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Although comprehensive understanding of the rates and mechanisms of intracrystalline diffusion is vital to a wide range of geological endeavors (e.g., determination of heating/ cooling rates, burial/ uplift rates, and P-T-t paths; geochronology; thermochronology), our knowledge of the fundamental atomic-scale phenomena that govern diffusion remains rudimentary.
In particular, the elastic-strain theory (EST) of diffusion predicts that in a given mineral structure, larger ions will diffuse more slowly than smaller ones. But measurements of diffusivities in several important silicates and oxides illustrate that EST is commonly violated. A robust new data set for Mg, Fe, Mn and Ca diffusion in aluminosilicate garnet reveals that for each quaternary end-member there exists a certain optimum radius -- close to or slightly larger than the radius for the ion in the dodecahedral site in the end-member -- for which diffusion is fastest; both smaller and larger ions diffuse more slowly than ions of the optimum radius. Similar behavior is observed in forsterite, tephroite, and periclase.
No existing theory predicts slower diffusion for smaller ions, pointing to a fundamental gap in our understanding of diffusion in solid state. One hypothesis to explain these observations is that greater potential energy barriers to diffusion exist not only for atoms larger than the optimum (due to the larger local strains needed to move the atom through the saddlepoint between sites, as in EST), but also for atoms smaller than the optimum (due to shorter bonds, and thus stronger bonding, in the site).
Molecular dynamics (MD) simulations of diffusion in garnet were undertaken as a possible means of testing this hypothesis. The simulations used a common formulation for the interatomic potentials (IAPs) in ionic crystals that sums contributions from coulombic attraction/ repulsion, Born-Mayer-type repulsion, and dipole attraction. A new set of potential parameters for Mg, Fe, Mn, and Ca in garnet was derived by using a genetic algorithm to fit data on molar volumes, thermal expansivity and compressibility.
Results of the simulations fail to match experimental observations, but are qualitatively in agreement with the predictions of EST. Self-diffusion coefficients retrieved from the MD simulations (Mg in pyrope, Fe in almandine, Mn in spessartine, Ca in grossular) are systematically lower for end-members with larger molar volumes, and "tracer" diffusion coefficients (e.g, ∼10 mole % Fe, Mn, or Ca in pyrope) retrieved from the simulations show a parabolic inverse dependence on ionic radius. These results indicate that MD simulations using the formulation for IAPs employed here encompass relevant strain effects, but fail to capture the essential physics of whatever process leads to slower diffusivity for smaller ions. This suggests the importance of factors not included in the IAPs, such as changes in polarization for atoms near vacancies, as key determinants of diffusion rates.
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