Precision Peak Determination in X-ray Powder Diffraction

Abstract

A systematic study of the derivative methods for peak search analysis of X-ray powder diffraction data was made to evaluate the relative merits of the methods. Results of analysing computer simulated diffraction peaks show that the peak positions can be precisely determined by the first derivative of a least-squares fitted cubic polynomial. The technique has an accuracy of 0 . 00 1" and precisions ranging from ±0·003" to 0·02" depending on the levels of counting statistical noise. The study also shows that reliable resolution of overlaps has been obtained using the second derivative of a quadratic/cubic polynomial. A method of combining the first derivative of a cubic polynomial and the second derivative quadratic/cubic polynomial has thus been used for precision peak search analysis. The combined first/second derivative method has been tested with experimental diffraction patterns recorded with various step sizes, levels of counting statistical noise and degrees of overlaps. Analysis results agree with those obtained from the computer simulated data. A comparison between the peak search and the profile fitting results showed good matches in the peak positions but relatively poor agreements in the peak intensities especially for the heavily overlapping peaks