Ab Initio Study of Surface Stresses of Charged Au films
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0924-Z01-09
Ab Initio Study of Surface Stresses of Charged Au films Yoshitaka Umeno1,2, Joerg Weissmueller3,4, Christian Elsaesser2,5, Bernd Meyer6, and Peter Gumbsch2,5 1 Dept. of Mechanical Engineering and Science, Kyoto University, Yoshida-hommachi, Sakyo-ku, Kyoto, Kyoto, 606-8501, Japan 2 IZBS, Universitaet Karlsruhe, Karlsruhe, Karlsruhe, 76131, Germany 3 Forschungszentrum Karlsruhe GmbH, Karlsruhe, Karlsruhe, 76021, Germany 4 Universitaet des Saarlandes, Saarbruecken, Saarbruecken, 66041, Germany 5 Fraunhofer-Institut fuer Werkstoffmechanik IWM, Freiburg, Freiburg, 79108, Germany 6 Ruhr-Universitaet Bochum, Bochum, Bochum, 44780, Germany ABSTRACT It has been observed in experiments that charging of nanometer-sized porous material can lead to expansion or contraction of this material. This effect can be explained by a change in surface stress as a function of surface electron charge density. Here, we employ ab initio density functional calculations using a mixed-basis pseudopotential approach to study the change in surface stresses, f, as a function of surface charge density, q for Au thin films with (111) and (100) surfaces. The derivative of the surface stress with respect to the charge, ∂f/∂q, at equilibrium is related to and can be evaluated from ∂µ/∂e of an uncharged slab, where µ is the chemical potential of the electrons in the slab and e the tangential strain. The responses of the (111) and (100) surfaces to charging are evaluated in this way as –1.86 V and –0.90 V, respectively. The calculated values compare well to experimental observations (–0.9 V). INTRODUCTION Experiments have shown that charging of nanometer-sized porous material can lead to expansion or contraction of this material [1,2]. This can be explained as an effect of surface charge on surface stress, which has been experimentally observed in experiments on macroscopic single crystal surfaces of some metals, as reviewed in Refs. [3,4]. The aim of this paper is to study the effect of charging on surface stress by ab initio methods in order to test whether this explanation is appropriate. While ab initio simulations of surface properties like relaxation of charged or uncharged surfaces have been performed before, surface stress response to electronic charging has not been directly calculated so far. We employ ab initio density functional calculations using a mixed-basis pseudopotential approach [5-7] for Au slab models with (111) and (100) surfaces to calculate the change in surface stress with changing surface charge. METHODOLOGY Surface stress response to surface charge What is to be studied is how the surface free energy density, ψ(q, e), reacts to variations in surface excess charge density, q, and in tangential strain, e. We refer the densities ψand q to the area, A, of the undeformed surface, in other words, we use Lagrangian coordinates. Note that a positive q indicates a deficit of electrons. We consider only biaxial strain, exx = eyy, and write e = exx+ eyy. The subscripts x and y relate to the two coordinate axes in the plane. T
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