Géométrie des relations d'orientation dans la symétrie hexagonale. Dimension de la coïncidence

The main characteristics of the orientation relationship between two hexagonal lattices are simply denoted by four parameters (M, U, V, W). In the case of a tridimensional coincidence orientation relationship, for a rational value of (c/a)², these four parameters become four prime integers (m, un, vn, wn). The equivalence class of the orientation relationship may be represented by 12 equivalent descriptions for which the indices of the rotation axes are noted on the basis of one crystal. This original representation can lead to the concept of spatial distribution of the equivalent rotation axes, a distribution which is strongly related to the c/a ratio. In real materials (c/a irrational), bidimensional coincidence orientation relationships can describe a large number of grain boundaries.