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DOE OSTI2018

First-principles study of structural, elastic, electronic, vibrational and thermodynamic properties of uranium aluminides

The structural, elastic, electronic, vibrational and thermodynamic properties of uranium aluminides UAl x (x = 2, 3, 4) were studied by density functional theory calculations. The single crystal elastic constants of UAl x were predicted using the stress-strain method, which were further used to calculate the polycrystalline aggregate properties of UAl x , including bulk modulus, shear modulus, Young’s modulus, and Poisson’s ratio, etc. The calculated electronic density of states confirm that UAl x compounds are metallic phases with majority states at the Fermi level contributed by U 5 f electrons. The phonon dispersion relations and density of states show that the low frequency acoustic phonon modes of UAl x are dominated by the lattice vibration of uranium atoms while high frequency optical phonon modes are from the vibration of aluminum atoms. Using quasiharmonic approximation, thermodynamic properties of UAl x , including Gibbs free energy, entropy, heat capacity, and linear thermal expansion coefficient, were predicted by including both lattice vibrational and thermal electronic contributions. The thermal electronic energy was found to be crucial for the description of the temperature dependence of the thermodynamic properties. In conclusion, the derived Gibbs energy functions of UAl x are expected to be useful to the thermodynamic modeling of the ternary U-Mo-Al system.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Critical evaluation and thermodynamic modeling of the Pd–Sn system

The single crystalline material PdSn 4 , a homologue of the Dirac nodal arc semimetal PtSn 4 , is a promising candidate to search for new topological states with fascinating quantum physical properties. In the present work, the thermochemistry and phase diagram information of the Pd–Sn system published in the literature was collected and critically reviewed, two thermodynamic reassessments of the Pd–Sn system were carried out in the frame of the CALPHAD approach to optimize the Gibbs free energy of each phase presented in the system. The liquid phase was described using respectively the Bragg-Williams random mixing model and the associate solution model. All the reliable thermodynamic property and phase equilibria data can be generally described using the presently obtained thermodynamic descriptions of the Pd–Sn system. Issues related to the further improvement of the thermodynamic descriptions of the Pd–Sn system are discussed.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Complementing a continuum thermodynamic approach to constitutive modeling with symbolic regression

Here, an interpretable machine learning method, physics-informed genetic programming-based symbolic regression (P-GPSR), is integrated into a continuum thermodynamic approach to developing constitutive models. The proposed strategy for combining a thermodynamic analysis with P-GPSR is demonstrated by generating a yield function for an idealized material with voids, i.e., the Gurson yield function. First, a thermodynamic-based analysis is used to derive model requirements that are exploited in a custom P-GPSR implementation as fitness criteria or are strongly enforced in the solution. The P-GPSR implementation improved accuracy, generalizability, and training time compared to the same GPSR code without physics-informed fitness criteria. The yield function generated through the P-GPSR framework is in the form of a composite function that describes a class of materials and is characteristically more interpretable than GPSR-derived equations. The physical significance of the input functions learned by P-GPSR within the composite function is acquired from the thermodynamic analysis. Fundamental explanations of why the implemented P-GPSR capabilities improve results over a conventional GPSR algorithm are provided.

42 ENGINEERING↗

DOE OSTI2017

Electronic structural, optical and phonon lattice dynamical properties of pure- and La-doped SrTiO 3 : An ab initio thermodynamics study

To better understand the electronic, optical, and thermodynamic behaviors of lanthanum doped strontium titanate (La-STO) with different doping levels at high temperature, ab initio thermodynamics have been employed to investigate their electronic structures and thermodynamic evolutions versus temperatures. Here, the results show that with increasing La-doping level, the corresponding structures of La-STO become less stable with an increasing number of phonon soft modes. The calculated thermodynamic properties show that with increasing La-doping levels, the free energy and enthalpy changes of La-STOs are decreased at given temperature. For all La-STOs with different La-doping levels investigated, we found that in three cases doping with 25%, 37.5% and 75% La over Sr, the diagonal elements of their dielectric constant matrix are not all equal, which means these crystal structures are uniaxial and anisotropic. Our results indicate that doping La into STO could alter the optical properties of pure STO to be birefringent.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2024

Thermodynamically consistent Cahn–Hilliard–Navier–Stokes equations using the metriplectic dynamics formalism

