the time of the chain reaction. Of particular importance is the fact
that oxides with ao = 5.43-5.44 A occur mainly in the reaction zone which is also characterized by a sharp
deficit of radiogenic lead.
The appearance of coffinite, which, according to our assumptions, was subsequently replaced by
nasturan with a() = 5.39 A, was preceded by the precipitation of kaolinite or illite (see Fig. 4) which de-
veloped in the form of transversely fibrous veins in coarse uraninite grains. The formation of recent
uranium minerals, which are associated with the metasomatic replacement of uraninite, could cause a
repeated purification of uraninite from several or all preceding generations of radiogenic lead. In any
_case, galenite accompanies the recent ?nasturan-and coffinite:? .
P13 Pb ,Pb
(U, Pb)02+s,-- (U, Pb)02+x.,--* [USi041 (U, USiO4.
ao= 5.48 A. a, -= 5.44 A ao = 5.39 A
Thus,three varieties of uranium oxide were found in the contaminated zone. One variety seems to
have developed it the course of the formation of the primary bed; another variety is associated with the
response to some recrystallization processes (nuclear chain reaction); and the third variety reflects the
recent hydrothermal processes of local redistribution of uranium minerals.
The fact that the recent coffinite is well preserved does not rule out the possibility that this coffinite
was formed in the "cementation" zone in the present epoch, particularly since processes of surface mi-
gration were recognized: gummite, rutherfordine, and wolsendorfite were established on the site [13,17].
Table 4 lists the results of radiochemical investigations of the state of the radioactive equilibrium
in the decay of 238U and 235U. The results indicate that the ratio of 22613a to 238U is practically equal to one,
whereas the ratio of 236Th to 238U is in some cases substantially greater than one. Specifically, the 236Th
activity exceeds the 238U activity by approximately 20% in two samples taken from the zone of the chain
reaction. This detail, and the small geochemical mobility of the thorium isotopes relative to uranium,
suggest that uranium migrated in the present epoch (the time required for establishing equilibrium between
238U and 230Th amounts to -106 years). A missing equilibrium between 223Ra and 235U was experimentally
established. But in order to explain this phenomenon, one must have information on the concentration of
231Pa and 222AC in the samples. Work which is done for this purpose is in progress.
Since no lump samples from the zone of the chain reaction nor_from the zone of the bituminous nas-
turan ore are available, it is not possible to completely reconstruct the sequence of geochemical events.
But one can tentatively speak of mineral formation in the course of three metallogenetic epochs.
A. Precambrian processes corresponding to an age of 1.8 .109 years comprise the formation of the
primary sediments, evidently glauconites, their conversion into chlorite, the conversion of the chlorites
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before, or simultaneous with, the formation of uraninite and, possibly, coffinite, and the replacement of
silicates by uranium oxides. One can assume that this epoch is related to nuclear fission processes of
235U and reactions involving neutrons owing to the accumulation of both fission products and 232Th.
B. ?Events corresponding to an age of several hundred million years; vehement, intense recrystal-
lization and replacement of (U, Pb)02 +X1, accompanied by the separation and migration of lead. The mi-
gration of both uranium and radiogenic lead resulted in a zone of blending and mixing.
C. Recent processes, corresponding to an age of dozens of millions of years. These processes en-
compass the formation of coffinite and its decomposition, the formation of iron sulfides and galenite, the
regeneration of coffinite, and more recent supergene processes. The latter processes are related to
changes in the radioactive equilibrium between 238U and 23?Th, obviously owing to the migration of uranium.
Thus, preliminary investigations of samples from the Oklo site have shown that the uranium miner-
als from the various sections of the site are characterized by various compositions and ages. A 232Th
excess was found in samples from the zone of the chain reaction; the excess is directly related to the de-
gree of the 235U burnup. An excess 207Pb concentration was found in samples from the zone of mixing;
this concentration was also increased relative to the equilibrium concentration of 230Th.
The deviations which were observed indicate that the processes causing the disturbances are very
complicated and dissimilar and do not always conform to the accepted theories of the ore-formation pro-
cesses and the laws of radioactive equilibrium. The previously advanced hypotheses only partially explain
the deviations.
One must recognize that, in the ore of the Oklo site, there occurred and, possibly, occur to the pres-
ent time, strong, repeated migration processes involving elements which make it impossible to clearly
decide over several problems concerning the mechanism of the isotope replacement. The replacement
can originate from ancient nuclear processes, but some of the replacement processes must be ascribed to
a more recent time.
