International audienceThe structure of a near-Sigma 9 symmetrical tilt boundary of a silicon bicrystal is observed at atomic scale by high-resolution transmission electron microscopy using the [0,1,1] common tilt axis. The experimentally observed positions of atomic rows nearby the boundary are compared to theoretically predicted row positions using an elastic displacement field u generated by a planar semicoherent interface containing a periodic array of edge DSC dislocations. These dislocations accommodate a small angular departure (1.70 degrees) fromthe perfect Sigma 9 twin orientation, as a small-angle symmetrical tilt grain boundary accommodates the misorientation. The investigation includes a large region containing two successive dislocation cores (spacing 6.1 nm). A good agreement between the experimental and theoretical atomic rows is obtained, except in the vicinity of the dislocation cores. This observation shows that the elastic field of the DSC dislocation array behaves like that of a planar periodic semicoherent interface separating two different crystals: it does not generate a long-range displacement or rotation field. (C) 201
Inclined threading dislocations (TDs) piercing the oriented free surface of a crystal are currently observed after growth of oriented thin films on substrates. Up to date the unique way to treat their anisotropic elastic properties nearby the free surface region is to use the integral formalism, which assumes no dislocation core size and needs numerical double integrations. In a first stage of the work, a new and alternative approach to the integral formalism is developed using double Fourier series and the concept of a finite core size, which is often observed in high-resolution transmission electron microscopy. In a second stage, the integral formalism and the Fourier series approaches are applied to the important case of a TD piercing the basal free surface of a hexagonal crystal. For this particular geometry, easy-to-use expressions are derived and compared to a third approach previously known for a plate-like crystal. Finally, the numerical interest and the convergence of these approaches are tested using the basal free surface of the GaN compound, in particular for TDs with Burgers vectors c and (a + c).
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