SOVIET ATOMIC ENERGY VOL. 30, NO. 4

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• Document Creation Date: December 27, 2016
• Document Release Date: February 25, 2013
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• Publication Date: April 1, 1971
• Content Type: REPORT

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Russian Original Vol. 30, No. 4, April, 1971
Translation published November, 1971
ILLEGIB
SOVIET
ATOMIC
ENERGY
ATOMHAA 3HEP('VIA
(ATOMNAYA ENERGIYA)
TRANSLI4TED FROM RUSSIAN
CONSULTANTS BUREAU, NEW YORK
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t ~~
SOVIET
ATOMIC
ENERGY
Soviet Atomic Energy is acover-to-cover translation of Atomnaya
Energiya, a publication of the Academy of Sciences of the USSR:
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? i
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h
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ssue o
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ussian journal.
Editorial Board of Atomnaya ~nergiya:
Editor: M. D: Millionshchikov ~ _
Deputy C)irector
I. V. Kurchatov Institute of Atomic Energy
Academy of Sciences of the USSR
' Moscow, USSR
Associate Editors: N._A. Kolokol'tsov
' - N. A. Vlasov
A. I. Alikhanov
A. A. Bochvar
N. A. Dollezhal'
V. S. Fursov ,
I. N. Golovin
V. F. Kalinin
A. K. Krasin '
A. I. Leipunskii
V. V. Matveev
M. G. Meshcheryakov
~ P. N. Palei
V. B. Shevchenko
D. L. Simoneriko
V. (. Smirnov
A. P. Vitiogradov~
' A. P. Zefirov
Copyright ?1971 Consultants Bureau, New York, a division of Plenum Publishing
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SOVIET ATOMIC ENERGY
A translation of Atomnaya Energiya
Translation published November, 1971
Volume. 30, Number 4
April, 1971
C?INTElN~'~
f / Engl./Buss.
`On the Expediency of Operating an Atomic-Power Station at a Reduced Power before '"??~
.Recharging - Yu. I. Mityaev . .. ........... ........... ......... 419 339
Design and Optimization of Ion Exchange for Demineralization of Water for Nuclear
Reactors - I. V. Komarova, V. A. Nikashina, R. N. Rubinshtein,
and M. M. Senyavin ........... .......................... ... 424 343
Purification of Circulating Water by Distillation - V. F. Bagretsov
and S. I. Zakharov ..... . . ... ............................... 429 347 .....~;,,~.
Some Questions Relating to the Hydrodynamics of a Boiling Vessel-Type Reactor
- A. P. Sarygin, I. N. Sokolov, V. I. Kondrat'ev, E. V. Kulikov,
I. S. Dubrovskii, and E. V. Kozin ............................... 432 350
Temperature Effect in the Range from 20 to 250?C in the Case of, Some Strictly
Regular Heterogeneous U-Hz0 Critical Assemblies - G. A. Bat',
V. N. Gulimov, Yu. V. Zarubin, V. K. Obukhov, and Yu. V. Ushakov . ..... 436 354
Kinetics of Fission Yield from Ceramic Fuel - B. V. Samsonov and A. K. Frei ..... 441 358
Measurement of the Ratio of the Cross Sections for Radiative Capture and Fission (a)
for puzss in the Neutron Energy Range 0.1-30 keV - M. A. Kurov,
Yu. V. Ryabov, So Tong Hsik, N. Chikov, V. N. Kononov, E. D. Poletaev,
Yu. S. Prokopets, and Yu. Ya. Stavisskii .. ...... ......... .... .. ... 446 362
Cross Section of the Am241(n, y)Am2az Reaction for a Neutron Spectrum Similar to the
Fission Spectrum - N. I. Ivanova, A. N. Kobzev, N. G. Krylov, A. A. Lbov,
N. P. Martynov, A. E. Trikanov, and A. I. Shelamkov ... .. .... 452 369
Chemical and Phase Transformations in Uranium Hexafluoride at High Temperatures
- N. P. Galkin and Yu. N. Tumanov ... ... .. .. ... ............ . .
Tungsten Isotopes in Fresh Radioactive Fallout in December 1968 - Yu. A. Izrael',
A. A. Ter-Saakov, S. G. Malakhov, V. M. Kurganskaya, F. Ya. Rovinskii,
E. D. Stukin, S. B. Iokhel'son, V. N. Churkin, and Z. S. Shulepko ....... .
ABSTRACTS _
Reactivity Measurements by Rod Drop Method with Real Movement of Absorber Taken
into Account- J. Bouzik, S. Chwaszczewski, and J. Jablonski........... .. 465 381
Note on the Stability of Coupled Nuclear Reactors - V. D. Goryachenko ........... 466 381
Optimum Shutdown of a High-Flux Reactor - T. S. Zaritskaya and A. P. Rudik...... 467 382
Some Physicochemical Properties of the Compound XeFZ ? UF6 - V. K. Ezhov....... 468 383
The Interaction of Beryllium with Molten Sodium Fluoride and UF4-NaF Salt Mixtures.
- G. P. Novoselov, I. N. Kashcheev, and A. V. Zolotarev ....... ....... 468 383
Approximation of Photoelectric Absorption Cross Sections - L. V. Popova
and L. A. Sholokhova ... .. .... .... . ... . .... . ......... 469 384
y -Radiation from the Earth and Neutrino Experiments- V. I. Glotov .. .. .. .. .. ... 470 384
Determination of Thickness of y -Sources and Absorbers from the Deformation of the
Hard Part of the Energy Spectrum - V. A. Vorob'ev and Sh. D. Fridman..... 471 385
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CONTENTS
Engl./Russ.
Neutron Spectra from 0.05 to 10 MeV in Certain Shielding Materials - A. P. Vesel'kin,
E. V. Voskresenskii, Yu. A. Egorov, Yu. V. Pankrat'ev, and V. I. Piskunov. .
472
386
Distribution of Spontaneous Fission Neutrons from Uranium Nuclei in an Ore Bed Cut
by a Cylindrical Borehole - Yu. B. Davydov .................. ......
473
386
Dose Sensitivity of a Rhodium Neutron Detector - G. M. Obaturov
and Yu. K. Chumbarov ............. .. ...... ........ .... .. .. ..
474
387
Enhancing Effectiveness of Synchrotron Capture in Beam Bunching Outside of
Separatrix - G. G. Gurov, E. A. Myae, P. T. Pashkov, and K. A. Yakovlev ..
475
388
LETTERS TO THE EDITOR
Note on the Properties of the Integrated Reactor Characteristic K+ - A. I. Mogil'ner..
476
389
On the Physicochemical Reaction of Hafnium with Europium - E. M. Savitskii,
B. G. Arabei, V. I. Bakarinova, S. E. Salibekov, N. I. Timofeeva,
and V. M. Romashov ... ... .. .. .. .... .... .... ...... .... .. ....
479
390
Notes on Measurement of Tcssm Activity - Kh. Shtefan, V. A. Bazhenov,
V. V. Bochkarev, Yu. M. Golubev, and T. N. Sokolova .... .. .. ...... ..
48.1
392
Construction of Certain Injectors for Experiments with Radioactive Indicators
- J. Dobzhansky, K. Korbel, and T. Ovsjak .. . . .: . . . ...........
483
393
Dependence of Buildup Factor on Position of Shield between Bremsstrahlung Source
and Detector - V. P. Kovalev, V. P. Kharin, V. V. Gordeev,
and 5. P. Filipenok ............. .... ...... .... .......... .. ..
487
396
The Use of a (p, y) Reaction to Determine the Content of Light Elements in Thin
Surface Layers of Samples - S. S. Vasil'ev, Yu. A. Dzhemard'yan,
G. I. Mikhailov, and L. P. Starchik .. .. .. .... .. .. .. ..:. ..........
489
397
The Use of Accelerated Charged Particles (cx and p) to Determine the Content of
Certain Light Elements - K. A. Baskova, S. S. Vasil'ev, Yu. A. Dzhemard'yan,
G. I. Mikhailov, and L. P. Starchik .... .. .. ...... .. .... .. .. .. ....
491
398
Production of Strong, High-Energy Neutron Fluxes in a Cyclotron by Irradiating Thick
Lithium and Beryllium Targets with 22-MeV Deuterons - V. K. Daruga
and N. N. Krasnov ... .... .. .. .. .. .. .. .. .. .. .. .... .. .. .. ....
493
399
Method of Experimentally Determining the Magnetic-Well Depth in a System with
Minimum B - V. M. Glagolev, Yu. V. Skosyrev, and A. A. Shmarin........
495
401
NEWS
Vienna October 1970 IA EA Symposium on Cost Aspects of Nuclear Power Station
Hookup to Power Grids ......................... .......... ....
499
404
Grenoble September 1970 International Conference on Magnetism - V. I. Ozhogin ....
502
405
A Visit to Culham Laboratory - L. I. Artemenkov .... ...... .... .... ......
504
406
Resonance Transformer for Miniature Accelerator Facilities - B. I. Al'bertinskii,
A. T. Ermolaev, Ya. Ya. Pil'kevich and G. I. Polyakova ...... .... ....
506
407
The Kvant Data Transfer System - I. N. Ivanov, V. V. Eldashev,
and V. V. Filippov ..... .. .. .. .. .. .. .. .. .... .... .. .... ......
508
409
Miniature Hydraulically Powered Centrifugal Extractor - G. I. Kuznetsov,
M. F. Pushlenkov, and G. N. Yakovlev .... .. ..
...................
509
410
Proximate Analysis of Field Work Geological Samples with Portable Neutron
Generators - V. A. Kasatkin, D. I. Leipunskaya, S. I. Savosin,
and Yu. G. Chulanov ...... .. .. .... .. .. .... .. .... .... .. .. . . ..
511
411
BRIEF COMMUNICATIONS ... .. ...... .. .. .. .. .. .. .. ..... .. ...... .
514
413
BOOK REVIEWS
A. M. Petros'yants -From Scientific Research to Atomic Industry -Reviewed by
A. F. Tulinov and O. P. Shevchenko ..... .. .. .. .. .. .. .. .. ........
515
414
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CONTENTS
Engl./Russ.
A, I. Abramov, Yu. A. Kazanskii; and E. S. Matusevich -Fundamentals of
Experimental Nuclear Physics Techniques -Reviewed by A. F. Tulinov
and O. P. Shevchenko .... .... .. .. ............................ 516 415
The Russian press date (podpisano k pechati) of this issue was 4/ 2/ 1971.
Publication therefore did not occur prior to this date, but must be assumed
to have taken place reasonably soon thereafter.
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Yu. I. Mityaev UDC 621.039.566
The majority of atomic-power-station reactors have a negative power coefficient of reactivity c~,
ensuring the safe and stable operation of the reactors. Hence on reducing the .power of the reactor a cer-
tain amount of reactivity is released, and this may be used for the production of additional electrical energy
and for increasing the extent of fuel burn-up. Clearly this kind of operation is only possible for atomic-
power stations working in the basic mode, a reduction in power only being expedient after the exhaustion of
the reserve of reactivity for burn-up, i.e., immediately before the recharging of the fuel.
Certain atomic-power stations are in fact now operated with a reduced power prior to recharging
[l, 2] . Usually in this case the operation of the reactor is conducted as follows. After extracting all the
absorbers, the reactor is changed to the self-regulating mode of operation, in which the reduction in re-
activity due to the burn-up of the fuel is compensated by a spontaneous reduction in reactor power. Thus
the atomic-power station of the "Yankee Atomic" company (electrical power 200 MW) was regularly
.operated at a reduced power before recharging in 1961-1965 (four times). The maximum power reduction
was 75 MW (electrical). Altogether more than 1 billion kW ' h of electrical power was developed in the low-
power mode over this period [1]. In the fourth operation of the Novo-Voronezh atomic-power station, an
additional 110 million kW ? h of electrical power were developed by reducing the power from 210 to 160 MW
[2]
Let us determine the conditions under which the operation of an atomic-power station in the mode
under consideration will be economically desirable, understanding this to mean a reduction in the net cost
of producing electrical energy C. For this purpose we may consider the operation of the atomic-power
station under conditions of regular partial fuel recharging, with and without reducing the power from No to
Nn before each recharging (Fig. 1). 'In order to simplify the problem let us assume the following: 1) the
reactor is charged with identical fuel channels, the construction and manufacturing technology of which
admit a certain increase in the extent of burn-up of the fuel; 2) the neutron breeding factor keff is a linear
function of the burn-up of the fuel channels: keff = Ko-K15; this is quite frequently the case in the practice
of reactor building [3] (the notation is also that of the earlier paper [3]); 3) the operation of the atomic-
power station does not require any additional store of reactivity in order to avoid the "iodine depression,"
smoothing of the power distribution of the fuel channels, and so on; 4) the atomic power station is operated
without the reprocessing and secondary use of the burnt-up fuel, which is a characteristic feature of modern
nuclear-power techniques.
In contrast to an earlier paper [4], we shall compare the operation of the atomic-power station with
and without a reduction in power before recharging for the two cases of greatest practical interest: for the
same production of electrical power between rechargings, and for the same proportion of recharged fuel
channels.
Case 1. Production of Electrical Power between Rechargings (with and without Reducing the Power
of the. Atomic-Power Station) Kept Constant -and Equal to Eo GW ? h. In the reduced-power mode, (Eo-OE)
GW ? h of electrical energy are produced with the atomic-power station working at a power of No, and DE
GW ? h are produced with the power station working at a power of ON lower than- this, the difference being
ON = No-Np MW; here DE = ONa, where the coefficient a may be expressed as the amount of electrical
energy developed by the power station on reducing its power by 1 MW (electrical). For example, in the
case of the Novo-Voronezh and "Yankee Atomic" power stations, the value of cu is 2.2 and 5.5 GW ? h/MW
Translated from Atomnaya Energiya, Vol. 30, No. 4, pp. 339-343, April, 1971. Original article
submitted August 10, 1970.
m 1971 Consultants Bureau, a divisioa of Plenum Publishing Corporation, 227 West 17th Street, New York,
N. Y. 10011. All rights reserved. This article cannot be reproduced for aay purpose whatsoever without
permission of the. publisher. A copy of this article is available from the publisher for $15.00.
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TABLE 1. Reduction in the Net Cost of Electrical Energy OC/C and Increase in the
Burn-Up of the Discharged Fuel (Smax-Smax)/Smax on Operating an Atomic-Power
Station with the Optimum Reduction in Power before Fuel Recharging, for No = 200 MW,
Eo = 1200 GW ? h, and ~ = 1/3
a= 2 GW?h/MW
a=4GW?h/MW
a= 6 GW?h/MW
CT
Characteristics
case 1
I case 2
case 1
case 2
case 1
i case 2
`~G ?0
C'
4,99
3,48
8,47
6,41
11,1
8,93
2Cp
0 Nopt, MW
- 1'l0
113,4
--107
140,1
-- 98
107,2
Smax -Smax
. %
Smax
13,3
9,45
23,8
18,4
3'L,7
26,8
~~~,> %
C
2,41
1,59
4,26
3,01
5,76
4,29
Cp
p Nopt, M W
- 80
71, 7
~ 73
70,1
~ 67
68.6
Smax -Smax
- -, ''0
Smax
8,9
6,0
16,2
11,7
22,3
17,2
OG
I
"5
C'
0,96
0,60
1,76
1, 1(i
2.45
1,68
O,5Cp
ONopUMW
--49
41,Fi
--46
41.0
--43
40,4
~~ -Smax
"0
Smax
5,4
3,5
10,2
fi,8
14,3
10,1
(electrical) respectively [l, 2]. In the operating mode without a reduction in power, the burn-up of the
discharged fuel channels [3] is equal to
where ~] is the proportion of recharged fuel channels, So = (Ko -1) / Kf is the burn-up of the fuel channels
for the complete recharging of the reactor, i.e., for ~ = 1. The changes in the burn-up and keff in recharg-
ing will [3] .be equal to OS = Sm~r~ and Okeff = KiSm~r~. The operation of the atomic-power station at a
reduced power is equivalent to an increase of Skeff in the neutron-breeding coefficient, proportional to
OE. In this mode of operation (indicated by a prime), the burn-up of the discharged fuel channels equals
2 Ko-1+bkeff 2 _ (( bkeff l 2
Smax s01+TI' - Ki 1-1-+1~ - \S0+ Kt / 1-~rl~
`/ Skeff 2~ l 2 _ 0E 2r~ 1 2
S? `1+ 4keff 1~-rl i 1~-~1' So (11. Eo ~ 1-?-rl / 1+~?.
Since the two modes of operation are being compared for the same production of electrical energy, we have
DS' = OS or OS = SmaxT1 = Sp(2~7/1 + r~) and DS' = SI'll~r~' = So(1 + (pE/ Eo)(2~/1 + r~)) (27'/1 + ~+). It fol-
lows from the latter two relationships that
Eo
~ -- ~ Eo -~ 24Er~ '
DE
`Smax='Smax(i-`2 Eo ~l)
The ratio of the fuel components of the net cost of the electrical energy is inversely proportional to the
burn-up of the discharged fuel channels; hence
cT __ Smax
CT Smax
=1-}- 2 Eo ~l
and the reduction in the fuel component is
~Cr= Cr-C;.=C,. Eo-F20Et~ =CT Ea-{-ZONa
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Time
keff
y 1,0
Time
Nn
a b
20 40 60 BD 100 120 i40
~N, MW
Fig. 1 Fig. 2
Fig. 1. Loading graph and change in the effective neutron-breading factor keff during
the operation of an atomic-power station between fuel rechargings, with and without
reducing the power before recharging (b and a respectively).
Fig. 2. Relative change in the net cost of electrical energy DC/ C as a function of the
reduction in power before recharging ON for the first (1) and second (2) cases with
CT = Cp; ~1 = 1/3; Eo = 1200 GW ? h; No = 200 MW; ~ = 4 GW ? h/MW.
