# Inelastic X-ray Scattering as a Probe of Terahertz Phonon Propagation in Nanoparticle Suspensions
###### Abstract  
This paper reviews recent inelastic X-ray scattering investigations of simple inhomogeneous materials, such as nanoparticle suspensions in liquids. All studies reported emphasize the ability of immersed nanoparticles to dampen or attenuate acoustic waves through the hosting medium, the effect becoming even more pronounced upon freezing. Additionally, the results show that suspended nanoparticles can cause the onset of non-acoustic modes in the system. Also, the crucial role of Bayesian analysis in guiding spectral line shape modeling and interpretation is discussed. In summary, the presented results demonstrate that the simple inclusion of a sparse amount of nanoparticles profoundly influences sound propagation through a medium. This finding can inspire new avenues in the emerging field of terahertz acoustic steering and manipulation.  
inelastic X-ray scattering; phonon propagation; phononics +
Footnote †: journal:  
The works discussed in this review suggest that, as a potential alternative method to impact terahertz sound damping, one can include structural heterogeneities in a fluid, such as floating nano-objects. The mismatch of elastic properties between the floating colloids and the hosting liquid hinders the propagation of sound waves through the system, decreasing their lifetime. In this case, the arrangement of nano-objects is not present at all.  
Regardless of the strategy adopted to impact sound propagation, a pivotal concern is the identification of best-suited characterization methods. Natural candidates are high-resolution inelastic X-ray (IXS) [16] or neutron scattering (INS) [17; 18] techniques. Conceptually, an inelastic spectrometer resembles a microscope \"pointed on the dynamics\", which one can zoom in on dynamic events occurring in a given system over increasingly small distances and time lapses upon the increase of the energy, \(E\), and the momentum, \(\hbar\mathbf{Q}\), exchanged in the scattering event; here, \(\mathbf{Q}\) is the wavevector transfer and \(h=h/2\pi\) with \(h\) the Plank constant. Notice that, due to the inherent isotropy of a disordered or a partially ordered system, the direction of the exchanged momentum is irrelevant, the parameter of interest being rather \(Q=|\mathbf{Q}|\).  
When dealing with a hybrid (liquid and solid state) system as an NP suspension, by increasing \(Q\) and \(E\), one could map the whole dynamic crossover between the hydrodynamic response and the intra-NP one. A host of recent IXS studies carried out by my research group focused on the dynamics of liquid suspensions along this crossover, demonstrating several non-trivial effects, including the ability of immersed NPs to decrease the lifetime and the amplitude density waves propagating through the hosting medium.  
These findings have a broad general interest as, in principle, they may suggest a simple method to manipulate sound propagation in a simple liquid. More recently, a similar effect was observed in an IXS measurement on a frozen suspension, thus demonstrating that embedded nanoparticles can also impact the sound properties of solid-state aggregates. A critical review of these IXS investigations is the main focus of this paper. Before discussing these results, it is important to remark that, even at the lowest \(Q\) values covered by these works, the probed phonon wavelengths were smaller than the NP size by almost an order of magnitude. Therefore, it is safe to assume that, in all cases, acoustic waves perceived the nanoparticles as infinitely massive, thus experiencing merely elastic collision at their interface.