Growth and kinetic roughening of quasicrystals and other incommensurate systems

It is shown that in a simple model of surface dynamics of growing 3D quasicrystals, growth proceeds through the nucleation of steps whose heights hs diverse like ()-1/3 as the growth-driving chemical-potential difference. This large step size leads to very low growth velocities Vgxp{-1/3[T)/]4/3}.(T) defines a rounded kinetic roughening transition and is nonuniversal. For perfect-tiling models I find c(T)T-3/2 at high temperatures T, which fits recent numerical simulations, while in models with bulk phason Debye-Waller disorder, ln(c)- T. The growing interface is algebraically rough. © 1990 The American Physical Society.