Phase Equilibria Research Articles

Liquidus of SiO2 in the Li2O‐SiO2, Na2O‐SiO2, and K2O‐SiO2 systems

AbstractThe phase equilibria in the SiO2‐rich region of the Li2O‐, Na2O‐, and K2O‐SiO2 systems at 1550°C to 1650°C were experimentally studied to determine accurate liquidus of SiO2 in the systems. A classical equilibration/quenching method was used, and the equilibrated samples were analyzed by X‐ray diffraction (XRD) and electron probe microanalysis (EPMA). Samples were contained in sealed Pt crucibles and held at the target temperatures for 7–21 days to reach equilibrium condition. Sealed Pt crucibles were employed to avoid the volatile loss of alkali oxides during high temperature phase equilibration and hydration upon quenching. Accurate liquidus of SiO2 in alkali‐silicate systems was determined for the first time, and the results were analyzed using the limiting slope rule in order to understand the dissolution behavior of alkali oxides in SiO2 melt. It was confirmed that alkali oxide dissolves in SiO2 melt by producing Li+, Na+, and K+ cationic species rather than Li22+, Na22+ and K22+ species.

Thermodynamic study on the phase assemblage of MPC exposed to natural and accelerated carbonation conditions

AbstractMagnesium phosphate cement (MPC), which belongs to chemically bonded phosphate ceramics, is commonly applied as a repair material and waste stabilization/solidifications. However, studies on the influence of CO2 on the phase assemblages in MPC are limited. A thermodynamic simulation approach is employed to explore the influence of CO2 on the equilibrium phase assemblage of MPC. The mechanisms of natural and enforced carbonation of MPC have been investigated in this work. The results disclose that Mg carbonates are less likely to precipitate in magnesium ammonium phosphate cement (MAPC) cured under CO2, while MgCO3·3H2O is the only carbonation product of magnesium potassium phosphate cement (MKPC). The carbonation resistance of MAPC is better than that of MKPC. The increase of activity of magnesia employed in MPC obviously enhances the formation of brucite and slightly promotes the carbonation of MPC.

Mean Activity Coefficients of NaCl in the Ternary System NaCl–SrCl2–H2O at 288.15 K Determined by the Cell Potential Method and Their Application to the Prediction of Phase Equilibria

Mean Activity Coefficients of NaCl in the Ternary System NaCl–SrCl₂–H₂O at 288.15 K Determined by the Cell Potential Method and Their Application to the Prediction of Phase Equilibria

Distribution of Pb, Zn, Fe, As, Sn, Sb, Bi, and Ni Between Oxide Liquid and Metal in the ‘CuO0.5’-CaO-AlO1.5 System in Equilibrium with Cu Metal at 1400 °C

AbstractThe increasing complexity of ore resources and recycled materials in the feed of pyrometallurgical processes present a technical challenge to the metallurgical engineers working on maximizing the recovery of the valuable elements and minimizing the environmental impact of the processes. To address this challenge, the availability of computational tools that can predict the mass and energy balance in complex systems is required. Then, the accurate description of phase equilibria in the complex multicomponent systems describing the chemistry of the pyrometallurgical processes becomes critical for the correct implementation of the indicated tools and facing the outlined industrial challenges. In the present study, the distribution of selected elements (Pb, Zn, Fe, As, Sn, Sb, Bi, and Ni) between oxide liquid and metal in the ‘CuO0.5’–CaO–AlO1.5 system in equilibrium with Cu metal at 1400 °C (liquidus of CaAl2O4) was experimentally studied using the equilibration and quenching technique followed by the electron probe X-ray microanalysis of the resulted samples. The study covered a wide range of effective p(O2) over the system from 10−11 to 10−3.5 (corresponding to formation of immiscible CuO0.5-rich slag). To avoid loss of volatile elements (Pb, Zn, As, Sn, Sb, and Bi), a correlation between ‘CuO0.5’ in oxide liquid and p(O2) in open system was obtained first, followed by studying the volatile elements distribution in closed conditions (Al2O3 crucible sealed in SiO2 ampoule), where ‘CuO0.5’ concentration was used as a marker to evaluate the effective p(O2) over the system. The experimental results were then used for the optimization of the thermodynamic model parameters of the system as part of the integrated experimental and self-consisting thermodynamic modeling research program of phase equilibria in the Cu–Pb–Zn–Fe–Ca–Si–Al–Mg–O–S–(As, Sn, Sb, Bi, Ag, Au, Ni, Cr, Co, and Na) gas/oxide liquid/matte/speiss/metal/solids system. Graphical Abstract

Synthesis of long-chain polyester polymers and their properties as crude oil pour point depressant.

