Binary Subsystems Research Articles

Thermodynamics and Phase Equilibrium of the System CsCl–MgCl2–H2O at 298.15 K

Water activities of the CsCl–MgCl2–H2O ternary system and its sub-binary systems were elaborately measured by an isopiestic method at 298.15 K. The solubility of this ternary system at 298.15 K was also measured by two different methods, namely isothermal method and Flow-Cloud-Point method. The solubilities measured by the two different methods were consistent with each other. A Pitzer model was used to represent the thermodynamic properties and calculate the solubility isotherms for the CsCl–MgCl2–H2O ternary system at 298.15 K. Both the equal water activity lines and the solubility isotherms are calculated with parameters reported in literature. It was found that only the calculated equal water activity lines with the parameters reported by Scharge et al. are consistent with the experimental values of this work. However, all the calculated solubility isotherms deviated from the experimental data in this work. New set of ternary parameters were obtained by fitting the water activities and solubility data...

Scheil–Gulliver Constituent Diagrams

During solidification of alloys, conditions often approach those of Scheil–Gulliver cooling in which it is assumed that solid phases, once precipitated, remain unchanged. That is, they no longer react with the liquid or with each other. In the case of equilibrium solidification, equilibrium phase diagrams provide a valuable means of visualizing the effects of composition changes upon the final microstructure. In the present study, we propose for the first time the concept of Scheil–Gulliver constituent diagrams which play the same role as that in the case of Scheil–Gulliver cooling. It is shown how these diagrams can be calculated and plotted by the currently available thermodynamic database computing systems that combine Gibbs energy minimization software with large databases of optimized thermodynamic properties of solutions and compounds. Examples calculated using the FactSage system are presented for the Al-Li and Al-Mg-Zn systems, and for the Au-Bi-Sb-Pb system and its binary and ternary subsystems.

Modeling of some physicochemical properties in the liquid Au–Bi–Sn alloys relevant for Pb-free soldering

In this paper, some geometrical models such as Kohler, Muggianu, Toop, and Hillert have been used to estimate the molar volume of Au–Bi–Sn ternary systems based on the data of sub-binary systems over a wide temperature range (673–973[Formula: see text]K). The density of Au–Bi–Sn alloys was calculated from the calculated molar volume and using theoretical equation along three cross-sections [Formula: see text]/[Formula: see text]/2, 1/1 and 2/1. In addition, the viscosity of Au–Bi–Sn alloys was calculated by using Seetharaman–Sichen equation over a wide temperature range (673–1273[Formula: see text]K). The density of these alloys show linear dependence on temperature for all investigated compositions, while the molar volumes increase with increasing temperature and Sn compositions. The results show, as a function of temperature, that the increase in concentration of tin influences the viscosity of the Au–Bi–Sn alloys. The calculated values of density of Au–Bi–Sn alloys are compared with the experimental values reported in the literature, and a good agreement was observed.

Correlation of H2S solubility in aqueous MDEA solutions using electrolyte-modified Peng-Robinson plus association equation of state

ABSTRACTIn this survey, we use the emPR-CPA equation of state to model a ternary system of H2S solubility in MDEA aqueous solution at different solution compositions, temperatures, pressures, and acid gas loadings. For electrolyte part of the model, MSA theory and the Born term were used. There were 302 experimental data used in this work. To model a ternary system, at first pure components, then binary subsystems, and finally ternary system were modeled using a reactive bubble point pressure calculation method. An overall absolute average deviation percentage equal to 20.85 was achieved so that show the model efficiency for correlation of such systems.

Modeling of H2S solubility in aqueous MDEA solution using electrolyte SRK plus association equation of state

ABSTRACTH2S solubility in MDEA aqueous solution at different solution compositions, temperatures, pressures, and acid gas loadings was correlated using electrolyte SRK-cubic plus association equation of state. A total of 302 experimental data were used in this work. At first pure components parameters were obtained from literatures. Then binary interaction parameters were calculated through binary subsystems investigation. Finally, ternary system modeled using a reactive bubble point pressure calculation method. Considering number of binary interaction parameters that should be optimized, three scenarios were proposed. All of the scenarios present good results with acceptable absolute average deviation percentage (AAD%) but the third one shows better outputs. The AAD% in this scenario is 17.02.

