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Surface interactions and surface dynamics on a clean reconstructed W(100).

We have extended our study of the surface dynamics of a clean W(100) to the region T<T c . We have determined the surface phonon dispersion relations using a quasiharmonic approximation at low temperatures and a method of critical dynamics near T c . We demonstrate here how the phonon band gap opens at the surface Brillouin-zone boundary, as the surface goes into the c(2×2) phase. We also show how the surface phonon excitation differs from the harmonic picture under the presence of strong anharmonic interactions and large critical fluctuations