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DOE OSTI2025

First-principles thermodynamics of Al 10 ⁢V: An analytical treatment of localized anharmonic modes

Many complex intermetallic structures possess cagelike environments that can host additional guest atoms. In Al 10 ⁢V, these atoms give rise to low-frequency, localized vibrations (Einstein modes) that dominate the thermodynamic response at low temperature. They become imaginary under volume expansion as temperature rises, invalidating the harmonic approximation. Here, we develop a framework to incorporate these strongly anharmonic vibrational modes into first-principles thermodynamic calculations. By explicitly modeling the cage potential and solving the associated Schrödinger equation numerically, we compute the full anharmonic free energy contribution and demonstrate its impact on the thermodynamic behavior of Al 10⁢ V. This allows us to examine structures with different cage fillings and construct the Al-V phase diagram in the relevant composition range. Our results reproduce key experimental signatures, including the anomalous rise in the thermal expansion coefficient and heat capacity at low temperatures, and reveal that the presence and the extent of cage filling by guest atoms is essential to stabilizing the Al 10 ⁢V phase at elevated temperatures.

anharmonic lattice dynamics↗

DOE OSTI2025

Metriplectic four-bracket algorithm for constructing thermodynamically consistent dynamical systems

A unified thermodynamic algorithm is presented for constructing thermodynamically consistent dynamical systems, i.e., systems that have Hamiltonian and dissipative parts that conserve energy while producing entropy. The algorithm is based on the metriplectic 4-bracket given in Morrison and Updike [Phys. Rev. E 109, 045202 (2024)]. A feature of the unified thermodynamic algorithm is the force-flux relation 𝐉 𝛼 =−𝐿 𝛼⁢𝛽 𝛁(𝛿⁢𝐻⁡/𝛿⁢𝜉 𝛽 ) for phenomenological coefficients 𝐿 𝛼⁢𝛽 , Hamiltonian 𝐻, and dynamical variables 𝜉 𝛽 . The algorithm is applied to the Navier-Stokes-Fourier, the Cahn-Hilliard-Navier-Stokes, and Brenner-Navier-Stokes-Fourier systems, and significant generalizations of these systems are obtained.

Multiphase flows↗

DOE OSTI2026

Thermodynamics of grain-boundary phases

The past decade has seen a significant increase in research efforts aimed at understanding the thermodynamics of low-dimensional phases existing in many materials systems, ranging from two-dimensional materials to core regions of extended defects in crystalline solids. We review the current status of theoretical, computational, and experimental research on the “defect phases,” focusing on grain boundaries (GBs) in elemental and multicomponent polycrystalline materials. After reviewing the generalized concept of a phase of any dimensionality, we discuss recent progress in atomistic computer simulations of GB phase transformations and phase coexistences, including the observation of one-dimensional defects separating GB phases (defects in defects). Computational predictions compare well with experimental observations of multiple GB phases and segregation-induced phase transformations. An intriguing open question of GB thermodynamics is whether the GB free energy can be driven to a zero value by increasing solute segregation. We review recent efforts to understand this ultimate thermodynamic stabilization of GB phases and the possible polycrystalline microstructures that may arise. An outlook for future research in the field is discussed.

Materials science↗

DOE OSTI2025

First-Principles Thermodynamic Assessments of Sr-Containing Secondary Phase Formation in La1-xSrxMnO3±δ Perovskites for Solid Oxide Cell Applications

Sr-secondary phase formation is a potentially significant degradation mode threatening solid-oxide cell (SOC) commercial viability. A first-principles thermodynamic study was performed for rhombohedral perovskite (La1-xSrx) MnO3±δ (LSM) to assess its stability against Sr secondary phase formation in SOC applications. In this work, the Sr secondary phase formation reaction free energies were determined by combining ab initio lattice dynamics calculations for the solid phases and an ab initio thermodynamics approach for the gas phases. Furthermore, this approach goes beyond previous thermodynamic modeling studies by integrating first-principles based point-defect equilibria into the analyses. The modeling results indicate an increased tendency to form SrO oxide from LSM upon decreasing the oxygen partial pressure. Additionally, enhancing factors to form the Sr-related secondary phase from the associated SrO activity in LSM are further quantified by considering the equilibrium of SrO reacting with contaminant gas species as a function of temperature and gas pressure.

