Abstract
The equilibrium distribution of low-concentration impurities or vacancies is investigated in the region of a coherent phase boundary or antiphase boundary in a binary alloy. A general expression for the free energy of an inhomogeneous multicomponent alloy, which generalizes the expression previously derived for a binary alloy, is presented. Explicit formulas for the impurity concentration profile c im(x) in terms of the distribution of the principal components of the alloy near a boundary are obtained from this expression in the mean-field and pair-cluster approximations. The shape of this profile is determined by a “preference potential” P, which characterizes the attraction of an impurity to one of the alloy components, as well as by the temperature T and the phase transition temperature T c. At small values of P/T impurities segregate on a phase boundary, and the degree of this segregation, i.e, the height of the maximum of c im(x), in the region of the boundary increases exponentially as the ratio T c/T increases. For P ≠ 0 the c im(x) profile near a phase boundary is asymmetric, and as P/T increases, it takes on the form of a “worn step.” The maximum on the c im(x) curve then decreases, and at a certain |P|≳T c it vanishes. Segregation on an antiphase boundary is investigated in the case of CuZn ordering in a bcc alloy. The form of c im(x) near an antiphase boundary depends significantly both on the form of the potential P and on the stoichiometry of the alloy. At small P impurities segregate on an antiphase boundary, and at fairly large P “antisegregation,” i.e., a decrease in the impurity concentration on the antiphase boundary in comparison with the value within the antiphase domains, is also possible.
Similar content being viewed by others
References
H. Gleiter and B. Chalmers, High-Angle Grain Boundaries, Pergamon, Oxford (1972) [Russ. transl., Mir, Moscow (1975, Chap. 3)].
K. Yaldram and K. Binder, Acta Metall. Mater. 39, 707 (1991); J. Stat. Phys. 62, 161 (1991).
K. Yaldram and K. Binder, Z. Phys. B 82, 405 (1991).
P. Fratzl and O. Penrose, Phys. Rev. B 50, 3477 (1994).
E. Vives and A. Planes, Phys. Rev. B 47, 2557 (1993).
C. Frontera, E. Vives, and A. Planes, Z. Phys. B 96, 79 (1994).
C. Geng and L. Q. Chen, Scr. Metall. Mater. 31, 1507 (1994).
L. Q. Chen, Mater. Res. Soc. Symp. Proc. 319, 375 (1994).
L. D. Landau and E. M. Lifshitz, Statistical Physics, Vol. 1, 3rd. ed., Pergamon Press, Oxford-New York (1980).
L. Q. Chen, Phys. Rev. B 49, 3791 (1994).
V. G. Vaks, JETP Lett. 63, 461 (1996).
V. G. Vaks, S. V. Beiden, and V. Yu. Dobretsov, JETP Lett. 61, 68 (1995).
V. Yu. Dobretsov, G. Martin, F. Soisson, and V. G. Vaks, Europhys. Lett. 31, 417 (1995).
V. Yu. Dobretsov, V. G. Vaks, and G. Martin, Phys. Rev. B 54, 3227 (1996).
K. D. Belashchenko and V. G. Vaks, Phys. Lett. A 222, 345 (1996).
V. G. Vaks and V. G. Orlov, Fiz. Tverd. Tela (Leningrad) 28, 3627 (1986) [Sov. Phys. Solid State 28, 2045 (1986)].
V. G. Vaks, N. E. Zein, and V. V. Kamyshenko, J. Phys. F: Met. Phys. 18, 1641 (1988).
V. G. Vaks and V. V. Kamyshenko, Izv. Akad. Nauk. SSSR, Met. (2), 121 (1990).
J. M. Sanchez, F. Ducastelle, and D. Gratias, Physica A 128, 334 (1984).
V. G. Vaks, Introduction to the Microscopic Theory of Ferroelectrics [in Russian], Nauka, Moscow (1973).
R. Kikuchi and J. W. Cahn, J. Phys. Chem. Solids 20, 137 (1962); 27, 1305 (1966).
Author information
Authors and Affiliations
Additional information
Zh. Éksp. Teor. Fiz. 112, 714–728 (August 1997)
Rights and permissions
About this article
Cite this article
Belashchenko, K.D., Vaks, V.G. Segregation of impurities and vacancies on phase and antiphase boundaries in alloys. J. Exp. Theor. Phys. 85, 390–398 (1997). https://doi.org/10.1134/1.558289
Received:
Issue Date:
DOI: https://doi.org/10.1134/1.558289