However, on working at a reduced power, the constant component of the. cost of the electrical energy
increases and is equal to
Cp _ Cp ivno
where N = Eo/ [(Eo-OE)/No + 20E/(2No-ON)] is the average power of the reactor in the reduced-power
mode. Here we allow for the fact that, in this mode, the reduction in power from No to Np takes place al-
most in accordance with a linear law [1, 2]. The increase in the constant component is
OCp= Cp ONa 4N
Eo 2No-4N
Thus the reduction in the total net cost of the electrical energy is given by the equation
OC = 4C, - OC = a~N r 2CT,~ _ ~ ON
p 1 Eo-{-24Nar~ Eo 2No-4N/'
Case 2. Proportion of Recharged Fuel Channels (with or without Reducing the Power of the Atomic-
Power Station) Kept Constant and Equal to ~. In this case the burn-up of the discharged fuel channels will
also be greater in the reduced-power mode Smax than in the absence of power reduction (Smax)
akeff
+
S
Smax _
S~
o
. K~ _
i
1
~
Skeff
~keff
1
S
2r~
i
4E
2r~
Sinax
e reduct
So
ion i
So
n the fuel co
_
~
m
-.
So
pone
4keff
nt is eq
inax~l =
-F pkeff
'
ual to
_
_
1 ~~I
+ Eo
1-1-~I
-C
4C
C
C
C
T
,.
,.
T
~
oE
z,~
T Eo(1+~1)-}-
1-~
2ENar~ .
Eo 1--~I
Since the proportion of the recharged fuel channels is the same for both modes of operation, the production
of electrical energy between the rechargings will be proportional to the burn-up of the discharged fuel
channels: _
Eo Smax _ i 4E 2r~
Eo .._ ~n ax - .+ Eo 1 + ~
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~~
~~
~
~z
,,
i
~
~~.
///
=
_-ll
- _
3
-
3 4 Sa,GW?h/MW
2400Eo, GW ? h
{l~ (~l)
Fig. 3. Relative reduction in the net cost of electrical energy on operating on atomic-power sta-
tion with the optimum reduction in power before recharging for the first (---) and second ( )
cases, with No = 200 MW, Eo = 1200 GW ? h: l) CT = 2Cp; 2) CT = Cp; 3) CT = 0.5Cp.
Fig. 4. Relative fall in the net cost of electrical energy on operating an atomic-power station at
a lower power before recharging (second case) in relation to the development of energy between
the rechargings, with Na = 200 MW, CT = Cp (for corresponding proportions of recharged chan-
nels) and a _ equal to 6, 4, and 2GW ? h/ MW.
24Nar~
Eo Eo -r Eo (1-F- ~I)
N Eo-4E 24E E 1-r~
:Va ~ 2No-4N o-4E 1-f-r~ _~ 24[b'a
:~`o 2No-4N
and the increase in the constant component will be
4C - 1 ~~`Va (q ~ ~)
p 2No-4N ?Eo(1-Fri)-{-24:Vxr~'
Thus in this case the reduction in the total net cost of electrical power will be:
OC.:~CT-4Cp-: 4tya r2C -Cp4[V(1-r~l)
E'o(1-4-~1)-I-24Na~1L T~ 2Na-4N ].
It follows from formulas (1) and (2) that the reduction in the net cost of the electrical energy depends
on the power coefficient of reactivity, the ratio of the constant and fuel components, and the production of
electrical energy between the rechargings. It follows moreover from both formulas that, on operating
atomic-power stations at a reduced power, there is a certain optimum value ~Nopt for which the reduction
in the net cost of the electrical energy reaches a maximum (Fig. 2). For the second case the condition
dOC/dON = 0 readily yields an equation for determining ONopt~
ONapt {[2CTr~ -{- Cp (1- I- X1)1 Eo- 4NoCpxr~} -41Vapt4NoEo [2CTr~ -~- Cp (1-;- ~l)1 a- 8NoEoCTr~ - 0. (3)
In order. to obtain quantitative results, we considered a reactor with characteristics similar to those
of the Novo-Voronezh and "Yankee Atomic" power-station reactors. The change in the net cost of electrical
energy on operating the reactor at reduced power before recharging was studied in relation to the power
coefficient of reactivity and the ratio of the constant and fuel components of the net cost of electrical energy.
The results of the calculations are presented in Table 1 and Fig. 3. It follows from Table 1 and Fig. 3 that
the operation of the atomic-power station with a reduced power before recharging enables us to reduce the
net cost of electrical energy by an average of several percent. It should be noted that the economical ef-
fect will be somewhat smaller if we use, not the net cost of the electrical energy, but the reduced-expendi-
ture index, now widely employed in economic calculations [5] as an economic index. This is due to the fact
117.1 IS/ (3) ~2 /
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that, on increasing the extent of burn-up, the fuel component of the reduced expenditure will fall more
slowly than the fuel component of the net cost, since the run time of the fuel channels .will increase with
increasing burn-up, and hence so will the charges for the nuclear fuel.
Of the two cases considered, the former is the more advantageous. This is evidently due to the fact
that, in the first case, the proportion of recharged- channels is slightly smaller than in the second, which
leads to a greater reduction in the fuel component.
On operating atomic-power stations with a reduced power before recharging, the reserve of reac-
tivity for burn-up between rechargings diminishes, slightly more so in the first case than in the second.
Thus, on operating atomic-power stations with a reduced power before recharging, the unproductive
losses of neutrons in the absorbing control rods diminish, i.e., the advantages of this mode are due to the
same causal factors as the advantages of the operating mode with partial rechargings of the fuel: Thus if
the mode under consideration is advantageous for regular partial rechargings it will also be advantageous
during the transient stage, as well as on operating the atomic-power stations with repeated use of the fuel
channels.
Hence the reduction in the net cost of the electrical energy on operating atomic-power stations. at a
reduced power before recharging will be the greater, the greater the development of electrical energy
between the rechargings, i.e., the greater the proportion of channels recharged. This conclusion is illu-
strated by the computed data presented in Fig. 4.
The operation of atomic-power stations at a reduced power before fuel recharging is most expedient.
for light-water reactors of the vessel type, with relatively large power coefficients of reactivity; the pro-
portion of the recharged fuel channels is much greater i.n these than in channel reactors, being approxi-
mately equal to 1/ 3. In this case the increase in the burn-up of the discharged fuel becomes very sub-
stantial (Table 1); the question as to the permissibility of such an increase in burn-up accordingly assumes
a new importance.
In conclusion, the author wishes to thank V. K. Vikulov, A. D. Zhirnov, V. S. Smirnov, and V. M.
Shuvalov for interest in the work and useful comments, and L. G. Khristoforova for carrying out the calcu-
lations.
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 Declassified in Part -Sanitized Copy Approved for Release 2013/02/25 :CIA-RDP10-021968000300080003-1
DESIGN AND OPTIMIZATION OF ION EXCHANGE FOR
DEMINERALIZATION OF WATER FOR NUCLEAR REACTORS
I. V. Komar ova, V. A. Nikashina, ~ UDC 541.183+621.039
R. N. Rubinshtein, and M. M. Senyavin
Ion exchange is of well-established importance in the processing of water for thermal and atomic
electric power stations [1-3]. The large requirements of power stations for purified water, the stringent
demineralization requirements, and the tendency to reduce consumption of materials, reagents, and labor
to the economic limit all make it necessary to optimize the process of demineralization by ion exchange.
For water of given composition and a plant of given output, it is necessary to solve the problems of choosing
the ion-exchange resin, its amount and granularity, and the optimum water feed rate.
It is natural that optimization of such a complex group of parameters in multi component nonequili-
brial ion-exchange systems cannot be solved by direct experiment, but requires computational data. The
dynamics of ion-exchange sorption of multicomponent mixtures is represented, in the usual notation, by
the following well-known system of differential equations:
-v a`` xD a?`` - aut ~x 8c, is the balance equation; (1)
ax + a=2 - at at
aat - ~ (cl, cZ, , , ., ct; ai, a2, ..., aL; v, r) is the equation of kinetics; (2)
at
at == f (c~, cZ, ..., ct) is the equation of the ion- (3)
exchange isotherm
Equations (1)-(3) are solved for given initial conditions, ai(x, 0) = rV(x), and given boundary conditions, ci(0,
t) _ fi(t). However, so far this system of equations has not been solved in general form for exchange of
mixtures of ions, owing to the mathematical difficulties.
In this article we describe possible approaches to the problem of ion-exchange demineralization of
water in separate beds of ion-exchange resin, and the design analysis and optimization of this process.
We discuss optimization of the process for a sorption cycle with a completely regenerated column. This
problem, in particular, arises in the nuclear industry, in which .the resin is used only once in production
owing to its poor stability. Anyway, this problem is the first stage in any process of ion-exchange de-
mineralization.
The method of calculation for sorption of mixtures which we shall describe and discuss in this ar-
ticle is based on a law established as a result of layer-by-layer calculations for many systems [4]. The
law is that sorption of the least-sorbed ion in the parallel-transfer stage does not depend on the nature and
concentration ratio of the other components in the mixture, but depends only on their total concentration.
Thus the problem of sorption of a mixture of ions on an ion-exchange column can be reduced to the problem
of sorption of the one least-sorbed ion of the mixture. Previously [5] we have suggested a direct method
of calculating the dynamics of sorption of.one-component systems; characterized by any exchange constant,
in the region of external-diffusion kinetics.
Our results were plotted as a family of yield curves in dimensionless coordinates:
c
u-T Cu =-
co (4)
4-~ C4^ ao l
for various values of the exchange constant kij.
Translated from Atomnaya Energiya, Vol. 30, No. 4, pp. 343-347, April, 1971. Original article
submitted May 11, 1970; revision submitted October 26, 1970.
? 1971 Consultants Bureau, a division of Plenum Publishing .Corporation, 227 Nest 17th Street, New York,
N. Y. 10011. All rights reserved. This article cannot be reproduced /or any purpose whatsoever without
permission of the publisher. A copy of this article is available /rom the publisher /or $15.00.
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logl
0,5
0,4
03
D, 2
0,8
~~
0,6
x-r
S 6 789105
t, sec
I
I
210' 3 k 5 6 789102
Fig. 2
Fig. 1. Theoretical (x) and experimental (~) yield curves of sodium for cation ex-
change of water.
Fig. 2. Theoretical ( )and experimental (- - -) yield curves of chloride during
anion exchange of water.
In water processing we are dealing with dilute solutions; therefore, as we have shown, the kinetics
of ion-exchange demineralization of water will also be governed by external diffusion. Therefore to analyze
the sorption of the least-sorbed ion we used a method described in [5] for aone-component system. The
initial data for solving this problem are the exchange constant of the least-sorbed ion (or its sorption iso-
therm) and its kinetic coefficient.
Let us successively consider two stages of demineralization -cation exchange and anion exchange
- taking as an example the purification of chloride-sulfate water. In this case, in cation exchange the
least-sorbed ion is sodium. As we have shown [6], sorption of sodium on the hydrogen form of KU-2 cation
exchanger follows the Langmuir isotherm with an exchange constant of 1.25 [4]. The kinetic coefficient
a which depends on the flow rate v and the granularity d is given by
~ = 0.009w di,s ?
For sodium w = 1. With the aid of dimensionless graphs, for k = 1.25, by the above-described method [5]
we obtained the theoretical yield curve of sodium, which is plotted in Fig. 1. For comparison the same
graph shows the experimental yield curve of sodium from the mixture. We see that the experimental and
theoretical curves agree up to c/ co = 0.3. The maximum on the experimental yield curve is due to mutual
displacement during exchange of a mixture of ions.
In the anion-exchange stage the least-sorbed ion is the chloride ion. Let us consider the shape of the
exchange isotherm of the chloride ion on an anion exchanger in the OH form in .the presence of hydrogen
ions, i.e., in the case of exchange accompanied by neutralization.
The exchange isotherm of chloride in dimensionless variables is
I[ ucp
__ cOH
4 Kcou
1-~
pox
(6)
Here the right-hand side can be transformed in conformity with the condition of electrical neutrality, cpH
+ cCl = cH; thus cOH = cH-cCl? Clearly, cCl --Ointhefirststageof sorption (initial section of the isotherm),
therefore cpH = cH and cOH can be found from the equation cpg = cH = ~Kv, or cOH = mow; then the
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n/X, atm/cm isotherm takes the form
Fig. 3. Hydraulic resistance ver-
sus flow rate (bed depth 50 cm,
grain diameter 0.04 cm) .
Kco
-u
V Kw
q-
1-~ Kca u
V Kw
Let us define a coefficient Keff =Kco/fK",,. Then
Keff "
4- 1tKeff "
where Keff is the gradient of the initial section of the isotherm
of q versus u. It is known that if sorption follows the Langmuir
isotherm, then when Keff ~ 10 the isotherm practically merges,
with the axis of ordinates, i.e., the sorption process is repre-
sented by a nearly rectangular isotherm. Since Keff =Kco/~~
therefore Keff ~ 10 if co >_ 5.10-~ N. We are considering co = 5 ? 10-5-5.10-s N; the kinetic coefficient
of the chloride ion was calculated from Eq. (5), which gave W Cl = 1.1.
Figure 2 shows the theoretical and experimental yield curves for sorption of the chloride ion on AV-
17 anion exchanger in the OH form; the curves show good agreement. The above mathematical model was
here supplemented by the equation giving the hydraulic resistance h of the ion-exchanger bed in terms of the
experimental parameters. This equation, according to Bennet and Mayers [7], takes the form
h _ (150/Re ~-1.75) xu2 (1-x) j
~xs
(9)'
for any granular material; here j is the density of the solution in kg/cm3, and x is the porosity of the
sorbent.
To verify this approximate dependence of the hydraulic resistance on the flow rate, we performed
an experiment with a fairly wide range of velocities (0.8-4.0 cm/sec) for a bed of KU-2 cation exchanger, '.
50 cm in height, with a mean grain diameter of '0.04 cm (Fig. 3).
All the results so obtained confirm the adequacy of the mathematical model adopted, and we can thus!
use it to find the optimal conditions. ,
`- '' + 400
+++++
~l??
300
++
^
~ ? 350
+
++
+: +
+
? .
++
295
.'??
+ ? ~ +
~ + ? + 300
?
?
+
+? +
+
+ +
+? 755 +
+ ? ' + 250
? ? +
+ +
+ : t
t 293 +
+; +
+
+
+ ?. +
+ : +
?
+? ?? ++ 200
+ . +
?
+; ++
+t; +
++ 150
+
'
+
-
++++
+ .
+
100
++ +++
++++++
50
g8 1,6 2,4 0,8 1,6 2,4 3,2 4.0
v, cm/sec v, cm/sec
Fig. 4. Contour lines of optimization criterion Y for vary-
ing flow rate and bed depth (co = 5 ? 10-5 N, c/ co = 0.01, out-
put 200 m3/ h, d = 0.05 cm) . a) Cation exchange; b) anion
exchange.
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TABLE 1. Optimum Sorption Conditions, We calculated the optimal conditions with the aid
with Ion Exchanger Replaced after- Each of a computer, by the above scheme, with the optimization
Cycle, for Various Types of Water and criterion [8]:
Various Degrees of Purification (Output 10
Y==ECi~ ~ E'er-'-E'a-!-Eel, ( )
200 m3/ h)
~ where EC is the capital cost in thousands of rubles, EC
Cation exchanger Anion exchanger = f(v, X); a is the normative cost recovery time; EM is
the cost of materials (replacement of ion exchanger after
ca, N :i ? 10-5 5.10-8 5.10-5 5.10-5 5.10-8 5.10-5
each cycle of water purification) in thousands of rubles,
c, N ;i ? 10-~ 5.10-~ 5.10-8 5.10-7 5.10-7 5.10-8
EM = f1(v, x)/tfc(v, x, d); Ea is the depreciation cost in
c/ce 0,01 0,1 0,1 0,01 0,1 0,1
v, cm/sec 1,2 2,0 1,'L 2,0 2,0 2,0
thousands of rubles, Ea = f2(EC); and Eel is the cost of
x, cm 250 50 175 225 75 125
Y, thousand 75,5 9,85 71,4 293 30,58 285,9
rubles electrical energy in thousands of rubles, Eel = f3(v, x,
i
d) .
The process of sorption on a fully regenerated column is characterized by three input variables:
the flow rate v, the ion-exchange resin grain diameter d, and the bed depth x. We looked for the optimum
in the following ranges of these variables: 0.4 `I+vI)t ) -()`Xe~~vXe)i
-}-vXe-a'I-vI)-(NXe--vXe)e -~(a'I+v1 e (?
RXe(t) and R~h(t) were calculated from experimental data using the expressions
NXe - IRxe(t)J-7~IRIh(t)] (ti-F- G 1 (4)
NXe 1 = 7~IRIh(t) \~+ G 1
(specimen extracted from core).
Xel~ samples were counted using the technique described in [8].
The obtained results were plotted as a dependence of the reduced apparent diffusion coefficient D'
on the irradiation dose (Figs. 2 and 3). Since D' varies in approximately the same manner for all speci-
mens it is sufficient to cite only the steady-state values of D' at the beginning and end of the experiment
(Table 2).
/c m" hrraaiauon I olauon tope, % (adopted from [10]); ~ is the neutron flux intensity,
Radius of equiv-
alent sphere, ?
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FT
Fig. 1. Experimental setup.
TABLE 3. Comparison of Experimental D I S C U S S I O N
and Calculated Specimen Temperatures
An analysis of the results shown in Figs. 2 and 3 and
specimen tempera- in Table 2 leads to the conclusion that beginning with an
S ci- tt?e, ?K
pe z irradiation dose of ~2 ? lots dis/cm3 the diffusion of gas-
men Do, cm /sec E, cal/mole expeti- ~calcula-
i eous fission fragments decreases with increasing doses
~ ~ mental Ited
___ and stabilizes at 5 ? lOtB to 5.1019 dis/cm3. In the accepted
uoz 1,s?1o-e 70000 1/too 134o system of counting this decrease in diffusion manifests
Uc 10-2 7s o00 1400 isoo itself as an apparent reduction of diffusion coefficients.
