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We have performed a high-resolution electron-energy-loss study of the Si(111)-(~3x~3)R30':Al surface and have measured the dispersions of several surface phonons along the I'K direction. We interpret these using two different simple lattice dynamical models, both employing force constants from an ab initio electronic-structure calculation of Northrup. The first yields quantitative information at q = 0; the second is a semiquantitive estimate of the dispersion. These models have no adjustable parameters. The good agreement with the experiment for most of the observed modes indicates that a single theory can explain both the electronic structure and vibrational modes of this surface and also illustrates both the usefulness and limitations of simple models of lattice dynamics.

We calculate the optical response of a crystalline metal with a surface. Our model uses a single Fourier component of bulk potential, an infinite barrier at the surface, and the random-phase approximation to describe the many-body interactions. Within these constraints the calculations determine the full quantum-mechanical response. The results for an applied long-wavelength field parallel or perpendicular to the surface are characterized by the d parameters, d~i and d~. For the latter case we find novel long-ranged oscillations in the induced density near the surface. Although these arise from the simultaneous presence of the surface and lattice scattering, they extend far into the bulk and are incommensurate with the lattice. Using parameters appropriate for Li(110), we And that interband absorption causes both d& and d~~t o have frequency dependences significantly difFerent from the jellium limit.

In recent calculations of optical response at a metal surface, an unusual set of oscillations have been found in the induced charge density. These oscillations only appear when a crystal potential is included in the calculation. They propagate deep into the bulk, but are incommensurate with the lattice. We illustrate the occurrence of such oscillations in simple systems, and discuss their origin. For more general cases, we find that the amplitude of the oscillations is sensitive to the amount of spatial variation in directions parallel to the surface of either the crystal potential or the probing field. We also discuss the challenge of detecting this phenomenon experimentally.