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Electron correlations in the cubic paramagnetic perovskite Sr ( V , Mn ) O 3 : Results from fully self-consistent self-energy embedding calculations
In this study, we use the thermodynamically consistent and conserving self-energy embedding theory (SEET) to study the spectra of the prototypical undistorted cubic perovskites SrVO 3 and SrMnO 3 . In the strongly correlated metallic SrVO 3 we find that the usual attribution of the satellite peaks at –1.8 eV to Hund or Hubbard physics in the t 2 g orbitals is inconsistent with our calculations. In the strongly correlated insulator SrMnO 3 we recover insulating behavior due to a feedback effect between the strongly correlated orbitals and the weakly correlated environment. Our calculation shows a systematic convergence of spectral features as the space of strongly correlated orbitals is enlarged, paving the way to a systematic parameter-free study of correlated perovskites.
A Three-Dimensional, Thermodynamically and Variationally Consistent, Fully Coupled, Electro-Chemo-Thermo-Mechanical Model of Solid-State Batteries
Here we present a theoretical framework for high fidelity modeling of three-dimensional electro-chemo-thermo-mechanical coupled systems such as solid-state batteries. The framework provides a useful means of utilizing molecular level information to predict the overall performance of the system at the continuum level. The central statement of the theoretical framework is a thermodynamically consistent inf-sup problem. The total potential of the coupled system consists of the Helmholtz free energy, the electrical kinetic potential, the chemical potential, the Fourier potential, the chemical reaction potential, and the external power expenditure. All governing equations derive from variational principles. We also show that the resulting initial-boundary-value problem (IBVP) is consistent with existing, widely adopted equations for modeling batteries. Moreover, the IBVP can be naturally discretized using the (variational) finite element method to simulate practical solid-state batteries with arbitrary geometries. Several examples illustrate multiphysics coupling between pairs of the physical field equations, culminating in a comprehensive three-dimensional model of charge-discharge in a solid state battery.
Primal interface debonding formulation for finite strain isotropic plasticity
In this work, a framework is developed for modeling ductile damage of nonlinear materials whose plastic deformation is characterized using rate independent classical plasticity. This method relies on the assumption that the free energy can be decomposed into elastic, plastic and damage parts. A thermodynamically consistent method is derived which satisfies the second law of thermodynamics in the Clausius–Duhem inequality form. The dissipation associated with plasticity takes place in the domain only, while damage dissipation is localized to the interface. The method is developed using Variational Multiscale ideas to obtain definitions of the interface fluxes within a primal formulation analogous to the Discontinuous Galerkin method, which ensures weakly vanishing interface gap prior to reaching a damage initiation criterion. The local nonlinear problem to calculate both plastic deformation gradient and damage variable follows an incremental approach similar to classical plasticity return mapping algorithm. This elastoplastic damage formulation is developed for material undergoing finite strain, and it naturally accommodates a trapezoidal traction separation law (TSL) whose shape can be varied to model either ductile interface behavior or brittle interface behavior. The formulation's performance is assessed through modeling a patch test and a compact tension specimen.
Thermodynamic modeling of the Ti-Nb-Sn system and its preliminary applications in aging precipitation and solidification simulations
Abstract Gasping the thermodynamic and phase diagram of the materials being studied is essential for further guiding the development process, like composition design, heat treatment optimization and so on. Nb and Sn are common alloying elements in Ti-based biomedical alloys. In this work, the Ti-Nb-Sn system has been thermodynamically assessed based on experimental phase equilibria. A self-consistent thermodynamic description for the Ti-Nb-Sn system including two ternary compounds Ti 3 Nb 3 Sn 2 and Ti 3 NbSn has been obtained. Based on the comparison between the calculated and experimental phase equilibria, the reliability of the presently obtained thermodynamic description has been verified. The influence of Nb and Sn contents on the precipitation temperature and amount of hcp α -Ti phase in bcc β -(Ti, Nb) has been investigated based on thermodynamic calculations. Results show that the increase of Nb or Sn content in Ti-based alloys would significantly reduce the precipitation amount and transformation temperature of hcp α -Ti phase in bcc β -(Ti, Nb) and the influence of Nb content is more effective than that of Sn. The solidified phases in several as-cast alloys have been thermodynamically predicted based on Scheil solidification simulations. The presently developed thermodynamic description of the Ti-Nb-Sn system can serve as a sub-ternary one in the thermodynamic database for multicomponent Ti-based biomedical alloys.
