Rietveld whole-pattern-fitting method

YOUNG ET AL. Rietveld Whole-Pattern-Fitting Method... 

During the last five years, a powerful new method of getting crystal structural information from powder diffraction patterns has become widely used. Known variously as the Rietveld method, profile refinement1, or, more descriptively, whole-pattern-fitting structure refinement, the method was first introduced by Rietveld (X, 2) for use with neutron powder diffraction patterns. It has now been successfully used with neutron data to determine crystal structural details of more than 200 different materials in polycrystalline powder form. Later modified to work with x-ray powder patterns (3, X) the method has now been used for the refinement of more than 30 crystal structures, in 15 space groups, from x-ray powder data. Neutron applications have been reviewed by Cheetham and Taylor (5) and those for x-ray by Young (6). 

The whole-pattern-fitting structure-refinement method, which was first introduced by Rietveld and used for neutron diffraction powder patterns, does yield from x-ray diffraction patterns correct, refined structural information for linear polymers. Remarkably precise lattice parameters are obtained incidentally in the use of the method. The method lends itself to improved estimations of the fraction of amorphous and crystalline materials, or of two polymorphic forms, present. As improved profile functions come in to use, the method promises to provide crystallite size information, almost as a spin-off benefit. 

In the pharmaceutical community, quantitative analyses has conventionally been based on the intensity of a characteristic peak of the analyte. It is now recognized that phase quantification will be more accurate if it is based on the entire powder pattern.This forms the basis for the whole-powder-pattern analyses method developed in the last few decades. Of the available methods, the Rietveld method is deemed the most powerful since it is based on structural parameters. This is a whole-pattern fitting least-squares refinement technique that has also been extensively used for crystal structure refinement and to determine the size and strain of crystallites. 

Since the early 1980s, a new way of quantifying structural defects has appeared. It consists of applying the developments implemented in stmctural analysis to the increase in peak width [KEl 83, LUT 90, THO 87b, LEB 92, LEB 99], This method, which relies on Rietveld s stmctural analysis method, consists of a whole pattern fitting of the diffraction pattern. 

The Rietveld Fit of the Global Diffraction Pattern. The philosophy of the Rietveld method is to obtain the information relative to the crystalline phases by fitting the whole diffraction powder pattern with constraints imposed by crystallographic symmetry and cell composition. Differently from the non-structural least squared fitting methods, the Rietveld analysis uses the structural information and constraints to evaluate the diffraction pattern of the different phases constituting the diffraction experimental data. 

Rietveld refinement [25, 26] is a method of whole pattern refinement, where a calculated diffraction pattern for a structure model is a least-squares fit to an observed diffraction pattern. Originally, it was used as a means of verifying proposed structure models. For zeolites, Rietveld refinement is still used for the same purpose and provides details of the structure including atomic positions of framework atoms and cation sittings. Data with accurate intensities and well-resolved peaks are needed for the most accurate work, and so often a synchrotron source is used for data collection since it can provide higher intensity and peak resolution than an in-house diffractometer. However, modern in-house diffractometers often provide good enough data for some refinements. 

The view about line profile analysis given in this chapter is pessimistic, it is the consequence of the complexity of the Bragg peak shapes as they occur from poorly-crystallized material. More optimistic is the future of the main whole powder pattern fitting applications (decomposition or Rietveld methods) that have moved beyond the initial stages, enabling structure determinations (almost routinely) and refinements (routinely) of moderately complex structures to even complex crystal structures such as proteins (sometimes). 

The Rietveld method is a refinement technique in which the whole powder pattern is fitted by varying a number of instrumental and stmctural-model parameters. The successful use of the method is directly related to the quality of both the diffraction data and the structural model being refined. The Rietveld method is widely available for the structure refinement of powder data through such programs such as GSAS, FullProf, and Rietan. ... 

The strength of the Rietveld method lies in the refinement of the structure parameters of the whole powder sample not just of one single crystal. Rietveld [114] recognized that it is by no means necessary to allocate the measured intensities to individual reflections in a one-dimensional powder pattern. Instead, it is better to measure a diffraction pattern as exactly as possible and use it in its entirety as the basis for refinement of the structure parameters. Parameters such as the atom coordinates, temperature coefficients, and scaling factors are fitted to the diffraction data by a least-squares procedure. 

---