Topological Signature of Dislocations

Historically, one of the most ingenious venues within which to view lattice defects was through the use of bubble rafts. The basic idea is that a series of soap bubbles arrange themselves in a crystalline form which is occasionally disturbed by defects including dislocations. A more modem analog is provided by colloidal crystals in which colloidal particles crystallize and may be viewed via optical microscopy. As a supplement to the schematic of fig. 8.9, fig. 8.11 shows a dislocation in a colloidal crystal. 

A dislocated crystal has a distinct geometric character from one that is dislocation-free. From both the atomistic and continuum perspectives, the boundary between slipped and unslipped parts of the crystal has a unique signature. Whether we choose to view the material from the detailed atomic-level perspective of the crystal lattice or the macroscopic perspective offered by smeared out displacement fields, this geometric signature is evidenced by the presence of the so-called Burgers vector. After the passage of a lattice dislocation, atoms across the slip plane assume new partnerships. Atoms which were formerly across from 

The Burgers circuit concept introduced above from the discrete perspective has a continuum analog. Mathematically, the origin of this analog is the fact that there is a jump in the continuum displacement fields used to characterize the geometric state of the body. Recall that above we described the Volterra procedure in which the body is cut and rejoined after a relative translation operation. The resulting displacement jump reveals itself upon consideration of the integral 

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