Cahn–Hilliard–Navier–Stokes (CHNS) systems describe flows with two-phases, e.g., a liquid with bubbles. Obtaining constitutive relations for general dissipative processes for such systems, which are thermodynamically consistent, can be a challenge. We show how the metriplectic 4-bracket formalism (Morrison and Updike, 2024) achieves this in a straightforward, in fact algorithmic, manner. First, from the noncanonical Hamiltonian formulation for the ideal part of a CHNS system we obtain an appropriate Casimir to serve as the entropy in the metriplectic formalism that describes the dissipation (e.g. viscosity, heat conductivity and diffusion effects). General thermodynamics with the concentration variable and its thermodynamics conjugate, the chemical potential, are included. Having expressions for the Hamiltonian (energy), entropy, and Poisson bracket, we describe a procedure for obtaining a metriplectic 4-bracket that describes thermodynamically consistent dissipative effects. The 4-bracket formalism leads naturally to a general CHNS system that allows for anisotropic surface energy effects. Furthermore, this general CHNS system reduces to cases in the literature, to which we can compare.

Cahn–Hilliard↗

DOE OSTI2022

Overcoming significant challenges in extracting off-stoichiometric thermodynamics using the compound energy formalism through complementary use of experimental and first principles data: A case study of Ba 1-x Sr x FeO 3-δ

The compound energy formalism (CEF) is a powerful framework to describe the thermodynamics of metal oxides as a function of off-stoichiometry, temperature, and composition. The thermodynamic properties are crucial materials design attributes in metal oxide-based oxygen-exchange chemical processes. Despite the richness of information an accurate CEF model provides, a method to determine a unique and accurate fit for oxygen exchange materials remains elusive. This contribution details a method for fitting the CEF model that overcomes the current fitting challenges through three innovations: 1) the combination of density functional theory calculations with experimental data decorrelates excess terms and delineates the enthalpic/entropic contributions to the Gibbs free energy; 2) a systematic determination of the important CEF model terms, removing thermodynamic predetermining human intervention; 3) a self-consistent solution of the starting oxygen offstoichiometry (δ 0 ) of thermogravimetric measurements. Thus, our method enables the reliable extraction of off-stoichiometric metal oxide thermodynamic properties and facilitates rapid materials compositional screening, and reliable process design of systems dependent on off-stoichiometric redox-active metal oxides. We apply this method to a Ba x Sr 1-x FeO 3-δ test case. We find by systematically examining the performance of the CEF model fit with and without each innovation that all three innovations are necessary for an accurate fit. We determined that reduction enthalpy is higher and more sensitive to off-stoichiometry when the Sr fraction is large (139.5 and 185.3 kJ/mol O 2 for SrFeO 3 at δ = 0 and δ = 0.5, respectively vs. nearly constant 83 kJ/mol O 2 for BaFeO 3 ). However, the reduction entropy is mostly insensitive to Sr fraction, but highly dependent on δ suggesting larger contributions in the non-configurational entropy parameters.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Experimental Investigation of Thermodynamic Stabilization in Boron Imidazolate Frameworks (BIFs) Synthesized by Mechanochemistry

This study experimentally explores the energetics for the formation of boron–imidazolate frameworks (BIFs), which are synthesized by mechanochemistry. The topologically similar frameworks employ the same tetratopic linker based on tetrakis(imidazolyl)boric acid but differ in the monovalent cation metal nodes. This permits assessment of the stabilizing effect of metal nodes in frameworks with sodalite (SOD) and diamondoid (dia) topologies. The enthalpy of formation from endmembers (metal oxide and linker), which define thermodynamic stability of the structures, has been determined by use of acid solution calorimetry. The results show that heavier metal atoms in the node promote greater energetic stabilization of denser structures. Overall, in BIFs the relation between cation descriptors (ionic radius and electronegativity) and thermodynamic stability depends on framework topology. Thermodynamic stability increases with the metallic character of the cation employed as the metal node, independent of the framework topology. In conclusion, the results suggest unifying aspects for thermodynamic stabilization across MOF systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Proton, Electron, and Hydrogen-Atom Transfer Thermodynamics of the Metal–Organic Framework, Ti-MIL-125, Are Intrinsically Correlated to the Structural Disorder

