Diffusivities and atomic mobilities of an Sn–Ag–Bi–Cu–Pb melt
-
Weimin Chen
, Lijun Zhang , Yong Du and Baiyun Huang
Abstract
The recently developed Arrhenius formula of a modified Sutherland equation was employed to calculate the self- and impurity diffusivities in liquid Sn, Ag, Bi, Cu and Pb. The reliability of the calculated self- and impurity diffusivities was validated by comparing the calculated diffusivities with the critically reviewed literature data. Based on the reliable tracer, intrinsic and chemical diffusivities available in the literature, the atomic mobility parameters in an Sn–Ag–Bi–Cu–Pb melt were then evaluated by the DICTRA (DIffusion-Controlled TRAnsformations) software package with the aid of the available thermodynamic description for the liquid phase. Comprehensive comparisons show that most of the measured and theoretical diffusivities in Sn–Ag–Bi–Cu–Pb melts can be reasonably reproduced by the currently obtained atomic mobilities. The atomic mobilities were further verified by comparing the model-predicted concentration profiles with the measured ones in various liquid Ag–Pb, Bi–Pb and Sn–Bi–Pb diffusion couples. Finally, the simulation of dissolution of Ag and Cu substrates into liquid solder alloys during the reflow process was performed by using the presently obtained atomic mobilities in the Sn–Ag–Bi–Cu–Pb melts.
References
[1] H.-T.Ma, J.Wang, L.Qu, N.Zhao, A.Kunwar: J. Electron. Mater. 42 (2013) 2686. 10.1007/s11664-013-2615-ySearch in Google Scholar
[2] S.W.Chen, C.F.Yang, H.J.Wu, R.B.Chang, C.M.Hsu: Mater. Chem. Phys. 132 (2012) 481. 10.1016/j.matchemphys.2011.11.057Search in Google Scholar
[3] A.Milosavljević, D.Živković, D.Manasijević, Y.Du, N.Talijan, M.Bu, A.Kostov: Int. J. Mater. Res. 104 (2013) 452. 10.3139/146.110887Search in Google Scholar
[4] F.Hodaja, L.Petitb, L.Baggettoa, O.Boisiera, L.Verneyre: Int. J. Mater. Res. 104 (2013) 874. 10.3139/146.110932Search in Google Scholar
[5] Y.H.Wong, S.Ramesh, C.Y.Tan, B.Projjal: Int. J. Mater. Res. 105 (2014) 183. 10.3139/146.111011Search in Google Scholar
[6] U.S.Mohanty, K.L.Lin: J. Electron. Mater. 42 (2013) 628. 10.1007/s11664-012-2452-4Search in Google Scholar
[7] L.J.Zhang, Y.Du, I.Steinbach, Q.Chen, B.Y.Huang: Acta Mater. 58 (2010) 3664. 10.1016/j.actamat.2010.03.002Search in Google Scholar
[8] A.Borgenstam, A.Engström, L.Höglund, J.Ågren: J. Phase Equilibr. 21 (2000) 269. 10.1361/105497100770340057Search in Google Scholar
[9] W.M.Chen, L.J.Zhang, D.D.Liu, Y.Du, C.Y.Tan: J. Electron. Mater. 42 (2013) 1158. 10.1007/s11664-013-2549-4Search in Google Scholar
[10] W.M.Chen, W.Xie, L.J.Zhang, Y.Du, B.Y.Huang, G.H.Wen, S.Q.Wang: Int. J. Refract. Met. Hard Mater. 41 (2013) 531. 10.1016/j.ijrmhm.2013.07.003Search in Google Scholar
[11] W.M.Chen, L.J.Zhang, Y.Du, B.Y.Huang: Philos. Mag. 14 (2013) 1552. 10.1080/14786435.2014.890755Search in Google Scholar
[12] W.M.Chen, L.J.Zhang, Y.Du, B.Y.Huang: J. Electron. Mater. 43 (2014) 1131. 10.1007/s11664-014-3041-5Search in Google Scholar
[13] G.Ghosh: Acta Mater. 49 (2001) 2609. 10.1016/S1359-6454(01)00187-2Search in Google Scholar
[14] J.Henderson, L.Yang: Trans. Metall. Soc. AIME. 221 (1961) 72.Search in Google Scholar
