Surface effects associated with dislocations in layer crystals

Dislocation configurations in thin foils cannot be accurately interpreted unless the effects of anisotropy and surfaces on the stress and energies of edge and screw dislocations are known. Expressions for these effects are derived here for a semi-infinite hexagonal crystal with dislocations in the basal plane. It is then shown that in plate-like crystals, as used in electron-microscopic investigations,
the finite thickness of the specimen leads to observable effects on the dislocation patterns. In particular, the width of a ribbon decreases as it approaches the surface, due to the reduced repulsion between the partials, so that care is needed in deducing stacking fault energies from ribbon widths. Also the energy of a dislocation is a function of its distance from a surface, so that if it is crossed by a surface step it suffers a “refraction” which, in simple cases, follows Snell’s law. It is further shown that dislocations will tend to be aligned
with surface steps, and the interaction energy between a step and a parallel dislocation line can thus be derived from experimental data. Finally, a method is suggested for obtaining information on the elastic constants from electron microscopic data.