Excess Gibbs Energy Research Articles

Critical systematic investigation of the Cd–Ce system: phase stability and Gibbs energies of formation and equilibria via thermodynamic description

Abstract The CALPHAD (CAlculation of PHAse Diagrams) technique is used in the critical remodeling of the Cd–Ce system. On the basis of new experimental data in the literature, the excess Gibbs energies of the solution phase expression (liquid, bcc, fcc, and hcp_A3) are described using the Redlich–Kister equation. Four compounds (Cd3Ce, Cd6Ce, Cd11Ce, and Cd17Ce2) are treated as stochiometric compounds. Two intermetallic compounds (Cd2Ce and Cd58Ce13), which exhibit a little homogeneity range, are treated as a two-sublattice model. Two thermodynamic models are used for the CdCe and bcc. Model I is to model the compound CdCe and bcc-Ce separately. Model II is to use the formula (Cd, Ce)0.5(Cd, Ce)0.5(Va)3 to describe the compound CdCe with a CsCl-type structure (B2) and cope with the disorder–order transition from bcc-A2 to bcc-B2. The present work shows that four eutectic reactions, three peritectic reactions, two eutectoid reactions, one peritectoid transformation and three congruent reactions are observed, and the stoichiometric compound Cd17Ce2 is only stable from 804 to 882 °C in the Cd–Ce system.

Discrete Modeling Approach for Cluster-Based Excess Gibbs-Energy of Molecular Liquids.

The excess Gibbs-energy of a two-component liquid molecular mixture is modeled based on discrete clusters of molecules. These clusters preserve the three-dimensional geometric information about local molecule neighborhoods that inform the interaction energies of the clusters. In terms of a discrete Markov-chain, the clusters are used to hypothetically construct the mixture using sequential insertion steps. Each insertion step and, therefore, cluster is assigned a probability of occurring in an equilibrium system that is determined via the constrained minimization of the Helmholtz free energy. For this, informational Shannon entropy based on these probabilities is used synonymously with thermodynamic entropy. A first approach for coupling the model to real molecules is introduced in the form of a molecular sampling algorithm, which utilizes a force-field approach to determine the energetic interactions within a cluster. An exemplary application to four mixtures shows promising results regarding the description of a variety of excess Gibbs-energy curves, including the ability to distinguish between structural isomers.

A Numerical Algorithm for Calculating Critical Points and Its Application to Predictive Mixture Models and Binary CO_2 Mixtures

The use of supercritical fluids in technical applications requires an accurate knowledge of their critical points. For mixtures, these can deviate significantly and without a linear dependency from the critical points of its individual pure components. Since even small amounts of admixture can have noticeable effects, this not only concerns blends of targeted compositions, but also unintentional mixtures for example caused by impurities. Within this work, a method for the calculation of critical points is presented which focuses on numerical robustness promoting a fast and reliable generation of results. Implemented into the thermodynamic property software TREND, with its mixture modeling capabilities, the method allows a flexible combination of different equations of state and mixture models which also includes predictive approaches. Against the background of an increasing relevance of mixtures based on supercritical CO_2 (sCO_2) for energy applications, critical lines are calculated and compared against experimental results for selected sCO_2-based mixtures recently considered for power plant applications. Herein, several combinations of equations of state (EoS) and mixture models are compared. Critical lines are calculated for the first time in this work with the combination of the multi-fluid mixture model with excess Gibbs energy (g^text {E}) models. It was found that the critical lines calculated with the combination of the multi-fluid mixture model with the g^text {E}-model COSMO-SAC yields good predictive results for the investigated CO_2 mixtures.

Thermodynamic properties of the BaO-Al2O3 system

Synthesis of the samples in the BaO-Al2O3 system was carried out by solid state synthesis method at the temperature 1250 °C (all samples) and 1500 °C (samples NN 5–10). The characterization of the samples was performed with the use of XRD analysis. The vaporization and thermodynamic properties of BaO-Al2O3 system at 1815 °C from 0.10 to 0.90 Ba mole fractions have been studied by Knudsen effusion differential mass spectrometry.The formation enthalpies from the elements of Ba3Al2O6(s), BaAl2O4(s), BaAl12O19(s) were derived and the recommended values are the following: − 3515 ± 76, − 2338 ± 70 and − 10730 ± 25 kJ/mole respectively. The component activities, Gibbs energies of mixing and excess Gibbs energies were obtained. The thermodynamic properties of the BaO-Al2O3 system at high temperatures are characterized by the negative deviation from the ideal case.

