Study Of Phase Equilibria Research Articles

Evaluating atomic mobility and interdiffusivity based on two-dimensional diffusion simulations and diffusion triple experiments

Diffusion triples or multiples are commonly considered as high-throughput experiments to study phase equilibrium and diffusion. But when extracting diffusion coefficients, they are treated as diffusion couples with one-dimensional (1D) composition variation, never taking advantage of their two-dimensional (2D) composition distributions. In this work, we present an efficient numerical inverse approach to directly evaluate composition-dependent atomic mobilities and full matrix of interdiffusivities based on a novel 2D diffusion simulation scheme, which was applied to the Co–Fe–Ni alloys by analyzing only one diffusion triple over a wide composition range. Its reliability was confirmed by comparing with traditional methods.

Subsolidus phase equilibria in the GdFeO3-SrFeO3-δ system in air

The paper considers phase equilibria in the subsolidus region of the GdFeO3-SrFeO3-δ system in air. By using X-ray powder diffraction, SEM/EDS, and Mössbauer spectroscopy, a GdFeO3-SrFeO3-δ phase diagram was constructed in the 1300–1500 °C temperature range. The samples of Gd1-xSrxFeO3-α for this study were synthesized by solid-phase chemical reactions. The study of phase equilibria in the GdFeO3-SrFeO3-δ system showed the presence of three areas, that is, of solid solutions based on the strontium-poor GdFeO3 orthorhombic phase, of the strontium-rich SrFeO3-δ cubic phase, as well as of an intermediate region in the mixture of these phases. The miscibility gap width (Δx) decreases from 0.54 to 0.35 with an increase in temperature from 1300 to 1500 °C.

Phase Equilibria of Ferrous-Calcium Silicate Slags in the Liquid/Spinel/White Metal/Gas System for the Copper Converting Process

Ferrous calcium silicate (FCS) slags are reported to have high potential for use in the copper converting process. However, no phase equilibrium study has been carried out under a simulated converting gas atmosphere in the presence of SO2. In this study, under accurately controlled P(SO2) 0.4 atm and P(O2) 10−6 atm, the phase equilibria of FCS slags in a liquid/spinel/white metal/gas system were investigated for the copper converting process. The liquidus temperatures of slags in the Fe-Ca-Cu-Si-S-O system were quantified as well as the solid solubilities of Cu2O in the spinel phase. The experimental results were compared with the FactSage predictions, which provided clues for further improvement of the thermodynamic modelling. The applications of the FCS slags were further discussed and compared with iron silicate slags. The results obtained will contribute to slag development for converting operations and thermodynamic calculations.

Measurement and Correlational Study of Phase Equilibria in Aqueous Solutions of N,N-Dimethylacetamide with 1-Pentanol and 1-Hexanol at 298.15 and 308.15 K

Tie-line data were determined for the systems (water + N,N-dimethylacetamide + 1-pentanol) and (water + N,N-dimethylacetamide + 1-hexanol) at the temperatures of 298.15 and 308.15 K under 101.1 KPa. The phase diagrams for these systems are of type I according to the Treyball classification. The thermodynamic consistency of the measured tie-line data was verified using the Hand and Othmer–Tobias equations. The distribution ratios (D) and selectivity (S) values were computed according to the measured tie-line data to assess the extracting behaviors of the selected solvents. The experimental data were correlated using the nonrandom two liquid and the universal quasichemical activity coefficient equations and the Elephant Herding Optimization Algorithm (EHA). EHA is an emerging nature-inspired stochastic global optimization method, and it has been used for liquid–liquid equilibrium (LLE) parameter estimation of local composition models in multicomponent mixtures. The performance of this new swarm-based metaheuristic search method for LLE modeling with and without the closure equation has been analyzed.

