Vibrational modes of chemisorbed H on the W (001) surface

An attempt has been made to analyze some recent results for the vibrational model of H on the W (001) surface studied in electron-energy-loss experiments of Willis for different coverages on the basis of a number of structural models for the reconstructed surface, i.e., for $c(2\mathrm{}\times 2)$ superstructure. The phonon frequencies have been determined after taking into account the H-W central interactions up to third neighbors, H-W angular interactions up to first neighbors, and H-H central interactions up to the first neighbors. The central nearest-neighbor W-H interactions are seen to be dominant and the W-H angular interactions are weak. The interactions between the H and W atoms lying below the surface are quite feeble, most probably due to strong screening by the W-surface conduction electrons. For the unreconstructed $p(1\mathrm{}\times 1)$ W surface, the values of the W-H bond length, interbond angle, and the substrate-monolayer spacing are found to be 2.03 Å, 102°, and 1.28 Å, respectively. For the reconstructed $c(2\mathrm{}\times 2)$ H surface, the corresponding values are 2.19 Å, 78°, and 1.70 Å in the Debe and King model for the displacement of all surface atoms by 0.32 Å parallel to the surface and 2.24 Å, 78°, and 1.75 Å in a "puckered" layer model for the displacements of 50% surface atoms by 0.64 Å, both parallel and perpendicular to the surface. The values of these parameters in another model, where the W atoms are displaced in the surface in the $〈10〉$ direction (suggested by Barker and Estrup) by 0.21 Å, are 2.09 Å, 78°, and 1.70 Å.