Institute of Metals Division - Dislocations in Plastically Bent Germanium Crystals

Densities and distributions of dislocations in plastically bent germanium crystals before and after annealing were studied. In the bent and annealed crystals, the theoretical relationship between radius of curvature and density of dislocations is confirmed. Before annealing, however, more dislocations are present than required, and these are distributed with a minimum at the neutral axis and maxima at the top and bottom surfaces. On annealing, three significant changes occur in the bent bars: 1) the average dislocation density is reduced, presumably by the annihilation of opposite signs; 2) dislocations migrate from the high density outside regions toward the low density neutral axis, thus producing the equilibrium distribution of dislocations; and 3) a polygonized structure is formed by movement of the dislocations into walls normal to the slip plane. ETCHING to reveal edge dislocations'-" offers a unique opportunity to study, in germanium single crystals, the functioning of dislocations in plastic deformation. Plastic bending is ideally suited to this purpose because it produces a static array of edge dislocations in an ideally plastic material which is predictable from the theory." " Nye" has given a rather complete treatment of the geometry of bent crystals in terms of dislocations. The density of excess dislocations is related to the radius of curvature of the slip plane of a bent crystal, as shown in Fig. 1, assuming the absence of macroscopic elastic stresses. The curvature of any plane in the zone of the bend axis is found by resolving the Burgers vector into that plane, so that for the usual case where the slip plane is inclined at some angle 0 to the neutral plane of the bar, the equation applies, with T equal to the radius of curvature of the neutral plane of the bent crystal. Two predictions which are relevant to this study may be made from Eq. 1. First, in crystals bent to various radii, the average excess dislocation density is inversely proportional to the radius and second, for a bar bent to a radius which is large compared with its thick-