Using acrylic acid advanced ester and styrene as raw materials, the long-chain polyester polymer, polyacrylic acid advanced ester-styrene pour point depressant (P-PPD), was synthesized by molecular design, and its structure was characterized by infrared spectroscopy and nuclear magnetic resonance. In addition, this study experimentally investigated the effect of P-PPD on the phase equilibrium and induction time of natural gas hydrate inhibitors in deionized water (DW) and crude oil/water (O/W) systems, respectively. Polyvinylpyrrolidone (PVP) and mono ethylene glycol (EG) were selected as representatives of kinetic hydrate inhibitor (KHIs) and thermodynamic hydrate inhibitor (THIs), respectively. The results exhibit that P-PPD played a sight role in the phase equilibrium of hydrate, while the addition of P-PPD significantly prolonged the induction time of methane hydrate both in O/W + PVP, OW + EG and O/W + PVP + EG system, indicating that the addition of as-synthesized PPD has a synergistic inhibition effect on the nucleation ability of methane hydrate and can prevent hydrate from formatting during oil and gas transport process, and thus guarantee the flow assurance. The findings of this work will provide a data reference for the hybrid use of hydrate inhibitors and pour point depressants in oil and gas transport.

Microstructure and Phase Equilibria in BCC-B2 Nb-Ti-Ru Refractory Superalloys

Microstructure and Phase Equilibria in BCC-B2 Nb-Ti-Ru Refractory Superalloys

The Concept of the Estimation of Phase Diagrams (An Optimised Set of Simplified Equations to Estimate Equilibrium Liquidus and Solidus Temperatures, Partition Ratios, and Liquidus Slopes for Quick Access to Equilibrium Data in Solidification Software) Part I: Binary Equilibrium Phase Diagrams

This paper presents equations derived from thermodynamic equations for calculating the liquidus and solidus temperatures, the liquidus slope, and the partition ratio for solidification simulations. The constants of these equations can be easily determined from measurement data obtained by digitalisation from known diagrams or can be calculated using a CALPHAD-based software. ESTPHAD has a hierarchical system; the developed functions of the binary systems are used in the calculation of the functions of the ternary systems, the functions of the ternary systems in the calculation of the function of quaternary systems, and so on. The developed method is demonstrated by processing the liquidus and solidus of Si–Ge isomorphous and Al–Mg and Al–Si eutectic equilibrium phase diagrams. The use of this method for calculating the functions of ternary systems will be shown in Part II. The advantages of this method are that the equations are simple, can be determined very quickly, and can be built into the simulation software very easily. The most significant advantage is that the calculation time is shorter by some order of magnitude than that of a CALPHAD-type calculation.

A numerical study of internal transport in oxidizing liquid core–shell iron particles

In an effort to improve the understanding of the rate-limiting mechanisms in liquid iron particle combustion, this study investigates the impact of internal transport within a core–shell structure. The two-dimensional axisymmetric transient continuum model as presented in previous publication (Thijs et al., 2023) is extended, such that the boundary layer between the particle and the gas, surface processes at the particle–gas interface, as well as the internal oxide layer within the particle, considering the transport of reactive O and Fe ions, are resolved. Information from the equilibrium phase diagram, which is included as supplementary data, is used to determine oxidation rate of the particle. The study reveals that finite-rate internal transport significantly alters the temperature evolution compared to models assuming infinitely fast transport. At elevated oxygen concentrations, internal transport becomes rate-limiting, restricting the maximum particle temperature. The core–shell assumption leads to a higher local oxidation degree at the particle–gas interface than the average in the particle, reducing the overall oxygen consumption rate. The maximum particle temperature is reached when heat loss exceeds heat release. Although internal transport limits the maximum temperature, the initial heating rate remains overestimated, suggesting that the initial phase is not solely limited by external oxygen diffusion, and the L2-gas surface is not at thermodynamic equilibrium. The model does not account for the particle size effect on maximum temperature as observed in some experiments. A hypothetical explanation is that internal convection, more pronounced in larger particles, may reduce the internal transport limitation, leading to higher maximum temperatures in larger particles.Novelty and significanceThis study advances the understanding of oxidation rate-limiting mechanisms in liquid iron particle combustion by numerically investigating the impact of internal transport within a core–shell structure. By using a two-dimensional axisymmetric transient continuum model, the research reveals that finite-rate internal transport significantly affects temperature evolution of an oxidizing micron-sized iron particle, particularly at elevated oxygen concentrations where it becomes rate-limiting. The findings demonstrate that a finite-rate internal transport leads to a higher local oxidation degree at the particle–gas interface, reducing the oxygen consumption rates. The study highlights that finite-rate internal transport limits the maximum particle temperature at elevated oxygen concentrations, a trend observed in isolated iron particle combustion experiments. Furthermore, this study provides a hypothetical explanation for the experimentally observed particle size effects on the maximum particle temperature, emphasizing the role of internal convection in larger particles

