The influence of dislocations on crystal growth

The kinetic theory of the nucleation of new phases, developed especially by Volmer,l by Farkas,2 by Kaischew and Stranski3 and by Becker and DOring4 indicates that under typical conditions * the self-nucleation from vapour of new crystals, new liquid drops and fresh two-dimensional monolayers of molecules on a “ saturated ” crystal face require respectively supersaturations of the vapour by factors of typically 10, 5 and 1.5 respectively in order to proceed at appreciable rates. Experimentally, the first two of these figures are apparently correct : but the third is much larger than the actual supersaturation required to cause further growth of a crystal already formed. In fact, the existence of a critical finite supersaturation for further growth has only been established for a few materials, and then for individual faces of individual crystals, being different from case to case ; at the most it is about I yo. Volmer and S c h ~ l t z e , ~ who found a critical supersaturation of 0.8 yo for the growth of an iodine crystal from the vapour, interpreted this as the critical supersaturation for two-dimensional nucleation : but the quantitative discrepancy is far too great (for details of the growth rate formulzJ see the contributions of Burton and Cabrera to this Discussion). However, this discrepancy is not in the least surprising. One ought not to expect that any visible crystal will exhibit a completed perfect face needing fresh two-dimensional nucleation in order to grow. Investigation of the mechanical properties of solids shows that no macroscopic specimen ever exhibits the theoretical strength of the perfect crystal; and this enormous discrepancy (a factor of 100, say, and more for “good”