Electronic Structure of Disordered Alloys, Surfaces and Interfaces

At present, there is an increasing interest in the prediction of properties of classical and new materials such as substitutional alloys, their surfaces, and metallic or semiconductor multilayers. A detailed understanding based on a thus of the utmost importance for fu microscopic, parameter-free approach is ture developments in solid state physics and materials science. The interrela tion between electronic and structural properties at surfaces plays a key role for a microscopic understanding of phenomena as diverse as catalysis, corrosion, chemisorption and crystal growth. Remarkable progress has been made in the past 10-15 years in the understand ing of behavior of ideal crystals and their surfaces by relating their properties to the underlying electronic structure as determined from the first principles. Similar studies of complex systems like imperfect surfaces, interfaces, and mul tilayered structures seem to be accessible by now. Conventional band-structure methods, however, are of limited use because they require an excessive number of atoms per elementary cell, and are not able to account fully for e.g. substitu tional disorder and the true semiinfinite geometry of surfaces. Such problems can be solved more appropriately by Green function techniques and multiple scattering formalism.

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1 Introduction.- 1.1 Electronic Structure of Solids.- 1.2 Systems with Reduced Symmetry.- 1.3 Tight-Binding Approximation.- 1.4 Resolvents and Green Functions.- References.- 2 Linear Muffin-Tin Orbital (LMTO) Method.- 2.1 Secular Equation.- 2.2 Variational Principle.- References.- 3 Green Function Method.- 3.1 Green Functions in Solids.- 3.2 Tight-Binding LMTO Method.- 3.3 Relation to the KKR Method.- 3.4 Green Functions in Layered Systems.- 3.5 Calculation of Observables.- References.- 4 Coherent Potential Approximation (CPA).- 4.1 Configurational Average of Green Function.- 4.2 Single-Site Approximation.- 4.3 Calculation of Observables.- 4.4 Properties and Limitations of the CPA.- References.- 5 Selfconsistency Within Atomic Sphere Approximation.- 5.1 Charge Selfconsistency.- 5.2 Electrostatic (Madelung) Fields.- 5.3 Total Energy.- References.- 6 Relativistic Theory.- 6.1 Relativistic TB-LMTO Method: Non-Magnetic Case.- 6.2 Relativistic TB-LMTO Method: Spin-Polarized Case.- References.- 7 Bulk Systems, Overlayers and Surfaces.- 7.1 Bulk Elemental Metals.- 7.2 Bulk Transition-Metal Alloys.- 7.3 Clean Surfaces and Overlayers.- 7.4 Random Overlayers.- 7.5 Surfaces of Random Alloys.- References.- 8 Magnetic Properties.- 8.1 Ferromagnetic Bulk Alloys.- 8.2 Magnetism of Surfaces and Interfaces.- 8.3 Disordered Local Moments.- References.- 9 Effective Interatomic Interactions in Alloys.- 9.1 Ising Model for Alloys.- 9.2 Generalized Perturbation Method.- 9.3 Bulk Systems.- 9.4 Surfaces.- 9.5 Concluding Remarks.- References.- 10 Numerical Implementation.- 10.1 Tight-Binding Structure Constants.- 10.2 Radial Schrödinger and Dirac Equations.- 10.3 Complex Contour Energy Integration.- 10.4 Analytic Continuation.- 10.5 Brillouin Zone Integration.- 10.6 Surface Green Functions.-10.7 Coherent Potential Approximation.- 10.8 Local Spin Density Approximation.- References.