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Comparison of calculated helium production in stainless steel due to neutron irradiation with experiment
Jnaclaf ELSEVIER
Journal of Nuclear Materials 228 (1996) 207-214
Comparison of calculated helium production in stainless steel due to neutron irradiation with experiment V. Gopalakrishnan a, R.V. Nandedkar b, S. Ganesan c Indira Gandhi Centre for Atomic Research, Kalpakkam, India b Centre forAdvanced Technology, Indore, India c Bhabha Atomic Research Centre, Bombay, India
Received 16 May 1995; accepted 16 October 1995
Abstract
It is well known that helium produced during neutron irradiation through the (n, a ) reaction affects the mechanical properties and the amount of void swelling in nuclear reactor materials. In order to estimate the amount of helium produced in a high alloy stainless steel, which is used in fast reactors and is appropriate to be used in future fusion reactor structural materials, calculations have been performed using the neutron interaction cross sections of the steel constituents. Two austenitic steel specimens of type 1.4970 with high and low boron content, respectively, for which some experimental results are available have been chosen for the present calculations. Predominant nuclear reactions like l°B(n, a)7Li, and the two-step reaction viz. 58Ni(n, -y)S9Ni(n, a)S6Fe, and the details of the neutron spectrum are taken into account. The cross sections for 59Ni, the major contributor for higher irradiation times, are taken from the KEDAK-4 (German) and the most recent E N D F / B - V I (American) Evaluated Nuclear Data Libraries. The results show that the calculated and the measured estimates differ by a factor of 2 to 3. This difference may be due to uncertainties in the measurement as well as uncertainties in the reaction cross section, especially in the two-step reaction. I. Introduction
The production of helium due to neutron interactions with the constituent atoms of the structural materials of fusion reactors can cause detrimental effects on their mechanical properties [I]. Since helium is practically insoluble in most of the metals and alloys, the helium atoms generated during irradiation will precipitate in the grain boundaries and the interior as helium bubbles, and continuous accumulation of such bubbles would lead to significant changes in the mechanical properties. One of the ways the helium is introduced into structural materials is via (n, a ) reactions between the fusion neutrons and the nuclei of the bulk of structural components. The presence of mB in the stainless steel specimen can cause significant amount of helium production at low neutron energies due to its high (n, a) cross section. In addition, it is widely known that 59Ni atoms produced during irradiation contributes quite significantly to the helium generation at
high fluences, through the following two-step reaction [2]: 58Ni(n, y) --+59Ni(n, or) -+ 56Fe. All other nuclides in the steel have their respective contributions to helium production depending on their (n, a ) cross sections, but are usually less significant than the contributions from I°B and 59Ni. In principle, it is possible to estimate the exact amount of helium production by having the knowledge of the chemical composition of the specimen under study, the fluence of the irradiation and the cross sections for various neutron interactions involved. But the inevitable uncertainties in each of the above quantities put the limitation on the accuracy in the prediction. The cross sections of the materials generated during irradiation, i.e. not naturally occurring, 59Ni in our case, can have large uncertainties. A possible reason for the latter is that the sparsely measured cross
0022-3115/96/$15.00 © 1996 Elsevier Science B.V. All rights reserved SSDI 0022-3115(95)00214-6
V. Gopalakrishnan et aL /Journal of Nuclear Materials 228 (1996) 207-214
208
Table 1 Chemical composition of the steel specimens in wt% 1.4970
1.4970LB
Element
wt%
Element
wt%
Element
wt%
Element
wt%
Fe Cr Ti C N B
67.045 14.810 0.285 0.092 0.001 0.004
Ni Mo Mn Si V
14.640 1.150 1.600 0.350 0.023
Fe Cr Ti C N S V
65.4400 15.3000 0.2600 0.1120 0.0050 0.0024 0.0140
Ni Mo Mn Si P Cu B
15.400 1.1700 1.7700 0.4900 0.0140 0.0160 0.0023
2. Experimental details
sections are usually complemented by model based theoretical calculations and approximate fitting procedures. Experimental estimation also may have large uncertainty. The fluence of irradiation is among the difficult quantities to measure accurately. In the case of helium production very few integral experiments exist that would help better understanding of the physical processes that are happening and a validation of the basic physical data involved, cross sections for instance. Nevertheless, potential consequences of helium generation in structural materials have motivated many scientists, and so research papers based either on experiments or computations continually appear in literature [3]. The aim of the present work is limited to perform a theoretical calculation to estimate the amount of helium produced in the two specimens of austenitic stainless steel studied by Nandedkar and Kesternich [4], and make a comparison with their measurements, so as to have a feel of the agreement or otherwise of prediction and measurement of such an important quantity.
In the experiment of Nandedkar and Kesternich [4], two austenitic stainless steel specimens, one with composition of D I N 1.4970 containing about 40 wppm boron and another with a chemical composition close to D I N 1.4970, except having extremely low boron content of approximately 2 wppm, were irradiated in the F R J 2 reactor at K F A Julich, to thermal and fast ( E > 0.1 MeV) neutron fluences of 2.6 x 10 25 m 2 and 3.0 x 1025 m -2, respectively. The fast fluence corresponds to 1.5 dpa. The specimen containing low boron is designated as 1.4970LB. The chemical compositions of the two specimens are given in Table 1. The irradiation time is approximately 346.81 d, which is about 3 x 107 S. After the irradiation, the helium concentrations were measured, by degassing and mass spectrometry, to be 70 appm for specimen 1.4970 and 28 appm for 1.4970LB. These values have been obtained from two independent measurements each, giving 68 and 74 appm helium for 1.4970 and 28 and 28 appm for
10 ~s lethargy
neutron/sq.cm/sec/unit X b_ Y
o k--1 0 ~3I L~ Z
"~O121 ,,,HHq ,,,'~mI 10-2
10
~
1
ilil,q
10
I
Ilrl~l~
I
I
10 2
I rlllll
I
I
10 ~
I II~llJ I
10 ,
I
IIIf~ll
t
b I Jlllll
10 5
NEUTRON ENERCY (eV)
Fig. 1. Flux at B3 position of the FRJ 2 reactor.
I
I
10 6
IIIIIII
0 •
V. Gopalakrishnan et al. /Journal of Nuclear Materials 228 (1996) 207-214 1.4970LB. These measurements have been made at Rockwell International and the confidence in the measurements is understood to be well within 10%. The fluxes at the irradiation position [5], as reported by Weise [6] are used in the present calculations. The flux density per unit lethargy plotted against energy is given in Fig. 1 and corresponds to the B3 position [5,6] at which the irradiation took place in the FRJ 2 reactor at KFA Julich. The total (i.e. energy integrated) flux was 7.438 × 10 a8 m - 2 s 1. The fast ( > 0.1 MeV) fluence given in Ref. [4] was exactly reproduced from this data, for the sake of verification. The total fluence including thermal, intermediate and fast components is obtained as the product of the total flux and the time of irradiation to be 22.3 × 10 25 m -e. In the present work, helium production in each of the components of the steel specimens were calculated using appropriate information on flux, fluence and neutron cross sections and compared with this experiment. The theory, the data sources and the methods are briefly described below.