Studies of Phase Equilibria in Ternary KBr–SrBr<sub>2</sub>–H<sub>2</sub>O and NaBr–SrBr<sub>2</sub>–H<sub>2</sub>O Systems at 308 K

Studies of Phase Equilibria in Ternary KBr–SrBr<sub>2</sub>–H<sub>2</sub>O and NaBr–SrBr<sub>2</sub>–H<sub>2</sub>O Systems at 308 K

Thermodynamic and Topological Analysis of Phase Diagrams of Quaternary Systems with Internal Singular Points

A review of the literature published in Russia and abroad on the experimental studies of phase equilibria, methods for analyzing and predicting phase diagram structures, and simulating problems of the vapor–liquid equilibrium (VLE) of quaternary systems containing internal singular points is presented. A complete set of parameters that adequately describe the liquid–vapor and liquid–liquid equilibrium is obtained for the following four systems: acetone–chloroform–ethanol–water, acetone–chloroform–propanol-2–water, chloroform–ethanol–cyclohexane–water, and ethyl acetate–methyl ethyl ketone–cyclohexane–propanol-2. The methodology for determining the structure of the VLE diagram and predicting the presence of an internal azeotrope in the systems under study and in a model system that contains binary azeotropes and a quaternary azeotrope is illustrated. Possible ways for evolutionary changes in the structure of the VLE diagram with a variation in the pressure are shown, and the Poincare indices of boundary single azeotropes and a double tangential azeotrope are determined.

Phase equilibrium studies of high-pressure natural gas mixtures with toluene for LNG applications

To prevent possible freeze out in the main cryogenic heat exchanger (MCHE) used in liquefied natural gas (LNG) plants, new and accurate phase equilibrium data are required to improve the predictive reliability of existing models, in particular cubic equations of state (EOS). In this work, the vapor-liquid equilibrium (VLE) of a ternary methane + propane + toluene (methylbenzene) mixture was studied over a wide range of conditions with toluene as the minor component in both the liquid and vapor phases. Measurements were conducted along different isochoric paths at temperatures between (213 and 298 K) and pressures up to 8.3 MPa, to obtain data at conditions relevant to the operation of LNG scrub columns. The measured VLE data were compared to results calculated with the HYSYS Peng Robinson (PR) equation of state (EOS) that is used widely in LNG industry. The amount of toluene in the vapor phase was found to be under-predicted by the HYSYS PR EOS by an average of around 77% at lower temperatures, with the error increasing as temperature and toluene concentration decreased. The current work demonstrates that the HYSYS PR EOS as well as other cubic EOS substantially under-predict the possible toluene content of saturated vapours that could be present in the overhead of the LNG scrub column. Using the ThermoFAST model recently developed and optimised for the calculation of solid-liquid equilibrium conditions in LNG production, this work further demonstrates that the 77% increase in the toluene content of a saturated vapor entering the MCHE, corresponds to a 7 K increase in the solid formation temperature, which could significantly increase the likelihood of a blockage in the MCHE and thus possible shutdown of the LNG plant. The experimental and modelling work presented here underscores the importance of improving predictions of the allowable threshold concentration of heavy components in fluids entering cryogenic heat exchangers in LNG plants.

Application of GaInSn Liquid Metal Alloy Replacing Mercury in a Phase Equilibrium Cell: Vapor Pressures of Toluene, Hexylbenzene, and 2-Ethylnaphthalene

Mercury has been applied as a sealing and pressure transmission fluid in many experimental phase equilibrium studies employing the synthetic visual method as well as a moving piston in analytical isobaric and/or isothermal methods. However, mercury is highly toxic and therefore its use is restricted by authorities such as those of the European Union. A new apparatus employing nontoxic GaInSn liquid metal alloy as a sealing, moving piston, and pressure transmission fluid for phase equilibrium measurements with a nonvisual variable volume method is presented. The vapor pressures of toluene, hexylbenzene, and 2-ethylnaphtalene are provided within the applied temperature range of 400–620 K. New values for the parameters of the DIPPR 101 and Wagner equations, and PC-SAFT equation of state were regressed. The results demonstrate that GaInSn can be used in phase equilibrium cells as a very convenient substitute for mercury, especially at high temperatures.

Design and processing of drug delivery formulations of therapeutic deep eutectic systems for tuberculosis

Therapeutic deep eutectic systems (THEDES) emerged as alternative therapeutic agents that can enhance the bioavailability of the currently used active pharmaceutical ingredients. The use of THEDES in combination with supercritical CO2 has started to be explored to formulate drug delivery systems through green technology. This work aimed to develop THEDES-delivery systems for tuberculosis therapy, by encapsulating l-arginine-based THEDES in a lipidic matrix, through supercritical CO2 technology. From the phase equilibrium study of THEDES and CO2, PGSS was selected for THEDES encapsulation. Herein, THEDES encapsulation through PGSS was accomplished for the first time, with an average encapsulation efficiency of 75 %. The influence of the THEDES water-content in PGSS processing was also studied, suggesting no interference of the THEDES-water content in the formulation of the THEDES particles. Furthermore, the cell viability of the THEDES and the particles with THEDES encapsulated was measured in L929 fibroblasts and the systems prepared were non-cytotoxic.

