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Mechanical properties of phosphorene nanotubes: a density functional tight-binding study

机译：磷纳米管的机械性能：密度泛函紧密结合研究

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Using the density functional tight-binding method, we studied the elastic properties, deformation and failure of armchair (AC) and zigzag (ZZ) phosphorene nanotubes (PNTs) under uniaxial tensile strain. We found that the deformation and failure of PNTs are very much anisotropic. For ZZ PNTs, three deformation phases are recognized: the primary linear elastic phase-which is associated with interactions between neighboring puckers, succeeded by the bond rotation phase-where the puckered configuration of phosphorene is smoothed via bond rotation, and lastly the bond elongation phase-where the P-P bonds are directly stretched up to the maximally allowed limit and failure is initiated by the rupture of the most stretched bonds. For AC PNTs, the applied strain stretches the bonds up to the maximally allowed limit, causing their ultimate failure. For both AC and ZZ PNTs, their failure strain and failure stress are sensitive-while the Young's modulus, flexural rigidity, radial Poisson's ratio and thickness Poisson's ratio are relatively insensitive-to the tube diameter. More specifically, for AC PNTs, the failure strain decreases from 0.40 to 0.25 and the failure stress increases from 13 GPa to 21 GPa when the tube diameter increases from 13.3 angstrom to 32.8 angstrom; while for ZZ PNTs, the failure strain decreases from 0.66 to 0.55 and the failure stress increases from 4 GPa to 9 GPa when the tube diameter increases from 13.2 angstrom to 31.1 angstrom. The Young's modulus, flexural rigidity, radial and thickness Poisson ratios are 114.2 GPa, 0.019 eV . nm(2), 0.47 and 0.11 for AC PNTs, and 49.2 GPa, 0.071 eV . nm(2), 0.07 and 0.21 for ZZ PNTs, respectively. The present findings provide valuable references for the design and application of PNTs as device elements.
机译：使用密度泛函紧密结合方法，我们研究了单轴拉伸应变下扶手椅（AC）和之字形（ZZ）磷纳米管（PNT）的弹性，变形和破坏。我们发现PNT的变形和破坏是非常各向异性的。对于ZZ PNT，识别出三个变形阶段：主要的线性弹性阶段（与相邻的褶皱之间的相互作用相关联），接着是键旋转阶段（在该旋转过程中，磷的褶皱结构通过键旋转而变得平滑），最后是键伸长阶段-将PP键直接拉伸到最大允许极限，并通过拉伸最大的键的断裂来引发破坏。对于AC PNT，施加的应变将键拉伸到最大允许极限，从而导致其最终破坏。对于AC和ZZ PNT，其破坏应变和破坏应力都很敏感，而杨氏模量，挠曲刚度，径向泊松比和厚度泊松比对管径相对不敏感。更具体地，对于AC PNT，当管直径从13.3埃增加到32.8埃时，破坏应变从0.40降低到0.25，破坏应力从13 GPa增加到21 GPa。对于ZZ PNT，当管径从13.2埃增加到31.1埃时，破坏应变从0.66降低到0.55，破坏应力从4 GPa增加到9 GPa。杨氏模量，抗弯刚度，径向和厚度泊松比为114.2 GPa，0.019 eV。 nm（2），对于AC PNTs为0.47和0.11，以及49.2 GPa，0.071 eV。 ZZ PNT分别为nm（2），0.07和0.21。本发现为PNT作为设备元件的设计和应用提供了有价值的参考。

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