We investigate techniques for solving the wave equation which are based on the idea of obtaining exact local solutions within each potential cell, which are then joined to form a global solution. We derive full potential multiple scattering theory (MST) from the Lippmann-Schwinger equation and show that it as well as a closely related cellular method are techniques of this type. This cellular method appears to have all of the advantages of MST and the added advantage of having a secular matrix with only nearest neighbor interactions. Since this cellular method is easily linearized one can rigorously reduce electronic structure calculations to the problem of solving a nearest neighbor tight-binding problem.

We derive a relativistic full potential multiple scattering theory (MST) in direct analog to the non-relativistic full potential MST[1, 2]. The secular equation is derived fromi the Lippmann-Schwinger equation by expanding the wave function in terms of cell basis functions which are locally exact solutions of the Dirac equation. The relationship between this theory and currently widely used relativistic munffin-tin MST is also discussed.

Man has always been fascinated with the quest to understand the inner workings of nature at a fundamental level. According to Embedocles[1], a philosopher in ancient Greece, all material things consist of four basic elements (he called them “roots”), namely earth, water, air, and fire. Modern mail's interpretation of that statement is that earth, water and air refer to the three states of matter, i.e., solids, liquids and gasses, with fire designating a process for transforming one of those states into the other. Be that as it may, Embedocles' statement could be conceived as the first attempt to construct an alloy theory, i.e., a predictive capability of the behavior of composite systems.

We present a formulation of the Korringa-Kohn-Rostoker coherent potential approximation (KKPt-CPA) for the treatment of substitutionally disordered alloys within the KKR atomic-sphere approximation (ASA). This KKR-ASA-CPA represents the first step toward the implementation of a full cell potential CPA, and combines the accuracy of the KKR-CPA method with the flexibility of treating complex crystal structures. The accuracy of this approach has been tested by comparing the self-consistent-field (SCF) KKR-ASA-CPA calculations of Cu-Pd alloys with experimental results and previous SCF-KKR-CPA calculations.

We present a brief overview of the advanced methodology which has been recently developed to study phase stability properties of substitutional alloys, including order-disorder phenomena and structural transformations. The approach is based on the real space version of the Generalized Perturbation Method, first introduced by Ducastelle and Gautier, within the Korringa-Kohn- Rostoker multiple scattering formulation of the Coherent Potential Approximation. Temperature effects are taken into account with a generalized meanfield approach, namely the Cluster Variation Method. The viability and the predictive power of such a scheme will be illustrated by a few examples, among them: (1) the ground state properties of alloys, in particular the ordering tendencies for a series of equiatomic bcc-based alloys, (2) the computation of alloy phase diagrams with the case of fcc and bcc-based Ni-Al alloys, (3) the calculation of antiphase boundary energies and interfacial energies, and (4) the stability of artificial ordered superlattices.

A cluster expansion is used to predict the fcc groutnd states, i.e., the stable phases at zero Kelvin as a function of composition, for alloy systems. TFile internetallic structures are not assumed, but derived rigorously by minimizing the configurational energy subject to linear constraints. This ground state search includes pair and multiplet interactions which spatially extend to fourth nearest neighbor. A large number of these concentration-independent interactions are computed by the method of direct configurational averaging using a linearizedmuffin- tin orbital Hamiltonian cast into tight binding form (TB-LMTO). The interactions, derived without the use of any adjustable or experimentally obtained parameters, are compared to those calculated via the generalized perturbation method extention of the coherent potential approximation within the context of a KKR Hamiltonian (KKR-CPA-GPM). Agreement with the KKR-CPA-GPM results is quite excellent, as is the comparison of the ground state results with the fcc-based portions of the experimentally-determined phase diagrams under consideration.

