Epitaxial interfaces between half-crystals of quasicrystalline and periodic material

We recently demonstrated that epitaxial interfaces can be formed between periodic and quasiperiodic materials (Franke et al 2007 Phys. Rev. Lett. 99 036103). Such interfaces exhibit the same defining characteristic as epitaxial interfaces between commensurate periodic materials, namely the locking into registry of the two half-crystals' atomic structures. This real space characteristic is equivalent to the requirement of a coincidence of reciprocal lattice points. Here, we explore the characteristics of the potential interfaces within the class of quasicrystals exhibiting a periodic direction, including decagonal quasicrystals. We derive our results geometrically from a higher dimensional description, thus providing visual insight into the underlying concepts. Since the reciprocal lattice of quasicrystalline structures is generated by more basis vectors than their periodic counterparts', suitable quasicrystalline interlayers can be designed to epitaxially link incommensurate half-crystals. We give examples of selected model structures as illustrations.