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Results for “DEBYE FUNCTION”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

In situ high-temperature X-ray diffraction study of Sc-doped titanium oxide nanocrystallites

Titanium dioxide is an inexpensive wide-gap highly ionic semiconductor with striking photocatalytic capabilities in several heterogeneous photoredox reactions. A small crystal size is desirable to maximize the surface area, since photocatalytic reactions occur at the surface of a photocatalyst. Presented in this work are the synthesis and microstructural characterization of 4 at.% Sc-doped TiO 2 (4SDT) prepared by water-based co-precipitation. The crystal structure of 4SDT was examined via in situ high-temperature powder X-ray diffraction experiments from 25 to 1200°C. Rietveld analysis revealed single-phase anatase up to 875°C, while at 900°C the anatase-to-rutile phase transformation occurred and at higher temperatures additional reflections of Sc-rich phases (Sc 2 TiO 5 from 975°C and Ti 3 Sc 4 O 12 or Sc 2 O 3 at 1200°C) were observed. Debye function analysis (DFA) was applied to model the total scattering pattern directly in reciprocal space, allowing the reconstruction of Ti vacancies. Both Rietveld and DFA methods were applied to estimate the nanocrystallite size and shape with consistent growth in crystallite size with temperature: an ellipsoid shape with equatorial ~4.7 nm / axial (001) ~6.9 nm at 25°C to equatorial ~27.9 nm / axial (001) ~39.6 nm at 900°C refined by Rietveld analysis, versus a cylinder shape with D a , b = 4.3 nm and size dispersion σ ab = 1.5 nm, L c = 4.9 nm and σ c = 2.3 nm at 25°C to D a , b = 21.4 nm, σ ab = 8.3 nm, L c = 23.9 and σ c = 10.9 nm at 900°C estimated by DFA. The microstructural changes obtained by Rietveld and DFA methods were supported by high-resolution transmission electron microscopy image analysis, as well as by the less direct nitrogen sorption techniques that provide information on the size of non-agglomerated and dense particles. The Ti site-occupancy factor showed a linear increase from 0.6–0.8 at 25°C to unity at 900°C for anatase, and from ~0.7 at 900°C to unity at 1200°C for rutile, via Rietveld analysis and DFA.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Influence of Added Salt on Chain Conformations in Poly(ethylene oxide) Melts: SANS Analysis with Complications

Poly(ethylene oxide) (PEO)-based electrolytes have gained increasing attention in both the rechargeable battery industry and fundamental research, but any influence of the ions on the polymer conformation is not fully understood. Small-angle neutron scattering (SANS) is a powerful means to determine single-polymer chain conformations. We conducted SANS experiments on 50:50 blends of perdeuterated PEO (dPEO) and hydrogenous PEO (hPEO) of two different molecular weights (20 and 40 kDa) doped with two different salts (LiTFSI and LiClO 4 ) at various concentrations. An additional measurement with LiI is also reported. The scattering profiles of salt-doped dPEO/hPEO blends were measured, and the incoherent scattering from dPEO and hPEO doped with salt was measured separately. A strong low q upturn was observed in some of the blends and in the pure dPEO homopolymers. The statistical segment lengths of PEO–salt mixtures were derived using a Kratky analysis. The segment length decreases modestly with increasing amounts of LiTFSI but apparently first increases then decreases with added LiClO 4 . At the highest salt concentration examined (r = [Li+]/[EO] = 0.125), a roughly 10% decrease in the statistical segment length was observed in both LiTFSI and LiClO 4 -doped PEOs, for both molecular weights. This work confirms that added salt causes a contraction of the PEO chain dimensions, but the effect appears slightly weaker than reported recently. Certain difficulties in data analysis are also discussed, including the unexplained low q scattering even in pure deuterated polymers, uncertainties in background subtraction, and inappropriate application of the Debye function.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Discrete ion stochastic continuum overdamped solvent algorithm for modeling electrolytes

