Kinetics of crystalline configurations: III. An alloy that is inhomogeneous in one crystal direction

Abstract

The new theory of crystal kinetics, developed in two earlier papers (Physica 111A (1982) 591 and Physica 113A (1982) 117), here is applied to an alloy model with inhomogeneities. The latter are restricted to one crystal direction. Macroscopic rate equations are derived for the concentrations and for the nearest neigbour correlations. In a linearized form these are solved, with results that (for a positive interaction) closely agree with Cahn's macroscopic theory of spinodal decomposition. In systems with a negative interaction a long range order with a domain structure will develop below the transition temperature. In the limit of long.waves Fick's second law is recovered, with a diffusion coefficient depending on composition and temperature, but with a value for the associated nearest neighbour correlation that does not correspond to local equilibrium. For a few cases the full, non-linear, rate equations are integrated numerically. After an initially exponential growth, in agreement with the small amplitude analysis, the solutions show a rather sudden transition to a much slower coarsening process. The latter is markedly more sluggish for the ordering alloys than for the decomposing ones.