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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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At least 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Measurement of inclusive charged-particle b-jet production in pp and p-Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV

A measurement of the inclusive b-jet production cross section is presented in pp and p-Pb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV, using data collected with the ALICE detector at the LHC. The jets were reconstructed in the central rapidity region |η| < 0.5 from charged particles using the anti-k T algorithm with resolution parameter R = 0.4. Identification of b jets exploits the long lifetime of b hadrons, using the properties of secondary vertices and impact parameter distributions. The p T -differential inclusive production cross section of b jets, as well as the corresponding inclusive b-jet fraction, are reported for pp and p-Pb collisions in the jet transverse momentum range 10 ≤ p T,ch jet ≤ 100 GeV/c, together with the nuclear modification factor, $R^{b-jet}_{pPb}$. The analysis thus extends the lower p T limit of b-jet measurements at the LHC. The nuclear modification factor is found to be consistent with unity, indicating that the production of b jets in p-Pb at $\sqrt{s_{NN}}$ = 5.02 TeV is not affected by cold nuclear matter effects within the current precision. The measurements are well reproduced by POWHEG NLO pQCD calculations with PYTHIA fragmentation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Equipment List Comparing Balance of Plant Containing a Heat Pump against a Reference Electricity Generating Plant

Approximately two-thirds of U.S. energy consumption in the industrial and transportation sectors relies on fossil fuels. These sectors require high-quality heat, i.e., thermal energy at very high temperatures, for molecular transformation processes. The Integrated Energy Systems (IES) program aims to assess the economic potential of utilizing nuclear-grade heat from Advanced Reactors (ARs) to meet the high-quality heat demands. By having industrial processes (IPs) supplied with nuclear-generated heat, manufacturers could benefit from more stable and potentially lower energy costs, reducing reliance on volatile fossil fuel markets. The main outcome of the FY24 research was the thermodynamic assessment and gap analysis of steam generation for IP applications. The study completed in June 2024 demonstrated that the required steam temperatures could be achieved by integrating a heat pump into an AR power plant. After identifying the thermal demands of target IPs, multiple balance of plant configurations for the Xe-100 reactor by X-energy, incorporating a heat pump, were analyzed. Their technical feasibilities were assessed, including the design of suitable axial compressors for these applications. Comparative performance analysis showed that thermal efficiency alone is insufficient to evaluate system suitability. To address this, a new indicator (heat factor) was introduced in the report released in September 2024 to quantify the low-quality thermal power needed to produce one unit of high-quality heat for the IP. Results showed that integrating heat pumps into Rankine cycles enables higher steam temperatures, though at the expense of increased thermal energy input. This report builds upon and completes the foundational work previously undertaken. It focuses on the design of two Balance of Plant (BOP) configurations, both based on Rankine energy conversion cycles: “Case 1”, which involves electricity generation only, and “Case 2”, which combines electricity and high-temperature heat generation for industrial use. For each configuration, a comprehensive equipment list was developed, detailing all major components such as turbines, compressors, heat exchangers, pumps, and control systems. These lists will serve as the basis for future comparative cost analyses, with the goal of assessing the number and type of components required to integrate a heat pump into the Rankine cycle and to establish a heat transport system capable of delivering thermal energy from the nuclear plant to an industrial facility. Using the constitutive equations presented in the June 2024 milestone, the operating conditions of all BOP components for both “Case 1” and “Case 2” were evaluated. These parameters—such as temperature, pressure, mass flow rate, and steam quality—served as the basis for calculating the associated thermal and mechanical power flows. The net power required from the heat pump to raise the steam temperature to the target level was also determined. The thermodynamic performance of the configuration was then assessed using the heat factor metric. The key outcome of this analysis is a comparative table that presents the equipment that was used in the “Case 1” and “Case 2” configurations. This study offers a preliminary comparison of the two designs, providing insight into the impact of integrating a heat pump in terms of component requirements and thermal efficiency. This equipment list, together with the evaluated operating conditions, also serves as a foundation for the economic analyses scheduled for the current fiscal year.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

