Electronic Structure and Room Temperature Ferromagnetism in Gd‐doped Cerium Oxide Nanoparticles for Hydrogen Generation via Photocatalytic Water Splitting

Abstract Enhanced visible light photocatalytic activity of Gd‐doped CeO2 nanoparticles (NPs) is experimentally demonstrated, whereas there are very few reports on this mechanism with rare earth doping. All‐pure and Gd‐doped CeO2 NPs are synthesized using a coprecipitation method and characterized using X‐ray diffraction (XRD), absorption spectroscopy, surface‐enhanced Raman Spectroscopy (SERS), X‐ray photoelectron spectroscopy (XPS), and superconducting quantum interference device (SQUID). The effect of Gd‐doping on properties of CeO2 is discussed along with defects and oxygen vacancies generation. The XRD confirms the incorporation of Gd3+ at the Ce3+/Ce4+ site by keeping the crystal structure same. The average particle size from transmission electron microscopy (TEM) images is in the range of 5–7 nm. The XPS spectra of Ce 3d, O 1s, and Gd 4d exhibits the formation of oxygen vacancies to maintain the charge neutrality when Ce4+ changes to Ce3+. The gradual increase in hydrogen production is observed with increasing Gd concentration. The observed results are in good correlation with the characterization results and a mechanism of water splitting is proposed on the basis of analyses. The absorption spectra reveal optical band gap (2.5–2.7 eV) of samples, showing band gap narrowing leads to desired optical absorbance and photoactivity of NPs.


Introduction
Rare earth (RE) oxide-CeO 2 has attracted great interest of research due to their unique properties, including high oxygen storage capacity and ability to uptake and release oxygen (O 2− ) ions via conversion of oxidation state of cerium ion from Ce 4+ to Ce 3+ , due to formation of defect space such as oxygen vacancies in the lattice of CeO 2 . [1] On account of this uniqueness, CeO 2 has been widely used as three-way catalysts for eliminating vehicle exhaust gases, [2] UV blocker materials in sunscreens, UV-shielding used in cotton fabrics, [3] functionalize silk fiber for antibacterial activity, [4] oxygen sensors, [5] and oxygen ion conductors in solid oxide fuel cells (SOFCs). [6] Generally, it has been reported that type of dopant strongly influenced the electrical properties of ceria and high conductivity at low temperature is an essential requirement for SOFCs, therefore, rare earth (RE)-doped cerium oxide, Ce 1−x RE x O 2−δ (RE = Sm, Gd, Dy, Er, Lu) are preferable dopants used as electrolytes for intermediate-temperature SOFCs. [7,8] Alike TiO 2, bulk cerium dioxide (CeO 2 ) is a wide band gap (3.2 eV) cubic fluorite semiconductor, [9] which possesses the interesting properties such as a high dielectric constant (ε = 26), good transparency in the visible range, nontoxic, and capacity to exhibit the high photocatalytic activity under UV light irradiation. Therefore, CeO 2 seems to be a promising inorganic material that can be used for the UV filtration in sunscreen/cosmetic products and as a potential material for UV filtration. [10] Therefore, to enhance the workability of this compound in visible light some kind of structural engineering and doping of heavy metal might be done for reducing the band gap of CeO 2 .
Among all RE-doped CeO 2 , Sm and Gd-stabilized ceria has been extensively studied for utilization as electrolyte and anode material. [11,12] It has been reported that addition of Sm 3+ and Gd 3+ cations in CeO 2 system produced highest conductivity with least distortion of parent lattice, which is attributed to the smallest association enthalpy between the dopant cation and the oxygen vacancies in the CeO 2 lattice. [13][14][15] Besides of dopant type, theoretical and experimental observations have also suggested that the ionic conduction can be altered by the concentration of dopant. [16][17][18][19] Moreover, it is well known that material properties changes when particle size reduces to nanoscale, as reported by Kosacki et al. [20] in their nanocrystalline CeO 2 thin film, electrical conductivity has found to be enhanced due to reduced enthalpy of oxygen vacancy formation. Li et al. [21] have reported increase in catalytic activity as well as in optical and magnetic properties of porous Gd 3+ -doped CeO 2 (10 at% Gd) nanostructure due to Gd 3+ ions or formation of oxygen vacancies. In most of these studies, the local ordering of oxygen vacancies on grain boundaries in heavily RE-doped CeO 2 samples has been reported. [22][23][24] Chen et al. [25] have reported dopant-induced structural differences and defects in Sm-doped CeO 2 nanoparticles (NPs) with doping concentration 3%, 5%, 7%, 9%, and 11%. On the basis of their results based on X-ray absorption spectroscopy, extended X-ray absorption fine structure, Raman, and scanning transmission electron microscopeelectron energy loss spectroscopy measurements they have discussed that below 7% and above 7% distribution of defects strongly depend on the concentration of Sm 3+ ions in CeO 2 NPs. Since, there is a lack of literature available on the evidence of the distribution of defect study with small doping concentration of RE-doped CeO 2 NPs.
Metal oxide photocatalyst have attracted increasing attention due to their potential applications in the environmental protection and energy utilization, such as water splitting for hydrogen production. In the Zn-, Mg-, and Ca-doped CeO 2 materials the impurities tend to shift the band position and can tune the band gap because of their effects on electronic transition. [26] Gddoped CeO 2 is used for thermolysis of water that can produce 101.6 H 2 (µmol g −1 ) hydrogen. [27] It has been demonstrated experimentally that the rare earth dopants and oxygen vacancies greatly influenced the photocatalytic properties of CeO 2 ; however, the effect of interaction between the rare earth dopant and oxygen vacancy defects on enhanced visible light photocatalytic activity of CeO 2 is still not investigated so far.
