Growth and kinetic roughening of quasicrystals and other incommensurate systems

Abstract

It is shown that in a simple model of surface dynamics of growing 3D quasicrystals, growth proceeds through the nucleation of steps whose heights $h_s$ diverse like (Δμ${)}^{\mathrm{-}1/3}$ as the growth-driving chemical-potential difference Δμ→0. This large step size leads to very low growth velocities ${\mathit{V}}_{\mathit{g}}$∝exp{-1/3[Δ${\mathrm{\mu }}_{\mathit{c}}$(T)/Δμ${]}^{4/3}$}. Δ${\mathrm{\mu }}_{\mathit{c}}$(T) defines a rounded kinetic roughening transition and is nonuniversal. For ‘‘perfect-tiling models’’ I find Δ${\mu }_c$(T)∝$T^{\mathrm{-}3/2}$ at high temperatures T, which fits recent numerical simulations, while in models with bulk phason Debye-Waller disorder, ln(Δ${\mu }_c$)∝- √T . The growing interface is algebraically rough.