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Dislocations are line defects in crystals. Dislocation glide through the lattice causes one plane of molecules to slip over another, and this provides the mechanism of plastic deformation. The primary slip plane in ice is the basal (0001) plane. In ice the glide and multiplication of dislocations has been very effectively studied by X-ray topography, and dislocation velocities have been determined. A particular problem concerning dislocation glide in ice is that the proton disorder presents a barrier to motion; this topic is analysed and compared with experiment. Stacking faults occur where the sequence of the (0001) layers of molecules is incorrect. Such faults are planar defects. They can be formed by the condensation of molecular point defects and are bounded by prismatic dislocations. A dislocation on a basal plane may dissociate into two partial dislocations separated by a ribbon of stacking fault. Other planar defects are grain and sub-grain boundaries.

This chapter describes the various techniques for obtaining X-ray topographs: single-crystal reflection topography (Berg-Barrett), single crystal transmission topography (Lang, section and projection topographs, synchrotron white beam topographs), and double or multiple-crystal topography (plane-wave, synchrotron topography, high-resolution). The formation of the images of the different types of individual defects and their contrast are discussed for the different experimental settings: dislocations, stacking faults, planar defects, and twins. It is shown how long range strains and lattice parameter variations can be mapped. Equal-strain and equal lattice parameter contours are described. Many examples of the use of topography for the characterization of materials are given.

In a Volterra dislocation the relative displacement by the Burgers vector appears abruptly in the dislocation core so that the core has no width. This leads to divergent stresses and strains, which are unrealistic. Hybrid models correct this failure by considering a balance of forces that results in a finite core width, and finite stresses and strains throughout. Interatomic forces tend to constrict the core and elastic forces tend to widen it. The Frenkel-Kontorova model comprises two interacting linear chains of atoms as a representation of an edge dislocation, with linear springs between adjacent atoms of each chain. The Peierls-Nabarro model assumes the core is confined to two parallel atomic planes sandwiched between elastic continua. This model enables the stress to move the dislocation to be calculated, and it leads to the concept of dislocation kinks. These models highlight the role of atomic interactions in affecting ductility.

Plastic deformation involves planes of atoms sliding over each other. The sliding happens through the movement of linear defects called dislocations. The phenomenology of dislocations and their characterisation by the Burgers circuit and line direction are described. The Green’s function plays a central role in Volterra’s formula for the displacement field of a dislocation and Mura’s formula for the strain and stress fields. The isotropic elastic fields of edge and screw dislocations are derived. The field of an infinitesimal dislocation loop and its dipole tensor are also derived. The elastic energy of interaction between a dislocation and another source of stress is derived, and leads to force on a dislocation. The elastic energy of a dislocation and the Frank-Read source of dislocations are also discussed. Problem set 6 extends the content of the chapter in several directions including grain boundaries and faults.