LN single crystals display several excellent properties, such as high piezoelectric, electrooptical, photoelastic, acousto-optic, and nonlinear optical coefficients. They are known to have very low acoustic losses, offering a great versatility as a substrate for integrated optic systems: a considerable number of optical devices have been developed based on LN, such as wave guides, surface acoustic wave (SAW) devices, electrooptical wavelength filters and polarization modulators, nonlinear frequency converters (frequency doubling and second harmonic generation), nonvolatile memories, and ultrafast optical processing systems. Its combination of electrooptical and photogalvanic effects makes it photorefractive without the need of applying an external electrical field, thus being able to be applied in holographic data storage. It offers also the possibility of being easily doped, in a controllable way, with optical-active ionic species, using standard techniques such as ion implantation or thermal diffusion.

>1000 (1 kHz)

Melting temperature (°C) 1260 Curie temperature (°C) 1210

Refractive index (ordinary), *n*0 2.296 Electrooptical coefficient, r33 (m/V) 30 × 10−12 Transparency window (μm) 0.4–5

Dielectric constant at RT (*ε*′)—c-axis 80 (100 kHz)

Dielectric loss at RT (tan *δ*)—c-axis ≈0 (100 kHz)

Coercive field (at 1210°C) (V/m) 20 Spontaneous polarization at RT (*Ps* [×10−2 C m−2]) 70 Piezoelectric coefficient (d33 [pC/N]) 6 Thermal conductivity at RT (W m−1 K−1) 3.92 The physical properties aforementioned are optimized for the case where LN is grown as a single crystal and with stoichiometric composition. Regarding the stoichiometry, LN has a relatively broad composition range, and therefore, it can be labeled as congruent lithium niobate (cLN, 48.35–48.6 mol% Li2O) and stoichiometric (sLN, ~50 mol% Li2O). **Figure 1** displays the phase diagram of the Li2O-Nb2O5 binary system, showing the possibility of growing pure LN crystals by using 50% up to ~52% of Nb2O5. It also shows the transition of ferroelectric phase to paraelectric by increasing the synthesis temperature and Nb2O5 content. The large majority of LN single crystals are grown by the conventional Czochralski method, which yields cLN single crystals. Some competitor methods have been developed for growing stoichiometric crystals, including the vapor transport equilibration (VTE) method, which is a post-grown procedure [4]. The former is more suitable for thin and small samples, because for larger and thicker crystals, very large solid-state diffusion times are required for the Li/Nb ratio equilibration. To attain larger stoichiometric single crystals, more direct growth methods can be applied, such as the double crucible Czochralski method with an automatic power supply [5, 6] or the high-temperature top-seeded solution growth (HTTSSG) method from the K2O-Li2O-Nb2O5 ternary mixture, which is the one capable of yielding compositions closest to 50 mol% Li2O [5, 7].

The nonlinear and photorefractive properties will generally degrade with the loss of stoichiometry and consequent increase of defects and impurity density. As a matter of fact, the congruent composition range is regarded as having an intrinsic defect structure which is dominated by lithium vacancies, known as the lithium vacancy model, which translates in Eq. (1) [6]:

$$[L\ell\_{L\ell}]\_{1-5\chi}[Nb\_{L\ell}]\_{x}[V\_{L\ell}]\_{4\chi}Nb\_{Nb}O\_3\tag{1}$$

In this model, as depicted in Eq. (1), for every four lithium vacancies created, a niobium ion occupies a lithium network site, assuring electrical charge neutrality. The cLN is not suitable for high-temperature applications, because degradation processes can start to occur for temperatures starting from 300°C [6, 8]. On the other hand, studies show that sLN can be stable

**Figure 1.** Phase diagram of the Li2O-Nb2O5 binary system [3].

up to temperatures of at least 900°C [6, 9], because some properties like the electrical conductivity do not change under thermal cycling up to such temperatures.

As it was aforementioned, the dominant process in the growth of LN single crystals is the Czochralski method. However, this method is known for its technical and economic drawbacks, as well as being time-consuming. Thus, alternative preparation processes have been researched and explored. Solid-state reaction processes generally require high processing temperatures (>1000°C), which lead to the loss of lithium by evaporation [10]. As a consequence, secondary crystalline phases such as Li3NbO4 and LiNb3O8 can be formed, changing the stoichiometry and deteriorating the properties. Wet chemistry methods, such as sol-gel methodologies and hydrothermal methods, can be good alternatives because they require lower processing temperatures, such as calcination and thermal-sintering treatments, and thus the formation of secondary phases can be minimized [10, 11]. Single crystals in the nanometer and micrometer size ranges can be synthesized at low temperatures, such as 240°C, by these methods [11]. When such methods are applied, typically polycrystalline LN samples are produced, i.e., a material composed by small single crystals in the micrometric or nanometric range randomly distributed with no evident preferential orientation. Polycrystalline LN finds a lot of applications, especially as thin films for integrated optic applications, although generally the properties of polycrystalline materials are not as good as their single-crystalline counterpart. For example, the piezoelectric properties of polycrystalline LN are inferior to the single crystal, and in the best case, they might approach them if all of its domains are perfectly orientated. Further, relative to single-crystalline thin films, the grain boundaries in polycrystalline films may lead to increased light scattering and larger optical losses in wave guides, which may reduce their utility and potentiality in some applications [12]. However, their production is cheaper and easier compared with the growth processes for single crystals, and all these cons and drawbacks have to be considered and well balanced for potential applications.

Amorphous LN is also important for some applications. In an amorphous material, there is no long-range order, and the network can be described as distorted unitary cells randomly oriented. LN single crystals and polycrystals have low electrical conductivity (~10−12 S/cm at 500 K for single crystals [13]), and ionic diffusion or mobility is reduced in these materials. However, the amorphous structure is always a more open structure compared with the crystalline composition or, in other words, has a smaller density, which promotes and facilitates the ionic diffusivity, making them suitable for technical application such as solid-state electrolytes for Li-ion batteries. In fact, the reported activation energies for the ionic diffusivity are considerably smaller (half in the 25–150°C temperature range [13]) in amorphous LN.

In this chapter, the structural and electrical characterization of LiNbO3 nanosized particles prepared by the Pechini route, also known in the sol-gel methodologies as the polymeric precursor route, is discussed. The powders obtained by drying the gel (base powder) were heat-treated for 4 h at temperatures between 400 and 1000°C, according to the differential thermal analysis (DTA) results. The sintering temperature revealed to be, as expected, an important parameter in controlling the development of secondary crystalline phases, and it was found that the powders sintered at 450°C contain only the LN phase, while those heattreated at 500°C already contain the secondary LiNb3O8 phase. Their structural characterization was performed using X-ray diffraction (XRD) in conjunction with Rietveld refinement, Raman spectroscopy, and scanning electron microscopy (SEM). The grains observed have sizes lower than 100 nm and an approximately spherical geometry. The electrical characterization of pellets made from the base powder heat-treated at 450°C was made by measuring the dc and ac conductivities and measuring the complex impedance (*Z*\*) in the temperature range between 200 and 360 K and in the frequency range between 100 Hz and 1 MHz. From the measured complex impedance values, the complex permittivity (*ε*\*) was calculated, since the geometrical characteristics of the pellets legitimate the use of the parallel plate capacitor model. The correlation between the structure and morphology with the electrical and dielectric properties is one of the main topics of the present chapter.

## **2. Structural, morphologic, and electrical properties**

## **2.1. Structural properties**

up to temperatures of at least 900°C [6, 9], because some properties like the electrical conduc-

As it was aforementioned, the dominant process in the growth of LN single crystals is the Czochralski method. However, this method is known for its technical and economic drawbacks, as well as being time-consuming. Thus, alternative preparation processes have been researched and explored. Solid-state reaction processes generally require high processing temperatures (>1000°C), which lead to the loss of lithium by evaporation [10]. As a consequence, secondary crystalline phases such as Li3NbO4 and LiNb3O8 can be formed, changing the stoichiometry and deteriorating the properties. Wet chemistry methods, such as sol-gel methodologies and hydrothermal methods, can be good alternatives because they require lower processing temperatures, such as calcination and thermal-sintering treatments, and thus the formation of secondary phases can be minimized [10, 11]. Single crystals in the nanometer and micrometer size ranges can be synthesized at low temperatures, such as 240°C, by these methods [11]. When such methods are applied, typically polycrystalline LN samples are produced, i.e., a material composed by small single crystals in the micrometric or nanometric range randomly distributed with no evident preferential orientation. Polycrystalline LN finds a lot of applications, especially as thin films for integrated optic applications, although generally the properties of polycrystalline materials are not as good as their single-crystalline counterpart. For example, the piezoelectric properties of polycrystalline LN are inferior to the single crystal, and in the best case, they might approach them if all of its domains are perfectly orientated. Further, relative to single-crystalline thin films, the grain boundaries in polycrystalline films may lead to increased light scattering and larger optical losses in wave guides, which may reduce their utility and potentiality in some applications [12]. However, their production is cheaper and easier compared with the growth processes for single crystals, and all these cons and drawbacks have to be considered and well balanced for potential applica-

Amorphous LN is also important for some applications. In an amorphous material, there is no long-range order, and the network can be described as distorted unitary cells randomly oriented. LN single crystals and polycrystals have low electrical conductivity (~10−12 S/cm at 500 K for single crystals [13]), and ionic diffusion or mobility is reduced in these materials. However, the amorphous structure is always a more open structure compared with the crystalline composition or, in other words, has a smaller density, which promotes and facilitates the ionic diffusivity, making them suitable for technical application such as solid-state electrolytes for Li-ion batteries. In fact, the reported activation energies for the ionic diffusivity are considerably smaller (half in the 25–150°C temperature range [13]) in amorphous LN.

In this chapter, the structural and electrical characterization of LiNbO3 nanosized particles prepared by the Pechini route, also known in the sol-gel methodologies as the polymeric precursor route, is discussed. The powders obtained by drying the gel (base powder) were heat-treated for 4 h at temperatures between 400 and 1000°C, according to the differential thermal analysis (DTA) results. The sintering temperature revealed to be, as expected, an important parameter in controlling the development of secondary crystalline phases, and it was found that the powders sintered at 450°C contain only the LN phase, while those heat-

tivity do not change under thermal cycling up to such temperatures.

44 Applications of Molecular Spectroscopy to Current Research in the Chemical and Biological Sciences

tions.

LN belongs to a group of materials whose crystalline structure is a perovskite. This structure has the typical chemical formula ABO3, where the cation A usually is too large for an effective complete packaging, causing a distortion in the unit cell and leading to a displacement of the O2− anions from their expected sites. However, in the case of LN, the distortion is related with the small radius of the lithium ion. For temperatures lower than 1415 K, which is the Curie temperature (*Tc*) of sLN, this material is in its ferroelectric state, and consequently, it exhibits a spontaneous polarization, due to a nonuniform charge distribution of the lithium and niobium ions. In this ferroelectric phase, this material has a trigonal crystalline structure, with threefold rotation symmetry around its c-axis. **Figure 2(a)** and **(c)** shows the atomic model of LN in its ferroelectric crystalline phase. In this configuration, the crystalline structure consists in layers of oxygen atoms parallel to each other with the Li+ and Nb5+ cations lying along the

**Figure 2.** (a) and (c) Atomic model of the LN ferroelectric phase. (b) Atomic model of the LN paraelectric phase. ∆Li indicates the displacement along the c-axis of the Li+ cations, represented as black spheres, while ∆Nb indicates the displacement along the c-axis of the Nb5+ cations. Both displacements are represented relatively to the center of the oxygen (red spheres) planes [14].

c-axis, surrounded by oxygen octahedra: in the unitary cell, one-third of the octahedral interstices are occupied by Li+ cations; another one-third by Nb5+ cations and the remaining (one-third) interstices are structural voids [2, 14].

As depicted in **Figure 2**, in the ferroelectric state, the displacement of the Li+ and Nb5+ cations relatively to the center of the oxygen planes originates a spontaneous polarization along the c-axis with a magnitude of 0.7 C/m2 at 300 K (see **Table 1**). The displacement can be up or down with respect to the oxygen sublattice, and both cations are displaced in the same direction because of the Coulomb repulsion. Above the Curie temperature, due to the thermal expansion of the crystalline lattice axes, the structure is no longer distorted, because the Li+ and Nb5+ cations move to lattice sites lying in the planes of the oxygen layers, as **Figure 2(b)** displays. Thus, the transition to the paraelectric state occurs, and LN ceases to exhibit a permanent spontaneous polarization [2, 14].

As it was stated in Section 1, polycrystalline LN is also of great technological importance. In this form, the structure can be described as composed by small single crystals in the micrometric or nanometric range randomly distributed with no evident preferential orientation. Relatively to the ferroelectricity, it is composed by several ferroelectric domains, which are regions with different orientations of the spontaneous polarization *Ps*. In this case, the thermodynamic potential for describing the ferroelectric phase transition has to account with a nonuniform *Ps* distribution, organized in domains, and therefore the domain depolarization energy *WE* and the energy of the domain walls *WW* are introduced in the potential [3].

