**Abstract**

Gamma rays of energy 14.4 keV from excited 57Fe nuclei show a very narrow energy width of 4.67 neV by the Mössbauer effect. Mössbauer gamma rays are utilised as probe beams in unique quasi-elastic scattering spectroscopy with neVenergy resolution. The technique enables measurements of atomic/molecular dynamics on timescales between nanoseconds and microseconds for various condensed matter systems, such as supercooled liquids, glasses and soft materials. The microscopic dynamics is measured in time domain or energy domain based on synchrotron radiation using a time-domain interferometer or a nuclear Bragg monochromator, respectively. We introduce state-of-the-art spectroscopic techniques, application results and future perspectives of quasi-elastic Mössbauer gamma ray scattering based on synchrotron radiation.

**Keywords:** Mössbauer gamma ray, synchrotron radiation, quasi-elastic scattering, glass transition, slow dynamics

## **1. Introduction**

The recoilless nuclear excitation of a gamma ray and its reversal process of recoilless gamma ray emission were first reported by Mössbauer [1]. These phenomena occur in solids when the recoil momentum of gamma rays in absorption and emission processes is taken up by the whole crystal. Consistently, this physical phenomenon is referred to as the Mössbauer effect [2]. For 57Fe nuclei, the excitation energy to the first excited state is 14.4 keV, whereas the uncertainty width of the excited state *Γ*<sup>0</sup> 4*:*67 neV is relatively very narrow. Therefore, the gamma rays emitted from the excited 57Fe nuclei by the Mössbauer effect show an energy *E*<sup>0</sup>14.4 keV and a natural energy width *Γ*<sup>0</sup> 4.67 neV. The photon emitted by the nuclei is called the gamma ray because it originates at the nucleus. However, Mössbauer gamma rays have lower energy than gamma rays involved in astronomy physics and are, instead, closer to the energy range of hard X-rays. In this chapter, we refer to such gamma rays as Mössbauer gamma rays. In these cases, the ratio of the gamma rays' energy to the natural energy width reaches *<sup>Γ</sup>*0*=E*<sup>0</sup> <sup>10</sup>13, indicating that the Mössbauer gamma rays exhibit very high monochromaticity. The surrounding electrons affect nuclear excitation energies through hyperfine

interactions. Therefore, electronic states around the specific Mössbauer nuclei can be selectively studied from the measured nuclear excitation energies via the Mössbauer effect. This spectroscopic technique, known as Mössbauer spectroscopy, has been widely used for more than 40 elements and 70 nuclear species (referred to as the Mössbauer nuclear species) to resolve various challenges in the fields of chemistry, physics, geology and biology [2].

This chapter is organised as follows: In section 2, basic concepts of quasi-elastic scattering are introduced, and QEGS spectroscopic techniques are explained. In section 3, experimental results of application studies on several supercooled glass formers are described. In section 4, we conclude this chapter by describing future

*Synchrotron Radiation-Based Quasi-Elastic Scattering Using Mössbauer Gamma Ray…*

**2. Quasi-elastic scattering spectroscopy using Mössbauer gamma rays**

In this scattering process, gamma rays with wavevector *k* are emitted from the excited 57Fe nuclei by the Mössbauer effect and Mössbauer gamma rays impinge on a sample. The geometry of the resulting Rayleigh-scattering process is shown in **Figure 2**, where *k*<sup>0</sup> is the wavevector of the scattered gamma rays and *q* ¼ *k*<sup>0</sup> � *k* is the transferred momentum vector of the gamma rays to the sample [7]. The elec-

and *t* are the space coordinate and the time, respectively, *N* is the molecular number in the sample and *r<sup>i</sup>* is the centre position of atom *i*. In the momentum transfer

*<sup>i</sup>*¼<sup>1</sup> exp i*<sup>q</sup>* � *<sup>r</sup>i*ð Þ*<sup>t</sup>* � �. Due to atomic/molecular motions in the sample, the gamma rays transfer energy to the sample and vice versa. In quasi-elastic scattering processes, a neV-energy broadening of the gamma rays energy is observed, as shown in **Figure 2**. This peak broadening is due to energy transfers that occur at neVenergies, which are thus much smaller than the incident gamma rays' energy, for which we can thus assume j j *k* � *k*<sup>0</sup> j j. Consequently, the amplitude of the transferred momentum is *q* = 2 j j *k* sin(*θ*), where 2*θ* is the scattering angle. When the sample shows disordered structures, as in liquids and glasses, the relevant variable is the

