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Results for “equilibrium potential”

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 361 records · Page 20
All sourcesNASA NTRSDOE OSTI
NASA NTRS1981

On the equilibrium distribution of the elements in the gas in the Coma cluster

The equilibrium distribution of the elements for the case of an isothermal plasma in a gravitational potential well is given governing equations and a rapidly converging iterative procedure for their solution. Results are applied to the intracluster gas in clusters of galaxies, and implications are identified for the controversy as to whether iron nuclei settle out in the cluster core, and with respect to the interpretation of distribution size and shape for continuum X-ray emission from clusters. A model for the Coma cluster is considered in which the intracluster gas is in equilibrium and partially processed. It is found that this model can account for the angular dependence of the continuum X-ray emission from Coma, as determined by Einstein Observatory observations, at least as well as the uniform composition model.

Abramopoulos, F.↗
DOE OSTI2020

Far-from-equilibrium search for the QCD critical point

Initial conditions for relativistic heavy-ion collisions may be far from equilibrium (i.e., there are large initial contributions from the shear stress tensor and bulk pressure) but it is expected that on very short time scales the dynamics converge to a universal attractor that defines hydrodynamic behavior. Thus far, studies of this nature have only considered an idealized situation at LHC energies (high temperatures T and vanishing baryon chemical potential µ B = 0) but, in this work, we investigate for the first time how far-from-equilibrium effects may influence experimentally driven searches for the Quantum Chromodynamic critical point at RHIC. We find that the path to the critical point is heavily influenced by far from equilibrium initial conditions where viscous effects lead to dramatically different {T, µ B } trajectories through the QCD phase diagram. We compare hydrodynamic equations of motion with shear and bulk coupled together at finite µB for both DNMR and phenomenological Israel-Stewart equations of motion and discuss their influence on potential attractors at finite µ B and their corresponding {T, µ B } trajectories.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS2013

Global and Regional Temperature-change Potentials for Near-term Climate Forcers

We examine the climate effects of the emissions of near-term climate forcers (NTCFs) from 4 continental regions (East Asia, Europe, North America and South Asia) using results from the Task Force on Hemispheric Transport of Air Pollution Source-Receptor global chemical transport model simulations. We address 3 aerosol species (sulphate, particulate organic matter and black carbon) and 4 ozone precursors (methane, reactive nitrogen oxides (NOx), volatile organic compounds and carbon monoxide). We calculate the global climate metrics: global warming potentials (GWPs) and global temperature change potentials (GTPs). For the aerosols these metrics are simply time-dependent scalings of the equilibrium radiative forcings. The GTPs decrease more rapidly with time than the GWPs. The aerosol forcings and hence climate metrics have only a modest dependence on emission region. The metrics for ozone precursors include the effects on the methane lifetime. The impacts via methane are particularly important for the 20 yr GTPs. Emissions of NOx and VOCs from South Asia have GWPs and GTPs of higher magnitude than from the other Northern Hemisphere regions. The analysis is further extended by examining the temperature-change impacts in 4 latitude bands, and calculating absolute regional temperature-change potentials (ARTPs). The latitudinal pattern of the temperature response does not directly follow the pattern of the diagnosed radiative forcing. We find that temperatures in the Arctic latitudes appear to be particularly sensitive to BC emissions from South Asia. The northern mid-latitude temperature response to northern mid-latitude emissions is approximately twice as large as the global average response for aerosol emission, and about 20-30% larger than the global average for methane, VOC and CO emissions.

North America↗
DOE OSTI2022

Ab initio approaches to high-entropy alloys: a comparison of CPA, SQS, and supercell methods

In this work, we present a comparative study of different modeling approaches to the electronic properties of the Hf 0.05 Nb 0.05 Ta 0.8 Ti 0.05 Zr 0.05 high-entropy alloy. Common to our modeling is the methodology to compute the one-particle Green’s function in the framework of density functional theory. We demonstrate that the special quasi-random structures modeling and the supercell, i.e., the locally self-consistent multiple-scattering methods, provide very similar results for the ground state properties such as the spectral function (density of states) and the equilibrium lattice parameter. To reconcile the multiple-scattering single-site coherent potential approximation with the real space supercell methods, we included the effect of screening of the net charges of the alloy components. Based on the analysis of the total energy and spectral functions computed within the density functional theory, we found no signature for the long-range or local magnetic moments formation in the Hf 0.05 Nb 0.05 Ta 0.8 Ti 0.05 Zr 0.05 high-entropy alloy; instead, we find possible superconductivity below ~9K.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Equilibrium Fe isotope fractionation between olivine, pyroxene, spinel and MORB glass: Implications for mantle partial melting to generate MORBs

