Phenomenological coefficients for matter transport by vacancies from linear response theory: I. Derivation of Manning's equations for the impurity correlation factor

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Abstract
Liner response formulae for the phenomenological coefficients LAA, LAB, and LBB for matter transport by vacancies are calculated exactly for the five-frequency model of a very dilute FCC alloy of solute B in solvent A. The method reduces each formula to a set of random walk problems in the homogeneous system, and these are solved by Green function methods. In this paper the results for LBB are shown to be the same as that obtained by Manning in 1964 using the method of equivalent vacancy distributions. The key steps are noted and used in the following paper to calculate LAB and LAA.