Observation of a Zone-Center Gap in the Longitudinal Mode of an Adsorbate Overlayer: Xenon on Cu(111)

Abstract

Using inelastic scattering of thermal energy He atoms we have determined the phonon dispersion curves in commensurate ͑ p 3 3p 3 ͒R30 ± Xe monolayers adsorbed on Cu(111). In addition to the well known transverse acoustic mode the dispersion curve of the longitudinally polarized phonon branch could be measured. Since this is the first case where a finite zone-center phonon gap (here 0.4 6 0.15 meV) has been seen for a Q-resolved phonon branch, a normal mode analysis and theoretical calculations on the phonon excitation probabilities have been carried out to confirm the assignment. From the gap magnitude important information on the corrugation of the Xe-atom-substrate potential is derived. [S0031-9007(97)04932-6] PACS numbers: 68.35.Ja, 63.22. + mRecently the properties of monolayers of noble gas atoms, in particular Xe, adsorbed on solid substrates have attracted interest in connection with fundamental experiments on the microscopic origin of friction carried out by Krim and co-workers [1]. Up to now, however, no consensus has been achieved concerning the proper theoretical modeling of these layers. Two recent attempts to theoretically analyze the results of the friction experiments [1] using molecular dynamics have obtained rather different results [2,3]. These discrepancies may in part be due to uncertainties concerning the proper model potentials describing the corrugation of the metal substrate as seen by the Xe atoms. These uncertainties result from the lack of direct experimental information on the potential energy surface governing the lateral motion of Xe atoms on the substrate. So far it has only been possible to extract indirect information from, e.g., detailed analyses of thermodynamical properties and thermal desorption spectroscopy [4].In the present Letter we will describe the outcome of experiments where high resolution scattering of thermal energy He atoms (HAS) has been successfully used to determine the dispersion of the longitudinal phonon in the commensurate ͑ p 3 3p 3 ͒R30 ± Xe overlayer on Cu(111). A detailed analysis of this mode provides two important pieces of information: (1) At the zone center of the surface Brillouin zone [cf. Fig. 1(a)] this mode corresponds to a lateral displacement of the whole Xe layer, and the corresponding frequency thus directly measures the curvature of the potential energy surface describing the interaction of the individual Xe atoms with the substrate.(2) From the slope of the longitudinal phonon dispersion curve (or the velocity of sound) the force-constant coupling between adjacent Xe atoms can be obtained. As to (1) a Q-resolved phonon branch with a finite zone-center phonon gap has not yet been seen experimentally, although in previous neutron scattering studies this quantity has been extracted from the total density of states [5]. With regard to (2) one may expect the force-constant coupling of the adsorbed Xe atoms to be very similar to that predicted from accurate gas-phase potentials [6] or from the analysis of bulk phonon data [7], but recent work ha...

Onset of frictional slip by domain nucleation in adsorbed monolayers

“…We introduce a tunable factor δ in order to quantitatively reproduce the value of the potential corrugation obtained experimentally from phonon dispersion curves measured by inelastic scattering of He atoms (19). In particular, we tune δ so that the value of the corrugation along the sliding direction, corresponding to the minimum energy path between two equivalent potential minima, is V 0 ¼ 1.9 meV as reported in ref.…”

“…In particular, we tune δ so that the value of the corrugation along the sliding direction, corresponding to the minimum energy path between two equivalent potential minima, is V 0 ¼ 1.9 meV as reported in ref. (19). The functional form of the parameter A 0 is related to that of the parameter A 1 according to the following expression:…”

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

“…III C. Table IV from a thermally excited monolayer These data are formed from the data of Table IV by multiplying by the Debye-Waller factor at 50 K, including the Beeby correction. The Xe monolayer is a very corrugated target 33,34 and the scattering is the result of strong coupling of the 4 He to the monolayer. Thus, it was expected that there would be much diffracted strength in nonspecular g 0 channels.…”

“…Also we determine the time scales for transient trapping of the incident atom that has been noted in previous calculations 9, [11][12][13] and which extends over times of 20-80 ps in several cases. Our results are for the scattering of 4 He by a Xe/ Pt͑111͒ monolayer at incident energies of 2 -25 meV and the parameter space has been reduced by specifying that the geometry is such that the incident angle leads to an inelastic outgoing wave at an angle corresponding to the scan curve geometry of the principal experiments 6,8 ͑Fig. 1͒.…”

“…Thus, determining the phonon dispersion relations is basic to a fundamental characterization of the response of the lattice. 1,2 It is now feasible [3][4][5][6][7][8] to do such measurements on single monolayer solid domains using low energy inelastic helium atom scattering ͑HAS͒. 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.…”