CONTROLS ON DIFFUSION OF DIVALENT CATIONS IN GARNET: THE ROLES OF HOST-CRYSTAL COMPOSITION AND IONIC SIZE

A wealth of petrologic information can be derived from the changes in chemical zoning of garnet that result from modification by intracrystalline diffusion of gradients in concentration of its principal divalent cations, namely Mg, Fe, Mn, and Ca. Garnet is particularly useful in this way, because its breadth of possible compositions renders it stable in diverse lithologies over a wide range of P-T conditions. But this breadth of composition produces very large variations in cation diffusivity, so rigorous analysis of time-temperature relations in natural rocks requires explicit recognition and treatment of these compositional effects, and a theoretical understanding of their origin.

The effects on diffusivity of garnet composition are captured by a simple model ("C06": Carlson, 2006, Am Min 91:1) in which self-diffusion coefficients include pre-exponential frequency factors that are functions of unit-cell dimensions for the host crystal. The C06 model accounted for all reliable data then available, and also successfully predicted the diffusivities measured in a later experimental study on natural quaternary garnets. Compared to models without compositional dependence, this approach significantly improves fits to measured diffusion-induced profiles in several natural examples.

Host-crystal composition has varying effects on ions of different size. For example, when one compares alm-pyp to alm-sps couples, Mg displays almost identical diffusivity, but Fe diffusivity differs by nearly two orders of magnitude. The reason for this variation is made evident by the C06 synthesis, which yields a parabolic dependence of diffusivity on ionic radius: for each host-crystal composition, ions of "optimal" radius diffuse most rapidly, and both larger and smaller ions diffuse more slowly. This clear violation of elastic strain theory, which predicts that smaller ions should always diffuse more rapidly, is not an artifact of the model: it is mirrored, for example, in experimental data for forsterite, tephroite and periclase. A speculative origin for this effect in garnet is local relaxation of the structure around smaller-than-optimal ions, so that the four O2 oxygen atoms in the eightfold coordination polyhedron have shorter — and thus stronger — bonds to the smaller ion than exist for ions of the optimal size.