The Microstructure and Electronic Properties of Yttrium Oxide Doped With Cerium: A Theoretical Insight

Trivalent Cerium (Ce3+) doped Yttrium Oxide (Y2O3) host crystal has drawn considerable interest due to its popular optical 5d-4f transition. The outstanding optical properties of Y2O3:Ce system have been demonstrated by previous studies but the microstructures still remain unclear. The lacks of Y2O3:Ce microstructures could constitute a problem to further exploit its potential applications. In this sense, we have comprehensively investigated the structural evolutions of Y2O3:Ce crystals based on the CALYPSO structure search method in conjunction with density functional theory calculations. Our result uncovers a new rhombohedral phase of Y2O3:Ce with R-3 group symmetry. In the host crystal, the Y3+ ion at central site can be naturally replaced by the doped Ce3+, resulting in a perfect cage-like configuration. We find an interesting phase transition that the crystallographic symmetry of Y2O3 changes from cubic to rhombohedral when the impurity Ce3+ is doped into the host crystal. With the nominal concentration of Ce3+ at 3.125%, many metastable structures are also identified due to the different occupying points in the host crystal. The X-ray diffraction patterns of Y2O3:Ce are simulated and the theoretical result is comparable to experimental data, thus demonstrating the validity of the lowest energy structure. The result of phonon dispersions shows that the ground state structure is dynamically stable. The analysis of electronic properties indicate that the Y2O3:Ce possesses a band gap of 4.20 eV which suggests that the incorporation of impurity Ce3+ ion into Y2O3 host crystal leads to an insulator to semiconductor transition. Meanwhile, the strong covalent bonds of O atoms in the crystal, which may greatly contribute to the stability of ground state structure, are evidenced by electron localization function. These obtained results elucidate the structural and bonding characters of Y2O3:Ce and could also provide useful insights for understanding the experimental phenomena.

Trivalent Cerium (Ce 3+ ) doped Yttrium Oxide (Y 2 O 3 ) host crystal has drawn considerable interest due to its popular optical 5d-4f transition. The outstanding optical properties of Y 2 O 3 :Ce system have been demonstrated by previous studies but the microstructures still remain unclear. The lacks of Y 2 O 3 :Ce microstructures could constitute a problem to further exploit its potential applications. In this sense, we have comprehensively investigated the structural evolutions of Y 2 O 3 :Ce crystals based on the CALYPSO structure search method in conjunction with density functional theory calculations. Our result uncovers a new rhombohedral phase of Y 2 O 3 :Ce with R-3 group symmetry. In the host crystal, the Y 3+ ion at central site can be naturally replaced by the doped Ce 3+ , resulting in a perfect cage-like configuration. We find an interesting phase transition that the crystallographic symmetry of Y 2 O 3 changes from cubic to rhombohedral when the impurity Ce 3+ is doped into the host crystal. With the nominal concentration of Ce 3+ at 3.125%, many metastable structures are also identified due to the different occupying points in the host crystal. The X-ray diffraction patterns of Y 2 O 3 :Ce are simulated and the theoretical result is comparable to experimental data, thus demonstrating the validity of the lowest energy structure. The result of phonon dispersions shows that the ground state structure is dynamically stable. The analysis of electronic properties indicate that the Y 2 O 3 :Ce possesses a band gap of 4.20 eV which suggests that the incorporation of impurity Ce 3+ ion into Y 2 O 3 host crystal leads to an insulator to semiconductor transition. Meanwhile, the strong covalent bonds of O atoms in the crystal, which may greatly contribute to the stability of ground state structure, are evidenced by electron localization function. These obtained results elucidate the structural and bonding characters of Y 2 O 3 :Ce and could also provide useful insights for understanding the experimental phenomena.

