Temperature dependent elastic coefficients of Mg₂X (X = Si, Ge, Sn, Pb) compounds from first-principles calculations

Influence of temperature on the elastic properties of Mg₂X (X = Si, Ge, Sn, and Pb) compounds, has been studied using first-principles calculations, within the generalized gradient approximation, and compared with the available experimental data in the literature. Elastic stiffness coefficients calculated with respect to volume (c_ij(V)) have been correlated to the equilibrium volume as a function of temperature V(T) from phonon calculations to obtain temperature dependence of elastic stiffness coefficients c_ij(T). A good agreement between the thus predicted elastic constants and experimental data has been achieved. The general trend in the bulk modulus (B), shear modulus (G) and Young's modulus (E) seen for the compounds is Mg₂Ge > Mg₂Si > Mg₂Sn > Mg₂Pb. Elastic anisotropy, fracture toughness and stiffness of the compounds have been analyzed as a function of temperature based on their anisotropic ratio (2c₄₄/(c₁₁-c₁₂)), product of bulk modulus and volume (B × V^1/3), and Young's modulus. The results obtained herein provide a better understanding of the elastic behavior of antifluorite compounds as a function of temperature. The methodology used in this work acts as a benchmark for future first-principles work that involves calculating elastic constants as a function of temperature.