A Model for the Structure of the Decagonal Phase of Al-Mn Alloys

Abstract

In this letter the construction of a quasi-periodic thrse-dimensional tiling with onedimensional translational symmetry is described. The tiling is generated by the projection method. This quasi-lattice Can serve as a model of the structure of the decagonal phase of Al-Mn alloys, which has been recently discovered. The present construction is closely related to the projection of two-and three-dimensional Penrose tilings. A comparison is made with the model proposed by Ho.

Penrose patterns and related structures. II. Decagonal quasicrystals

“…1). This implies that their structure consists of several layers (Ho, 1986;Muller, 1987) and the projection along the axis gives the Penrose pattern. The Penrose pattern is divided into four kinds of subpatterns, which come from the four pentagonal atoms in the four-dimensional description of the Penrose pattern described in paper I.…”