Hence in this study, we systematically explore to develop the correlation between the rare earth dopants, its concentration and oxygen vacancy defects to enhance the photocatalytic activity of doped CeO 2 . To undertake this study we have investigated the structural properties, dopant distribution, and their association with oxygen vacancies in Gd-doped CeO 2 NPs. The CeO 2 NPs have been doped with different concentrations of Gd 3+ ions (2%, 4%, 6%, 8%, and 10%) to discuss the presence of defect induced oxygen vacancies (either intrinsic or extrinsic) and their association with doped cation with surface-enhanced Raman spectroscopy (SERS) measurements. Transmission electron microscopy (TEM) has been used to observe changes in the surface morphology and particle size with increased fluencies of Gd 3+ ions in CeO 2 lattice. The optical absorption spectra have been measured using ultraviolet-visible-near infrared (UV-Vis-NIR) spectrometer to find out the band gap energy. Finally, we have attempted to investigate how doping concentration affect the oxygen vacancies and cation (Ce 3+ ) defects, present in pure and Gd-doped CeO 2 NPs. These results offer a physical understanding for the available experimental results to explain the enhanced photocatalytic activities of Gd-doped CeO 2 NPs, which can be useful for designing and understanding the novel doped CeO 2 photocatalyst.

X-Ray Diffraction (XRD) Analysis
X-ray diffraction measurements have been made on Ce 1−x Gd x O 2 nanoparticles for x = 0.0, 0.02, 0.04, 0.06, 0.08, and 0.10 at room temperature are shown in Figure 1a. Nanocrystalline Gd-doped CeO 2 samples exhibit fundamental Bragg reflections corresponding to the fluorite type face centered cubic structure in the space group of Fm-3m, in which Ce and Gd atoms are located at 4a position, surrounded by eight O (located at 8b) positions. [28] Absence of any secondary phase corresponding to Gd 2 O 3 or other impurity peaks indicates well incorporation of Gd 3+ ions on CeO 2 lattice site, which confirms the single phase formation of all the Ce 1−x Gd x O 2 nanoparticles. The intensity of XRD diffraction peaks is found to vary with incorporation of Gd 3+ ions in CeO 2 NPs (as shown in Figure 1a).
The rising intensity signifies an improvement in the crystalline nature while falling intensity signifies low crystallinity of Ce 1−x Gd x O 2 samples. [29] Moreover, with fluency of Gd 3+ ions, no peak shifting is observed for x = 0.02 doping concentration, whereas with increasing concentration (x ≤ 0.06) diffraction peak (111) is shifted toward higher angle side (as shown inset of Figure 1a). For higher doping concentrations (x = 0.08 and 0.10) peak is again shifted toward lower angle side. This shifting of (111) peak toward lower and higher angle side is attributed to the lattice expansion and reduction, respectively, which is induced by incorporation of Gd 3+ ions in CeO 2 NPs. [30] Furthermore, it can be seen in Figure 1a, diffraction peaks become broader after doping and broadness of peaks are also observed to change with fluency of Gd 3+ ions in CeO 2 NPs, indicating that crystal size and crystallinity of the samples are affected with the fluencies of Gd 3+ ions. The average nanocrystalline particle size (D) of Gd-doped CeO 2 samples has been calculated with XRD diffraction spectra using the Debye-Scherrer's formula [31] D k cos where, all the parameters are as per the details given in ref. [15]. The lattice parameters of all the samples corresponding to (111) diffraction peak have been calculated by the following formula [32] a d h k l ( ) where "a" refers to the lattice parameter, d is the crystalline lattice spacing, and h, k, l, are the miller indices of crystal. The calculated value of lattice parameter with fluency of Gd 3+ ions in CeO 2 NPs is tabulated in Table 1.
Global Challenges 2019, 3, 1800090 The variation in the calculated values of lattice parameter can be directly related to the ionic radii of the dopant ion. Since, the larger ionic radii Gd 3+ (0.1053 nm) ions are substituted for the smaller ionic radii Ce 4+ (0.097 nm) ions and created the larger radii Ce 3+ ions (0.114 nm). [36] Furthermore, for maintaining charge neutrality in CeO 2 lattice, Gd 3+ and Ce 3+ ions are collectively creating oxygen vacancies in the CeO 2 lattice, which causes further lattice expansion. [30] Rietveld profile refinements (shown in Figure 1b(i-vi)) of all the samples are carried out and the results are listed in Table 1. The XRD patterns indicate that Gd-doping in CeO 2 does not affect the cubic fluorite structure of the CeO 2 , as no additional diffraction peaks related to possible impurity phases of Gd and oxides of Gd are observed in these Gd-doped CeO 2 samples. It is further confirmed the formation of a single phase of Ce 1-x Gd x O 2 . The refinement results clearly indicate that Gd ions are well incorporated in the CeO 2 matrix and Gd-doping in CeO 2 leads to small enhancement in the unit-cell volume.
It is clear from Table 1, the dislocation density is found to increase for x = 0.02 doping concentration but decreases for x = 0.04 and 0.06, which is again increased for x = 0.08 and decreased for x = 0.10 doping concentrations of Gd +3 cation. This variation in dislocation density is related to the promotion and reduction of disorder in the crystal structure. [29] Looking to Table 1, the values of strain indicates tensile strain for Gd-doped CeO 2 NPs. Due to incorporation of Gd 3+ (0.1053 nm) cations in CeO 2 NPs, the maximum value of strain is for x = 0.08 doping concentration. Some theoretical investigation revealed that tensile strain promotes the formation of oxygen vacancies rather than compressive strain. [37] Therefore, in Gd-doped CeO 2 samples, increased value of tensile strain can be directly related to the endorsement of oxygen vacancies in doped CeO 2 samples, which may be associated to the bonding length and the strength between the surface O and Ce atoms. [38] Since, for tensile strain, the bandwidth of the O 2p orbital decreases and overlapping between O 2p and Ce 5d as well as 4f orbital also decreases, which leads a weaker CeO bond and responsible for the formation of oxygen vacancies in doped CeO 2 system. [37] The crystallinity, morphology, and particle size of the Gd-doped CeO 2 samples are discussed in the next segment by TEM, high-resolution transmission electron microscopy (HRTEM), and selected area (electron) diffraction (SEAD) images.

Surface Morphology
The average crystallite particle size of all the samples is confirmed by electron microscopy investigations. TEM measurement is used to manifest the information about the shape, size, and the presence of any secondary phase in pure and Gd-doped CeO 2 NPs. The particle size and morphology of pure and Gd-doped CeO 2 NPs are analyzed by TEM as shown in Figure 3. From TEM analysis, it is observed that the particles are crystallized nanoparticles and agglomerated with spherical morphology. The average particle size calculated from TEM images are ranging from 5 to 7 nm for pure and Gd-doped CeO 2 NPs, which are in good agreement with the results obtained from Debye-Scherrer formula (listed in Table 1). It can be observed from TEM images that crystal growth is promoted with doping concentration of Gd-ions. However, the morphology of all samples is not changing but the agglomeration of particles is increased with the doping concentration of Gd-ions (as shown in Figure 2).
