## 3 The Chemical Synthesis Route to New Quasicrystals
Finally, it is worth noticing the existence of a great variety of stable i-QCs based on elements belonging to different blocks of the periodic table, but all of them bearing Sc atoms as their second or third constituent, as it is shown in Table 2. Taking into account that Sc atoms have two possible effective valences depending upon whether they are alloyed with non-TM or TM elements, respectively (see Figure 4), we can identify two different possible broad e/a intervals yielding stable QCs, namely, 1.8 e/a \(\leq\) 1.9 and 2.0 \(\leq\) e/a \(\leq\) 2.2. The important role played by the presence of a deep DOS minimum close to the Fermi energy in the stabilization of both icosahedral and decagonal QCs [16; 29; 34] inspired a chemical synthesis exploration project aimed at obtaining new quasicrystalline compounds via pseudogap electronic tuning, which has rendered successful results in the Zn-Sc-Cu, Ca-Au-In, and Mg-Cu-Ga systems [35; 36; 37; 38]. Indeed, for a given alloy composition the Fermi-surface-Brillouin-zone interaction mechanism can give rise to the formation of pseudogaps at energy values that are not close enough to the Fermi energy to significantly contribute to reduce its electronic energy. Now, if that pseudogap occurs above the Fermi energy then one can change the alloy's composition by properly alloying the original compound with electron-rich atoms in order to change its e/a ratio, shifting E\({}_{\text{F}}\) to properly match the Fermi level inside the deeper region of the pseudogap. This strategy was systematically applied to different compounds by [PERSON] and [PERSON], starting with Zn\({}_{17}\)Sc\({}_{3}\) alloy (e/a = 2.175) whose structure appeared to be isotypic with that of the prototypic Tsai-type 1/1 approximant (see Section 5). This alloy has an electron concentration ratio larger than that observed in Cd\({}_{85}\)(Ca,Yb)\({}_{15}\) i-QCs (e/a = 2.026), but substitution of some Zn by Cu yields a novel ternary icosahedral phase with the stoichiometry Zn\({}_{71.5}\)Sc\({}_{16.2}\)Cu\({}_{12.3}\) (e/a = 2.058). \begin{table}
\begin{tabular}{c c} \hline \hline
**Compound** & **e/a** \\ \hline Zn\({}_{88}\)Sc\({}_{12}\) & 2.148 \\ \hline Zn\({}_{71.5}\)Cu\({}_{12.3}\)Sc\({}_{16.2}\) & 1.797 \\ \hline Cu\({}_{46}\)Al\({}_{38}\)Sc\({}_{16}\) & 1.817 \\ \hline Zn\({}_{74}\)Sc\({}_{16}\)\(\left(\begin{array}{c}Ag\\ Au\end{array}\right)_{10}\) & 1.823 \\ \hline Zn\({}_{75}\)Sc\({}_{16}\)Pd\({}_{9}\) & 1.829 \\ \hline Zn\({}_{74}\)Sc\({}_{16}\)Ni\({}_{10}\) & 1.838 \\ \hline Zn\({}_{77}\)Sc\({}_{16}\)Fe\({}_{7}\) & 1.857 \\ \hline Zn\({}_{79}\)Sc\({}_{16}\)Co\({}_{6}\) & 1.866 \\ \hline Zn\({}_{72}\)Sc\({}_{16}\)Pt\({}_{10}\) & 1.885 \\ \hline Al\({}_{54}\)Pd\({}_{30}\)Sc\({}_{16}\) & 2.126 \\ \hline Zn\({}_{81}\)Sc\({}_{15}\)Mg\({}_{4}\) & 2.174 \\ \hline Zn\({}_{77}\)Sc\({}_{8}\)\(\left(\begin{array}{c}Ho\\ Er\\ Tm\end{array}\right)_{8}\) & 1.991 \\ \hline Cu\({}_{48}\)Ga\({}_{34}\)Sc\({}_{15}\)Mg\({}_{3}\) & 2.001 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Sc bearing icosahedral quasicrystals (i-QCs) belonging to different alloy systems grouped by their electron-per-atom e/a ratio value [5; 33]. The electronic tuning via the compositional change route was subsequently applied to Zn\({}_{11}\)Mg\({}_{2}\) alloy precursors to get the quaternary i-Cu\({}_{48}\)Ga\({}_{34}\)Sc\({}_{15}\)Mg\({}_{3}\) (e/a = 2.001) phase [36], and the ternary i-Zn\({}_{82.1}\)Sc\({}_{14.6}\)Mg\({}_{3.3}\) (e/a = 2.170) and i-Au\({}_{44.2}\)In\({}_{41.7}\)Ca\({}_{14.1}\) (e/a = 2.15) compounds [35; 37]. Remarkably enough, the systematic exploration of the active-metal-gold-post-transition-metal Na-Au-Ga system led to the discovery of the first Na-containing QC, i-Ga\({}_{37.5}\)Na\({}_{32.5}\)Au\({}_{30}\), which has a comparatively low e/a \(\simeq\) 1.753 value [38]. However, the existence of the stable phase i-Au\({}_{62.7}\)Al\({}_{23.0}\)Ca\({}_{14.3}\) with the even lower e/a \(\simeq\) 1.605 value was reported later on [39].