Site occupancy of chlorine on Cu„111… using normal-incidence x-ray standing waves: The energy difference between fcc and hcp hollow sites A. G. Shard* Department of Engineering Materials, Sir Robert Hadfield Building, University of Sheffield, Mappin Street, Sheffield S1 3JD, United Kingdom C. Ton-That Nanoscience Centre, University of Cambridge, 11 JJ Thomson Avenue, Cambridge CB3 0FF, United Kingdom P. A. Campbell School of Physics and Astronomy, St Andrews University, North Haugh, St Andrews, Fife KY16 9SS., United Kingdom V. R. Dhanak SRS Daresbury Laboratory and Physics Department, University of Liverpool, Warrington WA4 4AD, United Kingdom (Received 21 August 2003; revised manuscript received 21 April 2004; published 26 October 2004) It has previously been established that the lowest energy site for chlorine atoms on Cu111 is the “fcc” hollow. However, substantial population of the “hcp” hollow at room temperature indicates that there is a relatively small difference in energy between the two sites. We show that this energy difference must be less than 10 meV by measuring the relative populations using normal-incidence x-ray standing waves and compar- ing the results to Monte Carlo simulations. This result is consistent with recent density functional theory calculations which indicate an energy difference of approximately 5 meV. DOI: 10.1103/PhysRevB.70.155409 PACS number(s): 68.47.De, 68.49.Uv, 68.43.-h INTRODUCTION Most simple surfaces have well-defined sites which rep- resent the minimum energy position for adsorbate atoms. The position of such a site is usually amenable to experimental determination. Complexities arise when there are a number of different adsorption sites of similar energies which are thermally populated by adsorbate atoms. The relative popu- lation of each site is influenced by the temperature and the magnitude of energy differences between the sites. Knowl- edge of the size of these energy differences is essential to a full understanding of the system. Unfortunately, most struc- tural studies concentrate upon ordered phases in which a de- termination of such energy differences is impossible. In or- dered adlayers lateral interactions between adsorbate atoms are at least as important as adsorbate–substrate interactions in determining the populations of different sites. Therefore, one cannot deduce site energy differences by studying the site occupation of ordered phases alone and one must obtain additional information from disordered phases and from phase diagrams. To derive site energy differences from relative popula- tions it is necessary first to ensure that the system being investigated is at equilibrium and second to use an experi- mental technique that is able to quantitatively distinguish between adsorption at the various binding sites. The results must then be interpreted using simulations, since obtaining analytical solutions for site population in terms of interaction energies is generally not possible. X-ray standing wave (XSW) techniques are an excellent choice for such studies since they provide, with few assumptions, quantitative regis- try information for adsorbate atoms irrespective of order in the adsorbed over-layer. 1 This avoids a potential problem of using diffraction techniques, such as low-energy electron dif- fraction (LEED), in which ordered regions may dominate the data. In a series of experiments 2–4 Schwennicke et al. and Schwennicke and Pfnur investigated the lateral interactions of O/Ni111, using diffuse LEED results and the system phase diagram, demonstrating that both could be modeled using a Monte Carlo simulation and finding an energy differ- ence of 46 meV between the “hcp” and “fcc” hollow sites. Kadodwala et al. investigated the simultaneous adsorption of chlorine and bromine on Cu111. 5 While the main thrust of their investigation was a demonstration of the versatility of normal incidence XSW (NIXSW), a site energy difference between “fcc” and “hcp” hollows of 13.5± 5 meV was also calculated. Although details of the calculation were not pro- vided, this result is consistent with the two level partition function given in Eq. (1) in which N x is the number of atoms in site x and  is the energy difference between the two sites. N hcp N fcc = exp-   kT . 1 Use of this equation relies on the assumption that the number of available “hcp” sites is always equal to the number of available “fcc” sites. It is reasonable to suppose that adsorp- tion at a site will preclude another atom adsorbing at the same site. If one considers only the limitation of one adsorbed atom per site, the correct expression can be easily derived and is given in Eq. (2) where theta is fractional coverage following the standard definition (note that a frac- tional coverage of 2 is obtained when all hollow sites are occupied). PHYSICAL REVIEW B 70, 155409 (2004) 1098-0121/2004/70(15)/155409(8)/$22.50 ©2004 The American Physical Society 70 155409-1