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Abstract Characterization of material structure with X-ray or neutron scattering using e.g. Pair Distribution Function (PDF) analysis most often rely on refining a structure model against an experimental dataset. However, identifying a suitable model is often a bottleneck. Recently, automated approaches have made it possible to test thousands of models for each dataset, but these methods are computationally expensive and analysing the output, i.e. extracting structural information from the resulting fits in a meaningful way, is challenging. OurMachineLearning basedMotifExtractor (ML-MotEx) trains an ML algorithm on thousands of fits, and uses SHAP (SHapley Additive exPlanation) values to identify which model features are important for the fit quality. We use the method for 4 different chemical systems, including disordered nanomaterials and clusters. ML-MotEx opens for a type of modelling where each feature in a model is assigned an importance value for the fit quality based on explainable ML. 

Abstract Using Pair Distribution Function (PDF) analysis of in situ total scattering data, we investigate the formation of tungsten and niobium oxides in a simple solvothermal synthesis. We use Pearson Correlation Coefficient (PCC) analysis of the time resolved PDFs to both map the structural changes taking place throughout the synthesis and identify structural models for precursor and product through PCC‐based structure mining. Our analysis first shows that ultra‐small tungsten and niobium oxide nanoparticles form instantaneously upon heating, with sizes between 1.5 and 2 nm. We show that the main structural motifs in the nanoparticles can be described with structures containing pentagonal columns, which is characteristic for many bulk tungsten and niobium oxides. We furthermore elucidate the structure of the precursor complex as clusters of octahedra with O‐ and Cl‐ligands. The PCC based methodology automates the structure characterization and proves useful for analysis of large datasets of for example, time resolved X‐ray scattering studies. The PCC is implemented in ‘PDF in the cloud’, a web platform for PDF analysis. 

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 reportedClusterFinderalgorithm can screen 10⁴to 10⁵candidate 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. 

The pyrolysis of ZIF-67 is followedin situ, and the conditions are correlated with the structural evolution and electrocatalytic performance. 

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. 

We present a deep learning algorithm, DeepStruc, that can solve a simple nanoparticle structure directly from an experimental Pair Distribution Function (PDF) by using a conditional variational autoencoder. 

Motivated by some variational problems from a nonlocal model of mechanics, this work presents a set of sufficient conditions that guarantee a compact inclusion in the function space of $$ L^{p} $$ vector fields defined on a domain $$ \Omega $$ that is either a bounded domain in $$ \mathbb{R}^{d} $$ or $$ \mathbb{R}^{d} $$ itself. The criteria are nonlocal and are given with respect to nonlocal interaction kernels that may not be necessarily radially symmetric. Moreover, these criteria for vector fields are also different from those given for scalar fields in that the conditions are based on nonlocal interactions involving only parts of the components of the vector fields. The $$ L^{p} $$ compactness criteria are utilized in demonstrating the convergence of minimizers of parameterized nonlocal energy functionals.