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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 paper, we report that the results of the top-1 accuracy and top-6 accuracy are robust when applied to PDFs of different choices of experimental parameters $r_\text{max}$, $Q_\text{max}$, $Q_\text{damp}$ and atomic displacement parameters., Comment: 15 pages, 5 figures

We validate the use of matrix factorization for the automatic identification of relevant components from atomic pair distribution function (PDF) data. We also present a newly developed software infrastructure for analyzing the PDF data arriving in streaming manner. We then apply two matrix factorization techniques, Principal Component Analysis (PCA) and Non-negative Matrix Factorization (NMF), to study simulated and experiment datasets in the context of in situ experiment.

A new approach is presented to obtain candidate structures from atomic pair distribution function (PDF) data in a highly automated way. It fetches, from web-based structural databases, all the structures meeting the experimenter's search criteria and performs structure refinements on them without human intervention. It supports both x-ray and neutron PDFs. Tests on various material systems show the effectiveness and robustness of the algorithm in finding the correct atomic crystal structure. It works on crystalline and nanocrystalline materials including complex oxide nanoparticles and nanowires, low-symmetry and locally distorted structures, and complicated doped and magnetic materials. This approach could greatly reduce the traditional structure searching work and enable the possibility of high-throughput real-time auto analysis PDF experiments in the future., Comment: 41 pages, 8 figures

We present a method 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, we present a convolutional neural network (CNN) model which yields a promising result 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 on 12 out of 15 experimental PDFs. We discuss interesting aspects of the failed estimates, 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.

We present a novel approach for finding and evaluating structural models of small metallic nanoparticles. Rather than fitting a single model with many degrees of freedom, the approach algorithmically builds libraries of nanoparticle clusters from multiple structural motifs, and individually fits them to experimental PDFs. Each cluster-fit is highly constrained. The approach, called cluster-mining, returns all candidate structure models that are consistent with the data as measured by a goodness of fit. It is highly automated, easy to use, and yields models that are more physically realistic and result in better agreement to the data than models based on cubic close-packed crystallographic cores, often reported in the literature for metallic nanoparticles.

Systematic local structural studies of Ba$_{1-x}$K$_x$Fe$_2$As$_2$ system are undertaken at room temperature using atomic pair distribution function (PDF) analysis. The local structure of the Ba$_{1-x}$K$_x$Fe$_2$As$_2$ is found to be well described by the long-range structure extracted from the diffraction experiments, but with anisotropic atomic vibrations of the constituent atoms ($U_{11}$ = $U_{22} \ne U_{33}$). The crystal unit cell parameters, the FeAs$_4$ tetrahedral angle and the pnictogen height above the Fe-plane are seen to show systematic evolution with K doping, underlining the importance of the structural changes, in addition to the charge doping, in determining the properties of Ba$_{1-x}$K$_x$Fe$_2$As$_2$.

Here we show explicitly the relationship between the functions used in the atomic pair distribution function (PDF) method and those commonly used in small angle scattering (SAS) analyses. The origin of the sloping baseline, $-4\pi r\rho_0$, in PDFs of bulk materials is identified as originating from the SAS intensity that is neglected in PDF measurements. The non-linear baseline in nanoparticles has the same origin, and contains information about the shape and size of the nanoparticles., Comment: 19 pages, 0 figures

We have systematically studied the optimal real-space sampling of atomic pair distribution data by comparing refinement results from oversampled and resampled data. Based on nickel and a complex perovskite system, we demonstrate that the optimal sampling is bounded by the Nyquist interval described by the Nyquist-Shannon sampling theorem. Near this sampling interval, the data points in the PDF are minimally correlated, which results in more reliable uncertainty prediction. Furthermore, refinements using sparsely sampled data may run many times faster than using oversampled data. This investigation establishes a theoretically sound limit on the amount of information contained in the PDF, which has ramifications towards how PDF data are modeled., Comment: 10 pages, 4 figures

