Equilibrium surface segregation of interstitials on bcc (001) surfaces

Abstract

The surface segregation of interstitials X on free (001) surfaces of a body-centered cubic metal lattice M is studied by means of Monte Carlo modeling. It is assumed that interstitially dissolved X atoms occupy irregularly shaped octahedral bulk interstices characteristic of the bcc structure. Pairwise nearest and more distant neighbor couplings between adjacent M and X atoms ϕ MX (i) are used to calculate binding energies for X atoms at the various bulk and surface sites. Additional repulsive interactions between adjacent X atoms ϕ XX (i) are considered. Monte Carlo simulations are performed for three different sets of interaction parameters ϕ XX (i) .In all these cases the fourfold hollow sites of the bcc (001) surface are the most stable coordination sites. Ideal behavior in the bulk and at the surface is found if all interaction energies ϕ XX (i) = 0 . For slightly repulsive nearest and next nearest neighbor interactions ϕ XX (1) , ϕ XX (2) < 0 X atoms on the fourfold hollow sites of the surface still behave ideal while deviations from ideal behavior are observed in the bulk for concentrations x≳0.01. With additional repulsive fourth nearest neighbor interactions ϕ XX (4) < 0 c(2 × 2) ordering is induced at the surface for coverages θ ≈ 0.5. In this case interstitials segregated at fourfold hollow sites also display nonideal behavior. The excess Gibbs free energy of segregation ΔG Seg xs is evaluated according to the Langmuir-McLean equation. In the case of ϕ XX (1) , ϕ XX (2) = 0 we find − ΔG Seg xs = | ϕ MX (1) | . For ϕ XX (1) , ϕ XX (2) < 0 and low bulk concentrations x ≲ 0.01 there is still Langmuir-McLean behavior, i.e. − ΔG Seg xs = | ϕ MX (1) | = const , but with increasing bulk concentrations strong positive deviations from ideal behavior are found, − ΔG Seg xs = ƒ(θ,T) | ϕ MX (1) | . In contrast, negative deviations − ΔG Seg xs < | ϕ MX (1) | are observed in the case of c(2 × 2) ordered surface phases ( ϕ XX (4) < 0 ), which strongly depends on surface coverage.