Thermodynamics of metal nanoclusters (0D systems): Peculiarities of Binary and Ternary phase diagrams

The characteristics of the catalyst particles has been identified as a key parameter for controlling the structure and thereby the properties of grown carbon nanotubes. For deeper understanding of the impact of particle size we have focused on the investigation of Fe-C phase diagram as a function of the nanoparticle size. By applying a size-pressure relation and modeling with Young-Laplace equation, it was revealed for the first time the decreased solubility of carbon in Fe particles of decreasing size.

This phenomenon explains the experimental observation that reduction of catalyst size requires an increase in growth temperature.  Furthermore, we found that with reduced particle size the eutectic point shifts significantly not only toward lower temperatures, as expected from the Gibbs-Thomson law, but also toward lower concentrations of carbon.

The group deepened understanding of nanotube growth mechanism by considering the influence of Mo in Fe:Mo:C nanocatalysts, which are currently some of the most effective catalysts for nanotube growth. [Phys. Rev. B (2008)]. By using a size-pressure approximation and ab-initio modeling, we proved that, for Fe:Mo clusters that are both Fe-rich (80% Fe or more) and Mo-rich (50% Mo or more), the presence of carbon causes nucleation of Mo₂C. The formation of this phase enhances the activity of the particle since it releases Fe, which is initially bound in a stable Fe:Mo phase, so that it can catalyze nanotube growth.

We further investigated the phase diagrams for Fe nanoclusters supported by substrates, particularly alumina.  The studies showed that the supported Fe nanoparticles had higher melting points compared with unsupported ones, although both systems exhibited a reduction of melting temperature with decreasing diameter, in agreement with the Gibbs-Thomson law. The key factor was determined to be the porosity of the substrate, with the magnitude of the increase in melting point depending on the density, shape, and diameter of the pores. For example, the increase in melting point was greater for clusters supported on flat (nonporous) substrates than for clusters that straddled smaller pores.

Origin of helicity formation in single walled carbon nanotubes  (1D systems)

SWNTs can be classified as either metallic or semiconducting, depending on their conductivity, which is determined by their helicity. Despite more than two decades of intense research worldwide the underlying mechanism for the nucleation of carbon nanotubes as well as the formation of their helicity remains elusive, which is a huge challenge for broader applications. The reason is the great complexity and multidisciplinary of the problem with various hidden and function parameters that become even more apparent by simple consideration of pure math of the census of nanotubes and numerous permutation of nanotube walls and caps to form helicity. Achieving helicity controlled growth is the most challenging obstacle for unique applications of nanotubes. We have revealed the growth mechanism of single walled carbon nanotubes which led to the pioneering work on the preferential growth of carbon nanotubes that increased the abundance of tubes with metallic conductivity from about 30% (natural abundance) up to 90%. Based on in situobservations with an environmental transmission electron microscopy (ETEM) we have attributed this discovery to the dynamic reconstruction of catalyst particle morphology under various ambient, particularly the presence of H₂O vapor, which tuned the symmetry of grown tubes.

With our collaborators we have applied dislocation theory for chiral-controlled nanotube growth. We content that any nanotube can be viewed as having a screw dislocation along the axis. Consequently, its growth rate is shown to be proportional to the Burgers vector of such dislocation and therefore to the chiaral angle of the tube. The model has been supported by ab initio energy calculations.

Our further systematic ETEM studies considered within thermodynamic approach revealed carbon adsorption induced surface energy variation as a driving force for catalyst morphology reconstruction, carbon cap lift-off and thereby growth of nanotubes.  The metal catalyst can be viewed as an inorganic "heart' of the process, periodically changing its shape in the course of growth, when a single "heartbeat" is associated with the nucleation and lift-off of a single-walled carbon nanotube.

Careful detail in-situ analysis of nanotube nucleation led us to the conclusion that carbon cap forms first in the nanotube growth sequence and thereby dictates the helicity of grown nanotubes, which sheds the light on one of the most challenging tasks in the field.

The ETEM studies have been supported by studying energetics of carbon sp2 ebryo nucleation using van der Waals dispersion force calculations implemented within density functional theory. We conclude that  depending on the nucleation path the helicity of grown carbon nanotube can be mastered either by the symmetry of underlying low energy facet of catalyst along its tubular axis or by the curvature of the multifacet tip of catalyst. Consequently, capability of thorough control over the morphology of catalyst particle, i.e., aspect ratio and interfacial angular distributions of its tip, is the key that could lead to helicity controlled growth of carbon nanotubes. 

The role of dynamic thermal and solutal instabilities on graphene crystallinity (2D systems)

Strictly speaking a 2D system, such as a single carbon layer, is thermodynamically unstable and can exist only through the perturbations in the third direction. These fluctuations in the third direction result in a crumpled topography of the graphene sheet surface. Since graphene surface topography has significant impact on its physical and chemical properties, understanding the mechanism and controlling the formation of ripples is essential for exploiting their unique properties. Commonly the origin of graphene ripples is associated with 1) the problem of thermodynamic stability of 2D systems, 2) overlapping of adjacent graphene disoriented islands grown at different sites on a substrate and stitched together and 3) the thermal expansion coefficient difference between metal substrate and graphene. 

We have proposed a new origin for the formation of ripples in the course of graphene growth at elevated temperatures, where the topographic pattern formation is governed by dynamic instabilities on the interface of a carbon-substrate binary system. These non-equilibrium processes can be described based on Mullins-sekerka and benard-marangoni instabilities in diluted binary alloys, which offer the control over the ripple texturing through synthesis parameters such as temperature, imposed temperature gradient, quenching rate, and miscibility gap of metal(substrate)-carbon system.