Rayleigh Phonon Research Articles

Rayleigh mode in amorphous hydrogenated carbon films.

Brillouin-scattering experiments are performed on amorphous hydrogenated carbon (a-C:H) films grown by plasma deposition on silicon substrates at various bias voltages (-50 to -1400 V) and annealed after deposition at a bias of -400 V between 100 and 1100 \ifmmode^\circ\else\textdegree\fi{}C. Scattering from Rayleigh surface phonons is observed. The results show that the Reyleigh mode frequencies are between those of diamond and graphite. With increasing substrate bias voltage the Rayleigh mode frequency first increases to a maximum value at -200 V and then decreases monotonically. Upon annealing, the Rayleigh phonon frequency decreases drastically for temperatures above 500 \ifmmode^\circ\else\textdegree\fi{}C with minor changes below 400 \ifmmode^\circ\else\textdegree\fi{}C. These results correspond to the results of the ${\mathit{sp}}^{3}$-to-${\mathit{sp}}^{2}$ bonding ratio, indicating that the frequency variation of the Rayleigh phonon is due to phase transformations of a-C:H. The coupling between the relaxation mechanism and the phonon also confirms the phase transitions. Based on the hydrogen concentration, the ${\mathit{sp}}^{3}$-to-${\mathit{sp}}^{2}$ bonding ratio, and the phonon frequency, the correlated densities and elastic constants of annealed a-C:H films are calculated.

Inelastic He-atom scattering from the MgO(001) surface.

Dispersion curves of Rayleigh phonons on an in situ cleaved, room-temperature surface of MgO(001) are determined by time-of-flight measurements of inelastically scattered He atoms. Along both the \ensuremath{\Gamma}\ifmmode\bar\else\textasciimacron\fi{} X\ifmmode\bar\else\textasciimacron\fi{} and \ensuremath{\Gamma}\ifmmode\bar\else\textasciimacron\fi{} M\ifmmode\bar\else\textasciimacron\fi{} directions, the measured phonon frequencies agree fairly well with a shell-model calculation for an unrelaxed MgO(001) surface.

Surface phonon dispersion of Ni 90Pt 10(001)

The dispersion of surface phonons for a disordered metal alloy has been measured for the first time. High-resolution electron energy loss spectroscopy (HREELS) was used to investigate the surface phonon dispersion of Ni 90Pt 10(001) in the [110] direction. The Rayleigh wave was found to be rather similar to the Rayleigh phonon observed on the clean Ni(001) surface. For this mode a substantial broadening of the line width is observed which seems to arise from the Pt impurities at the surface. No low-frequency resonance mode (Pt impurity vibration) could be detected.

Rayleigh wave dispersion on Ag(100) along the direction.

Electron-energy-loss-spectroscopy measurements of Rayleigh phonon dispersion are reported for the \ensuremath{\Gamma}\ifmmode\bar\else\textasciimacron\fi{}-M\ifmmode\bar\else\textasciimacron\fi{} direction of the Ag(100) surface. The data are compared to lattice-dynamical calculations performed within a nearest-neighbor model. The comparison shows that a slight increase of the force constant between the first and second layer with respect to the bulk value is needed in order to fit the data. The force-constant change is, however, less than the accuracy with which one can reproduce the bulk phonon spectrum with this model and is therefore not physically significant. More sophisticated models are, on the other hand, shown to give wrong predictions for the surface spectrum. We conclude therefore that the Ag(100) surface exhibits smaller effects of surface relaxation, if indeed there are any effects, than the same surfaces of Cu and Ni.

Strong anisotropy in the Rayleigh phonon dispersion relation on Pt(111) induced by a p(2

Etude par diffusion inelastique de l'helium. La forte anisotropie s'explique par une absorption d'oxygene aux sites hexagonaux compacts surface Pt(111)

A surface stress induced (1×1) → (5×1) reconstruction of an Ir(1OO) surface

In the present study we have applied the phonon dispersion method to investigate the dynamics of the (1×1) → (5×1) reconstruction of an Ir(1OO) surface. The Ir(1OO) surface has been chosen here mainly because stable and atomicany clean surfaces of both uncreconstructed Ir(100)-(1×1) and reconstructed Ir(100)-(5×1) could be routinely obtained by controlling experimental conditions. The dispersion of surface phonons has been measured along both the \\ ̄ gG X̄ [011] and \\ ̄ gG M̄ [001] directions. Our results indicate that along both directions the frequency of the Rayleigh phonon near the zone boundary is significantly higher on the unreconstructed (1×1) surface. In addition, lattice dynamical calculations in a second nearest neighbour force constant model have also been performed for the unreconstructed Ir(100)-(1×1) surface. The comparison of theory with experimental results reveals that the unreconstructed surface possesses a substantial amount of tensile surface stress. The results presented here allow us to conclude that the surface stress is the major driving force for the surface reconstruction of Ir(100)-(1×1) to Ir(100)-(5×1).

