Validity criterion for evaluating the dimensionless figure of merit in ambient air using time-domain impedance spectroscopy

Abstract The performance of thermoelectric materials, which enable the direct conversion of heat into electricity, is quantified by the dimensionless figure of merit, zT , at temperature T . However, the reliable evaluation of zT remains a major experimental challenge in thermoelectric research. In this study, we address this research gap by developing a measurement science framework to evaluate the effective dimensionless figure of merit, zT eff ( P ), under atmospheric pressure using the time-domain impedance spectroscopy (TDIS) method. By explicitly incorporating convective heat loss and geometric factors, we define quantitative validity criteria that clarify the measurable range and limitations of ambient air TDIS measurements. Two dimensionless parameters—the Biot number Bi( P ) under pressure P and the geometric factor χ —are introduced to construct practical design maps for selecting appropriate sample geometries. In addition, a length scale-based criterion, expressed by the normalized parameter Λ( P ), is introduced to assess the validity of the one-dimensional (1D) heat-flow assumption along the thermoelectric element. The results show that zT eff ( P ) ≈ zT when Λ( P ) ⩽ 0.1. Although quantitative differences between the 1D model incorporating the correction factor and three-dimensional simulations appear at Λ( P ) ⩾ 0.1, qualitative agreement is still maintained. The proposed framework enables a geometry-corrected and measurement-oriented evaluation of zT eff ( P ), thereby establishing TDIS, when operated under ambient air conditions, as a measurement science-based screening-oriented tool for thermoelectric characterization under non-ideal environments.