Binary Subsystems Research Articles

Isopiestic measurements of water activities and thermodynamic modeling for CuCl2−MCl2−H2O (M = Mg, Ca) ternary system at t = 298.15 K

Water activities of the CuCl 2 −MCl 2 −H 2 O ( M = Mg, Ca) ternary systems and their sub-binary systems have been measured by the isopiestic method at 298.15 K. The maximum concentrations of the CuCl 2 −H 2 O, MgCl 2 −H 2 O and CaCl 2 −H 2 O binary systems are 5.28 mol•kg −1 , 5.25 mol•kg −1 and 6.61 mol•kg −1 , respectively. The concentrations of mixture solution rang from 0.91 mol•kg −1 to 5.69 mol•kg −1 for CuCl 2 −MgCl 2 −H 2 O system, and 1.29 mol•kg −1 to 6.87 mol•kg −1 for CuCl 2 −CaCl 2 −H 2 O system. The measured water activities of the sub-binary systems are consistent with the experimental results reported in literature. The measured equal water activities in the ternary systems strongly deviate from the Zdanovskii-Stokes-Robinson (ZSR) lines. The Pitzer model, Pitzer-Simonson-Clegg (PSC) model and Reaction model were selected to correlate and predict the water activity obtained in this work and the solubility reported in literature for the CuCl 2 −MCl 2 −H 2 O ( M = Mg, Ca) ternary systems at 298.15 K. It was found that, the Pitzer model and PSC model cannot consistently represent these thermodynamic properties, with the binary and mixing parameters that already reported or fitted in this work. However, the Reaction model, representing the different competition association ability of common-anions and water molecules with different cations, can successfully predictethe water activity and solubility isotherms in these ternary systems at 298.15 K with binary parameters only. Applying the Reaction model, some examples of the Cu-bearing species distribution as a function of MgCl 2 (CaCl 2 ) molalities are given and used to account for how the structure variation of a electrolyte solution influences its macroproperties.

Thermodynamic Properties of Gd–Sn and Gd–Sn–Ni Melt Systems

Enthalpies of mixing of liquid alloys are determined via isoperibol calorimetry for the Gd–Sn system throughout the range of concentrations at 1873, 1640, and 1510 K, and for the Gd–Sn–Ni system along the radial section with a constant ratio of atomic fractions of tin and nickel: xSn/xNi = 0.68/0.32 at 1873 ± 5 K up to xGd ∼ 0.25. It is found that the melts of the Gd–Sn system form with the release of a large amount of heat ( $$\Delta {{{H}}_{{\min }}}$$ = −68.4 ± 0.4 kJ/mol at xSn = 0.45). The calculations are performed using the geometric and analytical Redlich–Kister–Muggianu models of ΔH for melts of the ternary Gd–Sn–Ni system from similar data for binary boundary subsystems at 1873 K. The results show the minimum enthalpy of mixing of these ternary melts was established for the Gd0.55Sn0.45 alloy. It is shown that the experimentally investigated enthalpies of mixing of the Gd–Sn–Ni melts and calculated data using the Redlich–Kister–Muggianu model with ternary interaction parameter L = 500 kJ/mol agree satisfactorily with one another.

