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In materials with one-dimensional electronic bands, electron-electron interactions can produce intriguing quantum phenomena, including spin-charge separation and charge density waves (CDW). Most of these systems, however, are non-magnetic, motivating a search for anisotropic materials where the coupling of charge and spin may affect emergent quantum states. Here, electron doping the van der Waals magnetic semiconductor CrSBr induces an electronically driven quasi-1D CDW, which survives above room temperature. Lithium intercalation also increases the magnetic ordering temperature to 200 K and changes its interlayer magnetic coupling from antiferromagnetic to ferromagnetic. The spin-polarized nature of the anisotropic bands that give rise to this CDW enforces an intrinsic coupling of charge and spin. The coexistence and interplay of ferromagnetism and charge modulation in this exfoliatable material provides a promising platform for studying tunable quantum phenomena across a range of temperatures and thicknesses., Comment: Main text: 30 pages, 4 figures, 1 table. Supplementary Information: 21 pages, 11 figures, 2 tables

A quantitative measure of symmetry breaking is introduced that allows the quantification of which symmetries are most strongly broken due to the introduction of some kind of defect in a perfect structure. The method uses a statistical approach based on the Jensen-Shannon divergence. The measure is calculated by comparing the transformed atomic density function with its original. Software code is presented that carries the calculations out numerically using Monte Carlo methods. The behavior of this symmetry breaking measure is tested for various cases including finite size crystallites (where the surfaces break the crystallographic symmetry), atomic displacements from high symmetry positions, and collective motions of atoms due to rotations of rigid octahedra. The approach provides a powerful tool for assessing local symmetry breaking and offers new insights that can help researchers understand how different structural distortions affect different symmetry operations., Comment: 25 pages, 15 figures

We used interpretable machine learning to combine information from multiple heterogeneous spectra: X-ray absorption near-edge spectra (XANES) and atomic pair distribution functions (PDFs) to extract local structural and chemical environments of transition metal cations in oxides. Random forest models were trained on simulated XANES, PDF, and both combined to extract oxidation state, coordination number, and mean nearest-neighbor bond length. XANES-only models generally outperformed PDF-only models, even for structural tasks, although using the metal's differential PDFs (dPDFs) instead of total PDFs narrowed this gap. When combined with PDFs, information from XANES often dominates the prediction. Our results demonstrate that XANES contain rich structural information and highlight the utility of species-specificity. This interpretable, multimodal approach is quick to implement with suitable databases and offers valuable insights into the relative strengths of different modalities, guiding researchers in experiment design and identifying when combining complementary techniques adds meaningful information to a scientific investigation.

Complex contagion models that involve contagion along higher-order structures, such as simplicial complexes and hypergraphs, yield new classes of mean-field models. Interestingly, the differential equations arising from many such models often exhibit a similar form, resulting in qualitatively comparable global bifurcation patterns. Motivated by this observation, we investigate a generalized mean-field-type model that provides a unified framework for analysing a range of different models. In particular, we derive analytical conditions for the emergence of different bifurcation regimes exhibited by three models of increasing complexity -- ranging from three- and four-body interactions to two connected populations with both pairwise and three-body interactions. For the first two cases, we give a complete characterisation of all possible outcomes, along with the corresponding conditions on network and epidemic parameters. In the third case, we demonstrate that multistability is possible despite only three-body interactions. Our results reveal that single population models with three-body interactions can only exhibit simple transcritical transitions or bistability, whereas with four-body interactions multistability with two distinct endemic steady states is possible. Surprisingly, the two-population model exhibits multistability via symmetry breaking despite three-body interactions only. Our work sheds light on the relationship between equation structure and model behaviour and makes the first step towards elucidating mechanisms by which different system behaviours arise, and how network and dynamic properties facilitate or hinder outcomes., Comment: 23 pages, 9 figures

In this work, we explored data acquisition protocols and improved data reduction protocols using PDFgetX3 to obtain reliable data for atomic pair distribution function (PDF) analysis from a laboratory-based Mo x-ray source. A variable counting scheme is described that preferentially counts in the high-angle region of the diffraction pattern. The effects on the resulting PDF are studied by varying the overall count time, the use of Soller slits, and limiting the out-of-plane divergence of the incident beam. The protocols are tested using an amorphous silica and a quartz sample. We also present a modification to the current PDFgetX3 data corrections to take care of sample absorption, which was previously neglected in the use of that program for high-energy synchrotron x-ray data. We show that, despite limitations in the Q-range and flux of laboratory instruments, reasonable data for PDF model fits may be obtained using the best protocols in a few hours of counting.

