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At least 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

Wigner distribution function and entropy of the damped harmonic oscillator within the theory of the open quantum systems

The harmonic oscillator with dissipation is studied within the framework of the Lindblad theory for open quantum systems. By using the Wang-Uhlenbeck method, the Fokker-Planck equation, obtained from the master equation for the density operator, is solved for the Wigner distribution function, subject to either the Gaussian type or the delta-function type of initial conditions. The obtained Wigner functions are two-dimensional Gaussians with different widths. Then a closed expression for the density operator is extracted. The entropy of the system is subsequently calculated and its temporal behavior shows that this quantity relaxes to its equilibrium value.

Isar, Aurelian↗
NASA NTRS1980

Distribution function representation of energy spectra of H, He, C, O and Fe in corotating particle streams

From an analysis of nine corotating events observed near 1 AU during the 1974-1976 solar minimum, the spectral parameters for H, He, C, O and Fe and relative abundances of these elements and of Ne, Mg, Si, and S-Ca were determined. The distribution functions of H, He, O and Fe are well represented by an exponential in particle speed over the energy range of the measurements from 0.3 to 5 MeV/nucleon. The composition resembles that of the solar corona, particularly in the O/C ratio which is 0.95 + or - 0.19, and the He/H and He/Ne ratios are similar to the respective ratios in the solar wind. The results are consistent with interplanetary statistical acceleration of these particles out of the high-energy tail of the high-speed solar wind.

Gloeckler, G.↗
NASA NTRS1986

Determination of grain size distribution function using two-dimensional Fourier transforms of tone pulse encoded images

Microstructural images may be tone pulse encoded and subsequently Fourier transformed to determine the two-dimensional density of frequency components. A theory is developed relating the density of frequency components to the density of length components. The density of length components corresponds directly to the actual grain size distribution function from which the mean grain shape, size, and orientation can be obtained.

Generazio, E. R.↗
NASA NTRS1988

Determination of grain-size distribution function using two-dimensional Fourier transforms of tone-pulse-encoded images

Microstructural images may be tone pulse encoded and subsequently Fourier transformed to determine the two-dimensional density of frequency components. A theory is developed relating the density of frequency components to the density of length components. The density of length components corresponds directly to the actual grain-size distribution function from which the mean grain shape, size, and orientation can be obtained.

Generazio, E. R.↗
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)↗
NASA NTRS1977

Distribution functions for energetic oxygen atoms in the earth's lower atmosphere

Direct photolysis of O3 and quenching of O(1D) by N2 provide abundant sources of fast oxygen atoms for earth's lower atmosphere. The concentration of atoms with energy above 0.7 eV may exceed the concentration of O(1D) for all altitudes below 18 km, and these atoms may play an important role in lower-atmospheric chemistry. Distribution functions for O(3P) are given for the energy interval 0.1-1.3 eV and a range of altitudes from 0 to 62 km.

Logan, J. A.↗
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↗
NASA NTRS2016

A Proton-Cyclotron Wave Storm Generated by Unstable Proton Distribution Functions in the Solar Wind

We use audification of 0.092 seconds cadence magnetometer data from the Wind spacecraft to identify waves with amplitudes greater than 0.1 nanoteslas near the ion gyrofrequency (approximately 0.1 hertz) with duration longer than 1 hour during 2008. We present one of the most common types of event for a case study and find it to be a proton-cyclotron wave storm, coinciding with highly radial magnetic field and a suprathermal proton beam close in density to the core distribution itself. Using linear Vlasov analysis, we conclude that the long-duration, large-amplitude waves are generated by the instability of the proton distribution function. The origin of the beam is unknown, but the radial field period is found in the trailing edge of a fast solar wind stream and resembles other events thought to be caused by magnetic field footpoint motion or interchange reconnection between coronal holes and closed field lines in the corona.

instabilities - plasmas↗
NASA NTRS1982

Bidirectional reflectance distribution function of the Infrared Astronomical Satellite solar-shield material

The Infrared Astronomical Satellite (IRAS) telescope has an outer shield on it which is used to reduce the amount of thermal radiation that enters the telescope. The shield forms the first part of the baffle structure which reduces the photon incidence on the focal plane. It was, therefore, necessary to model this structure for scattering, and a required input for such modeling is the scattering characteristic of this surface. Attention is given to the measurement of the bidirectional reflectance distribution function (BRDF), the reflected radiance divided by the incident irradiance at 10.6 micrometers, 118 micrometers, and at several angles of incidence. Visual observation of the gold sample shows that there are striations which line up in a single direction. The data were, therefore, taken with the sample oriented in each of two directions.

