Phase Equilibrium Relations Research Articles

Introduction of Cyclic Structures into Phosphonium Salts As Potential Guest Substances for Ionic Clathrate Hydrates

An ionic clathrate hydrate composed of tri-n-butylbenzyl-phosphonium chloride has been investigated from the viewpoint of phase equilibrium (temperature-composition) relations in comparison with an ionic clathrate hydrate with tri-n-butyl(cyclohexylmethyl)phosphonium bromide. The highest dissociation temperature of the ionic clathrate hydrates composed of tri-n-butylbenzylphosphonium chloride and tri-n-butyl(cyclohexyl-methyl)phosphonium bromide were 274.4 ± 0.1 K and 276.0 ± 0.1 K, respectively at the atmospheric pressure. The dissociation enthalpy of tri-n-butylbenzyl-phosphonium chloride ionic clathrate hydrate was 192 ± 3 kJ·kg−1. These results allow us to suggest that controlling steric structures in the guest compounds might be one of the options for tuning the equilibrium temperatures of ionic clathrate hydrates.

Phase equilibria relations in the V2O5-rich part of the Fe2O3-TiO2-V2O5 system at 1200°C related to converter vanadium-bearing slag

Phase equilibria relations in the V2O5-rich part of the Fe2O3-TiO2-V2O5 system at 1200°C related to converter vanadium-bearing slag

Thermodynamic evaluation and optimization of the K2O‐Al2O3‐SiO2 system

AbstractThe K2O‐Al2O3‐SiO2 system is an important component of microcrystalline glass. The K2O‐Al2O3 and K2O‐SiO2 binary systems and the K2O‐Al2O3‐SiO2 ternary system were thermodynamically evaluated and optimized using the CALculation of PHAse Diagram (CALPHAD) method. The liquid phase is described by using the ionic two‐sublattice model, and the solid solutions involved in the ternary system are all described using the compound energy formalism (CEF) model. The new parameters obtained from the optimization are capable of describing the equilibrium phase relations of the ternary system and its subsystems, and the calculated thermodynamic properties of the ternary compounds are in good agreement with the experimental data.

Phase equilibria of SiO2–Al2O3–Fe3O4-5 wt.% CaO system at 1400 °C in air relevant to the production of continuous basalt fibers: Emphasis on spinel solid solution phase

A long-term foundational study aimed at developing a thermodynamic database for continuous basalt fiber systems is in progress. In this work, the equilibrium phase relations of the SiO2–Al2O3–Fe3O4-5 wt.% CaO system at 1400 °C in air atmosphere were determined experimentally using the equilibrium-quenching technique. Subsequent analyses were conducted using Electron Probe Micro-Analysis (EPMA), X-ray Diffraction (XRD), and Scanning Electron Microscopy (SEM) to validate the experimental results and further investigate the microstructural characteristics. The results revealed a single liquid region and three distinct two-phase regions as Liquid-Cristobalite, Liquid-Mullite solid solution, and Liquid-Spinel solid solution. Additionally, two three-phase regions were identified as liquid-cristobalite-mullite solid solution, and liquid-mullite solid solution-spinel solid solution. This work contributes to a deeper understanding of the phase behavior during the melting of basalt ore systems, which is crucial for optimizing their production and enhancing their applications.

Investigation of the multitemperature stable phase equilibria of alkali tetraborates and bromides and molecular thermodynamic modeling based on DFT

The multitemperature stable phase equilibria of alkali tetraborate and bromide were investigated by isothermal dissolution equilibrium method. Based on the experimental data, the phase diagrams and the density-composition diagrams of the ternary systems were drawn respectively. The results demonstrate that the phase diagrams of alkali tetraborate and bromide ternary systems with water as solvent at 273.2 K, 288.2 K and 308.2 K consist of one invariant point, two univariate solubility curves and two crystallization fields. The density at the invariant points is greater than that at the adjacent points. Additionally, based on density functional theory (DFT), a molecular model of phase equilibria of alkali tetraborate and bromide was creatively established to predict the phase equilibrium solubilities of the ternary systems. Based on results of Raman spectra identification of borate ions in the ternary mixed solutions, the primary forms of borate ions in solution, namely B(OH)3, B(OH)4−, B3O3(OH)4− and B4O5(OH)42− were comprehensively considered in this work. By comparing the experimental data of these ternary systems with the calculated results of the DFT model, it is found that the DFT model can describe the solid–liquid equilibria of the ternary systems well, and has high accuracy. The investigation of the multitemperature stable phase equilibria of alkali tetraborate and bromide can provide thermodynamic data for separation of alkali tetraborates and bromides in brines.

