A new force-constant model for graphite

Nicholson, Anthony P.; Bacon, David

doi:10.1088/0022-3719/10/13/006

Cited by 36 publications

(7 citation statements)

References 12 publications

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“…Molecular mechanistic modelling of single layer graphene sheets has been pursued by several authors. Simple lattice models with force constants derived from an assumed potential have been developed by Bacon and Nicholson [11] and Gillis [12]. Ab initio methods have been used by Kudin et al [13], who predict a Young's modulus of 1.02 TPa and Poisson's ratio of 0.149, and Van Lier et al [14], reporting a Young's modulus for graphene equal to 1.11 TPa.…”

Section: Introductionmentioning

confidence: 99%

Effective elastic mechanical properties of single layer graphene sheets

2009

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The elastic moduli of single layer graphene sheet (SLGS) have been a subject of intensive research in recent years. Calculations of these effective properties range from molecular dynamic simulations to use of structural mechanical models. On the basis of mathematical models and calculation methods, several different results have been obtained and these are available in the literature. Existing mechanical models employ Euler-Bernoulli beams rigidly jointed to the lattice atoms. In this paper we propose truss-type analytical models and an approach based on cellular material mechanics theory to describe the in-plane linear elastic properties of the single layer graphene sheets. In the cellular material model, the C-C bonds are represented by equivalent mechanical beams having full stretching, hinging, bending and deep shear beam deformation mechanisms. Closed form expressions for Young's modulus, the shear modulus and Poisson's ratio for the graphene sheets are derived in terms of the equivalent mechanical C-C bond properties. The models presented provide not only quantitative information about the mechanical properties of SLGS, but also insight into the equivalent mechanical deformation mechanisms when the SLGS undergoes small strain uniaxial and pure shear loading. The analytical and numerical results from finite element simulations show good agreement with existing numerical values in the open literature. A peculiar marked auxetic behaviour for the C-C bonds is identified for single graphene sheets under pure shear loading.

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Section: Introductionmentioning

confidence: 99%

Effective elastic mechanical properties of single layer graphene sheets

2009

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“…Several models 5,6,7,8,9,10,11,12 have been proposed to calculate the phonon dispersion in bulk graphite. Most improved ones 9,10 involve many (up to twenty) parameters.…”

Section: Introductionmentioning

confidence: 99%

“…Several models 5,6,7,8,9,10,11 have been proposed to predict the phonon dispersion in graphene and bulk graphite from empirical force-constant calculations. A simplest approach assumes the diagonal form of the force-constant matrix which contains three constants for the interaction of an atom with all its nth-nearest neighbor.…”

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confidence: 99%

Symmetry constraints on phonon dispersion in graphene

Falkovsky

2008

Physics Letters A

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Taking into account the constraints imposed by the lattice symmetry, we calculate the phonon dispersion for graphene with interactions between the first, second, and third nearest neighbors in the framework of the Born--von Karman model. Analytical expressions obtained for the dispersion of the out-of-plane (bending) modes give the nonzero sound velocity. The dispersion of four in-plane modes is determined by coupled equations. Values of the force constants are found in fitting with frequencies at critical points and with elastic constants measured on graphite.Comment: 5 pages, 2 figure

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“…That is to say structures with a smaller elastic strain energy under strain (e xx a 0, e yy = e xy = 0) would have a smaller elastic constant C 11 . Inspired by the force-constant model for graphite, 58,59 we realized that the elastic strain energy of carbon materials is closely related to the C-C bond-length and +CCC bond-angle variation. Therefore, when comparing the elastic properties of carbon materials with similar bonding features, those with smaller bond-length and bond-angle variation under strain (e xx a 0, e yy = e xy = 0) would sustain smaller elastic strain energies, and accordingly have a smaller elastic constant C 11 .…”

Section: Elastic Propertiesmentioning

confidence: 99%

2D carbon sheets with negative Gaussian curvature assembled from pentagonal carbon nanoflakes

Zhang

Wang

et al. 2018

Phys. Chem. Chem. Phys.

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Despite the good progress made in materials fabrication, it remains a big challenge to synthesize 2D sheets by assembling nanoflakes that are usually produced in experiments, and few theoretical studies have explored this topic. Based on the recent experimental synthesis of pentagonal graphene nanoflakes and the novel properties of penta-graphene, we report a series of 2D assembled carbon allotropes (CG568-80, CG568-180 and CG568-320) that have the following unusual properties: different from most other 2D carbon allotropes, the assembled carbon sheets have negative Gaussian curvatures, and exhibit ultra-softness and better chemical reactivity due to the curvature-induced misalignment of π-orbitals as compared with pristine graphene; all three studied carbon sheets are highly stable with binding energies comparable to those of phagraphene and ψ-graphene, and are semiconductors with tunable band gaps, displaying size-dependent carrier mobilities: ∼105 cm2 V-1 s-1 (CG568-80 and CG568-320) and ∼104 cm2 V-1 s-1 (CG568-180). These features indicate that assembling nanoflakes can effectively tune the structural morphology and properties to expand the family of 2D carbon materials for future applications.

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A new force-constant model for graphite

Cited by 36 publications

References 12 publications

Effective elastic mechanical properties of single layer graphene sheets

Effective elastic mechanical properties of single layer graphene sheets

Symmetry constraints on phonon dispersion in graphene

2D carbon sheets with negative Gaussian curvature assembled from pentagonal carbon nanoflakes

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