[15] H.A.Walls, W.R.Upthegrove: Acta Metall. 12 (1964) 461. 10.1016/0001-6160(64)90018-5Search in Google Scholar
[16] A.D.Pasternak, D.R.Olander: Am. Inst. Chem. Eng. J. 13 (1967) 1052. 10.1002/aic.690130604Search in Google Scholar
[17] P.Ascarelli, A.Paskin: Phys. Rev. 165 (1968) 222. 10.1103/PhysRev.165.222Search in Google Scholar
[18] P.Protopapas, H.C.Andersen, N.A.D.Parlee: J. Chem. Phys. 59 (1973) 15. 10.1063/1.1679784Search in Google Scholar
[19] S.M.M.Rahman, L.B.Bhuiyan: Phys. Rev. B33 (1986) 7243. 10.1103/PhysRevB.33.7243Search in Google Scholar PubMed
[20] J.Mei, J.W.Davenport: Phys. Rev. B40 (1990) 9682. 10.1103/PhysRevB.42.9682Search in Google Scholar
[21] K.Y.Chen, Q.C.Li: Chin. Phys. Lett. 9 (1992) 650. 10.1088/0256-307X/9/12/007Search in Google Scholar
[22] A.Pasquarello, K.Laasonen, R.Car, C.Lee, D.Vanderbilt: Phys. Rev. Lett. 69 (1992) 1982. 10.1103/PhysRevLett.69.1982Search in Google Scholar PubMed
[23] M.M.G.Alemany, C.Rey, L.J.Gallego: J. Chem. Phys. 109 (1998) 5175. 10.1063/1.477133Search in Google Scholar
[24] M.M.G.Alemany, O.Diéguez, C.Rey, L.J.Gallego: Phys. Rev. B60 (1999) 9208. 10.1103/PhysRevB.60.9208Search in Google Scholar
[25] A.B.Belonoshko, R.Ahuja, O.Eriksson, B.Johansson: Phys. Rev. B61 (2000) 3838. 10.1103/PhysRevB.61.3838Search in Google Scholar
[26] A.Z.Z.Ahmed, G.M.Bhuiyan: Int. J. Mod. Phys. B16 (2002) 3837. 10.1142/S0217979202013171Search in Google Scholar
[27] F.F.Chen, H.F.Zhang, F.X.Qin, Z.Q.Hu: J. Chem. Phys. 120 (2004) 1823. 10.1063/1.1636452Search in Google Scholar PubMed
[28] T.Iida, R.Guthrie, M.Isac, N.Tripathi: Metall. Mater. Trans. B37 (2006) 559. 10.1007/s11663-006-0039-2Search in Google Scholar
[29] Y.Mitrokhin: Comput. Mater. Sci. 36 (2006) 189. 10.1016/j.commatsci.2005.07.002Search in Google Scholar
[30] H.M.Lu, G.Li, Y.F.Zhu, Q.Jiang: J. Non-Cryst. Solids352 (2006) 2797. 10.1016/j.jnoncrysol.2006.03.049Search in Google Scholar
[31] S.Dalgıç: Mater. Chem. Phys. 103 (2007) 183. 10.1016/j.matchemphys.2007.02.013Search in Google Scholar
[32] G.Kaptay: Int. J. Mater. Res. 99 (2008) 14. 10.3139/146.101600Search in Google Scholar
[33] A.Meyer: Phys. Rev. B81 (2010) 012102. 10.1103/PhysRevB.81.012102Search in Google Scholar
[34] M.Mouas, J.G.Gasser, S.Hellal, B.Grosdidier, A.Makradi, S.Belouettar: EPJ Web of Conf. 15 (2011) 01013. 10.1051/epjconf/20111501013Search in Google Scholar
[35] C.H.Ma, R.A.Swalin: Acta Metall. 8 (1960) 388. 10.1016/0001-6160(60)90008-0Search in Google Scholar
[36] A.K.Roy, R.P.Chhabra: Metall. Mater. Trans. A19 (1988) 273. 10.1007/BF02652536Search in Google Scholar
[37] T.Ejima, T.Yamamura, N.Uchida: J. Jpn. Inst. Met. 41 (1977) 1041.10.2320/jinstmet1952.41.10_1041Search in Google Scholar
[38] A.Bruson, M.Gerl: Phys. Rev. B19 (1979) 6123. 10.1103/PhysRevB.19.6123Search in Google Scholar
[39] K.Niwa, S.Kado, T.Itoh, K.Tsuchiya: J. Jpn. Inst. Met. 26 (1962) 718.10.2320/jinstmet1952.26.11_718Search in Google Scholar
[40] T.V.Vasilenko, E.I.Khar'kov: Ukrains'kii Fizichnii Zhurnal7 (1962) 1345.Search in Google Scholar
[41] K.Niwa, S.Kado, T.Ohno: J. Jpn. Inst. Met. 26 (1962) 726.10.2320/jinstmet1952.26.11_726Search in Google Scholar
