High Frictional Anisotropy of Periodic and Aperiodic Directions on a Quasicrystal Surface

Anisotropic Friction in a Ligand-Protein Complex

The effect of an externally applied directional force on molecular friction is so far poorly understood. Here, we study the force-driven dissociation of the ligand-protein complex biotin-streptavidin and identify anisotropic friction as a not yet described type of molecular friction. Using AFM-based stereographic single molecule force spectroscopy and targeted molecular dynamics simulations, we find that the rupture force and friction for biotin-streptavidin vary with the pulling angle. This observation holds true for friction extracted from Kramers' rate expression and by dissipation-corrected targeted molecular dynamics simulations based on Jarzynski's identity. We rule out ligand solvation and protein-internal friction as sources of the angle-dependent friction. Instead, we observe a heterogeneity in free energy barriers along an experimentally uncontrolled orientation parameter, which increases the rupture force variance and therefore the overall friction. We anticipate that anisotropic friction needs to be accounted for in a complete understanding of friction in biomolecular dynamics and anisotropic mechanical environments.

Formation of a single quasicrystal upon collision of multiple grains

Quasicrystals exhibit long-range order but lack translational symmetry. When grown as single crystals, they possess distinctive and unusual properties owing to the absence of grain boundaries. Unfortunately, conventional methods such as bulk crystal growth or thin film deposition only allow us to synthesize either polycrystalline quasicrystals or quasicrystals that are at most a few centimeters in size. Here, we reveal through real-time and 3D imaging the formation of a single decagonal quasicrystal arising from a hard collision between multiple growing quasicrystals in an Al-Co-Ni liquid. Through corresponding molecular dynamics simulations, we examine the underlying kinetics of quasicrystal coalescence and investigate the effects of initial misorientation between the growing quasicrystalline grains on the formation of grain boundaries. At small misorientation, coalescence occurs following rigid rotation that is facilitated by phasons. Our joint experimental-computational discovery paves the way toward fabrication of single, large-scale quasicrystals for novel applications.

Friction Anisotropy of MoS2: Effect of Tip-Sample Contact Quality

Atomic-scale friction measured for a single asperity sliding on 2D materials depend on the direction of scanning relative to the material's crystal lattice. Here, nanoscale friction anisotropy of wrinkle-free bulk and monolayer MoS₂ is characterized using atomic force microscopy and molecular dynamics simulations. Both techniques show 180° periodicity (2-fold symmetry) of atomic-lattice stick-slip friction vs. the tip's scanning direction with respect to the MoS₂ surface. The 60° periodicity (6-fold symmetry) expected from the MoS₂ surface's symmetry is only recovered in simulations where the sample is rotated, as opposed to the scanning direction changed. All observations are explained by the potential energy landscape of the tip-sample contact, in contrast with nanoscale topographic wrinkles that have been proposed previously as the source of anisotropy. These results demonstrate the importance of the tip-sample contact quality in determining the potential energy landscape and, in turn, friction at the nanoscale.

Nonwetting Behavior of Al-Co Quasicrystalline Approximants Owing to Their Unique Electronic Structures

Good wetting is generally observed for liquid metals on metallic substrates, while poor wetting usually occurs for metals on insulating oxides. In this work, we report unexpected large contact angles for lead on two metallic approximants to decagonal quasicrystals, namely, Al₅Co₂ and Al₁₃Co₄. Intrinsic surface wettability is predicted from first principles, using a thermodynamic model based on the Young equation, and validated by the good agreement with experimental measurements performed under ultra-high vacuum by scanning electron microscopy. The atomistic details of the atomic and electronic structures at the Pb-substrate interface, and the comparison with Pb(111)/Al(111), underline the influence of the specific electronic structures of quasicrystalline approximants on wetting. Our work suggests a possible correlation of the contact angles with the density of states at the Fermi energy and paves the way for a better fundamental understanding of wettability on intermetallic substrates, which has potential consequences in several applications such as supported catalysts, protective coatings, or crystal growth.

