Abstract
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 ®.
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Notes
Lattice sites are identified by vector components in the x, y, and z directions; unit vectors in those directions are oriented parallel to crystallographic axes a 1, a 2, and a 3 in garnet, with magnitudes equal to 1/8 of the garnet unit-cell dimension.
In the course of our study, we replicated the calculations of K&I83 that produced their g matrices for the bcc, fcc, and dmd lattices. Doing so revealed four typographical errors, as follows. (1) In their Table 1, for element g 33, "(200)" should instead read "(220)". (2) In their Table 3, for element g 44, “(442)” should instead read "(422)". (3) In their Table 4, for element g 31, "g 13" should instead read “2g 13”. (4) In their Table 4, for element g 14, "(200)" should instead read "(220)". We verified that all further calculations used the correct lattice Green's function, so these errors are purely typographical and did not propagate into their final expressions for the correlation factors.
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The support of the Geology Foundation of the University of Texas at Austin is gratefully acknowledged.
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Carlson, W.D., Wilson, C.R. Correlation factors for impurity diffusion on the sublattice of dodecahedral sites in garnet. Phys Chem Minerals 43, 363–369 (2016). https://doi.org/10.1007/s00269-016-0800-2
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DOI: https://doi.org/10.1007/s00269-016-0800-2