Determination of Anisotropic Thermoelectric Properties of Bismuth Using a Tensor Inversion Method

Conventional methods for quantifying thermoelectric anisotropy rely on precisely aligned crystals, which are time-consuming and error-prone. To address this, we propose a tensor inversion method integrating transport measurements with EBSD-derived Euler angles to determine the intrinsic tensors of as-grown bismuth crystals. This method reconstructs the full second-rank thermoelectric tensors—including electrical resistivity, thermal conductivity, and the Seebeck coefficient—by transforming transport data between the sample coordinate system (SCS) and the crystal coordinate system (CSC). The inverted tensor components of pure bismuth show excellent agreement with reported principal-axis values, validating the accuracy of this method. Moreover, the reversibility of the tensor inversion approach allows for complete visualization of the directional dependence of the thermoelectric figure of merit (zT), revealing its full angular and crystallographic orientation distribution for the first time. This bidirectional framework not only provides a convenient pathway for the reconstruction of intrinsic transport tensors but also enables the prediction of orientation-dependent properties, thereby offering a robust tool for analyzing anisotropic transport behavior and guiding the optimization of thermoelectric performance.