Molecular-dynamics theory of the temperature-dependent surface phonons of W(001)

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Abstract
We study the temperature-dependent zone-boundary surface phonons across the c(2×2)→1×1 reconstruction phase transition of the clean W(001) surface. Velocity-velocity correlations and hence the phonon spectral densities are calculated by molecular dynamics for the surface atoms of a finite-thickness (001) slab, with interatomic potentials established in a previous study of the surface statics. Our calculated k=((1/2, 1) / 2 )(2π/a) surface phonon spectra are dominated by three main low-frequency modes. Of these, the longitudinal and the shear horizontal modes are reconstruction related and display critical broadening and softening at the phase transition, while the third, the shear vertical mode, is basically unaffected. The reconstruction phase mode, the shear horizontal, appears to be responsible for the phase fluctuations which destroy long-range order at the transition.