Neutron powder diffraction pattern information

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). 

Early data analysis attempted to extract values of the individual structure factors from peak envelopes and then apply standard single crystal methods to obtain structural information. This approach was severely limited because the relatively broad peaks in a powder pattern resulted in substantial reflection overlap and the number of usable structure factors that could be obtained in this way was very small. Consequently, only very simple crystal structures could be examined by this method. For example, the neutron diffraction study of defects in CaF2-YF3 fluorite solid solutions used 20 reflection intensities to determine values for eight structural parameters. To overcome this limitation, H. M. Rietveld realized that a neutron powder diffraction pattern is a smooth curve that consists of Gaussian peaks on top of a smooth background... 

The very existence of the powder diffraction pattern, which is an experimentally measurable function of the crystal structure and other parameters of the specimen convoluted with various instrumental functions, has been made possible by the commensurability of properties of x-rays and neutrons with properties and structure of solids. As in any experiment, the quality of structural information, which may be obtained via different pathways (two possibilities are illustrated in Figure 2.62 as two series of required steps), is directly proportional to the quality of experimental data. The latter is usually achieved in a thoroughly planned and well executed experiment as will be detailed in Chapter 3. Similarly, each of the data processing steps, which were described in this chapter and are summarized in Figure 2.62, requires knowledge, experience and careful execution, and we will describe them in practical terms in Chapters 4 through 7. 

Figure 8 shows the relatively simple powder diffraction pattern of polycrystalline silicon, measured by time-of-flight neutron diffraction. Each allowed Bragg peak for the crystal structure is observed as a sharp peak in the diffraction pattern. A fundamental difference between single crystal and powder diffraction is that the single crystal diffraction pattern has the full directional information described by Equation [28], whereas for the powder diffraction pattern this information has been collapsed down into a onedimensional function. This difference has two important consequences firstly, the loss of directional information makes it very much more difficult to... 

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. 

Although single crystal diffraction is the most powerful method for studying the structure of crystals, the powder diffraction method is also frequently used to reveal structural information for crystalline materials. In this case the sample is not a single crystal, but is instead a powder which contains numerous microcrystals, such that all orientations are equally likely. The observed diffraction pattern is then an average of Equation [28] over all possible relative orientations between the momentum transfer vector Q and the crystal lattice. The measured diffraction pattern does not depend on the orientation between the sample and the neutron beam, and it is usual to identify each Bragg peak in the diffraction pattern by its d-spacing, di,y, defined by... 

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