Nucleation of crystal surfaces with corner energy regularization

• Published in: Journal of crystal growth Vol. 503; pp. 20 - 27
• Main Authors: Philippe, T., Henry, H., Plapp, M.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.12.2018; Elsevier BV; Elsevier
• Subjects: A1. Crystal morphology; A1. Growth models; A1. Interfaces; A1. Nucleation; Binary mixtures; Chemical potential; Computer simulation; Condensed Matter; Crystal structure; Crystal surfaces; Crystallinity; Energy; Equations of motion; Euler-Lagrange equation; Nucleation; Organic chemistry; Phase separation; Physics; Regularization; Saddle points; Simulation; A1. Growth models; A1. Nucleation; A1. Interfaces; A1. Crystal morphology
• ISSN: 0022-0248; 1873-5002
• DOI: 10.1016/j.jcrysgro.2018.09.009

•Evolution of crystal surfaces is regularized by adding an energy to corners.•Nucleation of crystalline surfaces is analogous to the Cahn and Hilliard theory.•As compared with saddle point nucleation, ridge crossing is dynamically favoured. The thermodynamics of strongly anisotropic crystalline surfaces is analogous to that of a binary mixture exhibiting phase separation. On a metastable planar surface, formation of stable orientations requires a nucleation process, in which the energy associated with the presence of corners must be considered. In this context, a nucleation event corresponds to the formation of a critical shape for the crystalline surface before the system enters the growth regime. We first derive the Euler-Lagrange equation for crystal surface nucleation, in two dimensions, and show that the saddle-point condition corresponds to a vanishing chemical potential along this critical surface. We then perform numerical simulation of the equation of motion for the crystal surface and show that, as compared with saddle point nucleation, ridge crossing is dynamically favoured.