Triggered Nanoexplosions of Pd Hollow Spheres.

Gas filled Pd nanocontainers can serve as model nanochambers for reaction and phase equilibria studies. In the current study, palladium hollow spheres (PdHS) filled with oxygen are brought in intimate contact with hydrogen filled PdHS at room temperature (with internal pressure in both the spheres at 20 bar). The molecular hydrogen gets chemisorbed in the Pd shell and further diffuses into the oxygen filled sphere. The rapid reaction of hydrogen with oxygen in the inner wall of the oxygen filled sphere leads to a nanoexplosion, with the formation of water. This explosion results in either the complete breakage of the nanoshell or the formation of connected shells via the rupture of the internal wall connecting the shells. Transmission electron microscopy and Raman spectroscopy have been used to establish the sequence of processes. Further, the water in the nanochambers is cooled below sub-zero temperature to crystallize ice. This phenomenon is observed for the first time at room temperature.

Phase equilibrium, structural properties and separation process studies of potassium-ammonium-based solid solution in aqueous-solid solution (AQ-SS)

In order to solve the problem that potassium salt product is impure in industrial production. Phase equilibrium, structural properties and separation process of potassium ammonium sulfate in aqueous-solid solution (AQ-SS) was studied. First, we study solid-liquid equilibrium of K2SO4-(NH4)2SO4-H2O ternary system, which revealed complete miscibility in the solid phase. The type of solid solutions was determined by analysis of XRD further confirmed-it is infinite substitutional solid solution. Then, from the analysis of FT-IR, TG-DSC and mapping of [(NH4)0.104K1.896]SO4 and [(NH4)1.79K0.203]SO4 solid solution, we can conclude that two solid solutions are similar, but the absorption position have slight shift to low wave number direction as the increasing of K2SO4 content; the weightlessness decreases with the decrease of NH4+ content; the homogeneous distribution of K+ and NH4+ elements. Finally, based on the phase diagrams and the relevant mass balancing, multistage fractional crystallization experiment to obtain the purity of the K2SO4 is 95.28% after three times cycle operation and we can get about 99.04% K2SO4 in the fourth operation by theoretical analysis, which not only demonstrates the potential application of multistage crystallization to separate K2SO4 from AQ-SS, but also provides guidance and methods for the separation of AQ-SS systems.

Experimental study and theoretical simulation of fluid phase equilibrium in the subsystems of quinary system NaBr–KBr–MgBr2–SrBr2–H2O at 298 K

Abstract Underground brine known as one of special fluids existing in nature has been regarded as a kind of comprehensive mineral resource. After multi-step separation mining, it can realize the effective extraction and recovery of various mineral resources. Conducting a series of further studies on this kind of natural fluid, especially on the study of fluid phase equilibrium, will be of great significance to explore the rules of its geochemical evolution and formation, and to guide the follow-up fluid mineralization simulation. Based on the above considerations, stable phase equilibria and solubility data of unreported subsystems for quinary system NaBr–KBr–MgBr2–SrBr2–H2O at 298 K were determined by the method of isothermal dissolution equilibrium aiming at the compositions of the underground brine in western Sichuan Basin. The research contents in this work include two ternary systems (NaBr–SrBr2–H2O, KBr–SrBr2–H2O) and three quaternary systems (NaBr–KBr–SrBr2–H2O, NaBr–MgBr2–SrBr2–H2O, and KBr–MgBr2–SrBr2–H2O). The phase diagrams of listed above systems were all drawn by experimental data. The experimental results show that there are no solid solutions as well as any complex salts in the three ternary systems. These phase diagrams all contain two solid phase regions of crystallization, two isothermal dissolution curves and only one isothermal-isobaric invariant point. At 298 K, quaternary systems NaBr–KBr–SrBr2–H2O belongs to a simple type, and the phase diagram consists of only one isothermal-isobaric invariant point, three isothermal dissolution curves and three crystallization regions. In the phase diagram of quaternary system NaBr–MgBr2–SrBr2–H2O at 298 K, there are two isothermal-isobaric invariant points, five isothermal dissolution curves, and four crystallization regions. In the quaternary systems KBr–MgBr2–SrBr2–H2O at 298 K, it was found that one complex salt (KBr·MgBr2·6H2O) formed and the phase diagram has two isothermal-isobaric invariant points, five isothermal dissolution curves, and four crystallization regions. The solubilities of the above subsystems at 298 K were predicted accurately by referring to Pitzer's electrolyte solution theory. It was found that the predicted results were coincided basically with the experimental data.

