SOVIET ATOMIC ENERGY VOL. 59, NO. 1

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• Document Creation Date: January 4, 2017
• Document Release Date: February 20, 2013
• Sequence Number: 1
• Publication Date: July 1, 1985
• Content Type: REPORT

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Russian Original Vol. 59, No. 1, July, 1985
January, 1986
-SATEi6q 59(1) 531-630 (19_85).
SOVIET
ATOMIC
ENERGY
ATO.MHAfl 3HEFTWA
(ATOMNAYA tNERGIYA)
? TRANSLATED FROM RUSSIAN,
q)_}
CONSULTANTS BUREAU, NEW YORK
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,I I 1 LI iata imp Ul cnergiya, a
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SOVIET ATOMIC ENERGY
A translation of Atomnaya Energiya
January, 1986
Volume 59, Number 1
July, 1985
CONTENTS
Engl./Russ.
ARTICLES
Recommendations on Calculating the Heat-Transfer Crisis in Pipes on
the Basis of a Bank of Experimental Data ? P. L. Kirillov,
V. P. Bobkov, V. N. Vinogradov, A. A. Ivashkevich, O. L. Peskov,
and I. P. Smogalev 531
Energy-Liberation Field in the Active Zone of a Boiling-Water?Water
Reactor ? A. A. Marakazov, Yu. A. Styrin, and A. A. Suslov 539 9
Taking Account of Height Constraints in Problems of Optimizing the
Spatial Energy Distribution ? N. A. Kuznetsov, P. T. Potapenko,
G. N. Shelepin, O. L. Bozhenkov, and V. V. Mal'tsev 546 13
Reconstruction of the Fields of Physical Quantities in RBMK
? A. D. Zhirnov, V. D. Nikitin, A. P. Sirotkin,
and V. P. Shaposhnikov 553 18
Complex Radiation Monitoring of the Fuel Distribution in Vibration-
Packed Fuel Elements ? L. I. Kosarev, N. R. Kuzelev,
A. N. Maiorov, A. S. Shtan', and V. M. Yumashev 558 22
A Study of the High-Temperature Creep in Coarse-Grained Uranium
Dioxide ? A. A. Gridnev, D. N. Dzalandinov, P. V. Zubarev,
and A. S. Panov 565 27
Calculation of the Displacement Peaks in the Continuum Approximation
? V. P. Zhukov and A. V. Demidov 568 29
Effect of Helium Blistering on the Hydrogen Permeability of the
Kh18N1OT Stainless Steel ? V. M. Sharapov, A. I. Pavlov,
A. P. Zakhar9v, M. I. Guseva, and V. N. Kulagin 574 33
Growth of Helium Pores in the Vicinity of and at the Grain Boundaries
? A. I. Ryazanov, G. A. Arutyunova, V. A. Borodin, V. M. Manichev,
Yu. N. Sokurskii, and V. I. Chuev 577 35
Hydrogen Permeability in Stainless Steel Interacting with TM-4 Tokamak
Plasma ? V. I. Bugarya, S. A. Grashin, A. V. Pereslavtsev,
Yu. M. Pustovoit, V. S. Svishchev, A. I. Livshits, and M. E. Notkin 584 40
Microwave Beam Instability in Proton Synchrotrons ? V. I. Balbekov
and S. V. Ivanov 587 42
Calculation of the Effects of Neutron Activation of Nuclei for Cases
of Superposition of the Signal in Gamma Activation Analysis
? A. P. Ganzha, M. G. Davydov, E. M. Davydov, and E. M. Shomurodov 598 49
Excitation Cross Section of the Characteristic X Radiation by Protons
and "He Ions for Elements with Z in the Range 22 Z 83
? E. Brazevich, Ya. Brazevich, V. F. Volkov, S. A. Gerasimov,
Lyu Zai Ik, G. M. Osetinskii, and A. Purev 603 52
LETTERS TO THE EDITOR
Influence of Reactor Irradiation upon the Electrophysical Characteristics
of Heteroepitaxial p-Silicon-On-Sapphire Layers ? B. V. Koba,
V. L. Litvinov, A. L. Ocheretyanskii, V. M. Stuchebnikov,
I. B. Fedotov, N. A. Ukhin, V. V. Khasikov, and V. N. Chernitsyn 610 58
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CONTENTS
Calculation and Experimental Investigation of the Heat Removal Modes of a
Shutdown BN-600 Reactor of the Beloyarsk Nuclear Power Station
? A. I. Karpenko, A. A. Lyzhin, and A. G. Sheinkman
Influence of the Change in Moisture Content of Atmosphere Air on the
Distribution of the Cosmic-Background Neutron Fluxes above a Water
Surface ? E. M. Filippov
(continued)
Engl./Russ.
613 60
616 61
A Pyroelectric Detector of Gamma Radiation with Compensation for the
Compton-Electron Current ? V. A. Borisenok, E. Z. Novitskii,
E. V. Vagin, S. A. Pimanikhin, and V. D. Sadunov
620
63
Polynomial Representation of the Bremsstrahlung Spectra of a Thick
Target for Electrons of Energy 10-22 MeV ? V. E. Zhuchko
and Zen Chan Uk
622
65
Heat-Transfer Coefficient with Glancing Flow Around Fuel Elements and
Tubes ? Yu. S. Yurlev and A. D. Efanov
624
66
Using Cadmium Telluride Detectors for the X-Ray Fluorescence Analysis
of Uranium Solutions ? V. V. Berdikov, A. V. Vasil'ev,
0. I. Grigorlev, B. S. Iokhin, and A. Kh. Khusainov
626
67
Half-Lives of the Spontaneous Fission of 239Pu and 241Pu
? A. A. Druzhinin, V. N. Polynov, A. M. Korochkin, E. A. Nikitin,
and L. I. Lagutina
628
68
The Russian press date (podpisano k pechati) of this issue was 6/28/1985.
Publication therefore did not occur prior to this date, but must be assumed
to have taken place reasonably soon thereafter.
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ARTIC Declassified and Approved For Release 2013/02/20: CIA-RDP10-02196R000300070001-4
RECOMMENDATIONS ON CALCULATING THE HEAT-TRANSFER CRISIS IN PIPES
ON THE BASIS OF A BANK OF EXPERIMENTAL DATA
P. L. Kirillov, V. P. Bobkov,
V. N. Vinogradov, A. A. Ivashkevich,
0. L. Peskov, and I. P. Smogalev
UDC 536.2
Existing recommendations on calculating critical heat fluxes appear to have some dis-
advantages. For example, in the tables in [1] and in [2], data are recommended for calcu-
lating these fluxes over restricted ranges in mass flow rate and steam content at the exit
(x xli). It is not always convenient to use suchtables. The calculation method of [3]
is complicated for engineering purposes because of the multiplicity of tabulated values for
the properties of water and steam, which are dependent on temperature.
The most reliable recommendations can be derived from a large body of experimental data.
As has already been communicated [4], the Thermophysical Data Center at the Power Physics
Institute has formulated computerized data banks. About 23,000 experimental points have
been recorded in the bank on the heat-transfer crisis in the boiling of water, including
data for uniform and nonuniform heating. The bank includes the data of [3] (about 1500
experimental points) and the data from check experiments (2579 experimental points). Table
1 gives the ranges in working and geometrical parameters for uniform heating for the collec-
tion of about 14,200 experimental points in the bank.
Control experiments have been performed on the heat-transfer crisis for water in tubes
with uniform energy deposition in the USSR during 1979-1982. There were 10 organizations
participating. The experiments were performed with identical values of the working and geo-
metrical parameters involving the use of the methods for measuring flow rate, temperature,
pressure, and other parameters adopted in those organizations. The main purposes of the
experiments were to determine the discrepancies between organizations, to elucidate the rea-
sons for the discrepancies, and to check and refine the recommendations for calculating the
heat-transfer crisis.
Preliminary information has been given in [5] on these experiments. Table 2 gives the
distributions of the experimental points by mode and geometrical parameters. The following
are major points in the statistical analysis of the data set:
1) There are considerable differences in the numbers of points provided by the different
organizations (from 28 to 629), and these points (from 15 to 119) are unevenly distributed
over the working parameters (Table 3);
2) there was no preliminary researcher's evaluation of the data accuracy;
3) in some of the experiments, the working parameters deviated from the agreed nominal
values.
These features to some extent complicate the data processing. The values for diameters
differing from nominal (8 mm) were first referred to the nominal value via the formula Ncr =
Ncrd(B/d)n, where the values of n were taken in accordance with the recommendations of [6]:
p, f,Tia 6,9 9,8 13,7 17,7
0,673 0,511 0,201 0,021
As the deviations in tube diameter did not exceed 3.6%, this correction in most cases
was less than 2.1%.
The data from the control experiments were evaluated statistically as regards the con-
formity between organizations. A preliminary study of the dependence of the critical power
Translated from Atomnaya Energiya, Vol. 59, No. 1, pp. 3-8, July, 1985. Original ar-
ticle submitted January 30, 1984; revision submitted December 14, 1984.
0038-531X/85/5901-0531$09.50 ? 1986 Plenum Publishing Corporation 531
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TABLE 1. Data Structure in Bank
Pressure
MPa
Water
flow,
kg/h
Tube
diam.,
mm
Tube
length, m
No.
of exptl.
points
1,0-5,9
57-1200 2-- 11
0,04-0,05
930
6,9
85-1220 4-15,1
0,25-6,0
1470
7,3-7,8
57-1220 2-15,1
0,04-6,0
1020
9,8
57-2140 2--15,1
0,04-6,0
2250
11,8
100-2040 4-15,1
0,25-6,0
920
12,2-12,7
57-1280 2-16
0,04.-6,0
600
13,7
70-1900 4-15,1
0,25-6,0
2000
14,7
57-1490 2-15,1
0,04-6,0
1350
15,7
140-19503,8-15,1
0,25-6,0
840
17,1- 17,6
57-1940 2-15,1
0,04-0,0
2070
19,6
57-2070 2-15,1
0,04-6,0
730
TABLE 2. Results from Experimental Data
Provided by Various Organizations
Organization
No.