LITERATURE CITED
1. R. Bodu et al., Compt. Rend. Acad. Sc!., 275, D-1731 (1972).
2. M. Neuilly, Compt. Rend. Acad. Sci., 275, D-1847 (1972).
3. R. Naudet, Bul. Inform. Sc!. Techn., 193, 746 (1974).
4. A. P. Vinogradov, Introduction to the Geochemistry of the Ocean [in Russian], Nauka, Moscow
(1967).
5. G. V. Gorshkov et at., The Natural Neutron Background of the Atmosphere and the Crust [in Rus-
sian], Atomizdat, Moscow (1966).
6. V. V. Cherdyntsev, Geokhimiya, No. 4, 373 (1960).
7. D. Hoffman et al., Nature, 255, 19 (1971).
8. V. V. Cherdyntsev, N. B. Kadyrov, and N. V. Novichkova, Geokhimiya, No. 3, 16 (1970).
9. N. A. Vlasov, Atomnaya Energiya, 34, No. 5, 395 (1973).
10. R. S. Prasolov, Atomnaya Energiya, 36, No. 1, 57 (1974).
11. B. G. Dubovskii et al., Critical Parameters of Systems with Fission Substances and Nuclear Safety
(Handbook) [in Russian], Atomizdat, Moscow (1966).
12. A. K. Kruglov et al., in: Proc. IAEA Symp. "The Oklo Phenomenon," IAEA, Vienna (1975),p. 303.
13. J. Geffrey, in: Proc. IAEA Symp. "The Oklo Phenomenon," IAEA, Vienna (1975), p.133.
14. F. Weber and J. Geffrey, in: Proc. IAEA Symp. "The Oklo Phenomenon," IAEA, Vienna (1975), p.
173.
15. A. I. Tugarinov, E. V. Bibikova, and S. I. Zykov, Atomnaya Energiya, 16, No. 4, 332 (1964).
16. Yu. M. Dymkov, The Nature of Uranium Pitchblende [in Russian], Atomizdat, Moscow (1973).
17. J. Geffrey, Bul. Inform. Sc!. Techn., 193, 57 (1974).
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STUDYING THE INTERACTION OF MOLTEN FUEL
WITH SODIUM IN THE ACTIVE ZONE OF A
FAST REACTOR
Yu. K. Buksha, Yu. E. Bagdasarov, UDC 621.039.58
and I. A. Kuznetsov
An important prospective fault process in the operation of fast reactors is the thermal interaction of
molton fuel with sodium.
The upper limit of energy accompanying such an interaction can be estimated from the thermodynamic
relationships 11]. However, this approach yields very high results for the conversion of thermal energy into
mechanical energy, insofar as it assumes an instantaneous transmission of energy from the fuel to the coolant.
The evolution of such a process greatly depends on the rate of heat exchange between fuel and coolant.
Articles [2-6] propose various limitations on the heat exchange, which are determined in the main by
the heat resistance of the fuel particles. The approach to the problem of determining the effect of the resul-
tant sodium vapor on the process varies. It is suggested that the vapor envelopes the fuel fully, after which
the transmission of heat from the fuel to the coolant can be ignored [2], or that a film of sodium remains on
the surface of the fuel particles from which it also evaporates [3-5]. These models describe the boundary
cases of the process of heat transmission. Article [6] suggests what appears to be the most realistic model,
which takes into account the possibility of the formation of a thin vapor film on the surface of the fuel parti-
cles having finite heat resistance. The formation of such a film has been confirmed experimentally [7,8].
The present article suggests a model which enables us to take into account the condensation of vapor on
the cold parts of the channel and the effect of the initial quantity of vapor on the process of interaction. By
taking these effects into account, we are. able to arrive at a more realistic representation of the interaction of
the fuel with sodium. The results are given of a calculation applying to a reactor type BN-600.
Let us consider a certain volume which includes the coolant, its vapor, uncondensed gas, and finely dis-
persed fuel particles located somewhere within the active zone of a reactor. The process of interaction be-
tween the molten fuel and sodium can be described in the following manner. -
The variation of the thermodynamic parameters of the coolant, according to the first law of thermodynam-
ics, can be described by the following expressions
dQ dp
dt = dt 9
(1)
where v is the specific density; p is the pressure; Q is the quantity of heat acting on the sodium;
=i (P, vNa). (2)
The quantity of heat Q acting On the sodium can be determined by solving the heat conductivity equation
for the fuel particles
at)
cr PP = kFAE)+QT"
(3)
where c is the specific heat at constant pressure; A is the heat conductivity; o is the density; 0 is the temper-
ature of the fuel; Q is the heat generated per unit volume.
