Liquid-like clusters free energy

The free volume (Vf = V — Vcr) can be freely redistributed throughout the whole bulk of the system, and this redistribution does not involve any energy consumption. However, for this free redistribution Vf to be realized it is necessary that among the nearest neighbors of the liquid-like cell there should be a certain number of cells of the same type. It is assumed that in a cluster formed by liquid-like cells each cell has at least two such neighbors (the coordination number Z > 1). 

Figure 1.10. Thermodynamic properties of LJ55 in the canonical ensemble, (a) The heat capacity, C,. (b) The Landau free energy, Al( c)- (c) The probability of the cluster being in the Mackay icosahedron, with one or two defects, and liquid-like regions of configuration space, (d) Gn,( c). the number of minima with energy less than c. All these properties were calculated using the anharmonic form of the superposition method from a sample of 1153 minima generated from a microcanonical MD simulation. In (b) the results are compared with simulation data obtained by Lynden-Bell and Wales (data points) [218] with the zero of free energy chosen for clarity.

In water there are many possible hydrogen-bonded structures other than those like Ice I and indeed truly ice-like clusters must be comparatively rare to account for the observed metastability of supercooled water. Some clusters in water may correspond to bulk structures having a higher free energy than liquid water and hence are described by a curve like (b) in fig. 4.5. Others, like the clathrate cages of Pauling, have very favourable bonding for particular numbers of molecules but the structure cannot be extended continuously to a bulk phase. Such clusters have a behaviour described by a curve like (c). 

Fig. 10. Calculated free energy barrier for homogeneous crystal nucleation of hard-sphere colloids. The results are shown for three values of the volume fraction. The drawn curves are fits to the CNT-expression Eq. (1). For the identification of solid like particles we used the techniques described before. The cutoff for the local environment was set to Vq = 1.4

When the primary facets of ice are defect free, the relevant step generation mechanism is the formation of two-dimensional nuclei. The process is driven by thermally activated fluctuations of the liquid phase that create two-dimensional heterophase clusters with solid-like structure. The most probable cluster geometry is tiiat of a pillbox, for which the edge-to-surface free energy ratio will favor spreading at a given drive. In analogy with three-dimensions, the nucleation frequency /per unit facet area. 4 is of a Maxwell-Boltzmann form, / exp - n cr /Ap kbT), where [Pg.47]

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