Ca0.5Sr0.5TiO3弹性和热学性质的第一性原理研究

利用能量最小原理, 确定了Ca_0.5Sr_0.5TiO₃晶体中4c位置的Ca/Sr原子对称分布, 建立了Ca_0.5Sr_0.5TiO₃稳定的晶体结构, 在此基础上利用基于密度泛函理论第一性原理的平面波超软赝势方法, 采用局域密度近似和广义梯度近似函数, 计算了Ca_0.5Sr_0.5TiO₃的晶格参数、弹性常数、体弹模量、剪切模量、杨氏模量、泊松比, 并基于Christoffel方程的本征值研究了平面声波的特征, 基于Cahill和Cahill-Pohl模型研究了最小热导率的特征. 计算结果表明: Ca_0.5Sr_0.5TiO₃晶格参数和实验值很接近, 体弹模量大于剪切模量, 100], 010], 001]晶向的杨氏模量、泊松比、普适弹性常数(A^U)以及杨氏模量三维图均显示了弹性各向异性; 平面声波在(010), (001)平面呈现各向异性, 在(100)平面呈现各向同性, 平面声波大小与平均横波和平均纵波的数值很接近. Cahill模型最小热导率在各平面呈现各向同性, Cahill-Pohl模型最小热导率在高温时趋于恒定. 准谐德拜模型下Ca_0.5Sr_0.5TiO₃ 晶体的摩尔热容和热膨胀系数与CaTiO₃晶体的接近, 并且高温下具有稳定的热膨胀性能. 计算所得禁带宽度为2.19 eV, 导带底主要是Ti-3d与O-2p态电子贡献; 由电荷布居和电荷密度图理论证实Ca_0.5Sr_0.5TiO₃具有稳定的Ti-O八面体结构.

First-principles study on the elastic and thermal properties of Ca0.5Sr0.5TiO3

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 Ca_0.5Sr_0.5TiO₃ is built. The lattice parameters, elastic constants, bulk modulus, shear modulus, Young's modulus and Poisson's ratio of Ca_0.5Sr_0.5TiO₃ (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/B_LDA = 0.5789 and G/B_GGA = 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 A_LDA^U = 0.0235 and A_GGA^U= 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.