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. 8.6, p. 712

Preferred orientation is a formidable problem which can drastically affect the measured intensities. A simple correction formula for platelike morphology was given by Rietveld (1969). Ahtee, Nurmela, Suortti & Järvinen (1989) have shown how the effects of preferred orientation can be included in the refinement by expanding the orientation distribution in spherical harmonics. Quantitative texture analysis based on spherical harmonics has been implemented in the Rietveld refinement code by Von Dreele (1997). A general model of the texture has also been described by Popa (1992). It may be possible to remove or reduce the effect of preferred orientation by mixing the sample with a suitable diluent.
An additional problem is caused by particle size and strain broadening, which are not smooth functions of the diffraction angle. These effects can be taken into account by phenomenological models (e.g. Dinnebier et al., 1999; Pratapa, O'Connor & Hunter, 2002) or by an analytical approach such as that of Popa & Balzar (2002).
The determination of the elastic stresses and strains in polycrystals can be determined from diffraction line shifts using Rietveld refinement (Popa & Balzar, 2001).
References
Ahtee, M., Nurmela, M., Suortti, P. & Järvinen, M. (1989). Correction for preferred orientation in Rietveld refinement. J. Appl. Cryst. 22, 261–268.Dinnebier, R. E., Von Dreele, R. B., Stephens, P. W., Jelonek, S. & Sieber, J. (1999). Structure of sodium parahydroxybenzoate by powder diffraction: application of a phenomenological model of anisotropic peak width. J. Appl. Cryst. 32, 761–769.
Popa, N. C. (1992). Texture in Rietveld refinement. J. Appl Cryst. 25, 611–616.
Popa, N. C. & Balzar, D. (2001). Elastic strain and stress determination by Rietveld refinement: generalized treatment for textured polycrystals for all Laue classes. J. Appl. Cryst. 34, 187–195.
Popa, N. C. & Balzar, D. (2002). An analytical approximation for a sizebroadened profile given by the lognormal and gamma distributions. J. Appl. Cryst. 35, 338–346.
Pratapa, S., O'Connor, B. & Hunter, B. (2002). A comparative study of singleline and Rietveld strainsize evaluation procedures using MgO ceramics. J. Appl. Cryst. 35, 155–162.
Rietveld, H. M. (1969). A profile refinement method for nuclear and magnetic structures. J. Appl. Cryst. 2, 65–71.
Von Dreele, R. B. (1997). Quantitative texture analysis by Rietveld refinement. J. Appl. Cryst. 30, 517–525.