The brick layer model revisited: Introducing the nano-grain composite model

Brick layer models (BLMs), although applicable at the microscale, are inappropriate for characterizing electroceramics at the nanoscale. A new construct, the nano-grain composite model (n-GCM), has been developed to model/analyze the AC-impedance response of equiaxed polycrystalline electroceramics. The procedure employs a set of equations, based on the Maxwell-Wagner/Hashin-Shtrikman effective medium model, to calculate local electrical properties (conductivity, dielectric constant) for both "phases" (grain core, grain boundary) from experimental AC-impedance spectra and also, for the first time, grain core volume fraction. The n-GCM method was tested on a model system (a 3D-BLM material) and demonstrated with a test case (nanograined yttria-stabilized zirconia). The method appears to be applicable only at nanograin sizes, i.e., 10-100 nm. Limitations of the method, in terms of grain size (10-100 nm) and experimental uncertainty, are also discussed.