Templated three-dimensional growth of quasicrystalline lead

Hydrogen, Oxygen, and Lead Adsorbates on Al13Co4(100): Accurate Potential Energy Surfaces at Low Computational Cost by Machine Learning and DFT-Based Data

Intermetallic compounds are promising materials in numerous fields, especially those involving surface interactions, such as catalysis. A key factor to investigate their surface properties lies in adsorption energy maps, typically built using first-principles approaches. However, exploring the adsorption energy landscapes of intermetallic compounds can be cumbersome, usually requiring huge computational resources. In this work, we propose an efficient method to predict adsorption energies, based on a Machine Learning (ML) scheme fed by a few Density Functional Theory (DFT) estimates performed on n sites selected through the Farthest Point Sampling (FPS) process. We detail its application on the Al13Co4(100) quasicrystalline approximant surface for several atomic adsorbates (H, O, and Pb). On this specific example, our approach is shown to outperform both simple interpolation strategies and the recent ML force field MACE [arXiv.2206.07697], especially when the number n is small, i.e., below 36 sites. The ground-truth DFT adsorption energies are much more correlated with the predicted FPS-ML estimates (Pearson R-factor of 0.71, 0.73, and 0.90 for H, O and Pb, respectively, when n = 36) than with interpolation-based or MACE-ML ones (Pearson R-factors of 0.43, 0.39, and 0.56 for H, O, and Pb, in the former case and 0.22, 0.35, and 0.63 in the latter case). The unbiased root-mean-square error (ubRMSE) is lower for FPS-ML than for interpolation-based and MACE-ML predictions (0.15, 0.17, and 0.17 eV, respectively, for hydrogen and 0.17, 0.25, and 0.22 eV for lead), except for oxygen (0.55, 0.47, and 0.46 eV) due to large surface relaxations in this case. We believe that these findings and the corresponding methodology can be extended to a wide range of systems, which will motivate the discovery of novel functional materials.

DNA Structure and the Golden Ratio Revisited

B-DNA, the informational molecule for life on earth, appears to contain ratios structured around the irrational number 1.618…, often known as the “golden ratio”. This occurs in the ratio of the length:width of one turn of the helix; the ratio of the spacing of the two helices; and in the axial structure of the molecule which has ten-fold rotational symmetry. That this occurs in the information-carrying molecule for life is unexpected, and suggests the action of some process. What this process might be is unclear, but it is central to any understanding of the formation of DNA, and so life.

Two-dimensional oxide quasicrystal approximants with tunable electronic and magnetic properties

Recently, the discovery of the quasiperiodic order in ultra-thin perovskite films reinvigorated the field of 2-dimensional oxides on metals, and raised the question of the reasons behind the emergence of the quasiperiodic order in these systems. The effect of size-mismatch between the two separate systems has been widely reported as a key factor governing the formation of new oxide structures on metals. Herein, we show that electronic effects can play an important role as well. To this end, the structural, thermodynamic, electronic and magnetic properties of freestanding two-dimensional oxide quasicrystalline approximants and their characteristics when deposited over metallic substrates are systematically investigated to unveil the structure-property relationships within the series. Our thermodynamic approach suggests that the formation of these aperiodic systems is likely for a wide range of compositions. In addition, the magnetic properties and work functions of the thin films can be controlled by tuning their chemical composition. This work provides well-founded general insights into the driving forces behind the emergence of the quasiperiodic order in ternary oxides grown on elemental metals and offers guidelines for the discovery of new oxide quasicrystalline ultra-thin films with interesting physical properties.

The role of three-dimensional bulk clusters in determining surface morphologies of intermetallic compounds: Quasicrystals to clathrates

Nanostructured alloy surfaces present unique physical properties and chemical reactivities that are quite different from those of the close-packed low-index surfaces. This can be beneficial for the design of new catalysts and electronic and data-storage devices. However, the growth of such surface nanostructures is not straightforward at the atomic scale. The cluster-based bulk structure of intermetallic compounds presents an original alternative to build surfaces with specific morphologies, in comparison to more traditional methods based on mechanical, chemical, or plasma treatments. It relies on their specific electronic structures-built from a network of bonds with a combination of ionic, covalent-like, and metallic characters, and also depends on the experimental conditions. In this paper, a few surface structures of cluster-based intermetallics are reviewed, with a special emphasis on quasicrystals and clathrates. We show how the intrinsic electronic properties of such compounds, as well as the surface preparation conditions, impact their surface morphologies, which can further influence the growth of atomic and molecular thin films at their surface.