INTRODUCTION
The rare-earth Cerium ions doped crystals constitute an attractive class of materials that have been extensively used in many kinds of fields including scintillation phosphors, laser medium, and white light emitting diode phosphors (Han et al., 2019;Lin et al., 2019;Masanori et al., 2020). The outstanding optical behaviors of trivalent Cerium ion (Ce 3+ ) has drawn considerable interest due to its popular optical 5d-4f transition. Among various host materials, Yttrium Oxide (Y 2 O 3 ) crystal is considered to be the most promising sesquioxide host because of its unique chemical and thermal stability. The Y 2 O 3 host crystal is also one of the multifunctional materials that can give rise to many application areas owing to its fabulous capacity of incorporating the activated laser ions (Ming et al., 2018;Wang et al., 2018;Ju et al., 2020). The latest study has indicated that the Ce 3+ doped Y 2 O 3 crystals (Y 2 O 3 :Ce) exhibit dominant emission bands at around 380 nm and relatively low intensive band at 560 nm (Gieszczyk et al., 2019). The results further demonstrate the ideal applications of energy storage phosphors for Y 2 O 3 :Ce. The excellent advantages of Y 2 O 3 :Ce can also be evidenced by the effective use as various laser ceramics (Lupei et al., 2017).
It is well-known that the laser actions can be generally identified in the absorption and emission spectra of rareearth doped materials. In order to explore the luminescent properties of Y 2 O 3 :Ce, Jia et al. (2001) had synthesized the Y 2 O 3 :Ce nanoparticles in experiments and measured the photoluminescence spectra at room temperature. Their results revealed that the strong emissions cover the ultraviolet band from 240 nm to 380 nm. To explain the emission lines of the spectra, Loitongbam et al. (2013) measured the luminescence intensities of Y 2 O 3 :Ce and found that the characteristic blue color emissions at 424 and 486 nm are originated from Ce 3+ ion 5d (spectra terms) → 4f (spectra terms). An unexpected optical activity, including up and down conversions, for Y 2 O 3 :Ce crystal was firstly observed by Marin et al. (2013). Although the laser actions were established by a few studies, many researchers were motivated to probe the structural properties of Y 2 O 3 :Ce. The effect of doping Ce 3+ ion into Y 2 O 3 fibers was investigated by Zhu et al. (2008). They found that the obvious quenching of the luminescence occurred at Ce 3+ concentration of 5%. By using the solid-state-reactive method, Liu et al. (2020) carried out a study on the structures of a series of Ce 3+ doped Y 2 O 3 ternary ceramics. The results demonstrated that the solubility of Ce 3+ concentration at 4% could broaden emission spectra and lead to a large red-shift, which is attractive for the white light emitting. A recent research on the structural properties of Y 2 O 3 :Ce was conducted by Krutikova et al. (2020). The nanopowders were obtained by laser ablation and the X-ray diffraction (XRD) patterns of Y 2 O 3 :Ce crystal were reported. By looking at the investigations concerning Y 2 O 3 :Ce in the literatures, it can be concluded that the systematic electronic structures have not yet been explored, especially for the theoretical insights. Furthermore, the lacks of Y 2 O 3 :Ce microstructures constitute a problem to exploit its potential prospects in many applications.
In this paper, we have performed a systematic study on the stable structures and electronic properties for Y 2 O 3 doped with Ce 3+ system. By using the CALYPSO (Crystal structure AnaLYsis by Particle Swarm Optimization) structure search method (Wang et al., 2010(Wang et al., , 2012Li et al., 2014) combined with first-principle calculation, the low-lying energy structures of Y 2 O 3 :Ce are extensively searched. A large number of candidate structures are obtained and the ground state structure together with the first four metastable structures is analyzed in detail. Based on the obtained lowest energy structure of Y 2 O 3 :Ce, we thoroughly conduct a calculation of the electronic properties, which could provide powerful guidance for further experimental and theoretical studies.