Defect and phase stability↗

DOE OSTI2025

Thermodynamic Profiling Through ASSIST Observations and TROPoe Retrievals

This report reviews the most relevant theoretical aspects of thermodynamic profiling techniques based on spectral observations from ASSIST-II infrared radiometers and TROPoe retrievals. The ASSIST+TROPoe system is a cutting-edge remote sensing technology deployed during the AWAKEN and WFIP3 field campaigns to estimate high-frequency profiles of temperature and humidity in the atmosphere. These profiles are highly valuable for characterizing atmospheric stratification, improving wind models, and understanding the impacts of wind plants on the climate. In this document, we discuss the operating principles of ASSIST, the physics of atmospheric infrared radiation, and the mathematical framework and capabilities of TROPoe. Sources of uncertainties in both the instrument and the retrieval method are also thoroughly addressed. This guide is designed to help users of ASSIST, TROPoe, and thermodynamic data in collecting, estimating, and applying thermodynamic profiles rigorously and scientifically.

17 WIND ENERGY↗

DOE OSTI2025

Aerosol Thermodynamics (Aerosol Liquid Water Concentration and Aerosol pH) at S2 during CoURAGE

These data report aerosol liquid water content (ALWC) and aerosol pH for the S2 (Mt. Airy) site during CoURAGE for April - June 2025. The ISORROPIA-II aerosol thermodynamic equilibrium model was used to compute ALWC and pH. The model was run in forward mode, with solids formation disabled (metastable mode), according to Pye et al. (Atmospheric Chemistry and Physics, 2020). Information about the model can be found at https://www.epfl.ch/labs/lapi/models-and-software/isorropia/, and in Fountoukis and Nenes (Atmospheric Chemistry and Physics, 2007). Inputs to the model were: (1) measured Temperature and relative humidity, both from the DoE ARM “metwxt” data products at S2, (2) aerosol chemical composition from the ARM ACSM, and (3) gas-phase ammonia concentrations. For ISORROPIA-II, ambient RH values above 0.995 were input to the model as 0.995; therefore, caution should be exercised interpreting ALWC when RH was above 0.995. Aerosol composition or NH3(g) concentrations below the LOD were input into the model as 0.5*LOD. Model runs were only conducted for data points at 30-min resolution with all three inputs (meteorology, ACSM, and NH3). If any of the three model inputs were missing, aerosol thermodynamic outputs are flagged as -999. Similarly, aerosol thermodynamic outputs are flagged as -999 if measured NH3(g) and aerosol ammonium (NH4+) were simultaneously below the respective LODs. The ALWC includes liquid water from inorganic aerosol components, calculated directly by ISORROPIA-II, as well as liquid water from organics, estimated from the ACSM organics assuming a kappa value of 0.12 according to Guo et al. (Atmospheric Chemistry and Physics, 2015).

Aerosol Liquid Water Content↗

DOE OSTI2025

Surface Nanostructure Control and Thermodynamic Stability Analysis of Femtosecond Laser-Ablated CuCoMn 1.75 NiFe 0.25 Nanoparticles