Research Progress on the Relationship Between Microstructure and Properties of AISI 321 Stainless Steel

AISI 321 stainless steel is widely used in chemical pipelines and nuclear power, prompting research on its high-temperature performance and corrosion resistance. This review focuses on the effects of alloy elements, second-phase particle formation, and heat treatment processes on the microstructure and properties of AISI 321 stainless steel. Fine tuning of alloying elements can affect the mode and effect of dynamic recrystallization, altering the high-temperature flow deformation of AISI 321 stainless steel. In order to achieve phase equilibrium, the relationship between corrosion resistance and high-temperature creep behavior and high-temperature mechanical behavior in the presence of second-phase particles was also analyzed. This review outlines the basic heat treatment procedures for improving material properties, providing a new perspective for solution treatment and improving corrosion resistance. In addition, the latest research progress on other factors affecting the high-temperature performance of AISI 321, such as coatings, was briefly introduced.

Vapor–liquid phase equilibrium prediction for mixtures of binary systems using graph neural networks

AbstractVapor–liquid phase equilibrium (VLE) plays a crucial role in chemical process design, process equipment control, and experimental process simulation. However, experimental acquisition of VLE data is a challenging and complex task. As an alternative to experimentation, VLE data prediction offers great convenience and utility. In this article, an artificial intelligence network is proposed to predict the temperature and the vapor phase composition of binary mixtures. We constructed a graph neural network (GNN) and designed an uncertainty‐aware learning and inference mechanism (UALF) in the prediction process. The model was tested on both a self‐constructed dataset and a publicly available dataset. The results demonstrate that the proposed method effectively reveals the phase equilibrium properties of the target data. This work presents a novel approach for predicting vapor–liquid phase equilibrium in binary systems and proposes innovative ideas for investigating phase equilibrium mechanisms and principles.

Experimental data and thermodynamic modeling for n-propane + Brazil nut oil at high pressures

This research aimed to uncover essential phase transition data for the pseudo-binary system of n-propane and Brazil nut oil. Over a range of temperatures from 313 to 343 K and pressures up to 3.42 MPa, our study identified various phase equilibria, including liquid-vapor, liquid-liquid, and liquid-liquid-vapor, using the visual synthetic-static variable volume method. The observed phase transitions fall under the type III classification proposed by Scott van Konynenburg. Leveraging the cubic Peng-Robinson equation of state with the van der Waals mixing rule, we were able to construct isopleths for the proposed system. Additionally, we examined the fatty acid profile of Brazil nut oil to accurately quantify its composition and estimate critical properties of the pseudo component in line with Kay's rule. This research provides critical insights into the behavior of phase diagrams for pressurized fluid-based extraction and separation processes, which are crucial for achieving maximum yield and minimizing energy expenditure.

