Theoretical Analysis of IS of Polycrystalline Materials with Blocking or Conducting Grain Boundaries: From Microcrystals to Nanocrystals

Impedance spectra (IS) of a polycrystalline sample with macroscopic dimensions are analyzed based on the brick layer model with parallel and series grain boundaries (gb). The gb width is taken as 0.5 nm, in accordance with the classical Fisher model of gb diffusion. Three mean grain size values of 500, 50, and 5 nm are simulated, corresponding to a change from microcrystalline to nanocrystalline ceramics. A constant conductivity of the grain interior S/m) and of the series gb S/m) is assumed. Impedance spectra are simulated for parallel gb conductivity values between (blocking) and S/m (conducting). Two impedance arcs are observed in all cases, but the conventional attribution of the high-frequency arc to the grain interior and the low-frequency semicircle to the series gb is valid only when the parallel gb contribution is insignificant, i.e., for low parallel gb conductivity and/or large mean grain size.