SIMPLE-MODEL OF KINETIC ROUGHENING OF QUASI-CRYSTALLINE 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 h(s) of these steps diverge like (DELTA-mu)-1/3 as the driving chemical-potential difference DELTA-mu 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 V(g); i.e., V(g) is proportional to exp{- 1/3]DELTA-mu-c(T)/DELTA-mu-[4/3}. The quantity DELTA-mu-c(T), which defines a rounded kinetic roughening transition, is nonuniversal. For "perfect-tiling models" of quasicrystal growth, I find DELTA-mu-c(T) infinity T-3/2, which fits recent numerical simulations, while for models which allow bulk phason Debye-Waller disorder, ln(1/DELTA-mu-c) is proportional to T3/2. The growing interface is algebraically rough at all temperatures.