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 analyzing 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 0.001° and precisions ranging form ±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. Analysis results agree with those obtained from the computer simulated data.