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The Rietveld method
Albinati, A. and Willis, B. T. M.  International Tables for Crystallography (2006). Vol. C, ch. 8.6, pp. 710-712 [ doi:10.1107/97809553602060000614 ]
... by fitting the entire profile of the diffraction pattern to a calculated profile, is provided. The basic theory of Rietveld refinement ... by fitting the entire profile of the diffraction pattern to a calculated profile. There is no intermediate step of extracting structure ... 1967, 1969) to the refinement of neutron intensities recorded at a fixed wavelength. Subsequently, it has been used successfully for ...

Preferred orientation and texture
Albinati, A. and Willis, B. T. M.  International Tables for Crystallography (2006). Vol. C, Section 8.6.2.4, p. 712 [ doi:10.1107/97809553602060000614 ]
... and texture 8.6.2.4. Preferred orientation and texture Preferred orientation is a formidable problem which can drastically affect the measured intensities. A simple correction formula for plate-like morphology was given by ... in the Rietveld refinement code by Von Dreele (1997). A general model of the texture has also been described ...
     [more results from section 8.6.2 in volume C]

Basic theory
Albinati, A. and Willis, B. T. M.  International Tables for Crystallography (2006). Vol. C, Section 8.6.1, pp. 710-711 [ doi:10.1107/97809553602060000614 ]
... squares minimization of the residual is the intensity measured at a point i in the diffraction pattern corrected for the background ... matrix [equation (8.1.2.3) ]. The number of independent observations in a powder pattern is determined by the extent of overlapping of ... number has been proposed by Altomare et al. (1995) and a more rigorous statistical estimate has been described by Sivia ( ...

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