Elastic origin of the O/Cu(1 1 0) self-ordering evidenced by GIXD G. Pr  evot a, * , B. Croset a , Y. Girard a , A. Coati b , Y. Garreau b , M. Hohage c , L.D. Sun c , P. Zeppenfeld c a Groupe de Physique des Solides, UMR CNRS 75-88, Universit es Paris 6 et 7, Campus Boucicaut, 140, rue de Lourmel, 75015 Paris, France b LURE, CNRS-MRES-CEA, B^ at. 209D, Centre Universitaire Paris-Sud, BP 34, 91898 Orsay Cedex, France c Institut f€ ur Experimentalphysik, Johannes Kepler Universit€ at, A-4040 Linz, Austria Received 26 September 2003; accepted for publication 14 November 2003 Abstract We have studied by grazing incidence X-ray diffraction the self-ordering of the Cu–CuO stripe pattern. By com- paring the experimental results to molecular dynamics simulations and anisotropic linear elastic calculations, we have been able to determine the atomic relaxations within the Cu substrate. The results show the importance of the crys- talline anisotropy in the relaxation field. These relaxations are due to the surface stress difference Dr between oxygen- covered and bare Cu(1 1 0) regions. For the different oxygen coverages studied, we have always found Dr ¼ 1:0  0:1 Nm 1 . This surface stress difference is shown to be the origin of the self-ordering. Ó 2003 Published by Elsevier B.V. Keywords: X-ray scattering, diffraction, and reflection; Surface stress; Copper; Oxygen; Low index single crystal surfaces 1. Introduction Since the first theoretical predictions of self- ordering of two phases on a surface [1,2], different systems have been shown to exhibit stable 1D [3–6] or 2D patterns [7–11]. Such systems are considered promising templates for the growth of well-defined nanostructures [12]. In the model of Marchenko– Vanderbilt [1,13], self-ordering results from the competition between a long-range relaxation en- ergy and a short-range boundary creation energy. Until recently, it was generally assumed that the long-range term was a substrate-mediated elastic interaction, due to the difference in surface stress between the two phases, although an electrostatic dipolar interaction, due to a difference in work function should display the same functional dependence and thus be difficult to separate from the elastic contribution [13]. For the N/Cu(1 0 0) system, ion channelling [14] and grazing incidence X-ray diffraction (GIXD) [15] experiments have evidenced for the first time the origin of the long- range interaction. For this system, the elastic interaction energy is 3000 times larger than the * Corresponding author. Tel.: +33-1-44-27-46-53; fax: +33-1- 43-54-28-78. E-mail address: prevot@gps.jussieu.fr (G. Pr evot). 0039-6028/$ - see front matter Ó 2003 Published by Elsevier B.V. doi:10.1016/j.susc.2003.11.020 Surface Science 549 (2004) 52–66 www.elsevier.com/locate/susc