Critical thermodynamic evaluation and optimization of the CaO–MgO–SiO2 system

A complete literature review, critical evaluation and thermodynamic modeling of phase diagrams and thermodynamic properties of all oxide phases in the CaO–MgO–SiO₂ system at 1 bar pressure are presented. The molten oxide phase is described by the Modified Quasichemical Model, and the Gibbs energies of the olivine and pyroxene solid solutions are modeled using the compound energy formalism. A set of optimized model parameters of all phases is obtained which reproduces all available and reliable thermodynamic and phase-equilibrium data within experimental error limits from 25 °C to above the liquidus temperatures over the entire composition range. The complex phase relationships in the system have been elucidated, and discrepancies among the data have been resolved. The database of the model parameters can be used along with software for Gibbs energy minimization in order to calculate all thermodynamic properties and any phase diagram section or phase equilibrium of interest.     

Thermodynamic modeling of the NiO–SiO2, MgO–NiO,CaO–NiO–SiO2, MgO–NiO–SiO2, CaO–MgO–NiO and CaO–MgO–NiO–SiO2 systems

A complete literature review, critical evaluation and thermodynamic optimization of phase equilibrium and thermodynamic properties of all available oxide phases in the NiO–SiO₂, MgO–NiO, CaO–NiO–SiO₂, MgO–NiO–SiO₂, CaO–MgO–NiO and CaO–MgO–NiO–SiO₂ systems at 1 bar pressure are presented. The molten oxide phase is described by the modified quasichemical model, and the Gibbs energies of solid olivine and pyroxene solutions were modeled using the compound energy formalism. A set of optimized model parameters of all phases is obtained which reproduces all available and reliable thermodynamic and phase equilibrium data within experimental error limits from 25 °C to above the liquidus temperatures over the entire composition range. The unexplored ternaries and quaternary phase diagrams and activity of liquid phase in the CaO–MgO–NiO–SiO₂ system have been predicted for the first time. The database of the model parameters can be used along with software for Gibbs energy minimization to calculate all thermodynamic properties and any phase diagram section of interest.     

Critical Evaluation and Thermodynamic Modeling of the Mg–Mn–O (MgO–MnO–MnO2) System

All phase diagram and thermodynamic data of the MgO–MnO and MgO–MnO–MnO₂ systems were critically evaluated and thermodynamically optimized to obtain one set of thermodynamic model parameters. The MgMn₂O₄–Mn₃O₄ spinel solutions were modeled with two sublattices Compound Energy Formalism by considering the cation distribution between tetrahedral and octahedral sites. The slag phase and monoxide solid solution were also described using the Modified Quasichemical Model and Bragg–Williams random mixing model, respectively. The optimized thermodynamic model parameters can be used with a Gibbs energy minimization routine to calculate the phase diagram and thermodynamic properties of the system at oxygen partial pressures between metal saturation and 1 atm.     

Critical evaluation and thermodynamic optimization of the Na2O–FeO–Fe2O3–Al2O3–SiO2 system

A critical assessment and thermodynamic optimization of phase diagrams and thermodynamic properties of the entire Na₂O–FeO–Fe₂O₃–Al₂O₃–SiO₂ system were carried out at 1 atm total pressure. A set of optimized model parameters obtained for all phases present in this system reproduces available and reliable thermodynamic property and phase equilibrium data within experimental error limits from 298 K to above liquidus temperatures for all compositions and oxygen partial pressures from metallic Fe saturation to 1 atm. The Gibbs energy of liquid solution was described based on the Modified Quasichemical Model considering the possible formation of NaAlO₂ and NaFeO₂ associates in the liquid state. The solid solutions wüstite, spinel, feldspar, nepheline, carnegieite, mullite, corundum, clino-pyroxene, meta-oxides and Na-β″-alumina were treated within the framework of Compound Energy Formalism. The database of model parameters can be used to calculate any thermodynamic property and phase diagram section of the present system.     

Critical evaluation and thermodynamic optimization of the Li-O,and Li2O-SiO2 systems

A critical evaluation and thermodynamic optimization of all available experimental data of the Li-O and Li₂O-SiO₂ systems were performed to obtain one set of consistent Gibbs energy functions for all phases in the systems. The obtained Gibbs energy functions can reproduce all available and reliable experimental data from 298 K to above liquidus temperatures at one atm total pressure. It is the first time, to the best of our knowledge that the Gibbs energy of stoichiometric phases like Li₂O, Li₄SiO₄, Li₂SiO₃, and Li₂Si₂O₅ was comprehensively evaluated and optimized. The liquid oxide solution was modeled using the Modified Quasichemical Model to describe its thermodynamic behavior accurately considering the short range ordering. Discrepancies observed in the metastable liquid immiscibility and the liquidus in the SiO₂-rich region of the Li₂O-SiO₂ system was resolved. The phase diagram and thermodynamic data of all the solid and liquid phases were well reproduced within experimental error limits.     

