Phonons: Theory and Experiments I

Lattice Dynamics and Models of Interatomic Forces
Softcover Nachdruck of the original 1. Auflage 1982
ISBN: 978-3-642-81783-0
Verlag: Springer

Buch, Englisch, Band 34, 261 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 429 g

Reihe: Springer Series in Solid-State Sciences

This two-volume treatment grew out of lectures the author gave at the "Ecole Poly technique Federale de Lausanne" during the years 1975-1980 for graduate students in experimental physics in their last year of study. It is written by an experimentalist with some interest in theory and is ad­ dressed mainly to experimentalists, but also to theoreticians interested in experiments. This treatment tries to bridge the gap between theory and experiments; it should assist experimentalists in the interpretation of their data in the vast field of lattice dynamics. An attempt has been made to provide not only the basic concepts but also a working knowledge in this field of solid-state physics. In this first volume, the basic concepts of the physics of phonons are developed and illustrated by many examples; it provides the background necessary for the interpretation of most experimental results. The second volume, which is in preparation, is devoted to experimental techniques, the interpretation of experiments, and discussion of phenomena which are directly related with phonons. The book is designed for introductory courses at the graduate level. It is believed that the book will also prove useful to those graduate students starting research in this or related fields, as well as to many workers already active in this branch of solid-state physics.

Zielgruppe

Research

Autoren/Hrsg.

Brüesch, Peter

Inhaltsverzeichnis

1 Introduction.- 1.1 The Static Lattice Model and Its Limitations.- 1.2 Early History of Lattice Dynamics.- 1.3 The Adiabatic and Harmonic Approximations.- 1.4 Organization of the Book.- 1.5 Problems.- 2. Dynamics of the Linear Diatomic Chain.- 2.1 Classical Mechanics.- 2.2 Quantum Mechanics.- 2.3 Problems.- 3. Dynamics of Three-Dimensional Crystals.- 3.1 Equations of Motion and Atomic Force Constants.- 3.2 Dynamical Matrix and Eigenvectors.- 3.3 Periodic Boundary Conditions, Reciprocal Lattices and Brillouin Zones.- 3.4 Normal Coordinates, Phonons.- 3.5 Density of States and Specific Heat.- 3.6 Connection of Lattice Dynamics with the Theory of Elasticity.- 3.7 An Illustration: Phonon Dispersion of Monoatomic Crystals with fcc Structure.- 3.8 Problems.- 4. Interatomic Forces and Phonon Dispersion Curves.- 4.1 Lattice Dynamics of the Solid Inert Gases.- 4.2 The Rigid-Ion Model for Ionic Crystals.- 4.3 The Shell Model.- 4.4 The Adiabatic Bond Charge Model.- 4.5 The Valence Force Model.- 4.6 Internal and External Vibrations in Molecular Crystals.- 4.7 Phonons in Metals.- 4.8 Problems.- 5. Anharmonicity.- 5.1 The Anharmonic Diatomic Molecule.- 5.2 The Anharmonic Linear Chain.- 5.3 The Anharmonic Three-Dimensional Crystal.- 5.4 The Self-Consistent Harmonic Approximation (SCHA).- 5.5 Response Function and Perturbation Theory of Phonon-Phonon Interactions.- 5.6 Problems.- A Periodicity of Eigenfrequencies and Atomic Displacements in Reciprocal Space.- B An Important Lattice Sum.- C Hamiltonian for the Diatomic Chain in Terms of Normal Coordinates.- D Commutator Relations for Normal Coordinates.- E The Occupation Number Representation.- F Restriction on Atomic Force Constants Which Follow from the Space Group Symmetry of the Crystal.- G Dynamical Matrix.- J Force Constants forCentral Forces.- K Evaluation of the Coulomb Matrix Using Ewald’s Method.- L The Valence Force Model.- M The Saddle-Point Method.- N The Free Energy in the Harmonic or Quasiharmonic Approximation.- O The Self-Consistent Harmonic Approximation (SCHA).- P Expansion Coefficients of Anharmonic Terms.- Q Constants and Units.- General References.- References.