Segregation of impurities and vacancies on phase and antiphase boundaries in alloys

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 cim(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 cim(x), in the region of the boundary increases exponentially as the ratio Tc/T increases. For P ≠ 0 the cim(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 cim(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 cim(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.