Surface Phonons

1. Introduction.- 2. Surface Acoustic Waves.- 2.1 Surface Acoustic Waves on Various Media.- 2.1.1 Elastic Media.- 2.1.2 Piezoelectric Media.- 2.2 Generation and Detection of Surface Acoustic Waves.- 2.2.1 Electrical Generation and Detection in Piezoelectric Media.- 2.2.2 Generation on Non-piezoelectric Media.- 2.2.3 Acousto-optic Detection of Generated Surface Acoustic Waves.- 2.2.4 Brillouin Scattering from Surface Waves.- 2.3 Some Applications of Surface Acoustic Waves.- 2.3.1 Applications to Electronic Signal Processing.- 2.3.2 Measurements of Intrinsic Material Properties.- References.- 3. The Green’s Function Method in the Surface Lattice Dynamics of Ionic Crystals.- 3.1 Outline of the Time-Independent Green’s Function Method.- 3.2 The Green’s Function Method in Surface Dynamics.- 3.3 The Intrinsic Perturbation for a Semi-Infinite Lattice.- 3.4 The Electronic Contribution to Surface Dynamics in the Framework of Shell Models.- 3.5 Surface Phonon Polaritons.- 3.6 Surface Vibrations in Alkali Halides.- 3.7 Further Developments: The Study of Surface Phonon Anomalies.- References.- 4. Study of Surface Phonons by the Slab Method.- 4.1 Formalism.- 4.1.1 Slab Dynamics.- 4.1.2 Use of Symmetry.- 4.1.3 Slab Vibrational Modes and Their Dispersion Curves.- 4.1.4 Macroscopic and Microscopic Surface Modes.- 4.1.5 Attenuation Curves.- 4.1.6 Systematic Features of Surface Modes.- 4.2 Computational Considerations.- 4.2.1 Diagonalization Techniques.- 4.2.2 Surface Brillouin Zone Sampling.- 4.3 Interaction Models.- 4.3.1 Simple Pair Potentials (Molecular Crystals).- 4.3.2 Shell Models (Ionic Crystals).- 4.3.3 Force Constant Models (Semiconductors, Metals).- 4.4 Results.- 4.4.1 Relaxation and Dynamics of the (001) Surfaces of Alkali Halides.- 4.4.2 Results for fee and bcc Metals.- 4.4.3 Layered Structure — Graphite.- 4.5 Derived Physical Quantities.- 4.5.1 Mean-Square Amplitudes of Vibration and Vibrational Correlation Functions.- 4.5.2 Surface Debye Temperature.- 4.5.3 Surface Thermodynamic Quantities.- 4.6 Concluding Remarks.- References.- 5. Experimental Determination of Surface Phonons by Helium Atom and Electron Energy Loss Spectroscopy.- 5.1 Theoretical Background.- 5.2 Kinematics.- 5.3 Helium Scattering.- 5.3.1 General Considerations.- 5.3.2 Helium Nozzle Beam Source.- 5.3.3 Target Chamber.- 5.3.4 Detector.- 5.3.5 Typical Measurements and Resolution.- 5.4 Electron Scattering.- 5.4.1 Apparatus.- 5.4.2 Typical Measurements.- 5.5 Intensities.- 5.5.1 Helium Atom Scattering.- 5.5.2 Electron Scattering.- 5.5.3 Comparison of Experimental Intensities.- 5.6 Discussion of Experimental Results and Summary.- References.- 6. Theory of Helium Scattering from Surface Phonons.- 6.1 Kinematics.- 6.1.1 Kinematic Focusing.- 6.2 Dynamical Theory: General Considerations.- 6.2.1 Box Normalization and Scattering Geometry.- 6.2.2 Cross Sections and Reflection Coefficients.- 6.2.3 State-to-State Cross Sections vs Differential Cross Sections.- 6.3 One-Phonon Exchange Processes.- 6.3.1 The Distorted Wave Born Approximation.- 6.3.2 The Phonon Matrix Elements.- 6.3.3 The Atom-Surface Matrix Elements.- 6.3.4 The Differential Reflection Coefficient.- 6.3.5 Relation to Phonon Density of States and Correlation Functions.- 6.4 The Inelastic Atom-Surface Interaction.- 6.4.1 The Static Repulsive Potential.- 6.4.2 The Static Attractive Potential.- 6.4.3 The Total Static Potential.- 6.4.4 The Dynamic Repulsion and the Cutoff Factor.- 6.4.5 Dynamical Effects of the Attractive Potential.- References.- 7. The Study of Surface Phonons by Electron Energy Loss Spectroscopy: Theoretical and Experimental Considerations.- 7.1 A Brief Review.- 7.2 The Surface Phonon Excitation Mechanism in the Impact Regime.- 7.3 The Green’s Function Approach to Spectral Density Calculations.- 7.4 Calculations of the Cross Section for Surface Phonon Excitation.- 7.5 Concluding Remarks.- References.- 8. Vibrational Properties of Clean Surfaces: Survey of Recent Theoretical and Experimental Results.- 8.1 Ionic Crystals.- 8.1.1 Alkali Halides (Rock Salt Structure).- 8.1.2 Metal Oxides.- 8.1.3 Refractory Compounds.- 8.1.4 Perovskite Structure Compounds.- 8.2 Metals.- 8.2.1 Body Centered Cubic Metals.- 8.2.2 Face Centered Cubic Metals.- 8.3 Miscellaneous.- 8.3.1 Diamond Structure Crystals.- 8.3.2 Zinc-Blende Structure Crystals.- 8.3.3 Layered Structure Crystals.- References.