Excess properties, spectral analyses, and CO2 capture performance of N-methyldiethanolamine + polyethylene glycol 300 binary system

Density (ρ) and viscosity (η) data of polyethylene glycol 300 (PEG300) + N-methyldiethanolamine (MDEA) binary system at T = (298.15–318.15) K with a step of 5 K were measured at P = 1005 hPa. After that, the experimental ρ and η values were correlated and predicted by several semi-empirical models. Meanwhile, the Jouyban-Acree model presented a better fitting for the density, and the McAllister four-body equation presented a better fitting for the kinematic viscosity. Based on the ρ and η values, excess molar volume (VmE), partial molar volume (V1¯ and V2¯), viscosity deviation (Δη), and excess Gibbs energy of activation of viscous flow (ΔG∗E) of PEG300 (1) + MDEA (2) binary system were systematically calculated and analyzed. These excess properties showed the predominance of intermolecular self-conjugation in PEG300 (1) + MDEA (2) binary system, and it was further demonstrated by various spectral characterizations. Importantly, the PEG300 + MDEA aqueous system was used for 5 CO2 absorption (room temperature)-desorption (371.15 K) cycles at a CO2 flow rate of 200 mL/min, with the average CO2 capture performance of 0.65 mol CO2/mol MDEA of per cycle, demonstrating excellent absorption capability, and remained stable throughout the entire cycle.

Ternary Mixed Micelle Hexadecyltrimethylammonium Bromide-Dodecyltrimethylammonium Bromide-Sodium Deoxycholate: Gibbs Free Energy of Mixing and Excess Gibbs Energy of Mixing.

Pharmaceutical, food, and cosmetic formulations often contain binary or ternary surfactant mixtures with synergistic interactions amongst micellar building blocks. Here, a ternary mixture of the surfactants hexadecyltrimethylammonium bromide, dodecyltrimethylammonium bromide, and sodium deoxycholate is examined to see if the molar fractions of the surfactants in the ternary mixed micellar pseudophase are determined by the interaction coefficients between various pairs of the surfactants or by their propensity to self-associate. Critical micelle concentrations (CMC) of the analyzed ternary mixtures are determined experimentally (spectrofluorimetrically using pyrene as the probe molecule). Thermodynamic parameters of ternary mixtures are calculated from CMC values using the Regular Solution protocol. The tendency for monocomponent surfactants to self-associate (lower value of CMC) determines the molar fractions of surfactant in the mixed micelle if there is no issue with the packing of the micelle building units of the ternary mixed micelle. If a more hydrophobic surfactant is incorporated into the mixed micelle, the system (an aqueous solution of surfactants) is then the most thermodynamically stabilized.

Basic physicochemical properties, excess properties, and intermolecular interactions of n-propanol/isopropanol and ethylenediamine binary mixtures

Density (ρ) and viscosity (η) values of binary mixtures composed of n-propanol/isopropanol and ethylenediamine (EDA) were measured at T = (298.15–318.15) K and P = 1005 hPa (atmospheric pressure in Tianjin, China). The excess properties, including viscosity deviation (Δη), excess molar volume (VmE), and excess Gibbs energy of activation of viscous flow (ΔG*E), were then obtained. The least-squares method and Jouyban–Acree model were used to correlate the experimental ρ values and kinematic viscosity associated with three semi-empirical models, and a superior fitting was obtained by comparing the model parameters. VmE, Δη, and ΔG*E were fitted to the Redlich–Kister equation, and partial molar volumes, apparent molar volumes, and viscous activation parameters of n-propanol/isopropanol and EDA binary mixtures were calculated. Raman spectroscopy, fluorescence spectroscopy (FLS), 1H NMR spectroscopy, and computational chemistry methods were used to demonstrate the existence of intermolecular hydrogen bonds (IHBs) in n-propanol/isopropanol and EDA binary mixtures, and the form of IHBs was confirmed as –OH···NH2–. Finally, the CO2 uptake rate was measured for binary mixtures at the molar fractions with strong intermolecular interactions.