The thermodynamic model for the single-crystal case, an "ideal" ferroelectric, does not need to include the former energy terms *WE* and *WW* and can be described by Eq. (2) [3]:

$$G\{P,T\} = G\_0 + \frac{a(T)}{2}P^2 + \frac{\beta(T)}{4}P^4 \tag{2}$$

This model is based on the second-order phase transition as described by Landau-Ginsburg; with at least a fourth-order polynomial in *P*, the polarization. *G*(*P*,*T*) is the Gibbs function, and *α* and *β* are second- and fourth-order expansion temperature-dependent terms. As it was said, this rather simple form applies for the case when *Ps* is uniform for all the material, as in the case of a single crystal. In the ferroelectric/paraelectric phase transition, the behavior of the plots of the type *G*(*P*,*T*) versus *P*, for different temperatures, is shown in **Figure 3** [3]. As it can be seen, for *T*2 and *T*0,, there is only one minimum, while for *T*1, in the ferroelectric phase, two minimum values exist, which correspond to the values of the spontaneous polarization *Ps* (can be positive or negative, according to the direction—**Figure 2**). These values can be determined by solving the differential (∂*G*/∂*P*)*Ps* = 0, resulting in = ± − for temperatures lower than *Tc* and *Ps* = 0 for temperatures higher than *Tc* [3]. The parameters *α* and *β* are related with the dielectric constants of LN, and more specifically, *α* can be expressed above *Tc*, in the paraelectric phase, according to the Curie-Weiss law shown in Eq. (3) [3, 15]:

Raman Spectroscopy and Scanning Electron Microscopy Structural Characterization of Lithium Niobate Nanoparticles Prepared by the Sol-Gel Process, Using X-Ray and Raman Spectroscopy and Scanning Electron Microscopy http://dx.doi.org/10.5772/64395 47

c-axis, surrounded by oxygen octahedra: in the unitary cell, one-third of the octahedral

relatively to the center of the oxygen planes originates a spontaneous polarization along the

with respect to the oxygen sublattice, and both cations are displaced in the same direction because of the Coulomb repulsion. Above the Curie temperature, due to the thermal expansion

cations move to lattice sites lying in the planes of the oxygen layers, as **Figure 2(b)** displays. Thus, the transition to the paraelectric state occurs, and LN ceases to exhibit a permanent

As it was stated in Section 1, polycrystalline LN is also of great technological importance. In this form, the structure can be described as composed by small single crystals in the micrometric or nanometric range randomly distributed with no evident preferential orientation. Relatively to the ferroelectricity, it is composed by several ferroelectric domains, which are regions with different orientations of the spontaneous polarization *Ps*. In this case, the thermodynamic potential for describing the ferroelectric phase transition has to account with a nonuniform *Ps* distribution, organized in domains, and therefore the domain depolarization

energy *WE* and the energy of the domain walls *WW* are introduced in the potential [3].

to include the former energy terms *WE* and *WW* and can be described by Eq. (2) [3]:

The thermodynamic model for the single-crystal case, an "ideal" ferroelectric, does not need

This model is based on the second-order phase transition as described by Landau-Ginsburg; with at least a fourth-order polynomial in *P*, the polarization. *G*(*P*,*T*) is the Gibbs function, and *α* and *β* are second- and fourth-order expansion temperature-dependent terms. As it was said, this rather simple form applies for the case when *Ps* is uniform for all the material, as in the case of a single crystal. In the ferroelectric/paraelectric phase transition, the behavior of the plots of the type *G*(*P*,*T*) versus *P*, for different temperatures, is shown in **Figure 3** [3]. As it can

minimum values exist, which correspond to the values of the spontaneous polarization *Ps* (can be positive or negative, according to the direction—**Figure 2**). These values can be determined

*Tc* and *Ps* = 0 for temperatures higher than *Tc* [3]. The parameters *α* and *β* are related with the dielectric constants of LN, and more specifically, *α* can be expressed above *Tc*, in the paraelectric

by solving the differential (∂*G*/∂*P*)*Ps* = 0, resulting in = ± −

phase, according to the Curie-Weiss law shown in Eq. (3) [3, 15]:

there is only one minimum, while for *T*1, in the ferroelectric phase, two

of the crystalline lattice axes, the structure is no longer distorted, because the Li+

As depicted in **Figure 2**, in the ferroelectric state, the displacement of the Li+

46 Applications of Molecular Spectroscopy to Current Research in the Chemical and Biological Sciences

cations; another one-third by Nb5+ cations and the remaining

at 300 K (see **Table 1**). The displacement can be up or down

and Nb5+ cations

and Nb5+

(2)

for temperatures lower than

interstices are occupied by Li+

c-axis with a magnitude of 0.7 C/m2

spontaneous polarization [2, 14].

be seen, for *T*2 and *T*0,,

(one-third) interstices are structural voids [2, 14].

$$\chi = \frac{1}{a} = \frac{c}{r - \tau\_c} \tag{3}$$

**Figure 3.** The Gibbs free energy in function of the polarization *P. T*0 is equal to *Tc*, and the quantitative relation between the temperatures is *T*1 < *T*0 < *T*2 [3].

where *χ* is the dielectric susceptibility and *C* is a material-dependent constant.

The above-considered model fails when predicting quantities such as the coercive field, both for congruent and stoichiometric LN, because the inversion mechanisms of *Ps* occur through the formation of ferroelectric domains and the model does not account with *Ps* discontinuities. However, this thermodynamic model can be improved to better characterize a ferroelectric material containing domains, according to Eq. (4) [3]:

$$G\{P,T\} = G\_0 + \int\_V \left[\frac{a}{2}P^2 + \frac{\beta}{4}P^4 + \frac{1}{2}\delta\{\nabla P\}^2\right]dV + W\_E + W\_W \tag{4}$$

As it was stated, the terms depolarization energy *WE* and the energy of the domain walls *WW* are here introduced. The integration volume, *WE* and *WW* depend on the domain structure and geometry. In [3] the *WE* and *WW* expressions are described for a simple periodic domain structure model. The manipulation of the structure and geometry of the domain walls in a ferroelectric such as LN was, and still is, an important subject of study, because depending on the technological application, some geometries/shapes may be preferred over others: for example, acoustic and optical frequency conversion devices will benefit with periodic gratings of antiparallel domains [15]. The domain shape will depend on the temperature at which they are created, through the application of external electric fields and also on the crystal stoichiometry/composition. When created at room temperature, they can show different shapes due to small variation of stoichiometric composition [15]. **Figure 4** shows the preferred shapes of domains created at 25 and 125°C, for a congruent LN. It is visible that the domains have a polygonal shape with six sides, known as *y* walls. Curiously, the domain shape as depicted in **Figure 4(a)** is the same for stoichiometric LN, while in other ferroelectric materials such as LiTaO3, the same does not happen [15].

**Figure 4.** Piezoelectric force microscopy phase contrast images obtained in a congruent LN. The domains were created at 25 and 125°C [15].

**Figure 5.** XRD spectra revealing the effect of heat treatments on amorphous LN prepared by complete hydrolysis of the LN double alkoxide [16].

As for the structure of amorphous LN, it was said that the network can be described as distorted unitary cells randomly oriented. **Figure 5** reveals the effect of heat treatments (HTs) on amorphous LN prepared by complete hydrolysis of the LN double alkoxide [16]. The XRD spectra of amorphous LN have the typical form of the spectrum for 473 K displayed in **Figure 5**, with two broad bands around 30 and 50–60°. These broad bands are a trademark of amorphous materials, and they are typically visible for diffraction angles where the crystalline phase has the most intense diffraction peaks, revealing at least a short-range-order preservation. The heat treatments promote the reconfiguration of the amorphous phase to a more thermodynamically stable crystalline phase; although for low treatment temperatures and times, the material may be composed by a heterogeneous mixture of an amorphous and a crystalline phase: for the heat treatment at 573 K for 0.5 h, it is still noticeable the coexistence of a broad band with the diffraction peaks of the LN crystalline phase [16]. The structure of amorphous LN was also described by Kitabatake et al. to be constructed from the network of NbO6 octahedra which contains a micronetwork similar to crystalline LN [17]. The high dielectric constant and a relaxation mechanism were attributed to the high mobility of the Li+ ion in the LN structure [17].

Going further on the structural properties, the Raman spectroscopy is a useful nondestructive technique to access about the structure and composition of materials. The Raman spectrum of LN will generally depend on its stoichiometry, i.e., the shape, width, and position of some Raman shifts may change according to the Li/Nb ratio [18]. Furthermore, the Li/Nb ratio of a given LN sample may be determined by analyzing the width of some Raman lines, for a given temperature [18, 19].

**Figure 4.** Piezoelectric force microscopy phase contrast images obtained in a congruent LN. The domains were created

48 Applications of Molecular Spectroscopy to Current Research in the Chemical and Biological Sciences

**Figure 5.** XRD spectra revealing the effect of heat treatments on amorphous LN prepared by complete hydrolysis of

As for the structure of amorphous LN, it was said that the network can be described as distorted unitary cells randomly oriented. **Figure 5** reveals the effect of heat treatments (HTs) on amorphous LN prepared by complete hydrolysis of the LN double alkoxide [16]. The XRD spectra of amorphous LN have the typical form of the spectrum for 473 K displayed in **Figure 5**, with two broad bands around 30 and 50–60°. These broad bands are a trademark of amorphous materials, and they are typically visible for diffraction angles where the crystalline phase has the most intense diffraction peaks, revealing at least a short-range-order preservation. The heat treatments promote the reconfiguration of the amorphous phase to a more thermodynamically stable crystalline phase; although for low treatment temperatures and times, the material may be composed by a heterogeneous mixture of an amorphous and a crystalline phase: for the heat treatment at 573 K for 0.5 h, it is still noticeable the coexistence

at 25 and 125°C [15].

the LN double alkoxide [16].

**Figure 6** exhibits experimental full width at half maximum (FWHM) values of the Raman lines detected at about 153 and 876 cm−1, for samples with different lithium contents (mol%) [19]. The measurements were carried out at room temperature (note that the Raman lines' width also depends on the temperature). The FWHM dependency with the Li content is approximately linear, and hence a calibration line can be obtained. The uncertainty related with the Li content determination by this method was calculated to be 0.05 mol%, with an estimated uncertainty of 0.2 cm−1 in the 876 cm−1 line FWHM and 0.1 cm−1 in the 153 cm−1 line [19]. Therefore, this technique can be a simple nondestructive method to estimate the Li/Nb ratio in LN crystals, with an excellent accuracy.

**Figure 6.** Full width at half maximum of the Raman lines at the wavenumbers 153 and 876 cm−1. The dots are experimental values obtained for samples with different lithium contents (mol%), at room temperature, and the lines are the linear least-squares fits [19].

**Figure 7** displays the Raman spectra of a nearly stoichiometric LN crystal, with *xc* = 49.7 %, and a congruent LN crystal with *xc* = 48.5 %, where *xc* is given by = + × 100 % [18]. According to the group theory, when belonging to the *R3c* spatial group, eighteen vibrational modes are to be expected, which can be reduced in the representation 4A1 + 9E + 5A2 [18]. The A2 vibrational modes are not active in Raman and FTIR (silent modes), while both A1 and E modes are active in Raman and FTIR. The A1 modes are polarized along the Z-axis, while the E modes represent vibrations along the X- and Y-axes (see **Figure 4**). Therefore, in the XYZ coordinate system, as indicated in **Figure 7**, Z-axis lies in the c-axis direction while the X-axis in the *a*-axis crystallographic direction. The Y-axis is perpendicular to Z and X. The notation represented in the same figure is a universally used notation first described by Damen et al. For example, in X(YZ)Y, the symbols inside the parenthesis are, from left to right, the polarization of the incident and scattered light, while the ones outside the parenthesis, from left to right, represent the directions of the incident and scattered light, respectively [20]. As depicted in **Figure 7**, the E(TO) transversal modes can be detected in the X(ZY)Z configuration, while E(TO) and E(LO) can be detected in both X(ZY)Z and X(YZ)Y configurations [18]. The A1(TO) phonons, represented in **Figure 7**, at right, can be detected in the X(ZZ)Y configuration. The spectra clearly show that there is a broadening of the lines in the congruent composition, relatively to the nearly stoichiometric, i.e., the nearly stoichiometric spectrum lines are more resolved. Furthermore, there are lines that are only clearly visible in the nearly stoichiometric LN, and thus vibrational mode attribution in congruent LN can be an incomplete task [18]. As a final remark, when dealing with polycrystalline LN, the discussion about the different possible configurations to detect different vibrational modes is not applicable, since in the polycrystalline sample, we have nano- or micrometric single crystals randomly oriented, and thus interaction volume of the laser beam with the sample will include all these different orientations. In Section 2.4, the case study, we include the Raman spectra of polycrystalline LN, where a typical overlapping of vibrational modes is visible. The overlapping is due to the fact that, as **Figure 7** shows, some of the E(TO + LO) and A1(TO) vibration modes are in the same wavenumber range, and consequently, they will overlap in the polycrystalline LN samples.

**Figure 7.** At left: Raman spectra of two LN crystals with composition *xc* = 49.7 % (nearly stoichiometric) and *xc* = 48.5 % (congruent), exhibiting the E(TO) and E(LO) vibrational modes. The arrows highlight lines that are more clearly visible in the nearly stoichiometric composition. At right: the configuration X(ZZ)Y allows the detection of the A1(TO) phonons [18].

