Theoretical Analysis of the Thermodynamic, Structural, Surface and Transport Properties of PbSn Liquid Alloys at 1050 K

Article Preview

Abstract:

The thermodynamic, structural, surface and transport properties of PbSn eutectic alloys at 1050 K have been analyzed employing self association model. The model parameters have been evaluated on utilizing the experimental data of free energy of mixing of PbSn liquid alloys at 1050 K. For the validation of the model parameters, the calculated values of the excess free energy of mixing and activity of the components of PbSn liquid alloys have been compared with the experimentally measured data. Further, the estimated model parameters have been used to determine the thermodynamic functions i.e. the free energy of mixing, thermodynamic activity, entropy of mixing and heat (or enthalpy) of mixing, and the structural properties such as the concentration fluctuations and shortrange order parameter. The theoretical and experimental values are compared. A good agreement is observed. Again, the surface properties of PbSn liquid alloys at 1050 K have been investigated using the Butler model in the framework of self association model. The calculated values of surface tension of PbSn liquid alloys at 1050 K are in reasonable agreement with the data available in the literature. The transport properties like the diffusivity and viscosity of PbSn liquid alloys at 1050 K have been theoretically analyzed. For the computation of viscosity, the simple formula developed by Moelwin- Hughes has been used in conjunction with self association model. The present study reveals that PbSn eutectic liquid alloys at 1050 K are segregating in nature. Further, the model parameters are found to depend on temperature.Keywords: Gibbsfree energy; concentration fluctuations; short-range order parameter; surface tension; diffusivity; viscosity

You might also be interested in these eBooks

Info:

Periodical:

Pages:

127-139

Citation:

Online since:

October 2022

Export:

Price:

Permissions CCC:

Permissions PLS:

Сopyright:

© 2022 Trans Tech Publications Ltd. All Rights Reserved

Share:

Citation:

* - Corresponding Author

[1] https://fetsolder.com.

Google Scholar

[2] G. Gasior, Z. Moser and J. Pstrus, Density and surface tension of the Pb-Sn liquid alloys, J. Phase Equilibria, 22 (1): 20-25, (2001).

DOI: 10.1007/s11669-001-0051-9

Google Scholar

[3] Y. Xi, F.Q. Zu, L.J. Liu, R.R. Shen, X. F. Li and Z.H. Chen, ABNORMAL SOLIDIFICATION OF Pb-Sn ALLOY INDUCED BY LIQUID STRUCTURE TRANSITION, Kovove Mater. 43: 432-439, (2005).

Google Scholar

[4] R.Hultgren , P.D. Desai, D.T. Hawkins, M. Gleiser, and K.K. Kelley, Selected Values of the Thermodynamic Properties of Binary Alloys, ASM, Metal Park, Ohio, (1973).

Google Scholar

[5] T.L. Ngai and Y.A. Chang, A thermodynamic analysis of the Pb-Sn system and the calculation of the Pb-Sn phase diagram, CALPHAD 5(4):267-276,(1981).

DOI: 10.1016/0364-5916(81)90009-2

Google Scholar

[6] I. Karakaya and W.T. Thompson, The Pb-Sn (Lead- Tin) system, Bull. Alloy Phase Diagrams 9: 144-152, (1988).

DOI: 10.1007/bf02890552

Google Scholar

[7] D.R. Poirier, Densities of Pb-Sn alloys during solidification, Metall. Trans. A,19: 2349-2354,(1988).

DOI: 10.1007/bf02645059

Google Scholar

[8] L. Battezzati and A.L. Greer, The viscosity of liquid metals and alloys, Acta Metall. 37 (7): 1791-1802, (1989).

DOI: 10.1016/0001-6160(89)90064-3

Google Scholar

[9] Y. Plevachuk, V. Sklyarchuk, A. Yakymovych, B. Willers and S. Eckert, Electronic properties and viscosity of liquid Pb-Sn alloys, J. Alloys and Compounds 394: 63-68, (2005).

DOI: 10.1016/j.jallcom.2004.10.051

Google Scholar

[10] M.J. Assael, A.E. Kalyva, K.E. Antoniadis, R.M. Banish, I. Egry, P.N. Quested, J. Wu, E. Kaschnitz and W.A. Wakeham, Reference data for the density and viscosity for liquid copper and liquid tin, J. Phys. Chem. Ref. Data, 39(3): 033105-1- 033105-8,(2010).

DOI: 10.1063/1.3467496

Google Scholar

[11] S.A. Etesami, M.I. Baskes, M. Laradji, and E. Asadi, Thermodynamics of solid Sn and Pb-Sn liquid mixtures using molecular dynamics simulations, Acta Materialia, 161, 320-330, (2018).

