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We used molecular dynamics and the empirical potential for carbon LCBOPII to simulate the nucleation/growth process of carbon clusters both in vacuum and under pressure. In vacuum, our results show that the growth process is homogeneous and yields mainly sp2 structures such as fullerenes. We used an argon gas and Lennard–Jones potentials to mimic the high pressures and temperatures reached during the detonation of carbon-rich explosives. We found that these extreme thermodynamic conditions do not affect substantially the topologies of the clusters formed in the process. However, our estimation of the growth rates under pressure are in much better agreement with the values estimated experimentally than our vacuum simulations. The formation of sp3 carbon was negligible both in vacuum and under pressure which suggests that larger simulation times and cluster sizes are needed to allow the nucleation of nanodiamonds. [ABSTRACT FROM AUTHOR]

We review recent developments in the modelling of the phase diagram and the kinetics of crystallization of carbon. In particular, we show that a particular class of bond-order potentials (the so-called LCBOP models) account well for many of the known structural and thermodynamic properties of carbon at high pressures and temperatures. We discuss the LCBOP models in some detail. In addition, we briefly review the 'history' of experimental and theoretical studies of the phase behaviour of carbon. Using a well-tested version of the LCBOP model (viz. LCBOPI+) we address some of the more controversial hypotheses concerning the phase behaviour of carbon, in particular: the suggestion that liquid carbon can exist in two phases separated by a first-order phase transition and the conjecture that diamonds could have formed by homogeneous nucleation in Uranus and Neptune. [ABSTRACT FROM AUTHOR]

The stability of two-dimensional (2D) layers and membranes is the subject of a long-standing theoretical debate. According to the so-called Mermin–Wagner theorem, long-wavelength fluctuations destroy the long-range order of 2D crystals. Similarly, 2D membranes embedded in a 3D space have a tendency to be crumpled. These fluctuations can, however, be suppressed by anharmonic coupling between bending and stretching modes meaning that a 2D membrane can exist but will exhibit strong height fluctuations. The discovery of graphene, the first truly 2D crystal, and the recent experimental observation of ripples in suspended graphene make these issues especially important. Besides the academic interest, understanding the mechanisms of the stability of graphene is crucial for understanding electronic transport in this material that is attracting so much interest owing to its unusual Dirac spectrum and electronic properties. We address the nature of these height fluctuations by means of atomistic Monte Carlo simulations based on a very accurate many-body interatomic potential for carbon. We find that ripples spontaneously appear owing to thermal fluctuations with a size distribution peaked around 80 Å which is compatible with experimental findings (50–100 Å). This unexpected result might be due to the multiplicity of chemical bonding in carbon. [ABSTRACT FROM AUTHOR]