Analysis Strategy of Powder Diffraction Data with 2-D Detector

To gain a clearer understanding of orientation and grain deformation of crystalline materials, x-ray powder diffraction has played an integral role in extracting three-dimensional structural information from one-dimensional diffraction patterns. Powder diffraction models identical geometry to the intersection of a normal right cone with a plane. The purpose of this paper is to develop a general expression defining the conic sections based on the geometry of a powder diffraction experiment. Applying the derived formulation of a diffraction arc to experimental data will give insight to the molecular and structural properties of the sample in question. Instead of using complex three-dimensional Euclidian geometry, we define the problem solving technique with a simpler two-dimensional transformation approach to arrive at the final equation describing the conic sections. Using the diffraction geometry parameters, we can use this equation to calibrate the diffractometer from the diffraction pattern of a known reference material, or to determine the crystalline lattice structure of the compound