Single Crystal Diffuse Scattering Research Articles

Synchrotron X-ray diffuse scattering from a stable polymorphic material: terephthalic acid, C8H6O4

Terephthalic acid (TPA, C8H6O4) is an industrially important chemical, one that shows polymorphism and disorder. Three polymorphs are known, two triclinic [(I) and (II)] and one monoclinic (III). Of the two triclinic polymorphs, (II) has been shown to be more stable in ambient conditions. This paper presents models of the local order of polymorphs (I) and (II), and compares the single-crystal diffuse scattering (SCDS) computed from the models with that observed from real crystals. TPA shows relatively weak and less-structured diffuse scattering than some other polymorphic materials, but it does appear that the SCDS is less well modelled by a purely harmonic model in polymorph (I) than in polymorph (II), according to the idea that the diffuse scattering is sensitive to anharmonicity that presages a structural phase transition. The work here verifies that displacive correlations are strong along the molecular chains and weak laterally, and that it is not necessary to allow the —COOH groups to librate to successfully model the diffuse scattering – keeping in mind that the data are from X-ray diffraction and not directly sensitive to H atoms.

Monte Carlo Modelling of Single-Crystal Diffuse Scattering from Intermetallics

Single-crystal diffuse scattering (SCDS) reveals detailed structural insights into materials. In particular, it is sensitive to two-body correlations, whereas traditional Bragg peak-based methods are sensitive to single-body correlations. This means that diffuse scattering is sensitive to ordering that persists for just a few unit cells: nanoscale order, sometimes referred to as “local structure”, which is often crucial for understanding a material and its function. Metals and alloys were early candidates for SCDS studies because of the availability of large single crystals. While great progress has been made in areas like ab initio modelling and molecular dynamics, a place remains for Monte Carlo modelling of model crystals because of its ability to model very large systems; important when correlations are relatively long (though still finite) in range. This paper briefly outlines, and gives examples of, some Monte Carlo methods appropriate for the modelling of SCDS from metallic compounds, and considers data collection as well as analysis. Even if the interest in the material is driven primarily by magnetism or transport behaviour, an understanding of the local structure can underpin such studies and give an indication of nanoscale inhomogeneity.

Total scattering and pair distribution function analysis in modelling disorder in PZN (PbZn1/3Nb2/3O3).

The ability of the pair distribution function (PDF) analysis of total scattering (TS) from a powder to determine the local ordering in ferroelectric PZN (PbZn1/3Nb2/3O3) has been explored by comparison with a model established using single-crystal diffuse scattering (SCDS). While X-ray PDF analysis is discussed, the focus is on neutron diffraction results because of the greater extent of the data and the sensitivity of the neutron to oxygen atoms, the behaviour of which is important in PZN. The PDF was shown to be sensitive to many effects not apparent in the average crystal structure, including variations in the B-site-O separation distances and the fact that 〈110〉 Pb(2+) displacements are most likely. A qualitative comparison between SCDS and the PDF shows that some features apparent in SCDS were not apparent in the PDF. These tended to pertain to short-range correlations in the structure, rather than to interatomic separations. For example, in SCDS the short-range alternation of the B-site cations was quite apparent in diffuse scattering at (½ ½ ½), whereas it was not apparent in the PDF.

A Process for Modelling Diffuse Scattering from Disordered Molecular Crystals, Illustrated by Application to Monoclinic 9-Chloro-10-methylanthracene

Diffuse scattering from a crystal contains valuable information about the two-body correlations (related to the nanoscale order) in the material. Despite years of development, the detailed analysis of single crystal diffuse scattering (SCDS) has yet to become part of the everyday toolbox of the structural scientist. Recent decades have seen the pair distribution function approach to diffuse scattering (in fact, total scattering) from powders become a relatively routine tool. However, analysing the detailed, complex, and often highly anisotropic three-dimensional distribution of SCDS remains valuable yet rare because there is no routine method for undertaking the analysis. At present, analysis requires significant investment of time to develop specialist expertise, which means that the analysis of diffuse scattering, which has much to offer, is not incorporated thorough studies of many compounds even though it has the potential to be a very useful adjunct to existing techniques. This article endeavours to outline in some detail how the diffuse scattering from a molecular crystal can be modelled relatively quickly and largely using existing software tools. It is hoped this will provide a template for other studies. To enable this, the entire simulation is included as deposited material.

Diffuse scattering and partial disorder in complex structures.

The study of single-crystal diffuse scattering (SCDS) goes back almost to the beginnings of X-ray crystallography. Because SCDS arises from two-body correlations, it contains information about local (short-range) ordering in the sample, information which is often crucial in the attempt to relate structure to function. This review discusses the state of the field, including detectors and data collection and the modelling of SCDS using Monte Carlo and ab initio techniques. High-quality, three-dimensional volumes of SCDS data can now be collected at synchrotron light sources, allowing ever more detailed and quantitative analyses to be undertaken, and opening the way to approaches such as three-dimensional pair distribution function studies (3D-PDF) and automated refinement of a disorder model, powerful techniques that require large volumes of low-noise data.

