Real-space Multiple-scattering Theory Research Articles

Real-space multiple-scattering theory of XMCD including spin-orbit interaction in scattering process

The effects of the spin-orbit interaction on surrounding atoms for XMCD spectra are studied by a real-space multiple-scattering theory. The present numerical calculation for Fe K-edge XMCD spectra from BCC iron demonstrates the importance of the spin-orbit interaction on scattering atoms, which has been disregarded in previous works. These effects will be inevitable for K-edge XMCD analyses of light elements surrounded by heavy magnetic atoms.

Electronic structure of GaInN semiconductors investigated by x-ray absorption spectroscopy

We have investigated the electronic structure of GaInN semiconductors by performing x-ray absorption near-edge fine structure (XANES) spectroscopy at Ga K-edge and self-consistent-field real-space multiple-scattering theory calculations. It was demonstrated that the nondestructive Ga K-edge XANES spectra can be used as the fingerprints of structure and composition for GaInN. The theoretical calculations gave a reasonable reproduction of the experimental spectral features. The results revealed that the combination of the experimental XANES and the theoretical calculations is a powerful tool for studying the electronic structure of GaInN semiconductors.

X-ray absorption near-edge fine structure study of AlInN semiconductors

We have carried out the x-ray absorption near-edge fine structure (XANES) measurements of AlInN at AlK edge and the self-consistent-field real-space multiple-scattering theory calculations. It was demonstrated that the AlK-edge XANES spectra of AlInN are the fingerprints of their composition. The theoretical results could give a reasonable reproduction of the experimental spectral structures. This type of combined use of the experimental XANES and the theoretical calculations must be a powerful tool for systematic and qualitative analysis of the structural and electronic structures of nitride semiconductors.

Mass absorption coefficient of tungsten for 1600–2100 eV

The transmission of soft x rays with photon energies from 1606 eV to 2106 eV was measured for tungsten using thin-film samples and a synchrotron source. This region includes the ${M}_{\mathrm{IV}}$ and ${M}_{\mathrm{V}}$ edges. The two tungsten films had thicknesses of $107.7\ifmmode\pm\else\textpm\fi{}10 \mathrm{nm}$ and $51.5\ifmmode\pm\else\textpm\fi{}10 \mathrm{nm};$ the intensity of the transmitted x rays was measured with a silicon photodiode. The values for the mass absorption coefficient reported here were determined from the ratios of the transmission through the two samples, i.e., through a net $56.2\ifmmode\pm\else\textpm\fi{}14 \mathrm{nm}$ of tungsten, and some additional constant factors. The ${M}_{\mathrm{V},\mathrm{I}\mathrm{V}}$ edges have widths (10%--90% after background subtraction) of $33\ifmmode\pm\else\textpm\fi{}5 \mathrm{eV}$ and $28\ifmmode\pm\else\textpm\fi{}5 \mathrm{eV},$ respectively, compared to zero width in all x-ray tables based on atomic form factors and to 41 eV and 44 eV within a real-space multiple-scattering theory. The measurements are relevant to microspectroscopy and microtomography of integrated circuit interconnects and may be applicable to accurate measurement of the mass absorption coefficients of similar dense elements.

Efficient determiniation of multilayer relaxation in the Pt(210) stepped and densely kinked surface.

The multilayer relaxation of the Pt(210) stepped and kinked surface is analyzed by low-energy-electron diffraction. This is the first application of the new real-space multiple-scattering theory of LEED, designed specifically for such open surfaces where conventional theories fail. Combined with an automated tensor LEED method, it efficiently detects nonalternating atomic relaxations which are oriented primarily perpendicular to the surface. These relaxations are in qualitative agreement with new embedded-atom-method results.

The Real-Space Multiple-Scattering Theory and the Electronic Structure of Grain Boundaries.

AbstractWe describe the recently developed real-space multiple-scattering theory (RSMST), which is designed for performing first-principles electronic-structure calculations of extended defects, such as surfaces and interfaces including atomic relaxations and with or without impurities, without using artificial periodic boundary conditions. We present the results of non-charge-selfconsistent RSMST calculations of the local electronic densities of states at twist and tilt grain boundaries in fcc Cu and bcc Nb, and report on progress towards the implementation of charge self-consistency and total-energy capabilities.