## **2.2. Morphological characteristics**

modes are to be expected, which can be reduced in the representation 4A1 + 9E + 5A2 [18]. The A2 vibrational modes are not active in Raman and FTIR (silent modes), while both A1 and E modes are active in Raman and FTIR. The A1 modes are polarized along the Z-axis, while the E modes represent vibrations along the X- and Y-axes (see **Figure 4**). Therefore, in the XYZ coordinate system, as indicated in **Figure 7**, Z-axis lies in the c-axis direction while the X-axis in the *a*-axis crystallographic direction. The Y-axis is perpendicular to Z and X. The notation represented in the same figure is a universally used notation first described by Damen et al. For example, in X(YZ)Y, the symbols inside the parenthesis are, from left to right, the polarization of the incident and scattered light, while the ones outside the parenthesis, from left to right, represent the directions of the incident and scattered light, respectively [20]. As depicted in **Figure 7**, the E(TO) transversal modes can be detected in the X(ZY)Z configuration, while E(TO) and E(LO) can be detected in both X(ZY)Z and X(YZ)Y configurations [18]. The A1(TO) phonons, represented in **Figure 7**, at right, can be detected in the X(ZZ)Y configuration. The spectra clearly show that there is a broadening of the lines in the congruent composition, relatively to the nearly stoichiometric, i.e., the nearly stoichiometric spectrum lines are more resolved. Furthermore, there are lines that are only clearly visible in the nearly stoichiometric LN, and thus vibrational mode attribution in congruent LN can be an incomplete task [18]. As a final remark, when dealing with polycrystalline LN, the discussion about the different possible configurations to detect different vibrational modes is not applicable, since in the polycrystalline sample, we have nano- or micrometric single crystals randomly oriented, and thus interaction volume of the laser beam with the sample will include all these different orientations. In Section 2.4, the case study, we include the Raman spectra of polycrystalline LN, where a typical overlapping of vibrational modes is visible. The overlapping is due to the fact that, as **Figure 7** shows, some of the E(TO + LO) and A1(TO) vibration modes are in the same wavenumber range, and consequently, they will overlap in the polycrystalline LN

50 Applications of Molecular Spectroscopy to Current Research in the Chemical and Biological Sciences

**Figure 7.** At left: Raman spectra of two LN crystals with composition *xc* = 49.7 % (nearly stoichiometric) and *xc* = 48.5 % (congruent), exhibiting the E(TO) and E(LO) vibrational modes. The arrows highlight lines that are more clearly visible in the nearly stoichiometric composition. At right: the configuration X(ZZ)Y allows the detection of the A1(TO) pho-

samples.

nons [18].

Morphology means "the study of form or pattern," and morphological characterization techniques, such as scanning electron microscopy (SEM) or transmission electron microscopy (TEM), allow to characterize the morphology of a given material. The morphological characteristics of LN will obviously rely upon the synthesis process, stoichiometry, and concentration of intrinsic defects. Depending on the synthesis process and crystal growth conditions, the grains observed for polycrystalline LN can display well-defined symmetries and a different range of sizes.

**Figure 8.** At left: SEM micrograph of polycrystalline LN prepared by a low-temperature hydrothermal route [21]. At right: SEM micrograph of polycrystalline LN prepared by the reactive molten salt synthesis (RMSS) process [10].

Zhan et al. [21] report in their work a low-temperature hydrothermal route to prepare polycrystalline LN. The XRD characterization revealed the formation of a pure hexagonal single phase of stoichiometric LN. The SEM micrograph of the LN powder, presented in **Figure 8**, shows a regular rhombohedral grain morphology, in agreement with the XRD results, although some imperfections, such as bended surfaces, are visible. The grain size ranges from 300 nm to approximately 1 μm. Kamali et al. [10] prepared polycrystalline LN using a modification of the molten salt synthesis (MSS): in conventional MSS, the mixed powders are heated above the liquids' temperature of the salt mixture, and this molten salt acts as the reaction medium, remaining inert during the synthesis. Salt mixtures such as KCl-NaCl are typically used. In the MSS modification approached by [10], the salt can react with other reagents during the synthesis process, being labeled as reactive molten salt synthesis (RMSS). They heat-treated at 973 K Nb2Cl5 powder in a LiCl molten salt, in a water-containing atmosphere, whereby the molten salt is one of the precursors for LN synthesis [10]. Using this RMSS approach, they produced single-phased LN, i.e., the loss by evaporation of Li2O was avoided. A SEM micrograph of the obtained LN particles is shown in **Figure 8**, on the right side [10]. The revealed morphology shows grains with dimensions ranging from several hundreds of nanometers to a few micrometers. The rhombohedral symmetry is also visible, although cleavages and bends are visible.

In **Figure 9**, it is visible a TEM bright-field micrograph of the polycrystalline LN prepared by the RMSS process. The inset on the right top shows a selected area electron diffraction pattern, being the area marked by the black arrow. The diffraction pattern is consistent with singlecrystalline rhombohedral LN. The inset on the left bottom shows a high-resolution micrograph of the area marked by the white arrow. The rhombohedral LN (104) atomic plane patterns are visible, with an interplanar spacing of 0.27 nm [10].

**Figure 9.** TEM bright-field micrograph of the LN particles prepared by the reactive molten salt synthesis (RMSS). Inset on the top right: selected area electron diffraction pattern of the area marked by the black arrow. Inset on the left bottom: high-resolution micrograph of the area marked by the white arrow [10].

The grain morphology will be determined by the growth conditions in such a way that the final morphology reflects the configuration with the minimum surface energy. In crystalline solid materials, the surface tension will depend on the crystallographic planes and direction, because to create a new surface, it is necessary to break bonds. At a constant pressure and temperature, the work required to create a new portion of surface *dAs* in a one-component system is given by Eq. (5) [22]:

$$dW\_{T,p} = \chi dA\_s \tag{5}$$

where *γ* is the surface energy (J/m2 ). This represents an excess of energy relatively to the bulk and will depend on the number of bonds of the surface (crystallographic plane) and their bond energy. The change of the Gibbs free energy can be written according to Eq. (6) [22]:

$$dG = -SdT + Vdp + \chi dA\_s \tag{6}$$

where *γ* is defined as in Eq. (7) [22]:

$$\boldsymbol{\chi} = \begin{pmatrix} \frac{\partial G}{\partial A\_{\boldsymbol{\beta}}} \end{pmatrix}\_{\boldsymbol{T}, \boldsymbol{P}} \tag{7}$$

The formation of new surfaces leads to a positive Gibbs energy contribution, whereby smaller particles will be unstable when compared with larger particles. The equilibrium morphology of the crystal will be determined by the surfaces with lower Gibbs energy, while surfaces of higher energy are sacrificed. Different crystallographic planes will have a different number of bonds per unit of area, and the bond strengths can also change according to the composition. Actually, very often when a surface energy value of a given crystalline material is indicated, it is in fact an average of the surface energy of the different crystalline faces. Taking as example a face-centered cubic lattice, when increasing the Miller indices, typically the atomic density of the planes decreases. The exception is that in the plane family [1 1 1], which contains six nearest neighbors, three bonds for each surface atom have to be broken when cutting the crystal along such direction, while for [1 0 0] and [1 1 0] planes, with lower atomic density, four and six bonds have to be broken, respectively [22]. Therefore, the surface energy of the former planes is larger relatively to the [1 1 1] plane family. Planes with the highest density have a lower surface energy and rate of growth, and therefore the final morphology of the crystal growth will be defined by the high-density atomic planes [21, 22]. However, several studies have indicated that a spherical morphology, which is the configuration that minimizes the surface area, is energetically more favorable for solids at high temperatures, and the difference of surface energy between different crystallographic planes becomes a less important factor [22].

#### **2.3. Electrical and dielectric properties**

crystalline rhombohedral LN. The inset on the left bottom shows a high-resolution micrograph of the area marked by the white arrow. The rhombohedral LN (104) atomic plane patterns are

52 Applications of Molecular Spectroscopy to Current Research in the Chemical and Biological Sciences

**Figure 9.** TEM bright-field micrograph of the LN particles prepared by the reactive molten salt synthesis (RMSS). Inset on the top right: selected area electron diffraction pattern of the area marked by the black arrow. Inset on the left bot-

The grain morphology will be determined by the growth conditions in such a way that the final morphology reflects the configuration with the minimum surface energy. In crystalline solid materials, the surface tension will depend on the crystallographic planes and direction, because to create a new surface, it is necessary to break bonds. At a constant pressure and temperature, the work required to create a new portion of surface *dAs* in a one-component

and will depend on the number of bonds of the surface (crystallographic plane) and their bond

The formation of new surfaces leads to a positive Gibbs energy contribution, whereby smaller particles will be unstable when compared with larger particles. The equilibrium morphology

energy. The change of the Gibbs free energy can be written according to Eq. (6) [22]:

). This represents an excess of energy relatively to the bulk

(5)

(6)

(7)

visible, with an interplanar spacing of 0.27 nm [10].

tom: high-resolution micrograph of the area marked by the white arrow [10].

system is given by Eq. (5) [22]:

where *γ* is the surface energy (J/m2

where *γ* is defined as in Eq. (7) [22]:

In this section, we will start to address the electrical properties of LN single crystalline and polycrystalline. Afterward, we will address polycrystalline LN. However, for both cases, it is important to analyze the properties for different temperature ranges and different stoichiometries, since both parameters have influence on the mechanisms of electrical conduction.

**Figure 10.** Dependence of a LN stoichiometric sample (sample 3 of **Figure 12**) total electrical conductivity with the oxygen partial pressure *p*0, at 1173 K (900°C). The solid line is the linear fit of the experimental values, while the dotted line is the extrapolation [6].

It is well known that the electrical conductivity of LN single crystals, as well as some optical properties, is strongly dependent on the surrounding environmental characteristics, in particular the partial oxygen pressure *p*0, as well as the Li/Nb ratio (stoichiometry). It was demonstrated that the electrical conductivity in high temperature ranges, between 600 and 1300 K, has a dependency of the type *p*0 −1/4 for low *p*0 ≲1 torr (1 torr ≈ 1/760 of a standard atmosphere). **Figure 10** presents the dependence of a sample with [Li]/[Nb] = 1 (sample 3; see inset table of **Figure 12**) total electrical conductivity with *p*0, at 1173 K (900°C) [6]. The solid line, which represents the linear fit of the experimental values, has a slope of approximately ¼ [6].

**Figure 11.** Dependence of *σ*dc and *E*A at room temperature with reduction temperature for different reduced congruent LN single crystals [23].

**Figure 12.** Arrhenius representation of the electrical conductivity of single-crystalline LN samples with different lithium contents, in the temperature range between 500 and 900°C. [VLi] represents the mol% of lithium vacancies, calculated through the lithium vacancy model (Eq. (1)). The activation energies (*E*A) for the different samples are also indicated (adapted with permission from [6]).

The electrical properties of LN are conditioned by the oxidation or reduction atmosphere, during thermal annealing: in a low *p*0 (≲1 torr) environment, it will consist of a reducing atmosphere. The effects of a reducing atmosphere on LN crystals are typically referred in the literature to originate the following modifications: the first is loss of oxygens from the structure, which leads to the release of electrons which are trapped by Nb5+ cations, consequently originating Nb4+ cations; the second is that the reducing atmosphere leads to the diffusion and loss of lithium cations, creating more lithium vacancies and an excess of niobium cations relatively to lithium, thus leading to the occupation of Li+ lattice sites by the Nb5+ species (the so-called anti-site niobium defects NbLi), according to the lithium vacancy model, presented in Eq. (1) [6, 23]. Dhar et al. studied the low temperature (77–373 K) dependency of dc electrical conduction in reduced congruent LN single crystals [23]. The samples had different levels of oxygen reduction according to the temperature of reduction, in a vacuum of approximately 10−5 mbar. **Figure 11** shows the dependence of the dc conductivity (*σ*dc) and activation energy (*E*A) at room temperature with the reduction temperature for different samples [23].

The presence of a maximum in *σ*dc and a minimum in *E*A can be explained by the Mott's variable range hopping (VRH) mechanism: the oxygens released during reduction can produce free electrons according to Eqs. (8) and (9) [23]:

$$2Nb^{5+} + O^{2-} \leftrightarrow 2Nb^{4+} + O\_v^{2-} + 1/2O\_2 \tag{8}$$

and

particular the partial oxygen pressure *p*0, as well as the Li/Nb ratio (stoichiometry). It was demonstrated that the electrical conductivity in high temperature ranges, between 600 and

54 Applications of Molecular Spectroscopy to Current Research in the Chemical and Biological Sciences

atmosphere). **Figure 10** presents the dependence of a sample with [Li]/[Nb] = 1 (sample 3; see inset table of **Figure 12**) total electrical conductivity with *p*0, at 1173 K (900°C) [6]. The solid line, which represents the linear fit of the experimental values, has a slope of approximately

**Figure 11.** Dependence of *σ*dc and *E*A at room temperature with reduction temperature for different reduced congruent

**Figure 12.** Arrhenius representation of the electrical conductivity of single-crystalline LN samples with different lithium contents, in the temperature range between 500 and 900°C. [VLi] represents the mol% of lithium vacancies, calculated through the lithium vacancy model (Eq. (1)). The activation energies (*E*A) for the different samples are also indicated

−1/4 for low *p*0 ≲1 torr (1 torr ≈ 1/760 of a standard

1300 K, has a dependency of the type *p*0

¼ [6].

LN single crystals [23].

(adapted with permission from [6]).

$$Nb^{4+} \leftrightarrow Nb^{5+} + e^- \tag{9}$$

and therefore the release of oxygen during reduction originates free electrons that can get trapped in niobium ions, and the conduction mechanism is assigned to polaronic hopping between Nb5+ and Nb4+ cations [23]. The maximum and minimum observed in **Figure 11** can be explained according to the ratio of Nb4+/Nb5+ states: for low reduction temperatures, few Nb4+ states will be created, while for high reduction temperatures, Nb4+ will predominate. However, for intermediate reduction temperature, there will be a case where we will get Nb4+/Nb5+ = 0.5. In that case, a maximum in the conductivity and a minimum in *E*A are to be expected, because the different oxidation states through which the polaronic hopping occurs are closer to each other [23]. They also concluded that actually the reduction annealing in low *p*0 does not lead to a significant loss of lithium ions, as it was aforementioned (and is frequently mentioned in the literature), because they have shown that when reheating the reduced samples in an oxygen-rich atmosphere, without any content of lithium vapor, the conductivity decreases and regains practically the same value as unreduced samples, which imply that annealing at low *p*0 does not have an important role in lithium loss [23]. For a polaronic VRH, the conductivity has a dependency as expressed in Eq. (10):

$$
\sigma\_{dc} = \sigma\_0 \exp\left[-\left(\frac{T\_0}{T}\right)^S\right] \tag{10}
$$

where *σ*0 is the pre-exponential factor, *T*0 is Mott's characteristic temperature, and *s* is the exponent for the VRH model. For reduced LN single crystals, the exponent *s* = ¼ is the one which better describes the temperature dependency of *σ*dc (check on [23] to see a log(*σ*dc) vs *T* − 1/4 plot).

