The Transformation of the Structure at Heating and Mechanism of Thermal Expansion of Sn-Bi Eutectic Alloy


  • I.I. Shtablavyi Ivan Franko National University of Lviv
  • S.I. Mudry Ivan Franko National University of Lviv
  • U.I. Liudkevych Ivan Franko National University of Lviv



short range order structure, thermal expansion, free volume


The short range order structures of Sn-Bi eutectic melt has been studied by means of X-ray diffraction and reverse Monte-Carlo methods within 420 – 1120 К temperature range. Temperature dependences of interatomic distances and thermal expansion coefficient within first coordination sphere were calculated. Free volume temperature variation was investigated using Voronoi-Delone statistic-geometric method. Obtained data allowed us to find the occurrence of smeared structure transformation in Sn-Bi liquid eutectic and determine the temperature range of this transformation. Results of this study have a potential application in soldering technologies, particularly at improving of interface region properties.  


[1] M.E. Loomans, S. Vaynman, G. Ghosh, M.E. Fine, J Electron Mater. 23, 741 (1994).
[2] A. Rahn, The basics of soldering (NewYork: John Wiely & Sons, 1993).
[3] K.N. Tu, Solderjointtechnology: material, properties, andreliability.(NY, USA: Springer 2007).
[4] H.R. Kotadia, P.D. Howes, S.H. Mannan, 54, 1253 (2014)
[5] T. Laurila, V. Vuorinen, JK. Kivilahti, Mater Sci Eng R – Rep.49, 1 (2005).
[6] T. Laurila, V. Vuorinen, M. Paulasto-Krockel, Mater Sci Eng R – Rep. 68, 1(2010).
[7] M. Abtew, G. Selvaduray,Mater Sci Eng R – Rep27, 95 (2000).
[8] F. Hua, Z. Mei, A. Lavagnino, Eutectic Sn–Bi asan alternative Pb-freesolder. In: Proceedings of aninternational summiton lead-freeelectronic sassemblies, IPC Works’99; S/03/08/01/06(1999).
[9] J. F. Li, S. H.Mannan, M. P. Clode, D. C. Whalley, D. A. Hutt, ActaMater 54, 2907 (2006).
[10] T. B. Massalski, Binary alloy phase diagram(Metals Park, OH: ASM., 1990).
[11] J. Li, S. H. Mannan, M. P. Clode, C. Liu, K. Chen, D. C. Whalley, Trans Compon Packag Technol. 31, 574 (2008).
[12] M. S.Suh, C. J. Park, H. S.Kwon, Materials Chemistry and Physics 110, 95 (2008).
[13] P.T. Vianco, A.C. Kilgo, and R. Grant, JournalofElectronicMaterials, 24 (10), (1995).
[14] H. Xiaowu,L. Yulong, Z. Min, MaterSci: MaterElectron, 24, 2027 (2013).
[15] W.H. Tao, Chem. Mater.13, 1051(2001).
[16] Y. Waseda, The structure of non crystalline materials(Mc. Graw-Hill, New York, USA, 1980).
[17] S. Takeda, S. Tamakiand Y. Waseda, Journal of the Physical Society of Japan 53(10), 3447 (1984).
[18] S. Mudry, I. Shtablavyi and I. Shevernoga, Physics and Chemistry of Liquids 50(5), 630 (2012).
[19] S. Mudry, I. Shtablavyi, I. Shevernoga,PolishJournalofChemical Technology, 15(3), 61 (2013).
[20] L. Mingyang, G. Haoran, L. Fang, Z. Min, L. Rongxue, L. Shujing, Journal of Molecular Liquids 204, 27 (2015).
[21] V.K. Pecharsky, P.Y. Zavalij, Fundamentals of powder diffraction and structural characterization of materials (Springer, 2008).
[22] D.T. Cromer, J.T. Waber, Acta Crystallogr. 18(5), 104(1965).
[23] N.N. Medvedev, V.P. Voloshin, V.A. Luchnikov, M.L. Gavrilova, J. Comput Chem. 27, 1676 (2006).
[24] W. Aiqing, L. Guo, L. Changsong, J. Erguang, Z. Zhengang, Physica B 369, 51 (2005).



How to Cite

Shtablavyi, I., Mudry, S. ., & Liudkevych, U. (2017). The Transformation of the Structure at Heating and Mechanism of Thermal Expansion of Sn-Bi Eutectic Alloy. Physics and Chemistry of Solid State, 18(2), 198–205.



Scientific articles