Dodecagonal quasicrystal silicene: preparation, mechanical property, and friction behaviour

In this study, we obtained dodecagonal monolayer silicene with three-fold and four-fold coordination by melt quenching via molecular dynamics (MD) simulations. Stretching simulation of the pre-strained dodecagonal silicene showed lower critical stress than the honeycomb silicene and resulted in an increase in six-fold rings during the plastic deformation since the four-coordinated atom sites are less mechanically favoured than the three-coordinated sites. The friction behaviours with an AFM tip sliding on the dodecagonal and honeycomb surfaces under different loads and tip sizes were simulated and compared. For all the investigated cases, the dodecagonal surface always showed a lower mean friction force than the honeycomb surface. The lower friction of the quasicrystal was observed, and the mechanism was illuminated successfully for the first time by MD simulations. The reduced friction of dodecagonal silicene can be explained by the morphology of the one-dimensional potential energy surface (PES). The 1D PES of dodecagonal silicene has longer potential corrugation lengths than honeycomb silicene, which induce mild motion of the tip in the stick process and lower friction force. Considering the close density of the employed dodecagonal and honeycomb structure, the longer potential corrugation length is a consequence of the quasiperiodic morphology rather than the interspace between atoms. Besides, with a larger tip size, the 1D PES on the dodecagonal surface has a flatter area, which contributes further to the reduced friction force on the dodecagonal surface.

A universal state and its relaxation mechanisms of long-range interacting polygons

Using polygonal magnetic particles, we conduct experiments to explore the space-filling properties of anisotropic blocks with long-range interactions. In contrast to previous studies, we obtain the surprising finding that our systems' structures do not depend on the shape of building blocks: a single state, the hexagonal plastic crystal, appears as a universal attractor for a wide range of different polygons. This robust particle-shape independency appears as the interactions go beyond nearest neighbors. Particle shape plays an essential role in system relaxation, and determines the basic relaxation dynamics through a microscopic control parameter, internal roughness, produced by particle vertices. Thus our study reveals a new pattern-forming paradigm, in which particle shape plays little role in the static structure but determines the essential relaxation dynamics. Due to the ubiquity of long-range interactions and anisotropic building blocks, our discovery may shed new light on diverse problems involving structure formation, self-assembly, and packing.

Bioinspired 3D Printed Locomotion Devices Based on Anisotropic Friction

Anisotropic friction plays a key role in natural systems, particularly for realizing the purpose of locomotion and strong attachment for the survival of organisms. Of particular interest, here, is the observation that friction anisotropy is promoted numerous times by nature, for example, by wild wheat awn for its targeted and successful seed anchorage and dispersal. Such feature is, however, not fully exploited in man-made systems, such as microbots, due to technical limitations and lack of full understanding of the mechanisms. To unravel the complex dynamics occurring in the sliding interaction between anisotropic microstructured surfaces, the friction induced by asymmetric plant microstructures is first systematically investigated. Inspired by this, anisotropic polymer microactuators with three-dimensional (3D) printed microrelieves are then prepared. By varying geometric parameters, the capability of microactuators to generate strong friction anisotropy and controllable motion in remotely stretched cylindrical tubes is investigated. Advanced theoretical models are proposed to understand and predict the dynamic behavior of these synthetic systems and to shed light on the parameters and mechanisms governing their behavior. Finally, a microbot prototype is developed and cargo transportation functions are successfully realized. This research provides both in-depth understanding of anisotropic friction in nature and new avenues for developing intelligent actuators and microbots.

Exploring load, velocity, and surface disorder dependence of friction with one-dimensional and two-dimensional models

