The electronic structures of the stable face-centered-icosahedral alloy Alzppd2pMnqp and of a hierarchy of rational approximants to the icosahedral phase have been calculated using ab initio pseudopotential, linear-muKn-tin-orbital (LMTO), and tight-binding (TB)-LMTO techniques. The description of the atomic structure is based on a projection from six-dimensional space, with acceptance volumes chosen such as to reproduce the observed di8'raction 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 Qattened 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 facecentered 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 6nd 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.

Ab initio density-functional calculations have been used to study the response of two face-centered-cubic metals ͑Al and Cu͒ to shearing parallel to the close-packed ͑111͒ planes along two different directions, ͓112͔ and ͓110͔. Two different types of deformations-affine and alias-have been investigated. Under an affine shear deformation, all atoms are shifted parallel to the shearing direction by a distance proportional to their distance from the fixed basal plane. In the alias regime, only the top layer is displaced in the shearing direction. In both regimes, calculations have been performed with ͑pure shear͒ and without ͑simple shear͒ relaxation. For a pure alias shear, due to the interaction between the atoms, the displacement propagates through the sample; this is certainly the most realistic description of the shearing processes. In the pure alias regime, shear deformation, theoretical shear strength, and stacking fault formations may be described on a common footing. For small strains ͑in the elastic region͒, affine and alias shears lead to very similar results. Beyond the elastic limit, relaxation has a strong influence of the response on an applied shear strain. The elastic shear moduli are significantly larger for Cu than for Al, but a much higher shear strength is calculated for Al, although the shear strength is limited by the occurrence of a stacking fault instability before the stress maximum is reached. Under ͗110͘ ͕111͖ shear the analysis of the atomistic deformation mechanism shows that in this case the formation of a stacking fault leads to a splitting of the 1 2 ͓110͔ dislocation into two partial Shockley dislocations. Due to the repulsive interaction between the atoms in adjacent close-packed planes, the atoms in the top A layer move along 1 6 ͓211͔ to a position directly above the B layer such that the stable intrinsic stacking fault configuration is the same for both slip systems. The analysis of the variation in the lattice parameters under strain reveals significant differences in the relaxation behavior of both metals: Al is very stiff, but Cu is rather soft along the ͗112͘; in-plane relaxation is very strong for Cu but modest for Al. This much stronger relaxation explains that while the differences in the unstable stacking fault energies of both metals are only modest, the intrinsic stacking fault energies differ by as much as a factor of 4. A detailed comparison of the response to shear and tensile deformations has been performed. A phonon instability of the uniaxial tensile deformation along the ͓110͔ direction has been explained by the close connection with the shear system ͗112͘ ͕111͖.