BATCH CRYSTALLIZATION UNDER CONTINUOUS COOLING - ANALYTICAL SOLUTION FOR DIFFUSION-LIMITED CRYSTAL-GROWTH

The kinetic equations of nucleation and crystal growth in a multicompo nent system undergoing continuous cooling are solved for asymptoticall y slow cooling rates meaning that the maximum supercooling Delta T-m i s much smaller than the exponent A in the nucleation rate I similar to exp(-A Delta T-2). The growth rate is controlled by chemical diffusio n so that it depends not only on the supercooling but also on the crys tal size. The periods of metastable cooling, nucleation and relaxation are related as 1:p(-1):p(-1/3), where p = A <D Delta T-m(-2) approxim ate to 30-80 is a parameter characterizing the maximum supercooling De lta T-m. It is a weak (logarithmical) function of all the parameters i ncluding the cooling rate T. The crystal sizes are determined by the d ensity of nuclei produced during the nucleation period and depend on t he cooling rate approximately as T--0.5. The theoretical predictions a re found in a good agreement with experimental data for Al-Cu, Al-Si, Sn-Pb, and CaMgSi2O6-CaAl2Si2O8-NaAlSi3O8.