Vapor–Liquid Equilibrium Phase Behavior for Binary Mixtures Isopropyl Alcohol and Methyl Ethyl Ketone with Dimethyl Sulfoxide

Vapor–Liquid Equilibrium Phase Behavior for Binary Mixtures Isopropyl Alcohol and Methyl Ethyl Ketone with Dimethyl Sulfoxide

Adsorption Removal of Organophosphates from Water by Steel Slag: Modification, Performance, and Energy Site Analysis

Organophosphates are a type of emerging environmental contaminant, which can be removed effectively by adsorption. Here, modified steel slag was examined for its adsorptive performance in the removal of hydroxyethylidene diphosphonic acid (HEDP) from water. Compared to acid (55.3%, maximum removal rate) and base (85.5%) modification, high-temperature modification (90.6%) significantly enhanced steel slag’s adsorption capacity for HEDP, surpassing that of unmodified slag (71.2%). Kinetic analyses elucidated a two-phase adsorption process—initial rapid adsorption followed by a slower equilibrium phase. The results of adsorption energy analysis showed that modified steel slag preferentially occupied the sites with higher energy, which promoted the adsorption. After five regeneration cycles, the adsorption properties of the material were not significantly reduced, which indicates that the material has good application potential. Microscopic and spectroscopic techniques, including SEM-EDS, FTIR, and XPS, were employed to uncover the surface chemistry and structural changes responsible for the enhanced adsorption efficiency. The adsorption mechanism of HEDP on steel slag is a complete process guided by hydrogen bonding interactions, strengthened surface complexation, and optimized ligand exchange. This study advances the sustainable utilization of industrial waste materials and contributes significantly to the development of innovative water treatment technologies.

Phase equilibrium and separation process of byproduct vinyl acrylate in the ethylene vapor phase method producing vinyl acetate

Vinyl acrylate is one of the byproducts in the ethylene vapor phase method for the production of vinyl acetate (VAc), which not only has a toxic effect on the catalyst but also affects the purity of the product. Currently, phase equilibrium data for vinyl acrylate with water are missing, making the destination of vinyl acrylate in the distillation process uncertain. This has led to a lack of effective removal means, which restricts the optimization of the ethylene vapor phase method. This paper uses a method combining quantum chemistry and molecular dynamics simulation (MD) to investigate the existential form of the water molecule. And based on the ab initio calculation of the first principle, the force field parameters of the special water molecular structure are calculated, and the TIP4P-P force field that can describe the special water structure is established. Using the Gibbs Ensemble Monte Carlo (GEMC) method, the reliability of the improved water molecule force field for modeling the phase equilibrium of a binary system is first verified. Further, vapor–liquid phase equilibrium data for the vinyl acrylate-water binary system at 110 kPa and 150 kPa are calculated and the corresponding x-y and T-x-y phase diagrams are plotted. After performing the thermodynamic consistency test, the phase equilibrium data are fitted to obtain the binary interaction parameters of vinyl acrylate with water. The fitted parameters are applied to the process simulation of the VAc refining process to optimize the conditions and obtain an effective separation scheme for vinyl acrylate. The concentration distribution of vinyl acrylate in the distillation column is investigated, thus clarifying the destination of vinyl acrylate in the distillation process and facilitating the optimization of the ethylene vapor phase method.

Phase equilibria of ternary systems: LiCl–MClx (M = Na+, Mg2+, Sr2+)–H2O systems at 1 bar and volume properties investigating from 1 to 1000 bar (T = 298.2 K)

There are abundant lithium resources in seawater and brines. The thermodynamic phase equilibria of salt-water systems containing lithium have significant advantages to separation lithium from brines. Consequently, measurement and prediction of phase equilibria of LiCl–MClx (M = Na+, Mg2+, Sr2+)–H2O ternary systems are investigated at 298.2 K and 1 bar. The phase equilibria are determined using the isothermal dissolution equilibrium method and the solubilities of salts in the ternary systems are predicted using the Pitzer model. The predicted solubilities agree well with experimental data at 298.2 K and 1 bar.Then, the changes of volume properties (ΔV¯dis0) and compressibility (Δκ¯dis0) of three ternary solutions at high pressure of 1–1000 bars were obtained in this work. The solubility product constants Ksp of salts at high pressure are calculated in detail. The thermodynamic prediction model of the phase equilibria is developed at high pressure of 1–1000 bar accordingly. The predicted phase equilibria at high pressure of 1–1000 bar are discussed and compared detailly.

