Geometry and Fundamentals

The geometry of a two-dimensional X-ray diffraction (XRD2) system can be explained by three distinguishable and interrelated geometry spaces, each defined by a set of parameters. The three geometry spaces are the diffraction space, detector space, and sample space. This chapter compares conventional X-ray diffraction and XRD2. It describes the geometric definition of diffraction cones in the laboratory coordinate system. In an XRD2 system, three rotation angles are necessary to define the orientation of a sample in the diffractometer. These three rotation angles can be achieved either by a Eulerian geometry, a kappa geometry or other kind of geometry. The three angles in Eulerian geometry are 𝜔 (omega), 𝜓 (psi), and 𝜙 (phi). The diffraction patterns displayed in reciprocal space have been frequently used to visualize or analyze samples with highly oriented structures, diffuse scattering from crystal defects, and thin films.