Segregation of substitutional bulk S to the Fe(100) surface and the Fe–Fe oxide interface: Molecular-orbital theory

A molecular-orbital study of the binding of S atoms in bulk iron and on the (100) surface is performed with ${\mathrm{Fe}}_{47}$ bulk and ${\mathrm{Fe}}_{41}$ surface cluster models to understand the commonly observed surface segregation of impurities. An atom-spin-polarization rule for ferromagnetic iron is suggested wherein each atom’s contribution to the cluster-spin polarization is dependent on its coordination number. Its predictions are in satisfactory agreement with recent theoretically calculated values for Fe(100) and Fe(110) surfaces. The calculated binding energies are found to agree best with experiment when S is included in determining the Fe coordination number, thereby decreasing the spin polarization. The interaction of the filled S 3s orbital with occupied a-symmetry orbitals in a bulk substitutional site results in a closed-shell repulsion, while on the surface the S 3$p_z$ orbital is symmetry allowed to mix with the S 3s orbital, reducing the repulsion. The S 3s orbital is largely responsible for sulfur bonding more strongly on the surface than to a bulk substitutional site; respective calculated values are 3.98 (4.20) eV and 3.10 eV, where the value in parentheses is experimental. Taking into account the predicted vacancy-formation energy of 0.79 eV, the calculated S dissolution energy 2.31 eV is close to the experimental value (2.56 eV). The difference, 1.67 eV, compares well with experimental estimates (1.64 and 1.71 eV). It is concluded that half of the S segregation energy is caused by the closed-shell repulsion and the other half by the bulk Fe-vacancy-formation energy. The fact that S dissolves substitutionally in Fe suggests an explanation for a recent experimental observation that S will not segregate to an Fe–Fe-oxide interface: doing so would break strong Fe-O bonds and might introduce repulsive ${\mathrm{O}}^{2\mathrm{-}}$-${\mathrm{S}}^{2\mathrm{-}}$ interactions.