No. of
e?pti.
points
Arithmetic
mean devia.
A, %
SD a, %
1
249
1,33
6,76
2
60
-6,84
11,12
3
190
0,96
6,15
4
477
2,18
6,7
5
629
-1,03
6,43
6
33
-1,15
5,3
7
273
-0,4
6,14
8
223
-2,5
6,22
9
28
3,0
4,99
10
417
-0,68
6,5
For all organ-
izations
2579
-0,16
6,6
For all organ-
izations apart
from No. 2
2519
-0,00045
6,46
Ozerzhinskii
Power Institute
on the inlet temperature showed that this was close to linear. A detailed analysis showed
that the quadratic term was not statistically significant. The dependence of Ner on the
working and geometrical parameters is more complicated. The following approximation was
used:
where
532
Ncr (p, pw, 1, tin) = a (p, pw, 1)11 - b (p, pw, tin].
At the stage of preliminary analysis, we selected the form of the functions
a (p, pw, andb (p, pw, 1),
a = a, + a2p a,pw a4 (pw)2+ a, (pw)3+ a6pwp a7 -F a, + a9 (Pw)2 + a10 + a1 1 ?
'p 1p2 4,2 p3 Upw)2
+ (1121 a?lpw (1141 (pw)2 a151PPw a1912 a1712Pw (11812 (pw)2 a19 (PPw)2;
b = b21 b,pw b41pw ? b5(pw)2 1)61 (pw)2 b7 ppw b,Ipw p3 b, (PW)3up), .
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(1)
(2)
(3)
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lAnch J. comparison or tne critical Power Calculated from (1) with Experimental Data;
A and a Defined by Organization No. 5 (Table 2)
P.
MPa
pw,
kg/m2.
sec
1,
mm
No. of
exptl:
points
p
A, %,
from
(1)
a, %,
from
(1)
A,W,
from
(10)-
(11)
a.%
from
(10)-
(to
P.
MPa
, PY.
-kg/m2.
sec
/,
mm
No. of
eXpti.
points
A %,
from
(1)
(F,%,
from
(1)
A,%. '
from
(10)-
(11)
(r. (X,
from
(10)-
(11)
6,9
500
1000
44
5,40
7,08
-6,77
8,02
13,7
1000
3000
89
3,48
4,70
1,39
3,73
6,9
1000
1000
78
-4,19
8,13
-1,37
5,25
13,7
2000
3000
99
5,3
6,2
3,16
4,70
6,9
2000
1000
101
3,32
8,0
0,25
4,89
13,7
4000
3000
58
0,29
4,73
-1,98
8,45
6,9
4000
1000
56
-3,76
6,52
0,81
10,71
17,6
500
3000
43
-0,46
5,27
-3,70
5,6
9,8
500
1000
45
0,61
3,33
0,57
3,57
17,6
1000
3000
62
3,07
4,56
-0,05
3,27
9,8
1000
1000
83
-4,92
7,35
-4,22
6,87
17,6
2000
3000
77
-4,0
5,69
-2,20
4,08
9,8
2000
1000
114
2;17
6,06
-1,92
6,46
17,6
4000
3000
53
-2,99
4,82
1,97
5,71
9,8
4000
1000
49
4,79
9,93
7,13
12,02
6,9
500
6000
13
-9,3
16,8
-0,68
1,10
13,7
500
1000
47
1,09
5,52
-8,84
9,72
6,9
1000
6000
41
-3,65
8,0
10,02
12,13
13,7
1000
1000
71
1,9
6,63
--4,07
6,54
6,9
2000
6000
42
--2,46
5,32
7,08
8,68
13,7
2000
1000
108
2,42
6,97
1,82
6,12
6,9
4000:)
6000
15
-6,68
8,23
-4,49
9,58
13,7
4000
1000
35
-0,83
4,99
--1,75
5,03
9,8
500
6000
16
2,68
5,48
5,09
6,02
17,6
500
1000
49
-4,02
7,4
--6,72
8,63
9,8
1000
6000
43
0,38
3,66
11,30
13,13
17,6
1000
1000
52
4,64
8,2
2,99
5,18
9,8
2000
6000
42
3,05
5,9
4,08
7,24
17,6
2000
1000
81
--1,11
5,96
--1,10
6,40
9,8
4000
6000
21
-3,29
5,55
3,62
7,73
17,6
4000
1000
41
--1,01
8,67
-2,27
8,04
13,7
500
6000
17
1,73
2,3
9,09
11,16
6,9
500
3000
36
5,7
7,7
-2,67
4,11
13,7
1000
6000
45
2,70
7,71
13,82
18,35
6,9
1000
3000
65
-9,4
10,33
3,23
5,18
13,7
2000
6000
45
3,26
5,02
6,66
8,19
6,9
2000
3000
72
-6,3
7,5
1,32
4,4
13,7
4000
6000
27
2,83
5,9
-3,64
8,89
6,9
4000
3000
49
-6,6
8,41
--4,10
7,19
17,6
500
6000
18
-6,9
7,48
2,70
3,18
9,8
500
3000
38
--0,28
4,55
2,29
4,38
17,6
1000
6000
31
-4,7
5,52
1,99
4,22
9,8
1000
3000
85
--4,04
4,7
1,18
3,33
17,6
2000
6000
25
-5,0
7,06
0,68
4,13
9,8
2000
3000
119
-1,6
4,63
--4,18
5,51
17,6
4000
6000
15
-1,79
9,79
-1,17
6,67
9,8
4000
3000
81
3,34
5,14
9,00
10,00
For complete set
2579
--0,16
6,6
13,7
500
3000
43
4,64
7,17
-0,92
4,7
of data from
control expt.
We used the following scales for the numerical data:
Ncr=Nci./100; p = p/10; pw-pw/1000; t 0100;
/ = 111000. ?
(4)
Here Ncr is in kW, p in MPa, pw in kg/m2-sec, t in ?C, and 9, in mm.
Although the functions of (1)-(3) are linear in the parameters ai and bi, the linear
problem could not be handled by least squares since the values of the variables p, pw,
and tin differed from the nominal values and did not cover the necessary ranges. To deter-
mine the optimum coefficients in (2) and (3), we used unconditional nonlinear Davidson-
Fletcher-Powell minimization [7]. There was no evaluation of the experimental errors by
the original researchers, which meant that a minimizing functional had to be used. There
are only comparatively small changes in the critical power (by factors of 2-3), and this
with the study of the methods led us to choose the relative standard deviation as the func-
tional fitted to the experimental points:
AIL c-Ag12,
n-28 1 Al n-2'28 [ 1178r.
i=1
(5)
which gives an estimator for the relative (weighted) variance. Here n = 2579 is the number
of experimental points, 28 is the number of coefficients in (2) and (3), Ncer.iare the experi-
mental values of the critical power, and IsTccr.i are the calculatedapproximatingvalues at the
corresponding points.
Table 4 gives the optimized coefficients. The general results in Tables 2 and 3 indi-
cate a satisfactory approximation by groups and for the data as a whole.
The results in Table 2 deserve separate analysis; it implies that the data from all
organizations apart from one are statistically in agreement. One can use Dixon's criterion
[8] to analyze for anomalies in the sample elements from the organizations. This criterion
is of ranking type for small sets and characterizes the deviations of one or more elements
in a series from the adjacent terms. The test indicates reliably that the data from organiza-
tion No. 2 (Table 2) are statistically anomalous at the 95% confidence level: on average
533
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TABLE 4. Optimal Values of the Coefficients ai and bi
i
1
2
3
4
5
ai
0,447688
-0,214717
0,2444943
0,0508382
-.0,00348812
bi
0,144131
0,00857681
0,0610103
_0,00482804
-0,00882715
i
6
7
8
9
10
ai
0,0844160
--0,0940023
0,142995
_0,0338257
0,00164519
bi
0,32836.10A
--0,00858400
-0,329807.103
0,138139.103
I
11
12
13
14
15
al
-0,999607.103
-0,961122.104
0,243949
--0,0419301
-0,0030037
i
16
17
18
19
ai
--0,00125827
-0,0243218
0,00437281
0,00340208
TABLE 5. Deviations in the Dzerzhinskii
Power Institute Data by Groups of Working
Parameters
1,M
P,MPa
Pw,
kg/m2.sec
No. of
points
%
a, %
1
9,8
9,8
13,7
13,7
13,7
17,6
17,6
17,6
From all the
Dzerzhinskii
Power Insti-
tute data
1000
2000
1000
2000
4000
1000
2000
4000
8
10
6
8
7
7
6
8
--15
-8,7
-5,19
--8,83
-0,66*
5,66
--3,48*
--13,72
17
9,68
9,45
10,18
3,17
12,66
10,02
15,07
GO -6,84 11,12
they are higher than those from the other organizations. Dixon's test applied to the data
from the other organizations indicates statistical homogeneity. The following point is
notable: out of the 48 matched groups of working parameters, organization No. 2 presented
data only for 8 groups and for one length (Table 5). Table .5 shows that small deviations
occur only in one group of the data (indicated by asterisks). Here we do not examine the
reasons for the deviations, although separate consideration should be given to various points
in the design of the Power Institute system and the method of producing the two-phase flow
in it.
