Physica B 405 (2010) 4687–4690
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Physica B
journal homepage: www.elsevier.com/locate/physb
First-principles study of the (0 0 1) surface of cubic BiAlO3
Jie Cui a,n, Wei Liu b
a
b
School of Materials Science and Engineering, Xi’an University of Technology, Xi’an 710048, Shaanxi, PR China
Department of Construction Engineering, Yulin University, Yulin 719000, Shaanxi, PR China
a r t i c l e in fo
abstract
Article history:
Received 12 June 2010
Accepted 26 August 2010
The BiO and AlO2 terminations have been constructed for the BiAlO3 (0 0 1) surface. The cleavage and
surface energies, surface relaxation and surface electronic structure have been calculated for the two
types of (0 0 1) terminations using first principle plane waves ultrasoft pseudopotential method based
on local density approximation. The results show that compared with the BiO termination, the AlO2
termination corresponds to the lower surface energies and is more easily constructed. For the BiO
termination, some states in the conduction band are remarkably lowered and pulled down in the band
gap region; however, for the AlO2 termination the valence band exhibits an upward shift, intruding into
the lower part of the band gap, especially at the M point.
& 2010 Elsevier B.V. All rights reserved.
Keywords:
First-principles
Surface energy
Surface relaxation
Surface electronic structure
1. Introduction
ABO3 perovskite ferroelectrics are important for many hightech applications, including spintronic devices, optical waveguides, laser-host crystals, high-temperature oxygen sensors,
surface acoustic wave devices, non-volatile memories, dynamic
random access memories, frequency doublers, piezoelectric
actuator materials, catalyst electrodes and integrated optics
applications [1–4]. Lead zirconate titanate (PZT)-based materials
having good piezoelectric and ferroelectric properties are widely
used as sensor materials in smart structures and micro-electromechanical systems (MEMS). However, environmental problems
resulting from the toxicity of lead seem to be the limiting factors
for the further application of PZT-based materials. Of late,
Bi-based compounds are of particular interest as individual
lead-free piezoelectric and have been identified as the candidate
for Pb-based compounds, because they are non-toxic and also
have 6s2 lone pairs [5], which may be thought to be the origin of
the large ferroelectric polarization in Pb-based compounds.
BiAlO3 is non-centrosymmetric with space group R3c (a ¼5.38
and c ¼13.40 Å) [6]. Recently, a number of experimental and
theoretical studies have examined BiAlO3. Some theoretical
studies predicted the possibility of high performance ferroelectricity with a large spontaneous polarization of about 76 mC/cm2
[7,8]. However, experimental results showed a relatively lower
remanent polarization of about 9.5 mC/cm2 than the theoretical
data [5]. The structural, elastic, electronic and optical properties of
the cubic perovskite-type BiAlO3 have been studied by Bouhema-
n
Corresponding author. Tel.: + 86 29 82312557.
E-mail address: cuijieccjj@yahoo.com (J. Cui).
0921-4526/$ - see front matter & 2010 Elsevier B.V. All rights reserved.
doi:10.1016/j.physb.2010.08.063
dou et al. [9] using the pseudopotential plane waves method
within the local density approximation . The results show that
BiAlO3 has an indirect band gap between the occupied O 2p and
unoccupied Bi 6p states and a strong hybridization has been
found between the Al–O and Bi–O covalent bonds.
Since the properties of bulk BiAlO3 have been studied extensively,
in the present work, we focus only on the surface properties of BiAlO3.
It is noted that the R3c structure of BiAlO3 is a distorted form of the
ideal perovskite structure. Thus, study of the cubic phase, a hightemperature or hypothetical phase, is of importance for deeply
understanding the origin of ferroelectricity in perovskite. This paper is
organized as follows. Some details of the calculation method and the
structure of BiAlO3 (0 0 1) surfaces are given in Section 2. The
calculated cleavage and surface energies, surface relaxation and
surface electronic structure of BiAlO3 (0 0 1) surfaces are discussed in
Section 3. The conclusions of this work are summarized in Section 4.
2. Method
All calculations were performed within the framework of
density functional theory (DFT) using a basis set consisting of
plane waves, as implemented in the Cambridge Serial Total
Energy Package (CASTEP) [10]. The electron–ion interactions were
described by ultrasoft pseudopotentials and electron exchange
and correlation energies were calculated with the CA–PZ
formulation of the local density approximation (LDA) [11] and
the Perdew, Burke and Ernzerhof (PBE) formulation of the
generalized gradient approximation (GGA). [12]. The geometric
structure was optimized with the Broyden–Fletcher–Goldfarb–
Shanno (BFGS) method [13], and the forces on each ion converged
to less than 0.01 eV/Å. The pseudopotentials used for bulk and
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J. Cui, W. Liu / Physica B 405 (2010) 4687–4690
slab were constructed by the electron configurations as Bi 6s26p3
states, Al 3s13p1 states and O 2s22p4 states. The kinetic energy
cutoff (400 eV) of the plane wave basis was used throughout and
the Brillouin zone was sampled with special k-points of a 8 8 8
grid for cubic structure and a 8 8 2 grid for slab structure, as
proposed by Monkhorst and Pack [14].