For higher temperature ranges, in reduced LN single crystals, the VRH of polarons continues to be one of the mechanisms for the electrical conduction. However, and especially for congruent samples, lithium diffusion starts to be thermally activated, and when increasing the temperature, the main contribution for the total electrical conductivity may become ionic, assigned to lithium diffusion through lithium vacancies in the network (once again, we recall the lithium vacancy model) [6]. **Figure 12** shows the Arrhenius representation of the total electrical conductivity of LN single-crystalline samples with different lithium oxide molar percentages, in the temperature range between 773 and 1173 K [6]. The conductivity increases with the decrease of the Li2O content, indicating the influence of lithium diffusion through lithium vacancies. The ionic conductivity will be larger for congruent LN, because the density of lithium vacancies is larger.

With respect to the frequency dependency of the electrical properties, typically studied by means of impedance spectroscopy (IS), some results of the work done by Mansingh and Dhar will be addressed, namely, those related with the ac electrical conductivity (*σ*ac) and the dielectric constant (*ε*′) of congruent LN single crystals [24]. This work was published in 1985; however, more recent papers reporting dielectric studies as a function of frequency and temperature for LN single crystals are surprisingly not that easy to find, because most of them deal with polycrystalline LN or with LN doped with other elements.

**Figure 13.** Dependence of σac and σdc with the temperature (77–700 K) for different fixed frequencies (kHz): (•) DC, (○) 0.1, (x) 1, (Δ) 10, (□) 100 [24].

**Figure 13** shows for a congruent LN single crystal the dependence of *σ*ac and also *σ*dc (although in a more limited temperature range relatively to *σ*ac) with the temperature (77–700 K) for different frequencies, between 100 Hz and 100 kHz. It is visible that for lower temperatures *σ*ac presents high-frequency dispersion, and it is considerably higher than *σ*dc, while for higher temperatures it becomes practically frequency-independent and strongly temperaturedependent. Moreover, the temperature at which *σ*ac starts to have the same value as *σ*dc increases with the increase of the frequency. The mechanism for lower temperatures was found to be well described by a hopping-over-the-barrier (HOB) mechanism, and it was correlated with electron hopping between different valence states of the niobium, because of the reduction of Nb5+ due to oxygen deficiencies (as it was referred before) [24].

where *σ*0 is the pre-exponential factor, *T*0 is Mott's characteristic temperature, and *s* is the exponent for the VRH model. For reduced LN single crystals, the exponent *s* = ¼ is the one which better describes the temperature dependency of *σ*dc (check on [23] to see a log(*σ*dc) vs *T*

56 Applications of Molecular Spectroscopy to Current Research in the Chemical and Biological Sciences

For higher temperature ranges, in reduced LN single crystals, the VRH of polarons continues to be one of the mechanisms for the electrical conduction. However, and especially for congruent samples, lithium diffusion starts to be thermally activated, and when increasing the temperature, the main contribution for the total electrical conductivity may become ionic, assigned to lithium diffusion through lithium vacancies in the network (once again, we recall the lithium vacancy model) [6]. **Figure 12** shows the Arrhenius representation of the total electrical conductivity of LN single-crystalline samples with different lithium oxide molar percentages, in the temperature range between 773 and 1173 K [6]. The conductivity increases with the decrease of the Li2O content, indicating the influence of lithium diffusion through lithium vacancies. The ionic conductivity will be larger for congruent LN, because the density

With respect to the frequency dependency of the electrical properties, typically studied by means of impedance spectroscopy (IS), some results of the work done by Mansingh and Dhar will be addressed, namely, those related with the ac electrical conductivity (*σ*ac) and the dielectric constant (*ε*′) of congruent LN single crystals [24]. This work was published in 1985; however, more recent papers reporting dielectric studies as a function of frequency and temperature for LN single crystals are surprisingly not that easy to find, because most of them

**Figure 13.** Dependence of σac and σdc with the temperature (77–700 K) for different fixed frequencies (kHz): (•) DC, (○)

deal with polycrystalline LN or with LN doped with other elements.

− 1/4 plot).

of lithium vacancies is larger.

0.1, (x) 1, (Δ) 10, (□) 100 [24].

**Figure 14.** Frequency dependence of σac for some fixed temperatures (K): (◑) 77, (▼) 220, (▽) 320, (■) 415, (□) 475, (▲) 530, (∆) 580, (●) 625, (○) 650, (x) 680 [24].

**Figure 14** shows the frequency dependence of *σ*ac for some fixed temperatures. For lower temperatures, up to 530 K, the dependency of *σ*ac with the frequency can be expressed by the relation presented in Eq. (11) [24]:

(11)

**Figure 15.** Frequency dependency of the dielectric constant (ε') for different fixed temperatures (K): (◑) 77, (▲) 530, (∆) 580, (●) 625, (○) 650, (x) 680 [24].

This is the well-known relation found by Mott and Davis which describes the frequency dependency of *σ*ac for many amorphous and crystalline materials. The HOB mechanism presents a frequency dependency which can be described by Eq. (11). Furthermore, the HOB mechanism predicts a decrease of the frequency exponent *s* with the increase of temperature, and the values of *s* calculated by Mansingh and Dhar (~1 for 77 K and ~0.6 for 530 K) agree satisfactorily with the HOB model [24]. For higher temperatures, as it was aforementioned, *σ*ac becomes practically frequency-independent and with a magnitude close to *σ*dc. At the same time, for the same high temperature range (relatively to *σ*ac, see **Figure 14**), *ε*′ is characterized by a strong frequency dispersion, as shown in **Figure 15**.

The temperature dependence of *ε*′ for different fixed frequencies, between 100 Hz and 100 kHz, is also shown in **Figure 16**.

It can be noted in **Figure 16** that the temperature from which *ε*′ shows a sharp increase increases with the increase of frequency. So, from the presented plots of *σ*ac and *ε*′, it is evident that the temperature dependences show evidence of two distinct mechanisms for the conductivity. At low temperatures, the mechanism was already identified, the HOB mechanism with a high distribution of relaxation times. For higher temperatures, the strong *ε*′ dispersion is probably associated with the dc conduction mechanisms, while both ac and dc conductivities are determined by the same mechanism, long-range hopping of charge carriers [24]. A sample with thickness reduced to half, keeping the electrode surface area constant, was included in **Figure 16** to demonstrate that the sharp increase of *ε*′ is not related with the electrode barriers and spatial charge accumulation at the electrode/sample interface [24].

Raman Spectroscopy and Scanning Electron Microscopy Structural Characterization of Lithium Niobate Nanoparticles Prepared by the Sol-Gel Process, Using X-Ray and Raman Spectroscopy and Scanning Electron Microscopy http://dx.doi.org/10.5772/64395 59

(11)

**Figure 15.** Frequency dependency of the dielectric constant (ε') for different fixed temperatures (K): (◑) 77, (▲) 530, (∆)

58 Applications of Molecular Spectroscopy to Current Research in the Chemical and Biological Sciences

This is the well-known relation found by Mott and Davis which describes the frequency dependency of *σ*ac for many amorphous and crystalline materials. The HOB mechanism presents a frequency dependency which can be described by Eq. (11). Furthermore, the HOB mechanism predicts a decrease of the frequency exponent *s* with the increase of temperature, and the values of *s* calculated by Mansingh and Dhar (~1 for 77 K and ~0.6 for 530 K) agree satisfactorily with the HOB model [24]. For higher temperatures, as it was aforementioned, *σ*ac becomes practically frequency-independent and with a magnitude close to *σ*dc. At the same time, for the same high temperature range (relatively to *σ*ac, see **Figure 14**), *ε*′ is characterized

The temperature dependence of *ε*′ for different fixed frequencies, between 100 Hz and 100 kHz,

It can be noted in **Figure 16** that the temperature from which *ε*′ shows a sharp increase increases with the increase of frequency. So, from the presented plots of *σ*ac and *ε*′, it is evident that the temperature dependences show evidence of two distinct mechanisms for the conductivity. At low temperatures, the mechanism was already identified, the HOB mechanism with a high distribution of relaxation times. For higher temperatures, the strong *ε*′ dispersion is probably associated with the dc conduction mechanisms, while both ac and dc conductivities are determined by the same mechanism, long-range hopping of charge carriers [24]. A sample with thickness reduced to half, keeping the electrode surface area constant, was included in **Figure 16** to demonstrate that the sharp increase of *ε*′ is not related with the electrode barriers

580, (●) 625, (○) 650, (x) 680 [24].

is also shown in **Figure 16**.

by a strong frequency dispersion, as shown in **Figure 15**.

and spatial charge accumulation at the electrode/sample interface [24].

**Figure 16.** Temperature dependency of the dielectric constant (ε') for different fixed frequencies (kHz): (○) 0.1, (x) 1, (Δ) 10, (■) 100, (●) Sample with half of the thickness, keeping the same area [24].

We will end this section by briefly addressing the electrical and dielectric properties of polycrystalline LN. In such case, the behavior of the referred properties can reflect the presence of grain boundaries in the material. This effect of grain boundaries can be more clearly seen in IS measurements, because the characteristic frequencies (or times) at which grain boundary processes occur are different from those that occur in the bulk of the grains, and therefore Nyquist diagrams [plot of the negative of the imaginary part of the impedance, −Im(Z), in the y-axis over the real part of the impedance, Re(Z), in the x-axis] originate successive semicircles, where each point of the semicircle corresponds to a different frequency value which increases counterclockwise. Lanfredi and Rodrigues report in their work IS studies of the electrical conductivity and dielectric constant of polycrystalline LN [25]. **Figure 17** presents Nyquist diagrams for different temperatures of two polycrystalline LN samples *a* and *b*. Sample *b* has approximately half of the thickness to electrode surface area ratio (*l*/A) relatively to sample *a*.

**Figure 17.** At left: Nyquist diagram for different temperatures for a polycrystalline LN sample with a thickness to electrode surface area ratio *l*/A = 0.200 cm−1 (sample *a*). At right: Nyquist diagram for different temperatures for sample *a* polycrystalline LN sample with a thickness to surface area ratio l/A = 0.105 cm−1 (sample *b*), approximately half of sample *a*. For both samples, the smallest semicircle corresponds to a measurement performed at 700°C [25].

Comparing both diagrams, it is visible that for the same temperature, the real part of the complex impedance Re(Z) of sample *b* is approximately half of sample *a*, thus confirming that the high-frequency semicircle is the bulk response of the samples, since the resistance is directly proportional to the path length [25]. Furthermore, the frequency value distribution in the bulkresponse semicircle is the same for both samples, indicating the homogeneity of the bulk response, and that the relaxation frequency, given by the peak of the bulk semicircle (in the peak, the relation 2π*f*0*R*b*C*b = 1 is fulfilled, where *R*b and *C*b are bulk resistance and capacitance, respectively), is an intrinsic property of the material and does not depend on geometrical factors [25]. As expected, the bulk resistance decreases with the increase of the temperature. The low-frequency semicircle is assigned to the response of grain boundaries, and its depressed shape is an indicator of a nonhomogeneous electrical behavior of grain boundaries [25]. This nonhomogeneous behavior can be related with an existence of a distribution of relaxation times.

The complex impedance semicircle for the bulk response can be well fitted by simple *R*b*C*b equivalent circuit. A bulk electrical conductivity *σ*b can be defined according to Eq. (12):

$$
\sigma\_{\rm b} = \frac{1}{\kappa\_{\rm b}} \frac{\iota}{A} \tag{12}
$$

**Figure 18.** Arrhenius representation of the bulk electrical conductivity *σ*b of the polycrystalline LN samples *a* and *b*, in the temperature range between 450 and 800°C [25].

Raman Spectroscopy and Scanning Electron Microscopy Structural Characterization of Lithium Niobate Nanoparticles Prepared by the Sol-Gel Process, Using X-Ray and Raman Spectroscopy and Scanning Electron Microscopy http://dx.doi.org/10.5772/64395 61

**Figure 19.** Frequency dependency, in the range of 5–107 Hz, of *ε*′ for some fixed high temperatures, for sample *b* [25].

*R* b can be determined through the Nyquist plots by the second interception (just before the grain boundary response) of the bulk semicircle with the real axis. **Figure 18** displays for both samples *a* and *b* the Arrhenius representation of *σ*b in the temperature range between 450 and 800°C [25]. The activation energies are very similar.

To conclude this section, it is included in **Figure 19** the frequency dependency, between 5 and 107 Hz, of *ε*′ for some fixed high temperatures, for sample *b*.

For lower frequencies, a strong dispersion of *ε*′ is observed. This is due to spatial charge accumulation at the grain boundaries, and the charge accumulation at interface electrode/ sample may also contribute to the sharp increase of *ε*′ for lower frequencies. This behavior is often observed for polycrystalline materials.

## **2.4. Case study: preparation and characterization of polycrystalline LN by the Pechini method**

## *2.4.1. Preparation process: the Pechini route*

Comparing both diagrams, it is visible that for the same temperature, the real part of the complex impedance Re(Z) of sample *b* is approximately half of sample *a*, thus confirming that the high-frequency semicircle is the bulk response of the samples, since the resistance is directly proportional to the path length [25]. Furthermore, the frequency value distribution in the bulkresponse semicircle is the same for both samples, indicating the homogeneity of the bulk response, and that the relaxation frequency, given by the peak of the bulk semicircle (in the peak, the relation 2π*f*0*R*b*C*b = 1 is fulfilled, where *R*b and *C*b are bulk resistance and capacitance, respectively), is an intrinsic property of the material and does not depend on geometrical factors [25]. As expected, the bulk resistance decreases with the increase of the temperature. The low-frequency semicircle is assigned to the response of grain boundaries, and its depressed shape is an indicator of a nonhomogeneous electrical behavior of grain boundaries [25]. This nonhomogeneous behavior can be related with an existence of a distribution of relaxation

60 Applications of Molecular Spectroscopy to Current Research in the Chemical and Biological Sciences

The complex impedance semicircle for the bulk response can be well fitted by simple *R*b*C*b equivalent circuit. A bulk electrical conductivity *σ*b can be defined according to Eq. (12):

**Figure 18.** Arrhenius representation of the bulk electrical conductivity *σ*b of the polycrystalline LN samples *a* and *b*, in

the temperature range between 450 and 800°C [25].

