Preface

The characterization of microscopic properties of materials over distances comparable with, or smaller than, the nearest atoms'separations and time-lapses roughly matching "in-shell" rattling periods has become of critical relevance in our society and has been the focus of intensive research, having both fundamental and applicative aspects. From the experimental side, a relevant portion of these studies is routinely carried out using large-scale X-ray of neutron facilities research and relies on the use of sources, as well as more conventional X-ray instrumentation.

Rather than providing a comprehensive overview of scientific opportunities offered by this field of research, this book aims to give the reader a taste of a few novel applications of two complementary scattering methods: high-resolution Inelastic X-ray Scattering (IXS) and Powder Diffraction (XPD), respectively characterizing dynamic (time-dependent) and static (structural) properties of materials at mesoscopic scales.

In a scattering measurement, a beam of particles-waves impinges on a sample at thermal equilibrium exchanging with it both **energy** and **momentum**, and being, as a result, scattered in all directions. If the perturbation induced on the target sample is weak, the dependence of the scattered beam intensity on the energy and momentum exchanged is uniquely informative of equilibrium properties of the sample. When the beam's particles involved are X-rays, such a scattering intensity ultimately conveys information on the positions and the movements of the target sample's molecules.

Conceptually, a scattering instrument resembles a microscope pointed on either the structure or the dynamics of the target sample. Indeed, it can be zoomed in or out to focus on various distances and time-lapses by a suitable variation of momentum and energy transfers, respectively. Since the latter variables both increase upon decreasing the incident beam wavelength, the use of short wavelength radiation, as X-rays, can shed light phenomena occurring over extremely short distances and timescales.

It is customary to distinguish between diffraction and inelastic scattering methods: the first elucidates static properties of materials through the scanning of the exchanged momentum, while the second offers the additional option of varying the frequency, as required to investigate dynamic phenomena.

As mentioned, this book mainly deals with two specific examples of inelastic scattering and a diffraction technique (IXS and XPD) and its chapters are organized as follows.

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).

In summary, we believe that this book is a useful reference for those who want to use these techniques to improve the current knowledge of microscopic properties of

> **Alessandro Cunsolo** Department of Physics,

Cidade Universitária, São Paulo (SP), Brazil

**Fabiano Yokaichiya**

Curitiba (PR), Brazil

United States

University of Wisconsin–Madison,

Instituto de Pesquisas Energéticas e Nucleares-IPEN,

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

Universidade Federal do Paraná,

materials.

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 preferable.

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 of the fabrication parameters.

In summary, we believe that this book is a useful reference for those who want to use these techniques to improve the current knowledge of microscopic properties of materials.