Development of a customized computer Program for the construction of ternary diagram for liquid-liquid extraction process

The Liquid-Liquid Extraction (LLE) is a liquid-liquid phase mass transfer process in which solute chemicals are transferred between two immiscible or partially miscible liquids due to difference in solubility of the solutes in the two liquids. The phase equilibrium relationships are generally inconvenient to handle algebraically, therefore, LLE computational analyses are usually made graphically. Manual construction of ternary diagram becomes cumbersome, tedious and time consuming when used for a process that requires large number of stages. Therefore, the aim of this work was to develop a customized computer package for the ternary diagram. The customized computer package for the ternary diagram construction was achieved with the use of fuzzy inference system toolbox and primitive line function in MATLAB. The computer program was test-run using data from literature to determine theoretical number of stages for a given LLE separation process. The result compared well with the existing literature result.

Phase stability of W-containing high-entropy carbide with silicon addition at high temperatures

Reactive melt infiltration (RMI) is a typical method to produce carbon fiber-reinforced ultra-high temperature ceramic matrix composites (Cf/UHTCs), for which the molten Si is a very general and practical infiltrator. High-entropy carbide (HE-carbide) is a newly developed promising matrix phase of Cf/UHTCs. Understanding the phase equilibrium relation in the HE-carbide and Si reaction system can provide accurate guidance on designing the RMI process for preparing HE-carbide matrix composites with controlled phases and microstructure. This study systematically investigates W-containing HE-carbide and Si addition reactions at high temperatures. Samples with nominal starting compositions of (Ti0.2Zr0.2Hf0.2Ta0.2W0.2)C-xSi (HEC-xSi, x = 2.5, 5 and 10 wt%) are prepared by spark plasma sintering technique at 1500 °C and 1700 °C with an axial pressure of 40 MPa for 10 min. The results show that adding 2.5 wt% or 5 wt% Si removes carbon from the HEC matrix, forming SiC and stable equimolar (Ti0.2Zr0.2Hf0.2Ta0.2W0.2)C1-x phase with carbon deficiency at high temperatures. In contrast, besides the SiC phase, the addition of 10 wt% Si in the HEC matrix may form unstable transient phases of (Ti0.2Zr0.2Hf0.2Ta0.2W0.2)C1-x with supersaturated carbon deficiencies at high temperatures, which finally decomposes into non-equimolar HE-carbide (Ti0.2Zr0.2Hf0.2Ta0.2W0.2-y)C1-z and metal silicide WSi2 phases. The effects of the HEC and Si reactions on the microstructure evolution of the samples during sintering are discussed. Meanwhile, the mechanical properties of the samples with the reaction resulting microstructure are measured and briefly discussed.

Effect of ZrO2 on the phase relations for CaO-SiO2-TiO2 system related to efficient extraction of titanium from titania-bearing slag

The selective crystallization and phase separation process has been regarded as a promising process for the recycling of titanium from titania-bearing furnace slag, however, the composition modification mechanism still remains unclear due to the lack of fundamental thermodynamic data. In the present work, the influence of ZrO2 addition on the equilibrium phase relations and the 1400 °C isotherm for CaO-SiO2-TiO2 system were experimentally determined by using the high temperature equilibration-quenching technique, and Scanning Electron Microscopy-Energy Dispersive X-ray Spectrometry, and X-ray diffraction analysis. The equilibrium solid phases of rutile (TiO2), perovskite (CaTiO3), and tridymite (SiO2) are determined to be coexisting with the liquid phase. In addition, comparisons of present results with thermodynamic calculation by FactSage show significant discrepancies. The present work is important for enriching the thermodynamic database of titania-bearing slag oxide systems as well as optimizing the selective crystallization and phase separation process.

Determination and molecular simulation of ternary solid–liquid phase equilibrium of succinic acid + maleic acid + water from 283.15 K to 333.15 K

This study used the isothermal saturation gravimetric method to examine the solid–liquid phase equilibrium relationships composed of succinic acid + maleic acid + water spanning from 283.15 K to 333.15 K. The experimental data were utilized for the purpose of plotting the equilibrium phase diagrams of ternary systems in the studied temperature range. There were three crystalline regions in each isothermal ternary phase diagram, two saturation boundary curves, and a co-saturation point. To broaden the use of data from binary and ternary phase equilibrium measurements, Wilson and NRTL models were utilized for correlation and expectation, while relative average deviation (RAD) and root mean square deviation (RMSD) were utilized to evaluate the computational exactness. The results show that the theoretically calculated values were found to be in near agreement with the experimental values, and both models were able to obtain more precise theoretical data under different experimental conditions. In addition, molecular simulation was employed to elucidate the interaction between succinic acid, maleic acid, and water. This study provides accurate and reliable data for the separation of succinic acid and maleic acid mixture in water. These findings can be utilized to make sense of the dissolvability conduct of succinic acid and maleic acid in aqueous solution.

