Yee, S.K., Leblanc, S., Goodson, K.E., Dames, C., 2014, “Reply to the comment on “$ per W metrics for thermoelectric power generation: beyond ZT” by G. Nunes, Jr., Energy Environ. Sci., 2014, 7 DOE:10.1039/C3EE43700K,” Energy and Environmental Science, Vol. 7., 3441.
The comment by Nunes suggests a welcome reﬁnement to an approximation made in the original paper. We show here that Nunes’ reﬁnement is identical to a modiﬁed eﬀective thermal conductivity, keﬀ ¼ k(1 + gZT), where k is the thermal conductivity, ZT is the usual material ﬁgure of merit, and g is in the range 0.4–0.5. This form of keﬀ was already identiﬁed in Section 3.3 of our original paper as an option to improve the accuracy of the calculations and is itself an approximation to the more sophisticated keﬀ analysis of Baranowski, Snyder, and Toberer [J. Appl. Phys. 113, 204904 (2013)]. As noted by Nunes and ourselves, the main downside of such reﬁnements is that they complicate the universality of the main result, the universal cost surface in Fig. 2 of the original paper. The simpliﬁed results in the original manuscript are justiﬁed and reasonable for ZT ~1 or less, for physical insight, scaling, and rapid screening. For the best accuracy in real systems, exact numerical solutions of the coupled cost and power equations are most appropriate, examples of which we have recently published for 30 bulk and thin ﬁlm materials in Renewable Sustainable Energy Rev., 32, 31.