Influence of the crystal field effect on chemical transport in Earth's mantle: Cr 3+ and Ga 3+ diffusion in periclase

Abstract

Experiments were performed to determine concentration-dependent diffusion coefficients of Cr 3+ and Ga 3+ in periclase at temperatures of 1563–2273 K. Diffusion profiles measured in the quenched samples are consistent with a theoretical model in which the mobile species is a bound M 3+-vacancy pair, and each profile was fitted to determine the binding energy and diffusion coefficient of the pair. Trivalent chromium-vacancy pairs diffuse more slowly than Ga 3+-vacancy pairs, and with higher migration energy, 237 kJ/mol vs. 190 kJ/mol. Cation vacancies also bind less tightly to Cr 3+ than to Ga 3+, with average binding free energies of −22 and −83 kJ/mol, respectively. At all concentrations and temperatures, Cr 3+ diffuses much more slowly than Ga 3+, by up to two orders of magnitude. The differences between Cr 3+ and Ga 3+ cannot be explained by differences in ionic radius or dipole polarizability, but are consistent with the influence of the crystal field on the partially occupied 3d orbitals of Cr 3+. The crystal field splitting stabilizes Cr 3+ on the octahedral cation site, increasing the energy required for Cr 3+ to exchange positions with an adjacent vacancy. It also makes Cr 3+-vacancy pairs less favorable, with the presence of a nearest-neighbor vacancy disrupting the symmetry of the octahedral site, thus diminishing the crystal field stabilization. Trends in the diffusion of first-row divalent transition metals in periclase can also be explained by the crystal field effect. High-spin to low-spin transitions in Fe 2+, Co 2+ or Mn 2+ would significantly enhance their crystal field stabilization in periclase, and if such spin transitions occur in the deep mantle, they would be expected to slow the diffusivity of these ions significantly, perhaps by several orders of magnitude.