Uncertainty Quantification for a High Temperature Z-Meter Characterization System

Few systems have been developed for simultaneous measurement of thermal, electrical, and thermoelectric properties at high temperatures (> 600K) relevant to high temperature waste heat recovery applications. The Z-Meter approach enables simultaneous measurements of the three thermoelectric properties from which the figure of merit, ZT, is calculated. The method combines an ASTM D5470 reference bar measurement for thermal conductivity (often used for thermal interface materials) with the added functionality of electrical measurements for electrical conductivity and Seebeck Coefficient. Traditionally, this technique has been employed utilizing a very small temperature difference across the sample (ΔT ≈ 1 - 2K) and test temperatures between approximately 300 - 600K, but thermoelectric materials must generally have sizable temperature gradients across them to achieve desirable performance as increased operating temperatures generally allow access to higher grade waste heat, and the relevant properties are also significantly temperature dependent. Here, we design a Z-meter system to evaluate the performance of materials under large temperature differences relevant to such applications. The design of the instrument is driven by uncertainty quantification to minimize measurement error. A detailed design of experiments model enables informed decisions regarding the component and system designs (e.g. placement of the temperature sensors). This design of experiments model includes effects of radiative losses in the meter bars as well as the losses due to the measurement probes installed along the bars. The system as designed is capable of hot side temperatures of 1350K with the thermoelectric material to temperature gradients on the order of 500K. The elevated temperatures are necessary to fill a gap in characterization equipment for very high temperature thermoelectric applications. The measurement system requires vacuum pressure of 1 μTorr for suppression of convection losses and to prevent of oxidation of the hot system components. The system design employs a loading platform that allows the interfacial sample/bar loading to be changed in situ without breaking system vacuum allowing for high measurement throughput. Additionally, a triad of integrated load cells ensure repeatable loading conditions for the sample interface. The combination of simultaneous thermal, electrical, and thermoelectric properties at high temperatures with controlled mechanical loading opens the doors to new understanding of thermoelectrics for high temperature waste heat recovery. Ultimately, this uncertainty analysis coupled with the design process demonstrates the limits of using this system and guides operating conditions for given expected sample properties.