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The influence of stoichiometry on compression creep of polycrystalline UO2+x
JOURNAL
OF NUCLEAR
44 (1972)
MATERIALS
331-336.
0 NORTH-HOLLAND
PUBLISHINC3
CO.,
AMSTERDAM
THE INFLUENCE OF STOICHIOMETRYON COMPRESSIONCREEP OF POLYCRYSTALLINEUOa+, M. S. SELTZER, Metal
Compressive
Science
creep
Group,
tests
have
Battelle
been
polycrystalline
hyperstoichiometric
as a function
of temperature,
from
stoichiometry.
steady-state
Under
A. H. CLAUER Columbus
Laboratorierr,
Received
4 May
performed
stresses
d’activation
de
maniere
dioxyde
lin&irement
en fonction
de la contrainte,
de fluage est une fonction
1.75
and
of the form
increase
with
est
where
stress dependence
stresses,
the
creep
activation
for
uranium
activation
dioxide
single
energy,
crystals.
region,
different
creep behavior
processes
control
but values
in the two different
the
Abhiingigkeit
for
und
der
niedrigen
stress regimes.
wurden
Stochiometrie von
durchgefiihrt.
UOZ+~
angelegten
Spannung
c
metrischen
Sauerstoffgehalt gemessene
steigt
und x
an.
fonction
de la contrainte
de fluage
de UOZ+~ mesurees
dans
und steigt gem&s
an. Die Ubergangsspannung und
le
hoheren
steigendem
Die
in
Die
unter Kriech-
mit
der
iiberstochiobei
hohen
Kriechgeschwindigkeit
mit 4
et des
poly-
Spannung
linear
dem
sur-stoechiometrique
Sous de faibles contraintes,
der
gemessene station&e
sur du dioxyde polycristallin
en
an
Urandioxid
der Temperatur,
Spannungen
geschwindigkeit
observed
Druck
horcht einer Spennungsabhiingigkeit
les vitesses
11
diffusion
Studies.
Des essais de fluage sous compression ont Bte r&Ii&s de la temperature,
de
au fluage observe dans
de contreintes
unter von
Spennungen
&arts & la stoechiometrie.
de l’effort.
processus
iiberstiichiometrischem
kristallinem,
stress region. It is suggested that
diffusion
puissance
differents
le comportement
Kriechversuche
Creep
Qe are lower at a given x than are values obtained in the power-law
que
Qc,
energies also decrease with increasing x in
the linear stress-dependence
de x
tested at
decreases with increasing x in the same manner as found
suggere
les deux domaines
behavior decreases
with increasing O/U ratio. For polycrystsls
mais les
8. celles obtenues dans la region 06 la vitesse
controlent
The transition stress, ut, between linear
and power-law high
E dc u”
xm
energies
vrtleurs de Qc sont inferieures pour une vdeur
excess, 2.
a power-law
stress dependence
Les
du fluage diminuent aussi avec x croissant
don&e
4
que dans le cas des
d’uranium.
Creep rates for UOs+% tested at high stresses follow where
USA
dans la region 06 la vitesse de fluage second&ire varie
measured
stress, u, and with oxygen
43201,
1972
monocristaux
creep rates for UOs+= increase linearly
with applied
Columbus, Ohio
croissant de la m6me
on
uranium dioxide,
stress and deviation
low
and B. A. WILCOX
x*
ge-
der Art E a mit
an
1,75
ut zwischen der linearen
Spannungsabhiingigkeit
O/U-Verhiiltnis.
sinkt
mit
Die Aktivierungsenergie
stade secondaire augmentent lineairement en fonction
des Kriechens Qc nimmt fiir das bei hohen Spannungen
de l’effort
untersuchte polykristalline
oxygene
applique
u et de l’exces
2. Les vitesses
contraintes
de teneur
de fluage pour UOs+,
en
sous
Blevees obeissent & une loi en puissance
de la forme P:o( on ob 4
et augmentent
La contrainte
&pare le comportement
Die Aktivierungsenergie sinkt ebenfalls mit steigendem
avec
de transition
x im Bereich
qui
die Werte
obeissant iL la loi lineaire &
der linearen
polycristallins
den beiden verschiedenen
de
fluage
Qc diminue
avec
l’ecart
SpannungsabhGrgigkeit
x
x
gewonnen wurden. Vermutlich
unterschiedliche
achtete Kriechverhalten. 331
fur ein bestimmtes
niedriger als diejenigen, die im Bereich einer hijheren bestimmen
testes aux contraintes Blevees, l’energie
Spannungsabhiingigkeit,
fur Qc sind jedoch
celui regi par une loi en puissance de l’effort diminue avec le rapport O/U croissant. Pour les Bchantillons d’activation
Material mit steigendem x
in derselben Weise ab wie fur Urandioxid-Einkristalle.