UCZ 4,6.10-8 68 000 1400 1370
This reduction is different for the different xenon iso-
topes: it is highest for X8133 (by a factor of 104 to 106),
less for X8135 (102 to 103 times), and the lowest for X8138 (5 to 20 times). This reduction can only be ex-
plained by assuming that the fragments are trapped in internal pores that are formed during irradiation of
ceramic materials. Assumption of a decrease of the surface of "equivalent" grains would lead to an equal
reduction of the yield for all isotopes and to a much less pronounced effect.
However, the experimental values of D' at the beginning of irradiation are very high. It is hardly
reasonable to assume that xenon atoms, which are of a relatively great size, can diffuse so easily in the
dense crystalline lattice of the investigated materials [9]. The processes taking place can be given the
following qualitative interpretation. It is known [12] that the presence of point defects in irradiated ma-
terials facilitates diffusion. It can be thus assumed that the initial (at an irradiation dose of lots dis/cm3)
high value of the apparent diffusion coefficient of xenon isotopes depends on easy "transport" of the iso-
topes through point defects that tend to accumulate at grain boundaries in the crystalline lattice which still
does not contain a great number of traps. At the same time, since the half-life of Xetss is very long, of
XetsS shorter, and of X8138 the shortest, point defects transport Xe13s atoms from very deep layers of the
grain and in an amount much greater than follows from the equivalent-spheres model. Correspondingly,
the effect of point defects should be less for Xet35, and the least for X8138? The lowest (at a dose of 1019
dis/ cm3) steady-state values of apparent diffusion coefficients for xenon isotopes are also different; the
least for Xet33, higher for Xet35, and the highest for Xet38. This can also be explained by their different
half-lives. Coming from the deepest grain layers, X8133 meets on its path the highest number of traps and
thus becomes most "sensitive" to them. Similarly, the effect of traps is less on Xet35, and the least on
X8138
The generally accepted (at present) diffusion parameters Do and E for ceramic fuel. [3, 6] are listed
in Table 3. The specimen temperatures alsolistedinTable3were calculated from these parameters and
from the experimental values of the final steady-state diffusion coefficients of Xetss
Good agreement between the calculated and experimental temperature has been observed for both
UOZ and UCZ. The difference observed in the case of monocarbide is somewhat higher than the experimen-
tal error. For this value of D an activation energy of 65,000 cal/mole corresponds to a temperature of
1400?K. It has been reported [6] that for carbides the activation energy is 55,000 cal/mole. The average
value of energy between the maximum of 75,000 cal/mole and the minimum of 55,000 cal/mole agrees with
the suggested value of 65,000 cal/mole.
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Fig. 2. Reduced apparent dif-
fusion coefficient D' of UOZ-I
specimens as a function of if-
irradiation dose: 1) Xe133; 2)
Xe135; 3) Xe13&; 4) I133; 5) 1135
1016 10'~ 108 k~
Irradiation dose, dis/cm3
2
1
a
i
4
?
9
5 ~
3
x
0
?
0
Fig. 3. Reduced apparent diffusion coefficient D' of UCz-II specimen as a function of
irradiation dose: 1) Xe133. 2) Xe135; 3) Xe13a; 4) I133~ 5) 1135 The curves b and c show
data obtained for intermittent irradiation.
10~~ >01B 5?f0~~ 1016 10'`
Irradiation dose, dis/cros
A noteworthy fact is the intense diffusion of iodine isotopes. At the end of the experiments the number of
atoms of Xe133 and X135 produced by iodine atoms escapingfrom the specimens and precipitating in the channel
was 3 to 5 times the number of atoms directly escaping from the specimens.
The results indicate that the yield of gaseous fission fragments from ceramic fuel decreases notice-
ably in the course of irradiation. This effect can be explained by the appearance as a result of irradiation
of internal porosities that act as traps capturing gaseous fission fragments and hindering their escape
from the specimen.
The authors thank S. T. Konobeevskii, N. V. Krasnoyarov, V. A. Tsykanov, and V. N. Raetskii
for their advice and help, and A. I. Kashtanov for preparing the specimens.
LITERATURE CITED
1. R. Carroll and P. Reagan, Nucl. Sci. and Engng., 21, 141 (1965).
2. F. Felix et al., Report P/427, by the FRG Delegation to the Third Intern. Conf. on Peaceful Uses
of Atomic Energy, Geneva (1964).
b
c
1
4
? x
5?
~ .~
x v
?
5
4
?
,
x
v
? e
2
x
2 ? p x
3 x
o 1
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 Declassified in Part -Sanitized Copy Approved for Release 2013/02/25 :CIA-RDP10-021968000300080003-1
3. B. Eastman, Radiation Effects in Uranium Dioxide [in Russian], Atomizdat, Moscow (1964).
4. V. I. Polikarpov et al., Testing the Airtightness of Fuel Elements [in Russian], Atomizdat, Moscow
(1964).
5. L. Zumwalt et al., Nucl. 5ci. and Engng., 21, 1 (1965).
6. I. Wiliams, AECR, T1D-7546, 2 (1958).
7. I. MacEwan and W. Stevens, J. Nucl. Materials, 11, 77 (1964).
8. C. Townley et al., Nucl. Sci. and Engng., 10, 346 (1961).
9. S. T. Konobeevskii, The Effect of Radiation on Materials [in Russian], Atomizdat, Moscow (1967).
10. Yu. A. Zysin, A. A. Lbov, and L. I. Sel'chenkov, Fission Yield and Its Mass Distribution [in Rus-
sian], Gosatomizdat, Moscow (1963).
11. I. V. Gordeev, D. A. Kardashev, and A. V. Malyshev, Nuclear. Physics Constants [in Russian],
Gosatomizdat, Moscow (1963).
12. A. C. Damask and G. J. Dienes, Point Defects in Metals, Gordon and Beach (1964).
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 Declassified in Part -Sanitized Copy Approved for Release 2013/02/25 :CIA-RDP10-021968000300080003-1
MEASUREMENT OF THE RATIO OF THE CROSS SECTIONS
FOR RADIATIVE CAPTURE AND FISSION (a) FOR Puz3s IN
THE NEUTRON ENERGY RANGE 0.1-30 keV
M.
A, Kurov, Yu. V. Ryabov,
So Tong Hsik,
N.
Chikov, V. N. Kononov,
E.
D. Poletaev, Yu. S. Prokopets,
The value of ~ for puz3s is one of the fundamental constants that determines the technical and economic
basis of modern nuclear power. This constant largely determines the value of the reproduction coefficient
of nuclear fuel and detailed information about ~ is, therefore, of fundamental importance for the choice
of the optimal design of industrial fast-neutron reactors. The experimental accuracy in the determination
of a for puz3s required for the design of large reactors has been analyzed in several investigations. In
Table 1 we give the results of the analysis of Gribler et al. [1]. The table also contains an estimate of the
accuracy of all the experimental data published prior to 1968.
In view of the unsatisfactory state of the experimental data on cx(E), especially in the neutron energy
range 0.1-30 keV, we measured the values of cz(E) for Puz39 in this energy range in the present investiga-
tion.
Apparatus. The cross section cx(E) = rrny(E)/6f(E) was measured by the time-of-flight method with
a base line of 250 m and a resolution equal to 220 and ~15 nsec/m. The source of resonance neutrons in
the first case was a pulsed fast reactor of the Joint Institute of Nuclear Research and in the second case
a pulsed fast reactor with an electron microtron-injector [2].
The experimental method consisted of comparing the number of counts of an ionization fission cham-
ber containing "thin" Puz39 layers and a large liquid scintillation detector that measured the radiative cap-
ture and fission y-rays from a "thick" Puz39 sample as a function of the neutron time of flight.
In the experiments we employed ahigh-efficiency ionization fission chamber [3] containing 120 mg
of Puz39. Approximately 70% of the fission events in the chamber were detected. An increase in the ef-
ficiency of detection of the fission fragments despite the presence of a large background of c~-particles
(3.2 ? 108 a-particles/sec) was achieved by an appreciable increase in the speed of response of the ioniza-
tion chamber. The duration of the pulses from the chamber at the output of the amplifier, which deter-
mined the background of the multiple superpositions of cx-particles, was < 20 nsec. An appreciable in-
crease in the speed of response of the chamber was achieved by making direct use of the current pulses
that arose in the chamber, these pulses being subsequently amplified and discriminated by means of wide-
band current devices.
The capture and fission y-rays were detected by a large 500 liter scintillation tank. The detector
contained a central channel through which the neutron beam passed. The sample was placed in this channel,
the geometry being almost 4~r. To decrease the background due to the radioactivity of the sample and
cosmic rays the detector was split into two halves, these being connected for coincidence. Boron was.
introduced into the scintillator to decrease the background due to the detection of neutrons scattered by
the sample. A special experiment showed that not more than 0.3% of the neutrons scattered by the sample
Translated from Atomnaya Energiya, Vol. 30, No. 4, pp. 362-369, April, 1971. Original article
submitted June 1, 1970.
? 1971 Consultants Bureau, a division of Plenum Publishing Corporation, 227 !Vest 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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Ng? lOZ
0 ~ ~~~ ~ ~~~ `^~ ~ ~ ~ ~ ~ o~
200 400 600 800 1000 1200 1400 1600
Channel number
Fig. 1. Time-delay spectrum of pulses from the fission chamber (resolution
15 nsec/m).
TABLE 1. Accuracy in the Determination
of ~ (E) for plIZ39
Neutron energy, keV o,i t io ioo iooo io 000
Required accuracy ~- 5?0 -+~- 3?0 -~ ' obtained in the present investigation
are given in Table 5. In the experiments we used. a Puz39
sample of thickness 0.7 ~ lOZI nuclei/ cmZ. The results
for the microtron conditions were obtained by averaging
over three series of measurements and the specified er-
rors characterize the root-mean-square spread of the
data of these series. The indeterminacy in the value of ~ due to the statistical error in the measurements
of the ratio Ny/Nf and also allowance for the background of each series amounts to 20-50.%. The final data
for the microtron conditions were obtained by averaging the fission and radiative capture cross sections
over the intervals 0.1, 1, 20 keV. For the reactor conditions an estimate of the accuracy of the results of
the measurements based on allowance for the statistical errors in the ratio Ny/Nf, the statistical error
in the determination of the background level, and the errors associated with the calibration lead to an in-
determinacy in the value of a that ranges from t15 to f20%.
Comparison of our results with those already published (Fig. 5) reveals satisfactory agreement with
the data of [10] and discrepancies (that exceed the limits of the errors) with the results of [11] in the energy
range 2-5 keV and (12] in the energy range 2-30 keV. Note the good agreement of our data in the whole energy
range with the recent measurements made at Dubna with a resolution of 60 nsec/m [14]. Note also that in
the cases when the energy resolution of the spectrometers was sufficiently high (the energy range below 1
keV) the structure in the energy dependence of c>!(E) due to the fluctuations of the fission widths is well re-
produced.
It is clear that the considerable discrepancy between the results of measurements of c>!(E) in different
laboratories in the neutron energy range 1-30 keV cannot be explained solely by the inadequate accuracy of
the values of the resonance parameters used for the calibration: The -cause of these discrepancies is most
probably to be found in an inadequate procedure for measuring the background level by the method of re-
sonance filters. This applies particularly to experiments with linear accelerators, for which the shor-
test base lengths are used (25-35 m) since the variable component of the background associated with neu-
trons scattered in the measuring section may be appreciable for times of flight less than 200 ?sec. There-
fore, to obtain more reliable data on ~ in the neutron energy range 1-30 keV it is best to use spectrometers
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 Declassified in Part -Sanitized Copy Approved for Release 2013/02/25 :CIA-RDP10-021968000300080003-1
-
- ~
i
I
j
~~J?b-
- -
s
~- ,
~ J I
I
~
~
~ ~ \~
~~~,
i ~ ~ ~ ~ ~ ~
i ~
2 3 4 S 7 10 20 30 40 50 7CEn, keV
Fig. 5. Results of measurements of ~ in the range 0.1-100 keV: - ~-) present
investigation, resolution 220 nsec/m; -?-) present investigation, resolution
15 nsec/m (sample with 0.7 ? 1021 nuclei/cm2); ?) data of [9]; ---D---) [1.1];
-O-) [12] (the mean result for several series of measurements is given);
with long base lines. A promising development would be to make experiments with pulsed van der Graaf ac-
celerators in the range of lower neutron energies.
The authors would like to express their sincere gratitude to A. I. Leipunskii, F. L. Shapiro, and
L. N. Usachev for their constant interest in the investigation; to L. B. Pikel'ner for making it possible
to carry out the measurements with the scintillation (n, y) detector; and to L. N. Sedlakova, Ts. Pante-
leev, and Yu. Kolgin for assistance in evaluating the results with a computer and for helping with the mea-
surements.
1.
2.
3.
4.
P.
Gribler et al., Nucl. Applic., No. 5, 297 (1968).
V.
L.
Anan'ev et al., At. Energ., 20, 106 (1966).
V.
N.
Kononov et al., Prib. Tekh. Eksp., No. 6, 51 (1969).
Yu.
A.
Aleksandrov, Yu. V. Ryabov, and G. S. Samosvat, Preprint JINR R-2014 [in Russian], Dubna
(1965).
5. H. Darrien et al., Nucl. Data for Reactors, Vol. 11, IAEA, Vienna (1967), p. 195.
6. Yu. V. Ryabov et al., Yad. Fiz., 5, 925 (1967).
7. BNL-325, Suppl. 2 (1965).
8. G. James and B.' Patrick, A ERE-M2068 (1968) .
9. L. M. Bollinger et al., Proceedings of the Second United Nations International Conference on the
Peaceful Uses of Atomic Energy, Geneva, 1958, Published by the United Nations, Geneva (1958).
10. Proceedings of the Conference of Experts of the International Atomic Energy Agency on cu (Pu-239),
Winfrith (England) (1969).
11. Yu. V. Ryabov et al., At. Energ., 4, 351 (1968).
12. M. Sowerby et al., Fast Reactor Phys., Vol. 1, IAEA, Vienna (1968), p. 289.
13. G. de Saussure et al., Nucl. Data for Reactors, Vol. 11, IAEA, Vienna (1967), p. 233.
14. M. A. Kurov et al., Preprint JINR R3-5002 [in Russian], Dubna (1970).
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CROSS SECTION OF THE Amz41(n, y)Am24z REACTION- FOR
A NEUTRON SPECTRUM SIMILAR TO THE FISSION.5PECTRUM
N. I. Ivanova, A. N. Kobzev,
N. G. Krylov, A. A. Lbov,
N. P. Martynov, A. E. Trikanov,
and A. I. Shelamkov
This investigation is concerned with the use of the activation method for measuring the cross sec-
tion of the Am24i(n, y)Amzaz reaction (Tl/z = 16.01 h) for neutrons having a spectrum similar to the fission
spectrum. * Existing data [1] relating to the cross sections of the (n, y) reaction of Amz41 only refer to
thermal neutrons. There are no such data for fast neutrons.
EXPERIMENTAL METHOD
The use of the activation method for measuring the cross section of the Amz41(n, y)Amz4z reaction
encounters.serious difficulties associated with the necessity of recording the /3-activity of the developing
Am242 on the much greater background of the intrinsic cz- and y-activity of the irradiated Amz41 and the
fission fragments formed.
For the 1 mg samples of Amzal here studied, the a-activity equalled 7.2.109 decays/min, and the
y-activity, which was almost entirely determined by a line with an energy of 59.57 keV (quantum yield 0.37
[2j) was equal to X2.7 ? 109 quanta/min. An estimate of the expected (3-activity of the Amz4z, based on an
integrated flux of 2.1015 neutrons/ cmz at the sample and a possible cross section of the (n, 1') reactions of
^'0.3 b, amounted to ~0.9 ? 106 decays/min at the end of the irradiation period. Here it was assumed that
83.6% and (16.4 f 0.3)% of the total were associated with a-decay and electron capture respectively [2].
Taking account of the time (some 20 h) needed to separate the americium chemically and purify it
from fission products, -the /3-activity, of Amz42 at the target may be equated to (3-4) ? 105 decays/min.
In order to measure the a-activity of the Amz4z, we used a sensor containing a plastic scintillator
53 x 1 mm in size and an FEU-11B photomultiplier. The pulses from the sensor fell on asingle-channel
amplitude analyzer, operating in the integrated mode of recording.
In order to eliminate the influence of the background a-activity of the sample when making the mea-
surements, an aluminum absorber was employed; the contribution of the y-activity and x-radiation was
reduced by pulse discrimination in the recording system. An aluminum absorber 100 ? thick was placed
between the sample and the the crystal; the measurements were made with differing registration thresholds,
corresponding to ER ~ 150-300 keV. For the preliminary calibration of the apparatus with respect to ef-
ficiency, we used the following isotopes: Sr90 (ER = 0.54 MeV), T1204 (ER = 0.765 MeV), and Au198 (E~3 = 0.963
MeV). The choice of these isotopes for the calibration was determined by the fact that the Amzaz had ER
= 0.667 MeV (40%) and Eft = 0.625 MeV (60%) [2]. The recording efficiency for Am24z under the measuring
conditions chosen was 13.7 and 11%, depending on the value of the threshold. In order to eliminate the in- '
fluence of the activity arising from the fragments, radiochemical purification was incorporated.
*The neutron spectrum is characterized by the following energy distribution: 0-0.1 MeV 3.8%; 0.1-0.4
MeV 19.3%; 0.4-0.9 MeV 26.9%; 0.9-1.4 MeV 15.0%; 1.4-3.0 MeV 23.8%; over 3.0 MeV 11:2%.
- ---
Translated from Atomnaya Energiya, Vol. 30, No. 4, pp. 369-372, April, 1971. Original article
submitted October 15, 1970.
? 1971 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 pwblisher for $15.00.
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~r
~. rr
~
~
I
~
2
_
~
_
.
i
-
~_
-
-{
~_.
~_.1
~
--
~-
~
T1
/p =
16 h
I i
_._
_
~-
-~
~
3/19/1968 3/20/1968 3/21/1968 3/22/1968
Fig. 1. Decay curve of Amz42 (sample No. 3).