Pseudo-2-Fold Surface of the Al13Co4 Catalyst: Structure, Stability, and Hydrogen Adsorption

A few low-order approximants to decagonal quasicrystals have been shown to provide excellent activity and selectivity for the hydrogenation of alkenes and alkynes. It is the case for the Al₁₃Co₄ compound, for which the catalytic properties of the pseudo-2-fold orientation have been revealed to be among the best. A combination of surface science studies, including surface X-ray diffraction, and calculations based on density functional theory is used here to derive an atomistic model for the pseudo-2-fold o-Al₁₃Co₄ surface, whose faceted and columnar structure is found very similar to the one of the 2-fold surface of the d-Al-Ni-Co quasicrystal. Facets substantially stabilize the system, with energies in the range 1.19-1.31 J/m², i.e., much smaller than the ones of the pseudo-10-fold (1.49-1.68 J/m²) and pseudo-2-fold (1.66 J/m²) surfaces. Faceting is also a main factor at the origin of the Al₁₃Co₄ catalytic performances, as illustrated by the comparison of the pseudo-10-fold, pseudo-2-fold and facet potential energy maps for hydrogen adsorption. This work gives insights toward the design of complex intermetallic catalysts through surface nanostructuration for optimized catalytic performances.

Influence of differences in orientational planar density on the growth of Pb on the i-Ag-In-Yb quasicrystal

Metal adsorption upon the 3-fold and 5-fold symmetric surfaces of the i-Ag-In-Yb quasicrystal has led to the observation of unique growth modes. Here, we present a study of the growth of Pb upon the 2-fold i-Ag-In-Yb surface, where the growth mechanism is found to be different from those observed on the other, higher symmetry surfaces of the same system. Initial Pb atoms occupy non-chemically-specific surface sites before forming a row structure. At higher coverages, the Pb atoms form a dense wetting layer before 1D Pb chains of limited size are self-assembled as a second layer. We therefore consider the Pb atoms to exhibit a type of Stranski-Krastanov growth mode. Substrate-adsorbate interaction is favoured in the wetting layer, before adsorbate-adsorbate interaction promotes chain growth. The difference in growth modes upon the three high symmetry surfaces is discussed with respect to their respective atomic densities.

Quantum Spin Hall Effect and Spin Bott Index in a Quasicrystal Lattice

Despite the rapid progress in the field of the quantum spin Hall (QSH) effect, most of the QSH systems studied up to now are based on crystalline materials. Here we propose that the QSH effect can be realized in quasicrystal lattices (QLs). We show that the electronic topology of aperiodic and amorphous insulators can be characterized by a spin Bott index B_{s}. The nontrivial QSH state in a QL is identified by a nonzero spin Bott index B_{s}=1, associated with robust edge states and quantized conductance. We also map out a topological phase diagram in which the QSH state lies in between a normal insulator and a weak metal phase due to the unique wave functions of QLs. Our findings not only provide a better understanding of electronic properties of quasicrystals but also extend the search of the QSH phase to aperiodic and amorphous materials that are experimentally feasible.

A molecular overlayer with the Fibonacci square grid structure

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.

Quasicrystals possess long range order but no translational symmetry, and rotational symmetries that are forbidden in periodic crystals. Here, a fullerene overlayer deposited on a surface of an icosahedral intermetallic quasicrystal achieves a Fibonacci square grid structure, by selective adsorption at specific sites.

Fullerene adsorption on intermetallic compounds of increasing structural complexity

Compared to elemental crystals (Al, Cu, Ag, etc.), the local atomic arrangement within Al-based complex intermetallics is usually best described by highly symmetric clusters decorating the unit cell. With the latter containing tens to several thousand atoms (or an infinite number for the case of quasicrystals), this translates to structurally complex surfaces exhibiting unique potential energy landscapes. This review will focus on the different studies reporting the adsorption of C60 molecules on such complex metallic alloy surfaces, aiming to benefit from this complexity to create exotic molecular nanostructures. First, we will recall the main adsorption mechanisms and surface phases that have been identified when fullerene adsorption is carried out on single crystal surfaces. Second, we will discuss how surfaces of increasing structural complexity impact the film properties. The presence of five-fold symmetric adsorption sites is another intrinsic property of these complex intermetallic surfaces. As will be presented in this review, this leads to specific molecular orientations to maximize substrate–adsorbate symmetry matching, hence introducing another degree of freedom to create new 2-D molecular architectures. The local electronic interactions at the adsorption site interface will also be introduced. Furthermore, the different fullerene structures formed upon adsorption on aperiodic surfaces of varying chemical composition and on Bi allotropes will be discussed. Finally, suggestions will be given for future work along with the foreseen area of interests.

