High frequency dynamics in liquids and supercritical fluids: A comparative inelastic x-ray scattering study.

The microscopic dynamics of four prototype systems (water, ammonia, nitrogen, and neon) across the critical temperature has been investigated by means of high-resolution inelastic x-ray scattering. The experimental line shape has been described using a model based on the memory function formalism. Two main relaxations, the thermal and the structural one, were observed in all the investigated systems. We found that the microscopic mechanism driving the structural relaxation clearly changes, being mainly governed by intermolecular bond rearrangements below the critical temperature and by binary collisions above it. Moreover, we observed that the relative weight of the thermal relaxation systematically increases on approaching the critical temperature, thus allowing for the observation of a transition from an adiabatic to an isothermal regime of sound propagation. Finally, we found the presence of an additional instantaneous relaxation, likely related to the coupling between collective vibrational modes and intramolecular degrees of freedom.

Nonlinear optics in the X-ray regime: nonlinear waves and self-action effects.

We study the nonlinear refraction of X-rays in highly ionized condensed matter by using a classical model of a cold electron plasma in a lattice of still ions coupled with Maxwell equations. We discuss the existence and stability of nonlinear waves. As a real-world example, we consider beam self-defocusing in crystalline materials (B, C, Li, Na). We predict that nonlinear processes become comparable to the linear ones for focused beams with powers of the order of mc(3)/ro (approximately 10 GW), the classical electron power. As a consequence, nonlinear phenomena are expected in currently exploited X-ray Free-Electron Lasers and in their future developments.

High frequency dynamics and structural relaxation process in liquid ammonia.

The dynamic structure factor S(Q,omega) of liquid ammonia has been measured by inelastic x-ray scattering in the terahertz frequency region as a function of the temperature in the range of 220-298 K at a pressure P=85 bars. The data have been analyzed using the generalized hydrodynamic formalism with a three term memory function to take into account the thermal, the structural, (alpha) and the microscopic (mu) relaxation processes affecting the dynamics of the liquid. This allows to extract the temperature dependence of the structural relaxation time (tau(alpha)) and strength (Delta(alpha)). The former quantity follows an Arrhenius behavior with an activation energy E(a)=2.6+/-0.2 kcal/mol, while the latter is temperature independent suggesting that there are no changes in the interparticle potential and arrangement with T. The obtained results, compared with those already existing in liquid water and liquid hydrogen fluoride, suggest the strong influence of the connectivity of the molecular network on the structural relaxation.

High-frequency dynamics of liquid and supercritical water.

The dynamic structure factor S(Q,omega) of water has been determined by high-resolution inelastic x-ray scattering (IXS) in a momentum (Q) and energy (E) transfer range extending from 2 to 4 nm{-1} and from +/-40meV . IXS spectra have been recorded along an isobaric path (400bar) in a temperature (T) interval ranging from ambient up to supercritical (T>647K) conditions. The experimental data have been described in the frame of the generalized hydrodynamic theory, utilizing a model based on the memory function approach. This model allows identifying the active relaxation processes which affect the time decay of density fluctuations, as well as a direct determination of the Q , T , and density (rho) dependencies of the involved transport parameters. The experimental spectra are well described by considering three different relaxation processes: the thermal, the structural, and the instantaneous one. On approaching supercritical conditions, we observe that the microscopic mechanism responsible for the structural relaxation is no longer related to the making and breaking of intermolecular bonds, but to binary intermolecular collisions.

Structural and collisional relaxations in liquids and supercritical fluids.

The dynamic structure factor S(Q,omega) of both associated (water and ammonia) and simple fluids (nitrogen and neon) has been determined by high-resolution inelastic x-ray scattering in the 2-14 nm(-1) momentum transfer range. A line-shape analysis with a generalized hydrodynamic model was used to study the involved relaxation process and to characterize its strength and time scale. We observe that in the liquid phase such a process is governed by rearrangements of intermolecular bonds, whereas in the supercritical region it assumes a collisional nature.

High-frequency subsurface and bulk dynamics of liquid indium.

We have performed bulk and surface-sensitive inelastic x-ray scattering experiments on liquid indium with 3 meV energy resolution. The experimental data are well reproduced within a generalized hydrodynamic model including structural and microscopic relaxation processes. We find a longitudinal viscosity of 22 mPa s in the near-surface region compared to 7.4 mPa s in the bulk. The origin of the increase is associated with a slowing down of the collective dynamics in a subsurface region of 4.6 nm.

Evidence for a crossover in the frequency dependence of the acoustic attenuation in vitreous silica.

