Two two-dimensional atomic models were constructed to test the application of Direct Methods for solving surface crystal structures (atomic positions are listed in Table 1). The use of Direct Methods to solve three dimensional structures from X-ray diffraction has been well established for several years. However to the best of our knowledge never before had this technique been applied to 2-D surface structures. A Genetic Algorithm (GA) search routine was implemented for exploring possible solutions.

The models were constructed using electron scattering factors to calculate the intensities and phases for beams out to 1 Å resolution (Fig. 1). Since electron diffraction from surfaces has been shown to be nearly kinematical X-ray and electron scattering can be handled identically. An error term was applied to the generated intensities to simulate realistic sampling errors. The generated phases for each model were removed and later used to monitor the solutions calculated by the direct methods.