Translated from Atomnaya nergiya, Vol. 41, No. 1, pp. 9-14, July, 1976. Original article submitted
May 4, 1975.
This material is protected by copyright registered in the name of Plenum Publishing Corporation, 227 West 17th Street, New York, N.Y. 10011. No part
of this publication may he reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying,
microfilming, recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $7.50.
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The relationship between the volume of uncondensed gases and pressure can be described by the
, polytropic equation
pvnG = (4)
Additional ratios between the pressure and the volume of the zone of interaction are determined by
the equation of motion of the coolant surrounding the reaction zone
dV d2V
P = ( ) ?
(5)
The process of thermal interaction between the fuel and the coolant can be divided into two phases.
In the first phase, the sodium is in the liquid state, while in the second phase the sodium is boiling. Let
us consider the first phase. The volume occupied by the zone of interaction can be expressed by the for-
mula
M F M Na MG
P F ? PNa P G
(6)
where MF, MNa, and MG represent the weights of fuel, sodium and gas, respectively. We differentiate
this equation with respect to time, assuming the density of the fuel to be constant. As shown by calcula-
tion, the effect of variations of fuel density on the pressure does not exceed 10%:
dV M Na dpNa MG dpG
dt pfsla dt dt ?
By using the equation of state of the gas (4) and of the sodium (2) in the form p = f(p, T), we find that
n+1
1 dp 1
dt pGonpo ( Pp? ) n ddtP ;
dPNa 13F dp 2p di'
Pa de PNa de PNa dt
where ap is the coefficient of thermal expansion of sodium; 13F is the coefficient of isothermal compres-
sion of sodium. Equation (7) can be written as
(7)
(8)
(9)
n-r1
dV _( MG ? a
___ 1 Po " -Pm),
Na \ dp _t_ aPMNa dr
di PG0.,,P0 1 P PNa 1 dt ' PNa dt '
taking (8) and (9) into account. By using the expression for enthalpy di(1/PNa)dpdT,
= cNadT + (1/6Na)dp ?
(10)
the equation for the first law of thermodynamics (1) for sodium can be written in the form
dT MNaap dp dQ
MNaella dt?
PNa di dt
Let us consider the equation for the variations of volume and energy in the second phase of the process.
In this case, equation of state (2) will take the form p = p(T). Using the expression for enthalpy and the
specific density of the coolant in the form*
I =xi"? (1 ?
VNa = XV" + ? V',
and differentiating these with respect to time gives us
dvNa
dt
di' dT . , ., dr
di r di"
dt = (1 X) --dT dt ? ) dt
x dp" (1? x) dp' , I 1 1 \ dx
L p"2 dT p'2 dr _1 dt p" p'J dt ?
Let us write the .energy equation taking (12) into account
dp di dx dT dQ
.
MNa[X --dr ? (1 dT ? UNa ] j_ N dr dt a (in _ dt dt
(12)
(13)
(14)
*One and two apostrophes refer to parameters of sodium and vapor on the saturation line, respectively.
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A
atm
fo3
102
10-6
lo-5 10-4
10-2 ; sec
Fig. 1 Fig. 2
Fig. 1. Relationship of pressure in interaction zone with respect to time:
R = 0.03 cm; 2) zo = 5 cm; R = 0.03 cm; 3) zo = 5 cm; R = 0.06 cm.
Fig. 2. .Relationship of pressure in zone of interaction with respect to time for zo = 5
cm, R = 0.03 cm, and el. = 3.5; ? ? ?) and ?) taking into account and ignoring vapor
condensation, respectively.
