## Introduction to Lattice DynamicsThe 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. |

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### Contents

Some fundamentals | 1 |

The harmonic approximation and lattice dynamics | 18 |

general principles | 36 |

How far do the atoms move? | 55 |

Lattice dynamics and thermodynamics | 64 |

Formal description | 80 |

Acoustic modes and macroscopic elasticity | 95 |

Anharmonic effects and phase transitions | 101 |

Formal quantummechanical description of lattice vibrations | 167 |

Time and position dependence | 174 |

Appendix A The Ewald method | 195 |

Appendix B Lattice sums | 202 |

Landau theory of phase transitions | 210 |

Appendix E Classical theory of coherent neutron scattering | 221 |

Appendix F Time correlation functions | 229 |

Appendix H Published phonon dispersion curves | 236 |

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### Common terms and phrases

absorption acoustic modes amplitude anharmonic interactions atomic displacements average behaviour Brillouin zone Bruce and Cowley calculated Chapter classical correlation function corresponding cubic Debye defined density described dispersion curves displacive phase transitions dynamical matrix effects eigenvectors elastic constant electrons equations of motion example experimental data factor fluctuations force constants Fourier transform free energy give given by equation Hamiltonian heat capacity high-temperature phase infrared interatomic potential internal modes Landau free energy Landau theory lattice dynamics lattice energy lattice vibrations low-temperature measured method mode frequency molecular crystals neutron scattering normal mode normal mode coordinates obtained optic modes order parameter particle phase transitions phonon phonon frequencies polarisability quantity quantum mechanics quency Raman reciprocal space Reduced wave vector Salje sample shell model shown in Figure simulation soft mode spectroscopy spectrum symmetry directions temperature dependence thermal expansion thermodynamic tion transition temperature transverse unit cell velocity wave vector zero zone boundary

### Popular passages

Page 247 - Glass AM 1977 Principles and Applications of Ferroelectrics and Related Materials (Oxford: Oxford University Press) [179] von Hippel A, Breckenridge RG, Chesley FC and Tisza L 1946 Ind.