Experimental investigation of the CaO-Al2O3-TiO2 system: Isothermal section of 1500 °C and liquidus projection

The CaO-Al2O3-TiO2 phase diagram is of great guiding significance for the comprehensive utilization of Ti-bearing mineral resources and the design of metallurgical slag for Al-Ti alloy steel. In this paper, the high-temperature phase equilibrium experimental method was adopted; the types and compositions of phases were identified by Electron Probe Micro Analysis (EPMA) and X-ray diffraction (XRD). A total of 12 equilibrium phases were determined, including CaO, Al2O3, TiO2, 3CaO2TiO2, 4CaO3TiO2, CaOTiO2, Al2O3TiO2, 3CaOAl2O3, CaOAl2O3, CaO2Al2O3, CaO6Al2O3, and Liquid; they formed a total of 16 phase equilibrium relations. The isothermal section of CaO-Al2O3-TiO2 system at 1500 °C in atmosphere was constructed for the first time. There are 10 three-phase fields (Liquid+CaO+3CaO2TiO2, Liquid+3CaO2TiO2+4CaO3TiO2, CaOTiO2+CaOAl2O3+CaO2Al2O3, CaO2Al2O3+CaOTiO2+CaO6Al2O3, Liquid+CaOTiO2+ CaO6Al2O3, Liquid+CaO6Al2O3+Al2O3, Liquid+Al2O3+Al2O3TiO2, Liquid+TiO2+Al2O3TiO2, Liquid+CaOAl2O3+4CaO3TiO2, 4CaO3TiO2(ss)+CaOTiO2(ss)+CaOAl2O3), 13 two-phase fields (Liquid+CaO, CaO+3CaO2TiO2, Liquid+3CaO2TiO2, Liquid+4CaO3TiO2, Liquid+TiO2, Liquid+CaOTiO2, Liquid+Al2O3TiO2, Liquid+Al2O3, Liquid+CaO6Al2O3, Liquid+CaOAl2O3, CaOTiO2(ss)+CaO2Al2O3, 4CaO3TiO2(ss)+CaOTiO2(ss), 4CaO3TiO2(ss)+3CaO2TiO2(ss)), 2 single-phase solid solution fields (4CaO3TiO2(ss), 3CaO2TiO2(ss)), and 2 disconnected single liquid phase fields. On this basis, the liquidus projection of the CaO-Al2O3-TiO2 system was revised. The types of relevant invariant reactions were identified by the Lever Rule; the types of relevant univariant reactions were determined by the original method proposed in this paper.

Determination of Citronellal-geraniol Phase Equilibrium Data and Distillation Simulation Study based on Aspen Plus Software

Aspen Plus is an efficient, reliable, and scalable large-scale process simulation software suitable for a variety of applications. It boasts excellent computational efficiency, high-quality physical property data, and comprehensive system integration, earning consistent acclaim within the industry. The separation of citronella oil components is increasingly expensive due to their thermal sensitivity and high separation difficulty. This study utilizes gas chromatography to analyze the volatile oil components and investigates the phase equilibrium relationship of citronellal -geraniol system in citronella oil. Experimental phase equilibrium data for the citronellal-geraniol system in citronella oil are obtained to provide the thermodynamic basis for the separation of the citronellal-geraniol system in citronella oil. Aspen Plus process simulation software is used to estimate the physical property parameters of the citronellal-geraniol system and optimize the distillation separation, providing support for the industrial production of high-purity separation of the citronellal-geraniol system.

