Anisotropic buckling of few-layer black phosphorus

TL;DR

This study investigates the anisotropic buckling behavior of few-layer black phosphorus under compression, revealing direction-dependent ripple periods and enabling measurement of its Young's modulus along different crystal axes.

Contribution

It provides a quantitative analysis of black phosphorus buckling, linking ripple patterns to its anisotropic elastic properties, which was not previously characterized in detail.

Findings

Buckling ripple period is 40% longer along zig-zag direction.

Young's modulus along armchair is 35.1 GPa, zig-zag is 93.3 GPa.

Buckling behavior is governed by the puckered crystal structure.

Abstract

When a two-dimensional material, adhered onto a compliant substrate, is subjected to compression it can undertake a buckling instability yielding to a periodic rippling. Interestingly, when black phosphorus flakes are compressed along the zig-zag crystal direction the flake buckles forming ripples with a 40% longer period than that obtained when the compression is applied along the armchair direction. This anisotropic buckling stems from the puckered honeycomb crystal structure of black phosphorus and a quantitative analysis of the ripple period allows us to determine the Youngs's modulus of few-layer black phosphorus along the armchair direction (EbP_AC = 35.1 +- 6.3 GPa) and the zig-zag direction (EbP_ZZ = 93.3 +- 21.8 GPa).