First-principles investigation of the structural and mechanical properties of β″ phase in Mg–Gd alloy system

We have performed a first-principles calculation within the generalized gradient approximation to investigate the β″ phase in Mg–Gd alloy system. The lattice parameters are determined theoretically by structural optimization of full relaxation and the β″ phase Mg3Gd is found to be energetically favorable from the calculated formation enthalpy. The nine independent elastic constants are calculated, indicating the proposed Mg3Gd structure is mechanically stable. Then the polycrystalline bulk modulus B, shear modulus G, Young's modulus E and Poisson ratio ν are gained by the Voigt–Reuss–Hill (VRH) approximation. The elastic anisotropy is discussed in detail. The electronic density of states and charge density distribution are analyzed, indicating the existence of covalent bonding in Mg3Gd. The Debye temperature is also estimated for the investigation in the future.