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At least 109 records · Page 6

A Thermodynamic Model for ZrO 2 (am) Solubility at 25 °C in the Ca 2+ –Na + –H + –Cl - –OH - –H 2 O System: A Critical Review

Zirconium is an important element in the nuclear fuel cycle. Thermodynamic data and models to reliably predict Zr-OH system behavior in various conditions including high ionic strengths are required and currently are unavailable. Most available experimental data are rather old, obtained using inadequate methodologies, and provide equilibrium constant values that differ by many orders of magnitude. Previous reviews have recommended values based on available data. These reviews used all of the available data, including poor quality data, in a global fit to determine these values. This has resulted in recommended thermodynamic models with a large number of polynuclear species and a number of mononuclear species with values of thermodynamic constants for the solubility product of ZrO 2 (am) and Zr-OH hydrolysis constants that are many orders of magnitude different than those for the reliable analogous Hf reactions. In this critical review, we have evaluated the quality of the available data, selected only those data that are of high quality, and reinterpreted all of the high quality data using SIT and Pitzer models for applications to high ionic strength solutions. Herein for 25°C we 1) present formation constant values for ZrOH 3+ , Zr(OH) 2+ 2 , Zr(OH) 4 (aq), Zr(OH) 5 - , and Zr(OH) 6 2- , and the solubility product for ZrO 2 (am) which are consistent with the Hf system, 2) report a revised value for the formation of Ca 3 Zr(OH) 6 4+ , 3) show that several hypothetical polynuclear species (Zr 3 (OH) 9 3+ , Zr 4 (OH) 15 + , and Zr 4 (OH) 16 (aq)) proposed in previous reviews are not needed, and 4) show that polynuclear species (Zr 3 (OH) 4 8+ and Zr 4 (OH) 8 8+ ) are not important in a very extensive H + concentration range (0.1 to 10 -15.4 mol·kg -1 ). Our review has also resulted in SIT and Pitzer ion-interaction parameters applicable to as high ionic strength solutions as 5.6 mol·kg -1 in NaCl, 2.11 mol·kg -1 in CaCl 2 , and 23.5 mol·kg -1 in NaOH.

solubility, ZrO2(am), solubility product, thermody↗

First-principles calculations and thermodynamic modeling of the Yb-Ni binary system

A complete thermodynamic description of the Yb-Ni binary system is developed by means of the CALculation of PHAse Diagram (CALPHAD) method in combination with first-principles calculations based on density functional theory (DFT) and available experimental data in the literature. Finite temperature thermodynamic properties of the Yb-Ni intermetallic compounds are predicted using the quasi-harmonic approach, where first-principles phonon calculations are performed to calculate the lattice vibrational entropy. Here, the associate solution model is used to describe the complex thermodynamic behavior of the liquid phase. The calculated phase diagram agrees well the experimental phase equilibrium data in the literature. By the coupling of CALPHAD modeling with first-principles calculations, the present work provides a more thermodynamically accurate model of the Yb-Ni system when compared to previous models.

36 MATERIALS SCIENCE↗

Thermodynamic Model of Solvent Effects in Semiflexible Diblock and Random Copolymer Assembly

Here, we present a field-theoretic model to predict the equilibrium thermodynamic behavior of semiflexible diblock copolymers and random copolymers in the presence of solvent. We find that in both systems polymer–solvent contacts dramatically influence the thermodynamic behavior with decreasing the copolymer segment length (i.e., molecular weight). When a copolymer has unequal monomer composition, both polymer length and solvent concentration have a strong influence on the phase transition spinodal and magnitude of the critical wave modes. Diblock copolymers exhibit an expanded region of the lamellar phase in the phase diagram with decreasing chain length and polymer concentration. Such effects suggest a breakdown of the dilute approximation for solutions of short diblock copolymers. Random copolymer solutions also exhibit changes in the phase-transition spinodal and critical wave mode at asymmetric chemical compositions. This effect is highly relevant to most random copolymer materials, since a monomer is typically a low-molecular-weight chemical unit.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Solute induced relaxation in glassy polymers: Experimental measurements and nonequilibrium thermodynamic model

Data for kinetics of mass uptake from vapor sorption experiments in thin glassy polymer samples are here interpreted in terms of relaxation times for volume dilation. To this result, both models from non-equilibrium thermodynamics and from mechanics of volume relaxation contribute. Different kind of sorption experiments have been considered in order to facilitate the direct comparison between kinetics of solute induced volume dilation and corresponding data from process driven by pressure or temperature jumps.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

