Introduction to Lattice Dynamics (Cambridge Topics in Mineral Physics and Chemistry, Series Number 4)

The vibrations of atoms inside crystals - lattice dynamics - is basic to many fields of study in the solid-state and mineral sciences. Lattice dynamics is becoming increasingly important for work on mineral stability. This book provides a self-contained text that introduces the subject from a basic level and then takes the reader through real applications of the theory. The book is aimed at advanced undergraduates, graduate students and research workers in the earth and solid-state sciences who need to incorporate lattice dynamic treatments into their work. Applications include the use of lattice dynamics instabilities to study the origin of phase transitions in crystals and the use of vibrational spectra to obtain information about inter-atomic forces. Contents......Page 9 Preface......Page 13 Acknowledgements......Page 16 Physical constants and conversion factors......Page 17 Some fundamentals......Page 19 The harmonic approximation and lattice dynamics of very simple systems......Page 36 Dynamics of diatomic crystals: general principles......Page 54 How far do the atoms move?......Page 73 Lattice dynamics and thermodynamics......Page 82 Formal description......Page 98 Acoustic modes and macroscopic elasticity......Page 113 Anharmonic effects and phase transitions......Page 119 Neutron scattering......Page 150 Infrared and Raman spectroscopy......Page 169 Formal quantum-mechanical description of lattice vibrations......Page 185 Molecular dynamics simulations......Page 197 The Ewald method......Page 213 Lattice sums......Page 220 Bose-Einstein distribution and the thermodynamic relations for phonons......Page 225 Landau theory of phase transitions......Page 228 Classical theory of coherent neutron scattering......Page 239 Time correlation functions......Page 247 Commutation relations......Page 251 Published phonon dispersion curves for non-metallic crystals: update of previous compilation......Page 254 References......Page 258 Index......Page 272 The vibrations of atoms inside crystals - lattice dynamics - are basic to many fields of study in the solid state and mineral sciences, and lattice dynamics is becoming increasingly important for work on mineral stability. This book provides a self-contained text that introduces the subject from a basic level and then takes the reader, through applications of the theory, to research level. Simple systems are used for the development of the general principles. More complex systems are then introduced and later chapters look at thermodynamics, elasticity, phase transitions and quantum effects. Experimental and computational methods are described and applications of lattice dynamics to specific studies are detailed. Appendices provide supplementary information and derivations for the Ewald method, statistical mechanics of lattice vibrations, Landau theory, scattering theory and correlation functions. The book is aimed at students and research workers in the earth and solid state sciences who need to incorporate lattice dynamics into their work Foreword Acknowledgements Definitions of symbols used 1. Some fundamentals 2. The harmonic approximation and lattice dynamics of very simple systems 3. Dynamics of diatomic crystals: general principles 4. How far do the atoms move? 5. Lattice dynamics and thermodynamics 6. Formal description 7. Acoustic modes and macroscopic elasticity 8. Anharmonic effects and phase transitions 9. Neutron scattering 10. Infrared and Raman spectroscopy 11. Formal quantum mechanical description of lattice vibrations 12. Molecular dynamics simulations Appendices Problems Bibliography Index This is a terrific introduction to lattice dynamics. It is highly readable but very substantive. It's a great place to start learning this topic, and for many it may have all that one needs to know about the field.