Phase-field modeling of rate-dependent fluid-driven fracture initiation and propagation
The rate-dependent behavior associated with deformation and fracturing of materials, such as natural rocks, poses significant challenges for modeling. In addition to the complications of the viscoelastic response, the speed of fracture propagation reflects micromechanical mechanisms in the fracture process zone(FPZ). In order to represent these complicated behaviors, a thermodynamically consistent, rate-dependent fracture model is required. Based on rigorous thermodynamic principles, we derive a rate-dependent phase-field mechanical model coupled with single-phase fluid flow in both the matrix and the fracture. The model is guaranteed to satisfy energy conservation during fracture propagation. Here, the system of equations is solved using the introduced solution procedure and a novel preconditioner that accounts for the complex fluid-structure interaction. The proposed phase-field model is tested against several benchmark problems on solid-fluid coupling, fluid-driven fracture propagation and rate-dependent viscoelastic deformation. The model serves as a strong basis for investigating rate-dependent fracturing experiments and for making predictions of material behaviors under new conditions.
Evaluation of thermodynamic closure models for partially reacted two-phase mixture of condensed phase explosives
One of the key fundamental issues that is crucial in the continuum modeling of reactive flow phenomena is the thermodynamically consistent description of reaction mixture properties. To define the mixture properties, thermodynamic closure rules that relate the properties of the individual reaction components to the mixture properties are required. In the context of reactive two-phase modeling approaches, various strategies to define the thermodynamic closures have been adopted such as pressure temperature (PT) equilibrium between the individual reaction components, pressure (specific) volume (PV) equilibrium, etc. The choice of closure rules determines the relative distribution of specific volume and energy across the reaction components that comprise the mixture. Therefore, depending on the choice of the closure, the mixture thermodynamic behavior can vary. The present work examines the effect of different closure approaches on the thermodynamic properties of the reaction mixture. The analysis is performed for a condensed phase HMX (octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine) based plastic bonded explosive (PBX) 9501 explosive using four different thermodynamic closures, viz., PT equilibrium, PV equilibrium, volume temperature (VT) equilibrium, and pressure (P) equilibrium with reactants on an isentrope. Furthermore, the relative variations in the thermodynamic properties of the mixture are analyzed and compared under both compression and expansion loading regimes. It is shown that out of the four closure models, only PT equilibrium and P equilibrium closures lead to a thermodynamically accurate description of the mixture under both compression and expansion.
An analytic and complete equation of state for condensed phase materials
Analytic equations of state (EOS) are intended to reproduce theoretical and experimental data in a single phase portion of the thermodynamic space. We devise a complete and thermodynamically consistent model with four distinct features: (1) a reference isotherm that remains thermodynamically stable, (2) a flexible specific heat model based on a fourth-order rational polynomial, (3) a Grüneisen parameter that depends on specific volume and temperature, and (4) pressure and internal energy functions that can be inverted analytically in temperature. The model aims to improve the accuracy of existing equations of state while remaining computationally efficient. To demonstrate its features, we include calibrations for single-crystal pentaerythritol tetranitrate (PETN), liquid nitromethane (NM), and hexagonal close-packed beryllium (Be) metal. The parameter optimization uses the specific heat capacity, Grüneisen parameter, and static compression curves obtained from density functional theory for the crystalline solids and molecular dynamics simulations for liquid NM. We also present a velocity autocorrelation function that yields accurate phonon densities of states for the EOS calibration from the molecular dynamics trajectories. Each of the three calibrations is constrained to enforce the ambient state from experimental measurements and validated against experimental Hugoniot data from multiple sources. We also include one-dimensional hydrodynamic simulations of the isentropic compression experiments for beryllium conducted at the Z facility.
HANNA: hard-constraint neural network for consistent activity coefficient prediction
We introduce HANNA, the first hybrid neural network model that strictly complies with all thermodynamic consistency criteria for predicting activity coefficients and outperforms current benchmark methods in terms of accuracy and applicability.
