Simple model of kinetic roughening of quasicrystalline surfaces

A simple relaxational model of the dynamics of the surface of a growing quasicrystal is studied. As in a crystal, growth proceeds through the nucleation of steps on the surface. Unlike the crystal, the heights hs of these steps diverge like ()-1/3 as the driving chemical-potential difference between quasicrystal and fluid goes to zero. The exponent 1/3 is universal for all quasicrystals with structures derived from quadratic irrationals. This large step size leads to unusually low growth velocities Vg; i.e., Vgexp{-1/3[uc(T)/]4/3}. The quantity c(T), which defines a rounded kinetic roughening transition, is nonuniversal. For perfect-tiling models of quasicrystal growth, I find c(T) T-3/2, which fits recent numerical simulations, while for models which allow bulk phason Debye-Waller disorder, ln(1/c)T3/2. The growing interface is algebraically rough at all temperatures. © 1991 The American Physical Society.