High Temperature Stability of BaZrO
: An Ab Initio
Nadarajan Raja, Deveraj Murali, Matthias Posselt,
and Satyavolu Venkata Maruthi Satyanarayana*
exhibits excellent proton conductivity and good high-temperature
stability. It is therefore a promising electrolyte material for solid oxide fuel
cells. The stability of BaZrO
at high temperatures is generally explained by
the low diffusivity of O vacancy. Present first principle density functional
theory calculations show that the slow migration of the doubly charged O
vacancy at high temperature cannot be solely caused by the ground-state
migration energy but by the contribution of phonon excitations to the free
migration energy. With increasing temperature, the effective barrier for
oxygen vacancy migration increases. At about 1000 K, which is the operating
temperature of fuel cells, the calculated O vacancy diffusivity is more than
one order of magnitude lower than that determined using ground-state
migration barrier. The calculated diffusivity data agree well with experimental
results from literature. The present work reveals that the high-temperature
stability of BaZrO
is mainly due to the phonon contribution to the free
migration energy of the O vacancy.
(BZO), a cubic perovskite, is a promising electrolyte
material in solid oxide fuel cells (SOFC).
BZO exhibits good
proton conductivity at high temperatures.
materials that exhibit high ionic conductivity tend to be less
stable at high temperature.
However, BZO shows a good
chemical and mechanical stability at these temperatures.
This may be explained by the relatively low diffusivity of the O
vacancy observed at high temperatures.
reason for low diffusion of O vacancy observed in experi-
is not fully understood. Therefore, the present
work is focused on using ﬁrst-principles density functional
theory (DFT) and ab initio thermodynam-
ics to compute free migration energy and
the diffusivity of the doubly charged O
vacancy in BZO. Most previous DFT
studies on BZO were limited to ground
state properties. However, recent investi-
gations clearly demonstrate the inadequacy
of using ground state data to explain ﬁnite
temperature effects and emphasize the
importance of considering phonon excita-
Bjørheim et al.
calculations to understand the effect of
phonon excitations on the free formation
energy of neutral as well as doubly charged
O vacancies in BZO and showed that these
contributions strongly affect the relative
stability of both vacancy types. Further,
Bjørheim et al.
also showed the signiﬁ-
cance of phonon contribution to surface
segregation enthalpies and entropies of
the doubly charged O vacancy and the
hydroxide ion (OH
). Hydrogen diffusion was studied by
Sundell et al.
using DFT calculations and it was found that
zero point vibrations effectively reduce activation enthalpies
and make the prefactors similar for translation and rotation
motion of H atom. While the effect of phonon excitations on the
formation of the O vacancy has been studied,
to the best of
our knowledge, only ground state DFT calculations are used for
O vacancy migration.
Therefore, in this work we
determine the phonon contribution to free migration energy
of the doubly charged O vacancy and compute the correspond-
2. Calculation Method
DFT calculations were performed using Vienna Ab Initio
Simulation Package (VASP) based on plane wave basis sets.
The pseudopotentials were based on projected augmented wave
(PAW) method with exchange and correlation effects described
using generalized gradient approximation (GGA-RPBE).
Brillion Zone sampling was done using Monkhorst–Pack
Ground state calculations for bulk as well as
calculations involving a single doubly charged O vacancy were
performed in 40 atom supercell with 4 Â 4 Â 4 k-points and 135
atom supercell with 2 Â 2 Â 2 k-points. Plane wave basis cutoff of
500 eV was chosen for all calculations. Atomic position as well as
N. Raja, Dr. S. V. M. Satyanarayana
Department of Physics,
Pondicherry University, Puducherry 605 014, India
Dr. D. Murali
Department of Physics, Indian Institute of
Technology Madras, Madras 600 036, India
Dr. M. Posselt
Institute of Ion Beam Physics and Materials
Research, Bautzner Landstr. 400, 01328 Dresden,
Perovskite Electrolytes www.pss-b.com
Phys. Status Solidi B 2018, 255, 1700398 © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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