First-principles Study On Near-stoichiometry Ca_0.5Sr_0.5TiO₃ Crystal

Ca_xSr_1-xTiO₃ Perovskite materials were widely used in electronic, mechanical and ceramic industries due to their high dielectric constant, low dielectric loss, and heat stability. CaxSr（1-x）TiO3 with photocatalytic activity and redox catalytic activity and electromagnetic properties are excellent functional materials. They can be used in the photocatalytic water decomposition for hydrogen production, photocatalytic degradation of organic pollutants and photochemical cells.In this study, the stable crystal structure of Ca_0.5Sr_0.5TiO₃（CST50） was built as Ca/Sr atoms was confirmed to have symmetric distributions on 4c sites by using the minimum energy principle. The lattice parameters and elastic constants were investigated with the plane wave pseuedopotential method based on the first-principles density functional theory within the local density approximate（LDA） and generalized gradient approximation（GGA） functions. The results showed that the calculated lattice parameters were consistent with the corresponding experimental and other theoretical values. The direct band gap of CST50 was 2.19 eV and the bottom of the valence band was mainly determined by the electron orbitals of Ti-3d and O-2p.The analysis of the charge populations, contours of charge density and charge density difference proved that CST50 had the stable Ti—O octahedral structure.The bulk modulus, shear modulus, Young’s modulus and Poisson’s ratio of CST50 were calculated with the stress-strain method. The calculated elastic constants C11, C22, C33 suggested the incompressibility along the principle axes, and the bulk modulus was larger than the shear modulus.LDAG/ B =0.5789 and GGAG/ B =0.5999 indicated that CST50 was a brittle material. The calculated Young’s modulus along [100], [010], [001] crystal orientations, the three-dimensional images of Young’s modulus in XOY, XOZ and YOZ planars, the Poisson’s ratio and the universal elastic anisotropy indexes all suggested the weak elastic anisotropy of CST50.The properties of the planar acoustic wave of CST50 were studied by Christoffel equation. The plane acoustic wave was consisting of a longitudinal wave and two transverse waves. The phase velocity of the longitudinal wave was fast than that of the transverse waves. The phase velocities of the longitudinal wave and the transverse waves were anisotropic in XOY and YOZ planes and isotropic in XOZ plane. It also displayed that the group velocity of the longitudinal wave was larger than its phase velocity, and the group velocities of the transverse waves were almost equal to their phase velocities. The group velocities of the longitudinal wave and one of the transverse waves were isotropy in all planes, and the velocities of the other transverse wave were strongly anisotropic in XOY and YOZ planes and isotropic in XOZ plane.Moreover, the optical properties, including refractive index, reflectivity, absorption function, energy loss function, optical conductivity, extinction coefficient, and transmittance of CST50 were calculated by the complex dielectric function. The calculated results showed that the absorption coefficient, the extinction coefficient, the energy-loss spectrum, and the optical conductivity approached to zero in low energy. In high energy, the absorption coefficient, the optical conductivity, and the extinction coefficient were sensitive to the incident light energy. The energy-loss function spectrum was limited to a particular range of the energy, and the theoretical transmittance of CST50 thin film was high in the 0-2.19 eV energy range.The density of phonon states, Gibbs free energy, enthalpy of CST50 were calculated by Norm-conserving pseudopotentials. The molar heat capacities and thermal expansion coefficient of CST50 were studied with the quasi harmonic Debye model. The thermal properties of CST50 were close to those of calcium titanate and had the stable thermal expansion property at high temperatures. The minimum thermal conductivity properties were investigated with Cahill and Slack models. The minimum thermal conductivity in Cahill model was weak anisotropic in each plane, while the minimum thermal conductivity in Slack model decreased with the increasing external temperature, and reached to a constant at high temperatures. In addition, the projections of Debye temperatures in XOY, YOZ and XOZ planes indicated the lattice vibrations were weak anisotropic.