Influence of crystallography upon critical nucleus shapes and kinetics of homogeneous F.C.C.-F.C.C. nucleation—II. The non-classical regime

Abstract

In a previous paper, the shape of the critical nucleus and its influence upon nucleation kinetics were studied at near zero supersaturation, i.e. in the classical nucleation regime, using a discrete lattice plane model of the coherent interphase boundary energy. In order to extend these studies to higher supersaturations, a discrete lattice point model, based on a formalism developed by Cook, de Fontaine and Hilliard, is employed in the present paper and applied to homogeneous nucleation of coherent f.c.c. precipitates in an f.c.c. matrix. Concentration profiles and free energies of formation of critical nuclei are calculated from this model as a function of temperature and supersaturation and compared with results obtained from the Cahn-Hilliard continuum non-classical model and the previously used discrete lattice plane classical model. As predicted in effect by Cahn and Hilliard, the three models converge at very low supersaturations, and the continuum and the discrete lattice point (but not the classical discrete lattice plane) models also do so near the spinodal. Thus the most important differences between the continuum and the discrete lattice point models develop at intermediate supersaturations. The main advantages of the discrete lattice point model are that it allows the influence of crystalline anisotropy to be taken into account, permits treatment of arbitrarily steep variations in composition and provides a more convenient milieu for the incorporation of volume strain energy, as is done in the next paper in this series.