Interfacial charge transfer reactions involving protons and/or electrons are fundamental to heterogeneous catalysis and many other reactions relevant to energy, chemical, and biological sectors. Metal–organic frameworks (MOFs) with redox-active metal-oxo nodes have emerged as candidate materials to examine these reactions with near-atomic-level precision, given their crystalline nature. Here, we employed a colloidally stable, Ti-based MOF, Ti-MIL-125, with different crystal sizes to examine catalytically relevant charge transfer thermodynamics. The Ti 8 (μ 2 -O) 8 (μ 2 -OH) 4 nodes structurally mimic TiO 2 , which has shown some PCET reactivity toward reactions of H 2 , O 2 , and others. In this report, we have demonstrated that a change in crystal size induces different amounts of structural disorder to the Ti-oxo node, further changing the thermodynamics of proton/electron/hydrogen-atom transfer reactions. Using electrochemical open-circuit potential (E OCP ) measurements, we have determined that all crystallites undergo a 1H + /1e – redox reaction, which, given the stoichiometry, can be considered as a net H atom transfer (HAT) reaction. The thermodynamics of this HAT reaction, the Ti 3+ O–H bond dissociation free energy (BDFE), was dependent on the crystal size of the MOF, as the decrease in crystal size induced more structural disorder. Our computational calculations have indicated that this difference in BDFE is due to a local change in the geometry of Ti cations, rather than the commonly invoked defects, such as the “missing-linker” defect sites. Individual proton/electron transfer (PT/ET) thermodynamics were also highly dependent on the crystal sizes. These were probed using pK a or band gaps (E g ), respectively. These findings suggest that, particularly when MOFs are nanosized with a large amount of structural disorder, they should no longer be considered “true” single-site catalysts; this is an implicit, but widespread assumption within the MOF-based catalysis field. Implications of these findings will be contrasted with structurally similar metal oxides like TiO 2 and other redox-active MOFs.

Bond dissociation free energy↗

DOE OSTI2014

Irreversible thermodynamics of open chemical networks. I. Emergent cycles and broken conservation laws

In this paper and Paper II, we outline a general framework for the thermodynamic description of open chemical reaction networks, with special regard to metabolic networks regulating cellular physiology and biochemical functions. We first introduce closed networks “in a box”, whose thermodynamics is subjected to strict physical constraints: the mass-action law, elementarity of processes, and detailed balance. We further digress on the role of solvents and on the seemingly unacknowledged property of network independence of free energy landscapes. We then open the system by assuming that the concentrations of certain substrate species (the chemostats) are fixed, whether because promptly regulated by the environment via contact with reservoirs, or because nearly constant in a time window. As a result, the system is driven out of equilibrium. A rich algebraic and topological structure ensues in the network of internal species: Emergent irreversible cycles are associated with nonvanishing affinities, whose symmetries are dictated by the breakage of conservation laws. These central results are resumed in the relation a + b = s{sup Y} between the number of fundamental affinities a, that of broken conservation laws b and the number of chemostats s{sup Y}. We decompose the steady state entropy production rate in terms of fundamental fluxes and affinities in the spirit of Schnakenberg's theory of network thermodynamics, paving the way for the forthcoming treatment of the linear regime, of efficiency and tight coupling, of free energy transduction, and of thermodynamic constraints for network reconstruction.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2014

Statistically optimal analysis of state-discretized trajectory data from multiple thermodynamic states

We propose a discrete transition-based reweighting analysis method (dTRAM) for analyzing configuration-space-discretized simulation trajectories produced at different thermodynamic states (temperatures, Hamiltonians, etc.) dTRAM provides maximum-likelihood estimates of stationary quantities (probabilities, free energies, expectation values) at any thermodynamic state. In contrast to the weighted histogram analysis method (WHAM), dTRAM does not require data to be sampled from global equilibrium, and can thus produce superior estimates for enhanced sampling data such as parallel/simulated tempering, replica exchange, umbrella sampling, or metadynamics. In addition, dTRAM provides optimal estimates of Markov state models (MSMs) from the discretized state-space trajectories at all thermodynamic states. Under suitable conditions, these MSMs can be used to calculate kinetic quantities (e.g., rates, timescales). In the limit of a single thermodynamic state, dTRAM estimates a maximum likelihood reversible MSM, while in the limit of uncorrelated sampling data, dTRAM is identical to WHAM. dTRAM is thus a generalization to both estimators.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

Thermodynamics of a lattice gas with linear attractive potential

We study the equilibrium thermodynamics of a one-dimensional lattice gas with interaction V(|i−j|)=−1/(μn) (ξ−1/n |i−j|) given by the superposition of a universal attractive interaction with strength −1/(μn) ξ<0, and a linear attractive potential 1/(μn{sup 2}) |i−j|. The interaction is rescaled with the lattice size n, such that the thermodynamical limit n → ∞ is well-behaved. The thermodynamical properties of the system can be found exactly, both for a finite size lattice and in the thermodynamical limit n → ∞. The lattice gas can be mapped to a system of non-interacting bosons which are placed on known energy levels. The exact solution shows that the system has a liquid-gas phase transition for ξ > 0. In the large temperature limit T ≫ T{sub 0}(ρ) = ρ{sup 2}/(4μ) with ρ the density, the system becomes spatially homogeneous, and the equation of state is given to a good approximation by a lattice version of the van der Waals equation, with critical temperature T{sub c}{sup (vdW)}=1/(12μ) (3ξ−1)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

