Temperature Dependent Thermodynamical and Thermoelectric Behaviour of Hafnium Based Insulators: An Ab-inito Characterization

This study aims to conduct a comprehensive investigation into the thermodynamic and thermoelectric potential of the (Ca,Sr,Ba)HfO\(_3\) family. This family has been selected for recognition because of their remarkable achievements in the areas of solar cell and energy storage applications using perovskites. The materials showcased exceptional efficiency and displayed immense potential in these areas of research. Our study delves into the thermodynamically assisted intruding thermoelectric properties of (Ca,Sr,Ba)HfO\(_3\) compounds. We thoroughly investigate their thermoelectric response, analyzing the impact of carrier concentrations and temperature effects. Our study reveals the noteworthy influence of the high entropic behavior of BaHfO\(_3\), leading to a reduction in thermal conductivity and ultimately enhancing thermoelectric performance. This study utilizes Density Functional Theory to analyze the structural, electronic, thermodynamic, and thermoelectric properties of the hafnium based perovskite oxide family (Ca,Sr,Ba)HfO\(_3\). Compounds confirm their cubic symmetry through the calculated tolerance factors (\(\tau\)). The lack of negative frequencies in the phonon dispersion curves suggests the thermal stability of this group. The decrease in Helmholtz free energy reliably indicates the thermodynamic stability of the system. This study explores the thermoelectric properties of (Ca,Sr,Ba)HfO\(_3\) under various levels of electron and hole doping. Variation in carrier concentration and temperature lead to a rise in the power factor. At a temperature of 700 K, the figure of merit (zT) exhibits a correlation with the electron doping concentration, ranging from 77 to 99%. The zT factor achieved a peak value of 88% within the temperature range of 300–700 K, accompanied by hole carrier concentrations ranging from 10\(^{17}\) to 10\(^{22}\). The zT value remains relatively constant within a specific temperature range, typically between 500 and 700 K, despite variations in hole carrier concentration. Furthermore, BaHfO\(_3\) demonstrates a significantly greater entropy in comparison to the other two members of its family. It appears that BaHfO\(_3\) has the potential to provide a substantial response in thermoelectric applications.