At the 2- and 10-fold-symmetry surfaces of the two-dimensional quasicrystal Al-Co-Ni an epitaxial cubic layer is induced by preferential sputtering of Al using Al+ ions. Annealing the sample at 760 K restores the Al concentration at the surface and, thereby, the quasicrystalline structure. Simultaneous observations of the surface chemistry by Auger electron spectroscopy and of its atomic structure by secondary-electron imaging reveal that the transition is a two-step process. The replenishment of Al at the surface is limited by high-temperature mediated diffusion of Al from bulk, while the assembly kinetics of the quasicrystalline structure proceeds at lower temperatures. Thus, the underlying bulk Al-Co-Ni quasicrystal acts as an Al reservoir and as a structural template for the recovery of the quasicrystal. The paper also presents a discussion of different cubic orientations of the surface phase formed by different sputtering conditions. (C) 2003 Published by Elsevier Science B.V.