Structure-mining: screening structure models by automated fitting to the atomic pair distribution function over large numbers of models

MLstructureMining: a machine learning tool for structure identification from X-ray pair distribution functions

Synchrotron X-ray techniques are essential for studies of the intrinsic relationship between synthesis, structure, and properties of materials. Modern synchrotrons can produce up to 1 petabyte of data per day. Such amounts of data can speed up materials development, but also comes with a staggering growth in workload, as the data generated must be stored and analyzed. We present an approach for quickly identifying an atomic structure model from pair distribution function (PDF) data from (nano)crystalline materials. Our model, MLstructureMining, uses a tree-based machine learning (ML) classifier. MLstructureMining has been trained to classify chemical structures from a PDF and gives a top-3 accuracy of 99% on simulated PDFs not seen during training, with a total of 6062 possible classes. We also demonstrate that MLstructureMining can identify the chemical structure from experimental PDFs from nanoparticles of CoFe2O4 and CeO2, and we show how it can be used to treat an in situ PDF series collected during Bi2Fe4O9 formation. Additionally, we show how MLstructureMining can be used in combination with the well-known methods, principal component analysis (PCA) and non-negative matrix factorization (NMF) to analyze data from in situ experiments. MLstructureMining thus allows for real-time structure characterization by screening vast quantities of crystallographic information files in seconds.

Structure and phase transitions in niobium and tantalum derived nanoscale transition metal perovskites, Ba(Ti,MV)O3, M=Nb,Ta

The prospect of creating ferroelectric or high permittivity nanomaterials provides motivation for investigating complex transition metal oxides of the form Ba(Ti, MV)O3, where M = Nb or Ta. Solid state processing typically produces mixtures of crystalline phases, rarely beyond minimally doped Nb/Ta. Using a modified sol-gel method, we prepared single phase nanocrystals of Ba(Ti, M)O3. Compositional and elemental analysis puts the empirical formulas close to BaTi0.5Nb0.5O3-δ and BaTi0.5Ta0.5O3-δ. For both materials, a reversible temperature dependent phase transition (non-centrosymmetric to symmetric) is observed in the Raman spectrum in the region 533-583 K (260-310 °C); for Ba(Ti, Nb)O3, the onset is at 543 K (270 °C); and for Ba(Ti, Ta)O3, the onset is at 533 K (260 °C), which are comparable with 390-393 K (117-120 °C) for bulk BaTiO3. The crystal structure was resolved by examination of the powder x-ray diffraction and atomic pair distribution function (PDF) analysis of synchrotron total scattering data. It was postulated whether the structure adopted at the nanoscale was single or double perovskite. Double perovskites (A2B'B″O6) are characterized by the type and extent of cation ordering, which gives rise to higher symmetry crystal structures. PDF analysis was used to examine all likely candidate structures and to look for evidence of higher symmetry. The feasible phase space that evolves includes the ordered double perovskite structure Ba2(Ti, MV)O6 (M = Nb, Ta) Fm-3m, a disordered cubic structure, as a suitable high temperature analog, Ba(Ti, MV)O3Pm-3m, and an orthorhombic Ba(Ti, MV)O3Amm2, a room temperature structure that presents an unusually high level of lattice displacement, possibly due to octahedral tilting, and indication of a highly polarized crystal.

ClusterFinder: a fast tool to find cluster structures from pair distribution function data

A novel automated high-throughput screening approach, ClusterFinder, is reported for finding candidate structures for atomic pair distribution function (PDF) structural refinements. Finding starting models for PDF refinements is notoriously difficult when the PDF originates from nanoclusters or small nanoparticles. The reported ClusterFinder algorithm can screen 104 to 105 candidate structures from structural databases such as the Inorganic Crystal Structure Database (ICSD) in minutes, using the crystal structures as templates in which it looks for atomic clusters that result in a PDF similar to the target measured PDF. The algorithm returns a rank-ordered list of clusters for further assessment by the user. The algorithm has performed well for simulated and measured PDFs of metal-oxido clusters such as Keggin clusters. This is therefore a powerful approach to finding structural cluster candidates in a modelling campaign for PDFs of nanoparticles and nanoclusters.

POMFinder: identifying polyoxometallate cluster structures from pair distribution function data using explainable machine learning

Characterization of a material structure with pair distribution function (PDF) analysis typically involves refining a structure model against an experimental data set, but finding or constructing a suitable atomic model for PDF modelling can be an extremely labour-intensive task, requiring carefully browsing through large numbers of possible models. Presented here is POMFinder, a machine learning (ML) classifier that rapidly screens a database of structures, here polyoxometallate (POM) clusters, to identify candidate structures for PDF data modelling. The approach is shown to identify suitable POMs from experimental data, including in situ data collected with fast acquisition times. This automated approach has significant potential for identifying suitable models for structure refinement to extract quantitative structural parameters in materials chemistry research. POMFinder is open source and user friendly, making it accessible to those without prior ML knowledge. It is also demonstrated that POMFinder offers a promising modelling framework for combined modelling of multiple scattering techniques.

Machine learning for analysis of experimental scattering and spectroscopy data in materials chemistry

The rapid growth of materials chemistry data, driven by advancements in large-scale radiation facilities as well as laboratory instruments, has outpaced conventional data analysis and modelling methods, which can require enormous manual effort. To address this bottleneck, we investigate the application of supervised and unsupervised machine learning (ML) techniques for scattering and spectroscopy data analysis in materials chemistry research. Our perspective focuses on ML applications in powder diffraction (PD), pair distribution function (PDF), small-angle scattering (SAS), inelastic neutron scattering (INS), and X-ray absorption spectroscopy (XAS) data, but the lessons that we learn are generally applicable across materials chemistry. We review the ability of ML to identify physical and structural models and extract information efficiently and accurately from experimental data. Furthermore, we discuss the challenges associated with supervised ML and highlight how unsupervised ML can mitigate these limitations, thus enhancing experimental materials chemistry data analysis. Our perspective emphasises the transformative potential of ML in materials chemistry characterisation and identifies promising directions for future applications. The perspective aims to guide newcomers to ML-based experimental data analysis.

