Estudo Geralhttps://estudogeral.sib.uc.ptThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Sat, 04 Jul 2020 12:42:04 GMT2020-07-04T12:42:04Z5021Formation energies of metallic voids, edges, and steps: Generalized liquid-drop modelhttp://hdl.handle.net/10316/12331Title: Formation energies of metallic voids, edges, and steps: Generalized liquid-drop model
Authors: Perdew, John P.; Ziesche, Paul; Fiolhais, Carlos
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 Padé 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 θ is estimated to be γ(π-θ)/4, where γ is the intrinsic curvature energy. The step energy is estimated as (n-2+π/2)σd, where σ is the intrinsic surface energy, n≥1 is the number of atomic layers at the step, and d is the layer height
Tue, 15 Jun 1993 00:00:00 GMThttp://hdl.handle.net/10316/123311993-06-15T00:00:00ZSpherical voids in the stabilized jellium model: Rigorous theorems and Padé representation of the void-formation energyhttp://hdl.handle.net/10316/12333Title: Spherical voids in the stabilized jellium model: Rigorous theorems and Padé representation of the void-formation energy
Authors: Ziesche, Paul; Perdew, John P.; Fiolhais, Carlos
Abstract: We consider the energy needed to form a spherical hole or void in a simple metal, modeled as ordinary jellium or stabilized jellium. (Only the latter model correctly predicts positive formation energies for voids in high-density metals.) First we present two Hellmann-Feynman theorems for the void-formation energy 4πR2σRv(n¯) as a function of the void radius R and the positive-background density n¯, which may be used to check the self-consistency of numerical calculations. They are special cases of more-general relationships for partially emptied or partially stabilized voids. The difference between these two theorems has an analog for spherical clusters. Next we link the small-R expansion of the void surface energy (from perturbation theory) with the large-R expansion (from the liquid drop model) by means of a Padé approximant without adjustable parameters. For a range of sizes (including the monovacancy and its ‘‘antiparticle,’’ the atom), we compare void formation energies and cohesive energies calculated by the liquid drop expansion (sum of volume, surface, and curvature energy terms), by the Padé form, and by self-consistent Kohn-Sham calculations within the local-density approximation, against experimental values. Thus we confirm that the domain of validity of the liquid drop model extends down almost to the atomic scale of sizes. From the Padé formula, we estimate the next term of the liquid drop expansion beyond the curvature energy term. The Padé form suggests a ‘‘generalized liquid drop model,’’ which we use to estimate the edge and step-formation energies on an Al (111) surface
Tue, 15 Mar 1994 00:00:00 GMThttp://hdl.handle.net/10316/123331994-03-15T00:00:00Z