Towards a direct method for low energy electron diffraction

A direct method for crystallography is an algorithm that leads directly from a set of measured diffraction intensities to an atomic-scale structure without the need for guesswork or iterative model building. Recently there has been considerable progress towards the development of such a method in the area of surface x-ray diffraction, where knowledge of the bulk structure allows the problem to be treated as one of structure completion. The algorithm involves iteratively satisfying constraints in real and reciprocal space. Extension of such a methodology to LEED is much more difficult as there is no invertible Fourier transform relationship between relevant quantities in the two spaces, due to multiple scattering. Nevertheless, we have made significant progress towards the solution of this inverse problem. We will describe the algorithm and give examples of practical applications to measured experimental data.