Primitive mid-ocean ridge basalts (MORBs) exhibit Fe isotopic compositions heavier than the upper mantle by +0.074 ± 0.028 ‰ for δ 56 Fe. The processes responsible for this isotopic difference remain unclear. Modeling of Fe isotope fractionation during mantle partial melting requires reliable equilibrium Fe isotope fractionation factors between minerals and melts, for which consistent data are still lacking. Here, in this study, we used Nuclear Resonant Inelastic X-ray Scattering (NRIXS) technique to measure Fe force constants for a MORB glass (ALV 519-4-1) and natural mantle minerals (olivine, orthopyroxene, clinopyroxene, and spinel) to determine the equilibrium Fe isotope fractionation factors between them. The force constants determined in this study, in increasing order, are 167 ± 26 N/m for spinel, 175 ± 17 N/m for olivine, 176 ± 20 N/m for MORB glass, 205 ± 26 N/m for clinopyroxene, and 219 ± 36 N/m for orthopyroxene. We evaluated the previously proposed mechanisms for the heavy Fe isotopic composition of MORBs, including (i) mantle partial melting, (ii) mantle lithological heterogeneity, with pyroxenite in the source, (iii) mantle metasomatism by low-degree melts, and (iv) fractional crystallization of olivine from melts. For (i), we used the pMELTS program to simulate adiabatic decompression melting of mantle peridotites, and calculated Fe isotope fractionation based on Fe 3+ –Fe 2+ equilibrium-controlled fractionation, where Fe 3+ forms stronger bonds and is more incompatible than Fe 2+ . At 10 wt% peridotite melting, corresponding to MORB generation, only +0.03 ‰ Fe isotope fractionation between the melt and the original bulk composition (Δ 56 Fe = δ 56 Fe melt - δ 56 Fe 0 ) was produced, insufficient to account for the observed MORB-upper mantle difference. For (ii), melting of pyroxenites yields smaller Fe isotope fractionation than melting of peridotites, making it unlikely the cause for the MORB-upper mantle isotopic difference. For (iii), both the Fe 3+ /ΣFe ratio and the δ 56 Fe of melts increase with the degree of partial melting, indicating that low-degree melts are not isotopically heavy enough to significantly alter the isotopic composition of lithospheric mantle through metasomatism. For (iv), equilibrium isotope fractionation between olivine and melt is near zero. These results suggest that equilibrium Fe isotope fractionation alone cannot explain the MORB isotopic signature, highlighting the potential role of kinetic isotope fractionation. Using a diffusion model, we calculated kinetic Fe and Mg isotope fractionations associated with (iv) olivine crystallization from a melt, and found that the predicted Fe and Mg isotope fractionations were inconsistent with observations in MORBs. Qualitatively, two processes could have induced kinetic Fe isotope fractionation during MORB generation: (a) Fe-Mg interdiffusion between melt and solid during melt migration and (b) reactive melt-rock interactions during melt focusing. However, a quantitative understanding of their role in modifying the melt isotopic composition remains limited and requires further investigation.

Fe isotopes↗
DOE OSTI2025

Investigation of residual stress distribution in wire-arc directed energy deposited refractory molybdenum alloy utilizing numerical thermo-mechanical analysis and neutron diffraction method

