The Stability of the Low Temperature Surface Reconstruction in Au(111)
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The Stability of the Low Temperature Surface Reconstruction in Au(111) Todd M. Trimble, Robert C. Cammarata Johns Hopkins University, Department of Materials Science and Engineering, Baltimore, MD 21218, USA ABSTRACT We have performed computer simulation studies on the 22x√3 surface reconstruction of Au(111). This reconstruction involves a uniaxial contraction of the top monolayer corresponding to a surface strain of about 4.3% and has been observed to be the stable structure for clean surfaces at low temperatures. A continuum model yields a stability criterion that depends on the knowledge of a small number of measurable physical quantities: surface stress f, surface free energy γ, lattice parameter a0 and shear modulus µ . The simulations using EAM potentials accurately reproduce many observed features of the reconstruction and tend to support the continuum model and the resulting stability criterion. INTRODUCTION Several of the low-index surfaces of the 4d and 5d transition and noble metals are known to reconstruct. These include Au and Pt (111), and Au, Pt and Ir (100) and (110) surfaces. For (111) oriented surfaces reconstructions can be considered incorporative (or contractive) since they involve an increase in the atomic density of the top monolayer, resulting in a contraction of the surface layer with respect to the underlying lattice. This contraction can be isotropic (as in Au and Pt(111) above 0.65Tm, where Tm is the melting temperature) or uniaxial (as in Au(111) at lower temperatures). In either case the thermodynamic surface quantities of surface stress f and surface free energy γ of the corresponding unreconstructed 1x1 surfaces are seen as important physical parameters in the stabilization of the higher density surface phase. A continuum analysis of the energetics of the reconstruction that extended an analysis by Herring [2] was given in [1]. Restricting attention to the case of uniaxial contraction seen on clean Au(111) at room temperature (as well as locally on Pt(111)), the free energy difference per unit area between the reconstructed and unreconstructed systems is given by: ∆F = (f-γ)ε - αµbε +Ehε2/2(1-ν2),
(1)
where ε is the one-dimensional strain associated with the contraction, µ is the shear modulus, b is the Burgers vector, E is Young’s modulus, h is the thickness of the surface layer, ν is Poisson’s ratio and α=[4π(1-ν)]-1. The first term on the right-hand side represents to first order in ε the change in surface free energy upon reconstruction and is the driving force. The other term linear in ε is the energy cost associated with the disregistry, here modeled as a series of misfit dislocations. Finally, the third term represents the elastic energy of the strained surface layer, which presumably is important only for large enough contractions. By setting ∆F = 0, and considering small ε, a condition for the instability of the unreconstructed surface is: β = (f-γ)/µb > α=[4π(1-ν)]-1 ≈ 0.1. P3.22.1
(2)
When used with ab initio values for f and γ this criterion is very successful in pred
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