The low-friction properties of quasicrystal surfaces suggest their use as coatings on moving machine parts, including those in internal combustion engines. In such applications, additional lubricants are typically used. Since the low-friction properties of quasicrystals are thought to depend on their aperiodic structures, the interactions of lubricants on quasicrystalline surfaces may have an i...

We have observed the configuration and motion of surface steps on the aperiodic icosahedral (i-) Al-Pd-Mn quasicrystal using low-energy electron microscopy and scanning tunneling microscopy. As the quasicrystal is cooled from high temperature, bulk vacancies migrate to the surface causing the surface to be etched. Surprisingly, this etching occurs by two types of steps with different heights mo...

We identify several new quasicrystal approximants in alloy systems in which quasicrystals have not been previously reported. Some occur in alloys with large size contrast between the constituent elements, either containing small Boron atoms, or large Ca/Eu atoms, leading to quasicrystal structures quite different from currently known systems where the size contrast is smaller. Another group of ...

2014 We present a new algorithm for the generation of quasicrystalline structures. It is related to the cut and projection method, but allows a direct generation of the structure in the « physical » space E. The orthogonal space site selection is replaced by a direct check in a periodic array of « acceptance » regions in E. This method shows that there is a sort of underlying crystalline lattic...

After the first couple years of quasicrystal papers, and especially after the discovery of long-range-ordered equilibrium quasicrystals, theorists began to address their stabilisation. But this was mostly in terms of abstract tilings – with inter-tile matching rules (as in Penrose’s tiling), or without (as in the random-tiling models); it was implicitly understood that the tiles’ interactions w...

Inverse x-ray fluorescence holography was used to explore the local atomic order of a nearly perfect quasicrystal with composition Al70. 4Pd21Mn8.6. We have demonstrated the possibility of direct 3D imaging of the atomic decoration in a quasicrystal. We have obtained the average 3D environment of selected coordination shells around the Mn atoms. These results open the way to obtaining further a...

We interpret experimentally known B-Mg-Ru crystals as quasicrystal approximants whose deterministic decoration of tiles by atoms can be extended quasiperiodically. Experimentally observed disorder corresponds to phason fluctuations. First-principles total energy calculations find many distinct tilings close to stability and suggest a phase transition from a crystalline state at low temperatures...

We discuss a new general phenomenon pertaining to tiling models of quasicrystal growth. It is known that with Penrose tiles no (de-terministic) local matching rules exist which guarantee defect-free tiling for regions of arbitrary large size. We prove that this property holds quite generally: namely, that the emergence of defects in quasicrystal growth is unavoidable for all aperiodic tiling mo...

Quasicrystals are metallic alloys that possess long-range, aperiodic structures with diffraction symmetries forbidden to conventional crystals. Since the discovery of quasicrystals by Schechtman et al. in 1984, there has been considerable progress in resolving their geometric structure. For example, it is well known that the golden ratio of mathematics and art occurs over and over again in thei...

This paper reviews the empire problem for quasiperiodic tilings and the existing methods for generating the empires of the vertex configurations in quasicrystals, while introducing a new and more efficient method based on the cut-and-project technique. Using Penrose tiling as an example, this method finds the forced tiles with the restrictions in the high dimensional lattice (the mother lattice...