Growth rate of crystal surfaces with several dislocation centers
Provides refined theoretical estimates for crystal growth rates with multiple dislocations, relevant to materials science and crystal growth modeling.
The paper studies the growth rate of crystal surfaces with multiple screw dislocations, proposing improved estimates that match numerical simulations, and analyzes the influence of dislocation distribution and spiral orientation.
We study analytically and numerical the growth rate of a crystal surface growing by several screw dislocations. To describe several spiral steps we use the revised level set method for spirals by the authors (Journal of Scientific Computing 62, 831-874, 2015). We carefully compare our simulation results on the growth rates with predictions in a classical paper by Burton et al. (Philos Trans R Soc Lond Ser A Math Phys Sci 243,299-358, 1951). Then, we propose improved estimates on the growth rate with several different configurations, which are in agreement with our numerical simulations. The influence of distribution of screw dislocations in a group on a line to the growth rate, and the growth rate by a group including different rotational orientations of spirals are also studied in this paper.