Thermodynamic stability of Fe/O solid solution at inner-core conditions

We present a new technique which allows the fully ab initio calculation of the chemical potential of a substitutional impurity in a high-temperature c rystal, including harmonic and anharmonic lattice vibrations. The technique uses the combination of thermodynamic integration and reference models dev eloped recently for the ab initio calculation of the free energy of liquids and anharmonic solids. We apply the technique to the case of the substitut ional oxygen impurity in h.c.p. iron under Earth's core conditions, which e arlier static ab initio calculations indicated to be thermodynamically very unstable. Our results show that entropic effects arising from the large Vi brational amplitude of the oxygen impurity give a major reduction of the ox ygen chemical potential, so that oxygen dissolved in h.c.p. iron may be sta bilised at concentrations up a few mol % under core conditions.