Structural characterisation of amorphous solid dispersions via metropolis matrix factorisation of pair distribution function data

Exploring porous structures without crystals: advancements with pair distribution function in metal- and covalent organic frameworks

The pair distribution function (PDF) is a versatile characterisation tool in materials science, capable of retrieving atom-atom distances on a continuous scale (from a few angstroms to nanometres), without being restricted to crystalline samples. Typically, total scattering experiments are performed using high-energy synchrotron X-rays, neutrons or electrons to achieve a high atomic resolution in a short time. Recently, PDF analysis provides a powerful approach to target current characterisation challenges in the field of metal- and covalent organic frameworks. By identifying molecular interactions on the pore surfaces, tracking complex structural transformations involving disorder states, and elucidating nucleation and growth mechanisms, structural analysis using PDF has provided invaluable insights into these materials. This review article highlights the significance of PDF analysis in advancing our understanding of MOFs and COFs, paving the way for innovative applications and discoveries in porous materials research.

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.

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.

Towards scanning nanostructure X-ray microscopy

This article demonstrates spatial mapping of the local and nanoscale structure of thin film objects using spatially resolved pair distribution function (PDF) analysis of synchrotron X-ray diffraction data. This is exemplified in a lab-on-chip combinatorial array of sample spots containing catalytically interesting nanoparticles deposited from liquid precursors using an ink-jet liquid-handling system. A software implementation is presented of the whole protocol, including an approach for automated data acquisition and analysis using the atomic PDF method. The protocol software can handle semi-automated data reduction, normalization and modeling, with user-defined recipes generating a comprehensive collection of metadata and analysis results. By slicing the collection using included functions, it is possible to build images of different contrast features chosen by the user, giving insights into different aspects of the local structure.

Mapping short-range order at the nanoscale in metal-organic framework and inorganic glass composites

Characterization of nanoscale changes in the atomic structure of amorphous materials is a profound challenge. Established X-ray and neutron total scattering methods typically provide sufficient signal quality only over macroscopic volumes. Pair distribution function analysis using electron scattering (ePDF) in the scanning transmission electron microscope (STEM) has emerged as a method of probing nanovolumes of these materials, but inorganic glasses as well as metal-organic frameworks (MOFs) and many other materials containing organic components are characteristically prone to irreversible changes after limited electron beam exposures. This beam sensitivity requires 'low-dose' data acquisition to probe inorganic glasses, amorphous and glassy MOFs, and MOF composites. Here, we use STEM-ePDF applied at low electron fluences (10 e^- Å^-2) combined with unsupervised machine learning methods to map changes in the short-range order with ca. 5 nm spatial resolution in a composite material consisting of a zeolitic imidazolate framework glass a_gZIF-62 and a 0.67([Na₂O]_0.9[P₂O₅])-0.33([AlO_3/2][AlF₃]_1.5) inorganic glass. STEM-ePDF enables separation of MOF and inorganic glass domains from atomic structure differences alone, showing abrupt changes in atomic structure at interfaces with interatomic correlation distances seen in X-ray PDF preserved at the nanoscale. These findings underline that the average bulk amorphous structure is retained at the nanoscale in the growing family of MOF glasses and composites, a previously untested assumption in PDF analyses crucial for future non-crystalline nanostructure engineering.

Harnessing interpretable and unsupervised machine learning to address big data from modern X-ray diffraction

The information content of crystalline materials becomes astronomical when collective electronic behavior and their fluctuations are taken into account. In the past decade, improvements in source brightness and detector technology at modern X-ray facilities have allowed a dramatically increased fraction of this information to be captured. Now, the primary challenge is to understand and discover scientific principles from big datasets when a comprehensive analysis is beyond human reach. We report the development of an unsupervised machine learning approach, X-ray diffraction (XRD) temperature clustering (X-TEC), that can automatically extract charge density wave order parameters and detect intraunit cell ordering and its fluctuations from a series of high-volume X-ray diffraction measurements taken at multiple temperatures. We benchmark X-TEC with diffraction data on a quasi-skutterudite family of materials, (CaxSr[Formula: see text])3Rh4Sn13, where a quantum critical point is observed as a function of Ca concentration. We apply X-TEC to XRD data on the pyrochlore metal, Cd2Re2O7, to investigate its two much-debated structural phase transitions and uncover the Goldstone mode accompanying them. We demonstrate how unprecedented atomic-scale knowledge can be gained when human researchers connect the X-TEC results to physical principles. Specifically, we extract from the X-TEC-revealed selection rules that the Cd and Re displacements are approximately equal in amplitude but out of phase. This discovery reveals a previously unknown involvement of [Formula: see text] Re, supporting the idea of an electronic origin to the structural order. Our approach can radically transform XRD experiments by allowing in operando data analysis and enabling researchers to refine experiments by discovering interesting regions of phase space on the fly.

