Advancing reverse Monte Carlo structure refinements to the nanoscale

Mapping Polar Distortions using Nanobeam Electron Diffraction and a Cepstral Approach

Measuring local polar ordering is key to understanding ferroelectricity in thin films, especially for systems with small domains or significant disorder. Scanning nanobeam electron diffraction (NBED) provides an effective local probe of lattice parameters, local fields, polarization directions, and charge densities, which can be analyzed using a relatively low beam dose over large fields of view. However, quantitatively extracting the magnitudes and directions of polarization vectors from NBED remains challenging. Here, we use a cepstral approach, similar to a pair distribution function, to determine local polar displacements that drive ferroelectricity from NBED patterns. Because polar distortions generate asymmetry in the diffraction pattern intensity, we can efficiently recover the underlying displacements from the imaginary part of the cepstrum transform. We investigate the limits of this technique using analytical and simulated data and give experimental examples, achieving the order of 1.1 pm precision and mapping of polar displacements with nanometer resolution.

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.

New capabilities for enhancement of RMCProfile: instrumental profiles with arbitrary peak shapes for structural refinements using the reverse Monte Carlo method

Reported here are the development and application of new capabilities in the RMCProfile software for structural refinements using the reverse Monte Carlo (RMC) method. An algorithm has been implemented to enable the use of arbitrary peak-shape functions in the modeling of Bragg diffraction patterns and instrumental resolution effects on total-scattering data. This capability eliminates the dependence of RMCProfile on preset functions, which are inadequate for data produced by some total-scattering instruments, e.g. NOMAD at the Spallation Neutron Source (SNS) at Oak Ridge, Tennessee, USA. The recently developed procedure for the instrument-resolution correction has been modified to improve its accuracy, which is critical for recovering nanoscale structure. The ability to measure fine details of local and nanoscale structures with high fidelity is required because such features are increasingly exploited in the design of materials with enhanced functional properties. The new methodology has been tested via RMC refinements of large-scale atomic configurations (distances up to 8 nm) for SrTiO3 using neutron total-scattering data collected on the Polaris and NOMAD time-of-flight powder diffractometers at the ISIS facility (Didcot, Oxfordshire, UK) and SNS, respectively. While the Polaris instrument is known to provide the high-quality data needed for RMC analysis, the similar and sound atomic configurations obtained from both instruments confirmed that the NOMAD data are also suitable for RMC refinements over a broad distance range.

Using In-Situ Laboratory and Synchrotron-Based X-ray Diffraction for Lithium-Ion Batteries Characterization: A Review on Recent Developments

Renewable technologies, and in particular the electric vehicle revolution, have generated tremendous pressure for the improvement of lithium ion battery performance. To meet the increasingly high market demand, challenges include improving the energy density, extending cycle life and enhancing safety. In order to address these issues, a deep understanding of both the physical and chemical changes of battery materials under working conditions is crucial for linking degradation processes to their origins in material properties and their electrochemical signatures. In situ and operando synchrotron-based X-ray techniques provide powerful tools for battery materials research, allowing a deep understanding of structural evolution, redox processes and transport properties during cycling. In this review, in situ synchrotron-based X-ray diffraction methods are discussed in detail with an emphasis on recent advancements in improving the spatial and temporal resolution. The experimental approaches reviewed here include cell designs and materials, as well as beamline experimental setup details. Finally, future challenges and opportunities for battery technologies are discussed.

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 simple correction for the parallax effect in X-ray pair distribution function measurements

Total scattering and pair distribution function (PDF) analysis has created new insights that traditional powder diffraction methods have been unable to achieve in understanding the local structures of materials exhibiting disorder or complex nanostructures. Care must be taken in such analyses as subtle and discrete features in the PDF can easily be artefacts generated in the measurement process, which can result in unphysical models and interpretation. The focus of this study is an artefact called the parallax effect, which can occur in area detectors with thick detection layers during the collection of X-ray PDF data. This effect results in high-Q peak offsets, which subsequently cause an r-dependent shift in the PDF peak positions in real space. Such effects should be accounted for if a truly accurate model is to be achieved, and a simple correction that can be conducted via a Rietveld refinement against the reference data is proposed.