Discrete stochastic model of point defect-dislocation interaction for simulating dislocation climb
Dislocation climb is an important high temperature process in metals plasticity, responsible for the phenomena such as creep, swelling, or hardening. Climb is defined by the ability of dislocations to leave their original glide plane by interacting with point defects. As such, dislocation climb is controlled by point defect diffusion/absorption/emission, all of which involve thermal activation. The existing thermodynamically consistent models for climb are generally formulated in a continuum framework, through the definition of effective defect fluxes and climb propensities in response to thermodynamic driving forces. However, the point-wise discrete nature of vacancies (and/or self-interstitials) confers a highly discrete nature to the climb dynamics, which is also strongly affected by elastic forces. The combination of discreteness, thermal activation, and elasticity makes this process too challenging for direct atomistic methods such as molecular dynamics. Here we develop a kinetic Monte Carlo model that captures vacancy generation and transport kinetics acting in conjuction with the evolving elastic fields provided by discrete dislocation dynamics simulations. The two models are coupled via the applied stresses and stress gradients generated by dislocation structures at vacancy locations. Our simulations reveal two surprising results. First that climb is dominated by vacancy emission even when the background vacancy concentration is much higher than the equilibrium one. And, second, that climb velocities might be much faster than otherwise believed when one uses the classical theories of climb. These effects are due to the locality of vacancy-dislocation processes, which are not captured in classical treatments that assume smooth vacancy fluxes and homogeneous concentrations. We apply the method to study elementary climb processes in body-centered cubic iron and furnish climb mobility functions to be used in parametric dislocation dynamics and/or crystal plasticity simulations. Here, we apply the technique to study non-conservative plastic bypass of spherical precipitates by edge dislocations and point out the differences between our discrete approach and existing continuum formulations.
Multiphase phase-field approach for solid–solid phase transformations via propagating interfacial phase in HMX
In this study, a thermodynamically consistent multiphase phase-field theory has been formulated to describe temperature-induced solid–solid phase transformations via an interfacial phase. This theory satisfies all thermodynamic equilibrium and stability conditions. It allows us to formulate the analytical solutions of the interface profile, energy, width, and velocity for each of the propagating solid–melt and solid–solid interfaces. The formation of the intermediate melt during solid–solid phase transformation has been studied hundreds of degrees below melting temperature in the HMX energetic crystal. The effect of the penalizing term in the phase-field model and two nanoscale material parameters on the appearance and degree of disordering of intermediate melt has been analyzed for the non-equilibrium interface. The developed approach is applicable to phase transitions in geological, pharmaceutical, ferroelectric, colloidal, and superhard materials where phase transformations occur via the intermediate phase.
Effects of local order parameter dependent transport coefficient in diblock copolymers under applied electric fields
In this work, we present an approach for constructing thermodynamically consistent time-dependent models relevant to thin films of diblock copolymers in applied electric fields. The approach is based on the principles of linear irreversible thermodynamics, and, in this work, it is applied to study the effects of electric fields on thin films of incompressible diblock copolymers. Enforcement of local incompressibility constraint at all times leads to a local order parameter dependent transport coefficient in the model for the diblock copolymers. The dependence of the transport coefficient on the local order parameter is used to relate it with the diffusion constant of Rouse chains and leads to sensitivity of the model to initial conditions. In addition, transient behavior is found to be affected when compared with an ad hoc model assuming a constant transport coefficient. Numerical results such as electric field induced alignment of lamellae domains due to the field are found to be in qualitative agreement with experiments. This approach opens up a systematic way of developing kinetic models for simulating effects of electrolytes added to thin films containing diblock copolymers in the presence of applied electric fields.