The size-dependent structure of CdSe nanoparticles, with diameters ranging from 2 to 4 nm, has been studied using the atomic pair distribution function (PDF) method. The core structure of the measured CdSe nanoparticles can be described in terms of the wurtzite atomic structure with extensive stacking faults. The density of faults in the nanoparticles ~50% . The diameter of the core region was extracted directly from the PDF data and is in good agreement with the diameter obtained from standard characterization methods suggesting that there is little surface amorphous region. A compressive strain was measured in the Cd-Se bond length that increases with decreasing particle size being 0.5% with respect to bulk CdSe for the 2 nm diameter particles. This study demonstrates the size-dependent quantitative structural information that can be obtained even from very small nanoparticles using the PDF approach., Comment: 10 pages, 7 figures and 3 tables. Phys. Rev. B, submitted (2007)

The frst neutron powder diffraction based atomic pair distribution functions (PDFs) are reported from the new wide angular-range chopper spectrometer ARCS at the Spallation Neutron Source at Oak Ridge National Laboratory. The spectrometer was run in white-beam mode, with no Fermi chopper. The PDF patterns of Si, Ni, and Al2O3 were refined using the PDFfit method and the results compared to data collected at the NPDF diffractometer at Los Alamos National Laboratory. The resulting fits are of high quality demonstrating that quantitatively reliable powder diffraction data can be obtained from ARCS when operated in this configuration., Comment: 4 pages, 5 figures, submitted to Journal of Applied Crystallography

The mean-square relative displacements (MSRD) of atomic pair motions in crystals are studied as a function of pair distance and temperature using the atomic pair distribution function (PDF). The effects of the lattice vibrations on the PDF peak widths are modelled using both a multi-parameter Born von-Karman (BvK) force model and a single-parameter Debye model. These results are compared to experimentally determined PDFs. We find that the near-neighbor atomic motions are strongly correlated, and that the extent of this correlation depends both on the interatomic interactions and crystal structure. These results suggest that proper account of the lattice vibrational effects on the PDF peak width is important in extracting information on static disorder in a disordered system such as an alloy. Good agreement is obtained between the BvK model calculations of PDF peak widths and the experimentally determined peak widths. The Debye model successfully explains the average, though not detailed, natures of the MSRD of atomic pair motion with just one parameter. Also the temperature dependence of the Debye model largely agrees with the BvK model predictions. Therefore, the Debye model provides a simple description of the effects of lattice vibrations on the PDF peak widths., Comment: 9 pages, 11 figures

Many crystalline materials show chemical short range order and relaxation of neighboring atoms. Local structural information can be obtained by analyzing the atomic pair distribution function (PDF) obtained from powder diffraction data. In this paper, we present the successful extraction of chemical short range order parameters from the x-ray PDF of a quenched Cu_3Au sample., Comment: 4 pages, 4 figures

The structure of LiMoS2 has been experimentally determined for the first time. The approach of atomic pair distribution function (PDF) analysis was used because of the lack of well defined Bragg peaks due to the short structural coherence (~ 50 A) in this intercalation compound. This represents one of the first instances where the structure of such poorly diffracting material was determined from the total scattering including diffuse as well as Bragg scattering. The reduction of Mo by Li results in Mo-Mo bonding with the formation of chains of distorted Mo-S6 octahedra. Using the refined structural parameters the electronic band-structure for this material has been calculated and is in good agreement with observed material properties., Comment: 4 pages, 5 figures

Many disordered crystalline materials show chemical short range order and relaxation of neighboring atoms. Local structural information can be obtained by analyzing the atomic pair distribution function (PDF). The viability of reverse Monte Carlo (RMC) simulations to extract quantitative information about chemical ordering as well as displacements is investigated. The method has been applied to simulated PDFs of disordered structures showing chemical disorder alone as well as in combination with displacements., Comment: 8 pages, 8 postscript figures