Alessandro Cunsolo

By Alessandro Cunsolo

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.

Part of the book: Neutron Scattering

By Alessandro Cunsolo

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.

Part of the book: X-ray Scattering

By Alessandro Cunsolo

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.

Part of the book: Inelastic X-Ray Scattering and X-Ray Powder Diffraction Applications

By Alessio De Francesco, Luisa Scaccia, Martin Bohem and Alessandro Cunsolo

Nowadays, an increasing number of scattering measurements rely on the use of large-scale research facilities, which is usually granted after highly competitive peer-reviewing and typically for short-time lapses. The optimal use of the allocated time requires rigorous estimates on the reliability of the data analysis, as inferred from the limited statistical accuracy of the measurement. Bayesian inference approaches can significantly help this endeavor by providing investigators with much-needed guidance under challenging decisions on experimental time management. We propose here a method based on the real-time data analysis of running experiments, which fully exploits the core strengths of Bayes theorem. The procedure is implemented in sequential steps in which the spectral measurement is adjourned by summing to it successive acquisition runs, and the spectral modeling is upgraded accordingly. At each stage, the statistical accuracy of the measurement improves, and a more grounded joint posterior distribution is drawn and used as a prior in the subsequent data acquisition stage. The gradual reduction in the model parameters’ uncertainty down to the targets set a priori by experimenters provides a quantitative “success criterion,” which helps prevent oversampling during acquisition. A similar “on the fly” data modeling, might substantially change the way large-scale facilities operate.

Part of the book: Bayesian Inference