General solution model and its new progress

Abstract

The physicochemical properties of multicomponent systems are involved in all fields of chemistry and have received attention from various related areas such as minerals, metallurgy, material science, environment, biology, and agriculture. At present, the relevant data can be obtained by using two major calculation methods, namely, the first principle method and the empirical method. Though the former has achieved recent great progress, it is still a long way to offer practical data; while the latter has not received progress for almost half a century. Therefore, a new method that is theoretically reasonable and accurate in practical application is necessary to obtain practical and precise physicochemical data for ternary and multicomponent systems. In this paper, a new theoretical model is suggested based on its corresponding binary ones. The feasibility of this theoretical model is discussed in terms of both theoretical analysis and practical performance.

Keywords

multicomponent system / physicochemical properties / solution model / phenomenological theory

References

[1] HildebrandJH. Solubility. XII. regular solutions. J. Am. Chem. Soc., 1929, 51(1): 66

[2] J.H. Hildebrand, The term ‘regular solution’, Nature, 168(1951), No. 4281, art. No. 868.

[3] ScatchardG, WoodSE, MochelJM. Vapor-liquid equilibrium. V. Carbon tetrachloride-benzene mixtures. J. Am. Chem. Soc., 1940, 62(4): 712

[4] ScatchardG, WoodSE, MochelJM. Vapor-liquid equilibrium. VI. Benzene-methanol mixtures. J. Am. Chem. Soc., 1946, 68(10): 1957

[5] ScatchardG, WoodSE, MochelJM. Vapor-liquid equilibrium. VII. Carbon tetrachloride-methanol mixtures. J. Am. Chem. Soc., 1946, 68(10): 1960

[6] ScatchardG, TicknorLB. Vapor-liquid equilibrium. IX. The methanol-carbon tetrachloride-benzene system. J. Am. Chem. Soc., 1952, 74(15): 3724

[7] RedlichO, KisterAT. Algebraic representation of thermodynamic properties and the classification of solutions. Ind. Eng. Chem., 1948, 40(2): 345

[8] ScatchardG, TicknorLB, GoatesJR, McCartneyER. Heats of mixing in some non-electrolyte solutions. J. Am. Chem. Soc., 1952, 74(15): 3721

[9] ScatchardG, KavanaghGM, TicknorLB. Vapor-liquid equilibrium. VIII. Hydrogen peroxide-water mixtures. J. Am. Chem. Soc., 1952, 74(15): 3715

[10] ScatchardG. Solutions of nonelectrolytes. Annu. Rev. Phys. Chem., 1952, 3: 259

[11] KohlerF. Zur berechnung der thermodynamischen daten eines ternären systems aus den zugehörigen binären systemen. Monatshefte Für Chemie Und Verwandte Teile Anderer Wissenschaften, 1960, 91(4): 738

[12] ToopGW. Predicting ternary activities using binary data. Trans. Metall. Soc. AIME, 1965, 233: 850

[13] C. Colinet, Thesis University of Grenoble, France, 1967.

[14] MuggianuYM, GambinoM, BrosJP. Enthalpies de formation des alliages liquides bismuth-étain-gallium à 723 K. Choix d’une représentation analytique des grandeurs d’excès intégrales et partielles de mélange. J. Chim. Phys., 1975, 72: 83

[15] HillertM. Empirical methods of predicting and representing thermodynamic properties of ternary solution phases. Calphad, 1980, 4(1): 1

[16] ChouKC. A new solution model for predicting ternary thermodynamic properties. Calphad, 1987, 11(3): 293

[17] AnsaraI. Comparison of methods for thermodynamic calculation of phase diagrams. Int. Mater. Rev., 1979, 24(1): 20

[18] ChouKC, Austin ChangY. A study of ternary geometrical models. Berichte Der Bunsengesellschaft Für Physikalische Chemie, 1989, 93(6): 735

[19] KaliesG, ReichenbachC, RockmannR, EnkeD, BräuerP, JaroniecM. Further advancements in predicting adsorption equilibria using excess formalism: Calculation of adsorption excesses at the liquid/solid interface. J. Colloid Interface Sci., 2010, 352(2): 504

[20] PrasadLC, MikulaA. Surface segregation and surface tension in Al−Sn−Zn liquid alloys. Phys. B Condens. Matter, 2006, 373(1): 142

[21] IloukhaniH, KhanlarzadehK. Physicochemical properties of quaternary systems and comparison of different geometrical models. J. Chem. Eng. Data, 2011, 56(11): 4244

[22] NikolaevVF, SatgaraevAN, SultanovaRB. Predicting property isotherms of ternary mixtures on isotherms of the binary mixtures, presented by a non-stoichiometric model. J. Solut. Chem., 2012, 41(6): 953

[23] PrasadLC, JhaRK. Correlation between bulk and surface properties of ternary Ag−Sn−Zn liquid alloys and concerned binaries. Phys. Chem. Liq., 2007, 45(2): 149