Marinelli [9] reported a special study performed in Western European laboratories and
designed to estimate the reproducibility in data on the heat-transfer crisis. There were
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m/sec
Hfrml
sec
0,05
4044
0,01
0,02
0,07
0,1
0,1
0,10
0, 0
gos
402
in.Kkg/m?sec
500
\
1000
1500
_
? 2000
2500
3000
\ i'000
5000
_
N
_
_
8
10
p MPa
_
\
_
\\
pm0(g/m2
5000
WO
sec
3000
2500
2000
1500
_
1000
_
,
i
I
SOO,
1
1
12 14' 16 18 p,MPa
Fig. 1. Graph (nomogram) for determining K.
589 experiments on identical circular tubes (din = 10 mm, t = 2m) at 3-9 MPa and pw = 200-
6000 kg/m2.sec. A comparison of 363 points covering the range of parameters represented
by the data from all laboratories showed that there were discrepancies of up to 30% for cer-
tain data groups from two laboratories by comparison with the results from the others. If
we neglect these anomalous data, the standard deviation for the 268 points is 4.2%, the
maximum deviations being 14 and 19% on comparing the critical power levels by relation to
the optimized dependence on this data set.
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K2 m/
sec
414,
ppilkF/m2 sec
SOO
sec
0,02
0,07
8 S 10 77 12 ?M Pa
1ov,kg/m2 'sec
5000
0000 -
2700
2500
2250
2000
1500
1000
14,
500
15
18
p, MPa
Fig. 2. Graph.(nomogram) for determining K2.
Practical use of the data bank requires simple and reliable relationships for the crit-
ical power. These should be based primarily on the reliable results following a detailed
analysis and should have adequate accuracy and the widest possible working range. We de-
vised a simple method for calculating the critical power for the flow of unheated water and
for a steam?water flow. The method is based on the formula
where
NCr arlIKrp" xe? xin
Xe+C
C ? Kip"
d (pw) '
(6)
in which K and xe are empirical functions of the pressure and mass velocity, r is the latent
heat of evaporation, p" is the steam density, d is diameter, and 9, is length.
The physical basis of these formulas is given in [10]. The numerous empirical formulas
given in the literature at various times [11, 121 confirm the relationship, since they can
be reduced to (6).
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0,9
0,8
0,7
0,5
0,5
0,4
500 1000
Approved For
Release 2013/02/20:
CIA-RDP10-02196
s7%
N
IN
- Ampa
.....15,,
....:',,,,,15,7,.....
zy
11,75
12,7
'.0
70,70
5',' 5,85
8,8
5,80
??? . .
_.....,... .... ..?_,....
-........'
,...
12,5 ?
'
R000300070001-4
1500 2000 .pkt e.g/m2 *sec
Fig 3. Graph (nomogram) for determining xel.
From our viewpoint, the working formulas for the critical power as a function of the
stream content (or inlet temperature) are more reliable than the values for the critical
heat flux density as a function of the critical steam content and are of greater practical
value. This is mainly because Ncr and tin are primary experimental data. On the other
hand, the critical power in a uniformly heated tube is much the same as that in a tube
with a cosine distribution of the heat flux along the length (the discrepancies do not ex-
ceed ?10%) if the distribution is not too sharply varying (qmax/clav < 1.5) [6].
On solving (6) with the heat-balance equation for the tubes, we find that the relation
between qcr and xcr is linear:
qcr/Krp" = I ?(xer /x.). (7)
Usually [3], the entire range in the critical steam content is split up into three
characteristic zones. The first is the region of underheating and of steam contents less
than xii, which extends up to the kink in the qii = f(xii) relation. The second is the regionof
dispersed annular flow. In that range, qcr = f(xcr) may have a slope differing from that
in the first zone. In the third zone, which corresponds to large values of the critical
steam content, the slope of qcr = f(xcr) also alters. The third zone is of little practical
significance and is usually not considered. This division is now obvious, since it is re-
lated to modes of flow in the steam-water mixture and differences in the nature of the crisis.
Therefore, the suggestions made in [3] are advantageous.
The linear relationship of (7), but with a relatively large slope, was used to simplify
the calculations without altering the form of the relationship in the second zone when xcr
x. In general, this does not correspond to the actual situation, but it greatly simpli-
fies the calculations without increasing the error substantially.
Therefore, we divide the entire range of critical steam contents into two basic zones.
In each of these zones, qcr = f(xcr) istakenas linear. The slope in each zone is defined by
the empirical parameter K, while the point of intersection with the steam content axis
is defined by xe, and the boundary between the zones is defined by the point of intersection
between the two straight lines, which is close to x not only in physical signifi-
cance but also in absolute value [2, 13, 14]. The empirical tunctions Kl, K2, Xel, Xe2 are
derived from the experimental data [3, 6]. It is found that one can take xel = 0.7 xe2, no
matter what the values of p and pw. The values of these parameters are given in Figs. 1-3.
As the qcr = f(xcr) dependence is only slightly affected by the tube diameter, we introduced
a factor reflecting the effects of the diameter on K1 and K2 in the form
12.10-3 0,4
d m=(\
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The critical power is calculated as follows:
1) One determines the boundary xii between the first and second zones. Here it is neces-
sary to find the point of intersection between the straight lines from the formula
where
KI?K2
Xe2 K1-1,43K2 ?
2) One finds the approximate value of the critical steam content from
x. ==x
cr e2 C2m+xe2 9
C2m xin
C2 ==-- AK21p"Idpw.
(8)
(9)
This formula has been obtained on solving (7) with the heat-balance equation. The values
of the empirical parameters correspond to the first zone. Therefore, the formula is exact
for the second zone but approximate for the first one. As it is necessary to calculate xcr
in this case only to determine the region or zone, this simplification does not introduce
a substantial error.
3) The zone in which xcr falls (the first if xcr < xli and the second if xcr > xii) is
used to determine the critical power from the formula
in p
Ncr.i= irP"
( xe,?
where i = 1 for the first zone and i = 2 for the second. In (10)
c 4K1/p" c 4K2ip"
dpiv ' 2 '
F - nz? (12.10-3 )0.4 ;
xei 0.7xe2
(here K is in m/sec, r in kJ/kg, p" in kg/m3, 2. in m, Ncr in kW, pw in kg/m2-sec, and din
m).
If routine calculations are required, the graphical information for these parameters
can be loaded into the computer by standard programs.
We compared the calculated and observed Ncr over wide ranges in the working and geo-
metrical parameters (4.90 14 //1'>0.
U u , L. L
Replacingthevariablesopjal uj . and u . -i- a . , respectively, in all the conditions
J J J J
in Eqs. (7) and (8) and transforming them as shown above, a canonical form of the linear-pro-
gramming problem is obtained. The inequality in Eq. (13) may then take the form of an equa-
tion, with the following form
UUL LLL
uUj + xiU 13j ?cei; ui xj-=-13i?a ?,, 1, ...,n.
(14)
whemx and x. are additional nonnegative variables.
j
It follows from an analysis of Eq. (14) that, if in any iteration of the simplex algor-
ithm the variable ut! = 0 = 0), i.e., falls outside the basis, then the corresponding HIlj
U/ L
is at its lower boundary (completely immersed), according to Eq. (12). If x(x) is not in the
U xj L _ J J
basis,however,i.e. _ (), it follows from Eqs. (14) and (12) that the corresponding
HRj is at its upper limit (completely withdrawn). It is readily evident that, if both the
L
variables imixU - J (u-andx1Oarenonzero(inthebasis),thecorresponding HRj takesanintermediate
113 J J
position within the limits of its range of displacement. Thus, from the presence or absence
UULL
ofthevariables u?' x-' u-' J
x-inthebasis at each iteration of the computational .process, the
J J J
position of the HRj may be monitored within the limits of its range of displacement. This
allows the logic of the simplex algorithm to be corrected in determining the current variable,
which is introduced in the basis in such a way that the specified sequence of HRj displacements
is not disrupted.
In accordance with simplex-method theory, each iteration is accompanied by successive?
transition from one basis solution to another (at the stage of determining the permissible
basis solution) or from one permissible basis solution to another (at the stage of searching
for an optimal plan) [9]. In both cases, this transition is associated with the replacement
of one of the basis variables by a variable not belonging to the current basis. The criter-
ion for choice of the variable to be introduced in the basis is a maximum (in modulus) nega-
tive value of the characteristic difference. Since the characteristic differences are cal-
culated independently for all the independent variables, all the nonbasis variables are
equally correct for introduction in the basis from the viewpoint of the usual simplex-algor-
ithm scheme. Therefore, using this scheme cannot ensure the required sequence of HR dis-
placements in the course of solving the optimization problem.
At the same time, in the given problem of optimizing the spatial energy distribution,
the physical meaning of the successive transition from one basis to another by replacing a
basis variable by a nonbasis variable is that, within the limits of a single iteration of
the computational process, the position of only one of the rods HR, HRY.(j = 1, n)
J J
may be changed. If it is also taken into account that the presence or absence of the vari-
ables u., x., u., x. (j = 1, n) in the current basis may be used to unambiguously
J J J J
judge the position of any of the HRj before the beginning of each iteration of the simplex
algorithm, the possibility of governing the sequence of HR displacements in the course of
the whole computational process emerges.
This may be accomplished if the selection rule for the variable to be introduced into
U U L L /. _
the basis is corrected as follows. From among the variables u. xJ., u' kJ . x. - 1, n)
J' J J
not belonging to the current basis, a preliminary choice is made of those associated with the
URj for which the change in position in the next iteration is permissible in accordance with
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the established rule. To this subset are added nonbasis variables unrelated to HRj. Next,
the usual selection rule for the variable to be introduced into the basis is applied to the
set of nonbasis variables limited in this way, and the next iteration of the computational
process is performed in complete agreement with the standard scheme of the simplex algorithm.
