First-principles study of decagonal quasicrystals

This thesis studies the energetics of decagonal quasicrystals using ab-initio methods. First, we extend the generalized pseudopotential theory (GPT) to treat ternary transition metal (TM) aluminides. The GPT interactions are decomposed to pair and many-body interactions that allow efficient calculations of total energies. In aluminum-rich systems treated at the pair-potential level, one practical limitation is a transition-metal over-binding that creates an unrealistic TM-TM attraction at short separations. An additional potential term is added for systems with short TM atom separations, formally folding repulsive contributions of the three- and higher-body interactions into the pair potentials. To do this, we have performed numerical ab-initio total-energy calculations using an Al-Co-Ni compound in a particular quasicrystalline approximant structure. The results allow us to fit a short-ranged, many-body correction of the form a( r0/r)b to the GPT pair potentials for Co-Co, Co-Ni, and Ni-Ni interactions. We employ the corrected potentials to predict the structure of a decagonal quasicrystal from first-principles considerations. The resulting structure obeys a nearly deterministic decoration of tiles on a hierarchy of length scales related by powers of tau, the golden mean.; Second, an investigation of matching rules in Al-Co-Cu quasicrystals using a form of tile Hamiltonian (TH) reveals several results. Phason flips that replace a star-hexagon pair with a pair of boats lower the energy. In Penrose tilings, quasiperiodicity is forced by arrow matching rules on rhombus edges. The edge orientation in Al-Co-Cu is due to Co/Cu chemical ordering. Tile edges meet in vertices with 72° or 144° angles. We find strong interactions between edge orientations at 72° vertices that force a type of matching rule. Comparisons between the ab-initio methods and pair potentials are presented.; Lastly, we explore the applicability of the locally self-consistent multiple scattering method (LSMS) in the energy calculations of our quasicrystal models. This is an O(N) all-electron method, which makes calculations both faster and more accurate, in principle, than other available ab-initio methods.