Excitation of the shear horizontal mode in a monolayer by inelastic helium atom scattering

Abstract

Inelastic scattering of a low-energy atomic helium beam ͑HAS͒ by a physisorbed monolayer is treated in the one-phonon approximation using a time-dependent wave packet formulation. The calculations show that modes with shear horizontal polarization can be excited near high symmetry azimuths of the monolayer, in agreement with recent experiments. The parameters of the calculations are chosen to match the conditions of HAS experiments for triangular incommensurate monolayer solids of xenon, krypton, and argon adsorbed on the ͑111͒ face of platinum, and the results show many of the systematic experimental trends for relative excitation probability of the shear horizontal and longitudinal acoustic phonon branches. The inelastic scattering at beam energies near 8 meV is exceedingly sensitive to small misalignment between the scattering plane and the high symmetry directions of the monolayer solid. The diffraction and inelastic processes arise from a strong coupling of the incident atom to the target and the calculated results show large departures from expectations based on analogies to inelastic thermal neutron scattering.

Atomic scattering from an adsorbed monolayer solid with a helium beam that penetrates to the substrate

“…(11) of Ref. 4. This implies that the norm of the wave function 1 for having excited a single specific phonon mode is O(1/N) and very small.…”

“…1,2 The theory is relatively complex because the processes that make a thermal energy He beam an exquisitely surface sensitive probe require treating the scattering as a strong coupling event. [3][4][5][6] For example, the simply commensurate monolayer solid p(1 × 1) H 2 /NaCl(001) is such a corrugated target that some experimental diffraction peaks are more intense than the specular peak 7 and the theory 6 shows this too. Further, that monolayer solid is so dilated that there is only a low potential energy barrier for the He to penetrate to the interlayer region that is between the plane of the monolayer molecule centers and the plane of the centers of surface ions of the substrate and there may be paths with no barrier for a more dilated conjectured commensurate monolayer solid p(1 × 1) H 2 /KCl(001) that has not yet been observed.…”

“…This is in marked contrast to low energy electron diffraction experiments, where interference between reflections at the monolayer and at the substrate is analyzed to determine the adsorption-site geometry. 11 Our previous work (Papers I-III) [4][5][6] is in the context of the time-dependent evolution of a scattering wave packet and starts from the one-phonon scattering approximation of Choi and Poe. 12 The time-dependent theory exhibits the dynamic interplay of the elastic and inelastic processes.…”

Enhanced creation of dispersive monolayer phonons in Xe∕Pt(111) by inelastic helium atom scattering at low energies

“…The misalignment of the scattering plane relative to the ⌫M azimuth of the monolayer is ␣ = 2.6°, the Novaco-McTague orientational alignment angle at L nn = 4.33 Å determined in the Xe/ Pt͑111͒ experiments. 6 This value is not crucial because a misalignment ␣ = 0.5°also gives strong symmetry-breaking SH-mode excitation 9 Mostly, the phonon wave vectors are directed antiparallel to k iʈ because of the experimental experience 6 that this led to better resolved SH-mode excitation.…”

“…An unanticipated result of the experiments was that all branches of the dispersion relations were accessed for wave vectors near high-symmetry azimuths in the first Brillouin zone. 6 In a previous paper, 9 denoted as Paper I, we demonstrated that the anomalous excitation of shear horizontal ͑SH͒ phonon modes by HAS from a physically adsorbed monolayer can be understood using a strong coupling inelastic scattering theory and known atomic interactions. The basic calculation was to generate the time-dependent solution for wave packet scattering, with the inelastic processes treated in the one-phonon creation approximation.…”