Estimation of the surface tensions of binary liquid alloys
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I.
INTRODUCTION
V A R I O U S models for binary solutions have been developed to predict the surface tension of the alloys. For alloys with weak chemical interactions, Defay and Prigogine ~1 applied a regular solution model to describe the surface tension; however, the model cannot be applied to the alloys with strong chemical interactions. Joud et al.,~21 based on the "surrounded atom" concept and a surface monolayer introduced by Mathieu et al. ,[3] developed a partition function of a binary solution and then derived expressions for the surface tensions of binary alloys. Laty et al. [41 extended this statistical approach and correlated thermodynamic data with the potential energies varying with coordination number. They considered a surface monolayer, as well as the layer just below the surface layer bridging the surface layer to the bulk solution. The numbers of A - A , B - B , and A - B bonds were correlated to the potential energies and then to the thermochemical data of the alloy. They introduced a "privileged surrounded atom," which represents the preference for certain types of neighbors, and the perturbation energy, which measures the extent of the preference. A number of probabilities involved in their model are functions of the potential energies, perturbation energy, and the privileged surrounded atoms. In their treatment, these probabilities were computed for complete atomic disorder. Because this assumption is in conflict with the probability expressions dependent on potential energy, their chemical potentials do not satisfy the GibbsDuhem relation. Goumiri and Joud ts] enhanced the model to eliminate the inconsistency and computed the probabilities rigorously. Their model can be used to interpret experimental data, if the parameters involved in their model are properly adjusted. However, the parameters, which must be consistent with thermochemical data, cannot be easily obtained.
K.S. YEUM, Research Metallurgist, R. SPEISER, Adjunct Professor, and D.R. POIRIER, Professor, are with the Department of Materials Science and Engineering, The University of Arizona, Tucson, AZ 85721. Manuscript submitted January 3, 1989. METALLURGICAL TRANSACTIONS B
This paper presents a simple method of predicting the surface tensions of binary alloys, starting with the surface tensions of pure components and the excess free energies of the alloy. The success of this method is demonstrated by applying it to ten binary alloys that collectively show positive deviations, positive as well as negative deviations, depending on composition, and strong negative deviations from ideal solution behavior. In an earlier paper, t61 we applied the model to two binary alloys. To demonstrate general applicability, this model has been refined and applied to the ten binary alloys in this paper. II.
SURFACE TENSION MODEL
The surface of a multicomponent solution can be treated as a "phase." If the components in the surface and bulk phases are in thermodynamic equilibrium, the chemical potential of each component in the surface phase is e
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