Parametric interatomic potential for graphene

Tewary, Vinod K.; Ye, Bo

doi:10.1103/physrevb.79.075442

Cited by 71 publications

(67 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…We found a GR Debye temperature of 1495 AE 50 K, between the values of diamond (2240 K) and graphite (402 K) [32]. This is in good agreement with the calculated out-of-plane Debye temperature of GR (1287 K) [33], thus suggesting that the out-of-plane atomic fluctuations, as found in the simulations [see Fig. 1(c)], play an important role.…”

supporting

confidence: 84%

Thermal Expansion of Supported and Freestanding Graphene: Lattice Constant versus Interatomic Distance

Pozzo

Alfè

Lacovig³

et al. 2011

Phys. Rev. Lett.

164

159

View full text Add to dashboard Cite

By using ab initio molecular dynamics calculations, we show that even where the graphene lattice constant contracts, as previously reported for freestanding graphene below room temperature, the average carbon-carbon distance increases with temperature, in both free and supported graphene. This results in a larger corrugation at higher temperature, which can affect the interaction between graphene and the supporting substrate. For a weakly interacting system as graphene=Irð111Þ, we confirm the results using an experimental approach which gives direct access to interatomic distances. DOI: 10.1103/PhysRevLett.106.135501 PACS numbers: 81.05.ue, 68.65.Àk, 65.80.Ck Graphene's (GR) mechanical [1] and thermal [2,3] properties are crucial for applications such as the cooling of electronic devices [4,5], but their microscopic mechanism is often not well understood [6], in contrast to that of many electronic phenomena [7][8][9][10]. A particular challenge lies in the fact that graphene, while being two dimensional, exists in a three-dimensional world, permitting low-lying vibrational excitations and the formation of large-scale ripples perpendicular to the plane [11,12]. This is also important because it introduces a difference between freestanding GR and the technologically more important supported material.In particular, the thermal expansion coefficient of GR and the underlying microscopic mechanism is currently being debated. For freestanding GR and below % 500-700 K, a state-of-the-art atomistic simulation [13], a nonequilibrium Green's function approach [14], and a harmonic density functional theory (HDFT) calculation [15,16] all show a decreasing in-plane lattice parameter a, i.e., a thermal contraction. Above 900 K or so, the two former techniques show a trend reversal with a thermal expansion, while in HDFT the contraction persists over the entire temperature range studied (up to 2500 K). Experiments clearly confirm the thermal contraction of a below room temperature [3,17], but no high temperature measurements have been reported.In order to clarify this issue and to gain insight into its microscopic origin, we present a study based on ab initio simulations and core level photoelectron spectroscopy. Temperature-dependent ab initio molecular dynamics (AIMD) calculations were performed on both freestanding and supported GR. We have used the VASP code [18] with the projector-augmented wave method [19,20], the Perdew-Burke-Ernzerhof exchange-correlation energy [21], and an efficient extrapolation for the charge density [22]. Single particle orbitals were expanded in plane waves with a cutoff of 400 eV. We used the NPT ensemble (constant particles number N, pressure P, and temperature T), as recently implemented in VASP [23,24]. For the present slab calculations, we only applied the constant pressure algorithm to the two lattice vectors parallel to the surface, leaving the third unchanged during the simulation.In the case of freestanding GR the calculations were done using unit cells of different sizes (8 Â 8, 10 Â...

show abstract

supporting

confidence: 84%

Thermal Expansion of Supported and Freestanding Graphene: Lattice Constant versus Interatomic Distance

Pozzo

Alfè

Lacovig³

et al. 2011

Phys. Rev. Lett.

164

159

View full text Add to dashboard Cite

show abstract

“…38 (c) Thermal conductance G per cross-sectional area A for graphene and related materials (symbols), compared to the theoretical ballistic limit, G ball /A (solid line). 8,11,74 (d) Expected scaling of thermal conductivity κ with sample length L in the quasi-ballistic regime, at T  300 K. The solid line is the ballistic limit, κ ball = (G ball /A)L, and dashed lines represent κ estimated with phonon mean free paths as labeled (see text), chosen to match experimental data for suspended graphene, 31 supported graphene, 39 and GNRs; GNR showing different types of defects (vacancies, grain boundaries, StoneWales defects, substitutional and functionalization defects, and wrinkles or folds), 22 that have a profound effect in tuning thermal transport in graphene. Also see Table I.…”

Section: Discussionmentioning

confidence: 99%

“…However, phonons dominate the specific heat of graphene at all practical temperatures 19,20 (>1 K), and the phonon specific heat 4 increases with temperature, [17][18][19][20] as shown in Figure 2. At very high temperatures 21 (approaching the in-plane Debye temperature 17,22 Θ D  2100 K), the specific heat is nearly constant at…”

