X-ray scattering by anisotropic elastic deformations around vacancies in ordered smectic phases

Smectic B phases are 3D ordered phases, but they are not perfect crystals. In these phases there exist strings of molecules, the order of which is easily disturbed by the existence of vacancies. We have shown in previous papers that a significant signature of these defects on X-ray diffraction pattems is the presence of a white diffuse line. The hexagonal symmetry of the medium generates an anisotropic deformation field around each defect. We relate the shape of the white diffuse zone to the elastic constants of the material.