The XRD patterns of the samples prepared by hydrothermal reaction at 160°C for 12 h are shown in Figure 1a. The sample obtained with CeCl₃·7H₂O as the starting agent shows no XRD peaks, indicating that it is amorphous, whereas the sample from Ce(NO₃)₃·6H₂O exhibits XRD peaks that correspond to the (111), (200), (220), (311), (222), and (400) planes, which are consistent with the face-centered cubic fluorite structure of CeO₂ in the standard data from the Joint Committee on Powder Diffraction Standards (JCPDS) 34–0394, indicating that pure CeO₂ was successfully synthesized via these procedures.

In this study, we found that the type of cerium source has a great effect on the morphology of the final product. The cerium source from Ce(NO₃)₃·6H₂O shows that the sample consisted of sphere-like particles with diameters of 100 to 250 nm (Figure 1b), whereas other cerium sources such as CeCl₃·7H₂O, Ce(CH₃CO₂)₃·xH₂O, and Ce₂(SO₄)₃·8H₂O resulted in irregular shapes and agglomerated particles as shown in Figure 1c,d,e, respectively. Therefore, it is clearly seen that cerium source from nitrate is most favorable for the formation of uniformly sized CeO₂ nanospheres. It is possible that the absorption of PVP molecules on various crystallographic planes of cerium source played a major role in determining the product morphology, due to the fact that the supersaturation degree has a significant influence on the crystal nucleation rate and crystal growth rate 19. However, the real reason for the morphology variation of the cerium source and surfactants has yet to be fully understood.

Figure 2 shows the XRD patterns of the pure CeO₂ from cerium nitrate at various hydrothermal treatment durations and temperatures. All the samples exhibited six typical peaks corresponding to the (111), (200), (220), (311), (222), and (400) planes, which are consistent with the face-centered cubic fluorite structure of CeO₂ in the standard data from JCPDS 34–0394, and this is in agreement with the selected area electron diffraction (SAED) patterns shown in Figure 3d. The values of the lattice constant calculated from the XRD spectra are shown in Table 1. The average crystallite size of all the samples was calculated from X-ray line broadening of the peaks at the (111), (200), (220), and (311) planes using Scherrer’s equation, (as listed in Table 1). We observed that the lattice parameter decreases with increasing crystallite size. This decrease is possibly due to the introduction of Ce³⁺ ions into the crystal lattice. Ce³⁺ ions have a higher ionic radius (1.034 Å) compared with the Ce⁴⁺ ions (0.92 Å) and introduce oxygen vacancies. Therefore, the concentration of Ce³⁺ ions increases, and there is also an increase in the number of oxygen vacancies. It is observed that the pure CeO₂ nanoparticles experience considerable lattice distortion, which is in good agreement with earlier reports on CeO₂ nanoparticles 920, which indicated that this causes a change in the Ce-O bond length (lattice distortion) and the overall lattice parameter.

E_g, bandgap energy; M_s, saturation magnetization. Data of magnetization of pure CeO₂ nanospheres is before and after Ar annealing.

The formation of a cubic structure in the CeO₂ nanospheres was further supported by the Raman spectra. Figure 4 shows typical spectra of CeO₂. The Raman active modes are shifted from 458 to 461 cm⁻¹ for the CeO₂ samples heated at 160°C to 200°C. These Raman active modes are attributed to a symmetrical stretching mode of the Ce-80 vibrational unit, and therefore, they are very sensitive to any disorder in the oxygen sublattice that resulted from thermal, doping, or grain size 21222324. The effect of the microstructure of CeO₂ on the shape of the Raman spectra was observed by the broadening of the line and by increases in its asymmetry, which are attributed to the reduction of the phonon lifetime in the nanocrystalline regime 25 26. The particle size of the CeO₂ sample can be also estimated from the Raman line broadening using the following Equation 1 23 24 27:

Γ ( cm − 1 ) = 10 + 124.7 D R ,

where Γ ( cm − 1 ) is the full width at half maximum of the Raman active mode peak and D_R is the particle size of a CeO₂ sample. This relation can be used to determine the crystal size of the CeO₂ samples as shown in Table 1. This calculated crystal size is near that obtained from X-ray line broadening.

The morphology and structure of CeO₂ nanospheres were investigated by FE-SEM and TEM as shown in Figure 3. TEM bright field images show that the samples contain monodisperse nanospheres with a narrow size distribution. The high-magnification TEM image of a single particle (Figure 3b) indicates that the sphere has a diameter of about 218 nm. This result is similar to the work reported by Zhou et al. 28, in which spherical CeO₂ crystallites assembled by nanoparticles were synthesized by hydrothermal treatment because small nanoparticles of CeO₂ aggregated and gradually evolved into a spherical assembly, achieving a low surface energy. The corresponding SAED patterns (inset in Figure 3d of the products show spotty ring patterns indicative of a face-centered cubic structure of CeO₂ (JCPDS 34–0394), which is in agreement with the XRD results. The HRTEM images of the CeO₂ sample prepared at 200°C for 12 h and the CeO₂ sample prepared at 200°C for 12 h followed by annealing in Ar at 400°C for 2 h, are shown in Figure 5a,b, respectively. The d spacings of the lattice fringes of approximately 0.30 and 0.31 nm for the CeO₂ sample prepared at 200°C for 12 h (Figure 5a) calculated from the HRTEM images correspond to the (111) plane of CeO₂, whereas the d spacings of approximately 0.31 and 0.32 nm (Figure 5b) for the CeO₂ sample prepared at 200°C for 12 h followed by annealing in Ar at 400°C for 2 h match with (111) plane of CeO₂. This is in good agreement with the standard data (JCPDS 34–0394).

