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.

Neutron inelastic scattering has been used to measure the magnetic excitations in powdered NiPS3, a quasi-two-dimensional antiferromagnet with spin S=1 on a honeycomb lattice. The spectra show clear, dispersive magnons with a ~7 meV gap at the Brillouin zone center. The data were fitted using a Heisenberg Hamiltonian with a single-ion anisotropy assuming no magnetic exchange between the honeycomb planes. Magnetic exchange interactions up to the third intraplanar nearest neighbor were required. The fits show robustly that NiPS3 has an easy-axis anisotropy with ?=0.3 meV and that the third nearest neighbor has a strong antiferromagnetic exchange of J3=-6.90 meV. The data can be fitted reasonably well with either J1<0 or J1>0, however, the best quantitative agreement with high-resolution data indicates that the nearest-neighbor interaction is ferromagnetic with J1=1.9 meV and that the second nearest-neighbor exchange is small and antiferromagnetic with J2=-0.1 meV. The dispersion has a minimum in the Brillouin zone corner that is slightly larger than that at the Brillouin zone center, indicating that the magnetic structure of NiPS3 is close to being unstable. © 2018 American Physical Society.

We have investigated how the propagation of sound-like modes in liquid water is affected by the presence of nanoparticles at low concentration. Inelastic X ray scattering spectra clearly show the drastic effect of the immersion of 50 nm sized golden nanoparticles on the collective dynamics of room temperature water, despite the very diluted character of the suspension. By using a Bayesian approach implemented through a Reversible Jump - Markov Chain Monte Carlo algorithm, the data analysis provided evidence about the switching-off of the water THz dynamics and that only the excitations propagating inside the nanoparticles survive in the solution. These results may open new perspectives on the design and development of new materials, especially when the tuning of the heat transport properties needs to be implemented.

The control of phonon propagation in nanoparticle arrays is one of the new frontiers of nanotechnology, potentially enabling the discovery of materials with unknown functionalities for potential innovative applications. The exploration of the terahertz window appears quite promising as phonons in this range are the leading carriers of heat transport in insulators and their control is the key to implement devices for heat flow management. Unfortunately, this scientific field is still in its infancy and even a basic topic such as the influence of floating nanoparticles on the terahertz phonon propagation of a colloidal suspension still eludes a firm answer. Shedding some light on this topic is the main motivation of the present work, which focuses an Inelastic X-Ray Scattering (IXS) measurements on a dilute suspension of Au nano-spheres in water. Measured spectra showed a non-trivial and unexpected shape displaying multiple inelastic features that, based on a Bayesian inference analysis, we assign to phonon modes propagating throughout the nanoparticle interior. Surprisingly, the spectra bear no evidence of propagating modes, which are known to dominate the spectrum of pure water, owing to the scattering that these modes suffer from the sparse nanoparticles in suspension. In perspective, this finding may inspire simple routes to manipulate high-frequency acoustic propagation in hybrid - liquid and solid- materials.

Very recent papers about the self dynamics of Lennard-Jones model fluids clearly demonstrated that the properties of the spectrum Z(w) of the velocity autocorrelation function (VAF) fully justify the identification of Z(w) with the density of states (DoS) of the liquid and that access to this single-particle quantity is of invaluable help for the characterization of the whole dynamics of the system. Based on this identification and on the recent progress in the theory of correlation functions we verified the effectiveness of a method that opens the way to the experimental determination of the DoS of a liquid, otherwise only accessible by simulations of the VAF. We show that by means of multi-Lorentzian fits of the self dynamic structure factor Sself(Q,w) at various Q values, the Q to 0 extrapolation required to determine Z(w) from Sself(Q,w) can be performed smoothly, with the further advantage of by-passing completely the problems related to resolution broadening of either experimental (through incoherent neutron scattering measurements) or simulated self spectra. In the test-case we considered to probe the applicability of the method, and regarding the self dynamics of liquid Au as provided by ab initio simulations, further analysis of Z(w) revealed the presence, along with propagating sound waves, of lower frequency modes in liquid gold that were not observed before by means of dynamic structure factor measurements. Additional inspection of the transverse current-current correlation spectra definitely confirmed the transverse nature of such low-frequency excitations. As an unexpected and remarkable by-product of this work, we also demonstrate that only non-hydrodynamic modes contribute to the DoS of a liquid, thus establishing its purely microscopic origin.

