Modeling crystallization dynamics when the Avrami model fails

Recent experiments on the formation of crystalline CO2 from a newly discove red binary phase consisting of CO2 and C2H2 at 90 degrees K fail to be adeq uately simulated by Avrami equations. The purpose of this note is to develo p an alternative to the Avrami model which can make accurate predictions fo r these experiments. The new model uses empirical approximations to the dis tribution densities of the volumes of three-dimensional Voronoi cells defin ed by Poisson-generated crystallization kernels (nuclei). Inside each Voron oi 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 C2 H2 (thought of as a waste product). The cumulative growth curve is computed by averaging these individual growth curves with respect to the distributi on density of the volumes of the Voronoi cells. Agreement with the experime nts is excellent.