Interface-driven formation of a two-dimensional dodecagonal fullerene quasicrystal.
ABSTRACT: Since their discovery, quasicrystals have attracted continuous research interest due to their unique structural and physical properties. Recently, it was demonstrated that dodecagonal quasicrystals could be used as bandgap materials in next-generation photonic devices. However, a full understanding of the formation mechanism of quasicrystals is necessary to control their physical properties. Here we report the formation of a two-dimensional dodecagonal fullerene quasicrystal on a Pt3Ti(111) surface, which can be described in terms of a square-triangle tiling. Employing density functional theory calculations, we identify the complex adsorption energy landscape of the Pt-terminated Pt3Ti surface that is responsible for the quasicrystal formation. We demonstrate the presence of quasicrystal-specific phason strain, which provides the degree of freedom required to accommodate the quasicrystalline structure on the periodic substrate. Our results reveal detailed insight into an interface-driven formation mechanism and open the way to the creation of tailored fullerene quasicrystals with specific physical properties.
Project description:Considerable progress in the fabrication of quasicrystals demonstrates that they can be realized in a broad range of materials. However, the development of chemistries enabling direct experimental observation of early quasicrystal growth pathways remains challenging. Here, we report the synthesis of four surfactant-directed mesoporous silica nanoparticle structures, including dodecagonal quasicrystalline nanoparticles, as a function of micelle pore expander concentration or stirring rate. We demonstrate that the early formation stages of dodecagonal quasicrystalline mesoporous silica nanoparticles can be preserved, where precise control of mesoporous silica nanoparticle size down to <30?nm facilitates comparison between mesoporous silica nanoparticles and simulated single-particle growth trajectories beginning with a single tiling unit. Our results reveal details of the building block size distributions during early growth and how they promote quasicrystal formation. This work identifies simple synthetic parameters, such as stirring rate, that may be exploited to design other quasicrystal-forming self-assembly chemistries and processes.Probing the growth pathways of quasicrystalline materials, where tiling units arrange with local but no long-range order, remains challenging. Here, the authors demonstrate that dodecagonal tiling of mesoporous silica nanoparticles occurs via irreversible packing of micelles with non-uniform size distribution.
Project description:The atomically resolved real-space structure of a long-range-ordered dodecagonal quasicrystal is determined based on scanning tunnelling microscopy. For the BaTiO3-derived oxide quasicrystal which spontaneously forms on a Pt(111) surface, 8100 atomic positions have been determined and are compared with an ideal Niizeki-Gähler tiling. Although the Niizeki-Gähler tiling has a complex three-element structure, the abundance of the triangle, square and rhomb tiling elements in the experimental data closely resembles the ideal frequencies. Similarly, the frequencies of all possible next-neighbour tiling combinations are, within the experimental uncertainty, identical to the ideal tiling. The angular and orientational distributions of all individual tiling elements show the characteristics of the dodecagonal quasicrystal. In contrast, the analysis of the orientation of characteristic and more complex tiling combinations indicates the partial decomposition of the quasicrystal into small patches with locally reduced symmetry. These, however, preserve the long-range quasicrystal coherence. The symmetry reduction from dodecagonal to sixfold is assigned to local interaction with the threefold substrate. It leads to atomic flips which preserve the number of quasicrystal tiling elements.
Project description:Quasicrystals have been discovered in a variety of materials ranging from metals to polymers. Yet, why and how they form is incompletely understood. In situ transmission electron microscopy of alloy quasicrystal formation in metals suggests an error-and-repair mechanism, whereby quasiperiodic crystals grow imperfectly with phason strain present, and only perfect themselves later into a high-quality quasicrystal with negligible phason strain. The growth mechanism has not been investigated for other types of quasicrystals, such as dendrimeric, polymeric, or colloidal quasicrystals. Soft-matter quasicrystals typically result from entropic, rather than energetic, interactions, and are not usually grown (either in laboratories or <i>in silico</i>) into large-volume quasicrystals. Consequently, it is unknown whether soft-matter quasicrystals form with the high degree of structural quality found in metal alloy quasicrystals. Here, we investigate the entropically driven growth of colloidal dodecagonal quasicrystals (DQCs) via computer simulation of systems of hard tetrahedra, which are simple models for anisotropic colloidal particles that form a quasicrystal. Using a pattern recognition algorithm applied to particle trajectories during DQC growth, we analyze phason strain to follow the evolution of quasiperiodic order. As in alloys, we observe high structural quality; DQCs with low phason strain crystallize directly from the melt and only require minimal further reduction of phason strain. We also observe transformation from a denser approximant to the DQC via continuous phason strain relaxation. Our results demonstrate that soft-matter quasicrystals dominated by entropy can be thermodynamically stable and grown with high structural quality--just like their alloy quasicrystal counterparts.
