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A user-friendly open-source Monte Carlo regression package (McSAS) is presented, which structures the analysis of small-angle scattering (SAS) using uncorrelated shape-similar particles (or scattering contributions). The underdetermined problem is solvable, provided that sufficient external information is available. Based on this, the user picks a scatterer contribution model (or 'shape') from a comprehensive library and defines variation intervals of its model parameters. A multitude of scattering contribution models are included, including prolate and oblate nanoparticles, core-shell objects, several polymer models, and a model for densely packed spheres. Most importantly, the form-free Monte Carlo nature of McSAS means it is not necessary to provide further restrictions on the mathematical form of the parameter distribution; without prior knowledge, McSAS is able to extract complex multimodal or odd-shaped parameter distributions from SAS data. When provided with data on an absolute scale with reasonable uncertainty estimates, the software outputs model parameter distributions in absolute volume fraction, and provides the modes of the distribution (e.g. mean, variance etc.). In addition to facilitating the evaluation of (series of) SAS curves, McSAS also helps in assessing the significance of the results through the addition of uncertainty estimates to the result. The McSAS software can be integrated as part of an automated reduction and analysis procedure in laboratory instruments or at synchrotron beamlines.
Ultra-SAXS can enhance the capabilities of existing synchrotron SAXS/WAXS beamlines. A compact ultra-SAXS module has been developed, which extends the measurable q-range with 0.0015 ≤ q (nm−1) ≤ 0.2, allowing structural dimensions in the range 30 ≤ D (nm) ≤ 4000 to be probed in addition to the range covered by a high-end SAXS/WAXS instrument. By shifting the module components in and out on their respective motor stages, SAXS/WAXS measurements can be easily and rapidly interleaved with USAXS measurements. The use of vertical crystal rotation axes (horizontal diffraction) greatly simplifies the construction, at minimal cost to efficiency. In this paper, the design considerations, realization and synchrotron findings are presented. Measurements of silica spheres, an alumina membrane, and a porous carbon catalyst are provided as application examples.
Data correction is probably the least favourite activity amongst users experimenting with small-angle X-ray scattering: if it is not done sufficiently well, this may become evident only during the data analysis stage, necessitating the repetition of the data corrections from scratch. A recommended comprehensive sequence of elementary data correction steps is presented here to alleviate the difficulties associated with data correction, both in the laboratory and at the synchrotron. When applied in the proposed order to the raw signals, the resulting absolute scattering cross section will provide a high degree of accuracy for a very wide range of samples, with its values accompanied by uncertainty estimates. The method can be applied without modification to any pinhole-collimated instruments with photon-counting direct-detection area detectors.
This paper presents the first worldwide inter-laboratory comparison of small-angle X-ray scattering (SAXS) for nanoparticle sizing. The measurands in this comparison are the mean particle radius, the width of the size distribution and the particle concentration. The investigated sample consists of dispersed silver nanoparticles, surrounded by a stabilizing polymeric shell of poly(acrylic acid). The silver cores dominate the X-ray scattering pattern, leading to the determination of their radius size distribution using (i) the generalized indirect Fourier transformation method, (ii) classical model fitting using SASfit and (iii) a Monte Carlo fitting approach using McSAS. The application of these three methods to the collected data sets from the various laboratories produces consistent mean number- and volume-weighted core radii of Rn = 2.76 (6) nm and Rv = 3.20 (4) nm, respectively. The corresponding widths of the lognormal radius distribution of the particles were σn = 0.65 (1) nm and σv = 0.71 (1) nm. The particle concentration determined using this method was 3.0 (4) g l−1 or 4.2 (7) × 10−6 mol l−1. These results are affected slightly by the choice of data evaluation procedure, but not by the instruments: the participating laboratories at synchrotron SAXS beamlines, commercial and in-house-designed instruments were all able to provide highly consistent data. This demonstrates that SAXS is a suitable method for revealing particle size distributions in the sub-20 nm region (at minimum), out of reach for most other analytical methods.
A round-robin study has been carried out to estimate the impact of the human element in small-angle scattering data analysis. Four corrected datasets were provided to participants ready for analysis. All datasets were measured on samples containing spherical scatterers, with two datasets in dilute dispersions and two from powders. Most of the 46 participants correctly identified the number of populations in the dilute dispersions, with half of the population mean entries within 1.5% and half of the population width entries within 40%. Due to the added complexity of the structure factor, far fewer people submitted answers on the powder datasets. For those that did, half of the entries for the means and widths were within 44 and 86%, respectively. This round-robin experiment highlights several causes for the discrepancies, for which solutions are proposed.