Skip to main content
SpringerLink
Log in

Structure–Property Relations in Pb-Supersaturated Metastable Sn-Rich Pb-Sn Alloys

  • Original Research Article
  • Published:
Metallurgical and Materials Transactions A Aims and scope Submit manuscript

Abstract

We have performed a theoretical study of three polymorphs of Pb-supersaturated Sn-rich Pb-Sn alloys with the \(\alpha \)-Sn, \(\beta \)-Sn, and a simple-hexagonal \(\gamma \)-Sn structure employing quantum-mechanical calculations. We focused on structure–property relations in the case of lattice parameters, thermodynamic stability, elastic properties, and mechanical stability as well as electronic-structure density of states. Compositional trends in structural, thermodynamic, and electronic properties were found nearly linear. Our study also sheds new light on a decades-long controversy surrounding the existence of \(\gamma \)-phase and \(\beta \)-phase supersaturated Sn-rich Pb-Sn alloys. We suggest that the experimental difficulties when synthesizing them are caused by their high formation energy and mechanical instability of the \(\beta \)-phase.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

Data Availability

The data will be made available upon request.

References

  1. L. Zhang, and K.N. Tu: Mater. Sci. Eng.: R Rep., 2014, vol. 82, pp. 1–32. https://doi.org/10.1016/j.mser.2014.06.001

    Article  Google Scholar 

  2. S. Dammu, A.P. Singh, S.R.F. Lala, and C. Srivastava: Metall. Mater. Trans. A, 2023, vol. 54, pp. 3928–39. https://doi.org/10.1007/s11661-023-07143-4

    Article  Google Scholar 

  3. A.P. Singh, A. Gupta, K.S. Jyotheender, and C. Srivastava: Metall. Mater. Trans. A, 2022, vol. 53, pp. 2743–53. https://doi.org/10.1007/s11661-022-06704-3

    Article  CAS  Google Scholar 

  4. S.R.F. Lala, A. Gupta, and C. Srivastava: Metall. Mater. Trans. A 2022, vol. 53, pp. 3795–806. https://doi.org/10.1007/s11661-022-06786-z

    Article  CAS  Google Scholar 

  5. P. Peng, W. Chen, Y. Xu, X. Pei, and J. Wang: Metall. Mater. Trans. A, 2022, vol. 53, 382–87. https://doi.org/10.1007/s11661-021-06542-9

    Article  CAS  Google Scholar 

  6. B. Rheingans, L.P.H. Jeurgens, and J. Janczak-Rusch: Metall. Mater. Trans. A, 2022, vol. 53, 2195–207. https://doi.org/10.1007/s11661-022-06660-y

    Article  CAS  Google Scholar 

  7. Y. Wang, Z. Ye, X. Peng, J. Huang, J. Yang, S. Chen, and X. Zhao: Metall. Mater. Trans. A, 2022, vol. 53, 1704–16. https://doi.org/10.1007/s11661-022-06625-1

    Article  CAS  Google Scholar 

  8. N. Hou, J.W. Xian, A. Sugiyama, H. Yasuda, and C.M. Gourlay: Metall. Mater. Trans. A, 2023, vol. 54, 909–27. https://doi.org/10.1007/s11661-022-06937-2

    Article  CAS  Google Scholar 

  9. S. Cui, J. Wang, and I.-H. Jung: Metall. Mater. Trans. A, 2022, vol. 53, 4296–14, https://doi.org/10.1007/s11661-022-06825-9

    Article  CAS  Google Scholar 

  10. I. Karakaya, and W.T. Thompson: J. Phase Equilibria, 1988, vol. 9, pp. 144–52. https://doi.org/10.1007/BF02890552

    Article  Google Scholar 

  11. J.A. Lee, and G.V. Raynor: Proc. Phys. Soc. Sect. B, 1954, vol. 67, pp. 737

    Article  Google Scholar 

  12. R.P. Frankenthal, and D.J. Siconolfi: Surf. Sci., 1982, vol. 119, pp. 331–48. https://doi.org/10.1016/0039-6028(82)90301-6

    Article  CAS  Google Scholar 

  13. R.H. Kane, B.C. Giessen, and N.J. Grant: Acta Metall., 1966, vol. 14, pp. 605–609. https://doi.org/10.1016/0001-6160(66)90068-X

