Modified mean-field potential approach to thermodynamic properties of a low-symmetry crystal: Beryllium as a prototype

We extend the mean-field potential (MFP) approach for evaluating the vibrational contribution of the lattice ion of high-symmetry metals, and present a modified MFP approach which can be applied to low-symmetry or complex structure crystals. Based on the modified MFP approach in which the effect of the structural parameters on the free energy is taken into account, a first-principles scheme for calculating thermodynamic properties of a crystal dependent on the crystal structure is developed. By taking hexagonal close-packed beryllium as a prototype, we demonstrate that our scheme is suitable for investigating the structural properties and equation of state of low-symmetry crystals.