Surface nanostructure control is the key to functionalizing nanomaterials. This paper presents a characterization with thermodynamic stability analysis of CuCoMn 1.75 NiFe 0.25 high-entropy alloy (HEA) nanoparticles synthesized by femtosecond laser ablation in ethanol and liquid nitrogen (LN2). Using multimodal electron microscopy and spectroscopy, we examine phase, particle size, defect structure, chemical distribution, and surface composition and relate them to HEA stability. Elemental distributions are uniform in both media, but LN2 produces smaller particles with a narrower size distribution and mainly single- or few-domain interiors, whereas ethanol yields larger particles built from 2–4 nm crystallites with domain aggregation. Edge defects appear in both but energy-dispersive X-ray spectroscopy (EDS) is broadly uniform with local fluctuations in ethanol. X-ray photoelectron spectroscopy (XPS), supported by an attenuation model, indicates an ∼1 nm oxide overlayer that suppresses Mn 2p intensity; correcting for it returns Mn toward the bulk value. UV–NIR and photoluminescent spectra independently support a thin oxide shell. Composition-based thermodynamic descriptors place LN2 closer to bulk mixing parameters, while ethanol raises ΔH_mix and lowers Ω. Cooling simulations are consistent (LN2 ∼ 0.1 μs quench, ethanol ∼1 μs). In conclusion, these results connect solvent-controlled kinetics and thermodynamics to crystalline state and surface chemistry, informing surface control of HEA nanoparticles.

Femtosecond Laser Ablation↗

DOE OSTI2026

Thermodynamic Control of Interface Directs MnO 2 Nucleation Chemistry for Dense and Conformal Electrodeposition

Manganese dioxide (MnO 2 ) is widely recognized as a promising material for high-energy-density energy storage systems due to its broad applicability and facile electrodeposition. However, achieving uniform, thin, and high-mass-loading MnO 2 coatings on high-surface-area electrodes remains a significant challenge. Conventional electrodeposition methods typically yield nonuniform, thick layers with poor conductivity and limited material utilization, restricting their practical use. Here, we uncover a thermodynamically engineered vanadyl/pervanadyl (VO 2+ /VO 2 + ) interface that fundamentally reshapes MnO 2 electrodeposition chemistry, enabling highly uniform and dense coatings. Here, combining in situ AFM measurement, Classical Nucleation Theory, and Johnson–Mehl–Avrami–Kolmogorov modeling, we show that this interface reduces early-stage detectable MnO 2 island size by 35-fold and shifts the MnO 2 growth from diffusion-limited to reaction-limited progressive nucleation. This thermodynamically controlled interface yields highly dense and conformal MnO 2 films with record-high mass loading of 241 mg cm –2 (1607 mg cm –3 ) on 3D-printed graphene aerogels, without compromising porosity or inducing thickness gradient. As a prototype demonstration, the resulting MnO 2 electrodes deliver record-setting volumetric performance in both capacitors (106 F cm –3 ) and Zn//MnO 2 pouch cells (162 mAh cm –3 ). Beyond energy storage, our findings demonstrate the significance of thermodynamic interface control in MnO 2 nucleation chemistry for achieving dense and uniform coatings on various substrates, with implications for electrocatalysis, semiconductor processing, and advanced materials manufacturing.

Batteries↗

DOE OSTI2025

Circuit complexity and functionality: A statistical thermodynamics perspective

Circuit complexity, defined as the minimum circuit size required for implementing a particular Boolean computation, is a foundational concept in computer science. Determining circuit complexity is believed to be a hard computational problem. Recently, in the context of black holes, circuit complexity has been promoted to a physical property, wherein the growth of complexity is reflected in the time evolution of the Einstein-Rosen bridge (“wormhole”) connecting the two sides of an anti-de Sitter “eternal” black hole. Here, we are motivated by an independent set of considerations and explore links between complexity and thermodynamics for functionally equivalent circuits, making the physics-inspired approach relevant to real computational problems, for which functionality is the key element of interest. In particular, our thermodynamic framework provides an alternative perspective on the obfuscation of programs of arbitrary length—an important problem in cryptography—as thermalization through recursive mixing of neighboring sections of a circuit, which can be viewed as the mixing of two containers with “gases of gates.” This recursive process equilibrates the average complexity and leads to the saturation of the circuit entropy, while preserving functionality of the overall circuit. The thermodynamic arguments hinge on ergodicity in the space of circuits which we conjecture is limited to disconnected ergodic sectors due to fragmentation. The notion of fragmentation has important implications for the problem of circuit obfuscation as it implies that there are circuits of same size and functionality that cannot be connected via a polynomial number of local moves. Furthermore, we argue that fragmentation is unavoidable unless the complexity classes NP and coNP coincide, a statement that implies the collapse of the polynomial hierarchy of computational complexity theory to its first level.