COMPUTATIONAL DETAILS
We have carried out an unbiased structure search for Y 2 O 3 doped with Ce 3+ system based on the CALYPSO method (Wang et al., 2010(Wang et al., , 2012Li et al., 2014). The CALYPSO is able to successfully predict the stable structures only with given chemical composition of the system (Lu et al., 2013. The detailed method of CALYPSO has been reported in many papers (Ju et al., 2016(Ju et al., , 2017(Ju et al., , 2019a. In this work, the structure searches are performed for Y 2 O 3 doped with Ce system at 80 atoms in one unit cell. The obtained lowlying energy structures are used to perform further geometric optimizations. We conduct the ab initio structural relaxations and electronic properties calculations in the framework of density functional theory (DFT) by using the local density approximation (LDA) exchange correlation functional, as implemented in the Vienna Ab Initio Simulation Package (VASP) (Kresse and Hafner, 1993;Kresse and Furthmuller, 1996;Perdew et al., 1996). Considering the strong f-electrons correlations within the heavy Ce 3+ ion, an onsite Coulomb repulsion U = 5.0 eV is employed in the calculations (Herbst and Waston, 1978). We use the projector-augmented wave method to simulate the valence electron space of Ce, Y, and O atoms. The used electrons are 4f 1 5s 2 5p 6 5d 1 6s 2 , 4s 2 4p 6 4d 1 5s 2 , and 2s 2 2p 4 , respectively. Sufficiently fine Monkhorst-Pack k meshes and 500 eV cutoff energy have been chosen to make sure that the calculated enthalpy of each atom is <1 meV. By using a super cell approach, the phonon dispersion spectra are calculated in PHONOPY code (Atsushi et al., 1993). The electron localization function (ELF) (Becke and Edgecombe, 1990;Savin et al., 1992) analysis of Y 2 O 3 :Ce is performed and the results are depicted in the VESTA software (Momma and Izumi, 2011). The projected Crystal Orbital Hamilton Population (COHP) (Richard and Peter, 1993) are calculated by the LOBSTER code (Volker et al., 2011;Stefan et al., 2016).

Crystal Structures
The stable structures for Y 2 O 3 :Ce system are favorably identified by using the method described in section Computational Details. On the basis of total energies from low to high, we have plotted the lowest-energy structure of Y 2 O 3 :Ce in Figure 1, together with the local [CeO 6 ] 9− complex ligand. Noticeably, the ground state structure of Y 2 O 3 :Ce possesses a novel structure with R-3 (No. 148) space group. To the best of our knowledge, the rhombohedral phase of Y 2 O 3 :Ce crystal is uncovered for the first time. This result indicates an interesting phase transition that the crystallographic symmetry of Y 2 O 3 changes from cubic (Ia-3) to rhombohedral (R-3) when the impurity Ce 3+ is doped into the host crystal. It is clearly seen from Figure 1 that the host Y 3+ ion can be naturally occupied by the impurity Ce 3+ ion. Interestingly, the Wyckoff position of Ce 3+ is 1b (0.5, 0.5, 0.5), suggesting that the ground state Y 2 O 3 :Ce is a standard cage-like structure. This result is different from that of Y 2 O 3 :Nd system (Ju et al., 2020). For reference, the coordinates of all atoms for the ground state Y 2 O 3 :Ce are summarized in Table 1. The estimated unit cell parameters and volume for Y 2 O 3 :Ce are a = b = c = 10.541 Å and 1171.371 Å (Han et al., 2019), respectively. These values are slightly smaller than those of pure Y 2 O 3 but are comparable to the results reported by Kumar et al. (2017). As regard to the local structure, the Ce 3+ ion is calculated to be 6-fold coordinated by O 2− , forming the [CeO 6 ] 9− complex ligand. The cationic site symmetry of Ce 3+ is C 3i with six equal Ce-O bonds of 2.369 Å. This bond length is similar with that of Y-O bonds because the effective radius of Ce 3+ (1.03 Å) is very close to Y 3+ (0.90 Å).