    Article  CAS  Google Scholar 

  14. P.R. Sarode, and A.R. Chetal: Curr. Sci., 1974, vol. 43, pp. 339–39

    CAS  Google Scholar 

  15. H.J. Fecht, and J.H. Perepezko: Metall. Trans. A, 1989, vol. 20, pp. 785–94. https://doi.org/10.1007/BF02651645

    Article  Google Scholar 

  16. G. Kresse, and J. Hafner: Phys. Rev. B, 1993, vol. 47, pp. 558–61. https://doi.org/10.1103/PhysRevB.47.558

    Article  CAS  Google Scholar 

  17. G. Kresse, J. Furthmüller: Phys. Rev. B, 1996, vol. 54, pp. 11169–86. https://doi.org/10.1103/PhysRevB.54.11169

    Article  CAS  Google Scholar 

  18. Hohenberg, P., Kohn, W.: Phys. Rev. B, 1964, vol. 136, pp. 864–71. https://doi.org/10.1103/PhysRev.136.B864

    Article  Google Scholar 

  19. W. Kohn, and L.J. Sham: Phys. Rev. A, 1965, vol. 140, pp. 1133–38. https://doi.org/10.1103/PhysRev.140.A1133

    Article  Google Scholar 

  20. P.E. Blöchl: Phys. Rev. B, 1994, vol. 50, pp. 17953–79. https://doi.org/10.1103/PhysRevB.50.17953

    Article  Google Scholar 

  21. G. Kresse, and D. Joubert: Phys. Rev. B, 1999, vol. 59, pp. 1758–75. https://doi.org/10.1103/PhysRevB.59.1758

    Article  CAS  Google Scholar 

  22. J.P. Perdew, K. Burke, and M. Ernzerhof: Phys. Rev. Lett. 1996, vol. 77, pp. 3865–68. https://doi.org/10.1103/PhysRevLett.77.386

    Article  CAS  PubMed  Google Scholar 

  23. A. Zunger, S. Wei, L. Ferreira, and J. Bernard: Phys. Rev. Lett., 1990, vol. 65, 353–56. https://doi.org/10.1103/PhysRevLett.65.353

    Article  CAS  PubMed  Google Scholar 

  24. A.R. Oganov, and C.W. Glass: J. Chem. Phys., 2006, vol. 124, p. 244704. https://doi.org/10.1063/1.2210932

    Article  CAS  PubMed  Google Scholar 

  25. A.O. Lyakhov, A.R. Oganov, H.T. Stokes, and Q. Zhu: Comput. Phys. Commun., 2013, vol. 184, pp. 1172–82. https://doi.org/10.1016/j.cpc.2012.12.009

    Article  CAS  Google Scholar 

  26. A.R. Oganov, A.O. Lyakhov, and M. Valle: Acc. Chem. Res., 2011, vol. 44, 227–37. https://doi.org/10.1021/ar1001318

    Article  CAS  PubMed  Google Scholar 

  27. L. Zhou, D. Holec, and P.H. Mayrhofer: J. Appl. Phys., 2013, vol. 113. https://doi.org/10.1063/1.4793084

  28. M.J. Mehl, M. Ronquillo, D. Hicks, M. Esters, C. Oses, R. Friedrich, A. Smolyanyuk, E. Gossett, D. Finkenstadt, and S. Curtarolo: Phys. Rev. Mater. 2021, vol. 5, p. 083608. https://doi.org/10.1103/PhysRevMaterials.5.083608

    Article  CAS  Google Scholar 

  29. R. Gaillac, P. Pullumbi, and F.-X. Coudert: J. Phys.: Condens. Matter, 2016, vol. 28, p. 275201. https://doi.org/10.1088/0953-8984/28/27/275201

    Article  CAS  PubMed  Google Scholar 

  30. M. Friák, N. Masničák, O. Schneeweiss, P. Roupcová, A. Michalcová, Š. Msallamová, and M. Šob: Comput. Mater. Sci., 2022, vol. 215, p. 111780. https://doi.org/10.1016/j.commatsci.2022.111780

    Article  CAS  Google Scholar 

  31. M. Friák, D. Lago, N. Koutná, D. Holec, T. Rebok, M. Šob: Comput. Phys. Commun., 2019, p. 106863. https://doi.org/10.1016/j.cpc.2019.106863

  32. F. Tran, J. Stelzl, and P. Blaha: J. Chem. Phys., 2016, vol. 144, p. 204120. https://doi.org/10.1063/1.4948636

    Article  CAS  PubMed  Google Scholar 

  33. G.-X. Zhang, A.M. Reilly, A. Tkatchenko, and M. Scheffler: New J. Phys., 2018, vol. 20, p. 063020. https://doi.org/10.1088/1367-2630/aac7f0