Project description:In traditional approaches to form quasicrystals, multiple competing length scales involved in particle size, shape, or interaction potential are believed to be necessary. It is unexpected that quasicrystals can be formed by monodisperse, isotropic particles interacting via a simple potential that does not contain explicit multiple length scales to stabilize quasicrystals. Here, we report the surprising finding of the formation of such quasicrystals in high-density systems of soft-core particles. Although there are length scales naturally introduced in our model systems, they do not establish the quasicrystalline order. In two dimensions, we find not only dodecagonal but also octagonal quasicrystals, which have not been found yet in soft quasicrystals. In such unexpected quasicrystals, particles tend to form pentagons, which are essential elements to develop the quasicrystalline order. Our findings thus pave an unexpected and simple way to form quasicrystals and pose a challenge for theoretical understanding of quasicrystals.
Project description:The electronic and topological properties of materials are derived from the interplay between crystalline symmetry and dimensionality. Simultaneously introducing "forbidden" symmetries via quasiperiodic ordering with low dimensionality into a material system promises the emergence of new physical phenomena. Here, we isolate a two-dimensional (2D) chalcogenide quasicrystal and approximant, and investigate their electronic and topological properties. The 2D layers of the materials with a composition close to Ta<sub>1.6</sub>Te, derived from a layered transition metal dichalcogenide, are isolated with standard exfoliation techniques, and investigated with electron diffraction and atomic resolution scanning transmission electron microscopy. Density functional theory calculations and symmetry analysis of the large unit cell crystalline approximant of the quasicrystal, Ta<sub>21</sub>Te<sub>13</sub>, reveal the presence of symmetry-protected nodal crossings in the quasicrystalline and approximant phases, whose presence is tunable by layer number. Our study provides a platform for the exploration of physics in quasicrystalline, low-dimensional materials and the interconnected nature of topology, dimensionality, and symmetry in electronic systems.
Project description:A delicate balance of noncovalent interactions directs the hierarchical self-assembly of molecular amphiphiles into spherical micelles that pack into three-dimensional periodic arrays, which mimic intermetallic crystals. Herein, we report the discovery that adding water to a mixture of an ionic surfactant and <i>n</i>-decane induces aperiodic ordering of oil-swollen spherical micelles into previously unrecognized, aqueous lyotropic dodecagonal quasicrystals (DDQCs), which exhibit local 12-fold rotational symmetry and no long-range translational order. The emergence of these DDQCs at the nexus of dynamically arrested micellar glasses and a periodic Frank-Kasper (FK) σ phase approximant sensitively depends on the mixing order of molecular constituents in the assembly process and on sample thermal history. Addition of <i>n</i>-decane to mixtures of surfactant and water instead leads only to periodic FK A15 and σ approximants with no evidence for aperiodic order, while extended ambient temperature annealing of the DDQC also reveals its transformation into a σ phase. Thus, these lyotropic DDQCs are long-lived metastable morphologies, which nucleate and grow from a stochastic distribution of micelle sizes formed by abrupt segregation of varied amounts of oil into surfactant micelles on hydration. These findings indicate that molecular building block complexity is not a prerequisite for the formation of aperiodic supramolecular order, while also establishing the generic nature of quasicrystalline states across metal alloys and self-assembled micellar materials.