Note that the method of preliminary selection of nonbasis variables here proposed is analo-
gous to the method of simultaneous calculation of the characteristic differences or suboptimi-
zation, described in [10], in which successive solution of the optimization problem is per-
formed with limited sets of nonbasis variables. The only difference here is that the selec-
tion criterion for the nonbasis variables is subject to a set rule of HR displacement.
The proposed method of solving the radial problem, taking account of the height con-
straint in Eq. (5), is also applicable, without any changes, in the case when each of the
CRj is replaced not by two but by a large number of HR with permissible displacement regions,
uniformly distributed within the limits of each half of the active zone. The condition of
nonexcitation of the first axial harmonic may be written here in the following form
\-1
( U L?=-1 ?Pli) + ? ? ? + ( 6PUij - 6Pt;) 01)
I -sr I.
In addition, for the time being, we shall assume that
0, e>o IQ; WI ? - q
(46)
However, when several multipoles are excited simultaneously this representation can strongly
distort the result. If
AQ, fIX
Qo nicr ,
(47)
then the series (38) contains a large number of terms, and the sum can be replaced by an
integral, which leads to the microwave dispersion equation and the formula (35) for A. In
this case, the expression (43) determines the maximum value of a separate term and thus gives
an estimate of the error of the result:
SA? Q" P" 12/3.
AO, 1 n/cr /
(48)
Formula (47) refines the microwave condition (20), which was used above. Inequality (21)
follows from it automatically also.
If neither of the inequalities (45) and (47) holds, then the series (38) contains a
relatively small number of terms, i.e., coupled oscillations of several multipoles with
indices close to m, appear. The calculation of the threshold requires the general formula
(38), which in this case cannot be simplified.
The study of other representations leads to analogous results, though the number of
coefficients can change somewhat. In this case, it is significant that all real distribu-
tion functions satisfy the condition F'(0) = 0. The role of this condition can be clarified
for the example of the distribution p(f),-.- __I-, for which the formulas (41)-(42) give
ea
1 52?
max
m2/3 APc
(49)
Therefore, the term in = 1 dominates in the sum (38), and the maximum is reached at IQI = 00,
which gives A = 00/A0c. Thus the instability begins with dipolar oscillations of the bunch.
Microwave oscillations cannot appear, because the condition (20) does not hold. Increasing
the resonator frequency leads to the fact that the excitation of the bunch, remaining dipolar,
is pulled toward its center. At very high frequencies, only the central core oscillates,
while the periphery of the bunch remains almost stationary.
It is evident from the formula (43) and the subsequent analysis that when the frequency
of the resonator is increased the factor A decreases and approaches the microwave limit (35),
if SA/Tritcr 1. In other words, the beam is most stable in the microwave zone. This asser-
tion follows in a more general form from the results examined in Secs. 3 and 5. We present
the main idea of the proof without details. The threshold curve C [see (30)], generally
speaking, encompasses the region of strong instability, since the latter is described by Eq.
(19). The full region of instability, of course, is wider and both regions coincide only in
the microwave limit.
In conclusion, we shall evaluate the error in the calculation of the microwave value of
A associated with the use of the formula (24) near the resonance point (see Fig. 2). At this
point the conditions (22) and (39) must be satisfied simultaneously. Taking into account (23)
also, it is evident that in calculating A with the help of (24) terms lying in the interval
I m - m? SmQ, where
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lki iki v
q "C (r0) Y, 62 inE2 q
MQ
(eQH e k --1113
6 do Qiq rQl
(50)
give the largest error. Now, using the formulas (24) and (40), we can find the correction
to A:
mg-I-6mu
Qs IF' (')I
SA [2
(e,2)1 lint,g, (r&I)140) 6mg ? (rm) 12,,, den] ,
7;?
where m and tm are related by the relation (39). A calculation leads to
SA -12L)1"
nier
(51)
(52)
In the microwave zone, where the condition (47) holds, this error is, for all practical
purposes, negligible.
APPENDIX
We shall study a chamber whose impedance is determined by several narrow-band resonant
elements with approximately the same coupling resistances. First of all, it is clear that
there is no mutual effect of elements if their resonant frequencies satisfy the conditions
(Al)
where t is an arbitrary integer. The resonant terms not satisfying (Al) must be examined
simultaneously. In this case, the dispersion equation has the form
det RShk, zk;,(0) kh, (52) = 0.
(A2)
A calculation of the matrix elements using the procedure described in Sec. 3 leads to the
following result:
c'nG' (u) du
kie (Q) i k"s" h?k. ?
aPs
Q+ r 11(os u
Ps
Gh(u)= 2n vio. F (x, u)] exp (i ?kg x dx.
This gives an estimate of the relative value of the matrix elements:
Ykk' I q k .
I YkkI k xmax
(A3)
(A4)
(A5)
If this value is small, then the nondiagonal matrix elements can be neglected, which
reduces (A2) to dispersion equation in the text (10). A calculation in the near threshold
region using the procedure examined in Sec. 4 leads to the same conclusion.
Next, we take into account the fact that only the matrix elements with indices kj
?wj/ws are actually different from zero. This leads to the following condition of applicabil-
ity of the results obtained: for each resonant frequency and for each pair of frequencies
the relations
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(0;>> ?(0;1> ,
the first of which coincides with the microwave condition (21), must hold.
LITERATURE CITED
(A6)
1. A. N. Lebedev, "Coherent synchrotron oscillations in the presence of space charge,"
At. Energ., 25, No. 2, 100-104 (1968).
2. F. Sacherer, IEEE Trans. Nucl. Sci., NS-20, 825 (1973).
3. P. T. Pashkov and A. V. Smirnov, "Longitudinal short-wavelength instability of proton
bunches interacting with the resonator," At. Energ., 50, No. 6, 480-412 (1981).
4. D. Boussard, CERN LAB II/RF/Int 75-2 (1975).
5. G. G. Gurov, Preprint No. 80-109, Institute of High Energy Physics (1980).
6. D. Boussard et al., IEEE Trans. Nucl. Sci., NS-24, 1399 (1977).
7. A. A. Kolomenskii and A. N. Lebedev, Theory of Cyclical Accelerators [in Russian], Fiz-
matgiz, Moscow (1962).
8. E. T. Copson, Asymptotic Expansions, Cambridge Univ., Press (1965).
CALCULATION OF THE EFFECTS OF NEUTRON ACTIVATION OF NUCLEI FOR CASES
OF SUPERPOSITION OF THE SIGNAL IN GAMMA ACTIVATION ANALYSIS
A. P. Ganzha, M. G.,Davydov, UDC 543.0
E. M. Davydov, and E. M. Shomurodov
When a sample is activated by bremmstrahlung from an electron accelerator, the photonu-
clear [zA(y, x)C] and neutron [zB(n, y)C] reactions on isotopes of a single element Z can
form the same radionuclides C. The analytical signal in the spectrum of the gamma radiation
of the activated sample will be formed by the superposition of signals from the radiation
of radionuclides ? products of y and neutron activation. This signal amplification effect
must be taken into account in y activation analysis when selecting the optimum energy of
the bremmstrahlung spectrum Eym. In calculating the effect, the activation from both the
background photoneutrons of the accelerator ("external") and from photoneutrons formed in-
side the sample itself ("internal") must be taken into account. The calculation for differ-
ent pairs of reactions (y, y')?(n, n'), (y, n) ? (n, 2n), (y, n) ? (n, y) and others is sim-
ilar, though in each case it has peculiarities which are determined by the energy dependence
of the reaction cross sections.
For definiteness, we shall study the proposed method for calculating the contribution
of neutron activation to the analytical signal for the pair of reactions (y, y'), which is
of special interest for y activation analysis. In spite of the relatively small cross sec-
tions of the reactions (y, y'), they in many cases make it possible to develop exceedingly
selective and fast methods for experimentally determining commercially valuable elements
in samples with a complicated composition [1, 2]. The prospects for the exploitation of
the reactions (y, y') in y activation analysis is demonstrated, for example, in [3-8]. In
addition, the neutron activation effect under study must be especially significant in this
case because of the peculiarities of the cross sections of the reactions (y, y') and (n, n'
The yield of nuclei in the isomeric state with activation of a sample in a real bremm-
strahlung beam from an electron accelerator (with an admixture of internal and external
photoneutrons) will contain three components which depend differently on Eym.
The first component is determined by the cross section cry,y1 of the reaction (y, y')
on nuclei of the sample under study. If the bremmstrahlung spectrum is described by the
product of the integrated spectrum W(Ey, Eym) [9] and the angular distribution of the bremm-
strahlung [10], then the expression for the yield of the photonuclear reaction can be writ- '
ten in the form [11]
Translated from Atomnaya Energiya, Vol. 59, No. 1, pp. 49-52, July, 1985. Original
article submitted February 13, 1984.
598 0038-531X/85/5901-0598$09.50 @ 1986 Plenum Publishing Corporation
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YY, v' (Evm) = aiD (Eym)Q (Evm, 0)>< ov, (E OW (Er, E',") dE,
(1)
where al is the coefficient of proportionality; D(Eym) is a function describing the dependence
of the bremmstrahlung dose on Eym; Q is a function determining the relative fraction of the
average intensity of the bremmstrahlung on the sample, subtending an angle 219, relative to the
intensity at the center of the sample; and, EII,Y is the threshold of the reaction (y, y').