Thermodynamic description and quaternary miscibility gap of the C–Hf–Ti–W system

The C–Hf–Ti, C–Hf–W and C–Hf–Ti–W systems have been assessed by means of the CALPHAD (CALculation of PHAse Diagram) approach. All of the experimental phase diagram and thermodynamic data available from the literature are critically reviewed. According to the available experimental data, no ternary or quaternary compound has been found in these systems. The liquid is modeled as a substitutional solution phase, while the solid solution phases including βHf, αHf, βTi, αTi, W, HfC1-x, TiC1-x, WC1-x, WC, W2C and HfW2 are described by sublattice models. The modeling of C–Hf–Ti and C–Hf–W systems covers the whole composition range. A set of self-consistent thermodynamic parameters for the C–Hf–Ti and C–Hf–W systems are then obtained. Comprehensive comparisons between the calculated and experimental data show that the experimental information is satisfactorily accounted for by the present thermodynamic description. The liquidus projection and reaction scheme of the C–Hf–Ti and C–Hf–W systems are generated by using the present thermodynamic parameters. Due to limited experimental data, the simple Hf–Ti–W system is extrapolated from its sub-binary systems. Based on the present work and the previous assessment of the C–Ti–W system, a thermodynamic description of the quaternary C–Hf–Ti–W system is extrapolated, and the experimental phase equilibria can also be well reproduced by the present thermodynamic modeling. For the first time, the miscibility gap of the quaternary cubic carbides is calculated in the quaternary C–Hf–Ti–W system. A high potential in industrial applications such as in bulk cemented carbide, cermet cutting tools and hard-coatings is discussed mainly in terms of the miscibility gap.

Thermodynamics and phase equilibrium of the high concentration solid solution-aqueous solution system KCl–RbCl–H2O from T = 298.15 K to T = 323.15 K

Water activities of the high concentration solid solution-aqueous solution system (SS-AS) KCl–RbCl–H2O and its sub-binary systems at T=298.15K and T=323.15K have been elaborately measured by an isopiestic method. The solubility of this ternary system at T=(298.15, 308.15 and 323.15)K was also measured by a Flow-Cloud-Point method. A Pitzer model was used to estimate the reliability of the solubility reported in the literature, and to judge the type of solid phase, by correlating the measured water activity and the reported solubility values. The binary model parameters as a function of temperature between T=298.15K and T=323.15K were obtained by fitting the water activities in the binary systems. The predicted water activities at T=298.15K and T=323.15K with the obtained binary parameters only, are in good agreement with the experimental values, which indicate that the Pitzer model can reliably represent the properties of the ternary system, with binary parameters only within the temperature range from T=298.15K to T=323.15K. Under the different assumptions that the equilibrium solid phase involved the pure salts (KCl(s) and RbCl(s)) for the ideal solid solution or regular solid solution (K, Rb)Cl(ss), the solubility isotherms at T=(298.15, 308.15 and 323.15)K were calculated and compared to experimental results, respectively. It was found that only the calculated solubility isotherms for (K, Rb)Cl(ss) regular solid solution are consistent with the corresponding experimental values. The solid phase equilibrated with the aqueous solution in the KCl–RbCl–H2O ternary system should be a regular solid solution (K, Rb)Cl(ss). This conclusion also can be verified from the Lippman log∑K−Xs−Xact and Φ∑m−Xs−Xaq equilibrium diagrams.

