Theoretical calculation of surface tension and its temperature coefficient associated with liquid Cu–Ti alloys

References

• N. Eustathopoulos, N. Sobczak, A. Passerone, and K. Nogi, Measurement of contact angle and work of adhesion at high temperature, J. Mater. Sci. 40 (2005), pp. 2271–2280. doi: 10.1007/s10853-005-1945-4
   Web of Science ®Google Scholar
• J. Butler, The thermodynamics of the surfaces of solutions, Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character 135 (1932), pp. 348–375.
   Google Scholar
• A. Bhatia and R. Singh, Thermodynamic properties of compound forming molten alloys in a weak interaction approximation, Phys. Chem. Liq: an Int. J. 11 (1982), pp. 343–351. doi: 10.1080/00319108208080755
   Web of Science ®Google Scholar
• E. Guggenheim, Mixtures, Oxford University Press, Oxford, 1952.
   Google Scholar
• R. Speiser, D. Poirier, and K. Yeum, Surface tension of binary liquid alloys, Scripta. Metall. Mater. 21 (1987), pp. 687–692. doi: 10.1016/0036-9748(87)90385-1
   Google Scholar
• K. Yeum, R. Speiser, and D. Poirier, Estimation of the surface tensions of binary liquid alloys, Metall. Trans. B. 20 (1989), pp. 693–703. doi: 10.1007/BF02655927
   Google Scholar
• R. Singh, Short-range order and concentration fluctuations in binary molten alloys, Can J Phys. 65 (1987), pp. 309–325. doi: 10.1139/p87-038
   Web of Science ®Google Scholar
• A. Bhatia and R. Singh, Short range order and concentration fluctuations in regular and compound forming molten alloys, Phys. Chem. Liq.: an International Journal. 11 (1982), pp. 285–313. doi: 10.1080/00319108208080752
   Web of Science ®Google Scholar
• R. Novakovic, E. Ricci, D. Giuranno, and A. Passerone, Surface and transport properties of Ag–Cu liquid alloys, Surf Sci. 576 (2005), pp. 175–187. doi: 10.1016/j.susc.2004.12.009
   Web of Science ®Google Scholar
• R.N. Singh and F. Sommer, Simple model for demixing binary liquid alloys, Z Metallkd. 83 (1992), pp. 533–540.
   Google Scholar
• F. Sommer and R. Singh, Temperature dependence of the thermodynamic functions for demixing liquid binary alloys, Z. Metallkd. 85 (1994), pp. 621–624.
   Google Scholar
• J. Li, L. Coudurier, and N. Eustathopoulos, Work of adhesion and contact-angle isotherm of binary alloys on ionocovalent oxides, J. Mater. Sci. 24 (1989), pp. 1109–1116. doi: 10.1007/BF01148806
   Web of Science ®Google Scholar
• J. Miyazaki, J. Barker, and G. Pound, A new Monte Carlo method for calculating surface tension, J. Chem. Phys. 64 (1976), pp. 3364–3369. doi: 10.1063/1.432627
   Web of Science ®Google Scholar
• J.K. Lee, J. Barker, and G. Pound, Surface structure and surface tension: perturbation theory and Monte Carlo calculation, J Chem. Phys. 60 (1974), pp. 1976–1980. doi: 10.1063/1.1681303
   Web of Science ®Google Scholar
• L. Prasad, R. Singh, V. Singh, and G. Singh, Correlation between bulk and surface properties of AgSn liquid alloys, J Phys. Chem. B. 102 (1998), pp. 921–926. doi: 10.1021/jp971042l
