Faulkner, J. Samuel

Within the Green's function approach to the multiple scattering theory, we present a different formalism for the screened Korringa-Kohn-Rostoker (KKR) scheme. In addition, we investigate the convergence properties of the screened KKR by performing total energy and density of states calculations for a fcc copper. Finally, we introduce a new approach to (near) tight binding calculations of the screened tau-matrix that yields total energies within the desired accuracy.

The embedded cluster Monte Carlo (ECMC) method which combines the Korringa-Kohn-Rostoker coherent potential approximation embedded cluster method (KKR-CPA-ECM) and the Monte Carlo method has been developed in order to study phase diagrams of binary alloys. The KKR-CPA-ECM provides interchange energies to the Monte Carlo code. In this thesis, a pair-interaction (PI) method is used to provide interchange energies to the Monte Carlo code. The code of the PI method is obtained based on the KKR-CPA-ECM code. The interchange energies of Cu0.5 Zn0.5 alloys are calculated with the PI method. The critical temperature and the phase boundary of Cu-Zn alloys are obtained by carrying out both Monte Carlo calculations with above interchange energies and the ECMC calculations. A comparison between the results of both methods is made.

The QKKR method is a recently invented band theory with remarkable advantages of fast computational speed and no special requirements on the one electron potential. It has been successfully applied to the band structure calculation for simple crystals. A program for QKKR band theory calculations for complex crystals (more than one atom per unit cell) is developed and applied to PdH. It is shown that, compared with the KKR method, the QKKR method is more efficient and yields very accurate results in the range of energies in which we are interested. Unlike other band theories, the QKKR requires the expansion of a three dimensional step function in real spherical harmonics. A general method for evaluating this expansion is established in this thesis.

The purpose of this thesis is to generate a starting potential from Thomas-Fermi theory and verify that this leads to expedient convergence of the energy eigenvalues. The potential was generated for various elements, representative of the 3d and 4d elements, as well as the simple metals, for different lattice constants. They were inserted into a quadratic Korringa-Kohn-Rostoker band theory program. They lead to self-consistent results at a faster rate than the potentials given by Moruzzi, Janak, and Williams for lattice constants for which the lattice was not in equilibrium.