Full text of DOI:10.1557/JMR.2002.0302

Predictions of strontium accommodation in
A2B2O7 pyrochlores
Mohsin Pirzada
Department of Materials, Imperial College, London SW72BP, United Kingdom
Robin W. Grimes
Department of Materials, Imperial College, London SW72BP, United Kingdom, and Los Angeles
National Laboratory, Los Alamos, New Mexico 87545
John Maguire
AFRL/MLMR, Air Force Research Laboratory, Wright Patterson Air Force Laboratory, Ohio 45433
Kurt Sickafus
Los Alamos National Laboratory, Los Alamos, New Mexico 87545
(Received 14 March 2002; accepted 16 May 2002)
A2B2O7 pyrochlore oxides are being considered as potential host materials for the
immobilization of fission products. It is therefore important to establish the relative
ability of these compounds to accommodate fission product ions. We address this issue
by using computer simulations to predict the structures and relative equilibrium
energies associated with solution of Sr2+ over an extensive compositional range.
Results indicate that strontium is accommodated via substitution for A host cations
with oxygen vacancy compensation. This results in a nonstoichiometric composition.
Optimum compositions and defect clusters structures are identified by constructing
contour energy maps.
I. INTRODUCTION
interstitial-vacancy recombination or the formation of
clusters precipitating as interstitial dislocation loops and
voids. The latter is well known to cause void swelling.6,7
The activation energies for oxygen migration in pyro-
chlore oxides have also been studied through atomistic
simulation.8 As with fluorites, oxygen migration in the
pyrochlore lattice proceeds via a vacancy-mediated
mechanism.9 Interestingly in certain compositions the
oxygen vacancy can form a split configuration.8 Since
we expect a suitable host for fission products or actinides
to allow its anion lattice to perturbate, restore, and ac-
commodate radiation damage, it has been suggested that
compounds with small energy barriers for anion migra-
tion should best facilitate the mechanism for damage
recovery.10
Although the criteria discussed above are critical to the
long-term performance of an immobilization host, it is
equally important to establish the relative ability of the
various pyrochlore compounds to accommodate fission
product ions. This is of particular interest for plutonium
immobilization because it has been proposed that radio-
nuclides such as Cs137 or Sr90 are incorporated as part of
the host lattice. These form a radiological barrier, which
acts as a safe-guard preventing access to plutonium.11
However, the common fission product isotope of stron-
tium for immobilization is 90Sr, which has a half-life of
29 years.3 Given this half-life, important issues are the
A. Radiation tolerance
A2B2O7 pyrochlore oxides have attracted considerable
attention as potential host materials for the immobiliza-
tion of fission products and plutonium.1,2 Most of the
interest has focused on the ability of pyrochlore and
the related fluorite lattice to tolerate radiation damage.
Indeed, pyrochlores were initially considered because
natural pyrochlore (NaCaNb2O6F) contains U and Th
and its long-term tolerance to self-irradiation could there-
fore be studied.3–5 Recently the radiation tolerance of an
extensive series of A2B2O7 oxides was predicted by re-
lating tolerance to the ability of the lattice to accommo-
date point defects, in particular cation antisite pairs,
which form when trivalent cations swap sites with tetra-
valent cations.2 The previous study, which used energies
calculated by atomic-scale computer simulations, con-
cluded that the propensity of a material with composition
A2B2O7 to accommodate radiation-induced defects de-
pended strongly on the choice of A and B cations. Fol-
lowing experimental verification,2 Sickafus et al.
suggested that damage evolution through irradiation de-
pends upon (i) the ability of the crystal structure to ac-
commodate elevated defect concentrations and (ii) the
nature of consequential interactions between the defects.
Defect interactions can include annihilation through
J. Mater. Res., Vol. 17, No. 8, Aug 2002
© 2002 Materials Research Society
2041
http://journals.cambridge.org
Downloaded: 18 Mar 2015
IP address: 140.182.176.13

M. Pirzada et al.: Predictions of strontium accommodation in A2B2O7 pyrochlores
immediate solution of the element, its influence on
formation. Depending upon the composition of the py-
rochlore, this single 48f oxygen vacancy may adopt a
lower energy split vacancy configuration.8 Alternative
the host stoichiometry, and its retention over hundreds
rather than tens of thousands of years. Here we will ad-
dress this issue by investigating the detailed structures
and relative equilibrium energies associated with stron-
tium ion accommodation.
