Growth rate of crystal surfaces with several dislocation centers

TL;DR

This paper combines analytical and numerical methods to study how multiple screw dislocations influence crystal surface growth rates, improving existing estimates and exploring the effects of dislocation arrangements.

Contribution

It introduces improved estimates for growth rates with multiple dislocations and analyzes the impact of dislocation distribution and orientations on growth.

Findings

Numerical results align with classical predictions by Burton et al.

Dislocation distribution significantly affects growth rates.

Different spiral orientations influence overall growth dynamics.

Abstract

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.