Atomistic theory of stationary nucleation

The first attempt to overcome the quantitative contradiction between the classical nucleation theory and the experimental results was made by Walton [2.56, 2.57] who derived an explicit expression for the stationary nucleation rale valid for small critical nuclei. Walton s theory was developed for the case of heterogeneous nucleation from a vapor phase but we consider it here 

Similarly to the classical theory the Walton s treatment is based on the idea for a critical nucleus the formation of which is the rate-determining step of the phase transition. However, the definition of the critical nucleus is conformed to the specificity of the small clusters and the high supersaturations. Thus it is assumed that the critical nucleus may consist of a very low number of atoms - two, one and even zero atoms in the case of very active substrates. The c-atomic critical nucleus is considered as a cluster having a probability of decay higher than or equal to the probability 

Here accounts for the number of possible ways of attachment of single 

In equation (2.67) E(rtc) is the total bonding energy of the c-atomic cluster and the number Z of single adsorbed atoms on the substrate reads  

Namely equation (2.69) is used to determine the size rtc of the critical nucleus by studying experimentally the Ig Ri) relationship at a constant 

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