3. Theoretical background For any nuclide which produces helium due to a neutron fluence ~bt, ~b being the flux, the total number of helium atoms produced per unit volume of the sample during the irradiation period of t seconds is given by
Nf
-N~fo0-~, _
k
t
k
exp(-0-kth/) dt,
(1)
which reduces to N f = Nok0-f/0-ak for a large irradiation time, where, Nok is the number of atoms of the nuclide k per unit volume of the entire specimen, 0-f is the helium production cross section, and 0-f is the activation cross section which includes all neutron reactions by which the nuclide is destroyed. In the case of 59Ni, which is produced during the irradiation, the amount of helium atoms produced in the two-step reaction is given by 58 5 9 J 59 -- N 5 8 0-'¢ 0-c~ ~9 f0t{
Nd -
0 0-a59_0-a58
exp(--°'a586t)
-- exp( --0-a59q~/)} dt,
(2)
where No58 is the initial number of 58Ni atoms, 0-v58 is the (n, ~) cross section of 58Ni, 0-f8 is the activation cross section of 5SNi, 0-59 is the (n, a ) cross section of 59 Ni, and 0-a59 is the activation cross section of 59 Ni. Since 59Ni is produced during irradiation, its contribution to helium production will increase with the time of irradiation reaching an asymptotic or saturation value of 0- 58O. 59
N59
r~/58-'t -a = " 0 0-a590-58•
(3)
209
Eqs. (1) and (2) can now be used for helium estimation from steel provided the effective cross sections of neutron interactions and the fluence of irradiation are known. In an evaluated nuclear data file (ENDF), cross sections are given as a function of energy, from subthermal energies to about 20 MeV, in a tabular form, along with some interpolation schemes to be used between the tabulated points. In the resonance energy region, cross sections are often given through 'resonance parameters', from which it is possible to construct the cross sections in tabular form. For the sake of brevity in explaining the method used to calculate effective cross sections, let us assume that the microscopic cross sections for any desired reaction are initially made available as a function of energy. Since the irradiation was done in a mixed neutron spectrum, a knowledge of the flux spectra is essential to properly account for the structures shown, as a function of neutron energy, by each of the constituents of steel in their neutron interaction cross sections at intermediate energies. If the fluxes at the irradiation position are known in multigroup form, the effective (one-group) cross section, for any reaction x can be obtained as
0-X=~g0-Xg~bg/~gdpg,
(4,
where 0-xg is the average cross section in an energy group g, with lower limit Eg+l and upper limit Eg, and ~bg is the known multigroup flux. The multigroup cross sections for the above purpose may be obtained from the basic cross section 0-x(E) as
0-x =f +10-x(E)S(F )dE/fEg S(e) dE, Eg+l
(5)
where S(E), which approximates the shape of the neutron collision density at energy E, is the standard weighting spectrum usually used in cross section averaging for reactor physics applications. For the present calculations, we used a 53 energy group structure whose boundaries are given by Neef [7]. The multigroup cross sections were obtained, as defined in Eq. (5) above, using the code REX1-87 [8]. The neutron interaction cross sections were taken from the basic evaluated nuclear data library, ENDL/84-V [9] of the Lawrence Livermore Laboratory, USA, for all the nuclides of the specimens except for 14N and 59Ni. E N D F / B - I V [10] (American) library was used for 14N. The KEDAK-4 [11] (German) and also the most recent E N D F / B - V I [12] (American) libraries were tried for 59Ni. All these data libraries were obtained through the Nuclear Data Section of the International Atomic Energy Agency, Vienna, Austria. The energy
210
V. Gopalakrishnan et al. /Journal of Nuclear Materials 228 (1996) 207-214
Table 2 Weighting spectrum used for cross section averaging Energy region
4.
Weighting function
Upper limit (eV)
Lower limit (eV)
S(E) ~
1.49180+07 b 2.46600 + 06 4.07620 + 05 5.24750 + 04 2.03470 + 03 2.26030 + 01 3.75000-01
2.46600+06 4.07620 + 05 5.24750 + 04 2.03470 + 03 2.26030+ 01 3.75000- 01 Thermal
7E exp(- E/1.4 x 10 6) E 2 1/ E 1/dE constant in E E E exp(- E/0.0253)
variation of the (n, a ) cross section of 1°B and 59Ni are given in Fig. 2. The shapes used for S ( E ) are given in Table 2 for various energy regions. The 53 group fluxes, ~bg, are obtained from the values of flux density per unit lethargy, ~b'(E), given by Weise [6] as (6)
J~'g+l
Further, the 'activation cross section' is defined for the present work as the cross section for that process in which the target nuclide does not appear as a reaction product, and is computed as (7)
Ora : O',.¢ - F O p q- O"d q- O'T "~'- O"~ q- O'2n -]- O'3n.
and
discussion
Plots of the accumulated helium atoms produced per every million atoms of the sample upto a given irradiation time in X°B, 58Ni, and 5 9 N i ( E N D F / B - V I ) are given in Fig. 3 for the two specimens. For 58Ni and 59Ni, the helium production in 1.4970LB is only slightly higher than in 1.4970, due to higher initial concentration of 58Ni in 1.4970LB; the corresponding curves for the two specimens nearly coincide and hence these are not shown in Fig. 3. From Fig. 3 the following points can be noted: - Each of the curves shows saturation behaviour at high irradiation times, as expected. - ~°B is the most important helium producer at low irradiation times. - 59Ni is the dominant producer at high irradiation times. It was initially not present, but its concentration and hence its contribution to helium production increase with time. High initial concentration of 58Ni, over four orders of magnitude higher than that of I°B, together with its significant (n, -/) cross section contribute to the dominance of 59Ni, even though the (n, c~) cross sections of 59Ni are lower than those of l°B by more than two orders. Production from 58Ni exceeds that from 1°B at high irradiation times for which l°B shows saturation, due to the high concentration of 58Ni in the specimen. However, 58Ni itself is not a significant helium producer, as l°B at short irradiation times, and 59Ni at large irradiation times become dominant helium producers. Production from 5SNi is comparable to that from l°B for the 1.4970LB specimen, for the fluence considered in the present study. It could become signif-
a See Eq. (5). Weighting function is proportional to S(E), where E is neutron energy in eV. b Read as 1.49180x 10 7.
¢bg = leg
Results
The effective cross sections obtained as above are given in Table 3.
10 E k_
g z © I--
10" .......
--
-
......
10 3.
Ni-59 Ni-59 B-IO
(ENDF/B-Vl) .(KEDAK-4) (ENDL/84-V)
10 2 10
LLJ fJ3
"'""--'"--..
_
---_
1
Lf3 10 gO (:3 O:5 C)
'
"
'-"
1(3
10 10 -2
10 -~
1
10
10 2
103
10"
10 s
NEUTRON ENERCY (eV) Fig. 2. The (n, a) cross sections versus neutron energy.
