Experimental study of thermodynamic properties and phase equilibria in Na2CO3–K2CO3 system

Sodium and potassium carbonates and their mixtures are important for different applications, e.g. for latent thermal energy storage, die-casting processes and molten carbonate fuel cells. In this work the phase diagram and thermodynamic properties of Na₂CO₃–K₂CO₃ system were studied by differential thermal analysis, differential scanning calorimetry and high temperature X-ray diffraction. Three carbonate mixtures (56, 25 and 75 mol% of Na₂CO₃) have solid-solid transition in a wide temperature range between 648 K and 823 K. The high temperature XRD analysis has shown that this transition is a continuous process of changing of the unit cell volume without structural changing of the hexagonal lattice. This phenomenon has also been observed on the measured heat capacity curves. The obtained experimental results were compared with calculations performed using the previous thermodynamic datasets. The comparison of these results shows that further thermochemical assessment of this system needs to be performed to achieve better agreement with the available experimental data.     

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.     

Experimental investigation and thermodynamic calculation of the phase equilibria in the Fe–Ni–V system

The phase equilibria in the Fe–Ni–V ternary system were investigated by means of electron probe microanalysis (EPMA) and X-ray diffraction (XRD). Three isothermal sections of the Fe–Ni–V ternary system at 1000 °C, 1100 °C and 1200 °C were established. On the basis of the obtained experimental data, the phase equilibria in the Fe–Ni–V system were thermodynamically assessed using (CALculation of PHAse Diagrams) CALPHAD method, and a consistent set of thermodynamic parameters leading to reasonable agreement between the calculated results and experimental data was obtained.     

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.     

Solution properties and salt-solution equilibria in the H-Li-Na-K-Ca-Mg-Cl-H2O system at 25 °C: A new thermodynamic model based on Pitzer's equations

A large part of Li production comes from the exploitation of saline lakes and salars. Industrial processes for Li recovery from such resources have to deal with highly saline waters. It is therefore necessary to develop the knowledge of Li chemistry adapted to these contexts. The present work aims to present a new set of Pitzer interaction parameters able to describe the chemical behavior of the H-Li-Na-K-Ca-Mg-Cl-H₂O system up to salt solubility, at 25 °C. In a previous work, the model was limited to the H-Li-Na-K-Cl-H₂O system. It is extended here by including Ca and Mg, taking into account recently revised parameters allowing the thermal properties of the binary CaCl₂-H₂O and MgCl₂-H₂O systems to be represented. The consistent extension of the thermodynamic database was made possible by the study of the binary CaCl₂-H₂O system up to the supersaturated metastable region and of nine ternary systems, namely X-Ca-Cl, X-Mg-Cl and Ca-Mg-Cl (where X = H, Li, Na, K). The model was finally tested on five quaternary systems.     

Effect of CaO on the liquid/spinel/matte/gas equilibria in the Si–Fe–O–Cu–S system at controlled P(SO2) 0.3 and 0.6 atm

Herein the phase equilibria in the Si–Fe–Ca–O–S–Cu system in equilibrium with matte at controlled P(SO₂) of 0.3 and 0.6 atm and fixed matte grade of 72 wt % Cu were experimentally investigated in the spinel primary phase field. The high-temperature equilibrations were realized in spinel substrate and the sample after quenching were characterized using Electron Probe Micro-analysis (EPMA). The effect of CaO on the liquidus temperature of slags was quantified with varying CaO content from 0 to 6 wt %. It was found that, the presence of CaO increased the liquidus temperature of slags and moreover, the increment effect got enhanced with increasing CaO content in the present range. The influence of P(SO₂) was further clarified and it was found that, the equilibrium SiO₂ content in the liquid phase, at the same temperature, remarkably increased with increasing P(SO₂). The present study will not only deepen the understanding of the equilibration in the present liquid/spinel/matte/gas system, but also provide useful guidance for the industrial operations.     

Effect of MgO on the liquid/spinel/matte/gas equilibria in the Si–Fe–Mg–O–Cu–S system at controlled P(SO2) 0.3 and 0.6 atm

In this study, the effect of MgO on the phase equilibria of iron silicate slags in equilibrium with Fe₃O₄ spinel and matte of fixed 72 wt % Cu were identified at controlled P(SO₂) 0.3 and 0.6 atm. The experimental process includes equilibration, quenching and Electron Probe X-ray Micro Analysis (EPMA). Spinel (Fe₃O₄) substrates were applied to confirm the equilibrium was achieved in the primary phase field of spinel. It was found that the presence of MgO increases the liquidus temperature of slag under a constant SiO₂ content, i.e., more SiO₂ is required to be fluxed to keep a stable smelting temperature with MgO. The effects of CaO and MgO on the liquidus of the system were further compared and found that the influence of MgO is stronger than CaO at 1250 °C under the same weight content while opposite situation occurs at 1200 °C, which is different from the FactSage predictions. Thus, the present study provides important information not only for the industrial smelting process but also for the thermodynamic modelling.     