High-Temperature Thermodynamics Modeling of Graphite

We present high-temperature thermodynamic properties for graphite from first-principles anharmonic theory. The ab initio electronic structure is obtained from density-functional theory coupled to a lattice dynamics method that is used to model anharmonic lattice vibrations. This combined approach produces free energies and specific heats for graphite that compare well with available experiments and results from models that empirically represent experimental data, such as CALPHAD. We show that anharmonic theory for the phonons is essential for accurate thermodynamic quantities above about 1000 K.

36 MATERIALS SCIENCE↗

An improved thermodynamic model for the complexation of trivalent actinides and lanthanide with oxalic acid valid to high ionic strength.

The dissociation constants of oxalic acid (Ox), and the stability constants of Am 3+ , Cm 3+ and Eu 3+ with Ox 2– have been determined at 25 °C, over a range of concentration varying from 0.1 to 6.60 m NaClO4 using potentiometric titration and extraction techniques, respectively. The experimental data support the formation of complexes, M(Ox) n 3 – 2n , where (M = Am 3+ , Cm 3+ and Eu 3+ and n = 1 and 2). The dissociation constant and the stability constant values measured as a function of NaClO 4 concentration were used to estimate the Pitzer parameters for the respective interactions of Am 3+ , Cm 3+ and Eu 3+ with Ox. Furthermore, the stability constants data of Am 3+ –Ox measured in NaClO 4 and in NaCl solutions from the literature were simultaneously fitted in order to refine the existing actinide–oxalate complexation model that can be used universally in the safety assessment of radioactive waste disposal. The thermodynamic stability constant: log β 0 101 = 6.30 ± 0.06 and log β 0 102 = 10.84 ± 0.06 for Am 3+ was obtained by simultaneously fitting data in NaCl and NaClO 4 media. Additionally, log β 0 101 = 6.72 ± 0.08 and log β 0 102 = 11.05 ± 0.09 for the Cm 3+ and log β 0 101 = 6.67 ± 0.08 and log β 0 102 = 11.15 ± 0.09 for the Eu 3+ were calculated by extrapolation of data to zero ionic strength in NaClO 4 medium only. For all stability constants, the Pitzer model gives an excellent representation of the data using interaction parameters β (0) , β (1) , and CΦ determined in this work. The thermodynamic model developed in this work will be useful in accurately modeling the potential solubility of trivalent actinides and early lanthanides to ionic strength of 6.60 m in low temperature environments in the presence of Ox. Furthermore, the work is also applicable to the accurate modeling transport of rare earth elements in various environments under the surface conditions.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Experimental investigation and thermodynamic modeling of the binary Pt–Sn system

Here, the thermodynamics of the Pt–Sn system is revisited with attention to phase equilibria involving PtSn 4 , a topological quantum material with interesting physical properties. The phase relationship in the Sn-rich region of the Pt–Sn binary system was investigated by a combination of differential scanning calorimetry and equilibration experiments. Based on the present experiments and a critical evaluation of the available thermodynamic and phase diagram data reported in the literature, thermodynamic assessments of the entire Pt–Sn system were performed using the CALPHAD approach. Two sets of thermodynamic parameters were optimized, where the liquid phase was described using the Bragg-Williams random mixing model and the associate solution model, respectively. The modeling results are compared with the reliable experimental data and are shown to provide good representations of the phase equilibria and thermodynamic properties in this system.

36 MATERIALS SCIENCE↗

Ab Initio Thermodynamic Model for Magnesium Carbonates and Hydrates

An ab initio thermodynamic framework for predicting properties of hydrated magnesium carbonate minerals has been developed using density-functional theory linked to macroscopic thermodynamics through the experimental chemical potentials for MgO, water, and CO2. Including semiempirical dispersion via the Grimme method and small corrections to the generalized gradient approximation of Perdew, Burke, and Ernzerhof for the heat of formation yields a model with quantitative agreement for the benchmark minerals brucite, magnesite, nesquehonite, and hydromagnesite. The model shows how small differences in experimental conditions determine whether nesquehonite, hydromagnesite, or magnesite is the result of laboratory synthesis from carbonation of brucite, and what transformations are expected to occur on geological time scales. Because of the reliance on parameter-free first principles methods, the model is reliably extensible to experimental conditions not readily accessible to experiment and to any mineral composition for which the structure is known or can be hypothesized, including structures containing defects, substitutions, or transitional structures during solid state transformations induced by temperature changes or processes such as water, CO2, or O2 diffusion. Demonstrated applications of the ab initio thermodynamic framework include an independent means to evaluate differences in thermodynamic data for lansfordite, predicting the properties of Mg analogs of Ca-based hydrated carbonates monohydrocalcite and ikaite which have not been observed in nature, and an estimation of the thermodynamics of barringtonite from the stoichiometry and a single experimental observation.