Multivariate analysis of disorder in metal-organic frameworks

The rational design of disordered frameworks is an appealing route to target functional materials. However, intentional realisation of such materials relies on our ability to readily characterise and quantify structural disorder. Here, we use multivariate analysis of pair distribution functions to fingerprint and quantify the disorder within a series of compositionally identical metal–organic frameworks, possessing different crystalline, disordered, and amorphous structures. We find this approach can provide powerful insight into the kinetics and mechanism of structural collapse that links these materials. Our methodology is also extended to a very different system, namely the melting of a zeolitic imidazolate framework, to demonstrate the potential generality of this approach across many areas of disordered structural chemistry.

Structural disorder in materials is challenging to characterise. Here, the authors use multivariate analysis of atomic pair distribution functions to study structural collapse and melting of metal–organic frameworks, revealing powerful mechanistic and kinetic insight.

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.

Recovering local structure information from high-pressure total scattering experiments

High pressure is a powerful thermodynamic tool for exploring the structure and the phase behaviour of the crystalline state, and is now widely used in conventional crystallographic measurements. High-pressure local structure measurements using neutron diffraction have, thus far, been limited by the presence of a strongly scattering, perdeuterated, pressure-transmitting medium (PTM), the signal from which contaminates the resulting pair distribution functions (PDFs). Here, a method is reported for subtracting the pairwise correlations of the commonly used 4:1 methanol:ethanol PTM from neutron PDFs obtained under hydro-static compression. The method applies a molecular-dynamics-informed empirical correction and a non-negative matrix factorization algorithm to recover the PDF of the pure sample. Proof of principle is demonstrated, producing corrected high-pressure PDFs of simple crystalline materials, Ni and MgO, and benchmarking these against simulated data from the average structure. Finally, the first local structure determination of α-quartz under hydro-static pressure is presented, extracting compression behaviour of the real-space structure.

A multimodal analytical toolkit to resolve correlated reaction pathways: the case of nanoparticle formation in zeolites

Unraveling the complex, competing pathways that can govern reactions in multicomponent systems is an experimental and technical challenge. We outline and apply a novel analytical toolkit that fully leverages the synchronicity of multimodal experiments to deconvolute causal from correlative relationships and resolve structural and chemical changes in complex materials. Here, simultaneous multimodal measurements combined diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS) and angular dispersive X-ray scattering suitable for pair distribution function (PDF), X-ray diffraction (XRD) and small angle X-ray scattering (SAXS) analyses. The multimodal experimental data was interpreted via multi-level analysis; conventional analyses of each data series were integrated through meta-analysis involving non-negative matrix factorization (NMF) as a dimensional reduction algorithm and correlation analysis. We apply this toolkit to build a cohesive mechanistic picture of the pathways governing silver nanoparticle formation in zeolite A (LTA), which is key to designing catalytic and separations-based applications. For this Ag-LTA system, the mechanisms of zeolite dehydration, framework flexing, ion reduction, and cluster and nanoparticle formation and transport through the zeolite are elucidated. We note that the advanced analytical approach outline here can be applied generally to multimodal experiments, to take full advantage of the efficiencies and self-consistencies in understanding complex materials and go beyond what can be achieved by conventional approaches to data analysis.

Multimodal in situ experimental data probing a complex reaction have been integrated via a multi-level analysis involving non-negative matrix factorization and correlation analysis. This strategy can be applied generally to multimodal experiments.

Implications of the Conformationally Flexible, Macrocyclic Structure of the First-Generation, Direct-Acting Anti-Viral Paritaprevir on Its Solid Form Complexity and Chameleonic Behavior

Direct-acting antiviral regimens have transformed therapeutic management of hepatitis C across all prevalent genotypes. Most of the chemical matter in these regimens comprises molecules well outside the traditional drug development chemical space and presents significant challenges. Herein, the implications of high conformational flexibility and the presence of a 15-membered macrocyclic ring in paritaprevir are studied through a combination of advanced computational and experimental methods with focus on molecular chameleonicity and crystal form complexity. The ability of the molecule to toggle between high and low 3D polar surface area (PSA) conformations is underpinned by intramolecular hydrogen bonding (IMHB) interactions and intramolecular steric effects. Computational studies consequently show a very significant difference of over 75 Ų in 3D PSA between polar and apolar environments and provide the structural basis for the perplexingly favorable passive permeability of the molecule. Crystal packing and protein binding resulting in strong intermolecular interactions disrupt these intramolecular interactions. Crystalline Form I benefits from strong intermolecular interactions, whereas the weaker intermolecular interactions in Form II are partially compensated by the energetic advantage of an IMHB. Like Form I, no IMHB is observed within the receptor-bound conformation; instead, an intermolecular H-bond contributes to the potency of the molecule. The choice of metastable Form II is derisked through strategies accounting for crystal surface and packing features to manage higher form specific solid-state chemical reactivity and specific processing requirements. Overall, the results show an unambiguous link between structural features and derived properties from crystallization to dissolution, permeation, and docking into the protein pocket.

