Mapping of individual dislocations with dark field x-ray microscopy

We present an x-ray microscopy approach for mapping deeply embedded dislocations in three dimensions using a monochromatic beam with a low divergence. Magnified images are acquired by inserting an x-ray objective lens in the diffracted beam. The strain fields close to the core of dislocations give rise to scattering at angles where weak beam conditions are obtained. We derive analytical expressions for the image contrast. While the use of the objective implies an integration over two directions in reciprocal space, scanning an aperture in the back focal plane of the microscope allows a reciprocal space resolution of DQ/Q < 5 · 10^-5 in all directions, ultimately enabling high precision mapping of lattice strain and tilt. We demonstrate the approach on three types of samples: a multi-scale study of a large diamond crystal in transmission, magnified section topography on a 140μm thick SrTiO₃ sample and a reflection study of misfit dislocations in a 120 nm thick BiFeO₃ film epitaxially grown on a thick substrate. With optimal contrast, the full width of half maximum of the dislocations lines are 200 nm, corresponding to the instrumental resolution of the microscope.