A space-charge model is applied to describe the equilibrium effects of
segregation of double-donor oxygen vacancies to grain boundaries in dry and wet
acceptor-doped samples of the perovskite oxide BaZrO3. The grain boundary core
vacancy concentrations and electrostatic potential barriers resulting from
different vacancy segregation energies are evaluated. Density-functional
calculations on vacancy segregation to the mirror-symmetric \Sigma 3 (112)
[-110] tilt grain boundary are also presented. Our results indicate that oxygen
vacancy segregation can be responsible for the low grain boundary proton
conductivity in BaZrO3 reported in the literature

Adachi M.

B. Joakim Nyman

Edit E. Helgee

Göran Wahnström

English

arXiv

Crossref

Applied Physics Letters

Oxygen vacancy segregation and space-charge effects in grain boundaries of dry and hydrated BaZrO<sub>3</sub>

A space-charge model is applied to describe the equilibrium effects of segregation of double-donor oxygen vacancies to grain boundaries in dry and wet acceptor-doped samples of the perovskite oxide BaZrO3. The grain boundary (GB) core vacancy concentrations and electrostatic potential barriers resulting from different vacancy segregation energies were evaluated. Density-functional calculations on vacancy segregation to the mirror-symmetric Σ3 (112) [-110] tilt grain boundary are also presented. Our results indicate that oxygen vacancy segregation can be responsible for the low grain boundary proton conductivity in BaZrO3 reported in the literature

Nyman, Joakim

Ahlberg Helgee, Edit

Wahnstr\uf6m, G\uf6ran

Chalmers Research

Oxygen vacancy segregation and space-charge effects in grain boundaries of dry and hydrated BaZrO3

Nyman, B. Joakim

Helgee, Edit E.

Wahnström, Göran

Chalmers Publication Library

  
 
 
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downloaded for personal use only. Any other use requires prior 
permission of the author and the American Institute of Physics.  
 
The following article appeared in Applied Physics Letters and 
may be found at http://dx.doi.org/10.1063/1.3681169.  
 
