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1. Using a machine learning approach to determine the space group of a structure from the atomic pair distribution function

   https://doi.org/10.1107/S2053273319005606  

   Liu, Chia-Hao; Tao, Yunzhe; Hsu, Daniel; Du, Qiang; Billinge, Simon J. (July 2019, Acta Crystallographica Section A Foundations and Advances)

   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. 

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2. A new method for in situ structural investigations of nano-sized amorphous and crystalline materials using mixed-flow reactors

   https://doi.org/10.1107/S2053273319008623  

   Hoeher, Alexandria; Mergelsberg, Sebastian; Borkiewicz, Olaf J.; Dove, Patricia M.; Michel, F. Marc (September 2019, Acta Crystallographica Section A Foundations and Advances)

   Structural investigations of amorphous and nanocrystalline phases forming in solution are historically challenging. Few methods are capable of in situ atomic structural analysis and rigorous control of the system. A mixed-flow reactor (MFR) is used for total X-ray scattering experiments to examine the short- and long-range structure of phases in situ with pair distribution function (PDF) analysis. The adaptable experimental setup enables data collection for a range of different system chemistries, initial supersaturations and residence times. The age of the sample during analysis is controlled by adjusting the flow rate. Faster rates allow for younger samples to be examined, but if flow is too fast not enough data are acquired to average out excess signal noise. Slower flow rates form older samples, but at very slow speeds particles settle and block flow, clogging the system. Proper background collection and subtraction is critical for data optimization. Overall, this MFR method is an ideal scheme for analyzing the in situ structures of phases that form during crystal growth in solution. As a proof of concept, high-resolution total X-ray scattering data of amorphous and crystalline calcium phosphates and amorphous calcium carbonate were collected for PDF analysis. 

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3. Characterising the atomic structure of mono-metallic nanoparticles from x-ray scattering data using conditional generative models

   https://doi.org/10.26434/chemrxiv.12662222.v1  

   Anker, Andy S.; Kjaer, Emil T.; Dam, Erik B.; Billinge, Simon J.; Jensen, Kirsten M.; Selvan, Raghavendra (July 2020, ChemRxiv)

   null (Ed.)

   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 the 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. 

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4. Symmetry-mode analysis for local structure investigations using pair distribution function data

   https://doi.org/10.1107/S1600576723005794  

   Hamilton, Parker K.; Moya, Jaime M.; Hallas, Alannah M.; Morosan, E.; Baral, Raju; Frandsen, Benjamin A. (August 2023, Journal of Applied Crystallography)

   Symmetry-adapted distortion modes provide a natural way of describing distorted structures derived from higher-symmetry parent phases. Structural refinements using symmetry-mode amplitudes as fit variables have been used for at least ten years in Rietveld refinements of the average crystal structure from diffraction data; more recently, this approach has also been used for investigations of the local structure using real-space pair distribution function (PDF) data. Here, the value of performing symmetry-mode fits to PDF data is further demonstrated through the successful application of this method to two topical materials: TiSe 2 , where a subtle but long-range structural distortion driven by the formation of a charge-density wave is detected, and MnTe, where a large but highly localized structural distortion is characterized in terms of symmetry-lowering displacements of the Te atoms. The analysis is performed using fully open-source code within the DiffPy framework via two packages developed for this work: isopydistort , which provides a scriptable interface to the ISODISTORT web application for group theoretical calculations, and isopytools , which converts the ISODISTORT output into a DiffPy -compatible format for subsequent fitting and analysis. These developments expand the potential impact of symmetry-adapted PDF analysis by enabling high-throughput analysis and removing the need for any commercial software. 

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5. Proximity Effect Correction for Fresnel Holograms on Nanophotonic Phased Arrays

   https://doi.org/10.1109/VR50410.2021.00058  

   Sun, Xuetong; Zhang, Yang; Huang, Po-Chun; Acharjee, Niloy; Dagenais, Mario; Peckerar, Martin; Varshney, Amitabh (March 2021, 2021 IEEE Virtual Reality and 3D User Interfaces (VR))

   null (Ed.)

   Holographic displays and computer-generated holography offer a unique opportunity in improving optical resolutions and depth characteristics of near-eye displays. The thermally-modulated Nanopho-tonic Phased Array (NPA), a new type of holographic display, affords several advantages, including integrated light source and higher refresh rates, over other holographic display technologies. However, the thermal phase modulation of the NPA makes it susceptible to the thermal proximity effect where heating one pixel affects the temperature of nearby pixels. Proximity effect correction (PEC) methods have been proposed for 2D Fourier holograms in the far field but not for Fresnel holograms at user-specified depths. Here we extend an existing PEC method for the NPA to Fresnel holograms with phase-only hologram optimization and validate it through computational simulations. Our method is not only effective in correcting the proximity effect for the Fresnel holograms of 2D images at desired depths but can also leverage the fast refresh rate of the NPA to display 3D scenes with time-division multiplexing. 

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