Energy harvesting with thermoelectric materials has been investigated with increasing attention over recent decades. However, the vast number of various material classes makes it difficult to maintain an overview of the best candidates. Thus, we revitalize Ioffe plots as a useful tool for making the thermoelectric properties of a material obvious and easily comparable. These plots enable us to consider not only the efficiency of the material by the figure of merit zT but also the power factor and entropy conductivity as separate parameters. This is especially important for high-temperature applications, where a critical look at the impact of the power factor and thermal conductivity is mandatory. Thus, this review focuses on material classes for high-temperature applications and emphasizes the best candidates within the material classes of oxides, oxyselenides, Zintl phases, half-Heusler compounds, and SiGe alloys. An overall comparison between these material classes with respect to either a high efficiency or a high power output is discussed.

Dense Ca 3 Co 4 O 9 -Na x CoO 2 -Bi 2 Ca 2 Co 2 O 9 (CCO-NCO-BCCO) nanocomposites were produced from sol-gel derived powder by three methods: Spark plasma sintering, hot-pressing and pressureless sintering under O 2 atmosphere. The SPS processed product showed a thermoelectric power factor of 6.6 µW • cm -1 • K -2 at 1073 K in air. A dense nanocomposite with all-scale hierarchical architecture and enhanced thermoelectric properties is only obtained from pressureless sintering under O 2 atmosphere. The resulting nanocomposite enables the simultaneous increase in isothermal electrical conductivity σ and Seebeck coefficient α, and it delivers a thermoelectric power factor of 8.2 µW • cm -1 • K -2 at 1073 K in air. The impact of materials with enhanced electrical conductivity and power factor on the electrical power output of thermoelectric generators was verified in prototypes. A high electrical power output and power density of 22.7 mW and 113.5 mW•cm -2 , respectively, were obtained, when a hot-side temperature of 1073 K and a temperature difference of 251 K were applied. Different p-and n-type materials were used to verify the effect of the thermoelectric figure of merit zT and power factor on the performance of thermoelectric generators.

Schemes, diagrams both SEM and TEM micrographs were created using Orig-inPro 9.1G, ImageJ, Diamond and Digital Micrograph. Figures were arranged, merged and saved using PowerPoint 2010 and Photoshop CS5. Table S 1 shows the ionic radii of the substituted elements and inserted dopants. According to the similarity of the ionic radii of the elements used, doping should be possible. The XRD patterns of the Na x CoO 2 (NCO) and Bi 2 Ca 2 Co 2 O 9 (BCCO) phases, shown in Figure S 1 refer to Figure 2 in the main text. A step size of 0.003942, a time per step of 1.1 seconds, a voltage of 40 kV and a current of 40 mA were used in the XRD experiments. Pure NCO and nearly pure BCCO phases were subjected to SEM and elemental distribution analyses of polished cross-sections, as shown in Figure S 2a-d.Vibration-polished cross-section specimens were prepared by a multistep (30 µm, 15 µm, 6 µm, 3 µm and 1 µm diamond lapping films) polishing program using a Techprep from Allied -High Tech Products, Inc., followed by vibration polishing using a Buehler Vibromet-2 and a 50 nm colloidal alumina suspension. TEM specimens were prepared similar to SEM specimens and put on a TEM grid. The specimens were pinched out using a precision ion polishing system (Ar-ion) Model 691 from Gatan. The BCCO phase decomposes at approximately 1023 K, and Ca-containing phases are formed; see Figure S 1 [1] . Figure S 3 gives detailed elemental distribution information referring to Figure 4a-c in the main document. The interdiffusion of Ca into the NCO phase is clearer, and the very thin layers of NCO and BCCO are clearly visible in the Na, Ca and Bi signals shown in Figures S 3d-f and 4a-d. The insets of Figure 4d-f in the main document are enlarged for a better readability in Figure S 5a-f. Additional TEM micrographs of other sites of the CCO-30-35-10 nanocomposite ceramic are shown in Figures S 6, 7 and 8. These other sites clarify the composition and thickness of different layers within the material. These sequences continue throughout the ceramic. Comparing Figure S 6 and Figure S 7shows that the amount of interdiffusion of Ca into the NCO phase is not constant, suggesting that the degree of interdiffusion might also depends on thickness and surroundings (e.g., being embedded between BCCO phases). Figure S 9 illustrates the measured heat capacities C P of CCO and nanocomposite ceramics as a function of temperature in the range from 313 K to 1173 K. The C P values reached approximately 0.83 J • g -1 • K -1 at 1073 K for a CCO-30-35-10 nanocomposite ceramic. The nanocomposite ceramics showed only small differences in C P from those of undoped CCO. The system was calibrated and the sapphire method was used. The sensitivity S and heat capacity C P were calculated as described by Jankovsky et al. [2] . Samples of bar geometry were

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