Relative stability of theAl12W structure in Al–transition-metal compounds

The structural stability of the prototypical complex ${\mathrm{Al}}_{12}$W structure, relative to the ${\mathrm{Cu}}_3$Au structure, is computed for Al compounds with 3d and 4d transition metals. The calculated structural energy differences are on the order of an eV per transition-metal atom, have their largest negative magnitude for the transition metals with nearly half-filled d bands, and have larger magnitudes for the 4d transition metals than for the 3d metals. These results suggest that electronic effects are more important than atomic-size effects. It is shown that a large part of the structural energy differences is due to the presence of a Fermi-level nonbonding peak in the electronic density of states (DOS) for the ${\mathrm{Cu}}_3$Au structure, which destabilizes that structure. The energy associated with the nonbonding peak has comparable contributions from a term in the energy that favors large unit-cell sizes, and from a local term that penalizes 90° bond angles around the transition-metal atoms. A significant additional contribution comes from the appearance of the dip in the DOS around the Fermi level for the ${\mathrm{Al}}_{12}$W structure. It is shown that the energetic factors developed here likely contribute to the relative stability of binary Al–transition-metal icosahedral phases.