Reliable evaluation of bulk thermoelectric materials requires the Seebeck coefficient, electrical resistivity, and thermal conductivity to be measured under mutually comparable conditions. For millimeter scale specimens, measurements using different instruments or mounting states are susceptible to deviations caused by anisotropy, contact conditions, and temperature gradient differences. In steady state thermal conductivity measurements, lateral radiative heat loss also makes the axial heat flow position dependent. To address these issues, a steady state multiparameter apparatus using a dual reference configuration and radiative heat loss correction is developed.
The test specimen is placed between two Inconel 600 reference specimens of known thermal conductivity. The heat flows entering and leaving the specimen are determined independently from the temperature gradients in the upper and lower references. Their imbalance is used to estimate the radiation dominated effective lateral heat loss and to correct the axial heat flow at the specimen mid plane. Thermal conductivity is calculated from the corrected heat flow, specimen geometry, and temperature difference. Without changing the mounting configuration, the Seebeck coefficient and electrical resistivity are subsequently measured, allowing the dimensionless figure of merit ZT to be evaluated for the same specimen under comparable thermal boundary conditions. A three dimensional steady state finite element model is established, and the simulated temperatures at the thermocouple positions are processed using the same data reduction procedure as in the experiment.
The simulation shows that lateral radiation produces a nonlinear axial temperature distribution. The intrinsic algorithmic error increases with temperature, surface emissivity, specimen aspect ratio, and thermocouple spacing, and is more pronounced for low thermal conductivity materials. Under the geometry and thermal boundary conditions of the present apparatus, this error remains below 1% for specimens with a thermal conductivity of 0.5–20 Wm^-1K^-1, a cross section of 5 mm×5 mm, and a length of 5–10 mm. This value describes the data reduction error under ideal inputs and does not include experimental uncertainties.
An Inconel 600 specimen is used to assess the thermal conductivity measurement. Between 296 and 313K, the measured values reproduce the literature temperature dependence but are 3.5%–4.6% higher. Bulk Bi₂Te₃, Bi₈₅Sb₁₅, and PbTe specimens are then measured and compared with commercial systems. For the recommended specimen geometry of 5 mm×5 mm×10 mm over 296–315 K, the maximum absolute relative deviations in thermal conductivity, Seebeck coefficient, electrical resistivity, and ZT are all below 5%. Repeated mounting of a Bi₂Te₃ specimen near 320 K gives a relative standard deviation of 0.57% in thermal conductivity. The relative expanded uncertainty of the room temperature thermal conductivity measurement is estimated to be 9.9% at a coverage factor of k = 2.
The apparatus enables rapid and internally consistent characterization of millimeter scale bulk thermoelectric materials. Its present uncertainty level is appropriate for material screening, trend evaluation, and engineering comparison rather than primary standard thermal conductivity metrology.