[Paper Review] McSAS: A package for extracting quantitative form-free distributions

Ingo Breßler, Brian R. Pauw+1 more|arXiv (Cornell University)|Dec 5, 2014

Corrosion Behavior and Inhibition2 references3 citations

TL;DR

McSAS is a user-friendly software package that extracts quantitative, form-free size distributions from small-angle X-ray scattering (SAXS) data using a Monte Carlo rejection sampling method. It enables model-independent retrieval of volume-weighted size distributions with uncertainty estimates and minimum evidence limits, supporting various particle shapes and complex systems like densely packed spheres, significantly improving accessibility and reliability over classical fitting approaches.

ABSTRACT

A reliable and user-friendly characterisation of nano-objects in a target material is presented here in the form of a software data analysis package for interpreting small-angle X-ray scattering (SAXS) patterns. When provided with data on absolute scale with reasonable uncertainty estimates, the software outputs (size) distributions in absolute volume fractions complete with uncertainty estimates and minimum evidence limits, and outputs all distribution modes of a user definable range of one or more model parameters. A multitude of models are included, including prolate and oblate nanoparticles, core-shell objects, polymer models (Gaussian chain and Kholodenko worm) and a model for densely packed spheres (using the LMA-PY approximations). The McSAS software can furthermore be integrated as part of an automated reduction and analysis procedure in laboratory instruments or at synchrotron beamlines.

Motivation & Objective

• To develop a reliable, user-friendly software package for quantitative analysis of small-angle X-ray scattering (SAXS) patterns.
• To overcome limitations of classical model-based fitting by enabling form-free size distribution extraction without assuming a specific functional form for dispersity.
• To provide absolute volume fractions with uncertainty estimates and minimum evidence limits for improved data interpretation.
• To support complex systems such as core-shell particles, polymers, and densely packed spheres through flexible modeling.
• To enhance accessibility and adoption of advanced SAXS analysis by integrating a graphical user interface and modern software practices.

Proposed method

• The McSAS method employs Monte Carlo rejection sampling to iteratively sample particle parameters (e.g., radius, length) from a user-defined range.
• For each sampled particle set, the scattering intensity is computed using analytical form factors (e.g., sphere, rod, ellipsoid) and structure factors (e.g., LMA-PY for hard-sphere interactions).
• The algorithm weights contributions inversely by particle volume to improve convergence and reduce required sampling iterations.
• A rejection criterion is applied based on the agreement between simulated and experimental scattering patterns, ensuring statistical consistency.
• The final output includes volume-weighted size distributions, absolute volume fractions, and uncertainty estimates derived from the posterior distribution.
• The software integrates with laboratory and synchrotron beamline workflows and supports automated data reduction and analysis pipelines.

Experimental results

Research questions

• RQ1 Can a form-free method extract reliable size distributions from SAXS data without assuming a specific functional form for dispersity?
• RQ2 How does the performance of the McSAS method compare to classical least-squares fitting in terms of accuracy and robustness for polydisperse and complex systems?
• RQ3 To what extent can the method resolve multiple populations in a distribution when the data is noisy or the system is highly polydisperse?
• RQ4 How do uncertainty estimates and evidence limits in McSAS improve confidence in the retrieved size distributions compared to conventional approaches?
• RQ5 Can the method be effectively integrated into automated data analysis pipelines for high-throughput SAXS experiments?

Key findings

• McSAS successfully retrieves volume-weighted size distributions with absolute volume fractions from SAXS data, even for complex systems such as densely packed SiO2 spheres.
• The method achieves a good fit to experimental data (within uncertainty) for a system of 75 nm SiO2 spheres packed at a volume fraction of ~0.63, with a number-weighted mean radius of 76.1(2) nm.
• A minor secondary peak at approximately half the main particle size was observed, suggesting potential limitations in the LMA-PY structure factor or sample heterogeneity.
• The solution is sensitive to the assumed volume fraction, with acceptable fits obtainable across a range of 0.5 ≤ vf ≤ 0.7, highlighting the need for external constraints to ensure uniqueness.
• The software demonstrates a significant improvement over classical fitting by avoiding assumptions about size distribution shape and providing uncertainty estimates.
• The integration of a graphical user interface and support for multiple particle models enhances usability and broadens accessibility for non-expert users.