The particle-size distribution histogram (shown in the inset of Figure 2) shows that the distribution is quite narrow in the size range of 5-7 nm for Gd-doped CeO 2 NPs. This agglomeration of particles with smaller particle-size (<7 nm) indicates that the obtained particles are nanocrystalline. Furthermore, HRTEM and SAED analysis are also used to decipher the information about the nanocrystallinity and impurity phases, if any present in Gd-doped CeO 2 NPs. HRTEM images (shown in Figure 3) indicate that the lattice fringes are well developed and randomly oriented with respect to each other. Most of the lattice fringes of Gd-doped CeO 2 samples are about at a distance of 0.31 nm (values are tabulated in Table 1) that corresponding to the (111) lattice plane of the fluorite like cubic structure.
As shown in Table 1, no significant change is observed in the interplanar distance (d) for Gd-doped CeO 2 samples but for 8% Gd-doped CeO 2 sample, the interplanar distance (d = 0.32 nm for (111) plane) is slightly increased, which again promotes the crystal growth and indicates the low crystallinity. Some defects, such as dislocations (shown in Figure 3c,d, marked with a red ring) are also observed in the HRTEM image of 4% and 6% Gd-doped CeO 2 samples. Moreover, SAED patterns are also taken (shown in the insets of Figure 3) for Gd-doped CeO 2 samples. SAED pattern exhibits four broad rings, which could be attributed to (111) Table 1. Calculated values of lattice parameter (a), lattice spacing (d) for (111) plane, average crystalline size (D) measured from TEM, XRD line broadening, and Raman line broadening, dislocation density (δ), lattice strain (ε), absorbance wavelength (λ), optical band gap energy (E g ), and refractive index (n) are summarized in this indicate that the particles are crystallized and diffraction rings are very well matched with the XRD measurement results. The fluency of Gd 3+ ions in CeO 2 NPs also affect the optical band gap energy, which is further discussed in the next segment by UV-Vis-NIR spectroscopy. Figure 4a shows the UV-Vis-NIR absorption spectra of Ce 1−x Gd x O 2 samples (x = 0.00, 0.02, 0.04, 0.06, 0.08, and 0.10). These samples exhibit a strong absorption below 400 nm with an absorption peak in UV-range corresponding to the different doping concentration of Gd 3+ ions in CeO 2 NPs as tabulated in Table 1. These peaks are originated due to direct charge transfer transition from 2p valance band of O 2− to 4f conduction band of Ce 4+ ions. [39] It is well known that CeO 2 have wide band gap semiconductor with a forbidden gap of 5.5 eV. [40] The valance band consists of O 2p level with a width of 4 eV and conduction band consist of Ce 5d level. Ce 4f level is present in between these two states, just above the Fermi level, that lies about 3 eV higher than the valance band (O 2p). [41] Hence there is direct recombination of the electrons in Ce 4+ (4f) conduction band with the holes in the O 2− (2p) valance band. It can be seen from Figure 4a, the absorbance peak is obtained at 367 nm for pure CeO 2 but after incorporation of Gd 3+ ions peak is shifted toward lower wavelength (blue shift) up to optimal doping concentration x = 0.04, while for further fluencies x = 0.06 to 0.10 peak is shifted toward higher wavelength (red shift) side. It has been reported that when metal NPs are forming smaller size particles, the λ max shifts toward shorter wavelength (blue shift) side, whereas, when the smaller particles aggregate to form bigger/larger size particles, the λ max value shifts toward longer wavelength (red shift) side. [42] This may indicate that smaller-sized particles have been formed up to doping concentration (x = 0.04), while with increasing fluencies of Gd-ions (for x = 0.06 to 0.10) in CeO 2 NPs, these smaller sized particles are agglomerated (as shown in Figure 2). As Hu et al. reported that the agglomeration of nanoparticles occurs because nanoparticles have a tendency to decrease the exposed surface in order to lower the surface energy, which results decreases in particle size with strong agglomeration. [43] Furthermore, blue shifting in the absorption spectra with the fluency of Gd 3+ ions in CeO 2 NPs can be due to change of Ce 4+ to Ce 3+ state, that increases the direct charge-transfer transition gap between O 2p and Ce 4f bands and reduces the particle size. [21,44] In addition of that the average particle size obtained from TEM images for Gd-doped CeO 2 NPs is in the range of 5-6 nm at lower doping concentration (x = 0.02 and 0.04), which is smaller than the predictable Bohr exciton radius for CeO 2 (7-8 nm). [21,45] Global Challenges 2019, 3, 1800090 Therefore, the quantum confinement effect may also be taken place that contributes to the blue shift of the absorption spectra with small fluencies of Gd-ions in CeO 2 NPs. Generally, quantum confinement effect results when the Bohr radius of an exciton approaches the grain or particle size, spatially confining the electron-hole pair. When this happens, the energy of the lowest excited state increases and the increased band gap produces a blue shift in the absorption spectra. Now at the higher fluencies (for x = 0.06 to 0.10) of Gd 3+ ions, the contribution of blue shifting from Ce 4+ to Ce 3+ valance state change will become small. Therefore, red shifting is occurred in the absorption spectra of Gd-doped CeO 2 (for 6%, 8%, and 10%)   samples. This red shifting may be the outcome of an interfacial polaron effect arising from electron-phonon coupling phenomenon. [46,47] Form all above absorption data, the band gap energy (E g ) of pure CeO 2 and Ce 1−x Gd x O 2 (x = 0.02, 0.04, 0.06, 0.08, and 0.10) NPs has been calculated using Tauc's equation

Optical Absorption
where all the parameters have their usual meaning. For direct transition n = 1/2 and for n = 2 for indirect transition. [48] Figure 4b displays the measured values of (αhν) 2 as a function of the incident photon energy (hν). Table 1 contains the calculated value of band gap energy (E g ) of all samples. Pure CeO 2 NPs shows band gap energy of 2.60 eV that is smaller than the band gap energy reported for bulk ceria, i.e., 3.15 eV. [49] This decrease in band gap energy may be attributed due to increase in the concentration of Ce 3+ states on grain boundaries. Moreover, the optical band gap energy is found to increase for low fluency of Gd 3+ ions (for x = 0.02 and 0.04) in CeO 2 NPs while it decreases subsequently with increasing fluencies of Gd 3+ ions (for x = 0.06 to 0.10) in CeO 2 NPs (as shown in Table 1). This blue shift in the band gap energy at lower doping concentration (for x = 0.02 and 0.04) of Gd 3+ ions may be correlated with the decrease of Ce 3+ concentration as well as oxygen vacancies