Structure and Dynamics of Surfaces II

1. Introduction: Surface Phenomena and Their Analysis by Scattering Experiments.- 1.1 Surface Phenomena.- 1.1.1 Reconstruction and Relaxation.- 1.1.2 Phase Transitions.- 1.1.3 Defects.- 1.1.4 Phonons and Mean Vibrational Amplitudes.- 1.1.5 Bound Resonant States.- 1.1.6 Vibrations of Adsorbed Species.- 1.1.7 Diffusion, Adsorption and Desorption.- 1.1.8 Segregation.- 1.1.9 Interfaces and Superlattices.- 1.1.10 Magnetism and Electronic States.- 1.2 Scattering Methods for Surface Analysis.- 1.2.1 Electron Scattering.- 1.2.2 Scattering of He Atoms.- 1.2.3 Neutron Scattering.- 1.2.4 X-Ray Scattering.- 1.2.5 Scattering of Ions.- 1.2.6 Comparison of Different Scattering Methods.- 1.2.7 Conclusion and Outlook.- 1.3 On the Temperature-Dependence of Surface Properties.- 1.3.1 Pair Potentials at the Surface.- 1.3.2 Density-Functional Formalism for Nonzero Temperatures.- 1.3.3 Conclusions.- 1.4 Book Outline.- References.- Additional References with Titles.- 2. Study of Surface Phonons by Means of the Green's Function Method.- 2.1 Introductory Remarks.- 2.2 The Time-Independent Green's Function Method in Summary.- 2.3 The Green's Function Method in Surface Dynamics.- 2.4 From a Slab to a Semiinfinite Lattice: Selfconsistent Definition of the Perturbation Matrix.- 2.5 The Electronic Contribution to Surface Dynamics in the Framework of Shell Models.- 2.6 Surface Vibrations in Alkali Halides.- 2.6.1 LiF and NaF.- 2.6.2 NaCl and NaI.- 2.6.3 Potassium Halides.- 2.7 Further Developments: The Study of Surface Phonon Anomalies.- References.- 3. Surface Diffusion and Layer Growth.- 3.1 Mass Transport and Growth Phenomena at Surfaces.- 3.2 Description of Surface Diffusion.- 3.3 Experimental Methods for the Study of Surface Diffusion and Typical Results.- 3.3.1 Direct Observation of Diffusing Atoms.- 3.3.2 The Study of Particle Correlations in Equilibrium Systems.- 3.3.3 Diffusion Studies in a Concentration Gradient.- 3.3.4 Anisotropy of Surface Diffusion.- 3.3.5 Surface Diffusion Near the Melting Point.- 3.4 Growth Modes.- 3.5 Layer-Growth Techniques.- 3.6 Methods for the Examination of Growth Processes and Typical Results.- 3.6.1 Detection of Growth Modes by Electron Spectroscopy.- 3.6.2 Observation of Layer Growth by Diffraction Experiments.- 3.6.3 Examination of Surface and Interface Layers by High-Energy Ion Scattering.- 3.6.4 The Growth of Metal Layers on Semiconductor Substrates.- 3.6.5 Examination of Superlattices.- 3.7 Model Calculations and Simulations.- 3.8 Conclusion and Outlook.- References.- Additional References with Titles.- 4. Phase Transitions on Single-Crystal Surfaces and in Chemisorbed Layers.- 4.1 Background.- 4.2 Theoretical Foundations.- 4.2.1 Phases in Two Dimensions.- 4.2.2 Origin of Surface Phases and Relation to Magnetic Models.- 4.2.3 Models and Nomenclature.- 4.2.4 Continuous Order-Disorder Transitions.- a) Critical Behaviour and Exponents, Universality and Scaling Laws.- b) Symmetry Analysis and Symmetric Lattice Models.- c) Asymmetric and Anisotropic Models.- 4.2.5 Order-Order Transitions.- 4.2.6 Commensurate-Incommensurate Transitions.- 4.2.7 Melting in Two Dimensions.- 4.2.8 Interface Delocalization Transitions in Two Dimensions.- 4.2.9 Systems with Long-Range Repulsive Interactions.- 4.2.10 Systems with Purely Attractive Interactions.- 4.3 Experimental Techniques.- 4.3.1 Diffraction Methods.- 4.3.2 Scattering Methods.- 4.3.3 Work Function Change Measurement.- 4.3.4 Thermal Desorption Methods.- 4.3.5 Electron Microscopy.- 4.3.6 Experimental Limitations.- 4.4 Results.- 4.4.1 Clean Surfaces.- a) The Si(111)-(7 × 7)?(1 × 1) Transition.- b) The Au(110)-(1 × 2)?(1 × 1) Transition.- c) W(100)-c(2 × 2)?(1 × 1) Transition.- d) Other Transitions on Clean Surfaces.- 4.4.2 Chemisorbed Layers with Repulsive Nearest-Neighbour Interactions.- a) Two-Dimensionally Densely Packed Surfaces.- b) One-Dimensionally Densely Packed Surfaces (p2mm).- c) Open Surfaces.- 4.4.3 Chemisorbed Layers with Attractive Nearest-Neighbour Interactions.- 4.5 Concluding Remarks and Outlook.- References.- Additional References with Titles.- 5. Solid and Liquid Surfaces Studied by Synchrotron X-Ray Diffraction.- 5.1 Reflectivity and Density Profile.- 5.1.1 Master Formula.- 5.1.2 Fresnel Reflectivity.- 5.1.3 Derivation of Master Formula.- 5.1.4 Traditional Calculation Scheme for R(Q).- 5.2 Experimental Reflectivity Set Up.- 5.2.1 General Wave-Vector Transfer.- 5.2.2 Resolution.- 5.3 Examples of Reflectivity Measurements.