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1. Robustness test of the spacegroupMining model for determining space groups from atomic pair distribution function data

   https://doi.org/10.1107/S1600576722002990  

   Lan, Ling; Liu, Chia-Hao; Du, Qiang; Billinge, Simon J. (June 2022, Journal of Applied Crystallography)

   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. 

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2. In Situ Studies of the Formation of Tungsten and Niobium Oxide Nanoparticles: Towards Automated Analysis of Reaction Pathways from PDF Analysis using the Pearson Correlation Coefficient

   https://doi.org/10.1002/cmtd.202200034  

   Kjær, Emil_T_S; Aalling‐Frederiksen, Olivia; Yang, Long; Thomas, Nancy_K; Juelsholt, Mikkel; Billinge, Simon_J_L; Jensen, Kirsten_M_Ø (August 2022, Chemistry–Methods)

   Abstract Using Pair Distribution Function (PDF) analysis of in situ total scattering data, we investigate the formation of tungsten and niobium oxides in a simple solvothermal synthesis. We use Pearson Correlation Coefficient (PCC) analysis of the time resolved PDFs to both map the structural changes taking place throughout the synthesis and identify structural models for precursor and product through PCC‐based structure mining. Our analysis first shows that ultra‐small tungsten and niobium oxide nanoparticles form instantaneously upon heating, with sizes between 1.5 and 2 nm. We show that the main structural motifs in the nanoparticles can be described with structures containing pentagonal columns, which is characteristic for many bulk tungsten and niobium oxides. We furthermore elucidate the structure of the precursor complex as clusters of octahedra with O‐ and Cl‐ligands. The PCC based methodology automates the structure characterization and proves useful for analysis of large datasets of for example, time resolved X‐ray scattering studies. The PCC is implemented in ‘PDF in the cloud’, a web platform for PDF analysis. 

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3. 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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4. 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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5. Special quasirandom structures description of the local structure of disordered Bi _0.5 K _0.5 TiO ₃

   https://doi.org/10.1063/5.0123468  

   Jiang, Bo; Lin, De-Ye; Wang, Xin; Selbach, Sverre M.; Page, Katharine (December 2022, Journal of Applied Physics)

   Polar nanoregions (PNRs) are believed to play a decisive role in the local and macroscopic polarization in relaxor ferroelectrics. The limited microscopic understanding of the structure and dynamics of PNRs hampers the rational design of new lead-free materials. Here, the local structure of A-site disordered Bi 0.5 K 0.5 TiO 3 (BKT) is investigated using synchrotron x-ray and neutron pair distribution function (PDF) analysis and density functional theory (DFT) optimized special quasirandom structures (SQSs). DFT-relaxed SQS with a 4 × 4 × 4 supercell size can reproduce the experimental PDFs of disordered BKT, as well as the partial PDFs and total polarization, with comparable results to those reported from a combined analysis of x-ray and neutron PDF data with large-box reverse Monte Carlo methods. We find that small Bi 3+ -rich polar clusters are likely to be the microscopic origin of relaxor behavior in disordered BKT, and that the existence of large polar nanoregions (PNRs) is not necessary to explain the relaxor properties. Our results also highlight the great potential of the SQS approach to gain a nanoscale-to-microscopic understanding of other relaxor solid solutions. 

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