ABSTRACT
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At the nanoscale, it is not so obvious that the notions valid in the bulk limit are still relevant, especially in the context of phase transitions that are associated with divergences in some thermodynamic functions. Strictly speaking, there can be no divergence in the thermodynamical properties of a nite system, because for a well-behaved and physically realistic potential energy surface, the partition function varies smoothly with increasing temperature unless any limit N → ∞ is taken. However, even in small systems the concept of phases seems to hold in many situations. For the melting problem, to which much of this chapter will be devoted, it is rather clear that a solid phase can be dened when the internal energy (or temperature) is very low, even though it does not correspond to a periodic crystal. Likewise, it is expected that the same system may undergo some global transformation if a sucient amount of energy is pumped into it, losing its atomistically resolved shape in favor of something more disordered and uxional. Unfortunately, contrary to the case of the solid phase, it is not straightforward to dene a liquid at the nanoscale, because the denition used in the macroscopic limit (a phase in which the system adopts the shape of its container) does not apply. We will show at the end of this chapter that the uid phases of a nanoscale system are not well dened without knowledge of the time scale of observation.