Directed energy deposition (DED), a metal additive manufacturing (AM) technique, offers higher deposition rates and energy efficiency, making it suitable for fabricating components from refractory molybdenum alloys, such as molybdenum-titanium-zirconium (TZM). However, large thermal gradients and non-equilibrium thermal cycles in DED could generate high residual stress in the component, potentially deteriorating quality and performance. Thus, this study aims to investigate residual stress generation and its distribution in wire-arc DED of TZM thin-wall, utilizing thermo-mechanical analysis and high-fidelity neutron diffraction (ND) method. Two interpass temperatures (50°C and 200°C) have been considered to investigate their impact on residual stress formation. During experiments, in-situ thermal data has been recorded using thermocouples, which have been utilized for calibrating the thermal model. Thermocouple data shows a good agreement with the simulation results, having a difference of less than 10 %. Post-deposition part deformation has been observed, which is measured using a coordinate measuring machine, showing maximum values of 0.93 mm and 0.78 mm for interpass temperatures of 50°C and 200°C, respectively. Numerical predictions of distortion deviated by less than 15% from the experimental results. ND measurement and simulation results indicate that residual stress magnitude and evolution vary across the TZM deposits, revealing microstructural anisotropy in both conditions. Notably, lower interpass temperatures resulted in higher residual stresses, confirmed by experimental and simulation data. Further, this study demonstrated that an integrated experimental and thermo-mechanical analysis can potentially reveal the temperature history, part deformation, and residual stress formation in wire-arc DED TZM alloy.

36 MATERIALS SCIENCE↗
DOE OSTI2022

How Cooperatively Folding Are Homopolymer Molecular Knots?

Detailed thermodynamic analysis of complex systems with multiple stable configurational states allows for insight into the cooperativity of each individual transition. In this work, we derive a heat capacity decomposition comprising contributions from each individual configurational state, which together sum to a baseline heat capacity, and contributions from each state-to-state transition. We apply this analysis framework to a series of replica exchange molecular dynamics simulations of linear and 1-1 coarse-grained homo-oligomer models, which fold into stable, configurationally well-defined molecular knots, in order to better understand the parameters leading to stable and cooperative folding of these knots. We find that a stiff harmonic backbone bending angle potential is key to achieving knots with specific 3D structures. Tuning the backbone equilibrium angle in small increments yields a variety of knot topologies. Populations of different knotted states as a function of temperature can also be manipulated by tuning the backbone torsion stiffness or by adding side-chain beads. We find that sharp total heat capacity peaks for the homo-oligomer knots are largely due to a coil-to-globule transition rather than a cooperative knotting step. Furthermore, in some cases, the cooperativity of globule-to-knot and coil-to-globule transitions is comparable, suggesting that highly cooperative folding to knotted structures can be achieved by refining the model parameters or adding sequence specificity.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Thermalization and criticality on an analogue–digital quantum simulator

Abstract Understanding how interacting particles approach thermal equilibrium is a major challenge of quantum simulators 1,2 . Unlocking the full potential of such systems towards this goal requires flexible initial state preparation, precise time evolution and extensive probes for final state characterization. Here we present a quantum simulator comprising 69 superconducting qubits that supports both universal quantum gates and high-fidelity analogue evolution, with performance beyond the reach of classical simulation in cross-entropy benchmarking experiments. This hybrid platform features more versatile measurement capabilities compared with analogue-only simulators, which we leverage here to reveal a coarsening-induced breakdown of Kibble–Zurek scaling predictions 3 in theXYmodel, as well as signatures of the classical Kosterlitz–Thouless phase transition 4 . Moreover, the digital gates enable precise energy control, allowing us to study the effects of the eigenstate thermalization hypothesis 5–7 in targeted parts of the eigenspectrum. We also demonstrate digital preparation of pairwise-entangled dimer states, and image the transport of energy and vorticity during subsequent thermalization in analogue evolution. These results establish the efficacy of superconducting analogue–digital quantum processors for preparing states across many-body spectra and unveiling their thermalization dynamics.

