Complete-path matrix equations for tracer diffusion coefficients and correlation factors

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Abstract
General complete-path matrix equations are derived for the tracer diffusion coefficient and correlation factor by taking into account the frequency with which defects encounter a tracer atom and the possibility of multiple exchanges of a defect with the atom. These equations apply even when mirror symmetry and rotational symmetry of the crystal and defect are lacking, as for example when diffusion occurs via complex defects in noncubic crystals. They also are valid for diffusion along any diffusion direction and where the individual atom jumps provide a variety of jump distances. It is shown that the general equations reduce to those of Stark and of Howard in the special case where there is mirror symmetry across the diffusion place.