单层黑磷弯曲变形的各向异性及其失稳现象

Anisotropic bending behaviors and bending induced buckling in single-layered black phosphorus

利用密度泛函理论系统地研究了单层黑磷的纯弯变形特性,揭示了单层黑磷沿锯齿型方向弯曲时的失稳现象,并与石墨烯和单层二硫化钼的弯曲变形行为进行了比较.在此基础上,从连续介质力学的角度引入等效原子面积,计算了3种材料的弯曲刚度,并且与实测值和经验势的结果很好地符合.结果表明,单层黑磷的弯曲变形体现了明显的各向异性,刚度过大的锯齿型弯曲是导致其失稳区过早出现的力学根源,而单层黑磷孤电子对的排斥作用是弯曲变形呈现各向异性的主要物理机制.

The bending behavior of single-layered black phosphorus was systematically studied using density functional theory. Graphene, containing a single layer of molybdenum disulfide, was studied by considering changes in the bending strain energies as a function of the radius of the curvature. Bending-induced buckling in single-layered black phosphorus and its bent states were found along a zigzag direction as shown by the critical radius of the curvature. Combing the bending strain energies from first-principle calculations of the corresponding single-wall nanotubes of grapheme, single-layered black phosphorus and single-layered molybdenum disulfide with the strain energy densities using pure bending plate theory and by the introduction of a simple equivalent atomic area, the bending stiffnesses of three kinds of two-dimensional crystals were calculated and found to be in good agreement with experimental and empirical results. We also show that the bending stiffness is 5.336 eV under zigzag bending and 1.251 eV under armchair bending in single-layered black phosphorus. Apparent anisotropic bending behavior was found where high bending stiffness under zigzag bending leads to a buckling phenomenon. With insight into the physical mechanism of the anisotropic bending behavior, electron density distributions in the single-layered black phosphorus and the corresponding armchair （11,0） and zigzag （0,15） black phosphorus nanotubes with a similar curvature radius were further analyzed. We show that the anisotropic bending behavior can be attributed to repulsive phosphorus lone pair interactions, which are stronger under zigzag bending compared with armchair bending. When a critical curvature radius is attained, the hybridized sp3 orbitals in single-layered black phosphorus will be affected by the lone pairs according to Pauli＇s exclusion principle. The local equilibrium conditions of the electron clouds are thus disrupted and bending-induced buckling finally occurs.