Analytical evaluation of thermal diffuse scattering contributions to integrated X-ray intensities in the vicinity of a Bragg reflection

The first order thermal diffuse scattering contribution to integrated Bragg scattering intensities for monatomic, crystalline lattices has been analytically evaluated. Parallel arguments for evaluation of the integrated Bragg intensity and the integrated thermal diffuse scattering intensity are developed for a general diffractometer intensity scan. The resulting general expressions are reduced to a simplified form for several situations. In particular, the two standard integrated intensity scans, an ω-scan and an ω/2θ-scan, are considered. Comparison is made between the results of this calculation and previously published calculations, as well as with recently published experimental measurements of thermal diffuse scattering effects. The variation of the thermal diffuse scattering contributions to the measured intensity is discussed through consideration of a dimensionless parameter, which is independent of both temperature and the diffracting material. This parameter depends only on the experimental constants relating to the intensity measurement and is examined as a function of the detection window size, the scan width and type, and the diffraction angle. It is found, for the situations considered, that the ratio of the thermal diffuse scattering to the Bragg scattering tends to show a pronounced maximum in the intermediate-high angle region (60 ° ≲ 0 ≲ 80 °).