Front. Mater. Sci. China 2007, 1(3): 316–318 DOI 10.1007/s11706-007-0058-1

RESEARCH ARTICLE

Electronic structure of nanograin barium titanate ceramics DENG Xiangyun ( )1, WANG Xiaohui2, LI Dejun1, LI Longtu2 1 College of Physics and Electronic Information, Tianjin Normal University, Tianjin 300387, China 2 State Key Lab of New Ceramics and Fine Processing, Department of Materials Science and Engineering, Tsinghua University, Beijing 100084, China

© Higher Education Press and Springer-Verlag 2007

Abstract The density of states and band structure of 20 nm barium titanate (BaTiO3, BT) ceramics are investigated by first-principles calculation. The full potential linearized augmented plane wave (FLAPW) method is used and the exchange correlation effects are treated by the generalized gradient approximation (GGA). The results show that there is substantial hybridization between the Ti 3d and O 2p states in 20 nm BT ceramics and the interaction between barium and oxygen is typically ionic. Keywords nanocrystalline BaTiO3 ceramics, electronic structure, first-principles calculation

1

Introduction

Barium titanate (BaTiO3, BT), as a ferroelectric material with perovskite structure, has been extensively used in the electronics industry including a number of dielectric, electro-optic and other electronic devices [1]. The continuous advance in microelectronics and communications is leading to the miniaturization and integration of ferroelectric components, and the properties of BT with small size will ultimately become dominant [2]. Consequently, the study of sizedependent properties in the nanometric range is important both to find the possible limit of ferroelectricity and to elucidate the microstructural characteristics of the ferroelectric components. Many efforts have been done about the size effect on the ferroelectric properties of BT materials in forms of particles [3], thin films [4], composite and bulk ceramics [5]. The causes of size effect in BT materials are numerous, and it is difficult to separate true size effect from other factors, such as the microstructure, defect chemistry, boundary conditions, etc. Therefore, theoretical investigations play a crucial role Received March 19, 2007; accepted March 28, 2007 E-mail: [email protected]

in determining true intrinsic effect. In recent years, firstprinciple calculations have been very successful in the experimental and theoretical studies of BT materials [6]. There has been considerable progress in achieving an understanding of the lattice dynamics and greatly deepened our comprehension of the origin of ferroelectricity [7]. From these investigations, it has been shown that Ti–O hybridization is essential to the ferroelectric instability in BT [8] and the ferroelectric instability occurs as a result of the delicate balance between longrange Coulomb interactions that favour the ferroelectric state, and the short-range forces that favour the cubic paraelectric phase [9]. To our knowledge, less data on theoretical investigation of dense nanocrystalline BT ceramics are available, mainly due to the difficulty of obtaining ceramics with high relative density >95% at this scale. In order to know well the role of atoms on the origin of ferroelectricity in nanograin BT ceramics, we calculated the electronic structure of 20 nm BT ceramics by the first principles.

2

Calculation procedures

The 20 nm bulk nanocrystalline BT ceramics with relative density 97% has been successfully prepared by spark plasma sintering (SPS) process (Dr. Sinter 2050, Sumitomo Coal Mining Co., Tokyo, Japan). Figure 1 shows the scanning electron microscopy (SEM, Model XL30 S-FEG, FEI Co., America) micrograph of 20 nm BT ceramics. The average grain size was determined by linear intercept method from SEM micrographs of surfaces by counting at least 500 grains, which was combined with calculation of (111) peak broadening of X-ray diffraction (XRD) data. Detailed description of the preparation is discussed elsewhere. The calculations presented in this work are performed within the generalized gradient approximation (GGA) [10] to density functional theory using the full potential linear augmented plane wave (FLAPW) [11] method. In this study no shape approximation on either potential or the electronic charge density is made.

