A simple solid-on-solid model is proposed to study various interfacial properties in two-dimensional (2D) aperiodic structures. Height-difference correlations, step free energies, and polar-surface free-energy plots (γ plots) are discussed. We find that interfaces in 2D aperiodic systems are always less rough than those of crystals except in a particular class of random structures studied by Lipowsky and Henley [Phys. Rev. Lett. 60, 2394 (1988)]. In some systems interfaces are found to be localized. Those localized interfaces may migrate to search for lower surface free energy. Modifications of the Fibonacci sequence potential are introduced to emulate two-dimensional quasicrystals. For systems that resemble the Penrose tiling most closely, we find a new type of roughening transition, while for another type of quasiperiodic modification the interfaces may always be localized.

• Received 7 April 1989

DOI:https://doi.org/10.1103/PhysRevB.40.7167