Crystal symmetry, lattice vibrations, and optical spectroscopy of solids : a group theoretical approach

"This book provides a comprehensive treatment of the two fundamental aspects of a solid that determine its physical properties: lattice structure and atomic vibrations (phonons). The elements of group theory are extensively developed and used as a tool to show how the symmetry of a solid and the vibrations of the atoms in the solid lead to the physical properties of the material. The uses of different types of spectroscopy techniques that elucidate the lattice structure of a solid and the normal vibrational modes of the atoms in the solid are described. The interaction of light with solids (optical spectroscopy) is described in detail including how lattice symmetry and phonons affect the spectral properties and how spectral properties provide information about the material's symmetry and normal modes of lattice vibrations. The effects of point defects (doping) on the lattice symmetry and atomic vibrations and thus the spectral properties are discussed and used to show how material symmetry and lattice vibrations are critical in determining the properties of solid state lasers."--pub. desc Machine-generated Contents Note: Ch. 1 Introduction -- 1.1. The Hamiltonian Of A Crystalline Solid -- 1.2. The Adiabatic Approximation -- 1.3. The Role Of Symmetry -- 1.4. The Symmetries Of The Hamiltonian -- Reference -- Ch. 2 Concepts Of Group Theory -- 2.1. Properties Of A Group -- 2.2. Subgroups, Cosets, And Classes -- 2.3. Theory Of Representations -- 2.4. Orthogonality Relations -- 2.5. Characters Of A Matrix Representation -- 2.6. Reduction Of A Reducible Representation -- 2.7. Basis Functions For Irreducible Representations -- 2.8. Direct Product Representations -- 2.9. The Fundamental Theorem For Functions Transforming Irreducibly -- 2.10. Product Groups And Their Representations -- 2.11. Connection Of Quantum Mechanics With Group Theory -- Ch. 3 Crystal Symmetries -- 3.1. Unit Cells And Space Lattices -- 3.2. Miller Indices -- 3.3. The Crystal Systems -- 3.3.1. The Four Two-dimensional Crystal Systems -- 3.3.2. The Seven Three-dimensional Crystal Systems -- 3.4. The Bravais Lattices -- 3.4.1. The Five Bravais Lattices In Two Dimensions -- 3.4.2. The Fourteen Bravais Lattices In Three Dimensions -- Ch. 4 Group Theoretical Treatment Of Crystal Symmetries -- 4.1. Space Groups -- 4.2. The Crystallographic Point Groups -- 4.2.1. Two-dimensional Crystallographic Point Groups -- 4.2.2. Three-dimensional Crystallographic Point Groups -- 4.2.3. Site Groups -- 4.3. The Invariant Subgroup Of Primitive Translations: Bravais Lattices -- 4.4. The Compatibility Of Rotational And Translational Symmetries And Its Relevance To Space Groups -- 4.5. The Irreducible Representations Of A Group Of Primitive Translations Brillouin Zones -- 4.6. The Irreducible Representations Of Space Groups -- 4.6.1. Effects Of Translational Symmetry -- 4.6.2. Effects Of Rotational Symmetry -- 4.6.3. General Properties Of The Irreducible Representations -- 4.6.4. Small Representations For Different Points Of The Brillouin Zone -- 4.7. Example I. Symmorphic Group C14v -- 4.8. Example Ii. Non-symmorphic Group C24v -- References -- Ch. 5 Scattering Of X-rays By Crystals -- 5.1. Introduction -- 5.2. Scattering From A Single Electron -- 5.3. Scattering From A Single Atom -- 5.4. Scattering From The Atoms In The Unit Cell Of A Crystal -- 5.5. Scattering From A Crystal -- 5.6. Interpretation Of Laue Equations In Reciprocal Space -- 5.7. Methods Of X-ray Diffraction -- 5.7.1. The Laue Method (see Fig. 5.8a) -- 5.7.2. The Bragg Method (see Fig. 5.8b) -- 5.7.3. The Debye-scherrer Method (see Fig. 5.8c) -- References -- Ch. 6 Lattice Vibrations Of Crystals -- 6.1. The Infinite Linear Crystal -- 6.2. The Finite Linear Crystal -- 6.3. Normal Modes Of Vibration Of A Linear Crystal -- 6.4. Linear Crystal With A Basis -- 6.5. Lattice Vibrations In Three Dimensions -- 6.5.1. The Equations Of Motion -- 6.5.2. Allowed Values Of K. Density Of Phonon Modes -- 6.5.3. Normal Modes Of Vibration -- 6.5.4. Energy Levels -- 6.5.5. Particular Modes Of Vibration -- 6.5.6. Spectrum Of Lattice Vibrations -- 6.6. Group Theory And Lattice Vibrations -- 6.6.1. Properties Of The Normal Coordinates -- 6.6.2. The Frequency Eigenvalues And The Polarization Vectors -- 6.6.3. Additional Degeneracies Not Due To Spacelike Symmetries -- 6.6.4. Time-reversal Degeneracy -- 6.7. Group-theoretical Analysis Of The Lattice Vibrations Of A Linear Crystal -- 6.7.1. Case Of