Mapping grain boundary heterogeneity at the nanoscale in a positive temperature coefficient of resistivity ceramic

Despite being of wide commercial use in devices, the orders of magnitude increase in resistance that can be seen in some semiconducting BaTiO₃-based ceramics, on heating through the Curie temperature (T_C), is far from well understood. Current understanding of the behavior hinges on the role of grain boundary resistance that can be modified by polarization discontinuities which develop in the ferroelectric state. However, direct nanoscale resistance mapping to verify this model has rarely been attempted, and the potential approach to engineer polarization states at the grain boundaries, that could lead to optimized positive temperature coefficient (PTC) behavior, is strongly underdeveloped. Here we present direct visualization and nanoscale mapping in a commercially optimized BaTiO₃-PbTiO₃-CaTiO₃ PTC ceramic using Kelvin probe force microscopy, which shows that, even in the low resistance ferroelectric state, the potential drop at grain boundaries is significantly greater than in grain interiors. Aberration-corrected scanning transmission electron microscopy and electron energy loss spectroscopy reveal new evidence of Pb-rich grain boundaries symptomatic of a higher net polarization normal to the grain boundaries compared to the purer grain interiors. These results validate the critical link between optimized PTC performance and higher local polarization at grain boundaries in this specific ceramic system and suggest a novel route towards engineering devices where an interface layer of higher spontaneous polarization could lead to enhanced PTC functionality.