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Fission gas yield in uranium metal
JOURNAL
OF NUCLEAR
MATERIALS
FISSION
19, No.
1 (1963)
GAS YIELD
67-69,
NORTH-HOLLAND
IN URANIUM
PUBLISHING
METAL
CO., AMSTERDAM
7
J. W. WEBER
Received
13 February
Volume increases in uranium during irradiation at temperat~es above 400” C are attributed primarily to the agglomeration of fission gases 192).Values given in the literature for the volume of fission gases present in unalloyed uranium, irradiated in a thermal neutron flux, expresses as cm3 gas STP/cm” uraniLl~n per at O/oburnup, range from 3 to 4.95 g-5). Because of this wide range of values, an independent investigation was made by Merckx 6) based on the latest available values of fission product yields. His anaIysis took into account the formation of stable Xe134 and Xel36 from Xe133 and Xe135, respectively, by neutron capture. The analysis and results described here refine the yields by accounting for the differences in fission product yield between plutonium and urani~~m and the build-up of pluto~lium as a function of burnup. The yields of each xenon and krypton fission gas isotope for the thermal fissioning of both U235 and Pu23@ are given in table 1 7). The difference in total gas yield between geranium and plutonium is seen to be about 3 percent. To determine if this difference would make a significant change in the volume of fission gas over a range of burnups, the fraction of U235 and Pu23@ fissioning was computed for several enrichments and for burnups to 1 at O/&It was found that for enrichments of 0.72 percent, or greater, the difference in the total gas yield between assuming all 17235fissioning or taking the actual fraction of plutonium and uranium 7
This work performed
and General Electric
under
Contract
TABLE 1 Fission
67
product
yields
for thermal
fission of
II235
and Pu239 7) Fission product
o/0 Yield
isotope
u235
0.54 1.00
c
y/, Yield
0.30
Pu239 0.29 0.47 0.13
2.02
0.76
0.07
Insignificant
3.93
A/ I
1.65 3.78
Xe'3'
2.93
X&z"
4.38
5.26
X0133
6.62
6.91
Xe’34
8.06
7.47
Xel35
6.30
5.70
Xe13F Xe’3”
6.46
6.63
0.25
0.25
35.00
36.00
L
fissioned, is 3 percent or less at 1 at y. burnup. This small difference is neglected, and the fission yields of U235 in table 1 were used in the subsequent calculations of gas volume. In the normal radioactive decay, the Xel33 and Xe135 decays to C&33 and Ca135,respectively. However> in a reactor neutron field, these two Xe isotopes can capture neutrons forming stable Xe13” and Xe136, respectively. The proportion of stable xenon isotopes formed thus is a function of the neutron flux. The yields of Xe134 and Xels@ from this source are given by:
ND. AT(45-I)-1350
Company.
1963
between
the
Atomic
Energy
Commission
J.
08
W.
.__-_--
Wk!.~l!An,
chains
has
reached equilibrium. By more calc~~lat,ions it can be shown that for
[aJ(A/9: -t-o,)] [% yield of Xei”” or Xeia5]. where cr,= capture cross-se&ions for neutrons ; A = radioactive decay collsta~lt ; q~=: l~e~lt,r~n flus. The nuclear const,ants used for X$33 and iye
irradiatio~l periods of 24 hours or more the error in the total gas volume generated due to
are given in table 2.
the startup
TABLE Nuclear
constants
Xe133 and
Xe135 *)
Xe1s3 nr
Half-life /.
190 *
transient
are insignificant.
Another error is introduced by the loss of X+3” and Xei36 which would occur each time
2
for
rigorous
a reactor is shut down as a result of the decay
Xe""5
’ 2.72 x 10” barils
90 barns
9.2 hours / j 2.09 x IO-5/set
5.27 days 1.52 x lOP/sec
In table 3 are presented the yields and volumes of fission gases at “C! and 1 atmosphere as a function of thermal neut’ron flux. The gas volume was calculated from the yields. The gas volume as a function of neutron flux on a logarithmic scale is plotted in fig. 1. The expression used to calculate the yields of Xeia* and Xei36 from their respective precursor is an approximatio~l and assumes that decay and neukon capture in the two decay TABLE Calerdated yields
and
Fig.
1.
Inert
gas
from
fission
of
l~raxli~~.rn.
3
volume of fission gases neutron flux for -27235
as a function
of
Volume-cm3/cm3-
1 cpnoat./cm2-see
Gas
I
Yield “5
Uranium
at :&
Blwnup I
Krypton
.
and xenon
3.93
. 1012 5 x 101”
22.80 24.56
1013
25.65
.‘i x 1013
27.68
gas .
.
.
.
I .
