Formation energies of metallic voids, edges, and steps: Generalized liquid-drop model

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 Pad\'e 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 \ensuremath{\theta} is estimated to be \ensuremath{\gamma}(\ensuremath{\pi}-\ensuremath{\theta})/4, where \ensuremath{\gamma} is the intrinsic curvature energy. The step energy is estimated as (n-2+\ensuremath{\pi}/2)\ensuremath{\sigma}d, where \ensuremath{\sigma} is the intrinsic surface energy, n\ensuremath{\ge}1 is the number of atomic layers at the step, and d is the layer height.