Phason-elastic energy in a model quasicrystal Ulrich Koschella, Franz G¨ahler, Johannes Roth, and Hans-Rainer Trebin Institut f¨ ur Theoretische und Angewandte Physik, Universit¨at Stuttgart, D-70550 Stuttgart, Germany 06.09.2002 Abstract The standard two-dimensional decagonal binary tiling quasicrystal with Lennard-Jones potentials is metastable at zero temperature with respect to one phason strain mode. By calculating the frequencies of local environments as a function of phason strain, a correction for the potentials is predicted, which stabilizes the quasicrystal. PACS: 61.44.Br, 62.20.Dc 1. Introduction In a previous paper [1] we have measured the five generalized phason-phonon elastic constants at zero temperature for the standard two-dimensional decagonal binary tiling quasicrystal with Lennard- Jones potentials, using molecular dynamics relax- ation simulations. One of the phason elastic con- stants turned out to be negative, rendering the sys- tem metastable. Lee et al. [2] have shown, that the ground state of this system is a phase separation into various crystalline states without any five- or tenfold motifs. To improve on those results, we analyze in Sec- tion 2 the phason elastic constants in dependence of the two-body interaction potentials, by counting the frequencies of atomic neighborhoods as a function of phason strain. These calculations suggest a modifica- tion of the potentials, presented in Section 3, which stabilizes the binary tiling quasicrystal. For these new potentials the elastic constants are determined with the same simulation method as in [1]. The elastic constant for stoichiometry preserving phason strains becomes positive, and the system is stable. The ground state structure for both potentials is obtained by Monte-Carlo cooling simulations, briefly discussed in Section 4. With the unmodi- fied Lennard-Jones potentials the results of Lee et al. [2] are reproduced, whereas the modified potentials strongly prefer tenfold clusters. The cooling simula- tions yield a ground state structure which is a super- tile random tiling with mainly doubly inflated thick Penrose rhombs. 2. Calculation of the zero temperature phason elastic constants We consider here a model quasicrystal without phonon strain or local relaxations of atom positions, but with an arbitrary phason strain. Such structures include both periodic approximants and the perfect quasicrystal. If we consider a cutoff radius R c for the atomic interactions, the potential energy E i of a single atom depends only on the potentials φ and the atomic configuration inside the ball B Rc,xi with radius R c around the position x i of the atom. There-