Estimation of mixing enthalpy of the liquid Sn-Ag-Cu system at 1423 K from data on the properties of binary subsystems using geometric models of solutions

Cover Page

Cite item

Full Text

Open Access Open Access
Restricted Access Access granted
Restricted Access Subscription Access

Abstract

The article considers the estimation of mixing enthalpy ΔНmix of the Sn-Ag-Cu ternary system melts at a temperature of 1423 K from the calorimetric data on the mixing enthalpy of binary subsystems Ag-Cu, Ag-Sn and Cu-Sn measured earlier. The geometric models by Toop, Kohler and Muggianu, where binary data is jointly processed in each case according to a specific mathematical procedure, were applied to the ΔНmix assessment. The results of calculations by these models are presented by the compositional dependences of ΔНmix of the ternary system in the form of 3D surfaces, projections of these surfaces onto the plane of the compositional triangle, as well as isotherms plotted for individual quasi-binary sections. It was found that modeling using the Kohler’s and Muggianu’s methods gives insignificantly different results, whereas the values of the mixing enthalpy of ternary compositions in the Toop’s model are noticeably more immersed into the negative (exothermic) region. As it is known from the scientific literature, the right choice of a geometric model depends on whether the ternary system under study belongs to a “symmetric” or “asymmetric” type. The shape of the available ΔНmix isotherms of binary subsystems indicates that the Sn-Ag-Cu system is “asymmetric”. The results calculated using the Toop’s model are recognized as the most correct ones, since that model is recommended in the literature for describing “asymmetric” systems. The common limitation of all geometric models, considering only binary interparticle interactions, and the advisability of extra experimental study of three-component melts formation to reveal the possible contribution of ternary interactions to the mixing enthalpy are noted.

About the authors

А. S. Bykov

Institute of Metallurgy, Ural Branch, RAS

Author for correspondence.
Email: 1007o1007@gmail.com
Russian Federation, Yekaterinburg

К. I. Oleinik

Institute of Metallurgy, Ural Branch, RAS

Email: 1007o1007@gmail.com
Russian Federation, Yekaterinburg

References

  1. Rogachev A.S. Struktura, stabil’nost’ i svoystva vysokoentropiynykh splavov // Fizika metallov i metallovedeniye. 2020. 121. № 8. P. 807–841.
  2. Decterov S.A. Thermodynamic database for multicomponent oxide systems // Chim. Techno Acta. 2018. 5. P. 16–48.
  3. Toop G.W. Predicting ternary activities using binary data // Trans. Metall. Soc. AIME. 1965. 233. P. 850–855.
  4. Kohler F. Zur berechnung der thermodynamischen daten eines ternären systems aus den zugehörigen binären systemin // Monatsh. Chem. Verw. Anderer Wiss. 1960. 91. P. 738–740.
  5. Muggianu Y.M., Gambino M., Bros J. 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. Phys.-Chim. Biol. 1975. 72. P. 83–88.
  6. Oleinik K.I., Bykov A.S. Kalorimetricheskoe issledovanie obrazovaniya zhidkih splavov Ag–Cu–Sn. Ental’piya smesheniya v granichnyh binarnyh sistemah Cu–Ag, Cu–Sn i Ag–Sn pri 1150°C // Rasplavy. 2019. 5. С. 12–17.
  7. Oleinik K.I., Bykov A.S. Calorimetric study of the formation of liquid Ag–Cu–Sn alloys. Enthalpy of mixing for the boundary binary Cu–Ag, Cu–Sn, and Ag–Sn systems at 1150° C // Russian Metallurgy (Metally). 2019. 2019. P. 131–134.
  8. Sharkey R.L., Pool M.J., Hoch M. Thermodynamic modeling of binary and ternary metallic solutions // Metall. Trans. 1971. 2. P. 3039–3046.
  9. Pool M.J., Predel B., Schultheiss E. Application of the Setaram high temperature calorimeter for the determination of mixing enthalpies of liquid alloys // Thermochim. Acta. 1979. 28. P. 349–358.
  10. Luef C., Flandorfer H., Ipser H. Lead-free solder materials: experimental enthalpies of mixing in the Ag-Cu-Sn and Cu-Ni-Sn ternary systems // Z. Metallkd. 2004. 95. P. 151–163.
  11. Nazeri M.F.M., Ismail A.B., Mohamad A.A. Effect of polarizations on Sn-Zn solders alloys in alkaline electrolyte // J. Alloys Compd. 2014. 606. P. 278–287.
  12. Ho C.-Y., Tsai M.-T., Duh J.-G., Lee J.-W. Bump height confinement governed solder alloy hardening in Cu/SnAg/Ni and Cu/SnAgCu/Ni joint assemblies // J. Alloys Compd. 2014. 600. P. 199–203.
  13. Huang M., Zhao N, Liu S., He Y. Drop failure modes of Sn–3.0Ag–0.5Cu solder joints in wafer level chip scale package // Trans. Nonferrous Met. Soc. China. 2016. 26. P. 1663–1669.
  14. Shnawah. D.A., Said S.B.M., Sabri M.F.M., Badruddin I.A., Che F.X. High-reliability low-Ag-content Sn–Ag–Cu solder joints for electronics applications // J. Electron. Mater. 2012. 41. P. 2631–2658.
  15. Amin N.A.A.M., Shnawah D.A., Said S.M., Sabri M.F.M., Arof H. Effect of Ag content and the minor alloying element Fe on the electrical resistivity of Sn–Ag–Cu solder alloy // J. Alloys Compd. 2014. 599. P. 114–120.
  16. Elhosiny Ali H., El-Taher A.M., Algarni H. Influence of bismuth addition on the physical and mechanical properties of low silver/lead-free Sn-Ag-Cu solder // Mater. Today Commun. 2024. 39. 109113.
  17. Zhao X., Zhao M., Cui X., Xu T., Tong M. Effect of cerium on microstructure and mechanical properties of Sn-Ag-Cu system lead-free solder alloys // Trans. Nonferrous Met. Soc. China. 2007. 17. P. 805-810.
  18. Zhang R.F., Zhang S.H., He Z.J., Jing J., Sheng S.H. Miedema Calculator: A thermodynamic platform for predicting formation enthalpies of alloys within framework of Miedema’s Theory // Comput. Phys. Commun. 2016. 209. P. 58–69.
  19. Hillert M. Empirical methods of predicting and representing thermodynamic properties of ternary solution phases // Calphad. 1980. 4. P. 1–12.

Supplementary files

Supplementary Files
Action
1. JATS XML

Copyright (c) 2024 Russian Academy of Sciences