Local order in wüstite. Fe1-xO, using a PDF approach

Many minerals (and materials more widely) show evidence of strong and complex local structural ordering. This local ordering can affect a material's mechanical properties, its transport properties (for example, how vacancies relate to oxygen transport through the structure) and its thermodynamics, and so is clearly of prime importance. For crystalline materials the analysis of single crystal diffuse scattering (SCDS) is the most definitive way of determining local structure but for many minerals (and materials more widely) single crystals of a sufficient size for such studies are often not readily obtainable and powder diffraction data must suffice. While conventional powder XRD (e.g. using Rietveld refinement) can provide information about the average crystal structure, total scattering (TS) – which includes both Bragg peaks and diffuse scattering – is needed if information about the local structure and short-range order is to be gained. The pair distribution function (PDF) analysis of such total scattering data has become a widely used technique for extracting such local structural information from a wide variety of materials including crystalline powders, nano-materials, amorphous materials, glasses and liquids. The aim of the present work is to explore the sensitivity of the PDF methodology to various aspects of disorder and short-range order for a mineral system for which the local structure has been characterised previously using SCDS. The system chosen for this study is the non-stoichiometric iron oxide wüstite, (Fe1–xO, x = 0.057). The X-ray diffraction patterns obtained from a single crystal of wüstite show strong and richly structured diffuse scattering (see Fig. 1). This has enabled a detailed model of the defect structure to be established. The aim is to assess to what extent this defect structure model could have been established using PDF analysis of powder diffraction data.

Nanoscale Order in Molecular Systems from Single Crystal Diffuse Scattering

Diffuse scattering – the coherently scattered intensity that is not localised on the reciprocal lattice – contains a wealth of information about the local order (order on the nanoscale) in crystalline materials. Since molecules and atoms will respond most strongly to their local chemical environments, it is a valuable tool in understanding how structure leads to properties. However, at present its collection and analysis are relatively specialised. Monte Carlo (MC) computer simulation of a model structure has become a powerful and well-accepted technique for aiding the interpretation and analysis of diffuse scattering patterns. Its great strength is its flexibility – as long as an MC energy can be defined, a model can be developed and tested. At one extreme a very simplified model may be useful in demonstrating particular qualitative effects, while at the other a quantitative and very detailed description of disordered structures can be obtained. Examples discussed include new results concerning p-chloro-N-(p-chloro-benzylidene)aniline, a molecule showing various degrees of molecular flexibility.

Diffuse Scattering from Lead-Containing Ferroelectric Perovskite Oxides

Ferroelectric materials rely on some type of non-centrosymmetric displacement correlations to give rise to a macroscopic polarisation. These displacements can show short-range order (SRO) that is reflective of the local chemistry, and so studying it reveals important information about how the structure gives rise to the technologically useful properties. A key means of exploring this SRO is diffuse scattering. Conventional structural studies use Bragg peak intensitiesto determine the average structure. In a single crystal diffuse scattering (SCDS) experiment, the coherent scattered intensity is measured at non-integer Miller indices, and can be used to examine the population of local configurations. This is because the diffuse scattering is sensitive to two-body averages, whereas the Bragg intensity gives single-body averages. This review outlines key results of SCDS studies on several materials and explores the similarities and differences in their diffuse scattering. Random strains are considered, as are models based on a phonon-like picture or a more local-chemistry oriented picture. Limitations of the technique are discussed.

Distinguishing Types of Disorder in Diffuse Scattering: A Numerical Simulation Study

Using numerical simulation tools such as DISCUS and ZMC, the signatures in simulated pair distribution function (PDF) and single-crystal diffuse scattering (SCDS) of various types of disorders in a range of model systems are explored by observation of the evolution of calculated PDF and SCDS. Disordered crystalline materials may show a variety of types of short-range correlations in occupancies, displacements, and (if a molecular system) orientations of constituents. Further, the correlation between occupancy and displacement (the size effect) will often also be present. This work provides some insight into the abilities of the two data types to distinguish and quantify these different aspects of disorder in materials, with a view to guide the analysis of real systems.

Scientific Review: Prospects and Challenges in Single Crystal Diffuse Scattering

Scientific Review: Prospects and Challenges in Single Crystal Diffuse Scattering

Scientific Review: Prospects and Challenges in Single Crystal Diffuse Scattering

Until comparatively recently, condensed matter physics was mostly concerned with understanding the properties of ideally crystalline solids, and this has led to a detailed understanding of both the structure and dynamics of well-ordered materials. There is however growing interest in understanding complex materials in which disorder, and the nanoscale self-organization associated with it, plays an important role in their bulk properties, as many new phenomena that are attracting considerable interest in materials science are enhanced by the controlled introduction of quenched disorder [1]. Examples include magnetoresistive oxides, superconducting cuprates, ferroelectric relaxors, and fast-ion conductors.