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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Novel Relaxation Time Approximation: A Consistent Calculation of Transport Coefficients with QCD-inspired Relaxation Times

We use a novel formulation of the relaxation time approximation to consistently calculate the bulk and shear viscosity coefficients using QCDinspired energy-dependent relaxation times and phenomenological thermal masses obtained from fits to lattice QCD thermodynamics. The matching conditions are conveniently chosen to simplify the computations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Uniqueness of relaxation times determined by dielectric spectroscopy

Dielectric spectroscopy is extremely powerful to study molecular dynamics, because of the very broad frequency range. Often multiple processes superimpose resulting in spectra that expand over several orders of magnitude, with some of the contributions partially hidden. For illustration, we selected two examples, (i) normal mode of high molar mass polymers partially hidden by conductivity and polarization and (ii) contour length fluctuations partially hidden by reptation using the well-studied polyisoprene melts as example. The intuitive approach to describe experimental spectra and to extract relaxation times is the addition of two or more model functions. Here, we use the empirical Havriliak-Negami function to illustrate the ambiguity of the extracted relaxation time, despite an excellent agreement of the fit with experimental data. We show that there are an infinite number of solutions for which a perfect description of experimental data can be achieved. However, a simple mathematical relationship indicates uniqueness of the pairs of the relaxation strength and relaxation time. Sacrificing the absolute value of the relaxation time enables to find the temperature dependence of the parameters with a high accuracy. For the specific cases studied here, the time temperature superposition (TTS) is very useful to confirm the principle. However, the derivation is not based on a specific temperature dependence, hence, independent from the TTS. We compare new and traditional approaches and find the same trend for the temperature dependence. The important advantage of the new technology is the knowledge of the accuracy of the relaxation times. Relaxation times determined from data for which the peak is clearly visible are the same within the experimental accuracy for traditional and new technology. However, for data where a dominant process hides the peak, substantial deviations can be observed. Finally, we conclude that the new approach is particularly helpful for cases in which relaxation times need to be determined without having access to the associated peak position.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Regularizing the linearly extrapolated BDF2 scheme for incompressible flows with time relaxation

This paper presents a highly-efficient finite element scheme for the time relaxation model (TRM). The efficiency is achieved through the second-order BDF2 time-stepping scheme with linear extrapolation (BDF2LE). The accuracy of the scheme is also greatly enhanced through the use of the divergence-free Scott-Vogeulis finite elements, and van Cittert approximate deconvolution. A complete finite element analysis is provided, which includes rigorous proofs for the stability, well-possessedness, and convergence of both velocity and pressure solutions. Furthermore, we also demonstrate that the inclusion of the linear time relaxation term preserves the long-time stability of the unregularized BDF2LE scheme. Finally, numerical experiments are presented that demonstrate the added stability and accuracy that time relaxation can provide.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Analysis of Niobium Electropolishing Using a Generalized Distribution of Relaxation Times Method

Using electrochemical impedance spectroscopy, we have devised a method of sensing the microscopic surface conditions on the surface of niobium as it is undergoing an electrochemical polishing (EP) treatment. The method uses electrochemical impedance spectroscopy (EIS) to gather information on the surface state of the electrode without disrupting the polishing reaction. The EIS data is analyzed using a so-called distribution of relaxation times (DRT) method. Using DRT, the EIS data can be deconvolved into discrete relaxation time peaks without any a priori knowledge of the electrode dynamics. By analyzing the relaxation time peaks, we are able to distinguish two distinct modes of the EP reaction. As the polishing voltage is increased, the electrode transitions from the low voltage EP mode, characterized by a single relaxation time peaks, to the high voltage EP mode, characterized by two relaxation time peaks. We theorize that this second peak is caused by the formation of an oxide layer on the electrode. We also find that this oxide induced peak transitions from to a negative relaxation time, which is indicative of a blocking electrode process. By analyzing EPed samples, we show that samples polished in the low voltage mode have significantly higher surface roughness due to grain etching and faceting. We find that the surface roughness of the samples only improves when the oxide film peak is present and in the negative relaxation time region. This shows that EIS combined with DRT analysis can be used to predict etching on EPed Nb. This method can also be performed before or during the EP, which could allow for adjustment of polishing parameters to guarantee a smooth cavity surface finish.

