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An ab initio study of the relative stabilities and equations of state of Fe₃S polymorphs

P. Martin¹, L. Voadlo², D. Alfè^2,3 and G. D. Price²

¹ Department of Physics, University of Cambridge, Cavendish Laboratory, Madingley Road, Cambridge CB3 0HE, UK
² Department of Earth Sciences, University College London, Gower Street, London WC1E 6BT, UK
³ Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK

^* E-mail: paula.martin{at}phy.cam.ac.uk

An investigation of the relative stabilities and equations of state of possible Fe₃S polymorphs was conducted using first-principles pseudopotential calculations. These calculations were based on density functional theory and performed using ultrasoft Vanderbilt pseudopotentials within the generalized gradient approximation. In accord with experiment, we found that the tetragonal Fe₃P-type polymorph is the only stable phase along the 0 K isotherm as a function of pressure. Fe₃S exhibits permanent magnetism at ambient conditions (Fei et al., 2000), but magnetism is suppressed by pressure and temperature, and therefore non-magnetic data are appropriate ones to use for modelling planetary interiors. For this reason, and because the Fe₃P-type polymorph of Fe₃S contains 32 atoms per unit cell it was impractical to incorporate magnetic properties into the simulations of this phase, we studied the behaviour of the non-magnetic phase. We obtained values of 250 GPa for the bulk modulus, K₀, and 4.61 for its first derivative with respect to pressure, K₀', by fitting a 3^rd order Birch-Murnaghan equation of state to the calculated internal energy as a function of volume for the non-magnetic Fe₃P- type Fe₃S. This suggests that a pressure far greater than that expected in the Martian interior would be needed to achieve a density comparable to that of the Martian core. We therefore conclude that it is unlikely that the core of Mars contains significant amounts of solid Fe₃S.

KEYWORDS: equation of state, Fe₃S polymorph, Mars, non-magnetic data

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