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3

Fig. 1 The SEM micrograph of 20 nm BT ceramics

Results and discussion

The total and partial density of states (DOS) of 20 nm BT ceramics is shown in Fig. 3. There is a sharp peak arising from Ti 3d and two broad peaks from O 2p between 0 and 8 eV. In the energy range from −5 to 0 eV, there are two sharp peaks of O 2p and a broad peak of Ti 3d. The DOS of O 2p and Ti 3d have nearly the same peaks and characters in the energy range from −17 to −15 eV. From the analysis of the partial DOS of O 2p and Ti 3d, it means Ti 3d and O 2p have nearly the same valence density of states and there is hybridization between Ti 3d and O 2p, demonstrating that the interaction between Ti and O is covalent.

We use WIEN2k [12,13] implementation of the method, which allows the inclusion of local orbits in the basis, improving upon linearization and making a possible consistent treatment of semicore and valence states in one energy window, hence ensuring proper orthogonality. The lattice parameter we used in this study of 20 nm BT ceramics is a = b = c = 4.0198 nm, taken from our experimental results of SPS. The atomic coordinates are Ba (0, 0, 0), Ti (0.5, 0.5, 0.5), O(1) (0, 0.5, 0.5), O(2) (0.5, 0, 0.5) and O(3) (0.5, 0.5, 0). Figure 2 shows the unit cell of BT ceramics for this structure. The muffin-tin sphere radii (Ri) 2.0, 1.8 and 1.5 a.u. are respectively used for Ba, Ti, O in the calculations. Ba 6s, Ti 3d and O 2p orbitals are treated as valence orbitals. The convergence parameter RKmax (RmtKmax, where Kmax is the plane wave cutoff and Rmt is the smallest one of all atomic sphere radii), which controls the size of the basis sets in these calculations, is set to be 8.0. This gives well converged basis sets consisting of approximately 4,719 plane waves.

Ba y x

Ti

O

Fig. 2 The unit cell of 20 nm BT ceramics

The calculations are iterated to self-consistency with the specified energy convergence criterion 10−5 Ryd. Integrations in reciprocal space are performed using special point method. We use 5x5x5 meshes, which represent 125 k points in the first Brillouin zone, which makes our calculation with a good precision.

Fig. 3 Calculated DOS for 20 nm BT ceramics: The top panel shows total DOS in unit of states/(eV cell), and other panels show orbital decomposed partial DOS (PDOS) in unit of states/(eV atom) (the zero of the energy scale shows the position of the Fermi level)

The calculated band structure for 20 nm BT ceramics in the high-symmetry direction in the Brillouin zone is shown in Fig. 4. The energy scale is in eV, and the origin of energy was arbitrarily set to be at the valence band maximum. There are eight conduction bands (CBs) between 0 and 8 eV seen in Fig. 4. Comparing these bands with Fig. 3, it is assessed that they consist of Ti 3d and O 2p and the eight bands overlap each other. From −5 to 0 eV, there are five bands seen in Fig. 4. Comparing these bands with Fig. 3, around −5 to 0 eV, it is assessed that they consist of Ti 3d and O 2p and the two bands also

318 863-2001AA325010, and the Ministry of Science Technology, China through 973-project under Grant No. 2002CB613301.

References

Fig. 4 The calculated energy-band structure for 20 nm BT ceramics (the zero of the energy was set at the top of the valence band)

overlap each other. It means that there is hybridization between the Ti 3d and O 2p. The same conclusion has been obtained from the band structure analysis from −17 to −15 eV. At the bottom of the valence region, there are three bands. They arise from the Ba 6s and O 2p because there are two peaks around −55 and −25 eV in the DOS of Ba 6s (Fig. 3), there are a peak around −33 eV in the DOS of O 2p (Fig. 3). There is no overlapping among them; therefore, it appears that the Ba−O is typically ionic.

4

Conclusions

In summary, we have performed FLAPW calculations to investigate the electronic structure of 20 nm BT ceramics. The density of states and band structure are obtained. From the calculated DOS and band structure, it is shown that in the 20 nm BT ceramics, there are two kinds of electronic interactions; the interaction between Ti 3d and O 2p is covalent and the bonding between titanium and oxygen is ionic. Acknowledgements This

work was supported by the High Technology Research and Development Project, China under Grant No.

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