Abstract
A general formulation of cluster methods applied to calculations of thermodynamic quantities of alloys in terms of renormalizing fields describing interaction between a cluster and its environment is given. We have shown that the well-known cluster variation method and the cluster field method, which was suggested earlier, are special cases of our approach. These methods have been used in calculations of phase diagrams of fcc alloys with L12 and L10 ordering transitions with several realistic interaction models. It turns out that, for all these models, the simple tetrahedron version of the cluster field method suggested in this paper describes the phase diagrams almost as accurately as more complicated cluster variation techniques. Possible applications of the tetrahedron version of the cluster field method to inhomogeneous states and kinetics of phase transitions in fcc alloys are discussed.
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References
D. de Fontaine, Solid State Phys. 34, 74 (1979).
P. E. A. Turchi, in Intermetallic Compounds, Vol. 1, Principles, J. H. Westbrook and R. L. Fleischer (Eds.), Wiley, New York (1994), p. 21.
A. Zunger, in Statics and Dynamics of Alloy Phase Transformations, Vol. 319 of NATO Advanced Study Institute, Series B: Physics, A. Gonis and P. E. A. Turchi (Eds.), Plenum, New York (1994), p. 361.
A. Finel, in Statics and Dynamics of Alloy Phase Transformations, Vol. 319 of NATO Advanced Study Institute, Series B: Physics, A. Gonis and P. E. A. Turchi (Eds.), Plenum, New York (1994), p. 495–540.
K. Binder, in Statics and Dynamics of Alloy Phase Transformations, Vol. 319_of NATO Advanced Study Institute, Series B: Physics, A. Gonis and P. E. A. Turchi (Eds.), Plenum, New York (1994), p. 467–493.
L. Q. Chen, Y. Z. Wang, and A. G. Khachaturyan, in Statics and Dynamics of Alloy Phase Transformations, Vol. 319 of NATO Advanced Study Institute, Series B: Physics, A. Gonis and P. E. A. Turchi (Eds.), Plenum, New York (1994), p. 587–604.
K. D. Belashchenko, V. Yu. Dobretsov, and V. G. Vaks, in Properties of Complex Inorganic Solids, Proc. of 1st Intern. Alloy Conf., A. Gonis, A. Meike, and P. E. A. Turchi (Eds.), Plenum, New York (1997), p. 101.
R. Kikuchi, Phys. Rev. 81, 988 (1951).
T. Morita, J. Math. Phys. 13, 115 (1972).
J. M. Sanchez and D. de Fontaine, Phys. Rev. B 17, 2926 (1978).
T. Mohri, J. M. Sanchez, and D. de Fontaine, Acta Metall. 33, 1171 (1985).
J. M. Sanchez, F. Ducastelle, and D. Gratias, Physica A 128, 334 (1984).
A. Finel, Thése de Doctorat d’Etat, Universite’ Paris VI, Note Technique ONERA 1987-3 (1987).
F. Ducastelle, in Cohesion and Structures, Vol. 3, F. R. de Boer and D. G. Pettifor (Eds.), North Holland, Amsterdam (1991), Ch. 4.
V. G. Vaks and V. V. Kamyshenko, Izv. Akad. Nauk SSSR, Ser. Metally No. 2, 121 (1990).
B. H. Kear, Sci. Am., No. 12, 99 (1986).
V. G. Vaks, JETP Lett. 63, 471 (1996).
K. D. Belashchenko and V. G. Vaks, J. Phys. F 10, 1965 (1998).
V. G. Vaks, N. E. Zein, V. I. Zinenko, and V. G. Orlov, Zh. Éksp. Teor. Fiz. 87, 2030 (1984) [Sov. Phys. JETP 60, 1171 (1984)].
V. G. Vaks and V. G. Orlov, Fiz. Tverd. Tela 28, 3627 (1986) [Sov. Phys. Solid State 28, 2045 (1986)].
V. G. Vaks and V. G. Orlov, J. Phys. F 18, 883 (1988).
V. G. Vaks and V. I. Zinenko, J. Phys.: Condens. Matter 1, 9085 (1989); 3, 4533 (1991).
V. G. Vaks, N. E. Zein, and V. V. Kamyshenko, J. Phys. F 18, 1641 (1988).
V. G. Vaks, N. E. Zein, V. V. Kamyshenko, and Yu. V. Tkachenko, Fiz. Tverd. Tela 30, 477 (1988) [Sov. Phys. Solid State 30, 270 (1988)].
V. G. Vaks, N. E. Zein, and V. V. Kamyshenko, J. Phys.: Condens. Matter 1, 2115 (1989).
V. G. Vaks and V. V. Kamyshenko, J. Phys.: Condens. Matter 3, 1351 (1991).
C. N. Yang, J. Chem. Phys. 13, 66 (1945).
Y. Y. Li, J. Chem. Phys. 17, 447 (1949).
V. Yu. Dobretsov, V. G. Vaks, and G. Martin, Phys. Rev. B 54, 3227 (1996).
K. D. Belashchenko and V. G. Vaks, Zh. Éksp. Teor. Fiz. 112, 714 (1997) [JETP 85, 390 (1997)].
J. Dennis and R. Schnabel, Numerical Methods of Unconditional Optimization and Solution of Nonlinear Equations [Russian translation], Mir, Moscow (1988).
W. H. Press, S. A. Teukolsky, W. T. Vettering et al., Numerical Recipes in C, Camb. Univ. Press (1996), Ch. 10.
A. Finel, V. Mazauric, and F. Ducastelle, Phys. Rev. Lett. 65, 1016 (1990).
F. Chassagne, M. Bessiere, Y. Calvayrac et al., Acta Metall. 37, 2329 (1989).
A. G. Khachaturyan, Theory of Phase Transformations and Structure of Solid Solutions [in Russian], Nauka, Moscow (1974).
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Zh. Éksp. Teor. Fiz. 115, 158–179 (January 1999)
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Vaks, V.G., Samolyuk, G.D. On accuracy of different cluster models used in describing ordering phase transitions in fcc alloys. J. Exp. Theor. Phys. 88, 89–100 (1999). https://doi.org/10.1134/1.558769
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DOI: https://doi.org/10.1134/1.558769