Crystal chemical and energy analysis of partition coefficients of impurities during melt crystallization: The case of olivine

Abstract

Partition coefficients (K) between forsterite crystal and melt are experimentally determined for many univalent, bivalent, trivalent, and tetravalent trace elements. Using numerical modeling, we calculated the energies of intrinsic and impurity defects in forsterite (Edf) and the energies of dissolution of univalent, bivalent, trivalent, and tetravalent impurities (Eds). These results are compared with literature data. A linear dependence is established for the energy of defects on the charge of the impurity ion and the relative difference in the radii of the impurity and matrix ions Δr/d, where d is the average interatomic distance in the matrix. Partition coefficients are described by parabolic dependences on Δr/d and charge of the impurity ion using literature data on K of impurity elements in olivines and impurity ion dissolution energies. Linear dependences-RTlnK-(Δr/d)2 and Eds-(Δr/d)2 pass through the origin for isovalent substitutions and are well apart from it for heterovalent substitutions. Linear dependence (Δr/d)2 has a free term of about 200 kJ/mol, which is approximately equal to a half of the energy of formation of the Frenkel defect in forsterite; this defect maintains electroneutrality. If valency is compensated due to addition into the melt of an ion with another charge (than that of the impurity ion), Eds-(Δr/d)2 and-RTlnK-(Δr/d)2 lines at low (Δr/d)2 shift to the origin. This means that energy consumption for coupled isomorphism is lower than that for the formation of intrinsic structural defects. Correlation dependences are proposed for the distribution of impurities and the energy of their dissolution. They indicate the increasing contribution of the entropy components of impurity ion dissolution energy during heterovalent isomorphism.