Surface composition of ternary cu-ag-au alloys: part ii. a comparison of experiment with theoretical models
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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. [~-9t This is because the vast majority of experimental studies of surface composition has 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 ll~ and Guttmann and McLean [11] on grain boundaries, little attention has thus far been devoted to the prediction of equilibrium surface composition in ternary solid solutions. Licata [121 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. This article presents the results obtained by applying a recently developed regular solution nearest-neighbor bond model [13] of the equilibrium surface composition of ternary alloys to the Cu-Ag-Au system. It also presents the results of Monte Carlo simulations of surface segregation behavior performed with interatomic forces described by the embedded atom method (EAM). The results of the two models are compared with the experimental measurements reported in Part I.[34] As in Part I, the approach taken will be to compare the surface solute (silver and gold) concentrations with those of binary alloys having the same bulk solute content so as to identify clearly any ternary trends in surface segregation. We being by providing brief backgrounds on the nearest-neighbor bond model employed and on the Monte Carlo technique and the EAM. II.
NEAREST-NEIGHBOR
x~
In
1 -X~ - X ~
~
- In
A~, ~
1 -x~-x~
kT
[1]
and In
xl
1 -X~-X~
- In
~
a~ g
1 -X~-X~
kT
[2]
where X~ and X b are the atom fractions of the ith component at the surface and in the bulk, respectively, A/-/~/eg a r e the enthalpies of segregation of the ith c o m p o n e n t , k is Boltzmann's constant, T is the absolute temperature, and the components are taken to be 1 -- Ag, 2 = Au, and 3 = Cu, respectively. In the limit of a twocomponent system (X) = X~2 = 0 in Eq. [1] or X~ = X~I -- 0 in Eq. [2]), the expressions reduce to the binary solution expression obtained previously. [4] Note that the excess entropies of segregation do not appear in Eqs. [1] and [2], because these are assumed to be zero in the regular solution approximation. In this approximation, the enthalpies of segregation of the two surface-active species are given by A ~ eg = (~g - ~,3)A
BOND MODEL
In this section, we present the equations describing the equilibrium surface composition of ternary solutions based M.A. HOFFMANN, Graduate Student, and P. WYNBLATT, Professor, are with the Department of Metallurgical Engineering and Materials Science, Carnegie Mellon University, Pittsburgh, PA 15213. Manuscript submitted August 17, 1990. METALLURGICAL TRANSACTIONS A
on a previously derived regular solution nearest-neighbor bond model t13] together with the parameters used
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