Abstract
The evolution of atomic ordering processes in Fe3Al has been modeled by the Monte Carlo (MC) simulation method combined with the electronic theory of alloys in pseudopotential approximation. The magnitude of atomic ordering energies of atomic pairs in the Fe3Al system has been calculated by means of electronic theory in pseudopotential approximation up to sixth coordination spheres and subsequently used as input data for MC simulation for more detailed analysis for the first time. The Bragg-Williams long-range order (LRO) and Cowley-Warren short-range order (SRO) parameters have been calculated from the equilibrium configurations attained at the end of MC simulation for each predefined temperature and Al concentration levels, which reveal the evolution of the system from DO3→B2→disordered state as temperature increases. The variation of ordering parameters with temperature has identified the transition temperature from DO3→B2 type superlattice, and from B2→disordered (α) solid solution at about 540 °C and >900 °C, respectively, showing good qualitative agreement with experimental results. The results of the present study imply that combination of electronic theory of alloys in pseudopotential approximation with MC simulation can be successfully applied for qualitative or semiquantitative analysis of energetical and structural characteristics of atomic ordering processes in Fe3Al intermetallics.
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References
M.A. Krivoglaz and A. Smirnov: The Theory of Order-Disorder in Alloys, MacDonald, London, 1964.
M.J. Marcinkowski: Treatise on Materials Science and Technology, Academic Press, New York, NY, 1974, p. 333.
U. Prakash, R.A. Buckley, H. Jones, and C.M. Sellars: Iron Steel Inst. Jpn. Int., 1991, vol. 31, pp. 1113–26.
C.G. McKamey and C.T. Liu: Scripta Metall., 1990, vol. 24, pp. 2119–22.
S.M. Allen and J.W. Cahn: Acta Metall., 1975, vol. 23, pp. 1017.
N.S. Stoloff and R.G. Davies: Acta Metall., 1964, vol. 12, p. 473.
M.G. Mendiratta, S.K. Ehlers, D.K. Chatterjee, and H.A. Lipsitt: Metall. Trans. A, 1987, vol. 18A, pp. 283–91.
A.O. Mekhrabov, A. Ressamoğlu, and T. Oüztuürk: J. Alloys Compounds, 1994, vol. 205, pp. 147–56.
Computer Simulation Methods in Theoretical Physics: An Introduction, K. Binder and W. Heermann, eds., Springer-Verlag, Berlin, 1988.
M. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.N. Teller, and E. Teller: J. Chem. Phys., 1953, vol. 21, p. 1087.
A. Baumgartner and W. Schweika: Monte Carlo Simulations, reprinted from IFF Bulletin, IFF, Julich, Germany, 1988, pp. 3–32.
N.S. Golosov, L.E. Popov, and L.Y. Pudan: J. Phys. Chem. Solids, 1973, vol. 34, pp. 1149–56.
N.S. Golosov, L.E. Popov, and L.Y. Pudan: J. Phys. Chem. Solids, 1973, vol. 34, pp. 1157–62.
N.S. Golosov, A.M. Tolstik, and L.Y. Pudan: J. Phys. Chem. Solids, 1976, vol. 37, pp. 273–77.
N.S. Golosov and A.M. Tolstik: J. Phys. Chem. Solids, 1976, vol. 7, pp. 279–83.
N.S. Golosov and A.M. Tolstik: J. Phys. Chem. Solids, 1974, vol. 35, pp. 1575–80.
N.S. Golosov and A.M. Tolstik: J. Phys. Chem. Solids, 1974, vol. 35, pp. 1581–86.
N.S. Golosov and A.M. Tolstik: J. Phys. Chem. Solids, 1975, vol. 36, pp. 899–902.
N.S. Golosov and A.M. Tolstik: J. Phys. Chem. Solids, 1975, vol. 36, pp. 903–07.
K. Binder: in Statics and Dynamics of Alloy Phase Transformations, P.E. Turchi and A. Gonis, eds., Plenum Press, New York, NY, 1994, pp. 467–93.
F. Schmid and K. Binder: in Metallic Alloys: Experimental and Theoretical Perspectives. J.S. Faulkner and R.G. Jordan, eds., Kluwer Academic Publisher, Dordrecht, The Netherlands, 1994, pp. 261–70.
Applications of the Monte Carlo Methods in Statistical Physics, K. Binder, ed., Springer-Verlag, Berlin, 1984.