The UV–vis absorption spectra of the pure CeO₂ nanospheres are shown in Figure 6a. All the samples show a strong absorption below 400 nm (3.10 eV) with a well-defined absorbance peak at approximately 302 nm (4.10 eV). The direct bandgap energy (E_g) is determined by fitting the absorption data to the direct transition as shown in Equation 2:

α hν = A hν − E g 1 / 2

where α is the optical absorption coefficient, hν is the photon energy, E_g is the direct bandgap, and A is a constant 29. The extrapolation of the linear portions of the curves towards absorption equal to zero (y = 0) gives E_g for direct transitions (Figure 6b). The estimated direct bandgaps of all the samples are shown in Table 1. The bandgap of CeO₂ reported in this work is lower than that reported in the literature. Chen and Chang 30 reported direct bandgap values ranging from 3.56 to 3.71 eV for CeO₂ nanoparticles synthesized by precipitation method. Maensiri et al. 21 reported direct bandgap values ranging from 3.57 to 3.61 eV for CeO₂ nanoparticles synthesized by the sol–gel method using egg white. Similarly, Masui et al. reported direct bandgap values of 4.1 and 2.6 nm for CeO₂ nanoparticles prepared using reverse micelles to be 3.38 and 3.44 eV 31, respectively, due to quantum confinement effect 32. This phenomenon has been well explained for particle sizes down to less than a few nanometers, but for our results, the bandgaps increased with increasing crystal size, which exhibit blueshifts in the UV absorption spectra inferred from the bandgap calculated for pure CeO₂ nanospheres. This blueshift has been reported to be an electrostatic potential effect due to a cerium valence change when the particle size is larger than a few nanometers (e.g., ≥8 nm). The Ce⁴⁺ ions coexist with Ce³⁺ ions, and these ions can be attributed to oxygen vacancies at the surface 33. Therefore, in our work, the bandgaps increased with increasing crystal size. The crystallite size is in the range of 9 to 19 nm as indicated by the existence of the blueshift for our CeO₂ nanospheres.

Figure 7 shows the room temperature PL spectra obtained using a Xenon laser of 290 nm as the excitation source of the CeO₂ nanospheres. The spectra of all the samples are almost identical and mainly consist of five emission bands: a strong blue emission band at 422 nm (2.93 eV), a weak blue band at 446 nm (2.78 eV), a blue band at 460 nm (2.69 eV), a strong blue-green band at 485 nm (2.55 eV), and a green band at 529 nm (2.35 eV). Our results are consistent with that reported for CeO₂ in the literature. The strong emission peak at 410 nm 34 and 422 nm 35 observed for CeO₂ nanoparticles as-prepared at λ_ex = 290 nm. Maensiri et al. 21 reported a blue band at approximately 443 nm, along with a green band at 529 nm for 400°C to 500°C calcined sample, and a strong UV emission band at 392 nm for 600°C calcined sample. The dependence of the PL blueshift peak on CeO₂ particle concentration has also been observed by Sathyamurthy et al. 34 for CeO₂ nanoparticles synthesized by a reverse micelle route. This phenomenon has been explained by charge transitions from the 4f band to the valence band of the CeO₂ in both nanoparticles and thin films 36. In addition, it is well known that the emission energy from the 4f band to the valence band energy gap of CeO₂ is about 3.0 to 3.38 eV, as determined from the calculation of the electronic structure of CeO₂3537. Therefore, the emission in our CeO₂ samples could be assumed to be the transition from the Ce 4f band to the O 2p band (valence band) in CeO₂. The broad PL band ranging from 300 to 550 nm of all the samples could be the result of defects, including oxygen vacancies in the crystal with electronic energy levels below the 4f band 38. This is confirmed by the enhanced absorption tail below 3 eV in nonstoichiometric CeO₂ that was previously observed and attributed to the presence of oxygen vacancies 39.