Diffusionsprozesse
das in
Spannungsbereichen
beob-
332
1.
M. S. SELTZER
ET AL.
Introduction
STRESS,
The effects of varying
stoichiometry
psi
on the
high-temperature creep properties of hyperstoichiometric uranium dioxide single crystals were discussed in a previous paper 1). In order to investigate the influence of grain boundary contributions
to the creep process, these experi-
ments were extended creep of depleted
to include
and enriched
compression
polycrystalline
UO2+z.
2.
Experimental procedures
The experimental procedures employed have been described previously 1). Both high-density, coarse-grained, enriched specimens and lowerdepleted samples were density, fine-grained, used in this study. The final sintering operation for the enriched specimens consisted of pressing 24.48% enriched powder at 137.8 MN/m2 (20 000 psi) and 1700 “C for 15 h in flowing dry hydrogen. These specimens had a density of 97.8 * 0.5% of theoretical and an average grain size of 27 pm. They had an initial O/U ratio of 2.002 ~_t0.003, with iron and silicon being the major impurities at 100 and 150 ppm, respectively. Experiments were also conducted on 95% dense specimens with an average grain size of 6 ,um, which were ultrasonically trepanned from a boule produced by the hot pressing of depleted UO2 at 1400 “C under 96.5 MN/ma (14 000 psi) for 30 min.
3.
4 1
I
I
I
I
STRESS,
Fig.
1.
Steady-state
II
690
6.90
69
I
MN/m2
creep rate versus applied stress
for enriched uranium dioxide tested in compression at 1300 “C; grain size=27 /Am.
Experimental results
3.1. ENRICHED U02+%
Results obtained from creep tests conducted at 1100 “C and 1300 “C are included in figs. 1 and 2, respectively, in which steady-state creep rates, &, are plotted versus stress, u. Tests at constant O/U values of 2.001, 2.01 and 2.10 were performed by equilibrating the creep specimens in flowing CO/CO2 gas mixtures and oxygen partial maintaining the desired pressure 2) as the test progressed. The data for an O/U ratio of 2.10 at 1300 "C
(fig. 1) best illustrate how the stress dependence for steady-state creep varies with stress. At the lowest stresses used, 1.03 to 3.45 MN/ma (150 to 500 psi), the creep rates increase linearly with stress, but this dependence increases with increasing stress so that above 20.67 MN/m2 (3000 psi) creep rates are best fit by a power-law stress dependence of the form i oc ‘in, where n = 7. These results are similar to those obtained by other investigators s-5), where the high stress dependence suggests a dislocation creep
THE
INFLUENCE STRESS,
10s I
I
I
III
OF
STOICHIOMETRY
COMPRESSION
given temperature,
psi
105
ON
333
CREEP
stress, O/U ratio and grain
size are several orders of magnitude higher than
I
those reported by investigators who studied creep of uranium dioxide containing natural or depleted uranium s-5). The reason for this
to-’ -
behavior is not known. Although the absolute values for creep rates obtained
from the enriched
specimens
are not
in agreement with data from natural or depleted uranium-dioxide specimens, the observed dependence for creep rates of enriched UOs on composition is similar to that found for the unenriched specimens. Furthermore, the activation energies for creep of enriched, polycrystalline uranium dioxide are similar to those for creep of UO z+~ single crystals 1). Fig. 3 shows the creep activation energies for UOZ+~ single crystals l) as a function of logisz. Superimposed on these data are the activation energies for creep of enriched polycrystalline as determined from the high-stress UOZ,, portions of the data given in figs. 1 and 2 for O/U ratios of 2.001, 2.01, and 2.10. These values, shown as squares in fig. 3, are 117, 75, and 54 * 10 kcal per mole. It should be noted
o/u 10-3-
A
2.10
v 0
2.01 2.001
‘i
2
c” 2 4
E to-4-
10-5-
I
I
III
I
STRESS,
Fig.
2.