Thermodynamic assessment of the Ga–Gd, Ga–Nb and Gd–Nb binary phase diagrams towards the Ga–Gd–Nb system

The present work gives a thermodynamic optimization of the Ga–Gd, Ga–Nb and Gd–Nb binary systems based on the CALPHAD method. Redlich-Kister polynomials are used to describe the excess Gibbs energy of the liquid phase and the solid solutions. The Ga2Gd (ϵ) and GaNb3 (A15) phases, which present a large homogeneity range, were described using a two-sublattice model with the formula (Ga)2(Ga,Gd)1 and (Nb)3(Ga,Nb)1 respectively. The remaining intermediate phases, ht_Ga4Nb, Ga3Nb, Ga13Nb5, Ga5 Nb4, Ga4 Nb5, Ga3Nb5, Ga6Gd, GaGd, Ga2Gd3 and Ga3Gd5, were treated as stoichiometric compounds. The generated thermodynamic parameters relative to the involved phases were critically discussed and used to build the Ga-Gd-Nb ternary system.

Thermodynamic Model of the Fluid System H2O–CO2–NaCl–CaCl2 at P-T Parameters of the Middle and Lower Crust

Based on the earlier obtained equations of state for the ternary systems H2O–CO2–CaCl2 and H2O–CO2–NaCl, an equation of state for the four-component fluid system H2O–CO2–NaCl–CaCl2 is derived in terms of the Gibbs excess free energy. A corresponding numerical thermodynamic model is built. The main part of the numerical parameters of the model coincides with the corresponding parameters of the ternary systems. The NaCl–CaCl2 interaction parameter was obtained from the experimental liquidus of the salt mixture. Similar to the thermodynamic models for H2O–CO2–CaCl2 and H2O–CO2–NaCl, the range of applicability of the model is pressure 1–20 kbar and temperature from 500 to 1400°C. The model makes it possible to predict the physicochemical properties of the fluid involved in most processes of deep petrogenesis: the phase state of the system (homogeneous or multiphase fluid, presence or absence of solid salts), chemical activities of the components, densities of the fluid phases, and concentrations of the components in the coexisting phases. The model was used for a detailed study of the phase state and activity of water on the H2O–CO2–salt sections when changing the ratio {{{{x}_{{{text{NaCl}}}}}} mathord{left/ {vphantom {{{{x}_{{{text{NaCl}}}}}} {({{x}_{{{text{NaCl}}}}} + {{x}_{{{text{CaC}}{{{text{l}}}_{{text{2}}}}}}})}}} right. kern-0em} {({{x}_{{{text{NaCl}}}}} + {{x}_{{{text{CaC}}{{{text{l}}}_{{text{2}}}}}}})}} from 1 to 0. Changes in the composition and density of coexisting fluid phases at a constant activity of water and changes in the total composition of the system are studied. A set of phase diagrams on sections H2O–NaCl–CaCl2 for different mole fractions of CO2 is obtained. Pressure dependencies of the maximal activity of water in the field of coexisting unmixable fluid phases are obtained for several salt compositions of the system. Due to removal of restrictions resulting from a smaller number of components in ternary systems, the thermodynamic behavior of systems with a mixed composition of the salt significantly differs from the behavior of those with a single salt component.

Thermodynamic Model of the Fluid System H<sub>2</sub>O–CO<sub>2</sub>–NaCl–CaCl<sub>2</sub> at <i>P-T</i> Parameters of the Middle and Lower Crust

Based on the earlier obtained equations of state for the ternary systems H2O–CO2–CaCl2 and H2O–CO2–NaCl, an equation of state for the four-component fluid system H2O–CO2–NaCl–CaCl2 is derived in terms of the Gibbs excess free energy. A corresponding numerical thermodynamic model is build. The main part of the numerical parameters of the model coincides with the corresponding parameters of the ternary systems. The NaCl–CaCl2 interaction parameter was obtained from the experimental liquidus of the salt mixture. Similar to the thermodynamic models for H2O–CO2–CaCl2 and H2O–CO2–NaCl, the range of applicability of the model is pressure 1–20 kbar and temperature from 500°C to 1400°C. The model makes it possible to predict the physicochemical properties of the fluid involved in most processes of deep petrogenesis: the phase state of the system (homogeneous or multiphase fluid, presence or absence of solid salts), chemical activities of the components, densities of the fluid phases, and concentrations of the components in the coexisting phases. The model was used for a detailed study of the phase state and activity of water on the H2O–CO2–salt sections when changing the ratio \( {{{{x}_{{{\text{NaCl}}}}}} \mathord{\left/ {\vphantom {{{{x}_{{{\text{NaCl}}}}}} {\left( {{{x}_{{{\text{NaCl}}}}} + {{x}_{{{\text{CaC}}{{{\text{l}}}_{{\text{2}}}}}}}} \right)}}} \right.} {\left( {{{x}_{{{\text{NaCl}}}}} + {{x}_{{{\text{CaC}}{{{\text{l}}}_{{\text{2}}}}}}}} \right)}} \) from 1 to 0. Changes in the composition and density of coexisting fluid phases at a constant activity of water and changes in the total composition of the system are studied. A set of phase diagrams on sections H2O–NaCl–CaCl2 for different mole fractions of CO2 is obtained. Pressure dependencies of the maximal activity of water in the field of coexisting unmixable fluid phases are obtained for several salt compositions of the system. Due to removal of restrictions resulting from a smaller number of components in ternary systems, the thermodynamic behavior of systems with a mixed composition of the salt is significantly differ from the behavior of those with a single salt component.

