Structure of graphite by neutron diffraction

Trucano, P.; Chen, Ruey

doi:10.1038/258136a0

Cited by 455 publications

(326 citation statements)

References 6 publications

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“…The narrow and intense Bragg spots confirm the good quality of the crystal investigated. From these patterns we obtained the lattice dimensions of a b 2:46 A, and c 6:7 A, which are in agreement with the reported values obtained from static neutron diffraction [14]. In order to enhance the contribution of interferences of bulk layers, we tuned the angle of incidence of the electrons so that the beam specular reflection coincides with the (0 0 14) Bragg spot, whose profile is displayed as an inset in Fig.…”

supporting

confidence: 74%

Structural Preablation Dynamics of Graphite Observed by Ultrafast Electron Crystallography

Carbone

Baum

Rudolf³

et al. 2008

Phys. Rev. Lett.

141

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By means of time-resolved electron crystallography, we report direct observation of the structural dynamics of graphite, providing new insights into the processes involving coherent lattice motions and ultrafast graphene ablation. When graphite is excited by an ultrashort laser pulse, the excited carriers reach their equilibrium in less then one picosecond by transferring heat to a subset of strongly coupled optical phonons. The time-resolved diffraction data show that on such a time scale the crystal undergoes a contraction whose velocity depends on the excitation fluence. The contraction is followed by a large expansion which, at sufficiently high fluence, leads to the ablation of entire graphene layers, as recently predicted theoretically. DOI: 10.1103/PhysRevLett.100.035501 PACS numbers: 61.82.ÿd, 07.78.+s, 63.20.Kÿ, 78.47.ÿp The unique semimetal physical properties of graphite and its chemical inertness make possible numerous applications [1][2][3] including the use in nuclear reactors [4,5]. When subjected to a shock, the structure distorts, and the ablation to form graphene [6] may result from its instability. It is of fundamental importance to visualize the associated dynamics with atomic-scale spatial and temporal resolutions. Here, by means of ultrafast electron crystallography, we report direct observation of the structural dynamics of graphite following an impulsive near infrared excitation. The diffraction shows that the structure of graphite first contracts perpendicular to the layer planes on the time scale of 0.5 to 3 ps, depending on fluence, and then nonthermally expands in 7 ps. The excitation fluence dependence of both processes indicates a distinct behavior. The highly anisotropic transfer of carrier energy to a subset of phonons of the quasi-2D-structure alters the forces between layers which control the time scale and amplitude of structural change. These atomic motions on different time scales for compression, expansion and restructuring determine the degree of the instability, which at sufficiently high fluences reaches that of graphene ablation [7,8], as predicted theoretically [9].Previous optical studies have focused on the carrier dynamics induced by both high [10,11] and low fluence [12] optical excitation, revealing features of the unique phonon excitations in quasi-two-dimensional graphite and the coherent modes involved. In order to resolve details of the structure, diffraction is our method of choice. In ultrafast electron crystallography, the probing wavelength is 0.07 Å at 30 keV electron acceleration energy, and we use femtosecond (fs) near infrared pulses (800 nm) for the optical excitation of the system of graphite. The overall resolution is determined by group velocity mismatch [13], but as shown here, by tilting the optical wave front, see the inset in Fig. 4, we are able to resolve subpicosecond coherent dynamics. Highly oriented and single crystal graphite were studied, and indeed the static diffraction patterns of both display the characteristic structural features...

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supporting

confidence: 74%

Structural Preablation Dynamics of Graphite Observed by Ultrafast Electron Crystallography

Carbone

Baum

Rudolf³

et al. 2008

Phys. Rev. Lett.

141

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“…For ideal graphene, the lattice constant found with our computational setup amounts to 2.47 Å which compares well to the experimental lattice constant of graphite, 2.46 Å. 71 Maxima correspond to class 1CF structures, minima to class nCF configurations.…”

Section: Edge Strainsupporting

confidence: 78%

Clar’s Theory, π-Electron Distribution, and Geometry of Graphene Nanoribbons

et al. 2010

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We show that Clar's theory of the aromatic sextet is a simple and powerful tool to predict the stability, the π-electron distribution, the geometry, the electronic/magnetic structure of graphene nanoribbons with different hydrogen edge terminations. We use density functional theory to obtain the equilibrium atomic positions, simulated scanning tunneling microscopy (STM) images, edge energies, band gaps, and edge-induced strains of graphene ribbons that we analyze in terms of Clar formulas. Based on their Clar representation, we propose a classification scheme for graphene ribbons that groups configurations with similar bond length alternations, STM patterns, and Raman spectra. Our simulations show how STM images and Raman spectra can be used to identify the type of edge termination.

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“…24. The experimental lattice parameters at room temperature obtained by several authors 48,[50][51][52][53] are consistent with one another. The in-plane negative thermal expansion at low temperatures 25,54 implies that the zero-temperature value of a is at most 0.001 Å larger than the room-temperature one and a Ϸ 2.462-2.464 Å.…”

Section: Density Functional Theory Calculationssupporting

confidence: 72%

Energetics of interlayer binding in graphite: The semiempirical approach revisited

2007

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We have developed a semiempirical method to obtain interlayer binding energy of graphite in the previous work ͓M. Hasegawa and K. Nishidate, Phys. Rev. B 70, 205431 ͑2004͔͒. In the present paper, we revisit this approach and develop an improved method, in which ab initio calculations based on the density functional theory ͑DFT͒ are also corrected through an empirical atom-atom van der Waals ͑vdW͒ interaction. The local density approximation ͑LDA͒ and generalized gradient approximation ͑GGA͒ are used in the DFT calculations. The parametrized damping function introduced to modify the asymptotic atom-atom vdW interaction is more flexible than the previous ones and covers a wider range of possibility in correcting for the approximate DFT calculations. The damping function is determined empirically by imposing the condition that the experimental interlayer spacing, in-plane lattice constant, and c-axis elastic constant are reproduced. We also require consistency between the LDA-and GGA-based methods ͑LDA+ vdW, GGA+ vdW͒ as the theoretically motivated necessary condition. The interlayer binding energy obtained by this method is 60.4 meV/atom at T = 0 K. The result of ϳ54 meV/atom at room temperature corrected by the thermal effect is consistent with the most recent experiment, 52± 5 eV/atom ͓R. Zacharia et al., Phys. Rev. B 69, 155406 ͑2004͔͒. The atom-atom vdW interaction obtained by the present semiempirical method favorably corrects for the overbinding and underbinding nature of the LDA and GGA, respectively, in the in-plane energetics of graphite. That interaction also provides a useful starting point for the studies of energetics of other graphitic systems such as fullerenes and carbon nanotubes.

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Structure of graphite by neutron diffraction

Cited by 455 publications

References 6 publications

Structural Preablation Dynamics of Graphite Observed by Ultrafast Electron Crystallography

Structural Preablation Dynamics of Graphite Observed by Ultrafast Electron Crystallography

Clar’s Theory, π-Electron Distribution, and Geometry of Graphene Nanoribbons

Energetics of interlayer binding in graphite: The semiempirical approach revisited

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