Advertisement

Saddle-point equilibrium lines between fcc and bcc phases in Al and Ca from first principles

  • S. L. QiuEmail author
  • P. M. Marcus
Regular Article

Abstract

Phase equilibrium lines (denoted ph-eq lines) of face-centered-cubic (fcc) and body-centered-cubic (bcc) phases, as well as saddle-point equilibrium lines (denoted sp-eq lines) in Al and Ca are studied by first-principles total-energy calculations. For a non-vibrating crystal of Al we determine the transition pressure p t = 2.62 Mbar from fcc to bcc phase. The sp-eq line lies between the two ph-eq lines, merges with the bcc-eq line at V = 61 au3/atom (p = 1.64 Mbar) and with the fcc-eq line at V = 42.4 au3/atom (p = 5.50 Mbar), gives the Gibbs free energy barrier ΔG = 0.64 mRy/atom at p t . The bcc phase is unstable below 1.64 Mbar, while the fcc phase is unstable above 5.50 Mbar. In a non-vibrating crystal of Ca two sp-eq lines (denoted sp1-eq line and sp2-eq line, respectively) are found corresponding to two phase transitions: one is from fcc to bcc at p t1 = 89.6 kbar, the other is from bcc to fcc at p t2 = 787 kbar. The sp1-eq line merges with the bcc-eq line at V = 231 au3/atom (p = 50 kbar) and with the fcc-eq line at V = 183 au3/atom (p = 174 kbar), gives a barrier of Δ G 1 = 0.62 mRy/atom at p t1. The sp2-eq line merges with the bcc-eq line at V = 90 au3/atom (p = 981 kbar) and with the fcc-eq line at V = 110 au3/atom (p = 624 kbar), gives a barrier of Δ G 2 = 1.1 mRy/atom at p t2. The bcc phase is stable in the range from 50 kbar to 981 kbar but unstable outside this range, while the fcc phase is unstable in the range from 174 to 624 kbar but stable outside this range. This work confirms all the features of the sp-eq line described in our recent work [S.L. Qiu, P.M. Marcus, J. Phys.: Condens. Matter 24, 225501 (2012)] and finds two additional features: (1) there are two sp-eq lines corresponding to the two phase transitions between fcc and bcc phases in Ca; (2) fcc phase of Ca is unstable between the two merge points on the fcc-eq line but stable beyond them, while bcc phase of Ca is stable between the two merge points on the bcc-eq line but unstable beyond them.