The valence state of Ce in pure CeO₂ nanospheres was determined by XANES spectra measured at Ce L₃ edge. Figure 8a shows the edge energies of the Ce(NO₃)₃·6H₂O standard and CeO₂ standard. The standard Ce(NO₃)₃·6H₂O has a single peak illustrated by one intense white line at approximately 5,726.8 eV, which can be associated with the final state of 2

p

L

L

L

Figure 8b shows the XANES spectra of pure CeO₂ for various hydrothermal treatment durations and temperatures before and after annealing in Ar. The quantitative analysis of the valence state of Ce in each of the three states of the CeO₂ nanospheres was performed using multi-peak Gaussian fitting obtained from the XANES spectra, as shown in Figure 8c. The analysis shows that Ce in the samples is in a mixed valence state of Ce³⁺ and Ce⁴⁺. From these results, we can obtain the valence state of Ce according to the fitting parameters of the peak positions and areas listed in Table 2. It is observed that the percentage of Ce³⁺ ranges from 7% to 13.7% in the pure CeO₂ samples. These results provide confirmation of the formation of oxygen vacancies on the surface of the CeO₂ samples. It is possible that the concentration and distribution of oxygen vacancies play an important role in the magnetism of our CeO₂ nanospheres. The highest percentage of Ce³⁺ is 13.7% for CeO₂ prepared at 200°C for 24 h, with the increase in the number of oxygen vacancies, leading to the highest M_s values. The concentration of Ce³⁺ in our pure CeO₂ sample is higher than the values reported in the literature for CeO₂. Zhang et al. 41 reported the average Ce³⁺ concentration of 10- and 6-nm CeO₂ nanoparticles prepared by mixing cerium nitrate and hexamethylenetetramine in aqueous solution at room temperature to be 1% and 6.5%, respectively. Chen et al. 17 reported that the concentration of Ce³⁺ was higher than 21% for CeO₂ nanoparticles synthesized by the thermal decomposition method, which is higher than the value for pure CeO₂ nanospheres reported in this study.

Figure 9a,b shows the field dependence of the specific magnetization (M-H curve) of pure CeO₂ samples prepared at 160°C and 200°C for 12 h and prepared at 160°C and 200°C for 24 h, respectively, obtained from room temperature VSM measurements. The sample of CeO₂ prepared at 160°C for 12 h exhibits mixed behaviors of ferromagnetism and diamagnetism having hysteresis loops at low field. The samples that were prepared at 200°C for 12 h showed weak RT-FM with magnetization (M) of approximately 0.0026 emu/g, and the samples that were prepared at 160°C and 200°C for 24 h showed weak RT-FM with saturation magnetization (M_s) of approximately 0.0053 and 0.016 emu/g, respectively (as listed in Table 1). These values are higher than the M_s values reported in the literature for pure CeO₂ nanospheres 1517. Sundaresan et al. 15 reported an RT-FM with an M_s value of approximately 0.0019 emu/g for CeO₂ nanoparticles with an average size of approximately 15 nm. Ge et al. 18 reported weak ferromagnetic behavior at an ambient temperature with an M_s value of approximately 0.0007 emu/g for pure CeO₂ nanoparticles with an average size of approximately 100 nm obtained commercially from Sigma-Aldrich Corporation (purity of 99.9%). However, magnetic behavior (M_s of approximately 0.0057 emu/g) was also observed in monodisperse CeO₂ nanocubes with an average size of approximately 5.3 nm prepared by a chemical method. The results obtained here (experimental and theoretical) provide evidence that pure CeO₂ samples can indeed have a magnetic moment due to oxygen vacancies. This direct ferromagnetic coupling is called F-center exchange (FCE) 45, as cerium can have both variable valence states (Ce⁴⁺/Ce³⁺) and oxygen vacancies on the surface of the CeO₂ nanoparticles. It is possible that oxygen vacancies can create magnetic moments on neighboring Ce ions 46. In this work, the effect of Ar annealing at 400°C for 2 h on the magnetic properties was also performed to confirm the effect of oxygen vacancies on magnetic properties of the annealed samples. However, this effect was clearly observed only on the CeO₂ sample prepared at 200°C for 12 h and followed by annealing in argon atmosphere at 400°C for 2 h, as its magnetization increased from 0.0025 emu/g to 0.010 emu/g as (see inset of Figure 9b). It is noted that for the samples prepared at 160°C and 200°C for 24 h, annealing did not affect much their magnetic behavior due to the short time of annealing.

To explain the origin of the ferromagnetic contribution in the CeO₂ nanostructures, the following arguments are proposed. The annealing of samples in an Ar atmosphere at 400°C for 2 h could possibly increase the number of oxygen vacancies and Ce³⁺ ions in the samples. The high concentration of Ce³⁺ (approximately 13.3% Ce³⁺ for the sample prepared at 200 °C for 24 h) suggests that defects could be present in the majority of the samples, which activate more coupling between the Ce ions, leading to an increase in M_s. Wen et al. 9 reported the variation of RT-FM in oxygen and H₂ (10%)/Ar (90%) annealed samples of 1% Co-doped CeO₂ powder. They found that the sample showed little hysteresis loop after O₂ annealing and that the FM signal decreased significantly, while the H₂ (10%)/Ar (90%) annealed sample showed an enhanced FM with M_s of about 0.4 emu/g. However, further work is needed to achieve a thorough understanding, and this will be of great interest to researchers in the field of dilute magnetic oxides.