CXXXIII. Impurity diffusion in crystals (mainly ionic crystals with the sodium chloride structure)

In this paper elementary lattice kinetic theory is applied to the problem of impurity diffusion by the vacancy mechanism, special attention being paid to the case where there are appreciable attractions between impurity atoms and vacancies. We make use of the approximate methods of association theory, in which we treat impurity-vacancy pairs at small distances of separation (‘complexes’) on a different footing from pairs at farther separations. Detailed formulae are presented for (i) the diffusion coefficient of impurities in face-centred cubic metals, for which the association model should be very good (Johnson mechanism), and (ii) the diffusion coefficient of divalent ions in polar crystals of the NaCL type. One important aspect of the results on divalent ions in polar crystals is the dependence of the diffusion coefficient D(c) on impurity concentration, c, when there is appreciable association. At low concentrations D(c) is proportional to c but at higher concentrations D increases more and more slowly finally tending to a saturation value. In the absence of appreciable association D(c) remains proportional to c at all concentrations and temperatures. The form of our results shows that experimental determinations of impurity diffusion coefficients are capable of throwing a very direct light on the conditions existing within many of the systems of interest in the field of colour centres (e.g. NaCl and KCl containing alkaline earth chlorides).