Experimental Phase Equilibrium Data Research Articles

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.

Influence of excipients on solubility of oxcarbazepine: Modeling and prediction based on thermodynamic models

In this work, the solubility of oxcarbazepine in polymers (PEG 6000, PEG 20,000, PVP K25, and PVP K30) and their aqueous solutions was investigated by experimental measurement and thermodynamic modeling. Firstly, the solubility of oxcarbazepine in water and polymers was modeled and the corresponding binary interaction parameters (oxcarbazepine + water and oxcarbazepine + polymer) were determined based on the experimental phase equilibrium data. Furthermore, the solubility of oxcarbazepine in the polymer aqueous solution (the mass ratios of polymers in water were 2 %, 4 %, and 6 %) was predicted by the solid-liquid equilibrium (SLE) coupled with the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT). It was observed that the predicted results agreed well with the experimental data, and the average relative deviation (ARD) was <7 %. In this study, the solubility of oxcarbazepine in polymer aqueous solution was successfully predicted through the SLE coupled with the PC-SAFT, which was expected to provide theoretical guidance for the selection of pharmaceutical excipients and the rational design of preparations.

A new activity model for biotite and its application

A new activity model for biotite is formulated in the system K2O-FeO-MgO-Al2O3-SiO2-H2O-TiO2-O2 (KFMASHTO), which extends that for the KFMASH system by introducing a titanium-biotite and a ferric-biotite end-member (tbio: K(TiMg2)[(O)2(AlSi3)O10] and fbio: K(Fe3+Mg2)[(OH)2(Al2Si2)O10]), as well as a pyrophyllite end-member (pyp: Al2[(OH)2Si4O10]) that accounts for the presence of octahedral excess-Al in natural biotites. Phonon calculations applying density functional theory (DFT) using the software Castep yielded the standard entropies of tbio and fbio as Sotbio = 328.06 J/(mol·K) and Sofbio = 301.69 J/(mol·K), and their heat capacity functions. From experimental phase-equilibrium data, the enthalpy of formation value of tbio was constrained as ΔHf,tbioo\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta {H}_{f,tbio}^{o}$$\\end{document} = −6124.68 ± 3.33 kJ/mol. Natural data were used to derive ΔHf,fbioo\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta {H}_{f,fbio}^{o}$$\\end{document}= −5935.3 ± 6.6 kJ/mol. The single-defect DFT method was applied to parameterize important macroscopic mixing properties (macro-W’s) involving tbio and pyp end-members in the model (fbio was treated ideal). Castep-derived microscopic interaction energies (micro-w’s) are presented herein for KFMASH-biotite. The octahedral same-site (M1) Mg–Al mixing micro-w (wMgAl(M1)), the same-site tetrahedral Si-Al mixing parameter (wSiAl(T1)) and the related cross-site term are: wMgAl(M1) = 82.5 kJ/mol, wSiAl(T1) = 95.6 kJ/mol (two T1-sites) and wMgAlAlSi(M1T1)=\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${w}_{MgAlAlSi(M1T1)}=$$\\end{document} 175.1 kJ/mol. The linear combination of these micro-w’s gives a macroscopic Wphleas = 18.8 kJ/mol, that is not transferable to other mineral groups. Micro w’s for Mg-Fe mixing in biotite (wMgFe(M1), wMgFe(M2),wMgMgFeFe(M1M2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${w}_{MgMgFeFe(M1M2)}$$\\end{document}), are all close to ideality. The biotite activity model of this study is thus a first example of next-generation activity models that use DFT- and thus physically based micro-w’s and reassembled macro-W’s for petrological calculations. Test calculations on 5 samples from low- to high-grade metamorphic environments covering metapelite to greywacke bulk-compositions using Perple_X suite of programs illustrate the performance of the new biotite activity model. Computed mineral-chemistries are in all cases in better agreement with measured compositions than resulting from published activity models of biotite.

