**Alessandro Cunsolo**

Department of Physics, University of Wisconsin–Madison, United States

## **Margareth K. K. D. Franco**

Instituto de Pesquisas Energéticas e Nucleares-IPEN, Cidade Universitária, São Paulo (SP), Brazil

### **Fabiano Yokaichiya**

Universidade Federal do Paraná, Curitiba (PR), Brazil

The first, introductory chapter outlines relevant analytical steps toward a formal expression of the IXS cross-section, eventually demonstrating its direct link with spontaneous density fluctuations in fluids at equilibrium. It also provides an estimate of the count rate achievable in typical IXS measurements, succinctly comparing the outcome of an IXS measurement with a similar determination achieved by the complementary terahertz technique, Inelastic Neutron Scattering (INS).

Even from this introductory chapter, it readily appears that the IXS signal from disordered materials has a nearly structureless shape, whose interpretation is often hampered by a limited energy resolution and count statistics accuracy. Not uncommonly, these inherent difficulties are overlooked when analyzing the measured lineshape, while assuming overly invasive and inherently biased hypotheses on the analytical form of such a profile. Furthermore, these models are sometimes arbitrary or contain an unreasonably large number of free parameters. This course of events makes especially critical the need for a probabilistically grounded modeling of the lineshape. A substantial improvement can be achieved by implementing Bayesian inference methods, as discussed in Chapter 2. This chapter shows how Bayesian inference principles can be used to perform hypothesis tests involving competitive lineshape models. This approach inherently embodies, as a selection criterion, the "Occam razor" principle, which states that, among alternative explanations of some evidence, the one containing less adjustable parameters is always

Overall, the chapter illustrates the benefits of this approach for the interpretation of both frequency and time-resolved scattering results. This inherent versatility is of special value for IXS, which can also be implemented as time-domain spectroscopy, as discussed in Chapter 3. This chapter deals with the representation of IXS results in the direct (space-time) domain, rather than in the more conventional reciprocal (frequency-wave vector) one. Specifically, it shows how this representation makes the interpretation of results more straightforward. Chapter 4 illustrates the potentialities of ultra-high-resolution quasi-elastic Mössbauer gamma-ray spectroscopy with energy resolution in the neV-window. This unique performance enables the study of the microscopic dynamics over timescales included between nanoseconds and microseconds. Results can be obtained either in the time or the energy domain using either a time-domain interferometer or a nuclear Bragg monochromator, respectively.

As mentioned, the second technique dealt with in this book is the X-Ray Powder Diffraction (XPD), presented in Chapters 5 and 6. These chapters focus on the characterization of manufacturing materials using conventional X-ray laboratory instruments. Chapter 5 explores the XPD from steels to identify and quantify the phases, using the Rietveld method, a method potentially applicable in industrial environments. Chapter 6 illustrates in situ XPD results, aiming at studying the formations of secondary phases in titanium composite materials under the influence

preferable.

of the fabrication parameters.

**IV**

Section 1

Inelastic X-Ray Scattering

**1**

Section 1
