Impedance/dielectric spectroscopy of electroceramics-part 1: Evaluation of composite models for polycrystalline ceramics

In the microcrystalline regime, the electrical (impedance/dielectric) behavior of grain boundary-controlled electroceramics is well described by the "brick-layer model" (BLM). In the nanocrystalline regime, however, grain boundary layers can represent a significant volume fraction of the overall microstructure. Simple boundary-layer models no longer adequately describe the electrical properties of nanocrystalline ceramics. The present work describes the development of a pixel-based finite-difference approach to treat a "nested-cube model" (NCM), which is used to investigate the validity of existing models for describing the electrical properties of polycrystalline ceramics over the entire range of grain core vs. grain boundary volume fractions, from the nanocrystalline regime to the microcrystalline regime. The NCM is shown to agree closely with the Maxwell-Wagner effective medium theory.