Thermodynamic study of the KMgAlClSO4H2O system at the temperature 298.15 K

The Pitzer ion-interaction model has been used for thermodynamic simulation of the binary AlCl₃H₂O, Al₂(SO4)₃H2O, ternary KClAlCl₃H₂O, K₂SO₄Al₂(SO₄)₃H₂O, MgCl₂AlCl₃H₂O, MgSO₄Al₂(SO₄)₃H₂O, and the quaternary KClMgCl₂AlCl₃H₂O systems at T=298.15 K. The optimum values of the binary parameters of ionic interactions for aluminum solutions have been calculated using activity data up to saturation of solutions. The ternary parameters have been chosen on the basis of the compositions of saturated ternary solutions taking into account the unsymmetrical mixing terms. Good agreement between experimentally determined and calculated solubilities has been found. Important thermodynamic characteristics (thermodynamic solubility product, standard molar Gibbs energy of formation) of the solid phases (simple and double salts) crystallizing in the systems under consideration are determined.     

Thermodynamic study of the NaCl  Na2SO4  Na2Cr2O7  H2O system at the temperature 298.15 K

The Pitzer ion-interaction model has been used for thermodynamic simulation of the ternary NaClNa₂Cr₂O₇H₂O and Na₂SO₄Na₂Cr₂O₇H₂O, and the quaternary NaClNa₂SO₄-Na₂Cr₂O₇-H₂O systems at T=298.15 K. The necessary thermodynamic functions (binary and ternary parameters of interionic interaction and thermodynamic solubility products) have been calculated and the theoretical solubility isotherms have been plotted. Good agreement between experimentally determined and calculated solubilites has been found.     

Revisiting the thermodynamic properties of the LiCl–NaCl–KCl–H2O quaternary and its sub-ternary systems at 298.15 K

The phase diagram of the quaternary system LiCl–NaCl–KCl–H₂O have been predicted with a Pitzer–Simonson–Clegg thermodynamic model by combining the binary and ternary model parameters, which were determined by simulating reliable experimental data. The predicted phase diagram shows a good agreement with the available experiment data from the literature. The other thermodynamic properties (e.g. water activity) of the quaternary and its sub-ternary systems have been investigated by the model and compared with the experimental data in literature. Significant improvements have been made in comparison with assessments.     

Measurements and calculations of solid–liquid equilibria in the quaternary system NaBr–KBr–CaBr2–H2O at 298 K

The solubilities and densities of the quaternary system NaBr–KBr–CaBr₂–H₂O were investigated by the method of isothermal solution saturation at 298 K. On the basis of the experimental data, the phase diagram, water content diagram and the density-composition diagram were plotted, respectively. In the phase diagram of quaternary system NaBr–KBr–CaBr₂–H₂O at 298 K, no complex salt or solid solution was found. There are two invariant points, five univariant curves, and four crystallization fields corresponding to NaBr, NaBr·2H₂O, KBr and CaBr₂·6H₂O. Pitzer's equations based model has been applied to calculate bromide minerals solubilities in the quaternary system NaBr–KBr–CaBr₂–H₂O at 298 K. All binary and mixing ion interaction parameters and solubility products of bromide solids are taken from previously published T-variation model for the system under study, adapted to 298 K. The predicted and experimental solubilities are in a very good agreement up to a very high total concentration of the quaternary system.     

Thermodynamic properties of sodium pyrovanadate (Na4V2O7) at high temperature (298.15–873 K)

The sodium pyrovanadate (Na₄V₂O₇) powder was synthesized by solid-state reaction using sodium carbonate (Na₂CO₃) and vanadium pentoxide (V₂O₅) as raw materials. X-ray powder diffraction (XRD), scanning electron microscope (SEM), and differential scanning calorimeter (DSC) were used to accurately characterize the synthesized sample. The solid-state phase transformation from α-Na₄V₂O₇ to β-Na₄V₂O₇ occurs at the temperature 696 K and the enthalpy is equals to 1.03 ± 0.01 kJ/mol, the endothermic effect at 931 K and the enthalpy is equals to 31.35 ± 0.31 kJ/mol, which is related to the melting of Na₄V₂O₇. The high-temperature heat capacity of Na₄V₂O₇ was measured using a Multi-high temperature calorimeter 96 line and DSC. The obtained high-temperature heat capacity of Na₄V₂O₇, as a function of temperature, was modeled as: Cp=314.62+0.05T-5494390T^-2 J·mol^-1·K^-1 (298.15-873 K). The temperature dependence on heat capacity was then used for computing changes in the enthalpy, entropy, and Gibbs free energy at the specific temperature internal.     