[24] PrasadLC, MikulaA. Thermodynamics of liquid Al-Sn-Zn alloys and concerned binaries in the light of soldering characteristics. Phys. B Condens. Matter, 2006, 373(1): 64

[25] BonnierE, CabozR. Sur l’estimation de l’entalpie libre de me’lange de certaines alliages metalliques liquides ternaires. Comptes Rendus Hebdomadaires Des Seances De L Academie Des Sciences, 1960, 250: 527

[26] TsaoCC, SmithJM. Applied thermodynamics. Chem. Eng. Prog. Symp., Ser., 1953, 49: 107

[27] ChouKC. A general solution model for predicting ternary thermodynamic properties. Calphad, 1995, 19(3): 315

[28] ChouKC, WeiSK. A new generation solution model for predicting thermodynamic properties of a multicomponent system from binaries. Metall. Mater. Trans. B, 1997, 28(3): 439

[29] ChouKC, LiWC, LiFS, HeMH. Formalism of new ternary model expressed in terms of binary regular-solution type parameters. Calphad, 1996, 20(4): 395

[30] FanP, ChouKC. A self-consistent model for predicting interaction parameters in multicomponent alloys. Metall. Mater. Trans. A, 1999, 30(12): 3099

[31] GomidželovićL, ŽivkovićD, KostovA, MitovskiA, BalanovićL. Comparative thermodynamic study of Ga-In-Sb system. J. Therm. Anal. Calorim., 2011, 103(3): 1105

[32] ŽivkovićD, ŽivkovićŽ, VučinicB. Comparative thermodynamic analysis of the Bi−Ga_0.1Sb_0.9 section in the Bi−Ga−Sb system. J. Therm. Anal. Calorim., 2000, 61(1): 263

[33] ŽivkovićD, ŽivkovićŽ, StuparevićL, RančićS. Comparative thermodynamic investigation of the Bi−GaSb system. J. Therm. Anal. Calorim., 2001, 65(3): 805

[34] TrumicB, ZivkovicD, ZivkovicZ, ManasijevicD. Comparative thermodynamic analysis of the Pb−Au_0.7Sn_0.3 section in the Pb−Au−Sn ternary system. Thermochim. Acta, 2005, 435(1): 113

[35] ManasijevićD, ŽivkovićD, ŽivkovićŽ. Prediction of the thermodynamic properties for the Ga−Sb−Pb ternary system. Calphad, 2003, 27(4): 361

[36] BeheraCK, SonayeA. Measurement of zinc activity in the ternary In−Zn−Sn alloys by EMF method. Thermochim. Acta, 2013, 568: 196

[37] BalanovićL, ŽivkovićD, MitovskiA, ManasijevićD, ŽivkovićŽ. Calorimetric investigations and thermodynamic calculation of Zn−Al−Ga system. J. Therm. Anal. Calorim., 2011, 103(3): 1055

[38] YanLJ, ZhengSB, DingGJ, XuGT, QiaoZY. Surface tension calculation of the Sn−Ga−In ternary alloy. Calphad, 2007, 31(1): 112

[39] PiñeiroMM, MascatoE, MosteiroL, LegidoJL. Mixing properties for the ternary mixture methyl tert-butyl ether + 1-butanol + decane at 298.15 K. J. Chem. Eng. Data, 2003, 48(4): 758

[40] CasasH, SegadeL, García-GarabalS, PiñeiroMM, FranjoC, JiménezE, Paz AndradeMI. Excess molar enthalpies for propyl propanoate + cyclohexane + benzene at 298.15 and 308.15 K. Fluid Phase Equilib., 2001, 182(1–2): 279

[41] ArslanH. Analytical determination of partial and integral properties of the six components systems Ni−Cr−Co−Al−Mo−Ti and their subsystems. Phys. B Condens. Matter, 2014, 438: 48

[42] ArslanH, DoganA, DoganT. An analytical approach for thermodynamic properties of the six-component systems Ni−Cr−Co−Al−Mo−Ti and their subsystems. Phys. Met. Metallogr., 2013, 114(12): 1053

[43] HindlerM, MikulaA. Calorimetric investigations of liquid gold-antimony-tin alloys. Int. J. Mater. Res., 2012, 103(7): 858

[44] KnottS, LiZ, MikulaA. Integral enthalpy of mixing of the liquid ternary Au−Cu−Sn system. Thermochim. Acta, 2008, 470(1–2): 12

[45] A. Mikula and S. Knott, Thermodynamic investigations of ternary liquid alloys, J. Phys.: Condens. Matter, 20(2008), No. 11, art. No. 114109.

