Electrothermal Instabilities in Barium Titanate Based Ceramics

An electrothermal analysis for barium titanate based ceramics is presented combining the Heywang–Jonker model for the electric resistivity with a heat dissipation mechanism based on natural convection and radiation in a one dimensional model on the device level with voltage as the control parameter. Both PTC and NTC effects are accounted for through the double Schottky barriers at the grain boundaries of the material. The problem formulated in this way admits uniform and non–uniform multiple steady state solutions that do not depend on the external circuit. The numerical bifurcation analysis reveals that the PTC effect gives rise to several multiplicites above the Curie point, whereas the NTC effect is responsible for the thermal runaway (temperature blowup). The thermal runaway phenomenon as a potential thermal shock could be among the possible reasons for the observed thermomechanical failures (delamination fracture). The theoretical results for the NTC regime and the thermal runaway are in agreement with experimental flash sintering results obtained for 3% and 8% yttria stabilized zirconia.