Transient Thermal Gradients in Barium Titanate Positive Temperature Coefficient (PTC) Thermistors

Barium titanate positive temperature coefficient (PTC) ceramic disk thermistors can suffer major mechanical damage if inhomogeneous heating occurs under voltage. The steady-state and transient temperature distributions for thin disk samples (radius of 5 mm, thickness of 2 mm) have been studied with an infrared microscope, using a spatial resolution of 35 µm. The transient temperature distribution is observed to be particularly sensitive to the electrical boundary conditions during the initial heating period after application of a voltage. Small variations in electrode symmetry can lead to axial asymmetric thermal gradients up to 25 K/mm across the entire rim when an ac voltage of 100 V is applied. A finite-difference model in two dimensions, based on solution of the heat equation with a local-temperature-dependent Joule heating-source term, has been developed to describe the axial and radial transient temperature distributions in the cylindrical geometry. The predictions reveal current concentration at the edge of an electrode when the metal layer coverage is slightly smaller than that of the opposite face. This phenomenon results in stronger localized heating in a ring that initiates the thermal gradient.