Paper Titles

Preface and Editiorial Board

Investigation of the Kinetic of a Bainitic Reaction upon Heating in a CuAlNiMn and a CuAlNiMnFe Shape Memory Alloy
p.3

A Unified Theoretical Framework to Model Bulk, Surface and Interfacial Thermodynamic Properties of Immiscible Liquid Alloys
p.10

Comparative Study of Precipitation Hardened and Equal Channel Angular Pressed Powder Metallurgical Al-Alloy Samples
p.20

Hf Particles Reinforced Cu-Zr-Al Amorphous Powder Produced by Milling
p.30

Analysis of Lead in SnAg Based Solders Using X-Ray Fluorescence
p.37

The Role of Pb Impurity in SAC Solder Alloy
p.42

Description of the PM Process by Using Ishikawa-Analysis
p.48

Effect of High Rotating Magnetic Field on the Solidified Structure of Al–7wt.%Si–1wt.%Fe Alloy
p.57

HomeMaterials Science ForumMaterials Science Forum Vol. 752A Unified Theoretical Framework to Model Bulk,...

A Unified Theoretical Framework to Model Bulk, Surface and Interfacial Thermodynamic Properties of Immiscible Liquid Alloys

Article Preview

Abstract:

Bulk, surface and interface thermodynamics of immiscible liquid alloys are considered within a unified theoretical framework. For bulk thermodynamic functions the exponential and the combined linear-exponential equations are discussed, obeying the 4th law of thermodynamics. Surface phase transition is discussed in details. For surface and interface thermodynamics the monolayer Butler equation is compared to the multilayer model. During further assessment of bulk thermodynamic data of immiscible liquid alloys their experimentally measured surface tension and interfacial energy should be also taken into account, coupled with the models presented here.

You might also be interested in these eBooks

Materials Science at University of Miskolc

Info:

Periodical:

Materials Science Forum (Volume 752)

Pages:

10-19

DOI:

https://doi.org/10.4028/www.scientific.net/MSF.752.10

Citation:

Cite this paper

Online since:

March 2013

Authors:

Ádám Végh, Csaba Mekler, György Kaptay

Keywords:

CALPHAD, Immiscible Liquids, Interfacial Energy, Monotectic Alloys, Surface Phase Transition, Surface Tension, Thermodynamic

Export:

RIS, BibTeX

Price:

Permissions:

Request Permissions

[1] T.B. Massalski (ed), Binary Alloy Phase Diagrams, 3 volumes, ASM International, (1990).

[2] J.Z. Zhao, S. Drees, L. Ratke, Strip casting of Al-Pb alloys - a numerical analysis, Mater. Sci and Eng. A, 282 (2000) 262-290.

DOI: 10.1016/s0921-5093(99)00755-8

[3] C.P. Wang, X.J. Liu, I. Ohnuma, R. Kainuma, K. Ishida, Formation of immiscible alloy powders with egg-type microstructure, Science, 297 (2002) 990-993.

DOI: 10.1126/science.1073050

[4] G. Kaptay, On the wettability, encapsulation and surface phase transition in monotectic liquid metallic systems, Mater. Sci. Forum, 537-538 (2007) 527-532.

DOI: 10.4028/www.scientific.net/msf.537-538.527

[5] M. Wu, A. Ludwig, L. Ratke, Modeling of Marangoni-induced droplet motion and melt convection during solidification of hypermonotectic alloys, Metall. Mater. Trans. A, 34A (2003) 3009-3019.

DOI: 10.1007/s11661-003-0200-3

[6] J.Z. Zhao, J. He, Z.Q. Hu, L. Ratke, Microstructure evolution in immiscible alloys during rapid directional solidification, Z. Metallkd, 95 (2004) 362-368.

DOI: 10.3139/146.017967

[7] M. Svéda, A. Roósz, G. Buza, Formation of lead bearing surface layers on aluminum alloys by laser alloying, Mater. Sci. Forum, 508 (2006) 99-104.

DOI: 10.4028/www.scientific.net/msf.508.99

[8] I. Budai, G. Kaptay, A new class of engineering materials: particles stabilized metallic emulsions and monotectic alloys, Metall. Mater Trans A, 40A (2009) 1524-1528.

DOI: 10.1007/s11661-009-9857-6

[9] I. Budai, O.Z. Nagy, G. Kaptay, Inversion of a liquid Bi/Al metallic emulsion stabilized by solid SiC particles, Coll Surf A, 377 (2011) 325-329.

DOI: 10.1016/j.colsurfa.2011.01.028

[10] O.Z. Nagy, J.T. Szabo, G. Kaptay, Stabilization of metallic emulsions by in-situ precipitating intermetallic layers, Intermetallics, 26 (2012) 26-30.

DOI: 10.1016/j.intermet.2012.03.048

[11] G. Kaptay, On the equation of the maximum capillary pressure induced by solid particles to stabilize emulsions and foams and on the emulsion stability diagram, Coll Surfaces A, 282-283 (2006) 387-401.