The Monte Carlo Method in Condensed Matter Physics, K. Binder, ed., Springer-Verlag, Berlin, 1992.
P. Oramus, R. Kozubski, M.C. Cadeville, V. Pierron-Bohnes, and W. Pfeiler: Mater. Sci. Eng. A, 1997, vols. 239A–240A, pp.777–83
E. Kentzinger, M. Zemirli, V. Pierron-Bohnes, M.C. Cadeville, H. Bouzar, M. Benakki, and M.A. Khan: Mater. Sci. Eng. A, 1997, vols. 239A–240A, pp. 784–89.
W. Schweika and H.G. Haubold: Phys. Rev., 1988, vol. B37, pp. 9240–48.
W. Schweika: in Structure and Phase Stability of Alloys, J.L. Moran-Lopez, F. Mejia-Lira, and J.M. Sanchez, eds., Plenum Press, New York, NY, 1992, pp. 53–64.
J.W.D. Connolly and A.R. Williams: Phys. Rev. B, 1983, vol. 27, pp. 5169–72.
Z.W. Lu, S.H. Wei, and A. Zunger: Phys. Rev. Lett., 1991, vol. 66, pp. 1753–56.
A. Zunger: in Statics and Dynamics of Alloy Phase Transformations, P.E.A. Turchi and A. Gonis, eds., NATO ASI Series B: Physics, Plenum Press, New York, NY, 1994, vol. 319, pp. 361–420.
F. Ducastelle and F. Gaultier: J. Phys. F: Met. Phys., 1976, vol. F6, pp. 2039–62.
A. Gonis, A.J. Freeman, D.M. Nicholson, G.M. Stocks, P. Turchi, and X.G. Zhang: Phys. Rev., 1987, vol. B36, pp. 4630–46.
G.M. Stocks, D.M.C. Nicholson, W.A. Sheiton, B.L. Gyorffy, F.J. Pinski, D.D. Johnson, J.B. Staunton, B. Ginatempo, P.E.A. Turchi, and M. Sluiter: in Statics and Dynamics of Alloys Phase Transformations, P.E.A. Turchi and A. Gonis, eds., NATO ASI Series B: Physics, Plenum Press, New York, NY, 1994, vol. 319, pp. 305–59.
B.L. Gyorffy and G.M. Stocks: Phys. Rev. Lett., 1983, vol. 50, pp. 374–77.
W.M.C. Foulkes, L. Mitas, R.J. Needs, and G. Rajagopal: Rev. Mod. Phys., 2001, vol. 73, pp. 33–83.
Monte Carlo Methods in Statistical Physics, K. Binder, ed., Springer-Verlag, Berlin, 1979, vol. 7.
Applications of the Monte Carlo Methods in Statistical Physics, K. Binder, ed., Springer-Verlag, Berlin, 1987, vol. 36.
F. Ducastelle: Order and Phase Stability in Alloys, North Holland, Amsterdam, 1991.
A.O. Mekhrabov, M.V. Akdeniz, and M.M. Arer: Acta Mater., 1997, vol. 45 (3), pp. 1077–83.
M.V. Akdeniz and A.O. Mekhrabov: Acta Mater., 1998, vol. 46 (4), pp. 1185–92.
A.O. Mekhrabov and M.V. Akdeniz: Acta Mater., 1999, vol. 47 (7), pp. 2067–75.
E.Z. Ising: Z. Phys., 1925, vol. 31, p. 253.
F. Schmid and K. Binder: J. Phys.: Condens. Matter. 1992, vol. 4, pp. 3569–88.
S.K. Bose, J. Kudrnovsky, V. Drchal, O. Jepsen, and O.K. Andersen: Mater. Sci. Eng. B, 1996, vol. 37, pp. 237–41.
J.A. Plascak, L.E. Zamora, and G.A.P. Alcazar: Phys. Rev. B, 2000, vol. 61, pp. 3188–91.
V.M. Danilenko, D.R. Rizdvyanechkiy, and A.A. Smirnov: Fiz. Met. Metalloved., 1963, vol. 15, pp. 194–202.
V.M. Danilenko, D.R. Rizdvyanechkiy and A.A. Smirnov: Fiz. Met. Metalloved., 1963, vol. 16, pp. 3–12.
D.R. Rizdvyanechkiy: Metallofizikal, 1977, No. 68, pp. 31–37.
Z.A. Matysina, A.O. Mekhrabov, Z.M. Babaev and S.Y. Zaginaichenko: J. Phys. Chem. Solids, 1987, vol. 48, pp. 419–23.