Ab initio atomistic thermodynamics study on the oxidation mechanism of binary and ternary alloy surfaces

Utilizing a combination of ab initio density-functional theory and thermodynamics formalism, we have established the microscopic mechanisms for oxidation of the binary and ternary alloy surfaces and provided a clear explanation for the experimental results of the oxidation. We construct three-dimensional surface phase diagrams (SPDs) for oxygen adsorption on three different Nb-X(110) (X = Ti, Al or Si) binary alloy surfaces. On the basis of the obtained SPDs, we conclude a general microscopic mechanism for the thermodynamic oxidation, that is, under O-rich conditions, a uniform single-phase SPD (type I) and a nonuniform double-phase SPD (type II) correspond to the sustained complete selective oxidation and the non-sustained partial selective oxidation by adding the X element, respectively. Furthermore, by revealing the framework of thermodynamics for the oxidation mechanism of ternary alloys through the comparison of the surface energies of two separated binary alloys, we provide an understanding for the selective oxidation behavior of the Nb ternary alloy surfaces. Using these general microscopic mechanisms, one could predict the oxidation behavior of any binary and multi-component alloy surfaces based on thermodynamics considerations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2015

On the thermodynamic efficiency of a nickel-based multiferroic thermomagnetic generator: From bulk to atomic scale

A model is developed to correlate the effects of size on the thermodynamic efficiency for a nickel-based multiferroic thermomagnetic generator device. Three existing models are combined in order to estimate this correlation, they are (1) thermodynamic efficiency relations, (2) a model of ferromagnetic transition behavior, and (3) the bond-order length strength correlation. At the smallest size considered, a monolayer of nickel atoms shows a reduction in Curie temperature from its bulk value of T{sub c,Bulk}=630 K to T{sub c,ML}=240 K. This difference is analytically shown to affect the thermodynamic efficiency values when compared to bulk. Various nickel nanofilms are considered as a working body, such that the combined model predicts relative efficiency values that are comparable to the bulk scale, but operating closer to room-temperature when compared to bulk form. This result is unexpected since the absolute efficiency is shown to increase as a function of decreasing size, this discrepancy is explained as a consequence of Curie point suppression. The combined model is also applied to a hypothetical composite made of separated layers of nickel with distinct thicknesses. This composite material is predicted to spread the ferromagnetic transition across a much larger temperature range as compared to bulk nickel, such that this material may be better suited for different applications; for example, as a sensor or thermal switch. Moreover, this combined model is also shown to give a lower-bound estimate for thermodynamic efficiency, since the actual performance depends on material characterizations that have yet to be determined.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

Fluids confined in wedges and by edges: From cluster integrals to thermodynamic properties referred to different regions

Recently, new insights into the relation between the geometry of the vessel that confines a fluid and its thermodynamic properties were traced through the study of cluster integrals for inhomogeneous fluids. In this work, I analyze the thermodynamic properties of fluids confined in wedges or by edges, emphasizing on the question of the region to which these properties refer. In this context, the relations between the line-thermodynamic properties referred to different regions are derived as analytic functions of the dihedral angle α, for 0 < α < 2π, which enables a unified approach to both edges and wedges. As a simple application of these results, I analyze the properties of the confined gas in the low-density regime. Finally, using recent analytic results for the second cluster integral of the confined hard sphere fluid, the low density behavior of the line thermodynamic properties is analytically studied up to order two in the density for 0 < α < 2π and by adopting different reference regions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2013

Thermodynamic behavior of particular f(R,T)-gravity models

We investigate the thermodynamics at the apparent horizon of the FRW universe in f(R, T) theory in the nonequilibrium description. The laws of thermodynamics are discussed for two particular models of the f(R, T) theory. The first law of thermodynamics is expressed in the form of the Clausius relation <##> } T h d } S }^ h = δ Q $ T{sub h} d/hat S{sub h} = /delta Q $ T{sub h}d S-hat {sub h}=δQ </##>, where δQ is the energy flux across the horizon and <##> } d } S }^ $ d/hat S $ d S-hat </##> is the entropy production term. Furthermore, the conditions for the generalized second law of thermodynamics to be preserved are established with the constraints of positive temperature and attractive gravity. We illustrate our results for some concrete models in this theory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Pyrophosphate-free glycolysis in Clostridium thermocellum increases both thermodynamic driving force and ethanol titers