Fluid Phase Equilibria Carbon Dioxide + Decane + Hexadecane Ternary System

The interest in understanding reservoir fluids' phase behavior is to increase hydrocarbon production without any flow assurance issues. Due to its opacity, the evident complexity of determining phase equilibrium data revolves around the thermodynamic modeling of model systems. The article presents experimental phase equilibrium data and thermodynamic modeling for the CO2 + decane + hexadecane ternary system at 283.15, 298.15, and 323.15 K and pressures up to 20 MPa. The transitions observed during this study were liquid-liquid (LL), vapor-liquid (VL), and vapor-liquid-liquid (VLL). The Peng-Robinson equation of state was used to model this ternary system for various compositions. The temperature-dependent binary interaction parameters (kij) for the CO2 + n-alkane mixtures were adjusted to the experimental data. Additionally, a binary interaction parameter for the n-C16H34/n-C10H22 pair, independent of temperature, was obtained through the critical volume of the components. The results reveal complex behaviors as the mixture's composition of hexadecane progressively increases. Adding this longer-chain linear hydrocarbon influences the phase behavior, leading to the emergence of liquid-liquid transitions and barotropic inversion in the system. This study contributes valuable data on model systems representing crude oil, highlighting complex behaviors in ternary systems with high carbon dioxide content.

Experiment investigation and thermodynamic assessment of the ternary Ti–Mo-Hf system

Based on experimental data measured by scanning electron microscope (SEM), X-ray diffraction (XRD) and electron probe microanalysis (EPMA), isothermal sections of Ti–Mo-Hf system at 800 °C and 1000 °C were constructed. Four and three three-phase regions were derived in the isothermal sections at 800 and 1000 °C, respectively. In addition, a new ternary compound named τ was discovered. The maximum solubilities of the three elements, Ti, Mo and Hf in τ were measured at 800 °C and 1000 °C. At the same time, the solid solubilities of Ti in HfMo2_C15 and Mo in Hcp were also obtained. According to the measured experimental data, the Ti–Mo-Hf system was optimized using the CALPHAD (CALculation of PHAse Diagrams) method. The solution phases, liquid, Bcc and Hcp, were treated as substitutional solution, while the intermetallic compounds were modeled using sublattice models. HfMo2_C15 was treated as (Hf, Mo, Ti)1(Hf, Mo, Ti)2. The ternary phase τ was considered as a stoichiometric compound and its thermodynamic modeling was defined as (Ti)3(Mo)3(Hf)14. The calculated results showed good agreement with the experimental phase equilibrium data, leading to the derivation of a set of self-consistent thermodynamic parameters for the Ti–Mo-Hf system.

High-pressure phase equilibrium for carbon dioxide solubility with biofuels: Experimental and thermodynamic insights in 2,5-dimethylfuran and methyl levulinate

The solubility of carbon dioxide in two solvents, 2,5-dimethylfuran and methyl levulinate, were measured to high pressure, up to 9.1 MPa, at three different temperatures (283.15, 303.15 and 323.15) K. The new data were measured using both the isothermal synthetic technique and the variable volume synthetic method. Two methods were utilised to provide a level of data validation. The uncertainties in the measured data were critically estimated. The experimental phase equilibrium data were modeled using the Peng-Robinson equation of state and the Wong-Sandler mixing rule with a single set of binary interaction parameters for each system. The data indicated that the solubility of carbon dioxide in both 2,5-dimethylfuran and methyl levulinate at high pressures was relatively low, suggesting a low capacity of these biofuels to dissolve carbon dioxide at high pressure.

Transferable Anisotropic Mie Potential Force Field for Alkanediols.

The development of force fields for polyfunctional molecules, such as alkanediols, requires a careful account of different average intramolecular conformations for gas states compared to dense liquid states, where intra- and intermolecular hydrogen bonds compete. In the present work, the transferable anisotropic Mie (TAMie) potential is extended to 1,n-alkanediols. Using the convention that intramolecular nonbonded interactions up to and including the third neighbor are excluded, all force field parameters developed previously for 1-alcohols were transferred to 1,5-pentanediol and beyond, with good agreement with experimental phase equilibrium data. To obtain trans-gauche ratios of 1,2-ethanediol and 1,3-propanediol that are consistent with experimental results, the propensities for intra- and intermolecular hydrogen bonds had to be balanced. This was achieved by parameterizing the intramolecular dihedral energy functions governing the O-C-C-O and O-C-C-C angles while intramolecular charge-charge interactions were active. All partial charges belonging to a functional group are collected in a charge group and all interactions among two charge groups are evaluated even if they are separated by less than three bonds. With this approach, it is possible to apply the nonbonded parameters from 1-alcohols to alkanediols without further refinement. The agreement with experimental phase equilibrium and shear viscosity data is of similar quality as for the 1-alcohols and the trans-gauche ratio agrees with literature results from spectroscopic measurements and ab initio calculations.

