Coincidence and Near-Coincidence Grain Boundaries in HCP Metals

Coincidence concepts, commonly used in treating the structures of grain boundaries in cubic metals, are used to develop coincidence structural-unit models for grain boundaries in hcp metals. In doing this the concept of coincidence is extended to one of near- coincidence, in which the shared atoms at the boundary need not occupy exact coincidence sites but instead occupy compromise positions between two nearly coincidence lattice sites. This extension allows one to define near-coincidence-site lattices (near-CSL’s) from which are derived short-period near-coincidence structural units. Exact and near-CSL’s in the common hcp metals are tabulated for rotations about [0001], <1010>, and <1120>, and short-period coincidence structural units are presented. Geometric models of a variety of symmetric and asymmetric <1010> tilt boundaries are developed as examples to show how a relatively few coincidence structural units are combined in the structures of both simple and complex boundaries. Although hcp boundaries are treated here, the approach is quite general and can be applied to any crystal structure.