Growth and kinetic roughening of quasicrystals and other incommensurate systems

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 (Δμ)-1/3 as the driving chemical potential difference Δμ 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., Vg is proportional exp (-(Δμc(T)/Δμ)4/3). The quantity Δμc(T), which defines a ''rounded'' kinetic roughening transition, is non-universal. For ''perfect-tiling models'' of quasicrystal growth, I find Δμc(T) is proportional to T-3/2 at high temperatures T, which fits recent numerical simulations, while for models which allow bulk phason Debye-Waller disorder, Δμc is proportional to e-√T. The growing interface is algebraically rough at all temperatures. (author). 23 refs, 1 fig