Steady-state
I
I 69.C
6.90
0.69
MN/m*
creep rate versus applied stress
for enriched uranium dioxide tested in compression at 11OO’C; grain size=27 pm.
mechanism based on diffusion-controlled dislocation climb or some other diffusion-controlled process while the linear stress dependence indicates the predominance of Nabarro-Herring diffusional creep or some grain-boundary sliding process. For the lower O/U ratios at 1300 “C and in all cases at 1100 “C, the linear stress dependence was not observed because creep rates were too low at the stress levels required to reach this regime. The absolute values for the creep rates at a
60-
-4(2.0001)
-3(2.001)
-2(2.01)
-I(2.10)
LOG,, x
Fig.
3.
Activation
energies for creep of UOa+,
as a
function of logroz: polycrystals; depleted
0 Single crystals (l), 0 enriched 27 ,am grain size, this study, +, A
polyorystals;
x , V polycrystals, crystals,
6 pm grain size, this study,
4 to 35 ,am grain size (5), D poly-
6 ,am grain size, in bending
(6).
M. 5. SELTZER
334
that
these
obtained
activation
from
possibility determined
but
energies two
have
been
temperatures.
The
ET AL. STRESS, psi
for large errors in Qc values this way is somewhat reduced by
the fact t’hat they were calculated from a number of data points obtained at various stresses
at
agreement
1100 “C and between
1300 “C.
activation
The
energies
good de-
termined from single crystals and polycrystalline materials suggests that the same creep mechanism is operative in both cases. Since the single crystals are free of grain boundaries, the implication is that creep in the high-stress region is controlled by uranium volume diffusion. The dependence of creep rates for enriched, polycrystalline UOa on O/U ratio is also similar to that found for creep of single crystals 1). At 1100 “C, i oc x2 in the high-stress region, while at 1300 “C, the value for the exponent is between 1 and 2. 3.2.
STRESS, MN/m”
Pig.
4.
Steady-state
creep rate versus applied stress
for depleted polycrystalline tested
on compression
UOz+%, 6 pm grain size,
at 1100 “C and
1300 “C.
DEPLETED UOa+,
Tests with depleted UOZ+~ were conducted at 1100 “C and 1300 “C under stresses of 1.03 to 165.36 MN/ ms (150 to 24 000 psi). Results are included in fig. 4 for specimens having compositions in the range of 2.001
regions. In the region of linear stress dependence the creep rates increase linearly with x. In the power-law stress-dependence region, on the other hand, creep rates increase with x1.75. This is close to the x2 dependence found in singlecrystal creep studies l), which suggests t’hat similar processes control creep of single crystals and polycrystals in the power-law stress region, with possibly some grain-boundary contribution entering into the polycrystalline results. An estimate of the creep activation energies can be obtained from the data in fig. 4 for the two temperatures studied. For an O/U ratio of 2.001, in the high-stress region Qc = 108 kcal per mole *, while in the low-stress region Qc w 68.5 kcal per mole. For O/U values of 2.01 and 2.05, Qc values in the low-stress region are N 55 kcal per mole and N 45 kcal per mole, respectively. These activation energies have been plotted as triangles (A) and pluses (+) in fig, 3. Also included in fig. 3 are creep activation energies obtained by Bohaboy et a1.5), *
In order to obtain this value it was necessary
to extrapolate and
to higher stresses for both
1300 “C tests.
1100 “C
THE
INFLUENCE
OF
STOICHIOMETRY
ON
It
uranium
is assumed that their Qc of 132 kcal per mole for the power-law regime corresponds to an
decrease
for polycrystalline
UOZ tested in hydrogen.
o/u RS2.0001based on our results. Their Qc for the linear stress region, 90 kcal per mole, has
been
accordingly
O/U ratio. Activation
placed
at
t,he same
energies obtained
by Armstrong of the effect
of
stoichiometry on the bending creep rate of UOZ+$ have also been included in fig. 3. These experiments were performed in the low stress region where creep rates increased linearly with stress, and where creep rates were proportional to x. For values of 0.02
via
a
vacancy
in Qc with
335
CREEP
mechanism.
increasing
x was
The then
attributed 1) to a decrease in the apparent energy of formation of uranium vacancies with increasing x. The creep activation energies of approximately 60 kcal/mol found at O/U levels above
and Irvine 6) in their study
COMPRESSION
2.01
migration While
were
assumed
to
energy for uranium this interpretation
represent
the
vacancies.
