Symmetry superposition studied by surface second-harmonic generation

The components of a third-rank χ⁽²⁾ tensor have been split into contributions due to 1-fold, 2-fold, 3-fold, and {∞}-fold or isotropic rotation axes for a surface of Cₛ symmetry. Theoretical analysis of the rotation patterns obtained by the surface second-harmonic (SH) generation indicates that a complete symmetry analysis cannot be performed without knowledge of the relevant distribution functions. Rotation axes of lower symmetry create via ``overtones'' or ``harmonics'' contributions apparent in the analysis of the rotation axes of higher symmetry. An experimental example is the observation of structural changes of Au(111) surfaces in an aqueous electrolytic environment. Potential-dependent buildup and removal of a Au(111)-(1×{}23) surface could be monitored in situ and in real time. Symmetry analysis of the SH rotation patterns reveals both contributions due to a 3-fold axis due to the regular (1×{}1) structure and simultaneously a 1-fold and a 2-fold axis due to the (1×{}23) reconstruction.