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##### Formation energies of metallic voids, edges and steps

**Authors**: J. P. Perdew, P. Ziesche, and C. Fiolhais

**Ref.**: Physical Review B **47**, 16460-16463 (1993)

**Abstract**: The void formation energy is the work needed to create the curved surface of a void. For a spherical hole in a homogeneous metal (jellium or stabilized jellium), the void formation energy is calculated for large radii from the liquid-drop model (surface plus curvature terms), and for small radii from Perturbation theory. A Pade approximation is proposed to link these limits. For radii greater than or equal to that of a single atom or monovacancy, the liquid-drop model is found to be usefully accurate. Moreover, the predicted monovacancy formation energies for stabilized jellium agree reasonably well with those measured for simple metals. These results suggest a generalized liquid-drop model of possible high accuracy and explanatory value for the energetics of stable metal surfaces curved on the atomic scale (crystal faces, edges, corners, etc.). The bending energy per unit length for an edge at angle theta is estimated to be gamma(pi - theta)/4, where gamma is the intrinsic curvature energy. The step energy is estimated as (n - 2 + pi/2)sigmad, where or is the intrinsic surface energy, n greater-than-or-equal-to 1 is the number of atomic layers at the step, and d is the layer height.