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  1. Structural modelling of octahedral tilts in perovskites is typically carried out using the symmetry constraints of the resulting space group. In most cases, this introduces more degrees of freedom than those strictly necessary to describe only the octahedral tilts. It can therefore be a challenge to disentangle the octahedral tilts from other structural distortions such as cation displacements and octahedral distortions. This paper reports the development of constraints for modelling pure octahedral tilts and implementation of the constraints in diffpy-CMI , a powerful package to analyse pair distribution function (PDF) data. The model in the program allows features in the PDF that come from rigid tilts to be separated from non-rigid relaxations, providing an intuitive picture of the tilting. The model has many fewer refinable variables than the unconstrained space group fits and provides robust and stable refinements of the tilt components. It further demonstrates the use of the model on the canonical tilted perovskite CaTiO 3 which has the known Glazer tilt system α + β − β − . The Glazer model fits comparably to the corresponding space-group model Pnma below r = 14 Å and becomes progressively worse than the space-group model at higher r due to non-rigidmore »distortions in the real material.« less
    Free, publicly-accessible full text available September 1, 2023
  2. Machine learning models based on convolutional neural networks have been used for predicting space groups of crystal structures from their atomic pair distribution function (PDF). However, the PDFs used to train the model are calculated using a fixed set of parameters that reflect specific experimental conditions, and the accuracy of the model when given PDFs generated with different choices of these parameters is unknown. In this work, the results of the top-1 accuracy and top-6 accuracy are robust when applied to PDFs of different choices of experimental parameters r max , Q max , Q damp and atomic displacement parameters.
    Free, publicly-accessible full text available June 1, 2023
  3. The development of new nanomaterials for energy technologies is dependent on understanding the intricate relation between material properties and atomic structure. It is, therefore, crucial to be able to routinely characterise the atomic structure in nanomaterials, and a promising method for this task is Pair Distribution Function (PDF) analysis. The PDF can be obtained through Fourier transformation of x-ray total scattering data, and represents a histogram of all interatomic distances in the sample. Going from the distance information in the PDF to a chemical structure is an unassigned distance geometry problem (uDGP), and solving this is often the bottleneck in nanostructure analysis. In this work, we propose to use a Conditional Variational Autoencoder (CVAE) to automatically solve the uDGP to obtain valid chemical structures from PDFs. We use a simple model system of hypothetical mono-metallic nanoparticles containing up to 100 atoms in the face centered cubic (FCC) structure as a proof of concept. The model is trained to predict the assigned distance matrix (aDM) from a simulated PDF of the structure as the conditional input. We introduce a novel representation of structures by projecting them inside a unit sphere and adding additional anchor points or satellites to help in themore »reconstruction of the chemical structure. The performance of the CVAE model is compared to a Deterministic Autoencoder (DAE) showing that both models are able to solve the uDGP reasonably well. We further show that the CVAE learns a structured and meaningful latent embedding space which can be used to predict new chemical structures.« less
  4. SASPDF, a method for characterizing the structure of nanoparticle assemblies (NPAs), is presented. The method is an extension of the atomic pair distribution function (PDF) analysis to the small-angle scattering (SAS) regime. The PDFgetS3 software package for computing the PDF from SAS data is also presented. An application of the SASPDF method to characterize structures of representative NPA samples with different levels of structural order is then demonstrated. The SASPDF method quantitatively yields information such as structure, disorder and crystallite sizes of ordered NPA samples. The method was also used to successfully model the data from a disordered NPA sample. The SASPDF method offers the possibility of more quantitative characterizations of NPA structures for a wide class of samples.
  5. A method is presented for predicting the space group of a structure given a calculated or measured atomic pair distribution function (PDF) from that structure. The method utilizes machine learning models trained on more than 100 000 PDFs calculated from structures in the 45 most heavily represented space groups. In particular, a convolutional neural network (CNN) model is presented which yields a promising result in that it correctly identifies the space group among the top-6 estimates 91.9% of the time. The CNN model also successfully identifies space groups for 12 out of 15 experimental PDFs. Interesting aspects of the failed estimates are discussed, which indicate that the CNN is failing in similar ways as conventional indexing algorithms applied to conventional powder diffraction data. This preliminary success of the CNN model shows the possibility of model-independent assessment of PDF data on a wide class of materials.