A Machine-Learning-Based Approach for Solving Atomic Structures of Nanomaterials Combining Pair Distribution Functions with Density Functional Theory

Determination of crystal structures of nanocrystalline or amorphous compounds is a great challenge in solid-state chemistry and physics. Pair distribution function (PDF) analysis of X-ray or neutron total scattering data has proven to be a key element in tackling this challenge. However, in most cases, a reliable structural motif is needed as a starting configuration for structure refinements. Here, an algorithm that is able to determine the crystal structure of an unknown compound by means of an on-the-fly trained machine learning model, which combines density functional theory calculations with comparison of calculated and measured PDFs for global optimization in an artificial landscape, is presented. Due to the nature of this landscape, even metastable configurations and stacking disorders can be identified.

DeepStruc: towards structure solution from pair distribution function data using deep generative models

Structure solution of nanostructured materials that have limited long-range order remains a bottleneck in materials development. We present a deep learning algorithm, DeepStruc, that can solve a simple monometallic nanoparticle structure directly from a Pair Distribution Function (PDF) obtained from total scattering data by using a conditional variational autoencoder. We first apply DeepStruc to PDFs from seven different structure types of monometallic nanoparticles, and show that structures can be solved from both simulated and experimental PDFs, including PDFs from nanoparticles that are not present in the training distribution. We also apply DeepStruc to a system of hcp, fcc and stacking faulted nanoparticles, where DeepStruc recognizes stacking faulted nanoparticles as an interpolation between hcp and fcc nanoparticles and is able to solve stacking faulted structures from PDFs. Our findings suggests that DeepStruc is a step towards a general approach for structure solution of nanomaterials.

nmfMapping: a cloud-based web application for non-negative matrix factorization of powder diffraction and pair distribution function datasets

A cloud-hosted web-based software application, nmfMapping, for carrying out a non-negative matrix factorization of a set of powder diffraction or atomic pair distribution function datasets is described. This application allows structure scientists to find trends rapidly in sets of related data such as from in situ and operando diffraction experiments. The application is easy to use and does not require any programming expertise. It is available at https://pdfitc.org/.

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.

Structure determination of organic compounds by a fit to the pair distribution function from scratch without prior indexing

A method for the ab initio crystal structure determination of organic compounds by a fit to the pair distribution function (PDF), without prior knowledge of lattice parameters and space group, has been developed. The method is called 'PDF-Global-Fit' and is implemented by extension of the program FIDEL (fit with deviating lattice parameters). The structure solution is based on a global optimization approach starting from random structural models in selected space groups. No prior indexing of the powder data is needed. The new method requires only the molecular geometry and a carefully determined PDF. The generated random structures are compared with the experimental PDF and ranked by a similarity measure based on cross-correlation functions. The most promising structure candidates are fitted to the experimental PDF data using a restricted simulated annealing structure solution approach within the program TOPAS, followed by a structure refinement against the PDF to identify the correct crystal structure. With the PDF-Global-Fit it is possible to determine the local structure of crystalline and disordered organic materials, as well as to determine the local structure of unindexable powder patterns, such as nanocrystalline samples, by a fit to the PDF. The success of the method is demonstrated using barbituric acid as an example. The crystal structure of barbituric acid form IV solved and refined by the PDF-Global-Fit is in excellent agreement with the published crystal structure data.

Validation of non-negative matrix factorization for rapid assessment of large sets of atomic pair distribution function data

The use of the non-negative matrix factorization (NMF) technique is validated for automatically extracting physically relevant components from atomic pair distribution function (PDF) data from time-series data such as in situ experiments. The use of two matrix-factorization techniques, principal component analysis and NMF, on PDF data is compared in the context of a chemical synthesis reaction taking place in a synchrotron beam, applying the approach to synthetic data where the correct composition is known and on measured PDFs from previously published experimental data. The NMF approach yields mathematical components that are very close to the PDFs of the chemical components of the system and a time evolution of the weights that closely follows the ground truth. Finally, it is discussed how this would appear in a streaming context if the analysis were being carried out at the beamline as the experiment progressed.

A cloud platform for atomic pair distribution function analysis: PDFitc

A new web platform is presented for the pair distribution function (PDF) community to use and share advanced PDF analysis software in the cloud.

A cloud web platform for analysis and interpretation of atomic pair distribution function (PDF) data (PDFitc) is described. The platform is able to host applications for PDF analysis to help researchers study the local and nanoscale structure of nanostructured materials. The applications are designed to be powerful and easy to use and can, and will, be extended over time through community adoption and development. The currently available PDF analysis applications, structureMining, spacegroupMining and similarity­Mapping, are described. In the first and second the user uploads a single PDF and the application returns a list of best-fit candidate structures, and the most likely space group of the underlying structure, respectively. In the third, the user can upload a set of measured or calculated PDFs and the application returns a matrix of Pearson correlations, allowing assessment of the similarity between different data sets. structureMining is presented here as an example to show the easy-to-use workflow on PDFitc. In the future, as well as using the PDFitc applications for data analysis, it is hoped that the community will contribute their own codes and software to the platform.

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.