We report measurements of the sound attenuation coefficient in vitreous silica, for sound waves of wavelength between 50 and 80 nm, performed with the new inelastic UV light scattering technique. These data indicate that in silica glass a crossover between a temperature-dependent (at low frequency) and a temperature-independent (at high frequency) acoustic attenuation mechanism occurs at Q approximately equal to 0.15 nm(-1). The absence of any signature in the static structure factor at this Q value suggests that the observed crossover should be associated with local elastic constant fluctuations.

Observation of structural anisotropy and the onset of liquidlike motion during the nonthermal melting of InSb.

The melting dynamics of laser excited InSb have been studied with femtosecond x-ray diffraction. These measurements observe the delayed onset of diffusive atomic motion, signaling the appearance of liquidlike dynamics. They also demonstrate that the root-mean-squared displacement in the [111] direction increases faster than in the [110] direction after the first 500 fs. This structural anisotropy indicates that the initially generated fluid differs significantly from the equilibrium liquid.

Relaxation dynamics in (HF)x(H2O)1-x solutions.

The high-frequency dynamics of (HF)(x)(H(2)O)(1-x) solutions has been investigated by inelastic x-ray scattering. The measurements have been performed as a function of the concentration in the range x = 0.20-0.73 at fixed temperature T = 283 K. The results have been compared with similar data in pure water (x = 0) and pure hydrogen fluoride (x = 1). A viscoelastic analysis of the data highlights the presence of a relaxation process characterized by a relaxation time and a strength directly related to the presence of a hydrogen-bond network in the system. The comparison with the data on water and hydrogen fluoride shows that the structural relaxation time continuously decreases at increasing concentration of hydrogen fluoride passing from the value for water to the one for hydrogen fluoride tau(alphaHF), which is three times smaller. This is the consequence of a gradual decreasing number of constraints of the hydrogen-bond networks in passing from one liquid to the other.

Clocking femtosecond X rays.

Linear-accelerator-based sources will revolutionize ultrafast x-ray science due to their unprecedented brightness and short pulse duration. However, time-resolved studies at the resolution of the x-ray pulse duration are hampered by the inability to precisely synchronize an external laser to the accelerator. At the Sub-Picosecond Pulse Source at the Stanford Linear-Accelerator Center we solved this problem by measuring the arrival time of each high energy electron bunch with electro-optic sampling. This measurement indirectly determined the arrival time of each x-ray pulse relative to an external pump laser pulse with a time resolution of better than 60 fs rms.

Atomic-scale visualization of inertial dynamics.

The motion of atoms on interatomic potential energy surfaces is fundamental to the dynamics of liquids and solids. An accelerator-based source of femtosecond x-ray pulses allowed us to follow directly atomic displacements on an optically modified energy landscape, leading eventually to the transition from crystalline solid to disordered liquid. We show that, to first order in time, the dynamics are inertial, and we place constraints on the shape and curvature of the transition-state potential energy surface. Our measurements point toward analogies between this nonequilibrium phase transition and the short-time dynamics intrinsic to equilibrium liquids.

High-frequency longitudinal and transverse dynamics in water.

High-resolution, inelastic x-ray scattering measurements of the dynamic structure factor S (Q,omega) of liquid water have been performed for wave vectors Q between 4 and 30 nm(-1) in distinctly different thermodynamic conditions ( T=263-420 K ; at, or close to, ambient pressure and at P=2 kbar ). In agreement with previous inelastic x-ray and neutron studies, the presence of two inelastic contributions (one dispersing with Q and the other almost nondispersive) is confirmed. The study of their temperature and Q dependence provides strong support for a dynamics of liquid water controlled by the structural relaxation process. A viscoelastic analysis of the Q -dispersing mode, associated with the longitudinal dynamics, reveals that the sound velocity undergoes a complete transition from the adiabatic sound velocity ( c(0) ) (viscous limit) to the infinite-frequency sound velocity ( c(infinity) ) (elastic limit). On decreasing Q , as the transition regime is approached from the elastic side, we observe a decrease of the intensity of the second, weakly dispersing feature, which completely disappears when the viscous regime is reached. These findings unambiguously identify the second excitation to be a signature of the transverse dynamics with a longitudinal symmetry component, which becomes visible in S (Q,omega) as soon as the purely viscous regime is left.

Structural relaxation in liquid water by inelastic UV scattering.

Using the novel synchrotron radiation based inelastic ultraviolet scattering technique, the dynamic structure factor of normal and supercooled liquid water has been measured at a momentum transfer Q approximately equal to 0.1 nm(-1), in the temperature range 260-340 K. The structural (alpha) relaxation has been observed in the supercooled temperature region (T< or =273 K), where the inverse relaxation time matches the frequency of the probed sound modes. The T dependence of the relaxation time shows a diverging behavior with a critical temperature T approximately equal to 220 K. These results provide a unique experimental opportunity to frame the dynamics of water in the mode-coupling theory.