Science & Technology - Other Topics↗

DOE OSTI2026

Generative Thermodynamic Computing

Here, we introduce a generative modeling framework for thermodynamic computing, in which structured data are synthesized from noise by the natural time evolution of a physical system governed by Langevin dynamics. While conventional diffusion models use neural networks to perform denoising, here the information needed to generate structure from noise is encoded by the dynamics of a thermodynamic system. Training proceeds by maximizing the probability with which the computer generates the reverse of a noising trajectory, which ensures that the computer generates data with minimal heat emission. We demonstrate this framework within a digital simulation of a thermodynamic computer. If realized in analog hardware, such a system would function as a generative model that produces structured samples without the need for artificially injected noise or active control of denoising.

Whitelam, Stephen [Lawrence Berkeley National Labo↗

DOE OSTI2024

Formation kinetics and thermodynamic stability of the Aurivillius compounds in Bi 4 Ti 3 O 12 –BiFeO 3 system

Abstract The Aurivillius compounds in the Bi 2 O 3 –Fe 2 O 3 –TiO 2 system, combining ferroelectric, semiconducting, and ferromagnetic properties, have attracted particular interest. Formation kinetics and thermodynamic stability are the fundamental knowledge needed for modeling and predicting the temporal microstructure and property evolution during materials processing but have not yet been addressed by quantitative experimental measurement. This article focuses on the Bi n +1 Fe n –3 Ti 3 O 3 n +3 Aurivillius compounds on the Bi 4 Ti 3 O 12 –BiFeO 3 tie‐line to elucidate the mechanisms and thermodynamic controls responsible for phase formation of compounds with various perovskite‐like layers. Five high‐purity Aurivillius compounds Bi 4 Ti 3 O 12 , Bi 5 FeTi 3 O 15 , Bi 6 Fe 2 Ti 3 O 18 , Bi 7 Fe 3 Ti 3 O 21 , and Bi 8 Fe 4 Ti 3 O 24 with integer n = 3–7 values were synthesized and their phase transformation properties and enthalpies of formation were studied by X‐ray diffraction in situ, high temperature differential scanning calorimetry, and high temperature oxide melt solution calorimetry. Thermodynamic stability of the compounds decreases with increasing n , and formation kinetics gradually slow down, demonstrating the inherent difficulty to synthesize pure Aurivillius compounds with n larger than 8. This difficulty was confirmed by an impurity phase coexisting with Bi 9 Fe 5 Ti 3 O 27 .

Gong, Weiping↗

DOE OSTI2025

Thermodynamics of gallium-stabilized delta-plutonium: A high-temperature drop calorimetry study

Throughout the Cold War (1947–1991), both the United States and the former Soviet Union independently derived a phase diagram for the Pu-Ga system that has different implications on Pu phase stability. In the phase diagram produced by the United States, the Pu δ-phase is thermodynamically stable at room temperatures when Ga content is between 2 and 9 at. %. The diagram produced by the Soviet Union shows the δ-phase undergoing an eutectoid decomposition into the α-Pu + α-Pu 3 Ga at 7.9 at. % Ga and 370 K. This would suggest that Ga-stabilized δ-Pu is metastable with respect to α-Pu + α-Pu 3 Ga at 298 K. To investigate this, and the thermodynamic behavior of Ga in the FCC lattice of δ-Pu, we have utilized high-temperature drop calorimetry to study the enthalpy of formation of two δ-Pu 1−x Ga x compositions. In doing so, mixing models (regular and subregular) were developed to understand the thermodynamic behavior of Ga in the FCC lattice of δ-Pu and found a strong departure from ideal conditions, which suggests Ga ordering in the FCC lattice of δ-Pu. Overall, it was found that δ-Pu 1−x Ga x is enthalpically metastable with respect to α-Pu + Pu 3 Ga at 298 K.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Quantifying the regime of thermodynamic control for solid-state reactions during ternary metal oxide synthesis