Hubbs, J. E.↗
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↗
NASA NTRS1994

Modeling the bidirectional reflectance distribution function of mixed finite plant canopies and soil

An analytical model of the bidirectional reflectance for optically semi-infinite plant canopies has been extended to describe the reflectance of finite depth canopies contributions from the underlying soil. The model depends on 10 independent parameters describing vegetation and soil optical and structural properties. The model is inverted with a nonlinear minimization routine using directional reflectance data for lawn (leaf area index (LAI) is equal to 9.9), soybeans (LAI, 2.9) and simulated reflectance data (LAI, 1.0) from a numerical bidirectional reflectance distribution function (BRDF) model (Myneni et al., 1988). While the ten-parameter model results in relatively low rms differences for the BRDF, most of the retrieved parameters exhibit poor stability. The most stable parameter was the single-scattering albedo of the vegetation. Canopy albedo could be derived with an accuracy of less than 5% relative error in the visible and less than 1% in the near-infrared. Sensitivity were performed to determine which of the 10 parameters were most important and to assess the effects of Gaussian noise on the parameter retrievals. Out of the 10 parameters, three were identified which described most of the BRDF variability. At low LAI values the most influential parameters were the single-scattering albedos (both soil and vegetation) and LAI, while at higher LAI values (greater than 2.5) these shifted to the two scattering phase function parameters for vegetation and the single-scattering albedo of the vegetation. The three-parameter model, formed by fixing the seven least significant parameters, gave higher rms values but was less sensitive to noise in the BRDF than the full ten-parameter model. A full hemispherical reflectance data set for lawn was then interpolated to yield BRDF values corresponding to advanced very high resolution radiometer (AVHRR) scan geometries collected over a period of nine days. The resulting parameters and BRDFs are similar to those for the full sampling geometry, suggesting that the limited geometry of AVHRR measurements might be used to reliably retrieve BRDF and canopy albedo with this model.

Schluessel, G.↗
NASA NTRS2019

Experimentally-Derived Bidirectional Reflectance Distribution Function Data in Support of the Orbital Debris Program Office

The NASA Orbital Debris Program Office (ODPO) has used various optical assets to acquire photometric data of Earth-orbiting objects to define the orbital debris environment. To better characterize and model optical data acquired from ground-based telescopes, the Optical Measurements Center (OMC) at NASA Johnson Space Center emulates illumination conditions seen in space by using equipment and techniques that parallel telescopic observations and source-target-sensor orientations. One of the OMC goals is to improve the size calculation used for optical data by developing an optical-based Size Estimation Model. The current size estimation requires applying a Lambertian phase function, a set albedo value, and range to the observed magnitude. The first step to improving the sampled brightness of laboratory targets is to remove aspect-angle dependencies. Then, the volume of possible object viewing angles is sampled at 21 combinations of azimuth and zenith angles for each solar phase angle. Finally, the acquired images are input into an image processing program that generates approximations for the object’s Bidirectional Reflectance Distribution Function (BRDF) and phase function. The BRDF is a radiometric concept that identifies an object’s material composition by matching a BRDF approximated with photometric data collected by ground-based telescopes with a BRDF generated experimentally from a known object in the laboratory. This paper discusses the validation of experimental BRDF and phase function approximations produced in the OMC and how the findings will be incorporated into ODPO models. A Lambertian sphere is imaged and the subsequent experimental functions are scrutinized to confirm that they correspond to an object that has an isotropic luminance. With the image processing algorithm validated, test objects with varying optical properties are then imaged to confirm that the produced photometric functions are both unique and repeatable. Once the validation is complete, the OMC will be used to evaluate a subset of fragments from a hypervelocity impact test of a mock-up satellite and assess the appropriate phase function and size estimates using BRDF measurements for a large volume of targets composed of various shapes, sizes, and materials.

Orbital Debris Program Office (ODPO)↗
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.↗
NASA NTRS1980

Distribution functions of type III electrons observed in interplanetary space

Simultaneous energetic electron and solar radio observations from the ISEE-3 spacecraft of several solar type III radio bursts are analyzed and discussed. Two types of electron events are found: (1) normal flare associated electron events in the 20 to greater than 100 keV range, and (2) low energy, 2 to 10 keV, electron events which appear to be associated with individual type III bursts from low frequency type III storms. The arrival direction and frequency of the radio emission are identified and the temporal behavior of the in situ radio intensity and the electron intensity are compared. Calculations of the electron velocity distribution function parallel to the magnetic field are made, implying that for electron events above 20 keV, scattering in the pitch angle is significant in modifying this function.

Lin, R. P.↗