(12)

times.

The sol-gel process is a well-known route for the synthesis of different types of materials, and in its basic description, it can be referred as a technique that synthesizes a solid compound through a chemical reaction in solution at low temperatures. There are different sol-gel methodologies according to the type of precursors used and the chemical reactions leading to the formation of the gel: there is the sol-gel methodology based on the hydrolysis-condensation of metal alkoxides, the "chelate-gel" route, involving aqueous solutions containing metal chelates, and the Pechini route. The sol-gel methodologies have general advantages such as the very good control of the stoichiometry and purity of the final material, low processing temperatures, possibility, and good flexibility in developing thin films as well as the possibility to have control over some important characteristics, such as the size and shape of the particles and homogeneity.

The Pechini route takes its name on its developer, Maggio Pechini in 1967 [26]. In particular, it was developed to include metals which are not suitable for traditional sol-gel reactions due to their unfavorable hydrolysis equilibria, and thus this method has the advantage of not requiring that the metallic species involved form stable hydroxo-complexes. This method is known for its use on the synthesis of multicomponent metal oxide materials [26], and basically this method uses an R-hydroxycarboxylic acid, such as citric acid (CA), to lead the formation of stable metal complex, i.e., the metallic cations of interest form stable complexes known as chelates. After this step, a polyalcohol, such as ethylene glycol (EG), is used to promote the polyesterification of the chelates, leading to the formation of a polymeric resin, where the metallic cations are trapped in the organic polymeric network. In other words, the polyalcohol is able to create links between the chelates by polyesterification reactions. The formation of the polymeric resin results in the formation of the gel. The subsequent drying process leads to the pyrolysis of the organic compounds, resulting in the formation of multicomponent metal oxide [26].

In this case study, the precursors lithium nitrate (LiNO3) and niobium chloride (NbCl5) (purity > 99%) were chosen. A molar ratio of 1:1 between LiNO3 and NbCl5 was established in order to enhance the formation of the LiNbO3 stoichiometric phase. Firstly, the LiNO3 and NbCl5 were dissolved in deionized water and in a hydrogen peroxide solution (H2O2, 3%, V/V), respectively. For each gram of NbCl5, 3.2 ml of H2O2 was used, originating a yellow transparent and clear solution. Both precursor solutions were mixed with citric acid (CA), fixing a molar ratio of 1:1 between the CA and the metallic cations, in order to form the metal complexes (chelates). The mixing was performed using a magnetic stirrer for 30 min at room temperature. After the mixing process, ethylene glycol (EG) was added to promote the polyesterification of the chelates. A mass ratio of 2:3 was established between the CA and EG to determine the quantity of EG to use. The final solution was mixed again with a magnetic stirrer for about 3 h, and the final gel was yellow and transparent, maintaining its macroscopic appearance for a long time period (>1 month). **Figure 20** outlines the entire preparation process.

The base powder was obtained after drying the gel at 300°C for 1 h, with a heating ramp of 5°C/min, yielding a black/grayish powder.

#### *2.4.2. Thermal, structural, and morphological properties*

The base powder was subjected to several heat treatments (HTs) at temperatures between 400 and 1000°C. These temperatures were chosen according to the differential thermal analysis (DTA) results, presented in **Figure 21**. This thermal technique was performed between room temperature and 1200 °C using a Linseis 63A apparatus. The heating rate was 20 °C/min and Al2O3 powder as used as reference. In **Figure 21**, the thermogram shows the presence of three exothermic thermal processes at the temperatures of 490, 790, and 1050°C, approximately. Consequently, HTs were performed at 450, 500, 800, and 1000°C, for 4 h.

Raman Spectroscopy and Scanning Electron Microscopy Structural Characterization of Lithium Niobate Nanoparticles Prepared by the Sol-Gel Process, Using X-Ray and Raman Spectroscopy and Scanning Electron Microscopyhttp://dx.doi.org/10.5772/64395 63

to have control over some important characteristics, such as the size and shape of the particles

62 Applications of Molecular Spectroscopy to Current Research in the Chemical and Biological Sciences

The Pechini route takes its name on its developer, Maggio Pechini in 1967 [26]. In particular, it was developed to include metals which are not suitable for traditional sol-gel reactions due to their unfavorable hydrolysis equilibria, and thus this method has the advantage of not requiring that the metallic species involved form stable hydroxo-complexes. This method is known for its use on the synthesis of multicomponent metal oxide materials [26], and basically this method uses an R-hydroxycarboxylic acid, such as citric acid (CA), to lead the formation of stable metal complex, i.e., the metallic cations of interest form stable complexes known as chelates. After this step, a polyalcohol, such as ethylene glycol (EG), is used to promote the polyesterification of the chelates, leading to the formation of a polymeric resin, where the metallic cations are trapped in the organic polymeric network. In other words, the polyalcohol is able to create links between the chelates by polyesterification reactions. The formation of the polymeric resin results in the formation of the gel. The subsequent drying process leads to the pyrolysis of the organic compounds, resulting in the formation of multicomponent metal

In this case study, the precursors lithium nitrate (LiNO3) and niobium chloride (NbCl5) (purity > 99%) were chosen. A molar ratio of 1:1 between LiNO3 and NbCl5 was established in order to enhance the formation of the LiNbO3 stoichiometric phase. Firstly, the LiNO3 and NbCl5 were dissolved in deionized water and in a hydrogen peroxide solution (H2O2, 3%, V/V), respectively. For each gram of NbCl5, 3.2 ml of H2O2 was used, originating a yellow transparent and clear solution. Both precursor solutions were mixed with citric acid (CA), fixing a molar ratio of 1:1 between the CA and the metallic cations, in order to form the metal complexes (chelates). The mixing was performed using a magnetic stirrer for 30 min at room temperature. After the mixing process, ethylene glycol (EG) was added to promote the polyesterification of the chelates. A mass ratio of 2:3 was established between the CA and EG to determine the quantity of EG to use. The final solution was mixed again with a magnetic stirrer for about 3 h, and the final gel was yellow and transparent, maintaining its macroscopic appearance for a long time period (>1 month). **Figure 20** outlines the entire preparation process.

The base powder was obtained after drying the gel at 300°C for 1 h, with a heating ramp of

The base powder was subjected to several heat treatments (HTs) at temperatures between 400 and 1000°C. These temperatures were chosen according to the differential thermal analysis (DTA) results, presented in **Figure 21**. This thermal technique was performed between room temperature and 1200 °C using a Linseis 63A apparatus. The heating rate was 20 °C/min and Al2O3 powder as used as reference. In **Figure 21**, the thermogram shows the presence of three exothermic thermal processes at the temperatures of 490, 790, and 1050°C, approximately.

Consequently, HTs were performed at 450, 500, 800, and 1000°C, for 4 h.

5°C/min, yielding a black/grayish powder.

*2.4.2. Thermal, structural, and morphological properties*

and homogeneity.

oxide [26].

**Figure 20.** Diagram of the Pechini method used for the synthesis of the LN base powder. CA, citric acid; EG, ethylene glycol.

**Figure 21.** DTA thermogram of the base powder synthesized by the Pechini method. This thermal analysis was performed between room temperature and 1200 °C, with a heating rate of 20 °C/min.

The XRD measurements performed on these powders (not shown here) revealed that for the HT at 500°C, the LN and LiNb3O8 crystalline phases are present and that the increase of the HT temperature promotes the development of the LiNb3O8 phase. However, the powder HT at 450°C only contained the LiNbO3 phase, whereby this powder was used to prepare pellets which were then sintered at 450°C for 4, 12, 24, 48, and 96 h. Thirty milligrams of powder was used for the preparation of the 10-mm diameter pellets, resulting in a thickness of about 1 mm when applying a uniaxial pressure of 1.5 tons. Hereafter, we will refer to these pellets as samples.

**Figure 22.** XRD patterns of the base powder HT at 450°C and of the samples sintered for 4, 12, 24, 48, and 96 h (× LiNbO3; O LiNb3O8).

**Figure 22** depicts the XRD patterns of the samples sintered during the aforementioned time intervals. The patterns show that the sintering process activated the formation of the LiNb3O8 phase. The XRD technique was performed on a Philips X'Pert MPD (CuKα radiation, *λ* = 1.54056 Å), with a step 0.02° in 1 s, in the 2*θ* angle range of 10–60°. The identification of the crystalline phases was made using the database of the Joint Committee on Powder Diffraction Standards–International Center for Diffraction Data. To get a further insight about the contents of each phase in the samples as well as to calculate the crystallite sizes associated with each phase, a Rietveld refinement was performed for all the diffraction patterns shown in **Figure 22**, using the PowderCell software. In **Figure 23**, the Rietveld fits of the samples 4 h and 4 h + 96 h are presented.

**Figure 23.** The Rietveld fits of the XRD patterns for the powder HT at 450°C, containing only the LN crystalline phase and the sample sintered for 96 h, containing both LN and LiNb3O8.

The Rietveld fit parameters indicate a good fit of the structural models to the experimental data (**Table 2**). Although the XRD patterns shown in **Figure 22** may suggest that the LiNb3O8 phase is present in small amounts, the mass percentages shown in **Table 2** show that the presence of this phase is relevant, reaching the maximum value for the sample 4 h + 96 h. In fact, both LN and LiNb3O8 have reflections lying in close diffraction angles, and some of the observed peaks contain a contribution of the LiNb3O8 phase, besides the LN phase, explaining the relatively high mass percentages. The crystallite size of both phases stands approximately constant for the different samples, especially for the LiNb3O8 phase, which has larger sizes relatively to the LN phase.

at 450°C only contained the LiNbO3 phase, whereby this powder was used to prepare pellets which were then sintered at 450°C for 4, 12, 24, 48, and 96 h. Thirty milligrams of powder was used for the preparation of the 10-mm diameter pellets, resulting in a thickness of about 1 mm when applying a uniaxial pressure of 1.5 tons. Hereafter, we will refer to these pellets as

64 Applications of Molecular Spectroscopy to Current Research in the Chemical and Biological Sciences

**Figure 22.** XRD patterns of the base powder HT at 450°C and of the samples sintered for 4, 12, 24, 48, and 96 h (× LiN-

**Figure 22** depicts the XRD patterns of the samples sintered during the aforementioned time intervals. The patterns show that the sintering process activated the formation of the LiNb3O8 phase. The XRD technique was performed on a Philips X'Pert MPD (CuKα radiation, *λ* = 1.54056 Å), with a step 0.02° in 1 s, in the 2*θ* angle range of 10–60°. The identification of the crystalline phases was made using the database of the Joint Committee on Powder Diffraction Standards–International Center for Diffraction Data. To get a further insight about the contents of each phase in the samples as well as to calculate the crystallite sizes associated with each phase, a Rietveld refinement was performed for all the diffraction patterns shown in **Figure 22**, using the PowderCell software. In **Figure 23**, the Rietveld fits

**Figure 23.** The Rietveld fits of the XRD patterns for the powder HT at 450°C, containing only the LN crystalline phase

samples.

bO3; O LiNb3O8).

of the samples 4 h and 4 h + 96 h are presented.

and the sample sintered for 96 h, containing both LN and LiNb3O8.

**Table 2.** The initial three parameters are the weighted profile *R*-factor (*R*wp), the expected *R*-factor (*R*exp), and the "chi squared" *χ*2 . The crystallite size and mass percentage of each crystalline phase in all the samples are also indicated. The last two columns show the dielectric constant (*ε*′) and loss tangent (tan *δ*) at 10 kHz and room temperature (300 K).

**Figure 24.** The Raman spectra of the samples sintered for different times between the time range 4 and 96 h, performed at room temperature.

In **Figure 24**, the Raman spectra of the sintered samples are presented. The spectra show the presence of vibrational bands which are the result of an overlapping of vibrational models of LN and also of the LiNb3O8 crystalline phase, as a consequence of the polycrystalline structure of the prepared samples. For a further analysis of the LN and LiNb3O8 vibrational modes, the authors suggest the reading of Bartasyte et al. report [27]. The room-temperature Raman spectroscopy was performed in backscattering geometry using a T64000 Jobin-Yvon spectrometer. A microscope objective (50×) focused the exciting light (Ar+ laser, *λ* = 532 nm) onto the sample (spot diameter <0.8 μm).

**Figure 25.** SEM micrographs of the LN polycrystalline samples prepared by the Pechini method, sintered at 450°C for 4, 12, 24, 48, and 96 h.

In **Figure 25**, SEM micrographs of the samples are shown, as well as the variation of the grain size with the sintering time. The grain size increases significantly with the sintering time from 4 to 12 h and then decreases slightly up to 96 h. As for the morphology, the grains show an approximate spherical geometry. The SEM was executed on a HITACHI S4100-1. All samples were sputtered with carbon before the analysis.

#### *2.4.3. Electrical and dielectric properties*

The electrical analysis of these types of samples is not evident. **Figure 26** shows the temperature dependence of the dc conductivity (*σ*dc) for all samples, revealing a decrease of the conductivity with the increase of the sintering time. This suggests a probable decrease in the number of charge carriers.

However, **Figure 27** shows that the activation energy, calculated in the high-temperature region (marked by the Arrhenius regression line in **Figure 26**), decreases substantially from sample sintered at 4 h to the sample sintered at 96 h. This profile indicates that the height of the potential barriers, from which the charge carriers must pass through, decreases, which should promote an increase in their mobility. Therefore, this analysis indicates a decrease in the number of charge carriers and also an increase in their mobility.

