Partial dislocations

Abstract: Dislocations are common defects in solids, yet all crystals begin as dislocation-free nuclei. The mechanisms by which dislocations form during early growth are poorly understood. When nanocrystalline materials grow by oriented attachment at crystallographically specific surfaces and there is a small misorientation at the interface, dislocations result. Spiral growth at two or more closely spaced screw dislocations provides a mechanism for generating complex polytypic and polymorphic structures. These results are of fundamental importance to understanding crystal growth.

Abstract: When an ultrasonic pulse, containing, say, ten quasi-sinusoidal oscillations, is reflected in air from a rough surface, it is observed experimentally that the scattered wave train contains dislocations, which are closely analogous to those found in imperfect crystals. We show theoretically that such dislocations are to be expected whenever limited trains of waves, ultimately derived from the same oscillator, travel in different directions and interfere - for example in a scattering problem. Dispersion is not involved. Equations are given showing the detailed structure of edge, screw and mixed edge-screw dislocations, and also of parallel sets of such dislocations. Edge dislocations can glide relative to the wave train at any velocity; they can also climb, and screw dislocations can glide. Wavefront dislocations may be curved, and they may intersect; they may collide and rebound; they may annihilate each other or be created as loops or pairs. With dislocations in wave trains, unlike crystal dislocations, there is no breakdown of linearity near the centre. Mathematically they are lines along which the phase is indeterminate; this implies that the wave amplitude is zero.