Unfortunately, the equilibrium concentrations of im-
purities in refractory-like ceramic materials are generally
low, except at high temperatures. Consequently, the
practical operating loading of strontium in a ceramic
immobilization host is likely to be above equilibrium.
Nevertheless, solution energy is still an important
parameter—it is a measure of the thermodynamic driving
force for dissolution with small energies being prefer-
able. High impurity concentrations will, however, mean
that cluster formation is practically inevitable (as we
mechanisms involving charge compensation by Sr¨ de-
i
fects are all much higher energy processes. This follows
from a consideration of the intrinsic defect reactions14
whose energies were reported previously.19
In order that reactions (1–5) can be compared, their
energies must be normalized to yield an energy related to
the equilibrium concentration of strontium [Sr]. For ex-
ample, a mass action analysis15 of reaction (4) will yield
[Vꢀ]2[SrЈ ]4 ꢁ exp(−⌬H4/kT)
,
(6)
o
A
where ⌬H4 is the internal energy for solution calculated
for reaction (4), k is Boltzmann’s constant, and T is the
absolute temperature. If the solution reaction yields a
greater concentration of oxygen vacancies than the in-
trinsic disorder reaction then electroneutrality will dictate that
shall see, the clusters that form are between SrЈ and
A
charge compensating oxygen vacancies). Therefore, so-
lution with respect to clusters must also be determined, as
it is the driving force for dissolution at high defect con-
centrations. Cluster formation is also important as it hin-
ders oxygen ion migration through the lattice (the effect
on cation motion should be negligible as oxygen motion
in these compounds is so much greater12). To facilitate
recovery mechanisms for radiation damage, lower bind-
ing energies are preferable.
[Voꢀ] ס 2[SrЈ ]
,
(7)
A
substituting back into Eq. (6) yields
[SrЈ ] ס 4−1/6exp(−⌬H4/6kT)
.
(8)
A
The normalization factor for Eq. (4) is therefore 6. The
equivalent factor for Eqs. (1) and (2) is 9, for reaction (3)
it is 7, and for reaction (5) it is 8.
B. Solution mechanisms
The analysis must be extended to include the possibil-
ity that the solution mechanism may not be dominant
over intrinsic processes. To achieve this, we must con-
sider the equilibria that exists between the intrinsic and
extrinsic reactions. If the solution is not the dominant
process in forming oxygen vacancies, then
The five lowest energy solution mechanisms [Eqs. (1–5)]
for strontium incorporation in A2B2O7 are described be-
low using Kro¨ger–Vink notation.13
4SrO + 4Ax + 2Bx + 3Ox
A
O
ꢀ 4SrЈ + 2AЉ + B3Voꢀ+ A2B2O7
,
,
(1)
(2)
(3)
(4)
(5)
A
B
4SrO + 4Ax + 2Bx + 3Ox
[Vꢀ] ס exp(−⌬HFrenkel/2kT)
,
(9)
and via substitution of Eq. (9) into Eq. (6) we arrive at
[SrЈ ] ס exp−(⌬H4 − ⌬HFrenkel)/4kT (10)
o
A
O
ꢀ 4SrЉ + 2B˙ + B3Voꢀ+ A2B2O7
B
A
4SrO + 2Ax + 2Bx + 3Ox
A
O
ꢀ 2SrЈ + 2SrЉ +B3Voꢀ+ A2B2O7
,
,
A
A
B
4SrO + 4Ax + 2Ox
which describes the equilibrium solution if intrinsic proc-
esses dominate the oxygen vacancy concentration. We
can now determine if Eq. (8) (i.e., solution) dominates
over Eq. (10) (i.e., intrinsic). This follows if the exponent
in Eq. (8) is less than the exponent in Eq. (10). This
simplifies to:
A
O
ꢀ 4SrЈ + 2Voꢀ + 2A2O3
,
A
4SrO + 4Bx + 4Ox
B
ꢀ 4SrЉ + 4Voꢀ + O4BO2
.
B
Examining mechanisms (1–5), we can categorize them
into two groups: (i) mechanisms (1–3), which yield the
stoichiometric pyrochlore A2−xB2−xSr2xO7−3x/2 and (ii)
mechanism (4), forming excess A2O3 and a nonstoichio-
metric pyrochlore of formula A2−xB2SrxO7−x/2 or mecha-
nism (5) forming excess BO2 and a nonstoichiometric
pyrochlore of formula A2B2−xSrxO7−x. Each mechanism
involves defect compensation through oxygen vacancy
(⌬H4/12) < (⌬HFrenkel/4)
.