of the creep rate
The results of this investigation confirm a number of previously reported observations regarding the influence of stoichiometry on the creep of polycrystalline uranium dioxide. Thus the early results of Armstrong and Irvine 6) which showed that creep rates for UOZ,, varied linearly with x in the low stress region for 0.02
and activation energy dependence on deviation from stoichiometry at high stresses is selfconsistent, the magnitude and variation with composition for the creep activation energies cannot be correlated with existing uranium self-diffusion activation energies. Thus Hawkins and Alcock 8) found activation energies for uranium diffusion in UOS+~ to increase from 89 kcal/mol to 105 kcal/mol as the O/U ratio was increased from 2.01 to 2.10, in contrast to creep activation energies which decrease from 65 kcal/mol to 55 kcal/mol over the same range of compositions. No explanation can be offered for the differences obtained in creep and diffusion experiments. Matzke lo), however, has pointed out that the increase in diffusion activation energies and pre-exponential constants, DO, with increasing deviation from stoichiometry found by Hawkins and Alcock is inconsistent with our present understanding of diffusion in highly defective oxides.
from stoichiometry, x > 0.01, are in good agreement with the values obtained in previous studies. The activation energies of 45 kcal/mol
If the creep activation energies in the highstress region corresponds to uranium volume diffusion activation energies, how are the lower
and 55 kcal/mol found in this study for O/U ratios of 2.01 and 2.05 may be compared with the value of 56 f 5 kcal/mol for 0.02
creep activation energies obtained in the linear stress dependency region to be interpreted? One possibility is to attribute these low Qc values to a grain boundary diffusion process. This assumption leads to the conclusion that creep in the low-stress region occurs not by the classical Nabarro-Herring diffusional creep mechanism, which involves volume diffusion, but rather by the modified Nabarro-Herring, or Coble creep mechanism, which is controlled by a grain boundary diffusion process. Measurements of the grain size dependence for creep rates can be used to distinguish between Nabarro-Herring and Coble creep. In the
4.
Discussion
336
M.
S.
SELTZER
former case creep rates are proportional to l/L2 while in the latter theory a l/La dependence is predicted
where
L is the grain size. While
the grain size dependence
was not established
ET
AL.
values obtained
in the power-law
Thus Qc= 90 kcal/mole for 45 kcal/mole for x= 0.05.
stress region.
x= 0.0001,
and
in the present study, previous investigators51 12)
(5) Creep rates for enriched UOZ+~ were found to be several orders of magnitude greater
have found
than values obtained
to
that creep rates are proportional
l/L2for polycrystalline
UOs. These results
would imply that the creep activation
energies
in the low stress region do correspond to volume diffusion energies. If this is the case the higher creep activation energies measured in the highstress region could correspond to a composite of the volume diffusion activation energy plus some additional term, such as the jog formation energy (if creep in the high stress region is governed by the diffusion controlled motion of jogged 5.
screw dislocations).
UOs,, under conditions.
a
for depleted
given
set
of
or natural
experimental
Acknowledgements The authors wish to thank Mr. James Bibler for his assistance with various aspects of the experimental program. The investigation was supported by the United States Atomic Energy Commission, Division of Reactor Development and Technology, and by the Argonne National Laboratory, under Contract W-7405-eng-92.
Conclusions
(1) Creep rates for polycrystalline U02+Z tested at low stresses increase linearly with applied stress, 0, and with oxygen excess, x. Creep rates for polycrystalline UOS+~ tested at high stresses follow a power-law stress dependence of the form i oc (in where 4
References 1) M. S. Seltzer, A. H. Clauer and B. A. Wilcox, J. Nucl.
‘) 3)
P. 0.
Mater.
44 (1972)
43
Perron, Thermodynamics
L. E. Poteat
and C. S. Yust,
reactions during deformation, structures, (Wiley,
4,
of non-stoichio-
metric uranium dioxide, AECL-3072
R.
A.
in Ceramic micro-
eds. R. M. Fulrath
New York, Wolfe
and
(May, 1968)
Grain boundary and J. A. Pask
1968) p. 646 S. F.
Kaufman,
Mechanical
properties of oxide fuels, WAPD-TM-587
5)
1967) P. E. Bohaboy, Compressive
R. R. Asamoto
creep
and A. E. Conti,
characteristics
of
metric uranium dioxide, GEAP-10054
6) W. M. Armstrong Mater.
