Instability, Distortion, and Dynamics of the W(100) Surface

A model for the reconstructions of the W(100) surface is presented. Four types of distortions are obtained, along $〈011〉$, $〈001〉$, $〈100〉$ (commensurate), and (×{} 10) (incommensurate). The $〈011〉$ distortion, corresponding to the observed (√2×√2)45^∘ clean surface, is worked out in detail. A distortion magnitude of {~} 0.35 {} is found, and a surface coherence length ξ15^∘ {} close to experiment. The full vibrational spectrum, the distortion penetration, and the anisotropic surface anharmonic energies are also obtained.