Profile shape functions in Rietveld refinements

Reflection profile functions used or suggested for use in Rietveld refinements with fixed-angle or fixed-wavelength powder diffraction data, obtained with neutrons or with X-rays, are reviewed briefly. The fixed-wavelength X-ray case is considered in detail. In tests of fitting to individual resolved reflection profiles, at least eight different profile functions, including some representations consisting of "learned' differentiable number arrays, have been show to be satisfactory at the less than 3% misfit level. Several authors have made comparative studies of subsets of the six analytic functions, Gaussian (G), Lorentzian (L), modified Lorentzian (ML), intermediate Lorentzian (IL), pseudo-Voigt (p-V), and Pearson VII (PVII). In this work, the performance of all six, in Rietveld refinements with data sets from seven different specimens with differing degrees of broadening, have been intercompared on the basis of difference plots, R_wp, and R_B. The Gaussian function was consistently the worst performer, while the pseudo-Voigt and Pearson VII were the best. For this reason, for reasons of simplicity, and for convenient though crude physical interpretation of the Lorentz-fraction parameter, the pseudo-Voigt is identified as the function of choice among these six. It is emphasized that a need still exists for a better profile function soundly based on physical reality.