Cluster-Based Solidification and Growth Algorithm for Decagonal Quasicrystals

A novel approach is used for the simulation of decagonal quasicrystal (DQC) solidification and growth. It is based on the observation that in well-ordered DQCs the atoms are largely arranged along quasiperiodically spaced planes parallel to the tenfold axis, running throughout the whole structure in five different directions. The structures themselves can be described as quasiperiodic arrangements of decagonal columnar clusters (cluster covering) that partially overlap in a systematic way. Based on these findings, we define a cluster interaction model within the mean field approximation, with effectively asymmetric interactions ranging beyond the nearest neighbors. In our Monte Carlo simulations, this leads to a long-range ordered quasiperiodic ground state. Indications of two finite-temperature unlocking phase transitions are observed, and are related to the two fundamental length scales that are characteristic for the system.