Nucleation of crystal surfaces with corner energy regularization

TL;DR

This paper investigates the nucleation process of crystal surfaces considering corner energy effects, deriving key equations and demonstrating through simulations that ridge crossing is dynamically favored over saddle point nucleation.

Contribution

It introduces a novel analysis of crystal surface nucleation with corner energy regularization, deriving the Euler-Lagrange equation and comparing dynamic pathways.

Findings

Saddle-point nucleation involves a critical shape with zero chemical potential.

Numerical simulations show ridge crossing is dynamically favored over saddle point nucleation.

The study provides insights into the energetics and dynamics of crystal surface formation.

Abstract

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.