Title: Introduction to lattice dynamics /
Authors: Dove, Martin T.
Date: 1993
Publisher: Cambridge University Press,
Physical description: xvii, 258 pages : illustrations ; 24 cm.
Language: English
LC classification: Q
Contents: 1. Some fundamentals -- Indications that dynamics of atoms in a crystal are important: failure of the static lattice approximation -- Interatomic forces -- The variety of interatomic forces -- Lattice energy -- Worked example: a simple model for NaCl -- Transferable models -- Waves in crystals -- The wave equation -- Travelling waves in crystals -- 2. The harmonic approximation and lattice dynamics of very simple systems -- The harmonic approximation -- The equation of motion of the one-dimensional monatomic chain -- Reciprocal lattice, the Brillouin zone, and allowed wave vectors -- The long wavelength limit -- Extension to include distant neighbours -- Three-dimensional monatomic crystals -- Worked example: the lattice dynamics of the rare-gas solids -- 3. Dynamics of diatomic crystals: general principles -- The basic model -- Equations of motion -- Solution in the long-wavelength limit -- Some specific solutions -- Generalisation to more complex cases -- Examples --^ 4. How far do the atoms move? -- Normal modes and normal mode coordinates -- The quantisation of normal modes -- Vibrational energies and normal mode amplitudes -- So how far do the atoms actually move? -- The crystallographic temperature factor -- 5. Lattice dynamics and thermodynamics -- The basic thermodynamic functions -- Evaluation of the thermodynamic functions and the density of states -- The heat capacity -- Worked example: the heat capacity of NaCl -- Free energy minimisation methods and the quasi-harmonic approximation -- Reconstructive phase transitions -- 6. Formal description -- Review and problems -- The diatomic chain revisited -- The equations of motion and the dynamical matrix -- Extension for molecular crystals -- The dynamical matrix and symmetry -- Extension for the shell model -- Actual calculations of dispersion curves -- Normal mode coordinates -- 7. Acoustic modes and macroscopic elasticity -- The behaviour of long-wavelength acoustic modes --^ Acoustic mode frequencies and the elastic constant tensor -- Worked example: acoustic waves in a cubic crystal -- 8. Anharmonic effects and phase transitions -- Failures of the harmonic approximation -- Anharmonic interactions -- Simple treatment of thermal conductivity -- Temperature dependence of phonon frequencies -- Displacive phase transitions and soft modes -- Soft modes and the Landau theory of phase transitions -- The origin of the anharmonic interactions -- 9. Neutron scattering -- Properties of the neutron as a useful probe -- Sources of thermal neutron beams -- Interactions of neutrons with atomic nuclei -- The neutron scattering function -- Conservation laws for one-phonon neutron scattering -- Experimental inelastic neutron scattering -- Advantages of neutron scattering and some problems with the technique -- 10. Infrared and Raman spectroscopy -- Vibrational spectroscopy by infrared absorption -- Raman spectroscopy -- Advantages and disadvantages of spectroscopy --^ Qualitative applications of infrared and Raman spectroscopy -- Quantitative applications of infrared and Raman spectroscopy -- 11. Formal quantum-mechanical description of lattice vibrations -- Some preliminaries -- Quantum-mechanical description of the harmonic crystal -- The new operators: creation and annihilation operators -- The Hamiltonian and wave function with creation and annihilation operators -- Time and position dependence -- Applications -- 12. Molecular dynamics simulations -- The molecular dynamics simulation method -- Details of the molecular dynamics simulation method -- Analysis of the results of a simulation -- Model systems -- Limitations of the molecular dynamics simulation method -- Appendix A The Ewald method -- The Ewald sum for the Coulomb energy -- Extension for other terms of the functional form r[superscript -n]: the case n=6 -- Appendix B Lattice sums -- Two fundamental results -- Derivation of equation (4.13) -- Derivation of equation (4.20) --^ Derivation of equation (6.44) -- Derivation of equation (A.5) -- Appendix C Bose-Einstein distribution and the thermodynamic relations for phonons -- Appendix D Landau theory of phase transitions -- The order parameter -- Landau free energy for second-order phase transitions -- First-order phase transitions -- Tricritical phase transitions -- Interaction between the order parameter and other variables -- Landau free energy functions with cubic terms -- Critique of Landau theory -- Appendix E Classical theory of coherent neutron scattering -- General scattering formalism -- Time dependence and the inelastic scattering function -- Scattering cross section -- Appendix F Time correlation functions -- Time-dependent correlation functions -- Power spectra -- Example: the velocity autocorrelation function and the phonon density of states -- Appendix G Commutation relations -- Appendix H Published phonon dispersion curves for non-metallic crystals: update of previous compilation --^ Molecular crystals -- Silicates -- Ionic crystals.
Subject headings (LCSH): Lattice dynamics.; Solid state physics.