Jan H. Los

Intrinsic ripples in graphene

The stability of two-dimensional (2D) layers and membranes is the subject of a long-standing theoretical debate. According to the so-called Mermin-Wagner theorem, long-wavelength fluctuations destroy the long-range order of 2D crystals. Similarly, 2D membranes embedded in a 3D space have a tendency to be crumpled. These fluctuations can, however, be suppressed by anharmonic coupling between bending and stretching modes meaning that a 2D membrane can exist but will exhibit strong height fluctuations. The discovery of graphene, the first truly 2D crystal, and the recent experimental observation of ripples in suspended graphene make these issues especially important. Besides the academic interest, understanding the mechanisms of the stability of graphene is crucial for understanding electronic transport in this material that is attracting so much interest owing to its unusual Dirac spectrum and electronic properties. We address the nature of these height fluctuations by means of atomistic Monte Carlo simulations based on a very accurate many-body interatomic potential for carbon. We find that ripples spontaneously appear owing to thermal fluctuations with a size distribution peaked around 80 A which is compatible with experimental findings (50-100 A). This unexpected result might be due to the multiplicity of chemical bonding in carbon.

Melting of graphene: from two to one dimension

The high temperature behaviour of graphene is studied by atomistic simulations based on an accurate interatomic potential for carbon. We find that clustering of Stone-Wales defects and formation of octagons are the first steps in the process of melting which proceeds via the formation of carbon chains. The molten state forms a three-dimensional network of entangled chains rather than a simple liquid. The melting temperature estimated from the two-dimensional Lindemann criterion and from extrapolation of our simulation for different heating rates is about 4900 K.

Atomistic simulations of structural and thermodynamic properties of bilayer graphene

Radboud University Nijmegen, Institute for Molecules and Materials,Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands(Dated: April 2, 2010)We study the structural and thermodynamic properties of bilayer graphene, a prototype two-layer membrane, by means of Monte Carlo simulations based on the empirical bond order potentialLCBOPII. We present the temperature dependence of lattice parameter, bending rigidity and hightemperature heat capacity as well as the correlation function of out-of-plane atomic displacements.The thermal expansion coefficient changes sign from negative to positive above ≈ 400 K, which islower than previously found for single layer graphene and close to the experimental value of bulkgraphite. The bending rigidity is twice as large than for single layer graphene, making the out-of-plane fluctuations smaller. The crossover from correlated to uncorrelated out-of-plane fluctuationsof the two carbon planes occurs for wavevectors shorter than ≈ 3 nm

Scaling properties of flexible membranes from atomistic simulations: Application to Graphene

Structure and thermodynamics of crystalline membranes are characterized by the long-wavelength behavior of the normal-normal correlation function G(q). We calculate G(q) by Monte Carlo and molecular dynamics simulations for a quasiharmonic model potential and for a realistic potential for graphene. To access the long-wavelength limit for finite-size systems (up to 40 000 atoms) we introduce a Monte Carlo sampling based on collective atomic moves (wave moves). We find a power-law behavior G(q)alpha q(-2+eta) with the same exponent eta approximate to 0.85 for both potentials. This finding supports, from the microscopic side, the adequacy of the scaling theory of membranes in the continuum medium approach, even for an extremely rigid material such as graphene.

Melting temperature of graphene

We present an approach to the melting of graphene based on nucleation theory for a first order phase transition from the two-dimensional (2D) solid to the 3D liquid via an intermediate quasi-2D liquid. The applicability of nucleation theory, supported by the results of systematic atomistic Monte Carlo simulations, provides an intrinsic definition of the melting temperature of graphene,

State-of-the-art models for the phase diagram of carbon and diamond nucleation

{T}_{m}

Scaling Behavior and Strain Dependence of In-Plane Elastic Properties of Graphene

, and allows us to determine it. We find

Thermal rippling behavior of graphane

{T}_{m}\ensuremath{\simeq}4510

Theoretical study of the nucleation/growth process of carbon clusters under pressure

K, about 250 K higher than that of graphite using the same interatomic interaction model. The found melting temperature is shown to be in good agreement with the asymptotic results of melting simulations for finite disks and ribbons of graphene. Our results strongly suggest that graphene is the most refractory of all known materials.

Liquid carbon: structure near the freezing line

We review recent developments in the modelling of the phase diagram and the kinetics of crystallization of carbon. In particular, we show that a particular class of bond-order potentials (the so-called LCBOP models) account well for many of the known structural and thermodynamic properties of carbon at high pressures and temperatures. We discuss the LCBOP models in some detail. In addition, we briefly review the ‘history’ of experimental and theoretical studies of the phase behaviour of carbon. Using a well-tested version of the LCBOP model (viz. LCBOPI+) we address some of the more controversial hypotheses concerning the phase behaviour of carbon, in particular: the suggestion that liquid carbon can exist in two phases separated by a first-order phase transition and the conjecture that diamonds could have formed by homogeneous nucleation in Uranus and Neptune.