[42] T.Yamamura, T.Ejima: J. Jpn. Inst. Met. 37 (1973) 901.10.2320/jinstmet1952.37.8_901Search in Google Scholar
[43] G.W.Preckshot, R.E.Hudrlik: Trans. Metall. Soc. AIME. 218 (1956) 516.Search in Google Scholar
[44] M.Tanigaki, N.Komatsu, M.Harada, W.Eguchi: J. Chem. Eng. Jpn. 16 (1983) 167. 10.1252/jcej.16.167Search in Google Scholar
[45] R.W.Smith, X.H.Zhu, M.C.Tunnicliffe, T.J.N.Smith, L.Misener, J.Adamson: Ann. N.Y. Acad. Sci. 974 (2002) 57. 10.1111/j.1749-6632.2002.tb05896.xSearch in Google Scholar PubMed
[46] K.Niwa, M.Shimoji, S.Kado, Y.Watanab: J. Jpn. Inst. Met. 19 (1955) 294.10.2320/jinstmet1952.19.4_294Search in Google Scholar
[47] S.J.Rothman, L.D.Hall: Trans. Metall. Soc. AIME. 206 (1956) 199.Search in Google Scholar
[48] G.Döge: Z. Naturforsch. A20 (1965) 634.10.1515/zna-1965-0426Search in Google Scholar
[49] S.J.Rothman, L.D.Hall: J. Metals8 (1956) 1580.Search in Google Scholar
[50] J.W.Gorman, G.W.Preckshot: Trans. Metall. Soc. AIME. 212 (1958) 367.Search in Google Scholar
[51] X.Su, S.Yang, J.Wang, N.Y.Tang, F.Yin, Z.Li, M.Zhao: J. Phase Equilib. Diffus. 31 (2010) 333. 10.1007/s11669-010-9726-4Search in Google Scholar
[52] G.P.Grinevich, L.M.Kapitanchuk, T.V.Polishchuk: Russ. Phys. J. 21 (1978) 1369.Search in Google Scholar
[53] Y.Y.Liu, G.B.Jia, B.Yang, D.C.Liu: Mater. Rev. 25 (2011) 1.Search in Google Scholar
[54] K.Niwa, S.Kado, H.Nakajima, K.Ichikawa: J. Jpn. Inst. Met. 28 (1964) 353.10.2320/jinstmet1952.28.6_353Search in Google Scholar
[55] K.Niwa, S.Kado, S.Inagaki: J. Jpn. Inst. Met. 28 (1964) 348.10.2320/jinstmet1952.28.6_348Search in Google Scholar
[56] R.V.G.Rao, A.Satpathy. Phys. Rev. B41 (1990) 995. 10.1103/PhysRevB.41.995Search in Google Scholar
[57] J.-G.Kohl, B.Predel: Z. Metallkde69 (1978) 248.Search in Google Scholar
[58] S.Palchaudhui, R.N.Joarder, R.V.G.Rao: Phys. Stat. Sol. B126 (1984) 443. 10.1002/pssb.2221260202Search in Google Scholar
[59] S.Suzuki, K.-H.Kraatz, G.Frohberg, R.Roşu, W.Wendl, G.Müller-Vogt: Ann. N.Y. Acad. Sci. 1077 (2006) 380. 10.1196/annals.1362.028Search in Google Scholar PubMed
[60] R.E.Grace, G.Derge: Trans. Metall. Soc. AIME. 203 (1955) 839.Search in Google Scholar
[61] M.Yagaki, H.Toyoda, M.Harada, W.Eguchi: Kyoto Daigaku Genshi Enerugi Kenkyusho Iho48 (1975) 45.Search in Google Scholar
[62] K.Niwa, M.Shimoji, S.Kado, Y.Watanabe: J. Jpn. Inst. Met. 18 (1954) 276.10.2320/jinstmet1952.18.5_276Search in Google Scholar
[63] Y.Du, Y.A.Chang, B.Y.Huang, W.P.Gong, Z.P.Jin, H.H.Xu, Z.Yuan, Y.Liu, Y.He, F.-Y.Xie: Mater. Sci. Eng. A363 (2003) 140. 10.1016/S0921-5093(03)00624-5Search in Google Scholar
[64] J.O.Andersson, J.Ågren: J. Appl. Phys. 72 (1992) 1350. 10.1063/1.351745Search in Google Scholar
[65] J.Ågren: Curr. Opin. Solid State Mater. Sci. 1 (1996) 355. 10.1016/S1359-0286(96)80025-8Search in Google Scholar
[66] T.Iida, R.I.L.Guthrie: The Physical Properties of Liquid Metals, Oxford University Press, Oxford (1993).Search in Google Scholar
[67] U.Kattner, Solder Database (solder.tdb) available from NIST, (http://www.metallurgy.nist.gov/phase/solder/solder.html).Search in Google Scholar
[68] S.Chada, R.A.Fournelle, W.Laub, D.Shangguan: J. Electron. Mater. 29 (2000) 1214. 10.1007/s11664-000-0015-6Search in Google Scholar
