Low-Energy Electron Diffraction

1. The Relevance and Historical Development of LEED.- 1.1 The Relevance of Surface Crystallography.- 1.2 The Historical Development of LEED.- 1.2.1 The Period Before Wave Mechanics.- 1.2.2 The Discovery of Electron Diffraction.- 1.2.3 The Aftermath of the Discovery of Electron Diffraction.- 1.2.4 The Period 1930 - 1965.- 1.2.5 The Renaissance of LEED: Experimental Advances in the Mid-1960s.- 1.2.6 The Theoretical Solution: The Late 1960s and Early 1970s.- 1.2.7 The Era of Structural Determination: The 1970s and 1980s.- 2. The LEED Experiment.- 2.1 General Features of LEED Experiments.- 2.2 Sample Mounting.- 2.3 Electron Gun and Display System.- 2.3.1 Electron Gun.- 2.3.2 Display System.- 2.4 Methods of Data Acquisition.- 2.4.1 Faraday-Cup Collector and Spot Photometer.- 2.4.2 Photographic Technique.- 2.4.3 Vidicon Camera Method.- 2.4.4 Position-Sensitive Detector.- 2.5 Instrumental Response Function.- 2.5.1 Basic Concepts.- 2.5.2 Contributions to the Response Width.- 2.6 Determination of Angle of Incidence.- 2.6.1 Different Methods.- 2.6.2 Theory.- 2.6.3 An Example.- 2.7 Determination of the Debye Temperature.- 2.7.1 The Debye Temperature Normal to the Crystal Surface.- 2.7.2 The Debye Temperature Parallel to the Crystal Surface.- 3. Ordered Surfaces: Structure and Diffraction Pattern.- 3.1 Two-Dimensional Periodicity and the LEED Pattern.- 3.1.1 Miller and Miller-Bravais Indices.- 3.1.2 Lattice and Basis.- 3.1.3 Direct and Reciprocal Lattices.- 3.2 Superlattices at Surfaces.- 3.3 Stepped and Kinked Surfaces.- 3.3.1 The Step Notation.- 3.3.2 The Microfacet Notation for Cubic Materials.- 3.3.3 Unit Cells of Stepped and Kinked Surfaces.- 3.4 Symmetries and Domains at Surfaces.- 3.4.1 Symmetries in Two Dimensions.- 3.4.2 Domains.- 3.5 Interpretation of LEED Patterns.- 3.5.1 Patterns with a Bravais Array of Spots.- 3.5.2 Patterns with Multiple Bravais Arrays of Spots - Domains.- 3.5.3 Patterns Exhibiting Extinctions Due to Glide-Plane Symmetry.- 3.5.4 Rationally Related Lattices and Coincidence Lattices.- 3.5.5 An Instructive Example of Pattern Interpretation.- 3.5.6 Incommensurate Lattices.- 3.5.7 Split Spots.- 3.5.8 An Example: Compact Structures vs. Antiphase Domain Structures of Adsorbed Carbon Monoxide Overlayers.- 3.5.9 Patterns with Multiple Specular Spots.- 3.5.10 Laser Simulation of LEED Patterns.- 4. Kinematic LEED Theory and Its Limitations.- 4.1 Definition of Kinematic Theory.- 4.1.1 Atomic Scattering Factor.- 4.1.2 Elastic Scattering.- 4.1.3 Amplitude of Diffraction.- 4.1.4 Surface Sensitivity.- 4.1.5 From Amplitudes to Intensities of Diffraction.- 4.2 The Kinematic Structure Factor for Ordered Surfaces.- 4.2.1 Two-Dimensional Bragg Conditions.- 4.2.2 General Derivation of Two-Dimensional Bragg Conditions in LEED from the Schrodinger Equation.- 4.2.3 Plane Waves, Beams, and the LEED Pattern.- 4.2.4 I-V, I-?, I-?, and Other Collections of Data.- 4.2.5 Kinematic Diffraction by Bravais Lattices of Atoms.- 4.2.6 The Case of Non-Bravais Lattices.- 4.2.7 Surface Structures Deviating from the Bulk Structure.- 4.2.8 Surfaces with Superlattices.- 4.2.9 Modulated Structures.