Quasichemical Model Research Articles

Amine blending optimization for maximizing CO2 absorption capacity in a diisopropanolamine – methyldiethanolamine – H2O system using the electrolyte UNIQUAC model

Experimental data on CO2 solubility in diisopropanolamine (DIPA) and methyldiethanolamine (MDEA) blended aqueous solutions were measured at different amine blending ratios and working temperatures. The successive (iterative) substitution method was implemented to calculate the molar fractions of all chemical species, including molecules and electrolytes, from equilibrium along with four material balances and one electroneutrality equation. The electrolyte universal quasi-chemical (electrolyte UNIQUAC) model was used to consider the nonideality in the liquid phase. The partial pressures of CO2 in the gas phase and molar fractions of all components in the liquid phase were recalculated using thermodynamic models. In addition, the effect of the blending ratio of DIPA, MDEA, and H2O was investigated and expressed using the newly applied triangular diagrams of pH, heat of absorption, and cyclic capacity of CO2 according to the absorption and stripping conditions.

Structural Evaluation of Silicate Melts by Performing Impedance Measurements and Quasichemical Model Calculations

Structural Evaluation of Silicate Melts by Performing Impedance Measurements and Quasichemical Model Calculations

Thermodynamic optimization of the Cu–As–S system

A literature review, critical assessment and thermodynamic modeling of matte, metal (speiss) and solid phases in the Cu–As–S system are presented. The literature data include enthalpies and entropies of formation, activity measurements using vapor pressure, phase equilibrium and element distribution data. The model for the liquid phase was developed within the framework of the Modified Quasichemical Model (MQM) in pair approximation. Liquid metal and matte phases were described using the single solution with a miscibility gap. Previously published model parameters for the liquid phase in the Cu–S system were modified to achieve agreement with the data for the Cu–As–S system. The resulting set of model parameters was incorporated into a large multicomponent thermodynamic database intended for predictions of phase equilibria, heat balance and distribution of arsenic in the course of pyrometallurgical processing of copper- and lead-containing materials.

Experimental investigation and thermodynamic modeling of the Mg–Sn–Sr ternary system

The isothermal sections of the Mg–Sn–Sr ternary system in the Mg-rich region at 415 and 350 °C have been determined using the scanning electron microscopy (SEM) equipped with energy dispersive X-Ray spectrometry (EDS). The existence of the MgSnSr ternary compound was confirmed in these two isothermal sections. Two new compounds, named Mg5Sn3Sr and Mg25Sn24Sr14, were found in the present work based on the SEM/EDS results. Thermodynamic optimization of the Sn–Sr binary and Mg–Sn–Sr ternary systems were carried out using the CALPHAD (CALculation of PHAse Diagrams) technique. The Modified quasi-chemical model (MQM) was used for the liquid solution which exhibits a high degree of short-range ordering behavior. The solid phases were described with the Compound energy formalism (CEF). Finally, a self-consistent thermodynamic databases for the Mg–Sn–Sr ternary system has been constructed in the present work, which can be an efficient and convenient guidance to investigate and develop the Mg-based alloys.

Thermodynamic optimization of the As–S system

Literature review, critical assessment and thermodynamic modeling of the liquid and solid phases in the As–S system are presented. A set of optimized model parameters was obtained to reproduce previously published experimental data. The literature data included enthalpies of formation, heat capacity, vapor pressure and phase equilibrium data. A significant discrepancy among different sets of literature data was revealed. The model for the liquid phase was developed within the framework of the Modified Quasichemical Model (MQM) in pair approximation. The resulting set of model parameters was merged and tested within a larger multicomponent thermodynamic database for pyrometallurgical copper, lead and recycling industrial operations.