   Web of Science ®Google Scholar
• S. Amore, J. Brillo, I. Egry, and R. Novakovic, Surface tension of liquid Cu–Ti binary alloys measured by electromagnetic levitation and thermodynamic modelling, Appl. Surf. Sci. 257 (2011), pp. 7739–7745. doi: 10.1016/j.apsusc.2011.04.019
   Web of Science ®Google Scholar
• R. Novakovic, E. Ricci, M. Muolo, D. Giuranno, and A. Passerone, On the application of modelling to study the surface and interfacial phenomena in liquid alloy–ceramic substrate systems, Intermetallics. 11 (2003), pp. 1301–1311. doi: 10.1016/S0966-9795(03)00172-9
   Web of Science ®Google Scholar
• E. Ricci, D. Giuranno, R. Novakovic, T. Matsushita, S. Seetharaman, R. Brooks, L. Chapman, and P. Quested, Density, surface tension, and viscosity of CMSX-4® superalloy, Int. J. Thermophys. 28 (2007), pp. 1304–1321. doi: 10.1007/s10765-007-0257-0
   Web of Science ®Google Scholar
• L. Battezzati and D. Baldissin, The thermo lab project: thermophysical properties of superalloys, High Temp. Mater. Proc. 27 (2008), pp. 423–428. doi: 10.1515/HTMP.2008.27.6.423
   Web of Science ®Google Scholar
• R. Aune, L. Battezzati, R. Brooks, I. Egry, H.-J. Fecht, J.-P. Garandet, M. Hayashi, K.C. Mills, A. Passerone, and P.N. Quested, Thermophysical properties of in738Lc, Mm247Lc and Cmsx-4 in the liquid and high temperature solid phase, Superalloys. 718 (2005), pp. 625–706.
   Google Scholar
• R. Aune, S. Seetharaman, L. Battezzati, I. Egry, F. Schmidt-Hohagen, J. Etay, H. Fecht, R. Wunderlich, A. Passerone, and E. Ricci, Surface tension measurements of Al-Ni based alloys from ground-based and parabolic flight experiments: results from the ThermoLab project, Microgravity-Sci. Tec. 18 (2006), p. 73. doi: 10.1007/BF02870383
   Web of Science ®Google Scholar
• H.-J. Fecht, R. Wunderlich, L. Battezzati, J. Etay, E. Ricci, S. Seetharaman, and I. Egry, Thermophysical properties of materials, Europhys. News. 39 (2008), pp. 19–21. doi: 10.1051/epn:2008501
   Google Scholar
• F. Kohler, Zur Berechnung der thermodynamischen Daten eines ternären Systems aus den zugehörigen binären Systemen, Monatsh. Chem. Verw. Tl. 91 (1960), pp. 738–740. doi: 10.1007/BF00899814
   Google Scholar
• Y.-M. Muggianu, M. Gambino, and J.-P. Bros, 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. 72 (1975), pp. 83–88. doi: 10.1051/jcp/1975720083
   Web of Science ®Google Scholar
• K.-C. Chou, A general solution model for predicting ternary thermodynamic properties, Calphad. 19 (1995), pp. 315–325. doi: 10.1016/0364-5916(95)00029-E
   Web of Science ®Google Scholar
• M. Hillert, Empirical methods of predicting and representing thermodynamic properties of ternary solution phases, Calphad. 4 (1980), pp. 1–12. doi: 10.1016/0364-5916(80)90016-4
   Web of Science ®Google Scholar
• G. Toop, Predicting ternary activities using binary data, T Metall. Soc. AIME. 233 (1965), pp. 850–854.
   Google Scholar
• The thermodynamics of the surfaces of solutions, Vol. 135, 827, The Royal Society.