(11)
A similar analysis can be conducted for the remaining
solution mechanisms. Finally a note of caution. Here we
consider solution into synthetic stoichiometric ceramic
materials. The situation for natural pyrochlore minerals is
much more complex.16
2042
J. Mater. Res., Vol. 17, No. 8, Aug 2002
http://journals.cambridge.org
Downloaded: 18 Mar 2015
IP address: 140.182.176.13

M. Pirzada et al.: Predictions of strontium accommodation in A2B2O7 pyrochlores
II. METHODOLOGY
connects equal energies over the cation radii surface. The
advantage of these maps is that they allow us to compare
trends and identify compositional regions of interest.
Calculations presented here are based upon a classical
Born-like description of an ionic crystal lattice.17 The
interatomic forces acting between ions are resolved into
two terms: long-range columbic forces, which are
summed using Ewalds’ method,18 and short-range forces,
which are modeled using parameterized pair potentials.
We define the perfect lattice using a unit cell, which is
repeated throughout space using periodic boundary con-
ditions as defined by the usual crystallographic lattice
vectors.
III. RESULTS AND DISCUSSION
A. Solution mechanisms assuming isolated ions
Figures 1(a)–1(e) delineate the results for solution
mechanisms (1–5), respectively. In each case, the cal-
culations assume that each constituent defect remains
isolated. Figures 1(a), 1(b), and 1(c) concern the mecha-
nisms that yield stoichiometric pyrochlores, whereas
Figs. 1(d) and 1(e) relate to mechanisms that result in
nonstoichiometric materials. It is immediately clear from
these figures that for all pyrochlore compositions only
mechanisms (1) and (4) [i.e., Figs. 1(a) and 1(d)] can be
of significance. That is, strontium ions are never pre-
dicted to substitute onto the tetravalent B-site; they oc-
cupy only trivalent A-sites.
We must now consider Figs. 1(a) and 1(d) in detail.
Across the majority of pyrochlore compositions, the so-
lution energies for both mechanisms remain below
2.5 eV. However, these energies become considerably
lower (<0.5 eV) as compositions approach the pyrochlore–
fluorite order/disorder composition boundary,19 indicat-
ing that the extent of strontium incorporation becomes
considerably greater. At this point it is important to stress
that when using the dilute limit approximation and a
computational technique that employs a simple pair
potential description of forces (as we have here), one
should pay attention primarily to relative energies. Our
approximations lead to an overestimation of absolute
solution energies, although for the pyrochlores we find
that relative energies show excellent agreement with
experiments.2,8,19
If we now compare the energies in Figs. 1(a) and 1(d),
it appears that the normalized solution energies for
mechanism (4) are lower than the values exhibited
by mechanism (1), for stable pyrochlore formers, but
energy differences become negligible where compounds
lie on the pyrochlore-to-fluorite composition boundary.19
Consequently, in this region the actual solution mecha-
nism will be complex, involving defects from both reac-
tions. Nevertheless, the contour maps can be used with
confidence to identify compositional regions that will
exhibit greater solution of SrO. In particular we see that
of those compounds that form a stable pyrochlore struc-
ture,19 zirconates in combination with Gd, Sm, and Eu or
stannates in combination with Lu and Yb exhibit excep-
tionally low solution energies. If these materials are not
chemically or physically compatible with other elements
of the containment assembly, alternative materials within
the compositional vicinity described should be investigated.
