Experimental Pair Distribution Function Research Articles

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

We present MLstructureMining, a machine learning tool that identifies a structural model from an experimental pair distribution function. We show how the method can be used for structure analysis of both crystalline and nanocrystalline materials.

Atomistic-Scale Simulations Toward the Understanding of the Conversion–Alloying Mechanism in Li-Ion Battery Anodes

The increasing demands for energy storage call for improved capacity and cycling stability of modern Li-ion batteries (LIBs). However, the application of the state-of-the-art LIB anode material – graphite is limited as graphite underperforms as a high-rate/high-storage-capacity anode. Alternatively, materials capable of alloying with Li-ions have attracted attention as a promising pathway to solve high-rate and high-capacity challenges. Furthermore, when alloying reaction in a material is coupled with irreversible conversion reaction, the materials operating under such mechanism exhibit a high Li-ion storage capacity and long-term stability during electrochemical cycling. However, despite the optimistic performance of these materials, a number of parameters need to be optimized and fundamentally understood.Among the unknowns for the conversion/alloying materials are the atomistic details of the reaction mechanism - understanding the atomistic structure during transformations is a pre-requisite for the future rational optimization of the materials. Furthermore, amorphization, which is prevalent in these materials, severely limits the conventional characterization methods essentially impeding further development and understanding the degradation mechanisms. Hence, to investigate the atomistic structure changes, we proposed a computational methodology for these conversion-alloying materials and their reaction mechanism by taking amorphous substoichiometric silicon nitride as a showcase system [1]. The molecular dynamics (MD) simulations utilized the ReaxFF parameter set which was specifically developed for the investigation. Subsequently, the experimental pair distribution functions (PDF) were used to verify the modeling results.While the reactive molecular dynamics was coupled with the PDF simulation to complement the experimental measurements, the effective and practical approach guided us to the atomistic structure evolution understanding for LIBs in a conversion–alloying process, revealing the bond coordinations around the Si atoms in the active material. Consequently, the analysis opened an in-depth understanding of the cycling stability of substoichiometric a-SiNx anode materials by revealing the atomistic features relevant to the changes this material undergoes during lithiation and delithiation processes in a LIB. Furthermore, the proposed approach allows modeling of the changes at the atomistic scale for the amorphous materials and predicting the experimental PDF at different cycling stages, verifying the modeling outcome. The topic also addresses the applications of the approach for other anode materials.

Multilevel atomic structural model for interstratified opal materials

The structure of opal has long fascinated scientists. It occurs in a number of structural states, ranging from amorphous to exhibiting features of stacking disorder. Opal-CT, where C and T signify cristobalite- and tridymite-like interstratification, represents an important link in the length scales between amorphous and crystalline states. However, details about local atomic (dis)order and arrangements extending to long-range stacking faults in opal polymorphs remain incompletely understood. Here, a multilevel modeling approach is reported that considers stacking states in correlation with the abundance of C and T segments as a high-level structural parameter (i.e. not each atom). Optimization accounting for inter-tetrahedral bond lengths and angles and the regularity of the silicate tetrahedra is included as lower levels of structural parameters. Together, a set of parameters with both coarse-grained and atomistic features for different levels of structural details is refined. Structural disorder at the ∼10–100 Å distance scale is evaluated using experimental pair distribution function and diffraction datasets, comparing peak intensities, widths and asymmetry. This work presents a complete multilevel structural description of natural opal-CT and explains many of the unusual features observed in X-ray powder diffraction patterns. This modeling approach can be adopted generally for analyzing layered materials and their assembly into 3D structures.

