A bird's eye view on the flat and conic band world of the honeycomb and Kagome lattices: towards an understanding of 2D metal-organic frameworks electronic structure.

We present a thorough tight-binding analysis of the band structure of a wide variety of lattices belonging to the class of honeycomb and Kagome systems including several mixed forms combining both lattices. The band structure of these systems are made of a combination of dispersive and flat bands. The dispersive bands possess Dirac cones (linear dispersion) at the six corners (K points) of the Brillouin zone although in peculiar cases Dirac cones at the center of the zone [Formula: see text] point) appear. The flat bands can be of different nature. Most of them are tangent to the dispersive bands at the center of the zone but some, for symmetry reasons, do not hybridize with other states. The objective of our work is to provide an analysis of a wide class of so-called ligand-decorated honeycomb Kagome lattices that are observed in a 2D metal-organic framework where the ligand occupy honeycomb sites and the metallic atoms the Kagome sites. We show that the p x -p y graphene model is relevant in these systems and there exists four types of flat bands: Kagome flat (singly degenerate) bands, two kinds of ligand-centered flat bands (A2 like and E like, respectively doubly and singly degenerate) and metal-centered (three fold degenerate) flat bands.

Size Dependent Phase Diagrams of Nickel-Carbon Nanoparticles.

The carbon rich phase diagrams of nickel-carbon nanoparticles, relevant to catalysis and catalytic chemical vapor deposition synthesis of carbon nanotubes, are calculated for system sizes up to about 3 nm (807 Ni atoms). A tight binding model for interatomic interactions drives the grand canonical Monte Carlo simulations used to locate solid, core shell and liquid stability domains, as a function of size, temperature, and carbon chemical potential or concentration. Melting is favored by carbon incorporation from the nanoparticle surface, resulting in a strong relative lowering of the eutectic temperature and a phase diagram topology different from the bulk one. This should lead to a better understanding of the nanotube growth mechanisms.

Magnetism: the driving force of order in CoPt, a first-principles study.

CoPt equiatomic alloy orders according to the tetragonal L1(0) structure which favors strong magnetic anisotropy. Conversely, magnetism can influence the chemical ordering. We present here ab initio calculations of the stability of the L1(0) and L1(2) structures of Co-Pt alloys in their paramagnetic and ferromagnetic states. They show that magnetism strongly reinforces the ordering tendencies in this system. A simple tight-binding analysis allows us to account for this behavior in terms of some pertinent parameters.

Importance of carbon solubility and wetting properties of nickel nanoparticles for single wall nanotube growth.

Optimized growth of single wall carbon nanotubes requires full knowledge of the actual state of the catalyst nanoparticle and its interface with the tube. Using tight binding based atomistic computer simulations, we calculate carbon adsorption isotherms on nanoparticles of nickel, a typical catalyst, and show that carbon solubility increases for smaller nanoparticles that are either molten or surface molten under experimental conditions. Increasing carbon content favors the dewetting of Ni nanoparticles with respect to sp(2) carbon walls, a necessary property to limit catalyst encapsulation and deactivation. Grand canonical Monte Carlo simulations of the growth of tube embryos show that wetting properties of the nanoparticles, controlled by carbon solubility, are of fundamental importance to enable the growth, shedding new light on the growth mechanisms.

Many-body effects in electronic bandgaps of carbon nanotubes measured by scanning tunnelling spectroscopy.

Single-walled carbon nanotubes provide an ideal system for studying the properties of one-dimensional (1D) materials, where strong electron-electron interactions are expected. Optical measurements have recently reported the existence of excitons in semiconducting nanotubes, revealing the importance of many-body effects. Surprisingly, pioneering electronic structure calculations and scanning tunnelling spectroscopy (STS) experiments report the same gap values as optical experiments. Here, an experimental STS study of the bandgap of single-walled semiconducting nanotubes, demonstrates a continuous transition from the gap reduced by the screening resulting from the metal substrate to the intrinsic gap dominated by many-body interactions. These results provide a deeper knowledge of many-body interactions in these 1D systems and a better understanding of their electronic properties, which is a prerequisite for any application of nanotubes in the ultimate device miniaturization for molecular electronics, or spintronics.

