This article presents 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. Analytical expressions are derived 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 ÁQ/Q < 5 Â 10 À5 in all directions, ultimately enabling highprecision mapping of lattice strain and tilt. The approach is demonstrated on three types of samples: a multi-scale study of a large diamond crystal in transmission, magnified section topography on a 140 mm-thick SrTiO 3 sample and a reflection study of misfit dislocations in a 120 nm-thick BiFeO 3 film epitaxially grown on a thick substrate. With optimal contrast, the half-widths at half-maximum of the dislocation lines are 200 nm. A. C. Jakobsen et al. Mapping of dislocation networks 127 Figure 5Projection images of a large single-crystal diamond in the transmission experiment. (Left) Nearfield detector image with no X-ray objective and (right) corresponding dark-field image acquired with the diffraction microscope, both for À 0 = 0.002 . The magnification of the microscope is M ¼ 16:2. The direction of the rotation axis is marked by an arrow.q q 2 andq q roll are parallel to the x and y axes of these subfigures, respectively.

No abstract

Dark-field X-ray microscopy is a new full-field imaging technique for nondestructively mapping the structure of deeply embedded crystalline elements in three dimensions. Placing an objective in the diffracted beam generates a magnified projection image of a local volume. By placing a detector in the back focal plane, high-resolution reciprocal space maps are generated for the local volume. Geometrical optics is used to provide analytical expressions for the resolution and range of the reciprocal space maps and the associated field of view in the sample plane. To understand the effects of coherence a comparison is made with wavefront simulations using the fractional Fourier transform. Reciprocal space mapping is demonstrated experimentally at an X-ray energy of 15.6 keV. The resolution function exhibits suppressed streaks and an FWHM resolution in all directions of ÁQ/Q = 4 Â 10 À5 or better. It is demonstrated by simulations that scanning a square aperture in the back focal plane enables strain mapping with no loss in resolution to be combined with a spatial resolution of 100 nm.