Twist,tilt, and symmetric grain boundaries in hexagonal materials

Grain boundaries of characteristic geometry, e.g., twist, tilt, and symmetric boundaries are often used as reference boundaries in analyses of boundary networks in polycrystalline materials. This article deals with the issue of proper identification of characteristic boundaries in the case of materials with hexagonal D _6h symmetry. To identify all boundaries of characteristic types, both analytical calculations and numerical searches are used. The first approach provides exact parameters of the characteristic boundaries, whereas the second one gives boundaries which can be classified as characteristic if some tolerance is allowed. In both methods, all symmetrically equivalent boundary representations are taken into consideration. The obtained sets of twist, tilt, symmetric, and 180°-tilt boundaries are presented in the form of two-dimensional maps containing stereographic projections of the corresponding boundary plane normals for selected grain misorientations. These diagrams facilitate interpretation of experimental distributions of grain boundaries; with the representation used, they can be directly linked to experimental distributions. Examples of such diagrams for lattice parameter ratios c/a of $\sqrt{5/2}$ and $\sqrt{20/21}$ are presented. They are compared to example boundary distributions in Ti alloy and distributions of WC/WC boundaries in WC–Co composites available in the literature.