Hydrogen bonding plays an essential role on intermolecular forces, and consequently on the thermodynamics of materials defined by this elusive bonding character. It determines the property of a vital liquid as water as well as many processes crucial for life. The longstanding controversy on the nature of the hydrogen bond (HB) can be settled by looking at the effect of a vanishing HB interaction on the microscopic properties of a given hydrogen-bonded fluid. This task suits the capabilities of computer simulations techniques, which allow to easily switch off HB interactions. We then use molecular dynamics to study the microscopic properties of methanol, a prototypical HB liquid. Fundamental aspects of the dynamics of methanol at room temperature were contextualised only very recently and its rich dynamics was found to have striking analogies with that of water. The lower temperature (200 K) considered in the present study led us to observe that the molecular centre-of-mass dynamics is dominated by four modes. Most importantly, the computational ability to switch on and off hydrogen bonds permitted us to identify which, among these modes, have a pure HB-origin. This clarifies the role of hydrogen bonds in liquid dynamics, disclosing new research opportunities and unexplored interpretation schemes.

To date, the BRISP spectrometer represents the state-of-the-art for every instrument aiming to perform Brillouin neutron scattering. Exploiting accurate ray-tracing McStas simulations, we investigate an improved configuration of the BRISP primary spectrometer to provide a higher flux at the sample position, while preserving all the present capabilities of the instrument. This configuration is based on a neutron guide system and is designed to fit the instrument platform with no modifications of the secondary spectrometer. These evaluations show that this setup can achieve a flux gain factor ranging from 3 to 6, depending on the wavelength. This can expand the experimental possibilities of BRISP towards smaller samples, possibly using also complex sample environments.

We show that by exploiting multi-Lorentzian fits of the self dynamic structure factor at various wavevectors it is possible to carefully perform the $Q \to 0$ extrapolation required to determine the spectrum $Z(\omega)$ of the velocity autocorrelation function of a liquid. The smooth $Q$-dependence of the fit parameters makes their extrapolation to $Q$=0 a simple procedure from which $Z(\omega)$ becomes computable, with the great advantage of solving the problems related to resolution broadening of either experimental or simulated self spectra. Determination of a single-particle property like the spectrum of the velocity autocorrelation function reveals crucial to understand the whole dynamics of the liquid. In fact, we demonstrate the clear link between the collective modes frequencies and the shape of the frequency distribution. In the specific case considered in this work, i.e. liquid Au, analysis of $Z(\omega)$ revealed the presence, along with propagating sound waves, of lower frequency modes that were not observed before by means of dynamic structure factor measurements. By exploiting ab initio simulations for this liquid metal we could also calculate the transverse current-current correlation spectra, and clearly identify the transverse nature of the above mentioned less energetic modes. Existence of propagating transverse excitations appears therefore to be quite a common feature of dense liquids. However, in some cases these are difficult to detect: we show here that the analysis of the single-particle dynamics is able to unveil their presence in a very effective way. The properties here shown to characterize $Z(\omega)$ and the information in it contained allow therefore to identify it with the density of states (DoS) of the liquid. Finally, as a side-output of this work, we provide our estimate of the self diffusion coefficient of liquid gold just above melting.

The relatively simple molecular structure of hydrogen-bonded (HB) systems is often belied by their exceptionally complex thermodynamic and microscopic behaviour. For this reason, after a thorough experimental, computational and theoretical scrutiny, the dynamics of molecules in HB systems still eludes a comprehensive understanding. Aiming at shedding some insight into this topic, we jointly used neutron Brillouin scattering and molecular dynamics simulations to probe the dynamics of a prototypical hydrogen-bonded alcohol, liquid methanol. The comparison with the most thoroughly investigated HB system, liquid water, pinpoints common behaviours of their THz microscopic dynamics, thereby providing additional information on the role of HB dynamics in these two systems. This study demonstrates that the dynamic behaviour of methanol is much richer than what so far known, and prompts us to establish striking analogies with the features of liquid and supercooled water. In particular, based on the strong differences between the structural properties of the two systems, our results suggest that the assignment of some dynamical properties to the tetrahedral character of water structure should be questioned. We finally highlight the similarities between the characteristic decay times of the time correlation function, as obtained from our data and the mean lifetime of hydrogen bond known in literature.

When the dynamics of liquids and disordered systems at mesoscopic level is investigated by means of inelastic scattering (e.g., neutron or x ray), spectra are often characterized by a poor definition of the excitation lines and spectroscopic features in general and one important issue is to establish howmany of these lines need to be included in the modeling function and to estimate their parameters. Furthermore, when strongly damped excitations are present, commonly used and widespread fitting algorithms are particularly affected by the choice of initial values of the parameters. An inadequate choice may lead to an inefficient exploration of the parameter space, resulting in the algorithm getting stuck in a local minimum. In this paper, we present a Bayesian approach to the analysis of neutron Brillouin scattering data in which the number of excitation lines is treated as unknown and estimated along with the other model parameters. We propose a joint estimation procedure based on a reversible-jump Markov chain Monte Carlo algorithm, which efficiently explores the parameter space, producing a probabilistic measure to quantify the uncertainty on the number of excitation lines as well as reliable parameter estimates. The method proposed could turn out of great importance in extracting physical information from experimental data, especially when the detection of spectral features is complicated not only because of the properties of the sample, but also because of the limited instrumental resolution and count statistics. The approach is tested on generated data set and then applied to real experimental spectra of neutron Brillouin scattering from a liquid metal, previously analyzed in a more traditional way.