The success of solid-state synthesis often hinges on the first intermediate phase that forms, which determines the remaining driving force to produce the desired target material. Recent work suggests that when reaction energies are large, thermodynamics primarily dictates the initial product formed, regardless of reactant stoichiometry. Here, we validate this principle and quantify its constraints by performing in situ characterization on 37 pairs of reactants. These experiments reveal a threshold for thermodynamic control in solid-state reactions, whereby initial product formation can be predicted when its driving force exceeds that of all other competing phases by ≥60 milli–electron volt per atom. In contrast, when multiple phases have a comparable driving force to form, the initial product is more often determined by kinetic factors. Analysis of the Materials Project data shows that 15% of possible reactions fall within the regime of thermodynamic control, highlighting the opportunity to predict synthesis pathways from first principles.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Thermodynamic Modeling of Point Defects in Triple Conducting Perovskite Ba 0.95 La 0.05 FeO 3- $_δ$ with Incorporation of the Hydride Defect Formation Reaction for Solid Oxide Cells

Distinct from the proton defect, the hydride defect species may be present in certain perovskite materials in reducing environments such as in fuel electrodes of solid oxide cells (SOCs) or on the reducing side of ceramic membranes. A generalized defect thermodynamic model was developed for the triple-conducting perovskites (La,Ba)Fe 1-x M x O 3-δ (M = Y and Zr) to allow inclusion of the hydride defect formation reaction in addition to the other three main defect reactions, namely, the oxygen vacancy formation, hydration, and charge disproportionation reactions. This comprehensive defect model also allows the incorporation of polynomial functional forms of oxygen nonstoichiometry δ to describe the defect reaction energies and entropies and to enable refinements of the defect reaction equilibrium constants in the defect thermodynamic analysis. As a first step, the developed model is applied to the Ba 0.95 La 0.05 FeO 3-δ material as an illustrative system to obtain its Brouwer diagrams with both the proton and hydride defects in relevant SOC conditions, particularly for more reducing environments. In conclusion, the results provide direct guidance on the influence of electronic and ionic defect concentrations upon thermodynamic properties and ultimately on the performance of Ba 0.95 La 0.05 FeO 3-δ and potentially other (La,Ba)Fe 1-x M x O 3-δ perovskite materials involved in SOC applications.

25 ENERGY STORAGE↗

DOE OSTI2025

Quantifying the Thermodynamic Impacts on the Atmospheric Boundary Layer due to the Sea Breeze in the Coastal Houston Region

The atmospheric boundary layer (ABL) is unique in coastal regions because of kinematic and thermodynamic influences from continental and marine environments. Sea-breeze (SB) circulations act to equilibrate the land–sea temperature gradient through advecting marine air onshore. The strength of the SB varies in terms of stability, temperature, and moisture advection and influences air quality and weather forecasts. The Tracking Aerosol Convection Interactions Experiment (TRACER) collected a wealth of data on coastal boundary layer evolution, including observations from uncrewed aerial systems (UASs). Vertical profiles of temperature, humidity, and winds were collected by the OU CopterSonde UAS from June to September in the coastal region of Houston. These profiles offer 5-m vertical resolution, on average, every 30 min through diurnal transitions, SB events, and nearby deep convection. During the campaign, CopterSonde observations were gathered through 17 SB events, six of which led to convection initiation. The UAS data can resolve the thermodynamic evolution and interactions between the SB and the preexisting convective boundary layer. Results show large variability across observed SBs and their impacts on temperature and moisture. The intensity of thermodynamic changes depends on the time of sea-breeze passage and influence from the Galveston Bay Breeze, a secondary marine circulation commonly observed in this region. In quantifying the spectrum of SB impacts, equivalent potential temperature θ e is used to contextualize its role in convection initiation and evolution. In conclusion, while all SBs tend to increase θ e from moisture advection, the rate and timing of the θ e rise can distinguish convective from nonconvective cases.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Elucidating the complex interplay between thermodynamics, kinetics, and electrochemistry in battery electrodes through phase-field modeling