The lattice energy (UL) can then be expressed as
follows:
−r
ij
1
qiqj
rij
C
␳
UL =
+ Ae
−
,
(12)
Α
6
8␲⑀0
rij
iꢀj
where A, ␳, and C are the adjustable parameters specific
to ions i and j, rij is the interionic separation and qi is the
charge on ion i. A multi-structural parameter-fitting ap-
proach was applied as discussed previously.19
Since the incorporation of strontium involves the for-
mation of defects, an approach is needed to model the
effect of a defect on the surrounding lattice ions. Indeed,
defect energies are not useful unless they include the
contribution due to lattice relaxation. However, this re-
laxation is greatest in the vicinity of the defect. Therefore
the lattice is partitioned into three regions.20 In region I,
centered around the defect, ions are treated explicitly and
relaxed iteratively to zero strain via a Newton–Raphson
procedure. Region IIa is an interfacial region in which
the forces between ions are determined via the Mott–
Littleton approximation,21 and ions are relaxed in one
step. The interaction energies of the ions between region
IIa and region I are calculated explicitly. Finally, the
outer region IIb is effectively a point charge array whose
relaxation energy is determined using the Mott–Littleton
approximation, this provides the Madelung field of the
remaining crystal. All calculations were carried out using
the CASCADE code.22
The electronic polarisability of ions is accounted for
via the shell model.23 This assumes a massless shell with
charge Y|e| coupled to a core of charge X|e| via an iso-
tropic harmonic force constant k. The net charge state of
each ion equals (X + Y)|e|. Values for the charges and
force constants have been published previously.8
The results for each solution mechanism are presented
in the form of energy contour maps. In these, the calcu-
lated normalized solution energies associated with a
pyrochlore compound A2B2O7 is a value on a two di-
mensional grid. The location of the energy value is de-
fined by B4+ and A3+ cation radii, plotted along the x and
y axes, respectively. The energy contours are then
generated using software,24 which interpolates and
J. Mater. Res., Vol. 17, No. 8, Aug 2002
2043
http://journals.cambridge.org
Downloaded: 18 Mar 2015
IP address: 140.182.176.13

M. Pirzada et al.: Predictions of strontium accommodation in A2B2O7 pyrochlores
FIG. 1. (a–e) Normalized solution energy maps for mechanisms 1–5.
It is unfortunate that the titanates, which are very stable
pyrochlore formers, are predicted to be particularly poor
for solution of SrO.
The question now arises whether solution via mecha-
nism (4) [or (1)] can be the dominant process for the
formation of oxygen vacancies. To address this, we must
return to and evaluate the assumption that we form oxy-
gen vacancies through solution and that the intrinsic
oxygen vacancy defect concentration is negligible. If this
is not so, an important equilibria is already in effect,
which would control the oxygen vacancy concentration
and change the solution energies. However, when we
evaluate Eq. (11) (the results are presented elsewhere),14
it is clear that the equilibrium oxygen vacancy concen-
tration resulting from mechanism (4) is considerably
greater than the intrinsic defect limits (Schottky or Fren-
kel). Titanates, ruthenates, and molybdenate compounds
Although solution energies for zirconates in combina-
tion with smaller trivalent cations are also predicted to be
low, these materials do not form ordered pyrochlores but
rather disordered fluorite solid solutions. As with the
results for oxygen migration,8 the results presented here
must be considered in conjunction with the structure sta-
bility map.19 Ultimately, solution energies for such dis-
ordered systems should be determined using a different
model; however, the generation of realistic distributions
of ions in disordered systems is computationally
demanding.26
2044
J. Mater. Res., Vol. 17, No. 8, Aug 2002
http://journals.cambridge.org
Downloaded: 18 Mar 2015
IP address: 140.182.176.13

M. Pirzada et al.: Predictions of strontium accommodation in A2B2O7 pyrochlores
show a preference for the solution reaction, by 1–2 eV,
compared with the intrinsic processes. For the stannates,
this preference is reduced to approximately 1 eV, and for
zirconates it is closer to 0.5 eV.
Finally, this investigation was extended to include the
accommodation of divalent barium ions, which are also
formed as fission products. Of particular concern is the
isotope Ba133 which exhibits a half life of 11 years.25
The solution energy results show a compositional distri-
bution qualitatively similar to those for strontium incor-
poration, although the normalized solution maps show a
slightly stronger preference toward mechanism (4) over
mechanism (1) for stable pyrochlore compositions. Fur-
thermore, the solution energies are slightly higher for
barium, indicating that the equilibrium extent of solu-
tion for barium will be slightly lower than that for
strontium.14
FIG. 2. Energy contour map of the lowest binding energies to form the
cluster (2SrЈ : Vꢀo )x in A2B2O7 compounds. The lowest energy cluster
A
geometries are indicated by filled, half-filled, or unfilled symbols on
the map.
