Excess energy and deformation along free edges of graphene nanoribbons

Lü, Qiang; Huang, Rui

doi:10.1103/physrevb.81.155410

Cited by 84 publications

(69 citation statements)

References 26 publications

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“…Some of the shapes we observe are similar to those reported in past studies, both at zero and finite temperature 11,12,16,40 . A key feature is that we observe two dominant morphological classes for each given set of parameters: in-phase or symmetrical ripples (S), and outof-phase or asymmetrical (AS) ripples, where the phase refers to the relative displacements of the edges.…”

Section: Past Experiments and Computationssupporting

confidence: 89%

Rippling instabilities in suspended nanoribbons

Wang

Upmanyu

2012

Phys. Rev. B

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Morphology mediates the interplay between the structure and electronic transport in atomically thin nanoribbons such as graphene as the relaxation of edge stresses occurs preferentially via outof-plane deflections. In the case of end-supported suspended nanoribbons that we study here, past experiments and computations have identified a range of equilibrium morphologies, in particular for graphene flakes, yet a unified understanding of their relative stability remains elusive. Here, we employ atomic-scale simulations and a composite framework based on isotropic elastic plate theory to chart out the morphological stability space of suspended nanoribbons with respect to intrinsic (ribbon elasticity) and engineered (ribbon geometry) parameters, and the combination of edge and body actuation. The computations highlight a rich morphological shape space that can be naturally classified into two competing shapes, bending-like and twist-like, depending on the distribution of ripples across the interacting edges. The linearized elastic framework yields exact solutions for these rippled shapes. For compressive edge stresses, the body strain emerges as a key variable that controls their relative stability and in extreme cases stabilizes co-existing transverse ripples. Tensile edge stresses lead to dimples within the ribbon core that decay into the edges, a feature of obvious significance for stretchable nanoelectronics. The interplay between geometry and mechanics that we report should serve as a key input for quantifying the transport along these ribbons.

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Section: Past Experiments and Computationssupporting

confidence: 89%

Rippling instabilities in suspended nanoribbons

Wang

Upmanyu

2012

Phys. Rev. B

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“…The simple formula E c = Z 2 E b with Z = 3 the number of nearest neighbors yields E b = 5.3 eV, which corresponds to a breaking energy G = 3.4 nJ/m to cut the bonds perpendicular to a zigzag direction. We note the excellent agreement with the excess energy reported for the zigzag edge of graphene (half the breaking energy G), λ = 1.7 nJ/m [18]. Using this value of λ together with C = 350 N/m [5] yields K c = 1.1 × 10 −3 Nm −1/2 , in fair agreement with the experimental value reported above for monolayer graphene.…”

Section: Mechanical Propertiessupporting

confidence: 90%

Graphene as a Prototypical Model for Two-Dimensional Continuous Mechanics

Lambin

2017

Applied Sciences

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This paper reviews a few problems where continuous-medium theory specialized to two-dimensional media provides a qualitatively correct picture of the mechanical behavior of graphene. A critical analysis of the parameters involved is given. Among other results, a simple mathematical description of a folded graphene sheet is proposed. It is also shown how the graphene-graphene adhesion interaction is related to the cleavage energy of graphite and its C 33 bulk elastic constant.

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“…However, using periodic boundary conditions removes the effects of free edges, which are known to cause dramatic changes in various physical properties for two-dimensional materials 25 . With regards to mechanical behavior, edge stresses resulting from undercoordinated edge atoms in graphene were shown to lead to warping of monolayer graphene 26,27 . However, in contrast to graphene, ab initio calculations showed that edge stresses in SLBP have been shown to induce bending rather than warping 18 .…”

Section: Cpi and Edge Stress-induced Bendingmentioning

confidence: 99%

A Stillinger–Weber potential for single-layered black phosphorus, and the importance of cross-pucker interactions for a negative Poisson's ratio and edge stress-induced bending

2015

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The distinguishing structural feature of single-layer black phosphorus is its puckered structure, which leads to many novel physical properties. In this work, we first present a new parameterization of the Stillinger-Weber potential for single-layer black phosphorus. In doing so, we reveal the importance of a cross-pucker interaction term in capturing its unique mechanical properties, such as a negative Poisson's ratio. In particular, we show that the cross-pucker interaction enables the pucker to act as a re-entrant hinge, which expands in the lateral direction when it is stretched in the longitudinal direction. As a consequence, single-layer black phosphorus has a negative Poisson's ratio in the direction perpendicular to the atomic plane. As an additional demonstration of the impact of the cross-pucker interaction, we show that it is also the key factor that enables capturing the edge stress-induced bending of single-layer black phosphorus that has been reported in ab initio calculations.

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Excess energy and deformation along free edges of graphene nanoribbons

Cited by 84 publications

References 26 publications

Rippling instabilities in suspended nanoribbons

Rippling instabilities in suspended nanoribbons

Graphene as a Prototypical Model for Two-Dimensional Continuous Mechanics

A Stillinger–Weber potential for single-layered black phosphorus, and the importance of cross-pucker interactions for a negative Poisson's ratio and edge stress-induced bending

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