Charge radii of the nucleon from its flavor dependent Dirac form factors

In this report we have determined the proton and the neutron charge radii from a global analysis of the proton and the neutron elastic form factors, after first performing a flavor decomposition of these form factors under charge symmetry in the light cone frame formulation. We then extracted the transverse mean-square radii of the flavor dependent quark distributions. In turn, these are related in a model-independent way to the proton and neutron charge radii but allow us to take into account motion effects of the recoiling nucleon for data at finite but high momentum transfer. In the proton case we find $\langle r_p \rangle$ = 0.852±0.002 (stat.) ± 0.009 (syst.) (fm), consistent with the proton charge radius obtained from muonic hydrogen spectroscopy. The current method improves on the precision of the $\langle r_p \rangle$; extraction based on the form factor measurements. Furthermore, we find no discrepancy in the $\langle r_p \rangle$ determination among the different electron scattering measurements, all of which, utilizing the current method of extraction, result in a value that is consistent with the smallest $\langle r_p \rangle$ extraction from the electron scattering measurements. Concerning the neutron case, past results relied solely on the neutron-electron scattering length measurements, which suffer from an underestimation of underlying systematic uncertainties inherent to the extraction technique. Utilizing the present method we have performed the first extraction of the neutron charge radius based on nucleon form factor data, and we find $\langle r^2_n \rangle$ = -0.122±0.004 (stat.) ± 0.010 (syst.) (fm 2 ).

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Attribution of the Australian bushfire risk to anthropogenic climate change

Abstract. Disastrous bushfires during the last months of 2019 and January 2020 affected Australia, raising the question to what extent the risk of these fires was exacerbated by anthropogenic climate change. To answer the question for southeastern Australia, where fires were particularly severe, affecting people and ecosystems, we use a physically based index of fire weather, the Fire Weather Index; long-term observations of heat and drought; and 11 large ensembles of state-of-the-art climate models. We find large trends in the Fire Weather Index in the fifth-generation European Centre for Medium-Range Weather Forecasts (ECMWF) Atmospheric Reanalysis (ERA5) since 1979 and a smaller but significant increase by at least 30 % in the models. Therefore, we find that climate change has induced a higher weather-induced risk of such an extreme fire season. This trend is mainly driven by the increase of temperature extremes. In agreement with previous analyses we find that heat extremes have become more likely by at least a factor of 2 due to the long-term warming trend. However, current climate models overestimate variability and tend to underestimate the long-term trend in these extremes, so the true change in the likelihood of extreme heat could be larger, suggesting that the attribution of the increased fire weather risk is a conservative estimate. We do not find an attributable trend in either extreme annual drought or the driest month of the fire season, September–February. The observations, however, show a weak drying trend in the annual mean. For the 2019/20 season more than half of the July–December drought was driven by record excursions of the Indian Ocean Dipole and Southern Annular Mode, factors which are included in the analysis here. The study reveals the complexity of the 2019/20 bushfire event, with some but not all drivers showing an imprint of anthropogenic climate change. Finally, the study concludes with a qualitative review of various vulnerability and exposure factors that each play a role, along with the hazard in increasing or decreasing the overall impact of the bushfires.

van Oldenborgh, Geert Jan (ORCID:0000000268989535)↗
DOE OSTI2024

Renormalization group improved photon impact factors and the high energy virtual photon scattering

We perform the renormalization group improved collinear resummation of the photon-gluon impact factors. We construct the resummed cross section for virtual photon-photon (γ ∗ γ ∗ ) scattering which incorporates the impact factors and BFKL gluon Green’s function up to the next-to-leading logarithmic accuracy in energy. The impact factors include important kinematical effects which are responsible for the most singular poles in Mellin space at next-to-leading order. Further conditions on the resummed cross section are obtained by requiring the consistency with the collinear limits. Our analysis is consistent with previous impact factor calculations at NLO, apart from a new term proportional to C F that we find for the longitudinal polarization. Finally, we use the resummed cross section to compare with the LEP data on the γ ∗ γ ∗ cross section and with previous calculations. The resummed result is lower than the leading logarithmic approximation but higher than the pure next-to-leading one, and is consistent with the experimental data.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Data-Driven Insights into the Structural Essence of Plasticity in High-Entropy Alloys

The heterogeneous mechanical response of a crystalline alloy with multiple principal elements was investigated using molecular dynamics simulations. The local configuration of the alloy in its quiescent state was characterized by the variables derived from the gyration tensor and the atomic electronegativity. A multivariate analysis identified the geometric and chemical factors that influenced the atomic packing variations. Further, upon straining, the non-affine displacement exhibited spatial heterogeneity. A statistical correlation was established between the local yield events and the specific features of the local configuration. Our findings, validated by the performance metrics analysis, provided a structural criterion for the instability mechanisms in high-entropy alloys (HEAs) and enhanced the understanding of their plasticity.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Statistical Significance Testing for Mixed Priors: A Combined Bayesian and Frequentist Analysis