Towards quantitative treatment of electron pair distribution function

The pair distribution function (PDF) is a versatile tool to describe the structure of disordered and amorphous materials. Electron PDF (ePDF) uses the advantage of strong scattering of electrons, thus allowing small volumes to be probed and providing unique information on structure variations at the nano-scale. The spectrum of ePDF applications is rather broad: from ceramic to metallic glasses and mineralogical to organic samples. The quantitative interpretation of ePDF relies on knowledge of how structural and instrumental effects contribute to the experimental data. Here, a broad overview is given on the development of ePDF as a structure analysis method and its applications to diverse materials. Then the physical meaning of the PDF is explained and its use is demonstrated with several examples. Special features of electron scattering regarding the PDF calculations are discussed. A quantitative approach to ePDF data treatment is demonstrated using different refinement software programs for a nanocrystalline anatase sample. Finally, a list of available software packages for ePDF calculation is provided.

Local atomic order and hierarchical polar nanoregions in a classical relaxor ferroelectric

The development of useful structure-function relationships for materials that exhibit correlated nanoscale disorder requires adequately large atomistic models which today are obtained mainly via theoretical simulations. Here, we exploit our recent advances in structure-refinement methodology to demonstrate how such models can be derived directly from simultaneous fitting of 3D diffuse- and total-scattering data, and we use this approach to elucidate the complex nanoscale atomic correlations in the classical relaxor ferroelectric PbMg_1/3Nb_2/3O₃ (PMN). Our results uncover details of ordering of Mg and Nb and reveal a hierarchical structure of polar nanoregions associated with the Pb and Nb displacements. The magnitudes of these displacements and their alignment vary smoothly across the nanoregion boundaries. No spatial correlations were found between the chemical ordering and the polar nanoregions. This work highlights a broadly applicable nanoscale structure-refinement method and provides insights into the structure of PMN that require rethinking its existing contentious models.

The understanding of relaxor ferroelectrics is hindered by the complexity of nanoscale perturbations of their structure. Here, a data set of independent techniques treated on common footing provides a multiscale description of atomic order which reconciles conflicting models derived from single methods.

decryst: an efficient software suite for structure determination from powder diffraction

Presented here is decryst, a software suite for structure determination from powder diffraction, which uses the direct-space method, and is able to apply anti-bump constraints automatically and efficiently during the procedure of global optimization using the crystallographic collision detection algorithm by Liu [Acta Cryst. (2017), A73, 414–422]. decryst employs incremental computation in its global-optimization cycles, which results in dramatic performance enhancement. It is also designed with parallel and distributed computing in mind, allowing for even better performance by simultaneous use of multiple processors. Owing to the parallelized usage of the equivalent position combination method [Deng & Dong (2009). J. Appl. Cryst. 42, 953–958] in decryst, it is particularly suitable for determination of structures with mostly unknown bonding relations, and offers some unprecedented opportunities for these structures. decryst is free and open-source software, and can be obtained at https://gitlab.com/CasperVector/decryst/; it strives to be simple yet flexible, in the hope that the underlying techniques could be adopted in more crystallographic applications.

Coupling of emergent octahedral rotations to polarization in (K,Na)NbO3 ferroelectrics

Perovskite potassium sodium niobates, K_1−xNa_xNbO₃, are promising lead-free piezoelectrics. Their dielectric and piezoelectric characteristics peak near x = 0.5, but the reasons for such property enhancement remain unclear. We addressed this uncertainty by analyzing changes in the local and average structures across the x = 0.5 composition, which have been determined using simultaneous Reverse Monte Carlo fitting of neutron and X-ray total-scattering data, potassium EXAFS, and diffuse-scattering patterns in electron diffraction. Within the A-sites, Na cations are found to be strongly off-centered along the polar axis as a result of oversized cube-octahedral cages determined by the larger K ions. These Na displacements promote off-centering of the neighboring Nb ions, so that the Curie temperature and spontaneous polarization remain largely unchanged with increasing x, despite the shrinking octahedral volumes. The enhancement of the properties near x = 0.5 is attributed to an abrupt increase in the magnitude and probability of the short-range ordered octahedral rotations, which resembles the pre-transition behavior. These rotations reduce the bond tension around Na and effectively soften the short Na-O bond along the polar axis – an effect that is proposed to facilitate reorientation of the polarization as external electric field is applied.