Thermodynamic properties of the ternary system (KBr + PEG 4000 + water) by potentiometric method at T = (288.2, 298.2, and 308.2) K

The goal of this research is to evaluate the mean ion activity coefficients (γ±) of the mixtures containing KBr + PEG 4000 + H2O (PEG stands for poly(ethylene glycol)) as well as some other thermodynamic quantities including solvent osmotic coefficients (φ), excess Gibbs energies (GE), standard Gibbs energies of transference (ΔGt0), and primary hydration number (nhydr). The experiment was employed by potentiometric measurement using the cell with two ion-selective electrodes (abbreviated as ISE) at (288.2, 298.2, and 308.2) K, and the mass fraction of PEG 4000 ranged from w = (0 to 0.20) with an increment of 0.05. The type of the cell is as follows:K–ISE | KBr (m), PEG 4000 (w), H2O (1-w) | Br–ISE.Nernst's equation was used to combine the Debye-Hückel and Pitzer models with potentiometric values. Pitzer ion interaction parameters (β0, β1, and Cφ) and Debye-Hückel model parameter (a) were evaluated. Moreover, the Bjerrum parameter (q) was calculated.

Thermodynamic Behavior of (2-Propanol + 1,8-Cineole) Mixtures: Isothermal Vapor-Liquid Equilibria, Densities, Enthalpies of Mixing, and Modeling.

Vapor pressures and other thermodynamic properties of liquids, such as density and enthalpy of mixtures, are the key parameters in chemical engineering for designing new process units, and are also essential for understanding the physical chemistry, macroscopic and molecular behavior of fluid systems. In this work, vapor pressures between 278.15 and 323.15 K, densities and enthalpies of mixtures between 288.15 and 318.15 K for the binary mixture (2-propanol + 1,8-cineole) have been measured. From the vapor pressure data, activity coefficients and excess Gibbs energies were calculated via the Barker's method and the Wilson equation. Excess molar volumes and excess molar enthalpies were also obtained from the density and calorimetric measurements. Thermodynamic consistency test between excess molar Gibbs energies and excess molar enthalpies has been carried out using the Gibbs-Helmholtz equation. Robinson-Mathias, and Peng-Robinson-Stryjek-Vera together with volume translation of Peneloux equations of state (EoS) are considered, as well as the statistical associating fluid theory that offers a molecular vision quite suitable for systems having highly non-spherical or associated molecules. Of these three models, the first two fit the experimental vapor pressure results quite adequately; in contrast, only the last one approaches the volumetric behavior of the system. A brief comparison of the thermodynamic excess molar functions for binary mixtures of short-chain alcohol + 1,8-cineole (cyclic ether), or +di-n-propylether (lineal ether) is also included.

Thermodynamics of K2HPO4/d-Sucrose/Water System at 298.15 K: Experiment and Modeling

Thermodynamic properties of K2HPO4/d-sucrose/water ternary solutions were investigated at 298.15 K. Water activity, osmotic coefficient, and electrolyte saturation points are determined by measuring relative humidities in the wide range of K2HPO4 molality (ranging from 0.1 to approximately 5 mol·kg–1) and for various d-sucrose contents (0.1, 0.3, 0.5, 1, 2, 3, 4, 5, and 5.5 mol·kg–1) in the ternary K2HPO4/d-sucrose/water system. The solid state was characterized using powder X-ray diffraction (XRD) and attenuated total reflection Fourier-transform infrared (ATR-FTIR) techniques. The obtained data were then analyzed using the Pitzer-Simonson-Clegg (PSC) model to determine several thermodynamic properties. These properties encompass the stoichiometric ionic mean activity coefficient of K2HPO4, excess Gibbs energy, solubility in aqueous solutions, and the Gibbs energy of transfer of K2HPO4 between water (W) and d-sucrose/water (W+S) mixtures. Furthermore, the interactions among water, d-sucrose, and K2HPO4 are also examined and discussed.