Before the irradiation, the original material, taken in the form of americium chloride, was sub-
jected to chemical processing in order to remove fission products and other possible impurities. After
evaporation to dryness in quartz cassettes, the americium chloride was irradiated. The amount of ma-
terial in each cassette was about 1 mg. In order to eliminate the influence of the thermal-neutron back-
ground, the quartz cassettes were placed in cadmium sheaths with a wall thickness of 0.5 mm; at the bot-
tom of each cadmium-shielded cassette was an Au197 foil approximately 2 mg in weight (for monitoring the
neutron flux) .
Three neutron irradiations were carried out. In each experiment two Amz4t cassettes were irra-
diated. The integrated neutron flux, measured by means of the fission, chambers, approximately equalled
2 ? 105 neutrons/ cmZ.
The active sample containing the americium and its fission products was subjected to chemical puri-
fication immediately after irradiation. In view of the comparatively short half life of the Am2az formed
(T1/z = 16.01 h), the principal requirement laid upon the method of chemical purification was that of maxi-
mum speed, with a reasonably high coefficient of purification from the fission products.
After irradiation, the americium was leached from the quartz cassette with concentrated hy-
drochloric acid, and the solution was passed through Dowex 2X8 resin, which retained many of the transi-
tion elements and also elements constituting fission products (operation 1).
After passing through the column, the solution was evaporated to dryness, the residue was dissolved
in concentrated hydrochloric acid, and operation 1 was then repeated (operation 2).
The separation of the americium- from the rare-earth and alkaline-earth elements and also from
various other fission products was effected in Dowex 2X8 resin in the thiocyanate form. We used columns
0.2 mm x 11 cm in size. For filling the column we used resin in the chloride form, the rate of deposition
of the particles in the water being 0.2-0.4 cm/min. The anion exchanger was converted into the thio-
cyanate form by prolonged washing with a solution characterized by a strength index of 5 M with respect to
NHgCNS and 0.1 M with respect to HCI. After operation 2, the eluate was evaporated to dryness, and the
residue was dissolved in two or three drops of a similar solution. The resultant solution was transferred to
the thiocyanate column for the sorption of the americium and the fission products.. The fission products
were washed from this column with a solution characterized by a strength index of 1 M with respect to
NH4CNS and 0.01 M with respect to HC1, containing40% of ethyl alcohol. Then the americium was washed from the
column with 0.1 M HCl (2-2.5 free volumes of the column) . The eluate was collected on a platinum substrate and
dried under an infrared heater in order to remove the solvents and a small amount of ammonium thiocyanate.
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TABLE 1. Principal Experimental Results
Serial No~
Serial No.
Integrated neutron
Amount of Amyl
(Absolute activ-
Measured
A
of irradi-
i
of sample
z
flux
neutrons/ctn
in the target,
tty of the Am2az,
cross sec-
verage- cross
ation
II
,
atoms
decays/min
tions, mb
section, mb
I J
1
1,96?fOts
2,32.1018
7,4.10
2'L8
t
2
1,96.1015
1,23.1018
4,0.105
232
II ~
3
.1,97.1016
2,06.1018
6,8.105
233
4
1,97.1015
4,9.1017
1,9.105
273
240-~30
III {
5
2,0.1015
1,89.1018
6,4.105
235
6
2,0.1015
4,22.1017
1,5.106
248
The foregoing chemical method of separating the americium yielded a coefficient of purification from
the fission products of about 105 (some 15-20 h after irradiation had ended); the chemical yield of americium
equalled 80-90%? The period required for the separation was 15-20 h. However, the actual chemical yield
was not over-important, since the calculation of the cross section was based on measurements of the n-
and /3-activity arising from the same sample.
The fall in the Q-activity of the samples with time was measured for a period equal to four or five
Am242 half lives. After this time the sensor recorded only the constant background activity of the target,
principally that due to the y-radiation of the Amz41, with an energy of 59.57 keV. After subtracting the
constant background activity, the ~?-activity due to the Am242 was readily distinguished (Fig. 1).
The amount of Amz11 in the target was determined from the total a-activity measured in the integrating
ionization chamber.
a (n, Y) _ .iTl~Z
noQ?U.693 '
where A is the absolute activity of the Am~2 in the target at the instant at which the irradiation ended (al-
lowing for the recording efficiency,' corrections for decays taking place during the irradiation period,
corrections for inaccuracies in the decay s theme) ; T 1~ 2 is the half life of the AmZ4z; no is the number of Amz41
atoms in the target; Q is the neutron flux of a spectrum closely resembling the fission spectrum.
We obtained the cross section corresponding to the radiative capture of neutrons in Amz41 for six
samples (Table 1). The results of the individual measurements had no appreciable scatter over and above
that of the experimental errors. The average cross section of the Am211(n, y)Amz4z reaction was equal to
Q(n, y)Amz41 = (240 f 30) ? 10-27 cm2.*
The errors committed in the cross-section measurements comprise inaccuracies in determining the
activity of the samples (2-4%), the half life of the Amza2 (2%), the neutron flux (7%), and the amount of
material in the target (4%), and also errors introduced when determining the efficiency of the sensor (3%);
the total measuring error is 10-12%.
In order to check for the presence of possible systematic errors in the measuring method, an Aufs~ `
sample was irradiated at the same time as the Amz11
The cross section for the Au197(n, y)Au1~ reaction measured with the plastic scintillator equalled
Q(n, y)Aui97 = (140 f 15) ? 10-27 cm2, in excellent agreement with the earlier value of rr(n, y)Au1s7 = 150 ? 10-?~
cm2 [3]; this verified the applicability of the method in question for measuring the capture cross section of
fast neutrons in Amza1
1. J. Stehr et al., Neutron Cross Sections, BNL-325 (1966).
2. V. M. Gorbachev et al., Fundamental Characteristics of the Isotopes of Heavy Elements [in Russian]?
Atomizdat, Moscow (1970).
3. I. V. Gordeev et al., Nuclear-Physics Constants [in Russian], Atomizdat, Moscow (1963), p. 316.
* That is, the cross section only leading to the formation of Am242 with T1~2 = 16.01 h.
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CHEMICAL AND PHASE TRANSFORMATIONS IN URANIUM
HEXAFLUORIDE AT HIGH TEMPERATURES
N. P. Galkin and Yu. N. Tumanov UDC 546.791:546.16
Uranium hexafluoride is a thermally stable compound. This is evidenced,, in particular, by the fact
that during the production of uranium hexafluoride in the fluorination of the tetrafluoride with elementary
fluorine, temperatures exceeding 1400?K are developed in the flame reactor [1].
In the work of Kudrin [2] it is indicated that in the temperature interval 5. 103-3.104?K, the basic
components of the plasma, produced from the initial gas uranium hexafluoride, are U, F2, F, and F ~.
The equilibrium constants of the reaction [3]
(UFa)gas-' (LF.~)gas+2(F)g~
were also calculated.
To resolve certain practical questions it is necessary to know the thermodynamic and kinetic, charac-
teristics of the process of gas phase decomposition of uranium hexafluoride, heated to a temperature of
3.103?K. Uranium tetrafluoride can be isolated under these conditions. In this work an attempt was
.made to determine the indicated characteristics.
Mechanism of the Decomposition of UFs
The mechanism of the decomposition of uranium hexafluoride to the tetrafluoride can evidently be
represented by the following scheme of potentially possible reactions:
(UFs~~-: (CJFS~gas-~(F)gas. O11zsa=80720 cal:
(1)
(UFs)gasy(UFa)gas+(F)gas' ~Hiee=93200ca1;
(2)
2~F)gas-'~Fz)gas, 4Hzna=-38000 cal;
(3)
(UFe~gas-~(F)gas-'NFs)gas-~-~Fz)gas, OH2sa=-4`L720ca1;
(4)
(UFs)gas-I- (F)gas -' (UF4) gas l- (Fz) gas? OH2E8 = - 55 200 cal.
(5)
Reactions (1) and (2) have a positive entropy change; reactions (3)-(5) have a negative entropy change.
Since reactions (1), (2), (4), and (5) are endothermic, we should consider only reactions (1), (2), and the
exothermic reaction (3) at high temperatures.
Thermodynamics of the Decomposition of UFO
To find the equilibrium partial pressures in the mixture obtained when uranium hexafluoride is heated,
it is necessary to solve a system of five equations:
Purb~e
K -
(6)
_
Pl PUry
PUr4Pg
K
(7)
pZ PUrb ,
Pp'z
8
PUFg J" PUN e ~ PUFq -I-' PUFy 1i' PF = i abS, atm;
(9)
pure-}'PUrfi-F'PUF} 1
(lo)
6PUre-I-SPOre+4pur,+2Prz+Pr 6
Translated from Atomnaya Energiya, Vol. 30, No. 4, pp. 372-376, April, 1971. Original article
submitted February 13, 1970; revision submitted May 4, 1970.
? 1971 Consultants Bureau, a division of Plenum. Publishing Corporation, 227 Rest 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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1
a-
-~5
3
2
~
iII
__ _
11 4
I
1
I
-y--
i
1000 2000 3000 T, ?K
Fig. 1. Partial pressures of
uranium fluorides as a func-
tion of the temperature: 1)
p1iFs; 2) pUFS; 3) pUF4; 4)
pFz; 5) pF.
values of ~UF were calculated in the approximation of a rigid rotator
s
- harmonic oscillator -according to the known values of the molecular constants, taken from [5]. The
thermodynamic properties of gaseous uranium tetrafluoride were calculated according to the equivalent
molecular constants Td of the model of the UF4 molecule [6].
The thermodynamic properties of uranium pentafluoride were calculated by the method outlined ih
[7], on the assumption that UF5 molecules, just like other pentafluoride molecules [8], have the structure
either of a trigonal bipyramid of the point group D3h or a tetragonal pyramid of the point group C4v'
Hoskins and Lord [9] have shown that pentafluoride molecules, for example, PF5 and AsFS, during
the process of intramolecular exchange of fluorine atoms, exist with some probability both in the form
of a trigonal bipyramid and in the form of a tetragonal pyramid. The frequency of exchange is determined
by the expression
TABLE 1. Values of the Reduced Thermo-
dynamic Potential of Gaseous Uranium
Fluorides (cal/mole ? deg)
? The UF5 molecule has one free electron, and its
ground state is assumed to be doublet.
t Asinglet state is assmned for -'the UFy molecule.
Here pi represents the partial pressures of the components of the high-
temperature gas mixture;
_ i/a (ern' eFin, it
K e T' 1 T , (11)
ei
where Kei are the equilibrium constants of reactions (1)-(3); ~4'T i
and OHo~ i are the changes in the reduced thermodynamic potential at
the temperature T and the enthalpies of the reaction at absolute zero;
R is the gas constant. The values of ~F~ and ~F are known [4]. The
k
v (sec's) = ti exp (-- ~ _RT )exp (4S/R);
(12)
where k and h are the Boltzmann and Planck constants, respectively; DS is the entropy difference of the
D3h and C4V structures; R is the gas constant; DE* is the difference of the potential energies of the D3h
and C4V structures..
According to the estimate of Hoskins and Lord [9], exp (OS/R) lies in the interval 1-10, but is closer
to 1, while OS lies in the interval 0-4.53 ca.l/mole ? deg. For heavy molecules .the values of (S,?r)D3h-(ST)C4v
and (~T)D3h-(~T)C4V -are less than 1 cal/mole ? deg [7j; therefore in the calculations we can use the ther-
modynamic properties of the D3h and C4V structures of UF5.
The molecular constants according to which the thermodynamic properties of the three uranium fluor
rides in the ideal gas state were calculated, are cited in [4, 6, 7]. The values of the reduced thermodynamic
potential of the three uranium fluorides are presented in Table 1. To calculate the equilibrium constants
Ket and Kee we used the values of ~T of the D3h model of the UF5 molecules, which is an analog of the
MoC15 and WC15 molecules, which have a trigonal bipyramid structure [10].
Figure 1 presents the calculated dependences of the partial pressures of fragments of the UFs mole-
cule on the temperature at a total pressure equal to 1 atm. The partial pressure of the hexafluoride
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Fig. 2
Fig. 2. Structural changes during reaction (1).
Fig. 3. Dependence of the logarithms of the rate constants of reactions (1) and (2) on the
reciprocals of the temperature.
decreases sharply after 2200?K; the uranium hexafluoride pressure has a maximum at T = 2.4 ? 103?K; the
pressure of the tetrafluoride has a maximum at T = 3.2 ? 103oK. For complete conversion of uranium hexa-
fluoride to the tetrafluoride and fluorine, it is necessary to heat the hexafluoride to 3200-3400?K.
Kinetics of the Decomposition of Uranium Fluorides
Complex polyatomic molecules with high energies of bond cleavage are characterized by a mono-
molecular mechanism of decomposition [11-13].
The rate constant of the monomolecular reaction can be estimated by the expression [14]
where ao i is the fraction of activated molecules reacting per unit time; ei is the activation energy; f is
the number of oscillators; k is Boltzmann's constant; T is the absolute temperature.
Reactions (1) and (2) represent the elementary step of the decomposition of UF6. It may be assumed
that the electronic levels of the UF6 and UF5 molecules lie rather high, and the dissociation of these mole-
cules occurs from the electronic ground state. In this case the activation energy of reactions (1) and (2)
is equal to the cleavage energy of the bond. -For reaction (1) El = 80,720 cal; for reaction (2) s2 = 93,200 cal.
In both cases fly < si. The values of ~ni can be estimated according to the following function [14]:
z :~.kT iii 14
?c
where n is the concentration of particles at which the order of the reaction changes; r1 z is the sum of the
radii of the colliding particles; m is the mass of the particle; ~_1~ i is the fraction of active particles de-
activated per unit time.
At low pressures, monomolecular reactions proceed according to second order, while at high pres-
sures they proceed according to first order. The upper and lower limits of ?the pressures, within which
the reaction order changes, were found according to the empirical dependence of the pressure of the transi-
tion on the number of excited oscillators in the molecule, constructed according to the literature data [14].
From this dependence it was found that in the pressure interval 0.3-150 mm Hg, for UFs and UF5 molecules,
second order changes to first. Above a pressure of 150 mm Hg, both reactions proceed according to first
order.
The possible structural changes that occur during reaction (1) are presented in Fig. 2. The cross
marks the bond to be broken in the octahedral UF6 molecule. From the standpoint of the principle of least
pressure [15], it makes no difference which bond in the iJFs molecule is broken, since they are all equivalent.
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Fig. 4
Fig. 4.. Structural changes during reaction (2).
Fig. 5. Dependence of the logarithms of the rate constants of reaction (3) on the values of
103/T: 1) calculation; 2) experiment.
TABLE 2. Rate Constants of Recombina- According to the same principle, both configurations of
tion (cm3 ? sec-1) of Uranium Fluorides the UF5 molecule (D3h and C4V) are equally probable.
and Fluorine By analogy with the MoCls and WCls molecules, we might
.expect a greater probability for the D3h model of the '
-~
Zoe--Td
Din
The mass of the UF5 molecule m2 = 5.526 ? 10-z2 g, ri,2 ~ 5.274 A, f = 2.
Reactions of Recombination
.. kF
The temperature dependence of the rate constant of the reactions FZ + Ne ? 2F + Ne is described
by an equation obtained experimentally by Diesen [17]:
ICFy- 2.0.1010e-35 000/RT~M]-1 S2C-1, (15)
where [M] is the neon concentration, M. With some approximation we can assume [MJ = const. Then
The activation energy of the reaction is close to the energy of cleavage of the F-F bond, equal to 38,000 cal.
The value of k3 can also be calculated according to formula (13), on the assumption that s3 = 38,000 cal,
f = 2, pressure of the transition 1 abs. atm, and the reaction mechanism is monomolecular. The results of
calculation according to formulas (13) and (15) are in satisfactory agreement (Fig. 5).
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The rate constants of recombination ~ the fluorine atoms k3 were calculated in terms of the equi-
librium constant of reaction (3), Kea, and the constant k3, and are cited in Table 2. There also are cited
the rate constants of the recombination of uranium flourides, calculated according to the formula
7c] .= kikTKei> (17)
where Kpi is the equilibrium constant of the corresponding recombination reaction.
Kinetics of the Condensation of Uranium Tetrafluoride
In the case of abrupt cooling of high-temperature gas mixtures of uranium fluorides, the partial
pressures of which are cited in Fig. 1, there is a condensation of uranium penta- and tetrafluoride. If the
mixture has a temperature of 3200?K, and if the cooling is performed sufficiently rapidly, uranium tetra-
fluoride may condense. For this the time of the elementary event of condensation must be less than the
time of recombination processes.
The rates of condensation (in reciprocal seconds/ molecule) can be estimated according to the Fren-
kel' equation [18]:
~norl ---
u%cond = e akT 2~r* kT V ^4~v3m4~c ~.
where v is the surface tension at the gas/condensed phase boundary; r* is the critical value of the radius
of the condensing particle; p is the pressure of the gas; k is Boltzmann's constant; m is the mass of the
particle; cpv and cpc are the thermodynamic potentials of the vapor and condensed phases, related to one
molecule; g* is the critical size of nuclei of the condensing substance.
.The values of the surface tension of uranium tetrafluoride are unknown. Depending on the complexity.
of the molecule, the temperature, and the volatility, the surface tension may vary in the range from several
erg/cm2 to 103 erg/cm2. Let r* ~ 3.10-$ sec, the temperature of the .condensing surface T = 3.? 102?K,
pUF4 = 0.30 atm, Q ~ 4 ? 10 erg ?cm2, g* ,~ 10, mUF4 = 5.85. 10-22 g, cpv-cpc = 4 ? 10-12 erg. In this case
the rate of condensation wcond = 1.6.10$ sec-1. The influence of the noncondensing gas (fluorine) is not con-
sidered here.
We should estimate what cooling of uranium tetrafluoride is provided by condensation. The rate of
cooling of the tetrafluoride on account of .condensation can be estimated according to the formula
d'L' T~--TZ
(deg/sec),
ac _-Vona
where T1 is the temperature of the gas; T2 is the temperature of the condensing surface, Tcond is the time
of condensation. If T1 = 3.2 ? 103oK, T2 = 3 ? 102?K, Tcond = 6.25 ? 10-9 sec, then dT/dt ~ 4.7 ? 1011 deg/sec.
