Analysis of the AC electrical response for (Ba,Pb)TiO₃ positive temperature coefficient ceramics

AC electrical properties of positive temperature coefficient of resistance (PTCR) ceramics of composition Ba_0.347Pb_0.65 La_0.003Ca_0.005Ti_0.995O₃ with Curie point T_c≈380°C were studied. A combined imaginary impedance/modulus plot was adopted to identify the appropriate equivalent circuit. Analysis of such circuit modified with a frequency dependent capacitor C_n gives satisfactory interpretation of the commonly observed inclined semicircle in the complex impedance plane. The exponent n, which is extracted from the depression angle and suggested to be associated with the “loss” degree of the material, shows a temperature dependence similar to that of a useful parameter extracted from the AC conductivity-frequency measurements. Both are ascribed to the conduction characteristics of the grain boundary, whose resistivity anomaly is the main contribution to PTCR jump. The validity of the present methodology is assessed not only by fitting well the observed non-ideality of real AC response, but also by confirming the Curie-Weiss behavior of the calculated grain boundary capacitance, which is the essence of well-accepted barrier theory (Heywang-Jonker model) proposed to explain the PTCR effect