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DOE OSTI2024

Parametric description of intermittent probability distribution functions in solar wind and magnetohydrodynamic turbulence

ABSTRACT In this work, we find empirical evidence that the scale-dependent statistical properties of solar wind and magnetohydrodynamic (MHD) turbulence can be described in terms of a family of parametric probability distribution functions (PDFs) known as Normal Inverse Gaussian (NIG). Understanding these PDFs is one of the most important goals in turbulence theory, as they are inherently connected to the intermittent properties of solar wind turbulence. We investigate the properties of PDFs of Elsasser increments based on a large statistical sample from solar wind observations and high-resolution numerical simulations of MHD turbulence. In order to measure the PDFs and their corresponding properties, three experiments are presented: fast and slow solar wind for experimental data and a simulation of reduced MHD (RMHD) turbulence. Conditional statistics on a 23-yr-long sample of WIND data near 1 au and high-resolution pseudo-spectral simulation of steadily driven RMHD turbulence on a $2048^3$ mesh are used to construct scale-dependent PDFs. The empirical PDFs are fitted to NIG distributions, which depend on four free parameters. Our analysis shows that NIG distributions accurately capture the evolution of the PDFs, with scale-dependent parameters, from large scales characterized by a Gaussian distribution, turning to exponential tails within the inertial range and stretched exponentials at dissipative scales. We also show that empirically-measured NIG parameters exhibit well-defined scaling properties that are similar across the three empirical data sets, which may be indicative of universal behaviour.

Astronomy & Astrophysics↗

DOE OSTI2024

Integrated analysis of X-ray diffraction patterns and pair distribution functions for machine-learned phase identification

Abstract To bolster the accuracy of existing methods for automated phase identification from X-ray diffraction (XRD) patterns, we introduce a machine learning approach that uses a dual representation whereby XRD patterns are augmented with simulated pair distribution functions (PDFs). A convolutional neural network is trained directly on XRD patterns calculated using physics-informed data augmentation, which accounts for experimental artifacts such as lattice strain and crystallographic texture. A second network is trained on PDFs generated via Fourier transform of the augmented XRD patterns. At inference, these networks classify unknown samples by aggregating their predictions in a confidence-weighted sum. We show that such an integrated approach to phase identification provides enhanced accuracy by leveraging the benefits of each model’s input representation. Whereas networks trained on XRD patterns provide a reciprocal space representation and can effectively distinguish large diffraction peaks in multi-phase samples, networks trained on PDFs provide a real space representation and perform better when peaks with low intensity become important. These findings underscore the importance of using diverse input representations for machine learning models in materials science and point to new avenues for automating multi-modal characterization.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Resolving local ordering and structure in Mn x Ge 1- x Te alloys through thermodynamic ensembles of pair distribution functions

Characterizing local bonding environments in complex materials is essential for understanding and optimizing their properties. Equally as important is the ability to predict local motifs as a function of synthesis conditions, enhancing chemists’ ability to design properties into materials. In this study, we present an approach to leverage statistical mechanics to generate temperature- and energy-informed ensemble averaged pair distribution functions (PDFs). This method, which we have named Thermodynamic Ensemble Averages of PDFs for Ordering and Transformations (TEAPOT), utilizes density functional theory (DFT) to relax supercells while incorporating energetic penalties for local order, enabling accurate and computationally efficient analysis of local structure. We apply this method to the neutron PDF measurements of the pseudobinary MnTe–GeTe (MGT) alloy, demonstrating its capability to resolve complex local distortions and chemical ordering. Our results reveal detailed insights into phase transformations and local distortions driven by Mn substitution. For compositions that globally present as rock salt, our analysis reveals that Ge coordination geometry is heavily impacted by synthesis temperature. We propose that high temperature synthesis conditions promote a lowered Ge polyhedra distortion, promoting high charge carrier mobility due to the alignment of local and global structure. Incorporating statistical mechanics and computation into experimental analysis thus guides synthesis of tailored local structure.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Small-scale signatures of primordial non-Gaussianity in k-nearest neighbour cumulative distribution functions

ABSTRACT Searches for primordial non-Gaussianity in cosmological perturbations are a key means of revealing novel primordial physics. However, robustly extracting signatures of primordial non-Gaussianity from non-linear scales of the late-time Universe is an open problem. In this paper, we apply k-Nearest Neighbour cumulative distribution functions, kNN-CDFs, to the quijote-png simulations to explore the sensitivity of kNN-CDFs to primordial non-Gaussianity. An interesting result is that for halo samples with $M_\mathrm{ h}\langle 10^{14}$ M$_\odot$ $h^{-1}$, the kNN-CDFs respond to equilateral PNG in a manner distinct from the other parameters. This persists in the galaxy catalogues in redshift space and can be differentiated from the impact of galaxy modelling, at least within the halo occupation distribution (HOD) framework considered here. kNN-CDFs are related to counts-in-cells and, through mapping a subset of the kNN-CDF measurements into the count-in-cells picture, we show that our results can be modelled analytically. A caveat of the analysis is that we only consider the HOD framework, including assembly bias. It will be interesting to validate these results with other techniques for modelling the galaxy–halo connection, e.g. (hybrid) effective field theory or semi-analytical methods.