106
10 7
I/.. Gopalakrishnan et aL /Journal of Nuclear Materials 228 (1996) 207-214
211
Table 3 Effective n e u t r o n cross sections No.
MAT a
Nuclide
Source b
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
7810 7811 7812 1275 7820 7821 7822 7828 7829 7830 7831 7832 7838 7844 7837 d 2828 2859
1°B UB t2C N Si P S Ti V Cr Mn Fe Cu Mo 58Ni 59Ni 59Ni
ENDL/84-V
Cross sections
e
(b)
tr~
~a
9,5460 4,4520 5.9660 6.0090 1.9020 1.1020 6.5670 8.0130 1.3290 4.3320 1.0770 2.2240 2.3720 0.0 1.2740 3.6110 4.0950
ENDF/B-IV ENDL/84-V
ENDF/B-VI KEDAK-4
+ -
02 c 06 05 03 04 04 03 06 06 05 05 05 05
9.5470 3.0010 1.2370 4.8090 4.3010 5.3750 1.6390 1.5220 1.2730 7.7280 3.2670 6.3680 9.6670 1.2610 1.1240 2.9730 3.1420
- 03 + 00 + 00
+ + + + + + + +
02 03 03 01 02 02 01 00 00 01 00 01 01 00 00 01 01
a M A T is the i d e n t i f i c a t i o n n u m b e r of the nuclide in the r e s p e c t i v e source. M A T for 59Ni in K E D A K - 4 is 280059. It is t a k e n 2859 for c o n v e n i e n c e . b T h e p r e v i o u s s o u r c e i m p l i e d if given blank. c R e a d as 9.546 x 102. d 58Ni ~r~ = 1,115 b.
Thermal cross sections: l ° B t r , = 3837 b t°Btra = 3837 b 58Nicrv = 4.6 b 58Nitra = 5 b 59Nitr,~ = 13 b 58Nit& = 110 b
E
10 s.
~ZL 0 10 3 r~ Ld (--)
B-IO B-IO Ni-58 Ni-59
...... ---
(DiN (,DIN
1.4970) 1.4970LB) ~ ::
10 -1
0103 cv O_
1 0 _5 T_ /
10_7.
J /
Ld ZE
/ /
1 0 -g
/ / / /
10 -"
I i lllllll
0
i i IIIEIII
10 2
i i lilllll
10 3
10 '
] I llllll I
I ; II11111
10 s
I I Itllll I
10 6
lll~.q
10
I I IllllI 1
10 a
I I IIIII
10 a
10
~o
IRRADIATION TIME ( s e c ) Fig. 3. H e l i u m p r o d u c e d in b o r o n a n d nickel ( T h e vertical line is to aid r e a d i n g the p r o d u c t i o n at the i r r a d i a t i o n t i m e considered).
212
V.
Gopalakrishnan et al. /Journal of Nuclear Materia& 228 (1996) 207-214
Table 4 H e l i u m p r o d u c e d in c o m p o n e n t s of steel 1.4970. N e u t r o n irradiation fluence used: 22.3 × 1025 m SI. no.
MAT
Nuclide
1 2
7810 7811
mB t 1B
3 4
7812 1275
tZC N
5 6 7 8
7820 7828 7829 7830
Si Ti V Cr
9 10
7831 7832
Mn Fe
11
7844
12 13 14
7836 7837 d 2828
15
Total
Nuclides p e r cm 3 a
~r/cr,,
0.0008 0.11032
3.753 + 18 b 1.503 + 19
I).0920 0.0010
wt%
z
Helium produced per cm 3
appm
9.999 -- 01 1.483 - / 1 3
3.752 + 18 1.491 + 12
4.442 + 01 1.765 05
3.601 + 211 3.355 + 18
4.824 02 1.251/- 02
4.788 + 14 4.469 + 14
5.668 - 03 5.291 03
/I.3500 0.2850 0.0230 14.8101/
5.871 2.789 2.118 1.338
4.423 5.264 1.044 5.605
2.488 + 15 4.897 + 13 6.188 + 11
2.945 02 5.797 - 04 7.326 - 06
1.6000 67.0450
1.366 + 21 5.623 + 22
3.297 - 06 3.492 - 05
1.280 + 16 3.164 + 14 2.767 + 16
1 . 5 1 6 - 01 3.745 03 3.273 - 01
Mo
1.15110
5.627 + 20
0.0
Ni ~" 5SNi 5'~Ni
4.6453 9.9947 0.0
3.626 + 21 8.094 + 21 0.0
6.151 - 04 1.134 - 03 1.215 - 01
0.0 1.246 + 16 2.270 + 17 6.509 + 18
0.0 1.476 - 01 2.687 + 00 7.706 + 01
1.055 + 19
1.248 + 02
7.300 + 18
8.642 + 01
1.134 + 19
1.342 + 02
+ + + +
20 20 19 22
-
(13 1/6 (16 05
8.452 + 22
W h e n d a t a for 59Ni is t a k e n f r o m K E D A K - 4 , Rows 14 and 15 r e a d as below: 14
2859
15
Total
5'~Ni
0.0
0.0
1.303 - 01
8.452 + 22
'~ Steel density a s s u m e d : 7.8 g / c m 3. i, R e a d as 3.753 × 10 TM. "58
•
c E l e m e n t a l nickel excluding ~ NL d 58Ni o.v/%, = 0.9922. Table 5 H e l i u m p r o d u c e d in c o m p o n e n t s of steel 1.4970LB. N e u t r o n irradiation fluence used: 22.3 × 10 25 m SI. no.
MAT
Nuclide
wt%
1 2 3
7810 7811 7812
mB iiB tic
0.00005 0.00018 0.11200
4 5 6 7 8 9 111 11 12 13 14 15 16 17
1275 7820 7821 7822 7828 7829 7830 7831 7832 7838 7844 7836 7837 d 2828
N Si P S Ti V Cr Mn Fe Cu Mo Ni ~ 5SNi 5'~Ni
0.00500 I).49000 0.01400 0.002411 1/.26000 0.01400 15.30000 1.77000 65.44430 0.01600 1.17000 4.88642 10.5136 0.0
18
Total
Nuclides p e r cm 3 a
%let,,
2.158 + 17 b 8.640 + 17 4.384 + 20 1.677 8.220 2.121 3.523 2.544 1.289 1.382 1.512 5.489 1.183 5.724 3.814 8.514 0.0
+ + + + + + + + + + + + +
19 20 19 18 20 19 22 21 22 19 211 21 21
•
Helium produced per c m 3
appm
9.999 - 01 1.483 - 03 4.824 - 02
2.158 + 17 8.573 + 10 5.829 + 14
2.548 + 00 1.013 - 06 6.884 - 03
1.250 4.423 2.051 4.007 5.264 1.044 5.605 3.297 3.492 2.454 0.0 6.151 1.134 1.215
2.235 3.483 5.207 5.146 4.467 3.767 1.323 3.500 2.701 6.185 1).0 1.311 2.388 6.847
2.639 4.1146.150 6.078 5.276 4.449 1.562 4.133 3.189 7.305 0.0 1.549 2.820 + 8.087 +
-
02 03 03 02 06 06 05 06 05 05
-/)4 - 03 - 01
8.471 + 22
+ + + + + + + + + +
15 15 13 14 13 11 16 14 16 12
+ 16 + 17 + 18
02 02 04 03 04 (16 01 03 01 115 01 00 01
7.363 + 18
8.696 + 01
7.679 + 18
9.069 + 01
8.194 + 18
9.678 + 01
W h e n d a t a for 59Ni is t a k e n f r o m K E D A K - 4 , Rows 17 and 18 r e a d as below: 17
2859
18
Total
59 Ni
Steel density a s s u m e d : 7.8 g / c m 3. b R e a d as 2.158 × 10 I7. c E l e m e n t a l nickel excluding 5SNi. d 58Ni o.v/o,a = 0.9922.