Predicting zeolites’ stability during the corrosion of nuclear waste immobilization glasses: Comparison with glass corrosion experiments
During the long-term corrosion of nuclear waste glasses under nuclear waste disposal conditions, the precipitation of zeolitic phases has been linked to a delayed acceleration in glass corrosion (known as “Stage III”). Hence, predicting the thermodynamic propensity for zeolites to form upon the dissolution of nuclear waste glasses is key to ensure their long-term performance. Here, we compile a unified, internally-consistent thermodynamic database “clay20” to estimate the stability of clay and feldspar phases relevant to nuclear waste immobilization glasses, including beidellite(Mg, Ca, Na, K), kaolinite, montmorillonite(Mg, Ca, Na, K), nontronite(Mg, Ca, Na, K), saponite(Ca, Na, K), and albite. Based on this, we report a geochemical modeling method allowing us to predict the stability of secondary phases (including zeolites, calcium–silicate–hydrate gels, and clays) upon the dissolution of nuclear waste immobilization glasses. We show that this approach offers a realistic description of the stability of the secondary phases forming during the dissolution of two archetypical model nuclear glasses (namely, the International Simple Glass, ISG, and WVUTh-203) under conditions relevant to nuclear waste disposal (T = 90°C, p = 1 bar) as a function of pH. We find that the formation of silica and clay secondary phases is thermodynamically favored at low pH (pH < 10), whereas, in contrast, zeolite (analcime) and calcium–silicate–hydrate phases are favored at high pH (pH > 10.5). This suggests that thermodynamics (i.e., not solely kinetics) plays a key role in determining the range of solution pH wherein stage III corrosion may occur, i.e., when zeolite formation is favored.
Revisiting the First, Second and Combined Laws of Thermodynamics
The present study revisits the first, second, and combined laws of thermodynamics by introducing partial internal energy in the first law, entropy production and partial entropy in entropy change, and partial volume in the context of work exchange. These developments yield a more rigorous and internally consistent thermodynamic framework, within which chemical potential is defined as the partial derivative of internal energy with respect to composition at constant entropy and volume, and is related to partial internal energy, partial entropy, and partial volume.
Decoding Zeolite Crystallization and Stage III in Nuclear Waste Glasses by Coupled Modeling and Experiments
Under specific conditions of pH and temperature, nuclear waste immobilization borosilicate glasses may exhibit a sudden acceleration in their corrosion kinetics (stage III)—a behavior that has been associated with the formation of zeolite crystals. Such accelerated dissolution may compromise the integrity of nuclear wasteforms placed in geological depositories. However, thus far, none of the available models is able to predict the thermodynamic propensity and kinetics of zeolite precipitation as a function of the solution conditions due to (i) a lack of fundamental knowledge regarding the nucleation & growth mechanisms of zeolitic phases, (ii) uncertainty regarding the compositions (types) of zeolites that may form and the rate-limiting step in their precipitation as a function of the solution conditions, and (iii) the complexities that arise due to the vast parametric space (i.e., solution chemistry, temperature, number of secondary phases, etc.) that encompass these systems under conditions of environmental exposure. To resolve these challenges, this project aimed to unambiguously identify the thermodynamic propensity for zeolite precipitation and the kinetics thereof as a function of the solution conditions (composition, pH, and temperature). To achieve this goal: 1) We identified the solution conditions and zeolite phases relevant to nuclear glass dissolution. 2) We performed a series of ab initio molecular dynamics (AIMD) simulations to compute the thermodynamic properties of a group of characteristic zeolites that features a large range of compositions, various hydration levels, a wide range of framework structures, and partial atomic site occupancies. 3) We released a first-of-a-kind self-consistent thermodynamic database that can be used to assess the kinetics and the stability fields of zeolitic phases within a Gibbs energy minimization (GEM) framework. 4) We developed a robust geochemical modeling method allowing us to predict the stability of secondary phases (including zeolites, calcium–silicate–hydrate gels, and clays) upon the dissolution of nuclear waste immobilization glasses. 5) We introduced a model that predicts the dissolution kinetics of a series of borosilicate nuclear waste immobilization glasses in terms of the topology of their atomic network. 6) We investigated the roles of the solution composition on the crystallization kinetics of phillipsite zeolites and tobermorite silicate hydrates. Via PNNL’s collaboration and engagement, this project directly supports DOE’s nuclear waste immobilization activities by offering a technical, science-based foundation that will (i) facilitate predictions of the long-term corrosion rates and extents of existing nuclear waste immobilization glasses to help ensure safe and successful vitrification operations, (ii) inform the development of advanced glass formulations with enhanced durability, and, (iii) enable cost-savings that result from making more decisive and hence less conservative predictions while offering higher levels of nuclear waste embedment in smaller, more compact glass volumes.