Coulton, William R. (ORCID:0000000212973673)↗

DOE OSTI2021

Bayesian estimations of orientation distribution functions from small-angle scattering enable direct prediction of mechanical stress in anisotropic materials

Properties of soft materials are influenced by their anisotropic structuring under nonequilibrium fields. Although anisotropic structure-property relationships have been extensively explored theoretically, comparison to experiments requires determination of the microstructural orientation probability distribution function (OPDF) of microstructural elements. Small angle scattering (SAS) measurements encode information about the OPDF, but tools to navigate this connection are incomplete. Here, we develop and validate an explicit framework to link arbitrary OPDFs to SAS measurements. Specifically, we propose, validate, and apply a method, maximum a posteriori scattering inference (MAPSI), whereby the OPDF may be obtained from SAS measurements using a Bayesian estimation method. Using this method, we obtain estimates of the full 3D OPDF for two model semidilute fd-virus (rodlike) dispersions at concentrations that are approximately equal to and twice the overlap concentration. From the OPDF, we calculate its second and fourth moments and compare these to predictions for a dilute suspension of rigid rods and to a recent theory for semidilute suspensions. Finally, we use both the theoretical and measured moments to calculate the stress, both for dilute and semidilute suspensions. These predictions are not only compared to each other, but also to measured values of the shear stress, and point to new insights into the behavior of suspensions of highly elongated particles in the transition between dilute and semidilute behavior. We also use this new framework to provide perspective on the connection between scalar parameterizations of scattering and the OPDF that have frequently been used in the past. Here, the new tools developed in this work provide an unprecedented path toward experimental validation of dynamical theories of rodlike colloids and polymers, and for measurement of nonequilibrium structures and stresses of other complex fluids and soft materials with SAS.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Absorption Correction for Reliable Pair Distribution Functions from Low Energy X-ray Sources

This paper explores the development and testing of a simple absorption correction model for processing powder X-ray diffraction data from Debye−Scherrer geometry laboratory X-ray experiments. This may be used as a preprocessing step before using PDFGETX3 to obtain reliable pair distribution functions (PDFs). Various experimental and theoretical methods for estimating μR were explored, and the most appropriate μR values for correction were identified for different capillary diameters and X-ray beam sizes. We identify operational ranges of μR where a reasonable signal-to-noise ratio is possible after correction. A user-friendly software package, DIFFPY.LABPDFPROC, is presented that can help estimate μR and perform absorption corrections with a rapid calculation for efficient processing.

Absorption↗

DOE OSTI2022

Time-resolved electron energy distribution functions at the substrate during a HiPIMS discharge with cathode voltage reversal

Abstract The time-dependent plasma properties of a high-power impulse magnetron sputtering plasma are investigated which include a positive ‘kick’ pulse on the sputtering target 2 μ s after the main negative pulse, this reversing the voltage on the cathode. At a substrate 15 cm distant from the magnetron, the time-dependent electron energy distribution function (EEDF), plasma potential, potential commute time and plasma diffusion properties are measured using a single Langmuir probe. Results show that the positive pulse on the target expels plasma and raises the plasma potential across the chamber on the order of 1 to 2 μ s, which is the time scale of the electron diffusion. The EEDF at the substrate fits a Druyvesteyn distribution during the main negative pulse rising slightly in average energy over time. The distribution is still Druyvesteyn and at the very start of the positive pulse, but then loses the higher energy electrons and drops in average electron energy as the positive pulse progresses. A Boltzmann equation solver, BOLSIG+, was used to predict the EEDF at the substrate during the positive pulse and it agrees best with the measurements assuming a value of 0.2 Td for the E / N (electric field/gas number density).

