## 1 Introduction
Is this unusual behavior uniquely related to the characteristic long-range quasiperiodic order (QPO) present in the underlying atomic structure of QCs? Figure 1: (**a**) Electron diffraction pattern of the d-Al\({}_{70}\)Ni\({}_{15}\)Co\({}_{15}\) quasicrystal (QC) showing a ten-fold symmetry axis around the origin and a dense distribution of Bragg reflections. A set of consecutive nested pentagons, exhibiting the Pythagorean pentagram self-similar design, depicted at the bottom right corner, can be clearly seen; (**b**) scanning electron image showing the decagonal prism habit growth morphology corresponding to a d-AlNiCo QC. Cross sections of the decaprism show ten faceted planes where atoms are quasiperiodically arranged. These quasiperiodic planes are periodically stacked along the prism axis (Courtesy of [PERSON]). It is certainly tempting to think of these properties as the fingerprints of QPO in condensed matter. An assumption which is apparently supported by the observation of remarkable anisotropies in the transport properties of d-QCs, which behave as metals when measurements are performed along their periodic direction, whereas they exhibit a non-metallic behavior in the quasiperiodically ordered perpendicular planes [16]. Furthermore, their electrical conductivity significantly _decreases_ as the structural quality of the sample is improved (e.g., by annealing), in striking contrast with periodic metallic alloys, whose electrical transport properties improve when structural imperfections are removed upon heating [12], thereby providing additional evidence on the role played by the novel kind of order present in these materials. Another suitable example is provided by the extremely low \begin{table}
\begin{tabular}{c c c} \hline
**Property** & **Metals** & **Quasicrystals** \\ \hline \multirow{3}{*}{Electrical} & High conductivity & Low conductivity \\  & Resistivity increases with & Resistivity decreases with \\  & temperature & temperature \\  & Small thermopower & Moderate thermopower \\ \hline \multirow{2}{*}{Thermal} & High conductivity & Very low conductivity \\  & Large specific heat & Small specific heat \\ \hline \multirow{2}{*}{Magnetic} & Paramagnetic & Diamagnetic \\  & Ferromagnetic & Diamagnetic \\ \hline Optical & Drude peak & No Drude peak \\ \hline Mechanical & Ductility, malleability & Brittle \\ \hline \multirow{3}{*}{Tribological} & Relatively soft & Very hard \\  & Moderate friction & Low friction coefficients \\ \cline{1-1}  & Easy corrosion & Corrosion resistant \\ \hline \end{tabular}
\end{table} 
Table 1: Comparison between the physical properties of typical metallic compounds and QC alloys. Figure 2: **(a)** Plot comparing the electrical conductivity temperature dependences for different quasicrystalline samples belonging to the i-AlCuFe (\(\square\)), i-AlCuRu (\(\triangledown\)), and i-AlPdMn (\(\square\)) alloy systems. From top to bottom their chemical compositions read as follows: Al\({}_{63}\)Cu\({}_{24.5}\)Fe\({}_{12.5}\), Al\({}_{62.8}\)Cu\({}_{24.8}\)Fe\({}_{12.4}\), Al\({}_{70}\)Pd\({}_{20}\)Mn\({}_{10}\), Al\({}_{62.5}\)Cu\({}_{25}\)Fe\({}_{12.5}\), Al\({}_{70}\)Pd\({}_{20}\)Mn\({}_{10}\), Al\({}_{65}\)Cu\({}_{21}\)Ru\({}_{14}\), Al\({}_{65}\)Cu\({}_{20}\)Ru\({}_{15}\), and Al\({}_{65}\)Cu\({}_{19}\)Ru\({}_{16}\). Data for i-AlCuFe samples were kindly provided by [PERSON]. Data for i-AlCuRu and i-AlPdMn samples were from [14; 15], respectively (reprinted figure with permission from [PERSON] Universal features in the electrical conductivity of icosahedral Al-transition-metal quasicrystals, _Phys. Rev. B_ 2002, 66, 174203 Copyright (2002) by the American Physical Society); **(b)** temperature dependence of the electrical conductivity for four different i-QCs up to \(\approx\)100 K. The inset illustrates the sensitivity of the residual conductivity value to minor variations in the sample composition (reprinted figure with permission from [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] Evidence for unconventional electronic transport in quasicrystals. _Phys. Rev.