Most stable structures and physical properties are studied for silicon-doped ${\mathrm{Al}}_{13},$ ${\mathrm{Al}}_{19},$ and ${\mathrm{Al}}_{23}$ clusters using the ab initio molecular-dynamics method within the framework of a plane-wave pseudopotential approach and the local density as well as the generalized gradient approximations. The lowest energy structures of the undoped clusters are found to be Jahn-Teller distorted icosahedron, double icosahedron, and decahedron, respectively. Substitutional doping with a Si impurity makes these clusters electronically closed shell and leads to a large gain in the binding energy, which decreases with an increase in the cluster size in a nonmonotonic way. The heat of solution of a Si atom in clusters is found to be exothermic as compared to endothermic behavior in bulk aluminum. Further, a Si impurity is found to stabilize the ${\mathrm{Al}}_{18}\mathrm{Si}$ cluster in cuboctahedral structure. However, a capped icosahedron as well as a double icosahedron are found to be nearly degenerate with about 1.77 eV higher binding energy. For ${\mathrm{Al}}_{22}\mathrm{Si},$ the decahedral isomer has the lowest energy with a highest-occupied lowest-unoccupied molecular-orbital gap of 0.82 eV. It is also found to be very stable when heated at 700 K. Similar results are likely to hold in the case of doping with germanium. We discuss the significance of these results for the understanding of the stability of silicon-doped quasicrystals.

• Received 27 September 1999

DOI:https://doi.org/10.1103/PhysRevB.61.8541