A method and a computer program were developed for deconvolution of overlapped X-ray powder diffraction spectra for quantitative mineral analysis. Removal of profile aberrations by unfolding spectral segments and overlapped profiles to deconvolute X-ray powder defraction patterns for quantitative analysis were considered. Sources of profile shape and distortion, convolution and its functions, the Lorentz polarization factor, folding and unfolding of profiles, the Fourier Transform method, Stokes' method and the Ergun method of iterative folding were examined, along with other methods of infinite series, linear representation, folding of Lorentzians and raw profile fitting. Deconvolution of overlapped profiles and Lorentzian profiles for least squares fitting also were considered. The author concludes that deconvolution of X-ray diffraction spectra requires correction for instrument aberrations and wave length dispersion. Correction of profiles, stripping, and least square fitting of overlapping peaks are needed to deconvolute overlapped profiles. The only practical and satisfactory methods for correcting aberrations are the Ergun and related methods, if unfolding is performed. Taupin, Parrish and Huang's folding methods of deconvolution are useful. The method presented is good for quantitative deconvolution and could serve as a basis for correcting integrated intensities and relating asymmetry to twinning and deformation faults.
NIOSH, Center for Disease Control, Public Health Service, U.S. Department of Health, Education and Welfare