Thermodynamic optimization of the Mn–P and Fe–Mn–P systems

Thermodynamic modeling of the Mn–P and Fe–Mn–P systems in the full composition was carried out using the CALculation of PHAse Diagrams (CALPHAD) method based on the critical evaluation of all available phase equilibria and thermodynamic data. The liquid and solid solutions were described using the Modified Quasichemical Model and Compound Energy Formalism, respectively. The Gibbs energies of the binary stoichiometric iron and manganese phosphides were determined based on reliable experimental data. The ternary (Fe,Mn)3P, (Fe,Mn)2P and (Fe,Mn)P phosphides were modeled as solid solutions with mutual substitution between Fe and Mn atoms. The Gibbs energy of the liquid solution was predicted using the Toop interpolation technique with P as an asymmetric component, without any ternary parameters. The thermodynamic properties of P in the entire composition region and the liquidus of the ternary system were well reproduced. Based on the thermodynamic models with optimized parameters, unexplored phase diagrams and thermodynamic properties of the Fe–Mn–P system were predicted.

Electron transport in dense degenerate plasmas

Within a unified approach, a method for calculating the tensors of electrical conductivity, the Seebeck coefficient and thermal conductivity of a nonideal plasma in a magnetic field were considered. Under this unified approach the kinetic coefficients are calculated together with the equation of state for a nonideal plasma within the framework of a quasi-chemical model. Various methods for determining the Coulomb logarithm in the kinetic theory of transport and various options for choosing the boundary value of the wave number of electrons are considered. The scattering of electrons by ions using the phase shift method has been considered and the appearance of values of the Coulomb logarithm less than unity are demonstrated. Electron scattering by the phase shift method is considered using the Buckingham potential which permits to describe the Ramsauer minimum in the transport cross section for electron scattering by noble gas atoms.

Thermodynamic Assessment of Liquid Fe-Ni-C Alloy Using Modified Quasichemical Model

The liquid solution properties in the Fe-Ni and Fe-Ni-C systems have been thermodynamically assessed using the modified quasichemical model in the pair approximation. The asymmetry of the Fe-Ni and Fe-Ni-C alloy melts was verified by measuring the melting points of Fe-Ni binary alloys on the Ni-rich side, and the C solubility limit in Fe-Ni melt over the entire concentration range at 1500°C and 1600°C. The solubility minimum of C and the maximum partial enthalpy of mixing of C in the ternary Fe-Ni-C system occurred at near the maximum short-range ordering composition of the binary Fe-Ni liquid solution. The extrema of the partial properties of C in the ternary Fe-Ni-C system were successfully reproduced with only one constant adjustable ternary parameter.

Thermodynamic evaluation and optimization of LiNO3–KNO3–NaNO3 ternary system

The phase diagram of LiNO3–KNO3 system was investigated with differential scanning calorimetry. Phase transitions data of LiNO3–KNO3 system were obtained. Using the measured phase equilibrium data as well as other available phase equilibrium and thermodynamic data in literature, the thermodynamic optimization of parameters for all phases and compounds in the LiNO3–NaNO3–KNO3 system was performed. The Modified Quasichemical Model was applied for the liquid phase, and Compound Energy Formalism was used for the NaNO3–KNO3 solid solutions. The compound KNO3·LiNO3 was treated with Neumann-Kopp rule. The optimized parameters were used to predict the phase diagram of LiNO3–NaNO3–KNO3 ternary system and the predicted ternary invariant points were experimentally verified.

Thermodynamic assessment of the Fe–V–O system

The Fe–V–O system over the whole composition range was optimized according to the reliable phase equilibria and thermodynamic data. The modified quasichemical model was used to describe the liquid phase from metal alloy to oxide melt. Based upon the Compound Energy Formalism, the FeV2O4–Fe3O4 spinel solution was described by a sublattice model considering the cation distribution between tetrahedral and octahedral sites. Wüstite, corundum and (VO2)s.s. were described using a simple Bragg-Williams model. A set of self-consistent model parameters was obtained and the available phase diagram and thermodynamic data were reproduced well within experimental error limits. The complex phase relations in the Fe–V–O system at various temperatures and oxygen partial pressures were elucidated.