9 (1963)
and W.
R.
(October,
stoichio-
(May, 1969)
Irvine,
J. Nucl.
121
7) K. W. Lay, J. Amer. Ceram. Sot. 54 (1971) 18 6) R. J. Hawkins and C. B. Alcock, J. Nucl. 9
Mater. 26 (1968) 112 J. M. Marin, H. Michaud Compt.-Rendu
264 (1967)
and
P.
Contamin,
1633
loI Hj. Matzke, J. Nucl. Mater. 30 (1969) 26 11) A. B. Lidiard, J. Nucl. Mater. 19 (1966) 106 12) W. M. Armstrong, W. R. Irvine and R. H. Martinson,
J. Nucl.
Mater.
7 (1962)
133
OF NUCLEAR
44 (1972)
MATERIALS
331-336.
0 NORTH-HOLLAND
PUBLISHINC3
CO.,
AMSTERDAM
THE INFLUENCE OF STOICHIOMETRYON COMPRESSIONCREEP OF POLYCRYSTALLINEUOa+, M. S. SELTZER, Metal
Compressive
Science
creep
Group,
tests
have
Battelle
been
polycrystalline
hyperstoichiometric
as a function
of temperature,
from
stoichiometry.
steady-state
Under
A. H. CLAUER Columbus
Laboratorierr,
Received
4 May
performed
stresses
d’activation
de
maniere
dioxyde
lin&irement
en fonction
de la contrainte,
de fluage est une fonction
1.75
and
of the form
increase
with
est
where
stress dependence
stresses,
the
creep
activation
for
uranium
activation
dioxide
single
energy,
crystals.
region,
different
creep behavior
processes
control
but values
in the two different
the
Abhiingigkeit
for
und
der
niedrigen
stress regimes.
wurden
Stochiometrie von
durchgefiihrt.
UOZ+~
angelegten
Spannung
c
metrischen
Sauerstoffgehalt gemessene
steigt
und x
an.
fonction
de la contrainte
de fluage
de UOZ+~ mesurees
dans
und steigt gem&s
an. Die Ubergangsspannung und
le
hoheren
steigendem
Die
in
Die
unter Kriech-
mit
der
iiberstochiobei
hohen
Kriechgeschwindigkeit
mit 4
et des
poly-
Spannung
linear
dem
sur-stoechiometrique
Sous de faibles contraintes,
der
gemessene station&e
sur du dioxyde polycristallin
en
an
Urandioxid
der Temperatur,
Spannungen
geschwindigkeit
observed
Druck
horcht einer Spennungsabhiingigkeit
les vitesses
11
diffusion
Studies.
Des essais de fluage sous compression ont Bte r&Ii&s de la temperature,
de
au fluage observe dans
de contreintes
unter von
Spennungen
&arts & la stoechiometrie.
de l’effort.
processus
iiberstiichiometrischem
kristallinem,
stress region. It is suggested that
diffusion
puissance
differents
le comportement
Kriechversuche
Creep
Qe are lower at a given x than are values obtained in the power-law
que
Qc,
energies also decrease with increasing x in
the linear stress-dependence
de x
tested at
decreases with increasing x in the same manner as found
suggere
les deux domaines
behavior decreases
with increasing O/U ratio. For polycrystsls
mais les
8. celles obtenues dans la region 06 la vitesse
controlent
The transition stress, ut, between linear
and power-law high
E dc u”
xm
energies
vrtleurs de Qc sont inferieures pour une vdeur
excess, 2.
a power-law
stress dependence
Les
du fluage diminuent aussi avec x croissant
don&e
4
que dans le cas des
d’uranium.
Creep rates for UOs+% tested at high stresses follow where
USA
dans la region 06 la vitesse de fluage second&ire varie
measured
stress, u, and with oxygen
43201,
1972
monocristaux
creep rates for UOs+= increase linearly
with applied
Columbus, Ohio
croissant de la m6me
on
uranium dioxide,
stress and deviation
low
and B. A. WILCOX
x*
ge-
der Art E a mit
an
1,75
ut zwischen der linearen
Spannungsabhiingigkeit
O/U-Verhiiltnis.