The convergences with respect to the cutoff energy and the kpoints mesh have been tested and the results show that the cutoff
energy and the k-points mesh used in this work are enough for
the system.
Before the surface calculations, the bulk lattice constant a,
elastic constants Cij and bulk modulus B are calculated first and
the results are listed in Table 1, along with the available
theoretical data. The calculated lattice constant of 3.658 Å
calculated by LDA is in good agreement with the available
theoretical values [9,15]. It is noted that GGA calculation seems
to overestimate a and underestimate B. Moreover, from the
present calculations, the LDA method looks the best for calculating the bulk and surface properties of ABO3 [15–17]. Therefore,
the lattice constant calculated by LDA is used in the following
surface calculations. The three independent elastic constants in
cubic symmetry (C11, C12 and C44) are also estimated by
calculating the stress tensors on applying strains to an equilibrium structure. All Cij constants for BiAlO3 are positive and
satisfy the generalized criteria [18] for mechanically stable
crystals: (C11 C12)40, (C11 +2C12)40 and C44 40.
Table 1
Calculated bulk lattice constant a, elastic constants Cij and bulk modulus B of cubic
BiAlO3, compared with the available theoretical values.
Method
This work
PP-PW [9]
FP-LAPW [15]
GGA
LDA
LDA
LDA
a (Å)
C11 (GPa)
C12 (GPa)
C44 (GPa)
B (GPa)
3.775
3.658
3.659
3.724
320
381
380
130
145
145
138
158
157
194
224
219
208
As in other cubic ABO3 materials, cubic BiAlO3 (0 0 1) surface
consists of two types of terminations, with the sequence of atomic
layers of BiO and AlO2. In this paper, we consider two types of
(0 0 1) terminations (shown in Fig. 1). The periodic boundary
condition is used in the repeated slab model calculations. For the
considered terminations, the slabs with seven atoms layer
thickness are separated by a 12 Å vacuum region. During the
surface structure optimization, all atoms are fully relaxed.
3. Results and discussion
3.1. Surface energy
It is noted that BiO- and AlO2-terminated surfaces are
complementary mutually; the cleavage energy of the complementary surface Ecl(BiO+AlO2) can be obtained from the total
energies computed for the unrelaxed slabs through the following
equation:
i
1 h unrel
Ecl ðBiOþ AlO2 Þ ¼
E
ð1Þ
ðBiOÞ þEunrel
slab ðAlO2 ÞnEbulk ,
4S slab
where S is the area of the (1 1) termination, Eunrel
slab ðaÞ the total
energy of unrelaxed a-terminated slab, Ebulk the bulk energy per
formula unit in the cubic structure, n the total number of bulk
formula units in the two slabs and 1/4 means that totally four
surfaces are created upon the crystal cleavage.
When both sides of the slab are allowed to relax, the relaxation
energies for each of the surfaces can be obtained by the equation
i
1 h rel
Erel ðaÞ ¼
Eslab ðaÞEunrel
ð2Þ
slab ðaÞ ,
2S
where S is the area of the a termination,Erel
slab ðaÞ the a-terminated
slab energy after relaxation and 1/2 means that two surfaces are
created upon the crystal cleavage. Now when the cleavage and
relaxation energies are calculated, the surface energy is just their
sum
Esurf ðaÞ ¼ Ecl ðaÞ þ Erel ðaÞ:
ð3Þ
Our calculated results of the cleavage, relaxation and surface
energies of the two types of (0 0 1) terminations are listed in Table 2.
It can be seen from the table that the cleavage energy Ecl for the two
terminations are the same at 1.65 eV. However, the relaxation
energy of AlO2 termination is larger than that of BiO termination,
which resulted in a lower surface energy Es (1.31 eV/a2) for the AlO2
termination. This means the AlO2 termination is more easily
constructed in vacuum between the two types of terminations.
3.2. Surface relaxation
The relaxed structures of the two types of BiAlO3 (0 0 1)
terminations have been calculated, and all the seven layers are
fully relaxed. The results are presented in Table 3. Displacements
of the ion on the ith layer from the surface are expressed as Dzi:
Dzi ¼ ðzi zi,bulk Þ=a 100%
ð4Þ
Table 2
Calculated cleavage, relaxation and surface energies (in eV per surface cell) for the
two types of (0 0 1) terminations.
Fig. 1. Two types of BiAlO3 (0 0 1) terminations: (a) BiO termination and (b) AlO2
termination.
Termination
Ecl
Erel
Es
BiO
AlO2
1.65
1.65
0.18
0.34
1.47
1.31
J. Cui, W. Liu / Physica B 405 (2010) 4687–4690
the first layer both move inward, and the surface rumpling s is
much smaller (1.54%) compared with that for the BiO termination.
