We present the full in-plane phonon dispersion of graphite obtained from inelastic x-ray scattering, including the optical and acoustic branches, as well as the mid-frequency range between the K and M points in the Brillouin zone, where experimental data have been unavailable so far. The existence of a Kohn anomaly at the K point is further supported. We fit a fifth-nearest neighbour force-constants model to the experimental data, making improved force-constants calculations of the phonon dispersion in both graphite and carbon nanotubes available.

According to textbook definitions 1 , there exists no physical observable able to distinguish a liquid from a gas beyond the critical point, and hence only a single fluid phase is defined. There are, however, some thermophysical quantities, having maxima that define a line emanating from the critical point, named 'the Widom line' 2 in the case of the constant-pressure specific heat. We determined the velocity of nanometric acoustic waves in supercritical fluid argon at high pressures by inelastic X-ray scattering and molecular dynamics simulations. Our study reveals a sharp transition on crossing the Widom line demonstrating how the supercritical region is actually divided into two regions that, although not connected by a first-order singularity, can be identified by different dynamical regimes: gas-like and liquid-like, reminiscent of the subcritical domains. These findings will pave the way to a deeper understanding of hot dense fluids, which are of paramount importance in fundamental and applied sciences. Throughout the past century great effort was devoted to the investigation of the physics of fluid systems: all of their thermodynamical properties in the phase diagram below the critical point are nowadays well known 3. On the other hand, experimental studies in the supercritical region have been limited so far, owing to technical difficulties. The fluid pressure-temperature (P-T) phase diagram includes a subcritical region with two different phases (liquid and gas, separated by the liquid-vapour coexistence line) and a single-phase supercritical region. Structural and dynamical investigations, aiming to extend the study of the fluid phase diagram well beyond the critical point play a crucial role in many fundamental and applied research fields, such as condensedmatter physics, Earth and planetary science, nanotechnology and waste management 4-8. From an experimental point of view, the challenge is to close the gap between studies on fluid and solid phases using diamond anvil cell (DAC) techniques 9-12 and studies on hot dense fluids by shock waves 13,14. As this gap typically overlaps with the supercritical fluid region, it is crucial to track the evolution of transport properties of fluids beyond the critical point. In the specific case of acoustic waves, most of the liquids show the so-called positive dispersion. This is an increase of the speed of sound as a function of wavelength from the continuum limit (λ → ∞)-in which the acoustic waves propagate adiabatically-to the short-wavelength limit, that is, on approaching the interparticle distances 15-17. The ultimate origin of this effect can be traced back to the presence of one (or more)

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The development of inelastic x-ray scattering with millielectron volt energy resolution at the European Synchrotron Radiation Facility in Grenoble, France, provides a method for studying high-frequency collective dynamics in disordered systems. This has led to the observation of propagating acoustic phonon-like excitations in glasses and glass-forming liquids down to wavelengths comparable to the interparticle distance. Using the inelastic x-ray scattering results on glycerol as a representative example, it is shown that the microscopic dynamic properties are related to the excess of vibrational states in glasses and to the consequences at the microscopic level of the liquid-glass transition. Moreover, they allow derivation of the infinite frequency sound velocity, a quantity related to the structural relaxation times and to the change of ergodicity at the liquid-glass transition.

The phonon dispersion relations of bulk hexagonal boron nitride have been determined from inelastic x-ray scattering measurements and analyzed by ab initio calculations. Experimental data and calculations show an outstanding agreement and reconcile the controversies raised by recent experimental data obtained by electron-energy loss spectroscopy and second-order Raman scattering. DOI: 10.1103/PhysRevLett.98.095503 PACS numbers: 63.20.Dj, 61.10.Eq, 63.10.+a, 71.15.Mb Besides their intermediate structure between twodimensional sheets and 3D crystals, layered compounds are relevant materials for storage of other compounds [1] and as potential building blocks for nanotubes [2]. Among these materials, graphite and hexagonal boron nitride (h-BN) have drawn most of the attention due to their simple hexagonal structure, their fascinating properties, and the successful realization of carbon-[3] and more recently BN [4 -6] nanotubes. A wide band gap semiconductor, h-BN, has been grown successfully very recently as a single crystal. It exhibits a lasing behavior at 5.8 eV that makes it attractive for optoelectronic applications in the ultraviolet energy range [7].Despite the tremendous effort devoted to the characterization of physical properties of h-BN, the lattice dynamics, responsible for the elastic and thermodynamic properties such as the heat capacity and the thermal expansion, are still under debate. First principles calculations are generally accepted as the most accurate theoretical description of the lattice dynamics [8]. Recently, for h-BN, the validity of state of the art ab initio calculations was put in doubt by two experiments: Rokuta et al. [9] reported the only experimental data available for the phonon dispersion relations by electron-energy loss spectroscopy (EELS) performed on a monolayer of h-BN deposited on a Ni(111) substrate. Among several deviations from ab initio calculations of the lattice dynamics both for a monolayer [10,11] and for bulk h-BN [12,13], the EELS data show a degeneracy at the K point between acoustic (ZA) and optical (ZO) modes polarized along the c axis. The origin of this degeneracy has not been clarified yet. More recently [14], second-order Raman spectra of single crystalline h-BN revealed two features that contested the predictions based on a simple doubling of the energy scale of ab initio calculations for the one-phonon density of states, suggesting deviations up to 40% for the calculated energy of the TA branch in the K-M region. Since h-BN is a relevant material for UV lasing, it is imperative to resolve the existing controversies and critically assess the quality of the ab initio calculations. Furthermore, we need exact information on the lattice dynamics in order to properly understand the contributions due to electron-phonon coupling observed in the cathodoluminescence and absorption spectra of h-BN [7] and BN nanotubes [15,16].In this Letter we address the above discrepancies in the vibrational properties by reporting inelastic x-ray scattering (IXS) measurements...

The five independent elastic moduli of single-crystalline graphite are determined using inelastic x-ray scattering. At room temperature the elastic moduli are, in units of GPa, C 11 = 1109, C 12 = 139, C 13 =0, C 33 = 38.7, and C 44 = 4.95. Our experimental results are compared with predictions of ab initio calculations and previously reported incomplete and contradictory data sets. We obtain an upper limit of 1.1 TPa for the on-axis Young's modulus of homogeneous carbon nanotube, thus providing important constraints for further theoretical advances and quantitative input to model elasticity in graphite nanotubes.

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