Background: Clostridium thermocellum is a promising candidate for production of cellulosic biofuels, however, its final product titer is too low for commercial application, and this may be due to thermodynamic limitations in glycolysis. Previous studies in this organism have revealed a metabolic bottleneck at the phosphofructokinase (PFK) reaction in glycolysis. In the wild-type organism, this reaction uses pyrophosphate (PP i ) as an energy cofactor, which is thermodynamically less favorable compared to reactions that use ATP as a cofactor. Previously we showed that replacing the PP i -linked PFK reaction with an ATP-linked reaction increased the thermodynamic driving force of glycolysis, but only had a local effect on intracellular metabolite concentrations, and did not affect final ethanol titer. Results: In this study, we substituted PP i -pfk with ATP-pfk, deleted the other PPi-requiring glycolytic gene pyruvate:phosphate dikinase (ppdk), and expressed a soluble pyrophosphatase (PPase) and pyruvate kinase (pyk) genes to engineer PP i -free glycolysis in C. thermocellum. We demonstrated a decrease in the reversibility of the PFK reaction, higher levels of lower glycolysis metabolites, and an increase in ethanol titer by an average of 38% (from 15.1 to 21.0 g/L) by using PP i -free glycolysis. Conclusions: By engineering PP i -free glycolysis in C. thermocellum, we achieved an increase in ethanol production. These results demonstrate that optimizing the thermodynamic landscape through metabolic engineering can enhance product titers. While further increases in ethanol titers are necessary for commercial application, this work represents a significant step toward engineering glycolysis in C. thermocellum to increase ethanol titers.

09 BIOMASS FUELS↗

DOE OSTI2014

Perform Thermodynamics Measurements on Fuel Cycle Case Study Systems

This document was prepared to meet FCR&D level 3 milestone M3FT-14IN0304022, “Perform Thermodynamics Measurements on Fuel Cycle Case Study Systems.” This work was carried out under the auspices of the Thermodynamics and Kinetics FCR&D work package. This document reports preliminary work in support of determining the thermodynamic parameters for the ALSEP process. The ALSEP process is a mixed extractant system comprised of a cation exchanger 2-ethylhexyl-phosphonic acid mono-2-ethylhexyl ester (HEH[EHP]) and a neutral solvating extractant N,N,N’,N’-tetraoctyldiglycolamide (TODGA). The extractant combination produces complex organic phase chemistry that is challenging for traditional measurement techniques. To neutralize the complexity, temperature dependent solvent extraction experiments were conducted with neat TODGA and scaled down concentrations of the ALSEP formulation to determine the enthalpies of extraction for the two conditions. A full set of thermodynamic data for Eu, Am, and Cm extraction by TODGA from 3.0 M HNO3 is reported. These data are compared to previous extraction results from a 1.0 M HNO3 aqueous medium, and a short discussion of the mixed HEH[EHP]/TODGA system results is offered.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2025

Thermodynamic Cloud Phase Classifications Using Machine Learning at NSA and ANX

Vertically resolved thermodynamic cloud phase classifications are essential for studies of atmospheric cloud and precipitation processes. The Department of Energy (DOE) Atmospheric Radiation Measurement (ARM) THERMOCLDPHASE Value-Added Product (VAP) uses a multi-sensor approach to classify thermodynamic cloud phase by combining lidar backscatter and depolarization, radar reflectivity, Doppler velocity, spectral width, microwave radiometer-derived liquid water path, and radiosonde temperature measurements. The measured voxels are classified as ice, snow, mixed-phase, liquid (cloud water), drizzle, rain, and liq_driz (liquid+drizzle). We use this product as the ground truth to train three machine learning (ML) models to predict the thermodynamic cloud phase from multi-sensor remote sensing measurements taken at the ARM North Slope of Alaska (NSA) observatory: a random forest (RF), a multilayer perceptron (MLP), and a convolutional neural network (CNN) with a U-Net architecture. Evaluations against the outputs of the THERMOCLDPHASE VAP with one year of data show that the CNN outperforms the other two models, achieving the highest test accuracy, F1-score, and mean Intersection over Union (IOU). Analysis of ML confidence scores shows ice, rain, and snow have higher confidence scores, followed by liquid, while mixed, drizzle, and liq_driz have lower scores. Feature importance analysis reveals that the mean Doppler velocity and vertically resolved temperature are the most influential datastreams for ML thermodynamic cloud phase predictions. The ML models’ generalization capacity is further evaluated by applying them at another Arctic ARM site in Norway using data taken during the ARM Cold-Air Outbreaks in the Marine Boundary Layer Experiment (COMBLE) field campaign. Finally, we evaluate the ML models’ response to simulated instrument outages and signal degradation.

54 ENVIRONMENTAL SCIENCES↗