Theory of diffusion in ordered alloys of the β-brass type

Abstract

The vacancy concentration and the migration energy in a β-brass type order-disorder alloy have been investigated using the Bragg-Williams theory, Kirkwood's second moment approximation and the quasi-chemical theory. The migration energy problem has been studied for both cases of first and second neighbor jump. A significant difference in the coefficients of the order-dependent terms exists between the first and the second neighbor jump mechanisms. An analysis of experimental data on diffusion in β-brass shows that a second neighbor jump mechanism should be operating. The conditions under which it is possible to apply Kirkwood's or the quasi-chemical theory to the problem of the migration energy are discussed. Formulae have been derived for the vacancy concentration, the migration energy and the activation energy for diffusion using Kirkwood's and the quasi-chemical theory. All of them contain a short range order dependent term above the critical temperature. Results obtained with Kirkwood's theory differ significantly from those obtained using Bragg-Williams theory only above and immediately below the critical temperature. The functional form of the activation energy for diffusion derived for β-brass should also be valid for b.c.c. ferromagnets. A good agreement of the activation energy vs. 1 T is obtained for the experimental data on self-diffusion in Fe above T c .