In this paper we develop a methodology for the mesoscale simulation of strong electrolytes. The methodology is an extension of the fluctuating immersed-boundary approach that treats a solute as discrete Lagrangian particles that interact with Eulerian hydrodynamic and electrostatic fields. In both algorithms the immersed-boundary method of Peskin is used for particle-field coupling. Hydrodynamic interactions are taken to be overdamped, with thermal noise incorporated using the fluctuating Stokes equation, including a "dry diffusion" Brownian motion to account for scales not resolved by the coarse-grained model of the solvent. Long-range electrostatic interactions are computed by solving the Poisson equation, with short-range corrections included using an immersed-boundary variant of the classical particle-particle particle-mesh technique. Also included is a short-range repulsive force based on the Weeks-Chandler-Andersen potential. This methodology is validated by comparison to Debye-Hückel theory for ion-ion pair correlation functions, and Debye-Hückel-Onsager theory for conductivity, including the Wien effect for strong electric fields. In each case, good agreement is observed, provided that hydrodynamic interactions at the typical ion-ion separation are resolved by the fluid grid.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

DFT Calculation of Thermal Expansion within Debye-Grüneisen Framework Made Simple and Accurate

The density functional theory (DFT) based Debye-Grüneisen approach is a computational method used to calculate the thermodynamic properties of materials by relating the volume dependence of the Debye frequency to the Grüneisen parameter. In this study, we propose a new model to describe the volume dependence of the Grüneisen parameter. This model offers a simple yet accurate approach to predict the thermal expansion of materials within the framework of the Debye-Grüneisen theory. Specifically, for pure elements or species used as a reference system, we calibrated the parameters to reproduce the experimental coefficient of thermal expansion, heat capacity, and entropy. For compounds with arbitrary compositions, the parameters are determined by taking the arithmetic or geometric average of those obtained from the pure elements or species based on their composition. We then compared the model prediction with experiments. This allowed for a comprehensive characterization of the thermal expansion behavior of various materials.

Wang, Yi↗
DOE OSTI2022

Modeling electrokinetic flows with the discrete ion stochastic continuum overdamped solvent algorithm

In this article we develop an algorithm for the efficient simulation of electrolytes in the presence of physical boundaries. In previous work the discrete ion stochastic continuum overdamped solvent (DISCOS) algorithm was derived for triply periodic domains, and was validated through ion-ion pair correlation functions and Debye-Hückel-Onsager theory for conductivity, including the Wien effect for strong electric fields. In extending this approach to include an accurate treatment of physical boundaries we must address several important issues. First, the modifications to the spreading and interpolation operators necessary to incorporate interactions of the ions with the boundary are described. Next we discuss the modifications to the electrostatic solver to handle the influence of charges near either a fixed potential or dielectric boundary. An additional short-ranged potential is also introduced to represent interaction of the ions with a solid wall. Finally, the dry diffusion term is modified to account for the reduced mobility of ions near a boundary, which introduces an additional stochastic drift correction. Herein, several validation tests are presented confirming the correct equilibrium distribution of ions in a channel. Additionally, the methodology is demonstrated using electro-osmosis and induced-charge electro-osmosis, with comparison made to theory and other numerical methods. Notably, the DISCOS approach achieves greater accuracy than a continuum electrostatic simulation method. We also examine the effect of under-resolving hydrodynamic effects using a “dry diffusion” approach, and find that considerable computational speedup can be achieved with a negligible impact on accuracy.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Enhancing the accuracy and generality of the Debye–Grüneisen Model: Optimizing the volume dependence for accurate predictions across varied compositions

In this work, we have introduced an optimized Debye-Grüneisen model that revolutionizes the determination of the Debye temperature and Grüneisen parameters. Unlike conventional methods, our model requires only the 0 K energy volume data for a material as input, eliminating the need to determine the bulk modulus and its pressure derivative, which often pose challenges due to numerical uncertainties. This unique feature sets our model apart from existing approaches and streamlines the process, enabling accurate predictions of thermal expansion behavior across various materials. To demonstrate its effectiveness, we showcase its excellent agreement with measured coefficients of thermal expansion (CTE) for the nickel-cobalt-chromium-aluminum-yttrium (Ni-Co-Cr-Al-Y) bond-coating system. Additionally, we apply our approach by conducting a high-throughput search for potential bond-coating materials among 90,000 compositions within the aluminum-cobalt-chromium-iron-nickel (Al-Co-Cr-Fe-Ni) system. From this extensive search, four compositions are synthesized, and the measured CTE values agree very well with theoretical predictions, hence validating our approach. In conclusion, the current optimized Debye-Grüneisen model combined with Density Functional Theory (DFT)-based thermodynamic database enables reliable and efficient high-throughput calculations of CTE of of a material without expensive phonon calculations.