Past studies show that coupled model biases in European blocking and North Atlantic eddy-driven jet variability decrease as one increases the horizontal resolution in the atmospheric and oceanic model components. This has commonly been argued to be related to an alleviation of sea surface temperature (SST) biases due to increased oceanic resolution in particular, with a physical pathway via changes to surface baroclinicity. On the other hand, many studies have now highlighted the key role of diabatic processes in the Gulf Stream region on blocking formation and maintenance. Here, following recent work by Schemm, we leverage a large multi-model ensemble to show that Gulf Stream precipitation variability in coupled models is tightly linked to the simulated frequency of European blocking and northern jet excursions. Furthermore, the reduced biases in blocking and jet variability are consistent with greater precipitation variability as a result of increased atmospheric horizontal resolution. By contrast, typical North Atlantic SST biases are found to share only a weak or negligible relationship with blocking and jet biases. Finally, while previous studies have used a comparison between coupled models and models run with prescribed SSTs to argue for the role of ocean resolution, we emphasise here that models run with prescribed SSTs experience greatly reduced precipitation variability due to their excessive thermal damping, making it unclear if such a comparison is meaningful. Instead, we speculate that most of the reduction in coupled model biases may actually be due to increased atmospheric resolution., Comment: Submitted for review

Structural modelling of $operando$ pair distribution function (PDF) data of functional materials can be highly complex. To aid the understanding of complex operando PDF data, we here demonstrate a toolbox for PDF analysis. The tools include the structureMining, similarityMapping, nmfMapping apps available through the online service 'PDF in the cloud' (PDFitc, www.pdfitc.org), as well as noise-filtering using principal component analysis (PCA). The tools are applied to both ex situ and operando PDF data for 3 nm $\mathrm{TiO_{2}}$-bronze nanocrystals, which function as the active electrode material in a Li-ion battery. The tools enable structural modelling of the ex situ and operando PDF data, revealing two pristine $\mathrm{TiO_{2}}$ phases (bronze and anatase) and two lithiated $\mathrm{Li_{x}TiO_{2}}$ phases (lithiated versions of bronze and anatase), and the phase evolution during Galvanostatic cycling is characterized., Comment: Preprint, 82 pages in total (front page: 1 page, abstract: 1 page, paper: 34 pages, supporting information: 40 pages, references: 5 pages, synopsis: 1 page), 35 figures in total (frontpage: 1 figure, paper: 8 figures, supporting information: 26 figures)

Material functionality can be strongly determined by structure extending only over nanoscale distances. The pair distribution function presents an opportunity to shift structural studies beyond idealized crystal models and investigate structure over varying length scales. Applying this method with ultrafast time resolution has the potential to similarly disrupt the study of structural dynamics and phase transitions. Here, we demonstrate such a measurement of CuIr$_{2}$S$_{4}$ optically pumped from its low temperature Ir-dimerized phase. Dimers are optically suppressed without spatial correlation, generating a structure whose level of disorder depends strongly on length scale. The re-development of structural ordering over tens of picoseconds is directly tracked over both space and time as a transient state is approached. This measurement demonstrates both the crucial role of local structure and disorder in non-equilibrium processes and the feasibility of accessing this information with state-of-the-art XFEL facilities., Comment: 14 page manuscript with 4 figures. 13 page Supplementary with 17 figures. 27 pages and 21 figures in total

Recently there has been an increasing interest in studying dynamical processes on networks exhibiting higher-order structures, such as simplicial complexes, where the dynamics acts above and beyond dyadic interactions. Using simulations or heuristically derived epidemic spreading models it was shown that new phenomena can emerge, such as bi-stability/multistability. Here, we show that such new emerging phenomena do not require complex contact patterns, such as community structures, but naturally result from the higher-order contagion mechanisms. We show this by deriving an exact higher-order SIS model and its limiting mean-field equivalent for fully connected simplicial complexes. Going beyond previous results, we also give the global bifurcation picture for networks with 3- and 4-body interactions, with the latter allowing for two non-trivial stable endemic steady states. Differently from previous approaches, we are able to study systems featuring interactions of arbitrary order. In addition, we characterise the contributions from higher-order infections to the endemic equilibrium as perturbations of the pairwise baseline, finding that these diminish as the pairwise rate of infection increases. Our approach represents a first step towards a principled understanding of higher-order contagion processes beyond triads and opens up further directions for analytical investigations., Comment: 19 pages, 14 figures

The open-source python package diffpy.mpdf, part of the DiffPy suite for diffraction and pair distribution function analysis, provides a user-friendly approach for performing magnetic pair distribution function (mPDF) analysis. The package builds on existing libraries in the DiffPy suite to allow users to create models of magnetic structures and calculate corresponding one-dimensional and three-dimensional mPDF patterns. diffpy.mpdf can be used to perform fits to mPDF data either in isolation or in combination with atomic PDF data for joint refinements of the atomic and magnetic structure. Examples are given using MnO and MnTe as representative antiferromagnetic compounds and MnSb as a representative ferromagnet.

