Bridging the water solubility and ion diffusivity in the mantle silicates by a thermodynamic model

摘要

Water solubility in Mg-endmember silicates is suggested to correlate with cation diffusivity. This study proposes a thermodynamic model by introducing the concept of transient Frenkel defect for Mg ions to quantify the relationship between water solubility and Mg diffusivity in mantle silicates. The formation of the Mg transient Frenkel defect is regarded as the escape of Mg from Mg-O polyhedron, and the concentration of Mg transient vacancy is considered as its statistical probability in silicate minerals. The proposed thermodynamic model reveals that the formation energy for Mg transient vacancy (Delta G(tr)) is approximately Delta G/6 (Delta G is activation energy for Mg diffusion in silicates) for silicates with Mg-O-6 octahedra, such as enstatite, forsterite, wadsleyite, and ringwoodite, and 5 Delta G/12 for bridgmanite and post-perovskite. This observation implies a possible diffusion mode of Mg through transient vacancies. Our model connects water solubility and ion diffusivity in silicates.