Thermodynamic Modeling of Ni-C, Co-C, and Ni-Co-C Liquid Alloys Using the Modified Quasichemical Model

The strong interactions between the metallic elements and C in liquid Ni, Co, and Ni-Co alloys have been thermodynamically analyzed. The liquid solution properties in Ni-C and Co-C systems showed significant asymmetry because of the short-range ordering of C exhibited in the liquid solution. Using the modified quasichemical model in the pair approximation, the Ni-C and Co-C systems were re-optimized to simultaneously reproduce the present experimental results of the C solubility and the reported thermodynamic properties in the liquid phases. In particular, the partial enthalpy data of C in liquid Ni and Co alloys were considered for the first time on the thermodynamic assessment of Ni-C and Co-C liquid solutions. The asymmetric interpolation method was introduced to evaluate the Gibbs free energy in the ternary system based on the binary Gibbs free energies in the Ni-C and Co-C systems. The C solubility data measured in the ternary Ni-Co-C alloy melt over a wide Co concentration range were successfully reproduced without any additional ternary model parameter by considering the short-range ordering of C.

Measurement and Thermodynamics of Carbon Solubilities in Molten Si–Fe, Si–Ni, and Si–Cr–Fe Alloys at 2073 K

The equilibrium phase relations of molten Si–Fe, Si–Ni, and Si–Fe–Cr alloys saturated with either silicon carbide (SiC) or graphite, which are candidates for the solvent for rapid solution growth of SiC, have been investigated. The measured carbon solubilities at 2073 K were 0.19–6.6 mol% for the Si–(24.1–70.1) mol% Fe, 0.061–5.2 mol% for Si–(30.0–85.0) mol% Ni, and 1.1–3.9 mol% for Si–(50−x) mol% Fe–x mol% Cr (x = 10.4–40.1) alloys. A quasi-chemical model that assumes that the carbon atoms are introduced into the interstitial sites of the Si–Fe, Si–Ni, and Si–Fe–Cr solvents and obstruct the bonding between solvent atoms was used to evaluate the activity coefficient of carbon in each alloy. The estimation reproduced the trends of the measured carbon solubilities fairly well. However, the estimation using the sub-regular solution model often overestimated the carbon solubilities. Thus, the carbon behavior in molten silicon–transition metal alloys is well described by the quasi-chemical model.

Critical Evaluation and Thermodynamic Optimization of the Fe-P System

Thermodynamic optimization of the Fe-P system was performed using the CALculation of PHAse Diagrams (CALPHAD) method based on critical evaluation of all available phase equilibria and thermodynamic data. The Gibbs energies of liquid phase and solid solutions were described using the Modified Quasichemical Model and Compound Energy Formalism, respectively. The Fe-P phase diagram, thermodynamic properties of P in liquid Fe and stability of intermediate iron phosphides (Fe3P, Fe2P, FeP and FeP2) in the entire composition range were reoptimized for resolving the discrepancies left in the previously optimized database. Several problems in previous assessments were resolved, and a more accurate and consistent description of the Fe-P system was achieved compared to experimental data. The distribution of P between molten Fe-P alloys and slag at different temperatures was also calculated to present the applicability of the present work to steel dephosphorization calculation.

Novel ethyl lactate based ATPS for the purification of rutin and quercetin

The application of new aqueous two-phase systems (ATPS) composed by a hydrophilic green solvent, ethyl lactate, and two low environmental impact salts: sodium and potassium citrate have been studied for the recovery of two flavonoids from aqueous solutions. First, to understand the phase formation process of the ATPS, binodal curves and tie-lines and their respective slopes and tie-line lengths were determined at T = 298.15 K and atmospheric pressure. The degree of consistency of the tie-lines was evaluated using Othmer-Tobias and Bancroft equations. Moreover, the influence of the change of the salt cation on the phase behaviour has been assessed. Furthermore, the UNIversal QUAsiChemical (UNIQUAC) thermodynamic model was applied to describe the phase equilibria presented in this work. Furthermore, the partitioning of two flavonoids, rutin and quercetin, in these ATPS {ethyl lactate (1) + citrate salts (2) + water (3)} was measured at T = 298.15 K and atmospheric pressure. Finally, the obtained results were compared with those found in literature.

