Influence of faceting upon the equilibrium shape of nuclei at grain boundaries-I. Two-dimensions

The exact equilibrium shape of two-dimensional nuclei (or of any other small particles) at a grain boundary which is constrained to remain planar, both in the presence and the absence of a facet at one orientation of the nucleus-matrix boundary, is found by minimizing the total interfacial free energy subject to the constraint of a constant volume. These shapes, as well as those obtained by allowing the grain boundary to pucker in order to achieve force balances at its junctions with the nucleus, are also derived graphically through a new generalization of the Wulff construction. The free energy of activation, ΔG*, for the formation of critical nuclei in these shapes is calculated as a function of the angle between the facet and the grain boundary under representative conditions of relative interfacial free energy; ΔG* is found to be significantly less at small values of this angle under most circumstances, and also to be smaller at puckered than at planar grain boundaries, though often by negligible amounts