First-Principles Study of Lattice Dynamics, Structural Phase Transition, and Thermodynamic Properties of Barium Titanate

Abstract Lattice dynamics, structural phase transition, and the thermodynamic properties of barium titanate (BaTiO 3 ) are investigated by using first-principles calculations within the density functional theory (DFT). It is found that the GGA-WC exchange-correlation functional can produce better results. The imaginary frequencies that indicate structural instability are observed for the cubic, tetragonal, and orthorhombic phases of BaTiO 3 and no imaginary frequencies emerge in the rhombohedral phase. By examining the partial phonon density of states (PDOSs), we find that the main contribution to the imaginary frequencies is the distortions of the perovskite cage (Ti-O). On the basis of the site-symmetry consideration and group theory, we give the comparative phonon symmetry analysis in four phases, which is useful to analyze the role of different atomic displacements in the vibrational modes of different symmetry. The calculated optical phonon frequencies at Γ point for the four phases are in good agreement with other theoretical and experimental data. The pressure-induced phase transition of BaTiO 3 among four phases and the thermodynamic properties of BaTiO 3 in rhombohedral phase have been investigated within the quasi-harmonic approximation (QHA). The sequence of the pressure-induced phase transition is rhombohedral→orthorhombic→tetragonal→cubic, and the corresponding transition pressure is 5.17, 5.92, 6.65 GPa, respectively. At zero pressure, the thermal expansion coefficient α V , heat capacity C V , Grüneisen parameter γ , and bulk modulus B of the rhombohedral phase BaTiO 3 are estimated from 0 K to 200 K.