during annealing process. This may eliminate some localized defect energy states within the band gap due to the corresponding decrease of vacancies content, which results increase in the band gap energy. [50] Another reason for explaining the increase in band gap energy may be correlated with the Burstein-Moss (BM) shift [49] Here, m vc * is effective mass of electrons, n e is the electron concentration, and h is the Plank constant. Now, according to BM effect, above the Mott critical density, the increased number of free electron concentration is leading to fill 4f level partially, which in turn blocks the lowest states and leads to band gap widening. [49,51] With incorporation of Gd 3+ ions into CeO 2 sample, the crystalline size is reduced (as shown in Table 1). Therefore, the charge carriers are more confined in the small sized particles, which in turn increasing the band gap energy at lower doping concentration of Gd-doped CeO 2 NPs. This implies that, both particle size and BM effect results in the increase in band gap energy. Besides that, the red shift in band gap energy with higher fluencies of Gd 3+ ions (x = 0.06, 0.08, and 0.10) is caused with the existence of Ce 3+ contents at the grain boundaries, which increases with decreasing particle size. [52] The refractive index of Gd-doped CeO 2 NPs has been calculated by using the following formula [53] n n E 1 2 1 20 The obtained values for the refractive index of pure and Gddoped CeO 2 NPs are tabulated in Table 1. These values indicates that the refractive index is found to decrease with fluency of Gd ions up to optimal doping concentration x = 0.04, whereas it is increased for further fluencies (x = 0.06, 0.08, and 0.10) of Gd 3+ ions in CeO 2 NPs. The variation in the refractive index and band gap energy has been shown in Figure 5 with different concentration of Gd-ions in CeO 2 NPs. Therefore, absorption of UV light at low concentration of Gd-ions (x = 0.02 and 0.04) in CeO 2 NPs has been increased due to reduction of particle size as well as refractive index, whereas, due to increasing doping concentration the transparency and UV protection qualities are decreased. [54]

Raman Spectra
Surface enhanced Raman spectroscopy is a powerful vibrational technique, which allows for highly sensitivity structural detection of low concentration analyses through the amplification of electromagnetic fields generated by the excitation of localized surface plasmons. [55] SERS provides the same information as traditional Raman spectroscopy does, but with enhanced signals. It can easily detect additional modes that cannot be observed in the traditional Raman spectrum. Therefore, SERS has been used for getting information of different modes presented in Gd-doped CeO 2 NPs. Figure 6 shows Raman active (F 2g ) mode for pure CeO 2 and Ce 1−x Gd x O 2 (x = 0.02, 0.04, 0.06, 0.08, and 0.10) samples, at 463.3 cm −1 and in the range of 461.4-459.5 cm −1 , assigned for firstorder scattering. [56] This Raman active mode is attributed to a symmetrical stretching mode of Ce-O8 vibration unit. Therefore, this mode is very sensitive for any disorder in the oxygen sublattice results from nonstoichiometry of ceria. [57] We can see from Figure 6 the absence of characteristic band for Gd 2 O 3 (360 cm −1 ) clearly indicating the incorporation of Gd 3+ ions into CeO 2 lattice, confirms the absence of any impurity phase in the lattice, in agreement with XRD results. [58,59] F 2g mode corresponding to pure CeO 2 and Ce 1−x Gd x O 2 is slightly shifted toward lower wavenumber side (or lower energy side) and broadening in its FWHM can also be observed with doping fluencies of Gd 3+ ions in CeO 2 sample. These structural changes in Raman spectra with Gd-doping are attributed to the inhomogeneous strain and defects caused by substitution at the smaller radii Ce 4+ (0.97 Å) site by larger ionic radii Gd 3+ (1.08 Å) ions. [60] In addition of Global Challenges 2019, 3, 1800090 F 2g mode, weak intensity second-order Raman peaks are also obtained at 598.5 and 595.6 cm −1 for pure CeO 2 and 2% Gddoped CeO 2 , respectively, generated due to nondegenerated longitudinal optical (LO) mode. [61] These peaks are assigned to defect space that include intrinsic oxygen vacancies due to nonstoichiometry of CeO 2 . The three possible defect induced mechanism for oxygen vacancies in pure CeO 2 sample can be given as [62] Since, these peaks are generated for maintaining the electrically neutrality in the system, therefore all Ce-ions not only shows Ce 4+ state but also Ce 3+ state. For doing so, oxygen (O 2− ) ions are released from the structure and finally oxygen vacancies are formed in the system. The intensity of this peak is increased with incorporation of Gd-ions indicates the rise of oxygen vacancies in ceria lattice. With increasing the fluency of Gd-ions, two weak second-order Raman modes in the range of 554.3-558 and 598-600.1 cm −1 are also obtained (as shown in the inset of Figure 6b). The Raman mode in the range of 554.3-558 cm −1 is related to the extrinsic oxygen vacancies, which are generated due to charge compensating defects due to substitution of Ce 4+ ions by Gd 3+ ions. The possible disorder mechanism for extrinsic oxygen vacancies in Ce 1−x Gd x O 2 (x = 0.02, 0.04, 0.06, 0.08, and 0.10) NPs can be given as [63] x x where symbols have the following meaning as: x Ce ce and Gd Ce ′ are Ce 4+ and Gd 3+ ions on the CeO 2 lattice site, respectively, x O O is O −2 ions on an oxygen lattice site, and V O •• is neutral oxygen vacancy site. In addition, another vacancy peak can also be observed in the range of 598-600.1 cm −1 , which is assigned to the defect space including intrinsic oxygen vacancies due to reduction of Ce 4+ to Ce 3+ , i.e., nonstoichiometry of ceria. [62] The possible disorder reaction for intrinsic oxygen vacancies in the sample can be given as [64] x x where symbols have the following meaning as: x Ce ce and Ce Ce ′ are Ce 4+ and Ce 3+ ions on the Ce lattice site, respectively, x O O is O −2 ions on an oxygen lattice site, and V O •• is neutral oxygen vacancy site. [65] As shown in the inset of Figure 6b, the intensity of intrinsic and extrinsic oxygen vacancies mode increases with doping fluency up to x = 0.04. With further increase in fluency, the intensity of this mode decreases and then again increases at x = 0.10 concentration. The variation of intensity of vacancy mode is related to the concentration of oxygen vacancies. The quantitative estimation of oxygen vacancies of pure CeO 2 and Gd-doped CeO 2 samples is made from the relative peak area of vacancy modes (intrinsic and extrinsic) with area of F 2g mode. For doing so, Lorentzian fitting is done for measuring the peak area of the respected peaks.