Phase equilibria and liquid phase behavior of the K2O-CaO-SiO2 system for entrained flow biomass gasification

Experimental data of solid-liquid phase equilibria in the K2O-CaO-SiO2 systems vital for many technologies and industrial applications are very limited and even not available at some primary phase fields. In the present study, by using Equilibration-Quenching-Phase compositional analysis (EPMA/EDS) method, liquidus compositions in equilibrium with pure solid SiO2, CaO·SiO2, 3CaO·2SiO2, 2CaO·SiO2, K2O·6CaO·4SiO2 and K2O·2CaO·2SiO2 compounds and 2CaO·SiO2 solid solution were measured. By knowing the evaporation behavior of K2O during the equilibration process, specific initial mixtures could be selected to obtain liquidus data for targeted final equilibrium assemblages. EPMA and EDS analysis results were compared. The experimental data obtained in the present study were discussed and compared with the results from previous experimental investigations and the assessed ternary phase diagrams. Some novel experimental data of the liquid at single and double solid phase saturations were obtained in the present study and they can be used to correct and support the predictions and thermodynamic assessments of the K2O-CaO-SiO2 system. Present investigation reports liquidus projections and detailed phase relations among the phases in isothermal sections at 1000, 1100, 1200, 1300 and 1400 °C. Viscosity calculations of the liquid at different compositions between 1000 and 1400 °C also have been made. A combination of phase equilibria study and the viscosity predictions in the present investigation provides suitable temperature and ash composition regions for optimal flow properties of the slag in entrained flow biomass combustion or gasification processes.

Eulytite-type solid solution in the LaPO4 – Ba3(PO4)2 system

Studies of phase equilibria in the LaPO4–Ba3(PO4)2 system were carried out in the whole concentration range in temperature scope up to 1950 °C using TGA/DSC, XRD and reflected light microscopy. Analysis of the results allowed to determine the phase relationships in the system. In the LaPO4–Ba3(PO4)2 system, there is an intermediate compound Ba3La(PO4)3 that divides the studied concentration range into two partial systems: LaPO4–Ba3La(PO4)3 and Ba3La(PO4)3–Ba3(PO4)2. They both have a eutectic character. Ba3La(PO4)3 is a thermodynamically stable phosphate at room temperature. At high temperature it forms a limited solid solution with Ba3(PO4)2. At 1450 °C, the maximum solubility of Ba3(PO4)2 in Ba3La(PO4)3 corresponds to phase of the Ba3.66La0.34(PO4)2.78 composition.

Application of phase equilibrium studies of CaO–SiO2–Al2O3–MgO system for oxide inclusions in Si-deoxidized steels

In the steelmaking process, the compositions of the oxide inclusions could be modified by refining slags to a large extent. The chemistries of the oxide inclusions and refining slags can be described by the system CaO–SiO2–Al2O3–MgO. Phase equilibria and liquidus temperatures in this system have been experimentally investigated in the composition and temperature ranges related to the oxide inclusions and refining slags by means of high-temperature equilibration, quenching and electron probe X-ray microanalysis. Isotherms in the interval of 20 °C between 1260 and 1560 °C were determined in the primary phase fields of wollastonite, anorthite, spinel, and melilite. Effects of the mass ratio of (Al2O3+SiO2)/((Al2O3+SiO2)+(CaO + SiO2)) and MgO content on the liquidus temperatures have been discussed to assist inclusion control. To obtain the lowest liquidus temperature of Al2O3–SiO2–CaO–MgO system inclusions, refining time ought to be properly controlled.

