Algorithm for distance list extraction from pair distribution functions

Towards the extraction of the crystal cell parameters from pair distribution function profiles

The approach based on atomic pair distribution function (PDF) has revolutionized structural investigations by X-ray/electron diffraction of nano or quasi-amorphous materials, opening up the possibility of exploring short-range order. However, the ab initio crystal structural solution by the PDF is far from being achieved due to the difficulty in determining the crystallographic properties of the unit cell. A method for estimating the crystal cell parameters directly from a PDF profile is presented, which is composed of two steps: first, the type of crystal cell is inferred using machine-learning approaches applied to the PDF profile; second, the crystal cell parameters are extracted by means of multivariate analysis combined with vector superposition techniques. The procedure has been validated on a large number of PDF profiles calculated from known crystal structures and on a small number of measured PDF profiles. The lattice determination step has been benchmarked by a comprehensive exploration of different classifiers and different input data. The highest performance is obtained using the k-nearest neighbours classifier applied to whole PDF profiles. Descriptors calculated from the PDF profiles by recurrence quantitative analysis produce results that can be interpreted in terms of PDF properties, and the significance of each descriptor in determining the prediction is evaluated. The cell parameter extraction step depends on the cell metric rather than its type. Monometric, dimetric and trimetric cells have top-1 estimates that are correct 40, 20 and 5% of the time, respectively. Promising results were obtained when analysing real nanocrystals, where unit cells close to the true ones are found within the top-1 ranked solution in the case of monometric cells and within the top-6 ranked solutions in the case of dimetric cells, even in the presence of a crystalline impurity with a weight fraction up to 40%.

A fast two-stage algorithm for non-negative matrix factorization in smoothly varying data

This article reports the study of algorithms for non-negative matrix factorization (NMF) in various applications involving smoothly varying data such as time or temperature series diffraction data on a dense grid of points. Utilizing the continual nature of the data, a fast two-stage algorithm is developed for highly efficient and accurate NMF. In the first stage, an alternating non-negative least-squares framework is used in combination with the active set method with a warm-start strategy for the solution of subproblems. In the second stage, an interior point method is adopted to accelerate the local convergence. The convergence of the proposed algorithm is proved. The new algorithm is compared with some existing algorithms in benchmark tests using both real-world data and synthetic data. The results demonstrate the advantage of the algorithm in finding high-precision solutions.

Structural Analysis of Molecular Materials Using the Pair Distribution Function

This is a review of atomic pair distribution function (PDF) analysis as applied to the study of molecular materials. The PDF method is a powerful approach to study short- and intermediate-range order in materials on the nanoscale. It may be obtained from total scattering measurements using X-rays, neutrons, or electrons, and it provides structural details when defects, disorder, or structural ambiguities obscure their elucidation directly in reciprocal space. While its uses in the study of inorganic crystals, glasses, and nanomaterials have been recently highlighted, significant progress has also been made in its application to molecular materials such as carbons, pharmaceuticals, polymers, liquids, coordination compounds, composites, and more. Here, an overview of applications toward a wide variety of molecular compounds (organic and inorganic) and systems with molecular components is presented. We then present pedagogical descriptions and tips for further implementation. Successful utilization of the method requires an interdisciplinary consolidation of material preparation, high quality scattering experimentation, data processing, model formulation, and attentive scrutiny of the results. It is hoped that this article will provide a useful reference to practitioners for PDF applications in a wide realm of molecular sciences, and help new practitioners to get started with this technique.

There's no place like real-space: elucidating size-dependent atomic structure of nanomaterials using pair distribution function analysis

The development of new functional materials builds on an understanding of the intricate relationship between material structure and properties, and structural characterization is a crucial part of materials chemistry. However, elucidating the atomic structure of nanomaterials remains a challenge using conventional diffraction techniques due to the lack of long-range atomic order. Over the past decade, Pair Distribution Function (PDF) analysis of X-ray or neutron total scattering data has become a mature and well-established method capable of giving insight into the atomic structure in nanomaterials. Here, we review the use of PDF analysis and modelling in characterization of a range of different nanomaterials that exhibit unique atomic structure compared to the corresponding bulk materials. A brief introduction to PDF analysis and modelling is given, followed by examples of how essential structural information can be extracted from PDFs using both model-free and advanced modelling methods. We put an emphasis on how the intuitive nature of the PDF can be used for understanding important structural motifs, and on the diversity of applications of PDF analysis to nanostructure problems.