The substantial upgrade in new generation reactor-based time-of-flight (ToF) spectrometers lies in their hugely increased detection area. For such instruments, the strong improvement is clearly the high neutron-collection power, and with this the count statistics achievable in relatively short times. Dealing with thousands of time channels and several tens of thousands of detection pixels is, however, quite punishing as soon as data handling and correction for various effects in real-geometry conditions are considered. Anisotropic multiple scattering evaluation, even in an approximate way, is surely the most demanding step in the general treatment of inelastic neutron data, and becomes a very hard task when "extreme" conditions are further imposed by a widely-extended detection geometry, as that typical of new or upgraded neutron ToF spectrometers such as BRISP, IN4C or IN5 at the Institut Laue Langevin in Grenoble. For this reason, we refreshed our approach to multiple scattering calculations, in order to obtain reasonably accurate real-geometry results in nearly real-time conditions. Our new code, though conceptually originating from a long standing experience of Monte Carlo (MC) integration techniques to extract (unnormalized) double and single scattering intensities, is now made particularly efficient in computing time both by a careful application of the "importance sampling" method used to calculate some of the required MC integrals, and by the choice of programming languages which allow for a heavy but efficient use of matrix algebra. The fast matrix manipulation performances offered by some languages thus allow to avoid the (far slower) nested-loop logic required by more traditional languages. The concepts at the basis of the algorithm and several implementation details are presented.

In this work we describe a Bayesian approach to the analysis of Neutron Brillouin Scattering (NBS) data. Specifically, when dealing with spectra related to liquids and disordered systems, which are typically characterized by a poor definition of the excitation lines and, generally speaking, of spectroscopic features, the central issue is to establish how many excitation modes are justified by the experimental data and to support the related choices about model parameters on a probability basis. Furthermore when overdamped excitations are present, commonly used and widespread fitting algorithms are particularly affected by the initial values of the parameters that may lead to an inefficient exploration of the parameters space and, consequently, to output results corresponding to a local minimum the algorithm is not able to escape from. The statistical method we discuss here could turn out of great importance in determining the reliability and significance of physical information extracted from experimental data, especially in those cases where the measurement of spectral features is rendered difficult not only by the kind of sample, but also by the limited instrumental resolution and count statistics. An algorithm based on Markov chain Monte Carlo and Reversible Jump techniques has been applied to model simulated data generated by different combination of several Damped Harmonic Oscillator functions. The output will be the most probable number of components in the simulated neutron Brillouin scattering spectra (and of course the posterior distribution function for the variable "number of lines") together with a posterior distribution function of all the relevant dynamical parameters. Finally we show how the algorithm manage to fit on real experimental data on liquid gold, collected on the Brillouin Spectrometer Brisp at the Institut Laue Langevin and how the results are consistent with the rigorous analysis already assessed in literature. We also envisage the very interesting possibility, offered by this approach, to apply physical constraints to fitting models, such as theoretically known sum rules or the finiteness of higher-order frequency moments of the dynamic structure factor.

Methanol is a hydrogen-bonded liquid of enormous importance in pure and applied physics and chemistry, and is the object of innumerable studies. Yet, the fundamental aspects of its molecular dynamics are still known only to a very poor extent. The study of the collective dynamics is hindered by the weakness of the acoustic excitations, which has led to the wrong conclusion that sound modes propagate only in a surprisingly narrow range of small wave vector values. Combined molecular dynamics simulations and neutron Brillouin scattering measurements reveal, however, quite a different situation. Methanol is shown, for the first time, to feature the normal viscoelastic behaviour typical of a large variety of liquids, including the arrest of acoustic propagation near the peak of the static structure factor. Besides this, however, two more excitations are detected in the molecular centre-of-mass dynamics structure factor, at frequencies, respectively, one lower and one higher than the acoustic frequency, both with negligible dispersion. The rich translational dynamics revealed by this study classifies methanol as a fluid partly similar to the most important hydrogen-bonded liquid: water.

Methanol is the simplest molecule containing a polar hydroxyl group and a non-polar methyl group, thus offering the possibility of studying the properties of small amphiphile systems in aqueous environments, as well as self-assembly phenomena. As for other alcohols it shows non-ideal behaviour when mixed with water and a large negative excess entropy that has been often attributed to an enhanced water ordering in the vicinity of hydrophobic groups. However the validity of such model has been questioned and alternative suggestions proposed. We have recently explored by means of quasielastic neutron scattering and MD simulations the possibility of observing anomalies in the dynamics of water and methanol in the mixtures that could be related with any of the available propositions. As part of this effort, the collective dynamics of pure methanol have also been measured using the BRISP spectrometer at the Institut Laue-Langevin (Grenoble, France). The experimental results have been analyzed in combination with the MD and show striking similarities with the collective dynamics of water. In particular a third high-frequency mode that in recent simulation results on supercooled water has been associated to four-coordinated molecules is also visible in methanol, suggesting that tetrahedrality is not an essential requisite for this mode to appear.