Experimental investigation of the Al-Mn-C system. Part II: Liquidus and solidus projections

Phase equilibria upon crystallization in the Al-Mn-C system were studied using DTA, X-ray diffraction, SEM and electron probe microanalysis. The liquidus and solidus projections and the melting diagram (liquidus + solidus) for this system were constructed covering the whole concentration range. The ternary compound Mn3AlC (κ) (antiperovskite structure CaTiO3-type, ≿Р5-Pm-3m) melts congruently at 1320 °C. The liquidus surface consists of the binary compounds, the ternary compound Mn3AlC (κ) and solid solutions primary crystallization fields. The carbide Mn5C2 in the ternary system participates in equilibrium with the liquid phase in contrary to the binary system where it is formed from the solid state equilibrium. The solidus surface of the Al-Mn-C system in the region up to 50 at.% Al is defined by the co-existence of the κ-carbide with almost all phases of the binary subsystems: (С), (γMn), (εAlMn), (Al4C3), (Mn7C3) and (Mn5C2). The solidus surface in the region >45 at.% Al is defined by the co-existence of the carbide Al4C3 with all phases from Al-rich region.The DTA curves of the alloys with compositions close to the homogeneity region of phase (εAlMn), exhibit (on heating) an exothermic effect at ∼570 °C. This exothermic effect corresponds to the formation of the ordered metastable τ-phase, which is formed by mechanism: ε → ε' (B19) → τ. τ-phase (AuCu, tP2-P4/mmm, a = 2.760, c = 3.600 Å) and which was observed in the alloys after heating up to 700 °C and slow cooling (5 °C/min).

How Many-Body Correlations andαClustering ShapeHe6

The Borromean $^6$He nucleus is an exotic system characterized by two `halo' neutrons orbiting around a compact $^4$He (or $\alpha$) core, in which the binary subsystems are unbound. The simultaneous reproduction of its small binding energy and extended matter and point-proton radii has been a challenge for {\em ab initio} theoretical calculations based on traditional bound-state methods. Using soft nucleon-nucleon interactions based on chiral effective field theory potentials, we show that supplementing the model space with $^4$He+$n$+$n$ cluster degrees of freedom largely solves this issue. We analyze the role played by the $\alpha$-clustering and many-body correlations, and study the dependence of the energy spectrum on the resolution scale of the interaction.

Thermodynamic evaluation of LiCl-KCl-PuCl3 system

The present study focuses on developing the phase diagram of LiCl-KCl-PuCl3 system based on the CALPHAD (CALculation of PHase Diagram) method. Sub-binary systems of LiCl-KCl, LiCl-PuCl3, and KCl-PuCl3 were developed first by optimizing the Gibbs energy parameters according to the experimental data from literature using the two-sublattice model. Then the enthalpy of mixing of the LiCl-KCl-PuCl3 system was estimated, to explore the ternary interactions, using an empirical correlation derived from the surrounded-ion model for the asymmetric salt system due to the scarcity of available data for the ternary system. Based on the phase diagram developed, the solubility of PuCl3 in the eutectic LiCl-KCl melt at different temperatures was obtained, as well as the Gibbs energy of formation of PuCl3 in the salt as a function of PuCl3 concentration. The present study extends the experimental data for dilutions to concentrated solutions for which no experimental data have been well reported.

Thermodynamic assessment of Si-P and Si-Fe-P alloys for solar grade silicon refining via vacuum levitation

Thermodynamic properties of phosphorus in Si and Si-Fe alloys were studied using the Molecular Interaction Volume Model (MIVM), aiming to better understand the behavior of phosphorus at low concentration during its removal from these alloys. The model parameters were optimized based on published results for the sub-binary systems of Si-Fe-P, and were shown to reproduce the experimental activity results with good reliability. A relationship between the Henrian activity coefficient, namely infinite dilute activity coefficient, of phosphorus in liquid Si and temperature was established as lnγPinSio=−2117/T+0.197. Further, the separation coefficients, removal efficiencies and equilibrium compositions during vapor-liquid equilibria of Si-P and Si-Fe-P were calculated under vacuum levitation refining conditions.

Thermodynamic Model of the Urea Synthesis Process

A thermodynamic model of the ammonia−carbon dioxide–water–urea system at urea synthesis conditions, that is, at t = (135 to 230) °C, p = (3.5 to 45) MPa, L = nN/nC = (2 to 5.5) and W = ( nH2O – n (NH2)2CO) = nO/nC – 2 = (−0.75 to 1.2) was developed. A liquid phase was described by the UNIQUAC model including urea, ammonium carbamate, and ammonium bicarbonate as compounds; the gas phase was described by a virial equation of state. Bubble point pressures and carbon dioxide to urea conversion data were used for the model parameters optimization. The unique features of the model are the correct description of the saddle azeotrope and intensive use of existing thermodynamic data about constituents and binary subsystems vapor–liquid equilibria data.