Keywords

Solid State and Materials 

References

  1. 1.
    S.L. Qiu, P.M. Marcus, J. Phys.: Condens. Matter 24, 225501 (2012) ADSCrossRefGoogle Scholar
  2. 2.
    P.M. Marcus, H. Ma, S.L. Qiu, J. Phys.: Condensed Matter 14, L525 (2002) ADSCrossRefGoogle Scholar
  3. 3.
    L.D. Landau, E.M. Lifshitz, Course of Theoretical Physics, Statistical Physics, 3rd edn. (Pergamon, 1980), Vol. 5, Part 1 Google Scholar
  4. 4.
    P.M. Marcus, S.L. Qiu, J. Phys.: Condens. Matter 16, 8787 (2004) ADSCrossRefGoogle Scholar
  5. 5.
    J.A. Moriarty, A.K. McMahan, Phys. Rev. Lett. 48, 809 (1982) ADSCrossRefGoogle Scholar
  6. 6.
    P.K. Lam, M.L. Cohen, Phys. Rev. B 27, 5986 (1983) ADSCrossRefGoogle Scholar
  7. 7.
    J.C. Boettger, S.B. Trickey, Phys. Rev. B 29, 6434 (1984) ADSCrossRefGoogle Scholar
  8. 8.
    G.V. Sin’ko, N.A. Smirnov, J. Phys.: Condens. Matter 14, 6989 (2002) ADSCrossRefGoogle Scholar
  9. 9.
    M.J. Tambe, N. Bonini, N. Marzari, Phys. Rev. B 77, 172102 (2008) ADSCrossRefGoogle Scholar
  10. 10.
    Li Li, Shao Jian-Li, Li Yan-Fang, Duan Su-Qing, Liang Jiu-Qing, Chin. Phys. B 21, 026402 (2012) ADSCrossRefGoogle Scholar
  11. 11.
    H. Olijnyk, W.B. Holzapfel, Phys. Lett. A 100, 191 (1984) ADSCrossRefGoogle Scholar
  12. 12.
    S. Arapan, H. Mao, R. Ahuja, Proc. Natl. Acad. Sci. 105, 20627 (2008) ADSCrossRefGoogle Scholar
  13. 13.
    A.M. Teweldeberhan, S.A. Bonev, Phys. Rev. B 78, 140101 (2008) ADSCrossRefGoogle Scholar
  14. 14.
    R. Ahuja, O. Eriksson, J.M. Wills, B. Johansson, Phys. Rev. Lett. 75, 3473 (1995) ADSCrossRefGoogle Scholar
  15. 15.
    H.L. Skriver, Phys. Rev. Lett. 49, 1768 (1982) ADSCrossRefGoogle Scholar
  16. 16.
    F. Jona, P.M. Marcus, J. Phys.: Condens. Matter 18, 4623 (2006) ADSCrossRefGoogle Scholar
  17. 17.
    R.M. Wentzcovitch, H. Krakauer, Phys. Rev. B 42, 4563 (1990) ADSCrossRefGoogle Scholar
  18. 18.
    A.N. Sofronkov, V.A. Drozdov, V.V. Pozhivatenko, The Physics of Metals and Metallography (Pergamon Press, 1992), Vol. 74, p. 140 (Engl. Transl.) Google Scholar
  19. 19.
    V.L. Sliwko, P. Mohn, K. Schwarz, P. Blaha, J. Phys.: Condens. Matter 8, 799 (1996) ADSCrossRefGoogle Scholar
  20. 20.
    S.L. Qiu, P.M. Marcus, J. Phys.: Condens. Matter 21, 435403 (2009) ADSCrossRefGoogle Scholar
  21. 21.
    P.M. Marcus, S.L. Qiu, J. Phys.: Condens. Matter 21, 125404 (2009) ADSCrossRefGoogle Scholar
  22. 22.
    P.M. Marcus, S.L. Qiu, J. Phys.: Condens. Matter 21, 115401 (2009) ADSCrossRefGoogle Scholar
  23. 23.
    P. Blaha, K. Schwarz, G.K.H. Madsen, D. Kvasnicka, J. Luitz, WIEN2k, An Augmented Plane Wave + Local Orbitals Program for Calculating Crystal Properties (Karlheinz Schwarz, Techn. Universität Wien, Austria, 2001) Google Scholar
  24. 24.
    P. Blaha, K. Schwarz, P. Sorantin, Comput. Phys. Commun. 59, 399 (1990) ADSCrossRefGoogle Scholar
  25. 25.
    K. Gaal-Nagy, A. Bauer, M. Schmitt, K. Karch, P. Pavone, D. Strauch, Phys. Stat. Sol. B 211, 275 (1999) ADSCrossRefGoogle Scholar
  26. 26.
    M. Hebbache, M. Mattesini, J. Szeftel, Phys. Rev. B 63, 205201 (2001) ADSCrossRefGoogle Scholar
  27. 27.
    J. Behler, R. Martoòák, D. Donadio, M. Parrinello, Phys. Stat. Sol. B 245, 2618 (2008) ADSCrossRefGoogle Scholar
  28. 28.
    V.P. Sakhnenko, V.M. Talanov, Fiz. Tverd. Tela (Leningrad) 21, 2435 (1979) [Sov. Phys. Solid State 21, 1401 (1979)] Google Scholar
  29. 29.
    J. Chang, Y. Cheng, M. Fu, J. At. Mol. Sci. 1, 243 (2010) Google Scholar
  30. 30.
    K. Mizushima, S. Yip, E. Kaxiras, Phys. Rev. B 50, 14952 (1994) ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of PhysicsFlorida Atlantic UniversityBoca RatonUSA
  2. 2.IBM Research DivisionT.J. Watson Research CenterYorktown HeightsUSA

Personalised recommendations