Modeling Short-Range Order in Disordered Rocksalt Cathodes by Pair Distribution Function Analysis

Pair distribution function (PDF) analysis is a powerful technique for the characterization of short-range order (SRO) in disordered materials. Accurate interpretation of experimental PDF data is critically reliant on the development of structural models that can account for local variations in site occupancies and bond lengths. To this end, we outline an approach to model SRO using first-principles calculations based on the cluster-expansion formalism. These methods are validated on neutron scattering data from two disordered rocksalt oxyfluorides, Li1.3Mn0.4Ti0.3O1.7F0.3 and Li1.3Mn0.4Nb0.2Ti0.1O1.7F0.3. For each composition, we demonstrate that an average structure without any SRO fails to reproduce several key features in the experimental PDF. To pinpoint the origin of the suspected SRO in these materials, configurational and displacive effects were separately investigated using two disparate models. Special quasi-random structures were relaxed using density functional theory to account for local changes in bond lengths while maintaining a near-random ionic configuration. This leads to slightly improved accuracy but still misrepresents asymmetry in the first few peaks of the PDF. Monte Carlo simulations were performed to model configurational SRO on a fixed lattice, which by itself is shown to have a minimal influence on the PDF. Instead, we find that it is the bond length relaxations within environments created by SRO which controls the details of the PDF, thereby highlighting the subtle but important coupling between configurational and displacive SRO in disordered materials.

A small-box approach to the local crystal structure of Y3NbO7

The local crystal structure of Y3NbO7 was probed using neutron total scattering. Five different structural models were fit to the experimental pair distribution function of this material up to 15 Å. Fits of defect fluorite (Fm3‾m), pyrochlore (Fd3‾m), and orthorhombic C weberite models (C2221) were attempted based on prior structural investigations of Y3NbO7 and related fluorite-based materials. Orthorhombic P weberite (P2221) and monoclinic weberite models (P1121) were derived via symmetry reduction of the orthorhombic C weberite structure. All models except monoclinic weberite failed to reproduce the experimental pair distribution function. Misfits were clearly visible for peaks arising from atom pairs within the first coordination shell (defect fluorite and pyrochlore) and beyond (orthorhombic C and P weberite). By contrast, monoclinic weberite (γ ≈ 91.8°) provided an excellent fit, with no major misfits observed. This unit cell features distorted YO8 dodecahedra, YO7 monocapped octahedra, and NbO6 octahedra as building blocks. Comparison between the topologies of the cationic and anionic substructures in monoclinic weberite and its parent orthorhombic C structure revealed displacements of the metal atoms along the [100] direction and a less compact spatial distribution of oxygen atoms along the a axis. The monoclinic weberite model presented herein may serve as a starting point to revisit structural modeling of fluorite-based materials with challenging local structures.

Pair distribution function analysis of discrete nanomaterials in PDFgui

Pair distribution functions (PDFs) are a leading tool for atomic structure analysis of nanomaterials. However, the most widely used programs for refining atomic structure against PDF data are based on extended crystallographic models, which cannot be applied to discrete, whole nanoparticles. This work describes a straightforward approach to simulate and refine atomistic models of discrete clusters and nanoparticles employing widely used PDF modelling programs such as PDFgui [Farrow et al. (2007). J. Phys. Condens. Matter, 19, 335219] that utilize extended crystallographic models. In this approach, the whole particle to be modelled is contained within an expanded, and otherwise empty, unit cell that is sufficiently large to avoid correlations between atoms in neighbouring unit cells over the r range analysed. The PDF of the particle is simulated as a composite using two conventional `phases': one that calculates the atom–atom correlations and one that approximates the local number density. This approach is first validated for large nanoparticles that are well modelled by a conventional shape factor model, and then applied to simulate the PDF of discrete particles and low-dimensional materials (graphene and MXene) and to model the experimental PDF data for single-layer FeS nanosheets. A comparison of this approach with the DiffPy-CMI program [Juhás et al. (2015). Acta Cryst. A71, 562–568], which calculates the PDF of discrete species, shows that the composite modelling approach is equally or more accurate. Example input files for implementing this approach within PDFgui and TOPAS [Coelho (2018). J. Appl. Cryst. 51, 210–218], and recommendations for selecting model parameters for reliable application of this refinement strategy, are provided.

