PROFVAL: functions to calculate powder-pattern peak profiles with axial-divergence asymmetry

Abstract

The crystallographic problem: In a powder diffractometer, the curvature of the Debye---Scherrer rings causes an asymmetry in the peak profiles as the Bragg angle approaches either 0 or 180 °. For accurate Rietveld refinement, this asymmetry, which is known as axial divergence, must be modeled correctly. Traditionally, empirical ad hoc functions such as a split-Pearson-VII function or multiple overlapping Gaussian peaks have been employed. Finger e t a / . (1994) extended the method of van Laar & Yellon (1984) for convolution of the ring shape with an intrinsic peak profile a procedure that describes extremely asymmetric profiles and involves only physically meaningful parameters. To date, however, only the program GSAS (Larson &von Dreele, 1990) has incorporated this method. This contribution makes available tested code for the convolution of the asymmetry function with the intrinsic line function in the hope that more Rietveld codes will incorporate this method.