Physics↗

DOE OSTI2024

Coordinate-based simulation of pair distance distribution functions for small and large molecular assemblies: implementation and applications

X-ray scattering has become a major tool in the structural characterization of nanoscale materials. Thanks to the widely available experimental and computational atomic models, coordinate-based X-ray scattering simulation has played a crucial role in data interpretation in the past two decades. However, simulation of real-space pair distance distribution functions (PDDFs) from small- and wide-angle X-ray scattering, SAXS/WAXS, has been relatively less exploited. This study presents a comparison of PDDF simulation methods, which are applied to molecular structures that range in size from β-cyclodextrin [1 kDa molecular weight (MW), 66 non-hydrogen atoms] to the satellite tobacco mosaic virus capsid (1.1 MDa MW, 81 960 non-hydrogen atoms). The results demonstrate the power of interpretation of experimental SAXS/WAXS from the real-space view, particularly by providing a more intuitive method for understanding of partial structure contributions. Furthermore, the computational efficiency of PDDF simulation algorithms makes them attractive as approaches for the analysis of large nanoscale materials and biological assemblies. The simulation methods demonstrated in this article have been implemented in stand-alone software, SolX 3.0 , which is available to download from https://12idb.xray.aps.anl.gov/solx.html.

Zuo, Xiaobing (ORCID:0000000201344804)↗

DOE OSTI2025

Local orthorhombic phase in zirconium oxide nanocrystals: insights from X-ray pair distribution function analysis

Zirconium dioxide (ZrO 2 ) and hafnium dioxide (HfO 2 ) have emerged as promising alternatives to conventional ferroelectric materials. Understanding the crystal phases of these oxides under different conditions is crucial for optimizing their properties. There are several theories for the (anti)ferroelectric properties; however, comprehensive analysis, particularly at the local structure level, is lacking. In this study, we investigate the local structure of ZrO 2 nanocrystals using X-ray pair distribution function (PDF) analysis, revealing an unexpected local orthorhombic distortion irrespective of crystallite size. This finding suggests the potential existence of an intermediate orthorhombic phase during the microscopic switching pathway observed in previous studies. Additionally, we explore the influence of crystallite size and surface effects on the PDF. These results contribute to a deeper understanding of the structural dynamics in ZrO 2 and offer insights for the design of next-generation ferroelectric materials.

Pokratath, Rohan (ORCID:0000000268383939)↗

DOE OSTI2022

Structure of Sulfuric Acid Solutions Using Pair Distribution Function Analysis

Solvation and mesoscale ordering of sulfuric acid and other strong acid solutions leads to suppressed freezing points and strong rheological changes with varying concentration. While the solid-state structures are well-understood, studies focused on the evolving solvation structure in the solution phase have probed a limited concentration range (~1–6 M). This study applies a total scattering approach in both the wide-angle X-ray scattering (WAXS) and pair distribution function (PDF) regimes to elucidate the evolving solvation structure over its full range of acid concentration (0–18 M). The emergence of a prepeak in the WAXS regime at intermediate concentrations indicates a transition from noninteracting sulfate molecules in the dilute limit to sterically limited sulfates at concentrations near its deep eutectic point. Fits to the PDF data quantify this trend, showing a transition from octahedrally hydrated sulfates up to 6–7 M concentrations, followed by gradual dehydration, and eventually reaching a solution structure similar to that of water-in-salt electrolyte systems at high acid concentrations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Structure refinement and anisotropic atomic displacement parameters of 1M Illite: Rietveld and pair distribution function analysis using synchrotron X-ray radiation

Illite, a widespread clay mineral, plays a pivotal role in geological processes, notably as an indicator in diagenetic and hydrothermal alteration environments, and possesses significant industrial relevance in applications including ceramics, construction and catalysis. However, challenges including its nanoscale crystallinity, structural disorder and frequent interstratification with other clay minerals have hindered detailed structural characterization using conventional X-ray diffraction (XRD) techniques. This study employs integrated synchrotron XRD and pair distribution function (PDF) analysis to elucidate the crystal structure of the 1M illite polytype, yielding the first determination of its anisotropic atomic displacement parameters (U aniso ). TheseU aniso parameters provide critical insights into atomic dynamics and static disorder within the structure, enabling a more refined understanding of structure–property relationships. This integrated approach, combining synchrotron XRD, Rietveld refinement and PDF analysis, yields a comprehensive structural characterization, capturing both average crystallographic and local atomic arrangements. Considering illite's widespread geological occurrence and industrial importance, this high-precision structural dataset, especially the determinedU aniso values, provides a crucial benchmark for future modeling and simulation efforts targeting accurate prediction of its physicochemical behavior.