Thermodynamic assessment of the CaO–Cu2O–FeO–Fe2O3 system

Thermodynamic assessment of the CaO–Cu₂O–FeO–Fe₂O₃ system is presented. Effects of temperature and P(O₂) on the phase equilibria involving slag, solubility of copper and the Fe³⁺/Fe²⁺ ratio in slag have been modeled using available experimental data. Subsolidus phase equilibria and concentration of iron in liquid copper were evaluated as well. Different ways of representing phase equilibria in a quaternary system are illustrated. The slag model, [Ca²⁺, Cu⁺, Fe²⁺, Fe³⁺][O²⁻], was developed using the Modified Quasichemical Model (MQM). Liquid metal phase is modeled using the MQM, but as a separate solution, (Cu^I, Fe^II, O^II). Spinel phase is modeled using the Compound Energy Formalism (CEF) and takes into account the solubility of copper and calcium. A thermodynamic database produced in the present study can be used for predictions in pyrometallurgical processing of copper involving calcium ferrite slags. The database is internally consistent with the binary and ternary sub-systems published earlier, as well as with higher-order systems. It works in the environment of FactSage, ChemApp, ChemSheet and SimuSage software packages.     

Critical thermodynamic re-evaluation and re-optimization of the CaO–FeO–Fe2O3–SiO2 system

Comprehensive literature review, critical re-assessment and thermodynamic re-optimization of phase diagrams and thermodynamic properties of all phases have been carried out for the CaO–FeO–Fe₂O₃–SiO₂ system. Thermodynamic assessments of this system were previously published, however some of them were incomplete or described only limited range of compositions. In addition, more recent important experimental data have been available after previous assessments. The Modified Quasichemical model is used to describe the Gibbs energy of the liquid slag. The monoxide, wollastonite, α-Ca₂SiO₄ and α’-Ca₂SiO₄ solid solutions are described using the random mixing Bragg-Williams model. Spinel, olivine, pyroxene and melilite solid solutions are modelled using sublattice model based on the Compound Energy Formalism. A set of optimized parameters for the thermodynamic models has been obtained which reproduces all available experimental data within the experimental uncertainties from sub-solidus to above the liquidus temperatures at all compositions and atmosphere conditions.     

Thermodynamic optimization of the PbO–FeO–Fe2O3–SiO2 system

Liquidus phase equilibrium data of the present authors for the PbO–FeO–Fe₂O₃ system at various oxygen potentials, PbO–“Fe₂O₃”–SiO₂ system in air, and PbO–“FeO”–SiO₂ in equilibrium with metallic Pb, combined with phase equilibrium and thermodynamic data from the literature, have been used to obtain a self-consistent set of parameters of the thermodynamic models for all phases in the PbO–FeO–Fe₂O₃–SiO₂ system. The modified quasichemical model is used for the liquid slag phase. For the liquid phase, the PbO–FeO, PbO–Fe₂O₃, PbO–FeO–Fe₂O₃, PbO–FeO–SiO₂ and PbO–Fe₂O₃–SiO₂ parameters are optimized in the present study. From these model parameters, the optimized ternary phase diagram is back calculated. Present set of parameters describe previous and new experimental data well, and can be used for predictions of the PbO–FeO–Fe₂O₃–SiO₂ phase equilibria over wide ranges of oxygen partial pressured, compositions and temperatures, as well as multicomponent systems.     

Thermodynamic optimization of the ZnO–FeO–Fe2O3–SiO2 system

Liquidus phase equilibria experimental data of the present authors for the ZnO–“Fe₂O₃”–SiO₂ system in air, ZnO–“FeO”–SiO₂ in equilibrium with metallic Fe, and ZnO–“FeO”–SiO₂–minor Cu₂O at p(O₂) ~10⁻⁷ … 10⁻⁸ atm (obtained as a part the research on the multicomponent PbO–ZnO–FeO–Fe₂O₃–Cu₂O–CaO–SiO₂ system), combined with phase equilibrium and thermodynamic data from the literature, have been used to obtain a self-consistent set of parameters of the thermodynamic models for all phases in the ZnO–FeO–Fe₂O₃–SiO₂ system for the whole range of compositions, p(O₂) between ~10⁻¹³ to 1 atm, and temperature range corresponding to liquid slag existence (1150–1700 °C). The modified quasichemical model is used for the liquid slag phase. From these optimized model parameters, the ternary phase diagrams are back calculated. The model based on the present set of parameters is in a good agreement with previous and new experimental data, and can be used for predictions of the ZnO–FeO–Fe₂O₃–SiO₂ phase equilibria over wide ranges of p(O₂), compositions and temperatures, as well as multicomponent systems.     