0.0
0.0 8.471 + 22
1.303 - 01
V. Gopalakrishnan et al. /Journal of Nuclear Materials 228 (1996) 207-214
icant when I°B concentration becomes very small ( < 1 wppm). - For the present study, the time of irradiation is 3 × 107 s and the helium accumulation in the specimen in this time can be roughly read out from Fig. 3. The calculated amounts of helium produced per cubic centimetre of the specimen for each of its constituents for the total fluence of 22 × 1025 m -2 are given in Table 4 and Table 5 for 1.4970 and 1.4970LB specimens respectively. From these tables one can see that as against the measured [4] helium production values of 70 appm for 1.4970 sample and 28 appm for the 1.4970LB sample, the calculated values stand at 125 appm and 87 appm, respectively, with 59Ni cross sections taken from the recent library E N D F / B - V I . With cross sections of this nuclide taken from the older library KEDAK-4, the corresponding values are 134 appm and 97 appm respectively. Though the recent cross sections give values closer to the measured than the older ones, the improvement is not significant. Using only the thermal cross sections (see Table 3) and the given thermal fluence of 2.6 × 1025 m -2, we obtained 62 appm of helium production for sample 1.4970 and 21 appm for sample 1.4970LB. With respect to the measured values, this appears to show that the majority of the helium production takes place at thermal energies. But these values are significantly smaller than the values of total production calculated with the mixed spectrum taken into account. Since thermal cross sections are normally known to a reasonable accuracy in contrast to the cross sections at higher energies, the values of 62 appm and 21 appm, corresponding to the thermal fluence may be assumed to be reliable. Remembering that the total fluence of 22 × 1025 m -2 is much larger than the thermal fluence and also noting the resonance structure in (n, a ) cross sections of 59Ni at higher energies, and the high initial concentration of 5SNi which can generate large concentrations of 59Ni for the given fluence, one would expect significantly large contribution to helium production from the fast component of the fluence. This reasoning supports the large calculated values and makes the measured values look too small. On the other hand, if one assumes the measurement to be fairly accurate (recall the confidence in the measurement, which is within 10%), the calculated total helium productions in the two specimens would appear too large, which in turn would suggest inaccuracies in the cross sections used. At the fluence of 22 × 1025 m -2, the major contributors to the helium production are 1°B and 59Ni as seen in Table 4 and Table 5. Of these, 1°B shows saturation in helium production and 59Ni dominates. This must indicate a large uncertainty in the 59Ni cross sections at high and intermediate energies, where this nuclide exhibits resonance structures in cross sections for reactions includ-
213
ing (n, a). In order to get a feel of the sensitivity, the effective (n, a ) and activation cross sections of 59Ni were reduced by 1 b, which decreased the helium production by over 20 appm. These observations, under the assumption that the helium measurement [4] is accurate enough, would suggest the need for a fresh look into the measurements and evaluations of 59Ni cross sections. A newer evaluation for this nuclide has already shown us a tendency to give better results as seen above. The two specimens differ essentially in their boron concentrations. The natural boron has 1°B and liB in the ratio 1:4. From the composition given in Table 1, and with the density of steel taken to be 7.8 g / c m 3, the l°B concentration in the 1.4970 specimen is found to be 44 appm and that in the 1.4970LB specimen, 2.5 appm. One can note that the difference of about 40 appm in the measured helium production in the two specimens seems to be fully accounted for by the difference of about 40 appm in the 1°B concentrations, assuming its complete burnup. Therefore, the present comparison does not throw any light on the confidence in the l°B(n, ct) cross sections. Nevertheless, l°B(n, a ) cross sections, being the standard for neutron cross section measurements below 100 keV, can be said to be adequately known. Discrepancies in SSNi (n, ~) cross sections could influence the results significantly. However, use of JENDL-2 [13] (Japanese Evaluated Nuclear Data Library Version 2) instead of ENDL/84-V for 1°B and 5SNi has been found to lead to the same results presented in this paper.
5. Conclusions
In this work, calculations were performed to estimate helium production in two stainless steel specimens irradiated in a mixed spectrum reactor, using the neutron interaction cross sections from different evaluated nuclear data libraries (ENDFs). The calculated values of helium production in these steels are compared with reported measured values. It was observed that calculated and measured estimates of helium produced in these two steels during neutron irradiation differ by a factor of 2 to 3. Since the actual error information in the data used were not available, the uncertainty in the calculation could not be quantified. The calculation made corresponding to the thermal component of the total fluence, using the thermal cross sections which are normally known to a reasonable accuracy, suggests that the measurements have given an underestimation of the helium produced. This may be due to the limitation in the accuracy of the measurement. At the same time, it is desirable to have very accurate neutron cross sections for 59Ni.
214
V. Gopalakrishnan et al. /Journal of Nuclear Materials 228 (1996) 207-214
Acknowledgement T h e authors are grateful to Dr. W. Kesternich for his valuable suggestions.
References [1] See for example: H. Ulmaier and H. Trinkhaus, Mater. Sci. Forum 97-99 (1992) 451. R.V. Nandedkar, Trans. lndian Inst. Metals 38(1985)64. [2] J. Weitman et al., Trans. Am. Nucl. Soc. 13(1970)2. M. Kangilaski and A.A. Bauer, Studies of the Effects of Irradiation on Cladding and Structural Alloys, BMI 1914, Battelle Memorial Institute (1971). G.J. Kirouac, Nucl. Sci. Eng. 46 (1971) 427. [3] See for example: B. Goel, Nucl. Sci. Eng. 69(1979)99. D.W. Kneff et al., Nucl. Sci. Eng. 92(1986)491. J.A. Grundl, Radiat. Eft. 93(1986)135.
