Efficient algorithms for calculating small-angle scattering from large model structures

• Published in: Journal of applied crystallography Vol. 47; no. 3; pp. 1077 - 1086
• Main Authors: Olds, Daniel P., Duxbury, Phillip M.
• Format: Journal Article
• Language: English
• Published: 5 Abbey Square, Chester, Cheshire CH1 2HU, England International Union of Crystallography 01.06.2014; Blackwell Publishing Ltd
• Subjects: Algorithms; Computer simulation; Crystallography; fast Fourier transforms; Fourier transforms; large morphological models; Mathematical models; Monte Carlo distribution function method; Monte Carlo methods; Monte Carlo simulation; Morphology; Nanostructure; SAS; Scattering; small-angle scattering
• ISSN: 1600-5767; 0021-8898; 1600-5767
• DOI: 10.1107/S1600576714005925

This paper compares Monte Carlo approaches and fast Fourier transform (FFT) methods to efficiently calculate small‐angle scattering (SAS) profiles from large morphological models. These methods enable calculation of SAS from complex nanoscale morphologies commonly encountered in modern polymeric and nanoparticle‐based systems which have no exact analytical representation and are instead represented digitally using many millions of subunits, so that algorithms with linear or near‐linear scaling are essential. The Monte Carlo method, referred to as the Monte Carlo distribution function method (MC‐DFM), is presented and its accuracy validated using a number of simple morphologies, while the FFT calculations are based on the fastest implementations available. The efficiency, usefulness and inherent limits of DFM and FFT approaches are explored using a series of complex morphological models, including Gaussian chain ensembles and two‐phase three‐dimensional interpenetrating nanostructures.