## 6 Chemical Fingerprints in the Physical Properties  
An abrupt change in certain physical properties in a series of compounds may indicate an abrupt change in the bond type (e.g., from mainly metallic to mainly covalent). For the sake of illustration, in Table 3 we list the melting temperatures of several i-QCs based on the three known cluster types (Bergman, Mackay, and Tsai). Broadly speaking one would expect relatively low melting points in molecular solids. Thus, the relatively high melting points observed in Al-based QCs may be indicating stronger than expected bonds among neighboring clusters. Alternatively, one may also think of the hierarchical spatial arrangement of clusters as precluding an easy separation from each other, even if they interact weakly among them. In this regard, it is interesting to note that the melting point of the Al\({}_{65}\)Cu\({}_{20}\)Fe\({}_{15}\) cubic approximant alloy is T\({}_{\rm m}\) = 1281 K, about 12% higher than that of the related icosahedral phase [56]. This may be indicative of long-range QPO effects in QCs. Figure 8: (**a**) Structure of a pseudo-Mackay cluster containing an inner cubic shell (1), followed by an icosahedron shell (2), and an icosidodecahedron (3) shell. The number of atoms in each shell is indicated in the figure. White (black) circles denote Al (TM) atoms, respectively. (Reprinted figure with permission from [PERSON] Conductivity in quasicrystals via hierarchically variable-range hopping. _Phys. Rev. B_**1996**, _53_, 181. Copyright (1996) by the American Physical Society); (**b**) A three-dimensional perspective of the \(\tau^{3}\)-inflated cluster forming the basic icosidodecahedron structural motif of i-CdYb phase. Its radius is about 12 nm. (Reprinted by permission from Springer Nature: _Nature Materials_, [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] Atomic structure of the binary icosahedral Yb-Cd quasicrystal. **2007**, \(6\), 58-63, Copyright (2007)). The electronic transport properties (electrical conductivity, Seebeck and Hall coefficients) of QCs critically depend on minute changes in the structural quality and chemical composition of the considered samples. For instance, high electrical resistivity values can only be obtained after a specific annealing process [56], applied to homogenize the chemical composition and to improve the structural order of the samples. This is a strong indication that a precise chemical composition and a high structural quality are required to attain the high resistivity reported values. It is also interesting to note that QCs belonging to the Mackay-type cluster generally exhibit significantly higher low temperature resistivities and resistivity ratios R = \(\varrho\)(4 K)/\(\varrho\)(300 K), than those observed in QCs containing either Bergman- or Tsai-type clusters, which display room temperature resistivity values comprised within the range 100-300 \(\upmu\Omega\)cm, typical of conventional ternary alloys. In a similar way, binary i-(Cd,Ca)Yb QC representatives and the i-AgInYb-related phases, characterized by a high-quality structural QPO with little chemical disorder, exhibit higher electrical conductivities, comparatively large electronic-specific heat coefficients, relatively low Debye temperatures, and higher magnetoresistance values than those reported for Al-based QCs [9; 33]. This remarkable behavior, combined with the relevant role of p-d hybridization effects in the emergence of a pseudogap close to the Fermi level, certainly points to a significant influence of chemical effects in the transport properties of this QC alloy system [66; 67]. Several chemical trends are also observed in the transport properties of i-QCs belonging to the AlCu(Fe,Ru,Os) and AlPd(Mn,Re) systems. This is illustrated in Table 4, where we clearly see a systematic increase of both the low temperature resistivity and the resistivity ratio maximum values by increasing the Z number of the group 7 (group 8) third element, respectively.