We have preformed the first-principles calculations for the mechanical properties, Born effective charge tensors and high frequency dielectric constants of the eight phases of BaTiO$_3$. The independent elastic constants, bulk modulus, shear modulus, Young’s modulus and Poisson’s ratio were obtained, which were consistent with the available theoretical and experimental values. The mechanical stability and brittle/ductile behaviors of the eight phases of BaTiO$_3$ have been discussed. The calculated results indicated that the eight phases were all mechanically stable and behaved in a brittle manner. The calculated Born effective charge tensors shown the covalent Ti-O bond and ionic Ba-O bond. Moreover, the high frequency dielectric constants have been given.
60.00.00 CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES
$^1$China Academy of Space Technology, Beijing 100094, People’s Republic of China
$^2$School of Physical Science and Technology, Southwest Jiaotong University, Key Laboratory of Advanced Technologies of Materials, Ministry of Education of China, Chengdu 610031, People’s Republic of China
$^3$Bond and Band Engineering Group, Sichuan Provincial Key Laboratory (for Universities) of High Pressure Science and Technology, Southwest Jiaotong University, Chengdu 610031, People’s Republic of China
$^4$State Key Laboratory of Solidification Processing, Northwestern Polytechnical University, Xi’an 710072, People’s Republic of China