Thermodynamic modeling of ZrO2–Y2O3–SiO2 and ZrO2-Gd2O3–SiO2 systems

Thermodynamic modeling in ZrO2–Y2O3–SiO2 and ZrO2-Gd2O3–SiO2 is part of a broader effort to develop thermodynamic databases that can help offer insight on reactions between thermal barrier coatings (TBCs) based on ZrO2–Y2O3/Gd2O3 and molten silicate deposits in gas turbine engines. The main purpose of the present work is devoted to providing a set of self-consistent thermodynamic parameters for ZrO2–Y2O3–SiO2 and ZrO2-Gd2O3–SiO2 systems by means of the CALPHAD (CALculation of PHAse Diagram) method. Firstly, the ZrO2–SiO2 and Gd2O3–SiO2 sub-systems are assessed. By combining with thermodynamic parameters of ZrO2–Y2O3, Y2O3–SiO2 and ZrO2-Gd2O3 in the literatures, phase equilibria in these two ternary systems are extrapolated and calculated. However, comparing the experimental data and the calculations reveals major inconsistencies, which contains three-phase equlibrium and a quaternary reaction. The bad predictions are mainly due to overestimating or underestimating phase stabilities of compounds in the binary sub-systems. Accordingly, Y2O3–SiO2 and ZrO2-Gd2O3 systems have been re-assessed based on new experiments. Finally, the experimental data for ternary systems are well reproduced by the improved thermodynamic descriptions. Our work exhibits that the accurate thermodynamic parameters of the sub-systems are significant to provide a reliable basis for thermodynamic extrapolations and calculations in higher-order systems.

3D computer model of the Co-Cu-CoS-Cu2S subsystem T-x-y diagram above 800°C

The three-dimensional computer model of the Co-Cu-CoS-Cu2S subsystem T-x-y diagram at temperatures above 800?C is represented. It is shown that the liquid immiscibility in the binary subsystem Cu-Cu2S is transformed within the ternary system with Co into the wide two-phase region of two immiscible melts, which interrupts the univariant curve of the Co and Cu2S co-crystallization. The special features of the structure of the solidus surface of cobalt, caused by liquid-phase immiscibility are considered.

Surface Properties of Al–Fe–Si Liquid Alloy Using Thermodynamic Database

Temperature-dependent interaction parameters for excess free energies of mixing of sub-binary systems of Al-Fe-Si ternary liquid alloys were optimised using the experiment data in the frame of Redlich-Kister (R-K) polynomials. These optimised parameters were then used to compute the partial excess free energy of sub-binary and ternary liquid alloys. The surface tension and surface concentration of sub-binary and the ternary liquid alloys were computed using Butler equation. The temperature dependent coefficients of R-K polynomials for excess surface tensions of the sub-binary systems were optimised which were then used to estimate the surface tension of ternary alloy using Chou, Kohler and Toop modelling equations at temperatures 1773, 1873, 1973 and 2073 K. The surface tension of the ternary alloy obtained using aforementioned models were found to be in good agreement from Fe and Al corners but some deviations were observed from Si corner.

Critical thermodynamic evaluation of the binary sub-systems of the core sulphate system Na2SO4–K2SO4–MgSO4–CaSO4

The binary subsystems of the quaternary system Na2SO4–K2SO4–MgSO4–CaSO4 were thermodynamically assessed using the available experimental information including own thermochemical and structure measurements. Phase equilibria and thermodynamic properties of all six binary systems were properly considered. The modified associate species model was successfully applied for the description of the liquid phase while the mutual solubility between various sulphates in the solid state was treated with appropriate multi-sublattice models. The resulting new databank being compatible with the general oxide database was used for the representation of the thermodynamic properties in the binary systems including phase equilibria, activity and mixing data. The calculations are in good agreement with the experimental data.

Immiscibility of Liquid Phases and Critical Phenomena in the Na2SO4–Na2B4O7–H2O System at 350–460°C and a Pressure of up to 100 MPa

The phase equilibria and critical phenomena in the Na2SO4–Na2B4O7–H2O system with the boundary subsystems Na2B4O7–H2O (type 1 with the phase separation of the solutions) and Na2SO4–H2O (type 2) at 350–460°C and a pressure of up to 100 MPa are studied. It is shown that there exist two three-phase regions L1–L2–S, which are adjacent to two water–salt subsystems and divided by a fluid region, at temperatures ranging from 440°C (the critical point Q (L1 = L2–S) of the type 2 binary system) to ~455°C (at which these regions unite). The ternary system has two critical curves in saturated solutions. The curves originate from different critical points of the type 2 binary subsystem, point p (G = L–S) and point Q (G = L1–L2–S), respectively, and end at the end ternary critical points pR (G = L1–L2–S) and QN (G–L1 = L2–S), respectively. Between the last two points, there is a four-phase equilibrium (G–L1–L2–S), which, according to the visual observations in the sealed quartz ampules, exists in the temperature range 350–380°C.

