Valence force model and nanomechanics of single-layer phosphorene

TL;DR

This paper develops a microscopic valence-force model and a macroscopic continuum model for single-layer phosphorene, linking atomic displacements to strain and stress, and explores its mechanical properties and response to pressure.

Contribution

It provides an improved valence-force parameter set and derives a comprehensive continuum model for phosphorene's nanomechanics, including bending rigidity.

Findings

Calculated phonon dispersion and elastic properties.

Derived continuum model including bending rigidities.

Analyzed properties of pressurized phosphorene sheets.

Abstract

In order to understand the relation of strain and material properties, both a microscopic model connecting a given strain to the displacement of atoms, and a macroscopic model relating applied stress to induced strain, are required. Starting from a valence-force model for black phosphorous (phosphorene) [Kaneta et al., Solid State Communications, 1982, 44, 613] we use recent experimental and computational results to obtain an improved set of valence-force parameters. From the model we calculate the phonon dispersion and the elastic properties of single-layer phosphorene. Finally, we use these results to derive a complete continuum model, including the bending rigidities, valid for long-wavelength deformations of phosphorene. This continuum model is then used to study the properties of pressurized suspended phosphorene sheets.