Equilibrium surface composition of ternary alloys
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I.
INTRODUCTION
THE theory of equilibrium
surface composition in solid solutions has been developed primarily for the case of two component solutions, l~-71 This is because the vast majority of experimental studies of surface composition have focused on binary alloys. While there has been some theoretical interest in the behavior of multicomponent segregation in the context of the equilibrium composition of other interfaces, such as the comprehensive work of Guttmann et al. [8,91on grain boundaries, little attention has thus far been devoted to the prediction" of equilibriumrml surface composition in ternary solid solutions. Licata has recently developed a formalism for interfacial segregation in ternary alloys, but this also seems to have been applied to grain boundaries rather than surfaces. Whereas the broad principles of interfacial thermodynamics apply indistinguishably to all interfaces, the existence of physical differences among different types of interfaces can lead to certain simplifications in one type of interface that are not possible in others. The application of Gibbs' adsorption isotherm to planar interfaces in substitutional binary solutions provides an example of the abovementioned differences among interfaces. In the case of a solid-vapor interface (i.e., a surface), it is possible to choose the position of the Gibbs dividing surface in such a manner as to set the surface excess of one of the two components in the solution to zero, thus simplifying considerably the integration of the adsorption isotherm. In contrast, in interfaces such as grain boundaries or stacking faults there is, in general, no choice of the dividing surface which simplifies the adsorption isotherm in the same manner, lul Similarly, as discussed in more detail below, the treatment of interfacial composition developed here for ternary solutions may be applied more simply to surfaces than to grain boundaries or certain other types of interface. The objective of the present paper is to extend the framework developed previously by Wynblatt and Ku t3] for the calculation of the enthalpy of surface segregation in binary alloys, to the case of ternary alloys. The approach is based on a modification of the regular solution approximation in which the usual nearest neighbor bond model description is corrected for solute strain energy effects. Thus it combines the nearest neighbor bond model approach developed by M.A. ItOFFMANN, Graduate Student, and P. WYNBLATT, Professor, are with the Department of Metallurgical Engineering and Materials Science, Carnegie Mellon University, Pittsburgh, PA 15213. Manuscript submitted October 26, 1987. METALLURGICAL TRANSACTIONS A
Defay and Prigogine D2] for describing the surface composition of liquid solutions, with the solute strain energy framework proposed by McLean t13J for interpreting grain boundary segregation phenomena in solids. It was demonstrated some time ago [14] that models of the equilibrium surface composition of alloys which employed either the bond model approach or the solute st
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