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Measurement of Crystalline Silica
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This information is taken from Smith and Gorter (1991). For addresses of authors, readers are directed to this reference.
With the availability of accurate digitized diffraction traces, peak analysis is becoming a very popular option for locating peaks and for determining the profile parameters. The terminology of profile analysis is confusing for diffractionists who are starting this type of analysis. The programs in this section are correctly classified as decomposition programs. Each of these programs uses a predetermined profile either defined analytically or "learned" from an isolated peak to fit all the other peaks in the pattern including the a2 component. This procedure is to be distinguished from deconvolution which is a Fourier analysis of the peak shape. There are several ways to approach the problem of decomposition.
First, the peaks can all be considered as independent, and each profile can be fit using free parameters. Usually, the profile shape is fixed and the parameters of peak intensity, profile half-width, and peak position are varied. The relative positions of the α1 and the α2 components are known, and their intensity ratios are fixed at 0.5. Where there is a mixture of phases, the peak shape may vary among the phases. If crystallite size is a factor and the crystallite shape is non-spherical, the half-width may vary within the peaks of the same phase. It should be apparent from this discussion that no single program can be optimized for all these options.
The programs listed under the heading "Profile Fitting - Decomposition" differ from the ones listed under "Profile Fitting - Full Pattern" in the way the peaks are treated. In the former category, each peak is generally considered as independent of the other peaks even in a cluster, and usually only a limited range of the pattern is considered during each application of the program. In the latter category, all the peaks (or a large number) in the pattern are considered at one time. If the sample is single phase, all the peak positions are related, and the program should constrain the peak locations to those compatible with a unit cell. Usually, the profile shape is also constrained. The purpose of this approach is to resolve individual peaks, so that the intensities can be determined. The single goal of this approach is to obtain intensities for crystal structure analysis. These intensities can then be used with the usual single-crystal analysis programs which employ direct methods and Patterson analysis. All the programs in this section operate on the full pattern to provide individual intensities.
Quantitative phase analysis by X-ray powder diffraction is one of the few techniques which is truly phase sensitive rather than element sensitive. The first applications followed the development of the theory by Alexander and Klug (1948). Although the technique was applied effectively to some special problems, the data collection was laborious and limited the general application of the method. When the APD became the data collector, the data was easier to analyze, and the technique saw enhanced use in the 1980's which has continued to the present time.
There are basically three ways of doing quantitative analysis at the present time. One technique uses integrated intensities (areas) of individual peaks for each of the phases in the mixture if peaks are resolvable and clusters of peaks when they are not. With the raw data in digitized form, it is easy to integrate the desired diffraction ranges for the calculation. QUANT85, PC/PEAKS, MicroQUANT and RIMPAC use this approach. GMQUANT and ARCOQUANT use the full diffraction trace with a reference database of digitized traces of reference patterns. The other programs are Rietveld programs modified to emphasize the quantification of phases in a mixture by adjusting the pattern scale factors for absorption effects. All these approaches are effective if the sample preparation problems can be overcome.