Clustering space

The rate of formation of stable nuclei can now be obtained by considering the rate at which clusters grow by adding (and sometimes losing) atoms as they advance through cluster space. If IVjy is the number of clusters of size Af in the system, the flux of clusters which are growing from size Af to size Af + 1 may be written as... 

The coefficients in Eq. 19.7 may be taken as constants independent of the form of the distribution of cluster sizes. The relationship between the two coefficients fa and qaa+i may then be obtained by imposing an artificial constraint on the system no clusters are allowed to grow beyond a limiting size, Af m, which is considerably larger than the critical size Afc. At the same time, all clusters of size below this limit are allowed to equilibrate with respect to one another so that detailed balance is achieved between them and all fluxes in cluster space go to zero. A new distribution of cluster sizes, N q, will be produced in this constrained system. It is assumed that the same free-energy minimization procedure used previously to find the size distribution under true equilibrium conditions, and which led to Eq. 19.6, may be used for the constrained system, resulting in... 

Cluster Space group Z Unit cell volume (V) AV M-M M Br Ref. 

Centroid Linkage Here, the centroid calculated by the average of a cluster is applied as the basis for aggregation without distorting the cluster space ... 

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