Inelastic X-Ray Scattering as a Probe of the Transition Between the Hydrodynamic and the Single Particle Regimes in Simple Fluids

In the last few decades, the study of the spectrum of density fluctuations in fluids at the transition from the continuous to the single particle regimes has attracted an increasing interest. Although the shape of the spectrum is well known in these two extreme limits, no theory firmly predicts its evolution in the broad crossover region. However, the development of inelastic X-ray scattering (IXS) has substantially expanded the potentialities of modern spectroscopy, thus, providing an unprecedented detailed mapping of such a crossover. A better understanding of the line-shape evolution in this intermediate regime is deemed to improve our knowledge of all dynamical processes occurring in a fluid from macroscopic to microscopic scales. The aim of this chapter is to review some relevant experimental contributions brought about by IXS in this field since its development toward the end of past millennium

Using X-ray as a Probe of the Terahertz Dynamics of Disordered Systems – Complementarity with Inelastic Neutron Scattering and Future Perspectivess

This Chapter is devoted to a general introduction of the high resolution (meV) inelastic x-ray scattering (IXS) technique. This starts from a theoretical derivation of the IXS cross section and the demostration of its link with the spectrum of density fluctuations. The complementarity of this technique with the other mesocopic spectrocopy method, inelastic neutron scattering (INS) is discussed in detail by emphasizing differences and similarities both from the practical and the teorethical points of view. Along with this general discussion, examples are given of both an existing IXS spectrometer and a new-concept one to be soon in operation. Finally, the result of a recent joint INS and IXS experiment on water, taking advantage of the complementarity of these two techniques, are described in the last paragraphs

The THz Spectrum of Density Fluctuations of Water: The Viscoelastic Regime

Relevant advances in the knowledge of the water dynamics at mesoscopic scales are reviewed, while mainly focusing on the contribution provided by high resolution inelastic X-ray scattering (IXS). In particular it is discussed how the use of IXS has improved our understanding of viscoelastic properties of water at THz frequencies. This specifically involves some solid-like features such as the onset of shear wave propagation, a sound velocity surprisingly similar to the one of ice, and an anomalously low sound absorption coefficient. All these properties can be explained by assuming the coupling of THz density fluctuations with a structural relaxation process connected to the breaking and forming of hydrogen bonds (HBs). This review also includes more recent IXS results demonstrating that, upon approaching supercritical conditions, relaxation phenomena in water gradually lose their structural character becoming essentially collisional in character. Furthermore, GHz spectroscopy results on supercooled water, suggesting the occurrence of a structural arrest, are discussed. An overview of the new opportunities offered by next generation IXS spectrometers finally concludes this review

High-Resolution Inelastic X-Ray Scattering: A Probe of Microscopic Density Fluctuations in Simple Fluids

The explicit form of the inelastic X-ray scattering, IXS, cross-section is derived within a time-dependent perturbative treatment of the scattering process. In this derivation, the double differential cross-section is obtained from the Fermi Golden Rule within a plane wave expansion of the vector potential. Furthermore, it is assumed throughout that the Thompson term of the perturbative Hamiltonian yields the overwhelming contribution to the scattering. The achievement of an explicit form for the double differential scattering cross-section rests on the validity of the adiabatic or Born-Oppenheimer approximation. As a result, it is here shown that that the IXS double differential cross-section is proportional to the spectrum of density fluctuations of the sample, which is thus the sample variable directly accessed by IXS measurements. Although the whole treatment is valid for monatomic systems only, under suitable approximations, it can be extended to molecular systems

Bayesian Approach for X-Ray and Neutron Scattering Spectroscopy

The rapidly improving performance of inelastic scattering instruments has prompted tremendous advances in our knowledge of the high-frequency dynamics of disordered systems, yet also imposing new demands to the data analysis and interpretation. This ongoing effort is likely to reach soon an impasse, unless new protocols are developed in the data modeling. This need stems from the increasingly detailed information sought for in typical line shape measurements, which often touches or crosses the boundaries imposed by the limited experimental accuracy. Given this scenario, the risk of a bias and an over-parametrized data modeling represents a concrete threat for further advances in the field. Being aware of the severity of the problem, we illustrate here the new hopes brought in this area by Bayesian inference methods. Making reference to recent literature results, we demonstrate the superior ability of these methods in providing a probabilistic and evidence-based modeling of experimental data. Most importantly, this approach can enable hypothesis test involving competitive line shape models and is intrinsically equipped with natural antidotes against the risk of over-parametrization as it naturally enforces the Occam maximum parsimony principle, which favors intrinsically simple models over overly complex ones

Application of a new ensemble conserving quantum dynamics simulation algorithm to liquidﾠpara-hydrogen andﾠortho-deuterium

We apply the Feynman-Kleinert Quasi-Classical Wigner (FK-QCW) method developed in our previous work [Smith et al., J. Chem. Phys. 142, 244112 (2015)] for the determination of the dynamic structure factor of liquid para-hydrogen and ortho-deuterium at state points of (T = 20.0 K, n = 21.24 nm−3) and (T = 23.0 K, n = 24.61 nm−3), respectively. When applied to this challenging system, it is shown that this new FK-QCW method consistently reproduces the experimental dynamic structure factor reported by Smith et al. [J. Chem. Phys. 140, 034501 (2014)] for all momentum transfers considered. This shows that FK-QCW provides a substantial improvement over the Feynman-Kleinert linearized path-integral method, in which purely classical dynamics are used. Furthermore, for small momentum transfers, it is shown that FK-QCW provides nearly the same results as ring-polymer molecular dynamics (RPMD), thus suggesting that FK-QCW provides a potentially more appealing algorithm than RPMD since it is not formally limited to correlation functions involving linear operators

Transverse dynamics of water across the melting point: A parallel neutron and x-ray inelastic scattering study

Joint inelastic neutron and x-ray scattering measurements have been performed on heavy water across the melting point. The spectra bear clear evidence of low- and high-frequency inelastic shoulders related to transverse and longitudinal modes, respectively. Upon increasing the momentum transfer, the spectral shape evolves from a viscoelastic regime, where the low-frequency mode is clearly over-damped, toward an elastic one where its propagation becomes instead allowed. The crossover between the two regimes occurs whenever both the characteristic frequency and the linewidth of the low-frequency mode match the inverse of the structural relaxation time. Furthermore, we observe that the frequency of the transverse mode undergoes a discontinuity across the melting, whose extent reduces upon increasing the exchanged momentum

Interpreting the Terahertz Spectrum of Complex Materials: The Unique Contribution of the Bayesian Analysis

In the last few decades, experimental studies of the terahertz spectrum of density fluctuations have considerably improved our knowledge of the mesoscopic dynamics of disordered materials, which also have imposed new demands on the data modelling and interpretation. Indeed, lineshape analyses are no longer limited to the phenomenological observation of inelastic features, as in the pioneering stage of Neutron or X-ray spectroscopy, rather aiming at the extraction from their shape of physically relevant quantities, as sound velocity and damping, relaxation times, or other transport coefficients. In this effort, researchers need to face both inherent and practical obstacles, respectively stemming from the highly damped nature of terahertz modes and the limited energy resolution, accessible kinematic region and statistical accuracy of the typical experimental outcome. To properly address these challenges, a global reconsideration of the lineshape modelling and the enforcement of evidence-based probabilistic inference is becoming crucial. Particularly compelling is the possibility of implementing Bayesian inference methods, which we illustrated here through an in-depth discussion of some results recently obtained in the analysis of Neutron and X-ray scattering results