Auxetic Black Phosphorus: A 2D Material with Negative Poisson’s Ratio

Abstract

The Poisson's ratio of a material characterizes its response to uniaxial strain. Materials normally possess a positive Poisson's ratio - they contract laterally when stretched, and expand laterally when compressed. A negative Poisson's ratio is theoretically permissible but has not, with few exceptions of man-made bulk structures, been experimentally observed in any natural materials. Here, we show that the negative Poisson's ratio exists in the low-dimensional natural material black phosphorus and that our experimental observations are consistent with first-principles simulations. Through applying uniaxial strain along armchair direction, we have succeeded in demonstrating a cross-plane interlayer negative Poisson's ratio on black phosphorus for the first time. Meanwhile, our results support the existence of a cross-plane intralayer negative Poisson's ratio in the constituent phosphorene layers under uniaxial deformation along the zigzag axis, which is in line with a previous theoretical prediction. The phenomenon originates from the puckered structure of its in-plane lattice, together with coupled hinge-like bonding configurations.

Black Phosphorus Rediscovered: From Bulk Material to Monolayers

“…1TPa for graphene). [141] The phenomenon originates from the puckered structure of its inplane lattice,t ogether with coupled hinge-like bonding configurations.I np ractical terms,s tretching results in the PB lattice opening up,t hereby generating more space between the Pa toms and it becoming thicker.T he outstanding mechanical flexibility of BP makes it an interesting material for engineering strain. [134][135][136][137] Single-layer BP has recently been shown to be auxetic [ *** ] when au niaxial stress along the zigzag direction is applied.…”

“…[140] Thea pplication of uniaxial strain along the armchair direction led to an egative cross-plane interlayer Poisson ratio for the first time being reported for BP. [141] The phenomenon originates from the puckered structure of its inplane lattice,t ogether with coupled hinge-like bonding configurations.I np ractical terms,s tretching results in the PB lattice opening up,t hereby generating more space between the Pa toms and it becoming thicker.T he outstanding mechanical flexibility of BP makes it an interesting material for engineering strain.…”

2D Elemental Nanomaterials Beyond Graphene

“…Mechanical properties . Phosphorene exhibits attractive mechanical flexibility and negative Poisson's ratio . First‐principles calculations by Wei et al .…”

Negative In‐Plane Poisson's Ratio for Single Layer Black Phosphorus: An Atomistic Simulation Study

“…[8][9][10] Recently, the investigation of auxetic property of nanoscale materials and structures using both numerical simulations and experiments have been received considerable attention. [11][12][13][14] The search for nanomaterials with negative Poisson's ratio (NPR) and the search for new mechanisms for NPR of nanomaterials have been significant. [15] Inspired by some existing mechanisms for bulk materials, some nanostructures involving defects or some specific engineered structures can show auxetic behavior such as patterned graphene structures based on rigid rotating unit model, [16] and wrinkled graphene structures based on de-wrinkling and unfolding mechanism.…”