The rate of cooling of the tetrafluoride obtained is several orders of magnitude greater than the required
level, determined by the time of recombination processes.
1. N. P. Galkin et al.,, The Technology of Uranium [in Russian], Atomizdat, Moscow (1964), p. 310.
2. L. P. Kudrin, At. Energ., 22, 265 (1967).
3. Yu. N. Tumanov, Zh. Neorgan. Khim., 13, 1488 (1968).
4. V. P. Glushko (editor), Thermodynamic Properties of Inorganic Substances [in Russian], Izd-vo AN
SSSR (1962).
5. B. Weinstock and G. Goodman, Advances Chem. Phys., 9, 169 (1965).
6. Yu. N. Tumanov and N. P. Galkin, Zh. Fiz. Khim., 43, 836 (1969).
7. N. P. Galkin, Yu. N. Tumanov, and Yu. P. Butylkin, Khim. Vys. Energ., 4, 512 (1970).
8. K. Hakamoto, Infrared Spectra of Inorganic and Coordination Compounds [Russian translation], Mir,
Moscow (1966), p. 162.
9. L. Hoskins and R. Lord, J. Chem. Phys., 46, 2406 (1967).
10. R. Bader, Kun Po Huang, J. Chem. Phys., 43, 3760 (1965).
11. F. B. Vurzel', L. S. Polak, and V.S. Shipachev, Kinetika i Kataliz, 7, No. 6 (1966).
12. V. N. Kondrat'ev, in: Chemical Kinetics and Catalysis [in Russian], V. N. Kondrat'ev (editor),
Nauka, Moscow (1966), p. 165.
13. V. N. Kondrat'ev, The Kinetics of Chemical Gas Reactions [in Russian], Izd-vo AN SSSR, Moscow
(1958), p. 263.
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14. M. S. Zakhar~evskii, Kinetics and Catalysis [in Russian], Izd-vo LGU, Leningrad (1963), p. 81.
15. F. Rice and E. Teller, J. Chem. Phys., 6, 489 (1938).
16. J. Leermakers, J. Amer. Chem. Soc., 55, 3098 (1938).
17. R. Diesen, J. Phys. Chem., 72., 108 (1968).
18. Ya. I. Frenkel', Collection of Selected Works [in Russian], Vol. 3, Izd-vo AN SSSR, Moscow-Lenin-
grad (1959), p. 358.
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TUNGSTEN ISOTOPES IN FRESH RADIOACTIVE
FALLOUT IN DECEMBER 1968
Yu. A. Izrael', A. A. Ter-Saakov,
S. G. Malakhov, V. M. Kurganskaya,
F. Ya. Rovinskii, E. D. Stukin,
S. B. Iokhel'son, V. N. Churkin,"
and Z: S. Shulepko
Fresh radioactive isotopes were detected in the ground air and precipitates, against the background
of global fallout, on the territory of the Soviet Union (European sector and Central Asia) in mid-December,
1968.
News of an underground nuclear explosion ("Schooner") carried out in the state of Nevada (USA) on
December 8, 1968 appeared in the press at that time. The nuclear explosion, 35 kiloton power, touched
off at a depth of 106 m, formed a crater 260 m in diameter and 60 m deep.. The radioactive products ejected
into the atmosphere were disseminated over considerable distances not only over the territories of the
USA but also outside its boundaries [1].
The trajectories of the airborne particles at a height of 5 km constructed from the site of the nu-
clear explosion, showed that the air masses from the region of the explosion reached the territories of
the Soviet Union on December 15 and moved over the USSR land mass over an approximate six-day period
(Fig. 1) .
Samples of air and fallout precipitation over some cities of the Soviet Union taken during December
1968 ,with" filters and horizontal planchets were subjected to y-ray spectrometric and radiochemical anal-
yses in early January 1969. The volume of one sample of air pumped through a filter in one month was
105 to lOs m3.
TABLE 1. Monthly Average Concentrations of Various Isotopes in the Ground Air
over the Territory of the Soviet Union in December 1968 (10-15 Ci/m3)
Translated from Atomna.ya Energiya, Vol. 30, No. 4, pp. 377-380, April, 1971. Original article.
submitted February 5, 1970.
? 1971 Consultants Bureau, a division of Plenum Publishing Corporation, 227 [Vest 17th Street, New York,
N. Y. 10011. All rights reserved. This article cannot be reproduced for any purpose whatsoever without
permission o(the publisher. A copy of this article is available from the publisher (or $15.00.
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Trajectory of air masses
at height of 5 km (dates
indicated)
Eastern troundazy of Wiat
fallout
Fig. 1. Trajectory of airborne particles formed in the state of Nevada [USA] on De-
cember 8, 1968, at a height of 5 km above the territory of the Soviet Union and neigh-
boring countries.
Figure 2 shows y-ray spectra of radioactive air samples taken in the region around Moscow before
the appearance of the radioactive products (curve. l) and during the December 13-21 period (curve 2). Com-
parison of these curves shows clearly that the 59 keV curve appeared in air samples taken after December
15. The half-life of the radioactive products in this sample, determined from the rates of decreases in the
intensity of this curve, were found to be 140 days. W181 was identified in the samples from these data.
The dynamics of the variation in W181 concentration at three points in the Moscow region are illu-
strated in Fig. 3. The onset of the appearance of Wtel in the ground air (December 15), and the first and
second waves of radioactivity enhancement (the second appearing after traveling completely around the
globe), stand out clearly in the diagram.
The monthly average concentrations of diverse isotopes in the ground air samples taken at several
cities in the Soviet Union are reproduced in Table 1. If we assume that the W181-contaminated air masses
traversed a given site over asix-day period, then the average Wlal concentration during the traversal of
any point can be found by multiplying by the five monthly-average values listed in Table 1.
Table 2 compares the average isotope composition in the fallout zone (in the form of the average
ratio of number of nuclei to Zr95 nuclei) according to data obtained at several points, and similar values
of global fallout from past tests measured in April-June, 1968 in the North Atlantic and over the territory
of the USSR in September, 1968. The isotope composition was also compared to characteristic fallout
values stemming from an underground nuclear explosion [2]. It is clear from Table 2 that Ba140 and Sr89
which are characteristic of fallout deriving from underground explosions with radioactive products ejected
into the atmosphere, are completely absentinthe fresh fallout (December, 1968). The composition of the
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~~
a
U
9,
400
Energy, keV
Fig. 2. Energy spectra of y-ray emission from samples of radioac-
tive fallout [curve 1) background sample; curve 2) sample of "fresh"
fallout in December 1968].
^ I III
.~
a IIL~lilll
C
v 15 20 25
c
o ~
III ~I~I~ Ili ~ ~~
30 5 f0 15 20
TABLE 2. Average Ratio of Number of Nu=
clei of Diverse Isotopes to Zr95 in Ground
Air Samples
.~.
~~
A. ~
?'
E,
a~
Sr89
O,U7
-
122
0,08
Balao
0
0
18
0
Sroo
310
-
51
320
Cst37
790
400
178
480
Ce144
55
70
I -
21
? Figures for December 1968,
t Ratio to Mo99, the behavior of which is presumed
c similaz to that of Zr95 (fractionation absent),
fission fragments in the December fallout is practically the
15 20 25 30 5 10 15 2v same as the composition typical of global fallout. The dis-
fDecember 1968 ~-Januazy 1969 -~
tinguishing feature of the December fallout is the consider-
Fig. 3. Daily average W1B1 concentra- able amount of W181 which, apparently, is a product of activa-
tions at three sites in the Moscow re- tion in nuclear explosions. Hence, the daily-average W18i con-
gion. centrations in the air in the Moscow region attained levels
of 4.6 ? 10-14 Ci/m3.
In the samples taken W165 was also identified, and the ratio of its activity to that of W1si at the time
of the explosion ranged from 0.9 to 4.6, depending on the sample; the average was ,-a____~
Considerable amounts of W181 were observed precisely in the region traversed~y airborne particles
deriving from the explosion (see Fig. 1). In regions to the east of Arkhangelsk, and at Novosibirsk, the
amount of W181 was insignificant, and none was detected at Chita or Vladivostok. During the preceding
months, no Wt$f at all had been observed over the territories of the Soviet Union.
The appearance of W181 and W185 over the territories of the Soviet Union in the period from December
15 through December 21, 1968 (at some sites still later), i.e., in the period during which the trajectory of
air masses deriving from the state of Nevada traversed those territories, proves that the tungsten isotopes
belong to the American underground nuclear explosion "Schooner" which was detonated on December 8,1968.
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The isotopes Weal and W185 are products of activation by the nuclear explosion neutrons, and were
observed in fallout samples of earlier date that were associated with aerial nuclear weapons tests or
American underground nuclear explosions [3-5].
The ratio of the activities of WlaS and Wlsl at the time of the explosion, in calculations of induced
activity based on the reaction (n, y), was 70 in the thermal approximation; this ratio is roughly 7.0 in the
case of neutron energies 10 to 100 eV, which corresponds to a temperature of 105 to 106?K.
The r 'o found by theoretical calculations based on the reaction (n, 2n) ' 2.06 r 14 MeV neutrons
[4], an~~ w en using the cross sections of the reaction [6]. The cross section lie (n, 2n) reactions
are slight reater than the cross sections of (n, y) reactions.
We now estimate the Weal activity in a cloud passing over the territory of the Soviet Union from De-
cember 15 through December 21, 1968. The average concentration of Wlal in a cloud about 1500 km wide,
according to data from 11 samples taken during that period, * was about 0.1 decay/min ? m3. When the ex-
plosion-derived cloud moved at a height of 5 km over the territory of the USSR over asix-day period, at
an average speed of about 40 km/h, and extent of about 6000 km, the total Wlal activity in the cloud
amounted to 5 ~ 1015 decays/min, or 2.3.103 Ci. If we assume that even as much as 10% of the total amount
of Wlsl was retained in that cloud, that would mean that not less than 2.3.104 Ci Wlsl was formed in the
. nuclear explosion. As a result of activation in the soil in the 35-kiloton underground nuclear explosion,
and with a 10-3% weight ratio of tungsten in the rock material affected by the explosion, not more than 2.4
? 102 Ci Wlal could have formed (taking into .account resonance absorption of neutrons at high temperatures
in the cavity scooped out by the nuclear explosion).
We may infer from the foregoing that the tungsten isotopes detected in radioactive fallout from the
American underground nuclear explosion "Schooner" over the. territories of the Soviet Union are products
of activation by neutrons released in the explosion which originated in elements directly incorporated in
the structure of the nuclear device.
LITERATURE CITED
1. Applied Atomics, No. 690, 7 (1968).
2. F. Cray and R. Fried, in: Radioactive Fallout from Nuclear Explosions, Yu. A. Izrael' (editor)
[Russian translationJ, Mir, Moscow (1968).
3. Yu. A. Izrael' and E. D. Stukin, y-Radiation of Radioactive Fallout [in Russian], Atomizdat, Mos-
cow (1967).
4. B. V. Kurchatov et al:, At. Energ:, 13, No. 6, 576 (1962).
5. E. Martell, J. Atoms. Sci., 25, No. 1, 113 (1968).
6. A. I. Aliev et al., Nuclear Physics Constants for Neutron Activation Analysis [in Russian], Atomiz-
dat, Moscow (1969).
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ABSTRACTS
REACTIVITY MEASUREMENTS BY ROD DROP METHOD WITH
REAL MOVEMENT OF ABSORBER TAKEN INTO ACCOUNT
J. Bouzik, S. Chwaszczewski,
and J. Jablonski
The real movement of absorber in the reactor must be taken into account when interpreting results
of reactivity- measurements by the rod drop method, particularly in measurements of high reactivity levels.
Using the single-point equations of reactor kinetics as point of departure, we can derive a general formula
which enables us to refine the results of reactivity measurements by the rod drop method (the formula is
readily extended to the method of neutron source removal):
~ (o) fps-I-x-11 (1)
Po =
j P~ (t) 6 (t) dt
0
Here the time dependence of reactivity assumes the form
P (t) _ -PoN (t) (2)
when the following initial and asymptotic conditions are satisfied: p' = 0 when t = 0 and .p' = 1 when t = ~,
while O(t) is the amplitude of the signal from the neutron detector placed inside the reactor. The remaining
designations in formula (1) are conventional ones. The proposed reactivity measurement method was veri-
fied experimentally on the critical assembly "Anna." The absorber is introduced into the reactor, in the
form of a cadmium cylinder, with the aid of a pneumatic device. The time required to get the absorber into
the reactor ranged from 0.5 to 15 sec. The' in-pile location of the absorber was recorded by measuring
voltages on a potentiometer connected to the absorber, and also by the number of pulses generated as the
absorber is moved. The conversion from the time dependence of the. in-pile position of the absorber to
reactivity was achieved either by means of additional calculations or additional measurements.
The basic reactivity measurements were taken by three methods. In the first, digital, method, ab-
sorber position pulses were compared to pulses from the neutron counter, using a 400-channel time dis-
tribution analyzer. In the second, analog-digital, method, the absorber position was placed synchronously,
by means of an x-y dataplotting recorder, across the input of an analyzer which simultaneously records
the time rate of change in the neutron detector count rate. The third, analog, method is based on the .use
of an analog computer connected to the setup. When the normalization of the input signal across the output
is properly selected, the reciprocal reactivity is obtained accurate to within a known coefficient.
The results of the measurements confirm the validity of the proposed method for application to exact
determinations of high reactivity levels. The results confirm the feasibility of utilizing an analog com-
puter system in reactivity measurements.
Translated from Atomnaya Energiya, .Vol. 30, No. 4, p. 381, April, 1971. Original article sub-
mitted May 14, 1970; abstract submitted November 25, 1970.
? 1971 Consultants Bureau, a division o/ Plenum Publishing Corporation, 227 Nest 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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NOTE ON THE STABILITY OF COUPLED
NUCLEAR REACTORS
V. D. Goryachenko UDC 621.039.515
The primary purpose of the article is to derive the sufficient stability conditions for the stationary
mode of operation of a reactor consisting of two different coupled cores.
The kinetics of coupled reactor cores have been described [l, 2] in terms of a multipoint model:
dNk Pk-1'k m ak/
dt = lit Nk'~ ~ kikCrk+ i f ~k~ (u) N~ (t-u) du ;
k
i=1 0 .
d~tk = ~k Nk-A,ikCik, i=1, ..., m; k=1, 2; 1=1, 2; I ~ k,
where Nk and pk are the neutron density and the reactivity in the k-th core; lk is the neutron lifetime; Cik~
~ik~ Rik are. respectively the concentration, decay constant, and fraction of the i-th group of emitters of
delayed neutrons; ak = ~ Qik~ akj are coupling coefficients; cpkj(t) is the distribution function (with respect
to the time) of the probability of transition of neutrons from the j-th core to the k-th core. Clearly, we
have
ski (i) > 0, ~ ~k j (~) dt -1. (2)
u
Intercore coupling is assumed weak, i.e., we assume akj = const, with the reactivity pk independent of the
variables describing the j-th core (j ~ k).
For the purpose of investigating the stationary mode:
Eqs. (1) were linearized and supplemented with the linearized feedback equations for each core. The latter
were presented in integral form: "
Pk lkPkO = - ~ fk ~t-Z) `Vk (~NkU Nk0 dZ,
Q
and the form of the kernels fk, dependent on the type of feedback equations, was not concretized. The
characteristic equation of the linearized system was set up and its analysis made it possible to derive the
following stability criterion.
The equilibrium state (3) is asymptotically stable at any positive coupling coefficients whenever
Re ml (p) ~ 0 and Re mZ (p)er 0 when Ro p~ 0, (5)
u?k (P)=P a- ~h -}-I~'k ~P)- ~ih kik /t=1, 2
/k ~ /k P'+~ik
{
Fk(p) is the feedback transfer coefficient for the k-th core [i.e., the Laplace transform of the kernel fk(t)].
The functions of the complex variable p which conform to the constraints (5) are positive real functions
[3], while the constraints (5) are equivalent [3] to the conditions: 1) Rewl(jw) > 0, Rew2(jw) > 0 for all w
0; 2) the functions wl and w2 do not have poles to the right of the imaginary axis or on the imaginary axis
itself (one exception is the case where there are only simple poles on the imaginary axis, and only poles
with positive residues).
Rcw(P)=13e LP-{-S-{-FOP)-~ SL p ~-~a,p,~0 when ReP7?U, (7)
Translated from Atomnaya Energiya, Vol. 30, No.. 4, pp. 381-382, April, 1971. Original article sub-
mitted May 11, 1970; abstract submitted October 26, 1970.
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written for a noncoupled ("point") critical reactor, is a sufficient condition of asymptotic stability for the
stationary mode of this reactor.
1. S. Gage et al., in: Neutron Dynamics and Control [Proceedings of the symposium on nuclear engineer-
ing held April 5-7, 1965, at the University of Arizona, Tucson] (1966).
2. H. Plaza and W. Kohler, Nucl. Sci. and Engng., 26, 419 (1966).
3. B. V. Bulgakov, Oscillations [in Russian], Gostekhizdat, Moscow (1954).
T. S. Zaritskaya and A.. P. Rudik UDC 621.039.56
We consider the problem of finding the optimum reactor shutdown regime ensuring maximum energy
release during the transient process. We choose the reactor power as the function to be varied -the con-
trol. We solve the problem by using the mathematical apparatus of the nonclassical calculus of variations
in the form of the L. S. Pontryagin maximum principle from which it follows that only four kinds of con-
trol are possible: l) maximum power; 2) complete reactor shutdown; 3) power varying with time in such
a way that the xenon concentration has its maximum admissible value; 4) power determined by the classical
calculus of variations.
By using L. S. Pontryagin's principle [1], which states that each portion of an optimum path is also
an optimum path, the general form of the optimum path in the present' problem can be found by a numerical
comparison of various combinations of admissible kinds of control. It turns out that in the present case
the optimum transient regime consists of the following three stages:.