[4] R.V. Nandedkar and W. Kesternich, J. Nucl. Mater 62( 1989)329. [5] W. Kesternich and R.V. Nandedkar, private communication. [6] L. Weise, Neutronenspektrumentfaltungen aus gemessehen Sondenaktivierungen Das FORTRAN-Rechenprogramm SAND-MX2, KFA Report, Kernforscbungsanlage Jiilieb, JUL-1837 (1983). [7] R.D. Neef, Berechnung der Anreicherung und der Bestrahlungszeit fur die Testplatten des AF-Pragramms, KFA Report, Kernforschungsanlage Julich, JUL-Spez160 (1982). [8] V. Gopalakrishnan and S. Ganesan, REXI-87, A Code for Multigrouping Neutron Cross Sections from Preprocessed E N D F / B Basic Data File, Internal Report IGC A R / R P D / N D S - 1 3 (1988). [9] IAEA Summary documentation: IAEA-NDS-11, Rev. 5. [10] IAEA Summary documentation: IAEA-NDS-23, Rev. 3. [11] B. Goel and B. Krieg, Status of the Nuclear Data Library KEDAK-4, October 1984, Report KFK-3838 (1985). IAEA Summary documentation: IAEA-NDS-21, Rev. 4. [12] IAEA Summary documentation: IAEA-NDS-100, Rev. 3. [13] IAEA Summary documentation: IAEA-NDS-18, Rev. 3.
Journal of Nuclear Materials 228 (1996) 207-214
Comparison of calculated helium production in stainless steel due to neutron irradiation with experiment V. Gopalakrishnan a, R.V. Nandedkar b, S. Ganesan c Indira Gandhi Centre for Atomic Research, Kalpakkam, India b Centre forAdvanced Technology, Indore, India c Bhabha Atomic Research Centre, Bombay, India
Received 16 May 1995; accepted 16 October 1995
Abstract
It is well known that helium produced during neutron irradiation through the (n, a ) reaction affects the mechanical properties and the amount of void swelling in nuclear reactor materials. In order to estimate the amount of helium produced in a high alloy stainless steel, which is used in fast reactors and is appropriate to be used in future fusion reactor structural materials, calculations have been performed using the neutron interaction cross sections of the steel constituents. Two austenitic steel specimens of type 1.4970 with high and low boron content, respectively, for which some experimental results are available have been chosen for the present calculations. Predominant nuclear reactions like l°B(n, a)7Li, and the two-step reaction viz. 58Ni(n, -y)S9Ni(n, a)S6Fe, and the details of the neutron spectrum are taken into account. The cross sections for 59Ni, the major contributor for higher irradiation times, are taken from the KEDAK-4 (German) and the most recent E N D F / B - V I (American) Evaluated Nuclear Data Libraries. The results show that the calculated and the measured estimates differ by a factor of 2 to 3. This difference may be due to uncertainties in the measurement as well as uncertainties in the reaction cross section, especially in the two-step reaction. I. Introduction
The production of helium due to neutron interactions with the constituent atoms of the structural materials of fusion reactors can cause detrimental effects on their mechanical properties [I]. Since helium is practically insoluble in most of the metals and alloys, the helium atoms generated during irradiation will precipitate in the grain boundaries and the interior as helium bubbles, and continuous accumulation of such bubbles would lead to significant changes in the mechanical properties. One of the ways the helium is introduced into structural materials is via (n, a ) reactions between the fusion neutrons and the nuclei of the bulk of structural components. The presence of mB in the stainless steel specimen can cause significant amount of helium production at low neutron energies due to its high (n, a) cross section. In addition, it is widely known that 59Ni atoms produced during irradiation contributes quite significantly to the helium generation at
high fluences, through the following two-step reaction [2]: 58Ni(n, y) --+59Ni(n, or) -+ 56Fe. All other nuclides in the steel have their respective contributions to helium production depending on their (n, a ) cross sections, but are usually less significant than the contributions from I°B and 59Ni. In principle, it is possible to estimate the exact amount of helium production by having the knowledge of the chemical composition of the specimen under study, the fluence of the irradiation and the cross sections for various neutron interactions involved. But the inevitable uncertainties in each of the above quantities put the limitation on the accuracy in the prediction. The cross sections of the materials generated during irradiation, i.e. not naturally occurring, 59Ni in our case, can have large uncertainties. A possible reason for the latter is that the sparsely measured cross
0022-3115/96/$15.00 © 1996 Elsevier Science B.V. All rights reserved SSDI 0022-3115(95)00214-6
V. Gopalakrishnan et aL /Journal of Nuclear Materials 228 (1996) 207-214
208
Table 1 Chemical composition of the steel specimens in wt% 1.4970
1.4970LB
Element
wt%
Element
wt%
Element
wt%
Element
wt%
Fe Cr Ti C N B
67.045 14.810 0.285 0.092 0.001 0.004
Ni Mo Mn Si V
14.640 1.150 1.600 0.350 0.023
Fe Cr Ti C N S V
65.4400 15.3000 0.2600 0.1120 0.0050 0.0024 0.0140
Ni Mo Mn Si P Cu B
15.400 1.1700 1.7700 0.4900 0.0140 0.0160 0.0023
2. Experimental details
sections are usually complemented by model based theoretical calculations and approximate fitting procedures. Experimental estimation also may have large uncertainty. The fluence of irradiation is among the difficult quantities to measure accurately. In the case of helium production very few integral experiments exist that would help better understanding of the physical processes that are happening and a validation of the basic physical data involved, cross sections for instance. Nevertheless, potential consequences of helium generation in structural materials have motivated many scientists, and so research papers based either on experiments or computations continually appear in literature [3]. The aim of the present work is limited to perform a theoretical calculation to estimate the amount of helium produced in the two specimens of austenitic stainless steel studied by Nandedkar and Kesternich [4], and make a comparison with their measurements, so as to have a feel of the agreement or otherwise of prediction and measurement of such an important quantity.
In the experiment of Nandedkar and Kesternich [4], two austenitic stainless steel specimens, one with composition of D I N 1.4970 containing about 40 wppm boron and another with a chemical composition close to D I N 1.4970, except having extremely low boron content of approximately 2 wppm, were irradiated in the F R J 2 reactor at K F A Julich, to thermal and fast ( E > 0.1 MeV) neutron fluences of 2.6 x 10 25 m 2 and 3.0 x 1025 m -2, respectively. The fast fluence corresponds to 1.5 dpa. The specimen containing low boron is designated as 1.4970LB. The chemical compositions of the two specimens are given in Table 1. The irradiation time is approximately 346.81 d, which is about 3 x 107 S. After the irradiation, the helium concentrations were measured, by degassing and mass spectrometry, to be 70 appm for specimen 1.4970 and 28 appm for 1.4970LB. These values have been obtained from two independent measurements each, giving 68 and 74 appm helium for 1.4970 and 28 and 28 appm for
10 ~s lethargy
neutron/sq.cm/sec/unit X b_ Y
o k--1 0 ~3I L~ Z
"~O121 ,,,HHq ,,,'~mI 10-2
10
~
1
ilil,q
10
I
Ilrl~l~
I
I
10 2
I rlllll
I
I
10 ~
I II~llJ I
10 ,
I
IIIf~ll
t
b I Jlllll
10 5
NEUTRON ENERCY (eV)
Fig. 1. Flux at B3 position of the FRJ 2 reactor.
