Atomistic simulation of trace element incorporation into garnets-comparison with experimental garnet-melt partitioning data

We have studied the energetics of trace element incorporation into pure almandine (Alm), grossular (Gros), pyrope (Py) and spessartine (Spes) garnets (X₃Al₂Si₃O₁₂, with X = Fe, Ca, Mg, Mn respectively), by means of computer simulations of perfect and defective lattices in the static limit. The simulations use a consistent set of interatomic potentials to describe the non-Coulombic interactions between the ions, and take explicit account of lattice relaxation associated with trace element incorporation. The calculated relaxation (strain) energies U(rel) are compared to those obtained using the Brice (1975) model of lattice relaxation, and the results compared to experimental garnet-melt trace element partitioning data interpreted using the same model. Simulated U(rel) associated with a wide range of homovalent (Ni, Mg, Co, Fe, Mn, Ca, Eu, Sr, Ba) and charge-compensated heterovalent (Sc, Lu, Yb, Ho, Gd, Eu, Nd, La, Li, Na, K, Rb) substitutions onto the garnet X-sites show a near-parabolic dependence on trace element radius, in agreement with the Brice model. From application of the Brice model we derived apparent X-site Young's moduli E(X)(1+, 2+, 3+) and the 'ideal' ionic radii r₀(1+, 2+, 3+), corresponding to the minima in plots of U(rel) vs. radius. For both homovalent and heterovalent substitutions r₀ increases in the order Py-Alm-Spes-Gros, consistent with crystallographic data on the size of garnet X-sites and with the results of garnet-melt partitioning studies. Each end-member also shows a marked increase in both the apparent E(X) and r₀ with increasing trace element charge (Z(c)). The increase in E(X) is consistent with values obtained by fitting to the Brice model of experimental garnet-melt partitioning data. However, the increase in r₀ with increasing Z(c) is contrary to experimental observation. To estimate the influence of melt on the energetics of trace element incorporation, solution energies (U(sol)) were calculated for appropriate exchange reactions between garnet and melt, using binary and other oxides to simulate cation co-ordination environment in the melt. U(sol) also shows a parabolic dependence on trace element radius, with inter-garnet trends in E(X) and r₀ similar to those found for relaxation energies. However, r₀(i+) obtained from minima in plots of U(sol) vs. radius are located at markedly different positions, especially for heterovalent substitutions (i = 1, 3). For each end-member garnet, r₀ now decreases with increasing Z(c), consistent with experiment. Furthermore, although different assumptions for trace element environment in the melt, e.g., REE³⁺ (VI) vs. REE³⁺ (VIII), lead to parabolae with differing curvatures and minima, relative differences between end-members are always preserved. We conclude that: 1. The simulated variation in r₀ and E(X) between garnets is largely governed by the solid phase. This stresses the overriding influence of crystal local environment on trace element partitioning. 2. Simulations suggest r₀ in garnets varies with trace element charge, as experimentally observed. 3. Absolute values of r₀ and E(X) can be influenced by the presence and structure of a coexisting melt. Thus, quantitative relations between r₀, E and crystal chemistry should be derived from well-constrained systematic mineral-melt partitioning studies, and cannot be predicted from crystal-structural data alone. Copyright (C) 2000 Elsevier Science Ltd.