*<sup>i</sup>*¼<sup>1</sup> *<sup>δ</sup>*ð Þ *<sup>r</sup>*�*ri*ð Þ*<sup>t</sup>* , where *<sup>r</sup>*

In this section, we introduce the quasi-elastic scattering technique using Mössbauer gamma rays. In section 2.1, basic concepts of the quasi-elastic scattering technique are described. In section 2.2, we introduce energy-domain spectroscopic techniques of QEGS using Mössbauer gamma rays from conventional RI and SR sources. In section 2.3, time-domain measurement techniques of QEGS spectros-

copy using single-line and multi-line TDI are described.

tron density field in the sample can be written as *<sup>ρ</sup>*ð Þ¼ *<sup>r</sup>; <sup>t</sup>* <sup>P</sup>*<sup>N</sup>*

(wavenumber) space, the density field *<sup>g</sup> <sup>q</sup>; <sup>t</sup>* � � is written as *<sup>g</sup> <sup>q</sup>; <sup>t</sup>* � � <sup>¼</sup> <sup>P</sup>*<sup>N</sup>*

*Schematic picture of the quasi-elastic scattering process of Mössbauer gamma rays from a sample.*

**2.1 Introduction to quasi-elastic scattering**

absolute value *q* rather than the vector *q*.

**Figure 2.**

**63**

perspectives of QEGS.

*DOI: http://dx.doi.org/10.5772/intechopen.88898*

Microscopic dynamics in condensed matter, which do not contain Mössbauer nuclear species, have been studied since the 1960s with Mössbauer gamma rays [3]. In these experiments, the Mössbauer effect is utilised to generate the monochromatic gamma rays from a radioactive isotope (RI) source, and a quasi-elastic scattering experiment is performed for some samples [3]. In this chapter, we refer to the methods as quasi-elastic gamma ray scattering (QEGS) spectroscopy based on conventional nomenclature, such as inelastic/quasi-elastic neutron/X-ray scattering though this method has often been referred to as the Rayleigh-scattering of Mössbauer radiation method. The neV-energy resolution of the gamma rays from 57Fe nuclei allows the dynamics to be measured on timescales of about 100 ns. However, the measurements require much longer times because gamma rays from RI sources do not have parallel beams with enough brilliance for the QEGS experiment.

Recently, synchrotron radiation (SR)-based QEGS spectroscopic techniques using a 57Fe-nuclear Bragg monochromator (NBM) [4, 5] and a time-domain interferometer (TDI) of 57Fe gamma rays [6] have been developed. These methods have enabled much faster measurements of the atomic/molecular dynamics than RIbased QEGS spectroscopy, owing to the high brilliance and directionality of the SR source. To date, alloys, supercooled molecular liquids, polymers, ionic liquid, liquid crystals and polymer nanocomposite systems have been studied by SR-based QEGS spectroscopy.

In this chapter, we consider Mössbauer gamma rays from 57Fe nuclei because the gamma ray is most frequently used for QEGS spectroscopy. The length scales of the density correlation function currently observable by SR-based QEGS spectroscopy using TDI range from 0.1 to 6 nm, and the fluctuation timescales vary from few nanoseconds to sub-microseconds, as shown in **Figure 1**. The figure demonstrates how QEGS spectroscopy enables us to study density fluctuations, which are quite difficult to study by conventional spectroscopies in the microscopic range. Many unsolved issues are related to these time and length scales, including microscopic activation processes, which are related to the nature of the glass transition, start to occur in glass-forming materials in the time and length scales with cooling.

#### **Figure 1.**

*Various experimental techniques and the covered time and length scales. Quasi-elastic scattering spectroscopy using gamma rays from 57Fe covers a unique time- and length-scale region.*

*Synchrotron Radiation-Based Quasi-Elastic Scattering Using Mössbauer Gamma Ray… DOI: http://dx.doi.org/10.5772/intechopen.88898*

This chapter is organised as follows: In section 2, basic concepts of quasi-elastic scattering are introduced, and QEGS spectroscopic techniques are explained. In section 3, experimental results of application studies on several supercooled glass formers are described. In section 4, we conclude this chapter by describing future perspectives of QEGS.