Phase equilibria of the Al2O3-SiO2-CrOx system at 1600 °C and pO2 of 10-10-10-11 atm

The equilibrium phase relations of the Al2O3-SiO2-CrOx system were experimentally studied at 1600 °C and pO2 of 10-10-10-11 atm. The high-temperature isothermal equilibration experiments were conducted in a vertical tube furnace, followed by drop quenching and direct phase composition analysis using an Electron Probe X-ray Microanalyzer. The single liquid equilibria, liquid-solid phase equilibria including liquid-corundum, liquid-mullite, and liquid-cristobalite, as well as the three-phase equilibria of liquid-cristobalite-corundum and liquid-corundum-mullite, were observed. The 1600 °C isothermal sections of the quasi-ternary Al2O3-SiO2-CrOx phase diagram at pO2 of 10-10 and 10-11 atm were constructed. The present experimental results display significant discrepancies with the simulations by MTDATA, FactSage, and Thermo-Calc.

Thermodynamic study of the Ca-Cu-Zn ternary system with key experimental measurements

Zinc-based alloys, particularly those alloyed with elements like Ca, Cu, and others, have emerged as promising candidates for biodegradable implants. Therefore, the purpose of this study was to investigate the phase equilibrium relationship of the Ca-Cu-Zn ternary system in the Cu-Zn rich region for Zn-based biodegradable materials development. In this work, 21 and 19 samples were prepared and annealed at the temperatures of 350 and 400 °C, respectively. And Then, these samples were analyzed using analytical techniques including scanning electron microscopy (SEM) coupled with energy dispersion spectroscopy (EDS), electron probe microanalysis (EPMA), and powder X-ray diffraction analysis (XRD). The present obtained results indicate the existence of five regions exhibiting three-phase equilibrium and sixteen regions exhibiting two-phase equilibrium within these two isothermal sections. Additionally, differential scanning calorimetry (DSC) was utilized to determine the phase transition temperatures of alloys with constant values of 12 at% Cu and 40 at% Ca, respectively. Moreover, the CALPHAD method was employed to optimize the thermodynamic parameters of the phases of Ca-Cu-Zn ternary system. The model of the liquid phase was performed using the modified quasi-chemical model (MQM). The compound energy formalism (CEF) model was used to represent the Gibbs free energy of the solid phases. Finally, the experimental measured results could be reproduced well using the present obtained thermodynamic parameters.

An experimental study on the phase equilibria of the CaO–MgO–SiO2–13%Al2O3–50%TiO2 system in air at 1450 °C

This study systematically investigates the phase equilibrium relations of the CaO–MgO–SiO2–13%Al2O3–50%TiO2 system in air at 1450 °C. Within the composition range, the coexistence of the liquid phase with anosovite and rutile, liquid-rutile (TiO2), liquid-anosovite (M3O5), liquid phase with anosovite and spinel, liquid-spinel, liquid phase with perovskite and spinel, and liquid-perovskite (CaTiO3) were found. Additionally, the 1450 °C isotherm in this system was obtained by comparing the experimental liquid phase results with the predicted results by FactSage 8.1. The experimental findings indicated that an increase in MgO content contributed to a higher concentration of MgTi2O5 in the anosovite solid solution. Notably, the predicted liquidus temperature was much lower than the experimentally determined liquidus temperatures within the primary of M3O5 and spinel area. This work would contribute to further refining the phase diagram of the titania-containing systems.

Equilibrium Phase Relationships of CaO-SiO2-TiO2 System with 5 wt% Cr2O3 Addition for Titania-Bearing Slag Recycling

Equilibrium Phase Relationships of CaO-SiO2-TiO2 System with 5 wt% Cr2O3 Addition for Titania-Bearing Slag Recycling

Solid-liquid phase equilibrium relationship of high salt wastewater of coal chemical industry and mechanism of crystallization and scaling process

Crystallization and scaling problem in the process of falling film evaporation was one of the key problems restricting the evaporation process in near-zero discharge of coal chemical wastewater. We studied the phase equilibrium data of the ternary system Na+, Mg2+//Cl--H2O at 303.15–373.15 K. And, the influencing factors of crystallization and scaling were investigated, the flow characteristics of high-salt wastewater descending film were analyzed and the scaling sites were predicted. Results showed the system was a simple ternary system. Both w(NaCl) and w(MgCl2) were linearly correlated with the temperature. The higher MgCl2 contents, the faster rates of crystallization and scaling; temperature and scaling rate showed a positive correlation; the fitted curve of scaling under different roughness was in accordance with y=ax+b. The flow characteristics in evaporation tubes of four high-salt wastewaters (10% NaCl+9, 11% CaCl2, 10% NaCl+9, 11% MgCl2) were simulated. The risk of precipitation scaling was obtained at 591 mm, 667 mm, 772 mm and 938 mm, which was also verified by falling film evaporation experiments. The phase equilibrium relationship was creatively combined with numerical simulation in this paper. Meanwhile, phase equilibrium data was introduced in the study of crystallization and scaling process. This study provided a theoretical basis for the reasonable control of salt scaling in evaporation process of coal chemical industry. It is benefit to ensure the efficient operation of the evaporator, achieve the recycling of inorganic salt products and maximize economic benefits. The goal of "near-zero discharge" would be achieved eventually.