Solubility of paracetamol in the ternary solvent mixtures of water + ethanol + glycerol at 298.2 and 303.2 K

ABSTRACT The solubility of paracetamol in the ternary mixtures of water + ethanol + glycerol at 298.2 and 303.2 K is determined via the shake-flask method. The reported data extend the solubility database for paracetamol in various solvent mixtures and also is employed to investigate the prediction capability of the cosolvency models for solubility prediction in the sub-binary and the ternary solvent systems. The solubility data are correlated with some cosolvency models and their accuracies are evaluated by the mean relative deviation (MRD) computed for back-calculated solubilities. The results show that the investigated models fit well and can be applied to the ternary solvent system, and the experimental data is relatively more consistent with the calculated values. The prediction ability of the trained Jouyban-Acree model for predicting drug solubility behaviour in the corresponding sub-binary systems is also investigated.

Development of a combined flash and binary geothermal system integrated with hydrogen production for blending into natural gas in daily applications

This paper concerns a novel integrated system for geothermal-based power and hydrogen generation and blending of hydrogen into natural gas to feed household devices, such as gas stove and combi boiler. The system includes a combined flash and binary geothermal subsystem, an alkaline electrolyzer, a blending unit and a combustion reactor. The design and modelling of the proposed system are conducted with Aspen Plus software. The overall energy and exergy efficiencies of the investigated system are found to be 46.8% and 77.9%, respectively. The highest exergy efficiency belongs to January as 86.63% when the average ambient temperature is 5.8 °C, while the lowest exergy efficiency belongs to July as 76.98% when the average ambient temperature is 27.2 °C in Denizli, Turkey. The hydrogen fraction into natural gas is changed from 0% to 20% and analysed the combustion of the blend. The results show that syngas composition has higher oxygen output rate and lower carbon dioxide, steam and heat release rates with higher hydrogen addition.

New expression for property difference in components for the Unified Extrapolation Model

As an important method to estimate the thermodynamic properties of a multi-component system from the sub-binary systems, many extrapolation models have been proposed in the past. However, lacking a clear rule to distinguish the applicability leads to much confusion in practice. Recently, a Unified Extrapolation Model (UEM) that can cover all traditional extrapolation models was built by introducing a contribution coefficient which depends on the property difference between two components in a multi-component system. In this paper, the definition of property difference between any two components was discussed and presented a new mathematical expression to describe it. The performance of the new mathematical expression was tested for prediction of the mixing enthalpy in multicomponent alloy systems. The results revealed that the new mathematical expression for the property difference between components makes the performance of the UEM stand out among all traditional extrapolation models.

The Other Metallic Phase in Spent Nuclear Fuel: A Complete Thermodynamic Evaluation of the U–Pd–Rh–Ru System

Abstract During burnup of nuclear fuel, fission products accumulate. Post-irradiation examination of burned up nuclear fuel has revealed the presence of several phases, namely, the fuel matrix of UO2, with dissolved oxides present; a white metallic phase consisting of the so-called “noble metals” (i.e., Mo–Ru–Pd–Rh–Tc); a gray oxide phase consisting of alkali or alkaline earth oxides (e.g., BaZrO3 or Cs2UO4); and an another metallic inclusion containing a mixture of UPd3–URh3–URu3, which is not completely assessed due to the lack of phase diagrams of the UPd3–URh3, URh3–URu3, and UPd3–URu3. Understanding how these phases behave becomes especially important from a safety perspective, if one considers a potential accident scenario. The quaternary system U–Pd–Rh–Ru has been evaluated and a thermodynamic model has been developed by first considering the six binary subsystems and the four ternary subsystems. A critical examination of the U–Pd, U–Rh, and U–Ru experimental phase diagrams has been made, with attention placed on both the solution phases, generally present on the uranium side of the diagrams and the UPd3–URh3–URu3 compounds. Finally, the implications of this new model and its potential refinements of the Royal Military College of Canada nuclear fuel treatment developed by previous authors (notably the RMCC group under Thompson and Lewis) will be explored.