Extracting interface correlations from the pair distribution function of composite materials

Using a non-negative matrix factorisation (NMF) approach, we show how the pair distribution function (PDF) of complex mixtures can be deconvolved into the contributions from the individual phase components and also the interface between phases. Our focus is on the model system Fe∥Fe3O4. We establish proof-of-concept using idealised PDF data generated from established theory-driven models of the Fe∥Fe3O4 interface. Using X-ray total scattering measurements for corroded Fe samples, and employing our newly-developed NMF analysis, we extract the experimental interface PDF ('iPDF') for this same system. We find excellent agreement between theory and experiment. The implications of our results in the broader context of interface characterisation for complex functional materials are discussed.

Revisiting metal fluorides as lithium-ion battery cathodes

Metal fluorides, promising lithium-ion battery cathode materials, have been classified as conversion materials due to the reconstructive phase transitions widely presumed to occur upon lithiation. We challenge this view by studying FeF₃ using X-ray total scattering and electron diffraction techniques that measure structure over multiple length scales coupled with density functional theory calculations, and by revisiting prior experimental studies of FeF₂ and CuF₂. Metal fluoride lithiation is instead dominated by diffusion-controlled displacement mechanisms, and a clear topological relationship between the metal fluoride F^- sublattices and that of LiF is established. Initial lithiation of FeF₃ forms FeF₂ on the particle's surface, along with a cation-ordered and stacking-disordered phase, A-Li_xFe_yF₃, which is structurally related to α-/β-LiMn²⁺Fe³⁺F₆ and which topotactically transforms to B- and then C-Li_xFe_yF₃, before forming LiF and Fe. Lithiation of FeF₂ and CuF₂ results in a buffer phase between FeF₂/CuF₂ and LiF. The resulting principles will aid future developments of a wider range of isomorphic metal fluorides.

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.

Non-equilibrium metal oxides via reconversion chemistry in lithium-ion batteries

Binary metal oxides are attractive anode materials for lithium-ion batteries. Despite sustained effort into nanomaterials synthesis and understanding the initial discharge mechanism, the fundamental chemistry underpinning the charge and subsequent cycles-thus the reversible capacity-remains poorly understood. Here, we use in operando X-ray pair distribution function analysis combining with our recently developed analytical approach employing Metropolis Monte Carlo simulations and non-negative matrix factorisation to study the charge reaction thermodynamics of a series of Fe- and Mn-oxides. As opposed to the commonly believed conversion chemistry forming rocksalt FeO and MnO, we reveal the two oxide series topotactically transform into non-native body-centred cubic FeO and zincblende MnO via displacement-like reactions whose kinetics are governed by the mobility differences between displaced species. These renewed mechanistic insights suggest avenues for the future design of metal oxide materials as well as new material synthesis routes using electrochemically-assisted methods.

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.

A thermal-gradient approach to variable-temperature measurements resolved in space

Temperature is a ubiquitous environmental variable used to explore materials structure, properties and reactivity. This article reports a new paradigm for variable-temperature measurements that varies the temperature continuously across a sample such that temperature is measured as a function of sample position and not time. The gradient approach offers advantages over conventional variable-temperature studies, in which temperature is scanned during a series measurement, in that it improves the efficiency with which a series of temperatures can be probed and it allows the sample evolution at multiple temperatures to be measured in parallel to resolve kinetic and thermodynamic effects. Applied to treat samples at a continuum of tem-peratures prior to measurements at ambient temperature, the gradient approach enables parametric studies of recovered systems, eliminating temperature-dependent structural and chemical variations to simplify interpretation of the data. The implementation of spatially resolved variable-temperature measurements presented here is based on a gradient-heater design that uses a 3D-printed ceramic template to guide the variable pitch of the wire in a resistively heated wire-wound heater element. The configuration of the gradient heater was refined on the basis of thermal modelling. Applications of the gradient heater to quantify thermal-expansion behaviour, to map metastable polymorphs recovered to ambient temperature, and to monitor the time- and temperature-dependent phase evolution in a complex solid-state reaction are demonstrated.

Local Structural Effects Due to Micronization and Amorphization on an HIV Treatment Active Pharmaceutical Ingredient

Processing procedures for inducing domain size reduction and/or amorphous phase generation can be crucial for enhancing the bioavailability of active pharmaceutical ingredients (APIs). It is important to quantify these reduced coherence phases and to detect and characterize associated structural changes, to ensure that no deleterious effects on safety, function, or stability occur. Here, X-ray powder diffraction (XRPD), total scattering pair distribution function (TSPDF) analysis, and solid-state nuclear magnetic resonance spectroscopy (SSNMR) have been performed on samples of GSK2838232B, an investigational drug for the treatment of human immunodeficiency virus (HIV). Preparations were obtained through different mechanical treatments resulting in varying extents of domain size reduction and amorphous phase generation. Completely amorphous formulations could be prepared by milling and microfluidic injection processes. Microfluidic injection was shown to result in a different local structure due to dispersion with dichloromethane (DCM). Implications of combined TSPDF and SSNMR studies to characterize molecular compounds are also discussed, in particular, the possibility to obtain a thorough structural understanding of disordered samples from different processes.