Calculation of effect of cation disorder on silicate spinel phase boundaries

The measured cation distributions in Fe₂SiO₄, Co₂SiO₄, and Ni₂SiO₄ (Yagi et al., 1974; Morimoto et al, 1974) are used to calculate interchange enthalpies (Navrotsky and Kleppa, 1967) of +28.8, +16.5, and +37.5 kcal, respectively, for the reaction: M²⁺_oct + Si⁴⁺_tet=M²⁺_tet + Si⁴⁺_oct. The octahedral site preference (Navrotsky and Kleppa, 1967) of Si⁴⁺ in spinels is estimated to be +24.3 ± 5 kcal (strong tetrahedral preference). The interchange enthalpy for Mg₂SiO₄ spinel is +23.3 kcal, leading to 5% inversion at 1500°C. The small degree of disorder in Fe₂SiO₄ and Mg₂SiO₄ is sufficient to account quantitatively for the curvature above 1000°C of the olivine-spinel phase boundary in Fe₂SiO₄ (Akimoto and Komada, 1967) and to cause positive values of ∂P/∂T above 1500°C for the decomposition of Mg₂SiO₄ to its component oxides. The volume change is estimated to be less than 0.5 cm³/mole for M₂SiO₄ (normal → inverse) leading to a very weak pressure dependence of the cation distribution in silicate spinels.