Structure determination of the (3sqrt{3}x3sqrt{3}) reconstructed   alpha-Al_2O_3(0001)
  Grazing-incidence X-ray diffraction data are combined with energy-minimization calculations to analyse the atomic structure of the Al-rich (3sqrt{3} x 3sqrt{3})R 30 deg reconstructed surface of sapphire alpha-Al_2O_3(0001). The experiments on the BM32 beamline of the ESRF provide the non-integer-order diffraction intensities and, after Fourier transform, an incomplete Patterson map. The computer simulations are implemented to obtain structural information from this map. In the simulations, the interactions between the Al overlayer atoms were described with the Sutton-Chen potential and the interactions between the overlayer and the sapphire substrate with a laterally modulated Lennard-Jones potential. We have shown that the hexagonal reconstructed unit cell is composed of triangles where the two layers of Al adatoms are FCC(111) ordered whereas between the triangles the stacking is FCC(001). 
Igor Vilfan, Thierry Deutsch, Frederic Lancon and Gilles Renaud