[46] RaghavanV. Al−Pb−Zn (aluminum-lead-zinc). J. Phase Equilib. Diffus., 2008, 29(2): 188

[47] ZhangLP, SongXL, SongYY, SunZB, LiQ, SongXP, WangLQ. A method to estimate the Gibbs free energy of non-equilibrium alloys by thermal analysis. J. Therm. Anal. Calorim., 2012, 110(3): 1153

[48] ŽivkovićD, GrgurićTH, GojićM, ĆubelaD, ŠimišićZS, KostovA, KožuhS. Calculation of thermodynamic properties of Cu−Al−(Ag, Au) shape memory alloy systems. Trans. Indian Inst. Met., 2014, 67(2): 285

[49] SunZB, GuoJ, LiY, ZhuYM, LiQ, SongXP. Effects of Ti addition on the liquid-phase separation of Cu₇₁Cr₂₉ alloy during rapid cooling. Metall. Mater. Trans. A, 2008, 39(5): 1054

[50] WanJF, ChenSP, Hsu Xu ZuyaoTY. The stability of transition phases in Fe−Mn−Si based alloys. Calphad, 2001, 25(3): 355

[51] MaX, QianYY, YoshidaF. Effect of La on the Sn-rich halo formation in Sn60−Pb40 alloy. J. Alloys Compd., 2001, 327(1–2): 263

[52] MaX, QianYY, YoshidaF. Effect of La on the Cu−Sn intermetallic compound (IMC) growth and solder joint reliability. J. Alloys Compd., 2002, 334(1–2): 224

[53] ZhangGH, WangLJ, ChouKC. A comparison of different geometrical models in calculating physicochemical properties of quaternary systems. Calphad, 2010, 34(4): 504

[54] ChouKC, ZhongXM, XuKD. Calculation of physicochemical properties in a ternary system with miscibility gap. Metall. Mater. Trans. B, 2004, 35(4): 715

[55] D.M. Pérez, Universidade da Coruna [Dissertation], 2006, p. 347.

[56] S.K. Yadav, U. Mehta, and D. Adhikari, Optimization of thermodynamic and surface properties of ternary Ti−Al−Si alloy and its sub-binary alloys in molten state, Heliyon, 7(2021), No. 3, art. No. e06511.

[57] DoganA, ArslanH. Estimation of viscosity of alloys using Gibbs free energy of mixing and geometric model. Russ. J. Phys. Chem., 2021, 95(3): 586

[58] H. Arslan, Prediction of excess molar volumes for quaternary liquid mixtures at 298.15 K, Süleyman Demirel Üniversitesi Fen Edebiyat Fakültesi Fen Dergisi, (2021), p. 96.

[59] V. Shrotri and L. Muhmood, Application of geometric models for calculation of viscosity and density of LiNO₃ and CsNO₃ based ternary nitrate salt systems, Calphad, 68(2020), art. No. 101749.

[60] ŚniadeckiZ. Glass-forming ability of Fe−Ni alloys substituted by group V and VI transition metals (V, Nb, Cr, Mo) studied by thermodynamic modeling. Metall. Mater. Trans. A, 2020, 51(9): 4777

[61] V. Kokotin, Technical University Dresden [Dissertation], 2010.

[62] ChouKC, ZhangGH. Calculation of physicochemical properties with limited discrete data in multicomponent systems. Metall. Mater. Trans. B, 2009, 40(2): 223

[63] MehtaU, YadavSK, KoiralaI, KoiralaRP, AdhikariD. Thermodynamic and surface properties of liquid Ti−Al−Fe alloy at different temperatures. Phys. Chem. Liq., 2021, 59(4): 585

[64] P. Sahu, S. Samal, and V. Kumar, Microstructural, magnetic, and geometrical thermodynamic investigation of FeCoNi(MnSi)_x (0.0, 0.1, 0.25, 0.5, 0.75, 1.0) high entropy alloys, Materialia, 18(2021), art. No. 101133.

[65] S.G. Sarwat and K.R. Ravi, Liquid phase as an indicator of glass-forming ability, Intermetallics, 133(2021), art. No. 107174.

[66] ŚniadeckiZ. The influence of 3d and 4d transition metals on the glass forming ability of ternary FeCo-based alloys. Metall. Mater. Trans. A, 2021, 52(5): 1861

[67] S.K. Yadav, U. Mehta, and D. Adhikari, Optimization of thermodynamic and surface properties of ternary Ti−Al−Si alloy and its sub-binary alloys in molten state, Heliyon, 7(2021), No. 3, art. No. e06511.

[68] DoganA, ArslanH. Estimation of viscosity of alloys using Gibbs free energy of mixing and geometric model. Russ. J. Phys. Chem., 2021, 95(3): 586

[69] H. Arslan, Prediction of excess molar volumes for quaternary liquid mixtures at 298.15 K, Süleyman Demirel Üniversitesi Fen Edebiyat Fakültesi Fen Dergisi, (2021), p. 96.

[70] V. Shrotri and L. Muhmood, Application of geometric models for calculation of viscosity and density of LiNO₃ and CsNO₃ based ternary nitrate salt systems, Calphad, 68(2020), art. No. 101749.

[71] ŚniadeckiZ. Glass-forming ability of Fe−Ni alloys substituted by group V and VI transition metals (V, Nb, Cr, Mo) studied by thermodynamic modeling. Metall. Mater. Trans. A, 2020, 51(9): 4777

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