Profile shape functions in Rietveld refinements

Abstract

Reflection profile functions used or suggested for use in Rietveld refinements with fixed-angle or fixedwavelength 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 3~0 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,,.p, and R e.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.

Microstructural and morphological analysis of pure and Ce-doped tin dioxide nanoparticles

“…The convergence parameters of the Rietveld refinement 10 and the results for microstructural characterization of the pure and Ce-doped SnO 2 nanopowders are displayed in Tables 1 and 2, respectively. In Fig.…”

Determinação de fase vítrea em bauxitas refratárias

“…Partindo da estrutura cristalina de um aluminossilicato de sódio, NaAlSiO 4 , e alargando os picos de maneira a formar bandas de difração, foi possível a aproximação de um modelo "estrutural" para a sílica vítrea. Considerando a fase amorfa como uma fase nanocristalina, é possível a sua inclusão no programa de refinamento de Rietveld, com a conseqüente determinação da quantidade de fases cristalinas e amorfas em uma amostra.…”

“…O programa utiliza um algoritmo baseado no ajuste por mínimos quadrados para refinar um modelo estrutural teórico em relação a difratogramas reais. Uma extensa bibliografia sobre o assunto pode ser encontrada, porém não é objetivo deste trabalho o aprofundamento teórico na técnica, que pode ser consultada nas diversas referências apresentadas [1][2][3][4][5][6].…”

A Re-Evaluation of the Morphology of a Bicontinuous Block Copolymer−Ceramic Material

“…Rotation series were used to evaluate I(q), and a plot for the calcined material is shown in Figure 3b. The intensity of scattering peaks was determined by fitting the 1-D scattering profile via nonlinear least-squares to the form, where I j and m j are the intensity and multiplicity of the j ) h 2 + k 2 + l 2 scattering peak, V is the Voigt function, 22,23 σ L0 , σ L1 , σ G0 , and σ G1 describe the width of each scattering peak, and B k are coefficients describing background scatter. The resulting peak intensities for as-made and calcined materials are reported in Table 1.…”