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Molten Salt Species Solubility Calculations Using Thermochimica's Gibbs Energy Minimizer (GEM)
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Monitoring the Structural Health of the Stage-Four Gibbs Resistor In Order to Maintain a Functioning Pulse-Forming Network
The Dual-Axis Radiographic Hydrodynamic Test (DARHT) facility at Los Alamos National Laboratory (LANL) is a critical facility used for nuclear weapons research and development (Los Alamos National Laboratory). Its primary function is to provide high-resolution, real-time images of the behavior of materials under extreme conditions, specifically during the hydrodynamic testing of nuclear weapons surrogates. The facility uses advanced radiographic techniques, such as dual-axis X-ray imaging, to capture detailed snapshots of these materials as they react to high-pressure environments. DARHT plays a key role in maintaining the safety, security, and reliability of the U.S. nuclear arsenal, supporting the Stockpile Stewardship Program. The facility helps ensure that nuclear weapons perform as designed without the need for nuclear tests. Its dual-axis radiography provides more precise data than traditional single-axis imaging, offering a comprehensive view of the internal dynamics of a weapon's primary stage.
Resource Estimates for Lindbladian-Based Gibbs State Preparation on Fault-Tolerant Quantum Computers
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Gibbs' third variational principle in statistical thermodynamics
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Elimination of Gibbs' phenomena from error analysis of finite element results
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On the Gibbs phenomenon 5: Recovering exponential accuracy from collocation point values of a piecewise analytic function
The paper presents a method to recover exponential accuracy at all points (including at the discontinuities themselves), from the knowledge of an approximation to the interpolation polynomial (or trigonometrical polynomial). We show that if we are given the collocation point values (or a highly accurate approximation) at the Gauss or Gauss-Lobatto points, we can reconstruct a uniform exponentially convergent approximation to the function f(x) in any sub-interval of analyticity. The proof covers the cases of Fourier, Chebyshev, Legendre, and more general Gegenbauer collocation methods.
Steps in Solution Growth: Revised Gibbs-Thomson Law, Turbulence and Morphological Stability
Two groups of new phenomena revealed by AFM and high resolution optical interferometry on crystal faces growing from solutions will be discussed. 1. Spacing between strongly polygonized spiral steps with low less than 10(exp -2) kink density on lysozyme and K- biphtalate do not follow the Burton-cabrera-Frank theory. The critical length of the yet immobile first Short step segment adjacent to a pinning defect (dislocation, stacking fault) is many times longer than that following from the step free energy. The low-kink density steps are typical of many growth conditions and materials, including low temperature gas phase epitaxy and MBE. 2. The step bunching pattern on the approx. 1 cm long { 110) KDP face growing from the turbulent solution flow (Re (triple bonds) 10(exp 4), solution flow rate approx. 1 m/s) suggests that the step bunch height does not increase infinitely as the bunch path on the crystal face rises, as is usually observed on large KDP crystals. The mechanism controlling the maximal bunch width and height is based on the drag of the solution depleted by the step bunch down thc solution stream. It includes splitting, coagulation and interlacing of bunches
What Would Gibbs Do If he Were Thinking of Nucleation of Protein Solid Phases
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Thermodynamics and its prediction and CALPHAD modeling: Review, state of the art, and perspectives
Thermodynamics is a science concerning the state of a system, whether it is stable, metastable, or unstable, when interacting with its surroundings. The combined law of thermodynamics derived by Gibbs about 150 years ago laid the foundation of thermodynamics. In Gibbs combined law, the entropy production due to internal processes was not included, and the 2nd law was thus practically removed from the Gibbs combined law, so it is only applicable to systems under equilibrium, thus commonly termed as equilibrium or Gibbs thermodynamics. Gibbs further derived the classical statistical thermodynamics in terms of the probability of configurations in a system in the later 1800's and early 1900's. With the quantum mechanics (QM) developed in 1920's, the QM-based statistical thermodynamics was established and connected to classical statistical thermodynamics at the classical limit as shown by Landau in the 1940's. In 1960's the development of density functional theory (DFT) by Kohn and co-workers enabled the QM prediction of properties of the ground state of a system. On the other hand, the entropy production due to internal processes in non-equilibrium systems was studied separately by Onsager in 1930's and Prigogine and co-workers in the 1950's. In 1960's to 1970's the digitization of thermodynamics was developed by Kaufman in the framework of the CALculation of PHAse Diagrams (CALPHAD) modeling of individual phases with internal degrees of freedom. CALPHAD modeling of thermodynamics and atomic transport properties has enabled computational design of complex materials in the last 50 years. Our recently termed zentropy theory integrates DFT and statistical mechanics through the replacement of the internal energy of each individual configuration by its DFT-predicted free energy. The zentropy theory is capable of accurately predicting the free energy of individual phases, transition temperatures and properties of magnetic and ferroelectric materials with free energies of individual configurations solely from DFT-based calculations and without fitting parameters, and is being tested for other phenomena including superconductivity, quantum criticality, and black holes. Those predictions include the singularity at critical points with divergence of physical properties, negative thermal expansion, and the strongly correlated physics. Furthermore, those individual configurations may thus be considered as the genomic building blocks of individual phases in the spirit of the materials genome®. This has the potential to shift the paradigm of CALPHAD modeling from being heavily dependent on experimental inputs to becoming fully predictive with inputs solely from DFT-based calculations and machine learning models built on those calculations and existing experimental data through newly developed and future open-source tools. Furthermore, through the combined law of thermodynamics including the internal entropy production, it is shown that the kinetic coefficient matrix of independent internal processes is diagonal with respect to the conjugate potentials in the combined law, and the cross phenomena that the phenomenological Onsager flux and reciprocal relationships are due to the dependence of the conjugate potential of a molar quantity on nonconjugate molar quantities and other potentials, which can be predicted by the zentropy theory and CALPHAD modeling.
