Linear response theory of correlation effects in anisothermal atomic transport in crystals

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Abstract
Linear response formulae are derived for the phenomenological coefficients for matter transport in a system characterised by a set of jump probabilities. The expressions for the isothermal transport coefficients are the same as those originally derived by Allnatt (1981-82) but the expressions for the anisothermal transport coefficients are different. The details of the derivation differ somewhat from those of the earlier work and are clearer and technically more satisfactory. The matrix method developed by Okamura and Allnatt (1983) for calculations of the isothermal transport coefficients in dilute binary alloys is extended to the anisothermal coefficients. As an example, new exact formulae for the terms in these coefficients which are of first order in the concentrations of paired and unpaired defects are calculated for the five-frequency model of the vacancy mechanism in a dilute FCC alloy. The results reduce to earlier less exact expressions in the appropriate limit.