New procedures for quantitative studies of diffuse X-ray scattering

Equations are derived for errors due to counting statistics in the determination of local order parameters and interatomic displacements from the diffuse X-ray scattering from solid solutions or nonstoichiometric compounds. The Georgopoulous–Cohen procedure is employed, which permits the determination of displacements for individual (AA and BB) pairs. It is shown that certain analysis procedures and a large variation in the ratio of scattering factors through the measured volume in reciprocal space improve the accuracy of the separation of the various contributions to the intensity with this procedure, particularly with respect to the terms due to displacements. Therefore, a short-wavelength radiation (Mo Kα, for example) is sometimes desirable. Weighting the measured intensities with respect to the counting errors also improves the separation. The new procedures also facilitate the analysis of high-temperature measurements and data from ternary systems.