Science & Technology - Other Topics↗
DOE OSTI2020

Calculation of the detonation state of HN 3 with quantum accuracy

HN 3 is a unique liquid energetic material that exhibits ultrafast detonation chemistry and a transition to metallic states during detonation. We combine the Chebyshev interaction model for efficient simulation (ChIMES) many-body reactive force field and the extended-Lagrangian multiscale shock technique molecular dynamics method to calculate the detonation properties of HN 3 with the accuracy of Kohn–Sham density-functional theory. ChIMES is based on a Chebyshev polynomial expansion and can accurately reproduce density-functional theory molecular dynamics (DFT-MD) simulations for a wide range of unreactive and decomposition conditions of liquid HN 3 . We show that addition of random displacement configurations and the energies of gas-phase equilibrium products in the training set allows ChIMES to efficiently explore the complex potential energy surface. Schemes for selecting force field parameters and the inclusion of stress tensor and energy data in the training set are examined. Structural and dynamical properties and chemistry predictions for the resulting models are benchmarked against DFT-MD. We demonstrate that the inclusion of explicit four-body energy terms is necessary to capture the potential energy surface across a wide range of conditions. Our results generally retain the accuracy of DFT-MD while yielding a high degree of computational efficiency, allowing simulations to approach orders of magnitude larger time and spatial scales. The techniques and recipes for MD model creation we present allow for direct simulation of nanosecond shock compression experiments and calculation of the detonation properties of materials with the accuracy of Kohn–Sham density-functional theory.

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

Resolved rotation–vibration non-equilibrium with rotational VIPA-CARS

Simultaneous rotational and vibrational temperatures are measured in an N 2 plasma with rotational coherent anti-Stokes Raman scattering (CARS) resolved with a virtually imaged phased array (VIPA)-based spectrometer. A VIPA spectrally separates rotational transitions for each vibrational state, allowing vibrational populations to be directly measured. VIPA-CARS is shown to provide more accurate measurements of non-equilibrium temperatures than grating-resolved rotational CARS. The general characteristics, limitations, and potential uses of VIPA-CARS are discussed.

Steinmetz, S. A. (ORCID:0000000311014662)↗
DOE OSTI2020

Microstructure study of U–35 wt.% Zr alloy after quick annealing at 650 °C

Uranium-35wt.%zirconium (U-35wt.%Zr) alloy was annealed for 1 hour and 24 hours at 650 ºC and characterized to understand the early stage microstructure evolution. Dendritic microstructure with fine (~300 nm in length) α-U precipitates clustered between dendrite branches were observed in the 1-hour annealed sample. After 24-hour annealing 650 ºC, the α-U precipitates coarsened, and the dendritic microstructure disappeared due to microstructure homogenization. Furthermore, microchemical homogenization observed with Energy-Dispersive X-ray Spectroscopy analysis suggests that α-U precipitates are approaching thermodynamic equilibrium in the 24-hour annealed sample. The findings from this study have potential impacts on the manufacturing and computer modeling of metallic nuclear fuel.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
NASA NTRS1972

Analytic prediction of airplane equilibrium spin characteristics

The nonlinear equations of motion are solved algebraically for conditions for which an airplane is in an equilibrium spin. Constrained minimization techniques are employed in obtaining the solution. Linear characteristics of the airplane about the equilibrium points are also presented and their significance in identifying the stability characteristics of the equilibrium points is discussed. Computer time requirements are small making the method appear potentially applicable in airplane design. Results are obtained for several configurations and are compared with other analytic-numerical methods employed in spin prediction. Correlation with experimental results is discussed for one configuration for which a rather extensive data base was available. A need is indicated for higher Reynolds number data taken under conditions which more accurately simulate a spin.

Adams, W. M., Jr.↗
DOE OSTI2021

Plutonium Co-precipitation with Calcite

The mobility of plutonium (Pu) in the environment is affected by Pu–mineral interactions, such as adsorption–desorption and structural incorporation. Calcite (CaCO 3 ) is a common secondary phase in near surface environments and a major component of many rocks and soils and is expected to form as an alteration product of cement-based materials planned for use in geological repositories. The reactivity of the calcite surface and its ability to tolerate significant variations in its chemical composition through substitution of Ca for other cations make calcite a potentially important sink for environmental contaminants. Here, single crystals of calcite were synthesized from aqueous solutions in equilibrium with air containing Pu as either Pu(VI) or Pu(IV) and characterized using a combination of laser ablation inductively coupled plasma mass spectrometry (LA–ICP–MS) and X-ray absorption spectroscopy (XAS). These data are used to assess the amount, structure, and oxidation state of Pu co-precipitated into calcite, providing insight into the potential for Pu sequestration in calcite precipitates. Overall, the XAS and LA–ICP–MS data support the co-precipitation of plutonyl [Pu(VI/V)] in the bulk calcite, although the exact nature of the co-precipitated Pu complex is difficult to elucidate in the synthesized material. Co-precipitated plutonyl could be incorporated in either distorted Ca lattice sites or defect sites, and we provide evidence to suggest that Pu(VI) is reduced mainly to Pu(V) in the precipitated solid. LA–ICP–MS additionally shows that the co-precipitation of Pu(VI/V) is favored over the co-precipitation of Pu(IV). Altogether, our results suggest that Pu sequestration in calcite under environmental conditions could immobilize Pu and isolate it from groundwater interactions in contaminated environments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRSDate not supplied

