Abstract
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.
Highlights
Quantification of nanoscale structures is set to become a requirement in industrial preparation of materials (EU, 2011)
While the general shape of the scatterer still has to be defined in order to arrive at a unique solution [see, for example, Rosalie & Pauw (2014)], the methods are no longer restricted to a limited set of model parameter distribution forms
The most important of these is the chi-squared criterion. While this is per default set to 1, it may prevent reaching a state of convergence (2r 1) for data whose uncertainty estimates are insufficiently large or poorly estimated
Summary
Quantification of nanoscale structures is set to become a requirement in industrial preparation of materials (EU, 2011). As TEM has remained largely resilient to automation efforts, this continues to be a tedious and labour-intensive task It is, beneficial to combine the localized resolving power of microscopy with another technique more suited for bulk-scale nanostructural quantification such as small-angle scattering (SAS) (ISO, 2014; Pauw, 2013). While the general shape of the scatterer still has to be defined in order to arrive at a unique solution [see, for example, Rosalie & Pauw (2014)], the methods are no longer restricted to a limited set of model parameter distribution forms Such modern methods include Titchmarsh (Fedorova & Schmidt, 1978; Botet & Cabane, 2012) or indirect Fourier transforms, based either on smoothness criteria (Glatter, 1977; Svergun, 1991), maximum entropy optimization (Hansen & Pedersen, 1991) or Bayesian hyperparameter estimation (Hansen, 2000). An attempt is made to replace one of the model contributions in order to improve the agreement between model and measured data
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