Equilibrium structure of decagonal AlNiCo
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Equilibrium structure of decagonal AlNiCo S. Naidu, M. Mihalkoviˇc1 and M. Widom, Department of Physics, Carnegie Mellon University, Pittsburgh, PA 15213 1 also at: Institute of Physics, Slovak Academy of Sciences, 84228 Bratislava, Slovakia ABSTRACT We investigate the high temperature decagonal quasicrystalline phase of Al72 Ni20 Co8 using a quasilattice gas Monte-Carlo simulation. To avoid biasing towards a specific model we use an over-dense site list with a large fraction of free sites, permitting the simulation to explore an extended region of perpendicular space. Representing the atomic surface occupancy in a basis of harmonic functions directly reveals the 5-fold symmetric component of our data. Occupancy is examined in physical and perpendicular space. INTRODUCTION AlNiCo exhibits quasicrystalline phases over a range of compositions and temperatures[1]. Of special interest is the Ni-rich quasicrystalline phase around the composition Al72 Ni20 Co8 . This is a decagonal phase with a period of 4.08 ˚ A along the periodic axis, making it a simple phase relative to other members of the Al-Ni-Co family. Additionally, it appears to be most perfect structurally, even though it is stable only at high temperatures around T=1000-1200K. Its structure has been extensively studied experimentally by X-ray diffraction[2, 3] and electron microscopy[4, 5]. Finally, since qualitatively accurate pair potentials are available[6], structural predictions can be made based on total energy considerations[7]. An idealized deterministic structure for this phase has been proposed by studying the total energy[7]. This prediction employed a multi-scale simulation method, in which small system sizes were simulated starting with very limited experimental input, then rules discovered through the small scale simulations were imposed to accelerate simulations of larger-scale models. Although efficient, this approach leaves open the question of how strongly the final model was biased by the chosen method. We adopt a different approach here, starting from slightly different experimental input and working directly at the relevant high temperatures. The experimental input is: (1) the density [2], composition and temperature at which the phase exists; (2) the hyperspace positions of atomic surfaces (these are simply the positions for a Penrose tiling, with AS1 at ν = ±1 and AS2 at ν = ±2); (3) the fact that the quasicrystal is layered, with space group 105 /mmc, and its lattice constants (we take aq = 6.427, c = 4.08˚ A ). The chief unknowns to be determined are the sizes, shapes and chemical occupancies of the atomic surfaces. Like the prior study [7], we employ Monte Carlo simulation using the same electronic-structure derived pair potentials[6]. Also, like the prior study, we employ a discrete list of allowed atomic positions. However, instead of using sparse decorations of fundamental tiles, where the configurational freedom arose largely from flipping of the decorated tiles, in the present study we employ a fixed site list based on a
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