We present a multiple-scattering Green's function method to calculate the electronic structure of ideal surfaces and surfaces with point defects. In our method we use the full potential in each atomic cell and describe the surface as a twodimensional defect of the bulk crystal by removing several (three to five) adjacent layers. We have implemented our method within density-functional theory in the local-spin-density approximation and present first results for the Cu (001)-surface, for magnetic monolayers on this surface and for such monolayers in bulk Cu.

Effective cluster interactions (ECI) at surfaces of substitutionally disordered alloys are determined using the generalization of the TB-LMTO-CPA method to inhomogeneous systems. Illustrative results are reported for the (Ag,Pd) alloy system.

The refractory transition metal—carbides commonly fail under stress by brittle fracture and the properties and nature of the fracture process are consequently of practical interest. We have calculated the fracture properties of titanium carbide under tensile stress using our full—potential LMTO method, a methodology which is closely related to multiple scattering theory (and includes a true interstitial region). The fracture calculation is accomplished by employing a repeated slab (or repeated cleavage separation) geometry. Within this geometry, the fracture process is simulated most simply by uniformly increasing the gap separation from zero to a distance on the order of a few atomic radii. A more sophisticated search for fracture instability involved stretching the ideal crystal and examining the separation energetics of the strained system.

Results of these calculations will be reported both for the ideal, stoichiometric titanium carbide crystal and also for systems containing carbon vacancies. We will discuss therole of such defects in modifying the bonding behavior at the cleavage plane and the resulting effect on resistance to fracture.

Two problems associated with the calculation of polar interface energies in semiconductors or insulators are discussed: (1) the stoichiometry of the associated interface region, and (2) the impossibility of constructing a supercell with two equivalent interfaces in certain cases. An approach for calculating the energy of a single interface is introduced. It utilizes local quantities obtained from supercell calcualtions and the electrostatic energy of the isolated single interface. Results are presented for GaAs inversion domain boundaries and NaCl antiphase boundaries. The problem associated with charge transfer between two different interfaces is discussed.

First principles electronic structure calculations, using the layer Korringa-Kohn-Rostoker method, are reported for isolated planar faults in TiAl. The calculated fault energies are discussed in the context of suggested superdislocation separation reactions. The influence of dilute impurities on fault energies are treated using the coherent potentialapproximation. Using this approach, the variation of fault energies in TiAl resulting from stoichiometry changes and from the addition of Mn axe calculated, and compared to recent experimental data.

Different 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.

We 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.

Within the framework of the muffin-tin multiple-scattering theory, the scattering path operators are given by the inverse of a matrix consisting of atomic t-matrices and a structural matrix. The influence of the displacement of an atomic centre on the structural matrix can be described analytically using Lie group techniques. From this analytical expression and the standard perturbation expansion of the Lippmann-Schwinger equation, it is possible to write the Green function of a disordered system as a series of terms whichare averages over configurations. These averages can be calculated analytically from themoments of the interatomic distances. Special terms of this series are then summed up toinfinity using Dyson equation. This formalism is computationally very effective to calculate electronic properties of systems with thermal or structural disorder. In this paper, the theoretical basis of this approach is briefly described and the convergence properties of the expansions are investigated.

The papers papers in this section were presented at a joint session of symposium V on Applications of Multiple Scattering Theory and of Symposium P on Disordered Systems. They show that the ideas of scattering theory can help us to understand a very broad class ofphenomena.

When light is very strongly multiply scattered by a medium, its propagation can be well described by a diffusion approximation. This allows important, measurable quantities to be calculated theoretically and interpreted. Thus, for example the total light transmitted through a sample can be used to determine the transport mean free path which characterizes the diffusive transport of the light. In addition, the distribution of path lengths followed by the diffusing light can be determined. This distribution can in turn be used to interpret the temporal fluctuations of the scattered intensity that arise due to the motion of the scattering medium. Therefore, traditional quasielastic, or dynamic, light scattering can be extended to the strongly multiple scattering limit. This technique is called Diffusing Wave Spectroscopy (DWS), and allows useful information about the dynamics of the medium to be determined. Furthermore, new physical processes can be studiedusing DWS. For example, DWS is sensitive to very small motions of colloidal particles: motion of 1 pm diameter particles can be resolved on lengths of∼ 5 Å using light with a wavelength of 0.5 μm. New physical phenomena are probed when motion on these length scales is observed. In particular, the time evolution of the hydrodynamic interaction between concentrated colloidal particles can be resolved. In addition, DWScan also probe spatially rare events since the light paths sample a large volume of the sample. This allows DWS to probe very slow dynamics, making it useful for the study of materials such as foams. This talk reviews the fundamentals of DWS and highlights some ofits unique applications.

We present a generalized coherent potential approximation for the identification of quasi propagating modes in dispersed random media and the calculation of their dispersion relations. The validity of this approach is supported by multiple-scattering calculations, numerical simulation, and comparison with experimental data on acoustic excitations in colloidal suspensions. Our theory yields excellent quantitative agreement with the measured dispersion relations and provides an explanation for the observed frequency gaps in the excitations spectra.