The second component depends on the cross section 0n,n1 of the reaction (n, n') on the
nuclei of the sample under study, the normalized spectrum of the background photoneutrons of
the accelerator fp(En, Eym), and their flux Yp and is proportional to the yield of the reac-
tion (n, n') from the sample, owing to the background photoneutrons:
Enmax
VP IP 1
4 n, n' \441,m,1 ".2-71) \? IFymi ip (EnEwra) on 01 (Er,) dEnl
(2)
where a, is the coefficient of proportionality; En is the energy of tl;le neutrons, Enmax is
the maximum energy of the background-photoneutron spectrum; and, Exill'n is the threshold of the
reaction (n, n'). A Maxwellian spectrum with an effective temperature i(Eym) is adopted for
the spectrum of the fast background photoneutrons:
fp (E nEym).- kE ? exp [ ? E?IT (Em)111'2 (3)
The third component is determined by the cross section on,nt of the reaction (n, n')
on nuclei of the sample under study, the normalized spectrum of the photoneutrons fi(En,
Eym) of nuclei of the i-th type in the sample, and their yields Yi(Eym), and is proportional
to the yield of the reaction (n, n') from the sample owing to photoneutrons formed in the
sample itself:
?11. max
(E ym) a3 n, (En) 2 1 (E,m) Ii (En, Eym) dE (x' Y') dV dV'
j r2
v v.
n'
(4)
where a3 is the coefficient of proportionality; V and V' are the volumes of integration over
the sample; -a(x', y') is a function describing the distribution of the intensity of thebremm-
strahlung over the surface of the sample; r2 = (x - x')2 + (y - y')2 + (z - z')2 is the
square of the distance between the elementary volumes dV and dV' with the coordinates (x, y,
z) and (x', y', z'), respectively. Writing r'2 = xt2 yr2 and using .a(0) from [121, we
obtain
m
* 1[1 E ? r') 2 2
arctg ,
moc2
(5)
where G is a normalization constant and L is the distance from the bremmstrahlung target
to the sample. The yields of photoneutrons on the nuclei of the sample Yi(Eym) are calculated
in a manner analogous to the calculation of the yield Yy,y1(Eym) from relation (1).
The internal photoneutron spectra fi(En, Eym) were calculated using the method described
in the monograph [12]. We assumed that this spectrum consists of two parts: the evaporative
Maxwellian part fim with the corresponding value T(Eym) and a part corresponding to the con-
tribution of direct processes fin; in addition, the relative fraction of neutrons from the
direct processes ai was assumed to be independent of Eym. The values of ai are taken from
[12]. The form of the photoneutron spectrum from direct processes, as in [12], was approxi-
mated in accordance with Wilkinson's model
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fin (E.)? Pi14/ (Bi+E, Eym) G1, n(Bi?E,,),
(6)
where oi is a normalization constant; Bi is the binding energy of the first neutron in the
i-th nucleus; and, En is the instantaneous neutron energy. The full spectrum of internal
photoneutrons of nuclei of the i-th type in the sample is
fi(En, Em)= +ai l exp [ ? ErilTi (Ev.)1
T(Em)
ai 4..
1.-I--at un
(7)
With an energy Eym > 18-20 MeV neutrons formed in the reactions (n, n') on nuclei in the
sample will make increasingly larger contributions to the yield of the reaction (y, 2n) from
the internal photoneutrons. Including the contribution of this reaction, the yield of the
reaction (n, n') is
En max
72, a3 Crn,In' (En) 2 Er' 'fn (Er, Ev,n) +231' 2n1i2n (E ,Evni)1dEn C15 (x' V)/r2 dV dV'. (8)
V
The calculation of the yield YYTI is analogous to the calculation of Y1,11 and
and the spectra of photoneutrons fi2n(En, Eym) from the reaction (y, 2n) are calculated by
the method described in [12].
It is obvious that the contributions of the second and third components of the yield of
the isomeric state, i.e., the contribution of the activation of these states, owing to the
reaction (n, n') from external and intvrnal photoneutrons, will grow rapidly with Eym when
Eym > EY'. Since the thresholds ETTII'n of the reactions (n, n') are low, the cross sections
as a rule, are substantially higher than Gy,yi, and the photoneutron (internal and
external) spectra become increasingly "harder" as Eym increases, the contribution of neutron
activation with respect to photoactivation of the isomer will increase rapidly with Eym and
can be very substantial at an energy of Eym = 20-25 MeV.
To check the validity of the proposed method for calculating the Eym dependence of the
contributions of neutron activation of isomeric states of nuclei to photoactivation of these
states by bremmstrahlung from electron accelerators, as a model variant we selected activa-
tion of the isomeric state of the 115In nucleus in the bremmstrahlung beam from the B-25/30
betatron. For this case, Yg,n,, Y151,n,, and Yy,n were calculated numerically for values of
Eym equal to 10, 13, 16, 19, and 22 MeV. The quantity Yg,n, was calculated using the rela-
tions (1) and (2) for L = 25 cm, a sample radius ro = 1.5 cm, and sample thickness t = 0.2
cm. The data on the dependence of the cross section of the reaction (n, n') on the energy
of the neutrons on,n1(En) are taken from the handbook [13] and were supplemented by new
data provided by the Center of Neutron Data of FEI.
The dependence of the effective temperature of the nucleus T on Eym, required for cal-
culating the background photoneutron spectrum using the formula (3), is obtained as follows.
According to the data of [14], the experimentally determined spectra of the background
photoneutrons of the betatron have a form which is typical for the spectrum of photoneu-
trons of a separate nucleus. The form of the spectrum is close to Maxwellian with T = 1.3
MeV at Eym = 25 MeV (if the presence of fast-neutron peaks on the high-energy side of the
spectrum is ignored). Keeping in mind the monotonic_dependences of the effective tempera-
ture in the photoneutron spectra of separate nuclei T(A) for fixed Eym (see the calculations
in [15]) as well as the low sensitivity of the spectra to a change in the cross sections of
photoneutron reactions, it may be assumed that the spectrum of the background photoneutrons
of the accelerator will be similar (equivalent) to the spectrum of photoneutrons for nuclei
with a value of A for which with fixed Eym the value of T will be equal to the experimental
value. The experimentally obtained value T = 1.3 MeV for Eym = 25 MeV is close to T ob-
tained by the calculation in [15] for the 59Co nucleus. It may therefore be assumed that
59Co is an acceptable equivalent for describing the dependence T(Eym) of background fast
photoneutrons of the betatron, and the dependence T(Eym) obtained in [15] for this nucleus
can be used in our calculations.
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'rel
4+
0,2
10 13
16
19 Er, MeV
Fig. 1. Dependence of the relative yield of the iso-
mer 115111Informedin the reactions (n, n') on the max-
imum energy of the bremmstrahlung Eym. The yield
YP
n owing to the background photoneutrons of the ac-
n,
accelerator (external): 1) the calculation;
.) the experimental values. The yield Y.,(1,n owing
to photoneutrons formed in the sample itself (in?
ternal): 2) calculation taking into account the spec?
tra of photoneutrons from the reactions (y, n) and
(y, 2n); 3) calculation taking into account the
spectra of photoneutrons from the reaction (y, n); 4)
calculation ignoring the photoneutron spectra; o)
the experimental points.
The yield of fast background photoneutrons Yp(Eym) for the B-25/30 betatron as a func-
tion of Eym was obtained previously in separate measurements for L = 25 cm with Eym = 25
MeV (the dosage was 0.7 A/kg). The yield of background photoneutrons of the electron ac-
celerator in the expression (2) was assumed to be independent of the angle, since within
the range of angles e Indeed, the curve of the yield Yi?r, calculated taking into
account the contribution of neutrons from the (y, 2n) reaction to the yield (see curve 2),
is steeper for high Eym than the yield curve calculated without this reaction (see curve 3).
The experimental values for Yl?,1en, within the limits of error of the measurements are
in agreement with both computed cur177es, though they lie closer to the curve Yiqcnr(y, 2n).
The computed and measured values of the yields Ywieft Yg,nl and YT?I,n,, which agree
within the limits of error of the measurements, were used to estimate the relative increase
in the yields of the isomer 115mIn due to the reaction (n, n') generated by the external
(YP 1/Y 1) and internal (Y? n f/Y'Y
Y I) photoneutrons. For the experimental conditions
n n Y'Y n
desCribed above, the relative increase for Yg,naYy,y1 was equal to 0.4, 0.7, 1.5, and 2.1%
for Eym equal to 13, 16, 19, and 22 MeV, respectively, and 5, 10, 20, and 25% for YA,n1/Y1,y,
for the same values of Eym, respectively. It should be underscored that these estimates are
meaningful only for the accelerator and the specific experimental conditions used in this work
and are presented only as an illustration of the possibility of making a quantitative evalua-
tion of the contribution of the reaction (n, n') to the yield of the isomeric state from
the reaction (y, y').
The experimental value of 14enf for Eym = 13 MeV is higher than the computed values
ygcnI.It should be noted that for low Eym the experimental determination of different con-
tributions to the yield of activation of isomeric states using the procedure in [18] is un-
reliable. The calculation of Yn,n1 neglecting the photoneutron spectra of indium Yc gives
Y'n
a dependence Yn,n,(Eym) differing appreciably from the values lel'icn,(Eym), calculated taking
into account the photoneutron spectra and from the experimental values Ylirilen,.
The computed dependences of YIP1,11, on Eym agree with the experimental dependences within
the limits of error.
Thus the proposed method for calculating the contributions of neutron activation of
isomeric states of nuclei for the model case of activation of indium samples studied here
in a real bremmstrahlung beam from an electron accelerator gives reasonable agreement for
both the relative contributions YR,nt/Y and YP dY and the energy dependence of these con-
tributions.
Using the proposed scheme with the appropriate data on the cross sections of the reac-
tions (y, x) and (n, y), it is possible to calculate the contributions of neutron activation
of nuclei on external and internal photoneutrons to the activation of a finite sample in
a bremmstrahlung beam from an electron accelerator. Such a calculation of the energy depen-
dence of the activation effects from the reactions (n, y) makes it possible to avoid performing
a large number of measurements of these contributions for different values of the bremmstrah-
lung energy. The experimental measurement can be performed at one quite high value of the
bremmstrahlung energy on the basis of the measurements of activation yields in two geometries
for three identical samples using the procedure described in [18]. For the remaining values
of the bremmstrahlung energy, the required contributions of the neutron activation are found
by calculating the energy dependence using the absolute experimental data for one value of
Eym.