Viscometric and refractive index study of intermolecular interaction between binary mixtures of terpinolene with o-, m- and p-cresol at 303.15, 308.15 and 313.15 K

Viscosities and refractive indexes  were experimentally measured for binary mixtures of terpinolene with o-, m- and p-cresol for entire composition range at 303.15, 308.15 and 313.15 K and at atmospheric pressure. Deviation in viscosity , excess Gibbs energy of activation for viscous flow , enthalpy  and entropy  of viscous flow, deviation in refractive index , molar refraction  and deviation in molar refraction  were also calculated. Various theoretical viscosity relations such as Dolezalek-Schulze ( , Grunberg-Nissan , Tamura-Kurata  Katti-Chaudhri ( , McAllister relation (  and ), Kendall-Munroe relation, Bingham relation and Arrhenius-Eyring relation were calculated. Similarly, nine theoretical refractive index relations such as Arago-Biot (A-B), Dale-Glastone (D-G), Lorentz-Lorentz (L-L), Eykman (Eyk), Weiner (WR), Heller (Hr), Newton (Nw), Oster (Os) and Eyring-John (E-J) were also calculated with their standard deviation  values. Results were discussed in terms of the presence of intermolecular interactions between the components of binary mixtures.

Thermodynamic Properties Data of Ternary System KBr–KH2PO4–H2O at 298.15 K

The OCP Group located in Morocco in Africa is one of the biggest producers of phosphates and fertilizers in the world and delivers products to more than 165 clients on five continents. These products include ammonium and di-ammonium phosphate, sodium phosphate, and others with added micronutrients (potassium–calcium–nitrogen) that are designed to effectively feed degraded soil. OCP has launched a new strategy in Africa called “Green Africa” to transform African agriculture and make it a platform for food production. Therefore, with the aim of developing new fertilizers and increasing the yield of soils and agriculture, we are interested in this work to study the influence of electrolytes on the fertilizer phosphate KBr–KH2PO4–H2O. This system was investigated with our developed hygrometric method at 298.15 K. The thermodynamic parameters of the studied system such as the water activity and osmotic coefficient are determined by measuring the relative humidity at various total molalities from 0.2 mol·kg–1 to about saturation, and for different ionic-strength fractions y of KH2PO4 (y = IKBr/(IKH2PO4+IKBr)) of 0, 1/4, 1/3, 1/2, 2/3, 3/4, and 1. The obtained measurements are compared to four models such the Dinane (ECA), Lin et al., Robinson and Stokes (RS), and Leitzke-Stoughton (LS II) equations. The solubilities of KBr and KH2PO4 in their aqueous mixture are also measured at 298.15 K. The solid state was characterized using powder X-ray diffraction (XRD). The PSC model was used to correlate the results and to predict the solute activity coefficients, excess Gibbs energy, and solubilities of the components in the mixture.

Activity coefficient acquisition with thermodynamics‐informed active learning for phase diagram construction

AbstractThis work explores the use of thermodynamics‐informed Gaussian processes (GPs) and active learning (AL) to model activity coefficients and construct phase diagrams. Relying on synthetic data generated from an excess Gibbs energy model, GPs were found to accurately describe the activity coefficients of several binary mixtures across large composition and temperature ranges. Moreover, GPs could estimate their own uncertainty and identify composition/temperature regions where activity coefficient data provide the most information to the models. This was leveraged to build AL algorithms targeted at modeling phase equilibria. In many cases, a single active‐learning‐acquired data point was sufficient to describe the phase diagrams studied. Finally, the ability of AL to greatly reduce the amount of data needed to obtain accurate models was further verified on experimental case studies, namely individual ion activity coefficients, the solid–liquid and vapor–liquid equilibrium of deep eutectic solvents, and phase equilibria in ternary mixtures.

