Dependence on pressure of conduction by hopping of small polarons in minerals of the Earth's lower mantle

Electrical conductivity of the lower mantle-like assemblage (Mg,Fe)SiO₃ perovskite-(Mg,Fe)O magnesiowüstite is usually analyzed using the quasi-chemical Arrhenian approach of diffusion. The conductivity of this assemblage has often been attributed to hopping of small polarons, because of the low value of the activation energy and the small negative activation volume. However, the solid-state physics approach can provide more arguments, for or against conduction by polarons. We have tried to bridge the gap between the two approaches and identify the physical quantities entering the phenomenological activation parameters. In particular, we have investigated the pressure dependence of the activation energy, and the physical meaning of the activation volume. Hopping is controlled by the binding energy of the polaron and by the value of the exchange integral, which increases with pressure causing the observed decrease of the activation energy. From the physical theory and the results of experiments at pressures up to 40 GPa and temperatures up to 400 ^∘C, we have estimated the values of parameters characteristic of polarons: radius, mobility, time between jumps and adiabaticity. These values are compatible with conduction by small adiabatic polarons. The consequences for extrapolations to lower mantle conditions of the presence of a temperature dependent preexponential term in the expression for conductivity have been examined. It was found that the extrapolations are not significantly different from those using the Arrhenius equation. Received: 5 November 1998 / Revised, accepted: 4 May 1999