Thermodynamic assessment of the pseudoternary Na2O–Al2O3–SiO2 system

Vitrified high‐level radioactive waste that contains high concentrations of Na₂O and Al₂O₃, such as the waste stored at the Hanford site, can cause nepheline to precipitate in the glass upon cooling in the canisters. Nepheline formation removes oxides such as Al₂O₃ and SiO₂ from the host glass, which can reduce its chemical durability. Uncertainty in the extent of precipitated nepheline necessitates operating at an enhanced waste loading margin, which increases operational costs by extending the vitrification mission as well as increasing waste storage requirements. A thermodynamic evaluation of the Na₂O–Al₂O₃–SiO₂ system that forms nepheline was conducted by utilizing the compound energy formalism and ionic liquid model to represent the solid solution and liquid phases, respectively. These were optimized with experimental data and used to extrapolate phase boundaries into regions of temperature and composition where measurements are unavailable. The intent is to import the determined Gibbs energies into a phase field model to more accurately predict nepheline phase formation and morphology evolution in waste glasses to allow for the design of formulations with maximum loading.     

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.     

Phase equilibria study and thermodynamic description of the BaO‐CaO‐Al2O3 system

A combined experimental investigation and thermodynamic assessment was performed for the BaO‐CaO‐Al₂O₃ system. By using a high‐temperature equilibration/quenching technique and scanning electron microscopy, electron probe microanalysis, and X‐ray powder diffraction analysis, the phase equilibria at 1500°C and phase stability of BaCa₂Al₈O₁₅ phase were determined. An extensive literature survey was conducted for the experimental and thermodynamic modeling data of the BaO‐CaO‐Al₂O₃ system. According to the literature data and the present measurements, a thermodynamic assessment was made in order to obtain a set of self‐consistent thermodynamic parameters to describe the BaO‐CaO‐Al₂O₃ system. Based on the thermodynamic parameters acquired in this work, isothermal sections at 1100°C, 1250°C, 1400°C, 1475°C, and 1500°C and the BaO·Al₂O₃‐CaO·Al₂O₃ and BaO·6Al₂O₃‐CaO·6Al₂O₃ joints were calculated and compared with the available experimental data.     

A practical approach to produce Mg‐Al spinel based on the modeling of phase equilibria for NH4Cl‐MgCl2‐AlCl3‐H2O system

Based on chemical modeling of phase equilibria for the NH₄Cl‐MgCl₂‐AlCl₃‐H₂O system, a practical approach to produce Mg‐Al spinel (MgAl₂O₄) (widely used as refractory brick, supports in catalysts, and inert material for oxygen carriers) is proposed and proven feasible. This novel process includes coprecipitation of Mg₄Al₂(OH)₁₄·3H₂O from the NH₃‐MgCl₂‐AlCl₃‐H₂O system; calcination of Mg₄Al₂(OH)₁₄·3H₂O to obtain Mg‐Al spinel and recovery of NH₄Cl from NH₄Cl‐rich solutions by feeding MgCl₂‐AlCl₃. A MSMPR reactor was applied to investigate the effect of temperature, feed concentration, and NH₄Cl addition on coprecipitation of precursor Mg₄Al₂(OH)₁₄·3H₂O from MgCl₂‐AlCl₃ solutions with Mg/Al ratio = 2 through gradual addition of NH₄OH. The phase equilibria of the NH₄Cl‐MgCl₂‐AlCl₃‐H₂O system were determined over the temperature range 283.2 to 363.2 K using dynamic method. The experimental solubilities were regressed to obtain new Bromley‐Zemaitis model parameters. These newly obtained parameters were verified by predicting the quaternary system. A chemical model for the NH₄Cl‐MgCl₂‐AlCl₃‐H₂O system has been established with the OLI platform. All the results generated from this study will provide the theoretical basis for Mg‐Al spinel production. The high quality Mg‐Al spinel was prepared by calcination of precursor from 773.2 to 1273.2 K, and the NH₄Cl was successfully recovered through the common ion effect of MgCl₂‐AlCl₃ addition. © 2012 American Institute of Chemical Engineers AIChE J, 59: 1855–1867, 2013     

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.     

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.     

