Modelling of thermo-chemical properties over the sub-solidus MgO–FeO binary, as a function of iron spin configuration, composition and temperature

Thermo-chemical properties and T–X phase relations diagram of the (Mg,Fe)O solid solution are modelled using mixing Helmholtz energy, ΔF(T,x)<inf>mixing</inf>, calculated by quantum mechanical and semi-empirical techniques. The sub-solidus MgO–FeO binary has been explored as a function of composition, with iron either in high-spin (HS) or low-spin (LS) configuration. 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: ΔF(T,x)<inf>mixing</inf> = x × y × [U<inf>0</inf>(T) + U<inf>1</inf>(T) × (x – y) + U<inf>2</inf>(T) × (x − y)²]−T × S(x,y)<inf>config</inf>, where y = 1−x and U<inf>j</inf>(T) are polynomials in T of the second order. ΔF(T,x)<inf>mixing</inf> exhibits a quasi-symmetric behaviour and allows one to build the T–X phase relations diagram over the MgO–FeO join. The HS model including vibrational contribution to the Helmholtz energy predicts a solid solution’s critical temperature of some 950 K, remarkably larger 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 structure degrees of freedom for atomic relaxation. From ΔF(T,x)<inf>mixing</inf>, we have then derived ΔH(T,x)<inf>excess</inf> and ΔS(T,x)<inf>excess</inf>. The former, characterized by a quasi-regular behaviour, has been parametrized through W × x × (1−x), obtaining W<inf>H,Mg–Fe</inf> of 17.7(5) kJ/mol. ΔS(T,x)<inf>excess</inf>, in turn, increases as a function of temperature, showing absolute figures confined within 0.1 J/mol/K. Mixing Gibbs energy, calculated combining the present issues with earlier theoretical determinations of the magnesio-wüstite’s elastic properties, has shown that the HS configuration is stable and promote Mg–Fe solid solution up to ≈15 GPa.