The Model for Icosahedral Al-Pd-Mn phase based on theT*(2F)Canonical Tiling

Abstract

AbstractThe icosahedral canonical tiling of the three-dimensional space by six golden tetahedraT*(2F)[1] is decorated for physical applications by the Bergman polytopes [2]. The model can be also formulated as the “primitive) tilingTP[3] decorated by alternating Bergman symmetry axis of and icosahedron, there appear the plans on three mutual distances following the rule of a decorated Fibonacci sequence. All these three distances among the terraces (mutually scaled by a factor τ) have been recently observed by shenet al. [5]. In particular they have measured also the shortest distance of 2.52Å that breaks the Fibonnaci-sequence of terrace like surfaces measured previously by schaubet al. [6]. We predict the frequencies for the appearance of the terraces of different heights in the model under the condition that the model of Boudardet al. [7.8], we decorate the atomic positions by Al, Pd and Mn. We present images of the predictedpossibleterrace-like surfaces on three possible distances in the fully decorated model by the atomic species.