Ice Its Nucleation in Undercooled Water

The occurrence of a phase transition requires a prior nucleation of the daughter phase within the mother phase. Thus, the growth of crystals in a saturated solution requires the prior generation of nuclei, composed of 

Most theoretical treatments of nucleation and crystal growth are based on a model of stepwise addition of molecules to an embryo, up to a critical size, at which the properties of the embryo (e.g. its surface free energy) are equated with those of the known solid phase, i.e. the crystal.  

In the case of water and ice, such a model might be realistic in treating the nucleation of liquid or solid from supersaturated vapour, as it occurs in the upper atmosphere. It seems doubtful, on the other hand, whether the model of stepwise molecular condensation can realistically be applied to the liquid - solid transition, because liquid water itself is already extensively associated and exists as a three-dimensional distorted network of hydrogen-bonded molecules, not too dissimilar from ice. Any mechanistic model of ice nucleation, based on the condensation of individual water molecules onto clusters of molecules with the properties of ice, should therefore be treated with caution. 

The value of r at which AGi g becomes negative, i.e. the cluster size for spontaneous crystal growth, is obtained as r by differentiation of Equation (2)  

Apart from the dimensions of critical nuclei under varying conditions, it is also important to consider the kinetics of nucleation, especially relative to the kinetics of crystal growth. The nucleation rate (/) is commonly estimated by means of transition state theory. With the aid of the best available values for transport properties of undercooled water,it has been estimated that in the neighbourhood of —40°C, J increases rapidly with decreasing temperature, by about a factor 20 per degree nucleation is thus a well-defined event that is hardly affected by the rate of cooling.  

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