sinkt
mit
Die Aktivierungsenergie
stade secondaire augmentent lineairement en fonction
des Kriechens Qc nimmt fiir das bei hohen Spannungen
de l’effort
untersuchte polykristalline
oxygene
applique
u et de l’exces
2. Les vitesses
contraintes
de teneur
de fluage pour UOs+,
en
sous
Blevees obeissent & une loi en puissance
de la forme P:o( on ob 4
et augmentent
La contrainte
&pare le comportement
Die Aktivierungsenergie sinkt ebenfalls mit steigendem
avec
de transition
x im Bereich
qui
die Werte
obeissant iL la loi lineaire &
der linearen
polycristallins
den beiden verschiedenen
de
fluage
Qc diminue
avec
l’ecart
SpannungsabhGrgigkeit
x
x
gewonnen wurden. Vermutlich
unterschiedliche
achtete Kriechverhalten. 331
fur ein bestimmtes
niedriger als diejenigen, die im Bereich einer hijheren bestimmen
testes aux contraintes Blevees, l’energie
Spannungsabhiingigkeit,
fur Qc sind jedoch
celui regi par une loi en puissance de l’effort diminue avec le rapport O/U croissant. Pour les Bchantillons d’activation
Material mit steigendem x
in derselben Weise ab wie fur Urandioxid-Einkristalle.
Diffusionsprozesse
das in
Spannungsbereichen
beob-
332
1.
M. S. SELTZER
ET AL.
Introduction
STRESS,
The effects of varying
stoichiometry
psi
on the
high-temperature creep properties of hyperstoichiometric uranium dioxide single crystals were discussed in a previous paper 1). In order to investigate the influence of grain boundary contributions
to the creep process, these experi-
ments were extended creep of depleted
to include
and enriched
compression
polycrystalline
UO2+z.
2.
Experimental procedures
The experimental procedures employed have been described previously 1). Both high-density, coarse-grained, enriched specimens and lowerdepleted samples were density, fine-grained, used in this study. The final sintering operation for the enriched specimens consisted of pressing 24.48% enriched powder at 137.8 MN/m2 (20 000 psi) and 1700 “C for 15 h in flowing dry hydrogen. These specimens had a density of 97.8 * 0.5% of theoretical and an average grain size of 27 pm. They had an initial O/U ratio of 2.002 ~_t0.003, with iron and silicon being the major impurities at 100 and 150 ppm, respectively. Experiments were also conducted on 95% dense specimens with an average grain size of 6 ,um, which were ultrasonically trepanned from a boule produced by the hot pressing of depleted UO2 at 1400 “C under 96.5 MN/ma (14 000 psi) for 30 min.
3.
4 1
I
I
I
I
STRESS,
Fig.
1.
Steady-state
II
690
6.90
69
I
MN/m2
creep rate versus applied stress
for enriched uranium dioxide tested in compression at 1300 “C; grain size=27 /Am.
Experimental results
3.1. ENRICHED U02+%
Results obtained from creep tests conducted at 1100 “C and 1300 “C are included in figs. 1 and 2, respectively, in which steady-state creep rates, &, are plotted versus stress, u. Tests at constant O/U values of 2.001, 2.01 and 2.10 were performed by equilibrating the creep specimens in flowing CO/CO2 gas mixtures and oxygen partial maintaining the desired pressure 2) as the test progressed. The data for an O/U ratio of 2.10 at 1300 "C
(fig. 1) best illustrate how the stress dependence for steady-state creep varies with stress. At the lowest stresses used, 1.03 to 3.45 MN/ma (150 to 500 psi), the creep rates increase linearly with stress, but this dependence increases with increasing stress so that above 20.67 MN/m2 (3000 psi) creep rates are best fit by a power-law stress dependence of the form i oc ‘in, where n = 7. These results are similar to those obtained by other investigators s-5), where the high stress dependence suggests a dislocation creep
THE
INFLUENCE STRESS,
10s I
I
I
III
OF
STOICHIOMETRY
COMPRESSION
given temperature,
psi
105
ON
333
CREEP
stress, O/U ratio and grain
size are several orders of magnitude higher than
I
those reported by investigators who studied creep of uranium dioxide containing natural or depleted uranium s-5). The reason for this
to-’ -
behavior is not known. Although the absolute values for creep rates obtained
from the enriched
specimens
are not
in agreement with data from natural or depleted uranium-dioxide specimens, the observed dependence for creep rates of enriched UOs on composition is similar to that found for the unenriched specimens. Furthermore, the activation energies for creep of enriched, polycrystalline uranium dioxide are similar to those for creep of UO z+~ single crystals 1). Fig. 3 shows the creep activation energies for UOZ+~ single crystals l) as a function of logisz. Superimposed on these data are the activation energies for creep of enriched polycrystalline as determined from the high-stress UOZ,, portions of the data given in figs. 1 and 2 for O/U ratios of 2.001, 2.01, and 2.10. These values, shown as squares in fig. 3, are 117, 75, and 54 * 10 kcal per mole. It should be noted
o/u 10-3-
A
2.10
v 0
2.01 2.001
‘i
2
c” 2 4
E to-4-
10-5-
I
I
III
I
STRESS,
Fig.