Bond coating materials↗
DOE OSTI2020

Generation of the Thermal Scattering Law of Uranium Dioxide with Ab Initio Lattice Dynamics to Capture Crystal Binding Effects on Neutron Interactions

Scattering of thermal neutrons and Doppler broadening of epithermal neutron resonances in uranium and its compounds may be sensitive to crystal binding. The thermal scattering law (TSL) for uranium dioxide, which captures crystal binding effects, has been reevaluated for ENDF/B-VIII.0. Phonon spectra were generated using ab initio lattice dynamics for the paramagnetic phase and validated against experiment. Improved agreement with the Debye-Waller coefficient as a function of temperature is found relative to the spectrum used for the ENDF/B-VII.1 evaluation. The TSL was generated using the phonon expansion method within the NJOY nuclear data processing package and was found to be in reasonable agreement with inelastic neutron scattering measurements. The present evaluation predicts a reduction in the inelastic scattering cross section relative to ENDF/B-VII.1 and a total scattering cross section consistent with neutron transmission experiments

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Local structure, bonding, and asymmetry of $\mathrm{((NH_2)_2CH)PbBr_3}$, $\mathrm{CsPbBr_3}$, and $\mathrm{(CH_3MH_3)PbBr_3}$

Here we report local structure measurements for CsPbBr 3 and ((NH 2 ) 2 CH)PbBr 3 (FAPbBr 3 ) and compare them with recent results for (CH 3 NH 3 )PbBr 3 (MAPbBr 3 ). The Pb-Br bonding is similar for all three systems; the effective spring constants, κ, are comparable (ranging from 1.20 to 1.95 eV/Å 2 ), but small in magnitude indicating very soft materials. However, there are also important differences between the three systems. Static disorder is very small for CsPbBr3 but increases somewhat with the size of the organic molecular ions MA + and FA + . At room temperature, dynamic disorder dominates in all compounds. The thermal disorder of the Pb-Br pair distribution function (PDF), i.e., the Debye-Waller factor σ 2 follows a correlated Debye or Einstein model up to 300 K in CsPbBr 3 (orthorhombic phase), but for FAPbBr 3 and MAPbBr 3 , there is a break in the σ 2 (T) curve at the orthorhombic-tetragonal transition (o-t) near 150 K, indicating a small change in the spring constant κ. κ increases for MAPbBr 3 but decreases in FAPbBr 3 at this transition. These changes are attributed to changes in the H-bonding between Br - and MA + or FA + at this transition, as a result of librations or rotations of these molecular cations. In addition, the Pb-Br PDF becomes asymmetric at a relatively low temperature for FAPbBr 3 and MAPbBr 3 , while this effect is significantly smaller for CsPbBr 3 . Finally, we address the question of a model to explain the asymmetric PDF. Two main models are discussed in the literature, an anharmonic pair potential and a split-pair distribution, possibly driven by the presence of a lone pair on the Pb ion. We show that the fourth cumulant C 4 can differentiate between these two models and other possible models. Experimentally C 4 is positive at 250 K and above, for all three systems and that is inconsistent with a split-peak model, for which C 4 is negative for splittings larger than 0.12 Å.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Impact of classical statistics on thermal conductivity predictions of BAs and diamond using machine learning molecular dynamics

Machine learning interatomic potentials (MLIPs) have greatly enhanced molecular dynamics (MD) simulations, achieving near-first-principles accuracy in thermal conductivity studies. In this work, we reveal that this accuracy, observed in BAs and diamond at sub-Debye temperatures, stems from an accidental error cancelation: classical statistics overestimates specific heat while underestimating phonon lifetimes, balancing out in thermal conductivity predictions. However, this balance is disrupted when isotopes are introduced, leading MLIP-based MD to significantly underpredict thermal conductivity compared to experiments and quantum statistics-based Boltzmann transport equation. This discrepancy arises not from classical statistics affecting phonon–isotope scattering rates but from its impact on the interplay between phonon–isotope and phonon–phonon scattering in the normal scattering-dominated BAs and diamond. In conclusion, this work underscores the limitations of MLIP-based MD for thermal conductivity studies at sub-Debye temperatures.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Specimen-displacement correction for powder X-ray diffraction in Debye–Scherrer geometry with a flat area detector

