ELECTRONIC STRUCTURE OF DISORDERED ALLOYS, SURFACES AND INTERFACES

Transcription

1 ELECTRONIC STRUCTURE OF DISORDERED ALLOYS, SURFACES AND INTERFACES llja TUREK Institute of Physics of Materials, Brno Academy of Sciences of the Czech Republic Vaclav DRCHAL, Josef KUDRNOVSKY Institute of Physics, Prague Academy of Sciences of the Czech Republic and Institute for Technical Electrochemistry Technical University of Vienna, Austria Mojmfr SOB Institute of Physics of Materials, Brno Academy of Sciences of the Czech Republic Peter WEINBERGER Institute for Technical Electrochemistry Technical University of Vienna, Austria KLUWER ACADEMIC PUBLISHERS Boston/London/Dordrecht

2 CONTENTS PREFACE X] INTRODUCTION Electronic Structure of Solids Born-Oppenheimer (Adiabatic) Approximation Selfconsistent Field Approximation Density Functional Theory Local Density Approximation to the Exchange-Correlation Functional Beyond the Local Density Approximation Methods of Electronic Structure Calculations for Perfect Solids Systems with Reduced Symmetry Tight-Binding Approximation Tight-Binding Hamiltonian Semiempirical and First-Principles Tight-Binding Calculations Resolvents and Green Functions 26 References 31 LINEAR MUFFIN-TIN ORBITAL (LMTO) METHOD Secular Equation Atomic Sphere Approximation Single-Site Problem Muffin-Tin Orbitals and Tail Cancellation Lattice Fourier Transformations 45 v

3 VI ELECTRONIC STRUCTURE 2.2 Variational Principle Energy Linearization Linear Muffin-Tin Orbitals Hamiltonian and Overlap Matrices Potential Parameters 54 References 58 GREEN FUNCTION METHOD Green Functions in Solids General Comments Green Functions within Atomic Sphere Approximation Green Functions in the LMTO Method Tight-Binding LMTO Method Basic Definitions and Properties Particular Representations Ab Initio Tight-Binding Hamiltonians Screening Transformations and Reference Potentials Relation to the KKR Method Green Functions in Layered Systems Principal Layers Partitioning Technique Surface Green Functions and Embedding Potentials Semiinfinite Homogeneous Systems Green Function in the Intermediate Region Concluding Remarks Calculation of Observables Charge Densities Densities of States Bloch Spectral Functions 108 References 111 COHERENT POTENTIAL APPROXIMATION (CPA) Configurational Average of Green Function Single-Site Approximation 120

4 Contents Vll Transformation Properties of the CPA A Few Additional Remarks Calculation of Observables Properties and Limitations of the CPA 131 References 133 SELFCONSISTENCY WITHIN ATOMIC SPHERE APPROXIMATION Charge Selfconsistency One-Electron Potentials Charge Densities Electrostatic (Madelung) Fields Crystalline Structures Layered Structures Total Energy 150 References 156 RELATIVISTIC THEORY Relativistic TB-LMTO Method: Non-Magnetic Case Dirac Equation Solution for a Single Spherically Symmetric Potential Well Potential Parameters Relativistic Structure Constants Green Functions and the Coherent Potential Approximation Charge Selfconsistency Symmetry of Non-Magnetic Systems Summary Relativistic TB-LMTO Method: Spin-Polarized Case Dirac Equation in the Presence of a Magnetic Field Spin-Polarized Solution for a Single Spherically Symmetric Potential Well Potential Parameters Relativistic Structure Constants The LMTO Hamiltonian and Green Functions 183

5 Vlll ELECTRONIC STRUCTURE Selfconsistency for Charge and Spin Densities Projected Local Densities of States Magnetic Field and Symmetry Spin-Orbit and Exchange Splitting Parameters Summary 192 References BULK SYSTEMS, OVERLAYERS AND SURFACES Bulk Elemental Metals Bulk Transition-Metal Alloys Local Densities of States and Bloch Spectral Functions Bulk Semiconductor Alloys Charge-Transfer Effects in Random Alloys: Al-Li System Clean Surfaces and Overlayers Surface-Related Properties Layer-Resolved Densities of States and Bloch Spectral Functions Random Overlayers Surfaces of Random Alloys 219 References MAGNETIC PROPERTIES Ferromagnetic Bulk Alloys Compositional Dependence of Magnetization Magnetic Moments and Atomic Order Exchange and Spin-Orbit Splitting Magnetism of Surfaces and Interfaces Magnetism at Transition Metal Surfaces Magnetic Overlayers on Non-Magnetic Substrates Interfaces and Grain Boundaries Disordered Local Moments Paramagnetic State of Metals in the Presence of Local Moments 247

6 IX Complex Magnetic Structures in Random Alloys 252 References 254 EFFECTIVE INTERATOMIC INTERACTIONS IN ALLOYS Ising Model for Alloys Ising Hamiltonian Determination of Parameters Determination of Phase Diagrams Generalized Perturbation Method Single-Site Approximation for Charge Densities Effective One-Electron Potential Total Energy Charge-Transfer Effects Band Term Derivation of the Generalized Perturbation Method Core Contributions Double-Counting Terms and Non-Spherical Corrections Madelung Contributions Bulk Systems Case Study: Cu 5 oni 5 o Alloy Surfaces Case Study: fee (001) Surface of Cu 5 oni 5 o Alloy Concluding Remarks 283 References 284 NUMERICAL IMPLEMENTATION Tight-Binding Structure Constants Radial Schrödinger and Dirac Equations Complex Contour Energy Integration Analytic Continuation Brillouin Zone Integration Surface Green Functions Reciprocal Space Approach Real Space Approach 296

7 X ELECTRONIC STRUCTURE 10.7 Coherent Potential Approximation Local Spin Density Approximation One-Electron Potentials Selfconsistency Iterations 305 References 306 INDEX 311