Many models in mathematical epidemiology are developed with the aim to provide a framework for parameter estimation and then prediction. It is well-known that parameters are not always uniquely identifiable. In this paper we consider network-based mean-field models and explore the problem of parameter identifiability when observations about an epidemic are available. Making use of the analytical tractability of most network-based mean-field models, e.g., explicit analytical expressions for leading eigenvalue and final epidemic size, we set up the parameter identifiability problem as finding the solution or solutions of a system of coupled equations. More precisely, subject to observing/measuring growth rate and final epidemic size, we seek to identify parameter values leading to these measurements. We are particularly concerned with disentangling transmission rate from the network density. To do this we define strong and weak identifiability and we find that except for the simplest model, parameters cannot be uniquely determined, that is they are weakly identifiable. This means that there exists multiple solutions (a manifold of infinite measure) which give rise to model output that is close to the data. Identifying, formalising and analytically describing this problem should lead to a better appreciation of the complexity involved in fitting models with many parameters to data., Comment: 14 pages, 3 figures

The paper contributes to strengthening the relation between machine learning and the theory of differential equations. In this context, the inverse problem of fitting the parameters, and the initial condition of a differential equation to some measurements constitutes a key issue. The paper explores an abstraction that can be used to construct a family of loss functions with the aim of fitting the solution of an initial value problem to a set of discrete or continuous measurements. It is shown, that an extension of the adjoint equation can be used to derive the gradient of the loss function as a continuous analogue of backpropagation in machine learning. Numerical evidence is presented that under reasonably controlled circumstances the gradients obtained this way can be used in a gradient descent to fit the solution of an initial value problem to a set of continuous noisy measurements, and a set of discrete noisy measurements that are recorded at uncertain times.

We investigate a prototype application for machine-readable literature. The program is called "pyDataRecognition" and serves as an example of a data-driven literature search, where the literature search query is an experimental data-set provided by the user. The user uploads a powder pattern together with the radiation wavelength. The program compares the user data to a database of existing powder patterns associated with published papers and produces a rank ordered according to their similarity score. The program returns the digital object identifier (doi) and full reference of top ranked papers together with a stack plot of the user data alongside the top five database entries. The paper describes the approach and explores successes and challenges., Comment: 27 pages, 4 figures

Structural modelling of octahedral tilts in perovskites is typically done using the symmetry constraints of the resulting space group. In most cases, this introduces more degrees of freedom than those strictly necessary to describe only the octahedral tilts. It can therefore be a challenge to disentangle the octahedral tilts from other structural distortions such as cation displacements and octahedral distortions. This paper reports on the development of constraints for modelling pure octahedral tilts and implemented the constraints in diffpy-CMI, a powerful package to analyse pair distribution function (PDF) data. The program allows features in the PDF that come from rigid tilts to be separated from non-rigid relaxations, provides an intuitive picture of the tilting, and as it has many fewer refinable variables than the unconstrained space-group fits, provides robust and stable refinements of the tilt components. It further demonstrates the use of the model on the canonical tilted perovskite CaTiO$_3$ which has a known Glazer tilt system $\alpha^+ \beta^- \beta^-$. The Glazer model fits comparably to the corresponding space group model $Pnma$ below $r$ = 14 A and becomes progressively worse than the space group model at higher $r$ due to non-rigid distortions in the real material., Comment: 17 pages, 5 figures, 2 tables

Machine learning models based on convolutional neural networks have been used for predicting space groups of crystal structures from their atomic pair distribution function (PDF). However, the PDFs used to train the model are calculated using a fixed set of parameters that reflect specific experimental conditions, and the accuracy of the model when given PDFs generated with different choices of these parameters is unknown. In this paper, we report that the results of the top-1 accuracy and top-6 accuracy are robust when applied to PDFs of different choices of experimental parameters $r_\text{max}$, $Q_\text{max}$, $Q_\text{damp}$ and atomic displacement parameters., Comment: 15 pages, 5 figures

Cubic energy materials such as thermoelectrics or hybrid perovskite materials are often understood to be highly disordered. In GeTe and related IV-VI compounds, this is thought to provide the low thermal conductivities needed for thermoelectric applications. Since conventional crystallography cannot distinguish between static disorder and atomic motions, we develop the energy-resolved variable-shutter pair distribution function technique. This collects structural snapshots with varying exposure times, on timescales relevant for atomic motions. In disagreement with previous interpretations, we find the time-averaged structure of GeTe to be crystalline at all temperatures, but with anisotropic anharmonic dynamics at higher temperatures that resemble static disorder at fast shutter speeds, with correlated ferroelectric fluctuations along the $<$100$>$c direction. We show that this anisotropy naturally emerges from a Ginzburg-Landau model that couples polarization fluctuations through long-range elastic interactions. By accessing time-dependent atomic correlations in energy materials, we resolve the long-standing disagreement between local and average structure probes, and show that spontaneous anisotropy is ubiquitous in cubic IV-VI materials., Comment: Published version, substantial changes, many references removed due to journal limits :-( Please see the supporting information online. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format (see conditions)