I I
I
4.05 4.40 4.59 4.33
28.01
/
5.01
5 x 10’4
28.67
j
5.13
10’5
29.07
10’4
Total
0.70 /
1
5.20
5 X 1Ol5
30.92
/
5.53
10’” .; x 10’”
Z6.73 28.49
I
4.78 5.10
I
5.29
10’3
29.58
6 x 10’3 10’4
31.51 31.34
5 x 10’4
32.60 33.00
10’5 5 x 1015
1
.5.63 5.71
/
34.85
5.83 5.90 6 .d. “4
I
TP”
in met;lllic
FISSION
QAS
YIELD
IN
inventory of precursor isotopes 1133, 1135, Xe133and Xe135 in equilibrium at the time ~al~ulat,io~~shave shown
that the irradiation cycles of ti days or longer the resuks given are valid within the practical range of reacbor fluxes. It is not suggested in this analysis that all t)he gas formed on fissioning is present in the pores found in irradiated uranium m&al; rather, the data presented are an upper limit of gas volume affecting uranium swelling.
3)
Int,. Conf.
Energy,
Geneva
A.
gas 4)
ura~nir~m, Proc. of the Second U’nit~x~
Nations J.
69
METAL
in irradiated
at the
of shutdo~~ll. However,
URilNIUM
Entlarhy~
btIbbles
on Pracefnl
(1958) Plastic
in
flow
uranium,
and the swelling
Rislry
IGN-R-R-198 (I 9.56) 1). Rhodes and V. \P. Eldred, 0.17 y:, brrrnq ncaling,
UKAEA
TN-\V-933, 5) A.
T.
prcssruY part
uranillm
on
Indnstrial
of Atornir
Uses
(1J.K.) The
swelling
llost’irradiat,ion Group
of
Report
Report
of an-
I(:%
l$JSX
Churc*hman
et al.,
on thcb swelling
1, Harwcxll
Effects of
of
irradiated
heat’
itnd
uranilun,
(U.K.) Report AERE-M-R-Z!)44
(1958)
References 1) S. F. Pugh, Damage bnrnnp,
Proc.
of the Int.
of At,omic Energy, Unit& 2)
Nations,
occxrring Conf.
Geneva New
York
R. S. Barnes et al., Swelling
in uranium on Peacefui
6)
K.
7)
(USA) Rqort~ HX-60431 (1959) gas:ls, Hanford S. Kat,coff, ~ission_I~r~~d~~et yields from neutrort18 (11)
Uses
(19!%) and inert gas diffusion
Mcrckx,
F&ion
induced fission, Rrferencc
during
1955, P/443 Vol. p. 441,
R.
*)
201-208,
J. E. Garrison capture
cross
Engineering
product
in&
1960
and B. TIT. Roes,
12 (1)
of
Data Manuai, Nncleonits
Novcmher sPctions,
yiehl
Nuclear
115-134,
Fission-prod,tc% Science>
,Janrlnry
196l!
ant1
OF NUCLEAR
MATERIALS
FISSION
19, No.
1 (1963)
GAS YIELD
67-69,
NORTH-HOLLAND
IN URANIUM
PUBLISHING
METAL
CO., AMSTERDAM
7
J. W. WEBER
Received
13 February
Volume increases in uranium during irradiation at temperat~es above 400” C are attributed primarily to the agglomeration of fission gases 192).Values given in the literature for the volume of fission gases present in unalloyed uranium, irradiated in a thermal neutron flux, expresses as cm3 gas STP/cm” uraniLl~n per at O/oburnup, range from 3 to 4.95 g-5). Because of this wide range of values, an independent investigation was made by Merckx 6) based on the latest available values of fission product yields. His anaIysis took into account the formation of stable Xe134 and Xel36 from Xe133 and Xe135, respectively, by neutron capture. The analysis and results described here refine the yields by accounting for the differences in fission product yield between plutonium and urani~~m and the build-up of pluto~lium as a function of burnup. The yields of each xenon and krypton fission gas isotope for the thermal fissioning of both U235 and Pu23@ are given in table 1 7). The difference in total gas yield between geranium and plutonium is seen to be about 3 percent. To determine if this difference would make a significant change in the volume of fission gas over a range of burnups, the fraction of U235 and Pu23@ fissioning was computed for several enrichments and for burnups to 1 at O/&It was found that for enrichments of 0.72 percent, or greater, the difference in the total gas yield between assuming all 17235fissioning or taking the actual fraction of plutonium and uranium 7
This work performed
and General Electric
under
Contract
TABLE 1 Fission
67
product
yields
for thermal
fission of
II235
and Pu239 7) Fission product
o/0 Yield
isotope
u235
0.54 1.00
c
y/, Yield
0.30
Pu239 0.29 0.47 0.13
2.02
0.76
0.07
Insignificant
3.93
A/ I
1.65 3.78
Xe'3'
2.93
X&z"
4.38
5.26
X0133
6.62
6.91
Xe’34
8.06
7.47
Xel35
6.30
5.70
Xe13F Xe’3”
6.46
6.63
0.25
0.25
35.00
36.00
L
fissioned, is 3 percent or less at 1 at y. burnup. This small difference is neglected, and the fission yields of U235 in table 1 were used in the subsequent calculations of gas volume. In the normal radioactive decay, the Xel33 and Xe135 decays to C&33 and Ca135,respectively. However> in a reactor neutron field, these two Xe isotopes can capture neutrons forming stable Xe13” and Xe136, respectively. The proportion of stable xenon isotopes formed thus is a function of the neutron flux. The yields of Xe134 and Xels@ from this source are given by:
ND. AT(45-I)-1350
Company.