High-Pressure Melting Experiments of Fe 3 C and a Thermodynamic Model of Fe-C Liquids for the Earth's Core
Melting experiments of Fe 3 C were conducted to 85 GPa in laser-heated diamond anvil cells with in situ X-ray diffraction and post-experiment textural observation. From the determined pressure-temperature conditions of the melting curve for Fe 3 C, together with literature data on the melting point of diamond and eutectic point of the system Fe-Fe 3 C/Fe 7 C 3 under high pressures, we established a self-consistent thermodynamic model for high-pressure melting of the system Fe-C including the mixing parameters for liquids. The results show that mixing of Fe and C liquids is negatively nonideal from 1 bar to the pressure at the center of the Earth. The departure from ideal mixing becomes progressively larger with increasing pressure, which leads to greatly stabilized liquids under core pressures. The modeled carbon content in eutectic melts under core pressures is 3.3–4.4 wt%. From the Gibbs free energy, we derived an internally consistent parameters for Fe-C outer cores which included the crystallizing points at their bottoms, isentropic thermal profiles, and densities and longitudinal seismic wave speeds (Vp). While the addition of carbon in excess of the eutectic melt composition effectively reduces the density of iron liquid, the Vp of iron liquid is not greatly changed. Therefore, the low density and high Vp of PREM relative to pure iron cannot be reconciled by an Fe-C liquid. Therefore, the Earth's core cannot be approximated by the system Fe-C and should include another light element.
A modified electrolyte non-random two-liquid model with analytical expression for excess enthalpy: Application to the MEA-H 2 O-CO 2 system
We report accurate thermodynamic properties of electrolyte systems are critical for the design and operation of many chemical processes. A comprehensive description of the thermodynamic framework for multi-electrolyte mixed solvent systems is presented, where the parameter structure of the symmetric electrolyte-Non-Random Two Liquid (e-NRTL) model is reformulated and a thermodynamically consistent and analytically derived formulation for the excess enthalpy is developed from the e-NRTL model. The refined parameter structure of the e-NRTL model avoids numerical singularities of the analytical formulation for the excess enthalpy in the absence of ionic species and extends the derived excess enthalpy formulation to non-electrolyte systems. The thermodynamic framework is demonstrated for the MEA-H 2 O-CO 2 case study using experimental data on thermodynamic quantities for the binary MEA-H 2 O system and the ternary MEA-H 2 O-CO 2 system. The model is implemented in Pyomo and will be available for release in the Institute for the Design of Advanced Energy Systems (IDAES) computational platform.
Computational investigation of water glasses using machine-learning potentials
The molecular origins of water’s anomalous properties have long been a subject of scientific inquiry. The liquid–liquid phase transition hypothesis, which posits the existence of distinct low-density and high-density liquid states separated by a first-order phase transition terminating at a critical point, has gained increasing experimental and computational support and offers a thermodynamically consistent framework for many of water’s anomalies. However, experimental challenges in avoiding crystallization near the postulated liquid–liquid critical point have focused attention to water’s canonical glassy states: low-density and high-density amorphous ice. Here, we use two Deep Potential machine-learning models, trained on the Strongly Constrained and Appropriately Normed density functional and the highly accurate Many-Body Polarizable potential, to conduct an investigation of water’s glassy phenomenology based on quantum mechanical calculations. Despite not being explicitly trained on amorphous ices, both models accurately capture the structure and transformation of the water glasses, including their interconversion along different thermodynamic paths. Isobaric quenching of liquid water at various pressures generates a continuum of intermediate amorphous ices and density fluctuations increase near the liquid–liquid critical pressure. The glass transition temperatures of the amorphous ices produced at different pressures exhibit two distinct branches, corresponding to low-density and high-density amorphous ice behaviors, consistent with experiment and the liquid–liquid transition hypothesis. Extrapolating transformation pressures from isothermal compressions to experimental compression rates brings our simulations into excellent agreement with data. Our findings demonstrate that machine-learning potentials trained on equilibrium phases can effectively model nonequilibrium glassy behavior and pave the way for studying long-timescale, out-of-equilibrium processes with quantum mechanical accuracy.