First-principle studies on the mechanical, thermodynamic and electronic properties of β″-Mg₃Gd and β′-Mg₇Gd alloys under pressure

A theoretical investigation on the mechanical, thermodynamic and electronic properties of β″-Mg₃Gd and β′-Mg₇Gd compounds at the effect of pressure have been conducted through the first-principles calculations. Since the shear modulus of β″ is less affected by pressure, its bulk modulus/shear modulus (B/G) is more sensitive to pressure than β′. Based on the analysis of vibrational heat capacity C_V, β′ can absorb more heat at high temperature. The pressure-induced distribution of charges is more localized between atoms, making stronger covalent bonds. Further, the inhomogeneous distributions of covalent and metal bonds may be the reason for the increased anisotropy based on the Ranganathan's anisotropy index (A^U). The Mg p and the Gd d states expand to both occupied and unoccupied states, whereas the lower energy Mg s and Gd s, p states expand primarily to bonding states under high pressures. The spatial distributions of Mg p and Gd d electrons hybridization at antibonding states act a crucial role in improving mechanical properties of alloys at the applied pressure.