One Atom Per Unit Cell -- 6.7.2. Case Of Two Atoms Per Unit Cell -- 6.8. Group-theoretical Analysis Of The Lattice Vibrations Of A Three-dimensional Crystal -- 6.9. Example I. Lattice Vibrations Of A Two-dimensional Crystal With Symmetry C14v -- 6.10. Example Ii. Lattice Vibrations Of A Two-dimensional Crystal With Symmetry C24v -- References -- Ch. 7 Thermodynamics Of Lattice Vibrations -- 7.1. Thermodynamics Of Specific Heats -- 7.2. The Classical Theory Of The Specific Heats Of Solids -- 7.3. The Einstein Theory Of Specific Heat -- 7.4. The Debye Theory Of Specific Heat -- 7.4.1. The Specific Heat Of A Linear Crystal -- 7.4.2. The Debye Theory Applied To A Linear Crystal -- 7.4.3. The Debye Theory Applied To A Three-dimensional Crystal -- 7.5. Temperature Dependence Of The Amplitude Of Vibrations Solids. The Lindemann Law Of Melting -- References -- Ch. 8 Effect Of Lattice Vibrations On X-ray Scattering And Neutron Scattering -- 8.1. Effect Of Lattice Vibrations On The Intensity Of The Scattered Radiation -- 8.1.1. The Intensity Of The Scattered Radiation -- 8.1.2. The Effect Of Lattice Vibrations: Einstein Model -- 8.1.3. The Effect Of Lattice Vibrations: Normal Mode Treatment -- 8.2. Theory Of Neutron Scattering -- 8.3. Elastic Neutron Scattering -- 8.4. Inelastic Neutron Scattering -- 8.5. Application Of Neutron Scattering To The Study Of Lattice Vibrations -- References -- Ch. 9 Interaction Of Radiation With Matter -- 9.1. The Classical Radiative Field -- 9.2. The Quantum Theory Of The Radiative Field -- 9.3. The Hamiltonian Of A Charged Particle In An Electromagnetic Field -- 9.4. The Interaction Between A Charged Particle And A Radiative Field -- 9.5. First-order Processes. Absorption And Emission Of Radiation -- 9.6. Second-order Processes -- 9.6.1. Matrix Element Due To H1 -- 9.6.2. Matrix Elements Due To H2 -- 9.6.3. Effective Matrix Element -- 9.6.4. Transition Rates Of Scattering Processes -- References -- Ch. 10 Optical Spectra Of Impurities In Solids I -- 10.1. Impurities In Crystals -- 10.2. Review Of The Theory Of Small Vibrations (classical) -- 10.3. Harmonic And Anharmonic Relaxation -- 10.4. Review Of The Theory Of Small Vibrations (quantum Mechanical) -- 10.5. The Effect Of Impurities On Lattice Vibrations -- 10.6. The Franck-condon Principle -- 10.7. Absorption And Emission In Crystals -- 10.8. Purely-electronic (zero-phonon) Transitions -- 10.9. Characteristics Of The Zero-phonon Lines -- 10.10. Phonon-assisted Transitions -- 10.11. Radiative Transitions In The Presence Of Localized Vibrations -- 10.12. Classification Of Vibronic Spectra -- References -- Ch. 11 Optical Spectra Of Impurities In Solids Ii -- 11.1. Summary Of Previous Results -- 11.2. Deviations From The Franck-condon Approximation -- 11.3. Deviations From The Adiabatic Approximation. Radiationless Transitions -- 11.4. A Simple Model For Laser Crystals: An Effective Hamiltonian -- 11.5. Radiative, Vibronic, And Radiationless Transitions Of Magnetic Impurities -- 11.6. Selection Rules For Vibronic Transitions -- 11.7. Effect Of Temperature On The Position And Shape Of A Purely-electronic Line -- 11.7.1. Thermal Line Shift -- 11.7.2. Thermal Broadening Of Sharp Lines -- References -- Ch. 12 Interaction Of Light With Lattice Vibrations: Infrared Absorption And Inelastic Light Scattering -- 12.1. General Characteristics Of Infrared Absorption By Crystals -- 12.2. Infrared Transitions In A Molecular System -- 12.3. Momentum And Energy Conservation In Infrared Absorption -- 12.4. Quantum Theory Of Infrared Absorption -- 12.5. Reststrahl (one-phonon) Absorption -- 12.6. Two-phonon Absorption -- 12.7. Selection Rules For Infrared Absorption -- 12.8. The Effect Of Impurities On Infrared Absorption Spectra -- 12.9. Infrared Absorption In Homopolar Crystals -- 12.10. General Characteristics Of Raman Scattering From Crystals -- 12.11. Theory Of Raman Scattering -- 12.12. Transition Polarizability -- 12.13. Energy Scattered In Raman Scattering Experiments -- 12.14. Selection Rules For Raman Scattering -- 12.15. The Effect Of Impurities On Raman Scattering -- 12.16. Brillouin Scattering -- References -- Ch. 13 Lattice Vibrations And Lasers -- 13.1. Non-radiative Transitions -- 13.2. Single-wavelength Lasers -- 13.2.1. Optical Transitions In Rare Earth Ion Lasers -- 13.2.2. Radiationless Decay Processes In Rare Earth Ion Lasers -- 13.3. Multiple-wavelength Lasers -- References. Baldassare Di Bartolo, Boston College, Usa, Richard C. Powell, University Of Arizona, Usa. Includes Bibliographical References And Index.