We report about residual resistivity calculations for dilute Ni alloys which are based on density-functional theory and the Korringa-Kohn-Rostoker Green's-function method. The transport is described quasiclassically by means of the Boltzmann equation using a two current model for the ferromagnetic host. In particular we consider 3d, 4d, 4sp and 5sp impurities in Ni and include in addition to the impurity atom one shell of perturbed host atoms in the calculation. For the residual resistivity satisfactory agreement with the experiments is obtained in practically all cases. We clarify the role of both subbands for the transport properties.

Both the electromigration wind valence and the residual resistivity for hydrogen in all row 5 (Y,….Ag) and row 6 (La,….Au) transition metals were calculated. Host metals with a hexagonal lattice have been treated in the FCC or BCC structure. The KKR-Green function method used to describe the multiple scattering of Bloch electrons, accounts for charge transfer and lattice deformation around the interstitial hydrogen.

The list of physical properties which are important in the design of materials and which are routinely calculated from first principles within the local density approximation to density functional theory is continually growing. In this paper we discuss the application of multiple scattering theory to the calculation of the residual resistivity of disordered alloys. Progress has been made on two fronts. First, the coherent potential approximation for the resistivity, which sums to all orders a limited set of multiple scattering diagrams, has given resistivities in agreement with experiment for alloys where the site occupation is roughly random. Second, the linearized KKR was used to evaluate the Kubo formula for several large configurations of atoms and obtain the resistivity with all multiple scattering paths included. This method is not limited to random alloys, but can be applied to short range ordered and amorphous alloys provided the resistivity is high enough to limit the mean free path to a single unit cell.

Chemical disorder leads to a variety of intriguing phenomena in alloys which have yet to be fully understood, particularly those phenomena occuring when chemical and magnetic effects interplay with one another. For example, magnetic order gives rise to chemical ordering in alloys, as in Ni-rich NiFe alloys. Two examples of the interplay of chemical disorder and magnetism will be discussed. Our recently developed ab-initio Landau (mean-field) theory for calculating the chemical-chemical, magneto-chemical, and magnetic-magnetic correlation functions in substitutional random alloys is used to describe electronic/magnetic mechanisms (e.g. in FeV) which give rise to the chemical short-range order as determined by neutron, X-ray, or electron diffuse scattering intensities. New developments within this approach that account for charge rearrangement effects will be mentioned. These calculations are performed within the multiplescatteringframework, developed by Korringa, Kohn, and Rostoker (KKR), combined with the coherent potential approximation (CPA) to describe the disorder. This approach allows a firstprinciples description of the electronic structure of the high-temperature, chemically disordered state and its instability to ordering at low temperatures. This method provides not only a direct comparison of diffuse scattering data with theory but a means to understand more fully the underlying mechanisms which drive chemical and/or magnetic ordering.

The interaction between atomic and magnetic order is very strong in Ni-Pt alloys, whereas Co-Pt alloys show local magnetic properties which are independent of the composition and state of order of the system. A multiple-scattering calculation on Ni-Pt alloys is used in this paper, together with band structures for ordered compounds of both Ni-Pt and Co-Pt, to discuss the origin of the difference in properties between both alloy systems.

Progress in the calculation of the phase diagram of the Ni-Pt compounds from "first-principles" is reported. Our procedure consists of: (1) calculating total energies for ordered structures as a function of volume and including internal relaxations by means of the linear muffin-tin orbitals method within the atomic sphere approximation; (2) mapping these results onto an Ising model with effective interaction parameters; and (3) calculating the phase diagram by means of the cluster variation method. We identify the elastic energy related to the difference in the Ni and Pt lattice constant as one of the major problems in this system and discuss the convergence of the cluster expansion of the energy.