[69] W.Gierlotka, Y.H.Chen, M.A.Haque, M.A.Rahman: J. Electron. Mater. 41 (2012) 3359. 10.1007/s11664-012-2330-0Search in Google Scholar
[70] P.T.Vianco, J.J.Martin, R.D.Wright, P.F.Hlava: Metall. Mater. Trans. A37 (2006) 1551. 10.1007/s11661-006-0099-6Search in Google Scholar
[71] G.Ghosh, Z.-K.Liu: J. Electron. Mater. 27 (1998) 1362. 10.1007/s11664-998-0098-zSearch in Google Scholar
[72] L.Zhang, Y.Du, Y.Ouyang, H.Xu, X.-G.Lu, Y.Liu, Y.Kong, J.Wang: Acta Mater. 56 (2008) 3940. 10.1016/j.actamat.2008.04.017Search in Google Scholar
[73] Y.Du, J.C.Schuster: Metall. Mater. Trans. A32 (2001) 2396. 10.1007/s11661-001-0214-7Search in Google Scholar
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Articles in the same Issue
- Contents
- Contents
- Original Contributions
- Diffusivities and atomic mobilities of an Sn–Ag–Bi–Cu–Pb melt
- Experimental study of the phase relations in the Fe–Cr–Si ternary system at 700°C
- Effect of molybdenum on the microstructure, mechanical properties and corrosion behavior of Ti alloys
- Mechanism of grain refinement and coarsening in undercooled Ni–Fe alloy
- Effects of copper content and liquid separation on the microstructure formation of Co–Cu immiscible alloys
- Influence of the solidification temperature range on Gasar structures made from Cu–Mn alloys
- Effect of ageing time on mechanical properties and tribological behaviour of aluminium hybrid composite
- Microstructure and tensile properties of a friction stir welded Al–Mg–Si alloy
- Lüders effect in Al 99.7% extruded via the KoBo method
- Reduced graphene oxide nanocomposites with different diameters and crystallinity of TiO2 nanoparticles – synthesis, characterization and photocatalytic activity
- Constitutive modelling of mill loads during hot rolling of AISI 321 austenitic stainless steel
- X-ray stress measurement with two-dimensional detector based on Fourier analysis
- People
- People
- People
- DGM News
- Personal
Articles in the same Issue
- Contents
- Contents
- Original Contributions
- Diffusivities and atomic mobilities of an Sn–Ag–Bi–Cu–Pb melt
- Experimental study of the phase relations in the Fe–Cr–Si ternary system at 700°C
- Effect of molybdenum on the microstructure, mechanical properties and corrosion behavior of Ti alloys
- Mechanism of grain refinement and coarsening in undercooled Ni–Fe alloy
- Effects of copper content and liquid separation on the microstructure formation of Co–Cu immiscible alloys
- Influence of the solidification temperature range on Gasar structures made from Cu–Mn alloys
- Effect of ageing time on mechanical properties and tribological behaviour of aluminium hybrid composite
- Microstructure and tensile properties of a friction stir welded Al–Mg–Si alloy
- Lüders effect in Al 99.7% extruded via the KoBo method
- Reduced graphene oxide nanocomposites with different diameters and crystallinity of TiO2 nanoparticles – synthesis, characterization and photocatalytic activity
- Constitutive modelling of mill loads during hot rolling of AISI 321 austenitic stainless steel
- X-ray stress measurement with two-dimensional detector based on Fourier analysis
- People
- People
- People
- DGM News
- Personal