#### **2. Quasi-elastic scattering spectroscopy using Mössbauer gamma rays**

In this section, we introduce the quasi-elastic scattering technique using Mössbauer gamma rays. In section 2.1, basic concepts of the quasi-elastic scattering technique are described. In section 2.2, we introduce energy-domain spectroscopic techniques of QEGS using Mössbauer gamma rays from conventional RI and SR sources. In section 2.3, time-domain measurement techniques of QEGS spectroscopy using single-line and multi-line TDI are described.

#### **2.1 Introduction to quasi-elastic scattering**

In this scattering process, gamma rays with wavevector *k* are emitted from the excited 57Fe nuclei by the Mössbauer effect and Mössbauer gamma rays impinge on a sample. The geometry of the resulting Rayleigh-scattering process is shown in **Figure 2**, where *k*<sup>0</sup> is the wavevector of the scattered gamma rays and *q* ¼ *k*<sup>0</sup> � *k* is the transferred momentum vector of the gamma rays to the sample [7]. The electron density field in the sample can be written as *<sup>ρ</sup>*ð Þ¼ *<sup>r</sup>; <sup>t</sup>* <sup>P</sup>*<sup>N</sup> <sup>i</sup>*¼<sup>1</sup> *<sup>δ</sup>*ð Þ *<sup>r</sup>*�*ri*ð Þ*<sup>t</sup>* , where *<sup>r</sup>* and *t* are the space coordinate and the time, respectively, *N* is the molecular number in the sample and *r<sup>i</sup>* is the centre position of atom *i*. In the momentum transfer (wavenumber) space, the density field *<sup>g</sup> <sup>q</sup>; <sup>t</sup>* � � is written as *<sup>g</sup> <sup>q</sup>; <sup>t</sup>* � � <sup>¼</sup> <sup>P</sup>*<sup>N</sup> <sup>i</sup>*¼<sup>1</sup> exp i*<sup>q</sup>* � *<sup>r</sup>i*ð Þ*<sup>t</sup>* � �. Due to atomic/molecular motions in the sample, the gamma rays transfer energy to the sample and vice versa. In quasi-elastic scattering processes, a neV-energy broadening of the gamma rays energy is observed, as shown in **Figure 2**. This peak broadening is due to energy transfers that occur at neVenergies, which are thus much smaller than the incident gamma rays' energy, for which we can thus assume j j *k* � *k*<sup>0</sup> j j. Consequently, the amplitude of the transferred momentum is *q* = 2 j j *k* sin(*θ*), where 2*θ* is the scattering angle. When the sample shows disordered structures, as in liquids and glasses, the relevant variable is the absolute value *q* rather than the vector *q*.

**Figure 2.** *Schematic picture of the quasi-elastic scattering process of Mössbauer gamma rays from a sample.*

interactions. Therefore, electronic states around the specific Mössbauer nuclei can be selectively studied from the measured nuclear excitation energies via the

*Inelastic X-Ray Scattering and X-Ray Powder Diffraction Applications*

Mössbauer effect. This spectroscopic technique, known as Mössbauer spectroscopy, has been widely used for more than 40 elements and 70 nuclear species (referred to as the Mössbauer nuclear species) to resolve various challenges in the fields of

Microscopic dynamics in condensed matter, which do not contain Mössbauer nuclear species, have been studied since the 1960s with Mössbauer gamma rays [3]. In these experiments, the Mössbauer effect is utilised to generate the monochromatic gamma rays from a radioactive isotope (RI) source, and a quasi-elastic scattering experiment is performed for some samples [3]. In this chapter, we refer to the methods as quasi-elastic gamma ray scattering (QEGS) spectroscopy based on conventional nomenclature, such as inelastic/quasi-elastic neutron/X-ray scattering though this method has often been referred to as the Rayleigh-scattering of Mössbauer radiation method. The neV-energy resolution of the gamma rays from 57Fe nuclei allows the dynamics to be measured on timescales of about 100 ns. However, the measurements require much longer times because gamma rays from RI sources do

not have parallel beams with enough brilliance for the QEGS experiment.

occur in glass-forming materials in the time and length scales with cooling.

