Ab Initio Studies On Phase Behavior of Barium Titanate
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Ab Initio Studies On Phase Behavior of Barium Titanate Mustafa Uludogan1, Tahir Cagin, William A. Goddard, III Materials and Process Simulation Center, Caltech, Pasadena, CA 91125, U.S.A. 1 Physics Department, METU, Ankara, TURKEY. ABSTRACT Using DFT methods we have studied structure, equation of state, and phase behavior of BaTiO3. We have identified the pressure induced phase transformations from the rhombohedral to orthorhombic structure at ca. 5 GPa and from tetragonal phase to cubic phase at ca. 7.5 GPa. INTRODUCTION BaTiO3 is an important example perovskite structured ceramic displaying ferroelectric property. At high temperature, BaTiO3 is stable in a paraelectric cubic structure with five atoms per unit cell (Pm3m). At lower temperatures, the crystal has three phase transitions from the paraelectric phase to ferroelectric phases. At 393 K, the symmetry changes to tetragonal (P4mm). The second phase transition, orthorhombic (Amm2) occurs at 278 K. Finally, the last phase transition, from orthorhombic to rhombohedral symmetry (R3m) takes place at 183 K. In these ferroelectric phases, the polar axis is aligned from tetragonal phase to rhombohedral phase along , and directions. BaTiO3 has been widely investigated since the discovery of its ferroelectric properties in 1945. To explain its ferroelectric behavior, there exists ample experimental data. For a long time, the theoretical studies depend on the empirical approaches but during the last decade, with the application of first-principles calculations to ABO3 compounds, computers have provided a theoretical understanding of the nature of ferroelectric perovskites. In this work, the characterization of four phases of BaTiO3, from cubic to rhombohedral phase, has been studied. Thus, we present zero temperature full equation of state (EOS) of BaTiO3 which is obtained using the commercial ab-initio program CASTEP. First we describe the methods used in the calculations and the EOS of different phases. In the succeeding section we present how we optimized the structures. Furthermore, we discuss the EOS and optimization results. CALCULATIONAL DETAILS We present ab-initio Quantum Mechanical calculations of the EOS of different phases of BaTiO3 using DFT in the GGA approximation; our calculations correspond to zero Temperature except that the zero point energy of the crystal in not considered. We use DFT [1,2,3], using PW-91 GGA for the exchange and correlation energy functional [4]. The k points sampled using a 5X5X5 Monkhorst-Pack mesh. Ultrasoft pseudopotentials are used for both Ba,Ti and O [5]. Energy cut-off for these potentials was chosen as 700 eV. In Figure 1, the zero temperature EOS of the different crystalline phases of BaTiO3 is shown, namely cubic, tetragonal, orthorhombic and rhombohedral. In the plot, the energy-volume curves of phases are plotted. The EOS is calculated in a volume range of 10 % expansion and 15 % compression. The details of how the total energy is obtained will be discussed in the optimization section. Our main objective in calculating
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