Thermodynamic Modeling of the HfO2–La2O3–Al2O3 System

Based on phase equilibria, thermodynamic, and crystal structure data, the thermodynamic modeling of HfO₂–La₂O₃–Al₂O₃ system is presented. Liquid phase is described by the modified quasichemical model considering the short‐range ordering in liquid solution. Solid solutions are described by the ionic sublattice model considering respective crystal structure. The model (La³⁺, Hf⁴⁺)₂(Hf⁴⁺, La³⁺)₂(O^2?, Va)₆(O^2?)₁(Va, O^2?)₁ successfully describes the structure defect, homogeneity range, and thermodynamic property of pyrochlore solid solution. A set of optimized model parameters is obtained which reproduces most experimental data well. Isothermal sections, liquidus and solidus projections, and Scheil reaction scheme are constructed.     

Thermodynamic assessment within the Zr–B–C–O quaternary system

Thermodynamic modeling of Zr–B–C–O quaternary system is conducted within the CALPHAD framework by employing data obtained from first-principle calculations and literature. The lower order binary B–O is assessed in this work by estimating the thermodynamic properties of stable solid phases of B₂O₃ and B₆O and by estimating the gas and liquid phases. First-principle calculations, in conjunction with special quasirandom structure were used to predict enthalpies of mixing for the ternary solid-solution phase of FCC-Zr(C, O). The calculated results were used to optimize the model parameters pertaining to the cubic phase, which is described by a two-sublattice model. The modeled Zr–C–O ternary phase diagrams calculated at 1923 and 2273 K under ambient pressure and 4 Pa, respectively, are in agreement with experimental phase diagrams.     

Experimental investigation of the LiAlSi2O6‐MgSiO3 and LiAlSi2O6‐CaMgSi2O6 isopleths at 1 atm

The phase diagrams of the LiAlSi₂O₆‐MgSiO₃ and LiAlSi₂O₆‐CaMgSi₂O₆ isopleths were experimentally investigated at 1 atm using the quenching method and differential scanning calorimetry and the phases produced were characterized with the help of X‐ray diffraction and electron probe microanalysis. With the help of thermodynamic optimization, the phase diagrams of both systems were more accurately reported. No detectable solubility of Li₂O in diopside and enstatite was found. However, both systems are not simple binary eutectic systems because their phase equilibria are somewhat complex due to the presence of some β‐spodumene solid solution. In the β‐spodumene solid solution, no notable solubility of MgO and CaO was detected; evidence of significant solubility of SiO₂ was confirmed.     

Coupled Experimental and Thermodynamic Optimization of the Na2O–FeO–Fe2O3–Al2O3 System: Part 1. Phase Diagram Experiments

As part of the complete thermodynamic modeling of the Na₂O–FeO–Fe₂O₃–Al₂O₃ system, the Na₂O–FeO–Fe₂O₃–Al₂O₃ phase diagrams in air (1583 and 1698 K) and at Fe saturation (1573 and 1673 K) were investigated using the quenching method followed by Electron Probe Micro‐Analyzer (EPMA) and X‐ray Diffraction (XRD) phase analysis. General features of the phase diagrams in this system were well revealed for the first time. A complete meta‐oxide solid solution between NaAlO₂ and NaFeO₂ was observed. An extensive solid solution of Na₂(Al,Fe)₁₂O₁₉ Na‐β?‐alumina was found and the existence of a miscibility gap in this solution was confirmed. Several compatibility triangles of three‐phase assemblages were also identified in air and at Fe saturation.     

Thermodynamic Modeling of the FeO–Fe2O3–MgO–SiO2 System

The liquid and solid phases in the FeO–Fe₂O₃–MgO–SiO₂ system are of importance in ceramics, metallurgy, and petrology. A complete critical evaluation and thermodynamic modeling of the phase diagrams and thermodynamic properties of this system are presented. Optimized equations for the thermodynamic properties of all phases are obtained that reproduce all available thermodynamic and phase equilibrium data within experimental error limits from 25°C to above the liquidus temperatures at all compositions and oxygen partial pressures. The optimized thermodynamic properties and phase diagrams are believed to be the best estimates presently available. The database of the model parameters can be used with software for Gibbs energy minimization to calculate any type of phase diagram section.     