Coupled Experimental Study and Thermodynamic Modeling of the Fe–Mn–Ti–O System

Thermodynamic optimization of phase diagrams and thermodynamic properties of the FeO–Fe2O3–MnO–Mn2O3–TiO2–Ti2O3 system at 1 atm pressure was performed based on the literature data and new phase diagram data in this study. Isothermal phase diagrams of the system at 1250–1600 °C in air atmosphere were experimentally determined for the first time using the equilibration and quenching method. The liquid phase and complex solid solutions like pseudobrookite, ilmenite and spinel were described using the Modified Quasichemical Model and Compound Energy Formalism, respectively. A set of optimized model parameters of all phases was obtained which reproduces all reliable thermodynamic data and phase equilibria within 3 mol% in composition and ± 25 °C in temperature. The present thermodynamic results can help the prediction of complex thermodynamic data and phase equilibria of the Fe–Mn–Ti–O system at 1 atm total pressure from 25 °C to above the liquidus temperatures over the entire range of composition and $$p_{{O_{2} }}$$ from metallic saturation to 1 atm.

Thermodynamic optimization of the binary PbO–CaO and ternary PbO–CaO–SiO2 systems

Liquidus phase equilibrium data from the recent study for the PbO–CaO and the PbO–CaO–SiO2 systems (as a part of research program on the characterization of the multicomponent PbO–ZnO–FeO–Fe2O3-“Cu2O”-CaO-SiO2 system), combined with phase equilibrium and thermodynamic data from the literature, have been used to obtain a self-consistent set of parameters of the thermodynamic models for all phases: liquid, (Ca,Pb)2SiO4, (Ca,Pb)3SiO5, (Ca,Pb)SiO3 (wollastonite and pseudowollastonite), Pb3(Ca,Pb)2Si3O11 (ganomalite) solutions, SiO2 (quartz, tridymite, cristobalite), Ca3Si2O7 (rankinite), CaO (lime), PbSiO3 (alamosite), Pb2SiO4, Pb11Si3O17, Pb5SiO7 lead silicates, PbO (massicot), Ca2PbO4, Pb8CaSi6O21 (barysilite), PbCa2Si3O9 (margarosanite) and Pb3Ca12Si5O25 compounds. Analysis of available data has shown the lack of data in the two immiscible liquids range over cristobalite, where several new experiments were done to support the model. The modified quasichemical model is used to describe the liquid slag phase. From these model parameters, the optimized ternary phase diagram is back calculated.

Critical Evaluation and Thermodynamic Optimization of the Al-P and Fe-Al-P Systems

The Al-P system and Fe-Al-P system have been thermodynamically optimized using the CALculation of PHAse Diagrams (CALPHAD) method based on critical evaluation of all available experimental data. The liquid phases and solid solutions were modeled using the Modified Quasichemical Model and Compound Energy Formalism, respectively. The Gibbs energies of stoichiometric AlP compound and liquid Al-P solution were critically optimized to reproduce the melting point of AlP and the liquidus of Al-P system on the Al-rich corner. In the ternary Fe-Al-P system, the behavior of P in the liquid was also well optimized with introduction of Toop interpolation technique (Al as an asymmetric component). In addition, various phase equilibria of Fe-Al-P alloys containing up to 30 wt.%Al and 15 wt.%P, isothermal sections at 450, 650 and 800 °C, and the solubility of P in BCC_A2 Fe-Al alloys were excellently described, compared to experimental data. According to the present optimization, an accurate and consistent thermodynamic database of the Fe-Al-P system has been developed.