Toward Atomistic Understanding of Materials with the Conversion–Alloying Mechanism in Li-Ion Batteries

The need for practical anodes for rechargeable batteries calls for new materials with improved storage capacity and cycling stability compared to the materials of today. Materials capable of alloying with alkali metals have been long viewed as a promising pathway to address this challenge. Meanwhile, severe drawbacks associated with the use of such materials led to the development of suitable alternatives, in which governing the reaction mechanism in a battery combines conversion and alloying reactions. These materials feature a high storage capacity and long-term stability during electrochemical cycling. However, the development of these materials is impeded by a lack of fundamental structural understanding due to the complexity of the chemical transformations taking place during battery cycling. Furthermore, amorphization, which is prevalent in these materials, also severely limits the conventional methods of characterization. In the present work, we propose a computational methodology for understanding the structure and reaction mechanism of these conversion–alloying materials by using amorphous substoichiometric silicon nitride as a model system. The developed ReaxFF parameter set allowed exploring the atomistic structure of this material and verify the resulting models through a comparison of calculated and experimentally obtained pair distribution functions (PDFs). The developed methodology also allowed exploring the structural changes occurring during lithiation and delithiation, i.e., operation mechanism in a battery. The analysis of the atomistic structure demonstrates that initial lithiation results in the formation of a Si network, which later participates in further lithiation process. Delithiation also influences the evolution of the amorphous Si network facilitating separation of nitrogen-rich and Si-rich regions and, therefore, confirming the conversion mechanism proposed earlier. Furthermore, the proposed approach allows modeling not only changes at the atomistic scale but also predicting the experimental PDF at different stages of cycling which allows experimentally verifying the outcome of modeling.

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.

Special quasirandom structures description of the local structure of disordered Bi0.5K0.5TiO3

Polar nanoregions (PNRs) are believed to play a decisive role in the local and macroscopic polarization in relaxor ferroelectrics. The limited microscopic understanding of the structure and dynamics of PNRs hampers the rational design of new lead-free materials. Here, the local structure of A-site disordered Bi0.5K0.5TiO3 (BKT) is investigated using synchrotron x-ray and neutron pair distribution function (PDF) analysis and density functional theory (DFT) optimized special quasirandom structures (SQSs). DFT-relaxed SQS with a 4 × 4 × 4 supercell size can reproduce the experimental PDFs of disordered BKT, as well as the partial PDFs and total polarization, with comparable results to those reported from a combined analysis of x-ray and neutron PDF data with large-box reverse Monte Carlo methods. We find that small Bi3+-rich polar clusters are likely to be the microscopic origin of relaxor behavior in disordered BKT, and that the existence of large polar nanoregions (PNRs) is not necessary to explain the relaxor properties. Our results also highlight the great potential of the SQS approach to gain a nanoscale-to-microscopic understanding of other relaxor solid solutions.

Atomic-Layer-Deposited Aluminum Oxide Thin Films Probed with X-ray Scattering and Compared to Molecular Dynamics and Density Functional Theory Models.

A better understanding of amorphous aluminum oxide's structure and electronic properties is obtained through combined experimental and computational approaches. Grazing incidence X-ray scattering measurements were carried out on aluminum oxide thin films grown using thermal atomic layer deposition. The corresponding pair distribution functions (PDFs) showed structures similar to previously reported PDFs of solid-state amorphous alumina and molten alumina. Structural models based on crystalline alumina polymorphs (PDFgui) and amorphous alumina (molecular dynamics, MD) were examined for structural comparisons to the experimental PDF data. Smaller MD models were optimized and verified against larger models to allow for quantum chemical electronic structure calculations. The electronic structure of the amorphous alumina models yields additional insight into the band structure and electronic defects present in amorphous alumina that are not present in crystalline samples.

