Width of a dislocation
The width of a dislocation gives a measure of the degree of disruption a dislocation creates with respect to the perfect lattice. If the dislocation is regarded as the transition between slipped and unslipped areas of a slip plane, then the width of the dislocation is a measure of the sharpness of the transition. Formally, the edge dislocation width w is defined as the distance over which the disregistry is greater than one quarter of the magnitude of the Burgers vector, b. The disregistry is the magnitude of the displacement of the atoms from their perfect crystal positions.
At the centre of a perfect edge dislocation, the disregistry is always b/2.
When w is several atomic spacings in dimension, the dislocation is wide; if w is of the order of one or two atomic spacings, it is narrow. Dislocation glide occurs most easily in wide dislocations - these are found in simple metals with simple close-packed crystal structures, hence these materials are ductile. Ceramics, for example, tend to have narrow dislocations, and are hard and brittle as a result. A mathematical treatment of this relationship can be seen here.