A MODEL FOR DIFFUSION ON CUBIC LATTICES AND ITS APPLICATION TO EARLY STAGES OF ORDERING

A theory is given for diffusion on cubic lattices in which an allowance is made for the effect of sharp composition gradients on the driving force. The treatment is similar in intent to those previously given by Hillert and by Cahn, but we have eliminated the regular-solution assumption of the former and the continuum approximation of the latter. An expression for diffusion is derived in the form of a differential-difference equation, and a simple analytic solution is obtained for the limiting case of small composition, fluctuations. This solution is then used to determine the kinetics and morphology at the early stages of ordering as described by the time dependence of the Fourier spectrum of the composition variation. It is found that many of the characteristics of ordering are the inverse of those for spinodal decomposition. © 1969.