43 PARTICLE ACCELERATORS↗
DOE OSTI2024

Revisiting shear stress tensor evolution: Nonresistive magnetohydrodynamics with momentum-dependent relaxation time

This study aims to develop second-order relativistic viscous magnetohydrodynamics (MHD) derived from kinetic theory within an extended relaxation time approximation (momentum/energy dependent) for the collision kernel. The investigation involves a detailed examination of shear stress tensor evolution equations and associated transport coefficients. The Boltzmann equation is solved using a Chapman-Enskog-like gradient expansion for a charge-conserved conformal system, incorporating a momentum-dependent relaxation time. The derived relativistic nonresistive, viscous second-order MHD equations for the shear stress tensor reveal significant modifications in the coupling with dissipative charge current and magnetic field due to the momentum dependence of the relaxation time. By utilizing a power law parametrization to quantify the momentum dependence of the relaxation time, the anisotropic magnetic field-dependent shear coefficients in the Navier-Stokes limit have been investigated. The resulting viscous coefficients are seen to be sensitive to the momentum dependence of the relaxation time.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Identifying electrochemical processes by distribution of relaxation times in proton exchange membrane electrolyzers

Distribution of relaxation time (DRT) is used to interpret electrochemical impedance spectroscopy (EIS) for proton exchange membrane (PEM) water electrolyzers, with an attempt to separate overlapped relaxation processes in Nyquist plots. By varying operating conditions and catalyst loadings, four main relaxation peaks arising from EIS can be identified and successfully separated from low to high frequencies as (P1) mass transport, (P2) oxygen evolution reaction kinetics, (P3) reaction kinetics (with faster time constant than P2), and (P4) ionic transport. Here, the shape, height, and frequency of the DRT peaks change with different membrane electrode assembly (MEA) configurations. Electron microscopy reveals distinct features from the cross-sectioned MEAs which verify critical DRT results in that increasing the iridium (Ir)-anode loading from 0.2 mgIr/cm 2 to 1.5 mgIr/cm 2 reduces kinetic losses due to higher site-access; a thick and compacted anode, however, also triggers higher ohmic resistances from membrane/catalyst layer hydration and increases transport losses due to longer ionomer pathways. DRT provides higher resolution to EIS for deconvoluting processes with different relaxation times and the quantification of DRT peaks improves the accounting of total losses from each process.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Relaxation time approximations in PAOFLOW 2.0

Abstract Regardless of its success, the constant relaxation time approximation has limited validity. Temperature and energy dependent effects are important to match experimental trends even in simple situations. We present the implementation of relaxation time approximation models in the calculation of Boltzmann transport in 2.0 and apply those to model band-structures. In addition, using a self-consistent fitting of the model parameters to experimental conductivity data, we provide a flexible tool to extract scattering rates with high accuracy. We illustrate the approximations using simple models and then apply the method to GaAs, Si, $$\hbox {Mg}_3\hbox {Sb}_2$$ Mg 3 Sb 2 , and $$\hbox {CoSb}_3$$ CoSb 3 .

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Transport coefficients of quasiparticle models within a new relaxation time approximation of the Boltzmann equation

We investigate the transport properties of a kinetic theory model that is tuned to describe the thermodynamic properties of QCD at zero chemical potential using a new formulation of the relaxation time approximation. In contrast to previous approaches, the latter is constructed to preserve the fundamental properties of the collision term of the Boltzmann equation for any energy dependence of the relaxation time. A novel choice of matching conditions is implemented to ensure that the background mean-field depends only on the temperature even when the system is out of equilibrium. We provide a consistent analysis of how the transport coefficients of relativistic Navier-Stokes theory vary with the energy dependence of the relaxation time. We also show that the entropy production of this theory is consistent with the second law of thermodynamics and verify that it is independent of the matching conditions employed. We used this fact to calculate the matching independent combination of transport coefficients.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Relaxation time approximation for a multispecies relativistic gas

We generalize a recent prescription for the relaxation time approximation for the relativistic Boltzmann equation for systems with multiple particle species at finite temperature. This is performed by adding counter-terms to the traditional Anderson-Witting ansatz for each particle species. Our approach allows for the use of momentum-dependent relaxation times and the obedience of local conservation laws regardless of the definition of the local equilibrium state. As an application, we derive the first order Chapman-Enskog corrections to the equilibrium distribution and display results for the hadron-resonance gas. We also demonstrate that our collision term ansatz obeys the second law of thermodynamics.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Novel Relaxation Time Approximation to the Relativistic Boltzmann Equation