The foregoing computational method can be used both in formulating experiments for de-
termining the yields of photoactivation of nuclei by electron accelerators and for optimizing
the conditions for determining elements in y activation analysis.
LITERATURE CITED
1. R. A. Kuznetsov, Activation Analysis [in Russian], Atomizdat, Moscow (1974), p. 126.
2. A. L. Yakubovich, E. I. Zaitsev, and S. M. Przhiyalgovskii, Nuclear-Physical Methods
of Analysis of Minerals [in Russian], Anergoizdat, Moscow (1982), pp. 102-106.
3. A. K. Berzin, Yu. A. Gruzdev, and V. V. Sulin, in: Nuclear Physical Methods of Analysis
of Matter [in Russian], Atomizdat, Moscow (1971), pp. 236-244.
4. 0. Abbosov, S. Kodiri, and L. P. Starchik, in: ibid., pp. 244-255.
5. Yu. N. Burmistenko, E. N. Gordeeva, and Yu. V. Feoktistov, in: Radiation Techniques
[in Russian], No. 11, Atomizdat, Moscow (1975), pp. 225-235.
602
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Declassified and Approved For Release 2013/02/20: CIA-RDP10-02196R000300070001-4
6. Yu. N. Burmistenko, B. N. Ryvkin, and Yu. V. Feoktistov, in: ibid. (1976), No. 13,
pp. 219-227.
7. B. M. Yakovlev and V. I. Lomonosov, in: Proceedings of the Scientific-Research Institute
of Nuclear Physics at the Tomsk Polytechnical Institute [in Russian], No. 6, Atomizdat,
Moscow (1976), p. 37.
8. Ph. Breban et al., Nucl Instrum. Methods, 158, 205-215 (1979).
9. L. Schiff, Phys. Rev., 83, 252 (1951).
10. L. Lanzl and A. Hanson, Phys. Rev., 83, 959 (1951).
11. M. G. Davydov and V. A. Shcherbachenko, "Calculation of the yield of photonuclear reac-
tions," At. Energ., 39, No. 3, 210 (1975).
12. V. P. Kovalev, Secondary Emission of Electron Accelerators [in Russian], Atomizdat,
Moscow (1979).
13. I. V. Gordeev, D. A. Kardashev, and A. V. Malyshev, Nuclear-Physical Constants (Handbook)
[in Russian], Atomizdat, Moscow (1963).
14. A. K. Berzin, B. M. Yakovlev, and A. A. Yatis, in: Electron Accelerators [in Russian],
Vysshaya Shkola, Moscow (1964), p. 435.
15. V. Emma et al., Nuovo Cimento, 21, No. 1, 135 (1961).
16. B. M. Yakovlev and R. P. Meshcheryakov, in: Electron Accelerators [in Russian], Vysshaya
Shkola, Moscow (1964), p. 430.
17. B. Berman, At. Data Nucl. Data Tables, 15, 313-390 (1975).
18. L. Meyer-Shutzmeister and V. Telegdi, Phys. Rev., 104, No. 1, 185 (1956).
EXCITATION CROSS SECTION OF THE CHARACTERISTIC X RADIATION BY
PROTONS AND 'He IONS FOR ELEMENTS WITH Z IN THE RANGE 22Ec, Z? 83
E. Brazevich, Ya. Brazevich, V. F. Volkov,
S. A. Gerasimov, Lyu Zai Ik, G. M. Osetinskii,
and A. Purev
UDC 539.17.012
The paper is devoted to the determination of the excitation cross section of the charac-
teristic x radiation (CXR) as during the bombardment of a number of elements with a beam of
protons and 'He ions with energy 1.5-3.8 MeV. The cross sections were determined for elements
for which, in this range of energies, data about as either are lacking or require refining.
Thin targets were used for the measurements. In this case, as is found by the formula
crs? NpNm'
(1)
where Np is the number of protons or He ions incident on the target; NM is the number of
atoms of the sample being investigated per cm2; y __is the yield of characteristic
Ea 80
Y,
x radiation for the a- and 0.-1ines of the K-series of the element being studied; 1-
Ea
Yo3 Y
++
eti3 Ev3
Y01+
is the same yield for the a-series; Ea, EB, etc. is the recording efficiency
of the CXR for the a-, 13-, 0,-,etc. lines of the K- or L-series, and Ei,s is the recording
efficiency of the i-th line of the S-series. The recording efficiency of the CXR is deter-
mined as Ei,S = cabcEA(4/410, where csbc is a coefficient taking into account the absorp-
tion of radiation on the path from the target to the detector (absorption in peepholes of
the detector chamber, in the air, and in the filters); EA is the recording efficiency by the
detector of the radiation with a wavelength A; AO is the solid detection angle. With con-
Translated from Atomnaya Energiya, Vol. 59, No. 1, 52-57, July, 1985. Original article
submitted July 4, 1984.
0038-531X/85/5901-0603$09.50 ? 1986 Plenum Publishing Corporation
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H-1- from ESA
To VN-2 -
pump
2
////777////7,///////// ,/%/77//////
Fig. 1. Layout of experiment: 1) vacuum seals; 2) nitrogen trap; 3) collimators; 4) inter-
mediate chamber; 5) plates for modulation of the beam; 6) high-vacuum pump; 7) device for
tracking the beam; 8) CXR chamber:9) Faraday cylinder; 10) Si-detector; 11) valve; D) CXR
detector; PA) preamplifier; M) target; ESA) electrostatic accelerator.
stant geometry of the experiment, the product cabc(AQ/47)EA is the magnitude of the constant
determined by calibration changes.
The characteristic features of the experiment being described are:
1. The CXR yield of the i-line (a, 13, etc.) of the S-series (K or L), denoted by us
in future as Yi,s, was determined from the area of the CXR energy spectrum obtained on a
multichannel pulse analyzer using the ACTIV program of JINR on the BASM-6 computer.
2. The number of particles incident on the target (Np) was found from the beam charge,
measured by the integral of the current. The error in the determination of the charge in
the working range of the beam current of 10-8-10-9 A is not greater than 1-1.5%.
3. The number of atoms of the target (NM) was determined by measuring the elastic scat-
tering of the He ions at an angle of 135? in the laboratory system of coordinates, in the
same geometry and for the same energy of the accelerated ions for which the CXR yield was
determined. Scattering was assumed to be Rutherford scattering. This assumption is com-
pletely valid in the range of energies investigated.
4. The detection efficiency Ei,s was determined by measuring the yield Its of CXR
from standard targets, for which the number of atoms is known. The calculation was performed
by the formula
Ei, s
Ys
NS tiv St? St. ,
P m -LS
(2)
where the number of atoms in the target-standards (per cm2) was found by measuring the inelas-
tic scattering of He ions with energy 2-3 MeV in the same target geometry in which the cross
section was measured. The value of at was calculated from special tables compiled by us
[2] as a result of averaging all the known data on a = f(E)J. The necessity for these aver-
aged tables originates because the discrepancies in the published data for one and the same
elements and energy, but obtained by different authors, sometimes exceed the experimental
errors by a factor of two to three or more, and because of this it is difficult to give pref-
erence to some or other method for their determination. The data were averaged by the method
of least squares on the SDS-6500 computer by the FUMILI program of JINR, using the polynomial
form
111
where A is the coefficient of the polynomial of (n?l)-power. The construction of these tables
is described in more detail in [2].
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TABLE 1. CXR Excitation Cross Sections for the K- and L-Series, during the Bombard-
ment of Elements with Protons in the Energy Range 1.46-3.8 MeV
Ele-
ment
Z
?
Proton energy, MeV
1,56
2,155
2,5
2,985
3,285 3,527
3,6
3,7
3,8
expt.1 [2]
expt.
[2]
expt. [2]
expt.1 [2]
,
expt. I [2] lexpt.1 [2]
expt.
[2]
expt.1 [2]
expt.
[2]
1
CXR K-series
Ti
22
89,95
117,9
213,9
219,9
285,6
298,8
364,5
387,3
440,5
Se
34
4,85
5,53
13,7
14,61
23,6
26,85
30,44
35,89
Bb
37
2,67
2,63
7,41
5,73
12,31
10,4
18,9
15,6
24,5P
Zr
40
1,15
1,77
3,20
3,45
5,39
4,61
8,67
5,77
11,36
Nb
41
0,94
0,85
2,59
2,52
4,50
4,20
7,18
10,43
11,18
Mo
42
0,71
0,80
1,97
2,31
3,40
3,98
5,55
5,52
4,96
Pd
46
0,30
0,29
6,86
1,69
2,43
4,11
4,46
Ag
47
0,20
0,27
(1,52
0,81
0,82
1,41
1,53
2,18
1,93
2,51
2,40
2,94
3,02
2,283,13
3,24
CXR L-series
SI)
51
307,0
506,12
676,8
802,8
892,4
Te
52
272,7
387,0
637,6
804,(.
847,3
.925,7
?
Ta
73
25,92
23,0
52,43
52,2
83,4
76,9
99,4
105,3
118,6
144,6
138,8
143,6
150,6168,3157,9
IV
74
26,2
53,9
81,3
405,7
122,2
161,7
Bi
83
7,53
7,15
15,68
16,9
29,46
26,3
39,7
37,9
43,6
49,00
52,2
54,2
57,0
59,8
The mean square error in the determination of Ei,S does not exceed 7%. It comprises
the error in the determination of Yi,s (not more than 2%), the number of target atoms ('4%),
in the measurement of Np (1.5%), and the error in ogt from the table of averaged values for
as = f(Z)IE "4.-..:5%. We note that the method chosen by us for obtaining the recording efficiency
of the CXR, based on the averaging of known tabular values of as, although it leads to slight-
ly overestimated errors in Et to a considerable degree eliminates the appearance of unac-
counted errors, which may arise in the determination of this quantity by other methods.
