Physica B 405 (2010) 4687–4690 Contents lists available at ScienceDirect 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: [email protected] (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 4688 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 4690 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. References [1] I.A. 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