Raman Spectroscopy and Scanning Electron Microscopy Structural Characterization of Lithium Niobate Nanoparticles Prepared by the Sol-Gel Process, Using X-Ray and Raman Spectroscopy and Scanning Electron Microscopy http://dx.doi.org/10.5772/64395 67

of the prepared samples. For a further analysis of the LN and LiNb3O8 vibrational modes, the authors suggest the reading of Bartasyte et al. report [27]. The room-temperature Raman spectroscopy was performed in backscattering geometry using a T64000 Jobin-Yvon spec-

**Figure 25.** SEM micrographs of the LN polycrystalline samples prepared by the Pechini method, sintered at 450°C for

In **Figure 25**, SEM micrographs of the samples are shown, as well as the variation of the grain size with the sintering time. The grain size increases significantly with the sintering time from 4 to 12 h and then decreases slightly up to 96 h. As for the morphology, the grains show an approximate spherical geometry. The SEM was executed on a HITACHI S4100-1. All samples

The electrical analysis of these types of samples is not evident. **Figure 26** shows the temperature dependence of the dc conductivity (*σ*dc) for all samples, revealing a decrease of the conductivity with the increase of the sintering time. This suggests a probable decrease in the number of

However, **Figure 27** shows that the activation energy, calculated in the high-temperature region (marked by the Arrhenius regression line in **Figure 26**), decreases substantially from sample sintered at 4 h to the sample sintered at 96 h. This profile indicates that the height of the potential barriers, from which the charge carriers must pass through, decreases, which should promote an increase in their mobility. Therefore, this analysis indicates a decrease in the

laser, *λ* = 532 nm) onto

trometer. A microscope objective (50×) focused the exciting light (Ar+

66 Applications of Molecular Spectroscopy to Current Research in the Chemical and Biological Sciences

the sample (spot diameter <0.8 μm).

4, 12, 24, 48, and 96 h.

charge carriers.

were sputtered with carbon before the analysis.

number of charge carriers and also an increase in their mobility.

*2.4.3. Electrical and dielectric properties*

**Figure 26.** Arrhenius representation of the dc conductivity (*σ*dc) for the samples sintered at 450°C for 4, 12, 24, 48, and 96 h.

**Figure 27.** Dc conductivity (*σ*dc) and activation energy (*E*a(dc)) of the samples sintered at 450°C for 4, 12, 24, 48, and 96 h, at room temperature (300 K).

As discussed in Section 2.3, the electrical conduction in crystalline LN can be due to oxygen vacancies, in low-pressure and/or high-temperature conditions (polaron-hopping mechanism), and due to lithium ions in high-pressure conditions (ionic conduction). In this case, the conduction will depend on the ratio between Li/Nb both for high and low pressures. Therefore, in this case context, the conduction related with the lithium-ion (Li+ ) hypothesis seems to be more relevant. The existence of the LiNb3O8 secondary phase, which is a reach niobium LN phase, implies an increase of the number of Li+ ions not connected to a crystalline structure, which allied to the decrease of the activation energy should improve the *σ*dc, which is not observed. This fact indicates that the number of Li+ ions inserted in the crystalline structure increases and is explained by two hypotheses: there is a possible existence of an amorphous phase in all samples and thus the number of lithium ions inserted in this amorphous phase should decrease with the increase of the sintering time, stimulating an increase of the crystalline amount. The second hypothesis is associated with the low-melting point of lithium (~454 K). The increase of the sintering time must raise the possibility of some Li+ ions to be released during sintering. Density measurements revealed that all samples have a density between 3.53 and 3.69 g/cm3 , which are values lower than the characteristic ones for LN (4.65 g/cm3 ) and LiNb3O8 (3.87 g/cm3 ). This fact increases the probabilities of the first hypothesis.

Both dc and ac conductivities (**Figures 26**–**29**) increase with the rise of the measurement temperature, showing that both mechanisms are thermally activated. However, with the increase in the sintering time, the *σ*ac shows the opposite trend of *σ*dc (it increases). This indicates that the conduction mechanism and dominant charge carriers are not the same in both processes. In our opinion, the *σ*ac increase should be related with the decrease of the grain size (**Figure 25**) observed from sample sintered at 12 h up to the sample sintered at 96 h.

**Figure 28.** Arrhenius representation of the ac conductivity (*σ*ac) for the samples sintered at 450°C for 4, 12, 24, 48, and 96 h.

**Figure 29.** Ac conductivity (*σ*dc) and activation energy (*E*a(ac)) of the samples sintered at 450°C for 4, 12, 24, 48, and 96 h, at 10 kHz and room temperature (300 K).

The dielectric constant is maximum for the sample sintered at 24 h (**Table 2**), measured at room temperature and 10 kHz, which is in accordance with the Rietveld refinement results (**Table 2**), by presenting the highest crystallite size. The sample sintered at 48 h shows a dielectric constant value very near the maximum, which should be related with the amount of LN phase present in the sample and not the size of their grains (**Table 2**). It must be noted that the values presented in **Table 2** were obtained without assuming the existence of the hypothetical amorphous phase. These two samples present a dielectric loss below 0.15 at room temperature and 10 kHz (**Table 2**), being almost constant for temperatures between 200 and 300 K.

should decrease with the increase of the sintering time, stimulating an increase of the crystalline amount. The second hypothesis is associated with the low-melting point of lithium

released during sintering. Density measurements revealed that all samples have a density

Both dc and ac conductivities (**Figures 26**–**29**) increase with the rise of the measurement temperature, showing that both mechanisms are thermally activated. However, with the increase in the sintering time, the *σ*ac shows the opposite trend of *σ*dc (it increases). This indicates that the conduction mechanism and dominant charge carriers are not the same in both processes. In our opinion, the *σ*ac increase should be related with the decrease of the grain size

**Figure 28.** Arrhenius representation of the ac conductivity (*σ*ac) for the samples sintered at 450°C for 4, 12, 24, 48, and

**Figure 29.** Ac conductivity (*σ*dc) and activation energy (*E*a(ac)) of the samples sintered at 450°C for 4, 12, 24, 48, and

, which are values lower than the characteristic ones for LN

). This fact increases the probabilities of the first hypoth-

ions to be

(~454 K). The increase of the sintering time must raise the possibility of some Li+

68 Applications of Molecular Spectroscopy to Current Research in the Chemical and Biological Sciences

(**Figure 25**) observed from sample sintered at 12 h up to the sample sintered at 96 h.

between 3.53 and 3.69 g/cm3

) and LiNb3O8 (3.87 g/cm3

(4.65 g/cm3

esis.

96 h.

96 h, at 10 kHz and room temperature (300 K).

The 3D plots (**Figures 30** and **31**) show the presence of a dielectric relaxation phenomenon practically independent on the measurement temperature. However, the frequency of the maximum observed in the loss tangent diagram decreases with the increase of the sintering time, which can be related to the suggested decrease of the amorphous phase content and consequent increase of the LN in crystalline form which is a material where the dielectric depolarization is very difficult, i.e., high-relaxation time characteristic.

**Figure 30.** At left: dependency of the dielectric constant with the temperature and frequency for the sample sintered at 450°C for 24 h. At right: dependency of the dielectric constant with the temperature and frequency for the sample sintered at 450°C for 96 h.

**Figure 31.** At left: dependency of the loss tangent with the temperature and frequency for the sample sintered at 450°C for 24 h. At right: dependency of the loss tangent with the temperature and frequency for the sample sintered at 450°C for 96 h.

## **Author details**

Pedro R.S. Prezas\* and Manuel P.F. Graça

\*Address all correspondence to<EMAIL_ADDRESS>
University of Aveiro/I3N—Physics Department, Aveiro, Portugal

## **References**

[11] Graça M.P.F., Prezas P.R., Costa M.M., Valente M.A., *Structural and dielectric characterization of LiNbO3 nano-size powders obtained by Pechini method*, J. Sol-Gel Sci. Technol., 2012, 64:78-85

**Author details**

Pedro R.S. Prezas\*

**References**

1989, 72(8):1311-1321

Croatia, ISBN: 978-953-307-350-7.

J. Cryst. Growth, 1992, 116:327-332

State Mater. Sci., 1998, 3(5):469-473

*synthesis method*, Ceram. Int., 2014, 40:1835-1841

Ionics, 2012, 225:26-29

360:181-184

8:6.1-6.7

and Manuel P.F. Graça

University of Aveiro/I3N—Physics Department, Aveiro, Portugal

70 Applications of Molecular Spectroscopy to Current Research in the Chemical and Biological Sciences

[1] Abouelleil M.M. and Leonberger F.J., *Waveguides in lithium niobate*, J. Am. Ceram. Soc.,

[2] Graça M.P.F. and Valente M.A. *Glass ceramics with para, anti or ferroelectric active phases*, Advances in Ceramics – Electric and Magnetic Ceramics, Bioceramics, Ceramics and Environment, Prof. Sikalidis C. (Ed.), InTech (2011). Janeza Trdine 9, 51000 Rijeka,

[3] Volk T. and Wohlecke (2008), Lithium Niobate: Defects, Photorefraction and Ferroelectric Switching*,* Springer-Verlag, Berlin, Heidelberg, ISBN: 978-3-540-70765-3.

[4] Bordui P.F., Norwood R.G., Jundt D.H., Fejer M.M., *Preparation and characterization of*

[5] Kitamura K., Yamamoto J.K., Iyi N., Kimura S., Hayashi T., *Stoichiometric LiNbO3 single crystal growth by double crucible Czochralski method using automatic powder supply system*,

[6] Weidenfelder A., Shi J., Fielitz P., Borchardt G., Becker K.D., Fritze H., *Electrical and electromechanical properties of stoichiometric lithium niobate at high-temperatures*, Solid State

[7] Szaller Zs., Péter Á., Polgár K., Szabó Gy., *High temperature top seeded solution growth of stoichiometric lithium niobate LiNbO3 (sLN) with planar interface*, J. Cryst. Growth, 2012,

[8] Damjanovic D., *Materials for high temperature piezoelectric transducers*, Curr. Opin. Solid

[9] Ohlendorf G., Richter D., Sauerwald J., Fritze H., *High-temperature electrical conductivity and electromechanical properties of stoichiometric lithium niobate*, Diff. Fundam., 2008,

[10] Kamali A.R. and Fray D.J., *Preparation of lithium niobate particles via reactive molten salt*

*off-congruent lithium niobate crystals*, J. Appl. Phys., 1992, 71(2):875-879

\*Address all correspondence to<EMAIL_ADDRESS>

## **Raman Spectroscopy, a Useful Tool to Study Nuclear Materials Raman Spectroscopy, a Useful Tool to Study Nuclear Materials**

Laura J. Bonales, Jone M. Elorrieta, Álvaro Lobato and Joaquin Cobos Joaquin Cobos Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

Laura J. Bonales, Jone M. Elorrieta, Álvaro Lobato and

http://dx.doi.org/10.5772/64436

#### **Abstract**

[26] Roque-Malherbe R.M.A. (2009), *The Physical Chemistry of Materials: Energy and Environmental Applications*, CRC Press, 6000 Broken Sound Parkway, NW Suite 300 Boca Raton,

72 Applications of Molecular Spectroscopy to Current Research in the Chemical and Biological Sciences

[27] Bartasyte A., Plausinaitiene V., Abrutis A., Stanionyte S., Margueron S., Boulet P., et al.*, Identification of LiNbO3, LiNb3O8 and Li3NbO4 phases in thin films synthesized with different deposition techniques by means of XRD and Raman spectroscopy*, J. Phys.: Condens.

FL 33487, United States, ISBN:<PHONE_NUMBER>722.

Matter., 2013, 25(20):205901.

The use of the Raman technique is nowadays being widely spread in many scientific and industrial disciplines. The rise of this spectroscopy is due to the technology developed in some of its main components (the laser, charge-coupled device (CCD) sensors, gratings, filters, etc.), what reduces the cost of the equipment. Characterization by Raman spectroscopy has long and well-established tradition in fields such as condensed matter physics and chemistry. In nuclear sciences, by contrast, it is far from being extensively applied, even though this technique can be especially useful. It is a fact that only a scarce number of Raman laboratories dealing with nuclear materials exist, and therefore a limited database related to these materials. In such a context, this chapter is devoted to the practical use of Raman spectroscopy for nuclear materials characterization.

**Keywords:** Raman, nuclear, uranium oxides, U-secondary phase

## **1. Introduction**

Nuclear power is a controversial subject that generates a debate in today's society; nevertheless, the existing 438 nuclear reactors [1] produce approximately 15% of the world's electricity [2], making it a major world energy source.

Proponents of nuclear energy describe nuclear power production as a low running costs and a nature friend since it can be considered a low carbon technology compared with fossil fuels such as coal, gas, and oil [3]. Opponents of nuclear power argue that this energy has very high initial costs, complex nuclear waste management, and high plant decommissioning costs, and

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

highlight the environmental and public risks and dangers associated with it [4, 5]. This debate has been mirrored by the number of nuclear power plant (NPP) constructions. For example [6], before the accident in Fukushima Daiichi in 2011, the number of NPPs was increasing due to the concerns over greenhouse gas emissions to avoid further global warming. Then, the accident impacted public acceptance of nuclear power and had an effect of decreasing the number of nuclear reactors [7]. In recent years, the number of constructions commencing are on the rise again [8], and the main concern is related to the nuclear waste management, mainly spent nuclear fuel (SNF).