Copyright 2012 by American Institute of Physics. The following article appeared in Appl. Phys. Lett. 100, 061903
(2012); doi: 10.1063/1.3681169 and may be found at http://dx.doi.org/10.1063/1.3681169
Oxygen vacancy segregation and space-charge eects in grain boundaries of
dry and hydrated BaZrO3
B. Joakim Nyman,a) Edit E. Helgee,b) and Goran Wahnstromc)
Dep. of Applied Physics, Chalmers University of Technology, Goteborg, SE-412 96,
Sweden
(Dated: 16 February 2012)
A space-charge model is applied to describe the equilibrium eects of segregation of double-donor oxygen va-
cancies to grain boundaries in dry and wet acceptor-doped samples of the perovskite oxide BaZrO3. The grain
boundary core vacancy concentrations and electrostatic potential barriers resulting from dierent vacancy
segregation energies are evaluated. Density-functional calculations on vacancy segregation to the mirror-
symmetric 3 (112) [110] tilt grain boundary are also presented. Our results indicate that oxygen vacancy
segregation can be responsible for the low grain boundary proton conductivity in BaZrO3 reported in the
literature.
PACS numbers: 61.72.Mm 61.72.jd 68.35.Dv 71.15.Nc 77.22.Jp
While the benets of ceramic materials make solid ox-
ide proton conductors like barium zirconate (BaZrO3,
BZO) desirable for use as electrolytes in electrochemical
devices such as hydrogen fuel cells, limitations in proton
conductivity have thus far prevented successful imple-
mentation.? ? It has become apparent that boundaries
between grains in the material are the prime source of
inhibited overall proton conductivity.? ? ?
Experiments have established that the grain boundary
(GB) proton resistivity is an intrinsic eect, not caused
by the segregation of secondary phases at the GB.? ?
Two dierent explanations have instead been put for-
ward? , in which the GB eects are believed to originate
in either a structural distortion in the GB region? , or
in the appearance of positively charged GBs, caused by
a change in chemical composition and leading to Schot-
tky barriers and the depletion of mobile protonic charge
carriers.? ? ? At present the latter explanation model
is the predominating one? ? ? , but the details of the
GB cores are neither well understood nor suciently ex-
plored.
In this letter we present an investigation concerning
the equilibrium segregation of oxygen vacancies to GBs
in dry and hydrated acceptor-doped BZO and the electro-
static potential barrier such segregation causes. Density-
functional theory (DFT) is used to evaluate the energy of
vacancy segregation to a 3 tilt GB and a space-charge
model is applied to describe the equilibrium barrier and
core vacancy concentration resulting from dierent segre-
gation energies. We show that segregation energies on the
a)joakim.nyman@chalmers.se
b)edit@chalmers.se
c)Corresponding author: goran.wahnstrom@chalmers.se
order that we nd can cause potential barriers consistent
with experimental ndings on GB proton conductivity in
BZO.
The system is modeled using the periodic supercell
technique and all DFT calculations are performed within
the plane-wave approach as implemented in the Vienna
ab-initio simulation package (VASP)? ? . Electron-ion
interactions are described by the projector augmented
wave method? and a generalized gradient approximation
(GGA) exchange-correlation functional due to Perdew
and Wang (PW91)? is used. More computational de-
tails have been reported elsewhere.? In the present work
all calculations are performed non-spin-polarized with a
plane-wave cuto of 400 eV (constant volume) or 520 eV
(volume relaxations), and a 4  2  1 Monkhorst-Pack
k-point grid is used to sample the Brillouin zone.
Theoretical and experimental work on the currently
considered 3 (112) [110] tilt GB has previously been
performed on strontium titanate? and this particu-
lar GB is well suited for DFT calculations. It con-
sists of alternating BaZrO and O2 planes and here we
consider the mirror-symmetric BaZrO terminated case,
which has the lowest energy. The interplanar distance is
d = a0=
p
24 = 0:87 A, with a computed value of the bulk
lattice constant a0 = 4:25 A. Our supercell has the di-
mensions (
p
3 a0; 2
p
2 a0; 3
p
6 a0) in the directions ([111],
[110], [112]) and consists of 180 atoms with the distance
18d = 15:6 A between the periodically repeated GBs.
To begin with, the system is optimized by relax-
ing the atomic structure, resulting in the conguration
shown in Fig. 1. The GB expands 0.135 A in the per-
pendicular direction and the calculated GB energy? is
GB = 0:78 J/m
2. Next, an oxygen vacancy is intro-
duced. Since double-donor vacancies are dominating in
acceptor doped BZO, we consider the q = +2 charge state
only. The vacancy formation energy EfGB is determined
2FIG. 1. The relaxed structure of the mirror-symmetric 3
(112) [110] tilt grain boundary.
0 1 2 3 4 5 6 7 8 9
−1.5
−1
−0.5
0
0.5
E
se
g
(e
V
)
at interface between interfacesLayer No. (-)
BaZrO O2 BaZrO O2 BaZrO O2 BaZrO O2 BaZrO O2
 