Phase Equilibrium and Interfacial Tension of Binary and Ternary Polymer Solutions

The liquid–liquid equilibrium (LLE) and interfacial tensions of binary and ternary polymer solutions of polystyrene in cyclohexane and methylcyclohexane are investigated. The chain length dependent modified double lattice model (MDL-CL) is applied to describe experimental phase diagrams measured by thermo-optical analysis. The proposed model is also combined with the modified density gradient theory to calculate interfacial tension between two coexisting liquid phases of the investigated systems. The calculated results of LLE and interfacial tensions using the MDL-CL model combined with the modified density gradient theory show good agreement with experimental data. The interfacial tension of the ternary system (polystyrene + cyclohexane + methylcyclohexane) is described with the parameters obtained from the binary subsystems (polystyrene + cyclohexane and polystyrene + methylcyclohexane). A comparison of experimental and theoretical phase behaviors and interfacial tensions demonstrates that the theoretic...

Thermodynamic assessment of the Nd2O3-CaO-SiO2 ternary system

In order to enable efficient recycling of rare earth metals through high temperature processes, the phase relations in rare earth oxide containing slags need to be understood. A thermodynamic description of the CaO-SiO2-Nd2O3 ternary system and its Nd-containing binary subsystems was, therefore, constructed in this study, based on existing phase diagram and thermodynamic data. The Gibbs energy of the liquid oxides in the CaO-SiO2-Nd2O3 system was modeled using the Modified Quasichemical Model. The solid phases Ca2-2xNd2xSiO4Ox, Ca3-3xNd2xSiO5, and Ca2+10xNd8-8x(SiO4)6O2-2x were modeled with polynomial expansions of the excess Gibbs energy. The optimized phase diagram of the CaO-SiO2-Nd2O3 system is in good agreement with the experimental data.

Thermodynamic Properties of Ternary Solutions in the Water–Nitric Acid–Rare Earth Nitrate (Pr, Nd, Sm) Systems at 298.15 K

The vapor pressure measurement unit from borosilicate glass was assembled for determination of partial pressures of water in aggressive acidic media using the transpiration method. Three ternary systems H2O–HNO3–RE(NO3)3 (RE = Pr, Nd, Sm) were investigated. The experimental results in ternary systems were compared with the estimation by the Pitzer model and Zdanovsky rule from the data of binary subsystems. In addition to vapor pressure measurements densities of investigated solutions were determined.

Thermodynamic modeling of the Al-Cr-Ni system over the entire composition and temperature range

A thermodynamic reassessment of the entire Al-Cr-Ni system has been made, according to the CALPHAD method. Compared to the previous assessments, more recent experimental results have been considered: in the binary subsystems Cr4Al11, CrNi2 and Ni3Al4 have been added and the model of the γ-L phase (hR26 –Cr5Al8 type) has been modified to four sublattices. The order-disorder model has been used to describe the A2/B2 and A1/L12 phase relations, respectively. Three ternary compounds in the Al-rich region have been introduced for the first time.Thermodynamic interaction parameters have been optimized using all the available experimental data. On the basis of the thermodynamic database implemented in this work stable isothermal and vertical sections have been calculated, which can fit experimental results in the whole composition range, including the aluminum-rich part of the system.

Densities, Viscosities, and Correlations for the Ternary System of Ethanol + Methylbenzene + 2-Methyl-2-propanol and Its Binary Subsystems at T = 298.15 and 318.15 K

Densities and viscosities of the ternary system (ethanol + methylbenzene + 2-methyl-2-propanol) and its binary subsystems were measured at T = 298.15 and 318.15 K and atmospheric pressure. Densities were determined using a vibrating-tube densimeter. Viscosities were found with an automatic microviscometer based on the rolling ball principle. From the experimental data, the excess molar volumes (VE) and deviations in viscosity (Δη) were derived. The binary VE and Δη data were correlated with the Redlich–Kister equation. The ternary VE and Δη data were fitted to the equation based on Cibulka and the equation of Singh et al., respectively. The values of VE and Δη were used to discuss the nature of mixing behaviors for the mixtures, and leading to these excess values is perhaps due to the complex formation and/or accommodation between molecules. To describe the ternary system, several mixtures with specially designated concentrations of 2-methyl-2-propanol were considered.

