Archimedean-like tiling on decagonal quasicrystalline surfaces

Abstract

Monolayers on crystalline surfaces often form complex structures with physical and chemical properties that differ strongly from those of their bulk phases 1 . Such hetero-epitactic overlayers are currently used in nanotechnology and understanding their growth mechanism is important for the development of new materials and devices. In comparison with crystals, quasicrystalline surfaces exhibit much larger structural and chemical complexity leading, for example, to unusual frictional 2 , catalytical 3 or optical properties 4,5 . Deposition of thin films on such substrates can lead to structures that may have typical quasicrystalline properties. Recent experiments have indeed showed 5-fold symmetries in the diffraction pattern of metallic layers adsorbed on quasicrystals 6,7 . Here we report a real-space investigation of the phase behaviour of a colloidal monolayer interacting with a quasicrystalline decagonal substrate created by interfering five laser beams. We find a pseudomorphic phase that shows both crystalline and quasicrystalline structural properties. It can be described by an archimedean-like tiling 8,9 consisting of alternating rows of square and triangular tiles. The calculated diffraction pattern of this phase is in agreement with recent observations of copper adsorbed on icosahedral Al 70 Pd 21 Mn 9 surfaces 10 . In addition to establishing a link between archimedean tilings and quasicrystals, our experiments allow us to investigate in real space how single-element monolayers can form commensurate structures on quasicrystalline surfaces.Quasicrystals are unusual materials: they are aperiodic but retain true long-range order 11 . Although quasicrystalline structures have been theoretically also predicted in systems with a single type of particle 12,13 , experimentally their spontaneous formation has been observed only in binary, ternary or even more complex alloys 14 . Accordingly, their surfaces exhibit a high degree of structural and chemical complexity and show unexpected mechanical, electrical and optical properties 15 . To understand the origin of those characteristics it is useful to disentangle structural and chemical aspects; this can be achieved by growing single-element monolayers to quasicrystalline surfaces 16,17 . Apart from adding to our understanding of how quasicrystalline properties can be transferred to such monolayers 18 , this approach might permit the fabrication of materials with previously unobserved properties. Heteroepictatic growth experiments on decagonal and icosahedral surfaces did indeed show the formation of Bi and Sb monolayers with a high degree of quasicrystalline order as determined by low-energy electron diffraction and elastic heliumatom scattering experiments 6,18 . In comparison with reciprocal space studies, it was only recently that scanning tunnelling microscopy permitted an atomic resolution of the adsorbate morphology 7 . Even then, however, it was difficult to relate the structure of the adsorbate to that of the underlying substrate.Here we report an experi...

Dynamic regimes for driven colloidal particles on a periodic substrate at commensurate and incommensurate fillings

“…Kink motion also occurs in experiments on colloidal particles moving over quasiperiodic substrates [39]. In addition, in studies of colloidal particles driven over corrugated 1D arrays, different dynamical transitions between pinned, smectic, and disordered flowing regimes were observed [33].…”

“…Experiments and computational studies have shown that in the absence of a drive, a variety of orderings can arise for colloidal particles interacting with one-dimensional (1D) periodic substrates [13,32,33], two-dimensional (2D) periodic substrates [15,20,21,[34][35][36][37][38], 2D quasiperiodic substrates [39][40][41][42][43], or 2D random substrates [44]. While these studies have provided a better understanding of several features of commensurateincommensurate behaviors, being able to dynamically control the particle ordering and dynamics could lead to a variety of applications, including self-assembled structures, particle separation, and photonic crystals.…”

Templated three-dimensional growth of quasicrystalline lead

“…S ince their discovery 1 , quasicrystalline phases have been found in 4100 intermetallic compounds, liquid crystals 2 , polymers 3 , colloids 4 and perovskite thin films 5 , and are recognized as universal phases of matter. A very important breakthrough was the discovery of stable intermetallic phases 6 , which enabled detailed experimental studies, including the determination of accurate atomic structures of quasicrystals and investigation of quasicrystalline surfaces and overlayers (ref.…”

Observation of kinks and antikinks in colloidal monolayers driven across ordered surfaces

“…This strong dependence of superlubric behaviour on the substrate lattice spacing is in agreement with atomic friction force experiments on incommensurate surfaces 15,23 . We also carried out friction experiments on nonperiodic substrate potentials with quasiperiodic order, which are strongly incommensurate with the periodic monolayer 22 . Here, we find almost the same behaviour as for triangular substrates with s = 4.8 μm, which is consistent with the small friction coefficient on atomic quasicrystalline surfaces reported from experiments and simulations [24][25][26] .…”

“…1a; ref. 22). To apply lateral forces to the colloidal crystal, the sample cell is translated with velocity u, which leads to a Stokes force F ∼ u acting on each particle (Methods).…”