International
Tables for Crystallography Volume C Mathematical, physical and chemical tables Edited by E. Prince © International Union of Crystallography 2006 |
International Tables for Crystallography (2006). Vol. C. ch. 2.5, p. 86
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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.
References
Buras, B., Gerward, L., Glazer, A. M., Hidaka, M. & Olsen, J. S. (1979). Quantitative structural studies by means of the energy-dispersive method with X-rays from a storage ring. J. Appl. Cryst. 12, 531–536.Google ScholarGlazer, A. M., Hidaka, M. & Bordas, J. (1978). Energy-dispersive powder profile refinement using synchrotron radiation. J. Appl. Cryst. 11, 165–172.Google Scholar
Neuling, H. W. & Holzapfel, W. B. (1992). Rietveld analysis for energy dispersive X-ray diffraction under high pressure with synchrotron radiation. High Press. Res. 8, 665–660.Google Scholar