Deconvolution of the instrumental functions in powder X-ray diffractometry

A novel method to deconvolute the instrumental aberration functions from the experimental powder X-ray data has been developed. The method is based on the combination of scale transformation, interpolation of data and fast Fourier transformation. The effects of axial divergence, flat specimen, sample transparency and spectroscopic profile of the source X-ray are eliminated from the entire observed diffraction pattern in three-step operations. The errors in the deconvoluted data propagated from the statistical uncertainty in the source data are approximated by the reciprocal of the square root of the correlation between the reciprocal of the variance in the source data and the squared instrumental function. The deconvolution of the instrumental aberration functions enables automatic correction of peak shift and line broadening, and supplies narrow and symmetric peak profiles for a well crystallized sample, which can be fitted by a simple model function. It will be useful in preparatory data processing for precise line profile analysis, accurate determination of lattice parameters and whole pattern fitting for crystal structure analysis.