Maximum density rule for bulk terminations of quasicrystals

Bravais' rule, of wide validity for crystals, states that their surfaces correspond to the densest planes of atoms in the bulk. Comparing a theoretical model of icosahedral Al-Pd-Mn with experimental results on sputter-annealed surfaces, we find that this correspondence breaks down, i.e., the surfaces parallel to the densest planes in the model are not necessarily the most stable bulk terminations. The correspondence is restored by recognizing that there is a contribution to the surface not just from a single geometrical plane but from a layer of stacked atoms, possibly containing more than one plane. We find that not only does the stability of high-symmetry surfaces match the density of the corresponding layerlike bulk terminations but the exact spacings between surface terraces can be determined and the typical area of the terraces can be estimated by a simple analysis of the density of layers predicted by the bulk geometric model.