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Abstract

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.