Atom surface phonons

The dispersion curves of surface phonons of short wavelength are calculated by lattice dynamical methods. First, the equations of motion of the lattice atoms are set up in terms of the potential energy of the lattice. We assume that thejxitential energy (p can be expressed as a function of the atomic positions 5( I y in the semi-infinite crystal. The location of the nth atom can be... 

Recently, we hav measured the surface phonon dispersion of Cu(l 10) along the rx, rF, and F5 azimuth of the surface Brillouin zone (Fig. 13) and analyzed the data with a lattice dynamical slab calculation. As an example we will discuss here the results along the TX-direction, i.e. the direction along the close-packed Cu atom rows. 

In addition to the acoustical modes and MSo, we observe in the first half of the Brillouin zone a weak optical mode MS7 at 19-20 me V. This particular mode has also been observed by Stroscio et with electron energy loss spectrocopy. According to Persson et the surface phonon density of states along the FX-direction is a region of depleted density of states, which they call pseudo band gap, inside which the resonance mode MS7 peals of. This behavior is explained in Fig. 16 (a) top view of a (110) surface (b) and (c) schematic plot of Ae structure of the layers in a plane normal to the (110) surface and containing the (110) and (100) directions, respectively. Along the (110) direction each bulk atom has six nearest neighbors in a lattice plane, while in the (100) direction it has only four. As exemplified in Fig. 17, where inelastic... 

Another class of techniques monitors surface vibration frequencies. High-resolution electron energy loss spectroscopy (HREELS) measures the inelastic scattering of low energy ( 5eV) electrons from surfaces. It is sensitive to the vibrational excitation of adsorbed atoms and molecules as well as surface phonons. This is particularly useful for chemisorption systems, allowing the identification of surface species. Application of normal mode analysis and selection rules can determine the point symmetry of the adsorption sites./24/ Infrarred reflectance-adsorption spectroscopy (IRRAS) is also used to study surface systems, although it is not intrinsically surface sensitive. IRRAS is less sensitive than HREELS but has much higher resolution. 

The choice of methods is a matter of convenience. Both will capture the essential features of the GLE, namely frictional energy loss from the primary atoms to the secondary atoms and thermal energy transfer from the secondary atoms to the primary atoms. Both will provide a reasonable description of the bulk and surface phonon density of states of the solid. Neither will provide the exact time-dependent response of the solid due to the limited number of parameters used to describe the memory function. 

Figure 44. Correction factor to the transition-state theory rate as a function of the frequency of the surface phonon, for H-atom diffusion on a W(IOO) surface, at T = 300 K. The horizontal dashed line is for a moveable surface. The various curves correspond to different multiplicative factors of the strength of copling to the phonon. The plot is from Jaquet and Miller (1985).

There are no gas—metal systems for which the dominant loss mechanism has been determined. However, it can be anticipated that developments in angle-resolved inelastic atom beam scattering experiments, exemplified by the recent work of Feuerbacher and Allison [380] with scattering from LiF 100, will make good this deficiency. In cases where single surface phonons are responsible for the inelasticity in He scattering, time-of-flight measurements with the detector scanned away from the molecular beam enable the dispersion curves for surface phonons to be constructed. 

Appelbaum and Hamann [209] produced a fully self-consistent first principles calculation for the chemisorption of H on Si lll, which showed that the Si—H bond potential is considerably greater than that for Si—Si. The force on the H atom is small and inward, with a bond length of 2.73 0.02 a.u. The Si-H bond force constant is 0.175a.u. compared with the measured value of 0.173 a.u. for SiH4. The corresponding surface phonon, as mentioned previously, has been observed by ELS [214]. In the calculated electronic structure of the Si—H surface, the most notable feature is the disappearance of states in the fundamental band gap and the corresponding appearance of a band of states, clearly connected with the Si- H bond, in the gap between the second and third valence bands. 

The harmonic-oscillator and elastic-continuum models can be used to explain the presence of surface phonons (Rayleigh waves and localized surface modes of vibration) and the larger mean-square displacement of surface atoms compared to that of atoms in the bulk. 

The situation at surfaces is more complicated, and richer in information. The altered chemical environment at the surface modifies the dynamics to give rise to new vibrational modes which have amplitudes that decay rapidly into the bulk and so are localized at the surface [33]. Hence, the displacements of the atoms at the surface are due both to surface phonons and to bulk phonons projected onto the surface. Since the crystalline symmetry at the surface is reduced from three dimensions to the two dimensions in the plane parallel to the surface, the wavevector characterizing the states becomes the two-dimensional vector Q = qy). (We follow the conventional notation using uppercase letters for surface projections of three-dimensional vectors and take the positive sense for the z-direction as outward normal to the surface.) Thus, for a given Q there is a whole band of bulk vibrational frequencies which appear at the surface, corresponding to all the bulk phonons with different values of (which effectively form a continuum) along with the isolated frequencies from the surface localized modes. 

Theoretical calculations of surface phonon dispersion have been carried out in two ways. One method is to use a Green s function technique which treats the surface as a perturbation of the bulk periodicity in the z-direction [34, 35]. The other is a slab dynamics calculation in which the crystal is represented by a slab of typically 15-30 layers thick, and periodic boundary conditions are employed to treat interactions outside the unit cell as the equations of motion for each atom are solved [28, 33, 35, 37]. In the latter both the bulk and the surface modes are found and the surface localized modes are identified by the decay of the vibrational amplitudes into the bulk in the former the surface modes can be obtained directly. When the frequency of a surface mode lies within a bulk band of the same symmetry, then hybridization can take place. In this event the mode can no longer be regarded as strictly surface localized and is referred to as a surface resonance [24]. Figure 8, adapted from Benedek and Toennies [24], shows how the bulk and surface modes develop as more and more layers are taken in a slab dynamics calculation. 

The next phase for the theorists in connection with this work lies in predictions of helium atom scattering intensities associated with surface phonon creation and annihilation for each variety of vibrational motion. In trying to understand why certain vibrational modes in these similar materials appear so much more prominently in some salts than others, one is always led back to the guiding principle that the vibrational motion has to perturb the surface electronic structure so that the static atom-surface potential is modulated by the vibration. Although the polarizabilities of the ions may contribute far less to the overall binding energies of alkali halide crystals than the Coulombic forces do, they seem to play a critical role in the vibrational dynamics of these materials. 

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