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

He-atom-beam scattering has been used to investigate the reconstruction of the W(001) surface. At low surface temperatures $T_s$ a sharp $(\sqrt{2}\times \sqrt{2})R45\mathrm{}°$ diffraction pattern is observed. When $T_s$ is raised, the fractional-order beams broaden and shift towards the specular. At $T_s\approx 450$ 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 $Q\sim 0.8Q_{\mathrm{BZ}}$. This mode softens with decreasing temperature, identifying the structural transformation as a continuous displacive transition.