The concept of atomic movement between neighboring sites was initially proposed by Wert, and has since been further developed by Vineyard. Vineyard's method builds upon the canonical ensemble of statistical mechanics, which considers the distribution of atomic positions and velocities. The process of an atomic jump can be understood as taking place within an energy landscape defined by the disparity in Gibbs free energy (G migr ) between the saddle-point barrier and the equilibrium position. Here, G migr represents the Gibbs free energy of atom migration (denoted as superscript migr) and can be divided into