The effect of dislocation cores on growth hillock vicinality and normal growth rates of KDP {1 0 1} surfaces

We present results from atomic force microscopy measurements on KDP {101} faces which show that over the range of supersaturations, 3% less than or equal to sigma less than or equal to 30%, the terrace widths on vicinal growth hillocks formed by dislocations are nearly independent of both supersaturation and dislocation structure, in contradiction to the predictions of simple BCF models. The data also show that, for Burgers vectors in excess of one unit step height, the dislocations generate hollow cores in accordance with theoretical predictions. Both analytical and numerical analyses are presented, which show that a model that takes into account the effect of these cores on the period of step rotation predicts a dependence of slope on supersaturation and Burgers vector, which is in good agreement with the experimental results. These calculations also show that the effect of the core perimeter on the step transit lime dominates the effect of reduced step velocity due to stresses near the core. Consequently, a simple analytical expression can be used to describe the slope even in the case of anistropic step kinetics. Finally, the results are used to explain the reproducible character of macroscopic growth rates and to rescale data on growth rate as a function of temperature and supersturation onto a single curve.