Experimental study and thermodynamic optimization of the ZnO–FeO–Fe2O3–CaO–SiO2 system

Liquidus phase equilibrium experimental data from the present study for the ZnO-“Fe₂O₃”-CaO-SiO₂ system in air, combined with phase equilibria and thermodynamic data from the literature on the ZnO-“Fe₂O₃”-CaO system in air and ZnO-“FeO”-CaO-SiO₂ system in equilibrium with metallic Fe, have been used to obtain a self-consistent set of parameters of the thermodynamic models for all phases in the ZnO–FeO–Fe₂O₃–CaO–SiO₂ system. The modified quasichemical model is used for the liquid slag phase; spinel (Fe,Zn,Ca)^tetr (Fe,Zn,Ca,Va)^oct₂O₄, melilite Ca₂(Fe²⁺,Fe³⁺,Zn)(Fe³⁺,Si)₂O₇ and olivine (Fe,Zn,Ca)^I(Fe,Zn,Ca)^IISiO₄ are described with compound energy formalism; lime and wustite (monoxide) (Ca,Fe,Zn)O, zincite (Zn,Fe,Ca)O_1+x, calcium-zinc ferrites Ca₂Fe₂O₅-“CaZnO₂” and CaFe₄O₇-“ZnFe₄O₇”, α- and α′-dicalcium silicate (Ca,Fe,Zn)₂SiO₄ and tricalcium silicate (Ca,Fe,Zn)₃SiO₅ and silicoferrite of calcium (SFC) Ca₉Fe₄₆SiO₈₀–Ca₁₂Fe₄₀Si₄O₈₀ are described within Bragg-Williams formalism; for other phases, previous assessments have been adopted. The phase diagrams are back calculated with the optimized model parameters. Present study is a part of research program on the characterization of the multicomponent PbO–ZnO–FeO–Fe₂O₃-“Cu₂O”-CaO-SiO₂ system.     

Critical evaluation and thermodynamic modeling of the Fe–V–O (FeO–Fe2O3–VO–V2O3–VO2–V2O5) system

Critical evaluation and optimization of the Fe–V–O ternary oxide system was carried out based on all the available phase equilibria and thermodynamic property data at 1 atm total pressure. The Fe₃O₄–FeV₂O₄ spinel solid solution was described within the framework of Compound Energy Formalism considering the cation distribution between tetrahedral and octahedral sites. The wüstite phase, corundum phase, and VO₂ solid solution were described using a simple random mixing model. The Modified Quasichemical Model was used to describe liquid oxide solution in consideration of all multivalence states of Fe and V (Fe²⁺, Fe³⁺, V²⁺, V³⁺, V⁴⁺ and V⁵⁺). The variation of phase equilibria depending on the oxygen partial pressures and thermodynamic data in the system were well reproduced in the present study.     

Thermodynamic properties of sodium hexatitanate (Na2Ti6O13) at high temperature (298.15–1573 K)

Sodium hexatitanate (Na₂Ti₆O₁₃) was reported as an anode side material for Sodium ion batteries owing to low material cost, high energy efficiency, good thermal stability and long cycle life. Therefore, studies pertaining to the thermodynamic properties of Na₂Ti₆O₁₃ are indispensable for improving its service performance. However, a significant number of literature reviews concerning thermodynamic properties indicated that heat capacity of Na₂Ti₆O₁₃ at high temperatures should be confirmed. In this study, the 99.5% purity of Na₂Ti₆O₁₃ sample was successfully prepared via solid-state reaction using TiO₂ and Na₂CO₃ as initial materials. Heat capacity of the as-synthesized samples in the temperature range of 573–1523 K was measured using a multi-high temperature calorimeter 96 line. Heat capacity, Cp, from 298.15 to 1573 K was modeled as a polynomial formula with a prediction error of 3%: Cp = 474.08143 + 0.06286T-8.04068 × 10⁶ T⁻² (J⋅mol⁻¹⋅K⁻¹). In combination with the low-temperature data, heat capacity of Na₂Ti₆O₁₃ from 0 to 1573 K was given in present study. Values of changes in enthalpy, Gibbs free energy and entropy in the temperature range of 298.15–1573 K were calculated based on the temperature dependence of heat capacity.     

Experimental study of the phase relationships in the SiO2–SrO–Al2O3 system

The phase relationships in silica rich area in the SiO₂–SrO–Al₂O₃ system were determined experimentally at 1723 K (1450 °C), 1823 K (1550 °C) and 1873 K (1600 °C) using quenching technique. Phases of the quenched samples were examined and identified using light optical microscopy (LOM), scanning electron microscope (SEM) and energy dispersive x-ray spectroscopy (EDS). X-ray Diffraction (XRD) was used to confirm the presence of solid phases. Based on the experimental results, the liquidus projections in the silica rich area for the studied temperatures were constructed.