Dispersionless single phonon creation and annihilation features have been observed across the entire Brillouin zone for the low density Hg monolayer adsorbed on Cu(001). This uncorrelated vibration of Hg atoms perpendicular to the surface contrasts sharply with the vibrational activity of most other chemisorbed metal atoms on metal substrates which exhibit correlated vibrations between groups of adsorbate atoms. The measured phonon energy has been used to build an interaction potential which incorporates both dynamical as well as static structural and thermodynamic properties of this system.

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