I
I
10 6
IIIIIII
0 •
V. Gopalakrishnan et al. /Journal of Nuclear Materials 228 (1996) 207-214 1.4970LB. These measurements have been made at Rockwell International and the confidence in the measurements is understood to be well within 10%. The fluxes at the irradiation position [5], as reported by Weise [6] are used in the present calculations. The flux density per unit lethargy plotted against energy is given in Fig. 1 and corresponds to the B3 position [5,6] at which the irradiation took place in the FRJ 2 reactor at KFA Julich. The total (i.e. energy integrated) flux was 7.438 × 10 a8 m - 2 s 1. The fast ( > 0.1 MeV) fluence given in Ref. [4] was exactly reproduced from this data, for the sake of verification. The total fluence including thermal, intermediate and fast components is obtained as the product of the total flux and the time of irradiation to be 22.3 × 10 25 m -e. In the present work, helium production in each of the components of the steel specimens were calculated using appropriate information on flux, fluence and neutron cross sections and compared with this experiment. The theory, the data sources and the methods are briefly described below.
3. Theoretical background For any nuclide which produces helium due to a neutron fluence ~bt, ~b being the flux, the total number of helium atoms produced per unit volume of the sample during the irradiation period of t seconds is given by
Nf
-N~fo0-~, _
k
t
k
exp(-0-kth/) dt,
(1)
which reduces to N f = Nok0-f/0-ak for a large irradiation time, where, Nok is the number of atoms of the nuclide k per unit volume of the entire specimen, 0-f is the helium production cross section, and 0-f is the activation cross section which includes all neutron reactions by which the nuclide is destroyed. In the case of 59Ni, which is produced during the irradiation, the amount of helium atoms produced in the two-step reaction is given by 58 5 9 J 59 -- N 5 8 0-'¢ 0-c~ ~9 f0t{
Nd -
0 0-a59_0-a58
exp(--°'a586t)
-- exp( --0-a59q~/)} dt,
(2)
where No58 is the initial number of 58Ni atoms, 0-v58 is the (n, ~) cross section of 58Ni, 0-f8 is the activation cross section of 5SNi, 0-59 is the (n, a ) cross section of 59 Ni, and 0-a59 is the activation cross section of 59 Ni. Since 59Ni is produced during irradiation, its contribution to helium production will increase with the time of irradiation reaching an asymptotic or saturation value of 0- 58O. 59
N59
r~/58-'t -a = " 0 0-a590-58•
(3)
209
Eqs. (1) and (2) can now be used for helium estimation from steel provided the effective cross sections of neutron interactions and the fluence of irradiation are known. In an evaluated nuclear data file (ENDF), cross sections are given as a function of energy, from subthermal energies to about 20 MeV, in a tabular form, along with some interpolation schemes to be used between the tabulated points. In the resonance energy region, cross sections are often given through 'resonance parameters', from which it is possible to construct the cross sections in tabular form. For the sake of brevity in explaining the method used to calculate effective cross sections, let us assume that the microscopic cross sections for any desired reaction are initially made available as a function of energy. Since the irradiation was done in a mixed neutron spectrum, a knowledge of the flux spectra is essential to properly account for the structures shown, as a function of neutron energy, by each of the constituents of steel in their neutron interaction cross sections at intermediate energies. If the fluxes at the irradiation position are known in multigroup form, the effective (one-group) cross section, for any reaction x can be obtained as
0-X=~g0-Xg~bg/~gdpg,
(4,
where 0-xg is the average cross section in an energy group g, with lower limit Eg+l and upper limit Eg, and ~bg is the known multigroup flux. The multigroup cross sections for the above purpose may be obtained from the basic cross section 0-x(E) as
0-x =f +10-x(E)S(F )dE/fEg S(e) dE, Eg+l
(5)
where S(E), which approximates the shape of the neutron collision density at energy E, is the standard weighting spectrum usually used in cross section averaging for reactor physics applications. For the present calculations, we used a 53 energy group structure whose boundaries are given by Neef [7]. The multigroup cross sections were obtained, as defined in Eq. (5) above, using the code REX1-87 [8]. The neutron interaction cross sections were taken from the basic evaluated nuclear data library, ENDL/84-V [9] of the Lawrence Livermore Laboratory, USA, for all the nuclides of the specimens except for 14N and 59Ni. E N D F / B - I V [10] (American) library was used for 14N. The KEDAK-4 [11] (German) and also the most recent E N D F / B - V I [12] (American) libraries were tried for 59Ni. All these data libraries were obtained through the Nuclear Data Section of the International Atomic Energy Agency, Vienna, Austria. The energy
210
V. Gopalakrishnan et al. /Journal of Nuclear Materials 228 (1996) 207-214
Table 2 Weighting spectrum used for cross section averaging Energy region
4.
Weighting function
Upper limit (eV)
Lower limit (eV)
S(E) ~
1.49180+07 b 2.46600 + 06 4.07620 + 05 5.24750 + 04 2.03470 + 03 2.26030 + 01 3.75000-01
2.46600+06 4.07620 + 05 5.24750 + 04 2.03470 + 03 2.26030+ 01 3.75000- 01 Thermal
7E exp(- E/1.4 x 10 6) E 2 1/ E 1/dE constant in E E E exp(- E/0.0253)
variation of the (n, a ) cross section of 1°B and 59Ni are given in Fig. 2. The shapes used for S ( E ) are given in Table 2 for various energy regions. The 53 group fluxes, ~bg, are obtained from the values of flux density per unit lethargy, ~b'(E), given by Weise [6] as (6)
J~'g+l
Further, the 'activation cross section' is defined for the present work as the cross section for that process in which the target nuclide does not appear as a reaction product, and is computed as (7)
Ora : O',.¢ - F O p q- O"d q- O'T "~'- O"~ q- O'2n -]- O'3n.
and
discussion
Plots of the accumulated helium atoms produced per every million atoms of the sample upto a given irradiation time in X°B, 58Ni, and 5 9 N i ( E N D F / B - V I ) are given in Fig. 3 for the two specimens. For 58Ni and 59Ni, the helium production in 1.4970LB is only slightly higher than in 1.4970, due to higher initial concentration of 58Ni in 1.4970LB; the corresponding curves for the two specimens nearly coincide and hence these are not shown in Fig. 3. From Fig. 3 the following points can be noted: - Each of the curves shows saturation behaviour at high irradiation times, as expected. - ~°B is the most important helium producer at low irradiation times. - 59Ni is the dominant producer at high irradiation times. It was initially not present, but its concentration and hence its contribution to helium production increase with time. High initial concentration of 58Ni, over four orders of magnitude higher than that of I°B, together with its significant (n, -/) cross section contribute to the dominance of 59Ni, even though the (n, c~) cross sections of 59Ni are lower than those of l°B by more than two orders. Production from 58Ni exceeds that from 1°B at high irradiation times for which l°B shows saturation, due to the high concentration of 58Ni in the specimen. However, 58Ni itself is not a significant helium producer, as l°B at short irradiation times, and 59Ni at large irradiation times become dominant helium producers. Production from 5SNi is comparable to that from l°B for the 1.4970LB specimen, for the fluence considered in the present study. It could become signif-
a See Eq. (5). Weighting function is proportional to S(E), where E is neutron energy in eV. b Read as 1.49180x 10 7.
