A Surface Diffusion Model for Nanotube Growth
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The problem of nanotube growth macrokinetics is viewed within the framework of the continuum surface diffusion equation combined with step-flow growth kinetics. The differences in incorporation rates of adatoms approaching the growth steps from 'upper" or "lower" terraces are taken into account. These differences can lead to the onset of surface island nucleation in front of a propagating step. This effect is able to cause formation of defects in the growing layer and even to inhibit stable step-flow modes of nanotube growth. The segregation effect of a second phase (BN) in front of the propagating of C layer step is considered, suggesting that it may cause increase in BN concentration and nucleation of islands leading to BN inclusions in C layers or the propagation of a BN layer over C layer. INTRODUCTION
Nanotube growth reveals an amazing variety of nanotubular structures and possible physical conditions for their synthesis [1-6]. The growth kinetics of nanotubes is a complicated phenomenon including atomic, surface microscopic and macroscopic effects, gas dymamics, laser interaction and plasma interaction with the source material. The nucleation and growth kinetics of nanotubes includes microkinetic processes of atomic-level interactions which are being actively studied by several groups dealing with ab initio simulations. However, ab initio approaches to theoretical treatment of growth kinetics of nanotubes is restricted to a small number of atoms, allowing investigation of only microenergetics and microkinetics [7-8]. Molecular dynamics simulations based upon empirical potentials for interatomic interactions have been shown to be effective in explaining various related effects [9]. However, the growth of nanotubes may also be considered within the framework of a continuum surface diffusion model which represents the next, "macro", level of formalization using ab initio values as "input" data and allows us to provide phenomenological insight into many growth kinetics effects [10, 11] which cannot be effectively treated by ab initio nor molecular dynamics approaches. In particular, in this paper, we consider two very important effects related to the growth of C and CBN nanotubes which have not so far been considered. First, we consider the possible inequality of incorporation kinetic constants for adatoms approaching the growth edge from the "lower" and "upper" terrace. The difference between these constants is shown to be crucial for understanding the onset of multi-island nucleation modes to which the external surface of nanotubes is known to be prone [4, 6]. However, the conditions and physical reasons responsible for this have not so far been specified. This effect, as will be shown, depends upon a combination of evaporation temperature as well as growth temperature and, as outlined, may be avoided in synthesis systems where strict temperature control is feasible. Second, our model allows us to formalize the effect of segregation of the second phase (BN), and the onset of nucleation of the BN layer over the
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