The effect of small changes in the specimen-to-detector distance on the unit-cell parameters is examined for synchrotron powder diffraction in Debye–Scherrer (transmission) geometry with a flat area detector. An analytical correction equation is proposed to fix the shift in 2θ values due to specimen capillary displacement. This equation does not require the use of an internal reference material, is applied during the Rietveld refinement step, and is analogous to the specimen-displacement correction equations for Bragg–Brentano and curved-detector Debye–Scherrer geometry experiments, but has a different functional form. The 2θ correction equation is compared with another specimen-displacement correction based on the use of an internal reference material in which new integration and calibration parameters of area-detector images are determined. Example data sets showing the effect of a 3.3 mm specimen displacement on the unit-cell parameters for 25°C CeO 2 , including both types of displacement correction, are described. These experiments were performed at powder X-ray diffraction beamlines at the National Synchrotron Light Source II at Brookhaven National Laboratory and the Advanced Photon Source at Argonne National Laboratory.

36 MATERIALS SCIENCE↗
DOE OSTI2020

EXAFS investigation of the local structure in URu 2-x Fe x Si 2 : Evidence for distortions below 100 K

X-ray absorption measurements at the U L III , Ru K , and Fe K edges are reported for the hidden order (HO) material URu 2 - x Fe x Si 2 ( x = 0 , 0.05, 0.08, 0.10, 0.12, 0.15, and 0.20) as a function of x and temperature T . Furthermore, when Fe is substituted for Ru, the local structure about Fe shrinks slightly and the first neighbor Fe-Si bond length decreases by ≈ 0.05 Å . More importantly excess disorder is observed below 80–100 K (the coherence temperature T * ) in plots of the Debye-Waller factor σ 2 ( σ is the width of the pair distribution function); at low T the data deviate from the usual Einstein or correlated-Debye model plots. This excess disorder is most prominent for the Ru-Si bond, and σ 2 actually increases below 80 K. These results suggest a local orthorhombic distortion with B 1 g -like symmetry that develops below 80–100 K. A model that describes these local distortions is presented, and discussed in terms of other measurements that indicate a breaking of fourfold symmetry at low T . In addition, the square root of the difference between σ 2 ( T ) for the Ru-Si pair and a Debye fit to these data serves as an order parameter for this orthorhombic distortion, in the temperature range below 100 K. This quantity is a length related to a - b , the difference between the a and b lattice constants in the orthorhombic phase, and provides a connection between this distortion and T * . X-ray absorption near edge structure (XANES) measurements also show that there are no changes in the edge positions down to 0.1 eV for any edge as a function of x , for T in the HO regime.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

Memsensing by surface ion migration within Debye length

Integration between electronics and biology is often facilitated by iontronics, where ion migration in aqueous media governs sensing and memory. However, the Debye screening effect limits electric fields to the Debye length, the distance over which mobile ions screen electrostatic interactions, necessitating external voltages that constrain the operation speed and device design. Here we report a high-speed in-memory sensor based on vanadium dioxide (VO2) that operates without an external voltage by leveraging built-in electric fields within the Debye length. When VO2 contacts a low-work-function metal (for example, indium) in a salt solution, electrochemical reactions generate indium ions that migrate into the VO2 surface under the native electric field, inducing a surface insulator-to-metal phase transition of VO2. The VO2 conductance increase rate reflects the salt concentration, enabling in-memory sensing, or memsensing of the solution. The memsensor mimics Caenorhabditis elegans chemosensory plasticity to guide a miniature boat for adaptive chemotaxis, illustrating low-power aquatic neurorobotics with fewer memory units.

Guo, Ruihan↗
DOE OSTI2020

Dimensional interpolation for metallic hydrogen

In this work, we employ a simple and mostly accurate dimensional interpolation formula using dimensional limits D = 1 and D = ∞ to obtain D = 3 ground-state energy of metallic hydrogen. We also present results describing the phase transitions for different symmetries of three-dimensional structure lattices. The interpolation formula not only predicts fairly accurate energies but also predicts a correct functional form of the energy as a function of the lattice parameters. That allows us to calculate different physical quantities such as the bulk modulus, Debye temperature, and critical transition temperature, from the gradient and the curvature of the energy curve as a function of the lattice parameters. These theoretical calculations suggest that metallic hydrogen is a likely candidate for high temperature superconductivity. The dimensional interpolation formula is robust and might be useful to obtain the energies of complex many-body systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
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 OSTI2023