DOI: 10.1016/j.colsurfa.2005.12.021

[12] I. Budai, G. Kaptay, Wettability of SiC and alumina particles by liquid Bi under liquid Al, J. Mater. Sci., 45 (2010) 2090-(2098).

DOI: 10.1007/s10853-009-3907-8

[13] C.R. Heiple, J.R. Roper, Mechanism for minor element effect on GTA fusion zone geometry, Welding J., 61 (1982) 97s-102s.

[14] Y. Wang, H.L. Tsai, Effects of surface active elements on weld pool fluid flow and weld penetration in gas metal arc welding, Metall. Mater. Trans. B, 32B (2001) 501-514.

DOI: 10.1007/s11663-001-0035-5

[15] S. Lu, H. Fujii, K. Nogi, Sensitivity of Marangoni convection and weld shape variations to welding parameters in O2-Ar shielded GTA welding, Scr. Mater, 51 (2004) 271-277.

DOI: 10.1016/j.scriptamat.2004.03.004

[16] Y. Zhao, Y. Lei, Y. Shi, Effects of surface-active elements sulphur on flow patterns of welding pool, J. Mater. Sci. Technol., 21 (2005) 408-414.

[17] T. Sándor, C. Mekler, J. Dobránszky, G. Kaptay, An improved theoretical model for A-TIG welding based on surface phase transition and reversed Marangoni flow, Metall. Mater. Trans. A, doi: 10. 1007/s11661-012-1367-2.

DOI: 10.1007/s11661-012-1367-2

[18] J.W. Cahn, Critical point wetting, J. Chem. Phys., 66 (1977) 3667-3672.

[19] P.G. de Gennes, Wetting: statics and dynamics, Rev. Modern Physics, 57 (1985) 827-863.

DOI: 10.1103/revmodphys.57.827

[20] W. Freyland, Wetting transitions in fluid metallic mixtures, J. Non-Cryst. Sol. 250-252 (1999) 199-204.

DOI: 10.1016/s0022-3093(99)00117-9

[21] D. Bonn, D. Ross, Wetting transitions, Rep. Prog. Phys., 64 (2001) 1085-1163.

DOI: 10.1088/0034-4885/64/9/202

[22] C. Serre, P. Wynblatt, D. Chatain, Study of wetting-related adsorption transition in the Ga-Pb system: 1. Surface energy measurements of Ga-rich liquids, Surf. Sci., 415 (1998) 336-345.

DOI: 10.1016/s0039-6028(98)00567-6

[23] H. Shim, D. Chatain, P. Wynblatt, Study of wetting-related adsorption transition in the Ga-Pb system: 2. Surface composition measurements of Ga-rich liquids, Surf. Sci., 415 (1998) 346-350.

DOI: 10.1016/s0039-6028(98)00568-8

[24] H. Shim, P. Wynblatt, D. Chatain, Wetting-related transitions in liquid Ga-Tl alloys, Surf. Sci. Lett., 476 (2001) L273-L277.

DOI: 10.1016/s0039-6028(01)00698-7

[25] A. Turchanin, D. Nattland, W. Freyland, Surface freezing in a liquid eutectic Ga-Bi alloy, Chem. Phys. Lett., 337 (2001) 5-10.

DOI: 10.1016/s0009-2614(01)00185-3

[26] G. Kaptay, A method to calculate equilibrium surface phase transition lines in monotectic systems, Calphad 29 (2005) 56-67 (+ Erratum, same volume, p.262).

DOI: 10.1016/j.calphad.2005.07.007

[27] C. Mekler, G. Kaptay, Calculation of surface tension and surface phase transition line in binary Ga-Tl system, Mater. Sci. Eng. A, 495 (2008) 65-69.

DOI: 10.1016/j.msea.2007.10.111

[28] J.A.V. Butler, The thermodynamics of the surfaces of solutions, Proc. Roy. Soc. A, 135 (1932) 348-375.

[29] T. Tanaka, K. Hack, S. Hara, Use of thermodynamic data to determine surface tension and viscosity of metallic alloys, MRS Bulletin, 24 (1999) 45-50.

DOI: 10.1557/s0883769400052180

[30] W. Gasior, Z. Moser, J. Pstrus, Density and surface tension of the Pb-Sn liquid alloys, J. Phase Equilibria, 22 (2001) 20-25.

DOI: 10.1007/s11669-001-0051-9

[31] R. Picha, J. Vrestal, A. Kroupa, Prediction of alloy surface tension using a thermodynamic database, Calphad, 28 (2004) 141-146.

DOI: 10.1016/j.calphad.2004.06.002

[32] J. Brillo, Y. Plevachuk, I. Egry, Surface tension of liquid Al-Cu-Ag ternary alloys, J. Mater. Sci., 45 (2010) 5150-5157.

DOI: 10.1007/s10853-010-4512-6

[33] P. Wynblatt, A. Saul, D. Chatain, The effects of prewetting and wetting transitions on the surface energy of liquid binary alloys, Acta mater., 46 (1998) 2337-2347.

DOI: 10.1016/s1359-6454(98)80015-3

[34] G. Kaptay, A CALPHAD-compatible method to calculate liquid/liquid interfacial energies in immiscible metallic systems, Calphad, 32 (2008) 338-352.