- 5.3.1 Thermal Roughness.- 5.3.2 Smectic Layering on Liquid Crystal Surfaces.- a) Smectic Layering in the Isotropic Phase.- b) Layer Penetration in the Nematic Phase.- c) Antiferroelectric Surface Layers.- 5.4 In-Plane Structures.- 5.4.1 Grazing Incidence Geometry.- a) Penetration Depth.- b) Field Strength.- c) Summary of Grazing Incidence.- 5.4.2 Principles of Surface Crystallography.- a) Bragg Scattering.- b) Unit Cell in Surface Geometry, InSb(111).- c) Reciprocal Lattice. Bragg Points.- d) Reconstructed (n × m) Surface Structure. Bragg Rods.- e) Bragg Rods from Termination at Surface.- f) Patterson Function.- 5.4.3 Reconstructed Surface of InSb(111)-(2 × 2).- a) Diffractometer Set Up.- b) Sample Preparation.- c) Results.- 5.4.4 Surface Structures Revealed by X-Ray Diffraction.- References.- 6. Statistical Mechanics of the Liquid Surface and the Effect of Premelting.- 6.1 The Structure of the Liquid Surface.- 6.1.1 General Remarks.- 6.1.2 Bulk Liquids.- 6.1.3 Liquid Surfaces.- a) Single-Particle Distribution Function.- b) The Two-Particle Distribution Function.- 6.1.4 Surface Thermodynamic Properties.- 6.1.5 Liquid Metals.- 6.2 Dynamics of the Liquid Surface.- 6.3 The Effect of Premelting. A Study for Krypton.- 6.3.1 Model.- 6.3.2 Results for the Distribution Functions.- a) Single-Particle Distribution Functions for Krypton.- b) Pair Correlation Function for Krypton.- 6.3.3 Discussion of the Results for the Distribution Functions.- a) Single-Particle Distribution Function for the Outermost Layer at T=7 K.- b) The Dynamics of the Particles of the Outermost Layer at T=102 K.- c) Melting Mechanism: Description at the Atomic Level.- 6.4 Final Remarks.- References.- Additional References with Titles.- 7. The Roughening Transition.- 7.1 Background.- 7.2 Macroscopic Description of Equilibrium Crystal Shapes.- 7.2.1 The Wulff Construction.- 7.2.2 Facets, Edges and Corners.- 7.2.3 The Roughening Transition and Other Phase Transitions.- 7.3 Microscopic Description of Crystal Surfaces.- 7.3.1 The Kossel Crystal, Lattice-Gas Models, Solid-on-Solid Models.- 7.3.2 Steps and Step Free Energies.- 7.3.3 Microscopic Characterization of Roughening Transitions.- 7.3.4 Equilibrium Shapes of Facets. General Criterium for Roughening.- 7.4 Statistical Mechanics of Interface Models.- 7.4.1 Renormalization-Group Results.- a) Roughening Temperature.- b) Surface Tension.- c) Step Free Energies.- d) Correlation Length.- e) Height-Height Correlation Function.- f) Jump in Curvature and Surface Stiffness.- 7.4.2 The BCSOS Model.- 7.4.3 The Terrace-Step-Kink Model.- 7.4.4 Universal Shape of Vicinal Areas.- 7.5 Discussion.- 7.5.1 Roughening Versus Surface Melting.- 7.5.2 Are All Roughening Transitions of Kosterlitz-Thouless Type?.- a) Inequivalent Layers.- b) Impurities and Lattice Faults.- c) First-Order Transitions.- 7.5.3 Multilayer Adsorption and Roughening.- Appendix 7.A: Surface Stiffness and Universal Jump in Curvature.- References.- Additional References with Titles.- 8. Structural and Dynamical Aspects of Adsorption and Desorption.- 8.1 General.- 8.2 Basic Experimental Facts.- 8.2.1 Elastic Scattering at Surfaces.- 8.2.2 Trapping and Sticking.- 8.2.3 Direct Inelastic Scattering.- 8.2.4 Desorption.- 8.3 Overview of the Different Theoretical Approaches.- 8.3.1 Classical and Classical-Stochastic Theories.- 8.3.2 Semiclassical Theories.- 8.3.3 Quantum Theories.- 8.4 Selected Problems.- 8.4.1 Structural and Dynamical Constraints.- 8.4.2 The Compensation Effect.- 8.4.3 The Sticking Coefficient - Definition and Zero Temperature/Zero Kinetic Energy Behaviour.- 8.4.4 Quantum Partitioning Techniques.- 8.4.5 Non-Adiabatic Adsorption and Desorption.- 8.5 Concluding Remarks.- References.- 9. Many-Body Description of Surface Elementary Excitations. Application to Semiconductors.- 9.1 Background.- 9.2 Elementary Excitations on Surfaces.- 9.2.1 Homogeneous Bethe-Salpeter Equations.- 9.2.2 Equation of Motion in the Local-Orbital Representation.- 9.2.3 Surface Density-Response Function.- 9.3 Surface Electromagnetic Response.- 9.3.1 Surface Macroscopic Dielectric Tensor.- 9.3.2 Microscopic Formulation of the Optical Response.- 9.3.3 Microscopic Theory of Surface Reflectivity.- 9.4 Electron-Phonon Interaction and Microscopic Theory of Lattice Dynamics on Surfaces.- 9.4.1 Surface Lattice Dynamics.- 9.5 Applications: Si(111).- 9.5.1 Electronic Instabilities in an Ideal Si(111) Slab.- 9.5.2 Microscopic Phonon Calculations for an Ideal Si(111)Slab.- 9.6 Summary and Perspectives.- References.