Grain Boundary Curvatures in Annealed Beta Brass
The polycrystalline structure experiences two mechanisms of grain boundary area reduction in the process of grain growth on annealing. One is the readjustment of junction angles on the occurrence of a grain encounter, i.e. the first time “Weting” of two grains. As soon as the threshold of a grain encounter is crossed a rather sharp but localized drop in boundary area ensues. This correction is relatively rapid at first, gradually slowing down as the equilibrium angles for the local junctions are approached. The various junction angles do not necessarily satisfy the angles required by the faces of various polyhedra involved and this discrepancy is satisfied energetically by producing a net spherical curvature of the boundaries. The actual curvature may not always be spherical because there are other geometrical requirements when the polyhedra are not regular or not symmetrical. But the net curvature tends toward spherical curvature because this yields the minimum surface for a given volume, which is dictated by the tendency toward minimization of boundary free energy. The second mechanism takes place as the grains with a net convex curvature diminish in size, the net diffusion favoring atomic escape from such grains. This is a relatively slow process in general but a necessary one, since it leads to further encounters, which repeat the cycle just described. The process may be somewhat rapid for those grains that are approaching extinction.
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