B. Defect cluster formation
the ratio increases to a magnitude of 10−4 since there is a
greater concentration of isolated defects. As mentioned
previously, it has been suggested that a full charge
model, as used here, will tend to consistently overesti-
mate solution energies (although relative energies are
still reliable). This would effect the prediction from
Eq. (16) since it employs absolute energies. An extreme
view would be to assume that the solution energies are
overestimated by a factor of two, but binding energies
remain unaltered. Even then, when these values are ap-
plied to Eq. (16), the amount of strontium present in clus-
ters is still relatively low compared to the concentration
found as isolated. Detailed results are shown else-
where.14 Thus, Fig. 1 remains an effective guide to com-
positional selection based on the criterion of equilibrium
solution limit. In addition, such low ratios indicate that
cluster formation will not greatly increase the relative
extent of SrO solution, at equilibrium.
It is important to establish the energetics associated
with cluster formation in a doped pyrochlore material. If
reaction (4) is considered, solution via this process, but
with cluster formation, will follow from
4SrO + 4Ax + 2Ox
A
O
ꢀ 2{2SrЈ : Voꢀ}x + 2A2O3
.
(13)
A
The interaction between the isolated and clustered de-
fects is described by
2SrЈA + Vꢀo ꢀ {2SrЈ : Vꢀo }x
,
(14)
A
and the equilibrium that is established is given by
[{2SrЈ : Voꢀ}x] / [SrЈ ]2[Vꢀo] ס exp −(⌬Hbinding)/kT
.
(15)
A
A
In this reaction ⌬Hbinding is the binding energy (see
Fig. 2). Since this internal energy to form the cluster is
less than that to form the isolated defects, the binding
energy is a negative number. Thus, the equilibrium
concentration of defect clusters will depend on the mag-
nitude of the binding energy and the absolute concentra-
tions of the isolated defects given by Eqs. (6) and (8).
Consequently, even if the binding energies are large, if
the concentration of isolated defects are small, the con-
centration of clusters at equilibrium will still be small.
To investigate this we need to consider the ratio of the
As stated in the introduction, it seems unlikely that
crystalline immobilization host materials will operate
with the fission product concentrations below the equi-
librium level. If this is the case then, Eq. (16) no longer
holds (even though it remains an indication of driving
force for dissolution). Now we should write
n ס 2[{2SrЈ : Voꢀ}x] + [SrЈ ]
,
(17)
A
A
concentration of strontium ions in clusters (i.e., 2[{2SrЈ :
A
Vꢀ}x]) compared to the concentration of isolated stron-
where n is the imposed concentration of strontium. Of
course, Eq. (15) still holds so that
o
tium dopant (i.e., [SrЈ ]). This ratio is determined by com-
A
bining Eqs. (6), (8) and (15).
n ס exp{−(⌬Hbinding)/kT}[SrЈ ]3 + [SrЈ ] . (18)
A
A
2[{2SrЈ : Vꢀo }x] / [SrЈ ] ס 22/3 и exp
A
A
This equation is cubic with respect to the isolated stron-
− (⌬Hbinding − 1/3⌬H4)/kT
.
(16)
tium ion concentration [SrЈ ] and can therefore be solved
A
Using Eq. 16, we find that for Gd2Ti2O7 at 1000 K (bind-
ing energy 2.03 eV), the ratio is of the order of 10−15
For Gd2Zr2O7, despite a lower binding energy (0.66 eV),
by the standard approach. Using these values and
Eq. (18), the ratio of strontium in clusters to that which
remains isolated can once again be determined. In
.
J. Mater. Res., Vol. 17, No. 8, Aug 2002
2045
http://journals.cambridge.org
Downloaded: 18 Mar 2015
IP address: 140.182.176.13

M. Pirzada et al.: Predictions of strontium accommodation in A2B2O7 pyrochlores
Gd2Ti2O7, if a loading of 1% of Gd sites with strontium
criterion. However, migration of oxygen may also facili-
tate vacancy or interstitial cluster formation so we should
treat this criterion with caution.
(i.e., n ס 0.01) is assumed, at 1000 K 98% of the stron-
tium ions will be in {2SrЈ : Voꢀ}x clusters. On the other
A
hand, in Gd2Zr2O7, only 8% of strontium ions will be in
clusters. Of course, loadings in excess of n ס 0.01 will
result in a greater proportion of strontium in clusters.