   Google Scholar
• J. Korozs, and G. Kaptay, Derivation of the Butler equation from the requirement of the minimum gibbs energy of a solution phase, taking into account its surface area, Colloids. Surf. A Physicochem. Eng. Asp. 533 (2017), pp. 296–301. doi: 10.1016/j.colsurfa.2017.09.010
   Web of Science ®Google Scholar
• G. Kaptay, Partial surface tension of components of a solution, Langmuir. 31 (2015), pp. 5796–5804. doi: 10.1021/acs.langmuir.5b00217
   PubMed Web of Science ®Google Scholar
• E. Guggenheim, Statistical thermodynamics of the surface of a regular solution, Trans. Faraday Soc. 41 (1945), pp. 150–156. doi: 10.1039/tf9454100150
   Google Scholar
• I. Egry, The surface tension of binary alloys: simple models for complex phenomena, Int. J. Thermophys. 26 (2005), pp. 931–939. doi: 10.1007/s10765-005-6675-y
   Web of Science ®Google Scholar
• F. Aqra, and A. Ayyad, Theoretical calculations of the surface tension of liquid transition metals, Metall. Mater. Trans. B. 42 (2011), pp. 5–8. doi: 10.1007/s11663-010-9456-3
   Web of Science ®Google Scholar
• R.F. Brooks, I. Egry, S. Seetharaman, and D. Grant, Reliable data for high-temperature viscosity and surface tension: results from a European project, High Temp High Press (UK) 33 (2001), pp. 631–637.
   Google Scholar
• J. Brillo and I. Egry, Surface tension of nickel, copper, iron and their binary alloys, J Mater Sci. 40 (2005), pp. 2213–2216. doi: 10.1007/s10853-005-1935-6
   Web of Science ®Google Scholar
• P. Shen, H. Fujii, T. Matsumoto, and K. Nogi, Influence of substrate crystallographic orientation on the wettability and adhesion of α-Al2O3 single crystals by liquid Al and Cu, J. Mater. Sci. 40 (2005), pp. 2329–2333. doi: 10.1007/s10853-005-1954-3
   Web of Science ®Google Scholar
• P. Laty, J. Joud, P. Desre, and G. Lang, Tension superficielle d’alliages liquides aluminium-cuivre, Surf. Sci. 69 (1977), pp. 508–520. doi: 10.1016/0039-6028(77)90130-3
   Google Scholar
• J. Schmitz, J. Brillo, I. Egry, and R. Schmid-Fetzer, Surface tension of liquid Al–Cu binary alloys, Int. J. Mater. Res. 100 (2009), pp. 1529–1535. doi: 10.3139/146.110221
   Web of Science ®Google Scholar
• B. Allen, The surface tension of liquid transition metals at their melting points, Trans. AIME. 227 (1963).
   Google Scholar
• J. Tille and J. Kelly, The surface tension of liquid titanium, Brit. J. Appl. Phys. 14 (1963), pp. 717–719. doi: 10.1088/0508-3443/14/10/332
   Web of Science ®Google Scholar
• V. Arkhipkin, A. Agaev, G. Grigorev, and V. Kostikov, Ind. Lab. 39 (1973), p. 1340.
   Google Scholar
• A. Peterson, H. Kedesdy, P. Keck, and E. Schwarz, Surface tension of titanium, zirconium, and hafnium, J. Appl. Phys. 29 (1958), pp. 213–216. doi: 10.1063/1.1723069
   Web of Science ®Google Scholar
• V. ELYUTIN, und MA MAURAKH: Izvest, Akad. Nauk SSSR, Otdel. Tekh. Nauk (1956), pp. 129–131.
   Google Scholar
• P.-F. Paradis, T. Ishikawa, and S. Yoda, Non-contact measurements of surface tension and viscosity of niobium, zirconium, and titanium using an electrostatic levitation furnace, Int. J. Thermophys. 23 (2002), pp. 825–842. doi: 10.1023/A:1015459222027
   Web of Science ®Google Scholar
• B. Vinet, L. Magnusson, H. Fredriksson, and P.J. Desré, Correlations between surface and interface energies with respect to crystal nucleation, J. Colloid. Interf. Sci. 255 (2002), pp. 363–374. doi: 10.1006/jcis.2002.8627
   PubMed Web of Science ®Google Scholar
• G. Kuppermann, The determination of the surface tension with the help of the levitierten reciprocating drop under terrestrial conditions and in space. Ph. D. thesis, 2000.
