THE DETERMINATION OF HYDROGEN IONS

By JENNIFER RAMIREZ

CONTENTS INTRODUCTION THE RADIO REVOLUTION METAL OXIDE MICROWAVE DIELECTRIC CERAMICS REVIEW OF DIELECTRIC LOSS STRUCTURE OF THESIS PUBLICATIONS BY THE AUTHOR REFERENCES MODELLING DIELECTRIC RESONATORS INTRODUCTION TO MICROWAVE DIELECTRICS MEASURING MICROWAVE DIELECTRIC PROPERTIES MODELLING SHIELDED DIELECTRIC RESONATORS MAXWELL EQUATIONS IN CYLINDRICAL COORDINATES MULTILAYER WAVEGUIDE EIGENVALUES THE RADIAL MODE MATCHING METHOD CALCULATING RESONATOR LOSSES EXAMPLE RESONATOR SUMMARY AND CONCLUSIONS MEASUREMENT OF DIELECTRIC PROPERTIES DIELECTRIC RESONATOR MEASUREMENTS CALCULATING DIELECTRIC PROPERTIES CRYOGENIC MEASUREMENTS CHARACTERISATION OF AG-PLATED CAVITY CHARACTERISATION OF SINGLE-CRYSTAL QUARTZ SUPPORT MAGNESIUM OXIDE — MGO LANTHANUM ALUMINATE — LAALO3 TITANIUM DIOXIDE (RUTILE) — TIO2 ALUMINIUM OXIDE (SAPPHIRE) — AL2O3 LATTICE DYNAMICS AND DENSITY FUNCTIONAL PERTURBATION THEORY LATTICE DYNAMICS HAMILTONIAN OF A SYSTEM OF IONS AND ELECTRONS THE BORN–OPPENHEIMER APPROXIMATION HELLMANN–FEYNMAN THEOREM HOHENBERG–KOHN THEOREM KOHN–SHAM ORBITALS THE LOCAL DENSITY APPROXIMATION LINEAR RESPONSE DFT PHONON MODES IN CRYSTALS LONG-WAVELENGTH PHONONS AND ELECTRIC FIELDS IMPLEMENTATION THE LYDANNE-SACHS-TELLER RELATION HARMONIC PROPERTIES OF METAL OXIDE DIELECTRICS ALUMINIUM OXIDE (SAPPHIRE) — A-AL2O3 THEORY OF ANHARMONIC PHONONS BEYOND THE HARMONIC APPROXIMATION ANHARMONIC HAMILTONIAN QUANTUM FIELD THEORY OF ANHARMONIC PHONONS THE EVOLUTION OPERATOR GRAPHICAL REPRESENTATION OF GREEN FUNCTIONS EVALUATING MATSUBARA SUMS THE SELF ENERGY, R LOOP INTERACTION BUBBLE INTERACTION HIGHER ORDER INTERACTIONS DYSON’S EQUATION AND DRESSED PHONONS ANHARMONIC PROPERTIES OF MGO SELF-ENERGY OF PHONONS THE EFFECT OF ISOTOPES ON SELF-ENERGY LINEAR COEF?CIENT OF THERMAL EXPANSION THERMAL STRAIN CONTRIBUTION TO PHONON SELF-ENERGY TEMPERATURE COEF?CIENT OF PERMITTIVITY DIELECTRIC LOSS PHONON–PHONON CONTRIBUTION TO THE SELF-ENERGY TWO-PHONON DENSITY OF STATES ENERGY CONSERVATION SURFACES WEIGHTED TWO-PHONON DENSITY OF STATES ANHARMONIC PHONON COUPLING TENSORS THE RELAXATION FREQUENCY, C FREQUENCY DEPENDENCE TEMPERATURE DEPENDENCE DISCUSSION AND CONCLUSIONS