Multipole electron-density modelling of synchrotron powder diffraction data: the case of diamond

Abstract

Accurate structure factors are extracted from synchrotron powder diffraction data measured on crystalline diamond based on a novel multipole model division of overlapping reflection intensities. The approach limits the spherical-atom bias in structure factors extracted from overlapping powder data using conventional spherical-atom Rietveld refinement. The structure factors are subsequently used for multipole electron-density modelling, and both the structure factors and the derived density are compared with results from ab initio theoretical calculations. Overall, excellent agreement is obtained between experiment and theory, and the study therefore demonstrates that synchrotron powder diffraction can indeed provide accurate structure-factor values based on data measured in minutes with limited sample preparation. Thus, potential systematic errors such as extinction and twinning commonly encountered in single-crystal studies of small-unit-cell inorganic structures can be overcome with synchrotron powder diffraction. It is shown that the standard Hansen-Coppens multipole model is not flexible enough to fit the static theoretical structure factors, whereas fitting of thermally smeared structure factors has much lower residuals. If thermally smeared structure factors (experimental or theoretical) are fitted with a slightly wrong radial model (s(2)p(2) instead of sp(3)) the radial scaling parameters (kappa' parameters) are found to be inadequate and the ;error' is absorbed into the atomic displacement parameter. This directly exposes a correlation between electron density and thermal parameters even for a light atom such as carbon, and it also underlines that in organic systems proper deconvolution of thermal motion is important for obtaining correct static electron densities.

Revisit: High resolution charge density study of α-rhombohedral boron using third-generation SR data at SPring-8

“…We have developed a method for determining accurate charge densities using multiple overlaid SR powder data sets [8,9,10]. The error of the structure factors determined by the method is less than 1.0%, which is comparable to that of the very accurate Pendellösung method [11].…”

Visualizing charge densities and electrostatic potentials in materials by synchrotron X-ray powder diffraction

“…For the more detailed analysis of charge densities, a combination of the MEM analysis with the multipole modelling [46] is preferable, in which wider Q range data are needed to optimize a large number of fitting parameters.…”

Experimental determination of core electron deformation in diamond

“…The vast majority of experimental ED studies are based on modelling of structure factors obtained from single-crystal X-ray diffraction (Koritsanszky & Coppens, 2001;Coppens et al, 2005). However, in a previous study of diamond, we showed that application of the HC model is also feasible in the case of powder diffraction data (Svendsen et al, 2010). There are pros and cons for both single-crystal and powder diffraction studies and, in the latter case, background subtraction as well as peak overlap have generally been considered as insurmountable challenges to the multipolar method.…”

“…In recent studies we explored the current limits of the X-ray ED method (Svendsen et al, 2010;Schmøkel et al, 2013). The vast majority of experimental ED studies are based on modelling of structure factors obtained from single-crystal X-ray diffraction (Koritsanszky & Coppens, 2001;Coppens et al, 2005).…”