Chemistry↗

DOE OSTI2020

Monte Carlo Global QCD Analyses of the Pion Parton Distribution Functions

As the lightest hadron, the pion presents itself as a dichotomy. While being the pseudo Goldstone boson associated with chiral symmetry breaking, it is simultaneously regarded as the lightest pseudoscalar meson typically composed of constituent quark and antiquark. As the chiral symmetry shares the same global symmetry as QCD, studying the pion and its internal structure is key in understanding one of the four fundamental forces of nature, namely the quantum chromodynamic strong interaction. We study the pion's parton distribution functions (PDFs), which are universal quantities that describe the structure of the pion in terms of its constituent quarks, antiquarks, and gluons. Our goal is to discover what the available data reveal for these universal quantities, namely the PDFs. Through the use of factorization theorems and perturbative QCD, we use Monte Carlo (MC) methods to extract the PDFs from the available Drell-Yan (DY) and leading neutron (LN) data. While the DY process involves two hadrons colliding, the LN electroproduction involves an electron beam incident on a target nucleon. We can constrain well the pion PDFs at large momentum fraction using DY data, and at low momentum fraction using LN data. We also use threshold resummation in the DY process to gather predictable higher order terms associated with the soft gluon radiation because their contributions to the cross section are nontrivial. In this dissertation, we parametrize the pion PDFs and fit those parameters to the available data. We make use of Bayesian inference and use MC techniques to sample the parameter space. Three sets of results are presented. We first extract the pion PDFs by fitting the DY and LN data. Then, we include transverse momentum dependent DY data in conjunction with the DY and LN data to extract the pion PDFs. Finally, we apply various methods of threshold resummation to the DY cross section and extract pion PDFs. The pion PDFs presented here are the first global QCD analyses performed as well as the first MC extracted pion PDFs, which are at the forefront of the pion PDF community.

Barry, Patrick↗

DOE OSTI2024

Decoding the Pair Distribution Function of Uranium in Molten Fluoride Salts from X-Ray Absorption Spectroscopy Data by Machine Learning

Thermal properties of actinides in molten salts are linked to the strongly disordered local environment of actinide ions. Here, we illustrate both the limitations of the commonly used fitting method for analysis of extended X-ray absorption fine structure (EXAFS) spectra in molten UF 4 and a possible solution using an "objective neural network - EXAFS" (ONNE) method. ONNE provides both extraction of the pair distribution function, as validated by its application to the EXAFS spectra calculated on molecular dynamics trajectory, and the EXAFS data reconstruction. The ONNE analysis of the molten UF4 has revealed reduction of the first nearest neighbor U-F coordination number, expansion of the U-F bond length and smaller contribution to the second shell compared to its crystalline counterpart. This method is therefore an attractive alternative to conventional EXAFS analysis and molecular dynamics simulations for studies of disordered environment of actinides in molten salts.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

DOE OSTI2020

In situ synchrotron pair distribution function analysis to monitor synthetic pathways under electromagnetic excitation

Electromagnetic (EM) fields, specifically microwave radiation (MWR), can significantly influence the synthesis of ceramic oxide materials and promote rapid, low-temperature growth. However, the mechanisms by which EM fields affect the phase formation process are not well understood. A major limitation to increasing this understanding has been the lack of information regarding dynamic changes in local atomic structure during MWR exposure compared to conventional hydrothermal synthesis routes. Here, we utilize in situ synchrotron X-ray pair distribution function (PDF) analysis to monitor MWR-assisted SnO 2 nanoparticle synthesis. A clear impact of the EM field is demonstrated, with MWR inducing changes in nearest neighbor distances and peaks in oxygen atomic displacement that do not occur during synthesis without MWR exposure. The observed local structural disorder serves as a precursor to rapid rutile SnO 2 nanoparticle crystallization, suggesting that EM field-assisted growth is mediated by changes to the oxygen sublattice. These findings further our understanding of the mechanisms underlying MWR-assisted synthesis and represent a step towards utilizing EM fields to engineer tailored atomic structures for a broad range of applications.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Local structure analysis of low-temperature neutron pair distribution function coupled with molecular dynamics simulations of CH 4 and CO 2 hydrates from 2 to 210 K

