Bimodal grain sized barium titanate dielectrics enabled under the cold sintering process

In barium titanate (BaTiO₃) the relative permittivity varies as a function of grain size due to the influence of various sizes and scaling effects. The cold sintering process (CSP) has been applied to sinter nanocrystalline BaTiO₃ (<200 nm), however in conventionally sintered BaTiO₃ a maximum relative permittivity is achieved at average grain sizes around 0.8 μm. In this work the feasibility of cold sintering 1 μm BaTiO₃ inclusions in ratios of fine-grained BaTiO₃ matrixes from 50 to 200 nm is investigated. Occurrences of both conformal sintering of inclusions into the matrix and constrained sintering with residual porosity are observed. Subsequently, electrical resistivities increased from 1 × 10⁸ Ω cm to approximately 1 × 10¹² Ω cm by a post CSP heat treatment of 500 °C. Relative permittivity of annealed samples increases systematically following a logarithmic mixing law as a function of matrix grain size and increasing the ratio of inclusions to matrix.