Evaluation of 3D small-angle scattering from non-spherical particles in single crystals

Three-dimensional small-angle scattering is discussed as a tool for investigation of anisometric particles in single-crystalline alloys. The measurement and evaluation methods take advantage of the well defined orientation relation between the precipitates and the matrix in alloys. The determination of shape, size and orientation of precipitates from the scattering in several planes of reciprocal space is discussed for the example of ellipsoids and plates. Shape and orientation of ellipsoids with small aspect ratio can be determined by deviations of the scattering intensity from spherical symmetry in certain planes of reciprocal space. Particle size is obtained from one-dimensional slices along certain directions. The small-angle scattering of plate-like particles with large aspect ratio is concentrated along radial streaks in reciprocal space. Slices along and across these streaks allow the determination of the plate thickness as well as size and aspect ratio of the plate surface. In addition, the evaluation of such `off-center' slices provides a resolution enhancement of almost one order of magnitude compared to the conventional Guinier method applied to spherically averaged data.