Resultant Seebeck coefficient formulated by combining the Thomson effect with the intrinsic Seebeck coefficient of a thermoelectric element

The resultant Seebeck coefficient αR(Tz) of a thermoelectric (TE) element was derived analytically from the temperature dependence of the intrinsic Seebeck coefficient αI(Tz) by taking into account the Thomson effect, where Tz is a temperature at z along a TE element. The analysis was performed by expanding αI(Tz) in a power series in (Tz − T), where T is a mean temperature. As a result, when αI(Tz) has a convex curve exhibiting a local maximum at Tz = T, αR(Tz) is increased at the interfaces of a TE element, while when it has a concave curve giving a local minimum at Tz = T, αR(Tz) deteriorates there. If the p-type (Bi0.4Sb0.6)2Te3 with a local maximum of αI(Tz) at T = 390 K is employed for a TE element, αR(Tz)/αI(T) at both interfaces is increased up to 1.53 under the condition of T = 390 K and ΔT = 200 K. A similar enhancement in αR(Tz)/αI(T) appeared even in the n-type (Zr–Hf)NiSn half-Heusler. When αI(Tz) varies nonlinearly with changes in Tz, therefore, the TE figure of merit ZR(Tz)Tz is found to be affected dramatically at the interfaces. The average resultants ZAR(T) estimated for the p-type Bi–Te and n-type half-Heusler compound reach great values of 1.46 and 1.26 times as large as their intrinsic Z(T), respectively. The experimental method to confirm such a phenomenon is also proposed here. The performance of a TE element is thus expected to be enhanced significantly not only by improving the intrinsic Z(Tz)Tz but also by optimizing the Tz-dependence of αI(Tz).