1) zero reactor power until the xenon concentration reaches its maximum admissible value.
2) power varying in such a way that the xenon concentration remains constant at its maximum ad-
missible value;
3) maximum power at which the reactor operates up to the time of planned shutdown. Quantitative
estimates are given of the gain in released energy during the optimum transient process.
1. L. S. Pontryagin et al., The Mathematical Theory of Optimum Processes [in Russian], Fizmatgiz,
Moscow (1961).
Translated from Atomnaya Energiya, Vol. 30, No. 4, p. 382, April, 1971. Original article sub-
mitted September 29, 1969; abstract submitted September 21, 1970.
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SOME PHYSICOCHEMICAL PROPERTIES OF
THE COMPOUND XeF2 ?'UFs
~~ ~ . r'; ?,.iJ ~ z ~ t.i? 1'it. y ~.r~~itl ~'~-:`?I1 i~tlJ 6 -
V. K. Ezhov* UDC 541.123
The possible existence of the compounds in the vapor phase has been investigated by either of two
methods.
The first technique relies on study of the behavior of a vapor-phase equimolar mixture of uranium
hexafluoride and xenon difluoride at different temperatures. The second technique involves investigating
the possibility of selective isolation of uranium hexafluoride from the compound with xenon difluoride exist-
ing in a condensed state. The existence of the compound XeF2 ?UFs in the vapor phase has not been detected
successfully by either of these techniques.
Processing of experimental data on determinations of the dissociation pressure of the compound XeF
? UFs as a function of the temperature has shown that the dependence described by the equation
~SPmm=9.30-T K'
holds in the temperature range from 24-100?C.
The heat of dissociation of the complex XeF2 ?UFs was calculated over that temperature range with
due attention to the fact that the pressure in the system studied is made up of equal contributions by the
partial pressures of uranium hexafluoride and xenon difluoride.. It was found to be a constant, 18.6 f 0.5
kcal /mole (77.9 f 2.1 kJ/mole) .
The heat of fusion of the compound XeF2 ?UFs was determined thermographically from the area under
the peak on the differential curve. The error allowed as a result of the approximations in those calcula-
tions was not greater than 0.3%.
The average heat of fusion of-the compound XeF2 ?UFs was 3.5 f 0.3 kcal/mole (14.6 f 1.3 kJ/mole)`
THE INTERACTION OF BERYLLIUM WITH MOLTEN
SODIUM FLUORIDE AND UF4 - NaF SALT MIXTURES
G. P. Novoselov, I. N Kashcheev, UDC 546.791.4
and A. V. Zolotarevt i
In [1] we investigated the possibility of reprocessing of irradiated uranium with molten fluorides of
the alkali metals. It was shown that uranium, plutonium, and the rare earth elements interact under non-
equilibrium conditions with the fluorides of the alkali metals, forming nonvolatile fluorides and liberating
the alkali metal.
In this work we investigated the interaction of beryllium with molten sodium fluoride and UFq-NaF
salt mixtures. It was established that under nonequilibrium conditions, at the temperature 1000?C, metallic
beryllium (0.2 g sample) interacts almost entirely with molten sodium fluoride within 30 min according to
* Translated from Atomnaya Energiya, Vol. 30, No. 4, p. 383, April, 1971. Original article sub-
mitted March 30, 1970; abstract submitted October 21, 1970; revision submitted October 21, 1970.
tTranslated from Atomnaya ~nergiya, Vol. 30, No. 4, p. 383, April, 1971. Original article sub-
mitted March 20, 1970; revision submitted August 31, -1970.
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In this case the interaction proceeds similarly to that described earlier,[1]; the main cause of the inter-
action is evaporation of metallic sodium from the reaction zone.
In the presence of an excess of sodium fluoride over the stoichiometrically necessary amount, the
salt phase was obtained in the form of a finely divided powder. The powder was formed as a result of
spontaneous pulverization of the low-temperature modification of sodium fluoberyllate [2] during cooling.
When salt mixtures UF4-NaF were melted in the presence of metallic beryllium for 60 min, beryl-
lium also interacted entirely with the salt melt, and the deposition of metallic sodium was observed. In
the case of subsequent cooling of the salt solution to room temperature (rate of cooling 33 deg/min), the
formation of two layers was observed. The lower layer represented a brown-colored melt and contained
96.5-98.7% by weight of the original amount of uranium. The upper layer was in the form of a white, readi-
ly separated powder.
1. G. P. Novoselov et al., At. Energ., 28, 48 (1970).
2. E. Tilo and H. Shreder, in: Beryllium [Russian translation], Vol. 1, Izd-vo IL, Moscow (1953), p. 32.
The experimental values of the photoelectric absorption .cross sections for hydrogen, .carbon, -alu-
minum, silicon, copper, tin, platinum, and water are approximated. The approximation functions have the
TABLE 1: Coefficients A, B, and C?for Calculating Photoelectric Absorption Cross Sections
by Eq. (1) (in units of 10-24 cm2/atom)
Element, ,
material I
Energy Lange
A
B
C
Element,
material
Ener ran e
$y g
A
B
_ __
C
_
Hydrogen
[0,01957;
0
4;310.10-9
3,53
[0;1566; 1,174`L)
957
1742
1
1
2,767.10-2
520
10-2
1
2,141.10-1
2
273
10-1
3,042
2
80
)
0,02925 ?
]
(
;
,
,
.
,
,
.
,
C azbon
[0,01957;
-0,0065
8,435.10-6
3,314
Tin
[0,01957;
-25
2,775.10-1
2,89
0,05871)
0,05724)
[0,05871;
-0,0004
7,026.10-6
3,376
[0,05724;
-39
3,8433
2,7
0,2935]
0,1174)
Aluminum
[0,01957;
-1,789
7,289.10-3
3,048
(0,1174; 0,5871)
'
0,1775
2,6207
2,874
0,07828)
(0,5871; 1,174
0
0,5267
2,3029
3,225
[0,07828;
2,667.10-a
4,032.10-3
3,23
[1,1742; 2,935]
0,1345
2,5532
2,412
0,3914)
Platinum
[0,02722;
-1,8791.102
2,5378
2,766
[0,3914; 0,7828)
5,4.10-3
1,712.10-3
4,024
0,078285
Silicon
[0,01957;
-2,725
1,088.10-2
3,023
(0,07828;
4,885
1,345
3,00
0,07828)
0,1538)
[0,07828;
3.33.10-3
5,569.10-3
3,24
[0,1538; 1,17~i2)
. 2,7273
17,4068
2,728
0,3914)
[1,1742; 2,935]
1,145
19,307
2,5
(0,3914; 0,7828]
5,010.10-3
7,307.10-3
'?,938
Water
[0,01957;
-9,35.10-2
4,268.10-a
3,24
0,09785)
Copper
[0,01957;
-6,14325.10
5,409.10-1
2,718
[0,09785;
4.10-3
2,55.10-?
3,425
0 05871)
0,1957)
[0,05871;
2,343
2,264
3,00
[0,1957; 0,3914)
4,5.10-3
1,873.10-a
3,6
0,1566)
? Square bracket denotes closed interval and parenthesis open interval.
0.01957 ~ a < 0.02925.
Translated from Atomnaya Energiya, Vol. 30, No. 4, p. 384, 1971. Original article submitted
May 25, 1970; abstract submitted July 3, 1070.
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form
where ~ is the y-energy in units.of mocz, and the-coefficients A, B, and C are listed in Table 1. The error
in the approximation does not exceed 1% over the whole energy range except at isolated points where it .
reaches 3%.
y-RADIATION FROM THE EARTH AND
NEUTRINO EXPERIMENTS
V. I. G l o t o v UDC 539.122.04: 539.123
The most important sources of natural terrestrial y-radiation constituting a basic component of the
external background in electronic neutrino detectors, and in particular in the lithium-drifted electronic
detector, are discussed. The discussion centers around the example of granite of average chemical com- ''
position containing 3.5.10-s g/g uranium, 1.8 ? 10-5 g/g of thorium, and 3.3.10-z g/g potassium. Yields
of y-photons generated through decay of uranium, thorium, and potassium, and in spontaneous fission of
U238 in (ay), (cx,a'y), (a, ny), (a, py), (ny), (n, n'y) reactions are estimated.
Fig. 1. Flux of unscat-
tered y-radiation from
granite, and magnitude
of electron background
in lithium neutrino de-
tector.
0 2 4 6 8 10 1
Ee, Me V
Translated from Atomnaya Energiya, Vol. 30, No. 4, pp. 384-385, April, 1971. Original article
submitted May 14, 1970; abstract submitted July 13, 1970.
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Experimental data on nuclear processes are borrowed from the literature in arriving at the esti=
mates. In other instances, the result is arrived at on the basis of general theoretical concepts, while
invoking assumptions simplifying the calculations. It is demonstrated that the decisive role in the forma-
tion of y-photons of energy < 3 MeV in granite is played by radioactive decay events, and that the decisive
role in the formation of >4 MeV y-photons is played by (ny), (a, py), and (cx, ny) processes. An experi-
mental investigation of the reactions Mg(c~, ny) and A1(a, py), in which energetically possible production of
y-photons up to 10 MeV is established, is carried out in order to lend greater precision to the estimates.
Curve 1 in the diagram shows the unscattered flux of photons ~unsc (Ey) obtained from a semiinfinite
granite slab. All of the y-radiation from the granite can be placed in two energy intervals in which the
integrated flux values contrast sharply: ~1 (Ey < 3 MeV) ~ 2.2 ? 105 cm-z/day and ~Z (Ey > 4 MeV) ~ 0.8
cm-z/day. When ~unsc impinges on a lithium detector (infinite lithium slab), background electrons of
density P(Ee) form as a result of the single Compton effect in the lithium slab (curve 2). Comparison of
the effect due to neutrino flux from the boron cycle of nuclear reactions on the sun (~v = 2.106 cm-2 ? sec-1)
and the value of P(Ee) shows .that the use of electron recording thresholds E~hr < 4 MeV is inadmissible in
electronic neutrino detectors, and that normal- performance of detectors of this type in an underground
mine gallery would beimpossiblewithoutheavy shielding to absorb the flux of y-photons of energy Ey > 4
MeV at least 106-fold to 10~-fold. This shielding may consist of combinations of pure (uranium and thorium
concentrations ~10-y g~g) and ultrapure (uranium and thorium concentrations ~10-12 g~g) materials. This
conclusion proves the necessity of an experimental search for shielding materials with an ultralow concen-
tration of uranium and thorium, as well as the need for a detailed analysis of the spectral composition of
background radiations.in such prospective materials.
DETERMINATION OF THICKNESS OF y-SOURCES
AND ABSORBERS FROM THE DEFORMATION OF
THE HARD PART OF THE ENERGY SPECTRUM
A method is described for determining the thickness of remote y-sources and absorbers by taking
account of the deformation of the hard part of the energy spectrum of the y-radiation from distributed
sources. This deformation is measured by a quantity ~ defined as the ratio of the intensity of the primary
y-radiation Jo of energy Eo to the. differential intensity of the hard scattered y-radiation Jo as E -- Ea, i.e.,
~ = Jp/ Jo
Relations are presented connecting the function ~ with the thickness of an inactive absorber, and in
the absence of an absorber, with the thickness of the radiation source for a plane isotropic source, a uni-
form half-space, and a uniform layer. Graphs of ~ (?x, 6) have been computed for a vertical collimated
detector with ahalf-angle aperture B -- 0?, and also for B equal to 30, 60, and 90? for a range of thicknesses
0.1 s ?x < 5.0.
The method is very sensitive.
Translated from Atomnaya Energiya, Vol. 30, No. 4, p. 385, April, 1971. Original article submitted
May 13, 1970; abstract submitted November 16, 1970.
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NEUTRON SPECTRA FROM 0.05 TO 10 MeV IN
CERTAIN SHIELDING MATERIALS
A.
P.
Veselkin, E. V. Voskresenskii,
Yu.
A.
Egorov, Yu. V. Pankrat'ev,
and
V.
I. Piskunov
A fast neutron. single-crystal scintillation spectrometer and a He3 spectrometer were used to mea-
sure neutron spectra in hydrogenous materials -lithium hydride and apolyethylene -lead mixture; in ma-
terials composed of elements of intermediate atomic weights -graphite, borated graphite, and serpen-
tine concrete; in heavy materials in whichthe moderation of fast neutrons is mainly by inelastic scattering
- titanium, steel, and lead.
The experimeht was performed at awater-cooled water-moderated research reactor. The measure-
ments with the He3 spectrometer were made under conditions close to semiinfinite geometry and those with
the scintillation spectrometer under conditions of shield geometry. The experimental results were normal-
ized in the 0.8-1.4 MeV energy region. The experimental error does not exceed 20-30%. As an example
the graphs of Fig. 1 show the spectra of neutrons transmitted through iron.
The neutron energy distributions are used to compute the attenuation functions and the relaxation
lengths of the neutron fluxes in nine energy groups. The error in determining the relaxation lengths is
5-8%?
'Z
f0
9
-
~'
-
-
2
g
1
~
`-
_
~
?~<
t
~.
~.
_. I
_
?~
2
'?m
i
g
--
zf
a
~
4
~
~
-
4
4
^oep
~
~
_
~
I
_
_
~
~
6
?.
5
g
4
2
~
0
_
4 sa10a 2 3 4 5 6 7 8
Neutron energy, MeV
Fig. 1. Spectra of neutrons
transmitted through iron (St.
3): 1) outside a 10 cm layer
of lead which remains in po-
sition; 2) outside a layer of
iron of thickness 10 cm; 3)
20 cm; 4) 40 cm; 5) 65 cm;
6) 82 cm.
Translated from Atomnaya Energiya, Vol. 30, No. 4, p. 386, April, 1971. Original article sub-
mitted August 6, 1970.
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DISTRIBUTION OF SPONTANEOUS .FISSION NEUTRONS
FROM URANIUM NUCLEI IN AN ORE BED CUT BY A
CYLINDRICAL BOREHOLE
Yu. B. Davydov UDC 539.125.52:551
The cylindrically symmetrical boundary problem dealing with the distribution of neutrons emitted
in spontaneous fission of uranium nuclei in a two-layer infinite medium, with a cylindrical interface, is
solved.
The internal medium simulates a borehole, the external medium the ore bed. This ore bed contains
neutron sources with aone-dimensional distribution, varying in the direction of the borehole axis. -The
assumption is thattliepresence of such sources, i.e., the variation in the chemical composition of the bed,
is without effect on the physical properties of the bed responsible for neutron transport (the bed consti-
tutes a quasihomogeneous medium in this sense).
The problem is solved in the two-group diffusion approximation. The solution in the general form is
found by the method of integral transformations. The Greens function method is applied in order to find
the concrete form of the solution [1].
A formula is derived for the density of thermal neutrons and fast neutrons in the borehole-bed sys-
tem, with an arbitrary pattern of source density variation. The solution of the boundary problem in the
general form serves as the starting expression for a further detailed analysis of the fission-neutron dis-
tribution in the cases of greatest practical interest, which are realized in actuality.
As an illustration, the fission-neutron distribution in a system comprising borehole and ore bed of
finite thickness with uniform mineralization is considered. Numerical calculations were carried out for
an ore stratum made up of porous limestone intersected by a borehole filled with fresh water. It is as-
sumed, in these calculations, that the pores in the limestone become filled up with fresh water.
Analysis of the results of the calculations provide evidence that treatment of the effect of the bore-
hole and intervening host rock can be handled independently in the first approximation, inasmuch as the
functions determining the effects of these two factors appeared as cofactors in the final solution. The con-
figuration of the neutron logging curves depends largely on the water content of the bed. Analysis of satura-
tion curves revealed that, as the hydrogen content increased, saturation set in earlier, i.e., at a lower
thickness of active ore stratum. It was also successfully demonstrated that, as the radius of the borehole
is increased, the fast-neutron density on the borehole axis declines, while a local density rise is observed
in the case of thermal neutrons, up to radii of 4-6 cm. This is explained by the anomalously high density
of dying-out of fast neutrons in the hydrogeneous medium.
LITERATURE CITED
1. D. Ivanenko. and A. Sokolov, Classical Field Theory [in Russian], Gostekhteorizdat, Moscow (1966).
Translated from Atomnaya Energiya, Vol. 30, No. 4, pp. 386-387, April, 1971. Original article
submitted April 21, 1970; abstract submitted July 23, 1970.
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DOSE SENSITIVITY OF A RHODIUM NEUTRON DETECTOR
G. M. Obaturov and Yu. K. Chumbarov UDC 539.12.08
To investigate the possibility of using a Rh103 detector for neutron dosimetry we have calculated the
average value of its dose sensitivity I'/ C (barns ? neutrons/ cmz ?rad) for various neutron spectra in the
energy ranges 0.4 eV-10 MeV, and 0.45-10 MeV.
The results of the calculations are shown in Table 1.
By measuring the activity (A, decays/sec) of a Rhlos detector and using the tabulated values of I'
/ C or t/ C the kerma of the neutrons K can be found from
K- .1
C (I'!C) '
where the constant C is 1.18 ? 10-T cmz/barn? sec for 1 g of Rhtos
It follows from Table 1 that dose can be measured with a rhodium detector to an accuracy which is
acceptable in practice, particularly if the shield material is known. The lower limit of the measurements
is ~1 rad.
TABLE 1. Values of Average Dose Sensitivity of a Rhodium De-
tector for Various Spectra
Translated from Atomnaya Energiya, Vol. 30, No. 4, p. 387, April, 1971. Original article sub-
mitted February 20, 1970; revision submitted November 30, 1970.
~~
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ENHANCING EFFECTIVENESS OF SYNCHROTRON CAPTURE
IN BEAM BUNCHING OUTSIDE OF SEPARATRIX
G. G. Gurov, E. A. Myae, UDC 621.384.634
P. T. Pashkov, and K. A. Yakovlev
The article cites results of calculations and experimental data on increases in the coefficient of
synchrotron capture of particles in the accelerator of IFVE [High-Energy Physics Institute]. The nonlinear
MN-7 analog simulation computer was used in the calculations. Numerical data on bunching time and the
parameters of the radio-frequency program were obtained, and the qualitative pattern of the capture pro-
cess was examined in relation to cases of beam injection above and below the separatrix.
