This thesis reports on surface and surface alloy structural and compositional determination with low-energy electron scattering and Monte Carlo simulations. Low-energy electron diffraction (LEED) technique and the newly developed low-energy electron microscopy (LEEM) IV technique are used to measure the electron scattering intensity spectra and dynamical multiple scattering analysis is performed to optimize the surface structural and non-structural parameters via comparison between the experimental spectra and calculated ones. My work focuses on the following four surface systems.

(111), (110) and (001) surface structures of the semimetal bismuth are determined with LEED. The unreconstructed (1×1) structure is revealed for all three surfaces. The interlayer spacings for several outermost layers are resolved. All results agree with those obtained by first-principles calculations. The Debye temperatures for the Bi(111) and Bi(110) surface are found to be lower than that of the Bi bulk. In conjunction with the LEED technique, scanning tunneling microscopy (STM) observation is performed on the Bi(001) surface. Surface topology images show dominant bilayer steps and no single layer step.

The newly developed LEEM-IV technique is used to investigate the PdCu surface alloy on the substrate Cu(001). Studies include quantifying the temporal evolution of Pd concentration on the Cu(001) terrace, mapping the 3D heterogeneous surface chemical composition, and identifying a step-overgrowth thin film growth mechanism. It is found that, at the initial deposition stages, Pd atoms reside in the second layer at the sample temperature of 473 K, and the Pd concentration increases exponentially with time. The heterogeneous structure and composition near the steps are found to be a result of the step-overgrowth. We highlight the LEEM-IV technique which provides a high lateral resolution at surfaces. We demonstrate a 3D profile of Pd concentration in the surface region by using the LEEM-IV technique.

The reconstructed Si(001)-2×1 surface has been intriguing due to its great scientific and technical significance. Unfortunately, no satisfactory agreement between the LEED experimental and theoretical data have been achieved. Some controversies over this surface, such as the flip-flop dimer dynamics and the ground-state structure, still require further study. Utilizing LEEM to get electron scattering spectra from a single domain, we get a refined asymmetric tilted dimer structure.

We investigate the 6H-SiC(0001) surface phase transition in order to ultimately understand the formation of graphene on it. LEEM diffraction data from a large single domain are analyzed for 3×3, 1×1 and [special characters omitted] phases. All the surface structures turn out to have an "A" bi-layer bulk termination. It is found that the amount of Si at the surface decreases with increased temperature. Adatom-trimer-adlayer model for the 3×3 surface does not give a satisfactory result and more work needs to be done to resolve this structure. A mixed Si-vacancy top-site overlayer on the 1×1 surface is found. A [special characters omitted] overlayer at the T4 registry on the substrate surface generates a best fit between experimental and calculated data.