Binding energy

Abstract: The aim of this paper is to advocate the usefulness of the spin-density-functional (SDF) formalism. The generalization of the Hohenberg-Kohn-Sham scheme to and SDF formalism is presented in its thermodynamic version. The ground-state formalism is extended to more general Hamiltonians and to the lowest excited state of each symmetry. A relation between the exchange-correlation functional and the pair correlation function is derived. It is used for the interpretation of approximate versions of the theory, in particular the local-spin-density (LSD) approximation, which is formally valid only in the limit of slow and weak spatial variation in the density. It is shown, however, to give good account for the exchange-correlation energy also in rather inhomogeneous situations, because only the spherical average of the exchange-correlation hole influences this energy, and because it fulfills the sum rule stating that this hole should contain only one charge unit. A further advantage of the LSD approximation is that it can be systematically improved. Calculations on the homogeneous spin-polarized electron liquid are reported on. These calculations provide data in the form of interpolation formulas for the exchange-correlation energy and potentials, to be used in the LSD approximation. The ground-state properties are obtained from the Galitskii-Migdal formula, which relates the total energy to the one-electron spectrum, obtained with a dynamical self-energy. The self-energy is calculated in an electron-plasmon model where the electron is assumed to couple to one single mode. The potential for excited states is obtained by identifying the quasiparticle peak in the spectrum. Correlation is found to significantly weaken the spin dependence of the potentials, compared with the result in the Hartree-Fock approximation. Charge and spin response functions are calculated in the long-wavelength limit. Correlation is found to be very important for properties which involve a change in the spinpolarization. For atoms, molecules, and solids the usefulness of the SDF formalism is discussed. In order to explore the range of applicability, a few applications of the LSD approximation are made on systems for which accurate solutions exist. The calculated ionization potentials, affinities, and excitation energies for atoms propose that the valence electrons are fairly well described, a typical error in the ionization energy being 1/2 eV. The exchange-correlation holes of two-electron ions are discussed. An application to the hydrogen molecule, using a minimum basis set, shows that the LSD approximation gives good results for the energy curve for all separations studied, in contrast to the spin-independent local approximation. In particular, the error in the binding energy is only 0.1 eV, and bond breaking is properly described. For solids, the SDF formalism provides a framework for band models of magnetism. An estimate of the splitting between spin-up and spin-down energy bands of a ferromagnetic transition metal shows that the LSD approximation gives a correction of the correct sign and order of magnitude to published $X\ensuremath{\alpha}$ results. To stimulate further use of the SDF formalism in the LSD approximation, the paper is self-contained and describes the necessary formulas and input data for the potentials.

Abstract: Ferrous (Fe2+) and ferric (Fe3+) compounds were investigated by XPS to determine the usefulness of calculated multiplet peaks to fit high-resolution iron 2p3/2 spectra from high-spin compounds. The multiplets were found to fit most spectra well, particularly when contributions attributed to surface peaks and shake-up satellites were included. This information was useful for fitting of the complex Fe 2p3/2 spectra for Fe3O4 where both Fe2+ and Fe3+ species are present. It was found that as the ionic bond character of the iron —ligand bond increased, the binding energy associated with either the ferrous or ferric 2p3/2 photoelectron peak also increased. This was determined to be due to the decrease in shielding of the iron cation by the more increasingly electronegative ligands. It was also observed that the difference in energy between a high-spin iron 2p3/2 peak and its corresponding shake-up satellite peak increased as the electronegativity of the ligand increased. The extrinsic loss spectra for ion oxides are also reported; these are as characteristic of each species as are the photoelectron peaks. Copyright © 2004 John Wiley & Sons, Ltd.

Abstract: Sputtering of a target by energetic ions or recoil atoms is assumed to result from cascades of atomic collisions. The sputtering yield is calculated under the assumption of random slowing down in an infinite medium. An integrodifferential equation for the yield is developed from the general Boltzmann transport equation. Input quantities are the cross sections for ion-target and target-target collisions, and atomic binding energies. Solutions of the integral equation are given that are asymptotically exact in the limit of high ion energy as compared to atomic binding energies. Two main stages of the collision cascade have to be distinguished: first, the slowing down of the primary ion and all recoiling atoms that have comparable energies---these particles determine the spatial extent of the cascade; second, the creation and slowing down of low-energy recoils that constitute the major part of all atoms set in motion. The separation between the two stages is essentially complete in the limit of high ion energy, as far as the calculation of the sputtering yield is concerned. High-energy collisions are characterized by Thomas-Fermi-type cross sections, while a Born-Mayer-type cross section is applied in the low-energy region. Electronic stopping is included when necessary. The separation of the cascade into two distinct stages has the consequence that two characteristic depths are important for the qualitative understanding of the sputtering process. First, the scattering events that eventually lead to sputtering take place within a certain layer near the surface, the thickness of which depends on ion mass and energy and on ion-target geometry. In the elastic collision region, this thickness is a sizable fraction of the ion range. Second, the majority of sputtered particles originate from a very thin surface layer (\ensuremath{\sim}5 \AA{}), because small energies dominate. The general sputtering-yield formula is applied to specific situations that are of interest for comparison with experiment. These include backsputtering of thick targets by ion beams at perpendicular and oblique incidence and ion energies above \ensuremath{\sim}100 eV, transmission sputtering of thin foils, sputtering by recoil atoms from $\ensuremath{\alpha}$-active atoms distributed homogeneously or inhomogeneously in a thick target, sputtering of fissionable specimens by fission fragments, and sputtering of specimens that are irradiated in the core of a reactor or bombarded with a neutron beam. There is good agreement with experimental results on polycrystalline targets within the estimated accuracy of the data and the input parameters entering the theory. There is no need for adjustable parameters in the usual sense, but specific experimental setups are discussed that allow independent checks or accurate determination of some input quantities.