Section 2.5.1.5. Corrections

(a) Temperature effects. The effect of thermal vibrations on the integrated intensities is expressed by the Debye–Waller factor in the same way as for standard angle-dispersive methods. Notice that irrespective of the method used. The contribution of the thermal diffuse scattering to the measured integrated intensities can be calculated if the elastic constants of the sample are known (Uno & Ishigaki 1975).

(b) Absorption. The transmission factor ) for a small sample bathed in the incident beam and the factor for a large sample intercepting the entire incident beam are the same as for monochromatic methods (Table 6.3.3.1 ). However, when they are applied to energy-dispersive techniques, one has to note that the absorption corrections are strongly varying with energy. In the special case of a symmetrical reflection where the incident and diffracted beams each make angles with the face of a thick sample (powder or imperfect crystal), one has where μ(E) is the linear attenuation coefficient evaluated at the energy associated with the Bragg reflection.

(c) Extinction and dispersion. Extinction and dispersion corrections are applied in the same way as for angle-dispersive monochromatic methods. However, in XED, the energy dependence of the corrections has to be taken into account.

(d) Geometrical aberrations. These are distortions and displacements of the line profile by features of the geometry of the apparatus. Axial aberrations as well as equatorial divergence contribute to the angular range of the Bragg reflections. There is a predominance of positive contributions to , so that the diffraction maxima are slightly displaced to the low-energy side, and show more tailing on the low-energy side than the high-energy side (Wilson, 1973).

(e) Physical aberrations. Displacements due to the energy-dependent absorption and reflectivity of the sample tend to cancel each other if the incident intensity, , can be assumed to be constant within the energy range of Bragg reflection. With synchrotron radiation, varies rapidly with energy and its influence on the peak positions should be checked. Also, the detector response function will influence the line profile. Low-energy line shapes are particularly sensitive to the deadlayer absorption, which may cause tailing on the low-energy side of the peak. Integrated intensities, measured as peak areas in the diffraction spectrum, have to be corrected for detector efficiency and intensity losses due to escape peaks.