    Article  CAS  Google Scholar 

  34. J.A. Lee, and G.V. Raynor: Proc. Phys. Soc. Sect. B, 1954, vol. 67, p. 737. https://doi.org/10.1088/0370-1301/67/10/301

    Article  Google Scholar 

  35. A. Levins, M. Straumanis, and K. Karlsons: Z. Phys. Chem., 1938, vol. 40, p. 347

    Google Scholar 

  36. L.-F. Zhu, M. Friák, A. Dick, B. Grabowski, T. Hickel, F. Liot, D. Holec, A. Schlieter, U. Kühn, J. Eckert, Z. Ebrahimi, H. Emmerich, and J. Neugebauer: Acta Mater., 2012, vol. 60, pp. 1594–602. https://doi.org/10.1016/j.actamat.2011.11.046

    Article  CAS  Google Scholar 

  37. S. Maisel, M. Höfler, and S. Müller: Nature, 2012, vol. 491, p. 740. https://doi.org/10.1038/nature11609

    Article  CAS  PubMed  Google Scholar 

  38. K. Momma, and F. Izumi: J. Appl. Crystallogr., 2011, vol. 44, pp. 1272–76. https://doi.org/10.1107/S0021889811038970

    Article  CAS  Google Scholar 

Download references

Acknowledgments

M.F., P.Č., P.R., I.M., Š.M., and A.M. acknowledge the Czech Science Foundation for the financial support received under the Project No. 22-05801S. Computational resources were provided by the e-INFRA CZ project (ID:90254), supported by the Ministry of Education, Youth and Sports of the Czech Republic. These resources were utilized through IT4Innovations National Supercomputing Center, MetaCentrum as well as CERIT Scientific Cloud. Figures 1, 3, 4, and 5 are visualized using the VESTA software[38] (version 3, National Museum of Nature and Science, 4-1-1, Amakubo, Tsukuba-shi, Ibaraki 305-0005, Japan). Fruitful discussions with MSc. Aiswarya Vijayakumar Thelappurath from IPM in Brno, Czech Republic, related to the text of our paper are gratefully acknowledged.

Author information

Authors and Affiliations

  1. Department of Experimental Studies and Modelling of Structure, Institute of Physics of Materials, Czech Academy of Sciences, v. v. i., Žižkova 22, Brno, 616 00, Czech Republic

    Martin Friák, Petr Čípek, Ondřej Zobač, Pavla Roupcová & Ivana Miháliková

  2. Department of Chemistry, Faculty of Science, Masaryk University, Kotlářská 2, Brno, 611 37, Czech Republic

    Petr Čípek & Jana Pavlů

  3. Central European Institute of Technology (CEITEC), Brno University of Technology, Purkyňova 123, Brno, 612 00, Czech Republic

    Pavla Roupcová

  4. Department of Materials Science, Montanuniversität Leoben, Franz-Josef-Straße 18, Leoben, 8700, Austria

    David Holec

  5. Department of Metals and Corrosion Engineering, University of Chemistry and Technology in Prague, Technická 5, Prague, 166 28, Czech Republic

    Šárka Msallamová & Alena Michalcová

Authors
  1. Martin Friák
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Petr Čípek
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jana Pavlů
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ondřej Zobač
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Pavla Roupcová
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Ivana Miháliková
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. David Holec
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Šárka Msallamová
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. Alena Michalcová
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Conceptualization: MF, JP, ŠM, AM; Data Curation: JP, OZ, PR, DH, ŠM, AM; Formal Analysis and Investigation and Methodology: MF, PČ, JP, OZ, PR, IM, DH, ŠM, AM; Project Administration and Funding Acquisition: MF, AM; Resources: MF, JP, AM; Supervision: MF, JP, OZ, ŠM, AM; Validation: JP, PČ, OZ, PR, DH, ŠM, AM; Visualization: MF, PČ, JP, and DH; Writing—Original Draft, Writing—Review and Editing: MF, PČ, JP, OZ, PR, IM, DH, ŠM, AM.

Corresponding author

Correspondence to Martin Friák.

Ethics declarations

Conflict of interest

The authors declare no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Appendix

Appendix

See Figure A1.

Fig. A1
figure 12

Example of XRD profiles detected in our experimental Pb-Sn samples

Full size image

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Friák, M., Čípek, P., Pavlů, J. et al. Structure–Property Relations in Pb-Supersaturated Metastable Sn-Rich Pb-Sn Alloys. Metall Mater Trans A (2024). https://doi.org/10.1007/s11661-024-07362-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11661-024-07362-3

Search

Navigation