2.
Steady-state
I
I 69.C
6.90
0.69
MN/m*
creep rate versus applied stress
for enriched uranium dioxide tested in compression at 11OO’C; grain size=27 pm.
mechanism based on diffusion-controlled dislocation climb or some other diffusion-controlled process while the linear stress dependence indicates the predominance of Nabarro-Herring diffusional creep or some grain-boundary sliding process. For the lower O/U ratios at 1300 “C and in all cases at 1100 “C, the linear stress dependence was not observed because creep rates were too low at the stress levels required to reach this regime. The absolute values for the creep rates at a
60-
-4(2.0001)
-3(2.001)
-2(2.01)
-I(2.10)
LOG,, x
Fig.
3.
Activation
energies for creep of UOa+,
as a
function of logroz: polycrystals; depleted
0 Single crystals (l), 0 enriched 27 ,am grain size, this study, +, A
polyorystals;
x , V polycrystals, crystals,
6 pm grain size, this study,
4 to 35 ,am grain size (5), D poly-
6 ,am grain size, in bending
(6).
M. 5. SELTZER
334
that
these
obtained
activation
from
possibility determined
but
energies two
have
been
temperatures.
The
ET AL. STRESS, psi
for large errors in Qc values this way is somewhat reduced by
the fact t’hat they were calculated from a number of data points obtained at various stresses
at
agreement
1100 “C and between
1300 “C.
activation
The
energies
good de-
termined from single crystals and polycrystalline materials suggests that the same creep mechanism is operative in both cases. Since the single crystals are free of grain boundaries, the implication is that creep in the high-stress region is controlled by uranium volume diffusion. The dependence of creep rates for enriched, polycrystalline UOa on O/U ratio is also similar to that found for creep of single crystals 1). At 1100 “C, i oc x2 in the high-stress region, while at 1300 “C, the value for the exponent is between 1 and 2. 3.2.
STRESS, MN/m”
Pig.
4.
Steady-state
creep rate versus applied stress
for depleted polycrystalline tested
on compression
UOz+%, 6 pm grain size,
at 1100 “C and
1300 “C.
DEPLETED UOa+,
Tests with depleted UOZ+~ were conducted at 1100 “C and 1300 “C under stresses of 1.03 to 165.36 MN/ ms (150 to 24 000 psi). Results are included in fig. 4 for specimens having compositions in the range of 2.001
regions. In the region of linear stress dependence the creep rates increase linearly with x. In the power-law stress-dependence region, on the other hand, creep rates increase with x1.75. This is close to the x2 dependence found in singlecrystal creep studies l), which suggests t’hat similar processes control creep of single crystals and polycrystals in the power-law stress region, with possibly some grain-boundary contribution entering into the polycrystalline results. An estimate of the creep activation energies can be obtained from the data in fig. 4 for the two temperatures studied. For an O/U ratio of 2.001, in the high-stress region Qc = 108 kcal per mole *, while in the low-stress region Qc w 68.5 kcal per mole. For O/U values of 2.01 and 2.05, Qc values in the low-stress region are N 55 kcal per mole and N 45 kcal per mole, respectively. These activation energies have been plotted as triangles (A) and pluses (+) in fig, 3. Also included in fig. 3 are creep activation energies obtained by Bohaboy et a1.5), *
In order to obtain this value it was necessary
to extrapolate and
to higher stresses for both
1300 “C tests.