Modelling the density of Al2O3–CaO–MgO–SiO2 system using the CALPHAD approach

The density of Al2O3–CaO–MgO–SiO2 system is calculated using a model for molar volume. The model is similar to the one used for enthalpy of a multicomponent solution in the CALPHAD approach. The expression for molar volume consists of two terms: one representing the volume contribution from pure components and the other the volume of mixing. The molar volume of mixing takes into account of the binary and the ternary interactions. A total of 565 experimental density data for the constituent unary, binary and ternary systems were collected from the literature. These were used as input to simultaneously optimise the model parameters describing the molar volume, after ensuring that the data belong to a fully molten state. During the optimisation 48 data points that showed significant deviation from the average trend were excluded. The optimised model parameters for the unary, binary and ternary subsystems were used to calculate the density of the quaternary system. The calculated results were compared with experimental data. Finally, it is shown that the volume of mixing of binary systems correlates well with the corresponding enthalpy of mixing.

Experimental study and thermodynamic modeling of solid-liquid equilibrium of binary and ternary mixtures formed by C11H24, C12H26 and C14H30 for cryogenic thermal energy storage

Abstract In this study, experimental investigations of solid-liquid phase diagram of binary and ternary mixtures formed by the C11H24, C12H26 and C14H30 were carried out to employ the potential phase change materials (PCMs) for cryogenic applications using the differential scanning calorimetry (DSC). In addition, the thermodynamic equilibrium was modeled employing the ideal model, and the Wilson and NRTL model were applied to correlate the liquidus line. The results show that the C11-C12 system exhibits a peritectic transition and the composition of possibly peritectic point is 60wt% C12 with the temperature of 251.65 K. The compositions of the eutectic points appear at 10wt% C14 for C11-C14 system and 18wt% C14 for C12-C14 system with eutectic temperatures of 246.85 K and 260.45 K, respectively. The C11-C12-C14 ternary system presents two possibly eutectic points at compositions of 67wt% C11/5wt% C12 and 86wt% C11/10wt% C12 with eutectic temperatures of 246.45 K and 248.05 K, and has the slight supercooling (1.7 ˚C and 0.5 ˚C), indicating miscibility in liquid phase and immiscibility in solid phase. Moreover, the liquidus lines calculated by the theoretical models are in good agreement with the experimental results. The best predicted results of the ternary mixture and C11-C12 binary subsystem are obtained by the ideal model, with deviations of 0.75% and 0.58% respectively.

Thermodynamic assessment of the Ni–Co–Cr system and Diffusion Study of its fcc phase

In the present work, the liquidus and solidus for a series of NixCo1-2xCrx alloys were measured by means of differential scanning calorimetry, and the first-principles calculations were performed to obtain total energies for all solid solutions and end-members of the intermediate phases in the Ni–Co–Cr ternary system. Various types of data from the present work and the literature were used in the assessments of the Ni–Co–Cr ternary system and sub-binary systems by the CALPHAD method, and were well reproduced by the present thermodynamic database. In addition, diffusion couples of fcc Co–Cr and Ni–Co–Cr alloys were assembled and annealed at different temperatures to extract interdiffusion coefficients. Experimental diffusion data from the present work and the literature, in conjunction with thermodynamic parameters, were adopted to assess the atomic mobilities of the fcc phase in the Ni–Co–Cr system. The calculated and experimental diffusion coefficients reach a satisfactory agreement. The diffusional kinetic database developed was further validated by appropriate predictions of composition profiles and diffusion paths.