- 4.2.10 The Simple Effect of Multiple Scattering on LEED Patterns.- 4.2.11 The Ewald Sphere.- 4.2.12 Further Applications of the Kinematic Theory of LEED.- 4.3 The Scattering Processes in LEED.- 4.3.1 Inelastic Scattering Processes.- 4.3.2 Modeling the Effect of the Mean Free Path.- 4.3.3 Spin Effects.- 4.4 The Elastic Scattering Potential.- 4.4.1 Atomic Potentials.- 4.4.2 The Muffin-Tin Constant.- 4.4.3 Potential Steps.- 4.5 Atomic Scattering.- 4.5.1 Spherical-Wave Scattering.- 4.5.2 Plane Wave Scattering.- 4.5.3 Phase Shifts.- 4.5.4 Atoms as Point Scatterers.- 4.6 The Inner Potential and the Muffin-Tin Constant.- 4.7 Temperature Effects.- 4.7.1 The Debye-Waller Factor.- 4.8 From Kinematic to Dynamical LEED.- 4.8.1 Clean Crystals and Bragg Reflections in One Dimension.- 4.8.2 Three-Dimensional Effects.- 4.8.3 Overlayer Effects.- 5. Dynamical LEED Theory.- 5.1 Multiple Scattering.- 5.2 Diffraction in Crystalline Lattices.- 5.2.1 Expansion in Spherical Waves.- 5.2.2 Expansion in Plane Waves.- 5.2.3 Expansion in Bloch Waves.- 5.2.4 Forward vs. Backward Scattering.- 5.3 Multiple Scattering in the Spherical-Wave Representation - Self-Consistent Formalism.- 5.3.1 Scattering by Two Atoms.- 5.3.2 Scattering by N Atoms.- 5.3.3 One Periodic Plane of Atoms.- 5.3.4 Several Periodic Planes of Atoms.- 5.3.5 Change to Plane-Wave Amplitudes.- 5.3.6 Layer Diffraction Matrices for Plane Waves.- 5.3.7 One-Center Expansion.- 5.4 Perturbation Expansion of Multiple Scattering in the Spherical-Wave Representation: Reverse-Scattering Perturbation (RSP) Method.- 5.4.1 The Principle of RSP.- 5.4.2 The Formalism of RSP.- 5.4.3 The Use of RSP.- 5.5 Diffraction by a Stack of Layers: Transfer-Matrix and Bloch-Wave Method.- 5.5.1 The Bloch Condition.- 5.5.2 The Bloch Functions.- 5.5.3 The Transfer Matrix.- 5.5.4 Wave Matching at the Surface.- 5.5.5 Small Layer Spacings.- 5.5.6 Relation to Band Structure.- 5.6 Diffraction by a Stack of Layers: Layer-Stacking and Layer-Doubling Method.- 5.6.1 The Case of Two Layers.- 5.6.2 The Case of Many Layers.- 5.7 Diffraction by a Stack of Layers: Renormalized-Forward-Scattering (RFS) Perturbation Method.- 5.7.1 The Principle of RFS.- 5.7.2 The Formalism of RFS.- 5.8 Efficiency of Computation and the Combined-Space Method.- 5.9 Superlattices and Domains.- 5.9.1 Diffraction and Superlattices.- 5.9.2 Domains.- 5.10 Symmetries.- 5.10.1 Types of Symmetry.- 5.10.2 The Formalism of Symmetrization.- 5.10.3 Glide-Plane Symmetry.- 5.11 Thermal Effects.- 5.11.1 Temperature-Dependent Phase Shifts.- 5.11.2 Illustrations of Multiple-Scattering Effects in Temperature-Dependent LEED.- 5.12 Potential Steps, Surface States, Surface Resonances and LEED Fine Structure.- 5.12.1 Potential Steps.- 5.12.2 Surface States, Surface Resonances and LEED Fine Structure.- 5.13 Relativistic and Spin-Dependent Effects in LEED.- 5.14 Some Other Theoretical Techniques.- 5.14.1 Bootstrapping.- 5.14.2 The Chain Method.- 5.14.3 Multiple Scattering in Disordered Systems.- 5.14.4 Pseudopotentials.- 5.14.5 A Semiclassical Theory of LEED.- 5.15 Outstanding Theoretical Problems in LEED.- 5.16 Application of LEED Theory to Other Electron Spectroscopies.