Factors Influencing the Stability of AFm and AFt in the Ca–Al–S–O–H System at 25°C

The stabilities of Al₂O₃–Fe₂O₃‐mono (AFm) and ‐tri (AFt) phases in the Ca–Al–S–O–H system at 25°C are examined using Gibbs energy minimization as implemented by GEM‐Selektor software coupled with the Nagra/PSI thermodynamic database. Equilibrium phase diagrams are constructed and compared to those reported in previous studies. The sensitivity of the calculations to the assumed solid solubility products, highlighted by the example of hydrogarnet, is likely the reason that some studies, including this one, predict a stable SO₄‐rich AFm phase while others do not. The majority of the effort is given for calculating the influences on AFm and AFt stability of alkali and carbonate components, both of which are typically present in cementitious binders. Higher alkali content shifts the equilibria of both AFt and AFm to lower Ca but higher Al and S concentrations in solution. More importantly, higher alkali content significantly expands the range of solution compositions in equilibrium with AFm. The introduction of carbonates alters not only the stable AFm solid solution compositions, as expected, but also influences the range of solution pH over which SO₄‐rich and OH‐rich AFm phases are dominant. Some experimental tests are suggested that could provide validation of these calculations, which are all the more important because of the implications for resistance of portland cement binders to external sulfate attack.     

Optimization of the Thermodynamic Properties and Phase Diagrams of the Na2O–SiO2 and K2O–SiO2 Systems

Available thermodynamic and phase diagram data have been evaluated for all phases in the Na₂O-SiO₂ and K₂O-SiO₂ systems at 1 bar pressure from 298 K to above the liq-uidus temperatures. All reliable thermodynamic and phase diagram data have been simultaneously optimized in order to obtain one set of model equations for the Gibbs energies of all phases as functions of temperature and composition. The thermodynamic properties and phase diagrams calculated from these parameters are self-consistent. The modified quasi-chemical model was used to represent the Gibbs energies of the molten slag phases.     

Coupled experimental phase diagram study and thermodynamic optimization of the Li2O–MgO–SiO2 system

A coupled key phase diagram study and critical evaluation and optimization of all available experimental data of the Li₂O–MgO–SiO₂ system was performed to obtain a set of Gibbs energy functions to reproduce all the reliable phase equilibria and thermodynamic data. Differential scanning calorimetry measurements and equilibration/quenching experiments were performed in the Li₂SiO₃–MgO and Li₄SiO₄–Mg₂SiO₄ sections, respectively, using sealed Pt capsules to prevent the volatile loss of Li. According to the present experimental results, Li₂MgSiO₄ is the only compound present in the Li₄SiO₄–Mg₂SiO₄ isopleth, which shows a peritectic melting at 1465 ± 6°C (1738 ± 6 K). The Modified Quasichemical Model, which considers short‐range ordering in the melt, was employed to describe the thermodynamic properties of the liquid phase. The Li₄SiO₄–Li₂MgSiO₄ and Mg₂SiO₄‐rich solid solutions were modeled using the Compound Energy Formalism.     

Combined experimental and computational investigation of thermodynamics and phase equilibria in the CaO–TiO2 system

Phase relations in the CaO–TiO₂ system are of considerable interest in geology, metallurgy, and ceramics. Despite a number of studies of phase equilibria in the CaO–TiO₂ system, there are still some open questions regarding the stability of intermediate compounds. In this work, a series of specimens with different CaO:TiO₂ ratios were prepared by solid‐state reaction. The heat capacities of Ca₃Ti₂O₇ and Ca₄Ti₃O₁₀ from 300 to 1073 K were measured by differential scanning calorimetry and their formation enthalpies from the component oxides at 298 K were measured by high temperature oxide melt solution calorimetry. Using phase diagram information and thermodynamic data from the literature and the present measurements, thermodynamic optimization of the CaO–TiO₂ system was carried out by the CALPHAD technique. The phase diagram and the thermodynamic properties of the CaO–TiO₂ system were calculated using the obtained thermodynamic database, which clarify the stable and metastable phase equilibria of the system. The thermodynamic stability of the various compounds was discussed.     

Slag Resistance of Al2O3–MgO Refractory Castables in Different Environmental Conditions

Although the corrosion performance of spinel‐containing castables has been extensively investigated in recent years, no previous studies accessed the different conditions present in the ladle bottom. In this region, strong variations in the atmospheric environment are often detected, which could drastically change the interactions between refractory and molten slag. In the present work, the main corrosion mechanisms of an alumina–magnesia castable in two environmental conditions (oxidizing – pO₂ = 0.21 atm—or reducing – pO₂ = 10^?15 atm— atmosphere) were evaluated by means of scanning electron microscopy and EDS analyses of the corroded samples and thermodynamic simulations. The attained results showed that the slag penetration was suppressed in the presence of oxygen due to the precipitation of a great amount of calcium monoaluminate (CA) crystals as the refractory interacted with slag. Conversely, the CA phase was not stable under reducing conditions and, therefore, many more refractory components (Al₂O₃, MgO, and MgAl₂O₄) had to be dissolved to precipitate calcium dialuminate (CA₂) by reacting with infiltrating slag. Thus, besides providing a suitable and more realistic understanding of the castable performance in service conditions, the results also indicated that the prediction of the environmental conditions is of utmost importance for the design of high performance refractories.