Environmental Molecular Sciences Laboratory↗

Thermodynamic modeling of the Pd–Zn system with uncertainty quantification and its implication to tailor catalysts

Pd–Zn intermetallic catalysts show encouraging combinations of activity and selectivity on well-defined active site ensembles. Thermodynamic description of the Pd–Zn system, delineating phase boundaries and enumerating site occupancies within intermediate alloy phases, is essential to determining the ensembles of Pd–Zn atoms as a function of composition and temperature. Combining the present extensive first-principles calculations based on density functional theory (DFT) and available experimental data, the Pd–Zn system was remodeled using the CALculation of PHAse Diagrams (CALPHAD) approach. High throughput modeling tools with uncertainty quantification, i.e., ESPEI and PyCalphad, were incorporated in the phase analysis. Here, the site occupancies across the γ phase composition region were given special attention. A four-sublattice model was used for the γ phase owing to its four Wyckoff positions, i.e., the outer tetrahedral (OT) site 8c, the inner tetrahedral (IT) site 8c, the octahedral (OH) site 12e, and the cuboctahedral (CO) site 24g. The site fractions of Pd and Zn calculated from the present thermodynamic model show the occupancy preference of Pd in the OT and OH sublattices in agreement with experimental observations. The force constants obtained from DFT-based phonon calculations further supports the tendency of Pd occupying the OH sublattice compared with the IT and CO sublattice. The catalytic ensembles changing from Pd monomers (Pd 1 ) to trimers (Pd 3 ) on the surface of γ phase are attributed to the increase of Pd occupancy in the OH sublattice.

36 MATERIALS SCIENCE↗

Thermodynamic Model of COREX Melter Gasifier Using FactSage™ and Macro Facility

In the current study, the thermochemical model of the COREX melter gasifier has been developed using the FactSage™ thermodynamic software, and macro programming facility. The melter gasifier was conceptually divided into various equilibrium zones dealing with the reactions happening in the reactor. The coal char and the coke being used are divided among them optimally. The model has been validated with respect to the plant data for the hot-metal, slag, and reducing gas composition. The effects of the variation in the degree of metallization, on the final hot metal, slag, and reducing gas, have been predicted using this model. The variations in the process parameters for the different industrial coal grades used in the COREX plant have been determined. The effects of the volatile, ash, and the moisture contents of the coal on the hot-metal and the reducing gas compositions have been reported.

36 MATERIALS SCIENCE↗

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↗

A coupled dynamic-thermodynamic model of an ice-ocean system in the marginal ice zone

Thermodynamics are incorporated into a coupled ice-ocean model in order to investigate wind-driven ice-ocean processes in the marginal zone. Upswelling at the ice edge which is generated by the difference in the ice-air and air-water surface stresses is found to give rise to a strong entrainment by drawing the pycnocline closer to the surface. Entrainment is shown to be negligible outside the areas affected by the ice edge upswelling. If cooling at the top is included in the model, the heat and salt exchanges are further enhanced in the upswelling areas. It is noted that new ice formation occurs in the region not affected by ice edge upswelling, and it is suggested that the high-salinity mixed layer regions (with a scale of a few Rossby radii of deformation) will overturn due to cooling, possibly contributing to the formation of deep water.