In many hypothesis testing applications, we have mixed priors, with well-motivated informative priors for some parameters but not for others. The Bayesian methodology uses the Bayes factor and is helpful for the informative priors, as it incorporates Occam’s razor via the multiplicity or trials factor in the look-elsewhere effect. However, if the prior is not known completely, the frequentist hypothesis test via the false-positive rate is a better approach, as it is less sensitive to the prior choice. We argue that when only partial prior information is available, it is best to combine the two methodologies by using the Bayes factor as a test statistic in the frequentist analysis. We show that the standard frequentist maximum likelihood-ratio test statistic corresponds to the Bayes factor with a non-informative Jeffrey’s prior. We also show that mixed priors increase the statistical power in frequentist analyses over the maximum likelihood test statistic. We develop an analytic formalism that does not require expensive simulations and generalize Wilks’ theorem beyond its usual regime of validity. In specific limits, the formalism reproduces existing expressions, such as the p-value of linear models and periodograms. We apply the formalism to an example of exoplanet transits, where multiplicity can be more than 10 7 . We show that our analytic expressions reproduce the $p$-values derived from numerical simulations. We offer an interpretation of our formalism based on the statistical mechanics. We introduce the counting of states in a continuous parameter space using the uncertainty volume as the quantum of the state. We show that both the $p$-value and Bayes factor can be expressed as an energy versus entropy competition.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Electrokinetic Analysis of Poorly Conductive Electrocatalytic Materials

While many factors can influence the activity of the electrochemical interface at atomic and molecular levels, the electron and ion transport have a big impact on the overall electrochemical performance. Here, we investigate how electrical resistance (conductivity) of the electrode affects the measured electrocatalytic activity using the hydrogen evolution reaction as a model reaction. We clearly demonstrate the effect of the poor electronic conductivity of MoS 2 on the electrochemical performance, as both values of the exchange current density as well as the Tafel slope depend on the level of utilization of the active material and the ohmic losses. A quantitative analysis using the composite electrode model is provided, showing the importance of the experimental conditions and good control of electrode/electrolyte system for the proper evaluation and comparison of electrocatalysts’ kinetic parameters.

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

Machine learning inversion from small-angle scattering for charged polymers

We develop Monte Carlo simulations for uniformly charged polymers and a machine learning algorithm to interpret the intra-polymer structure factor of the charged polymer system, which can be obtained from small-angle scattering experiments. The polymer is modeled as a chain of fixed-length bonds, where the connected bonds are subject to bending energy, and there is also a screened Coulomb potential for charge interaction between all joints. The bending energy is determined by the intrinsic bending stiffness, and the charge interaction depends on the interaction strength and screening length. All three contribute to the stiffness of the polymer chain and lead to longer and larger polymer conformations. The screening length also introduces a second length scale for the polymer besides the bending persistence length. To obtain the inverse mapping from the structure factor to these polymer conformation and energy-related parameters, we generate a large data set of structure factors by running simulations for a wide range of polymer energy parameters. We use principal component analysis to investigate the intra-polymer structure factors and determine the feasibility of the inversion using the nearest neighbor distance. We employ Gaussian process regression to achieve the inverse mapping and extract the characteristic parameters of polymers from the structure factor with low relative error.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Galaxy mergers in eagle do not induce a significant amount of black hole growth yet do increase the rate of luminous AGN

