Abstract
The $(2\ifmmode\times\else\texttimes\fi{}2)$ surface-${\mathrm{V}}_{2}{\mathrm{O}}_{3}$ layer, an interface-mediated vanadium oxide phase observed on Pd(111) in the submonolayer coverage range, has been investigated by means of angle scanned x-ray photoelectron diffraction (XPD), which gives a direct experimental confirmation of the model derived by scanning tunnelling microscopy (STM) and density functional calculations (DFT), with a quantitative determination of the V-O interlayer spacing. In addition, XPD measurements compared to single scattering cluster--spherical wave (SSC-SW) simulations revealed a peculiar broadening of V-O forward scattering (FS) maxima that is limited to azimuthal scans and that cannot be accounted for by isotropic Debye-Waller attenuation of the diffraction features. However, the existence of a soft phonon mode in the overlayer, associated with substantial in-plane displacements from equilibrium of O scatterers with respect to V emitters, could explain the experimental observation. The existence of such a soft mode has been confirmed by DFT calculations. It consists of an in-plane quasirotation around the V emitter of the three nearest-neighbor O atoms, and the estimated DFT frequency amounts to $15{\mathrm{cm}}^{\ensuremath{-}1}.$ The XPD data have been analyzed by means of SSC-SW simulations wherein a harmonic oscillator model has been employed to approximate the effect of the soft phonon mode on XPD curves. As a result, an experimental determination of the frequency of the mode has been obtained $(40\ifmmode\pm\else\textpm\fi{}25{\mathrm{cm}}^{\ensuremath{-}1}),$ which is of the same order of magnitude as the DFT predicted frequency. Moreover, the sensitivity of XPD scans to the correlation of soft-mode atomic displacements has been studied, leading to the estimate of a ``soft-mode XPD coherence length'' for the system under investigation. This work therefore explores an application of XPD as a surface spectroscopy sensitive to vibrational soft modes.
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