Ab initiothermodynamics of the hcp metals Mg, Ti, and Zr

The thermal properties of hcp metals Mg, Ti, and Zr are investigated by performing density functional theory and density functional perturbation theory calculations within the quasiharmonic approximation. The temperature dependence of various quantities such as the anisotropic thermal expansion, the heat capacity, bulk modulus, and Gr\"uneisen parameters are computed. The electronic contribution to the thermal expansion and heat capacity are discussed. Our results are in good agreement with available experimental data in a wide range of temperature.