Tuning the Stability of a Model Quasicrystal and its Approximants with a Periodic Substrate

Abstract

Quasicrystals and their periodic approximants are complex phases, which have by now been observed in many metallic alloys, soft matter systems, and particle simulations. In recent experiments of thin-film perovskites on solid substrates, the type of complex phase was found to change depending on thermodynamic conditions and the type of substrate used. Here, we investigate the effect of a substrate on the relative stability of a two-dimensional model quasicrystal and its approximants. Our numerical methods are molecular dynamics simulations and free energy calculations that take into account phason flips explicitly. For weak substrates, we observe an incommensurate-commensurate transition, in which a continuous series of QC approximants locks into a discrete number of approximants. For stronger substrates, an enhancement of the stability of the dodecagonal quasicrystal and a variants of square lattices were found. All phenomena can be explained by the interplay of the model system with the substrate. Our results demonstrate that designing novel complex periodic and quasiperiodic structures by choice of suitable substrates is a promising strategy.