Thermodynamic modeling of CsF with LiF-NaF-KF for molten fluoride-fueled reactors
Gibbs energy models were developed to describe the thermochemical behavior of CsF in molten FLiNaK (46.5LiF-11.5NaF-42KF mol%), a proposed molten salt reactor (MSR) fuel solvent and coolant, as cesium is of concern due to its high radiotoxicity and volatility. Initially, it was necessary to obtain a more accurate Gibbs energy function for CsF which required fitting parameters to reported vapor pressures over condensed phase CsF. The pseudo-binary systems CsF-LiF, CsF-NaF and CsF-KF were then evaluated utilizing phase equilibria and enthalpy of mixing (Δ mix H) values, together with original differential scanning calorimetry (DSC) measurements performed for the CsF-LiF and CsF-KF systems. The CsF-LiF-NaF, CsF-LiF-KF and CsF-NaF-KF pseudo-ternary system representations were obtained by interpolation of the constituent pseudo-binary systems, with DSC measurements performed for the CsF-LiF-NaF system to corroborate the calculated liquidus temperature. Ultimately, the pseudo-ternary systems were interpolated to obtain Gibbs energy models for the pseudo-quaternary CsF-LiF-NaF-KF system, supported by DSC measurements at low CsF compositions (1–10 mol%), yielding computed equilibria and cesium-containing vapor pressures that compare favorably with reported values. In conclusion, the Molten Salt Thermal Properties Database – Thermochemical (MSTDB-TC) was subsequently expanded to include these Gibbs energy models allowing description of the thermochemical behavior of the CsF-LiF-NaF-KF system.
dGPredictor: Automated fragmentation method for metabolic reaction free energy prediction and de novo pathway design
Group contribution (GC) methods are conventionally used in thermodynamics analysis of metabolic pathways to estimate the standard Gibbs energy change ( Δ r G ′ o ) of enzymatic reactions from limited experimental measurements. However, these methods are limited by their dependence on manually curated groups and inability to capture stereochemical information, leading to low reaction coverage. Herein, we introduce an automated molecular fingerprint-based thermodynamic analysis tool called dGPredictor that enables the consideration of stereochemistry within metabolite structures and thus increases reaction coverage. dGPredictor has comparable prediction accuracy compared to existing GC methods and can capture Gibbs energy changes for isomerase and transferase reactions, which exhibit no overall group changes. We also demonstrate dGPredictor’s ability to predict the Gibbs energy change for novel reactions and seamless integration within de novo metabolic pathway design tools such as novoStoic for safeguarding against the inclusion of reaction steps with infeasible directionalities. To facilitate easy access to dGPredictor, we developed a graphical user interface to predict the standard Gibbs energy change for reactions at various pH and ionic strengths. The tool allows customized user input of known metabolites as KEGG IDs and novel metabolites as InChI strings ( https://github.com/maranasgroup/dGPredictor ).
Impact of Anions and Water Content on [Li–Al] Layered Double-Hydroxide Stability
[Li–Al] layered double hydroxides (LDHs) are compounds with potential as sorbents for lithium extraction from brine solutions. Here, in this work, heat capacities were measured from approximately 2.5 to 300 K for six [Li–Al] LDHs with differing anions (Cl – , OH – , and SO 4 2– ) and water content (denoted A for air-dried and O for oven-dried). These measurements were used to calculate the standard entropy at 298.15 K, and the results were combined with previously performed enthalpy measurements to calculate Gibbs energies of formation from the binary compounds. The calculated order of stability based on Gibbs energies of formation was Cl-LDH-O > OH-LDH-O > Cl-LDH-A > SO 4 -LDH-O > SO 4 -LDH-A > OH-LDH-A. Results support previous findings that higher water content generally raises the Gibbs energy of the LDH.
Predicting Melt Curves of Energetic Materials Using Molecular Models
Here, in this work, the solid–liquid coexistence curves of classical fully flexible atomistic models of α-RDX and β-HMX were calculated using thermodynamically rigorous methodologies that identify where the free energy difference between the phases is zero. The free energy difference between each phase at a given state point was computed using the pseudosupercritical path (PSCP) method, and Gibbs–Helmholtz integration was used to evaluate the solid–liquid free energy difference as a function of temperature. This procedure was repeated for several pressures to determine points along the coexistence curve, which were then fit to the Simon–Glatzel functional form. While effective, this method is computationally expensive. An alternative approach is to compute the melting point at a single pressure via the PSCP method, and then use the Gibbs–Duhem integration technique to trace out the coexistence curve in a more computationally economical manner. Both approaches were used to determine the coexistence curve of α-RDX. The Gibbs–Duhem integration method was shown to generate a melt curve that is in good agreement with the PSCP-derived melt curve, while only costing ~10 % of the computational resources used for the PSCP method. For α-RDX, the predicted melting temperature increases significantly more for a given increase in pressure when compared to available experimental data.
