X-ray diffraction (XRD) techniques are uniquely capable of determining the structures of crystalline materials with an accuracy of the order of picometers or better. However, the main obstacle to determining structures using XRD is the so-called "phase problem" - XRD patterns provide the intensities of diffraction spots, but the relative phases are inaccessible. In order to retrieve the phases, traditionally a model is proposed, and the structure modified until a self-consistent solution is found. Although this approach, coupled with sound stereochemical constraints, can lead to an unambiguous solution for simple structures, increasingly it fails for more complex systems - the starting model is insufficiently close to reality that this iterative procedure can remove the structure out of a local minimum towards the real solution.
New techniques, however, based on direct methods, are model-free and can potentially overcome the problem of being trapped in a local minimum. This project is concerned with developing such methods in the technique of surface x-ray diffraction (SXRD), used to determine the structures of crystalline surfaces and interfaces.