Thermodynamic optimization of KCl-LiCl-LaCl3 with ionic two-sublattice model for liquid

The pyroprocessing technology can reduce nuclear waste by recovering uranium from spent nuclear fuels. To fully take advantage of this technique, it is crucial to have a better understanding of the thermodynamic behavior evolution of the eutectic KCl-LiCl electrolyte with the accumulation of impurities such as lanthanides. The present study carries out thermodynamic modeling for the KCl-LiCl-LaCl3 system and its binary subsystems using the CALPHAD (CALculation of PHAse Diagrams) approach for the first time to predict the liquidus temperatures of KCl-LiCl eutectic as a function of LaCl3 content. Three possible ionic two-sublattice models have been implemented to describe the liquid phase for comparison. Model 1 only involves simple cations and anions. Model 2 and 3 consider short-range ordering in the liquid and introduce species K2LaCl5 and LaCl63-, respectively. It was demonstrated that from the thermodynamics point of view, Model 1 is sufficient to reproduce both phase equilibria and enthalpy of mixing data, whereas Models 2 and 3 seem redundant and increase the number of parameters, which may further lead to poor extrapolation behavior towards multicomponent systems. To achieve better agreements with experimental phase equilibria data and estimated enthalpy of mixing data using the surrounded-ion model, three ternary parameters were optimized for the KCl-LiCl-LaCl3 system. The resultant calculations can well reproduce the experiments and provide insights into the liquidus temperature variation as the mole fraction of LaCl3 increases in the electrolyte.

Phase Behavior and Phase Equilibria for The Polydisperse Polyethylene + Ethylene + Hexane System at High Pressures and Temperature: Experiments and Correlations

This study aims to provide experimental phase equilibrium and phase behavior data for polydisperse PE + ethylene + hexane system. Polydisperse PE (Mw 30.0 kg/mol, PDI 4.2) was used with feed PE weight fraction, ⱳF,PE, of 0.02 to 0.20. The experiments based on a synthetic method were conducted at 473.2 K using an apparatus consisted of an equilibrium cell equipped with sampling tubes for solvent-rich and polymer-rich phases. The LL phase separation pressure increased by about 1 MPa for 1 wt% increase in ethylene concentration. The weight fraction of PE in solvent-rich phase, ⱳS,PE, decreased as the ⱳF,PE and pressure decreased. Similarly, the weight fraction of PE in polymer-rich phase, ⱳP,PE, also decreased as the ⱳF,PE decreased. The solvent-rich phase contained lower molecular weight fractions of PE, while the polymer-rich phase contained higher molecular weight fractions. These results were correlated and predicted with the Sanchez-Lacombe (S-L) EoS. Finally, the effects of pressure and ⱳF,PEon solvent recovery ratio were investigated with the S-L EoS. The results provided in this study could be used to obtain the higher hexane recovery by controlling the LL separation pressure.

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.

Experimental and thermodynamic modeling study of phase equilibria in the PbO–NiO–SiO2 system

AbstractAn integrated experimental and thermodynamic modeling investigation of the phase equilibria in the PbO–NiO–SiO2 system in air and also in equilibrium with liquid metal has been undertaken to better characterize the chemical reactions taking place in the Ni‐containing Pb processing slags. New experimental phase equilibria data at 720°C–1740°C were obtained for this system using high‐temperature equilibration of synthetic mixtures with predetermined compositions in sealed silica ampoules or in Au/Pt–Ir foils, a rapid quenching technique, and electron probe x‐ray microanalysis of the equilibrated phase compositions. Phase equilibria and liquidus isotherms in the quartz/tridymite/cristobalite (SiO2), olivine (Ni2SiO4), monoxide (NiO), Ni‐barysilite (Pb8NiSi6O21), massicot (PbO), and di‐lead silicate (Pb2SiO4) primary phase fields were revealed and the extent of the high‐SiO2 two‐liquid immiscibility gap in equilibrium with cristobalite was determined. New experimental data were used in the development of a thermodynamic database describing this ternary system. Also, modeling revision of the NiO–SiO2 binary system was conducted, resulting in a smaller miscibility gap in ternary systems that was closer to the experimental results.