High‐temperature calorimetric study of oxide component dissolution in a CaO–MgO–Al2O3–SiO2 slag at 1450°C

Blast‐furnace slags are formed, as iron ore is reduced to metal, as a molten a mixture of refractory and not easily reducible oxides, largely silica, alumina, lime, and magnesia. Their relatively low silica content makes them basic and poor glass formers. Their thermodynamic properties, though important for modeling their formation and reactivity, as well as furnace heat balance, are poorly known. Solution calorimetry of small amounts of solid oxides in a molten oxide solvent at high temperature (up to about 1500°C) permits direct assessment of energetics of dissolution. The enthalpies of solution of slag forming oxides: CaO, SiO₂, Al₂O₃, MgO, and Fe₂O₃ in a simplified model slag of composition: CaO (45.9 mol%), SiO₂ (35.1 mol%), Al₂O₃ (8.3 mol%), MgO (10.7 mol%) were measured by high‐temperature drop solution calorimetry at 1450°C. For this slag composition, enthalpies of solution become more exothermic in the order: Fe₂O₃ (279.3 ± 20.8 kJ/mol), MgO (56.7 ± 9.1 kJ/mol), Al₂O, (41.6 ± 11.3 kJ/mol), CaO (?4.3 ± 2.3 kJ/mol), and SiO₂, (?20.4 ± 4.4 kJ/mol), reflecting the relatively basic character of this low‐silica melt. Within these fairly large experimental errors, characteristic of calorimetry at this high temperature, there is little or no discernible concentration dependence for these heats of solution. The trends seen for these five solutes parallel those seen for heats of solution of the same oxides in other melts at various temperatures, with changes in magnitude reflecting the differences in acid‐base character of the melts. The new data for quartz show systematic behavior which extends the range of basicity studied for the enthalpy of dissolution of silica. The results provide reliable data for future modeling of the thermal balance of steel‐making furnaces and geologic and ceramic systems.     

二氧化碳和醇类体系相平衡的研究进展

CO2和醇类混合物的高压相平衡是化工、食品及药品工业设计和运行过程中的基础数据。笔者对CO2-醇类二元体系相平衡的实验测定和理论模型方面的进展进行了总结,并分析了适用于CO2和醇类体系高压相平衡计算的交叉缔合模型的发展方向。     

Thermodynamics of the CaO–SiO2–VOx system at 1873 K under the oxygen partial pressure of 6.9×10−11 atm

Based on the phase equilibria of the CaO–SiO₂–VO_x system determined experimentally at 1873 K and the oxygen partial pressure of 6.9×10^?11 atm, the isothermal section diagram of the system was constructed. Aside from the simple oxides SiO₂ and V₂O₃, three complex crystal phases CaV₂O₄, Ca₂SiO₄ dissolving V₂O₃, and CaVO₃ dissolving SiO₂ were found in the present investigated composition range. The solubility of V₂O₃ in Ca₂SiO₄ phase can reach 5 mass %, and the CaVO₃ phase dissolves about 5% mass SiO₂. Furthermore, the thermodynamic activities of VO_x and SiO₂ in the determined single liquid region were measured by equilibrating the melts with liquid copper. The activity coefficient of SiO₂ decreases linearly with the increase in the basicity of the melts and is almost irrelevant to the total content of vanadium oxides. The activities of vanadium oxides increase slightly with the increase in the basicity but are mainly determined by the total content of vanadium oxides in the melts. With the increase in the basicity, the activity coefficient of VO_1.5 increases almost linearly, whereas those of VO₂ and VO_2.5 decrease gradually.     

Experimental determination of phase equilibria in the CaO-BaO-SiO2-12 mol pct. Al2O3-13 mol pct. MgO system at 1573 K and 1623 K

Phase equilibria of the CaO-BaO-SiO₂-12mol pct. Al₂O₃-13mol pct. MgO system with a wide substitution range of CaO with BaO have been experimentally determined at 1623 K (1350°C) and 1573 K (1300°C) using high-temperature equilibration followed by X-ray diffraction (XRD), scanning electron microscopy (SEM), and electron probe microanalysis (EPMA) analysis. The (Ca,Ba)₃MgSi₂O₈, BaAl₂O₄, BaAl₂Si₂O₈ and Ca₂(Al_0.46Mg_0.54)(Al_0.46Si_1.54)O₇ phases have been designated within the phase diagram. The liquidus temperature initially decreased and then increased for the samples substituting CaO with BaO at a constant (C + B)/S ratio between 1.50 and 1.86. For samples with a constant BaO/CaO ratio, the liquidus temperature showed similar trends with a lower (C + B)/S ratio from 1.22 to 0.67. The volume fraction of crystal phases of the samples as-quenched from 1573 K (1300°C) correlated well with the variation of liquidus and the primary phases. In addition, the change in the Gibbs free energy of the reactions and the bond parameter (X_p × Z/R_k) of the cations were analyzed, where the maximum change in the Gibbs free energy was found for the formation of Ca₃MgSi₂O₈; furthermore, the stronger basic tendency of Ba²⁺ than Ca²⁺ facilitates Ba²⁺ substitution for Ca²⁺ and bonding with acidic tendency cations to form Ba-containing phases.     

