7 大晶系的力学稳定性判据及其应用：以 SiO₂ 为例

According to the positive definiteness of the quadratic type, and based on the mechanical stability criteria derived by Mouhat and Coudert, the mechanical stability criteria of monoclinic and triclinic crystal systems are supplemented. The mechanical stability criteria of the seven crystal systems are given. Based on the density functional theory of the first principle method, the elastic constants of nine kinds of SiO₂ belonging to different crystal systems are calculated. Combined with the mechanical stability criteria, the stabilities of SiO₂ in different space groups, including cubic P2₁3, hexagonal P6₃/mmc, trigonal P3₁21 and R3, tetragonal P4₁2₁2 and I4, orthorhombic Pbcn, monoclinic P2₁/c, and triclinic P1̄, are determined. The calculated results show that the nine types of SiO₂ are all mechanically stable at 0 GPa.