Thermodynamic descriptions of ternary Al–Si–Yb system and their application to understand solidification behaviors of Yb-modified Al–Si alloys

In this paper, thermodynamic descriptions of binary Si–Yb and ternary Al–Si-Yb system were assessed using the CALculation of PHAse Diagram (CALPHAD) technique, from which insights to the solidification behaviors of Yb-modified Al–Si alloys were attained. Firstly, all the experimental phase equilibria and thermodynamic properties in binary Si–Yb and ternary Al–Si-Yb systems were critically evaluated. Based on evaluated experimental data in the literature, the thermodynamic parameters of binary Si–Yb system were then updated, resulting in a better agreement with the experimental phase equilibrium data in Si-rich part than the previous assessment in the literature. Afterward, the thermodynamic descriptions of ternary Al–Si-Yb system were established on the basis of thermodynamic parameters of three boundary binaries, and their reliability was verified by comprehensively comparing the predicted thermodynamic properties/solidified behaviors with the literature data. Finally, the Scheil-Gulliver solidification simulations of different Yb-modified Al–Si alloys were conducted, from which the effect of Yb additions on the solidification sequences, phase transition temperatures, and phases/structures fractions in Al–Si-Yb alloys was analyzed.

Equilibria of the ternary systems CsBr–LnBr3 (Ln = Gd, Dy)–H2O and the quaternary system CsBr–GdBr3–HBr (∼12.1 mass %)–H2O at T = 298.15 K and standard molar enthalpies of formation for new compounds

As part of a series of studies, this paper reports experimental phase equilibrium data for CsBr–GdBr3–H2O, CsBr–DyBr3–H2O and CsBr–GdBr3–HBr (∼12.1 mass %)–H2O systems at T = 298.15 K. The phase diagrams were constructed based on the measured data. In the phase diagrams of the ternary system CsBr–GdBr3–H2O and the quaternary system CsBr–GdBr3–HBr (∼12.1 mass %)–H2O,there are all two invariant points, and three crystallization regions corresponding to CsBr, Cs3GdBr6·10H2O, and GdBr3·6H2O, respectively.There are two invariant points and three crystallization regions corresponding to CsBr, Cs3Dy2Br9·16H2O and DyBr3·6H2Oin the system CsBr–DyBr3–H2O.The experimental solubility values of gadolinium bromide and dysprosium bromide at 298.15 K were 65.42 mass % and 65.94 mass %. The compounds Cs3GdBr6·10H2O and Cs3Dy2Br9·16H2O are incongruently soluble in water or a medium of ∼ 12.1 mass % HBr, and were characterized by XRD and TG-DTG techniques. The standard molar enthalpies of solution for Cs3GdBr6·10H2O, Cs3Dy2Br9·16H2O, GdBr3·nH2O (n = 6.00) and DyBr3·nH2O (n = 5.99) were obtainedby means of microcalorimetric measurement, the values found for standard molar enthalpies of formation of Cs3GdBr6·10H2O, Cs3Dy2Br9·16H2O, GdBr3·nH2O (n = 6.00) and DyBr3·nH2O (n = 5.99) were – (5104.8 ± 3.2) kJ·mol−1, – (7827.3 ± 3.6) kJ·mol−1, – (2726.0 ± 2.7) kJ·mol−1 and – (2734.5 ± 3.3) kJ·mol−1, respectively.