DOI: 10.1016/j.calphad.2007.10.002

[35] G. Kaptay, On the interfacial energy of coherent interfaces. Acta Mater, 60 (2012) 6804-6813.

DOI: 10.1016/j.actamat.2012.09.002

[36] H.L. Lukas, S.G. Fries, B. Sundman, Computational Thermodynamics. The Calphad method. Cambridge University Press, Cambridge, UK, (2007).

DOI: 10.1017/cbo9780511804137

[37] G. Kaptay, On the tendency of solutions to tend toward ideal solutions at high temperatures, Metall. Mater. Trans. A, 43 (2012) 531-543.

DOI: 10.1007/s11661-011-0902-x

[38] C.H.P. Lupis, J.F. Elliott, Correlation between excess entropy and enthalpy functions, Trans. Met. Soc. AIME, 236 (1966) 130.

[39] L. Kaufman, H. Bernstein, Computer Calculation of phase diagrams (with special reference to refractory metals), Academic Press, NY, USA, (1970).

[40] B. Predel (ed. ), Phase Equilibria, Crystallographic and Thermodynamic Data of Binary Alloys, volume 5 of group IV of Landolt-Börnstein Handbook, Springer-Verlag, Berlin, 1991-(1997).

[41] V.T. Witusiewitz, F. Sommer, Estimation of the excess entropy of mixing and the excess heat capacity of liquid alloys, J. Alloys Comps., 312 (2000) 228-237.

DOI: 10.1016/s0925-8388(00)01158-0

[42] S.L. Chen, S. Daniel, F. Zhang, Y.A. Chang, W.A. Oates, R. Schmid-Fetzer, On the calculation of multicomponent stable phase diagrams, J. Phase Equi., 22 (2001) 373-378.

DOI: 10.1361/105497101770332910

[43] G. Kaptay, A new equation for the temperature dependence of the excess Gibbs energy of solution phases, Calphad 28 (2004) 115-124.

DOI: 10.1016/j.calphad.2004.08.005

[44] K. Arroyave, Z.K. Liu, Thermodynamic modelling of the Zn-Zr system, Calphad 30 (2006) 1-13.

DOI: 10.1016/j.calphad.2005.12.006

[45] X. Yuan, W. Sun, Y. Du, D. Zhao, H. Yang, Thermodynamic modelling of Mg-Si system with the Kaptay equation for the excess Gibbs energy of the liquid phase, Calphad 33 (2009) 673-678.

DOI: 10.1016/j.calphad.2009.08.004

[46] C.Y. Zhan, W. Wang, Z.L. Tang, Z.R. Nie, Thermodynamic Research on Solution Properties of Al-Er Alloys, Mater. Sci. Forum 610-613 (2009) 674-680.

DOI: 10.4028/www.scientific.net/msf.610-613.674

[47] C. Guo, C. Li, Z. Du, A thermodynamic modelling of the Gd-Tl system, J. Alloys Compds., 492 (2009) 122-127.

[48] Y. Tang, X. Yuan, Y. Du, Thermodynamic modeling of the Fe-Zn system using exponential temperature dependence for the excess Gibbs energy, JMM B 37 (2011) 1-10.

[49] Y. Tang, Y. Du, L. Zhang, X. Yuan, G. Kaptay, Thermodynamic description of the Al–Mg–Si system using a new formulation for the excess Gibbs energy, Thermochim. Acta 527 (2012) 131-142.

DOI: 10.1016/j.tca.2011.10.017

[50] J.W. Gibbs, On the Equlibrium of Heterogenous Substances, Trans. Conn. Acad. Arts Sci. 3 (1875-1878) 108-248 and 343-524.

[51] G. Kaptay, A unified model for the cohesive enthalpy, critical temperature, surface tension and volume thermal expansion coefficient of liquid metals of bcc, fcc and hcp crystals, Mater. Sci. Eng. A, 495 (2008).

DOI: 10.1016/j.msea.2007.10.112

[52] G. Kaptay, On the order–disorder surface phase transition and critical temperature of pure liquid metals originating from bcc, fcc and hcp crystal structures, Int. J. Thermophysics 33 (2012) 1177-1190.

DOI: 10.1007/s10765-012-1270-5

[53] D. Chatain, L. Martin-Garin, N. Eustathopoulos, Etude experimentale de la tension interfaciale liquide-liquide du systeme Ga-Pb entre le temperatures monotectique et critique, J. chim. phys., 79 (1982) 569-577.

DOI: 10.1051/jcp/1982790569

[54] M. Merkwitz, J. Weise, K. Thriemer, W. Hoyer, Liquid-liquid interfacial tension in the demixing metal systems Ga-Hg and Ga-Pb, Z. Metallkd., 89 (1998) 247-255.

[55] I. Kaban, W. Hoyer, M. Merkwitz, Experimental study of the liquid/liquid interfacial tension in immiscible Al-Bi system, Z. Metallkunde, 94 (2003) 831-834.

DOI: 10.3139/146.030831