- 5.17 Computer Programs.- 6. Methods of Surface Crystallography by LEED.- 6.1 The Kinematic Approach to Surface Crystallography.- 6.1.1 Kinematic Simulation of Intensity Data.- 6.1.2 Layer Spacings from Sequences of Bragg Peaks.- 6.2 Averaging Methods.- 6.2.1 Constant-Momentum-Transfer Averaging (CMTA).- 6.2.2 CMTA with Azimuthal Averaging at Constant Energy.- 6.3 Fourier-Transform Methods.- 6.3.1 The Patterson Function.- 6.3.2 The Convolution-Transform Method.- 6.3.3 The Transform-Deconvolution Method.- 6.3.4 Fourier Transform of Intensity Beats from Overlayer and Substrate.- 6.4 The Dynamical Approach to Surface Crystallography.- 6.4.1 Dynamical Effects on Intensity Data.- 6.4.2 Information Content of Measured Data.- 6.4.3 Extraction of Structural Information from Dynamical LEED Intensities.- 6.5 Reliability Factors (R-Factors).- 6.5.1 Various R-Factors.- 6.5.2 Reliability of Reliability Factors.- 6.5.3 Dealing with Different Experiments and Different Beams.- 6.5.4 Noise and Smoothing.- 6.5.5 The Use of R-Factors.- 6.6 Accuracy and Precision of Structural Determination.- 7. Results of Structural Analyses by LEED.- 7.1 Clean Unreconstructed Surfaces.- 7.1.1 The Rh(111) Surface.- 7.1.2 Multilayer Relaxations.- 7.2 Reconstructed Surfaces.- 7.2.1 The Ir(110)-(1 x 2) Reconstructed Surface.- 7.2.2 The Si(100)-(2 x 1) Reconstructed Surface.- 7.2.3 The GaAs(110)-(1 x 1) Reconstructed Surface.- 7.3 Adsorbed Atomic Layers.- 7.3.1 The Ir(110)-(2 x 2)-2S Atomic Overlayer.- 7.3.2 The Ir(110)-c(2 x 2)-O and Ir(111)-(2 x 2)-O Atomic Overlayers.- 7.3.3 The Ti(0001)-(1 x 1)-N Atomic Underlayer.- 7.4 Adsorbed Molecular Layers.- 7.4.1 The Ni(100)-c(2 x 2)-CO Molecular Overlayer.- 7.4.2 The Pd(100)-($$2sqrt 2 times sqrt 2$$)R45 -2CO Molecular Overlayer.- 7.4.3 Molecular Overlayers of C2H2 and C2H4 on Pt(111) and Rh(111).- 8. Two Dimensional Order-Disorder Phase Transitions.- 8.1 Introduction to Order-Disorder Phase Transitions at Surfaces...- 8.1.1 Chemisorption and Ordering Principles.- 8.1.2 Universality, Nonuniversality, Critical Exponents and Scaling.- 8.1.3 Applicability to Actual Surfaces.- 8.2 The Interaction of Hydrogen with the (111) Surface of Nickel.- 8.2.1 An Optimum Case.- 8.2.2 Experimental Results for Hydrogen Chemisorption on Ni(111).- 8.2.3 Parameters for LEED Analysis.- 8.2.4 The Geometry of Chemisorbed Hydrogen on Ni(111).- 8.2.5 Thermal Motion and Disorder in the Hydrogen Overlayer.- 8.2.6 The Order-Disorder Phase Transition and Adatom-Adatom Interaction Energies.- 8.2.7 A Renormalization-Group Theory Description of the Order-Disorder Transition of Hydrogen on Ni(111).- 8.2.8 A Cluster-Variational Description of the Order-Disorder Transition of Hydrogen on Ni(111).- 8.2.9 An Atomic Band Structure Description of Hydrogen on Ni(111).- 8.3 The Interaction of Hydrogen with the (100) Surface of Palladium.- 8.3.1 Significance of the H/Pd(100) System.- 8.3.2 An Experimental Characterization of Hydrogen on Pd (100).- 8.3.3 The Order-Disorder Phase Transition.- 8.3.4 The Connection Between the Ising Model and the Lattice-Gas Model.- 8.3.5 The Lattice-Gas Model with First- and Second-Neighbor Interactions.