The Physics of Phonons

Abstract

Elements of crystal symmetry: Direct lattice Reciprocal lattice Brillouin zone Crystal structure Point groups Space groups Symmetry of the Brillouin zone Jones zone Surface Brillouin zone Matrix representations of point groups. Lattice dynamics in harmonic approximation - semiclassical treatment: Introduction Lattice dynamics of a linear chain Lattice dynamics of three-dimensional crystals - phenomenological models Density of normal modes Numerical calculation of g(w) Lattice heat capacity. Lattice dynamics in the harmonic approximation - ab initio treatment: Introduction The frozen-phonon approach The linear response approach The planar force constant method. Anharmonicity: Introduction Hamiltonian of a general three-dimensional crystal Effect of anharmonicity on phonon states Effects of the selection rules on three-phonon processes Hamiltonian of an anharmonic elastic continuum Evaluation of three-phonon scattering strengths The quasi-harmonic approximation and Grueneisen's constant. Theory of lattice thermal conductivity: Introduction Relaxation-time methods Gree-Kubo linear response theory Second sound and Poiseuille flow of phonons. Phonon scattering in solids: Boundary scattering Scattering by static imperfections Phonon scattering in alloys Anharmonic scattering Phonon-electron scattering in doped semiconductors Phonon scattering due to magnetic impurities in semiconductors Phonon scattering from tunnelling states of impurities Phonon-photon interaction. Analysis of phonon relaxation and thermal conductivity results: Anharmonic decay of phonons Lattice thermal conductivity of undoped semiconductors and insulators Non-metallic crystals with high thermal conductivity Thermal conductivity of complex crystals Low-temperature thermal conductivity of doped semiconductors. Phonons in low dimensional solids: Introduction Surface vibrational modes Attenuation of surface phonons Phonons in superlattices Thermal conductivity of superlattices. Phonons in impure and mixed crystals: Introduction Localised vibrational modes in semiconductors Experimental studies of long-wavelength optical phonons in mixed crystals Theoretical models for long-wavelength optical phonons in mixed crystals Phonon conductivity of mixed crystals. Phonons in quasi-crystalline and amorphous solids: Introduction Phonons in quasi-crystals Structure and vibrational excitations of amorphous solids Vibrational properties of amorphous solids Low-temperature properties of amorphous solids. Phonon spectroscopy: Introduction Heat pulse technique Superconducting tunnel junction technique Optical techniques Phonons from Landau levels in 2DEG Phonon focusing and imaging Frequency crossing phonon spectroscopy Phonon echoes. Phonons in liquid helium: Introduction Dispersion curve and elementary excitations Specific heat Interactions between the excitations Kapitza resistance Quantum evaporation. Appendices: Density functional formalism The pseudopotential method Evaluation of integrals in sections 6.4.1.4 Negative-definitenss of the phonon off-diagonal operator ^D*L. References. Index.