Evidence for a soft-phonon mechanism in the reconstruction of the Mo(001) surface

Surface-phonon dispersion curves of Mo(001) have been measured with high-resolution helium-atom scattering at three different surface temperatures, 1000, 750, and 400 K, respectively. Time-of-flight spectra in the 〈100〉 and 〈110〉 directions reveal two distinct phonon modes. The mode at higher energies can only be observed in the first third of the Brillouin zone and disappears for larger phonon wave vectors. The low-energy mode shows a remarkable softening in the 〈110〉 direction from the 8 meV at 1000 K to about 2 meV at 400 K at the wave vector Q=1.1 A${̊}^{\mathrm{-}1}$, whereas, within experimental accuracy, no softening occurs in the 〈100〉 direction.