Atomic and electronic structure of icosahedral Al-Pd-Mn alloys and approximant phases

The electronic structures of the stable face-centered-icosahedral alloy ${\mathrm{Al}}_{70}$${\mathrm{Pd}}_{20}$${\mathrm{Mn}}_{10}$ and of a hierarchy of rational approximants to the icosahedral phase have been calculated using ab initio pseudopotential, linear-muffin-tin-orbital (LMTO), and tight-binding (TB)-LMTO techniques. The description of the aotmic structure is based on a projection from six-dimensional space, with acceptance volumes chosen such as to reproduce the observed diffraction data. For the lowest-order approximants (1/1 and 2/1 with 128 and 544 atoms in the periodically repeated cell), the electronic eigenvalues and eigenfunctions have been calculated self-consistently using LMTO and ab initio pseudopotential techniques. For the 1/1 approximant, we have also performed a relaxation of the idealized structure using the Hellmann-Feynman forces. For the higher-order approximants (we go up to the 8/5 approximants with 41 068 atoms), the electronic densities of states and the spectral functions have been calculated from the TB-LMTO Hamiltonian via a real-space recursion technique. The electronic density of states (DOS) of the higher-order approximants is characterized by a structure-induced minimum at the Fermi level, indicating the possibility of a Hume-Rothery-type electronic mechanism for the stabilization of the icosahedral phase. However, in the lowest-order approximants the DOS minimum is either flattened or shifted away from the Fermi energy. This is in contrast to the simple icosahedral alloys such as Al-Cu-Li, where the DOS minimum exists in the quasiperiodic phase and in the crystalline approximants. Hence it appears that for the face-centered icosahedral alloys, the structure-induced DOS minimum may be not only a generic, but also a specific property of the quasicrystalline phase. In addition to the spectral properties, we have also studied the character of the electronic states via a calculation of the participation ratio. We find that the states in the vicinity of the Fermi level tend to be more localized than in the rest of the valence band and that the localization is related to certain aspects of the quasicrystalline structure. This is important for understanding the anomalous transport properties of these alloys.