Surface Lattice Dynamics

It is intended for this chapter to be a brief introduction to surface lattice dynamics and to some of the kinds of information that one is able to obtain about the electronic and vibrational properties of surfaces through high-resolution helium atom scattering. Such information is critical to the understanding of many aspects of surface chemistry and to the design of novel materials with specifically desired properties. 

W. (2002) Anomalous surface lattice dynamics of a simple hexagonally close-packed surface. Phys. Rev. B,... 

At the same time, many lattice dynamics models have been constructed from force-constant models or ab-initio methods. Recently, the technique of molecular dynamics (MD) simulation has been widely used" " to study vibrations, surface melting, roughening and disordering. In particular, it has been demonstrated " " " that the presence of adatoms modifies drastically the vibrational properties of surfaces. Lately, the dynamical properties of Cu adatoms on Cu(lOO) " and Cu(lll) faces have been calculated using MD simulations and a many-body potential based on the tight-binding (TB) second-moment aproximation (SMA). " ... 

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. 

The obtained Ao gi = 5.7 x 10 is even larger than the value of Acr (Cu) X (= 4.7 X 10 A ), and of the hypothetical Co—Cu crystal with intermediate elastic properties than bulk cobalt and copper (4.1 x lO" A ). The derived effect of the effect of the lower coordination of the surface atoms on the mean-square relative displacement (perpendicular vs. parallel motions) is 1.4 times larger amplitude of the perpendicular vs. parallel motions, in agreement with lattice dynamics calculations. This SEXAFS study has produced a measure of the surface effect on the atomic vibrations. This has been possible due to the absence of surface or adsorbate reconstruction (i.e. no changes in bond orientations with respect to the bulk) and of intermixing. 

The surface Fuchs-Kliewer modes, like the Rayleigh modes, should be regarded as macroscopic vibrations, and may be predicted from the bulk elastic or dielectric properties of the solid with the imposition of a surface boundary condition. Their projection deep into the bulk makes them insensitive to changes in local surface structure, or the adsorption of molecules at the surface. True localised surface modes are those which depend on details of the lattice dynamics of near surface ions which may be modified by surface reconstruction, relaxation or adsorbate bonding at the surface. Relatively little has been reported on the measurement of such phonon modes, although they have been the subject of lattice dynamical calculations [61-67],... 

D. D. Koleske, Studies of surface vibrations and structure using molecular dynamics simulations, lattice dynamics calculations, and helium atom scattering, 1992)... 

Conventional infrared spectra of powdery materials are very often used for studying solid hydrates in terms of sample characterization (fingerprints), phase transitions, and both structural and bonding features. For the latter objects mostly deuteration experiments are included. However, it must be born in mind that the band frequencies observed (except those of isotopically dilute samples (see Sect. 2.6)) are those of surface modes rather than due to bulk vibrations, i.e., the transverse optical phonon modes, and, hence, not favorably appropriate for molecular and lattice dynamic calculations. 

Unfortunately, the analytical theory of surface melting has been so far not developed in a more explicit way, simply because one is lacking reliable quantitative theories of the melting transition in the bulk. Thus theories that locate the onset of surface melting from lattice-dynamical phonon instabilities (Pietronero and Tosatti, 1979 Jayanthi et al., 1985a, b Tosatti, 1988 Trayanov and Tosatti, 1988) need to be viewed with the caution that analogous treatments of melting in the bulk do not work. While computer simu-... 

Saito H, Kawase Y, Kira A et al (2007) Surface and dynamic structures of bacteriorhodopsin in a 2D crystal, a distorted or dismpted lattice, as revealed by site-directed solid-state 13C NMR. Photochem Photobiol 83 253-262... 

Fig. 22. Phonon dispersion curves for the (26x2) HOC monolayer of Xe on Cu(110) along the FX (a) and FY (b) directions. Notations used R Cu(110) surface Rayleigh wave 1, Ij, -L3 single and multiple excitation of the perpendicular Xe vibration mode H, Hi, H2 branches of the hybridized 1 and R modes. L, L longitudinal Xe modes, G gap mode. Dashed lines are the result of a lattice dynamics calculation [97R].

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