Abstract
Volume transforms for the collision of 3D crystals are calculated for the case where the crystal centres are distributed randomly in a 2D plane. The transforms connect the volumes of collided crystals with the volumes the crystals would have had if they had not collided. The results obtained are consistent with the known mathematical bounds on the problem, and they also connect with nearest-neighbour theory in 2D. Because the transforms are calculated on the basis of ‘almost catastrophic’ collisions, it is not necessary to explicitly consider the detailed mechanisms responsible for the termination of the crystal growth processes.
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Fletcher, S., Matthews, D.B. A new model for the nucleation and growth of thick polycrystal films. I Calculation of volume transforms. J Appl Electrochem 11, 1–6 (1981). https://doi.org/10.1007/BF00615315
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DOI: https://doi.org/10.1007/BF00615315