High-pressure phase equilibria and densities of the binary system carbon dioxide/methyl laurate

The equilibrium compositions and densities in the gaseous and liquid phases of the binary system carbon dioxide/methyl laurate (dodecanoic acid methyl ester) have been measured at 40 °C, 50 °C and 60 °C, and at pressures up to 120 bar. Equilibrium was attained by recirculating both phases through a high-pressure view cell. A vibrating sensor tube was used to determine densities. Compositions were measured by taking samples from both phases by means of six-way valves.     

Experimental phase equilibria studies of the PbO–SiO2 system

Phase equilibria of the PbO–SiO₂ system have been established for a wide range of compositions: (i) liquid in equilibrium with silica polymorphs (quartz, tridymite, and cristobalite) between 740°C and 1580°C, at 60‐90 mol% SiO₂; (ii) with lead silicates (PbSiO₃, Pb₂SiO₄, and Pb₁₁Si₃O₁₇) and lead oxide (PbO) between 700°C and 810°C. A high‐temperature equilibration/quenching/electron probe X‐ray microanalysis (EPMA) technique has been used to accurately determine the compositions of the phases in equilibrium in the system. Significantly, no liquid immiscibility has been found in the high‐silica range, and the liquidus in this high‐silica region has been accurately measured. The phase equilibria information in the PbO–SiO₂ system is of practical importance for the improvement of the existing thermodynamic database of lead‐containing slag systems (Pb–Zn–Fe–Cu–Si–Ca–Al–Mg–O).     

Phase equilibria in the La2O3-Sm2O3-ZrO2 system: Experimental studies and thermodynamic modeling

A series of ceramic samples were prepared to experimentally investigate sub-solidus phase relations in the La₂O₃-Sm₂O₃-ZrO₂ system at 1873 K and 1673 K. No ternary compounds have been observed, while the binary La₂Zr₂O₇ and Sm₂Zr₂O₇ pyrochlore phases form a continuous solid solution La_2?xSm_xZr₂O₇ in the ternary system at the selected temperatures. X-ray diffraction and microstructure results demonstrated that the pyrochlore phase is stable in the ZrO₂-rich corner. The homogeneity range of the pyrochlore phase was carefully determined and the phase boundary of the cubic ZrO₂ (fluorite phase) which extends into the ternary system was also constructed via electron probe microanalysis. The as-obtained data were adopted to determine the mixing parameters for the pyrochlore and fluorite phases in the present thermodynamic modeling. A self-consistent database of the La₂O₃-Sm₂O₃-ZrO₂ system was accordingly established for the first time and the calculations agree well with the experimental data in the current work.     

High quality factor microwave dielectric ceramics in the (Mg1/3Nb2/3)O2–ZrO2–TiO2 ternary system

Novel high quality factor microwave dielectric ceramics (1?x)ZrTiO₄?x(Mg_1/3Nb_2/3)TiO₄ (0.325≤x≤0.4) and (ZrTi)_1?y(Mg_1/3Nb_2/3)_yO₄ (0.2≤y≤0.5) with the addition of 0.5 wt% MnCO₃ in the (Mg_1/3Nb_2/3)O₂–ZrO₂–TiO₂ ternary system were prepared, using solid‐state reaction method. The relationship between the structure and microwave dielectric properties of the ceramics was studied. The XRD patterns of the sintered samples reveal the main phase belonged to α‐PbO₂‐type structure. Raman spectroscopy and infrared reflectivity (IR) spectra were employed to evaluate phonon modes of ceramics. The 0.65ZrTiO₄?0.35(Mg_1/3Nb_2/3)TiO₄?0.5 wt% MnCO₃ ceramic can be well densified at 1240°C for 2 hours and exhibits good microwave dielectric properties with a relative permittivity (ε_r) of 42.5, a quality factor (Q×f) value of 43 520 GHz (at 5.9 Ghz) and temperature coefficient of resonant frequency (τ_f) value of ?5ppm/°C. Furthermore, the (ZrTi)_0.7(Mg_1/3Nb_2/3)_0.3O₄?0.5 wt% MnCO₃ ceramic sintered at 1260°C for 2 hours possesses a ε_r of 31.8, a Q×f value of 35 640 GHz (at 6.3 GHz) and a near zero τ_f value of ?5.9 ppm/°C. The results demonstrated that the (Mg_1/3Nb_2/3)O₂–ZrO₂–TiO₂ ternary system with excellent properties was a promising material for microwave electronic device applications.     

