Mesoscopic structures in ferroelastic crystals: Needle twins and right-angled domains

The shape and orientation of twin walls are calculated within the limits of elasticity theory. Single twin walls are oriented along lattice planes which are determined by the condition that the variation in the spontaneous strain through the twin walls does nor generate secondary strain fields. The twin walls have a finite thickness which is described by the Landau-Ginzburg theory. Two twin walls can bend towards each other and form a wedge-shaped junction. The trajectories of the twin walls in the plane perpendicular to the junction are needle shaped so that domains enclosed by the twin walls are commonly called 'needle domains'. It is shown that the actual shape of the trajectory varies widely between straight lines (i.e. planar walls near the junction) to parabolic or exponential (i.e. curved twin walls near the junction which make the needle tip appear blunt). The essential physical parameters which determine the shape of the trajectory are, firstly, the energies to bend a wall segment, secondly, the energy required to rotate a planar wall segment in an elastically anisotropic medium and, thirdly, the Peierls energy which is required to move a walls segment laterally. Various characteristic trajectories are discussed including those of junctions between orthogonal walls.