Diffusion-controlled crystal growth in K₂OSiO₂ compositions

The growth of cristobalite dendrites in two K₂OSiO₂ glasses containing 10.3 and 15.0 mol% K₂O has been studied over a wide range of temperature. The kinetics of crystallization were linear; i.e. the growth rates were independent of time. The observed crystallization rates were consistent with a diffusion-controlled mechanism. Measurements of the tip radii of curvature of the dendrites are consistent, at low undercoolings, with the predictions of Horvay and Cahn for the growth of an isolated dendrite. However, at lower temperatures at which the dendrites are closely spaced, the predicted radii are seriously in error. A model is described which takes account of the overlapping diffusion fields of neighboring dendrites and gives improved agreement with the observed growth rates. The presence of a maximum in each of the crystal growth rate versus temperature curves has not been explained. This phenomenon is apparently related to changes in the size, shape and spacing of the dendrites, which occur in the same temperature range.