ABSTRACT We investigate the connection between galaxy–galaxy mergers and enhanced black hole (BH) growth using the cosmological hydrodynamical eagle simulation. We do this via three methods of analysis, investigating: the merger fraction of AGN, the AGN fraction of merging systems, and the AGN fraction of galaxies with close companions. In each case, we find an increased abundance of AGN within merging systems relative to control samples of inactive or isolated galaxies (by up to a factor of ≈3 depending on the analysis method used), confirming that mergers are enhancing BH accretion rates for at least a subset of the galaxy population. The greatest excess of AGN triggered via a merger are found in lower mass (M* ∼ 1010 M⊙) gas rich (fgas > 0.2) central galaxies with lower mass BHs (MBH ∼ 107 M⊙) at lower redshifts (z < 1). We find no enhancement of AGN triggered via mergers in more massive galaxies (M* ≳ 1011 M⊙). The enhancement of AGN is not uniform throughout the phases of a merger, and instead peaks within the early remnants of merging systems (typically lagging ≈300 Myr post-coalescence of the two galaxies at z = 0.5). We argue that neither major ($M_{\mathrm{*,1}} / M_{\mathrm{*,2}} \ge \frac{1}{4}$) nor minor mergers ($\frac{1}{10} \lt M_{\mathrm{*,1}} / M_{\mathrm{*,2}} \lt \frac{1}{4}$) are statistically relevant for enhancing BH masses globally. Whilst at all redshifts the galaxies experiencing a merger have accretion rates that are on average 2–3 times that of isolated galaxies, the majority of mass that is accreted on to BHs occurs outside the periods of a merger. We compute that on average no more than 15 per cent of a BHs final day mass comes from the enhanced accretion rates triggered via a merger.

McAlpine, Stuart↗
DOE OSTI2023

Combining Sparse Approximate Factorizations with Mixed-precision Iterative Refinement

The standard LU factorization-based solution process for linear systems can be enhanced in speed or accuracy by employing mixed-precision iterative refinement. Most recent work has focused on dense systems. We investigate the potential of mixed-precision iterative refinement to enhance methods for sparse systems based on approximate sparse factorizations. In doing so, we first develop a new error analysis for LU- and GMRES-based iterative refinement under a general model of LU factorization that accounts for the approximation methods typically used by modern sparse solvers, such as low-rank approximations or relaxed pivoting strategies. We then provide a detailed performance analysis of both the execution time and memory consumption of different algorithms, based on a selected set of iterative refinement variants and approximate sparse factorizations. Our performance study uses the multifrontal solver MUMPS, which can exploit block low-rank factorization and static pivoting. We evaluate the performance of the algorithms on large, sparse problems coming from a variety of real-life and industrial applications showing that mixed-precision iterative refinement combined with approximate sparse factorization can lead to considerable reductions of both the time and memory consumption.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Exploiting non-linear scales in galaxy–galaxy lensing and galaxy clustering: A forecast for the dark energy survey

ABSTRACT The combination of galaxy–galaxy lensing (GGL) and galaxy clustering is a powerful probe of low-redshift matter clustering, especially if it is extended to the non-linear regime. To this end, we use an N-body and halo occupation distribution (HOD) emulator method to model the redMaGiC sample of colour-selected passive galaxies in the Dark Energy Survey (DES), adding parameters that describe central galaxy incompleteness, galaxy assembly bias, and a scale-independent multiplicative lensing bias Alens. We use this emulator to forecast cosmological constraints attainable from the GGL surface density profile ΔΣ(rp) and the projected galaxy correlation function wp, gg(rp) in the final (Year 6) DES data set over scales $r_p=0.3\!-\!30.0\, h^{-1} \, \mathrm{Mpc}$. For a $3{{\ \rm per\ cent}}$ prior on Alens we forecast precisions of $1.9{{\ \rm per\ cent}}$, $2.0{{\ \rm per\ cent}}$, and $1.9{{\ \rm per\ cent}}$ on Ωm, σ8, and $S_8 \equiv \sigma _8\Omega _m^{0.5}$, marginalized over all halo occupation distribution (HOD) parameters as well as Alens. Adding scales $r_p=0.3\!-\!3.0\, h^{-1} \, \mathrm{Mpc}$ improves the S8 precision by a factor of ∼1.6 relative to a large scale ($3.0\!-\!30.0\, h^{-1} \, \mathrm{Mpc}$) analysis, equivalent to increasing the survey area by a factor of ∼2.6. Sharpening the Alens prior to $1{{\ \rm per\ cent}}$ further improves the S8 precision to $1.1{{\ \rm per\ cent}}$, and it amplifies the gain from including non-linear scales. Our emulator achieves per cent-level accuracy similar to the projected DES statistical uncertainties, demonstrating the feasibility of a fully non-linear analysis. Obtaining precise parameter constraints from multiple galaxy types and from measurements that span linear and non-linear clustering offers many opportunities for internal cross-checks, which can diagnose systematics and demonstrate the robustness of cosmological results.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Analyzing Prospects for Quantum Advantage in Topological Data Analysis

