A Novel Strategy for Anisotropic Thermoelectric Characterization: Tensor Inversion Method

Thermoelectric (TE) materials, which enable direct conversion between thermal and electrical energy, have long held promise for applications in waste heat recovery, solid-state refrigeration, and deep-space exploration.^1-3 Their energy conversion efficiency is governed by the dimensionless figure of merit zT=S²T/ρκ, where the Seebeck coefficient (S), electrical resistivity (ρ), and thermal conductivity (κ) are all second-rank tensors with values strongly dependent on crystallographic orientation.⁴ In layered materials such as Bi₂Te₃⁵ and SnSe⁶, this anisotropy is particularly pronounced, making accurate characterization of intrinsic properties a persistent challenge. Conventional methodologies rely on single crystals precisely cut along principal crystallographic axes, a process that is not only time-consuming but also prone to orientation errors, mechanical damage, and limitations in reproducing true anisotropic behavior. These constraints have led to significant discrepancies between measured and intrinsic properties, hindering the establishment of reliable structure-property relationships and impeding the development of orientation-optimized materials.