¢bg = leg
Results
The effective cross sections obtained as above are given in Table 3.
10 E k_
g z © I--
10" .......
--
-
......
10 3.
Ni-59 Ni-59 B-IO
(ENDF/B-Vl) .(KEDAK-4) (ENDL/84-V)
10 2 10
LLJ fJ3
"'""--'"--..
_
---_
1
Lf3 10 gO (:3 O:5 C)
'
"
'-"
1(3
10 10 -2
10 -~
1
10
10 2
103
10"
10 s
NEUTRON ENERCY (eV) Fig. 2. The (n, a) cross sections versus neutron energy.
106
10 7
I/.. Gopalakrishnan et aL /Journal of Nuclear Materials 228 (1996) 207-214
211
Table 3 Effective n e u t r o n cross sections No.
MAT a
Nuclide
Source b
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
7810 7811 7812 1275 7820 7821 7822 7828 7829 7830 7831 7832 7838 7844 7837 d 2828 2859
1°B UB t2C N Si P S Ti V Cr Mn Fe Cu Mo 58Ni 59Ni 59Ni
ENDL/84-V
Cross sections
e
(b)
tr~
~a
9,5460 4,4520 5.9660 6.0090 1.9020 1.1020 6.5670 8.0130 1.3290 4.3320 1.0770 2.2240 2.3720 0.0 1.2740 3.6110 4.0950
ENDF/B-IV ENDL/84-V
ENDF/B-VI KEDAK-4
+ -
02 c 06 05 03 04 04 03 06 06 05 05 05 05
9.5470 3.0010 1.2370 4.8090 4.3010 5.3750 1.6390 1.5220 1.2730 7.7280 3.2670 6.3680 9.6670 1.2610 1.1240 2.9730 3.1420
- 03 + 00 + 00
+ + + + + + + +
02 03 03 01 02 02 01 00 00 01 00 01 01 00 00 01 01
a M A T is the i d e n t i f i c a t i o n n u m b e r of the nuclide in the r e s p e c t i v e source. M A T for 59Ni in K E D A K - 4 is 280059. It is t a k e n 2859 for c o n v e n i e n c e . b T h e p r e v i o u s s o u r c e i m p l i e d if given blank. c R e a d as 9.546 x 102. d 58Ni ~r~ = 1,115 b.
Thermal cross sections: l ° B t r , = 3837 b t°Btra = 3837 b 58Nicrv = 4.6 b 58Nitra = 5 b 59Nitr,~ = 13 b 58Nit& = 110 b
E
10 s.
~ZL 0 10 3 r~ Ld (--)
B-IO B-IO Ni-58 Ni-59
...... ---
(DiN (,DIN
1.4970) 1.4970LB) ~ ::
10 -1
0103 cv O_
1 0 _5 T_ /
10_7.
J /
Ld ZE
/ /
1 0 -g
/ / / /
10 -"
I i lllllll
0
i i IIIEIII
10 2
i i lilllll
10 3
10 '
] I llllll I
I ; II11111
10 s
I I Itllll I
10 6
lll~.q
10
I I IllllI 1
10 a
I I IIIII
10 a
10
~o
IRRADIATION TIME ( s e c ) Fig. 3. H e l i u m p r o d u c e d in b o r o n a n d nickel ( T h e vertical line is to aid r e a d i n g the p r o d u c t i o n at the i r r a d i a t i o n t i m e considered).
212
V.
Gopalakrishnan et al. /Journal of Nuclear Materia& 228 (1996) 207-214
Table 4 H e l i u m p r o d u c e d in c o m p o n e n t s of steel 1.4970. N e u t r o n irradiation fluence used: 22.3 × 1025 m SI. no.
MAT
Nuclide
1 2
7810 7811
mB t 1B
3 4
7812 1275
tZC N
5 6 7 8
7820 7828 7829 7830
Si Ti V Cr
9 10
7831 7832
Mn Fe
11
7844
12 13 14
7836 7837 d 2828
15
Total
Nuclides p e r cm 3 a
~r/cr,,
0.0008 0.11032
3.753 + 18 b 1.503 + 19
I).0920 0.0010
wt%
z
Helium produced per cm 3
appm
9.999 -- 01 1.483 - / 1 3
3.752 + 18 1.491 + 12
4.442 + 01 1.765 05
3.601 + 211 3.355 + 18
4.824 02 1.251/- 02
4.788 + 14 4.469 + 14
5.668 - 03 5.291 03
/I.3500 0.2850 0.0230 14.8101/
5.871 2.789 2.118 1.338
4.423 5.264 1.044 5.605
2.488 + 15 4.897 + 13 6.188 + 11
2.945 02 5.797 - 04 7.326 - 06
1.6000 67.0450
1.366 + 21 5.623 + 22
3.297 - 06 3.492 - 05
1.280 + 16 3.164 + 14 2.767 + 16
1 . 5 1 6 - 01 3.745 03 3.273 - 01
Mo
1.15110
5.627 + 20
0.0
Ni ~" 5SNi 5'~Ni
4.6453 9.9947 0.0
3.626 + 21 8.094 + 21 0.0
6.151 - 04 1.134 - 03 1.215 - 01
0.0 1.246 + 16 2.270 + 17 6.509 + 18
0.0 1.476 - 01 2.687 + 00 7.706 + 01
1.055 + 19
1.248 + 02
7.300 + 18
8.642 + 01
1.134 + 19
1.342 + 02
+ + + +
20 20 19 22
-
(13 1/6 (16 05
8.452 + 22
W h e n d a t a for 59Ni is t a k e n f r o m K E D A K - 4 , Rows 14 and 15 r e a d as below: 14
2859
15
Total
5'~Ni
0.0
0.0
1.303 - 01
8.452 + 22
'~ Steel density a s s u m e d : 7.8 g / c m 3. i, R e a d as 3.753 × 10 TM. "58
•
c E l e m e n t a l nickel excluding ~ NL d 58Ni o.v/%, = 0.9922. Table 5 H e l i u m p r o d u c e d in c o m p o n e n t s of steel 1.4970LB. N e u t r o n irradiation fluence used: 22.3 × 10 25 m SI. no.