Atomic structure of an FeCrMoCBY metallic glass revealed by high energy x-ray diffraction

Amorphous bulk metallic glasses with the composition Fe48Cr15Mo14C15B6Y2 have been of interest due to their special mechanical and electronic properties, including corrosion resistance, high yield-strength, large elasticity, catalytic performance, and soft ferromagnetism. Here, we apply a reverse Monte Carlo technique to unravel the atomic structure of these glasses. The pair-distribution functions for various atomic pairs are computed based on the high-energy x-ray diffraction data we have taken from an amorphous sample. Monte Carlo cycles are used to move the atomic positions until the model reproduces the experimental pair-distribution function. The resulting fitted model is consistent with our ab initio simulations of the metallic glass. Our study contributes to the understanding of functional properties of Fe-based bulk metallic glasses driven by disorder effects.

Atomic-Spring-like Effect in Glassy Silica-Helium Composites

We determine the structural origin of an “atomic-spring-like effect” in a glassy silica-helium composite, which exhibits this mechanical property that reversibly accumulates and restores energy at the subnanoscale based on a high-pressure experimental pair distribution function study combined with atom-scale molecular simulations. These unexpected experimental results were obtained by using a 3 μm spot size 61 keV X-ray beam and large area detector and by subtracting the scattered intensity due to helium outside the sample from the silica signal at the same focal point for each pressure point. The compression behavior of the glassy silica-helium composite is characterized on a structural level by the change from a uni- to bimodal distribution in the inter-tetrahedral distances in the amorphous isotropic structure of silica. We propose a simple characterization of this atomic-spring-like glass property using impedance spectroscopy measurements.

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.

Detailed total scattering analysis of disorder in ZIF-8

This work investigates the X-ray scattering signatures of disorder in the zeolitic imidazolate framework ZIF-8. Two layer disorder models are examined in reciprocal space and compared with conventional Rietveld analysis. Stacking faults along the [001] direction of the cubic lattice are in poor agreement with experimental powder diffraction data, consistent with previously reported density functional theory studies showing that these defects are energetically unfavorable compared with amorphization. Meanwhile, fluctuation of layer position along the [110] direction of the cubic lattice shows a significant agreement with experimental data. This result is interpreted analogously to an anisotropic strain mechanism, suggesting links between elastic anisotropy and crystallographic imperfections found in metal–organic framework materials. In direct space, it is demonstrated that models accounting for the static position disorder amongst the linker and metal sublattices are required to fit the experimental pair distribution function data.

Local structure and distortions of mixed methane-carbon dioxide hydrates

A vast source of methane is found in gas hydrate deposits, which form naturally dispersed throughout ocean sediments and arctic permafrost. Methane may be obtained from hydrates by exchange with hydrocarbon byproduct carbon dioxide. It is imperative for the development of safe methane extraction and carbon dioxide sequestration to understand how methane and carbon dioxide co-occupy the same hydrate structure. Pair distribution functions (PDFs) provide atomic-scale structural insight into intermolecular interactions in methane and carbon dioxide hydrates. We present experimental neutron PDFs of methane, carbon dioxide and mixed methane-carbon dioxide hydrates at 10 K analyzed with complementing classical molecular dynamics simulations and Reverse Monte Carlo fitting. Mixed hydrate, which forms during the exchange process, is more locally disordered than methane or carbon dioxide hydrates. The behavior of mixed gas species cannot be interpolated from properties of pure compounds, and PDF measurements provide important understanding of how the guest composition impacts overall order in the hydrate structure.

X-ray scattering study of water confined in bioactive glasses: experimental and simulated pair distribution function.