The most common nuclear fuel consists of uranium dioxide, UO2, enriched from 0.7 to 3–5% of 235U depending on which reactor it will be loaded into [9]. After its irradiation in the reactor core, the fuel is composed of a matrix of UO2 (>95%) doped with fission products and transuranium elements [10], which are found as bubbles (Xe, Kr), metallic precipitates (Mo, Tc, Ru, Rh, and Pd), oxide precipitates (Rb, Cs, Ba, and Zr), solid solutions, and transuranium elements dissolved by U substitution in the UO2 matrix [11]. These elements are not distributed homogeneously as a consequence of the thermal gradient within the UO2 pellet (temperature as high as 1700°C at the center of the pellet and decreasing to 400°C outwards) [12, 13]. Besides, the spent nuclear fuel suffers substantial microstructural modifications from the initial fresh fuel such as coarsening of the grains and extensive microcracking. Thus, SNF can be described as a complex, hot, and radioactive waste and therefore extremely dangerous. Bruno et al. [14] provide a particularly suitable example to demonstrate how hazardous the SNF is, that is, …"*One year after discharge from a reactor…a person exposed to this level of radioactivity at a distance of one meter would receive a lethal dose in less than one minute…."*

After several thousands of years, the total radioactivity of the SNF equals the radioactivity of natural uranium [15]. Therefore, within the management of spent nuclear fuel, the safe storage of this radioactive waste from the discharge of the reactor until the decay reaches natural uranium radioactivity is considered. Countries adopt different stages of these nuclear storages according to their internal policies [16], but usually the following steps are suitable: (i) spent fuel pools [17], (ii) intermediate storage or reprocessing [18], and (iii) final storage [19].

After SNF is removed from the reactor, it is stored for the first few years on-side in water containers or pools, located close to the reactor in order to allow the spent fuel to decay, both radioactively and thermally. Then, it can be transported to a reprocessing facility or to a definitive storage facility. However, since final repositories for spent fuel do not exist for the moment, interim storage is required. NPPs use the spent fuel dry-cask storages, which are steel and concrete containers filled with an inert gas as a first step for interim storage. Although no ultimate storage in operation exists, the deep geological repository is internationally accepted as the best solution [20].

The performance of the mentioned repositories requires knowledge of the SNF stability at different storage conditions. Thereby, the studies of the spent fuel behavior can be mainly divided into dry and wet conditions, given the different evolution observed in each case. The studies of spent nuclear fuel under dry conditions are mainly focused on the oxidation of both the UO2 matrix and the AnO2 [21] present in the SNF.1 In case of shielding failure, the oxidation of AnO2 and UO2 takes place owing to its contact with the atmospheric oxygen and the high temperatures present (up to 400°C) [15]. This oxidation occurs via oxygen incorporation into the fluorite structure (fcc) of the stoichiometric oxide, for example, some actinides as plutonium and uranium can oxidize to AnO2+*x* (*x* < 0.25) maintaining the fcc structure [22]. Further oxidation to higher-oxidation states (V and VI) leads to different structures. For example, the transformation of UO2 into U3O8 via the two-step reaction [23] UO2→ U4O9/U3O7→ U3O8 entails an increase in the volume of around 36% and, consequently, it might cause the loss of the UO2 matrix integrity.

On the other hand, the studies of spent nuclear fuel under wet conditions are focused on the corrosion process of this waste. This might happen in case the SNF shielding fails while stored in pools or in the deep geological repository at timescales of the order of some thousands of years [24] when it is assumed that the barriers that protect the waste will be breached and SNF will be in contact with water [25]. The UO2 matrix of the spent nuclear fuel might dissolve with water and then the release to the biosphere of the SNF radioactive contents might occur [26–28].

This corrosion process is primarily described by the oxidation of uranium, U(IV) → U(VI), and then the alteration products formation, usually containing UO2 2+ in their crystal structures [29] U(VI) → UO2 2+ (s).

Great effort has been performed to analyze the reaction mechanism and to establish the key parameter that controls the corrosion of the SNF such as leaching/dissolution experiments [30–32] and studies of the uraninite, a natural analog of the spent nuclear fuel matrix [33, 34]. These stability studies require the characterization of the SNF and its reaction products, with O2 and/or water, which is a great challenge not only because these materials are very complicated (containing almost the entire periodic table) [11] but also because intense radiation field inherently associated to these materials makes it difficult to examine them in safe conditions.

In order to minimize radiation doses and the release of radioactive material, the working procedure employed to study these materials must fulfill the ALARA principle (acronym for "as low as reasonably achievable") [35]. Such a reliable procedure must, hence, minimize the time that radioactive materials are handled and maximize the distance to them. Raman spectroscopy is an analyzing technique that has been established in recent years as a useful tool since it fulfills the mentioned safe principles, as shown by the increase in the number of publications dealing with the characterization of nuclear materials by this technique [36–44]. This is due to some of its features as (1) that it does not require any special preparation of the sample, (2) it allows the analysis of a very small amount of sample, and (3) it is a nondestructive technique.

Besides these safety principles, the confinement of the whole apparatus in a glove box or a hot cell is also very common, which obviously complicates the measurements [45]. Despite the advantages mentioned above, the characterization of these SNF and related nuclear materials is far from being well established. Existing databases must be improved and new methods

highlight the environmental and public risks and dangers associated with it [4, 5]. This debate has been mirrored by the number of nuclear power plant (NPP) constructions. For example [6], before the accident in Fukushima Daiichi in 2011, the number of NPPs was increasing due to the concerns over greenhouse gas emissions to avoid further global warming. Then, the accident impacted public acceptance of nuclear power and had an effect of decreasing the number of nuclear reactors [7]. In recent years, the number of constructions commencing are on the rise again [8], and the main concern is related to the nuclear waste management, mainly

74 Applications of Molecular Spectroscopy to Current Research in the Chemical and Biological Sciences

The most common nuclear fuel consists of uranium dioxide, UO2, enriched from 0.7 to 3–5% of 235U depending on which reactor it will be loaded into [9]. After its irradiation in the reactor core, the fuel is composed of a matrix of UO2 (>95%) doped with fission products and transuranium elements [10], which are found as bubbles (Xe, Kr), metallic precipitates (Mo, Tc, Ru, Rh, and Pd), oxide precipitates (Rb, Cs, Ba, and Zr), solid solutions, and transuranium elements dissolved by U substitution in the UO2 matrix [11]. These elements are not distributed homogeneously as a consequence of the thermal gradient within the UO2 pellet (temperature as high as 1700°C at the center of the pellet and decreasing to 400°C outwards) [12, 13]. Besides, the spent nuclear fuel suffers substantial microstructural modifications from the initial fresh fuel such as coarsening of the grains and extensive microcracking. Thus, SNF can be described as a complex, hot, and radioactive waste and therefore extremely dangerous. Bruno et al. [14] provide a particularly suitable example to demonstrate how hazardous the SNF is, that is, …"*One year after discharge from a reactor…a person exposed to this level of radioactivity at a distance*

After several thousands of years, the total radioactivity of the SNF equals the radioactivity of natural uranium [15]. Therefore, within the management of spent nuclear fuel, the safe storage of this radioactive waste from the discharge of the reactor until the decay reaches natural uranium radioactivity is considered. Countries adopt different stages of these nuclear storages according to their internal policies [16], but usually the following steps are suitable: (i) spent fuel pools [17], (ii) intermediate storage or reprocessing [18], and (iii) final storage [19].

After SNF is removed from the reactor, it is stored for the first few years on-side in water containers or pools, located close to the reactor in order to allow the spent fuel to decay, both radioactively and thermally. Then, it can be transported to a reprocessing facility or to a definitive storage facility. However, since final repositories for spent fuel do not exist for the moment, interim storage is required. NPPs use the spent fuel dry-cask storages, which are steel and concrete containers filled with an inert gas as a first step for interim storage. Although no ultimate storage in operation exists, the deep geological repository is internationally accepted

The performance of the mentioned repositories requires knowledge of the SNF stability at different storage conditions. Thereby, the studies of the spent fuel behavior can be mainly divided into dry and wet conditions, given the different evolution observed in each case. The studies of spent nuclear fuel under dry conditions are mainly focused on the oxidation of both

of AnO2 and UO2 takes place owing to its contact with the atmospheric oxygen and the high

In case of shielding failure, the oxidation

*of one meter would receive a lethal dose in less than one minute…."*

the UO2 matrix and the AnO2 [21] present in the SNF.1

spent nuclear fuel (SNF).

as the best solution [20].

1 A meaning minor actinides such as Np, Pu, and Am.

must be developed. Due to the hazardous feature of nuclear materials, both the development of new protocols and Raman spectra acquisition (for the purpose of extending the databases) are usually performed first by analyzing the behavior of different SNF analogs and, once the method is feasible, by applying it to the real SNF. Such analogs can be divided into two kinds: synthetic analogs such as uranium dioxide (UO2) [46, 47] or SIMFUEL (simulated fuel) [48, 49], and natural analogs such as uraninite.

In this context, this chapter is structured as follows: In the first part, Raman spectroscopy is described. First, the theoretical aspects on an introductory level are explained. Second, the main components of the Raman spectrometers are presented and, as an example, the *LabRam HR Evolution* spectrometer is described in more detail. The "Results" section has been divided into two, corresponding to dry and wet conditions; in each part, the developed method and the results found for analogs of the SNF are shown. Namely, the materials studied in this section are the different uranium oxides, UO2+*x* (0 < *x* < 0.25), U4O9/U3O7, and U3O8, and several secondary phases such as rutherfordine, soddyite, uranophane alpha, or kasolite.

## **2. Raman spectroscopy technique**

#### **2.1. Description of the Raman phenomena**

Raman effect owes its name to the Indian physicist Chandrasekhara Venkata Raman [50] who won the Nobel Prize for its discovery. In his Nobel lecture, given on December 11, 1930, Sir C.V. Raman said…"*The frequency differences determined from the spectra, the width and character of the lines appearing in them, and the intensity and state of polarization of the scattered radiations enable us to obtain an insight into the ultimate structure of the scattering substance […]. It follows that the new field of spectroscopy has practically unrestricted scope in the study of problems related to the structure of matter*" [51].

As other molecular spectroscopy techniques, Raman scattering is based on the analysis of lightmatter interaction [52], that is, absorption, emission, or scattering of a photon. Two interpretations of this phenomenon can be considered: the quantum mechanical method and the classical interpretation. In the purely classical interpretation, the radiation is considered as an electromagnetic wave, and the matter as an assembly of independent classical rotors and vibrators. This model can explain satisfactorily the main features of the light scattering such as the frequency dependence and some key aspect related to their selection rules.

Raman effect is described as an inelastical scattering of light. From a macroscopic point of view, light scattering consists in a deviation of light from its straight trajectory (original direction of incident light). Molecules scatter light because the electric field of the incident light wave forces the electrons within the molecule to oscillate (see **Figure 1**), producing oscillating electric moments leading to the reemission of radiation in all directions [53].

must be developed. Due to the hazardous feature of nuclear materials, both the development of new protocols and Raman spectra acquisition (for the purpose of extending the databases) are usually performed first by analyzing the behavior of different SNF analogs and, once the method is feasible, by applying it to the real SNF. Such analogs can be divided into two kinds: synthetic analogs such as uranium dioxide (UO2) [46, 47] or SIMFUEL (simulated fuel) [48,

76 Applications of Molecular Spectroscopy to Current Research in the Chemical and Biological Sciences

In this context, this chapter is structured as follows: In the first part, Raman spectroscopy is described. First, the theoretical aspects on an introductory level are explained. Second, the main components of the Raman spectrometers are presented and, as an example, the *LabRam HR Evolution* spectrometer is described in more detail. The "Results" section has been divided into two, corresponding to dry and wet conditions; in each part, the developed method and the results found for analogs of the SNF are shown. Namely, the materials studied in this section are the different uranium oxides, UO2+*x* (0 < *x* < 0.25), U4O9/U3O7, and U3O8, and several

Raman effect owes its name to the Indian physicist Chandrasekhara Venkata Raman [50] who won the Nobel Prize for its discovery. In his Nobel lecture, given on December 11, 1930, Sir C.V. Raman said…"*The frequency differences determined from the spectra, the width and character of the lines appearing in them, and the intensity and state of polarization of the scattered radiations enable us to obtain an insight into the ultimate structure of the scattering substance […]. It follows that the new field of spectroscopy has practically unrestricted scope in the study of problems related to the*

As other molecular spectroscopy techniques, Raman scattering is based on the analysis of lightmatter interaction [52], that is, absorption, emission, or scattering of a photon. Two interpretations of this phenomenon can be considered: the quantum mechanical method and the classical interpretation. In the purely classical interpretation, the radiation is considered as an electromagnetic wave, and the matter as an assembly of independent classical rotors and vibrators. This model can explain satisfactorily the main features of the light scattering such

Raman effect is described as an inelastical scattering of light. From a macroscopic point of view, light scattering consists in a deviation of light from its straight trajectory (original direction of incident light). Molecules scatter light because the electric field of the incident light wave forces the electrons within the molecule to oscillate (see **Figure 1**), producing oscillating electric

as the frequency dependence and some key aspect related to their selection rules.

moments leading to the reemission of radiation in all directions [53].

secondary phases such as rutherfordine, soddyite, uranophane alpha, or kasolite.

49], and natural analogs such as uraninite.

**2. Raman spectroscopy technique**

**2.1. Description of the Raman phenomena**

*structure of matter*" [51].

**Figure 1.** Light scattering produced by the interaction of the incident light's electric field and the molecule electrons.

Such process produces two types of radiation, Rayleigh radiation, which has the same frequency that the incident light (*ν*0), and Raman radiation, which consists in a new set of frequencies with more or less energy than the incident radiation (*ν*0 ± *ν*1), where *ν*1 is typically related to the rotational, vibrational, and electronic levels of the molecule. In **Figure 2**, a general scheme of the scattering process and its difference with the absorption process from the point of view of the photons and the energy levels of the molecule are represented.

**Figure 2.** Energy level diagrams describing the physical phenomenon of (1) IR absorption, (2) Rayleigh scattering, and (3) Raman scattering.