The scheme of the experiment is shown in Fig. 1. It can be seen from the figure that
the beam of protons or 'He ions from the JINR electrostatic accelerator of the Van de Graaf
type, on traversing the section of the ion-conductor, falls on the multiposition target lo-
cated at the center of the measurement chamber. The beam, on this section, is shaped by four
diaphragms. A uniform distribution of the current at the target is provided by debunching
the beam in two mutually perpendicular directions by means of electrostatic lenses. The tar-
get is insulated from the housing and is connected with the current integrator. At an angle
of 90' relative to the incident beam and at a distance of 50 mm from the center of the target
the chamber has an opening covered with milar foil with a thickness of 25 um. Beyond the
milar window is installed a Si(Li)-detector, the pulses from which via a preamplifier and
an amplifier are recorded by a DIDAC multichannel pulse analyzer. The amplifier provides the
stability of the zero level at the output and an indication of self-pileup of pulses. The
structural scheme for recording the CXR has a "real time" counter, which sums the "dead" time
of detection in the preamplifier, amplifier, and multichannel pulse analyzer, and automaticall5
projects the real time count on the luminous light panel of this instrument. The energy res-
olution of the spectrometer, measured on the 6.4-keV line of 'Co, amounts to 220 eV. At an
angle of 135? in the chamber, a silicon surface-barrier detector is installed, used for the
simultaneous measurement of the elastic scattering of 'He ions and the yield of CXR
Experimental Results
Table 1 shows the excitation cross sections for the CXR of the K- and L-series during
the bombardment of the elements being investigated by a beam of protons with energy 1.46-3.8
MeV. The excitation cross sections for the K-series were measured for a number of elements
in the range 22< Z? 47, and for the L-series in the range SI.< Z...5,1-83. For the purpose of
verifying the validity of the measurement procedure, in the table are included our data for
Ag, Ti, and Bi, the CXR excitation cross sections for which in the range of energies investi-
gated were determined previously by other authors and coincide well with oneanother. For com-
parison, the averaged values of the curves as = f(E)lz from [2] are given in the same table.
It can be seen from the table that in the energy range where a comparison is possible, the
CXR excitation cross sections coincide, within the limits of error, with the averaged liter-
ature data.
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TAtiLE L. Wilt txcitation uross ections jot. anu 1,-oerles as a RUSU'L 01 Lfie
Bombardment of Elements with 'He Ions in the Energy Range 1.5-3.8 MeV
Energy of 4He ions, MeV
Ele-
z
1,5
5,009
2,477
2,a87
3 2
3,191
3,0
3,7
3,8
ment
expt.
[3]
expt.
1 [3]
expt. [3]
expti [3]
expt.1 [3]
expt.
[3]
I
expt.;I DI
expt] [3] lexpt
i 131
f'
CM K-series
Ti
22
4,71
8,12
18,0
21,5
32,6
41,6
55,9
73,2
89,6
90,5
115,0
126,0
136,3
147,1
Cr
24
4,17
4,45
10,7
11,4
23,1
26,3
41,1
63,6
83,4
69,05109,0
119,0
127,4
137,5
Co
27
1,16
1,39
3,28
3,81
6,75
7,63
12,31
13,2
15,5
16,1
19,91
20,8
22,9
24,9
27,1
Cu
29
0,962
0,810
3,15
2,25
6,55
4,48
12,29
8,12
10,1
20,3
13,1
14,4
15,7
17,0
Se
340,133
0,127
0,397
0,438
0,827
0,9141,58
1,67
2,00
2,15
2,68
3,00
2,86
3,36
3,05
3,68
3,98
Rb
37
0,555
0,185
0,41
0,816
1,48
Zr
40
0,0224
0,082
0,19
0,367
0,643
Ni)
41
0,02820,062
1,092
0,146
0,1960,301
0,503
0,626
Mo
42
,01910,049
1,066
0,113
0,15
0,2320,3030,1350,388
0,4
0,531
0,593
0,6560,5520,725
Pd
46
0,0040
0,0196
0,05
0,104
0,113
0,191
0,211
Ag
47
0,00270,00350,019
0,019
0,039
0,0380,0820,063
0,081
0,1430,120
0,1650,1320,1860,147
0,157
Sn
50
0,0002
0,00870,019
0,0190,0390,025
0,035
0,0720,049
0,054
0,058
0,063
C}at L-series
I'd
46
88,8
189,2
262,4
497,7
585,9
Ag
47
60,4
128,6
467,0
629
637,8
Su
50
39,12
196,3
313,8
452,7
Sb
51
43,7
90,7
158,7
238,8
271,8
325,0
Te
52
38,3
79,6
135,8
214,0
261,0
316,2
Ta
73
1,75
5,27
5,38
9,73
10,0
15,7
16,5
19,7
21,3
24,4
26,3
28,1
27,5330,0
W
74
3,93
6,71
11,3
16,5
21,39
Pt
78
0,893
2,60
4,82
8,46
10,4
12,4
14,8
Bi
83
0,429
0,504
1,22
1,93
2,43
2,69
3,11
3,88
4,82
6,80
6,56
7,30
7,97
8,60
The CXR excitation cross sections for the K- and L-series as a resdlt of the bombardment
of a number of elements with a beam of 'He ions in the energy range 1.5-3.8 MeV are given in
Table 2, and also the data of [3] averaged in the energy range of interest to us by the method
stated earlier.
The values of as from the bombardment of Co, Se, Ag, and Ta are considered by us to be
confirmation of the validity of the assumed method of measurement. The measurements were
repeated for a number of elements, as the data on the CXR cross sections published by differ-
ent authors disagree strongly. Thus, for example, in the tables of [3] for the excitation
of the CXR K-series by the bombardment of Cu with He ions with energy 2.6 MeV, two values are
given for the cross sections: 8.68 and 4.7 b, for the excitation of the K-series in the case
of the bombardment of Cr (E,He = 2.1 MeV) 1.35 and 21.0 b, and for excitation of the L-series
of Bi (E,He = 3.0 MeV) 5.1 and 16.1 b, etc.
The mean square error in the determination of the cross sections in all the measurements
does not exceed 10%. It comprises the errors in the determination of the CXR yield (42%),
(5-7%), the number of target atoms (4%), the number of particles incident on the target (1.5%),
and also the error in the determination of a (1%) due to the errors in the energy measurement
[determined from the curve of a = f(E)].
Discussion of the Results Obtained
The CXR excitation cross sections as a result of the bombardment of the elements investi-
gated, with a beam of protons and 'He ions, were compared with the results of theoretical
calculations performed in Born approximation of plane waves (BAPW) and on a model of binary
collisions (MBC). The calculations give the ionization cross section, and conversion to
the excitation cross sections was effected by multiplying these values by the fluorescence
yield and the probability of a Coster-Kronig transition [4]. It should be noted that the
experimental data on the ionization cross sections of the K- and L-shells in the MBC-approxi-
mation, known at the present time, have been given by a number of authors using the wave
function only of the is-state for all subshells [5, 6].
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For the calculations of the cross sections in BAPW, the tabular data of [7, 8] usually
have been used, containing the function f(g8), related with the ionization cross section
a by the equation
rneE
a (ilses); .11s m
0 . 112Eeb
zLR.
where Z1, M? and E are the atomic number, mass, and energy of the incident particle; me and
Eeb are the mass and energy of the electron bond in the shell; ao and Roo are the Born radius
and Rydberg constant; n is the principal quantum number of the shell; Z2 is the atomic number
of the target atom, and Os is the screening constant, 8 < 1.
It was assumed in the calculations that screening of the charge of the nucleus by elec-
trons of the atom can be taken into account by the introduction of the screened charge in
accordance with Sletter's rule: Z25 = Z2 ? 0.3 for the K-shell, and Z2s = Z2 ?4.15 for
the L-shell.
We note that this method of calculation has definite drawbacks as, in the first place,
the choice of 8 < 1 corresponds to negative values of the kinetic energy of the electron
knocked out, for the consideration of which there are no convincing reasons, and, secondly,
the determination of the effective charge Z25 according to Sletter's rule leads to very large
errors. In contrast from the stated method of calculation, in our case for the calculations
by MBC and BAPW the is-, 2s-, and 2p-wave functions of a hydrogenlike atom were used, and
screening of the charge of the nucleus of the target atom was taken into account by the in-
troduction of the effective charge Z2s, obtained from the relation
Z2
2.5
Eeb= ,i2 Roo,
where n is the principal quantum number; Eeb is the experimental value of the binding energy
of the electron in the shell.
As the consideration was conducted for a hydrogenlike atom, the results of the theoret-
ical calculations for each individual subshell both in MBC as well as in BAPW were presented
in the form of a scaling law
0- (n2Eeb)2 F t Ei
Zin,e
2w2Eeb
The energy dependencies of the ratios of the calculated and experimental CXR excitation
cross sections (GTI GE) for the K-shell of some of the atoms investigated by their excitation
with a beam of protons with energy 1.5-3.8 MeV are shown in Fig. 2. The values of GT, used
in the calculation of GT/GE, were calculated in MBC approximation since, as analysis of the
results of the present paper and the numerous publications showed, the accuracy of the experi-
mental determination of GE is inadequate for establishing which of the approximations ? MBC,
BAPW, or their various modifications, including those proposed in the present paper ? more
correctly describes the ionization process of the atoms by protons. It can be seen from
Fig. 2 that the calculations of GT within the limits of error coincide with the experimental
data (GT/GE1). Similar calculations of GT/GE for the ionization of the L-shell of the
atoms investigated by protons, independently of the method of calculation (by MBC or BAPW),
also give values close to 1 (these results are not shown in the figure).
