It was recalled that experiments showed that misfit dislocations were either distributed homogeneously, with an average spacing of b/f (where b was the magnitude of the Burgers vector and f was the lattice mismatch), or were clustered into pile-ups and periodic patterns if the film thickness was sufficiently great. A kinetic description of the dislocation dynamics in thin films had been proposed which did not consider spatial interactions in any great detail. A generalization of the description was presented here which included the spatial dependence of the internal stress. This permitted a relationship to be deduced between the wavelength of misfit dislocation patterns and the characteristic range of the misfit dislocation stress field. This was the main driving force for patterning. The full integral representation of the internal stress was used. This avoided certain phenomenological assumptions and led to a better understanding of the relationship, between length scales, that governed the selection of a well-defined misfit dislocation pattern wavelength.

Non-Local Interactions and Patterning of Misfit Dislocations in Thin Films. N.Liosatos, A.E.Romanov, M.Zaiser, E.C.Aifantis: Scripta Materialia, 1998, 38[5], 819-26