A finite temperature theory of rotationally inelastic diffraction: H2, HD, and D2 on Cu(100)

The rotationally inelastic diffraction probabilities for H2, HD, and D2 from Cu(100) were computed as a function of surface temperature. The surface is treated in a quantum mechanical fashion using a recently developed formalism. The center of mass molecular translational motion is treated semiclassically, using Gaussian wave packets (GWPs), and the rotations are described quantum mechanically. Strong attenuation of the phonon elastic diffraction peaks with temperature is observed. This Debye–Waller-like attenuation increases with increasing molecular mass and kinetic energy, and decreases as the peaks become more off-specular. The phonon summed rotation–diffraction probabilities show a moderate temperature dependence for the most part. The 0→2 rotational excitation of D2 appears to be strongly phonon assisted above 300 K. At low temperatures our method reproduces the selection rules predicted by previous studies. As the temperature is increased these selection rules become less restrictive. The probability distribution for a scattering molecule exchanging an amount of energy ΔE with the surface was also computed. Rayleigh phonons were found to dominate the energy transfer, with bulk vibrations becoming more important for larger molecular masses, beam energies, and surface temperatures.

Surface phonon dispersion in ultrathin epitaxial films of Co on Cu(001)

The Rayleigh phonon dispersion for ultrathin epitaxial Co films on a Cu(001) substrate has been measured by high resolution EELS. The phonon energies are higher than those of Cu and show substantial flattening near the zone boundary, suggestive of the surface stress in the films.

Surface phonon dispersion in ultrathin epitaxial films of Co on Cu(001)

The Rayleigh phonon dispersion for ultrathin epitaxial Co films on a Cu(001) substrate has been measured by high resolution EELS. The phonon energies are higher than those of Cu and show substantial flattening near the zone boundary, suggestive of the surface stress in the films.

Surface phonon dispersion in ultrathin nickel films on Cu(100)

Ultrathin epitaxial films of Ni are deposited on the Cu(100) surface by evaporation in UHV. The dispersion of the Rayleigh phonon in 1 and 2 monolayer films and of a surface resonance in 1 monolayer films is measured by high resolution EELS. Lattice dynamical slab calculations with nearest-neighbour pair potentials fit the experimental data when the Ni-Ni coupling in the layer adjacent to the Cu substrate is softened by 50%.

Application of the Embedded Atom Method to surface-phonon dispersions on Cu(100)

The surface lattice dynamical matrix has been derived from a new model within the framework of the Embedded Atom Method (EAM), which is based on results from density functional theory. The surface-phonon dispersions on Cu (100) in the direction Γ X was calculated. The obtained dispersion curve of the Rayleigh phonon on Cu (100) is in good agreement with experimental data by electron-energy-loss-spectroscopy (EELS).

Surface phonon dispersion of clean and oxygen covered Pt(111)

The dispersion of the vibrational modes of the Pt(111) surface in the absence of impurities as well as in the presence of oxygen has been measured by inelastic helium scattering along the \\ ̄ gG $ ̄ M azimuth. In the case of the ordered p(2×2)O superstructure, the additional dispersion branch appearing as a result of the Brillouin zone folding was also measured. The experimental results show the first direct evidence for the appearance of a surface Rayleigh phonon gap at the new zone boundary. The gap was determined to be ~ 0.85 meV at the M̄ 0 point. Lattice-dynamical calculations show that this relatively large gap is due to bond stretching interactions between the adsorbate and substrate atoms. The dispersion curve in the presence of disordered oxygen, obtained by annealing (1200 K) the Pt surface in an oxygen atmosphere and assumed to be located subsurface on the basis of ion scattering data has been measured. The frequency of the Rayleigh phonon at the M̄ point is 12% below the clean surface value. This is at variance with the case of disordered oxygen on metal surfaces (O/Ni(100)) which has been shown to have a negligible influence on the Rayleigh dispersion curve. According to the lattice dynamical calculations this 12% frequency lowering corresponds to a reduction of the interlayer force constant k 12 by about 30% and thus supports the subsurface location of the oxygen atoms.