Hakkinen, Sirpa↗

VESIcal Part I: An open-source thermodynamic model engine for mixed volatile (H2O-CO2) solubility in silicate melts

Thermodynamics has been fundamental to the interpretation of geologic data and modeling of geologic systems for decades. However, more recent advancements in computational capabilities and a marked increase in researchers’ accessibility to computing tools has outpaced the functionality and extensibility of currently available modeling tools. Here we present VESIcal (Volatile Equilibria and Saturation Identification calculator): the first comprehensive modeling tool for H 2 O, CO 2 , and mixed (H 2 O-CO 2 ) solubility in silicate melts that: a) allows users access to seven commonly used models, plus easy inter-comparison between models; b) provides universal functionality for all models (e.g., functions for calculating saturation pressures, degassing paths, etc.); c) can process large datasets (1,000’s of samples) automatically; d) can output computed data into an excel spreadsheet for simple post-modeling analysis; e) integrates advanced plotting capabilities directly within the tool; and f) provides all of these within the framework of a python library, making the tool extensible by the user and allowing any of the model functions to be incorporated into any other code capable of calling python. The tool is presented within this manuscript, which is a Jupyter notebook containing worked examples accessible to python users with a range of skill levels. The basic functions of VESIcal can also be access via a web app (https://vesical.anvil.app). The VESIcal python library is open-source and available for download at https://github.com/kaylai/VESIcal.

K. Iacovino↗

First-Principles Calculations, Experimental Study, and Thermodynamic Modeling of the Al-Co-Cr System

The phase relations and thermodynamic properties of the condensed Al-Co-Cr ternary alloy system are investigated using first-principles calculations based on density functional theory (DFT) and phase-equilibria experiments that led to X-ray diffraction (XRD) and electron probe micro-analysis (EPMA) measurements. A thermodynamic description is developed by means of the calculations of phase diagrams (CALPHAD) method using experimental and computational data from the present work and the literature. Emphasis is placed on modeling the bcc-A2, B2, fcc-γ, and tetragonal-σ phases in the temperature range of 1173 to 1623 K. Liquid, bcc-A2 and fcc-γ phases are modeled using substitutional solution descriptions. First-principles special quasirandom structures (SQS) calculations predict a large bcc-A2 (disordered)/B2 (ordered) miscibility gap, in agreement with experiments. A partitioning model is then used for the A2/B2 phase to effectively describe the order-disorder transitions. The critically assessed thermodynamic description describes all phase equilibria data well. A2/B2 transitions are also shown to agree well with previous experimental findings.

36 MATERIALS SCIENCE↗

Thermodynamic modeling of countercurrent chemical looping reverse water gas shift process for redox material screening

The reverse water gas shift (RWGS) reaction is a key pathway for CO 2 utilization, particularly within Power-to-X process chains aimed at sustainable fuel and chemical production. Countercurrent chemical looping (CL-RWGS) using non-stoichiometric oxides can overcome equilibrium limitations of conventional RWGS reactors, enabling significantly higher CO 2 conversions. However, modeling the limiting performance of such systems is challenging due to their multiphase nature and coupled spatial and temporal variation in chemical composition. In this work, we present a discretized batch equilibrium model that simulates CL-RWGS reactors as a series of localized equilibrium exchanges between gas and solid elements. The model is numerically stable, computationally efficient, and free of kinetic source terms, making it well-suited for parametric studies and system-level integration. It is validated against established convection–diffusion models and shown to predict reasonable upper bounds on experimental results. Application of the model to a range of oxygen carrier materials identifies cerium–zirconium solid solutions, particularly Ce 0.80 Zr 0.20 O 2 , as a promising class offering superior oxygen storage characteristics compared to state-of-the-art La 0.6 Sr 0.4 FeO 3 . This framework provides a robust platform for materials screening, reactor sizing, and performance optimization in chemical looping systems. The model implementation is available as open-source software to support further research and development.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Thermodynamic Modeling and Optimization of the Copper Flash Converting Process Using the Equilibrium Constant Method

Based on the principle of multiphase equilibrium, a mathematical model of the copper flash converting process was established by the equilibrium constant method, and a computational system was developed with the use of MetCal software platform. The mathematical model was validated by comparing simulated outputs, industrial data, and published data. To obtain high-quality blister copper, a low copper content in slag, and increased impurity removal rate, the model was then applied to investigate the effects of the operational parameters [oxygen/feed ratio (R{sub OF}), flux rate (R{sub F}), and converting temperature (T)] on the product weights, compositions, and the distribution behaviors of impurity elements. The optimized results showed that R{sub OF}, R{sub F}, and T should be controlled at approximately 156 Nm{sup 3}/t, within 3.0 pct, and at approximately 1523 K (1250 °C), respectively.

36 MATERIALS SCIENCE↗