 
unrelaxed
relaxed
FIG. 2. Segregation energies of oxygen vacancies in the 3
(112) [110] tilt grain boundary as function of the location of
the vacancy, calculated using DFT.
as function of vacancy position, both with and with-
out relaxing the structure. As reference, the vacancy
formation energy for the bulk system Efbulk with the
same size of the supercell is also determined. The seg-
regation energy is then obtained by taking the dierence
Eseg = E
f
GB  Efbulk. Note that the error due to in-
teraction between charged defect images in the periodic
supercell calculations is to a large degree cancelled for
the quantity Eseg.
We nd a signicant segregation tendency to layer 1 of
the GB, with an energy of Eseg =  1:25 eV (cf. Fig. 2).
A large part of this energy gain derives from ionic relax-
ation during vacancy formation. Referring to Fig. 1, the
high stability of vacancies in layer 1 is due to the close
proximity of the pair of oxygen ions on either side of the
interface and the electrostatic repulsion this causes. As
one of the oxygens in the pair is removed, the other ion
relaxes considerably, to a position in the symmetry plane.
Having established the existence of low-energy vacancy
positions close to the GB interface, we would now like
to evaluate the corresponding equilibrium vacancy seg-
regation and electrostatic potential barrier as function
of temperature. To do so, we apply a space charge
model? ? ? ? with an ideal depletion approximation to
two dierent cases: i) dry BZO, where a concentration
of single-acceptor dopants are perfectly compensated for
by double-donor vacancies, and ii) wet BZO, where dis-
sociative absorption of water molecules from a humid at-
mosphere is taken into account.
In both cases we consider a one-dimensional model,
with three regions of constant defect concentration: i)
the GB core (0 < x < x0), where an increased concen-
tration ccV of oxygen vacancies is expected and the pro-
ton concentration is assumed to vanish, ii) a compensat-
ing space charge layer (SCL) (x0 < x < x
), depleted of
oxygen vacancies and protons, and nally iii) the neu-
tral grain interior (x > x) with vacancy concentration
ciV and in the wet case proton concentration c
i
OH. The
dopant concentration cA is taken to be xed and equal
throughout all regions and a concentration correspond-
ing to occupation of 10% of the Zr sites is used in all
calculations. Motivated by the high stability of oxygen
vacancies in layer 1 (cf. Fig. 2), we dene a core region
enclosing that layer and denote the segregation energy for
those vacancies with Ecseg. Vacancies in layers 2,3,4,: : :
are treated as having zero segregation energy and the
symmetry plane, layer 0, is assumed void of vacancies.
For the core half-width we use the value x0 = 2 A. With
this description the density of active oxygen vacancy sites
in the core becomes about half that of the grain interior:
N c = 0:579N i, where N i = 3=a30 = 0:039 A
 3.
We begin with the dry case and consider electrochemi-
cal equilibrium between oxygen vacancies in the GB core
and grain interior for an ideal solution? :
Ecseg+2 e
c+kBT ln
ccV
N c   ccV
= kBT ln
ciV
N i   ciV
: (1)
The electrostatic potential dierence between core and
interior, c  (x0)   (x), is obtained by solv-
ing Poisson's equation in the SCL with the boundary
conditions (x) = 0(x) = 0. For the dielectric con-
stant we use the value  = 32 0
? and the size of the
SCL is determined from charge compensation with re-
spect to the core: (2eccV   ecA)x0 = ecA (x   x0), or
x = (2ccV=cA)x0. It follows that the present model is
applicable for ccV > cA=2 only. The solution for the po-
tential dierence is:
c  (x0)  (x) = e
2
(2ccV   cA)2
cA
x20: (2)
Eqs. ?? and ?? can now be solved iteratively to obtain ccV
and c as function of temperature. Using the neutrality
condition, the grain interior oxygen vacancy concentra-
tion is in the present, dry, case given by: ciV = cA=2. Our
numerical results are shown in Fig. 3 as dashed lines for
a few dierent values of the segregation energy Ecseg.
Next, the wet case. Hydration of the grain interior is
modeled by the hydration reaction (Kroger-Vink nota-
tion):
H2O(g) + V

O +O

O  ! 2OHO: (3)
Experimental values from the literature? are assigned to
the hydration enthalpy H0hydr =  0:82 eV and entropy
S0hydr =  0:92 meV/K and a water partial pressure of
pH2O = 0:025 bar is used in the calculations. The interior
hydroxide concentration ciOH is obtained from the law of
mass action, charge neutrality and site restriction? :
ciOH
N i
=