*Various experimental techniques and the covered time and length scales. Quasi-elastic scattering spectroscopy*

*using gamma rays from 57Fe covers a unique time- and length-scale region.*

Recently, synchrotron radiation (SR)-based QEGS spectroscopic techniques using a 57Fe-nuclear Bragg monochromator (NBM) [4, 5] and a time-domain interferometer (TDI) of 57Fe gamma rays [6] have been developed. These methods have enabled much faster measurements of the atomic/molecular dynamics than RIbased QEGS spectroscopy, owing to the high brilliance and directionality of the SR source. To date, alloys, supercooled molecular liquids, polymers, ionic liquid, liquid crystals and polymer nanocomposite systems have been studied by SR-based QEGS

In this chapter, we consider Mössbauer gamma rays from 57Fe nuclei because the gamma ray is most frequently used for QEGS spectroscopy. The length scales of the density correlation function currently observable by SR-based QEGS spectroscopy using TDI range from 0.1 to 6 nm, and the fluctuation timescales vary from few nanoseconds to sub-microseconds, as shown in **Figure 1**. The figure demonstrates how QEGS spectroscopy enables us to study density fluctuations, which are quite difficult to study by conventional spectroscopies in the microscopic range. Many unsolved issues are related to these time and length scales, including microscopic activation processes, which are related to the nature of the glass transition, start to

chemistry, physics, geology and biology [2].

spectroscopy.

**Figure 1.**

**62**

We introduce the spatial correlation function of the electron density *G*ð Þ*r* as *G*ð Þ¼ *r* h i *ρ*ð Þ *r***0**þ*r; t*<sup>0</sup> *ρ*ð Þ *r***0***; t*<sup>0</sup> *,* where h i ⋯ denotes the equilibrium average over *t*<sup>0</sup> and position *r***0**, and *r* is a distance. The static structure factor *S q* � � is defined as its space Fourier transform *S q* � � <sup>¼</sup> <sup>Ð</sup> *<sup>G</sup>*ð Þ*<sup>r</sup>* exp i*<sup>q</sup>* � *<sup>r</sup>* � �*dr*. For simple monoatomic liquids, the scattering intensity *I*(*q*) is related to *S q*ð Þ as *I*(*q*) = *NS q*ð Þ. From this definition, it appears that the scattering at a given *q* is mainly caused by atomic pair correlations roughly occurring over distances 2π/*q,* in a very simple picture. At atomic scales, *S q*ð Þ is obtained via X-ray and neutron diffraction experiments.

gamma rays from a sample is detected by an absorption spectroscopy method commonly used in Mössbauer spectroscopy (**Figure 3a**). A transmittance-type energy spectrum is obtained by scanning the velocity *v* of a movable 57Fe gamma ray absorber with a single-line excitation profile. The absorber acts as the energy analyser, since its velocity determines the relative energy shift *E* ¼ *E*0*v=*c via the Doppler effect, where c is the speed of light. RSMR measurements require ample measuring time (at least several weeks) to obtain a spectrum with enough statistics for analysis because the RI source emits gamma rays in all directions, and limited

*Synchrotron Radiation-Based Quasi-Elastic Scattering Using Mössbauer Gamma Ray…*

*2.2.2 SR-based QEGS spectroscopy using 57Fe-nuclear Bragg monochromator*

The QEGS-based energy-domain spectroscopic technique using an SR source was developed with the 57Fe-NBM [4, 5]. NBM is used for a specific condition, in which conventional X-ray diffraction by electrons is forbidden, while nuclear resonant diffraction with nuclear excitation and deexcitation processes is allowed. In such cases, we can detect almost pure Mössbauer gamma rays on a 10 neV-energy width scale due to the specific Bragg angle selectively from a very intense incident SR. Therefore, the SR-NBM system is often called as synchrotron Mössbauer source [10]. The SR-based QEGS experiment has higher efficiency than conventional RSMR using RI because the monochromatic gamma rays from the NBM exhibited high directivity [10]. Moreover, the energy width of the Mössbauer gamma ray probe could be controlled to be much larger than the natural-line width (i.e., up to μeV) [11]. This unique characteristic of SR-based QEGS spectroscopy using NBM allows us to measure microscopic dynamics up to sub-nanosecond timescales.

