Observation of a Soft Surface-Phonon Mode in the Reconstruction of Clean W(100)

Abstract

He-atom-beam scattering has been used to investigate the reconstruction of the W(001) surface. At low surface temperatures ${T}_{s}$ a sharp $(\sqrt{2}\ifmmode\times\else\texttimes\fi{}\sqrt{2})R45\ifmmode^\circ\else\textdegree\fi{}$ diffraction pattern is observed. When ${T}_{s}$ is raised, the fractional-order beams broaden and shift towards the specular. At ${T}_{s}\ensuremath{\approx}450$ K the time-of-flight spectra reveal two different surface phonons along the $〈110〉$ direction, a normal Rayleigh mode and a strongly anomalous mode with a maximum at a wave vector $Q$ at one-half of the zone boundary ${Q}_{\mathrm{BZ}}$ and an energy approaching zero at $Q\ensuremath{\sim}0.8{Q}_{\mathrm{BZ}}$. This mode softens with decreasing temperature, identifying the structural transformation as a continuous displacive transition.