Experimental investigation and thermodynamic modeling of the Cr–Zr–Si system

The phase equilibria of the Cr–Zr–Si ternary system were studied combined with the key experiments and thermodynamic assessment. Thirty-five ternary alloys were prepared to determine the isothermal sections at 900 and 1000 °C by means of X-ray diffraction (XRD) and scanning electron microscopy with energy dispersive X-ray spectroscopy (SEM/EDS). Five ternary compounds, i.e., τ1 (CrSi2Zr), τ2 (Cr4Si5Zr2), τ3 (Cr4Si7Zr4), τ4 (CrSiZr) and τ5 (Cr3SiZr2), were confirmed. The solubilities of the third element in binary compounds were determined. Based on the experimental phase equilibria data available in the present work and the literature, as well as the thermodynamic parameters of constitutive binary systems, the Cr–Zr–Si system was evaluated by using the CALPHAD (CALculation of PHAse Diagram) method. A set of self-consistent thermodynamic parameters was obtained. Three isothermal sections and liquidus projection were calculated and the reaction scheme was constructed. The calculated results are in agreement with the experimental data.

Modelling of the isothermal vapor-liquid equilibrium of alternative refrigerants: Determination of phase diagrams (high-pressure/low-pressure) and optimized binary interaction parameters

In this work, a thermodynamic model for prediction of Vapor-Liquid Equilibrium (VLE) at moderate pressures (up to 19 bar) and different temperatures (288-323 K) is developed by using Soave-Redlich-Kwong (SRK) and Peng-Robenson (PR) equations of state (EoS) in combination with the classical van der Waals (vdW) mixing rules. Four refrigerant binary systems have been considered in this study (R134a+ R1336mzz (E)), (R600a+R1234ze (Z)), (R600a+R1243zf), (R744+R152a). Also, a new method was used to improve binary interaction parameters (kij). A comparison of experimental phase equilibrium data in the literature with the predicted results showed very good representation for some mixing rules.

Experimental investigation and thermodynamic calculation of the Cu–Cr–Ti ternary system

The phase equilibria of the Cu–Cr–Ti ternary system were investigated based on key experiments coupled with thermodynamic modeling. Eighteen ternary alloys were prepared to determine the isothermal sections of the Cu–Cr–Ti system at 600 and 800 °C by means of X-ray diffraction (XRD) and scanning electron microscopy equipped with energy dispersive X-ray spectroscopy (SEM/EDS). Seven three-phase regions have been determined. A ternary compound τ1 was confirmed. The solubilities of Cr in the Cu–Ti binary compounds and Cu in the Cr–Ti binary compounds were measured. The substitutional and sublattice models were used to describe the solution phases and intermediate phases, respectively. Based on the thermodynamic descriptions of three binary systems as well as the experimental phase equilibria data available from the literature and the present work, thermodynamic assessment of the Cu–Cr–Ti system was carried out using the CALPHAD (CALculation of PHAse Diagrams) approach. A set of thermodynamic parameters was obtained and the isothermal sections and the liquidus projection of the Cu–Cr–Ti system were calculated. The calculated results agree well with the experimental data.

Modelling the solid–liquid–vapour phase behaviour of n-alkanes in a TPT-1 framework

We study the global phase behaviour of n-alkanes applying Wertheim's first order thermodynamic perturbation theory (TPT1). The molecules are modelled as homonuclear chains comprised of m freely jointed spherical segments interacting via the Lennard-Jones potential. Vega et al. [J. Chem. Phys. 116, 17 (2002)] have shown that the TPT1 is suitable to treat solid phases as well as fluid phases when model chains are considered, but that the adoption of a fully flexible chain model leads to the under-prediction of triple point temperatures and overestimation of the fluid ranges in comparison to experiment. Here, we propose a model in which a different number of segments are used to treat the fluid and the solid phase. The number of segments used to model the molecules in the fluid phase , and the LJ monomer potential parameters σ and ε are taken from published soft-SAFT values, whereas in the case of the solid phase a reduced temperature-dependent effective chain length is determined through a minimisation between theoretical and experimental liquid-solid phase equilibrium data. We refer to this model as effective-solid TPT1 (es-TPT1). We use the model proposed to calculate the solid–liquid–vapour phase diagrams of several n-alkanes and compare with experimental data. In the approach proposed, the conformation of chains in the solid phase is decoupled from the fluid phase, and an excellent description of the melting properties, as well as accurate predictions of the triple point temperatures for the n-alkanes examined is obtained. This simple solution provides an avenue to model the solid–liquid–vapour phase behaviour of other real substances in a TPT1 framework, and hence within the SAFT family of equations.

