Total scattering and the pair distribution function in crystallography

Abstract

The importance of total scattering and its Fourier transform, the pair distribution function, in crystallography was understood soon after it was shown that crystals diffract X-rays. However for the next fifty years or so other techniques based more firmly on the crystal lattice came to the fore and total scattering measurements were largely the domain of those studying liquid and amorphous structure. In the late 1980s it was 'rediscovered' as a way to uncover disorder within crystal structures and since then the combination of improved instrumentation and analysis has led to a resurgence of the total scattering method. This review sets out this journey, highlighting both the early origins and-more importantly-the ways that total scattering and pair distribution functions are routinely used within crystallography today.

Mixed hierarchical local structure in a disordered metal–organic framework

“…The observed damping of Fe-BTC’s PDF at higher r may also arise due to the partial nanocrystallinity of the material. Nanocrystallinity results in the increase of diffraction peak width in reciprocal space, which manifests as a damping of the peak heights in the PDF as a function of increasing r in real space 10 . An alternative interpretation may include the formation of partial tetrahedra, those which do not contain all four constituent trimer vertices, within Fe-BTC.…”

“…However, these techniques are limited by their spatial resolution, which is often restricted to nearest-neighbour atomic distances. Total scattering techniques probe the short- and long-range structure of a material through the simultaneous interpretation of Bragg and diffuse scattering obtained from a diffraction experiment 10 . The Fourier transform of the total scattering data yields the pair distribution function (PDF)—a real-space mapping of the two-body atom–atom correlations.…”

Illustrated formalisms for total scattering data: a guide for new practitioners. Corrigendum and addendum

“…therein; Keen, 2020), but it has stabilized over the past 20 years within the now mature total scattering community, in part through the cross-referencing of equations following Keen (2001). We as a community have a responsibility to ensure that we do not further compound any perceived notational confusion we might be trying to mitigate.…”

Multivariate Analysis of Disorder in Metal–Organic Frameworks

“…[15][16][17] Total scattering and pair distribution function (PDF) analysis has found itself at the forefront of this area of structural chemistry. [18][19][20][21] Total scattering data, which incorporates both Bragg and diffuse scattering, is obtained from a diffraction experiment and has been used extensively to probe the intermediate and extended length-scales of order within inorganic glasses such as Si and GeO2. [22][23][24][25] By making use of the Fourier transform of the total scattering, the PDF is obtained, which is a real-space mapping of the two-body interactions and is sensitive to both the local and extended structure.…”

“…26 Previously, the collection of total scattering data represented a significant bottleneck in performing PDF studies, requiring long measurement times. 18 However, with the advent of synchrotron radiation sources and rapid area detectors, high quality total scattering data can now be obtained within a matter of seconds. 27 PDF analysis has been used to provide insight into the negative thermal expansion behaviour in ZrW2O8, the structure of metal oxide nanoparticles, in-situ formation of hybrid materials, operando studies on battery materials and, of course, studies on structural disorder.…”