Pair distribution function analysis of nano-object assemblies

The atomic pair distribution function (aPDF) analysis technique, also known as the total scattering method, which considers both Bragg and diffuse scattering, has been used extensively to probe local atomic arrangements in crystalline and disordered materials. In contrast, there have been limited applications of the PDF in self-assembled nanomaterials, which represent a class of materials built from nanoscale objects, such as nano-colloids, micelles and proteins. As distinguished from atoms, nano-objects have polydispersity in size and shape, and such form-factor effects complicate the application of PDF analysis to nano-systems. Here, in this paper, the application of the PDF is extended to spherical nano-object assemblies and the formulae for the nano-PDF (nPDF) are derived, showing some differences from the aPDF. By numerical simulations, the properties of the nPDF (peak broadening and pattern profile) are studied systematically as a function of structural features, such as nano-object parameters (size and size polydispersity) and assembly structural features (size, shape, structure type and lattice disorder), and of data processing parameters ( q cut-off and `missing' data in ultra-small-angle regions). The nPDF analysis method is found to provide an effective route to revealing not only nanoscale but also mesoscale structural properties, for example the morphology of a nano-assembly.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2025

Lectures on statistical mechanics

Presented here is a transcription of the lecture notes from Professor Allan N. Kaufman’s graduate statistical mechanics course Physics 212A and 212B at the University of California Berkeley from the 1972–1973 academic year. 212A addressed equilibrium statistical mechanics with topics: fundamentals (micro-canonical and sub-canonical ensembles, adiabatic law and action conservation, fluctuations, pressure, and virial theorem), classical fluids and other systems (equation of state, deviations from ideality, virial coefficients and van der Waals potential, canonical ensemble and partition function, quasistatic evolution, grand-canonical ensemble and partition function, chemical potential, simple model of a phase transition, quantum virial expansion, numerical simulation of equations of state, and phase transition), chemical equilibrium (systems with multiple species and chemical reactions, law of mass action, Saha equation, chemical equilibrium including ionization and excited states), and long-range interactions (including Coulomb, dipole, and gravitational interactions, Debye–Hückel theory, and shielding). 212B addressed nonequilibrium statistical mechanics with topics: fundamentals (definitions: realizations, moments, characteristic function, and discrete variables), Brownian motion (Langevin equation, fluctuation–dissipation theorem, spatial diffusion, Boltzmann’s H-theorem), Liouville and Klimontovich equations, Landau equation (derivation, elaboration, and H-theorem, and irreversibility), Markov processes and Fokker–Planck equation (derivations of the Fokker–Planck equation and a master equation), linear response and transport theory (linear Boltzmann equation, linear response theory of Kubo and Mori, relation of entropy production to electrical conductivity, transport relations and coefficients, normal mode solutions of the transport equations, sketch of a generalized Langevin equation method for transport theory), and an introduction to nonequilibrium quantum statistical mechanics.

plasma dynamics↗
DOE OSTI2021

The imaginary part of the heavy-quark potential from real-time Yang-Mills dynamics

We extract the imaginary part of the heavy-quark potential using classical-statistical simulations of real-time Yang-Mills dynamics in classical thermal equilibrium. The r-dependence of the imaginary part of the potential is extracted by measuring the temporal decay of Wilson loops of spatial length r. We compare our results to continuum expressions obtained using hard thermal loop theory and to semi-analytic lattice perturbation theory calculations using the hard classical loop formalism. We find that, when plotted as a function of m D r, where m D is the hard classical loop Debye mass, the imaginary part of the heavy-quark potential shows little sensitivity to the lattice spacing at small m D r ≲ 1 and agrees well with the semi-analytic hard classical loop result. For large quark-antiquark separations, we quantify the magnitude of the non-perturbative long-range corrections to the imaginary part of the heavy-quark potential. We present our results for a wide range of temperatures, lattice spacings, and lattice volumes. This work sets the stage for extracting the imaginary part of the heavy-quark potential in an expanding non-equilibrium Yang Mills plasma.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Surface softening in palladium nanoparticles: effects of a capping agent on vibrational properties

The presence of a capping agent (CTAB) on Pd nanoparticles produces a strong static disorder in the surface region. This results in a surface softening, which contributes to an overall increase in the Debye–Waller coefficient measured by X-ray powder diffraction. Here, molecular dynamics and density functional theory simulations show that the adsorption-induced surface disorder is strong enough to overcome the effects of nanoparticle size and shape.

77 NANOSCIENCE AND NANOTECHNOLOGY↗