Near-coincidence orientations in hexagonal materials: from a unified twin approach to a quasiperiodic description

Abstract

In materials belonging to the hexagonal crystal family (hexagonal or trigonal crystal systems), for which the irrationality arises primarily from the lattice parameters, the concept of near-coincidence orientation has to be introduced in order to characterize experimental grain boundaries. The practical use of this concept can be simplified if a twin approach is introduced: high-Σ specific coincidence orientations are described as a deviation from very low-Σ twin orientations defined among a unique set of limiting Σ. Consequently, for real hexagonal or trigonal materials, each orientation relationship defined by a quaternion (m, u, v, w), all relatively prime integers, can be described, for any c/a, uniquely by a quasiperiodic arrangement of elementary `twin' coincidences. Experimental cases of interfaces in hexagonal and rhombohedral crystals (h.c.p. metals, tungsten carbide, alumina) are analysed.