 
Summary: Physics of the Earth and Planetary Interiors 152 (2005) 6777
The axial ratio of hcp iron at the conditions of the
Earth's inner core
C.M.S. Gannarellia, D. Alf`ea,b, M.J. Gillana,
a Physics and Astronomy Department, University College London, Gower Street, London WC1E 6BT, UK
b Department of Earth Sciences, University College London, Gower Street, London WC1E 6BT, UK
Received 26 September 2004; received in revised form 1 June 2005; accepted 3 June 2005
Abstract
We present ab initio calculations of the hightemperature axial c/a ratio of hexagonalclosepacked (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
functional theory, which is known to predict the properties of highpressure iron with good accuracy. The temperature dependence
of c/a 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. 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 highpressure, hightemperature diffraction measurements. This
result casts doubt on an earlier interpretation of the seismic anisotropy of the inner core.
© 2005 Elsevier B.V. All rights reserved.
PACS: 62.20.D; 62.50.+p; 71.15.Ap; 91.35.x
Keywords: Ab initio; Anisotropy; Core; Elasticity