Moreover, the AlO2 termination with smaller surface rumpling
possesses lower surface energy, which is opposite to that of other
ATiO3 (A ¼Ca, Sr, Ba) (0 0 1) surfaces [16]. This discrepancy may
come from the much larger displacement of the Bi atoms in the
second layer of AlO2 termination. It is noted that the calculated
surface relaxation seems to be larger, especially for AlO2terminated surface. Such large surface relaxation may lead to
surface reconstruction.
Here, zi is the z coordinate of Bi, Al and/or O in the ith layer
after relaxation and zi,bulk is the unrelaxed z coordinate determined from the theoretical lattice constant of cubic BiAlO3.
Dzi o0 indicates the direction inwards to the surface, on the
contrary; Dzi 40 means the direction outwards from the surface.
First of all, stronger relaxation of BiO-terminated surface is
found in the first layer atoms, whereas for the AlO2-terminated
surface, the largest relaxation is found in the second layer atoms.
The displacement of the Bi atoms in the second layer is outward
and about 8.16% and that of the Al atoms in the first layer is
inward and about 2.32%. For the BiO termination, Bi atoms in the
first layer move inward (3.47%), whereas O atoms move outward
(3.45%), which leads to a relative large surface rumpling s of
6.92%. On the other hand, for AlO2 termination, Al and O atoms in
3.3. Surface electronic structure
Before calculating the surface electronic structure, the surfaceprojected bulk band structure and density of state are calculated
and are shown in Fig. 2. Bulk BiAlO3 is found to have indirect band
gaps; the valence band maximum occurs at R point in the
Brillouin zone, whereas the conduction band minimum is at the X
point. The calculated bulk band gap is large with the value of
1.8 eV, indicating the presence of an insulating feature. It should
be noted that the LDA calculations usually underestimate
the fundamental gap. Therefore, cubic BiAlO3 may have a
larger gap than our prediction. There is hybridization
between Al and O atoms and between Bi and O atom in the
upper valence bands, which suggests covalent bonding contributions in BiAlO3.
The calculated energy band structure for the two (0 0 1)
terminations along the high symmetry directions in the
Brillouin zone is shown in Fig. 3: (a) BiO-terminated surface and
Table 3
Relaxation of the uppermost three layers for BiAlO3 (0 0 1) surfaces (as a
percentage of the bulk crystal lattice parameter a).
BiO-terminated
AlO2-terminated
Layer
Ion
Dz (%)
Layer
Ion
Dz (%)
1
Bi
O
Al
O
Bi
O
3.47
3.45
2.26
3.47
1.57
1.24
1
Al
O
Bi
O
Al
O
2.32
0.78
8.16
0.68
0.33
2.68
2
3
2
3
Density of State (electrons / eV)
9
6
Energy (eV)
4689
3
0
-3
-6
-9
X
M
R
-20
X
-10
0
Energy (eV)
10
20
Fig. 2. Band structure (left panel) and density of state (right panel) for the cubic BiAlO3 around the Fermi level. The Fermi level is indicated by the dashed line. (a) Band
structure of BiO termination and (b) band structure of AlO2 termination.
9
6
6
Energy (eV)
Energy (eV)
3
0
-3
3
0
-6
-3
-9
-6
Γ
X
M
band structure of BiO termination
Γ
Γ
X
M
band structure of AlO2 termination
Fig. 3. Band structure for the two types of (0 0 1) termination along the high symmetry directions.
Γ
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J. Cui, W. Liu / Physica B 405 (2010) 4687–4690
(b) AlO2-terminated surface. It is found that, for the BiOterminated surface, some states in the conduction band are
remarkably lowered and pulled down in the band gap region.
Therefore, the BiO-terminated surface becomes metallic. For the
AlO2-terminated surface, the valence band exhibits an upward
shift, intruding into the lower part of the band gap, especially at
the M point. Meanwhile, the conduction band is also increased
and the bottom of the conduction band is located at the G point.
Thus the AlO2 termination is also metallic.
4. Conclusions
In the present work, two types of terminations (BiO termination and AlO2 termination) have been constructed for the BiAlO3
(0 0 1) surface. The cleavage and surface energies, surface
relaxation and surface electronic structure have been calculated
for the two terminations using first principle method based on
local density approximation generalized (LDA). The following
conclusions are obtained:
1. compared with the BiO termination, the AlO2 termination
corresponds to the lower surface energies and is more easily
constructed in vacuum;
2. stronger relaxation of BiO-terminated surface is found in the
first layer atoms, whereas it is in the second layer ones that the
AlO2-terminated surface represents stronger relaxation;
3. both BiO termination and AlO2 termination are metallic.
Acknowledgments
The authors would like to acknowledge the Youth Foundation
of Xi’an University of Technology (Grant No. 101-210923) for
providing financial support for this research.
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