Correlation factors for impurity diffusion on the sublattice of dodecahedral sites in garnet

The method of Koiwa and Ishioka (Philos Mag A 47:927–938, 1983) is used, with slight modification, to evaluate the correlation factor for vacancy-mediated diffusion of impurity atoms on the sublattice of dodecahedral sites in garnet, as a function of the relevant vacancy-jump frequencies. The required values of the lattice Green’s function were obtained from multiple Monte Carlo simulations in lattices of progressively larger size, extrapolated to an infinite lattice using a model that linearizes the dependence of the functional value on lattice size. As Online Resources, codes are provided that permit evaluation of the correlation factor for any chosen set of vacancy-jump frequencies, for implementation in either Mathematica ^® or Matlab ^®.