- 8.3.6 Effects of Three-Body Interactions.- 8.3.7 Effects of Third-Neighbor Interactions.- 8.3.8 Comparison Between Experiment and Theory for Hydrogen on Pd (100).- 8.4 The Interaction of Hydrogen with the (110) Surface of Iron.- 8.4.1 Significance of the H/Fe (110) System.- 8.4.2 An Experimental Characterization of Hydrogen on Fe(110).- 8.4.3 LEED Observations and Order-Disorder Phase Transitions of Hydrogen on Fe(110).- 8.4.4 Theoretical Predictions: A Lattice Gas on a Centered-Rectangular Lattice.- 8.4.5 Comparison Between Experiment and Theory for Hydrogen on Fe(110).- 9. Chemical Reactions at Surfaces and LEED.- 9.1 Monitoring Surface Reactions by LEED.- 9.2 The Adsorption of Oxygen on Rh(111) at 335 K.- 9.2.1 First-Order Langmuir Adsorption.- 9.2.2 The Structure of Oxygen on Rh(111).- 9.2.3 LEED Intensity Proportional to Oxygen Coverage.- 9.3 The Reaction Between Hydrogen and Ordered Oxygen on Rh(111).- 9.3.1 Reaction Threshold Temperature.- 9.3.2 First-Order Catalytic Reaction.- 9.3.3 Model for the Catalytic Reaction.- 9.3.4 Activation Energies and Preexponential Factors.- 9.3.5 Experimental Determination.- 9.4 The Reaction Between Hydrogen and Both Ordered and Disordered Oxygen on Rh(111).- 9.4.1 Order-Dependent Kinetics.- 9.4.2 Relative Amounts of Ordered and Disordered Oxygen.- 10. Island Formation of Adspecies and LEED.- 10.1 The Nature of Islands on Surfaces.- 10.2 LEED Beam Profiles for Arrays of Ordered Islands.- 10.2.1 Distributions of Islands.- 10.2.2 One-Dimensional Overlayers.- 10.2.3 Two-Dimensional Overlayers.- 10.2.4 Dependence on Surface Coverage.- 10.2.5 Summary of Theoretical Results for Beam Profiles.- 10.3 Island Formation in a Real System: CO on Ru(0001).- 10.3.1 Conditions of Island Formation.- 10.3.2 Experimental Results.- 10.3.3 Analysis and Discussion of Results.- 10.3.3a The Step-Limited Model of Island Formation.- 10.3.3b Dissolution of Islands.- 10.3.4 Summary of Island Formation Properties for CO/Ru (0001).- 11. The Future of LEED.- 11.1 Experimental Outlook.- 11.1.1 Improvements in Experimental Techniques.- 11.1.2 New Experimental Directions.- 11.2 Theoretical Outlook.- 11.2.1 Survival of the Kinematic Theory.- 11.2.2 Partial Multiple Scattering.- 11.2.3 Developments in the Dynamical Theory.- 11.2.3a Coherent Kinematic Summation of Amplitudes over Different Local Configurations.- 11.2.3b Reduced Unit Cell.- 11.2.3c Asymptotic Regime.- 11.2.4 New Directions.- 11.3 Progress in Structural Determination.- 11.3.1 Degree of Completeness of Structural Determinations.- 11.3.2 R-Factors and Structural Search Techniques.- 11.3.2a Projection Improvement.- 11.3.2b Functional Fitting of R-Factors.- 11.3.2c Steepest Descent.- 11.3.2d Least Squares.- 11.4 LEED vs. Other Surface-Sensitive Techniques.- 11.4.1 Individual Techniques.- 11.4.2 Comparisons Between Surface-Sensitive Techniques.- 11.4.3 Complementary and Competitive Techniques.- 12. Reference List and Table for Surface Structures.- Appendix A: Acronyms of Techniques Related to Surface Science.- Appendix B: A Computer Program to Determine the Angle of Incidence in LEED.- List of Major Symbols.- References.