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Profile separation in complex powder patterns
Author(s) -
Naidu S. V. N.,
Houska C. R.
Publication year - 1982
Publication title -
journal of applied crystallography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.429
H-Index - 162
ISSN - 1600-5767
DOI - 10.1107/s0021889882011753
Subject(s) - smoothing , cauchy distribution , diffraction , range (aeronautics) , gaussian , distortion (music) , resolution (logic) , curve fitting , derivative (finance) , least squares function approximation , mathematics , algorithm , data set , set (abstract data type) , mathematical analysis , optics , materials science , computer science , physics , statistics , amplifier , optoelectronics , cmos , quantum mechanics , artificial intelligence , estimator , financial economics , economics , composite material , programming language
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 ~ 10 5 range using raw data, and the ~ 10 4 range with digital smoothing. The use of less accurate analog scans is also discussed. Examples are given with overlapping peaks in a 2 θ 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.