Activity of growth centers during spiral growth of KDP in aqueous solution: A statistical approach

Abstract

The observed growth rate of {101} KDP and similar solution-grown crystals is determined by the local conditions at a point where the dominant growth center for the whole face is located, and is proportional to the activity ϵm of that center. The dominant growth center can be identified and its activity determined if the sizes m (the number of cooperating growth spirals) of all groups of screw dislocations of the same sign representing a population of growth centers on a face, and the average separation D between dislocations within groups, can be obtained. In the case of randomly distributed dislocations, the probability distribution function for the size m of a group of dislocations of the same characterized by nearest neighbor distances less than lc (the critical distance controlling spiral cooperation) has been derived and confirmed via Monte Carlo simulations. The relationship between the group size m and the average internal distance D within the group has been established for the spectrum of group sizes having equal probability to be present on a crystal face. Based on the above, dislocation activity ϵ(m) has been determined as a continuous function of group size with maximum value ϵm corresponding to the dominant growth center. The theoretical results have been generalized by means of two parameters: the dimensionless crystal size X0 as a number of critical distances lc per physical crystal size X and the dimensionless dislocation density γ0 as a number of dislocations per area of size l2c. Activity of the dominant growth center ϵm, its size m(ϵm), its limiting dimensionless internal distance l0(ϵm) and the size of a largest possible group mm of cooperating spirals were shown to be unique functions of the above two dimensionless parameters. The results derived from this investigation are consistent with many phenomena either predicted theoretically or observed in experiments that arise from the activity of screw dislocations in the process of crystal growth from solutions.