The rapid phase shift in the accelerating field needed to bring about particle capture experimentally
was attained by introducing controlled amplitude and pulse width into the pattern of variation of the ejec-
tion frequency. Frequency deviation was measured by a broadband frequency discriminator which was
supplied with a signal proportional to the sum of the voltages of the resonators in the accelerator stations.
The pulse spreads of the beam-were t0.2, f0.24; f0.3% in the course of the experiments. Injection
current varied from 10 to 65 mA. The results of the calculations made with the accelerator operating at
low and medium intensities differed only slightly from the experimental results. With a f0.2% spread iri
beam pulse at the time of injection,. the capture coefficient increased 44% in injection above the separatrix
and 38% in injection below the separatrix. At an intensity level of 1012 protons/ pulse, or higher, the in-
Kcap
creased capture effectiveness with beam bunching
above the separatrix was found to be less than pre-
dicted, viz. ~10%. We may assume that particle bunch-
ing aggravated the space charge effect of the beam in
this case, and this would be important at that intensity
icv ci.
The calculations performed, and the results of
T experimental investigations (see Fig. 1), indicate that
Q50P F,?/u
Fig. 1. Dependence of maximum capture on
beam pulse spread: 1) capture with bunching;
2) conventional capture (experimental data
points indicated on predicted curves).
ayii~ui ~~i vu. ~.aN~ui c ciic~.~a v cucoo ~.c~.a. uv .a?.Ni v v..u .. v..
beyond that attainable by injection into asteady-state
separatrix, when the IFVE accelerator is operated at
medium intensity levels (up to 7 ? 1011 protons/pulse).
A considerable increase in capture effectiveness can
be achieved, by this method, even at the limiting accel-
erator intensity, it would seem, if the parametric reso-
nance bands are properly corrected.
Translated from Atomnaya Energiya, Vol. 30, No. 4, p. 388, April, 1971. Original article sub-
mitted May 18, 1970; abstract submitted October 12, 1970.
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LETTERS TO THE EDITOR
NOTE ON THE PROPERTIES OF THE INTEGRATED
REACTOR CHARACTERISTIC K+
A. I. Mogil'ner UDC 621.039.5
The integrated reactor characteristic K+, defined as
K+ = Average number of neutrons generated (1)
I Average losses through internal processes '
has been introduced in some earlier articles [1-3]. By internal processes, we mean those processes taking
place without involving any change in coordinates (absorption, slowing-down, scattering, fission). The
definition uses neutron worth, an adjoint function, as a weighting factor in the averaging process.
An expression has been derived [2] for K+ in the diffusion approximation, and it has been shown that
this quantity is close to the neutron multiplication factor in an infinite medium Kam, and the difference in the
two quantities alluded to is not below B4 in order of magnitude, in the two-group approximation, where BZ
is the buckling. Further, a relationship has been established, in the diffusion approximation, between K+
and S, the total contribution made to the reactivity (total statistical weight) by all the materials included
in the composition of the reactor (theorem on the total statistical weight of the reactor materials):
Keff - 1 g+-q
P Keff P+ K+ .
In a recent paper by Hungarian physicists [4], the above results have been extended to the rigorous
Boltzmann equation. In that case, it becomes necessary to add, to the two terms present in the denomina-
for of the ratio K+ in the diffusion approximation, still a third term.
It was demonstrated [4] that the addition of a thirdtermtol/K+ in the transport equation leaves Eq. (2)
unaltered in the many-group approximation of diffusion theory or transport theory, and does not affect the
relative conservatism of K+ with respect to dimensionality. This has been shown in the case of simple
one-dimensional geometry.
The purpose of the present note is to shed some light on the physical significance of the dependence
of K+ on the selection of the computational model, and to ascertain some possible limitations to be im-
posed on the relationship linking K+ to Kam.
In diffusion theory, the weight factor (worth 'or importance) varies at a given point for two reasons:
as a result of neutron losses or in response to a change in neutron energy. The two sources of possible
losses correspond to the two terms in the formula for 1~ K+. In the more general case, we also have to
deal with changes in neutron worth as the directions of motion (angles) change, leading to the appearance
of the third term in 1/K+.
Let us show that the similarity between the K+-characteristic of a real finite reflected reactor to the
Kam-characteristic of a reactor of the saxr~e composition (but of unbounded dimensions) is implied by the
most general properties of the Boltzmann equation.
The similarity theorem can be formulated as the equivalence of the effect, on the reactivity, of iden-
tical relative changes in the density ? and in the dimension R:
Translated from Atomnaya Energiya, Vol. 30, No. 4, pp. 389-390, April, 1971. Original article
submitted March 20, 1970.
? 1971 Consultants Bureau, a division of Plenum Publishing Corporation, 227 !Vest 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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u aP -R an (3)1
N
But the left-hand member of Eq. (3) is equal, by definition, to the total statistical weight of the reactor
materials [2]: S =?(8p/ 8?). It is convenient to make the substitution of variables
Bz = R2 = x, (4)
in the right-hand member of the equation; here C is an arbitrary constant, so that Bz = x has the meaning
of the buckling operator. We can then write
The dependence of the reactivity on the reactor dimensions is a certain function p(x) which can be
expanded in a power series:
p(x)=P(~)+x aP Io+ 2x2 a PP lo-I-... (6)
We shall assume that the conditions for differentiation of series (6) are fulfilled, so that, after differen-
tiation, we get
aP _ aP
8x ax
o+x axP lo+ 2x2 a P to+...
Multiplying the series (7) by x, and taking Eq. (5) into account, we represent the statistical weight S in
the form of the series
S pP aP _daP
2 - x 8x - x Jx o -F x2 8r2
s
P+=P-~ 2 .
If we recall that p(0) = p~ _ (K,o-1)/K,~, then we obtain, as a result, a formula for p,o:
2 a
S ~ 1 8p 1 a ~p _
Pro = P'+ 2 T 2 xy dr.`2 o F 3 x ax3 0~ .. .
But according to the theorem (2),
Substracting the preceding expression from the last one, we obtain the required formula
2
x2 ~ p
2 dx2
sP
o ~- ~ s ax3 0 -F .. .
~- ~ (?~) i
(1
(8)
1 8cn>p (12)
u'
n=3
The dependence (11) has an important physical meaning, in that it accounts for the importance of
the quantity K+ introduced here. -The value of p+ or K+ is a characteristic of the reactor core material.
(of its composition), and is a weak function of the reactor dimension (varying as ~1/R4) and of the com-
position of the reactor reflector, since the derivatives in Eq. (llj are taken at x = 0, i.e., for the case
of an infinite reactor where the reflector plays no role.
For experimental applications of the statistical weight theorem, the difference between p+ and p,o
can be taken into account by treating the fifthright-hand member of Eq. (11) as a correction calculated on
the basis of the dependence of p(x) for an unreflected reactor with the same core. Clearly, p+ = p~ in the
one-group approximation, given the absence of any dependence on xZ. The difference between p+ and p,o
shows up starting with the two-group approximation, for which
2 2
Pro=P-rx K,~ Fx2 Kro
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 Declassified in Part -Sanitized Copy Approved for Release 2013/02/25 :CIA-RDP10-021968000300080003-1 ,
in conformity with the data reported in [2]. It is clear from Eq. (14) that, in those cases where the two-
group approximation is valid, K+ will be greater than Kam.
For experimental applications of the total statistical weight theorem, the constants p+ can be ob-
tained from special measurements carried out on "bare" assemblies of the same composition. Comparison
of Eqs. (13) and (9) reveals that measurements of the total statistical weight make it possible to determine .
the migration area approximately: j!
i
:~i= - S2
When the values of p+ and p~ are far apart, we can resort to an estimate:
I,=i ~ P~ -P2 /_ Kam.
a
LITERATURE CITED
1. A. I. Mogil'ner, At. Energ., 21, 127 (1966).
2. A. I. Mogil'ner, At. Energ., 24, 78 (1968).
3. A. I. Mogil'ner, V. A. Osipov, and G. N. Fokin, At. Energ., 24, 42 (1968).
4. G. Kosai and Z. Szatmari, Nukleonik, 12, 243 (1969).
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 Declassified in Part -Sanitized Copy Approved for Release 2013/02/25 :CIA-RDP10-021968000300080003-1
E.
M.
Savitskii, B. G. Arabei,
V.
I.
Bakarinova, S. E. Salibekov,
N.
I.
Timofeeva, and V. M. Romashov
Hafnium and europium have high chemical activities, the former being. ahigh-melting element, the
latter aloes-melting element with a high vapor pressure [l, 2]. This explains the difficulty of obtaining
alloys of hafnium and europium.
Fusion of the elements by arc melting, and simultaneous .heating' of hafnium and europium in hafnium
containers, gave poor results owing to evaporation of europium. In the case of simultaneous heating,.
retention at 1800-2000?C led to the appearance of fissures in the containers, through which virtually all
the europium escaped by evaporation.
We succeeded in fusing these elements by heating in air-tight molybdenum capsules (diameter 35 .mm,
height 50 mm, wall thickness 4 mm), filled with hafnium chips (^?15 g) and europium metal (~5 g) in an
atmosphere of argon. Both elements were degreased before the experiments. These were performed with
hafnium iodide (98.7%), hafnium powder (^?99.5%), and europium metal (>99.7%). The capsule cover was
sealed by argon-arc welding to make an air-tight joint. The capsules were then annealed in a TVV-4
vacuum furnace at different temperatures in the interval 850-1600?C with a residence time of up to 100 h.
The alloys were subjected to spectral, chemical, x-ray structural, and microscopic analyses. Thin
sections of hafnium and its alloys for microscopic analysis were subjected to etching electropolishing at
1000
soo
200
0
Eu
Eu~ap+a-Hf ~" readily soluble in acids. The hafnium metal remained prac-
40 60
Hf, at, Q/a
75-85 V in a 20 : 1 mixture of CH3000H and HC1O4 with vigorous
mixing of the electrolyte. We used a stainless steel cathode.
The mutual solubility of hafnium and europium at the in-
L ~ vestigated temperatures was determined by chemical phase
22~s?to analvsis. The capsule was opened and the material immediately
Fig. 1. Hypothetical phase diagram
of the system europium-hafnium.
tically undissolved. The solution was used for deterxmmng the
europium and hafnium contents by gravimetric analysis (euro-
pium by precipitation with oxalic acid, hafnium with phenyl-
arsonic acid). To determine the amount of europium dissolved
in hafnium, a weighed sample (~10 g) of alloy chips was treated
with HCl, as described above, then dissolved in concentrated. HF
with heating for 1 h. The europium fluoride precipitate was
roasted at 1000?C, treated with 1 : 1 HCl and heated, and euro-
pium precipitated as the oxalate by oxalic acid. Table 1 gives the
results of chemical phase analysis of europium and hafnium after
isothermal boiling.
The mutual solubility of europium and hafnium is negligible,
The maximum solubility of hafnium in europium was ~1.7 wt. %
Translated from Atomnaya nergiya, Vol. 30, No. 4, pp. 390-391, April, 1971. Original article
submitted April 27, 1970; revision submitted August 3, 1970.
? 1971 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 /or $15.00.
Vap+L
I I
EuL+a-
Hf
826?10
u+a-Hf
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TABLE 1. Mutual Solubility of Elements of the System Europium-Hafnium from Chem-
ical Analysis Data
Heatingtem-
Initial composition, g
Content by analysis, g
Solubility,%
perature, ?C
(residence
hafnium
europium
hafnium
I
europium
hafnium in
europium
time 100 h)
free
combined
free
i combined I
europium
in hafnium
850
15
4,05
14,83
0,067
3,96
0,0035
1,66
0,025
1200
i5
5,17
13,79
0,034
4,97
0,0036
0,68
0,026
14,50
15
6,83
13,85
0,045
6,72
-- 0,0047
0,65
--- 0,034
1600
14
4,61
12,89
0,020
2,80
0,0032
0,71
0,025
at 850?C and ~0.7 wt. % at higher temperatures. The solubility of europium in hafnium at all the investi-
gated temperatures was about 0.03 wt. %.
X-ray structural and microscopic analyses of the hafnium-based alloys showed that treatment with
HCl did not lead to the appearance of any new phases or structural components. The lattice constants of the
alloys were almost the same as those of the initial hafnium, and displayed no change after heating at various
temperatures, an increase in temperature leading only to growth of the grains.
The mutual solubility of hafnium and europium at higher temperatures was not investigated owing to
possible reaction of the components with the material of the capsule. Microscopic and spectral- analyses re-
vealed that >1800?C a reaction occurs in the ternary system Eu-Hf-Mo.
On the basis of our results and data on the pure components [2, 3] and reactions in analogous sys-
tems (4-7], and taking into account the marked differences in the atomic radii and melting points, elec-.
trochemical properties, and crystal lattices of hafnium and europium, we suggested a hypothetical form
of the phase diagram of the system europium-hafnium (see Fig. 1); according to this diagram, europium
and hafnium do not form intermediate phases, and their mutual solubility is negligible.`
1. F. Spedding et al., Trans. Metallurg. Soc. AIME, 212, 379 (1958); Problems of Present-Day Metal-
lurgy, No. 3, 130 (1959).
2. F. Spedding and A. Daane, Metallurgical Reviews, 5, No. 19, 297 (1960).
3. D. E. Thomas and E. T. Hayes, The Metallurgy of Hafnium [Russian translation], F. M. Perelman'
(editor), Metallurgiya, Moscow (1967).
4. R. Lesser and E. Erben, Metall., 15, 30 (1961); Problems of Present-Day Metallurgy, No. 3, 146
(1961).
5. M Wright et al., Paper No. P/ 696, in: Proc. of the Second United Nations Intern. Conf. on the
Peaceful Uses of Atomic Energy, Vol. 5, IA EA, Geneva (1958), p. 390.
6. R. Elliott, Constitution of Binary Alloys, Suppl. I, McGraw-Hill (1965), p. 412.
7. I. Obiriata et al., Trans. Amer. Soc. Metals, 52, 1097, 1072 (1960).
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NOTES ON MEASUREMENT OF Tcssm ACTIVITY
Kh. Shtefan, V. A. Bazhenov,
V. V. Bochkarev, Yu. M. Golubev,
and T. N. Sokolova
To date, the activity of Tcssm has been measured primarily by a relative method, making comparisons
with the isotope Co57. The 4n/3-y-coincidence procedure has been used [1] in precision measurements.
This article presents a method for measuring Tcssm activitywith the aid of a 4~r(3 -counter to within f 2%
error (95% confidence interval).
The decay scheme of Tcssm is shown in Fig. 1. For convenience, the same scheme notation is used
here as in [1]: a is the transition probability, energy 2 keV; cal, a2, a3 are the internal conversion coef-
ficients of the corresponding y -lines; ERi is the sensitivity of the 4~r/3 -counter to radiation related to the
2 keV transition; Ea is the sensitivity of the 4~ra -counter to conversion electrons of the 140 keV and 142 keV
transitions; say is the sensitivity of the 47r(3-counter to y-emissions at 140 keV and 142 keV; Ey is the
sensitivity of the scintillation sensor to y-emissions at 140 keV and 142 keV.
N~=Np ~ae~l-'ra(1 -e~l)e~1_aaz-}-eH (11+xa3 -t-a(1-EHi) q+a2EHv-i (1-a) 1+a3EHv} ;
a 1-a
Nv=No ('1-EHv)EV (q-Paz+q.~a3/
1
Nc=Noa 1 + az (q -EBv) evE~l?
for the count rates in the R - and y -channels and in the coincidence channel. ,
Hence, assuming a2 ~ 0.1, a3 ~ 30 [2], ERy < 5.10-4, ERi < 0.5, and neglecting terms introducing
less than 1% distortion in the sum of the results, we obtain the approximate Goodier-Williams formula [1]:
IVBNv 1-eBi ( aaz (1 _ a) u3
Ne ,., No r1-~- FBi s~ `1-~az ~ 1-{~as / J ?
Figure 2 shows extrapolation curves obtained when ERi is varied, in the coordinates.
0
Fig. 1. Decay scheme of Tcssm
N~Ny 1-ell
J= N x= e
~ di
Curve 1 is borrowed from [1], while curve 2 was taken by the
authors. The Tcssm was obtained from aMoss-generator. The
Moss was absorbed, in the form of sodium phosphomolybdate, on
aluminum oxide. Proceeding along the axis from zero 3.5 times
closer than in [1] made it possible, to begin with, to use NH4C1 to
wash off the Tcssm, with subsequent decomposition of the ammo-,
nium chloride upon heating, and dissolution of the residue with
the Tcssm in HNO3. Secondly, use of a layer of gold for reflecting
the electrons derived from the 2 keV transition aided this purpose.
The coating of the source, applied to film 15 ?g/cmZthick, in
films of total thickness ~60 ?g/ cm` thick on both sides, rendered
Translated from Atomnaya 1?nergiya, Vol. 30, No. 4, pp. 392-393, April, 1971. Original article
submitted May 12, 1970.
m 1971 Consultants Bureau, a division of Plenum Publishing Corporation, 227 Nest 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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N~Ny/N~ ~
2,500
EAR
NaNy/N~
i i i i i
3 4 5 6 71-Ep,
EP.
Fig. 2. Dependence of NRNy /Nc on 1- ER1/ Eat'
possible absorption (103-fold) of the radiation associated with the 2 keV transition, while the conversion
electrons from the 140 keV and 142 keV transitions underwent practically no absorption. The count rate
of the 4~r(3-counter for radiation from a sealed source is
N~ = kN?,
h-EH [ aaz ~(1-a) a3 ].
1 -aaz 1 as
By measuring No by the extrapolation method, using 4~r~3-y-coincidences and subsequent measure-
ments of the count rates N~3 from those same sources sealed on both sides by layers 60 ?g/cm2 thick, we
found
aaz +~1-a) as J=0,1193
1 ~-az 1-r a3 J
to within f2% error in a 95% confidence interval.