Lloyd [Nat. Commun. , 10138 (2016)] were first to demonstrate the promise of quantum algorithms for computing Betti numbers, a way to characterize topological features of data sets. Here, we propose, analyze, and optimize an improved quantum algorithm for topological data analysis (TDA) with reduced scaling, including a method for preparing Dicke states based on inequality testing, a more efficient amplitude estimation algorithm using Kaiser windows, and an optimal implementation of eigenvalue projectors based on Chebyshev polynomials. We compile our approach to a fault-tolerant gate set and estimate constant factors in the Toffoli complexity. Our analysis reveals that superquadratic quantum speedups are only possible for this problem when targeting a multiplicative error approximation and the Betti number grows asymptotically. Further, we propose a dequantization of the quantum TDA algorithm that shows that having exponentially large dimension and Betti number are necessary, but insufficient conditions, for superpolynomial advantage. We then introduce and analyze specific problem examples which have parameters in the regime where superpolynomial advantages may be achieved, and argue that quantum circuits with tens of billions of Toffoli gates can solve seemingly classically intractable instances. Published by the American Physical Society 2024

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Spectroscopy of 13 Be through isobaric analog states in 13 B

Spectroscopy of the exotic, neutron-unbound beryllium isotope, 13 Be, is still a puzzle despite significant experimental efforts. To observe T = 5/2 states in 13 B, establish spin parities and spectroscopic factors, and use isospin symmetry to inform spectroscopy of 13 Be, excitation functions for resonance elastic scattering of 12 Be on protons were measured in the c.m. energy range from 1 MeV to 5 MeV. Two T = 5/2 states in 13 B at excitation energies 18.25 MeV and 19.95 MeV were observed. Unambiguous 1/2 + and 5/2 + spin-parity assignments were made, and spectroscopic factors were established using R-matrix analysis of the measured 12 Be + p excitation functions. Here, we provide the first direct and unambiguous spin-parity assignments and spectroscopic factor measurements for the resonances in the A = 13, T = 5/2 isobaric multiplet. This puts us on a solid footing to identify the 2.3 MeV state in 13 Be as 5/2 + and infer the existence of an s-wave (1/2 + ) resonance at around 0.6 MeV with a relatively small spectroscopic factor.

6 ≤ A ≤ 19↗
DOE OSTI2026

Optimizing bioenergy biofuel harvest: a comparative analysis of stepwise and integrated methods for economic and environmental sustainability

Switchgrass is a promising bioenergy feedstock due to its high biomass yield potential, adaptability to marginal lands, and low carbon intensity for feedstock production. However, accurate cost estimation and assessment of greenhouse gas (GHG) emissions for the energy-intensive harvesting process are essential for evaluating the sustainability of bioenergy. This study provides a comparative analysis of two harvesting methods: the Stepwise Method, which separates operations into multiple stages, and the Integrated Method, which combines mowing and raking into a single pass. The analysis was conducted under four scenarios based on field sizes and biomass yields. Using three years of field-scale switchgrass harvest data from 125 sites, GHG emissions, energy consumption, and harvesting costs were quantified using the GREET model and techno-economic analysis. Additionally, regression analysis identified key climate and operational factors affecting fuel consumption. The Stepwise method was the most cost-effective for large fields with high biomass yield, achieving the lowest harvesting costs ($37.70 per ton). In contrast, the Integrated Method performed better in small fields and low-yield conditions, reducing GHG emissions by 9 % and energy use by 5 %. Regression analysis confirmed that a larger field size reduced fuel consumption, while higher biomass yield and longer operational time increased fuel use. Maximum temperature also contributed to a slight increase in fuel consumption. Furthermore, these results provide actionable insights for optimizing harvesting strategies based on field-specific conditions and operational goals, contributing to the economic and environmental sustainability of bioenergy production.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2026

Extracting $B_s\to D_s^*\ellν_\ell$ form factors

Semileptonic $B_{(s)}$ decays are of great phenomenological interest because they allow to determine e.g. CKM matrix elements or test lepton flavor universality. Taking advantage of already existing lattice data, we demonstrate the analysis steps to extract the four form factors describing exclusive semileptonic $B_s\to D_s^*\ellν_\ell$ decays using the narrow width approximation. Our data are based on RBC/UKQCD's set of 2+1 flavor gauge field ensembles with Shamir domain-wall fermion and Iwasaki gauge field action featuring inverse lattice spacings of $a^{-1}=$1.785, 2.383, and 2.785 GeV as well as pion masses between 268 and 433 MeV. Light, strange and charm quarks are simulated using domain-wall fermions, whereas bottom quarks are generated with the relativistic heavy quark (RHQ) action.

