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VLSI Design
Volume 9 (1999), Issue 4, Pages 377-383

Modeling Crystallization Dynamics when the Avrami Model Fails

1Department of Chemistry, University of Victoria, P.O. Box 3065, Victoria B.C. V8W 3V6, Canada
2Department of Mathematics and Statistics, University of Victoria, P.O. Box 3045, Victoria B.C. V8W 3P4, Canada

Received 13 August 1997; Revised 1 December 1998

Copyright © 1999 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Recent experiments on the formation of crystalline CO2 from a newly discovered binary phase consisting of CO2 and C2H2 at 90° K fail to be adequately simulated by Avrami equations. The purpose of this note is to develop an alternative to the Avrami model which can make accurate predictions for these experiments. The new model uses empirical approximations to the distribution densities of the volumes of three-dimensional Voronoi cells defined by Poisson-generated crystallization kernels (nuclei). Inside each Voronoi cell, the growth of the crystal is assumed to be linear in diameter (i.e., cubic in volume) until the cell is filled by the CO2 crystals and the C2H2 (thought of as a waste product). The cumulative growth curve is computed by averaging these individual growth curves with respect to the distribution density of the volumes of the Voronoi cells. Agreement with the experiments is excellent.