Real-Space Multiple Scattering Theory Method: Formalism and Applications

ABSTRACTDifferent forms of the real-space multiple scattering theory (RS-MST) formalism are compared in order to understand its convergence behavior with respect to truncation in the angular momentum expansions. In particular the so-called “folding method” or (1,n) mode is considered, in which the renormalized t-matrix T of the semi-infinite system has the dimension of n (n > 1) repeating units and the self-consistent equation for T is constructed by adding and contracting one such unit. It has been demonstrated in previous studies of layered structures that the folding method converges rapidly in both angular momentum (L) and site (n) indices and yields accurate results. The convergence behavior is an important factor to be considered in applying the various forms of the RS-MST method to layered structures as well as other systems with extended defects.

Self-Consistent Electronic-Structure Calculations for Interface Geometries

ABSTRACTWe describe a technique for computing self-consistent electronic structures and total energies of planar defects, such as interfaces, which are embedded in an otherwise perfectcrystal. As in the Layer Korringa-Kohn-Rostoker approach, the solid is treated as a set of coupled layers of atoms, using Bloch's theorem to take advantage of the two-dimensional periodicity of the individual layers. The layers are coupled using the techniques of the Real-Space Multiple-Scattering Theory, avoiding artificial slab or supercell boundary conditions. A total-energy calculation on a Cu crystal, which has been split apart at a (111) plane, is used to illustrate the method.

A real-space multiple scattering theory of low energy electron diffraction: a new approach for the structure determination of stepped surfaces

A new theory of Low Energy Electron Diffraction (LEED) is presented in which the relevant multiple scattering equations are solved in the angular momentum representation within the framework of real-space multiple scattering theory (RS-MST). This approach avoids the plane wave basis used in many conventional LEED techniques and its associated limitations when applied to the calculation of LEED intensities from open surfaces containing small bulk interplanar spacings. In particular, high Miller index, stepped surfaces which lie beyond the present capabilities of conventional LEED, can now be treated in a relatively efficient and convergent manner. The new theory is tested by evaluating I–V spectra from the (100), (311), (331) surfaces of Cu which are compared with the results of a layer doubling (LD) LEED calculation. Excellent agreement is obtained in the (100) and (311) cases, for which the LD approach is expected to be applicable. The (311) surface is about the highest index fcc surface which can reasonably be attempted with the existing approaches. The results obtained for the case of the (331) surface using the LD and the RS-MST approaches agree up to about E = 100 eV, beyond which the LD process fails to converge. We discuss and contrast the convergence properties of both methods.

Electronic Structure Calculations of Σ5 Grain Boundaries in Cu

Extended AbstractIn a recent publication [1], we presented results of electronic-structure calculations on Σ5 grain boundaries in Cu. These calculations were performed using the real-space multiplescattering theory (RSMST), a first-principles method which does not rely on translational invariance and Bloch's theorem [2, 3], and hence avoids the problems associated with treating interfaces in a periodic repeating slab geometry. A brief summary of this method follows.The RSMST is based on the concept of semi-infinite periodicity (SIP), defined as the regular repetition along a given direction of a scattering unit (atom, planes of atoms, etc.), or a set of such units. Systems with SIP possess the property of removal invariance, which states that the scattering properties (scattering matrices) of any such system remain invariant when an integral number of scattering units is removed from, or added to, the free end of the system. Using this property in conjunction with multiple-scattering theory, one can determine the electronic Green function, and hence all one-particle quantities such as the density of states (DOS), directly in real space.The essence of the method consists in a prescription for the proper renormalization of the scattering properties of the boundary sites of a cluster of atoms. Unrenormalized or “bare” sites in the interior of the cluster describe the region of interest, such as a grain boundary, while the renormalized boundary sites represent the infinite medium surrounding the cluster. This “dressing up” of the cluster is done independently for each part of a system that is characterized by its own SIP, so that grain boundaries between essentially arbitrary crystal structures can be treated.The calculations described previously [1] used given atomistic configurations and electronic one-particle potentials and computed the local DOS at atoms of interest within the grain boundaries. We are currently extending our method to incorporate charge self-consistency and total-energy capabilities. In connection with this, we have implemented four different methods of expressing mathematically the invariance properties of semi-infinite systems, and are evaluating them for optimal rates of convergence and computational efficiency. Calculations on Cu (100) monolayers will be used to illustrate these methods.

