We review recent developments in the modelling of the phase diagram and thekinetics of crystallization of carbon. In particular, we show that a particularclass of bond-order potentials (the so-called LCBOP models) account well formany of the known structural and thermodynamic properties of carbon at highpressures and temperatures. We discuss the LCBOP models in some detail. Inaddition, we briefly review the ``history'' of experimental and theoreticalstudies of the phase behaviour of carbon. Using a well-tested version of theLCBOP model (viz. LCBOPI+) we address some of the more controversial hypothesesconcerning the phase behaviour of carbon, in particular: the suggestion thatliquid carbon can exist in two phases separated by a first-order phasetransition and the conjecture that diamonds could have formed by homogeneousnucleation in Uranus and Neptune.
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