The extraction of physical quantitative information from inelastic Brillouin neutron scattering data is often a challenging task, especially when dealing with specific samples or anytime the scattering signal is very weak. These limiting conditions together with the effect of both instrument resolution and finite statistics make sometimes the data analysis and the estimation of relevant dynamical parameters similar to the amazing job of a sculptor who carves a beautiful and well defined figure from an unshaped block of marble. Moreover, when the collected spectra are poorly structured, classical algorithms struggle to fit the data, easily fall in local minima and results strongly depend on initial parameter values. Thus several solutions are apparently possible and the discernment of the researcher plays a heavy role. In addition, measured spectra often comprise an unknown number of structures or peaks of known parametric family. Choosing the number of such structures is an important issue, which is commonly dealt with using various criteria. These criteria though fail to provide a probability measure associated with the number of peaks and sometimes different criteria lead to different conclusions. We suggest a Bayesian approach to tackle these problems. Prior researcher information on any parameter can be incorporated in a sensible and systematic way that will allow a better fit to the spectra. Moreover results from this approach are in the form of probabilities, which one can use to compare the different possibilities for the number of peaks characterizing the spectra.

Comment on the significance of the excitation at 5 meV found in water with neutron spectroscopy.

Inelastic neutron scattering was applied to measure the acoustic-type excitations in the molten alkali halide rubidium bromide. For molten RbBr neutron scattering is mainly sensitive to the number density fluctuation spectrum and is not influenced by charge fluctuations. Utilizing a dedicated Brillouin scattering spectrometer, we focused on the small-wave-vector range. From inelastic excitations in the spectra a dispersion relation was obtained, which shows a large positive dispersion effect. This frequency enhancement is related to a viscoelastic response of the liquid at high frequencies. Towards small wave vectors we identify the transition to hydrodynamic behavior. This observation is supported by a transition of the sound velocity from a viscoelastic enhanced value to the adiabatic speed of sound for the acoustic-type excitations. Furthermore, the spectrum transforms into a line shape compatible with a prediction from hydrodynamics.

The neutron Time-of-Flight BRIllouin SPectrometer BRISP for inelastic neutron scattering at small angles was developed and constructed at ILLs High Flux Reactor for investigating a host of open scientific problems in the low momentum region with relatively high incoming neutron energies. With this dedicated instrument, the high-frequency dynamics of atomic nuclei and electron spins is studied in rather different materials. Originally planned for the investigation of disordered and magnetic systems, BRISP has immediately found a natural experimental extension to the study of those systems that have attracted in recent years a growing interest in the scientific community e.g. confined liquids, glasses, and biological macromolecules. A presentation of the instrument will be provided together with the illustration of some recent promising experiments.

Methanol is a hydrogen-bond liquid of fundamental importance in pure and applied physics and chemistry, particularly in mixtures with water, and innumerable papers deal with its properties. Yet, the fundamental aspects of microscopic dynamics, even in pure methanol, have not been clearly elucidated so far. The study of the collective dynamics is hindered by the weakness of the acoustic excitations, which has led to the erroneous conclusion that sound modes propagate only in a surprisingly narrow range of small wave vector values. New, accurate, molecular dynamics simulations joint to neutron Brillouin scattering measurements reveal, however, a different situation, reported in this paper. We have determined energy and damping of the acoustic modes in the whole range between the hydrodynamic regime, where the fluid can be viewed as a continuum, and the regime where the excitation wavelength decreases down to the order of intermolecular distances. Methanol is shown, for the first time, to feature the "normal" viscoelastic behaviour characterizing the dynamics of a large variety of liquids, including the arrest of sound mode propagation in the vicinity of the peak of the static structure factor. In addition to this first result, however, the presence of a second excitation with lower frequency, smaller damping and negligible dispersion is displayed. The translational intermolecular dynamics emerging from this study classifies methanol as a fluid having properties similar to those of water, where the presence of a double excitation is a long standing result although its interpretation has remained controversial for long time. However, this study provides a further quite remarkable result, namely the fact that the low-frequency mode seems to be present in the single-molecule dynamics as well. This opens a wide space to further research work, in two directions: one is a better understanding of the effect of hydrogen bonds in the microscopic molecular motions; the other is the problem of the presence of inelastic components, i.e. of characteristic frequencies, in single-particle fluids dynamics.