Abstract This article highlights applications of phase-field modeling to electrochemical systems, with a focus on battery electrodes. We first provide an overview on the physical processes involved in electrochemical systems and applications of the phase-field approach to understand the thermodynamic and kinetic mechanisms underlying these processes. We employ two examples to highlight how realistic thermodynamics and kinetics can naturally be incorporated into phase-field modeling of electrochemical processes. One is a composite battery cathode with an intercalation compound (Li x FePO 4 ) as the electrochemically active material, and the other is a displacement reaction compound (Li–Cu–TiS 2 ). With the input parameters mostly from atomistic calculations and experimental measurements, phase-field simulations allowed us to untangle the interactions among transport, reaction, electricity, chemistry, and thermodynamics that lead to highly complex evolution of the materials within battery electrodes. The implications of these observations for battery performance and degradation are discussed. Graphical abstract

Andrews, W. Beck (ORCID:0000000287824621)↗

DOE OSTI2025

Tritium Trapping Thermodynamics by Point Defects at Interfacial Fe-Al Phases of the Aluminide Coating

Density functional theory (DFT) simulations have been carried out to evaluate the potential for tritium trapping by metal vacancies in four phases (i.e., (Fe, Cr, Ni), AlFe 3 , NiAl, and AlFe) identified near the interface between the Al coating and 316 stainless steel (316 SS) cladding. In addition, an ab initio thermodynamics approach has been employed to predict the temperature and T 2 -partial pressure dependence on the thermodynamics of tritiated defects. Key results in this work suggest that metal vacancies in the four phases have the potential to favorably trap tritium species. This thermodynamic trend can be correlated to the high energy cost of having an interstitial tritium in the lattice, which has been calculated to be at least 0.48 eV. By combining the results of this study with previous theoretical works investigating tritium behavior in other Fe-Al phases identified in the aluminide coating, suggest that metal vacancies are generally able to trap tritium in various Fe-Al aluminide phases. Especially, it was found that Al vacancies are the most efficient to trap tritium, followed by Fe vacancies, then Ni and Cr vacancies. Strong interactions between tritium and the metal vacancies are occurring by the formation of Fe—T bonds. The formation of Cr—T, Ni—T, or Al—T bonds are found less energetically favorable than Fe—T bonds.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2026

Thermodynamics of Tritium Trapping by Point Defects at Interfacial Cr-based Phases of the Al Coating

Density functional theory (DFT) simulations have been carried out to evaluate the potential for tritium trapping by metal vacancies in four phases Cr-containing phases (i.e., Cr3Si, Al0.3Cr0.7, Al8Cr5-HT, and Al8Cr5) identified near the interface between the Al coating and 316 stainless steel (316 SS) cladding. In addition, an ab initio thermodynamics approach has been employed to predict the temperature and T2-partial pressure dependence on the thermodynamics of singly tritiated defects. Key results in this work suggest that metal vacancies in the four phases have the potential to favorably trap tritium species, especially Si vacancies in Cr3Si phase. This overall thermodynamic trend can be correlated to the energy cost of having an interstitial tritium in the lattice, which has been calculated to range from 0.17 eV in Al8Cr5-HT to 0.89 eV in Cr3Si. A comparison of the results from this study with previous theoretical works investigating tritium behavior in other Fe-Al phases identified in the aluminide coating, suggests that metal vacancies are generally able to trap tritium in various Fe-Al aluminide phases. Especially, it was found that Si and Al vacancies would be the most efficient to trap for tritium, followed by Cr vacancies, then Fe and Ni vacancies. In the four Cr-based material phases investigated in this work, it is interesting to note that, in the absences of Fe or Ni species, strong interactions between tritium and the metal vacancies are always occurring by the formation of preferential Cr—T bonds (i.e., no Si—T or Al—T bonds were formed).

Sassi, Michel J.↗