1963
between
the
Atomic
Energy
Commission
J.
08
W.
.__-_--
Wk!.~l!An,
chains
has
reached equilibrium. By more calc~~lat,ions it can be shown that for
[aJ(A/9: -t-o,)] [% yield of Xei”” or Xeia5]. where cr,= capture cross-se&ions for neutrons ; A = radioactive decay collsta~lt ; q~=: l~e~lt,r~n flus. The nuclear const,ants used for X$33 and iye
irradiatio~l periods of 24 hours or more the error in the total gas volume generated due to
are given in table 2.
the startup
TABLE Nuclear
constants
Xe133 and
Xe135 *)
Xe1s3 nr
Half-life /.
190 *
transient
are insignificant.
Another error is introduced by the loss of X+3” and Xei36 which would occur each time
2
for
rigorous
a reactor is shut down as a result of the decay
Xe""5
’ 2.72 x 10” barils
90 barns
9.2 hours / j 2.09 x IO-5/set
5.27 days 1.52 x lOP/sec
In table 3 are presented the yields and volumes of fission gases at “C! and 1 atmosphere as a function of thermal neut’ron flux. The gas volume was calculated from the yields. The gas volume as a function of neutron flux on a logarithmic scale is plotted in fig. 1. The expression used to calculate the yields of Xeia* and Xei36 from their respective precursor is an approximatio~l and assumes that decay and neukon capture in the two decay TABLE Calerdated yields
and
Fig.
1.
Inert
gas
from
fission
of
l~raxli~~.rn.
3
volume of fission gases neutron flux for -27235
as a function
of
Volume-cm3/cm3-
1 cpnoat./cm2-see
Gas
I
Yield “5
Uranium
at :&
Blwnup I
Krypton
.
and xenon
3.93
. 1012 5 x 101”
22.80 24.56
1013
25.65
.‘i x 1013
27.68
gas .
.
.
.
I .
I I
I
4.05 4.40 4.59 4.33
28.01
/
5.01
5 x 10’4
28.67
j
5.13
10’5
29.07
10’4
Total
0.70 /
1
5.20
5 X 1Ol5
30.92
/
5.53
10’” .; x 10’”
Z6.73 28.49
I
4.78 5.10
I
5.29
10’3
29.58
6 x 10’3 10’4
31.51 31.34
5 x 10’4
32.60 33.00
10’5 5 x 1015
1
.5.63 5.71
/
34.85
5.83 5.90 6 .d. “4
I
TP”
in met;lllic
FISSION
QAS
YIELD
IN
inventory of precursor isotopes 1133, 1135, Xe133and Xe135 in equilibrium at the time ~al~ulat,io~~shave shown
that the irradiation cycles of ti days or longer the resuks given are valid within the practical range of reacbor fluxes. It is not suggested in this analysis that all t)he gas formed on fissioning is present in the pores found in irradiated uranium m&al; rather, the data presented are an upper limit of gas volume affecting uranium swelling.
3)
Int,. Conf.
Energy,
Geneva
A.
gas 4)
ura~nir~m, Proc. of the Second U’nit~x~
Nations J.
69
METAL
in irradiated
at the
of shutdo~~ll. However,
URilNIUM
Entlarhy~
btIbbles
on Pracefnl
(1958) Plastic
in
flow
uranium,
and the swelling
Rislry
IGN-R-R-198 (I 9.56) 1). Rhodes and V. \P. Eldred, 0.17 y:, brrrnq ncaling,
UKAEA
TN-\V-933, 5) A.
T.
prcssruY part
uranillm
on
Indnstrial
of Atornir
Uses
(1J.K.) The
swelling
llost’irradiat,ion Group
of
Report
Report
of an-
I(:%
l$JSX
Churc*hman
et al.,
on thcb swelling
1, Harwcxll
Effects of
of
irradiated
heat’
itnd
uranilun,
(U.K.) Report AERE-M-R-Z!)44
(1958)
References 1) S. F. Pugh, Damage bnrnnp,
Proc.
of the Int.
of At,omic Energy, Unit& 2)
Nations,
occxrring Conf.
Geneva New
York
R. S. Barnes et al., Swelling
in uranium on Peacefui
6)
K.
7)
(USA) Rqort~ HX-60431 (1959) gas:ls, Hanford S. Kat,coff, ~ission_I~r~~d~~et yields from neutrort18 (11)
Uses
(19!%) and inert gas diffusion
Mcrckx,
F&ion
induced fission, Rrferencc
during
1955, P/443 Vol. p. 441,
R.
*)
201-208,
J. E. Garrison capture
cross
Engineering
product
in&
1960
and B. TIT. Roes,
12 (1)
of
Data Manuai, Nncleonits
Novcmher sPctions,
yiehl
Nuclear
115-134,
Fission-prod,tc% Science>
,Janrlnry
196l!
ant1