The effect of surface disorder, load, and velocity on friction between a single asperity contact and a model surface is explored with one-dimensional and two-dimensional Prandtl-Tomlinson (PT) models. We show that there are fundamental physical differences between the predictions of one-dimensional and two-dimensional models. The one-dimensional model estimates a monotonic increase in friction and energy dissipation with load, velocity, and surface disorder. However, a two-dimensional PT model, which is expected to approximate a tip-sample system more realistically, reveals a non-monotonic trend, i.e. friction is inert to surface disorder and roughness in wearless friction regime. The two-dimensional model discloses that the surface disorder starts to dominate the friction and energy dissipation when the tip and the sample interact predominantly deep into the repulsive regime. Our numerical calculations address that tracking the minimum energy path and the slip-stick motion are two competing effects that determine the load, velocity, and surface disorder dependence of friction. In the two-dimensional model, the single asperity can follow the minimum energy path in wearless regime; however, with increasing load and sliding velocity, the slip-stick movement dominates the dynamic motion and results in an increase in friction by impeding tracing the minimum energy path. Contrary to the two-dimensional model, when the one-dimensional PT model is employed, the single asperity cannot escape to the minimum energy minimum due to constraint motion and reveals only a trivial dependence of friction on load, velocity, and surface disorder. Our computational analyses clarify the physical differences between the predictions of the one-dimensional and two-dimensional models and open new avenues for disordered surfaces for low energy dissipation applications in wearless friction regime.

Recent highlights in nanoscale and mesoscale friction

Friction is the oldest branch of non-equilibrium condensed matter physics and, at the same time, the least established at the fundamental level. A full understanding and control of friction is increasingly recognized to involve all relevant size and time scales. We review here some recent advances on the research focusing of nano- and mesoscale tribology phenomena. These advances are currently pursued in a multifaceted approach starting from the fundamental atomic-scale friction and mechanical control of specific single-asperity combinations, e.g., nanoclusters on layered materials, then scaling up to the meso/microscale of extended, occasionally lubricated, interfaces and driven trapped optical systems, and eventually up to the macroscale. Currently, this "hot" research field is leading to new technological advances in the area of engineering and materials science.

Nanoscale liquid crystal lubrication controlled by surface structure and film composition

Liquid crystals have emerged as potential candidates for next-generation lubricants due to their tendency to exhibit long-range ordering. Here, we construct a full atomistic model of 4-cyano-4-hexylbiphenyl (6CB) nematic liquid crystal lubricants mixed with hexane and confined by mica surfaces. We explore the effect of the surface structure of mica, as well as lubricant composition and thickness, on the nanoscale friction in the system. Our results demonstrate the key role of the structure of the mica surfaces, specifically the positions of potassium (K+) ions, in determining the nature of sliding friction with monolayer lubricants, including the presence or absence of stick-slip dynamics. With the commensurate setup of confining surfaces, when the grooves created between the periodic K+ ions are parallel to the sliding direction we observe a lower friction force as compared to the perpendicular situation. Random positions of ions exhibit even smaller friction forces with respect to the previous two cases. For thicker lubrication layers the surface structure becomes less important and we observe a good agreement with the experimental data on bulk viscosity of 6CB and the additive hexane. In case of thicker lubrication layers, friction may still be controlled by tuning the relative concentrations of 6CB and hexane in the mixture.

Campestarenes: new building blocks with 5-fold symmetry

New campestarene derivatives bear functional groups designed to facilitate the formation of supramolecular assemblies of these 5-fold symmetric building blocks.

Dependence of the sliding distance of a one-dimensional atom chain on initial velocity

In our daily lives, a body with a high initial velocity sliding freely on a rough surface moves a longer distance than that with a low initial velocity. However, such a phenomenon may not occur in the microscopic world. The dynamical behavior of a one-dimensional atom chain (1DAC) sliding on a substrate is investigated in this study by using a modified Frenkel–Kontorova model, in which the vibration of atoms on the substrate is considered. The dependence of sliding distance on initial velocity is examined. Result shows that although sliding distance is proportional to the initial value for most velocities, such a linear relation does not exist in some special velocities. This phenomenon is explained by a theoretical analysis of phonon excitation. The physical process is divided into three stages. The first stage is a superlubric sliding process with small amplitude of the vibrication of the atoms. The single-mode phonon is excited in the second stage. In the third stage, the system exhibits instability because of multiple-mode phonon excitations. In addition, the dependence of the coupling strength between 1DAC and the substrate is investigated. The findings are helpful in understanding the energy dissipation mechanism of friction.