An approach is described for studying texture in nanostructured materials. The approach implements the real space texture PDF, txPDF, laid out in [Gong and Billinge (2018) arXiv:1805.10342 [cond-mat]]. It is demonstrated on a fiber textured polycrystalline Pt thin film. The approach uses 3D PDF methods to reconstruct the orientation distribution function (ODF) of the powder crystallites from a set of diffraction patterns taken at different tilt angles of the substrate with respect to the incident beam directly from the 3D PDF of the sample. A real space equivalent of the reciprocal space pole figure is defined in terms of interatomic vectors in the PDF and computed for various interatomic vectors in the Pt film. Further, it is shown how a valid isotropic PDF may be obtained from a weighted average over the tilt series, and the measurement conditions for the best approximant to the isotropic PDF from a single exposure, which for the case of the fiber textured film was in a nearly grazing incidence orientation of around 10 degrees. Finally, we describe an open source Python software package, Fourigui, that may be used to help in studies of texture from 3D reciprocal space data, and indeed for Fourier transforming and visualizing 3D PDF data in general.

A cloud-hosted web-based software application, nmfMapping, for carrying out a nonnegative matrix factorization of a set of powder diffraction or atomic pair distribution function datasets is described. This app allows structure scientists to rapidly find trends 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 the pdfitc.org website., Comment: 19 Pages, 7 Figures, submitted to Acta Crystallographica Section A

Deep learning (DL) is one of the fastest growing topics in materials data science, with rapidly emerging applications spanning atomistic, image-based, spectral, and textual data modalities. DL allows analysis of unstructured data and automated identification of features. Recent development of large materials databases has fueled the application of DL methods in atomistic prediction in particular. In contrast, advances in image and spectral data have largely leveraged synthetic data enabled by high quality forward models as well as by generative unsupervised DL methods. In this article, we present a high-level overview of deep-learning methods followed by a detailed discussion of recent developments of deep learning in atomistic simulation, materials imaging, spectral analysis, and natural language processing. For each modality we discuss applications involving both theoretical and experimental data, typical modeling approaches with their strengths and limitations, and relevant publicly available software and datasets. We conclude the review with a discussion of recent cross-cutting work related to uncertainty quantification in this field and a brief perspective on limitations, challenges, and potential growth areas for DL methods in materials science. The application of DL methods in materials science presents an exciting avenue for future materials discovery and design.

Here we explore the use of scanning electron diffraction coupled with electron atomic pair distribution function analysis (ePDF) to understand the local order as a function of position in a complex multicomponent system, a hot rolled, Ni-encapsulated, Zr$_{65}$Cu$_{17.5}$Ni$_{10}$Al$_{7.5}$ bulk metallic glass (BMG), with a spatial resolution of 3 nm. We show that it is possible to gain insight into the chemistry and chemical clustering/ordering tendency in different regions of the sample, including in the vicinity of nano-scale crystallites that are identified from virtual dark field images and in heavily deformed regions at the edge of the BMG. In addition to simpler analysis, unsupervised machine learning was used to extract partial PDFs from the material, modeled as a quasi-binary alloy, and map them in space. These maps allowed key insights not only into the local average composition, as validated by EELS, but also a unique insight into chemical short-range ordering tendencies in different regions of the sample during formation. The experiments are straightforward and rapid and, unlike spectroscopic measurements, don't require energy filters on the instrument. We spatially map different quantities of interest (QoI's), defined as scalars that can be computed directly from positions and widths of ePDF peaks or parameters refined from fits to the patterns. We developed a flexible and rapid data reduction and analysis software framework that allows experimenters to rapidly explore images of the sample on the basis of different QoI's. The power and flexibility of this approach are explored and described in detail. Because of the fact that we are getting spatially resolved images of the nanoscale structure obtained from ePDFs we call this approach scanning nano-structure electron microscopy (SNEM), and we believe that it will be powerful and useful extension of current 4D-STEM methods.

We demonstrate spatial mapping of the local and nano-scale structure of thin film objects using spatially resolved PDF analysis of synchrotron x-ray diffraction data. This is demonstrated 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. We present a software implementation of the whole protocol including an approach for automated data acquisition and analyis using the atomic pair distribution function (PDF) method. The protocol software can handle semi-automated data reduction, normalization and modelling, with user-defined recipes generating a comprehensive collection of metadata and analysis results. By slicing the collection using included functions it was possible to build images of the 2D object containing using different quantities for contrast, allowing us to determine the spatial map relating to different aspects of the local structure on the array., Comment: 6 pages, 6 figures