Structural model and electronic structure of the icosahedral $\mathrm{Al}-\mathrm{Ga}-\mathrm{Pd}-\mathrm{Mn}$ quasicrystal

The structural model and the electronic structure of a newly discovered $i\text{−}\mathrm{Al}-\mathrm{Ga}-\mathrm{Pd}-\mathrm{Mn}$ icosahedral quasicrystal with composition ${\mathrm{Al}}_{67}{\mathrm{Ga}}_4{\mathrm{Pd}}_{21}{\mathrm{Mn}}_8$ were studied by density functional methods. Calculations are based on the Quandt-Elser periodic approximant model of $i\text{−}\mathrm{Al}-\mathrm{Pd}-\mathrm{Mn}$, which was fully relaxed. To determine which Al sites in the $i\text{−}\mathrm{Al}-\mathrm{Ga}-\mathrm{Pd}-\mathrm{Mn}$ are occupied by Ga, total energies were compared, showing that Ga substitutes two of the aluminum glue atoms, ${\mathrm{Al}}_5$ and ${\mathrm{Al}}_6$, but no Al atoms that are part of a Bergman cluster. Since only specific Al sites are substituted by Ga, $i-\mathrm{Al}-\mathrm{Ga}-\mathrm{Pd}-\mathrm{Mn}$ is predicted to be a true quaternary quasicrystal, structurally isomorphous with $i-\mathrm{Al}-\mathrm{Pd}-\mathrm{Mn}$. Calculation of the electronic density of states of $i\text{−}\mathrm{Al}-\mathrm{Ga}-\mathrm{Pd}-\mathrm{Mn}$ and its comparison to $i\text{−}\mathrm{Al}-\mathrm{Pd}-\mathrm{Mn}$ predicts that 4% $\mathrm{Al}\to \mathrm{Ga}$ substitution in the $i\text{−}\mathrm{Al}-\mathrm{Pd}-\mathrm{Mn}$ lattice should have negligible influence on the electronic properties of this quasicrystal.

Figure 1

(Color online) Unit cell of the Quandt-Elser model of $i\text{−}\mathrm{Al}-\mathrm{Ga}-\mathrm{Pd}-\mathrm{Mn}$ (Table ). Two Bergman clusters form the main building blocks of the structure. They consist of a central Pd atom and an Al icosahedron (light bonds), which is surrounded by a pentagonal dodecahedron (dark bonds). In addition, there is a smaller cluster, consisting of an Al cube (light bonds) and a central Mn atom. Atoms that are not part of a cluster are called glue atoms. Ga has substituted two Al glue atoms in $i\text{−}\mathrm{Al}-\mathrm{Pd}-\mathrm{Mn}$.

Figure 2

(Color online) Total DOSs of $i\text{−}\mathrm{Al}-\mathrm{Ga}-\mathrm{Pd}-\mathrm{Mn}$ (solid curve) and of $i\text{−}\mathrm{Al}-\mathrm{Pd}-\mathrm{Mn}$ (dotted curve). The inset shows the DOSs in the vicinity of the Fermi level on an expanded scale. All DOSs were smeared with a Gaussian of full width at half maximum of $60\mathrm{meV}$.