Project description:Aperiodic formations continue to focus interest in areas ranging from advanced scientific theories to practical everyday applications. Starting from diverse and tightly bonded intermetallic compounds, this world showed an important breakthrough toward the so-called soft systems of meso/macroscale: liquid crystals, thin films, polymers, proteins, etc. This work opens a route for making bulk quasicrystals (QC) in an unprecedented but very common area, with molecular ligands. Since these systems are, to a large extent, transparent, they extend the possible areas of QC application to previously unreachable corners, e.g., photonics. We combined efficient bridging ligands with uranyl pentagonal bonding centers and, unexpectedly, brought the unique attributes of f-element coordination chemistry to an interdisciplinary area of aperiodic formations. Taking advantage of the planar coordination of uranyl ions, we were able to direct the structure expansion solely in two directions with a characteristic snub square tiling, a predicted but previously unobtainable dodecagonal approximant.
Project description:The first test explosion of a nuclear bomb, the Trinity test of 16 July 1945, resulted in the fusion of surrounding sand, the test tower, and copper transmission lines into a glassy material known as "trinitite." Here, we report the discovery, in a sample of red trinitite, of a hitherto unknown composition of icosahedral quasicrystal, Si<sub>61</sub>Cu<sub>30</sub>Ca<sub>7</sub>Fe<sub>2</sub> It represents the oldest extant anthropogenic quasicrystal currently known, with the distinctive property that its precise time of creation is indelibly etched in history. Like the naturally formed quasicrystals found in the Khatyrka meteorite and experimental shock syntheses of quasicrystals, the anthropogenic quasicrystals in red trinitite demonstrate that transient extreme pressure-temperature conditions are suitable for the synthesis of quasicrystals and for the discovery of new quasicrystal-forming systems.
Project description:Quasicrystals differ from conventional crystals and amorphous materials in that they possess long-range order without periodicity. They exhibit orders of rotational symmetry which are forbidden in periodic crystals, such as five-, ten-, and twelve-fold, and their structures can be described with complex aperiodic tilings such as Penrose tilings and Stampfli-Gaehler tilings. Previous theoretical work explored the structure and properties of a hypothetical four-fold symmetric quasicrystal-the so-called Fibonacci square grid. Here, we show an experimental realisation of the Fibonacci square grid structure in a molecular overlayer. Scanning tunnelling microscopy reveals that fullerenes (C60) deposited on the two-fold surface of an icosahedral Al-Pd-Mn quasicrystal selectively adsorb atop Mn atoms, forming a Fibonacci square grid. The site-specific adsorption behaviour offers the potential to generate relatively simple quasicrystalline overlayer structures with tunable physical properties and demonstrates the use of molecules as a surface chemical probe to identify atomic species on similar metallic alloy surfaces.
Project description:We present evidence that a rock sample found in the Koryak Mountains in Russia and containing icosahedrite, an icosahedral quasicrystalline phase with composition Al(63)Cu(24)Fe(13), is part of a meteorite, likely formed in the early solar system about 4.5 Gya. The quasicrystal grains are intergrown with diopside, forsterite, stishovite, and additional metallic phases [khatyrkite (CuAl(2)), cupalite (CuAl), and ?-phase (AlCuFe)]. This assemblage, in turn, is enclosed in a white rind consisting of diopside, hedenbergite, spinel (MgAl(2)O(4)), nepheline, and forsterite. Particularly notable is a grain of stishovite (from the interior), a tetragonal polymorph of silica that only occurs at ultrahigh pressures (? 10 Gpa), that contains an inclusion of quasicrystal. An extraterrestrial origin is inferred from secondary ion mass spectrometry (18)O/(16)O and (17)O/(16)O measurements of the pyroxene and olivine intergrown with the metal that show them to have isotopic compositions unlike any terrestrial minerals and instead overlap those of anhydrous phases in carbonaceous chondrite meteorites. The spinel from the white rind has an isotopic composition suggesting that it was part of a calcium-aluminum-rich inclusion similar to those found in CV3 chondrites. The mechanism that produced this exotic assemblage is not yet understood. The assemblage (metallic copper-aluminum alloy) is extremely reduced, and the close association of aluminum (high temperature refractory lithophile) with copper (low temperature chalcophile) is unexpected. Nevertheless, our evidence indicates that quasicrystals can form naturally under astrophysical conditions and remain stable over cosmic timescales, giving unique insights on their existence in nature and stability.