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Thermodynamics of hexagonal-close-packed iron under Earths core conditions

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 نشر من قبل Dario Alf\\`e
 تاريخ النشر 1999
  مجال البحث فيزياء
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The free energy and other thermodynamic properties of hexagonal-close-packed iron are calculated by direct {em ab initio} methods over a wide range of pressures and temperatures relevant to the Earths core. The {em ab initio} calculations are based on density-functional theory in the generalised-gradient approximation, and are performed using the projector augmented wave (PAW) approach. Thermal excitation of electrons is fully included. The Helmholtz free energy consists of three parts, associated with the rigid perfect lattice, harmonic lattice vibrations, and anharmonic contributions, and the technical problems of calculating these parts to high precision are investigated. The harmonic part is obtained by computing the phonon frequencies over the entire Brillouin zone, and by summation of the free-energy contributions associated with the phonon modes. The anharmonic part is computed by the technique of thermodynamic integration using carefully designed reference systems. Detailed results are presented for the pressure, specific heat, bulk modulus, expansion coefficient and Gr{u}neisen parameter, and comparisons are made with values obtained from diamond-anvil-cell and shock experiments.



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{em Ab initio} techniques based on density functional theory in the projector-augmented-wave implementation are used to calculate the free energy and a range of other thermodynamic properties of liquid iron at high pressures and temperatures relevant to the Earths core. The {em ab initio} free energy is obtained by using thermodynamic integration to calculate the change of free energy on going from a simple reference system to the {em ab initio} system, with thermal averages computed by {em ab initio} molecular dynamics simulation. The reference system consists of the inverse-power pair-potential model used in previous work. The liquid-state free energy is combined with the free energy of hexagonal close packed Fe calculated earlier using identical {em ab initio} techniques to obtain the melting curve and volume and entropy of melting. Comparisons of the calculated melting properties with experimental measurement and with other recent {em ab initio} predictions are presented. Experiment-theory comparisons are also presented for the pressures at which the solid and liquid Hugoniot curves cross the melting line, and the sound speed and Gr{u}neisen parameter along the Hugoniot. Additional comparisons are made with a commonly used equation of state for high-pressure/high-temperature Fe based on experimental data.
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