In this work, we show that the widely used relaxation time approximation to the relativistic Boltzmann equation contains basic flaws, being incompatible with micro- and macroscopic conservation laws if the relaxation time depends on energy or general matching conditions are applied. We propose a new approximation that fixes such fundamental issues and maintains the basic properties of the linearized Boltzmann collision operator. We show how this correction affects transport coefficients, such as the bulk viscosity and particle diffusion.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Defect in diamond with millisecond-scale spin relaxation time at room temperature

Spin defects in diamond are promising platforms for quantum sensing. The longest electron spin relaxation times (T1) at room temperature for solid-state defects are observed in nitrogen vacancy centers in diamond, which can reach 6.67 ms [1], and substitutional nitrogen (“P1 centers”) in diamond, which exhibit a T1 of 2 ms [2]. No other solid-state defect has exhibited millisecond-scale spin relaxation times at room temperature thus far. Here, we characterize the spin properties of the WAR5 defect in diamond [3] with pulsed electron spin resonance. The observed T1 is one of the longest for solid-state spin defects: 0.97(27) ms at room temperature and 14.38(19) min at 4 K. The observed coherence time (T2) is 246(7) µs, which can be extended to 6.49(34) ms at 4 K with dynamical decoupling. Finally, we demonstrate optical spin polarization with a range of wavelengths from 405 nm to 500 nm and propose potential zero-phonon line candidates.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Monitoring the long-term performance of organic redox flow battery by a distribution of relaxation time analysis

Organic redox flow batteries hold great promise as an energy storage technology, but their intricate chemistry makes them vulnerable to various degradation mechanisms. Monitoring this degradation is essential for identifying the limiting processes within the cells. Electrochemical impedance spectroscopy (EIS) offers a straightforward, in-situ method for measuring the total resistance of an operating cell. However, to pinpoint the limiting processes during long-term cycling, EIS data must be complemented by other techniques. Distribution of relaxation time (DRT) analysis is particularly effective for differentiating resistance components. Here, in this study, we perform a comprehensive analysis of resistance evolution and the separation of anode and cathode contributions during long-term cycling of a full cell employing 7,8-dihydroxyphenazine-2-sulfonic acid (DHPS) as the anolyte. Separate analyses of the DHPS anolyte and ferri-/ferrocyanide catholyte were conducted using a symmetric cell setup. The relaxation times derived from symmetric cells facilitate the identification of peaks in the DRT profiles from the full cell. Importantly, the DRT profiles indicate a correlation between the evolution of charge transfer resistance and the chemical degradation of DHPS. The methodologies and results outlined in this study offer significant insights for developing diagnostic tools applicable to other types of redox flow batteries.

Distribution of relaxation time↗
DOE OSTI2025

Strategies for Superconducting Transmon Qubits with Millisecond T$_1$ Relaxation Time

Significant strides have been made in extending qubit lifetimes by mitigating lossy materials at various surfaces and interfaces of superconducting transmon qubits. We have recently demonstrated a five-fold improvement of T$_1$ energy relaxation time by encapsulating the Nb surface to prevent native oxide formation. To further extend qubit coherence to millisecond timescales and beyond, we are actively exploring novel strategies. Such strategies include substrate preparation, alternative materials as low loss platforms, novel non-oxide forming low loss capping layers, optimized qubit designs & qubit packaging, and optimized Josephson junction materials, processing, and design. Qubit relaxation time T$_1$ measurements will be reported with best T$_1$’s in excess of a millisecond. This material is based upon work supported by the U.S. Department of Energy, Office of Science, National Quantum Information Science Research Centers, Superconducting Quantum Materials and Systems Center (SQMS) under contract number DE-AC02-07CH11359.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Strategies for Superconducting Transmon Qubits with Millisecond T1 Relaxation Time

Enhancing coherence in superconducting transmon qubits requires suppressing dielectric loss and quasiparticle-mediated dissipation at metal–substrate, metal–vacuum, and substrate–vacuum interfaces. We recently demonstrated a five-fold enhancement of the energy relaxation time (T₁) by encapsulating Nb thin films with a low-loss passivation layer that inhibits NbOₓ formation, thereby reducing two-level system (TLS) participation at the metal surface. To extend T₁ into the millisecond regime, we are implementing a comprehensive materials- and process-level optimization strategy. This includes engineered substrate surface treatments, evaluation of alternative low-loss superconducting and dielectric material stacks, development of ultra-low-loss capping layers, and redesigns of transmon geometries to suppress electric-field participation ratio in lossy regions. Additionally, we are pioneering novel etching processes to further lower surface participation ratios. We are also exploring novel Josephson-junction materials and device layouts to enhance coherence further. We report T₁ measurements from these efforts, with the leading devices achieving relaxation times>1 ms.