  4
"
1 
s
1    4


2
cA
N i
 
 cA
N i
2#
;
(4)
35
10
15
20
c
c V
/
N
c
(%
)
0
2
4 OH
V
c
i
/
N
i
(%
)
300 400 500 600 700 800 900 1000 1100 1200
0
0.2
0.4
0.6
∆
φ
c
(V
)
T (K)
FIG. 3. Core vacancy site-concentration and poten-
tial barrier for vacancy segregation energies Ecseg =
f 0:25; 0:75; 1:25g eV, where the thick lines correspond
to  1:25 eV. Dashed/solid lines have been used for the
dry/hydrated case and dotted lines indicate the bound of the
present space-charge model, i.e. ccV > cA=2. The middle panel
shows interior vacancy- and hydroxide concentrations for the
hydrated case.
where  = pH2OK and the equilibrium constant
K = exp(S0hydr=kB) exp( H0hydr=kBT ). In the mid-
dle panel of Fig. 3 we show the result for the interior
hydroxide concentration ciOH, indicating the transition
between wet and dry grain interior around 900 K.
We are now in the position to determine the concen-
tration of core vacancies ccV and the electrostatic barrier
c as function of temperature in hydrated samples. In
this case ciV = (cA   ciOH)=2 and N i   ciV in Eq. ?? is
replaced by N i   ciOH   ciV. Eqs. ?? and ?? are solved
together with the expression for the hydroxide concen-
tration in Eq. ?? and our nal results for ccV and 
c in
hydrated samples are shown as solid lines in Fig. 3.
It is clear from Fig. 3 that, according to our model,
segregation energies on the order that we nd in the 3
tilt GB can lead to signicant electrostatic potential bar-
riers as a result of oxygen vacancy aggregation at the
GB. In dry BZO at 600 K, 21% of the oxygen sites hav-
ing a vacancy segregation energy of  1:25 eV in the GB
core are predicted to be vacant, giving rise to an electro-
static potential barrier of 0.55 V. In the hydrated case,
vacancies persist at the GB to the degree that, although
the interior vacancies have been annihilated at 600 K,
19% of the core sites are still vacant and the barrier is
0.45 V. Even if the sample is cooled to room temperature,
the number (assuming thermodynamic equilibrium) only
drops to 17% and a potential barrier of 0.33 V is still
present.
In recent work, Kjlseth et al? used a space-charge
model to evaluate the potential barrier corresponding to
experimental results on grain interior and grain bound-
ary proton conductivity in Y-doped BZO? ? ? . A bar-
rier on the order 0.4{0.6 V was found to match measure-
ments made at 200{300C. This agrees relatively well
with our results, where a barrier of 0.4{0.45 V is seen for
Ecseg =  1:25 eV in this temperature range. Similar po-
tential barriers tted to experimental conductivity data
were also found by Chen et al? for 10 mol% Y-doped
samples? ? ? ? and by Iguchi et al? . Interesting to point
out is the signicant dierence in potential barrier cal-
culated from conductivity measurements of Duval? , of
BZO annealed at high temperature and of convention-
ally sintered samples. Chen et al calculated a barrier of
0.77 V in the conventionally sintered material, while the
calculations of Kjlseth et al show a barrier of 0.46 V in
the annealed sample.
When comparing our results to barriers estimated from
experimental data it is important to keep in mind that
our results are based on DFT calculation on one single
grain boundary structure, while experimental results cor-
respond to an average eect in polycrystalline samples.
Theoretical investigations of additional GBs are there-
fore warranted to conclude whether the magnitude of the
present oxygen vacancy segregation energy is a general
trait of GBs in BZO. Furthermore an aggregation of ac-
ceptor dopants at GBs has been observed in BZO? ? ? ,
an eect which we do not take into account and which
would tend to diminish the positive charge due to oxygen
vacancies. In addition, there is reason to investigate the
segregation energy of protons in GBs, particularly con-
sidering that the stability of protons in solid oxides has
been seen to increase on oxygen sites where vacancies are
also increasingly stable? ? .
In conclusion, we present DFT calculations of oxy-
gen vacancy segregation to a 3 tilt grain boundary in
BZO. Using a space charge model we demonstrate that
at 600 K, where the sample is fully hydrated in a wet
atmosphere, the oxygen vacancies in the grain boundary
core are still present with a site concentration of about
20%. This corresponds to a Schottky barrier height
of 0.45 V and compares well with recent experimental
data? ? ? ? ? . Our results indicate that oxygen vacancy
segregation can be responsible for the low grain boundary
proton conductivity in BZO reported in the literature.
Since this paper was submitted for publication further
relevant work on space charge and blocking eects at
grain boundaries of BZO has been published? ? ? .
We would like to acknowledge Profs JoachimMaier and
Truls Norby for useful conversations. The computations
have been performed on SNIC resources and the Swedish
Energy Agency is acknowledged for nancial support.
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Oxygen vacancy segregation and space-charge effects in grain boundaries
  of dry and hydrated BaZrO3

Oxygen vacancy segregation and space-charge effects in grain boundaries of dry and hydrated BaZrO3

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