A.A. Katsnelson, A.O. Mekhrabov, and V.M. Silonov: Fiz. Met. Metalloved., 1981, vol. 52, pp. 661–63.
A.O. Mekhrabov and M. Doyama: Phys. Status Solidi (B), 1984, vol. 126, pp. 453–58.
A. Taylor and R.W. Jones: J. Phys. Chem. Solids, 1958, vol. 6, pp. 16–37.
A.O.E. Animalu and V. Heine: Phil. Mag., 1965, vol. 12, p. 1249.
A.O.E. Animalu: Phys. Rev. B, 1973, vol. 8, pp. 3542–54.
A.O.E. Animalu: Phys. Rev. B, 1973, vol. 8, pp. 3555–62.
J. Hubbard: Proc. R. Soc. (London), 1957, vol. A 240, p. 359.
J. Hubbard: Proc. R. Soc. (London), 1957, vol. A 243, p. 336.
L.J. Sham: Proc. R. Soc. (London), 1965, vol. A 283, p. 33
A.O.E. Animalu: Intermediate Quantum Theory of Crystalline Solids, Prentice-Hall, Englewood Cliffs, NJ, 1977.
J.A. Moriarty: Phys. Rev. B, 1977, vol. 16, p. 2537.
J.A. Moriarty: Phys. Rev. B, 1982, vol. 26, pp. 1754–80.
J.A. Moriarty: Phys. Rev. B, 1988, vol. 38, pp. 3199–3231.
J.A. Moriarty: Phys. Rev. B, 1990, vol. 42, pp. 1609–28.
K.M. Ho, S.G. Louie, J.R. Chelikowsky, and M.L. Cohen: Phys. Rev. B, 1977, vol. 15, pp. 1755–59.
A. Zunger and M.L. Cohen: Phys. Rev. B, 1978, vol. 18, pp. 5449–72.
A. Zunger and M.L. Cohen: Phys. Rev. B, 1979, vol. 19, pp. 568–82.
G.P. Kerker, K.M. Ho, and M.L. Cohen: Phys. Rev. B, 1978, vol. 18, pp. 5473–83.
L.I. Yastrebov and A.A. Katsnelson: Foundations of One-Electron Theory of Solids, Mir Publisher, Moscow, 1987.
P.A. Schultz and J.W. Davenport: J. Alloys Compounds, 1993, vol. 197, pp. 229–42.
A.A. Katsnelson, V.M. Silonov, and M.M. Khruschev: Fiz. Tverd. Tela, 1977, vol. 19, p. 691.
A.A. Katsnelson, V.M. Silonov, and M.M. Khruschev: Fiz. Tverd. Tela, 1978, vol. 20, p. 2812.
A.A. Katsnelson, A.O. Mekhrabov, and V.M. Silonov: Fiz. Met. Metaloved., 1976, vol. 42(2), pp. 278–83.
A.A. Katsnelson, A.O. Mekhrabov, and V.M. Silonov: Fiz. Met. Metaloved., 1978, vol. 45(1), pp. 33–37.
A.A. Katsnelson, A.O. Mekhrabov, and V.M. Silonov: Fiz. Met. Metaloved., 1979, vol. 47(5), pp. 993–97.
P.S. Rudman: Acta Metall., 1960, vol. 8, pp. 321–327.
J.M. Cowley: J. Appl. Phys., 1950, vol. 21, pp. 24.
B.E. Warren, B.L. Averbach, and B.W. Roberts: J. Appl. Phys., 1951, vol. 22, pp. 1493–1496.
Design and Analysis of Experiments, D.C. Montgomery, ed., John Wiley, New York, NY, 1976.
M.M. Arer: Master’s Thesis, Middle East Technical University, Ankora, 1996.
P.R. Swann, W.R. Duff, and R.M. Fisher: Metall. Trans., 1972, vol. 3, p. 409.
A. Lawley and R.W. Cahn: J. Phys. Chem. Solids, 1961, vol. 20, pp. 204–21.
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Mekhrabov, A.O., Akdeniz, M.V. Modeling of the atomic ordering processes in Fe3Al intermetallics by the monte carlo simulation method combined with electronic theory of alloys. Metall Mater Trans A 34, 721–734 (2003). https://doi.org/10.1007/s11661-003-0107-z
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DOI: https://doi.org/10.1007/s11661-003-0107-z