Hexagonal and tetragonal states of magnesium by first principles

Abstract

First-principles total-energy calculations on hexagonal-close-packed (hcp) and body-centered-tetragonal (bct) states of bulk elemental magnesium have been made with a full-potential electronic structure program with both the local-density approximation and the generalized gradient approximation. The unique paths [called epitaxial Bain paths (EBP's)] through hexagonal or tetragonal states produced by epitaxial strain on equilibrium states have been found. The hexagonal EBP reveals the existence of an hcp phase with axial ratio $c/a\ensuremath{\sim}0.72$ and about 20 mRy/atom higher energy than the hcp ground state. Structure parameters and elastic constants of both the ground state and the higher-energy state are determined, and the ground-state values are compared to experiment. Tests of the stability of the hcp phase at $c/a\ensuremath{\sim}0.72$ show that this phase is unstable. The tests for stability require calculations of the elastic constants, which in the case of hcp crystals are composed of a homogeneous and an inhomogeneous contribution. We describe a considerably simplified calculation of the inhomogeneous contribution obtained by using a symmetrical orientation of the unit cell and finding all the elastic constants with symmetrical strains. The tetragonal EBP shows the existence of a face-centered-cubic phase of Mg with about 1 mRy/atom higher energy than the hcp ground state. The elastic constants of this phase satisfy the stability conditions: hence, this phase is metastable.