Application of the 'direct methods' difference sum function to the solution of reconstructed surfaces

The determination of reconstructed surfaces from diffraction data is normal ly performed in two stages: (i) the (x, y) projection of the reconstruction is determined by direct interpretation of the two-dimensional partial Patt erson map computed with the intensities of the reconstruction in-plane refl ections only; and (ii) this projection is subsequently expanded to three di mensions by fitting the full data set (in-plane plus out-of-plane data). Un fortunately, interpretation of two-dimensional Patterson maps is not a triv ial task for reconstructions with large unit cells. Here, an alternative pr ocedure based on the application of the 'direct methods' difference sum fun ction is presented which reduces the two steps to one single highly automat ed step. This is achieved by simulating an extra periodicity normal to the surface which takes into account all atoms of the reconstruction. In this w ay a set of reconstruction reflections is generated which can be processed with the same methodology as for superstructure reflections in bulk superst ructures. Two known reconstructed surfaces have been selected as test examp les: Ge(001) c(4 x 2) and GaAs(001)-p(2 x 4). (C) 1999 Elsevier Science B.V . All rights reserved.