Thus it seems that for practical materials we should also
consider a driving force for dissolution based on solution
with respect to clusters, at least in the initial stages of
dissolution. However, results for this, which are pre-
sented elsewhere,14 follow the same trends shown in
Fig. 1. Furthermore, reaction (4) is still dominant with
reaction (1) close behind. Reactions (2), (3), and (5) re-
main much higher energy processes.
IV. CONCLUSIONS
The relative extent of strontium solution was exam-
ined for a wide range of pyrochlore compositions. Ener-
gies were calculated for five solution mechanisms, two of
which are energetically significant. The lowest energy
mechanism results in a B cation excess nonstoichiomet-
ric composition A2−xB2SrxO7−x/2. Common to these re-
actions is charge compensation through oxygen
vacancies. Furthermore, equilibrium solution of stron-
tium results in the formation of charge-compensating
oxygen vacancies whose concentrations are greater than
concentrations of oxygen vacancies that would be
formed through purely intrinsic disorder reactions. Re-
sults for barium dopant ions were very similar to the
predictions for strontium.
The study was extended to include the effect of defect
cluster formation associated with the preferred solution
mechanism. It was found that, assuming equilibrium,
cluster formation is unlikely to greatly increase the rela-
tive extent of SrO solution. However, equilibrium con-
centrations of strontium are low, and it is likely that
practical loadings of strontium will exceed equilibrium.
At such higher loadings, defect clusters will dominate.
Nevertheless the lowest solution energies exhibited by
pyrochlore forming materials remain around the Gd and
Eu zirconates compositions.
Binding energy results were also discussed in the con-
text of damage recovery mechanisms, and compositional
regions exhibiting the lowest cluster binding energies
were identified. Such compounds should be more suit-
able as immobilization host materials, although other is-
sues such as oxygen ion conduction are also important.
Finally, by comparing the contour maps generated in
this and other studies,2,8,19 we can identify useful com-
positional regions based on several criteria. As such, the
property maps represent a powerful tool for materials
selection.
C. Implications for oxygen migration
In the introduction we noted that oxygen ion migration
is regarded as important for damage recovery.10 Clearly
this will be ever more important at higher strontium load-
ings. Certainly solution of strontium should be beneficial
since it introduces oxygen vacancies into the lattice.
However, if these are trapped too strongly by the stron-
tium ions, it will effectively increase the overall activa-
tion energy for oxygen migration.
Figure 2 is a map that shows for each composition the
lowest binding energy for a {2SrЈ : Voꢀ}x defect cluster.
A
Calculations were carried out for all different geometries
which assume 1st–1st, 1st–2nd, or 2nd–2nd neighbors
configurations of the two strontium ions with respect to
the oxygen vacancy (as the origin). Further details of the
geometries investigated are described elsewhere.14 Inter-
estingly, Fig. 2 predicts that for most pyrochlores, a 1st–
1st neighbor configuration is preferred (shown as unfilled
symbols in Fig. 2). However, a strong B-site dependency
on the cluster configuration emerges with compounds
switching over to adopt 1st–2nd neighbor configurations
as we move towards the pyrochlore–fluorite composition
boundary (indicated by filled symbols in Fig. 2). This
change is gradual, with a belt of compositions for which
the energy difference between 1st–1st and 1st–2nd con-
figurations is only 0.5 eV (indicated by half-filled sym-
bols in Fig. 2). The result provides another example of
the complex nature of pyrochlore compounds as we ap-
proach the pyrochlore–fluorite boundary.
From Fig. 2, compounds containing the larger tetrava-
lent cations with small trivalent cations exhibit the lowest
binding energies for the neutral cluster {2SrЈ : Vꢀ}x.
ACKNOWLEDGMENTS
M.P. was supported through European Office of Aero-
space and Development (EOARD) Contract No. F61775-
00-WE016. R.W.G. gratefully acknowledges Los
Alamos National Laboratory for support through the
Bernd T. Matthias Scholarship. K.E.S. was supported
by the Department of Energy, Office of Basic Energy
Sciences, Division of Materials Sciences. The Engineering
Physical Science and Research Council (EPSRC) provided
computing facilities through Grant No. GR/M94427.