Crystal Orientation Dependence of Gallium Nitride Wear

We explore how crystallographic order and orientation affect the tribological (friction and wear) performance of gallium nitride (GaN), through experiments and theory. Friction and wear were measured in every direction on the c-plane of GaN through rotary wear experiment. This revealed a strong crystallographic orientation dependence of the sliding properties of GaN; a 60° periodicity of wear rate and friction coefficient was observed. The origin of this periodicity is rooted in the symmetry presented in wurtzite hexagonal lattice structure of III-nitrides. The lowest wear rate was found as 0.6 × 10⁻⁷ mm³/Nm with <1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\bar{1}$$\end{document}1¯00>, while the wear rate associated with <1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\bar{2}$$\end{document}2¯10> had the highest wear rate of 1.4 × 10⁻⁷ mm³/Nm. On the contrary, higher friction coefficient can be observed along <1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\bar{1}$$\end{document}1¯00> while lower friction coefficient always appeared along <1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\bar{2}$$\end{document}2¯10>. We developed a simple molecular statics approach to understand energy barriers associated with sliding and material removal; this calculated change of free energy associated with sliding revealed that there were smaller energy barriers sliding along <1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\bar{2}$$\end{document}2¯10> as compared to the <1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\bar{1}$$\end{document}1¯00> direction.

Giant and Tunable Anisotropy of Nanoscale Friction in Graphene

The nanoscale friction between an atomic force microscopy tip and graphene is investigated using friction force microscopy (FFM). During the tip movement, friction forces are observed to increase and then saturate in a highly anisotropic manner. As a result, the friction forces in graphene are highly dependent on the scanning direction: under some conditions, the energy dissipated along the armchair direction can be 80% higher than along the zigzag direction. In comparison, for highly-oriented pyrolitic graphite (HOPG), the friction anisotropy between armchair and zigzag directions is only 15%. This giant friction anisotropy in graphene results from anisotropies in the amplitudes of flexural deformations of the graphene sheet driven by the tip movement, not present in HOPG. The effect can be seen as a novel manifestation of the classical phenomenon of Euler buckling at the nanoscale, which provides the non-linear ingredients that amplify friction anisotropy. Simulations based on a novel version of the 2D Tomlinson model (modified to include the effects of flexural deformations), as well as fully atomistic molecular dynamics simulations and first-principles density-functional theory (DFT) calculations, are able to reproduce and explain the experimental observations.

Switchable friction enabled by nanoscale self-assembly on graphene

Graphene monolayers are known to display domains of anisotropic friction with twofold symmetry and anisotropy exceeding 200%. This anisotropy has been thought to originate from periodic nanoscale ripples in the graphene sheet, which enhance puckering around a sliding asperity to a degree determined by the sliding direction. Here we demonstrate that these frictional domains derive not from structural features in the graphene but from self-assembly of environmental adsorbates into a highly regular superlattice of stripes with period 4-6 nm. The stripes and resulting frictional domains appear on monolayer and multilayer graphene on a variety of substrates, as well as on exfoliated flakes of hexagonal boron nitride. We show that the stripe-superlattices can be reproducibly and reversibly manipulated with submicrometre precision using a scanning probe microscope, allowing us to create arbitrary arrangements of frictional domains within a single flake. Our results suggest a revised understanding of the anisotropic friction observed on graphene and bulk graphite in terms of adsorbates.

Surfaces of Al-based complex metallic alloys: atomic structure, thin film growth and reactivity

We present a review on recent work performed on periodic complex metallic alloy (CMA) surfaces. The electronic and crystallographic structures of clean pseudo-tenfold, pseudo-twofold, sixfold surfaces will be presented along with the recent findings on CMA of lower structural complexity, i.e. with a smaller unit cell. The use of CMA surfaces as templates for thin film growth and the formation of surface alloy will also be introduced. The reactivity of these complex surfaces and their impact in the field of heterogeneous catalysis will be discussed. Finally, common trends among these systems will be highlighted when possible and future challenges will be examined.

