Direct methods for surfaces

This paper reviews recent progress in the application of Direct Methods to solve surface structures using surface X-ray or transmission electron diffraction data. The basic ideas of (crystallographic) Direct Methods are presented, as well as the additional problems posed by trying to apply them to surfaces and how they connect to the mathematical theory of projections. Surface crystallography notation is presented, which differs from the widely used LEED notation in that it emphasizes the surface symmetry. This is followed by a description of methods for structure completion and refinement, followed by applications to some experimental systems, both those where the structure was previously known (calibration tests) and a few where it was not, concluding with problems and limitations.