A Bayesian Framework for Spectral Reprojection
Abstract Fourier partial sum approximations yield exponential accuracy for smooth and periodic functions, but produce the infamous Gibbs phenomenon for non-periodic ones. Spectral reprojection resolves the Gibbs phenomenon by projecting the Fourier partial sum onto a Gibbs complementary basis, often prescribed as the Gegenbauer polynomials. Noise in the Fourier data and the Runge phenomenon both degrade the quality of the Gegenbauer reconstruction solution, however. Motivated by its theoretical convergence properties, this paper proposes a new Bayesian framework for spectral reprojection, which allows a greater understanding of the impact of noise on the reprojection method from a statistical point of view. We are also able to improve the robustness with respect to the Gegenbauer polynomials parameters. Finally, the framework provides a mechanism to quantify the uncertainty of the solution estimate.
Modeling aqueous association constants and mineral solubilities at subcritical and supercritical temperatures
The need for sustainable power generation has increased interest in the use of hydrothermal fluids for industrial applications. New high-enthalpy geothermal systems and biowaste-to-fuel processes are two relevant examples that employ supercritical fluids which require an in-depth understanding of complex chemical reactions occurring near the supercritical temperature of water (374 °C). As these processes operate in thermodynamic regimes that are not currently covered by a standard molar Gibbs energy of formation model, only empirical fits for single reaction systems are available which limit the use of multi-component phase equilibria calculations that are standard practice for less extreme environments. Here, in this paper, we advance a standard molar Gibbs energy of formation model able to operate in these otherwise inaccessible thermodynamic states to include species needed for key mineral solubility systems and ion association reactions. This work extends a model based on molecular statistical thermodynamics (MST) into four new systems (Na 3 PO 4 -H 2 O, LiOH-H 2 O, KOH-H 2 O, and BaSO 4 -H 2 O) by extending the model to cover 10 new species. For each of these systems, model predictions were consistently within the experimental uncertainties for the new systems covered. A breakdown of MST contributions to the model revealed that electrostatic and hard sphere contributions were key to reproducing density dependencies of standard molar Gibbs energy of formation values around the critical point of water.
Thermal Weight Determination and Interstate Coupling in State-Averaged ADAPT-VQE
Characterizing electronic thermal states at low temperatures is an important but challenging task in quantum chemistry and condensed matter physics, making it a prime candidate for a useful application in quantum computing. One of the most successful methods for state preparation on quantum computers is the Adaptive, Problem-Tailored (ADAPT) Variational Quantum Eigensolver (VQE), which has recently been generalized to treat excited states within a state-averaged framework as well as Gibbs states. In this work, we introduce Helmholtz-Optimized Thermal (HOT) ADAPT-VQE, an ancilla-free strategy for preparing Gibbs states that directly minimizes the Helmholtz free energy by targeting the dominant eigenstates of the thermal ensemble. We demonstrate the usefulness of HOT-ADAPT-VQE by predicting the free energy of two model systems with strongly correlated ground states: (1) the Fe 2+ cation in a magnetic field and (2) a [Cu 2 O 7 ] 10– fragment of the Mott insulator La 2 CuO 4 . Our results demonstrate that HOT-ADAPT-VQE significantly improves upon Gibbs-state estimates from multistate variants of ADAPT-VQE, often with substantially shallower quantum circuits, making it a promising candidate for thermal-state calculations.
Semi-empirical model for Henry’s law constant of noble gases in molten salts
Henry’s law constant, which describes the proportionality of dissolved gas to partial pressure of free gas in liquid–gas equilibrium systems, can also be applied to mass transport applications. In this work, we investigated an approach for determining the solubility of noble gases in a molten salt liquid utilizing the equilibrium concept of Henry’s gas constant. Henry’s gas constant is described as a mathematical function dependent on the van der Waals radius of the noble gas and the temperature of the molten salt. The alteration in Gibbs free energy encompasses contributions from both surface and volume energies. Enthalpy and entropy are deduced from these surface and volume energies in the Gibbs free energy formulation. A comparative analysis was conducted between the conventional method and our proposed model. Moreover, useful chemical properties can be determined from examination of surface and volume energies. Our findings provide an accurate and general theory of Gibbs free energy that can be validated experimentally based on the model proposed herein. This work unifies the prediction of Henry gas constant and subsequently the entropy and enthalpy calculation for noble gases in a molten salt solution to a single functional form using van der Waals radius of the gas and temperature of the system. This functional form is then used to perform a multiple regression method to find two parameters corresponding to the surface energy and volume energy. These two parameters are consistent between all combinations of noble gas and molten salt.