Friction and solid-solid adhesion on complex metallic alloys

The discovery in 1987 of stable quasicrystals in the Al-Cu-Fe system was soon exploited to patent specific coatings that showed reduced friction in ambient air against hard antagonists. Henceforth, it was possible to develop a number of applications, potential or commercially exploited to date, that will be alluded to in this topical review. A deeper understanding of the characteristics of complex metallic alloys (CMAs) may explain why material made of metals like Al, Cu and Fe offers reduced friction; low solid-solid adhesion came later. It is linked to the surface energy being significantly lower on those materials, in which translational symmetry has become a weak property, that is determined by the depth of the pseudo-gap at the Fermi energy. As a result, friction is anisotropic in CMAs that builds up according to the translation symmetry along one direction, but is aperiodic along the other two directions. A review is given in this article of the most salient data found along these lines during the past two decades or so.

Faulting of rocks in a three-dimensional stress field by micro-anticracks

Nucleation and propagation of a shear fault is known to be the result of interaction and coalescence of many microcracks. Yet the character and rate of the microcracks' interactions, and their dependence on the three-dimensional stress state are poorly understood. Here we investigate formation of microcracks during sandstone faulting under 3D-polyaxial stress fields by analyzing multi-stationary acoustic waveforms. We show that in a true three-dimensional stress state (a) faulting forms in a orthorhombic pattern, and (b) the emitted acoustic waveforms from microcracking carry a shorter rapid slip phase. The later is associated with microcracking that dominantly develops parallel to the minimum stress direction. Our results imply that due to inducing the micro-anticracks, the three-dimensional (3D) stress state can quicken dynamic weakening and rupture propagation by a factor of two relatively to simpler stress states. The results suggest a new nucleation mechanism of 3D-faulting with implications for earthquakes' instabilities, as well as the understanding of avalanches associated with dislocations.

Measurement of the friction between single polystyrene nanospheres and silicon surface using atomic force microscopy

In the present work, the individual nanoparticles have been manipulated on a silicon surface, using atomic force microscope (AFM) techniques. As a model system, near-spherical polystyrene nanoparticles with radii from 28.85 nm to 228.2 nm were deposited on a nanosmooth silicon wafer. Experiments demonstrated that when the normal force is above a threshold load, nanoparticles could steadily be pushed by the tip of the AFM along the defined pathway. The tests allow us to quantitatively study the interfacial friction between the nanoparticle and the surface. It was found that the friction could be affected by various factors such as the load, the particle size, and the surface treatment. The results showed that the friction between particles and substrate is proportional to the two-third power of the radius, which is in agreement with the Hertzian theory. It can also be seen that the ratio between the kinetic and the static friction was slightly changed from 0.3 to 0.6, depending on the size of the particles. However, the value of the ratio was little affected by other factors such as the particles' location, the tip normal force and the surface modification. The results provided new insights into the intriguing friction phenomenon on the nanoscale.

Friction anisotropy with respect to topographic orientation

Friction characteristics with respect to surface topographic orientation were investigated using surfaces of different materials and fabricated with grooves of different scales. Scratching friction tests were conducted using a nano-indentation-scratching system with the tip motion parallel or perpendicular to the groove orientation. Similar friction anisotropy trends were observed for all the surfaces studied, which are (1) under a light load and for surfaces with narrow grooves, the tip motion parallel to the grooves offers higher friction coefficients than does that perpendicular to them, (2) otherwise, equal or lower friction coefficients are found under this motion. The influences of groove size relative to the diameter of the mating tip (as a representative asperity), surface contact stiffness, contact area, and the characteristic stiction length are discussed. The appearance of this friction anisotropy is independent of material; however, the boundary and the point of trend transition depend on material properties.

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

Friction between solids is responsible for many phenomena such as earthquakes, wear or crack propagation. Unlike macroscopic objects, which only touch locally owing to their surface roughness, spatially extended contacts form between atomically flat surfaces. They are described by the Frenkel-Kontorova model, which considers a monolayer of interacting particles on a periodic substrate potential. In addition to the well-known stick-slip motion, such models also predict the formation of kinks and antikinks, which greatly reduce the friction between the monolayer and the substrate. Here, we report the direct observation of kinks and antikinks in a two-dimensional colloidal crystal that is driven across different types of ordered substrate. We show that the frictional properties only depend on the number and density of such excitations, which propagate through the monolayer along the direction of the applied force. In addition, we also observe kinks on quasicrystalline surfaces, which demonstrates that they are not limited to periodic substrates but occur under more general conditions.

