Effect of linear and non-linear components in the temperature dependences of thermoelectric properties on the energy conversion efficiency

The new thermal rate equations were built up by taking the linear and non-linear components in the temperature dependences of the Seebeck coefficient α, the electrical resistivity ρ and thermal conductivity κ of a thermoelectric (TE) material into the thermal rate equations on the assumption that their temperature dependences are expressed by a quadratic function of temperature T. The energy conversion efficiency η for a single TE element was formulated using the new thermal rate ones proposed here. By applying it to the high-performance half-Heusler compound, the non-linear component in the temperature dependence of α among those of the TE properties has the greatest effect on η, so that η/η0 was increased by 11% under the condition of T = 510 K and ΔT = 440 K, where η0 is a well-known conventional energy conversion efficiency. It was thus found that the temperature dependences of TE properties have a significant influence on η. When one evaluates the accurate achievement rate of ηexp obtained experimentally for a TE generator, therefore, ηexp should be compared with ηthe estimated from the theoretical expression proposed here, not with η0, particularly when there is a strong non-linearity in the temperature dependence of TE properties.