Boushmelev, Anastasia [Siegen U.] (ORCID:000000033↗
DOE OSTI2024

Seroprevalence and risk factors for brucellosis amongst livestock and humans in a multi-herd ranch system in Kagera, Tanzania

Background Brucellosis remains a significant health and economic challenge for livestock and humans globally. Despite its public health implications, the factors driving the endemic persistence ofBrucellaat the human-livestock interface in Tanzania remain poorly elucidated. This study aimed to identify the seroprevalence ofBrucellainfection in livestock and humans within a ranching system and determine associated risk factors for disease endemicity. Methods A cross-sectional sero-epidemiological study was conducted in 2023 in Tanzania’s Karagwe District, involving 725 livestock (cattle, goats, sheep) from 10 herds and 112 humans from associated camps. Seroprevalence was assessed using competitive ELISA while epidemiological data were collected via questionnaires. Generalized Linear Models and Contrast Analysis were used to identify risk factors for infection. Results Overall seroprevalence was 34% in livestock and 41% in humans. Goats exhibited the highest prevalence (69.2%), while cattle had the lowest (22.6%). Mixed-species herds (Odds Ratio, OR = 2.96, CI [1.90–4.60]) and small ruminants-only herds (OR = 6.54, CI [3.65–11.72]) showed a significantly higher risk of seropositivity compared to cattle-only herds. Older cattle (OR = 5.23, CI [2.70–10.10]) and lactating females (OR = 2.87, CI [1.78–4.63]) represented significant risks for brucellosis in livestock. In humans, close contact with animals (OR = 7.20, CI [1.97–36.31]) and handling animals during parturition or aborted fetuses (OR = 2.37, CI [1.01–5.58]) were significant risk factors. Notably, no spatial association was found in seroprevalence between herds and nearby human communities. Conclusion The lack of spatial correlation between livestock and human seroprevalence suggests complex transmission dynamics, potentially involving endemic circulation in livestock and human infections from multiple sources of exposure to livestock. This study highlights the need for comprehensive zoonotic risk education and targeted intervention strategies. Further research is crucial to elucidate transmission pathways and improveBrucellainfection control. This includes developing robust methods for identifying infective species and implementing effective strategies to mitigateBrucellainfection in endemic regions.

Public, Environmental & Occupational Health↗
DOE OSTI2025

Extending the capillary wave model to include the effect of bending rigidity: X-ray reflectivity and diffuse scattering

The surface roughness of a thin film at a liquid interface exhibits contributions of thermally excited fluctuations. This thermal roughness depends on temperature (𝑇), surface tension (𝛾), and elastic material properties, specifically the bending modulus (𝜅) of the film. A nonzero 𝜅 suppresses the thermal roughness at small length scales compared to an interface with zero 𝜅, as expressed by the power spectral density of the thermal roughness. The description of the x-ray scattering of the standard capillary wave model (CWM), which is valid for zero 𝜅, is extended to include the effect of 𝜅. The extended CWM (eCWM) provides a single analytical form for both the specular x-ray reflectivity (XRR) and the diffuse scattering around the specular reflection, and recovers the expression of the CWM at its zero 𝜅 limit. This theoretical approach enables the use of single-shot grazing incidence x-ray off-specular scattering (GIXOS) measurements for characterizing the structure of thin films on a liquid surface. The eCWM analysis approach decouples the thermal roughness factor from the surface scattering signal, providing direct access to the intrinsic surface-normal structure of the film and its bending modulus. Moreover, the eCWM facilitates the calculation of reflectivity at any desired resolution (pseudo-XRR approach). The transformation into pseudo-XRR provides the benefit of using widely available XRR software to perform GIXOS analysis. The extended range of the vertical scattering vector (𝑄 𝑧 ) available with the GIXOS pseudo-XRR approach allows for a higher spatial resolution than with conventional XRR. Experimental results are presented for various lipid systems, showing strong agreement between conventional specular XRR and pseudo-XRR methods. This agreement validates the proposed approach and highlights its utility for analyzing soft, thin films.

36 MATERIALS SCIENCE↗