Thermodynamic assessment of the CaO–P2O5–SiO2–ZnO system with special emphasis on the addition of ZnO to the Ca2SiO4–Ca3P2O8 phase

The CaO–P₂O₅–SiO₂–ZnO system including all binary and ternary sub-systems has been thermodynamically assessed using all available experimental data. Particular attention was given to the phase C2S–C3P which forms a complete solid solution with end-members α-Ca₂SiO₄ and α′-Ca₃P₂O₈. In addition, the present modelling of the phase C2S–C3P allows the inclusion of experimentally determined solubility values of zinc oxide in both end-members of the phase C2S–C3P. The mutual solubility between different crystallographic modifications of calcium and zinc phosphates is also described in this work using available experimental data. 24 phospates as stoichiometric phases have also been included in the database.     

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.     

Necessary and sufficient conditions for the existence of positive definite solutions of the matrix equation X+A T X −2 A=I

Necessary and sufficient conditions for the matrix equation X+A ^T X ^?2 A=I to have a real symmetric positive definite solution X are derived. Based on these conditions, some properties of the matrix A as well as relations between the solution X and A are derived.     

Phase relationship in V2O3-rich region of the V2O3–CaO system between 1573–1773 K at PO2 = 10−10 and 10−11 atm

V₂O₃–CaO system is one of the fundamental systems in the fields of vanadium extraction and vanadium-containing alloys production. Due to the insufficient experimental study, the data of this system was limited. The present study was carried out between 1300 and 1500 °C (1573–1773 K) at the V2O3-rich region (>56 wt% V₂O₃), with the controlled partial pressure of oxygen (PO2) at 10-10 and 10–11 atm. High-temperature equilibration experiments, quenching technique and electron probe micro-analyser (EPMA) were adopted to determine the microstructures and compositions of phases at high temperature. The results of phase compositions obtained were used to plot a sub-solidus phase diagram, which showed a great discrepancy with existing publications, and 4 solid-phase regions with their phase boundaries were identified in the present study. The solubility of CaO in V2O3 was found to increase slightly with the temperature under both PO2. The study is expected to fulfil the gaps of thermodynamics information in the V₂O₃-containing systems.     

Experimental studies of liquid/spinel/matte/gas equilibria in the Si-Fe-O-Cu-S system at controlled P(SO2) 0.3 and 0.6 atm

In the present study, the phase equilibria in the “FeO”-SiO₂ system in equilibrium with matte at controlled P(SO₂) 0.3 and 0.6 atm and fixed matte grade 72 wt% Cu were experimentally investigated. The high-temperature equilibration using primary phase material as the substrate, quenching and Electron Probe Micro-analysis (EPMA) were applied in the experiments where the P(O₂) and P(SO₂) were accurately controlled by CO/CO₂/SO₂ gas mixtures. The correlations between oxygen partial pressure and the matte grade were determined at P(SO₂) 0.3 and 0.6 atm to obtain the target matte grade in the samples. The liquidus temperatures of this “FeO”-SiO₂ system in equilibrium with matte at controlled P(SO₂) 0.3 and 0.6 atm and fixed matte grade 72 wt% Cu were also reported. The present experimental results were also compared with the FactSage predictions and show the differences. The present results are expected to be useful for the copper smelting operations and also provide reliable information for the thermodynamic database.     

Phase equilibria of the Al2O3–CaO–SiO2-(0%, 5%, 10%) MgO slag system for non-metallic inclusions control

Al₂O₃–CaO-(MgO–SiO₂) inclusions are one of the dominant inclusions in Al-deoxidized spring steel, the compositions changes of which are closely related to refining slags and deoxidization process. The Al₂O₃–CaO–SiO₂–MgO system can represent the primary ingredients of the Al₂O₃–CaO inclusions. According to analyzed compositions and predicted liquidus temperature ranges of inclusions and refining slag, equilibra experiments under high temperature, water quenching technique and subsquent electron probe X-ray microanalysis (EPMA) has been conducted to ascertain detailed thermodynamic database for inclusions control. Liquidus temperatures within the dominant phase fields of Ca₃SiO₅, Ca₂SiO₄, CaAl₂O₄, Ca₃Al₄O₉, spinel and MgO with the intervals of 20 °C from 1350 to 1560°C were identified. To further promote inclusions control, the influences of mass ratios of Mass(Al2O3)Mass(Al2O3+SiO2+CaO) and MgO contents on equilibrated phases and liquidus temperature changes have been explored. To further enhance modification levels of Al₂O₃–CaO-(MgO–SiO₂) system inclusions, it is suggested that refining time could be suitably prolonged.