Physical properties and solid-liquid equilibria for hexafluorophosphate-based ionic liquid ternary mixtures and their corresponding subsystems

Mixing ionic liquids is a simple and economical method of exploiting their tunability and allows to use ionic liquids with high melting temperatures for low-temperature applications through the formation of eutectic mixtures. In this study, the phase diagrams of the [C4mpy][PF6]-[C4mpip][PF6]-[C4mpyrr][PF6] ternary system (where [C4mpyrr] = 1-butyl-1-methylpyrrolidinium; [C4mpy] = 1-butyl-3-methylpyridinium; [C4mpip] = 1-butyl-1-methyl-piperidinium) and all of its unary and binary subsystems were measured and modelled using the Modified Quasichemical Model and the Compound Energy Formalism for the liquid and relevant solid solutions, respectively. The phase diagram determination allowed for density and viscosity measurements over the entire composition range, from temperatures close to the liquidus up to about 110 °C. In addition, the thermal and physical properties of the ionic liquid [C4mim][PF6] ([C4mim] = 1-butyl-3-methylimidazolium) were measured. A new viscosity model was proposed to describe mixtures and was compared to the Grunberg-Nissan mixing law. The proposed model exhibited a better predictive ability for the viscosity data of ternary mixtures compared to the Grunberg-Nissan mixing law with the same number of adjustable parameters. The limits of the proposed viscosity model were analyzed in light of the Gibbs-Adam theory, using viscosity and configurational entropy data for [C4mim][PF6].

Vapor–Liquid Equilibria and Conceptual Design of Extractive Distillation for Separating Ethanol and Ethyl Propionate

Ethyl propionate is usually produced from esterification of propionic acid and ethanol in the industry. However, the purification of ethyl propionate remains a challenge because the unreacted ethanol forms an azeotrope with ethyl propionate. In this work, extractive distillation was adopted, and isobutyl acetate was chosen as the entrainer to separate the mixture of ethanol and ethyl propionate. The vapor–liquid equilibria for binary systems of ethanol/ethyl propionate + isobutyl acetate were measured at atmospheric pressure, and the experiment data were correlated with the nonrandom two-liquid model, universal quasi-chemical model, and Wilson model. Then, the thermodynamic analyses, using residue curves, isovolatility curves, and extractive composition profile of the ethanol + ethyl propionate + isobutyl acetate ternary system, were performed to confirm the feasibility of separating the azeotrope with isobutyl acetate as the entrainer. The extractive distillation process was designed and optimized by the sequential iterative procedure based on the total annual cost. Results of the extractive distillation simulation also verified the reliability of thermodynamic analysis.

Thermodynamic optimization of the binary CaO–ZnO and ternary CaO–ZnO–SiO2 systems

Liquidus phase equilibrium data of the present authors for the CaO–ZnO–SiO2 system (as a part of research program on the characterization of the multicomponent PbO–ZnO–FeO–Fe2O3-“Cu2O”-CaO-SiO2 system), combined with phase equilibrium and thermodynamic data from the literature, have been used to obtain a self-consistent set of parameters of the thermodynamic models for all phases. The modified quasichemical model is used for the liquid slag phase; lime (Ca,Zn)O, zincite (Zn,Ca)O, α- and α′-dicalcium silicate (Ca,Zn)2SiO4 and tricalcium silicate (Ca,Zn)3SiO5 are described within Bragg-Williams formalism; tridymite, cristobalite SiO2, wollastonite, pseudowollastonite CaSiO3, rankinite Ca3Si2O7, willemite Zn2SiO4, melilite (hardystonite) Ca2ZnSi2O7 and Ca–Zn feldspar CaZnSi3O8 are treated as stoichiometric compounds. From these model parameters, the optimized ternary phase diagram is back calculated.