Before the interaction of the radiation with the system, there are N photons of energy *hcν*0. In the case of the absorption process, the interaction of the radiation with the system leads to the excitation of the molecule to a higher energy state resulting in a radiation which consists in N − 1 photons of energy *hcν*0. This process can occur, if and only if the incoming photon has the same energy as the difference between the initial and final state of the molecule, *E*f − *E*i = *hcν*fi = *hcν*0, fulfilling the condition of energy conservation.

Let us now consider the scattering process, the interaction between the incident radiation and the system produces the annihilation of a photon of energy *hcν*0, and simultaneously the creation of a new photon with energy *E*s. Now the radiation consists in N − 1 photons of energy *hcν*0, a new photon of energy *hcν*s, and the transition to the molecule to a final state with energy *E*f . In the overall process, the energy must be conserved so, *hcν*0 = *hcν*s + *E*f .

This two-photon process can be visualized as two simultaneous stages. First, the annihilation stage which leads the molecule to a virtual high-energy state. Virtual states are created when the laser interacts with the molecule and causes polarization; hence, their energy is determined by the frequency of the incident light source used (*ν*0). At this stage, there is no energy conservation implying that the role of the incident radiation in the scattering is to perturb the molecule given the possibility to allow different spectroscopic transitions rather than the absorption process. Second, the creation stage, where the molecule reaches its final state with energy *E*f producing the new photon. At this point, we can consider two types of scattered light: (1) the Rayleigh scattering, or elastic scattering, where the final state of the molecule is its own initial state, *E*f = *E*i *,* and, correspondingly, the energy of the scattered light corresponds to the initial frequency value, *ν*s = *ν*0. (2) The Raman scattering, or inelastic scattering, in which the molecule reaches a final state different from its initial state; hence, the energy of the scattered light has a different frequency value from the incident radiation, *ν*s = *ν*0 ± *ν*fi. This process is much less probable than Rayleigh scattering (only 10−5 − 10−8 of the incident beam intensity). If the final state has a higher energy than the initial state, *E*f > *E*i , the scattered photon loses energy, *ν*s = *ν*0 − *ν*fi. This radiation is known as Stokes Raman scattering. By contrast, if the final state has a lower energy than the initial state, *E*f < *E*i , the scattered photon increases its energy, *ν*s = *ν*0 + *ν*fi, giving the anti-Stokes Raman scattering. Relative probabilities of Stokes and anti-Stokes radiation depend on the population of the molecule states, *f* and *i*, and therefore on temperature according to the Maxwell-Boltzmann distribution. As both give the same information, it is customary to measure only the "Stokes" side of the spectrum.

Even though this general scheme describes scattering phenomena in a qualitative way, it highlights some key aspect of the Raman spectroscopy and its differences with the absorption process. Nevertheless, it is worth to describe the classical treatment of the Raman scattering in order to provide a deeper insight in the frequency dependence and the microscopic origin of the scattered light. Classical wave interpretation [54, 55] of the Raman effect is based on the time-dependent polarizability of the molecules. Consider one of the simplest scattering systems, a vibrating diatomic AB molecule.

 According to Hook´s law, its relative movement can be described by the second Newton law as follows:

**Figure 3.** Simplified model of a diatomic AB molecule.

$$
\mu \left( \frac{d^2 \mathbf{x}\_1}{dt^2} + \frac{d^2 \mathbf{x}\_2}{dt^2} \right) = K \left( \mathbf{x}\_1 + \mathbf{x}\_2 \right) \tag{1}
$$

where *μ* represents the reduced mass of the molecule, *x* represents the displacement, and *K* represents the bond strength. For small vibrations, the harmonic approximation holds, and then the normal coordinates *q*(*t*) of the vibrating molecule can be expressed as

$$q = q\_0 \cos\left(2\pi\nu\_m t\right) \tag{2}$$

where *q0* is the amplitude and *ν*m is the natural vibration frequency which is defined in terms of its bond strength as

$$\nu\_m = \frac{1}{2\pi} \sqrt{\frac{K}{\mu}} \tag{3}$$

When incident light interacts with a molecule, induces a dipole moment, *P*, equal to the product of the polarizability of the molecule, *α*, and the electric field of the incident light source *E*

$$P = \text{ or } E\_0 \cos(2\pi\nu\_o t),\tag{4}$$

where *E*0 and *ν*o are the electric field amplitude and frequency, respectively. As far as the molecule is vibrating, its polarizability varies according to the relative displacement of these atoms and therefore we can express *α* as a power series *q*

$$\alpha = \left. \alpha\_0 + q \left( \frac{\partial \alpha}{\partial q} \right)\_0 + \dots \right. \tag{5}$$

which when combined with Eqs. (3) and (5) results in,

the laser interacts with the molecule and causes polarization; hence, their energy is determined by the frequency of the incident light source used (*ν*0). At this stage, there is no energy conservation implying that the role of the incident radiation in the scattering is to perturb the molecule given the possibility to allow different spectroscopic transitions rather than the absorption process. Second, the creation stage, where the molecule reaches its final state with

78 Applications of Molecular Spectroscopy to Current Research in the Chemical and Biological Sciences

light: (1) the Rayleigh scattering, or elastic scattering, where the final state of the molecule is

to the initial frequency value, *ν*s = *ν*0. (2) The Raman scattering, or inelastic scattering, in which the molecule reaches a final state different from its initial state; hence, the energy of the scattered light has a different frequency value from the incident radiation, *ν*s = *ν*0 ± *ν*fi. This process is much less probable than Rayleigh scattering (only 10−5 − 10−8 of the incident beam

loses energy, *ν*s = *ν*0 − *ν*fi. This radiation is known as Stokes Raman scattering. By contrast, if the

energy, *ν*s = *ν*0 + *ν*fi, giving the anti-Stokes Raman scattering. Relative probabilities of Stokes and anti-Stokes radiation depend on the population of the molecule states, *f* and *i*, and therefore on temperature according to the Maxwell-Boltzmann distribution. As both give the same

Even though this general scheme describes scattering phenomena in a qualitative way, it highlights some key aspect of the Raman spectroscopy and its differences with the absorption process. Nevertheless, it is worth to describe the classical treatment of the Raman scattering in order to provide a deeper insight in the frequency dependence and the microscopic origin of the scattered light. Classical wave interpretation [54, 55] of the Raman effect is based on the time-dependent polarizability of the molecules.  According to Hook´s law, its relative movement can be described by the second

( ) 2 2

2 2 1 2 *dx dx Kx x*

è ø (1)

1 2

*dt dt*

æ ö ç ÷ + =+

m

information, it is customary to measure only the "Stokes" side of the spectrum.

producing the new photon. At this point, we can consider two types of scattered

*,* and, correspondingly, the energy of the scattered light corresponds

< *E*i

> *E*i

, the scattered photon increases its

, the scattered photon

energy *E*f

its own initial state, *E*f

= *E*i

final state has a lower energy than the initial state, *E*f

systems, a vibrating diatomic AB molecule.

**Figure 3.** Simplified model of a diatomic AB molecule.

Newton law as follows:

intensity). If the final state has a higher energy than the initial state, *E*f

$$P = \alpha\_0 E\_0 \cos\left(2\pi\nu\_0 t\right) + q\_0 \cos\left(2\pi\nu\_n t\right) E\_0 \cos\left(2\pi\nu\_0 t\right) \left(\frac{\partial a}{\partial q}\right)\_0 \tag{6}$$

$$P = \alpha\_o E\_o \cos(2\pi \mathbf{v}\_o t) + \left(\frac{\partial \alpha}{\partial q}\right)\_0 q\_o E\_o \left[\cos\left(2\pi \left\{\mathbf{v}\_o - \mathbf{v}\_m\right\} t\right) + \cos\left(2\pi \left\{\mathbf{v}\_o + \mathbf{v}\_m\right\} t\right)\right] \tag{7}$$

From Eq. (7), it is evident that the induced electric dipole is formed by three different terms. The first one gives rise to an oscillating moment at the same frequency of the incident light, the Rayleigh scattering, and two additional terms which accounts for the Stokes and anti-stokes Raman scattering. Therefore, Rayleigh scattering arises from an electric dipole which oscillates at the same frequency induced in the molecule by the electric field of the incident radiation, whereas Raman scattering arises from the modulation of the electric dipole with the natural frequency of the vibrating molecule. This modulation is produced by the electrons of the molecule, whose rearrangement produces a coupling between the nuclear motion and the electric field of the radiation.

#### **2.2. Dispersive Raman spectrometer**

From the basis of the Raman effect described above, it is easy to deduce that in a conventional (or dispersive) Raman spectrometer,2 the main difficulty lies in separating the intense stray light of the Rayleigh scattering from the much weaker Raman-scattered light. Besides, as Raman scattering has low efficiency, the optimization of each of the instrumental components becomes critically important.

The main components of a Raman setup are as follows:

*1. Excitation source:* Traditionally, mercury arc lamps were used as light sources until being replaced by laser sources. Laser beams are highly monochromatic, present small diameter and, with the help of different optic devices, can be focused on small samples. Different lasers can be used as the light source in Raman spectrometry, as the ones shown in **Table 1** [56].

**Table 1.** Lasers used as light source in Raman spectroscopy.

In addition, in order to enhance the laser quality it is possible to employ a pass-band filter, designed to pass only a certain band of frequencies while attenuating all signals outside this band. This component is commonly known as interferometric filter.

*2. Sample illumination system and collection optics*: The collimation and focusing optics of the exciting radiation onto the sample depends on the experimental setup. In principle, excitation

2 Raman systems are subdivided into two principals according to the spectral analysis of the Raman light, namely Fouriertransform (FT) systems using an interferometer, and dispersive systems.

and collection from the sample can be accomplished in any geometry, although 90 and 180°C (backscattering) are more frequently employed. The use of fiber optics helps to make the spectrometers more versatile.

whereas Raman scattering arises from the modulation of the electric dipole with the natural frequency of the vibrating molecule. This modulation is produced by the electrons of the molecule, whose rearrangement produces a coupling between the nuclear motion and the

80 Applications of Molecular Spectroscopy to Current Research in the Chemical and Biological Sciences

From the basis of the Raman effect described above, it is easy to deduce that in a conventional

light of the Rayleigh scattering from the much weaker Raman-scattered light. Besides, as Raman scattering has low efficiency, the optimization of each of the instrumental components

*1. Excitation source:* Traditionally, mercury arc lamps were used as light sources until being replaced by laser sources. Laser beams are highly monochromatic, present small diameter and, with the help of different optic devices, can be focused on small samples. Different lasers can

In addition, in order to enhance the laser quality it is possible to employ a pass-band filter, designed to pass only a certain band of frequencies while attenuating all signals outside this

*2. Sample illumination system and collection optics*: The collimation and focusing optics of the exciting radiation onto the sample depends on the experimental setup. In principle, excitation

2 Raman systems are subdivided into two principals according to the spectral analysis of the Raman light, namely Fourier-

be used as the light source in Raman spectrometry, as the ones shown in **Table 1** [56].

**Laser Wavelength (nm)** Ar ion 530.9/647.1 He-Ne 632.8 Near IR diode 785/830 Nd-YAG 1064 Frequency-doubled Nd:YAG 532 Nd:YVO4 diode 532

band. This component is commonly known as interferometric filter.

transform (FT) systems using an interferometer, and dispersive systems.

the main difficulty lies in separating the intense stray

electric field of the radiation.

becomes critically important.

(1) Excitation source

(5) Recording device

(4) Detector

**2.2. Dispersive Raman spectrometer**

(or dispersive) Raman spectrometer,2

(3) Wavelength selectors and separators

**Table 1.** Lasers used as light source in Raman spectroscopy.

The main components of a Raman setup are as follows:

(2) Sample illumination systems and collection optics

*3. Wavelength selectors and/or separators:* The separation or removal of the intense Rayleigh scattering can be achieved by using two different types of filters: notch and edge filters. Notch filters allow the acquisition of the anti-Stokes and Stokes Raman spectra down to ~30 cm−1, but their use is expensive since they must be replaced very frequently (~2 years). For this reason, the use of edge filters is widespread. These are wide pass-band filters, which imply that the anti- Stokes Raman spectrum cannot be obtained and typical minimum wavenumbers are ~50 cm−1. After the removal or suppression of the Rayleigh radiation, the separation of the different Raman radiations scattered by the sample should be performed. The first Raman spectrometers used prisms, but nowadays these are replaced by gratings that are typically holographically produced. It is worth noting that filters can be neglected if coupling of two or three monochromators is set in a series. This configuration allows not only to separate the Raman lines but also to remove the Rayleigh scatter.

*4. Detectors:* Just like in other spectrometers, the former detectors, that is, photographic films, were substituted first by photodiode array detectors and then by charge transfer devices (CTDs) such as charge-coupled devices (CCDs). CCDs are silicon-based semiconductors arranged as an array of photosensitive elements, each one generating photoelectrons and storing them as an electrical charge. Charges are stored on each individual pixel as a function of the number of photons striking that pixel and then read by an analog-to-digital converter [54].

A schematic representation of a modern micro-Raman spectrometer is shown in **Figure 4**.

**Figure 4.** Descriptive scheme of the main components of a Raman microspectrometer.

In the micro-Raman technique, a microscope is integrated in a conventional Raman spectrometer, enabling both visual and spectroscopic measurements. As can be seen in **Figure 4**, in these types of equipment the focusing and collection optics of the scattered radiation are identical. In addition to the analysis of a single point, these spectrometers allow mapping and imaging measurements.

## **3. Results**

As explained before, this section has been divided into two parts corresponding to dry and wet conditions; into the corresponding part the developed methods and the results obtained for analogs of the spent nuclear fuel matrix and its alteration products are shown. Namely, the materials studied in this section are the different uranium oxides, UO2+*x* (0 < *x* < 0.25), U4O9/ U3O7, and U3O8, and several secondary phases such as rutherfordine, soddyite, uranophane alpha, and kasolite.