A
o
That is, pyrochlores such as Gd, Eu, and Sm zirconates or
Y, Er, Yb, and Lu stannates have low binding energies
and are stable pyrochlore structure formers. Unfortu-
nately, although stannates exhibit low binding energies,
previous predictions of oxygen migration indicate that
their oxygen ion activation energies are high.8 This will
make them less suitable as immobilization host materials
if we accept that fast oxygen migration is an important
2046
J. Mater. Res., Vol. 17, No. 8, Aug 2002
http://journals.cambridge.org
Downloaded: 18 Mar 2015
IP address: 140.182.176.13

M. Pirzada et al.: Predictions of strontium accommodation in A2B2O7 pyrochlores
12. R.E. Williford, W.J. Weber, R. Devanathan, and J.D. Gale,
REFERENCES
J. Electroceram. 3, 409 (1999).
1. S.X. Wang, B.D. Begg, L.M. Wang, R.C. Ewing, W.J. Weber,
and K.V. Godivan Kutty, J. Mater. Res. 14, 4470 (1999).
2. K.E. Sickafus, L. Minervini, R.W. Grimes, J.A. Valdez,
M. Ishimary, F. Li, K.J. McClellan, and T. Hartmann, Science
289, 748 (2000).
3. W.J. Weber, R.C. Ewing, C.R.A. Catlow, T. Diaz de la Rubia,
L.W. Hobbs, C. Kinoshita, Hj. Matzke, A.T. Motta, M. Nastasi,
E.H.K. Salje, E.R. Vance, and S.J. Zinkle, J. Mater. Res. 13, 1434
(1998).
4. G.R. Lumpkin, B.C. Chakoumakos, and R.C. Ewing, Am. Min-
eral. 71, 569 (1986).
5. G.R. Lumpkin and R.C. Ewing, Phys. Chem. Min. 16, 2 (1988).
6. W.J. Weber, Radiation Effects 77, 295 (1983).
13. F.A. Kro¨ger and H.J. Vink, Solid State Physics—Advances in
Research and Applications (Academic Press, New York, 1957).
14. M. Pirzada, Ph.D. Thesis, University of London, London, United
Kingdom, (2002, in preparation).
15. Y-M. Chiang, D.P. Birnie III, and W.D. Kingery, Physical Ce-
ramics: Principles for Ceramic Science and Engineering (John
Wiley & Son, Inc., Canada, 1997), p. 111.
16. G.R. Lumpkin and R.C. Ewing, Am. Mineral. 80, 732 (1995).
17. M. Born, Atomtheorie des Feten Zustandes (Teubner, Keipzig,
Germany, 1923).
18. P.P. Ewald, Ann. Phys. (Leipzig). 64, 253 (1921).
19. L. Minervini, R.W. Grimes, and K.E. Sickafus, J. Am. Ceram. 83,
1873 (2000).
7. F.W. Clinard, Jr., D.L. Rohr, and R.B. Roof, Nucl. Instrum. Meth-
20. C.R.A. Catlow and W.C. Mackrodt, Computer Simulation of Sol-
ids (Springer-Verlag, Berlin, Germany, 1982).
ods Phys. Res. B 1, 581 (1984).
8. M. Pirzada, R.W. Grimes. L. Minervini, S. LeClair, and
K.E. Sickafus, Solid State Ionics. 140, 201 (2001).
9. H.L. Tuller in Defects and Disorder in Crystalline and Amor-
phous Solids, edited by R.A. Catlow (Kluwer, Dordrecht, the
Netherlands, 1994), p. 189.
10. W.J. Weber and R.C. Ewing, Science 289, 2051 (2000).
11. Management and Disposition of Excess Weapons Plutonium:
Reactor-Related Options, Panel on Reactor-Related Options for
the Disposition of Excess Weapons Plutonium, National Research
Council (National Academy of Sciences Press, 1995).
21. N.F. Mott and M.J. Littleton, Trans. Faraday Soc. 34, 485 (1932).
22. M. Leslie, CASCADE௡, DL/SCI/TM31T, Technical Report
SERC Daresbury Laboratory, United Kingdom (1982).
23. B.G. Dick and A.W. Overhauser, Phys. Rev. 112, 90 (1958).
24. Microcal Origin௡ Microcal Software Inc., Northampton, MA 01060.
25. R.A. Tinker and J.D. Smith, Analy. Chim. Acta. 332, 291 (1996).
26. M.O. Zacate and R.W. Grimes, Philos. Mag. A 80, 797 (2000).
J. Mater. Res., Vol. 17, No. 8, Aug 2002
2047
http://journals.cambridge.org
Downloaded: 18 Mar 2015
IP address: 140.182.176.13