MELT PROPERTIES OF THE FOUR SALT SYSTEM AlF3-KF-NaF-ZrF4

The fusibility of salt mixtures in the anhydrous quadruple AlF3-KF-NaF-ZrF4 system was studied. The direction of lowering the melting point of substances in the tetrahedron of the composition of the quadruple system, the influence of complexation on lowering the melting point of salt mixtures, were clarified.
 The fusibility of salts in the ternary AlF3-NaF-ZrF4 system was investigated experimentally by methods of thermal phase analysis. The diagram of fusibility to the isotherm of 900 °C is constructed. Primary crystallization fields are represented by the phases of the initial salts (AlF3, KF, ZrF4) of the compounds that were formed in binary subsystems (2KF∙ZrF4, 7NaF∙6ZrF4, 3NaF∙4ZrF4, 5NaF∙3AlF3) and Na3AlF6-Na3ZrF7 solid solutions. The minimum melting point was 466 ° C in a triple eutectic.
 The fusibility of salt mixtures was experimentally studied in the subsystem K2ZrF6-Na2ZrF6-KAlF4-NaAlF4, which was a section of the tetrahedron of the composition of the quadruple system AlF3-KF-NaF-ZrF4. The fusibility diagram of this subsystem was constructed. A triple point with a melting point of 450 °C was found. Primary crystallization fields are represented by compounds K2ZrF6, Na2ZrF6 and solid solutions KAlF4-NaAlF4.
 The low-melting region of the compositions in the tetrahedron of the composition of the quadruple system was shifted to the faces NaF-KF-ZrF4 and AlF3-KF-ZrF4. The intense chemical interaction of the starting materials of the quadruple system with the formation of complex compounds and the extensive formation of solid solutions complicated the determination of crystallizing solid phases and the establishment of monovariant equilibria in quadruple mixtures.
 Quadruple eutectic in the four component system was formed by the merger of four monovariant lines. To calculate the composition of the quadruple eutectic by the melting temperature and the composition of the eutectic of the triple subsystems, the coordinates of the four triple points are necessary. The characteristic of two triple points was obtained as a result of an experimental study of the fusibility diagrams of auxiliary sections of a tetrahedron of the composition: K2ZrF4-Na2ZrF6-KAlF4-NaAlF4 and KZrF6-NaAlF4-(0,5NaF+0,5ZrF4)-KAlF4, which were located near the quadruple eutectic.

Thermodynamic and surface properties of Al–Li–Mg liquid alloy

The thermodynamic database of excess Gibbs free energy of mixing was theoretically reproduced at temperatures 1000 K, 1073 K 1150 K, and 1250 K for liquid Al–Li–Mg ternary alloy on the basis of GSM, Toop and Kohler models. For this purpose, the linear as well exponential T-dependent interaction parameters of Redlich-Kister (R–K) polynomials were optimised. These parameters were used to compute the activities of the monomers of the binary sub-systems. The enthalpy of mixing of the ternary system was computed using exponential T-dependent parameters. The surface tensions of binary sub-systems were calculated employing Butler's equations and using the theoretically determined partial excess Gibbs free energy of constituent elements of the alloy. Further, the optimised coefficients of R–K polynomials were obtained for excess surface tensions of binary sub-systems. With the aid of these coefficients, the surface tension of the ternary system was computed in the frame work of models mentioned above.

Soluting Effect in Ternary Aqueous Solutions of Ionic Liquids by Isopiestic Equilibrium Studies and Applying the Linear Isopiestic Relations for Estimating Their Speed of Sound, Density, and Surface Tension Data

In the present study, to investigate the soluting effect in ternary aqueous solutions of ionic liquids (ILs), experimental studies have been carried out on ionic liquid 1 + ionic liquid 2 + water systems that are in isopiestic equilibrium. The imidazolium-based ionic liquids 1-ethyl-3-methyl-imidazolium bromide ([C2MIM]­Br), 1-butyl-3-methylimidazolium bromide ([C4MIM]­Br), and 1-hexyl-3-methylimidazolium bromide ([C6MIM]­Br) were selected, and the vapor–liquid equilibria (VLE) of {[C2MIM]Br + [C6MIM]Br + water}, {[C2MIM]Br + [C4MIM]Br + water}, and {[C4MIM]Br + [C6MIM]Br + water} were investigated by the isopiestic method. The equations derived from the Zdanovskii–Stokes–Robinson rule were applied to predict the thermodynamic properties (density, speed of sound, and surface tension) of ternary solutions from the corresponding data of binary subsystems with the same water activity data, and the calculated thermodynamic properties were compared to the experimental data.

