Ab-initio investigation of the thermodynamic stability of the magnesio-wüstite solid solution under Earth's lower mantle conditions

Mg-wüstite, (Mg,Fe)O, is the second most abundant phase in the Earth's lower mantle. A profound understanding of the thermodynamic stability of this phase under deep mantle conditions is thus crucial for developing accurate models of the Earth's interior and the importance of drawing a complete picture of the stability fields of the Mg-wustite solid solution, especially at high pressure/temperature regimes, is straightforward. In the light of the above considerations, the present work has been undertaken where the thermo-chemical properties of the (Mg,Fe)O solid solution, over a wide PT range, have been modelled using mixing Helmholtz energy, ?F T, x mixing. Calculations have been performed by means of cluster expansion, quantum mechanical and semiempirical techniques. Both high-spin (HS) and low-spin (LS) configurations of iron have been explored as a function of composition (x: molar fraction of FeO) over the MgO-FeO binary. Only the HS-model provides physically sound results at room pressure, yielding a correct trend of cell edge versus composition, whereas LS's issues are at variance with observations. Mixing Helmholtz energy has been parametrized by the following relationship ?F T, x mixing = x×y×[(U T ! + U T ! × x - y + U T ! ± (x - y)!, where y = 1 - x and U!(T) are polynomials in T of the third order. ?F T, x mixing exhibits a quasi-symmetric behaviour and allows one to build the T-X phase relations diagram over the MgO-FeO join. On the basis of the HS-model including vibrational contribution to Helmholtz energy, a solid solution's critical temperature of some 950 K has been predicted, remarkably lower than olivine's and Mg-Fe-garnet's. All this points to a more difficult Mg-Fe mixing in periclase-like structure than olivine and garnet, which, in turn, provide more degrees of freedom for atomic relaxation. From ?F T, x mixing, the values of ?H T, x mixing and ?S T, x mixing have been derived, both exhibiting so modest a dependence on T as to be negligible. ?H T, x mixing and ?S T, x mixing exhibit quasi-regularity; either has been parametrized as W×x×(1 - x), obtaining W!,!"!!" and W!,!"!!" of 17.7 kJ/mol and 26.8 J/mol/K, respectively. ?S T, x excess has been estimated to be smaller than 0.5 J/mol/K in absolute Moreover, it has been observed that the HS-configuration is stable and promote Mg-Fe solid solution up to >>15 GPa better than LS does. At higher pressures, the LS-model becomes favourite and increasingly stabilizes (Mg,Fe)O upon rising P, whereas HS predicts ex-solving into the end members above >>40 GPa