The pressure dependence of the lattice and elastic constants of the orthorhombic YBa ${}_2$ Cu ${}_3$ O ${}_7$ are firstly investigated using the first principles calculations based on the density functional theory. The calculated lattice parameters at 0 GPa are in agreement with the available experimental data. By the elastic stability criteria under isotropic pressure, it is predicted that YBa ${}_2$ Cu ${}_3$ O ${}_7$ with and orthorhombic structure is mechanically stable under pressure up to 100 GPa. On the basis of the elastic constants, Pugh’s modulus ratio, Poisson’s ratio, elastic anisotropy, Debye temperature, and the minimum thermal conductivity of YBa ${}_2$ Cu ${}_3$ O ${}_7$ under pressure up to 100 GPa are further investigated. It is found that its ductility, Debye temperature, and minimum thermal conductivity increase with pressure.

The volume versus temperature relations for Ni ${}_3$ Si and Ni ${}_3$ Ge are obtained by using the first principles calculations combined with the quasiharmonic approach. Based on the equilibrium volumes at temperature T, the temperature dependence of the elastic constants, generalized stacking fault energies and generalized planar fault energies of Ni ${}_3$ Si and Ni ${}_3$ Ge are investigated by first principles calculations. The elastic constants, antiphase boundary energies, complex stacking fault energies, superlattice intrinsic stacking fault energies and twinning energy decrease with increasing temperature. The twinnability of Ni ${}_3$ Si and Ni ${}_3$ Ge are examined using the twinnability criteria. It is found that their twinnability decrease with increasing temperature. Furthermore, Ni ${}_3$ Si has better twinnability than Ni ${}_3$ Ge at different temperatures.