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MM: Fachverband Metall- und Materialphysik
MM 12: Poster I
MM 12.21: Poster
Monday, March 27, 2023, 18:15–20:00, P2/OG1+2
Thermodynamical Stability Analysis of a Model Quasicrystal — •Moritz Holzwarth, Johannes Roth, and Hans-Rainer Trebin — FMQ, Uni Stuttgart, Germany
The random tiling hypothesis, first proposed by Henley in 1991, states that quasicrystals are entropy-stabilized and, hence, are high temperature phases. We confirm the hypothesis for a two-dimensional Tübingen triangle tiling which arises in molecular dynamics simulations with a Lennard-Jones-Gauß potential, by investigating the temperature dependence of its two phason elastic constants λ6 and λ8. These are the second derivatives of the free energy F(χ6,χ8,T) with respect to the symmetrized phason strain modes χ6 and χ8. At T=0, F has a saddle point by descending along the χ8 direction. Therefore, λ8 < 0 characterizes the quasicrystal’s initial instability. The configurational entropy due to phason flips turns F upwards at higher temperatures, reverses the sign of λ8 and leads to a stable quasicrystal. We obtain this result by applying exclusively geometric methods in the form of the polar calculus, where the atomic domain (AD) is divided into sections for each vertex environment. We extend the calculus to a dynamic one by separating the AD into areas that characterize the different kinds of phason flips. By phasonic deformation of the AD, we can determine the types of flips and their frequency in dependence of phason strain, can perform energy relaxations by flips and compute the configurational entropy. We find that an important mechanism supporting the quasicrystal stability is the symmetric nearest neighbour coupling of phasonic flips.