Crystallography of deformation by twin boundary movements in indium-thallium alloys

Abstract

The geometrical effects of steps (“twinning dislocations”) in the (101) twin boundaries of facecentered tetragonal crystals are outlined. By introduction of edge-type twinning dislocations, a set of parallel twins may be tapered uniformly to give a single crystal lattice, rotated slightly with respect to one of the twin orientations. The tapering is equivalent to a macroscopic shear, approximately on the (101̄)-plane of the untwinned lattice. The deformation of specimens consisting of sets of fine parallel twins is considered in detail. A distribution of edge twinning dislocations gives uniform plane bending to a maximum curvature determined by the orientation of the specimen. The geometrical results are closely related to those derived by Nye for glide deformation, but the condition for maximum bending is different. The variation of strain energy with twin thickness is calculated; minimum total energy corresponds to a twin thickness of' ~10 −3 cm. Three-dimensional bending is possible if screw-type twinning dislocations are introduced, though Nye's tensor relations cannot be satisfied exactly. For pure screw bending, the specimen has the approximate shape of a solid torus. The predictions were confirmed by experimental work on indium-thallium alloys. At room temperature, the behaviour is perfectly plastic, but the material exhibits rubber-like elastic properties when deformed at lower temperatures. The transition between plastic and pseudo-elastic behaviour is governed by a temperature controlled relaxation process. There is also a high temperature rubber-like behaviour, which may be explained by postulating stress induced transformation from the cubic to the tetragonal form above the normal M s , temperature.