Viscosity estimation of ternary mixtures containing ionic liquid from their binary subsystems: A comparison of three viscosity equations

Viscosity of the mixture containing ionic liquid (IL) is important for engineering design and application. The modeling of viscosity of the ternary mixtures containing IL is still in its infancy. The aim of this work is to evaluate the predictive ability of the semi-theoretical viscosity equations based on Eyring’s absolute rate theory and excess Gibbs free energy model for the ternary mixtures containing IL in terms of the viscosity of their binary subsystems. Three viscosity equations namely Eyring-UNIQUAC, Eyring-NRTL, and Eyring-Wilson equations are employed and extended to estimate the viscosity of ternary mixtures of IL with two molecular solvents using the interaction parameters obtained from their binary subsystems. The results were compared and discussed. The correlation results of the viscosity for 30 binary subsystems with 444 data points show that the Eyring-Wilson equation has more applicability and precision than those of the Eyring-UNIQUAC and Eyring-NRTL equations. Accordingly, the prediction results of the viscosity for 13 ternary mixtures containing IL with 813 data points indicate that the Eyring-Wilson equation has much better predictive ability than that of the Eyring-UNIQUAC and Eyring-NRTL equations. Moreover, the Eyring-Wilson equation can be used to predict the ternary viscosity at other temperature such as 313.15 K using the interaction parameters obtained from their binary subsystems at 298.15 K.

Ab initio energetics for modeling phase stability of the Np-U system

The Np-U system has been rarely studied despite this alloy being a key binary subsystem of metallic nuclear fuels. This study aims to further the understanding of the phase stability of the Np-U system through ab initio calculations. We first examined an existing CALPHAD model based on available experimental phase boundary data. We then focused on phases of which the CALPHAD model reproduces reasonably the experimental data and examined if values of the effective Hubbard U (i.e., Ueff) parameter for Np and U fitted previously in the Np-Zr and U-Zr systems are also applicable to the Np-U system, using CALPHAD predicted enthalpies as references. We found that in general DFT + U predicts improved or at least similarly accurate enthalpies compared to standard DFT when the Ueff’s used are within the ranges of single-structure optimized Ueff’s (0.65–0.9 eV for Np and 1–1.5 eV for U)—for example, the multi-structure optimized Ueff’s (0.9 eV for Np and 1.24 eV for U)—determined in our previous U-Zr and Np-Zr studies. Finally, we focused on the intermediate phase ζ(Np,U), which at present is poorly characterized by experiments and unsatisfactorily described in the CALPHAD model. Based on ab initio calculated formation enthalpies for ordered end members and the compound energy formalism, we predicted its site occupations as functions of composition and temperature. Our study demonstrated that Ueff’s fitted for U and Np determined in the U-Zr and Np-Zr systems may be transferable to the Np-U system and also provided new prediction of the site occupations for ζ(Np,U), which may serve as reference for future experimental and modeling study of the Np-U system.

A Water–Urea–Ammonium Sulfamate system: Experimental investigation and thermodynamic modelling

The Water–Urea–Ammonium Sulfamate ternary system was investigated by means of experimental methods and thermodynamic modelling. Experimental part of the work includes (i) DSC measurements of liquidus and solidus of the Urea–Ammonium Sulfamate, the Water–Ammonium Sulfamate subsystems with the estimation of eutectic point position and a set of experiments on the phase boundaries in the ternary system; (ii) vapor pressure measurements in the binary Water–Ammonium Sulfamate and ternary Water–Ammonium Sulfamate–Urea systems at 298.15 K in a wide concentration range. Excess Gibbs energies of the Water–Ammonium Sulfamate–Urea system and its binary subsystems were described by the Pitzer-Simonson-Clegg model which is reduced to polynomial formalism in case of nonelectrolyte systems. Results of the Water–Urea subsystem reassessment are given.