Thermodynamics of hexagonal-close-packed iron under Earth's core conditions - art. no. 045123

The free energy and other thermodynamic properties of hexagonal-close-packe d iron are calculated by direct ab initio methods over a wide range of pres sures and temperatures relevant to the Earth's core. The ab initio calculat ions are based on density-functional theory in the generalized-gradient app roximation, and are performed using the projector augmented wave approach. Thermal excitation of electrons is fully included. The Helmholtz free energ y consists of three parts, associated with the rigid perfect lattice, harmo nic lattice vibrations, and anharmonic contributions, and the technical pro blems of calculating these parts to high precision are investigated. The ha rmonic part is obtained by computing the phonon frequencies over the entire Brillouin zone, and by summation of the free-energy contributions associat ed with the phonon modes. The anharmonic part is computed by the technique of thermodynamic integration using carefully designed reference systems. De tailed results are presented for the pressure, specific heat, bulk modulus, expansion coefficient and Gruneisen parameter, and comparisons are made wi th values obtained from diamond-anvil-cell and shock experiments.