Understanding the nucleation mechanisms of carbon nanotubes in catalytic chemical vapor deposition.

The nucleation of carbon caps on small nickel clusters is studied using a tight binding model coupled to grand canonical Monte Carlo simulations. It takes place in a well defined carbon chemical potential range, when a critical concentration of surface carbon atoms is reached. The solubility of carbon in the outermost Ni layers, that depends on the initial, crystalline or disordered, state of the catalyst and on the thermodynamic conditions, is therefore a key quantity to control the nucleation.

A tight-binding grand canonical Monte Carlo study of the catalytic growth of carbon nanotubes.

The nucleation of carbon nanotubes on small nickel clusters is studied using a tight binding model coupled to grand canonical Monte Carlo simulations. This technique follows the conditions of the synthesis of carbon nanotubes by chemical vapor deposition. The possible formation of a carbon cap on the catalyst particle is studied as a function of the carbon chemical potential, for particles of different size, either crystalline or disordered. We show that these parameters strongly influence the structure of the cap/particle interface which in turn will have a strong effect on the control of the structure of the nanotube. In particular, we discuss the presence of carbon on surface or in subsurface layers.

Optical transitions in single-wall boron nitride nanotubes.

Optical transitions in single-wall boron nitride nanotubes are investigated by means of optical absorption spectroscopy. Three absorption lines are observed. Two of them (at 4.45 and 5.5 eV) result from the quantification involved by the rolling up of the hexagonal boron nitride (h-BN) sheet. The nature of these lines is discussed, and two interpretations are proposed. A comparison with single-wall carbon nanotubes leads one to interpret these lines as transitions between pairs of van Hove singularities in the one-dimensional density of states of boron nitride single-wall nanotubes. But the confinement energy due to the rolling up of the h-BN sheet cannot explain a gap width of the boron nitride nanotubes below the h-BN gap. The low energy line is then attributed to the existence of a Frenkel exciton with a binding energy in the 1 eV range.

Nucleation and growth of single-walled nanotubes: the role of metallic catalysts.

We present a review of experimental and theoretical results on the nucleation and growth of single-walled nanotubes, with particular emphasis on the growth of nanotube bundles emerging from catalyst particles obtained from evaporation-based elaboration techniques. General results are first discussed. Experiments strongly suggest a root-growth process in which carbon, dissolved at high temperatures in catalytic particles, segregates at the surface at lower temperatures to form tube embryos and finally nanotubes through a nucleation and growth process. A theoretical analysis of the reasons carbon does not always form graphene sheets to wrap the particles suggests analogies with other surface or interface instabilities, in particular, with those found in epitaxial growth. In the second part, detailed experimental results for nickel-rare earth metal catalysts are presented. By using various electron microscopy techniques, it is shown that carbon and the rare earth metal co-segregate at the surface of the particle and form carbide platelets, providing nucleation sites for nanotubes growing in directions perpendicular to the surface. A simple theoretical model is then presented in which the role of the rare earth metal is just to transfer electrons from metal to carbon. The graphene sheet is shown to become unstable; pentagons and heptagons are favored, which can explain the occurrence of local curvatures and of tube embryos. Finally, a brief discussion of some recent atomistic models is given.

Root-growth mechanism for single-wall carbon nanotubes.

The catalytic growth of single-wall carbon nanotubes is investigated by high-resolution transmission electron microscopy. The similarities between the samples synthesized from different techniques suggest a common growth mechanism based on a vapor-liquid-solid model. Quantum-molecular-dynamics simulations support a root growth mechanism where carbon atoms are incorporated into the tube base by a diffusion-segregation process.