Achieving Equilibrium for Dense, Integrated, Vehicle Navigation

Drone usage has proliferated in recent years with many applications that have market-changing potential. Applications that include parcel delivery, wildlife protection, precision farming, law enforcement, and industrial inspection, just to name a few. In this paper, the term drone is used to mean both Unmanned Aerial Vehicle and small Unmanned Aircraft System vehicles. Flight infrastructure can currently only support a few thousand aircraft flying over the United States National Airspace System (NAS) at any given time. A delay atone airport sends ripple effects through the system, causing more delays and missed connections. Once regulations and safety policies are put in place to allow for the widespread use of unmanned drones, the number of aircraft in the NAS is expected to skyrocket to millions, potentially congesting the airspace resulting in possible separation violations. In air traffic control, separation is the concept of keeping an “ownship” aircraft outside a minimum distance from “intruder” aircraft to reduce the risk of the aircraft colliding, as well as preventing accidents due to secondary factors, such as wake turbulence. Maintaining proper separation is a safety critical property for drones in the airspace. This paper addresses separation in time and in distance for high volume corridors (en-route) and lanes(on ground). The requirements and necessary conditions for maintaining proper separation and reaching maximum throughput for a given corridor/lane are addressed assuming unidirectional corridors/lanes where an aircraft arrives from one side and departs from the opposite side. Simulation results are presented that show the presented solution guarantees a set of drones to reach the equilibrium state by adjusting their speed based on their distance to the aircraft in front of them. The equilibrium state is defined as a state when a set of n aircraft moving at a relatively constant speed and uniform spacing from each other in a congested system. A congested system is defined as a state when the aircraft cannot move at their maximum allowed speed. Unlike existing centralized and pre-planned approaches, the proposed solution is fully distributed and enables autonomous aircraft to decide to adjust their speed and distance with respect to the preceding aircraft, dynamically. Simulation results are presented that assess the feasibility of the approach using a large number of drones and evaluate the scalability of the proposed solution.

Mahyar R. Malekpour↗
DOE OSTI2023

Experimental determinations of carbon and hydrogen isotope fractionations and methane clumped isotope compositions associated with ethane pyrolysis from 550 to 600°C

Methane clumped isotope compositions signify the relative natural abundances of rare, doubly substituted isotopic species of methane ( 13 CH 3 D and 12 CH 2 D 2 ) and have emerged as a new isotopic tool to trace the sources, sinks, and lifecycles of methane in the environment. Such measurements can identify equilibration (or reequilibration) temperatures if found to be in isotopic equilibrium or non-equilibrium processes (e.g., kinetically controlled reactions or mixing) if not in isotopic equilibrium. Naturally occurring thermogenic methane—formed by the thermally activated breakdown of larger organic molecules—has been found to have clumped isotope compositions consistent with equilibrium at reasonable gas formation temperatures in some settings and non-equilibrium processes occurring during either formation, migration, storage, or extraction in others. To explore the potential controls on the isotopic composition of thermogenic methane, we conducted isothermal time-series ethane pyrolysis experiments at 550 and 600 °C to measure methane and ethane 13 C/ 12 C and D/H fractionations and methane clumped isotope compositions (resolved 13 CH 3 D and 12 CH 2 D 2 ). We explore the effects of modifying the initial clumped isotope composition of ethane and the addition of water vapor to pyrolysis experiments. We observe that ethane and methane 13 C/ 12 C are controlled by kinetic isotope effects and Rayleigh distillation processes. In contrast, ethane and methane D/H and methane clumped isotope compositions appear to be controlled by a combination of these processes and hydrogen isotope exchange. The hydrogen isotope exchange processes lead to isotopic equilibrium as reaction completion is approached for both D/H (ethane/methane) and methane clumped isotope compositions. Here, we develop a chemical model based on a mass balance approach that accounts for inheritance vs. hydrogen-abstraction formation pathways for singly and doubly substituted isotopologues of ethane and methane that is compared to the experimental data. The model allows the determination of carbon and hydrogen kinetic isotope effects associated with ethane cracking and hydrogen abstraction reactions that, where applicable, we compare to prior theoretical constraints. From the comparison of the model to the experimental data, we infer that the kinetically controlled ethane and methane bulk isotope compositions and methane clumped isotope compositions are controlled by kinetic isotope effects (both primary and secondary) associated with both C–C bond and C–H bond cleavage reactions. Specifically, the methane clumped isotope compositions likely result from a combination of clumped isotope effects associated with ethane breakdown and/or assembly of methane isotopologues (expressed in terms of γ-factor parameters ≠ 1) and combinatorial effects that arise probabilistically. We discuss our experimental results in the context of recent pyrolysis experiments and observations of naturally occurring thermogenic methane. We consider a proposal consistent with observations from nature that the hydrogen isotope exchange reactions that promote equilibration of methane isotopic molecules at or near formation temperature may be facilitated by free radicals generated by pyrolysis reactions. In this framework, isotope exchange effectively ceases when pyrolysis effectively ceases locking in compositions that can be consistent with peak formation temperatures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
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↗
NASA NTRS1991