CH 4 hydrates occur naturally and are an abundant potential fuel source with a corresponding risk of potent greenhouse gas release, due to their stability conditions at low temperature and high pressure. Byproduct CO 2 can be exchanged with CH 4 in these natural deposits and can potentially stabilize the hydrates at higher temperatures. CH 4 , CO 2 , and mixed CH 4 -CO 2 hydrates are studied with in situ neutron pair distribution function experiments from 2 to 210 K to investigate the impact of varying the CH 4 -CO 2 guest composition in the gas hydrate structure. These experiments combined with Reverse Monte Carlo analysis allow for the characterization of intermolecular CH 4 and CO 2 interactions with the water molecules which form the hydrate lattice and how they impact the local structure of the lattice itself. Results indicate that when CH 4 and CO 2 co-occupy the hydrate, the host is more strongly distorted than in the pure CH 4 and CO 2 hydrates, but this becomes less defined with increasing temperature. The presence of CO 2 in mixed hydrate increases the stability range and creates a barrier for CH 4 to completely leave the structure.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Improving the picture of atomic structure in nonoriented polymer domains using the pair distribution function: A study of polyamide 6

Abstract Investigations of the atomic structures within polyamides started over 80 years ago and continue today. These weakly ordered materials diffract X‐rays poorly and typically require postprocessing to obtain idealized samples for structural studies. An important goal remains to develop techniques to study the local structure in its natural state, with atomic resolution, and with sensitivity to subtle changes due to synthesis conditions or other technologically relevant processing procedures. Here, we compare the structures of as‐produced, nonoriented polyamide 6 ([C 6 H 11 NO] n ) from both hydrolytic and anionic processes. A total scattering pair distribution function approach is used to elucidate information about the atomic bonding, molecular conformation, chain packing, crystallite size, and ratio of ordered to disordered domain content. The results are compared with those from standard analytical methods.

Terban, Maxwell W.↗

DOE OSTI2021

Ab Initio Molecular Dynamics Simulations of Amorphous Calcium Carbonate: Interpretation of Pair Distribution Function and X-Ray Absorption Spectroscopy Data

The structure and transformation of hydrous amorphous calcium carbonate (ACC) are key to understanding biomineralization pathways and their relationship with the properties of the resulting material. Quantitative interpretation of scattering experiments aimed at elucidating the structure of ACC is challenging, due to the amorphous nature of this material, and, therefore, requires models for the structure and the scattering physics. Here, we generate physically realistic ensembles of hydrated ACC structures and their vibrational disorder from ab initio molecular dynamics (AIMD) simulations with an emphasis on enabling the consistent interpretation of the finer details of three complementary structural probes: neutron and x-ray pair distribution experiments and x-ray absorption spectroscopy (XAS). In each case, we simulate the signal directly in reciprocal space and then manipulate it into the real-space pair distribution function (PDF) or spectrum using the same procedures for the experimental and theoretical data. Good agreement with experiment was obtained across the three techniques with the simulations accounting well for all features in the spectra. Remaining small discrepancies pointed to differences between real samples and the idealized simulated systems such as deviations from the nominal CaCO3·nH2O stoichiometry. Additionally, the simulations offered a more accurate description of the local coordination environment of calcium than previous shell-by-shell fits to spectra of synthetic ACC and classical molecular dynamics simulations. This work demonstrates that AIMD is a powerful approach for extracting detailed structural information from neutron PDF, x-ray PDF, and XAS of amorphous carbonate phases.

Prange, Micah P.↗

DOE OSTI2024

Inverse bremsstrahlung absorption rate for super-Gaussian electron distribution functions including plasma screening

Here we provide analytic expressions for the effective Coulomb logarithm for inverse bremsstrahlung absorption which predict significant corrections to the Langdon effect and overall absorption rate compared to previous estimates. The calculation of the collisional absorption rate of laser energy in a plasma by the inverse bremsstrahlung mechanism usually makes the approximation of a constant Coulomb logarithm. We dispense with this approximation and instead take into account the velocity dependence of the Coulomb logarithm, leading to a more accurate expression for the absorption rate valid in both classical and quantum conditions. In contrast to previous work, the laser intensity enters into the Coulomb logarithm. In most laser-plasma interactions the electron distribution function is super-Gaussian [Langdon, Phys. Rev. Lett. 44, 575 (1980)], and we find the absorption rate under these conditions is increased by as much as ≈ 30% compared to previous estimates at low density. In many cases of interest the correction to Langdon's predicted reduction in absorption is large; for example at Z = 6 and Te = 400 eV the Langdon prediction for the absorption is in error by a factor of ≈ 2. However, we also account for the additional effect of plasma screening, which predicts a reduction in absorption by a similar amount (up to ≈ 30%). These two effects compete to determine the overall absorption, which may be increased or decreased, depending on the conditions. The corrections can be incorporated into radiation-hydrodynamics simulation codes by replacing the familiar Coulomb logarithm with an analytic expression which depends on the super-Gaussian order “M” and the screening length.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