B. Croset

Direct observation of elastic displacement modes by grazing-incidence X-ray diffraction

It is demonstrated that grazing-incidence X-ray diffraction is a direct tool for measuring the elastic displacement modes near the surface of a crystal. Due to the fact that X-ray diffraction is a Fourier transform of the electronic density, and thus, of the atomic positions, elastic displacement modes appear as additional spots in the reciprocal space. Their characteristics can be directly derived from the elastic constants of the material. Measuring the amplitude of the diffracted wave for these peaks allows direct determination of the force distribution at the surface, which is at the origin of the elastic displacements. Various examples of such determinations are given for self-organized surfaces and for vicinal surfaces.

EQUILIBRIUM CONFIGURATIONS OF TWO-DIMENSIONAL STRESSED DOMAINS ON THE SURFACE OF ISOTROPIC AND CUBIC CRYSTALS

In this paper, we derive analytical formulations of the elastic energy of a stressed domain on a crystalline substrate. Taking care of the singularity of the elastic Green function at r = 0, we obtain a universal expression for the isotropic case. By using the analogy between electric dipolar and elastic interactions, we developed similar analytical calculations for the (001) surface of a cubic crystal.We showed that the anisotropy of the boundary energy and the anisotropy of the substrate govern the shape of the domains, favoring either compact shapes or stripe configurations. The analytical approach adopted in this paper also allows us to discuss the role of elastic anisotropy for the existence of attractive interactions between domains.