Impedance and modulus spectroscopy of semiconducting BaTiO3 showing positive temperature coefficient of resistance

Polycrystalline barium titanate that has been doped to give a positive temperature coefficient of resistance (PTCR) effect is an inhomogeneous material electrically. Analysis of ac impedance data using the complex impedance plane representation gives the dc resistance of PTCR ceramics. By additional use of the complex electric modulus formalism to analyze the same data, the inhomogeneous nature of the ceramics may be probed. This reveals the presence of two, sometimes three elements in the equivalent circuit. Grain-boundary and bulk effects may be distinguished from capacitance data: grain-boundary effects have temperature-independent capacitances, whereas bulk effects show a capacitance maximum at the Curie point and Curie–Weiss behavior above the Curie point. Both grain-boundary and bulk effects appear to contribute to the PTCR effect. These results reveal limitations in current theories of the PTCR effect.