Equation of state modeling and force field-based molecular dynamics simulations of supercritical polyethylene + hexane + ethylene systems

The understanding of polymer solution thermodynamics and characterization of pressure effects on fundamental polymer physics of macromolecular systems is significant in the manufacturing of polyolefins. Consequently, numerous experimental and theoretical efforts have been made towards understanding phase behavior of polymer solutions at elevated pressures. Despite this progress, only limited efforts are directed towards understanding the underlying phenomena behind the influence of high pressure upon the thermophysical properties of ternary polymer solutions at a molecular level. The present paper, therefore, reports on the influence of supercritical ethylene on the density of PE + hydrocarbon solvent system by exploring ternary mixtures of PE + hexane + ethylene for ethylene concentrations up to 10 wt% at varied temperatures and in a pressure range from 100 to 1000 bar via fully-atomistic molecular dynamics (MD) simulations. Additionally, the modified Sanchez-Lacombe equation of state (EOS) model is iteratively solved to capture the pressure, concentration, and temperature dependence of ternary PE solution density. It is shown that the small amounts of ethylene dissolved in the liquid mixtures of PE + hexane significantly decreases the polymer solution density. The presence of unreacted monomer in the solution polymerization process utilized in PE manufacturing was found to substantially lower the PE solution density particularly at the lower end of the investigated pressure range. This noteworthy reduction in mixture density as a consequence impacts design and operation of the liquid-liquid phase separator in manufacturing of PE via solution polymerization. Another key point to bear in mind is that the mixture density exhibits fairly less sensitivity to ethylene amount as external pressure raises. Nevertheless, pressure, solvent composition, and temperature dependence of density display less sensitivity as pressure increases. In relation to the characterization of the impact of addition of ethylene an atomistic-level insight is provided, which proves to be of great value in revealing intermolecular interactions in the binary subsystems of polymer/solvent/monomer. The MD computations are shown to be in excellent agreement with the theoretical EOS model, confirming the validity of the proposed methodology. Furthermore, the adopted OPLS-AA has been found a reliable atomistic force field, which provides detailed molecular information on the thermophysical properties of polyolefin in hydrocarbon solutions. Ultimately, it is demonstrated that the MD simulations complement parametric EOS predictions and costly experimental approaches.

Study of surface tension and viscosity of Cu–Fe–Si ternary alloy using a thermodynamic approach

The surface tension and viscosity of Cu–Fe–Si ternary alloys were computed at different temperatures using thermodynamic approaches. The thermodynamic data of the alloy were optimized in the framework of the Redlich-Kister (R–K) polynomials and exponential temperature dependent coefficients of the R–K polynomial were obtained. These coefficients were used to compute the excess Gibbs free energy of mixing of the alloy and the partial excess free energy of the components. The partial excess free energy so obtained was used to compute the surface tension of the ternary Cu–Fe–Si alloy system and its binary sub-systems. The enthalpy of mixing was also optimized and it was used to compute the viscosity of the sub-binary and ternary alloys.

Influence of Temperature on Liquid–Liquid Equilibrium of Methanol + Aromatic + Isooctane Ternary Systems

The influence of temperature on the miscibility of the {methanol + p-xylene + isooctane} and {methanol + benzene + isooctane} ternary systems at atmospheric pressure are investigated. The effect of temperature on the phase equilibrium is discussed for each system. All chemicals are verified using gas chromatograph, density, viscosity and refractive index. Phase equilibrium are reached using a modified version of measurement equipment used previously. Some ternary systems and binary subsystems are taken from the literature at different temperatures to determine the influence of the temperature on the systems. The upper critical solution temperature for the methanol + isooctane binary system was determined by the constant-composition method with an accuracy of ± 0.1 K. Experimental data are compared with the literature. Calculated values by the non-random two liquids (NRTL) and universal quasi-chemical (UNIQUAC) equations are contrasted with experimental data for the ternary systems. Deviations from the experimental binodal curve have good adjustment of less than one per cent for all systems.