Concepts in Surface Physics

1. Introduction.- 2. Thermodynamical and Statistical Properties of Clean Surfaces.- 2.1 Thermodynamics of a Surface at Equilibrium.- 2.2 Equilibrium Shape of a Crystal.- 2.3 Facetting.- 2.4 The Roughening Transition.- Problems.- 3. Atomic Structure of Surfaces.- 3.1 Surface Crystallography.- 3.2 Experimental Techniques.- Problems.- 4. Vibrations at Surfaces.- 4.1 Elastic Forces in Crystals.- 4.2 Bulk Modes.- 4.3 Surface Modes.- 4.4 Spectral Densities of Modes.- 4.5 Vibrational Thermodynamical Functions.- 4.6 Mean Square Displacements.- Problems.- 5. Electronic Structure of Surfaces.- 5.1 Jellium Model.- 5.2 Nearly Free Electron Model-Surface States.- 5.3 Tight-Binding Approximation.- 5.4 Application of the Tight-Binding Approximation to Transition Metal Surfaces.- 5.5 Application of the Tight-Binding Approximation to Semiconductor Surfaces.- 5.6 Other Methods.- 5.7 Surface Plasmons in Metals.- 5.8 Image Potential.- 5.9 Some Further Remarks on Exchange and Correlation Energies.- 5.10 Experimental Techniques for Investigating the Electronic Structure.- Problems.- 6. Adsorption Phenomena.- 6.1 Thermodynamical Approach.- 6.2 Statistical Methods.- 6.3 Physisorption.- 6.4 Chemisorption.- 6.5 Interactions Between Adsorbates.- 6.6 Electronic Structure of Ordered Overlayers. An Example: O on Ni(100).- Problems.- Appendices.- A. Theory of Scattering by a Spherical Potential: Brief Summary.- A.1 Solution of the Schrödinger Equation for a Particle in a Spherical Potential.- A.2 Scattering of a Free Particle by a Spherical Potential.- A.3 Friedel's Sum Rule.- B. The Continued Fraction Technique.- B.1 Principle of the Recursion Method.- B.2 Principle of the Moment Method.- B.3 Practical Calculations.- C. Electromagnetic Waves in Matter.- C.1 Brief Summary of Maxwell Equations inVacuum.- C.2 Maxwell Equations and Dielectric Properties in a Homogeneous and Isotropic Medium.- C.3 An Equivalent Description of the Dielectric Properties of a Homogeneous and Isotropic Medium: Longitudinal and Transverse Dielectric Functions.- D. Calculation of the Variation of the Total Energy Due to a Perturbing External Charge Distribution Within the Density Functional Formalism.- E. Useful Relations for the Study of Many Body Interactions.- E.1 Relation Between the Expectation Value of the Interaction Energy and the Total Energy for a System of Interacting Particle.- E.2 Derivation of the Fredholm Formula.- F. Interaction of an Electron With an Electromagnetic Field and Theory of Angle-Resolved Ultra-Violet Photoemission (UPS).- F.1 The Optical Matrix Element.- F.2 Expression of the Photoemitted Current in UPS.- F.2.1 Some Useful Relations.- F.2.2 Calculation of the Photoemitted Current in UPS.- F.3 Conservation of the Wave Vector in Photoemission.- G. Calculation of the Current in a Scanning Tunneling Microscope.- H. Calculation of the Atomic Dynamic Polarizability.- I. Variation of the Density of States Due to a Perturbing Potential.- J. Energy of Chemisorption in the Anderson-Grimley-Newns Model Using Contour Integrals.- K. Elastic Constants and Elastic Waves in Cubic Crystals.- K.1 Elastic Strain.- K.2 Elastic Stress.- K.3 Elastic Constants.- K.4 Propagation of Elastic Waves in Cubic Crystals.- K.5 Elastic Energy.- References.