Crisa, Francesco↗
DOE OSTI2026

Strategies for Superconducting Transmon Qubits with Millisecond T1 Relaxation Time

Enhancing coherence in superconducting transmon qubits requires suppressing dielectric loss and quasiparticle-mediated dissipation at metal–substrate, metal–vacuum, and substrate–vacuum interfaces. We recently demonstrated a five-fold enhancement of the energy relaxation time (T₁) by encapsulating Nb thin films with a low-loss passivation layer that inhibits NbOₓ formation, thereby reducing two-level system (TLS) participation at the metal surface. To extend T₁ into the millisecond regime, we are implementing a comprehensive materials- and process-level optimization strategy. This includes engineered substrate surface treatments, evaluation of alternative low-loss superconducting and dielectric material stacks, development of ultra-low-loss capping layers, and redesigns of transmon geometries to suppress electric-field participation ratio in lossy regions. Additionally, we are pioneering novel etching processes to further lower surface participation ratios. We are also exploring novel Josephson-junction materials and device layouts to enhance coherence further. We report T₁ measurements from these efforts, with the leading devices achieving relaxation times>1 ms.

Crisa, Francesco↗
DOE OSTI2023

How reliable is distribution of relaxation times (DRT) analysis? A dual regression-classification perspective on DRT estimation, interpretation, and accuracy

The distribution of relaxation times (DRT) has gained increasing attention and adoption in recent years as a versatile method for analyzing electrochemical impedance spectroscopy (EIS) data obtained from complex devices like fuel cells, electrolyzers, and batteries. The DRT deconvolutes the impedance without a priori specification of a generative model, which is especially useful for interpretation and model selection when the governing principles of the system under study are not fully understood. However, DRT estimation is an ill-posed inversion problem that must be addressed with a subjective choice of regularization and tuning, which leaves substantial risk of misleading interpretations of EIS data. In this work, we suggest a new classification view of the DRT inversion to clarify DRT estimation and interpretation. We introduce a dual regression-classification framework that unifies the classification and regression views of the DRT inversion with wide-reaching implications for DRT analysis. The dual framework is employed to demonstrate a new kind of DRT inversion algorithm and develop novel evaluation metrics that capture previously ignored aspects of DRT accuracy. These approaches are applied to both synthetic data and experimental spectra collected from a protonic ceramic fuel cell and a lithium-ion battery to illustrate their broad utility. The dual inversion algorithm shows promising performance for accurate DRT estimation and autonomous model identification, while the dual evaluation approach produces metrics that meaningfully assess the strengths and risks of DRT algorithms. Here this work provides valuable insight for both practical application of the DRT to experimental data and further development of EIS analysis methods.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Advancing electrochemical impedance analysis through innovations in the distribution of relaxation times method

Electrochemical impedance spectroscopy (EIS) is a key tool across various scientific disciplines, including energy sciences, chemistry, and biology, enabling the analysis of electrochemical systems. However, conventional methods for interpreting EIS data are often complex and model dependent. The distribution of relaxation times (DRT) offers a non-parametric approach that simplifies the interpretation process by providing a timescale interpretation of EIS data. This article provides a comprehensive review of current methods for DRT inversion. Additionally, a survey of practitioners highlights key challenges in the field. Here, the findings underscore the need for standardized DRT analysis and benchmarks, as well as the development of automated analysis tools. These advancements would improve the usability and interpretability of EIS data. Ultimately, implementing these improvements could not only propel the field forward but also expand the application of DRT in scientific research by making it accessible to a broader range of researchers, including those without specialized expertise in programming or statistics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Stochastic fluctuations and the relaxation time in transient relativistic fluids

We argue that the ratio between the shear viscosity and the shear relaxation time, η/τ π , should be defined as a thermodynamic quantity obtained from the equal-time symmetric correlator of the shear-stress tensor. In kinetic theory, we show that this ratio does not depend on the type of interaction. Similarly, an exact expression for this ratio is obtained for holographic gauge theories. We also determine how stochastic fluctuations change η/τ π in transient relativistic hydrodynamics and show that thermal fluctuations do not spoil causality and stability.

Denicol, Gabriel S. [Universidade Federal Fluminen↗