The structure, stability, and electronic properties of a fivefold surface of an icosahedral $\left(i\right)$ Al-Pd-Mn alloy have been investigated using ab initio density-functional methods. Structural models for a series of rational approximants to the quasicrystalline structure of bulk $i$-AlPdMn have been constructed using the cut-and-projection technique with triacontahedral acceptance domains in the six-dimensional hyperspace according to the Katz-Gratias-Boudard model. This leads to a real-space structure describable in terms of interpenetrating Mackay and Bergman clusters. A fivefold surface has been prepared by cleaving the bulk structure along a plane perpendicular to a fivefold axis. The position of the cleavage plane has been chosen such as to produce a surface layer with a high atomic density. The atomic structure of these surfaces can be described by a P1 tiling by pentagons, thin rhombi, pentagonal stars, and a “boat”—in terms of a cut-and-projection model the decagonal acceptance domain of the P1 tiling corresponds to the maximal cross section of the triacontahedra defining the three-dimensional quasicrystal. The vertices of the P1 tiling are occupied by Pd atoms surrounded by pentagonal motifs of Al atoms. For the ab initio calculations we have prepared slab models of the surface based on the $3∕2$ and $2∕1$ approximants and containing up to 357 atoms in the computational cell. The analysis of the surface charge density shows flat minima at the vertices of the P1 tiling and strong charge depletion in some of the pentagonal tiles (“surface vacancies”). Both observations are in agreement with scanning tunneling microscopy studies of these surfaces. Structural relaxations have been performed only for the $2∕1$ models with up to 205 atoms/cell. The calculations demonstrate that the skeleton of the P1 tiling fixed by the transition-metal atoms represents a stable surface termination, but considerable rearrangement of the Al atoms and large relaxations of the interlayer distances. The analysis of the surface electronic structure shows that the deep structure-induced pseudogap just above the Fermi level is filled up at the surface as a consequence of the structural disorder in the arrangement of the Al atoms at the surface and of a shift of both the Pd and Mn $d$ band to lower binding energy. The $d$ band shift at the surface is in good agreement with observations based on photoelectron and Auger spectroscopies.

• Received 6 October 2004

DOI:https://doi.org/10.1103/PhysRevB.71.054202