The symmetry properties of the Dirac equation, which describes electrons in relativistic quantum mechanics, is rather different from that of the corresponding Schr6dinger equation. Consequently, even when the velocity of light, c, is much larger than the velocity of an electron Vk, with wave vector, k, relativistic effects may be important. For instance, while the exchange interaction is isotropic in non-relativistic quantum mechanics the coupling between spin and orbital degrees of freedom in relativistic quantum mechanics implies that the band structure of a spin polarized metal depends on the orientation of its magnetization with respect to the crystal axis. As a consequence there is a finite set of degenerate directions for which the total energy of the electrons is an absolute minimum. Evidently, the above effect is the principle mechanism of the magneto crystalline anisotropy [1]. The following session will focus on this and other qualitatively new relativistic effects, such as dichroism at x-ray frequencies [2] or Fano effects in photo-emission from non-polarized solids [3].

We review spin polarised multiple scattering theory and show how it can provide a description of magnetic anisotropic effects in metallic systems. An interpretation in terms of the leading relativistic corrections is given; namely the interaction between spin-orbit coupling and spin polarisation. It is pointed out that it is straightforward to vary the d-rection of spin polarisation within this formalism. As simple illustrations, the cases of two and three impurities in a non-interacting relativistic' electron gas are outlined and the origin of pseudo-dipolar and Dzyaloshinski-Moriya anisotropy highlighted. We go on to compare and contrast estimates of magneto-crystalline anisotropies of transition metals with those from alternative methods. Finally we discuss the paramagnetic spin susceptibility of metals within this framework and show that this work is complementary to magnetic anisotropy energy calculations. A generalised Stoner condition for the onset and direction of the magnetisation is given. Calculations for h.c.p. metals cobalt, scandium and yttrium are presented. We conclude by pointing out that this approach can be extended to set up a theory for the dynamical susceptibility with consequent implications for anisotropy of spin wave excitations.

A KKR program for self-consistent electronic structure and total energy calculations of complex solids has been developed. This program has been used to study structural, electronic and magnetic properties of a number of solids. In this paper, we give a description of several numerical techniques used in this KKR program which might be of use to other practitioners. We also present some results obtained using this program: c/a ratio of hexagonal Y, elastic constants of Mo, TiC and MgO, and static spin susceptibility of Pd.

Analytical expressions for the total energy derivative with respect to the magnetic moment rotations have been derived in the relativistic local-spin density functional approach and multiple scattering theory. The spin-wave stiffness constant as well as the gap in the spin-wave spectrum due to relativistic anisotropy effects is calculated in KKR-ASA approximation for bcc Fe. This is compared with other theoretical calculations and available experimental data.

Applications of the spin-polarized relativistic version of multiple scattering theory (SPRKKR) to study the electronic properties of dilute and concentrated disordered alloys are presented. This approach, developed recently, allows to investigate magnetic systems containing heavy elements and also gives access to a detailed discussion of phenomena, which are linked to the simultanous presence of spin-polarisation and spin-orbit coupling. This is demonstrated by discussing the hyperfine properties of 5d-transition metals dissolved substitutionally in Fe, where pronounced relativistic effects could be found. In addition the magnetic X-ray dichroism (MXD), denoting the difference in absorption of left and right circularly polarized radiation, is studied for these dilute alloys.

To be able to deal also with concentrated alloys, we have combined the Coherent Potential Approximation (CPA) alloy theory with the SPRKKR-formalism. Results for the spin-orbit induced orbital contributions to the magnetic moments as well as the MXD in FexCol-x and CoxPtl-x clearly show that remarkable relativistic effects are present even for relatively light elements.

The consideration of spin-orbit coupling in spin-polarized electronic structure calculations leads to magnetic anisotropies and reduces the symmetry of the problem. The theory of magnetic groups is required to make full use of the remaining symmetry, which in turn then is applied to the Green's function method.

A fully relativistic layer-KKR formalism is developed for calculating the single-particle Green function in atomic layers parallel to crystalline surfaces of magnetic and nonmagnetic materials. Its application to spin-polarized photoemission is also discussed.

This article presents a brief overview of applications of multiple scattering theory to surfaces and extended defects. Discussion is given of some key issues and their practical status, and this discussion is related to the papers in the session which covered this topic at Symposium V.