All calculated values are tabulated in Table 2, which indicates an Global Challenges 2019, 3, 1800090 Table 2. The position of Raman active modes (cm −1 ) from Raman spectra and relative peak area ratio.

Sample
Position of Raman active mode (cm −1 ) and vibrational mode Second-order scattering [66,67] Pure   Figure 7). [68] In addition to that, pure CeO 2 and Gd-doped CeO 2 samples also exhibit one more extra weak second-order Raman mode at 1064.9 cm −1 and in the range of 1173.9-1175.3 cm −1 , (as shown in Table 2), which are assigned to 2LO mode that emanate from the second-order scattering of the surface superoxide species (O ) 2 − , and has small additional contribution from F 2g symmetry (which is not mentioned in Figure 6). [56,65] The particle size of all the Ce 1−x Gd x O 2 samples has been calculated from Raman spectra using the equation where Γ (cm −1 ) is full width at half maximum (FWHM) of Raman active (F 2g ) mode and D is particle size of pure CeO 2 and Ce 1−x Gd x O 2 (x = 0.02, 0.04, 0.06, 0.08, and 0.10) samples. [61,69] The calculated particle size from Raman spectra is in good agreement with the particle size calculated from XRD and TEM images (as shown in Table 1). The quantitative estimation of the overall concentration of oxygen vacancies has been made by the peak area of the oxygen vacancies A Ov corresponding to 598. 5  + ratios are calculated for Ce 1−x Gd x O 2 (for x = 0.04, 0.06, 0.08, and 0.10) samples. From these calculated values one can infer that the relative oxygen vacancy concentration is found to gradually increase with fluencies of Gd 3+ ions in CeO 2 NPs.

XPS Spectra in Ce 3d Region
The chemical composition and the valence state of the pure CeO 2 and Gd-doped CeO 2 NPs have been further characterized using XPS measurements of Ce 3d, Gd 4d, and O 1s core levels. Figure 8 illustrates the Ce 3d core level XP spectra of Ce 1−x Gd x O 2 (x = 0.02, 0.04, 0.06, 0.08, and 0.10) samples. All binding energies have been corrected for the charge shift using the C 1s peak (binding energy = 284.6 eV) as reference. [70] The high-resolution Ce 3d core level spectra in the energy range of 880-930 eV have been deconvoluted by mean of Gaussian shape fitting as shown in Figure 8. These deconvoluted Ce 3d core-level spectra are generally characterized by distinct features which are related to the final-state occupation of Ce 4f level. [71] On Account of spin-orbit coupling, these deconvoluted Ce 3d core-level spectra are resolved into ten peaks, which include six and four structures arise from Ce 4+ and Ce 3+ ions, respectively. These series of peaks are labeled as "u" and "v," which are due to 3d 3/2 and 3d 5/2 spin-orbit states, respectively. [30] The four peaks labeled with v o , v′, u o , and u′ are characteristic peaks of Ce 3+ , whereas, the peaks labeled with v, v″, v‴, u, u″, and u‴ are characteristic peaks of Ce 4+ (shown in Figure 8). [72] The separation in binding energy between v and u spin-orbit doublets is found around ≈18.4 eV for pure CeO 2 , and for Ce 1−x Gd x O 2 (x = 0.02, 0.04, 0.06, 0.08, and 0.10) samples, which are in good agreement with the reported papers. [73,74] We can see from the Ce 3d core level spectra that Ce ions are present in mixed valance state of both Ce 3+ and Ce 4+ for pure CeO 2 and Ce 1−x Gd x O 2 (x = 0.02, 0.04, 0.06, 0.08, and 0.10) samples. All peak positions for "u" and "v" of pure CeO 2 and Ce 1−x Gd x O 2 (x = 0.02, 0.04, 0.06, 0.08, and 0.10) samples have been tabulated in Table 3. The total concentration of Ce 3+ and Ce 4+ in the samples has been calculated using the following formula [75] A A A % Ce 100%  Ce 3+ and Ce 4+ , respectively. These calculated values are tabulated in Table 3. The quantitative ratio of Ce 3+ /Ce 4+ shows that the concentration of Ce 3+ ions over Ce 4+ ions is gradually increasing for Ce 1−x Gd x O 2 (x = 0.00, 0.02, and 0.04) samples. While, at 6% Gddoping concentration Ce 3+ /Ce 4+ value is deceased, which is again increased and then decreased at 8% and 10% doping. This shows that due to incorporation of larger radii Gd 3+ ions (0.105 nm) in CeO 2 NPs, replacing the smaller radii Ce 4+ ions (0.97 Å) and for maintaining the charge neutrality, the concentration of Ce 3+ ions (0.114 nm) is gradually increased for x = 0.02 and 0.04 doping concentrations. The presence of Ce 3+ may be due to either the formation of Ce 2 O 3 or the creation of oxygen vacancies in CeO 2 lattice. This can be verified by calculating the stoichiometry ratios x = [O]/[Ce] and x′ = [O 1s ]/[Ce 3d ], which can be estimated from their integrated peak area while considering their sensitivity factor. In order to calculate oxygen content in the samples, we assume that the total oxygen content is the sum of the required oxygen to fully oxidize Ce 3+ Table 4 according to the following equation [52] x O Ce The stoichiometry calculated from Equation (14) has been compared with the actual stoichiometry determined from the XPS integrated area A O and A Ce of the O 1s and Ce 3d peaks, respectively, which has been calculated according to the following equation [76] x  Table 4).