Spatial localization of bending waves was observed on a steel plate (72"X72"X1") decorated with lucite blocks (3.5"X3.5"X3") arranged in either a periodic or a random array. The exponential decay length of the localized modes is as short as 12 cm at 2.8 kHz, and increases with frequency as (f0 - f)-1, where f0 = 3.5 kHz is a quasi-mobility edge. The experimental data and finiteelement calculations suggest that the observed localization ofbending waves is due to the strong resonant scattering of bending waves by the shear modes of lucite/steel system. The generic nature of this localization phenomenon suggests its potential use as a attenuation mechanism for bending waves.

The properties of electric double layers near curved surfaces of arbitrary shape and genus are obtained exactly within the Debye-Hückel theory by means of multiple-scattering expansion. For smooth membranes, geometric and topological feature of the electrostatic free energy then emerge through convergent expansions in inverse powers of the principal radii of curvature. Some consequences for the electrostatic stability of various membrane shapes are considered. We also study the effects of surface singularities, e.g., wedges, on the thermodynamics of electric double layers near a rough colloid. Each wedge yields an additive contribution to the free energy that is a functionof the angle. A probabilistic Brownian representation of is given, which is entirely similar to that of vibration eigenmodes given by M. Kac long ago in “Canone hear the shape of a drum?” [Amer. Math. Monthly 73S, 1 (1966)]. The analysis yields a universal scaling law for the free energy of a rough colloid with its fractal Minkowski dimension.

This study treats the optical properties of different two-dimensional inhomogeneous systems in which localized and delocalized surface modes excited by incident light can exist. The optical response is described with the use of kinetic equations linking together different types of surface and bulk modes. It is important that both electromagnetic interactions between local modes and the dependence of the optical characteristics of centers on the local geometrical structure are taken into account.

It is shown that the behavior of experimentally observable quantities (enhancement ratioof the electric field at the surface, surface absorption, etc.) as functions of the frequency and concentration of local centers depends essentially on the excitation mechanismof local modes.

The equations of the layer-KKR method for finding the intensities of electrons diffracted by a semi-infinite layered structure are derived in a simple way by use of three identities relating spherical and plane waves and by use of a compact notation. The third identity, which transforms a sum of outgoing spherical waves on a twodimensional array intoa sum of plane waves or beams, is a very useful simplification of the derivation, which does not appear in texts on LEED. Explicit linear equations are derived for amplitudes of outgoing spherical waves produced by diffraction of an incident beam first by a singleBravais net and then generalized to a composite layer made up of several Bravais nets; matrix elements of the beam reflection and transmission matrices for a single Bravais netand for a composite layer are given, and also the exact interlayer matrix equation for the reflection matrix of the semi-infinite structure.

Recent advances in the theory of low-energy electron diffraction (LEED) are reviewed. They primarily concern methods to handle the multiple scattering of electrons in an atomiclattice. These advances have allowed the structure determination by LEED of complex surface structures, including large-unit-cell overlayers of molecules, disordered and incommensurate overlayers, complex reconstructions and adsorbate-induced relaxations.

We present an application of multiple scattering theory with “muffin-tin” potentials to the calculation of X-ray absorption cross section. We have measured and calculated the K-edge spectra of atoms in compounds with zincblende structure : SiC, ZnS. We show that some spectral features can be precisely related to the local environnement around the absorbing atom.

Because it gives direct and convenient access to the Green's function, multiple scattering theory (MST) provides a powerful machinery for the calculation of I particle observables in general and electron spectroscopies in particular.

The two techniques in which multiple scattering methods have made the biggest impact areangle-resolved photoemission and x-ray spectroscopy (absorption and emission); here the essential point is that MST allows experimental data to be analysed and modelled on the same footing as calculations of the underlying electronic structure, for both ordered and disordered systems. Applications in these areas are briefly reviewed, drawing attention to the two outstanding current deficiencies of the methodology (the use of density functional theory to describe excited states and the approximate — muffin-tin — form of the effective 1—electron potential) as well as its successes.

Current developments, particularly the treatment of relativistic and magnetic systems, the possibilities opened up by third-generation synchrotron radiation sources, and the use of parallel computing techniques, are mentioned.

The Co/Cu(100) system is the first system known where the contributions to the spin polarisation of spin-orbit coupling and the ferromagnetic overlayer were clearly distinguished experimentally. In order to get a first understanding of the photoemission data non-relativistic spin-polarized photoemission calculations are performed for one and two overlayers of Co on Cu(100).

We have developed the charge and spin selfconsistent KKR-CPA approach for a first-principles parameter free treatment of disorder effects in complex multi-component alloys. Thenature of the KKR-CPA Green's function in the complex energy plane is discussed. A generalized Lloyd formula for the density of states is obtained and some subtle features of the formalism are pointed out. We illustrate our KKR-CPA methodology by giving a number of examples of magnetic as well as non-magnetic systems. The non-magnetic cases considered are the simple cubic perovskites BaxK1−0BiO3 and BaPb—1BixO3, and the high-Te superconductor La2—xSrxCuO4 for the body-centeredtetragonal phase. The examples of magnetic systems discussed are, the the Heusler alloys Co2—xFexMnSi (L21 structure), and the semi-magnetic semiconductor Cdl—xMnxTe in the zincblende structure.