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We solve a longstanding problem--determining structural information for disordered materials from their diffraction spectra--for the case of planar disorder in close-packed structures (CPSs). Our solution offers the most complete possible…

Disordered Systems and Neural Networks · Physics 2009-11-07 D. P. Varn , G. S. Canright , J. P. Crutchfield

The paper describes an extension of the Liga algorithm for structure solution from atomic pair distribution function (PDF), to handle periodic crystal structures with multiple elements in the unit cell. The procedure is performed in 2…

Whereas knowledge of a crystalline material's unit cell is fundamental to understanding the material's properties and behavior, there are not obvious analogues to unit cells for disordered materials despite the frequent existence of…

Computational Geometry · Computer Science 2020-05-27 Benjamin Schweinhart , David Rodney , Jeremy Mason

Equations for the reduced structure function and atomic pair distribution function (PDF) of a textured polycrystalline sample are formulated in terms of the orientational distribution function (ODF) and the structure function from a single…

Materials Science · Physics 2018-05-29 Zizhou Gong , Simon J. L. Billinge

Materials with bespoke properties have long been identified by computational searches, and their experimental realisation is now coming within reach through autonomous laboratories. Scattering experiments are central to verifying the atomic…

In the In recent times, the research community has explored diverse structures and novel fabrication methods for amorphous solids. This work investigates structural trends among different classes of amorphous materials to identify universal…

Determining atomistic structures from characterization data is one of the most common yet intricate problems in materials science. Particularly in amorphous materials, proposing structures that balance realism and agreement with experiments…

Disordered Systems and Neural Networks · Physics 2026-03-25 Jiawei Guo , Daniel Schwalbe-Koda

We describe the quantitative refinement of nanoparticle structures from gold nanoparticles probed by ultrafast electron crystallography (UEC). We establish the equivalence between the modified radial distribution function employed in UEC…

Materials Science · Physics 2011-04-06 Christopher L. Farrow , Chong-Yu Ruan , Simon J. L. Billinge

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…

Accurate structural analysis is essential to gain physical knowledge and understanding of atomic-scale processes in materials from atomistic simulations. However, traditional analysis methods often reach their limits when applied to…

In alloys exhibiting substitutional disorder, the variety of atomic environments manifests itself as a `disorder broadening' in their core level binding energy spectra. Disorder broadening can be measured experimentally, and in principle…

Materials Science · Physics 2014-07-14 T. L. Underwood , G. J. Ackland , R. J. Cole

Nanocrystalline n-AlO(OH) (Disperal P2(R) of Sasol) was investigated by means of the atomic pair distribution function (PDF). The PDF is derived from powder diffraction data, an ideally resolved PDF is obtained from a synchrotron source…

Materials Science · Physics 2008-04-24 Stefan Bruehne , Saskia Gottlieb , Wolf Assmus , Edith Alig , Martin U. Schmidt

Atomic-resolution imaging with scanning transmission electron microscopy is a powerful tool for characterizing the nanoscale structure of materials, in particular features such as defects, local strains, and symmetry-breaking distortions.…

Symmetry-adapted distortion modes provide a natural way to describe distorted structures derived from higher-symmetry parent phases. Structural refinements using symmetry-mode amplitudes as fit variables have been used for at least 10 years…

Determining the atomic-level structure of crystalline solids is critically important across a wide array of scientific disciplines. The challenges associated with obtaining samples suitable for single-crystal diffraction, coupled with the…

Understanding the structural origins of the properties of amorphous materials remains one of the most important challenges in structural science. In this study we demonstrate that local 'structural simplicity', embodied by the degree to…

This article presents a modern deterministic framework for the study of leading significant digit distributions in numerical data. Rather than relying on traditional probabilistic or mixture-based explanations, we demonstrate that the…

Machine Learning · Statistics 2025-08-20 Vladimir Berman

Amorphous solids exhibit structural short-range order despite lacking long-range crystalline order, with this structural descriptor found to be important for determining mechanical properties. Nanobeam electron diffraction offers a…

Materials Science · Physics 2026-05-21 Junjie Wu , Timothy J. Rupert

High angular resolution diffusion imaging data is the observed characteristic function for the local diffusion of water molecules in tissue. This data is used to infer structural information in brain imaging. Nonparametric scalar measures…

Applications · Statistics 2011-08-17 Sofia C. Olhede , Brandon Whitcher

Amorphous silica ($a-SiO_2$) is a widely used inorganic material. Interestingly, the relationship between the local atomic structures of $a-SiO_2$ and their effects on ductility and fracture is seldom explored. Here, we combine large-scale…

Mesoscale and Nanoscale Physics · Physics 2023-04-17 Jiahao Liu , Jingjie Yeo