RANDOM SPACE-FILLING BY NUCLEATION AND GROWTH

Space filling by nucleation and growth of clusters for dimensions d = 1, 2, 3 (for some cases up to 6) was simulated on a computer. The following models were considered: (1) simultaneous growth from randomly distributed centres; (2) free nucleation and growth according to the rule l(k) = at; (3) placing of clusters of fixed size; (4) nucleation at active centres and growth. For complete filling frequency distributions for the cluster sizes and (for d = 2) figures of the cluster texture are given. Further the spatial distributions and the pair-distribution functions for the cluster centres are investigated. The degree of filling theta(t) in general satisfies the theory of Kolmogorov-Johnson-Mehl-Arvami; only for theta almost-equal-to 1 and for k > 1 deviations are found. Besides the ''fictitious cluster sum'' sigma(f)(''extended area'' after Avrami), also the ''actual cluster sum'' sigma(a) is discussed, which gives the total volume (without overlapping) of the present clusters. The equation dtheta = (1 - theta)xdsigma(a) holds, where x is fixed by the spatial distribution of the clusters and increases with the dimension d and with 1/k. The experimental cluster densities agree with the results of the theoretical considerations.