Surface phonon dispersion and adsorbate induced reconstruction of Ni(100)

The Ni(100) surface reconstructs upon adsorption of half a monolayer of nitrogen. This observation is at variance with a previous report. The reconstructed phase consists of a c(2 × 2) overlayer of nitrogen with a clockwise and counterclockwise rotation of the nickel surface atoms around two nearest neighbor nitrogen atoms, respectively. The same p4g(2 × 2) reconstruction was also observed with carbon overlayers. Recent total energy calculations and lattice dynamic analysis have shown that this reconstruction is driven by internal stresses caused by a repulsive interaction between the first layer nickel atoms. We have measured the phonon dispersion branches of the p4g(2 × 2) nitrogen covered surface along the [110] direction. Two adsorbate induced phonon branches above the bulk phonon branch of nickel are found. The branches are similar to those found for the carbon covered surface and indicate that nitrogen sits close to the surface in the fourfold hollow site. In addition to the adsorbate associated modes surface resonances inside the bulk band and the Rayleigh phonon have been measured. The various modes are identified by comparing experimental results to lattice dynamical calculations.

Theory of resonant inelastic one-phonon scattering of He atoms from a LiF(001) single crystal surface

For the He–LiF(001) system, molecular beam measurements of the inelastically scattered intensity have revealed a large number of resonance structures. In this paper the theoretical description of these resonant inelastic one-phonon scattering processes is provided in the framework of the distorted wave Born approximation. In the first step the elastic diffractive scattering problem is solved exactly using close coupling calculations for a recently developed pairwise additive semi ab initio potential and a rigid lattice. As the potential contains both the attractive well and the corrugation in a realistic manner, bound state resonances are fully taken into account. In the next step the inelastic coupling due to one-phonon processes is treated as a perturbation of the elastic wave functions obtained from the close coupling solutions. The inelastic coupling potential is the same semi ab initio two-body potential used to describe the atom–static surface potential, and the LiF–surface lattice dynamics are described by realistic Green’s function calculations. The theoretical results provide a good description of most of the structures seen in experimental angular distributions and time of flight spectra. The resonant features can be interpreted in terms of one-phonon assisted adsorption into and desorption out of specified bound states of the atom–surface potential. In addition to the contributions of Rayleigh phonons the bulk phonons contribute about 40% to both the creation and annihilation inelastic scattering processes.

The Rayleigh phonon dispersion on Cu(100): A stress induced frequency shift?

The dispersion of the Rayleigh wave on Cu(100) has been measured by high resolution electron energy loss spectroscopy (EELS) throughout the two-dimensional Brillouin zone in the\(\overline {\Gamma M} {\text{ - direction}}\). The experimental data can be matched with a nearest neighbour central force model when the force constant between the first and second layerk12 is stiffened by 20%. However, the data are likewise explained by assuming stress within the surface layer. The stress could arise from a tendency of the surface layer to contract.

The Rayleigh phonon dispersion curve on Cu(100) in the [formula omitted] direction

The dispersion curve of the Rayleigh phonon on Cu(100) has been measured by high resolution electron energy loss spectroscopy throughout the two-dimensional Brillouin zone in the ΓX direction. Lattice dynamical slab calculations fit the experimental data when the force constant between the first and second layer is stiffened by 20%.

Observation of surface optical phonons in NaF(001) by inelastic He-atom scattering.

Previous time-of-flight experiments at 20-meV He beam energies, which provided the dispersion curve of Rayleigh surface phonons, have been extended to 90-meV energies on NaF(001) along $〈100〉$. Despite a large multiphonon background from the Rayleigh phonons it has been possible to detect small peaks due to optical surface phonons. The results provide the first direct experimental evidence in the dispersion curves of microscopic surface optical modes.

The Rayleigh phonon dispersion curve on Ni(100) in the [formula omitted] (〈100〉) direction

The dispersion curve of the Rayleigh phonon on Ni(100) has been measured by high resolution electron energy loss spectroscopy throughout the two-dimensional Brillouin zone in the ΓM direction. Lattice dynamical calculations, fitted to the experimental data, confirm a stiffening of the force constant between first and second layer of the crystal of the order of 20%.

The Rayleigh phonon dispersion curve on Ni(100) in the [formula omitted] (〈100〉) direction

The dispersion curve of the Rayleigh phonon on Ni(100) has been measured by high resolution electron energy loss spectroscopy throughout the two-dimensional Brillouin zone in the ΓM direction. Lattice dynamical calculations, fitted to the experimental data, confirm a stiffening of the force constant between first and second layer of the crystal of the order of 20%.

Brillouin scattering in thin film optical waveguides. I. Theory of the phonon modes

The phonon modes of a thick plate and a thick plate coated with a thin film are discussed in the light of recent experiments on Brillouin scattering in thin film optical waveguides. Using the reflection coefficients for bulk waves, we have obtained the field structures, the mode normalization for excitation by thermal fluctuations, and the density of states for these modes. Both bulk and surface (Rayleigh, Sezawa, and Love) phonons are discussed.