Phase Equilibrium Relationship of CaO–Al2O3–Ce2O3–MgO System at 1573 K

Phase Equilibrium Relationship of CaO–Al2O3–Ce2O3–MgO System at 1573 K

Phase relations of the MgO–SiO2–CrOx system at 1600°C in air and reducing atmospheres

AbstractThe equilibrium phase relations of the MgO–SiO2–CrOx system were investigated at 1600°C in air and at pO2 of 10–10 to 10–11 atm using a high‐temperature isothermal equilibration technique followed by rapid quenching and direct phase composition analyses with electron probe X‐ray microanalysis. Two‐phase equilibria (liquid–cristobalite, liquid–spinel, liquid–corundum, and liquid–olivine) and three‐phase equilibria (liquid–cristobalite–spinel, liquid–olivine–spinel, liquid–spinel–corundum, and cristobalite–spinel–corundum) were observed. The 1600°C isothermal sections at various oxygen partial pressures were constructed for the MgO–SiO2–CrOx system based on the experimentally determined liquid and solid compositions. Data from the literature and the predictions by FactSage and MTDATA software were compared with the present experimental results.

A soil freezing-thawing model based on thermodynamics

The freezing-thawing behavior of soil plays a crucial role in frozen soil engineering. In this study, a soil freezing-thawing model is proposed from the perspective of statistical thermodynamics. First, the phase equilibrium relation for pore ice-water interface is deducted by applying statistical thermodynamics and the theoretical relationship is defined between the freezing temperature (i.e., the temperature at the ice-water interface) and the potential energy (i.e., total suction) of pore-water. This relation reveals that the matric suction of pore-water solely depends on the negative temperature at the pore ice-water interface for a given soil with constant osmotic suction and air pressure. Further, using the aforementioned relation and regarding the ice content of soil as an unknown variable, the thermo-hydraulic field in the soil freezing-thawing process can be solved by the mass and heat conversation. The governing equations related to this model are proposed in detail. Finally, to enhance the applicability of the proposed model, simplified forms in three typical conditions are provided, including the freezing process of saturated soil in artificial ground freezing technique, the capillary water migration coupled with freezing process of unsaturated soil in subgrade engineering and the vapor migration coupled with freezing process of semidry coarse soil under airport runways. Overall, the proposed model can be applied to various conditions and to other types of porous media (such as rock or concrete) that undergo freezing-thawing processes.

A new ternary molybdenum phospho-silicide Mo3Si2P: Phase equilibria, structural, electronic, transport and thermal properties

Here we report the successful preparation and systematical characterization of a novel molybdenum compound Mo3Si2P. As the first genuine ternary molybdenum phospho-silicide, it augments the Mo–Si–P family and may be served as an innovative archetype to develop exotic electronic states. The phase-equilibrium relation of Mo–Si–P system was studied, which defines the phase-stability region of Mo3Si2P, and a phase diagram that makes reviews on the abundant material and electronic physics in the system was established. Mo3Si2P crystallizes in a non-centrosymmetric orthorhombic structure (space group: Ama2) that appears as alternately stacking flat (Mo1)3P3 sheets and buckled (Mo2)3Si3 double-layers along the a-axis direction. The Bloch-Grüneisen-Mott model is employed to describe the T-dependent multiband metallic-conduction which is principally governed by electrons at high temperatures. The thermal-conductivity components of charge carrier and lattice vibration were extracted from κtotal by following the extended Wiedemann-Franz law. Poor thermoelectric performance is evidenced by very low thermoelectric power factor and figure-of-merit that are ascribed to small Seebeck coefficient and high thermal conductivity. Sommerfeld coefficient (γ) and Wilson ratio (RW) demonstrate that the electron correlation is extremely weak. First-principles calculations predict significant contribution from Mo-4 dx2−y2 orbital electrons to the Fermi surface of Mo3Si2P which shows different band fillings from Mo3Ge2P where dz2 electrons take the maximal occupation. Electron-phonon coupling parameter λep was calculated as 0.74, which reveals a medium interaction strength.