DOI: 10.1016/j.actamat.2018.09.036

Google Scholar

[12] S.A. Trebukhov, V.N. Volodin, O.V. Ulanova, A.V. Nitsenko and N.M. Burabaeva, Thermodynamics of formation and evaporation of lead-tin alloys, Complex Use of Mineral Resources 316 (1): 82-90, (2021).

DOI: 10.31643/2021/6445.10

Google Scholar

[13] R.N. Singh and F. Sommer, Segregation and Immiscibility in liquid binary alloys, Rep. Prog. Phys 60: 57-150, (1997).

DOI: 10.1088/0034-4885/60/1/003

Google Scholar

[14] B.C. Anusionwu, C.A. Madu and C.E. Orji, Theoretical studies of mutual diffusivities and surface properties in Cd-Ga liquid alloys, PRAMANA, J. Physics 72 (6): 951-967, (2009).

DOI: 10.1007/s12043-009-0088-6

Google Scholar

[15] Y.A. Odusote, A.I. Popoola and S.S. Oluyamo, Bulk and surface properties of demixing liquid Al-Sn and SnTl alloys, Appl. Phys A: 122:80, (2016).

DOI: 10.1007/s00339-015-9591-4

Google Scholar

[16] O.E. Awe and A. A. Azeez, Temperature dependence of the bulk and surface properties of liquid Zn-Cd alloys, Appl. Phys. A, 123: 363, (2017).

DOI: 10.1007/s00339-017-0977-3

Google Scholar

[17] D. Giuranno and R. Novakovic, Surface and transport properties of liquid Bi-Sn alloys, J. Mater. Sci.: Mater. in Electro. 31: 5533-5545,(2020).

DOI: 10.1007/s10854-020-03118-y

Google Scholar

[18] A.B. Bhatia and D.E Thornton, Structural Aspects of the Electrical Resistivity of Binary Alloys, Phys. Rev. B, 2 (8): 3004-3012, (1970).

DOI: 10.1103/physrevb.2.3004

Google Scholar

[19] B.E. Warren, X-ray Diffraction, Reading M.A., Addition-Wesley Pub., (1969).

Google Scholar

[20] J.M. Cowley, An Approximate Theory of Order in Alloys, Phys. Rev. 77: 667-675, (1950).

Google Scholar

[21] J.A.V. Butler, The Thermodynamics of the Surfaces of the Solutions, Proc. Roy. Soc. A 135: 348-375, (1932).

Google Scholar

[22] Y. Plevachuk, V. Sklyarchuk, G. Gerbeth, S. Eckert and R. Novakovic, Surface tension and density of liquid Bi-Pb, Bi-Sn and Bi-Pb-Sn eutectic alloys, Surface Science 605: 1034- 1042, (2011).

DOI: 10.1016/j.susc.2011.02.026

Google Scholar

[23] C. Costa, S. Delsante, G. Borzone, D. Zivkovic and R. Novakovic, Thermodynamic and surface properties of liquid Co-Cr-Ni alloys, J. Chem. Thermodyn. 69: 73-84, (2014).

DOI: 10.1016/j.jct.2013.09.034

Google Scholar

[24] G. Kaptay, A method to calculate equilibrium surface phase transition lines in monotectic systems, CALPHAD 29 (1): 56-67,(2005).

DOI: 10.1016/j.calphad.2005.04.004

Google Scholar

[25] L.C. Prasad and R.N. Singh, Surface segregation and concentration fluctuations at the liquid-vapour interface of molten Cu-Ni alloys, Phys. Rev. B 44: 13768-13771, (1991).

DOI: 10.1103/physrevb.44.13768

Google Scholar

[26] L.S. Darken, Diffusion, mobility and their interrelation through free energy in binary metallic systems,Trans. AIME 175: 184-201, (1948).

DOI: 10.1007/s11661-010-0177-7

Google Scholar

[27] L.C. Prasad, R.N. Singh, V.N. Singh and G.P. Singh, Correlation between bulk and surface properties of g-Sn liquid alloys, J. Phys. Chem. B 102: 921, (1998).

DOI: 10.1021/jp971042l

Google Scholar

[28] E. Moelwyn-Hughes, Physical Chemistry, Pergamon Press, (1961).

Google Scholar

[29] G.K. Shrestha, B.K. Singh, I.S. Jha, B.P. Singh and D. Adhikari, Optimization method for the study of the properties of Al—Sn binary liquid alloys, Physica B, 514: 1-7, (2017).

DOI: 10.1016/j.physb.2017.03.005

Google Scholar

[30] R.P. Chaudhary, J. Mandal, I.S. Jha, Symmetries in the properties of Ag-Cu liquid alloys at 1423 K, Materials oday: Proceedings 49: 2283-2287, (2022).

DOI: 10.1016/j.matpr.2021.09.343

Google Scholar

[31] T. Iida, R.I.L. Guthrie, The Physical Properties of Liquid Metals, Clarendon Press, Oxford, (1988).

Google Scholar