Anisotropic buckling of few-layer black phosphorus

Abstract

When a two-dimensional material, adhered onto a compliant substrate, is subjected to compression it can undergo a buckling instability yielding to a periodic rippling. Interestingly, when black phosphorus (bP) 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 bP and a quantitative analysis of the ripple period allows the determination of the Youngs's modulus of few-layer bP along the armchair direction (E_{bP_AC} = 35.1 ± 6.3 GPa) and the zig-zag direction (E_{bP_ZZ} = 93.3 ± 21.8 GPa).