Defining shapes of 2D-crystals with undefinable edge-energies

TL;DR

This paper introduces a method to predict the equilibrium shapes of 2D crystals even when their edge energies are undefined due to lack of symmetry, demonstrated on complex materials like SnS and AgNO2.

Contribution

It presents a novel approach using latent edge energies to determine crystal shapes without requiring explicit edge energy calculations.

Findings

Successfully predicted shapes of low-symmetry 2D crystals.

Demonstrated method on materials with no symmetry, like AgNO2.

Provided a new framework for crystal shape prediction in challenging cases.

Abstract

The equilibrium shape of crystals is a fundamental property of both aesthetic appeal and practical import. It is also a visible macro-manifestation of the underlying atomic-scale forces and chemical makeup, most conspicuous in two-dimensional (2D) materials of keen current interest. If the crystal surface/edge energy is known for different directions, its shape can be obtained by geometric Wulff construction, a tenet of crystal physics. However, if symmetry is lacking, the crystal edge energy cannot be defined or calculated, so its shape becomes elusive, presenting an insurmountable problem for theory. Here we show how, in fact, one can proceed with "latent edge energies" towards constructive prediction of a unique crystal shape, and demonstrate it for challenging material-examples, like ${\rm SnS}$ of ${\rm C_{2v}}$ symmetry and even ${\rm AgNO_2}$ of ${\rm C_1}$-no symmetry at all.