Surface tension, compressibility, and surface segregation in liquid binary alloys

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Abstract
The phenomenological treatment of Cahn and Hilliard, which relates the product κTσ of the isothermal compressibility κT and the surface tension σ to the thickness l of the liquid surface is generalized to liquid alloys. The result obtained is σ∼ (l/κT)[1+δ2SCC(0)/nkBTκT] −1, where δ (1/V)(∂V/∂c) is the size difference factor, SCC(0) represents the concentration fluctuations nV< (Δc)2≳, while n is the number density in the alloy. This formula affords a ready explanation of the remarkable variation of surface tension in the amalgams of the alkali metals. Surface segregation occurs in a dilute alloy c→0 when dσ/dc is negative, from the Gibbs formula. The above result for σ yields, with ϑ=nkBTκT, (1/σ)(dσ/dc) ‖c=0∼ (1/l)(dl/dc)− (1/κT)(dκT/dc)−(δ2/ϑ) ‖c=0. Screening arguments due to Friedel suggest, at least for simple metals with a valence difference between components, that dl/dc‖c=0 will be zero. Then the above formula for dσ/dc‖c=0 shows that favorable circumstances for segregation are: (a) positive dκT/dc; (b) large size difference δ and small ϑ. Finally the relation of our work to that of Burton and Machlin, who correlate bulk phase diagrams and surface segregation, is briefly considered.

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