A more contradictory pattern is observed with the calculation of GT for the ionization
of the K-shell as a result of excitation by 'He ions. In this case, ifforthe CXR excitation
of the L-series by protons and 'He ions the calculated values of GT coincide with the experi-
mental values, then in the case of ionization of the K-shell by 'He ions the ratio GT/GE is
significantly different from unity (Fig. 3). These mechanisms can be traced in Figs.4 and
5 where, in order to exclude the effect of the individual features of the target atoms during
their interaction with the incident particles, averaging of GT/GE = f(E) with respect to
the atomic numbers Z2 is carried out. The curves of (aT/GE)a = f(E) are shown in Fig.
607
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Pc14,
?
Zr'
Rb
b
6,.
C'E
'1,0
0,5
,x
... -----------------
? ?
2,0
2,5
Fig. 2
J0
2
1
Cr. O.....
Cu
40 2,5 40 41
Fig. 3
o Co
----- At,,..,...4...._,szt????? 5C
bit
sti?vmo
Fig. 2. Dependence of GT/OE on the proton energy for the K-series (MeV): x?) cal-
culation performed in MBC approximation; A) Mo; x) Zr; o) Rb; A) Nb; A) Pd.
Fig. 3. Dependence of GT/UE on the energy of the 'He ion for the CXR of the K-ser-
ies (calculation performed in MBC approximation).
(
t T./
Ea
1,0
a
4-
Fig. 4
PC6E)a
1,0
0,5
a
1, 0
a
cr
1 S
1,5
2,0 2:5-
4 0 45
.1L
2, 0 2, 5 .3, 0
Fig. 5
t
Fig. 4. Dependence of (aT/GE)a on the energy of the incident ion for
ionization of the K-shell; a) ionization by proton; b) ionization by
'He; o) calculation in MBC-approximation; A) calculation in BAPW.
Fig. 5. Dependence of (oT/GE)a on the energy of the incident ion for
ionization of the L-shell: a) ionization by proton; b) ionization by
He; o) calculation in MBC approximation; A) calculation in BAPW.
4 in the case of ionization of the K-shell of the atoms investigated by protons and 'He ions.
The upper part of Fig. 4(a) is related to ionization by protons, and the lower part (b) to
ionization by 'He ions. In Fig. 5 (a, b) these same curves are for ionization of the L-shell.
It can be seen from Figs. 4a and 5a, b that in the case of ionization of the K- and L-shells
by protons, and ionization of the L-shell by He ions, the averaged values of (oT/oE)a are
considerably greater than unity and increasewithreduction of the energy. The reason for
this discrepancy of the theoretical and experimental cross section values in the case of
ionization of the K-shell by He ions is not altogether clear, and its explanation will re-
quire further investigations. It can be understood qualitatively if the deviation of the
trajectory of the incident particles from rectilinear (assumed in the BAPW theory) in the
Coulomb field of the nucleus is taken into consideration. As a result of this deviation, the
distance of maximum convergence (d) of the incident ion with the target atom is increased,
and which for the He ion will be greater than for the proton. And as the radius of the L-
shell is four times greater than the radius of the K-shell, the ionization cross section with
608
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increase of the distance of closest approach is reduced for the K-shell more considerably
than for the L-shell (in the discussion, it is supposed that ionization of the atom takes
place mainly by ions approaching the nucleus of the target at a distance d < a2, where
a2 = n2a0/Z2, and a, is the Bohr radius). By comparison with the distance according to the
BAPW, the ionization cross section in this case is reduced with decrease of the energy of
the incident ion and with increase of Z2, which can be tracked by considering the relation
connecting the parameter of maximum approach d of the ion with the target atom and the im-
pact parameter (b):
d (b) -
+ dnbon )2],
where drain = Z,Z2e2/2E1 is one-half of the distance of the maximum approach for a central
collision; and E is the energy of the ion. The discussion conducted is confirmed by the
results shown in Figs. 3 and 4b, from which it can be seen that aT/cE increases with increase
of Z2 and with reduction of the energy of the incident ion.
In conclusion, the authors thank M. Paiek of the Joint Institute of Nuclear Research
(JINR) for useful discussions.
LITERATURE CITED
1. E. Brazevich et al., Preprint JINR 18-81-503, Dubna (1981).
2. E. Brazevich et al., Preprint JINR B1-81-320, Dubna (1981).
3. At. Data Nucl. Data Tables, 17, No. 2 (1976); At. Data Nucl. Data Tables, 21, No. 6
(1978).
4. M. Krause, J. Phys. Chem. Ref. Data, 8, 307 (1979).
5. J. Garcia, R. Fortner, and T. Kavanagh, Rev. Mod. Phys., 45, 111 (1973).
6. F. McDaniel, T. Gray, and R. Gardner, Phys. Rev., 11, 1607 (1975).
7. R. Rece, G. Basbas, and F. McDaniel, At. Data Nuc17?Data Tables, 20, 503 (1977).
8. B. Choi, E. Merzbcher, and G. Khandelwal, At. Data, 5, 291 (1973).
609
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LET Declassified and Approved For Release 2013/02/20: CIA-RDP10-02196R000300070001-4
INFLUENCE OF REACTOR IRRADIATION UPON THE ELECTROPHYSICAL CHARACTERISTICS
OF HETEROEPITAXIAL p-SILICON-ON-SAPPHIRE LAYERS
B. V. Koba, V. L. Litvinov,
A. L. Ocheretyanskii, V. M. Stuchebnikov,
I. B. Fedotov, N. A. Ukhin,
V. V. Khasikov, and V. N. Chernitsyn
UDC 537.311.33,315.59:621.315.59
Strongly alloyed silicon-on-sapphire structures with p-type conductivity are promising
for highly sensitive strain transducers of mechanical quantities in automatic control sys-
tems; these transducers have excellent metrological characteristics and can work reliably
under the strenuous operational conditions of atomic power stations [1-5].
We report in this paper on the results of an investigation of the influence of n?y
reactor radiation upon the electrophysical properties and the coefficients m? of elasto-
resistivity of highly alloyed p-silicon-on-sapphire structures with concentrations of 5.3.
1018_1.8.1020 cm-3 of the alloying admixture; these elements were used as strain transducers
of mechanical quantities.
In order to measure the temperature dependencies of the specific resistivity p, the
concentration p of the holes, and their mobility p, we used silicon-on-sapphire structures
on which Hall samples were produced by photolithography. In order to measure the coeffi-
cient m?? of elastoresistivity, which determines the sensitivity of the strain transducer,
we used beam-shaped test samples which were cantileverwise attached by welding with rigid
PSR-72 solder and which had silicon resistors arranged parallel or perpendicular to the
axis of the beam. m? was measured with the technique which is the analog to that described
in [6]. We assumed in the calculation of the parameter m? that the elastic characteristics
of silicon and sapphire do not change during the irradiation [7].
Our samples were irradiated in a VVR-2000 reactor under normal conditions (Tirrad (
70?C, normal atmospheric pressure). The neutron-flux dosimetry was made with sulfuric
threshold indicators (Ethresh = 2.9 MeV); the darkening of SGD-9 glass was used for the
dosimetry of the gamma radiation. Stepwise irradiation was used until a certain flux (1)
between 101" and 4.5.1018 cm-2 had been reached (En 2.9 MeV). The neutron flux intensity
was 109- 1018 cm-2. sec-1; the intensity of the accompanying y radiation amounted to several
hundred R/sec (1 R = 2.58-10-" C/kg). In order to reduce the activation, the samples were
inserted into 0.5-mm-thick cadmium jackets during the irradiation. Before and after each
of the irradiation steps, the parameters under inspection were measured.
Figure 1 depicts the dose dependence of the specific resistivity, the concentration of
the holes, and their mobility in silicon-on-sapphire structures with an initial charge car-
rier concentration p, = 6.1019 cm-3. It follows from Fig. 1 that, by contrast to weakly
alloyed bulk silicon [8], the relative change in the mobility in strongly alloyed p-silicon-
on-sapphire structures becomes comparable with the relative change of the concentration due
to the irradiation. The maximum is at the temperature of liquid nitrogen. The resulting
dose dependencies of the parameters under inspection are logarithmic and therefore differ
from the dependencies of the same parameters in weakly alloyed bulk silicon.
Figure 2 depicts the temperature dependence of the mobility of holes in silicon-on-
sapphire structures with various degrees of doping and refers to various irradiation doses.
The form of the temperature dependence of the mobility is not affected by the irradiation
in all samples examined. A similar behavior is observed in the temperature dependencies
of the charge carrier concentration.
Table 1 lists the initial rate of change of the specific resistivity, the concentration,
and the mobility of the charge carriers in dependence upon the irradiation dose. It follows
Translated from Atomnaya Energiya, Vol. 59, No. 1, pp. 58-59, July, 1985. Original
article submitted April 16, 1984.
610 0038-531X/85/5901-0610$09.50 @ 1986 Plenum Publishing Corporation
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Declassified and Approved For Release 2013/02/20: CIA-RDP10-02196R000300070001-4
040
rel. units
80
50
'cj 40
0 20
10
0,4'
-04'
45 1 2
S0,1010=-2
Its
Fig. 1. Radiation-induced change of the specific resis-
tivity (o, is), of the concentration (A, A), and of the mo-
bility of holes (V, V) in silicon-on-sapphire structures
at 77 (*, A, V) and 300?K (o, A, V).
TABLE 1. Initial Rate of Change of the
Parameters*
Initial
concn.
(cm3) of
the
holes
74.
e
a