Nanoscale Equilibrium Crystal Shapes

TL;DR

This paper investigates how finite size and interface effects influence equilibrium crystal shapes, deriving new solutions that account for curvature and step interactions, and discusses metastable states and their energy barriers.

Contribution

It introduces a new model incorporating curvature and step interactions to predict equilibrium and metastable crystal shapes, extending traditional theories.

Findings

Derived explicit relationships for ECS and metastable states.

Identified the role of shape parameter c in determining crystal shapes.

Discussed energy barriers related to nucleation of metastable states.

Abstract

The finite size and interface effects on equilibrium crystal shape (ECS) have been investigated for the case of a surface free energy density including step stiffness and inverse-square step-step interactions. Explicitly including the curvature of a crystallite leads to an extra boundary condition in the solution of the crystal shape, yielding a family of crystal shapes, governed by a shape parameter c. The total crystallite free energy, including interface energy, is minimized for c=0, yielding in all cases the traditional PT shape (z x3/2). Solutions of the crystal shape for c≠0 are presented and discussed in the context of meta-stable states due to the energy barrier for nucleation. Explicit scaled relationships for the ECS and meta-stable states in terms of the measurable step parameters and the interfacial energy are presented.