Best thermoelectric efficiency of ever-explored materials.

A thermoelectric device is a heat engine that directly converts heat into electricity. Many materials with a high figure of merit Z T have been discovered in the anticipation of a high thermoelectric efficiency. However, there has been a lack of investigations on efficiency-based material evaluation, and little is known about the achievable limit of thermoelectric efficiency. Here, we report the highest thermoelectric efficiency using 12,645 published materials. The 97,841,810 thermoelectric efficiencies are calculated using 808,610 device configurations under various heat-source temperatures ( T h ) when the cold-side temperature is 300 K, solving one-dimensional thermoelectric integral equations with temperature-dependent thermoelectric properties. For infinite-cascade devices, a thermoelectric efficiency larger than 33% (≈⅓) is achievable when T h exceeds 1400 K. For single-stage devices, the best efficiency of 17.1% (≈1/6) is possible when T h is 860 K. Leg segmentation can overcome this limit, delivering a very high efficiency of 24% (≈1/4) when T h is 1100 K.

Thermoelectric degrees of freedom determining thermoelectric efficiency.

For over half a century, the development of thermoelectric materials has based on the dimensionless figure of merit z T , assuming that the efficiency is mainly determined by this single parameter. Here, we show that the thermoelectric conversion efficiency is determined by three independent parameters, Z gen , τ, and ß, which we call the three thermoelectric degrees of freedom (DoFs). Z gen is the well-defined mean of the traditional z T under nonzero temperature differences. The two additional parameters τ and ß are gradients of material properties and crucial to evaluating the heat current altered by nonzero Thomson heat and asymmetric Joule heat escape. Each parameter is a figure of merit. Therefore, increasing one of the three DoFs leads to higher efficiency. Our finding explains why the single-parameter theory is inaccurate. Further, it suggests an alternative direction in material discovery and device design in thermoelectrics, such as high τ and ß, beyond z T .

Dimension reduction of thermoelectric properties using barycentric polynomial interpolation at Chebyshev nodes.

The thermoelectric properties (TEPs), consisting of Seebeck coefficient, electrical resistivity and thermal conductivity, are infinite-dimensional vectors because they depend on temperature. Accordingly, a projection of them into a finite-dimensional space is inevitable for use in computers. In this paper, as a dimension reduction method, we validate the use of high-order polynomial interpolation of TEPs at Chebyshev nodes of the second kind. To avoid the numerical instability of high order Lagrange polynomial interpolation, we use the barycentric formula. The numerical tests on 276 sets of published TEPs show at least 8 nodes are recommended to preserve the positivity of electrical resistivity and thermal conductivity. With 11 nodes, the interpolation causes about 2% error in TEPs and only 0.4% error in thermoelectric generator module performance. The robustness of our method against noise in TEPs is also tested; as the relative error caused by the interpolation of TEPs is almost the same as the relative size of noise, the interpolation does not cause unnecessarily high oscillation at unsampled points. The accuracy and robustness of the interpolation indicate digitizing infinite-dimensional univariate material data is practicable with tens or less data points. Furthermore, since a large interpolation error comes from a drastic change of data, the interpolation can be used to detect an anomaly such as a phase transition.