Energy-saving research on the separation of isopropyl acetate and isopropanol azeotrope using pressure-swing distillation based on phase equilibrium

Energy-saving research on the separation of isopropyl acetate and isopropanol azeotrope using pressure-swing distillation based on phase equilibrium

Growth, structure and optical properties of Rb2CоCl4·2H2O crystals

Phase equilibria in the RbCl–CoCl2·2H2O–H2O system were investigated, single crystals of double rubidium–cobalt chloride dihydrate were obtained, and its structure and optical properties were studied. The regions of crystallization of compounds in the three-component system under study were delimited. Rb2CoCl4·2H2O crystals were grown by controlled decrease in the temperature of a saturated aqueous solution. Using X-ray diffraction analysis, the crystal lattice parameters of Rb2CoCl4·2H2O were obtained and the structure of the crystals was refined. The spectral characteristics of the obtained crystals and the corresponding aqueous solution were studied in the λ range 200–800 nm.

Thermodynamic re-optimisation of the CaO-FeO-Fe2O3 system integrated with experimental phase equilibria studies (Part II – Thermodynamic optimisation)

The Ca-Fe-O system is essential for understanding the chemical equilibria involved in copper production using calcium ferrite slags. It forms a core component of a complex 20-component Cu-Pb-Zn-Fe-Ca-Si-O-S-Al-Mg-Cr-Na-As-Sn-Sb-Bi-Ag-Au-Ni-Co system developed for diverse applications in ferrous and non-ferrous metallurgy. This study re-evaluates the Ca-Fe-O system using recent experimental phase equilibrium data acquired by the authors [1] through advanced equilibration, quenching, and Electron Probe X-ray Microanalysis (EPMA) techniques. Thermodynamic properties of solid phases have been revised in accordance with the recommendations for the third generation of Calphad databases. Liquid endmember heat capacities have been refined to describe glass transition behaviour in supercooled liquids. The updated properties of liquid endmembers significantly extend the applicability of the database, enabling lower-temperature applications related to toxic element leaching from amorphous and partially crystallized slags. The revised, higher melting temperature of CaO enhances predictive accuracy in multicomponent systems. Liquid slag phase has been modelled within the Modified Quasichemical Formalism to account for short-range ordering phenomena. Recent advances in modelling and optimization technique made it possible to assess experimental data within the Ca-Fe-O system as an integral part of a large multicomponent dataset, applicable for industrial conditions.

Pressure-temperature-time paths from metapelites reveal neoproterozoic continental crust underthrusting related to the West Gondwana amalgamation

In this contribution, we employed a petrochronological approach to investigate the tectonometamorphic evolution of Al-rich garnet-staurolite and garnet-staurolite-kyanite (biotite- and plagioclase-free) metapelites of the southernmost portion of the Neoproterozoic Brasília orogen. We have reconstructed the first prograde to peak pressure-temperature-time (P-T-t) paths reported for metamorphic units of the area, by combining petrographic analyses, quantitative compositional mapping of major elements, phase equilibrium modeling, and EPMA Th–U–Pb monazite chemical dating. The metamorphic reactions involved in the prograde metamorphic evolution are discussed, including the effects of garnet fractionation, exhaustion of reactants, and re-equilibration reactions on the major-element composition of garnet porphyroblasts, and their influence on P-T condition estimates. Raman spectroscopy on carbonaceous material (RSCM) thermometry provided insights into the synkinematic retrograde path. A steep prograde path marked by two stages is recorded by the garnet porphyroblasts of garnet-staurolite-muscovite (±kyanite) schists: (i) 555–585 °C and 0.60–0.90 GPa; (ii) 590–635 °C and 1.0–1.4 GPa. Monazite crystals record the prograde to peak path from ca. 630–625 Ma to ca. 605–595 Ma. Matrix graphite crystals suggest post-peak cooling to 400–500 °C concurrent with the late stages of development of the main foliation. The reconstructed P-T-t paths indicate an intermediate dT/dP metamorphism, and a burial rate of ~0.55 km/Ma, with garnet compositional zoning suggesting that the high-pressure P-T-t path resulted from a single metamorphic event. The corresponding geothermal gradients, and in-situ ages, combined with regional evidence, suggest that peak metamorphic conditions were attained during collisional underthrusting of the continental crust related to the West Gondwana amalgamation.

Hydrate phase equilibrium of hydrogen with THP, DCM, TBAB+THF and sulfur hexafluoride +TBAB aqueous solution systems

Hydrate phase equilibrium of hydrogen with THP, DCM, TBAB+THF and sulfur hexafluoride +TBAB aqueous solution systems