Temperature-dependent total X-ray scattering measurements for water confined in bioactive glass samples with 5.9 nm pore diameter have been performed. Based on these experimental data, simulations were carried out using the Empirical Potential Structure Refinement (EPSR) code, in order to study the structural organization of the confined water in detail. The results indicate a non-homogeneous structure for water inside the pore, with three different structural organizations of water, depending on the distance from the pore surface: (i) a first layer (4 Å) of interfacial pore water that forms a strong chemical bond with the substrate, (ii) intermediate pore water forming a second layer (4-11 Å) on top of the interfacial pore water, (iii) bulk-like pore water in the centre of the pores. Analysis of the simulated site-site partial pair distribution function shows that the water-silica (Ow-Si) pair correlations occur at ∼3.75 Å. The tetrahedral network of bulk water with oxygen-oxygen (Ow-Ow) hydrogen-bonded pair correlations at ∼2.8, ∼4.1 and ∼4.5 Å is strongly distorted for the interfacial pore water while the second neighbour pair correlations are observed at ∼4.0 and ∼4.9 Å. For the interfacial pore water, an additional Ow-Ow pair correlation appears at ∼3.3 Å, which is likely caused by distortions due to the interactions of the water molecules with the silica at the pore surface.

Cluster-mining: an approach for determining core structures of metallic nanoparticles from atomic pair distribution function data.

A novel approach for finding and evaluating structural models of small metallic nanoparticles is presented. Rather than fitting a single model with many degrees of freedom, libraries of clusters from multiple structural motifs are built algorithmically and individually refined against experimental pair distribution functions. Each cluster fit is highly constrained. The approach, called cluster-mining, returns all candidate structure models that are consistent with the data as measured by a goodness of fit. It is highly automated, easy to use, and yields models that are more physically realistic and result in better agreement to the data than models based on cubic close-packed crystallographic cores, often reported in the literature for metallic nanoparticles.

A real-space approach to the analysis of stacking faults in close-packed metals: G(r) modelling and Q-space feedback

An R-space approach to the simulation and fitting of a structural model to the experimental pair distribution function is described, to investigate the structural disorder (distance distribution and stacking faults) in close-packed metals. This is carried out by transferring the Debye function analysis into R space and simulating the low-angle and high-angle truncation for the evaluation of the relevant Fourier transform. The strengths and weaknesses of the R-space approach with respect to the usual Q-space approach are discussed.

Structure of liquid ammonia at high pressures and temperatures

The structure of liquid ammonia (${\mathrm{NH}}_{3}$) is investigated from 1 to 6.3 GPa and up to 800 K by means of synchrotron x-ray diffraction (XRD) and ab initio molecular dynamics (AIMD) simulations. The XRD data are used to extract the molecular structure factor ${S}_{\mathrm{mol}}(Q)$, pair distribution function (PDF) ${g}_{\mathrm{mol}}(r)$, and the density of ${\mathrm{NH}}_{3}$. There is an excellent agreement between present ${S}_{\mathrm{mol}}(Q)$ and ${g}_{\mathrm{mol}}(r)$ at our lowest density and those reported in reference neutron experiments. Our densities agree better with the equation of state (EoS) of Tillner-Roth et al. [DKV-Tagungsbericht (Hannover, New York, 1993), Vol. 20, p. 167] than with more recent EoS models. The experimental structure factor and PDF are well reproduced by AIMD simulations using either the Becke-Lee-Yang-Parr or the Perdew-Burke-Ernzerhof exchange-correlation functional. The shapes of ${S}_{\mathrm{mol}}(Q)$ and ${g}_{\mathrm{mol}}(r)$ vary little over the investigated pressure range and suggest a compact liquid with weak orientational correlations between molecules, which is corroborated by the coordination number varying from 12.7 to $\ensuremath{\sim}14$. The simulations are used to study the evolution of the site-site pair distribution functions, which reveals that the number of H bonds per molecule (between 1.5 and 2) do not evolve with density and that the distribution of H atoms around N atoms becomes more and more anisotropic with pressure.

Structural Analysis of Ligand-Protected Smaller Metallic Nanocrystals by Atomic Pair Distribution Function under Precession Electron Diffraction

Atomic pair distribution function (PDF) analysis has been widely used to investigate nanocrystalline and structurally disordered materials. Experimental PDFs retrieved from electron diffraction (eP...