Using the Compatibility Factor to Design High Efficiency Segmented Thermoelectric Generators

Using thermoelectric compatibility, efficient thermoelectric generators are rationally designed. With examples, compatible and incompatible systems are explained and materials proposed for targeted development. The compatibility factor explains why segmentation of TAGS with SnTe or PbTe produces little extra power, while filled skutterudite increases the efficiency from 10.5% to 13.6%. High efficiency generators are designed with compatible ntype La2Te3, and similar p-type material, while incompatible SiGe alloys actually reduce the efficiency. A refractory metal with high p-type thermopower (> 100 μV/K) is required for development. The Chevrel compound Cu4Mo6Se8 is a compatible p-type metal that provides a modest increase in efficiency. A fully segmented generator using Bi2Te3-type, PbTe, TAGS, Zn4Sb3, skutterudite, La2Te3, and Chevrel compounds between 25° C and 1000° C will achieve 18.1% conversion efficiency. INTRODUCTION The efficiency of a thermoelectric generator is governed by the thermoelectric properties of the generator materials and the temperature drop across the generator. The temperature difference, ∆T between the hot side (Th) and the cold side (Tc) sets the upper limit of efficiency through the Carnot efficiency ηC = ΔT TH . The thermoelectric material governs how close the efficiency can be to Carnot primarily through the thermoelectric figure of merit, z, defined by z = α 2 κρ . The relevant materials properties are the Seebeck coefficient α , the thermal conductivity κ, and electrical resistivity ρ, which all vary with temperature. Thus to achieve high efficiency, both large temperature differences and high figure of merit materials are desired. Since the material thermoelectric properties (α, ρ, κ ) vary with temperature it is not desirable or even possible to use the same material throughout an entire, large temperature drop. Ideally, different materials can be segmented together (Figure 1) such that a material with high efficiency at high temperature is segmented with a different material with high efficiency at low temperature. In this way both materials are operating only in their most efficient temperature range. We have shown [1] that for the exact calculation of thermoelectric efficiency, the thermoelectric compatibility must also be considered. The maximum efficiency (determined by z) is only achieved [1] when the relative current density u, (ratio of the electrical current density to the heat flux by conduction: u = J κ∇T ) is equal to the compatibility factor s = 1+ zT −1 αT . In an efficient generator the relative current density is roughly a constant throughout a segmented element (typically u changes by less than 20%). Thus the goal is to select high figure