Global Challenges 2019, 3, 1800090  Although, the calculated values of actual stoichiometry (x′) are higher than that (x) calculated by Equation (5)  This means that core level Ce 3d spectra prove the existence of Ce 2 O 3 in the Ce 1−x Gd x O 2 (x = 0.02, 0.04, 0.06, 0.08, and 0.10) samples, while from XRD analysis only CeO 2 is identified. This Ce 2 O 3 phase has amorphous character and indicates that this phase is located at the grain surface and at the grain boundaries. Patsalas et al. [52] have reported a dimensional analysis, which determined that Ce 2 O 3 and CeO 2 are located at grain surface and volume, respectively. A linear correlation can be established between third power of [Ce 4+ ] (grain volume distribution) as well as third power of D (which is proportional to the grain volume V g ) with square of [Ce 3+ ] (surface distribution). 3 that confirms the distribution of Ce 2 O 3 and CeO 2 at the grain surface and volume. While, the experimental points of D 3 versus [Ce 3+ ] 2 are more scattered around straight line of the dimensional analysis, which is attributed to the strain in the grain that affects the broadening of the XRD peaks with Gd-doping in CeO 2 samples. From Table 4, it can also be seen that the difference between x and x′ increases and decreases with increase and decrease of Ce 3+ ions for Ce 1−x Gd x O 2 (x = 0.04, 0.06, 0.08, and 0.10) samples, which show an up and down in the formation of oxygen vacancies in these samples.

O 1s XPS Spectra
The O 1s spectra for pure CeO 2 and Ce 1−x Gd x O 2 (x = 0.02, 0.04, 0.06, 0.08, and 0.10) samples are shown in Figure 11. The asymmetrical O 1s core level spectra in the binding energy range 526-540 eV are deconvoluted into four peaks to determine the surface concentration of oxygen ions for all samples. The deconvoluted binding energy peaks of O 1s core level spectra at ≈528.6-529.9 eV can be assigned to the lattice oxygen O 2− (denoted as O L ) in pure CeO 2 and Ce 1−x Gd x O 2 (x = 0.02, 0.04, 0.06, 0.08, and 0.10) samples, while peak at higher binding energy side ≈530.3-533.3 eV and ≈533.5-536.4 eV are possibly assigned to oxygen vacancies (denoted as O V ) corresponds to Ce 3+ species originated from Ce 2 O 3 [78] and formation of hydroxyl or absorbed H 2 O species [79] (denoted as O α and O β ) on the surface of the samples, respectively (as shown in Table 5). [80,81] As shown in Figure 11, all the samples are showing the similar O 1s core level spectra, which are also used as another source of information about Ce oxidation state. Since, it is well known that the electronegativity of Gd ion (1.21) is higher than Ce ion (1.12) on Pauling scale, therefore, O 1s peak from Gd 2 O 3 should be at higher binding energy than that from metal oxide CeO 2 . [82] Thus, due to incorporation of Gd 3+ ions in the lattice of CeO 2 , not only the intensity of the lattice oxygen peak (O L ) but also oxygen vacancies peak (O V ) are found to increase for 2% Gd-doped CeO 2 NPs. The quantitative estimation of O L and O V peaks shows that due to incorporation of Gd 3+ ions the oxygen vacancies are formed on the surface of the Gd-doped CeO 2 samples. These vacancies are found to show variation with change in the concentration of Gd-ions in the CeO 2 NPs. Furthermore, as 1s electron of oxygen atom attached more tightly bound to Ce 3+ rather than Ce 4+ oxidation state. Thus, change in the oxidation state of Ce-ions (+4 to +3) due to incorporation of Gd 3+ ions in the CeO 2 NPs, may also be responsible for the change in the formation of oxygen vacancies. The quantitative percentage of Ce 3+ oxidation state from core level spectra of Ce 3d for pure CeO 2 and Ce 1−x Gd x O 2 (x = 0.02, 0.04, 0.06, 0.08, and 0.10) samples, if compared with quantitative percentage of O V from O 1s core level spectra, one can infer that the increasing Ce 3+ concentration is also helpful in increasing the oxygen vacancies on the surface of samples (as shown in Tables 3 and 5) along with the percentage increase in the concentration of the Gd 3+ ions.

Gd 4d XPS Spectra
The deconvoluted Gd 4d core level XPS spectra are split into doublet (Gd 4d 5/2 and Gd 4d 3/2 ) due to spin-orbit coupling for Global Challenges 2019, 3,1800090   Although, it has been reported that bulk CeO 2 exhibit diamagnetic behavior where it is reported that at nanoregime the undoped CeO 2 NPs exhibit weak ferromagnetism with small value of saturation magnetization by few reports. [86][87][88][89][90][91][92] Since, a significant amount of coercivity H c = 77.95 Oe has been observed for pure CeO 2 NPs, which ensures the ferromagnetic nature in our pure CeO 2 sample. The weak ferromagnetic behavior in pure CeO 2 NPs at room temperature is associated with oxygen vacancies that have been originated by the conversion of Ce 4+ to Ce 3+ oxidation state of cerium. [93] Although, after incorporation of Gd 3+ ions in CeO 2 NPs, Ce 0. 