Skip to main content
Log in

Thermodynamic Calculation of Phase Equilibria in the Ti–Co and Ni–Sn Systems

  • Published:
Journal of Materials Science Aims and scope Submit manuscript

Abstract

A thermodynamic model for the titanium-cobalt system has been developed utilizing measured enthalpies of mixing of the liquid and evaluated phase-diagram data. The free energies of the liquid, bcc, fcc, and hcp solid solutions, and TiCo, Ti2Co, TiCo2, and TiCo3 compounds were calculated for a temperature of 400 K. The model and measured heats of crystallization have been used to predict the free energy of the metastable amorphous phase at 400 K, needed for comparison with experimental results on the mechanical alloying of Ti and Co. The predicted glass-forming range for alloys prepared by mechanical alloying is from 10 to 81.5 at. % Co. We adopted a similar approach for modeling the Ni–Sn system to calculate the free energies of Ni3Sn, and Ni3Sn2, and the liquid (amorphous) and fcc solid solutions in the nickel-rich region at 240 K. In this system the inclusion of the magnetic contribution to the free energy of the Ni-rich fcc solid solution is important in interpreting the results of mechanical alloying. We propose a simple transformation of the free-energy curves, which assists in the graphical identification of the glass-forming ranges.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. R. B. Schwarz, P. Nash and D. Turnbull, J. Mater. Res. 2 (1987) 456–60.

    Google Scholar 

  2. J. Murray, in “Phase Diagrams of Binary Titanium Alloys, ” edited by J. Murray, (Amer. Soc. for Metals Int., Metals Park, Ohio, 1987), p. 59.

    Google Scholar 

  3. L. Kaufman and H. Bernstein, in “Computer Calculation of Phase Diagrams” (Academic Press, New York, 1970).

    Google Scholar 

  4. M. W. Chase, Bull. Alloy Phase Diagrams 4 (1983) 123.

    Google Scholar 

  5. Y. O. Esin, M. G. Valishev, P. B. Gel'd and M. S. Petrushevskii, Zh. Fis. Khim. 54 (1980) 2267–2270.

    Google Scholar 

  6. H. Lukas, private communication, Max-Planck Institut fur Metallorschung, Stuttgart, 1984.

  7. R. B. Schwarz and C. C. Koch, Appl. Phys. Lett. 49 (1986) 146.

    Google Scholar 

  8. J. H. Perepezko and J. S. Paik, J. Non-Cryst. Solids 61&62 (1984) 113.

    Google Scholar 

  9. J. Rubin and R. B. Schwarz, Phys Rev. B 50 (1984) 795–804.

    Google Scholar 

  10. J. Vuorinen and T. Tiainen, Tampere University of Technology (unpublished results, 1994).

  11. E. Ma and M. Atzmon, Mater. Chem. and Phys. 39 (1995) 249–267.

    Google Scholar 

  12. B. P. Dolgin, M. A. Vanek, T. Mcgory and D. J. Ham, J. Non-Crystalline Solids, 87 (1986) 281–289.

    Google Scholar 

  13. H. Choo, M.S. Thesis (Illinois Institute of Technology, Chicago, 1991).

    Google Scholar 

  14. E. Hellstern and L. Schultz, Mater. Sci. And Engineering 93 (1987) 213–216.

    Google Scholar 

  15. R. E. Somekh, Z. H. Barber, C. S. Baxter, P. E. Donovan, J. E. Evetts and W. M. Stobbs, J. Mater. Sci. Lett. 3 (1984) 217.

    Google Scholar 

  16. K. H. J. Buschow, Solid State Communications 43 (1982) 171–174.

    Google Scholar 

  17. C. C. Koch and M. S. Kim, J. de Physique, Colloque C8 (1985) 573.

    Google Scholar 

  18. P. Nash and A. Nash, in “Phase Diagrams of Binary Nickel Alloys” edited by P. Nash (ASM International, Metals Park, Ohio, 1991), pp. 310–318.

    Google Scholar 

  19. V. N. Eremenko, G. M. Lukashenko and V. L. Pritula, Zh. Fiz. Khim. 45 (1971) 1993–1995.

    Google Scholar 

  20. V. N. Eremenko, G. M. Lukashenko and V. L. Pritula, Proc. 4th ICVM, Sec. 1, 44–46 (1973).

  21. F. Korber and W. Oelson, Mitt. Kaiser Willhelm Inst. F. Eisenforsch., 19 (1937) 209–219.

    Google Scholar 

  22. B. Predel and W. Vogelbein, Thermochim. Acta 30, (1979) 201–215.

    Google Scholar 

  23. T. J. Tianen and R. B. Schwarz, J. of Less-Common Met. 140 (1988) 99.

    Google Scholar 

  24. A. P. Miodownik, Calphad 1(2) (1977) 133.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nash, P., Choo, H. & Schwarz, R.B. Thermodynamic Calculation of Phase Equilibria in the Ti–Co and Ni–Sn Systems. Journal of Materials Science 33, 4929–4936 (1998). https://doi.org/10.1023/A:1004478101233

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1004478101233

Keywords

Navigation