Profile separation in complex powder patterns

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Abstract
Diffraction patterns from multi-element alloys, composite materials, enriched ores and other materials involving a mix of several phases often contain regions of overlapping diffraction peaks. In many cases, the peaks can be separated by a combination of numerical differentiation of the data and non-linear least-squares curve-fitting techniques. The derivative provides a powerful but simple technique for distinguishing the number of peaks and their locations within a scramble. These results are required as input to a least-squares curve-fitting routine. The end result of this two-step procedure is a set of parameters that define the positions, shape, width and areas of the separate peaks. A statistical analysis of the data requirements indicates that a good second derivative can be obtained with a peak count in the ~ 105 range using raw data, and the ~ 104 range with digital smoothing. The use of less accurate analog scans is also discussed. Examples are given with overlapping peaks in a 2θ range of less than 1° . The theoretical results describing the data requirements, resolution, distortion effects, and peak enhancement are based upon a Pearson VII function which is capable of describing all shapes continuously between the Cauchy, modified Lorentzian and the Gaussian.

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