98    decreased 22.48 Oe as compared to pure CeO 2 NPs. While, further increase in Gd 3+ ions concentration are not able to maintain this FM behavior, that can be clearly seen from the hysteresis curves (in Figure 13b) for Ce 1−x Gd x O 2 (x = 0.04, 0.06, 0.08, and 0.10) samples. The magnetization of the Gd-doped CeO 2 samples is increased with increasing dopant concentration (as shown in Table 6 and Figure 13b). Since, the electronic configuration of Gd 3+ is [Xe] 6s 2 5d 1 4f 7 with 7 unpaired electrons in the 4f shell. These unpaired 4f electrons polarize the 6s and 5d valence electrons, results high effective magnetic moment µ eff = 7.94 µ B (calculated by the formula where g J is the Lande g-factor and for Gd 3+ ion ground state 8 S 7/2 , S = 7/2, L = 0, J = 7/2, g J = 2). [94,95] With increasing dopant concentration, the interaction of these unpaired spins of 4f electrons with the outermost ligands or other Gd 3+ is anticipated to get weaker. These noninteracting and localized magnetic spins of Gd 3+ ions have induced the paramagnetism with increase in magnetization. [96,97] The paramagnetic moment from the Gd 3+ ions incorporated into the CeO 2 lattice increases with increasing the dopant concentration, which results in reduction of ferromagnetic ordering in Gd-doped samples. Therefore, 4%, 6%, 8%, and 10% Gd-doped samples have small ferromagnetic behavior in addition to linear paramagnetic signals, which is gradually increasing with the fluency of Gd 3+ ions in CeO 2 NPs. Though Raman and XPS analyses are showing an increase in the oxygen vacancies but this increase in oxygen vacancy concentration may not enhance the ferromagnetic ordering in Gd-doped samples. [98] Nithyaa and Jaya reported the ferromagnetic behavior of pure TiO 2 NPs but incorporation of Gd-ions enhanced the paramagnetic nature, which has been reported due to oxygen defects. [99] In other reports on Gd doping in ZnO, the paramagnetism in these samples is reported due to high magnetic moment of Gdions (µ = 7.1 µ B ) and due to presence of secondary phases of Gd 2 O 3 . [100][101][102] Now, the main issue herein is to understand the possible origin of ferromagnetic dominated paramagnetic behavior in pure CeO 2 and Gd-doped CeO 2 NPs, respectively. The origin of FM behavior has been discussed in this paper accounting the F-center exchange (FCE) mechanism as a subcategory of bound magnetic polaron (BMP) model. [103] The conception of FCE coupling is based on BMP model that has been interpreted with the presence of oxygen vacancies (V O ). These oxygen vacancies and magnetic ions constitute a BMP that produces the ferromagnetism in these systems. In pure CeO 2 NPs, the origin of ferromagnetism is supposed to the reduction of the oxidation state of Ce ions, i.e., Ce 4+ to Ce 3+ . The formations of oxygen vacancies give rise to the reduction of Ce 4+ to Ce 3+ state. The formation of oxygen vacancy left two electrons which may be transferred to a Ce 4+ ion converting Ce 4+ into Ce 3+ . Due to this process, mixed Ce 3+ and Ce 4+ states yield in the pure CeO 2 NPs, which has already been confirmed by Ce 3d core level spectra analysis. The ferromagnetism in pure CeO 2 NPs may be arise from the nearest-neighbor interaction, i.e., either double exchange (Ce 3+ -V O -Ce 4+ ) or superexchange (Ce 3+ -V O -Ce 3+ ), which is mediated by oxygen ions. [104] The double exchange interaction forms an F + center because the two electrons left by V O are trapped on Ce 4+ ion and V O (hydrogenic orbital), while superexchange interaction forms an F 2+ center due to the both electrons are trapped on Ce 4+ ions. [105] When Gd ion is incorporated into CeO 2 , it has suppressed the ferromagnetism of CeO 2 NPs (as shown in Figure 13b). Now, for Ce 0.98 Gd 0.02 O 2 sample, the F + center may be coupled with   the nearest Ce 3+ or Gd 4f orbital and form Ce 3+ -V O -Gd 3+ complex (BMP), which is dominated in this sample. When the size of this BMP is large enough to percolate through the lattice, long-range (weak) room temperature ferromagnetism can be realized with higher saturation magnetization. However, it is clearly observed that ferromagnetism has been suppressed with the increase in Gd-doping concentration up to x = 0.10. Due to increase in Gd-ion doping concentration, the number of Gd-ions in the interior of CeO 2 lattice is less than that on its surface or on the grain boundaries. Only those Gd-ions are allowed to enter the lattice that is permitted by the host ions and rest is expelled. Due to higher doping concentration the separation among Gd 3+ ions is decreased. These largely separated Gd 3+ ions suppress the ferromagnetism and undergo superexchange interaction with each other via O 2− ions and results in antiparallel alignment of the magnetic spins of Gd 4f shell present in the nearest-neighbor ions that do not negotiate in ferromagnetic ordering. Thus higher doping concentration of Gd 3+ ions tends to destroy the observed ferromagnetism in Gd-doped CeO 2 NPs. Hence in our case the increase in paramagnetic signals may be attri buted to increase in oxygen vacancy concentrations without enhancing the ferromagnetic ordering of the samples. This ferromagnetic ordering is further suppressed due to the increased concentrations of Gd 3+cation as the separation between these Gd 3+ -ions is decreased results in anti-parallel alignment of the spins of Gd 4f state due to superexchange interaction.

Water Splitting Analysis
The amount of photocatalytic H 2 evolved from the samples has been hourly monitored (  Figure 14a). According to the mechanism, when the surface of the molecular device Pt/GdCeO 2 exposed to the light, an electron of the valance band (VB) gets energized after receiving that energy of light and jumped from VB to conduction band (CB), which generates a pair of photohole (at VB) and photoelectron (at CB) at Gd/CeO 2 surface. Nascent photoelectrons of CB are arrived at the junction of Pt/electrolyte interface by passing through the electron-pool of the metallic Pt (that can segregate the photoelectrons from photoholes). These photoelectrons interact with H + ions [106] of the water at the interface and liberate the nascent H that combined with another nascent H atom to generate H 2 gas. Hole amassed at VB of the doped semiconductor is responsible for the breakdown of CH 3 OH in formaldehyde or formic acid or both as mentioned in Equations (16)- (26), [107,108] which can be used to depict the proposed electron transfer mechanism of the water splitting, as illustrated by Figure 14b.
