Influence of the crystal field effect on chemical transport in Earth's mantle: Cr3+ and Ga3+ diffusion in periclase

Experiments were performed to determine concentration-dependent diffusion coefficients of Cr³⁺ and Ga³⁺ 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 M³⁺-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 Ga³⁺-vacancy pairs, and with higher migration energy, 237 kJ/mol vs. 190 kJ/mol. Cation vacancies also bind less tightly to Cr³⁺ than to Ga³⁺, with average binding free energies of ?22 and ?83 kJ/mol, respectively. At all concentrations and temperatures, Cr³⁺ diffuses much more slowly than Ga³⁺, by up to two orders of magnitude. The differences between Cr³⁺ and Ga³⁺ 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 Cr³⁺. The crystal field splitting stabilizes Cr³⁺ on the octahedral cation site, increasing the energy required for Cr³⁺ to exchange positions with an adjacent vacancy. It also makes Cr³⁺-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 Fe²⁺, Co²⁺ or Mn²⁺ 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.