Coverage-dependent structural phase transformations in the adsorption of pentacene on an aperiodically modulated Cu film

Surface ordering of pentacene molecules adsorbed on an aperiodic Cu surface has been studied with density functional theory (DFT) and scanning tunnelling microscopy as a function of coverage. Below 0.73 ML (5.3 × 10¹³ molecules cm^-2), the adsorbate structure is row-like with the molecular axes aligned with the rows in the Cu structure. Between this coverage and 1 ML (7.3 × 10¹³ molecules cm^-2), a structural phase with a checkerboard structure is seen. At this coverage region, the molecules are very close to each other which leads to unusual bending. At higher coverages, a further phase transition to a high-density row structure is seen for most of the film. DFT with van der Waals functionals is employed to study how the molecule-molecule and molecule-surface interactions evolve as a function of coverage.

Effective substrate potentials with quasicrystalline symmetry depend on the size of the adsorbed particles

We explore the effective potential landscapes that extended particles experience when adsorbed on the surface of quasicrystals. Commonly, these are solids with long-ranged order but no translational symmetry. The effective potentials significantly depend on the size of the adsorbed particles. We show how changing the particle radius changes the so-called local isomorphism class of the effective quasicrystalline pattern. This means effective potentials for different particle sizes cannot directly be mapped onto each other. Our theoretical predictions are confirmed by Monte Carlo simulations. The results are important for colloidal particles with different sizes that are subjected to laser fields with quasicrystalline symmetry as well as for systems where extended molecules are deposited onto the surface of metallic quasicrystals.

Quantitative adsorbate structure determination for quasicrystals using x-ray standing waves

The quantitative structure determination of adsorbed species on quasicrystal surfaces has so far appeared to present insurmountable problems. The normal incidence standing x-ray wave field technique offers a simple solution, without extensive data sets or large computations. Its application to quasicrystals raises several conceptual difficulties that are related to the phase problem in x-ray diffraction. We demonstrate their solution for the case of Si atoms adsorbed on the decagonal Co-rich modification of the Al-Co-Ni quasicrystal to determine the local structure, comprising 6-atom clusters in particular hollow sites.

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.

Crystalline and quasicrystalline allotropes of Pb formed on the fivefold surface of icosahedral Ag-In-Yb

Crystalline and quasicrystalline allotropes of Pb are formed by evaporation on the fivefold surface of the icosahedral (i) Ag-In-Yb quasicrystal under ultra-high vacuum. Lead grows in three dimensional quasicrystalline order and subsequently forms fivefold-twinned islands with the fcc(111) surface orientation atop of the quasicrystalline Pb. The islands exhibit specific heights (magic heights), possibly due to the confinement of electrons in the islands. We also study the adsorption behavior of C60 on the two allotropes of Pb. Scanning tunneling microcopy reveals that a high corrugation of the quasicrystalline Pb limits the diffusion of the C60 molecules and thus produces a disordered film, similar to adsorption behavior of the same molecules on the clean substrate surface. However, the sticking coefficient of C60 molecules atop the Pb islands approaches zero, regardless of the overall C60 coverage.

Self-organized molecular films with long-range quasiperiodic order

Self-organized molecular films with long-range quasiperiodic order have been grown by using the complex potential energy landscape of quasicrystalline surfaces as templates. The long-range order arises from a specific subset of quasilattice sites acting as preferred adsorption sites for the molecules, thus enforcing a quasiperiodic structure in the film. These adsorption sites exhibit a local 5-fold symmetry resulting from the cut by the surface plane through the cluster units identified in the bulk solid. Symmetry matching between the C60 fullerene and the substrate leads to a preferred adsorption configuration of the molecules with a pentagonal face down, a feature unique to quasicrystalline surfaces, enabling efficient chemical bonding at the molecule-substrate interface. This finding offers opportunities to investigate the physical properties of model 2D quasiperiodic systems, as the molecules can be functionalized to yield architectures with tailor-made properties.

Templated quasicrystalline molecular ordering

Quasicrystals are materials with long-range ordering but no periodicity. We report scanning tunneling microscopy (STM) observations of quasicrystalline molecular layers on 5-fold quasicrystal surfaces. The molecules adopt positions and orientations on the surface consistent with the quasicrystalline ordering of the substrate. Carbon-60 adsorbs atop sufficiently separated Fe atoms on icosahedral Al-Cu-Fe to form a unique quasicrystalline lattice, whereas further C60 molecules decorate remaining surface Fe atoms in a quasi-degenerate fashion. Pentacene (Pn) adsorbs at 10-fold symmetric points around surface-bisected rhombic triacontahedral clusters in icosahedral Ag-In-Yb. These systems constitute the first demonstrations of quasicrystalline molecular ordering on a template.