NONCONNECTED ATOMIC SURFACES FOR QUASI-CRYSTALLINE SPHERE PACKINGS

The problem of maximizing the density of quasiperiodic sphere packings is investigated. The investigation is limited primarily to the case where the centers of the spheres are determined by a cut through a higher-dimensional Bravais lattice of a single atomic surface. For certain cases, the sphere packing obtained by the largest connected atomic surface can be made more dense by replacing it with an atomic surface that is nonconnected. The nonconnected atomic surfaces differ from the connected ones only in specific regions near the atomic surface boundaries. These regions are determined by the quasicrystalline point-group symmetry and by the radius of the spheres. This method of improving sphere packings is applied to find nonconnected atomic surfaces for the dodecagonal, octagonal, and icosahedral cases. Using this method in conjunction with other methods, a packing fraction of approximately 0.5645 for a simple icosahedral b-c network is achieved.