Surface phonons. Springer series in surface sciences; 21.

In recent years substantial progress has been made in the detection of surface phonons owing to considerable improvements in inelastic rare gas scattering tech- niques and electron energy loss spectroscopy. With these methods it has become possible to measure surface vibrations in a wide energy range for all wave vectors in the two-dimensional Brillouin zone and thus to deduce the complete surface phonon dispersion curves. Inelastic atomic beam scattering and electron energy loss spectroscopy have started to play a role in the study of surface phonons similar to the one played by inelastic neutron scattering in the investigation of bulk phonons in the last thirty years. Detailed comparison between experimen- tal results and theoretical studies of inelastic surface scattering and of surface phonons has now become feasible. It is therefore possible to test and to improve the details of interaction models which have been worked out theoretically in the last few decades. At this point we felt that a concise, coherent and self-contained guide to the rapidly growing field of surface phonons was needed.

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.