Extension of the free-energy concentration expansion method to surface segregation in multi-component alloys and its application to Ni-Al-Cu

Statistical-mechanical description of multi-layer surface segregation in multi-component alloys, based on the free-energy concentration expansion method (FCEM), is introduced. The generalized FCEM provides simple analytical expressions for numerical minimization of the alloy free energy in the presence of short-range order (SRO). As an example, this theoretical approach is applied to unravel segregation with site competition at the (1 1 1) surface of a ternary Ni-8 at.%Al-4 at.%Cu(1 1 1) solid solution. Compared to the corresponding Ni-Al and Ni-Cu binary alloys, the calculations predict significant enhancement of Cu surface segregation and Al desegregation due to the relatively strong Ni-Al attractive interactions and SRO effects. A compositional phase transition marks the onset of Al segregation at high temperatures.