The Electronic Structure of Grain Boundaries in NB

ABSTRACTWe present first-principles calculations of the electronic structure of Nb grain boundaries. These are the first such calculations for a bcc metal using the real-space multiple-scattering theory (RSMST). Local densities of states near a Σ5 twist grain boundary are compared to those for bulk Nb.

FIRST-PRINCIPLES CALCULATIONS OF THE ELECTRONIC STRUCTURE OF GRAIN BOUNDARIES

FIRST-PRINCIPLES CALCULATIONS OF THE ELECTRONIC STRUCTURE OF GRAIN BOUNDARIES

Electronic structure of grain boundaries.

We report the first application of the recently developed real-space multiple-scattering theory to the calculation of the local density of states (DOS) at metallic grain boundaries. Our method treats properly the semi-infiite nature of the material on either side of the boundary. We exhibit and compare local DOS's at selected sites for both unrelaxed and relaxed \ensuremath{\Sigma}5(100) 36.9\ifmmode^\circ\else\textdegree\fi{} twist and \ensuremath{\Sigma}5(310) tilt grain boundaries in Cu, where the atomic coordinates of the relaxed configurations were obtained with the Embedded Atom Method.

Multiple-scattering solutions to the Schrödinger equation for semi-infinite layered materials.

The electronic structure of a layered system, such as a bulk, its surface, or internal interface, is formulated solely in terms of the angular-momentum matrix elements of the isolated layer scattering operators and structural Green's functions that couple the layers together. In contrast to the traditional layer-doubling technique, based on plane-wave expansions, the scattering matrix of the semi-infinite solid is constructed from the solution of a self-consistent equation using the real-space multiple-scattering theory approach. Results of calculations using this new technique are presented and compared with those based on layer coupling with plane-wave expansions.

Real-space, multiple-scattering-theory method for the calculation of x-ray bremsstrahlung isochromat spectra.

We introduce a new method for the calculation of the x-ray bremsstrahlung isochromat spectra. The method is worked out within a real-space multiple-scattering theory and disposes of the conceptual and practical difficulties inherent in the band-structure calculations. Our concept makes possible to calculate spectra in both near and extended energy regions even for systems lacking translational symmetry. The method is illustrated through a calculation of four isochromat spectra of Cu and Pd. For the first time the extended x-ray-isochromat fine structure is calculated.

Real-space multiple-scattering theory and the electronic structure of systems with full or reduced symmetry.

We present a new real-space multiple-scattering-theory method for the solution of the Schr{umlt o}dinger equation and the calculation of the electronic structure of solid materials with full or reduced symmetry. The method is based on the concept of semi-infinite periodicity (SIP), rather than translational invariance, and on the property of removal invariance of the scattering matrix of systems with SIP. This latter property allows one to replace the usual Brillouin-zone integrals in reciprocal space by a self-consistency equation for the {ital t} matrix, which is sufficient for the determination of the Green function and related properties. Because it is developed entirely in direct space, the method provides a unified treatment of the electronic structure of bulk materials, surfaces, interfaces and grain boundaries (coherent or incoherent), impurities of interstitial or substitutional kinds, and can be easily extended to treat concentrated, substitutionally disordered alloys. One of its advantages over methods based on Bloch's theorem and reciprocal space is the great simplicity of setting up and running the associated computer codes even for complex structures, and structures with reduced or no symmetry that lie outside the realm of applicability of conventional methods. We present the results of model calculations for one-dimensional and three-dimensionalmore » model systems as well as for three-dimensional realistic materials. Where appropriate, these results are compared with those obtained through conventional techniques, and give an indication of the method's flexibility and reliability. Our applications of this method to this point are discussed, and our plans for future development are presented.« less

The Electronic Structure pf Σ5 Grain Boundaries in CU

ABSTRACTWe present first-principles calculations of the densities of states (DOS's) of unrelaxed and relaxed twist and tilt grain boundaries (GB's) in Cu. The relaxed configurations were obtained through the use of the Embedded Atom Method (EAM), while the DOS's were calculated using the real-space multiplescattering theory (RSMST) approach recently introduced in the literature. The DOS's of GB's are compared against those of bulk materials as well as against one another. Although the RSMST calculations are still not self-consistent, these comparisons allow us to verify certain expected trends in the DOS's, and to verify the usefulness and reliability of our method.