High-frequency acoustic modes in liquid gallium at the melting point.

The microscopic dynamics in liquid gallium at melting has been studied by inelastic x-ray scattering. We demonstrate the existence of acousticlike modes up to wave vectors above one-half of the first maximum of the static structure factor, at variance with earlier results from inelastic neutron scattering [F. J. Bermejo et al., Phys. Rev. E 49, 3133 (1994)]. Despite structural (extremely rich polymorphism) and electronic (mixed valence) peculiarities, the collective dynamics is strikingly similar to the one of van der Waals and metallic fluids. This result speaks in favor of the universality of the short time dynamics in monatomic liquids rather than of system-specific dynamics.

Evidence of short-time dynamical correlations in simple liquids.

We report a molecular dynamics study of the collective dynamics of a simple monatomic liquid--interacting through a two-body potential that mimics that of lithium--across the liquid-glass transition. In the glassy phase we find evidences of a fast relaxation process similar to that recently found in Lennard-Jones glasses. The origin of this process is ascribed to the topological disorder, i.e., to the dephasing of the different momentum Q Fourier components of the actual normal modes of vibration of the disordered structure. More important, we find that the fast relaxation persists in the liquid phase with almost no temperature dependence of its characteristic parameters (strength and relaxation time). We conclude, therefore, that in the liquid phase well above the melting point, at variance with the usual assumption of uncorrelated binary collisions, the short time particle motion is strongly correlated and can be described via a normal mode expansion of the atomic dynamics.

Pressure evolution of the high-frequency sound velocity in liquid water.

The high-frequency sound velocity v( infinity ) of liquid water has been determined to densities of 1.37 g/cm(3) by inelastic x-ray scattering. In comparison to the hydrodynamic sound velocity v(0), the increase of v( infinity ) with density is substantially less pronounced, indicating that, at high density, the hydrogen-bond network is decreasingly relevant to the physical properties of liquid water. Furthermore, we observe an anomaly in v( infinity ) at densities around 1.12 g/cm(3), contrasting the smooth density evolution of v(0).

Structural and microscopic relaxation processes in liquid hydrogen fluoride.

The high frequency collective dynamics of liquid hydrogen fluoride is studied by inelastic x-ray scattering on the coexistence curve at T = 239 K. The comparison with existing molecular dynamics simulations shows the existence of two active relaxation processes with characteristic time scales in the subpicosecond range. The observed scenario is very similar to that found in liquid water. This suggests that hydrogen bonded liquids behave similarly to other very different systems as simple and glass forming liquids, thus indicating that these two relaxation processes are universal features of the liquid state.

Deep inelastic atomic scattering of x rays in liquid neon.

An inelastic x-ray scattering (IXS) experiment in liquid neon has been performed in the +/-100 meV exchanged energy range and at exchanged wave numbers, q, comprised between 1 and 16 A(-1). At the highest probed q's a deep inelastic scattering regime is reached where the Ne core electrons, after collision with the x rays, recoil almost freely with an effective mass equal to the Ne atomic mass. IXS in this high q regime is here shown to provide quantitative information on the atomic momentum distribution of liquid Ne, thus supplying a complementary technique to neutron scattering. There are several open problems in quantum and classical liquids which can benefit from this complementarity.

Anomalous dispersion of longitudinal optical phonons in Nd(1.86)Ce(0.14)CuO(4+delta) determined by inelastic x-ray scattering.

The phonon dispersions of Nd(1.86)Ce(0.14)CuO(4+delta) along the [xi,0,0] direction have been determined by inelastic x-ray scattering. Compared to the undoped parent compound, the two highest longitudinal phonon branches, associated with the Cu-O bond stretching and out-of-plane oxygen vibration, are shifted to lower energies. Moreover, an anomalous softening of the bond-stretching band is observed at about q = (0.2,0,0). These signatures provide evidence for strong electron-phonon coupling in this electron-doped high-temperature superconductor.

Inelastic x-ray scattering study of the collective dynamics in liquid sodium.

Inelastic x-ray scattering data have been collected for liquid sodium at T=390 K, i.e., slightly above the melting point. Owing to the very high instrumental resolution, pushed up to 1.5 meV, it has been possible to determine accurately the dynamic structure factor S(Q,omega) in a wide wave-vector range, 1.5-15 nm(-1), and to investigate on the dynamical processes underlying the collective dynamics. A detailed analysis of the line shape of S(Q,omega), similarly to other liquid metals, reveals the coexistence of two different relaxation processes with slow and fast characteristic time scales. The present data lead to the conclusion that (i) the picture of the relaxation mechanism based on a simple viscoelastic model fails and (ii) although the comparison with other liquid metals reveals similar behavior, the data do not exhibit an exact scaling law as the principle of the corresponding state would predict.