1100 “C
THE
INFLUENCE
OF
STOICHIOMETRY
ON
It
uranium
is assumed that their Qc of 132 kcal per mole for the power-law regime corresponds to an
decrease
for polycrystalline
UOZ tested in hydrogen.
o/u RS2.0001based on our results. Their Qc for the linear stress region, 90 kcal per mole, has
been
accordingly
O/U ratio. Activation
placed
at
t,he same
energies obtained
by Armstrong of the effect
of
stoichiometry on the bending creep rate of UOZ+$ have also been included in fig. 3. These experiments were performed in the low stress region where creep rates increased linearly with stress, and where creep rates were proportional to x. For values of 0.02
via
a
vacancy
in Qc with
335
CREEP
mechanism.
increasing
x was
The then
attributed 1) to a decrease in the apparent energy of formation of uranium vacancies with increasing x. The creep activation energies of approximately 60 kcal/mol found at O/U levels above
and Irvine 6) in their study
COMPRESSION
2.01
migration While
were
assumed
to
energy for uranium this interpretation
represent
the
vacancies.
of the creep rate
The results of this investigation confirm a number of previously reported observations regarding the influence of stoichiometry on the creep of polycrystalline uranium dioxide. Thus the early results of Armstrong and Irvine 6) which showed that creep rates for UOZ,, varied linearly with x in the low stress region for 0.02
and activation energy dependence on deviation from stoichiometry at high stresses is selfconsistent, the magnitude and variation with composition for the creep activation energies cannot be correlated with existing uranium self-diffusion activation energies. Thus Hawkins and Alcock 8) found activation energies for uranium diffusion in UOS+~ to increase from 89 kcal/mol to 105 kcal/mol as the O/U ratio was increased from 2.01 to 2.10, in contrast to creep activation energies which decrease from 65 kcal/mol to 55 kcal/mol over the same range of compositions. No explanation can be offered for the differences obtained in creep and diffusion experiments. Matzke lo), however, has pointed out that the increase in diffusion activation energies and pre-exponential constants, DO, with increasing deviation from stoichiometry found by Hawkins and Alcock is inconsistent with our present understanding of diffusion in highly defective oxides.
from stoichiometry, x > 0.01, are in good agreement with the values obtained in previous studies. The activation energies of 45 kcal/mol
If the creep activation energies in the highstress region corresponds to uranium volume diffusion activation energies, how are the lower
and 55 kcal/mol found in this study for O/U ratios of 2.01 and 2.05 may be compared with the value of 56 f 5 kcal/mol for 0.02
creep activation energies obtained in the linear stress dependency region to be interpreted? One possibility is to attribute these low Qc values to a grain boundary diffusion process. This assumption leads to the conclusion that creep in the low-stress region occurs not by the classical Nabarro-Herring diffusional creep mechanism, which involves volume diffusion, but rather by the modified Nabarro-Herring, or Coble creep mechanism, which is controlled by a grain boundary diffusion process. Measurements of the grain size dependence for creep rates can be used to distinguish between Nabarro-Herring and Coble creep. In the
4.
Discussion
336
M.
S.
SELTZER
former case creep rates are proportional to l/L2 while in the latter theory a l/La dependence is predicted
where
L is the grain size. While
the grain size dependence
was not established
ET
AL.
values obtained
in the power-law
Thus Qc= 90 kcal/mole for 45 kcal/mole for x= 0.05.
stress region.
x= 0.0001,
and
in the present study, previous investigators51 12)
(5) Creep rates for enriched UOZ+~ were found to be several orders of magnitude greater
have found
than values obtained
to
that creep rates are proportional
l/L2for polycrystalline
UOs. These results
would imply that the creep activation
energies
in the low stress region do correspond to volume diffusion energies. If this is the case the higher creep activation energies measured in the highstress region could correspond to a composite of the volume diffusion activation energy plus some additional term, such as the jog formation energy (if creep in the high stress region is governed by the diffusion controlled motion of jogged 5.
screw dislocations).
UOs,, under conditions.
a
for depleted
given
set
of
or natural
experimental
Acknowledgements The authors wish to thank Mr. James Bibler for his assistance with various aspects of the experimental program. The investigation was supported by the United States Atomic Energy Commission, Division of Reactor Development and Technology, and by the Argonne National Laboratory, under Contract W-7405-eng-92.
Conclusions
(1) Creep rates for polycrystalline U02+Z tested at low stresses increase linearly with applied stress, 0, and with oxygen excess, x. Creep rates for polycrystalline UOS+~ tested at high stresses follow a power-law stress dependence of the form i oc (in where 4
References 1) M. S. Seltzer, A. H. Clauer and B. A. Wilcox, J. Nucl.
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Mater.
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43
Perron, Thermodynamics
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A.
in Ceramic micro-
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and
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