Skip to main content Accessibility help
×
Home

Energetics of Bcc-Fcc Lattice Deformation in Iron

  • Genrich L Krasko (a1) and G. B. Olson (a1)

Abstract

The lattice deformation of the BCC-FCC martensitic transformation in iron can be described as a continuous change of the c/a parameter of the body-centered tetragonal (BCT) lattice from c/a=1 (BCC) to c/a=√2 (FCC). Along this deformation path, the total energy (as a function of volume), the enthalpy (as a function of pressure), the pressure-volume relations--both for nonmagnetic (NM) and ferromagnetic (FM) states--were calculated using the ab initio LMTO method. The ground-state magnetic properties: ferromagnetic contributions to the total energy and magnetic moments, were found by making use of the Stoner theory of itinerant ferromagnetism, rather than spin-polarized calculations. This circumvents the difficulties of using the traditional local spin-density approximation which failes to describe correctly the energetics of iron phases. The Stoner exchange parameter, I, was calculated from the linear response theory for each c/a as a function of volume. Then a constant enhancement factor, β, was introduced and the new Stoner parameter, βl, as used in all the calculations. The factor β was found by fitting the equilibrium atomic volume of the FM BCC phase to its experimental value. No other adjustments of any quantities were performed. The calculations revealed a somewhat unusual behavior of enthalpy along the deformation path. Instead of a double-well curve with a barrier maximum somewhere at 1 < c/a < √2, the enthalpy of the NM phase exhibits a monotonic decrease with c/a, the BCC modification being unstable with respect to the shear deformation. Moreover, up to a certain c/a (depending on pressure), the nonmagnetic BCT phase is also unstable with respect to spontaneous magnetization. Ferromagnetism stabilizes the BCT phases. However, the FM FCC phase is unstable with respect to shear deformation. The enthalpy curve along the deformation path then has a cusp corresponding to a first-order phase transition between ferromagnetic and nonmagnetic states accompanied by an appreciable volume discontinuity. The bulk modulus, the magnetic moments and the BCC-FCC enthalpy differences are in good agreement with the available experimental data.

Copyright

References

Hide All
1. Olson, G. B. and Cohen, M. in Dislocations in Solids, vol. 7,(ed. Nabarro, F.R.N.), North-Holland, Amsterdam, 1986, pp 297407; G. B. Olson, in Proc. Intl. Conf. Mart. Transf. ICOMAT 86, Japan Institute of Metals, 1986, pp 25-34.
2. Roitburd, A. L., in Solid State Physics (Ed. Seitz, F., Turnbull, D. and Ehrenreich, H.), v 32, Acad. Press, 1978, p.317; A. L. Roitburd, Soviet Phys. -Usp. 1Z, 326 (1974)
3. Nishiyama, Z.. Martensitic Transformations, New York, 1978
4. Bain, E. C., Trans. Amer. Inst. Min. Metall. Eng. 70, 25 (1924)
5. Suzuki, T., and Ledbetter, H. M., Phil. Mag. A 48, 83 (1983), M. J. Kelly, J. Phys. F: Metal Physics,9, 1921 (1979); P. Beauchamp, J. P. Villain. Proc. Intl. Conf. on Solid State Phase Transformations, TMS-AIME, 1981, p1221; J. Watton, Thesis, Massachusetts Institute of Technology, 1983 (unpublished)
6. Milstein, F. and Farber, B., Phys. Rev. Lett. 44, 277 (1980)
7. Moruzzi, V. L., Janak, J. F. and Williams, A. R.. Calculated Electronic Properties of Metals, Pergamon Press, New-York, 1978
8. Hathaway, K. B., Jansen, H. J. F. and Freeman, A. J., Phys. Rev. B 31, 7603 (1985)
9. Moruzzi, V. L., Phys. Rev. Lett. 57, 2211 (1986)
10. Moruzzi, V. L., Marcus, P. M., Schwarz, K., and Mohn, P., Phys. Rev. B 34, 1784 (1986)
11. Jansen, H. J. F. and Peng, S. S.. Phys. Rev. B 37, 2689 (1988)
12. Stoner, E. C., Proc. R. Soc. London, Ser. A 16 339 (1939)
13. Andersen, O.K., Jepsen, O., and Gloetzel, D. in Highlights of Condensed Matter Theory, edited by Bassani, F., Fumi, F., and Tosi, M. P. (NorthHolland, New York, 1985); 0. K. Andersen in Electronic Structure of Complex Systems, edited by Phariseau, P. and Timmerman, W.M. (Plenum, New York, 1984) p. 1165; H. L. Skriver, The LMTO Method (Springer, Berlin, 1984)
14. Gloetzel, D. and O. K. Andersen (unpublished), N. E. Christensen, Phys. Rev. B 32, 207 (1985), H. L. Skriver, Phys. Rev. B U1,1909 (1985)
15 Barth, U. von and Hedin, L., J. Phys.C 5, 1629 (1972)
16. Barth, U. von and Gelatt, C. D. Jr., Phys. Rev. B 21, 2222 (1980)
17. Krasko, G. L., Phys. Rev. B 36, 8565 (1987)
18. Marcus, P. M., and Moruzzi, V. L., Phys. Rev. B 38,6949 (1988)
19. Krasko, G. L., to be published
20 Janak, J. F., Phys. Rev. B 16, 255 (1977)
21. Kaufman, L. and Bernstein, H. ,Computer Calculations of Phase Diagrams Academic Press, New York, 1970
22. Pearson, W. P., Handbook of Lattice Spacings and Structures of Metals and Alloys, Pergamon Press, Oxford, 1964
23. Landolt-Bdrnstein, Neue Series, Bd Il/11. Springer,Berlin, 1984
24. Bendick, W. and Pepperhoff, W., Acta Metall. 30, 679 (1982)
25. Tauer, K. G. and Weiss, R. J.. Bull. Am. Bhys. Soc. 6, 125 (1961); L. Kaufman, E.V. Clougherty and R. J. Weiss, Acta Metall. 11, 323 (1963)
26. Abrahams, C., Guttman, L., and Kasper, J.S., Phys. Rev. 127, 2052 (1962); G. Johnson, M.B. McGirr, and D.A. Wheeler, Phys. Rev B 1, 3208 (1970)
27. Gonser, U., Krischel, R., and Nasu, S.. J. Magn. Magn. Mater. 15–18, 1145 (1980)
28. Wright, J. G.. Phil. Mag. 24, 217 (1971); U. Gradmann, W. KOmmerle and P. Tillmanns. Thin Solid Films,.34, 249 (1976)

Energetics of Bcc-Fcc Lattice Deformation in Iron

  • Genrich L Krasko (a1) and G. B. Olson (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.