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Sense and sign in wave and crystal dislocations

Dislocations in waves and in crystals are compared, in tutorial style, with particular emphasis on signs and senses. Reconnection of dislocations and the disappearance of a closed loop are treated as examples. There is a fundamental difference between the regularized phase gradient of a wave dislocation or wave vortex, as defined in a recent paper, and the Burgers vector of a dislocation in a crystal; the latter, as is well known, is not strictly a vector at all, because, to define it, a sense of direction for the dislocation line has to be chosen arbitrarily. The Burgers vector in a crystal is more analogous to the phase circulation of ± 2π around a wave dislocation. The new vector now associated with a wave dislocation could be called, not the Burgers vector, but simply ‘the phase gradient vector’. A new result is to see that, by an isotropic scaling, two parallel straight dislocation lines of opposite sign have identical phase patterns in the plane normal to them, regardless of whether they are of pure edge, or mixed edge/screw type.