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PTC (positive temperature coefficient) heaters are used as independent heating systems to control the temperature of the passenger compartment in cars. They play a role not only in e-mobility, but also in fossil-fueled vehicles, where the heat generated during operation is not sufficient to heat the passenger compartment during a cold start, for example, or to ensure a clear view when if the windshield is fogged or even iced over. Generally, electric vehicles produce too little heat, making heating concepts dependent on the vehicle battery for power, which has a negative impact on range, making efficient use of resources a priority. At present, almost all PTC heaters in cars are made of a barium titanate based ceramics with a lead content of up to 70 mol%. Because of its toxicological properties, the EU has issued a RoHS (Restriction of Hazardous Substances) directive that aims to reduce or eliminate lead content. At this time, there are possible replacement candidates, but the desired operating temperatures of > 150 °C have not yet been achieved and there are production problems, so that there is currently no alternative to lead-containing ceramics for PTC applications. The main aim of our research is to understand the fundamental of PTC production using lead-free barium titanate based ceramics and to transfer these to mixed system barium bismuth potassium titanate (BTK) and barium bismuth sodium titanate.

The poster "Determination of the Curie temperature by temperature-dependent X-ray diffraction of barium bismuth potassium titanate" presented in Vilnius 2024, which won the best poster competition, provides a small insight into our work. I would like to take this opportunity to thank you again for the award. Special thanks go to our team from KIT (Karlsruhe Institute of Technology, Germany), who always invest a lot of time and effort in our research and create new ideas through scientific discussions.

Figure 1: The Processing Team of IAM-KWT involved as co-authors, from left to right: Günter Schell, Swen Subotić, Annika Eberwein, Tabea Weismann and Claudia Bucharsky.  

The most common method for determining Curie temperature (TC) is the investigation of the relative permittivity as a function of temperature. However, this approach is restricted by first to second-order phase transformation resulting in a diffuse transition over a wide temperature range, often lacking a clear maximum in permittivity. The phase transformation of barium titanate shifts from first to second order as the amounts of Bi and K are increased, shown in Figure 2. As a result, TC is overestimated, or the materials exhibit second-order behavior. 

Figure 2: Permittivity measurement at 1 kHz from BT to increasing BKT content; the index number is the mol% of BKT in BT

To overcome these challenges, TC is investigated by examining the phase transformation of the crystallographic structure. This can be accomplished through temperature-dependent X-ray diffraction. Still, the diffuse transformation over a broad temperature range complicates the accurate determination of TC. In this study we present a method for defining TC for materials showing second-order behavior, even in the absence of an order-independent phase transformation. A distinctive feature of the presented method is the mathematical determination of TC based on lattice parameters.

Figure 3: Temperature-dependent X-ray diffraction pattern, reducing 2theta area to characteristics reflections 002 and 200 also reduces measurement time by 91 %

To optimize the measurement time, the angular range 2θ was restricted to the characteristic reflections 002 and 200, see Figure 3. This reduced the measurement time from 94 h to 8 h while maintaining the same significance of the results.

Figure 4: Defining TC with maximum curvature for first and second order phase transition

The next step involves the mathematical definition of TC independent of the order of phase transition. For this purpose, the maximum curvature of the lattice parameters was determined over temperature, see Figure 4. A further advantage of this method is that only refinement data of the tetragonal phase are required.

The investigations were first carried out on pure BT and pure BKT (BTK100). The determined TC values agree with known literature for both systems as well as with our measurements shown in Figure 5.

Figure 5:Results of TC for different BKT amounts and comparison of LCR method and MC-Method

Furthermore, the method was tested on compositions with different BKT contents in BT. For a solid solution, a linear relationship between BKT content and TC is usually found according to Vegard's rule. This linear relationship was confirmed by mathematical determination using the developed MC method.