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

• Published in: Geochimica et cosmochimica acta 2000-05, Vol.64 (9), p.1629-1639
• Main Authors: van Westrenen, W, Allan, N.L, Blundy, J.D, Purton, J.A, Wood, B.J
• Format: Article
• Language: English
• ISSN: 0016-7037; 1872-9533
• DOI: 10.1016/S0016-7037(00)00336-7

We have studied the energetics of trace element incorporation into pure almandine (Alm), grossular (Gros), pyrope (Py) and spessartine (Spes) garnets (X 3Al 2Si 3O 12, 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 r 0 (1+, 2+, 3+), corresponding to the minima in plots of U rel vs. radius. For both homovalent and heterovalent substitutions r 0 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 r 0 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 r 0 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 r 0 similar to those found for relaxation energies. However, r 0 ( 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, r 0 now decreases with increasin