Lunar anorthosites, their equilibrium melts and the bulk moon

The present study uses plagioclase compositions and partition coefficients for several elements to estimate melts from which lunar anorthosites formed and the partition liquids from which these melts were derived. The Fe and Mg contents of the plagioclases are examined for their potential use as predictors of Fe and Mg in associated melts. Usable trace elements are employed with selected partition coefficients to predict the equilibrium melts for lunar anorthosites, and melts for anorthosites are used in various models to calculate the composition of the initial melt from which the lunar mantle and eventually the anorthosites evolved. The initial melts are compared with bulk moon compositions to evaluate the nature of the melting that could have produced the anorthosites. All the models indicate that extensive melting of all or nearly all of the lunar mantle is required to produce a lunar crust that constitutes 13-15 percent of the moon's volume.

Phinney, W. C.↗
DOE OSTI2023

Calorimetric Energies and Chemical Potentials of Metal Atoms in Catalytic Nanoparticles on Oxide and Carbon Supports: Improved Size Dependencies and Adhesion Energies

The chemical potential of metal atoms, μM, in supported metal nanoparticles is an important descriptor related to both the catalytic activity and the stability of the nanoparticles. Here, we derive an expression relating μM to the radius of the particle’s contact area with the support and the adhesion energy at the metal/support interface (E adh ) that assumes the particles have the shape of spherical caps but of arbitrary contact angle with the support (θ c ) and includes an empirical correction for the increase in metal surface energy and adhesion energy with decreasing radius of curvature. We then show that, at any assumed contact angle, we can simultaneously fit previously reported measurements of both calorimetric μ M (from heats of metal vapor adsorption during nanoparticle growth by vapor deposition) versus metal coverage data and the He + low-energy ion scattering (LEIS) intensities for the metal and/or support versus metal coverage (using our recently developed spherical cap model for quantitative LEIS intensities), to determine the particle size versus coverage and E adh . Only one choice of contact angle gives a pair of values for contact angle and E adh , which is consistent with the Young–Dupré equation for the equilibrium shape of a spherical particle. At this equilibrium shape, we then applied this spherical cap model (SCM) to reanalyze microcalorimetric metal chemical potentials and LEIS signals versus coverage data for nine metal/support combinations that were previously analyzed by assuming that the particles had the shape of hemispherical caps, i.e., with a contact angle of 90°. We show that this revised approach gives close agreement with the calorimetric and LEIS data; the best-fit contact angles vary from 64 to 84°, correcting the earlier assumption of 90°. Furthermore, these results provide significant accuracy improvements in particle size versus coverage, metal chemical potential versus size and coverage, metal/support adhesion energies and contact angles for Cu, Ag and Au on CeO 2 (111), Ni on MgO(100), Ag on Fe 3 O 4 (111) and TiO 2 (100), and Ag, Ni and Pd on Ni-supported graphene. This revised approach is much more broadly applicable than the earlier hemispherical cap model (HCM).

99 GENERAL AND MISCELLANEOUS↗