In this paper, Ca/Sr atoms are confirmed to have symmetric distributions on 4c sites by using the minimum energy principle, and the stable crystal structure of Ca0.5Sr0.5TiO3 is built. The lattice parameters, elastic constants, bulk modulus, shear modulus, Young’s modulus and Poisson’s ratio of Ca0.5Sr0.5TiO3 (CST50) are investigated by the plane wave pseuedopotential method based on the first-principles density functional theory within the local density approximate (LDA) and generalized gradient approximation. The properties of planar acoustic velocity are studied by Christoffel equation, and the minimum thermal conductivity is investigated with Cahill and Cahill-Pohl models. The results show that the calculated lattice parameters are consistent with the corresponding experimental values. The larger calculated elastic constasnts C11, C22, and C33 suggest the incompressibility along the principle axes. The bulk modulus B is larger than the shear modulus G; G/BLDA = 0.5789 and G/BGGA = 0.5999, indicating that CST50 is a brittle material. The three-dimensional image of Young’s modulus along [100], [010], and [001] crystal orientations shows the anisotropic elasticity of CST50. The planar projections of Young’s modulus in (001) and (010) planes show the stronger anisotropy than in (100) plane and all the planar projections have two-fold symmetry. The Poisson’s ratio exhibits the incompressbility of CST50. The universal elastic anisotropy indexes AULDA = 0.0235 and AUGGA = 0.0341 indicate the weak anisotropy of CST50. The planar acoustic wave which has a branch of longitudinal wave and two branches of transverse wave is anisotropic along (010) and (001) planes and isotropic along (100) plane, and all the corresponding planar projections have two-fold symmetry. The minimum thermal conductivity calculated in Cahill model is isotropic in each plane, while the minimum thermal conductivity calculated in Cahill-Pohl model is proportional to the second power of T under low temperatures and reaches a constant at high temperatures. In the quasi harmonic Debye model, the molar heat capacity and thermal expansion coefficient of CST50 are close to those of calcium titanate, indicating that CST50 has the stable thermal expansion property at high temperatures. The direct band gap of CST50 is 2.19 eV and the bottom of the valence band is mainly determined by the electron orbitals of Ti-3d and O-2p. The analysis of the charge populations shows that the covalence of Ti—O is stronger than those of Sr—O and Ca—O, and the band length of Ti—O is shorter than those of Sr—O and Ca—O;(200), (110) and (002) planar contour charge densities indicate that Ti atoms interact strongly with O atoms. The charge population and contour charge density prove that CST50 has a stable Ti—O octahedral structure.
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