Student Number : 0009815Y - PhD thesis - School of Physics - Faculty of Science / Determining the properties of composites and how these relate to those of the components and the microstructure is extremely useful as it enables the understanding of existing materials and the design of new materials with a variety of applications. However, the link between the ac conductivity data and the microstructure and composition of the composite is not a simple one. Simulations of binary composites are presented which show that from relatively simple component properties arise complex composite properties. Accurate identi¯cation of the components of composites, using characteristic frequencies, is demonstrated for simulated and actual experimental data. The Maxwell-Wagner and Brick Layer Models, which are often applied beyond the range of their original derivation, are found to consistently ¯t the data of yttria-stabilized zirconia ceramics measured at various tempera- tures. The results from ¯tting single crystal and polycrystalline sample data indicate that accurate modeling of the properties of the polycrystalline sam- ples requires more theoretical work on the conduction mechanisms in single crystals and the grains of the ceramics. Data from a polyester-resin/silicon system is found to be best ¯tted us- ing the Single Exponent Phenomenological Percolation Equation (SEPPE) with experimentally measured component properties as input. The percola- tion threshold obtained suggests a system where the insulator tends coat the conductor. The results show that, with the actual component properties as input, the SEPPE can be used to qualitatively and semi-quantitatively model and ¯t composite ac conductivity data. Analysis of the ac conductivity of liquid-phase-sintered silicon carbide ce- ramics showed that for this system, the features often observed in the imped- ance spectra are all due to a multi-component grain bondary/binder phase and not the SiC grains. This multi-component grain boundary phase can be ¯tted accurately to the Brick Layer Model, indicating a microstructure where an insulating component coats a more conducting component.