Profile Refinement of Single Crystal and Powder Data: The Accuracy of Crystallographic Parameters

Abstract

Sakata and Cooper have recently published a comparison between profile refinement (in which each ordinate of the diffraction pattern is included separately in the least squares analysis) and, what they term, integrated intensity refinement (in which the ordinates are first summed over each Bragg peak). They find different results for the two methods and conclude that the results obtained from profile analysis are wrong. We show analytically that the two methods give identical results, and that the Sakata and Cooper analysis is in error because of the method they used to estimate integrated intensity. It is verified, using simulated data, that profile analysis gives lower values for the standard deviations of crystallographic parameters than simple ordinate summation.