Mechanical properties, Born effective charge tensors and high frequency dielectric constants of the eight phases of BaTiO$_3$

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.