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Evolution of cluster size distribution in nucleation and growth processes

Journal of Non-Crystalline Solids
Publication Date
DOI: 10.1016/0022-3093(91)90489-s
  • Mathematics


Abstract Based on classical nucleation theory, a Fokker-Planck-type partial differential equation for the time evolution of the cluster size distribution is formulated. The numerical solution of this equation leads to a general scenario of first order phase transitions in systems with molecule conservation proceeding via nucleation and growth. For the initial stage of nearly constant supersaturation, the proportionality of the mean cluster radius, 〈 R〉, to the square root of time, t, is verified. The following transition to the stage of Ostwald ripening may proceed either by a continuous decrease of the growth rate or via a transient stage of 〈 R〉-growth considerable slower than t 1 3 . The explanation of such different possibilities is given detail. The analysis shows that, for growth processes proceeding via an attachment of single monomers and non-overlapping diffusion zones of the clusters, only one population of clusters with an unimodal size distribution should evolve. The small-angle-X-ray scattering (SAXS) experiment data from the present study show, however, the existence of two cluster populations with significantly different mean radii. Additional physical assumptions are deduced from which an explanation of a bimodal size distribution is proposed. To support this general scenario, a series of experimental results from electron microscopic, SAXS and other measurements are given for the case of silver halide precipitation from glass-forming sodium borate melts. They show the time evolution of characteristic kinetic quantities such as relative supersaturation, mean cluster size and total cluster number.

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