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We present first-principles calculations of elastic properties of multilayered two-dimensional crystals such as graphene, h-BN and 2H-MoS2 which shows that their Poissons ratios along out-of-plane direction are negative, near zero and positive, respectively, spanning all possibilities for sign of the ratios. While the in-plane Poissons ratios are all positive regardless of their disparate electronic and structural properties, the characteristic interlayer interactions as well as layer stacking structures are shown to determine the sign of their out-of-plane ratios. Thorough investigation of elastic properties as a function of the number of layers for each system is also provided, highlighting their intertwined nature between elastic and electronic properties.
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As a basic mechanical parameter, Poissons ratio ({ u}) measures the mechanical responses of solids against external loads. In rare cases, materials have a negative Poissons ratio (NPR), and present an interesting auxetic effect. That is, when a material is stretched in one direction, it will expand in the perpendicular direction. To design modern nanoscale electromechanical devices with special functions, two dimensional (2D) auxetic materials are highly desirable. In this work, based on first principles calculations, we rediscover the previously proposed {delta}-phosphorene ({delta}-P) nanosheets [Jie Guan et al., Phys. Rev. Lett. 2014, 113, 046804] are good auxetic materials with a high NPR. The results show that the Youngs modulus and Poissons ratio of {delta}-P are all anisotropic. The NPR value along the grooved direction is up to -0.267, which is much higher than the recently reported 2D auxetic materials. The auxetic effect of {delta}-P originated from its puckered structure is robust and insensitive to the number of layers due to weak interlayer interactions. Moreover, {delta}-P possesses good flexibility because of its relatively small Youngs modulus and high critical crack strain. If {delta}-P can be synthesized, these extraordinary properties would endow it great potential in designing low dimensional electromechanical devices.
Silicon dioxide or silica, normally existing in various bulk crystalline and amorphous forms, is recently found to possess a two-dimensional structure. In this work, we use ab initio calculation and evolutionary algorithm to unveil three new 2D silica structures whose themal, dynamical and mechanical stabilities are compared with many typical bulk silica. In particular, we find that all these three 2D silica have large in-plane negative Poissons ratios with the largest one being double of penta-graphene and three times of borophenes. The negative Poissons ratio originates from the interplay of lattice symmetry and Si-O tetrahedron symmetry. Slab silica is also an insulating 2D material, with the highest electronic band gap (> 7 eV) among reported 2D structures. These exotic 2D silica with in-plane negative Poissons ratios and widest band gaps are expected to have great potential applications in nanomechanics and nanoelectronics.
Most materials exhibit positive Poissons ratio (PR) values but special structures can also present negative and, even rarer, zero (or close to zero) PR. Null PR structures have received much attention due to their unusual properties and potential applications in different fields, such as aeronautics and bio-engineering. Here, we present a new and simple near-zero PR 2D topological model based on a structural block composed of two smooth and rigid bars connected by a soft membrane or spring. It is not based on re-entrant or honeycomb-like configurations, which have been the basis of many null or quasi-null PR models. Our topological model was 3D printed and the experimentally obtained PR was$-0.003,pm 0.001,$, which is one the closest to zero value ever reported. This topological model can be easily extended to 3D systems and with compression in any direction. The advantages and disadvantages of these models are also addressed.
We study the elastic response of composites of rods embedded in elastic media. We calculate the micro-mechanical response functions, and bulk elastic constants as functions of rod density. We find two fixed points for Poissons ratio with respect to the addition of rods in 3D composites: there is an unstable fixed point for Poissons ratio=1/2 (an incompressible system) and a stable fixed point for Poissons ratio=1/4 (a compressible system). We also derive an approximate expression for the elastic constants for arbitrary rod density that yields exact results for both low and high density. These results may help to explain recent experiments [Physical Review Letters 102, 188303 (2009)] that reported compressibility for composites of microtubules in F-actin networks.
We compute the absolute Poissons ratio $ u$ and the bending rigidity exponent $eta$ of a free-standing two-dimensional crystalline membrane embedded into a space of large dimensionality $d = 2 + d_c$, $d_c gg 1$. We demonstrate that, in the regime of anomalous Hookes law, the absolute Poissons ratio approaches material independent value determined solely by the spatial dimensionality $d_c$: $ u = -1 +2/d_c-a/d_c^2+dots$ where $aapprox 1.76pm 0.02$. Also, we find the following expression for the exponent of the bending rigidity: $eta = 2/d_c+(73-68zeta(3))/(27 d_c^2)+dots$. These results cannot be captured by self-consistent screening approximation.
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