Section: Specific Heat Of Graphene and Graphitementioning

confidence: 99%

Thermal properties of graphene: Fundamentals and applications

2012

View full text Add to dashboard Cite

this preprint draft may differ slightly from the final published versionGraphene is a two-dimensional (2D) material with over 100-fold anisotropy of heat flow between the in-plane and out-of-plane directions. High inplane thermal conductivity is due to covalent sp 2 bonding between carbon atoms, whereas out-of-plane heat flow is limited by weak van der Waals coupling.Herein, we review the thermal properties of graphene, including its specific heat and thermal conductivity (from diffusive to ballistic limits) and the influence of substrates, defects, and other atomic modifications. We also highlight practical applications in which the thermal properties of graphene play a role. For instance, graphene transistors and interconnects benefit from the high in-plane thermal conductivity, up to a certain channel length. However, weak thermal coupling with substrates implies that interfaces and contacts remain significant dissipation bottlenecks. Heat flow in graphene or graphene composites could also be tunable through a variety of means, including phonon scattering by substrates, edges or interfaces. Ultimately, the unusual thermal properties of graphene stem from its 2D nature, forming a rich playground for new discoveries of heat flow physics and potentially leading to novel thermal management applications.MRS Bull. 37, 1273Bull. 37, (2012 Pop/Varshney/Roy 2 IntroductionGraphene is a two-dimensional (2D) material, formed of a lattice of hexagonally arranged carbon atoms. Graphene is typically referred to as a single layer of graphite, although common references also exist to bilayer or trilayer graphene. (See the introductory article in this issue.) Most thermal properties of graphene are derived from those of graphite and bear the imprint of the highly anisotropic nature of this crystal. 1 For instance, the in-plane covalent sp 2 bonds between adjacent carbon atoms are among the strongest in nature (slightly stronger than the sp 3 bonds in diamond), with a bonding energy of approximately 2 5.9 eV. By contrast, the adjacent graphene planes within a graphite crystal are linked by weak van der Waals interactions 2 (~50 meV) with a spacing 3 of h ≈ 3.35Å. Figure 1a displays the typical ABAB (also known as Bernal) stacking of graphene sheets within a graphite crystal.The strong and anisotropic bonding and the low mass of the carbon atomsgive graphene and related materials unique thermal properties. In this article we survey these unusual properties and their connection with the character of the underlying lattice vibrations. We examine both specific heat and thermal conductivity of graphene and related materials, and the conditions for achieving ballistic, scattering-free heat flow. We also investigate the role of atomistic lattice modifications and defects in tuning the thermal properties of graphene. Finally we explore the role of heat conduction in potential device applications and the possibility of architectures that allow control over the thermal anisotropy. Phonon dispersion of grapheneTo understand the thermal ...

show abstract

“…In a wider temperature range (see the inset), the obtained TEC shows a strong temperature dependence below 1000 K (which is around half of the Debye temperature [32]). The obtained TEC decreases rapidly with decreasing temperature from 800 K and becomes negative at T α ≈ 358 K. At room temperature (300 K) its value is −6.64 × 10 −6 K −1 .…”

Section: -P1mentioning

confidence: 93%

Anharmonic effects on thermodynamic properties of a graphene monolayer

Silva¹,

Cândido²,

Rabelo³

et al. 2014

EPL

View full text Add to dashboard Cite

-We extend the unsymmetrized self-consistent-field method (USF) for anharmonic crystals to layered non-Bravais crystals to investigate structural, dynamical and thermodynamic properties of a free-standing graphene monolayer. In this theory, the main anharmonicity of the crystal lattice has been included and the quantum corrections are taken into account in an h-expansion for the one-particle density matrix. The obtained result for the thermal expansion coefficient (TEC) of graphene shows a strong temperature dependence and agrees with experimental results by Bao et al. (Nat. Nanotechnol., 4 (2009) 562). The obtained value of TEC at room temperature (300 K) is −6.4 × 10 −6 K −1 and it becomes positive for T > Tα = 358 K. We find that quantum effects are significant for T < 1000 K. The interatomic distance, effective amplitudes of the graphene lattice vibrations, adiabatic and isothermal bulk moduli, isobaric and isochoric heat capacities are also calculated and their temperature dependences are determined.

show abstract

Parametric interatomic potential for graphene

Cited by 71 publications

References 27 publications

Thermal Expansion of Supported and Freestanding Graphene: Lattice Constant versus Interatomic Distance

Thermal Expansion of Supported and Freestanding Graphene: Lattice Constant versus Interatomic Distance

Thermal properties of graphene: Fundamentals and applications

Anharmonic effects on thermodynamic properties of a graphene monolayer

Contact Info

Product

Resources

About