MAT
Nuclide
wt%
1 2 3
7810 7811 7812
mB iiB tic
0.00005 0.00018 0.11200
4 5 6 7 8 9 111 11 12 13 14 15 16 17
1275 7820 7821 7822 7828 7829 7830 7831 7832 7838 7844 7836 7837 d 2828
N Si P S Ti V Cr Mn Fe Cu Mo Ni ~ 5SNi 5'~Ni
0.00500 I).49000 0.01400 0.002411 1/.26000 0.01400 15.30000 1.77000 65.44430 0.01600 1.17000 4.88642 10.5136 0.0
18
Total
Nuclides p e r cm 3 a
%let,,
2.158 + 17 b 8.640 + 17 4.384 + 20 1.677 8.220 2.121 3.523 2.544 1.289 1.382 1.512 5.489 1.183 5.724 3.814 8.514 0.0
+ + + + + + + + + + + + +
19 20 19 18 20 19 22 21 22 19 211 21 21
•
Helium produced per c m 3
appm
9.999 - 01 1.483 - 03 4.824 - 02
2.158 + 17 8.573 + 10 5.829 + 14
2.548 + 00 1.013 - 06 6.884 - 03
1.250 4.423 2.051 4.007 5.264 1.044 5.605 3.297 3.492 2.454 0.0 6.151 1.134 1.215
2.235 3.483 5.207 5.146 4.467 3.767 1.323 3.500 2.701 6.185 1).0 1.311 2.388 6.847
2.639 4.1146.150 6.078 5.276 4.449 1.562 4.133 3.189 7.305 0.0 1.549 2.820 + 8.087 +
-
02 03 03 02 06 06 05 06 05 05
-/)4 - 03 - 01
8.471 + 22
+ + + + + + + + + +
15 15 13 14 13 11 16 14 16 12
+ 16 + 17 + 18
02 02 04 03 04 (16 01 03 01 115 01 00 01
7.363 + 18
8.696 + 01
7.679 + 18
9.069 + 01
8.194 + 18
9.678 + 01
W h e n d a t a for 59Ni is t a k e n f r o m K E D A K - 4 , Rows 17 and 18 r e a d as below: 17
2859
18
Total
59 Ni
Steel density a s s u m e d : 7.8 g / c m 3. b R e a d as 2.158 × 10 I7. c E l e m e n t a l nickel excluding 5SNi. d 58Ni o.v/o,a = 0.9922.
0.0
0.0 8.471 + 22
1.303 - 01
V. Gopalakrishnan et al. /Journal of Nuclear Materials 228 (1996) 207-214
icant when I°B concentration becomes very small ( < 1 wppm). - For the present study, the time of irradiation is 3 × 107 s and the helium accumulation in the specimen in this time can be roughly read out from Fig. 3. The calculated amounts of helium produced per cubic centimetre of the specimen for each of its constituents for the total fluence of 22 × 1025 m -2 are given in Table 4 and Table 5 for 1.4970 and 1.4970LB specimens respectively. From these tables one can see that as against the measured [4] helium production values of 70 appm for 1.4970 sample and 28 appm for the 1.4970LB sample, the calculated values stand at 125 appm and 87 appm, respectively, with 59Ni cross sections taken from the recent library E N D F / B - V I . With cross sections of this nuclide taken from the older library KEDAK-4, the corresponding values are 134 appm and 97 appm respectively. Though the recent cross sections give values closer to the measured than the older ones, the improvement is not significant. Using only the thermal cross sections (see Table 3) and the given thermal fluence of 2.6 × 1025 m -2, we obtained 62 appm of helium production for sample 1.4970 and 21 appm for sample 1.4970LB. With respect to the measured values, this appears to show that the majority of the helium production takes place at thermal energies. But these values are significantly smaller than the values of total production calculated with the mixed spectrum taken into account. Since thermal cross sections are normally known to a reasonable accuracy in contrast to the cross sections at higher energies, the values of 62 appm and 21 appm, corresponding to the thermal fluence may be assumed to be reliable. Remembering that the total fluence of 22 × 1025 m -2 is much larger than the thermal fluence and also noting the resonance structure in (n, a ) cross sections of 59Ni at higher energies, and the high initial concentration of 5SNi which can generate large concentrations of 59Ni for the given fluence, one would expect significantly large contribution to helium production from the fast component of the fluence. This reasoning supports the large calculated values and makes the measured values look too small. On the other hand, if one assumes the measurement to be fairly accurate (recall the confidence in the measurement, which is within 10%), the calculated total helium productions in the two specimens would appear too large, which in turn would suggest inaccuracies in the cross sections used. At the fluence of 22 × 1025 m -2, the major contributors to the helium production are 1°B and 59Ni as seen in Table 4 and Table 5. Of these, 1°B shows saturation in helium production and 59Ni dominates. This must indicate a large uncertainty in the 59Ni cross sections at high and intermediate energies, where this nuclide exhibits resonance structures in cross sections for reactions includ-
213
ing (n, a). In order to get a feel of the sensitivity, the effective (n, a ) and activation cross sections of 59Ni were reduced by 1 b, which decreased the helium production by over 20 appm. These observations, under the assumption that the helium measurement [4] is accurate enough, would suggest the need for a fresh look into the measurements and evaluations of 59Ni cross sections. A newer evaluation for this nuclide has already shown us a tendency to give better results as seen above. The two specimens differ essentially in their boron concentrations. The natural boron has 1°B and liB in the ratio 1:4. From the composition given in Table 1, and with the density of steel taken to be 7.8 g / c m 3, the l°B concentration in the 1.4970 specimen is found to be 44 appm and that in the 1.4970LB specimen, 2.5 appm. One can note that the difference of about 40 appm in the measured helium production in the two specimens seems to be fully accounted for by the difference of about 40 appm in the 1°B concentrations, assuming its complete burnup. Therefore, the present comparison does not throw any light on the confidence in the l°B(n, ct) cross sections. Nevertheless, l°B(n, a ) cross sections, being the standard for neutron cross section measurements below 100 keV, can be said to be adequately known. Discrepancies in SSNi (n, ~) cross sections could influence the results significantly. However, use of JENDL-2 [13] (Japanese Evaluated Nuclear Data Library Version 2) instead of ENDL/84-V for 1°B and 5SNi has been found to lead to the same results presented in this paper.
5. Conclusions
In this work, calculations were performed to estimate helium production in two stainless steel specimens irradiated in a mixed spectrum reactor, using the neutron interaction cross sections from different evaluated nuclear data libraries (ENDFs). The calculated values of helium production in these steels are compared with reported measured values. It was observed that calculated and measured estimates of helium produced in these two steels during neutron irradiation differ by a factor of 2 to 3. Since the actual error information in the data used were not available, the uncertainty in the calculation could not be quantified. The calculation made corresponding to the thermal component of the total fluence, using the thermal cross sections which are normally known to a reasonable accuracy, suggests that the measurements have given an underestimation of the helium produced. This may be due to the limitation in the accuracy of the measurement. At the same time, it is desirable to have very accurate neutron cross sections for 59Ni.
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Acknowledgement T h e authors are grateful to Dr. W. Kesternich for his valuable suggestions.
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