Surface scaling properties of decagonal quasicrystals under nonequilibrium vertical growth

Abstract

Restricted solid-on-solid (RSOS) growth models are studied on two different decagonal quasicrystal lattices, namely the Penrose tiling lattice and the random tiling lattice. There exist two types of growth blocks-fat and skinny tiles-which may have different sticking probabilities. We found that the RSOS growths on both lattices belong to the Kardar-Parisi-Zhang universality class when they have the same sticking probabilities in spite of the lack of periodicity in the substrates. However, when they have tile-type dependent sticking probabilities, the RSOS models on two lattices may produce different scaling behaviors. Growth on Penrose tiling shows that the roughness exponent is around 0.4 while that on random tiling is around 0.49. Our observation may provide an effective way to investigate the bulk structures of decagonal quasicrystals.

Roughening transition and universality of single step growth models in (2+1)-dimensions

“…Although we have used relatively large system sizes with adequate statistics in our computations, there may however exist systematic deviations from the true thermodynamic values. In order to eliminate the systematic errors, we compute size-dependent effective roughness exponent [40] for various values of p.…”

“…deviations from the true thermodynamic values. In orto eliminate the systematic errors, we compute sizedependent effective roughness exponent [39] for various values of p.…”