Grain Size Distribution for Competitive Growth with Nucleation

R. Hilfer, P. Meakin

Zeitschrift für Physik B 88, 223 (1992)

submitted on
Monday, November 25, 1991

The paper introduces and discusses an idealized competitive growth model with nucleation for the microstructure formation during dense branching phase separation in thin Al/Ge films. Grain size and grain length distributions for the new model are obtained analytically and by simulation. These distributions exhibit a characteristic scaling form similar to cluster size distributions in many other growth models. The cutoff functions in these scaling forms and their influence on the determination of effective exponents are studied in detail. It is found that nucleation introduces a new length scale into the other-wise selfsimilar competitive growth model. This length scale appears only inside the cutoff function and diverges algebraically as the nucleation rate vanishes. We find both analytically and by simulation that the cutoff functions can exhibit stretched exponential behaviour ∼exp(−x α) for large arguments. Our analytical and simulation results for grain size and grain length distributions are in excellent quantitative agreement.

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