There are many factors which can dominate the water splitting activity such as particle size of photocatalyst, binding energy, dopant concentration and position (either Gd 3+ ion is taking position of Ce 3+ or Ce 4+ ion), oxygen vacancies, band gap and band positions, and many more. All of the above factors collectively responsible for increase in hydrogen generation activity on increasing the dopant concentration in ceria. Usually the steady decrease in particle size increases water splitting activity with increase in Gd proportion due to the large. Introduction of dopant Gd into the CeO 2 lattice, also gradually increases the oxygen vacancy in the lattice arrangement of CeO 2 because Gd 3+ (radius of Gd 3+ = 0.105 nm and charge density = 91) replaced the high charged but small Ce 4+ ion(radius of Ce 4+ = 0.097 nm and charge density = 148) in 2%, 4%, and 8% doped samples but also replaced low charged but bigger sized Ce 3+ (radius of Ce 3+ cation = 0.114 nm and charge density = 75) in 6% and 10% Gd samples. [109] All of the above changes due to Gd-doping in ceria lattice maintained the phase purity (checked with XRD) with minor but favorable changes in lattice parameters and suggested the lattice arrangement of atoms with expanded electron clouds between high charge M(Ce 4+ /Ce 3+ ) and low charge M(Gd 3+ ) bonds through bridging O and O as shown in Figure 15a. That results into creating active side to generate more carriers that bring about the enhanced photocatalytic activity of the doped ceria.
Usually the steady decrease in particle size increases water splitting activity with increase in Gd proportion due to the large. Introduction of dopant Gd into the CeO 2 lattice also gradually increases the oxygen vacancy in the lattice arrangement of CeO 2 because Gd 3+ (radius of Gd 3+ = 0.105 nm and charge density = 91) replaced the high charged but small Ce 4+ ion (radius of Ce 4+ = 0.097 nm and charge density = 148) in 2%, 4%, and 8% doped samples but also replaced low charged but bigger sized Ce 3+ (radius of Ce 3+ cation = 0.114 nm and charge density = 75) in 6% and 10% Gd samples. [109] Global Challenges 2019, 3,1800090 Figure 14. a) Hydrogen production rate for pristine CeO 2 and 2%, 4%, 6%, 8%, and 10% Gd-doped CeO 2 compounds in 10% CH 3 OH under visible light exposure of 300 W Xe light source and b) charge transfer reaction at oxidative and reductive sites.
Local cluster framework of the tetrahedral coordinated groups of multivalent metal cations (Ce 4+ /Ce 3+ and Gd 3+ ) and anions (O 2 2− ) generates a strong local electrostatic field inside the tetrahedra, as confirmed by the XRD, XPS, and Raman results. Residual water molecules are captured by the strong local electrostatic field of the molecular device Ce 1−x Gd x O 2 (x = 0.02, 0.04, 0.06, 0.08, and 0.10). These water molecules attract the bridging oxygen through the protonic side and the metallic cation, i.e., Ce through the hydroxyl side ( Figure 15b).
Finally, we get bridging oxygen impregnated with a hydroxyl proton and the Ce metallic side with a hydroxyl group that function as Lewis acid sites, which create strong electron withdrawing centers neighboring bridging O-H groups [110] as shown by Figure 15b. These withdrawing centers can act as superacidic Brnsted acid sites (BAS) with a highly negative cluster framework. H 3 O + that detached from BAS to release the tension of the bulky species and generate H + . These H + reacts with the photoelectrons of the solid solutions and produce nascent H that couples with another H. Thus, hydrogen gas is generated.

Conclusion
In summary, Gd-doped CeO 2 nanoparticles have been successfully synthesized by the coprecipitation method. The structural and morphological studies have been made by XRD, TEM, HRTEM, and SEAD analysis. From the XRD analysis all the lattice parameters, volume, particle size of pure and Gd-doped CeO 2 NPs have been calculated, the particle size of these nanoparticles is further verified with TEM and SERS analysis and observed approximately similar to the results obtained with XRD analysis. The particles are spherical in shape and getting agglomerated with fluencies of Gd 3+ ions in CeO 2 sample and the particle size is in the range of 5-7 nm, which is confirmed from the TEM images. From the TEM results and analysis we have observed the broadening of diffraction rings, which indicates that the particles are small in size and crystallinity becomes low with increasing doping concentration of Gd 3+ ions in CeO 2 NPs.
From the analysis of the UV-Vis-NIR absorption spectra we have observed the variation in the refractive index and band gap energy with different concentration of Gd-ions in CeO 2 NPs. The reduction of refractive index with incorporation of Gd 3+ ions in CeO 2 NPs is beneficial to UV protection. Normally, UV protection ability is strongly depending on the particle size and at nanoregime UV absorption ability is stronger than that of microsized ones. From the SERS spectra on pure and Gddoped CeO 2 NPs, the particle size, oxygen vacancy concentrations, etc. have been made to understand the mechanism of other properties of these samples. From the SERS spectra we can say that no other impurity phases are present in our samples and hence the nature of ferromagnetism in these NPs is intrinsic in nature and derived from the defects and intrinsic and extrinsic oxygen vacancy concentrations, which is found to gradually increase with fluencies of Gd 3+ ions in CeO 2 NPs.
Further for electronic structure of these NPs the core level Ce 3d, O1s, and Gd 4d XPS spectra have been recorded and analyzed in detail. From this analysis the change of oxidation state of Ce +4 to Ce +3 ions, incorporation of the Gd +3 ions in the lattice and formation of oxygen vacancies are reported. From the core level Ce 3d spectra the presence of both Ce 3+ and Ce 4+ ions in all the samples and an increase in the Ce 3+ concentration can be seen with the fluencies of Gd 3+ dopant ions in CeO 2 NPs, due to the formation of defects or an amorphous phase of Ce 2 O 3 . From the O 1s core level spectra analysis we are able to demonstrate that doping of Gd 3+ ions in CeO 2 NPs can modify the rate of reduction of Ce 4+ to Ce 3+ oxidation state as well as affects the formation of oxygen vacancies in Ce 1−x Gd x O 2 (x = 0.02, 0.04, 0.06, 0.08, and 0.10) doped samples. However, the Gd 4d core level spectra cannot be recorded with good statistics due to very small concentrations but reports the presence of Gd ion in our NPs. In our magnetic measurements we can see that all the samples pure CeO 2 and Ce 1−x Gd x O 2 (x = 0.02, 0.04, 0.06, 0.08, and 0.10) are showing the weak ferromagnetism dominated paramagnetic behavior, which is assumed to be triggered due to change of oxidation state of Ce +4 to Ce +3 ions, incorporation of the Gd +3 ions in the lattice and formation of oxygen vacancies. From Raman and XPS analyses, the presence of oxygen vacancy related defects is apparent. From Ce 3d XPS spectra one can reveal that a significant increase in Ce 3+ ions is not only able to increase the oxygen vacancies due to formation of Ce 2