1) ozo = 10 cm;
The equation for the variation in volume can be written as
n+1
dV_fz dp" (1? x) dp' dr 1. , I dx MG po n dp dr
j-1Na [ dT p'2. dr 1 dt T p" p' dt j oPo,/ dT dt
P
(15)
taking (13) into account. To determine the heat flow acting on the sodium, we have to find the temperature
field within the fuel particle. The problem can be written in the following system of equations
ae ,azej , 2 ae ) , . (16)
cFPF7,7-= 7;---.2 1- T. -7c. vv,
ao
?0. (17)
ar
? RAF? aC1 (1+ y) 1(0 Ir_R T); (18)
r Y
0 (t = 0) = (19)
where y is the ratio of the thickness of the film of vapor on the surface of the fuel particles to the radius of
these particles; R is the radius of a particle of fuel. When y = 0, we can write 0/r ?.R = T in place of (18),
as the heat conductivity of sodium is significantly greater than that of the fuel. The heat transmission
process is in a large degree defined by the thickness of the vapor film on the surface of the fuel. On the
basis of data obtained experimentally, article [6] calculates theoretically the thickness of the vapor film
covering the fuel, for conditions in which the weight of the fuel particle is balanced by the hydrodynamic
lift caused by the vapor flowing past the particle
y_ / 1.51.aiNa dx Iva
T/'. pRgMjd '
(20)
where is the dynamic viscosity of the vapor; q is the acceleration in free fall. The total quantity of heat
acting on the coolant per unit time is
dQ 3MT ae
?
dt ?Or CCZ :Om T),
(21)
where Tx is the temperature of the cold parts of the channel; z is the length of the zone of interaction; D
is the diameter of the fuel element; a is the coefficient of heat extraction in the presence of condensation.
Let us consider the equation of motion of the coolant surrounding the zone of interaction. For a
melting zone of length zo in the individual packets, we assume that the molten fuel mixes with the coolant
throughout the entire section of the packet. The walls of the packet are absolutely rigid and the zone of
interaction extends only in the axial direction. In the initial stage of the process, we have to take into
consideration the compressibility of the sodium. For this, we can employ an acoustic approximation
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dz p (t)? p0 210
dt PNa0C0 for t < tac , (22)
in which Co is the speed of sound in sodium; subscript 0 refers to time zero. For times t
> we can
ignore the 'compressibility of the sodium and return to the usual expression for the motion of a column of
tac,
sodium
d2z P ? PB dz 2 i
`k
dtz = pNao(o? z? zo) q dt D ?
The initial conditions for equation (23) are
t a c
dz I f (p ? pp) dt
dt It=tac= PNaolo
0
(23)
(24)
For the sake of simplicity, let us consider the upwards expansion only; the relationship between the
rate of ejection of coolant from the channel and the rate at which the volume of interaction changes can be
determined from the expression;
dV Vo dz
dt zo 11 -a-,
(25)
where / is the height of the sodium column above the zone of interaction; n is the ratio of the cross-sec-
tional area of sodium flow to the cross-sectional area of the zone of interaction.
The mathematical expressions we have given above represent a closed system of control, which fully
describes the interaction process of the molten fuel with sodium.
Fig. 1 gives the results of calculation relating to the following parameters; To = 1110 K, 8= 3100
K, Cp = 13, CC = 0, x = 0; where el, is the ratio of the fuel weight to the weight of sodium in the zone of
interaction; EG is the ratio of the weight of gas to the weight of sodium in the zone of interaction. The
ratio of the fuel weight to the sodium weight corresponds to the proportion by volume of these components
in the fuel can. The maximum pressure is achieved during the first phase of the process. The rate of
rise of pressure in this period is determined by the temperature coefficient of pressure and the rate of
heat supply to the sodium, as the expansion of the zone of interaction is insignificant at this stage. The
zone of interaction expands depending on the propagation of the disturbance; it then reaches its maximum
and starts to fall. When the pressure has fallen to the saturation pressure at the temperature of the so-
dium, the latter begins to boil and the process advances to the second stage. When zo = 10 and R = 0.03
cm (curve 1), the maximum pressure in the zone of interaction reaches 3150 atm and the fuel packet is
free of sodium after -4.5- i0-3 sec. If the zone of interaction is reduced by half, zo = 5 cm, and at the
same fuel particle dimensions, the maximum pressure is reduced to -2200 atm and this process takes
place in 7 .10-3 sec (curve 2). By comparing curves 2 and 3, we can see the effect of the heat-transmis-
sion surface for a given ratio of fuel and sodium by weight. Curve 3 shows the pressure in the zone of in-
teraction at zo = 5, R = 0.06 cm. Increasing the dimensions of the fuel particles by a factor of two leads
to a fall in the maximum pressure, also by a factor of two. This is important, as in all the known experi-
ments, the particle dimensions have been quite small (