| Inner core: HCP-iron |
| 1 | The axial ratio of hcp iron at the conditions of the Earth's inner core Abstract We present ab initio calculations of the high-temperature axial ca ratio of hexagonal-close-packed (hcp) iron at Earth's core pressures, in order to help interpret the observed seismic anisotropy of the inner core. The calculations are based on density co functional theory, which is known to predict the properties of high-pressure iron with ^ good accuracy. |
| 2 | The temperature dependence of ca is determined by minimising the Helmholtz free energy at fixed volume and temperature, with thermal contributions due to lattice vibrations calculated using harmonic theory. Anharmonic corrections to the harmonic predictions are estimated from calculations of the thermal average ^ stress obtained from ab initio molecular dynamics simulations of hcp iron at the conditions of the inner core. |
| 3 | We find a very gradual increase of axial ratio with temperature. This increase is much smaller than found in earlier calculations, but ^ is in reasonable agreement with recent high-pressure, high-temperature diffraction ^^ measurements. This result casts doubt on an earlier interpretation of the seismic ю anisotropy of the inner core. ^ CO ^ Key words: Ab initio, Anisotropy, Core, Elasticity ^ PACS: 62.20.D, 62.50.+p, 71.15.Ap, 91.35.-x 1 Introduction In the last few years, there have been a number of ab initio studies of iron at high temperatures and pressures, in an effort to understand the proper- * Corresponding Author. |
| 4 | Tel: +44 (0)20 7679 7049; Fax: +44 (0)20 7679 1360 Email address: m.gillan@ucl.ac.uk (M. J. Gillan). URL: http:www.cmmp.ucl.ac.uk~mjg (M. J. Gillan). Preprint submitted to Elsevier Science 2 February 2008 ties of the Earth's solid inner core (Stixrude et al. (1994); Stixrude and Cohen (1995); Soderlind et al. (1996); Wasserman et al. (1996); Stixrude et al. (1997); VoCadlo et al. (1997); Steinle-Neumann et al. (1999); Vocadlo et al. (2000); Belonoshko et al. (2003); Laio et al. (2000); Alfe et al. (2001); Steinle-Neumann et al. (2001, 2002); VoCadlo et al. (2003)), including its elastic properties. |
| 5 | A controversial issue, addressed by some of this work, concerns the elastic anisotropy of the inner core (Creager (1992); Tromp (1993)), i.e. the fact that compres-sional waves are observed to traverse the core region some 3-4% faster along the Earth's rotational axis than in the equatorial plane. It is widely assumed that the phase of Fe in the inner core is hexagonal close packed (hcp), and it has become clear that to understand the elastic properties it is necessary to know how the axial ratio ca depends on temperature and pressure. |
| 6 | In order to provide information about this, we present here ab initio calculations of the axial ratio of hcp iron over a range of pressures and temperatures relevant to the inner core. Ab initio calculations on pure crystalline iron are very relevant for understanding the inner core, even though the core is known to contain light impurities (the leading candidates are O, Si and S), and is believed to contain Ni as well as Fe (Poirier (1994)). |
| 7 | Recent estimates (Alfe et al. (2002a)) suggest that the fraction of light impurities in the inner core is approximately 8.5 mol%, and this low fraction will probably not change its properties greatly. The Ni content will also probably make only a small difference, since the electronic structures of Ni and Fe are so similar. The determination of the properties of pure Fe is thus essential as a starting point for further refinements. |
| 8 | The common assumption that Fe in the inner core is in the hcp structure has recently been challenged (Vocadlo et al. (2003); Belonoshko et al. (2003)), and it is possible that the crystal structure is different in different parts of the core (Song and Helmberger (1998); Ishii and Dziewonski (2002); Beghein and Trampert (2003)). However, in order to make progress, it is clearly essential to understand the properties of the leading candidates, of which hcp is certainly one. |
| 9 | It is well established that density functional theory (DFT) (Hohenberg and Kohn (1964); Kohn and Sham (1965); Jones and Gunnarsson (1989)) gives a rather accurate description of Fe and other transition metals, both under ambient conditions, and under high pressures and temperatures. This is known from comparisons with experiment for a wide range of properties, including the equilibrium lattice parameter under ambient conditions, elastic constants, magnetic properties, phonon frequencies (Stixrude et al. (1994); Soderlind et al. (1996); Vocadlo et al. (1997); Vocadlo et al. (2000)); the pressure-volume relationship at high pressures, the phonon density of states and the Hugoniot (Wasserman et al. |
| 10 | (1996); Mao et al. (2001); Alfe et al. (2001)). A number of groups have used DFT calculations to investigate the elastic constants of hcp Fe under inner-core conditions. The early calculations were performed at zero temperature (Stixrude and Cohen (1995); Steinle-Neumann et al. 2 (1999)), and led to the suggestion that elastic anisotropy could be explained by a preferential alignment of crystalline c-axes with the Earth's rotational axis. |
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