Pseudomorphy, surface alloys and the role of elementary clusters on the domain orientations in the Cu/Al13Co4(100) system

We have used the pseudo-tenfold surface of the orthorhombic Al(13)Co(4) crystal as a template for the adsorption of Cu thin films of various thicknesses deposited at different temperatures. This study has been carried out by means of low energy electron diffraction (LEED), scanning tunnelling microscopy (STM), x-ray photoelectron spectroscopy (XPS) and x-ray photoelectron diffraction (XPD). From 300 to 573 K, Cu adatoms grow pseudomorphically up to one monolayer. At 300 K, the β-Al(Cu, Co) phase appears for coverages greater than one monolayer. For higher temperature deposition, the β-Al(Cu, Co) phase further transforms into the γ-Al(4)Cu(9) phase. Both β and γ phases grow as two (110) domains rotated by 72° ± 1° from each other. Instead of following the substrate symmetry, it is the orientations of the bipentagonal motifs present on the clean Al(13)Co(4)(100) surface that dictate the growth orientation of these domains. The initial bulk composition and structural complexity of the substrate have a minor role in the formation of the γ-Al(4)Cu(9) phase as long as the amount of Al and the Cu film thickness reach a critical stoichiometry.

Three-dimensional Green's functions for two-dimensional quasi-crystal bimaterials

Owing to their specific structure, which can neither be classified as crystalline nor amorphous, quasi-crystals (QCs) exhibit properties that are interesting to both material science and mathematical physics or continuum mechanics. Within the framework of a mathematical theory of elasticity, one major focus is on features evolving from the coupling of phonon and phason fields, which is not observed in classical crystalline or amorphous materials. This paper deals with the problems of combinations of point phonon forces and point phason forces, which are applied to the interior of infinite solids and bimaterial solids of two-dimensional hexagonal QCs. By using the general solution of QCs, a series of displacement functions is adopted to obtain the analytical results when the two half-spaces are supposed to be ideally bonded or to be in smooth contact. In the final expressions, we provide three-dimensional Green’s functions for infinite bimaterial QC solids in the closed form, which are very convenient to be used in the study of dislocations, cracks and inhomogeneities of the new solid phase. Furthermore, the paper is concluded by a discussion of some special cases, in which Green’s functions for infinite transversely isotropic solids and Green’s functions for a half-space with free or fixed boundary are given.

Temperature dependence of atomic-scale stick-slip friction

We report experiments of atomic stick-slip friction on graphite as an explicit function of surface temperature between 100 and 300 K under ultrahigh vacuum conditions. A statistical analysis of the individual stick-slip events as a function of the velocity reveals an agreement with the thermally activated Prandtl-Tomlinson model at all temperatures. Taking into account an explicit temperature-dependence of the attempt frequency all data points collapse onto one single master curve.

Proliferation of anomalous symmetries in colloidal monolayers subjected to quasiperiodic light fields

Quasicrystals provide a fascinating class of materials with intriguing properties. Despite a strong potential for numerous technical applications, the conditions under which quasicrystals form are still poorly understood. Currently, it is not clear why most quasicrystals hold 5- or 10-fold symmetry but no single example with 7- or 9-fold symmetry has ever been observed. Here we report on geometrical constraints which impede the formation of quasicrystals with certain symmetries in a colloidal model system. Experimentally, colloidal quasicrystals are created by subjecting micron-sized particles to two-dimensional quasiperiodic potential landscapes created by n = 5 or seven laser beams. Our results clearly demonstrate that quasicrystalline order is much easier established for n = 5 compared to n = 7. With increasing laser intensity we observe that the colloids first adopt quasiperiodic order at local areas which then laterally grow until an extended quasicrystalline layer forms. As nucleation sites where quasiperiodicity originates, we identify highly symmetric motifs in the laser pattern. We find that their density strongly varies with n and surprisingly is smallest exactly for those quasicrystalline symmetries which have never been observed in atomic systems. Since such high-symmetry motifs also exist in atomic quasicrystals where they act as preferential adsorption sites, this suggests that it is indeed the deficiency of such motifs which accounts for the absence of materials with e.g., 7-fold symmetry.

