A bimodal grain size model for predicting the dielectric constant of calcium copper titanate ceramics

The bimodal distribution of grain size is frequently observed in calcium copper titanate (CaCu3Ti4O12 or CCTO) ceramics that exhibit high dielectric constant. In this study, we propose an analytical model composed of grains of two different sizes to estimate the dielectric behavior of CCTO based on microstructural features. Important assumptions are (1) CCTO is a barrier layer dielectric and (2) the insulating layer thickness is the same in both large and small grains. Explicit expressions for the effective dielectric constant of serial, parallel, and logarithmic mixture models are given. When compared with experimental results, the present bimodal model appears to be acceptable for describing the dielectric behavior of CCTO.