Ternary Model of an Al-Cu-Co Decagonal Quasicrystal

Abstract

We propose a structural model for decagonal Al-Cu-Co quasicrystals based upon existing experimental diffraction data supplemented by total energy calculations. The model is a decoration of tiles related to the Penrose rhombus tiling. Strong chemical ordering between Cu and Co leads to chains of alternating Cu and Co atoms. These chains project onto tile edges, where they define arrows. At low temperatures, the interatomic potentials lead to rules fixing the relative orientation of a majority of the arrows. These rules are a subset of the Penrose rhombus matching rules. [S0031-9007(98)06685-X] PACS numbers: 61.44.Br, 61.50.Lt, 61.43.Bn, 61.66.Dk More than a decade after the discovery of quasicrystals [1] answers are emerging to the fundamental problem of structure determination [2]. X-ray and neutron diffraction experiments successfully determine the location of the majority of atoms in quasicrystals [3]. Still, important questions remain. Quasicrystal structure refinements based on a finite number of diffraction peaks exhibit split atoms and atoms whose chemical identity cannot be determined [4,5]. Species determination is especially difficult for compounds such as Al-Cu-Co that contain elements near each other in a row of the periodic table, since their x-ray form factors are nearly equal. Furthermore, chemical disorder and partial occupancy are not well described. For example, a partially occupied site of high atomic number may mimic a fully occupied site of low atomic number. The atomicity condition is insufficient to resolve these issues; additional methods are required to investigate quasicrystal structure in greater detail. Techniques have been developed to supplement experimental diffraction data with total energy considerations to resolve the above difficulties [6 ‐ 8]. Here, we apply these techniques to create a model of the decagonal quasicrystal phase of Al-Cu-Co [9]. This phase exhibits quasiperiodic atomic layers stacked with a net 4 A periodicity in the perpendicular direction. We focus on this compound because its stable quasicrystalline phase has been well studied by diffraction, but experimental information suffers difficulties of the type described above. Furthermore, the existence of electronic-structure-based pair potentials for Al-Co alloys [10] allows total energy calculations to discriminate among candidate structures. We deduce the ternary alloy structure using only Al-Co binary potentials. After we review the current experimental knowledge of Al-Cu-Co decagonal phases, we discuss our computational method and then our results. Our results include an ideal hyperspace model and a corresponding real space structure. We describe the real space structure from two perspectives: linked clusters and space-filling tilings. We show that chemical ordering between Cu and Co enforces a subset of the Penrose matching rules. The temperature- and composition-dependent phase diagram of Al-Cu-Co alloys is well studied experimentally [11]. While the full composition range of thermodynamic stability of the decagonal phase shifts and widens as temperature increases, the principal domain of phase stability surrounds a straight line in the composition plane Al73.520.5xCuxCo26.520.5x ,