Composite dielectrics and conductors: simulation, characterization and design

Very large networks of randomly positioned resistors and capacitors have been used to simulate the microstructures of real two-phase (conductor-insulator) materials. These networks are found to exhibit fractional power law frequency dependences of dielectric properties and ac conductivity, of the type reported for a wide range of materials. The network results are related to the resistor and capacitor values by a simple logarithmic mixing rule. The same mixing rule is used to model the electrical characteristics of two-phase electrical composites. The results are tested using water impregnated lead zirconate titinate (PZT) ceramics samples that have a microstructure that forms a complex interconnected random array of conducting (water) and insulating regions. Excellent agreement is obtained between the experimental data and the modelling predictions based on the network simulation results. The power law exponents for ac conductivity and relative permittivity are found to be equal to the proportions of the composite occupied by the insulating and conducting phases, respectively. Studies of conducting polymer impregnated PZT are also presented which show less good agreement with modelling predictions.