Electrical Conduction and Polaron Mobility In Fe-Bearing Olivine

Electrical conductivity σ of Mg2(1–γ)Fe2YSiO4 olivines was measured as a function of Fe content (Y= 0.09, 0.11, 0.18, 0.34) at temperatures between 1423-1573 K and at oxygen fugacities slightly below the wüstite-magnetite buffer. Conductivity was proportional to X1.8Fe for the conditions examined. In accord with current and previous experiments and defect models at these conditions, conductivity is dominated by small polaron hopping of holes from Fe3° to Fe2° on the Mg sublattice. From quantitative equilibrium defect chemistry calculations, we find that the Fe3° concentration is proportional to XFe0.73. From measured conductivity and calculated defect concentrations, the hopping mobility is proportional to XFe1.1 and is in the range (1–6) × 10−4 cm2 V−1 s−1. This 1.1 power dependence on Fe content for mobility is close to the value of ∼1.0 independently deduced from polaron hopping theory for mixed valence solid solution systems. Therefore, small polaron conduction self-consistently explains the observed 1.8 power dependence of σ on Fe content. Using the measured dependence of conductivity on Fe content, a change in composition from Fa10 to Fa12 produces a conductivity increase by a factor of 1.39; near 1473K such a conductivity change could be misinterpreted as an equivalent temperature increase of 52 K in the upper mantle.