## 8 Potential of Quasicrystals as Thermoelectric Materials
Copyright (1993) by the American Physical Society); (**b**) temperature dependence of the Seebeck coefficient for different i-QCs. (Courtesy of [PERSON]); (**c**) temperature dependence of the thermal conductivity for the i-Al\({}_{74,6}\)Re\({}_{17,4}\)Si\({}_{8}\) QC (solid line) and its 1/1-cubic approximant (dashed line). The contribution due to the electrons (estimated from the Wiedemann–Franz law, dotted line) is almost negligible as compared to that due to the phonons (Courtesy [PERSON]); (**d**) figure of merit (ZT) curves as a function of temperature for Al\({}_{71\to 7}\)Ga\({}_{8}\)Pd\({}_{20}\)Mn\({}_{9}\) (x = 0, 2, 3). (Reprinted from [PERSON]; [PERSON] Metallic-covalent bonding conversion and thermoelectric properties of Al-based icosahedral quasicrystals and approximants. Sci. Technol. Adv. Mater. 2014, 15, 044802; doi:10.1088/1468-6996/15/4/044802, Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License). that exhibiting the lowest thermal conductivity value. Then, the high sensitivity of QCs transport coefficients to minor stoichiometric changes was exploited in order to properly enhance the power factor of the selected QCs, without seriously compromising their characteristic low thermal conductivities. In Table 5 we list the transport coefficients for those representatives yielding the best ZT values at room temperature. By inspecting Table 5 we see that isostructural i-Al\({}_{71}\)Pd\({}_{20}\)Mn\({}_{9}\) and i-Al\({}_{71}\)Pd\({}_{20}\)Re\({}_{9}\) samples exhibit promising ZT values, which are comparable to those reported for half-Heusler, skutterudites, and clathrates compounds at room temperature. In this way, it was found that the more promising QCs belong to the AlPd(Mn,Re) system. Subsequent search was then focused on refining their stoichiometries to further increase the corresponding ZT values. Indeed, ZT values differing by more than two orders of magnitude can be attained in a single QC system by slightly changing the sample's composition by a few atomic percent (hence preserving the QP lattice structure). We also note that both positive and negative values of the Seebeck coefficient can be obtained in this way, which allows for both the n- and p-type legs present in a typical thermoelectric cell to be fabricated from the same material. Furthermore, enhanced ZT values (0.2-0.25) are obtained at higher temperatures (450-500 K) for related quaternary i-QCs, as it is shown in Figure 11d for i-Al\({}_{71-\kappa}\)Ga\({}_{x}\)Pd\({}_{20}\)Mn\({}_{9}\) representatives [91]. The main reason for this ZT enhancement is the lowering of phonon thermal conductivity by the weakening of the inter-cluster bonds along with the usual alloying effects [92]. At this point; however, we must highlight a main difference between QCs and other TEMs, such as skutterudites and clathrates, exhibiting similar ZT values at room temperature. This difference refers to the rapid increase of the thermal conductivity with the temperature in Al-based i-QCs (and related approximants) starting at temperatures above T \(\sim\)300-400 K [97; 98; 99]. By all indications this increase mainly arises from the electronic contribution, while the phonon contribution steadily decreases as T increases [97; 98; 99; 100; 101; 102]. This \(\kappa\)(T) increase leads to ZT curves which progressively decrease as the temperature is raised above the Debye temperature (\(\approx\) 450-500 K), as can be seen in Figure 11d. Conversely, the ZT(T) curves of both skutterudites and clathrates progressively increase within this temperature range, attaining high figure of merit values (within the interval ZT = 0.8-1.3) at temperatures around 800-900 K. The enhancement of the electronic contribution to the thermal conductivity in QCs may be accounted for, within the framework of a two-band electronic structure model, in terms of a bipolar diffusion term [98], along with a possible dependence of the charge carrier density with the temperature at high enough temperatures [103].