In the microcrystalline regime, the electrical (impedance/dielectric) behavior of grain boundarycontrolled 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.
The reduction of grain size from the microcrystalline regime into the nanocrystalline regime is known to produce significant changes in the transport properties of polycrystalline ceramics. Part 1 of this series [1] described the development of a pixel-based finite-difference "nested-cube model" (NCM), which was used to evaluate existing composite models for the electrical/dielectric properties of polycrystalline ceramics over the entire range of grain core vs. grain boundary volume fractions, from the nanocrystalline regime to the microcrystalline regime. Part 2 addresses grain shape and periodicity effects in such composite modeling, and the extraction of local materials properties (conductivity, dielectric constant) from experimental impedance/dielectric spectroscopy data.
In the microcrystalline regime, the 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boundary layers can represent a significant volume fraction of the overall microstructure and simple layer models are no longer valid. This work describes the development of a pixel-based finite-difference approach to treat a “nested cube model” (NCM), which more accurately calculates the current distribution in polycrystalline ceramics when grain core and grain boundary dimensions become comparable. Furthermore, the NCM approaches layer model behavior as the volume fraction of grain cores approaches unity (thin boundary layers) and it matches standard effective medium treatments as the volume fraction of grain cores approaches zero. Therefore, the NCM can model electroceramic behavior at all grain sizes, from nanoscale to microscale. It can also be modified to handle multi-layer grain boundaries and property gradient effects (e.g., due to space charge regions).
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