Gap opening in graphene by shear strain

We exploit the concept of strain-induced band structure engineering in graphene through the calculation of its electronic properties under uniaxial, shear, and combined uniaxial-shear deformations. We show that by combining shear deformations to uniaxial strains it is possible modulate the graphene energy gap value from zero up to $0.9$ eV. Interestingly enough, the use of a shear component allows for a gap opening at moderate absolute deformation, safely smaller than the graphene failure strain.Comment: to appear on PRB - Rapid Communicatio

The effect of the hydrogen coverage on the Young modulus of graphene

We blend together continuum elasticity and first principles calculations to measure by a computer experiment the Young modulus of hydrogenated graphene. We provide evidence that hydrogenation generally leads to a much smaller longitudinal extension upon loading than in pristine graphene. Furthermore, the Young modulus is found to depend upon the loading direction for some specific conformers, characterized by an anisotropic linear elastic behavior

Graphene under strain. A combined continuum-atomistic approach

By combining continuum elasticity theory and atomistic simulations, we provide a picture of the elastic behavior of graphene, which was addressed as a two-dimensional crystal membrane. Thus, the constitutive nonlinear stress-strain relations for graphene, as well as its hydrogenated conformers, have been derived in the framework of the two-dimensional elastic theory, and all the corresponding linear and nonlinear elastic moduli have been computed by atomistic simulations. Moreover, we discuss the effects of an applied stretching on graphene lattice to its electronic band structure, in particular regards the concept of strain-induced band gap engineering. Finally, we focus on the emergence of a stretching field induced on a graphene nanoribbon by bending, providing that such an in-plane strain field can be decomposed in a first contribution due to the actual bending of the sheet and a second one due to the edge effects induced by the finite size of the nanoribbon.------------------------------------------------------ABSTRACT ITA-------Combinando la teoria dell‘elasticità del continuo con calcoli eseguiti attraverso simulazioni atomistiche, si è affrontato lo studio del comportamento elastico del grafene, ovvero di una struttura cristallina bidimensionale a base carbonio. In tal modo, nell‘ambito della teoria elastica bidimensionale, sono state derivate le equazioni costitutive non lineari per il grafene e per il suo composto con l‘idrogeno, detto grafane; conseguentemente sono stati determinati per mezzo di simulazioni atomistiche tutti i relativi moduli elastici lineari e non lineari. Inoltre, abbiamo discusso gli effetti dovuti a deformazioni omogenee applicate al reticolo di grafene sulle sue bande elettroniche, con particolare attenzione al concetto di ingegnerizzazione della gap elettronica indotta da deformazione. Infine, discutiamo l‘insorgenza di un campo di deformazione su un campione di grafene finito sottoposto a piegamento, evidenziando come tale campo possa essere decomposto in un contributo causato della flessione reale subita e in un secondo dovuto ai soli effetti di bordo.

Folds and Buckles at the Nanoscale: Experimental and Theoretical Investigation of the Bending Properties of Graphene Membranes

The elastic properties of graphene crystals have been extensively investigated, revealing unique properties in the linear and nonlinear regimes, when the membranes are under either stretching or bending loading conditions. Nevertheless less knowledge has been developed so far on folded graphene membranes and ribbons. It has been recently suggested that fold-induced curvatures, without in-plane strain, can affect the local chemical reactivity, the mechanical properties, and the electron transfer in graphene membranes. This intriguing perspective envisages a materials-by-design approach through the engineering of folding and bending to develop enhanced nano-resonators or nano-electro-mechanical devices. Here we present a novel methodology to investigate the mechanical properties of folded and wrinkled graphene crystals, combining transmission electron microscopy mapping of 3D curvatures and theoretical modeling based on continuum elasticity theory and tight-binding atomistic simulations

Elastic properties of hydrogenated graphene

There exist three conformers of hydrogenated graphene, referred to as chair-, boat-, or washboard-graphane. These systems have a perfect two-dimensional periodicity mapped onto the graphene scaffold, but they are characterized by a $sp^3$ orbital hybridization, have different crystal symmetry, and otherwise behave upon loading. By first principles calculations we determine their structural and phonon properties, as well as we establish their relative stability. Through continuum elasticity we define a simulation protocol addressed to measure by a computer experiment their linear and nonlinear elastic moduli and we actually compute them by first principles. We argue that all graphane conformers respond to any arbitrarily-oriented extention with a much smaller lateral contraction than the one calculated for graphene. Furthermore, we provide evidence that boat-graphane has a small and negative Poisson ratio along the armchair and zigzag principal directions of the carbon honeycomb lattice (axially auxetic elastic behavior). Moreover, we show that chair-graphane admits both softening and hardening hyperelasticity, depending on the direction of applied load.Comment: submitted on Phys.Rev.

Nonlinear elasticity of monolayer graphene

By combining continuum elasticity theory and tight-binding atomistic simulations, we work out the constitutive nonlinear stress-strain relation for graphene stretching elasticity and we calculate all the corresponding nonlinear elastic moduli. Present results represent a robust picture on elastic behavior of one-atom thick carbon sheets and provide the proper interpretation of recent experiments. In particular, we discuss the physical meaning of the effective nonlinear elastic modulus there introduced and we predict its value in good agreement with available data. Finally, a hyperelastic softening behavior is observed and discussed, so determining the failure properties of graphene.Comment: 4 page

Interplay between bending and stretching in carbon nanoribbons

We investigate the bending properties of carbon nanoribbons by combining continuum elasticity theory and tight-binding atomistic simulations. First, we develop a complete analysis of a given bended configuration through continuum mechanics. Then, we provide by tight-binding calculations the value of the bending rigidity in good agreement with recent literature. We discuss the emergence of a stretching field induced by the full atomic-scale relaxation of the nanoribbon architecture. We further prove that such an in-plane strain field can be decomposed into a first contribution due to the actual bending of the sheet and a second one due to edge effects.Comment: 5 pages, 6 figure

Elastic Moduli in Graphene Versus Hydrogen Coverage

Through continuum elasticity we define a simulation protocol addressed to measure by a computational experiment the linear elastic moduli of hydrogenated graphene and we actually compute them by first principles. We argue that hydrogenation generally leads to a much smaller longitudinal extension upon loading than the one calculated for ideal graphene. Nevertheless, the corresponding Young modulus shows minor variations as function of coverage. Furthermore, we pThrough continuum elasticity we define a simulation protocol addressed to measure by a computational experiment the linear elastic moduli of hydrogenated graphene and we actually compute them by first principles. We argue that hydrogenation generally leads to a much smaller longitudinal extension upon loading than the one calculated for ideal graphene. Nevertheless, the corresponding Young modulus shows minor variations as function of coverage. Furthermore, we provide evidence that hydrogenation only marginally affects the Poisson ratio