Thermodynamic assessment of the hollandite high-level radioactive waste form

Hollandite has been studied as a candidate ceramic waste form for the disposal of high-level radioactive waste due to its inherent leach resistance and ability to immobilize alkaline-earth metals such as Cs and Ba at defined lattice sites in the crystallographic structure. The chemical and structural complexity of hollandite-type phases developed for high-level waste immobilization limits the systematic experimental research that is required to understand phase development due to the large number of potential additives and compositional ranges that must be evaluated. Modeling the equilibrium behavior of the complex hollandite-forming oxide waste system would aid in the design and processing of hollandite waste forms by predicting their thermodynamic stability. Thus, a BaO–Cs₂O–TiO₂–Cr₂O₃–Al₂O₃–Fe₂O₃–FeO–Ga₂O₃ thermodynamic database was developed in this work according to the CALPHAD methodology. The compound energy formalism was used to model solid solution phases such as hollandite while the two-sublattice partially ionic liquid model characterized the oxide melt. Results of model optimizations are presented and discussed including a 1473 K isothermal BaO–Cs₂O–TiO₂ pseudo-ternary diagram that extrapolates phase equilibrium behavior to regions not experimentally explored.     

Phase Equilibria in the ZrO2–MgO–MnOx System

Phase equilibria were experimentally investigated in the MgO–MnO_x and the ZrO₂–MgO–MnO_x systems for different oxygen partial pressures by powder X‐ray diffractometry, scanning electron microscopy, and differential thermal analysis. The formation of two compositionally and structurally different β‐spinel solid solutions was observed in the MgO–MnO_x system in air in the temperature interval 1473–1713 K. Isothermal sections of the ZrO₂–MgO–MnO_x phase diagram were constructed for air conditions ( = 0.21 bar) at 1913, 1813, 1713, 1613, and 1523 K. In addition, isothermal sections at 1913 and 1523 K were constructed for = 10^?4 bar. The β‐spinel and halite phases of the MgO–MnO_x system were found to dissolve up to 2 and 5 mol% ZrO₂. A continuous c‐ZrO₂ solid solution forms between the boundary ZrO₂–MnO_x and ZrO₂–MgO systems. It stabilizes in the ZrO₂–MgO–MnO_x system down to at least 1613 K in air and down to 1506 K at = 10^?4 bar.     

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.     

Thermochemistry of BaSm2O4 and thermodynamic assessment of the BaO–Sm2O3 system

The BaO–Sm₂O₃ system is of interest for the optimization of synthesis of electroceramics. The only systematic experimental study of phase equilibria in the system was performed more than 40 years ago. The reported experimental values of the enthalpy of formation of BaSm₂O₄ are in conflict, and the reported compound Ba₃Sm₄O₉ has never been confirmed. In this work we synthesized BaSm₂O₄ by solid‐state reaction and determined its heat capacity, enthalpy of formation, and phase transitions by differential scanning calorimetry, high‐temperature oxide melt solution calorimetry and ultra‐high‐temperature differential thermal analysis, respectively. We confirmed the existence of Ba₃Sm₄O₉ and its apparent stability from 1873 to 2273 K by X‐ray diffraction on quenched laser‐melted samples but were not able to obtain single‐phase material for calorimetric measurements. The CALPHAD method was used to assess phase equilibria in the BaO–Sm₂O₃ system, using both available literature data and our new measurements. A self‐consistent thermodynamic database and the calculated phase diagram of the BaO–Sm₂O₃ system are provided. This work can be used to model and thus to understand the relationships among composition, temperature, and microstructure for multicomponent systems with BaO and Sm₂O₃.