Crystal- and defect-chemistry of fine grained thermistor ceramics on BaTiO$_{3}$ basis with BaO-excess

Bulk thermistor ceramics on BaTiO$_{3}$-basis with positive temperature coefficient (PTC) are used for surge protection devices, self-regulating heaters or temperature sensing elements for a long time. The origin of their high current limiting electric insulation resistance that only appears upon heating above the Curie temperature T$_{C}$ of the ferroelectric compound BaTiO$_{3}$ relies on a resistive back-to-back Schottky barrier layer, a space charge zone formed at the grain boundaries. This insulating layer is due to the physical or chemical absorption of oxygen combined with segregated acceptor-type metal vacancies created at the interface during processing. Generally the material compositions under mass production are off stoichiometric, enriched in TiO$_{2}$ and must be sintered under oxidizing conditions, since the oxidation process is crucial for the defect chemical reactions involved in the formation of the insulating grain boundary layer. Only in very recent years BaTiO$_{3}$-based ceramic formulations with BaO-excess for multilayer PTC thermistors, that can be fired even under reducing atmosphere, preventing the oxidation of internal metallic Ni electrodes, have been developed and commercialized. Upon careful reoxidation after firing these materials also show a very high positive temperature coefficient of resistance. The mechanisms in terms of defect chemistry involved in this process have not been understood clearly yet. Therefore in the present study the defect chemical background of BaO-rich La-doped BaTiO$_{3}$ thermistor ceramics regarding to their chemical composition, processing conditions and microstructure has been systematically investigated in detail. In the first part, experiments using impedance spectroscopy were conducted for electrical analysis using suitable equivalent circuits that adequately describe the PTCR effect in these materials. Unlike the case of conventional TiO$_{2}$-rich compositions not only a single resistive and capacitive (RC) components representing the grain boundary layers is responsible for the PTCR effect. Also surface effects represented by additional RC components significantly determine or even dominate the temperature characteristics of resistivity. Annealing experiments revealed that this resistive surface layer only appears when the ceramics are annealed in oxidizing atmosphere. In order to understand the origin of this phenomenon diffusion profiles obtained from in-situ oxidation treatments using $^{18}$O isotope as oxygen source were analyzed by SNMS. The results indicate that bulk diffusion only plays a significant role at the very surface of the ceramic samples. Penetration of oxygen towards the interior mainly occurs via grain boundary diffusion. In the case of stoichiometric samples, without BaO-excess no grain boundary diffusion in the relevant temperature range was observed. On the basis of these findings a possible defect chemical explanation for the mechanism of grain boundary resistivity has been proposed. In order to confirm this defect chemical model investigations on the DC conductivity in dependence of the oxygen partial pressure p(O$_{2}$) were performed in the second part of this [...