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.