Section 2.5.1.6. The Rietveld method

The Rietveld method (see Chapter 8.6 ) for refining structural variables has only recently been applied to energy-dispersive powder data. The ability to analyse diffraction patterns with overlapping Bragg peaks is particularly important for a low-resolution technique, such as XED (Glazer, Hidaka & Bordas, 1978; Buras, Gerward, Glazer, Hidaka & Olsen, 1979; Neuling & Holzapfel, 1992). In this section, it is assumed that the diffraction peaks are Gaussian in energy. It then follows from equation (2.5.1.7) that the measured profile of the reflection k at energy corresponding to the ith channel of the multichannel analyser can be written where is a constant, is evaluated at the energy , and is the full width (in energy) at half-maximum of the diffraction peak. is a factor that accounts for the absorption in the sample and elsewhere in the beam path. The number of overlapping peaks can be determined on the basis of their position and half-width. The full width at half-maximum can be expressed as a linear function of energy: where U and V are the half-width parameters.