The time-domain spectroscopy of QEGS is achieved using TDI. In this section,

The measurement principles of QEGS using the simplest TDI (usually referred to as single-line TDI) are described here. We discuss TDI using Mössbauer gamma rays from 57Fe because it exhibits the highest utility among nuclear species potentially available for TDI. **Figure 4a** shows the schematic experimental setup [6, 12, 13]. First, we consider the nuclear forward scattering (NFS) case, which often provides a calibration for the QEGS measurement because it is not affected by the dynamics of the sample. In the upper panel of **Figure 4a**, we show the experimental design for the NFS experiment using TDI. The incident SR crosses two identical materials with a single-line 57Fe nuclear excitation profile corresponding to the nuclear time response function *G t*ð Þ ultimately detected by the detector. Most of the SR beam crosses the 57Fe materials without any interaction. A small portion

rays to emit when the excited 57Fe nuclei decay. The gamma rays travel undeflected towards the forward detector because of the high directivity inherited from the incident SR. The gamma rays can be distinguished from the much more intense SR because they are delayed from the SR pulse by a typical delay time coincident with the lifetime of the excited 57Fe nuclei (�100 ns). The upstream material is moved with a constant velocity to change the relative nuclear excitation energy *ΔE* through the Doppler effect and consequently the energy spectrum of the gamma rays at the detector position shows two peaks due to the difference in the gamma ray energy

) of SR excites the 57Fe nuclei in the materials, causing the gamma

flux is introduced to the sample.

*DOI: http://dx.doi.org/10.5772/intechopen.88898*

**2.3 Time-domain measurement of QEGS**

*2.3.1 SR-based QEGS using single-line TDI*

(typically �10�<sup>6</sup>

**65**

we introduce time-domain spectroscopic techniques.

We introduce the time and space correlation function *G*ð Þ¼ *r; t* h i *ρ*ð Þ *r***0**þ*r; t*<sup>0</sup> þ *t ρ*ð Þ *r***0***; t*<sup>0</sup> describing the microscopic structural dynamics. Its *q*domain representation, often called the intermediate scattering function, is *<sup>S</sup> <sup>q</sup>; <sup>t</sup>* � � <sup>¼</sup> <sup>Ð</sup> *<sup>G</sup>*ð Þ *<sup>r</sup>; <sup>t</sup>* exp i*<sup>q</sup>* � *<sup>r</sup>* � �*d<sup>r</sup>* and can be measured by neutron spin echo spectroscopy and photon correlation spectroscopy. The spectral intensity of the scattered gamma rays at a given *<sup>q</sup>* is *I q*ð Þ¼ *; <sup>E</sup> NS q*ð Þ *; <sup>E</sup>* , where *<sup>S</sup> <sup>q</sup>; <sup>E</sup>* � � <sup>¼</sup> <sup>Ð</sup> *<sup>G</sup>*ð Þ *<sup>r</sup>; <sup>t</sup>* exp i *<sup>q</sup>* � *<sup>r</sup>* � *tE=<sup>ħ</sup>* � � � � *dtd<sup>r</sup>* is called the dynamics structure factor*.* Inelastic/quasi-elastic X-ray scattering using meV-high energy resolution monochromators and neutron scattering using triple-axis spectrometers measure *S q*ð Þ *; E* . Both *S q*ð Þ *; E* and *S q*ð Þ *; t* show quantitatively equivalent information for *G r*ð Þ *; t* .

#### **2.2 Energy-domain spectroscopy of QEGS**

In this section, we consider QEGS-based energy-domain spectroscopic techniques using Mössbauer gamma rays from conventional RI and SR sources. **Figure 3a** shows the common experimental design of the technique [8, 9]. In the setup, monochromatic Mössbauer gamma rays impinge on the sample. The quasielastic broadening of the scattered gamma ray's energy is analysed by the 57Fe-Mössbauer absorber, as explained below. As **Figure 3b** shows, *S q*ð Þ *; E* is observed as a transmittance-type spectrum *I q*ð Þ *; E* , which is conceptually written as *I q*ð Þ *; <sup>E</sup>* <sup>∝</sup><sup>1</sup> � <sup>Ð</sup> *dE*0 *S q; E*<sup>0</sup> ð Þ*R E* � *E*<sup>0</sup> ð Þ*,* where *R E*ð Þ is the resolution function.