Estimation of Component Activities and Molar Excess Gibbs Energy of 19 Binary Liquid Alloys from Partial Pair Distribution Functions in Literature

This work proposes a new method for estimating the molar excess Gibbs energy and activity of liquid alloy based on recent research. The local composition theory provides a connection between the structures of liquid alloys and the thermodynamic models. The partial pair distribution function (PPDF) was utilized to calculate the parameters of the MIVM, RSM, Wilson, and NRTL. The statistics of the number of molecular pairs of MIVM and RSM were rewritten, which resulted in new forms of the two models. To enhance the NRTL’s estimation performance, the coordination number was incorporated into it (M-NRTL). The aforementioned model and Quasi-chemical model (QCM) were utilized to estimate the excess Gibbs energy and activity of 19 alloys. The alloys contained multiple sets of PPDFs, which enabled the calculation of multiple sets of model parameters. The work examined the impact of expressing the model parameters as first-order linear functions of the components or as constants on the accuracy of the estimation. The parameters were treated as constants. MIVM, RSM, and M-NRTL provided an average relative deviation (ARD) of activity of less than ±20% for 15, 10, and 9 alloys by estimation. When model parameters were expressed as a function of components, QCM showed the best estimation performance, having nine alloys with an ARD of less than ±20%. The number of alloys with an ARD of less than ±20% corresponding to MIVM, RSM, Wilson, NRTL, and M-NRTL was six, five, three, five, and two, respectively. This new method offers simplicity, numerical calculation stability, and excellent reproducibility.

Thermodynamic properties of the Na2O-BaO-B2O3 glasses and melts

The glass formation region in the system Na2O-BaO-B2O3 has been established. Thermodynamic properties for this system were derived. It is found that the lower border of glass formation region is limited to composition containing 10–30 mol.% Na2O, 10–30 mol.% BaO and 60 mol.% B2O3. A region with partial crystallization has been found inside the glass formation region. This region is limited to compounds 5 Na2O-20 BaO-75 B2O3 mol.% and 10 Na2O-20 BaO-75 B2O3 mol.%. The vaporization processes and thermodynamic properties of the Na2O-BaO-B2O3 melts were investigated by the Knudsen effusion mass spectrometry in the temperature range 1290–1750 K. The values of the component activities, Gibbs energies and excess Gibbs energies were derived from experimental data. It was shown that the studied system is characterized by a negative deviation from the ideal behavior.

СИНТЕЗ И ИССЛЕДОВАНИЕ ФИЗИКО-ХИМИЧЕСКИХ И ТЕРМОДИНАМИЧЕСКИХ СВОЙСТВ В СИСТЕМЕ Na2O-BaO-B2O3

38 samples were synthesized in the Na2O-BaO-B2O3 system, some of which were glasses, some crystallized. The degree of interaction of the initial reagents in the synthesis process was controlled by X–ray phase analysis on a DRON-3M diffractometer using CuKa radiation. Crystal phases were identified using X–ray phase analysis on a DRON-3M diffractometer using CuKa radiation and the PDF–2 powder diffractometry database. The following crystalline phases were identified in the crystallized samples: β-BaВ2O4, NaBO2, NaBaB9O15. Density, microhardness, refractive index were measured for glassy samples of the system under study and melting/liquidus temperatures were determined. It is established that the nature of the dependence of the above properties on the content of sodium oxide with a constant content of boron oxide is linear. The study of vaporization processes and thermodynamic properties of the Na2O-BaO-B2O3 system was carried out by differential high-temperature mass spectrometry on the MS–1301 mass spectrometer. The studied samples were evaporated from a twin Knudsen molybdenum effusion cell. The heating of the cell was carried out by electronic bombardment, the temperature was measured with an optical pyrometer EOP–66. It was shown that as a result of the interaction of Na2O, BaO and B2O3 oxides, sodium and barium borates are formed in the condensed phase. It is established that the studied system is characterized by selective evaporation of NaBO2 in the temperature range of 1290–1350 K. The activity values of NaBO2 and B2O3 were determined depending on the composition of the condensed phase at a temperature of 1330 K. The activity of BaB2O4 was calculated using the Gibbs-Dugem equation. The obtained values of the Gibbs mixing energies and excess Gibbs energies indicate significant deviations of the Na2O-BaO-B2O3 system from the ideal behavior.

Thermodynamic Evaluation and Optimization of the Ag-As-S system

A critical evaluation of all available phase diagram and thermodynamic data has been performed for Ag-As, Ag-S, As-S and Ag-As-S systems, including a detailed review of the gaseous species involved in the As-S system. Thermodynamic assessments over the whole composition range for these four systems are presented using the CALPHAD method. To predict thermodynamic properties and phase equilibria, the Modified Quasichemical Model for short range ordering was used for the liquid phases, and the Compound Energy Formalism was used for the solid solutions. For the As-S binary system, natural logarithm terms for the temperature dependence of the excess Gibbs energy of the liquid solution have been used. This led to a significant improvement compared with the previous assessment of this system. The optimization of Ag-As-S systems is in good agreement with the existing experimental data.