Stable Phase Equilibria of the Quaternary System LiBr-NaBr-KBr-H2O and the Ternary System LiBr-KBr-H2O at 323.15 K

According to the composition characteristics of lithium, potassium, bromine, and other resources rich in the salt lake brine of the Qinghai–Tibet Plateau, the phase equilibria of the quaternary system LiBr-NaBr-KBr-H2O and its ternary subsystem LiBr-KBr-H2O at 323.15 K are studied by an isothermal dissolution equilibrium method. The solubility of each system in equilibrium solution at the corresponding temperature is measured, and the corresponding phase diagrams are drawn according to the phase equilibrium experimental data. The results show that there is no complex salt or solid solution in the ternary system LiBr-KBr-H2O at 323.15 K. The phase diagram contains one invariant point (E1), two univariate curves (AE1 and BE1), and two equilibrium solid crystallization regions (corresponding to LiBr·H2O and KBr), belonging to the simple cosaturated type. The quaternary system LiBr-NaBr-KBr-H2O also has no formation of complex salt and solid solution. The phase diagram contains two invariant points (F1 and F2), five univariate curves (E1F1, E3F1, F1F2, E2F2, and E4F2), and four equilibrium solid-phase crystallization regions (corresponding to LiBr·H2O, KBr, NaBr·2H2O, and NaBr). At the same time, to further explain the phase equilibrium relationship of each system at different temperatures and the change rule of each component, comparison and discussion are carried out.

Thermodynamic assessment of the Mg-Ni-Gd system with a general model description the long-period stacking ordered phases

ABSTRACT The phase equilibria of the Mg-Ni-Gd ternary system were thermodynamically assessed by the CALPHAD (CALculation of PHAse Diagrams) method based on the thermodynamic descriptions of the constitutive binary systems and experimental phase equilibria data available in the literature. The substitutional model and sublattice model were employed to describe the solution phases and intermediate phases, respectively. The ternary phases τ1-τ6 were described as stoichiometric compound and the long-period stacking ordered phase 14H and 18R were described Mgx(TM, Mg)6(RE, Mg)8 model (TM = Transition Metal, RE = Rare Earth). A set of self-consistent thermodynamic parameters of the Mg-Ni-Gd system was obtained. Some representative isothermal section, liquidus projections and the related invariant reactions were calculated. Comparisons between the calculated results and experimental data show that almost all the reliable experimental data were satisfactorily reproduced by the present modeling. The reaction scheme for the whole ternary system is also presented.

Precipitation of methionine and ethyl cellulose in carbon dioxide + ethanol + acetic acid systems at high pressures: Phase equilibrium data for the GAS antisolvent process

This work reports experimental data on the phase transitions in the quaternary system involving carbon dioxide, ethanol, acetic acid and solute (methionine or ethyl cellulose) at high pressures. Experimental data were obtained by the synthetic method, with a variable volume visualization cell, in the temperature range of 308.15–328.15 K and pressures from 6.19 to 11.15 MPa. For the quaternary systems, the solutes were previously solubilized at two different concentrations, 0.1 mg/mL [0.0110% mass fraction] and 0.2 mg/mL [0.0221% mass fraction] for methionine and 2.5 mg/mL [0.2757% mass fraction] and 5.0 mg/mL [0.5514% mass fraction] for ethyl cellulose, in a 1:1 mass ratio solution of ethanol to acetic acid. Vapor-liquid-type phase transitions were observed, characterized as bubbles in the presence or absence of solid phase. A solid phase was observed for all solute concentrations evaluated in this study. Determination of the region of precipitation of methionine or ethyl cellulose is important to identify the optimal concentration of the solvent/solute mixture, where CO2 will act strongly as an antisolvent, ensuring a high efficiency of the GAS technique. Thermodynamic modeling presented satisfactory results, where it adequately described of experimental phase equilibrium data, neglecting the acetic acid dimerization effect.