Phase Equilibria of Flexible Polymer and Monomer Liquid Crystal Blends

In this study, we explored the phase equilibria in blends of a nematic liquid crystal monomer and a nematic liquid crystal flexible polymer within the whole composition of the phase diagram. The crystal-nematic and nematic-isotropic transition temperatures, as well as the transition enthalpies and entropies, indicated the total miscibility in this mesogenic blend system. We also extracted an empirical axial ratio of 4.52 for the polymer from the nematic-isotropic transitions of the blends. Further, from the biphasic nematic-isotropic transitions of the blends in low concentration regions, we estimated the entropies of pure monomer and polymer from a theoretical lattice model. The calculated and experimental results showed good agreement. This work will be continued with a more detailed study of phase equilibria and comparison with other theoretical models in nematic flexible polymer and non-mesogenic rigid-rod monomer blends will be made.

Experimental study of phase equilibria on Co–Fe-rich side of Co–Al–Fe system

Despite various studies on Co–Al–Fe ternary system, its phase equilibria are still in doubt. Phase equilibria, magnetic transition and bcc_A2/bcc_B2 order–disorder transformation at the Co–Fe-rich side of the Co–Al–Fe alloys were carefully investigated by means of electron probe microanalysis (EPMA), X-ray diffraction (XRD) and differential scanning calorimetry. The equilibrium phases and their compositions were determined by 18 alloy samples annealed at 900, 1000, 1100 and 1200 °C for 528, 336, 168 and 96 h, respectively, followed by quenching. However, by adopting the above traditional method, bcc_A2 and fcc_A1 phases are difficult to be distinguished through XRD analysis at room temperature due to the martensitic transformation of fcc_A1 phase during quenching. For this reason, high-temperature in situ XRD technique was utilized to correctly establish the phase relationships among bcc_A2, bcc_B2 and fcc_A1 phases. The phase transformation between bcc_A2 and B2 phases was determined to be second order instead of first order at temperatures higher than 900 °C. The equilibrium phases and compositions were further confirmed by fabricating 16 diffusion couples together with EPMA. Meanwhile, using three-dimensional differential scanning calorimetry method, bcc_A2/B2 and ferro-/paramagnetic transitions were determined with high accuracy.

Some Issues of Complex Studies of Phase Equilibria and Thermodynamic Properties in Ternary Chalcogenide Systems Involving Emf Measurements (Review)

We address the methodology of a complex study of phase equilibria and thermodynamic properties in ternary metal and semiconductor systems using the emf method. A focus is on the behavior of partial molar functions in heterogeneous phase fields in the context of Voronin’s concept of partial heterogeneous functions (PHFs). The applicability criteria of emf measurements in heterogeneous phase fields for thermodynamic calculations have been determined. The scheme for calculating the integral thermodynamic functions (ITFs) of ternary phases from the partial molar functions of one component and the phase diagram using the integration of the Gibbs–Duhem equation has been described. Numerous thermodynamic data for ternary chalcogenide and chalcohalide systems gained by various variants of the emf method are cited.

Development of Experimental Approach for the Phase Equilibria Study of Arsenic-Containing Systems

The technique of arsenic-contained compounds synthesis has been developed. The experimental samples synthesis is proposed to be divided in two stages. The first stage includes the long-term heating of samples in specially developed high-pressure furnace with the excessive pressure to 50 bar at 900 °C. The second stage relates to conventional heating process at 1 atm pressure and 1200 °C. Results of differential thermal analysis, scanning electron microscopy and energy-dispersive x-ray spectroscopy has shown the consistency of obtained data to the preset phases and their compositions. The developed method can be used for studies of phase equilibria in multicomponent arsenic-contained systems or any complex systems with volatile compounds.

Factors influencing the microstructures of iron ore sinters

ABSTRACT The phases and the phase assemblages present in selected industrial iron ore sinters have been analysed. A new experimental laboratory-based procedure has been developed that enables sintering experiments to be undertaken under controlled temperature and gas conditions. The results indicate that the formation of the complex silico ferrite of calcia and alumina phase (SFCA) phase is strongly influenced by the sinter bulk composition. Within the range of compositions of interest to industrial iron ore sintering, an increase of CaO/SiO2 ratio facilitates the growth of the SFCA phase and the addition of Al2O3 increases the stability of the SFCA at elevated temperatures. Decreasing the oxygen partial pressure not only decreases the liquidus temperature but also lowers the relative stability of the SFCA phase. These observations are consistent with results obtained from phase equilibria studies of these systems, and indicate clear links between phase equilibria, melt solidification processes and sinter product microstructures.