The surface science of quasicrystals

The surfaces of quasicrystals have been extensively studied since about 1990. In this paper we review work on the structure and morphology of clean surfaces, and their electronic and phonon structure. We also describe progress in adsorption and epitaxy studies. The paper is illustrated throughout with examples from the literature. We offer some reflections on the wider impact of this body of work and anticipate areas for future development.

Origin of friction anisotropy on a quasicrystal surface

Wearless friction force experiments [Science 309, 1354 (2005)10.1126/science.1113239] have recently demonstrated that tribological response in quasicrystals could be related to the exotic atomic structure of the bulk material. Here, by numerical simulations, we address the origin of the experimentally observed friction anisotropy on a twofold decagonal quasicrystal surface. We predict the distinct stick-slip patterns in the lateral force along the periodic and quasiperiodic directions, specifically exploring the temperature dependence that rules the transitions between single and multiple-slip regimes of motion.

Superglide at an internal incommensurate boundary

The intriguing possibility of frictionless gliding of one solid surface on another has been predicted for certain incommensurate interfaces in crystals, based on Aubry's solution to the Frenkel-Kontorova model of a harmonic chain in a periodic potential field. Here we test this prediction for grain boundaries by comparing atomistic simulations with direct experimental observations on the structure and load-deformation behavior of gold nanopillars containing a root-two incommensurate grain boundary. The simulations show supergliding at this boundary limited by finite-size effects which cause edges to act as defects of the incommensurate structure. Structural relaxation at the edges generates stacking faults, dislocations, and asymmetric surface steps. These features as well as the related load-displacement behavior are replicated by experimental observations on the compression of nanopillars using a quantitative nanoindentation device inside a transmission electron microscope. The good agreement between the observed and predicted behavior suggests that incommensurate interfaces could play an important role in the deformation of polycrystalline materials.

Comparison of frictional forces on graphene and graphite

We report on the frictional force between an SiN tip and graphene/graphite surfaces using lateral force microscopy. The cantilever we have used was made of an SiN membrane and has a low stiffness of 0.006 N m(-1). We prepared graphene flakes on a Si wafer covered with silicon oxides. The frictional force on graphene was smaller than that on the Si oxide and larger than that on graphite (multilayer of graphene). Force spectroscopy was also employed to study the van der Waals force between the graphene and the tip. Judging that the van der Waals force was also in graphite-graphene-silicon oxide order, the friction is suspected to be related to the van der Waals interactions. As the normal force acting on the surface was much weaker than the attractive force, such as the van der Waals force, the friction was independent of the normal force strength. The velocity dependency of the friction showed a logarithmic behavior which was attributed to the thermally activated stick-slip effect.

Structures and topological transitions of hydrocarbon films on quasicrystalline surfaces

Lubricants can affect quasicrystalline coating surfaces by modifying the commensurability of the interfaces. We report results of the first computer simulation studies of physically adsorbed hydrocarbons on a quasicrystalline surface: methane, propane, and benzene on decagonal Al-Ni-Co. The grand canonical Monte Carlo method is employed, using novel embedded-atom method potentials generated from ab initio calculations, and standard hydrocarbon interactions. The resulting adsorption isotherms and calculated structures show the films' evolution from submonolayer to condensation. We discover the presence and absence of the fivefold to sixfold topological transition, for benzene and methane, respectively, in agreement with a previously formulated phenomenological rule based on adsorbate-substrate size mismatch.

Colloidal ordering on a 2D quasicrystalline substrate

By using Monte Carlo simulations, we study the complex phase behavior of charged-stabilized colloidal particles in a two-dimensional substrate potential with quasicrystalline decagonal symmetry. In the regime where the strengths of the substrate and colloidal pair potential are comparable, we identify a novel and unexpected quasicrystalline phase with pure 20-fold bond order and a disordered structure without any apparent rotational symmetry. Furthermore, we demonstrate how phasonic displacements in the substrate potential induce phasonic flips in the colloidal monolayer.