Electrothermal Instabilities in Barium-Titanate-Based Ceramics

Abstract

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 positive-temperature-coefficient (PTC) and negative temperature coefficient (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 the experimental flash sintering results obtained for barium titanate, and 3% and 8% yttria-stabilized zirconia.

Keywords

• BaTiO₃ and titanates
• thermistor
• Joule heating
• non-local problem
• bifurcation analysis
• delamination fracture