Using the value so found, we measured the Tcssm activity with ease, with the aid of a 4~ra-counter,
and using the formula
_ ~~'a
N0 - 0.1193e~ '
where Na is the count rate of the 4~r/3-counter intercepting radiation from a source sealed on both sides
by layers 60 ?g/cmz thick, and corrected for background and dead time; E~3 is the recording effectiveness
of the 4~r(3 -counter for conversion electrons from the 140 keV and 142 keV transitions, and is usually close
to unity. I
LITERATURE CITED
1. I. Goodier and A, Williams, Nature, 210, No. 5036, 614 (1966).
2. R. Growther and J. Eldridge, Nucl. Phys., 66, No. 2, 272 (1965).
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CONSTRUCTION OF CERTAIN INJECTORS FOR EXPERIMENTS
WITH RADIOACTIVE INDICATORS
J. Dobzhansky, K. Korb el,
and T. Ovsjak
UDC 621.039.85
The constantly increasing use of tracer atoms in scientific research and technological measurements
compels experimental research workers to develop new types of injector construction. In this paper we
shall describe the construction of injectors in two cooperating Cracow institutes, the Institute of Nuclear
Fig. 1 Fig. 2.
Fig. 1. Section of a rapid-pulse injector: 1, 2) channels for supplying compressed air; 3)
piston; 4) axis of piston; 5) cylinder of pneumatic drive; 6) injection chamber; 7) channel
inserting indicator; 8) first reciprocating valve; 9) injector nozzle; 10) sheath of exten-
sion system; 11) leading flange; 12) seal of the "0" type; 13) slide=valve; 14) flange; 15)
transporting pipeline; 16) reciprocating valve of the extension system.
Fig. 2. General view of the rapid-pulse injector mounted on the pipe-line:
Institute of Nuclear Technology of the Mining and Metallurgical Academy, Cracow, Poland. Institute
of Nuclear Physics, Cracow, Poland. Translated from Atomnaya Energiya, Vol. 30, No. 4, pp. 393-396,
April, 1971. Original article submitted June 1, 1970.
? 1971 Consultants Bureau, .a division of Plenum Publishing Corporation, 227 (Vest. 17th Street, New York,
N. Y. 10011. 'All rights reserved. This artpcle cannot be reproduced /or any purpose whatsoever without
permission o/the publisher. A copy of this article is available from. the publisher /or ~p15.00.
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Fig. 3 Fig. 4 Fig. 5
Fig. 3. Throwing-in injector: 1) release rod; 2) sheath; 3) holder handle;
4) rotating spring of.the release mechanism; 5) cone of the release
mechanism; 6) lever; 7) injector rod catch; 8) pedal; 9) set of springs; 10)
axis of injector; 11) radioactive indicator; 12) block for tightening the in-
jector spring.
Fig. 4. Bore-hole pulse injector (simplified): 1) cable; 2) upper end piece;
3) electromagnet; 4) system of levers; 5) rack and pinion; 6) release (travel-
ing) wheel with dog; 7) rubber compensators; 8) lower end piece; 9) working
spring;; 10) lead sheath; 11) syringe.
Fig. 5. Bore-hole injector with a constant outflow of the indicator: 1) carrier
cable; 2) gear lever; 3) upper end piece; 4) electric switch; 5) electric motor;
6) universal shaft; 7) distributor box; 8) end switches; 9) gear-wheel drive;
10) push rod; 11) control device; 12) channel connecting the syringe with the
push rod; 13) interchangeable syringe; 14) protective stem.
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Technology of the Mining and Metallurgical Academy and the Institute of Nuclear Physics. These injectors
are intended for measuring the velocity of liquids and hydraulic mixtures under two conditions: 1) in pipe-
lines; 2) in bore-holes associated with hydro-geological and geophysical investigations. For the first prob-
lem, rapid-pulse and "throwing-in" injectors have been designed, for the second, pulse and continuous
injectors.
The Rapid-Pulse Injector. This was designed in order to introduce a tracer substance into the medium
under investigation (the medium moving through a pipeline) in a very short period of time so as to be uni-
formly distributed over the whole cross section of the flow. Figures 1 and 2 show a section and a general
view of the injector; the construction of this satisfied both the foregoing requirements.
The injector consists of three main elements: 1) atwo-chamber cylinder 5 with a piston 3, serving
as a pneumatic drive for the injector; 2) an injection chamber 6; 3) an injection nozzle 9 furnished with
reciprocating valves 8 and 16. The two chambers of the pneumatic-drive cylinder 5 and the injection
chamber 6 are arranged in series, facilitating the incorporation of a single common coaxial system. The
piston 3 in the drive cylinder 5 is reinforced by means of leather sleeves which automatically contract
during the operating period. The piston has a greater working area in the upper region; in alternate work-
ing cycles, compressed air from a compressor is forced against this through channels 1 and 2 by means
of distributor valves. The working cross section of the piston in the injection chamber 6 is some 100 times
smaller; thus a comparatively low pressure (3 atm) easily overcomes the internal pressure acting in the
pipeline, ensuring a high rate of injection. Three channels lead into the injection chamber. Two of these
(the second is not shown in the figure) communicate with the upper part of the chamber and serve to in-
troduce portions of tracer substance into the injector. These channels are opened each time before filling,
and after filling are firmly closed by means of special slides.. The working volume of the chamber 6 was
decided by considering the activity of the portion of indicator needed in order to match a specified sensi-
tivity of the detectors, and also by considering the practically feasible activities of the materials available.
The volume in question approximately equalled 12 cm3. The outlet of the injection chamber 6 was made in
the form of a jet 5 mm in diameter with a reciprocating valve 8. The injector was mounted on the pipeline
by means of a flange sealed tothe latter. During the fitting of the injector the pipeline accordingly had to
be evacuated, which in`practice caused many difficulties. In order to avoid this, an additional attachment
was designed so as to allow the injectors to be fitted during the normal operation of the pipeline. This
consisted of a slide valve 13, a flange 11 with a seal of the "0" type, an extension system comprising a
tube 9 terminating in the injector nozzle, and also a sheath 10. The slide 13 was mounted on the pipeline
during an interruption in the technological process (in the closed position). During the measurements,
the injector proper was attached to the slide, then the injector was moved up to the support through the
open channel of the slide and connected into a single whole.
The Throwing-In Injector_ Figure 3 illustratesthespecially designed throwing-in injector for mea-
suring the velocity of multiple-component hydraulic mixtures. The injector serves to introduce several
different indicators into the inlet of the pipeline at the same time, simulating various granulometric frac-
tions of the solid phase of the hydraulic mixture; it also serves to inject the liquid phase of the hydraulic
mixture. The injector is made from a steel tube with an outer diameter of about 30 mm and a length of
about 3 m. The injection of a portion of indicator (earlier prepared in the capsule 11) is effected as follows:
after introducing the device 12 into the holder of the injector, the pedal 8 is depressed with the foot and the
rod 10 is let down until the catch 7 connects with the lever 6. At the same time the pin enters into the
rod 1, which protects the system from any chance ejection of the charged capsule. Then the capsule,
closed on both sides by rubber pistons, is inserted into the bayonet holder of the injector. In order to
eject the capsule, the pin is removed by applying pressure to the head of the striking rod and the rod is
set in axial motion. The cone 5 seated on the end of the rod rotates the lever 6 and releases the catch 7.
The springs 9 expand, moving the piston, which expels the contents of the capsule together with the rubber
stoppers.
The Bore-Hole Pulse Injector. The bore-hole pulse injector (Fig. 4) has been specially developed
for measurements in bore holes, in which it is essential to provide for repeated injection after the simul-
taneous installation of the measuring probe. An injector of this type consists of two chambers: a closed
and an open one. The closed chamber is closed at the top with an end piece 2 accomodating a sealed cable
1, and at the bottom with an end piece 8, carrying a compensator to compensate for the volume of the
glycerin filling the chamber. A rod with a spring 9 passes into the lower end piece through an appropriate
gasket. Inside the closed chamber is an electromagnet 3, which, on receiving pulses along the cable 1,
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operates the catch of the release wheel 6. The wheel in turn is connected to the rack and pinion 5, and when
the spring 9 is released it produces forward motion in the plunger of the syringe 11. The open chamber
constitutes .a space in direct contact with the medium under examination. This accomodates the lead sheath
10 and the working spring 9, together with the plunger of the syringe 11, which squeezes out approxi-
mately 0.7 cm3 of the substance. The volume of the syringe is approximately 20 cm3, which provides for
some 27 injections. The next filling of the syringe is effected after removing the sheath 10.
This injector may also be used in hydro-geological installations for measuring the velocity and di- .
rection of motion of waters in open reservoirs. Practice has shown that, in the case of a small outlet
cross section of the syringe, no spontaneous outflow occurs; hence there is no need for a reciprocating
valve in the apparatus.
Bore-Hole Injector with a Steady Outflow of Indicator (Fig. 5): Like the injector which we have just
been describing, this is intended. for measurements in bore holes and in hydro-geological research. In
contrast to the pulse-type injector, which always inserts the same vclume, -this injector provides for con-
tinuous injection with a constant (steady) efflux of indicator. The injection time is changed by smoothly
regulating the period of operation of the drive motor. The operating principle of the injector is as follows:
when the gear lever is set in "reverse," the rod 10 moves to the position A until the upper end switch 8
operates. After a brief manipulation (associated with the fixing of the injector 13), the injector is con-
nected to the channel 12. Then the gear lever is set in the "forward" position, after which (in accordance
with the time of starting the drive motor) the indicator ejected by the injector plunger starts flowing out.
Motion is transmitted from the motor to the indicator plunger in the following manner: the motor 5 is con-
nected with the distributor box 7 by way of the universal shaft 6; the motion is transmitted from the box
7 by a drive system 9, which operates through a rack and pinion to produce forward motion of the rod 10
and the indicator plunger 13. When the indicator is completely discharged, the lower end switch 8 starts
operating. After the gear lever has been returned to the "reverse" position, the next portion of indicator
passes into the injector from an auxiliary container.
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 Declassified in Part -Sanitized Copy Approved for Release 2013/02/25 :CIA-RDP10-021968000300080003-1
DEPENDENCE OF BUILDUP FACTOR ON POSITION OF
SHIELD BETWEEN BREMSSTRAHLUNG SOURCE AND DETECTOR
V. P. Kovalev, V. P. Kharin, UDC 539.12.08:539.122
V. V. Gordeev, and S. P. Filipenok
From a consideration of the process of transmission of radiation through a shield it follows that a
change in the position of a shield between a source and a detector alters the conditions under which radia-
tion scattered in the shield is incident on the detector and therefore changes the dose buildup factor [l, 2].
Flattening absorbers of various materials are commonly used to produce uniform dose distributions of
bremsstrahlung from electron accelerators. A study of the dependence of the buildup. factor on the posi-
tion of the shield permits the location of the optimum position of the absorber between the target and the
irradiated object. The buildup factor for an isotropic y -source and a semiinfinite absorber may reach
values of several units [1]. If the angular distribution of the bremsstrahlung has a peak in the direction
of motion of the electrons and the absorbers are finite in size the buildup factor will be smaller.
We_ have measured the dependence of the dose on the position of the absorber between a bremsstrahlung
source and a detector for electron energies of 12.5, 15.7, and 21.8 MeV. The work was performed with a
type LYE-25 linear electron accelerator [3] using a tungsten target 1.8 radiation lengths thick. The angular
distribution of the bremsstrahlung from the target at selected values of the electron energy are shown in
~ ~
20 30 40 50 60 70 80
~---
90
14. f2 1D 8' 6 4 2 D 2 4 6 8 10 12 14 ngles Target- absorber distance, cm
Fig. 1 Fig. 2
Fig. 1. Angular distributions of bremsstrahlung from a tungsten target for electron ener-
gies of 22 (s); 15 (O); and 12.8 (0) MeV.
Fig. 2. Dose as a function of position of aluminum absorber of diameter: a) 50; b) 80; c)
120 mm for electron energies of 21.8 (e); 15.7 (O); and 12.5 (O) MeV.
Translated from Atomnaya Energiya, Vol. 30, No: 4, pp. 396-397, April, 1971. Original article
submitted April 6, 1970.
m 1971 Consultants Bureau, a division of Plenum Publishing Corporation, 227 Nest 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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 Declassified in Part -Sanitized Copy Approved for Release 2013/02/25 :CIA-RDP10-021968000300080003-1
Fig. 1. Aluminum, copper, and lead absorbers of various sizes were used. The detector was a thimble "~
chamber with a plastic lining 16 mm thick. The detector was 1 m from the target.
Figure 2 shows the results for aluminum absorbers. The figure shows that the maximum value of the
buildup factor occurs for the minimum electron energy of 12.5 MeV when the absorber is placed close to the
target. The buildup factor decreases with increasing electron energy and increases as the absorber diam- ~
eter increases. Thus for aluminum absorbing cylinders 120, 80, and 50 mm in diameter and 100 mm high
the differences in dose, depending on the position of the absorber between the source and detector, are ''
respectively 23, 8, and 4% for electron energies of 12.5 MeV.
The buildup factor also increases. when the absorber is close to the detector. However, it is dif-
ficult to make a quantitative estimate in this case because of the contribution to the dose made by secondary'
electrons from the absorber.
Similar results were obtained for equivalent thicknesses of copper and lead. No significant change in
the buildup factor with the atomic number of the absorber was observed.
1. D. P. Osanov, in: Instruments and Methods for Radiation Analysis [in Russian], Vol. 3, Gosatomiz-
dat, Moscow (1962), p. 53.
2. Yu. A. Kazanskii et al., Information Bulletin of the Nuclear Data Center [in Russian], No. 2, Atorruz-
dat, Moscow (1965), p. 305. -
3. V. I. Ermakov et al., Atomnaya Energiya, 29, 206 (1970).
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 Declassified in Part -Sanitized Copy Approved for Release 2013/02/25 :CIA-RDP10-021968000300080003-1
THE USE OF A (p, y) REACTION TO DETERMINE
THE CONTENT OF LIGHT ELEMENTS IN THIN
SURFACE LAYERS OF SAMPLES
S. S. Vasil'ev, Yu. A. Dzhemard'yan, UDC 539.1.06:621.039
G. I. Mikhailov, and L. P. Starchik
Resonance reactions (p, y) permit the detection of the presence of light elements in very thin sur-
facelayersof samples [lj, as well as the establishment of their depth distribution in the investigated layer
[2, 3] or sample [4].
For thick layers, the yield of y-quanta Y is determined by the function (the number of reactions per
incident proton)
~'= Fri as Ca-{-Yb~ (1)
0
where ?a = (~r /2) (NAvQ~I'r)/Aa; NAv is Avogadro's number; I'r is the true width of the resonance level r of
the compound nucleus; Ca and Aa are the content and atomic weight of the element to be analyzed; Ta is the
occurrence of the isotope, on the nuclei of which the reaction used is observed; S2o = ~ ~iCi+ ~i and Ci
2
are the stopping power (eV ? cm2/mg) and content of the i-th element present in the sample; n'ag, is the
cross section in resonance, determined by the element to be analyzed; Yb is the yield of y-quanta due to
the matrical elements, considering .the constant background of the pickup.
300 400 500 600
Proton energy, keV
/0
o'
ti
C
0
6
U
0 5,0
.
7
a
z
300 500 700 900 1100
Proton energy, keV
2
~~~--~
15
---
~ T
i
Fig. 1. Excitation functions obtained by
proton irradiation of targets of silicon,'
tantalum, and carbon (graphite): 1, 2)
samples of silicon; 3) tantalum target;
4) excitation function of carbon; 5) ex-
citation function of silicon (without
carbon impurity); 6) excitation function
of graphite.
Translated from Atomnaya Energiya, Vol. 30, No. 4, pp. 397-398, April, 1971. Original article
submitted April 6, 1970; revision submitted May 4, 1970.
? 1971 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 /or $15.00.
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The content of the element to be monitored, found in a thin layer (the energy loss by the protons
is comparable with the width of the resonance level DEp ~ rr), can be found by determining the area A (E)
of the resonance peak:
A ~E)=E ~S'-Yb)=vF'aTaCa? (2)
In this expression v is the thickness of the layer in g/cm2, while E is the thickness of the layer in .
energy units with the corresponding resonance energy of the protons. If the width of the real resonance
peak I'experim and the width of resonance on a "thick" target I'?r are known, then
2 Z 3
e- rexperim-rT? )
The largestyield of the (p, y) reaction in the case of thin targets is observed when
s
En=Eres~-2 (4)
An experimental verification of the method of analysis of the composition of thin layers was con-
ducted for the determination of the contamination with carbon of the surface of eight samples of semicon-
ductor silicon, subjected to various stages of technological treatment (cutting, grinding, diamond and
chemical polishing). An electrostatic accelerator was used to accelerate the protons. The cross-sectional
area of the beam incident on the target was ~1 cm2; the current of the beam did not exceed 3?A.
The determination of the carbon content was based on the use of the reaction C12(p, 'Y)Ni3 (Ti/2 = 10.1 '
min, Ea+ = 1..19 MeV, Ey ~ 2.4 MeV) . Since samples of silicon in which the impurities did not exceed 1%
were investigated, it may be considered that the value of Sto ~ const.
Figure 1 presents the experimental excitation functions of two samples of silicon 1 and 2, graphite
6, 'and tantalum 3. The presence of carbon in the surface layer of silicon can be concluded according to
the shape of the excitation functions 1 and 2, which was confirmed by an investigation of the curve of the
decomposition of one of the irradiated samples. On the basis of the excitation functions obtained in the
irradiation of samples of silicon (with the least positron activity) and tantalum, with the aid of theoretical
calculations we constructed the excitation function of hypothetically pure silicon 5, corresponding to the
conditions of this experiment. Deducting the function 5 from the function 1, we obtained the function of
excitation of carbon 4. On the basis of graph 4 we found the value of rexperim~ and on the basis of the
curve of escape due to pure graphite, 6, we found rT. It was determined according to formula (3) that
E ~ 100 keV. This corresponds to a layer of a silicon sample contaminated by carbon atoms,