   Google Scholar
• K.F. Man, Surface tension measurements of liquid metals by the quasi-containerless pendant drop method, Int. J. Thermophys. 21 (2000), pp. 793–804. doi: 10.1023/A:1006601821432
   Web of Science ®Google Scholar
• 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. Engin A. 495 (2008), pp. 19–26. doi: 10.1016/j.msea.2007.10.112
   Web of Science ®Google Scholar
• G. Kaptay, Corrigendum to ‘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) 19–26], Mater. Sci. Engin. A. 501 (2009), p. 255. doi: 10.1016/j.msea.2008.10.001
   Web of Science ®Google Scholar
• H. Eyring, M.S. Jhon, Significant Liquid Structures, John Wiley & Sons, New York, NY, USA, 1969.
   Google Scholar
• T.S. Ree, T. Ree, and H. Eyring, Significant structure theory of surface tension, J. Chem. Phys. 41 (1964), pp. 524–530. doi: 10.1063/1.1725902
   Web of Science ®Google Scholar
• S.W. Kim, M.S. Jhon, T. Ree, and H. Eyring, The surface tension of binary liquid mixtures, P Natl. A Sci. India A. 59 (1968), pp. 336–342. doi: 10.1073/pnas.59.2.336
   PubMed Web of Science ®Google Scholar
• A. Ayyad and F. Aqra, Theoretical consideration of the anomalous temperature dependence of the surface tension of pure liquid gallium, Theor. Chem. Acc. 127 (2010), pp. 443–448. doi: 10.1007/s00214-010-0731-9
   Web of Science ®Google Scholar
• F. Aqra and A. Ayyad, Surface tension of pure liquid bismuth and its temperature dependence: theoretical calculations, Mater. Lett. 65 (2011), pp. 760–762. doi: 10.1016/j.matlet.2010.11.038
   Web of Science ®Google Scholar
• T. Iida and R.I. Guthrie, The physical properties of liquid metals, Clarendon Press, Walton Street, Oxford OX 2 6 DP, UK, 1993.
   Google Scholar
• J.E. Schoutens, Some theoretical considerations of the surface tension of liquid metals for metal matrix composites, J. Mater. Sci. 24 (1989), pp. 2681–2686. doi: 10.1007/BF02385611
   Web of Science ®Google Scholar
• J. Brillo, I. Egry, and I. Ho, Density and thermal expansion of liquid Ag–Cu and Ag–Au alloys, Int. J. Thermophys. 27 (2006), pp. 494–506. doi: 10.1007/s10765-005-0011-4
   Web of Science ®Google Scholar
• S. Amore, S. Delsante, H. Kobatake, and J. Brillo, Excess volume and heat of mixing in Cu-Ti liquid mixture, J. Chem. Phys. 139 (2013), p. 064504. doi: 10.1063/1.4817679
   PubMed Web of Science ®Google Scholar
• T. Saito, Y. Shiraishi, and Y. Sakuma, Density measurement of molten metals by levitation technique at temperatures between 1800 and 2200 C, Trans. Iron Steel Inst. Japan. 9 (1969), pp. 118–126.
   Google Scholar
• R. Arroyave, T. Eagar, and L. Kaufman, Thermodynamic assessment of the Cu–Ti–Zr system, J. Alloy. Compd. 351 (2003), pp. 158–170. doi: 10.1016/S0925-8388(02)01035-6
   Web of Science ®Google Scholar
• V. Krasovskyy and Y. Naidich, Surface tension and specific volume of copper–titanium melts measured by the sessile drop method, J. Adhes. Sci. Technol. 18 (2004), pp. 465–471. doi: 10.1163/156856104323016360
   Web of Science ®Google Scholar
• Z. Moser, W. Gasior, and J. Pstruś, Surface tension of liquid Ag-Sn alloys: experiment versus modeling, J. Phase. Equilib. 22 (2001), pp. 254–258. doi: 10.1361/105497101770338734
   Web of Science ®Google Scholar
• F. Aqra and A. Ayyad, Theoretical calculations of the surface tension of Ag (1- x)–Cu (x) liquid alloys, J. Alloy. Compd. 509 (2011), pp. 5736–5739. doi: 10.1016/j.jallcom.2011.02.148
   Web of Science ®Google Scholar