Theoretical calculations of the linear, nonlinear elastic constants and the Grüneisen parameters of cubic perovskites (Sr, Ba, Pb)TiO3

The second-order, third-order and fourth-order elastic constants of SrTiO3, BaTiO3 and PbTiO3 cubic perovskites are calculated by using the first-principles total-energy method combined with the means of homogeneous deformation. The predicted results provide reasonable agreement with the reported experimental data, other theoretical results and Cauchy relations. The curved surfaces of Grüneisen parameters at various acoustic propagation modes are plotted by using predicted results. In addition, the Grüneisen parameters at low temperature limit, high temperature limit and Debye temperature are also calculated. Since nonlinear elastic constants are very difficult to be measured in experiments, the methods and results presented here provide a valuable guidance for experiments and the investigation of anharmonic properties for perovskite materials.