Thermal properties of iron at high pressures and temperatures

Abstract

We investigate the thermoelastic properties of close-packed phases of iron at pressures up to 400 GPa and temperature to 6000 K using a tight-binding total-energy method and the cell model of the vibrational partition function. The calculated properties are in good agreement with available static and shock-wave experimental measurements. The compressional behavior of a number of thermoelastic parameters is found to resemble that of a prototypical oxide ͑MgO͒ supporting some aspects of universal behavior at high compression: the product of thermal expansivity ␣ and bulk modulus is found to be nearly independent of compression at high pressure and the logarithmic volume derivative of ␣ is found to decrease with compression. In contrast to the behavior of MgO, ␣K T and ␦ T of iron are found to depend strongly on temperature due to contributions from the thermal excitation of electrons. Significant decrease of the elastic constants of hcp iron with temperature was found.

Thermal equation of state of tantalum

“…Interestingly these values are not that different from MgO 28 (δ T (η = 1, 1000K)) = 5.00 and κ = 1.48. The behavior is much different than for Fe, where δ T is constant to 150 GPa with values of 5.2 and 5.0 for fcc and hcp, respectively, after which it drops more slowly than a power law 17 . The difference between δ T and K ′ is an important anharmonic parameter, and is related to the change in the bulk modulus with temperature at constant volume and the thermal pressure with compression at constant temperature:…”

“…Therefore, integration over the Wigner-Seitz cell can be replaced by an integration over the inscribed sphere. Also, the radial part of the integrand is invariant under point group operations of the lattice, hence a numerical quadrature can be used for angular integration based on the method of special directions 17,23 . In this method, the radial integral is expanded in terms of lattice harmonics, cubic harmonics for a cubic lattice, then a quadrature rule is derived for the angular integration in terms of the radial integration by choosing special directions,r i , in such a way that the contribution from l = 0 terms, as many lattice harmonics as possible, is zero.…”

“…In order to compute the high temperature properties of Ta, we separated the Helmholtz free energy as 17 :…”

“…The particle-in-a-cell model 17,18 was used to calculate the partition function. In this model, the partition function is factored by neglecting atomic correlations.…”

Theoretical modeling of molar volume and thermal expansion

“…Three well-known approximations used to account for the Grüneisen parameter γ can be combined into the following expression (Zharkov and Kalinin, 1971;Wasserman et al, 1996),…”