In the structure prediction, we adopt the chemical composition of Ce:Y: O = 1: 31: 48 to obtain the stable structures with nominal concentration of Ce 3+ . In this sense, the impurity Ce 3+ in Y 2 O 3 crystal is equal to 3.125 at %. Apart from the ground state structure, the CALYPSO also identifies a large number of candidate isomers that can be useful to study the structural evolution of the Y 2 O 3 :Ce. Figure 2 illustrates the first four metastable structures of Y 2 O 3 :Ce. The isomer (a) has the same R-3 space group as the lowest energy structure while the impurity Ce 3+ ions are likely to substitute the Y 3+ at the lattice vertexes. The Ce 3+ ion of isomer (a) takes the 1a (0, 0, 0) position. It is evidenced that the calculated crystal lattice parameters (10.543 Å) are nearly same as those of lowest-energy structure. The group symmetry of isomer (b) is predicted to be P1 with a triclinic phase. The Wyckoff position of Ce 3+ is predicted to be 1a (0.25, 0.75, 0.25). Calculated result reveals that the isomer (c) exhibits a monoclinic structure which belongs to P2 symmetry. The impurity Ce 3+ ion occupies the 1b (0, 0.47157, Although the X-ray powder diffraction (XRD) patterns of Y 2 O 3 :Ce crystals have been extensively studied, there appears to be inconsistencies of the spectra (Chien and Yu, 2008;Taibeche et al., 2016;Kumar et al., 2017). In order to clarify the crystal characters of the lowest-energy structure, we simulate the XRD patterns of Y 2 O 3 :Ce in the 2θ range of 15-65 • . The result compared with experimental data is presented in Figure 3. It is evident that the calculated spectrum is in perfect agreement with the values measured by Kumar et al. (2017), demonstrating the validity of the lowest energy structure as well as the accuracy of our theoretical calculations. It should be pointed out that the simulated diffraction peak at 34 • is ascribed to the (400) plane direction. This is accord with the result obtained by Taibeche et al. (2016) but different from the measured value proposed by Chien and Yu (2008). For comparison, the XRD patterns of the four isomers (a), (b), (c), and (d) are also provided in Figure 3. Although the overall distribution of the peaks in isomers is closely similar with each other, there are minor differences in the relative intensities. To evaluate the dynamical stability of Y 2 O 3 :Ce, the phonon spectrum within the Brillouin zone of ground state structure are calculated. Figure 4 illustrates the phonon dispersion curves along the high-symmetry directions including F, Γ , and Z. Clearly, the overall values in Figure 4 are positive and no virtual frequencies are observed in the full Brillouin zone. It is concluded that the rhombohedral phase structure of Y 2 O 3 :Ce crystal is dynamically stable.

Electronic Properties
To further elucidate the electronic properties of Y 2 O 3 :Ce crystal, we have performed a series of ab initio calculations including the electronic band structures, total and partial electronic density of states and electron localization functions. The calculated band structure and density of states (DOS) are plotted together in Figure 5. Our calculated results show that both of the conduction band minimum and valence band maximum are identified at Γ site. The band structure is considered to be a typical of semiconductor with relatively flat top of the valence bands. According to the calculations, the band gap value of ground state Y 2 O 3 :Ce is equal to 4.20 eV directly at Γ point. This result is very close to the energy gap of Y 2 O 3 :Nd system (Ju et al., 2020) but significantly smaller than that of pure Y 2 O 3 crystal (Wilk and Wallace, 2002). The direct band gap of 4.20 eV suggests a semiconductor character of the Y 2 O 3 :Ce. In addition to the electronic band gap, the electronic calculations of high-symmetry directions are in accordance with the above analysis based on phonon spectrum. In Figure 5A, we can clearly see that the band structures can be divided into three parts. The high conduction band is above 4.20 eV while the low valence band is below −0.17 eV. Interestingly, an extremely narrow valence band is observed just below the Fermi level. This result is greatly different with the band structures of pure Y 2 O 3 . The calculations show that the narrow valence band is caused by the electronic Alpha states. In contrast, the Beta electrons are not identified near the Fermi level. In order to explore the origins of the electronic bands, we further calculate the partial DOS including s, p, d and f states. The calculated DOS are depicted in Figure 5B. It can be clearly seen that the high conduction bands are mainly formed by d and p states. The p electrons are calculated to be the strongest state in the low valence bands. Moreover, the partial DOS of Y 2 O 3 :Ce reveals that the extremely narrow valence band near Fermi level is ascribed to the f orbital, which suggests that the impurity Ce 3+ ion leads to a dramatic reduction of the band gap. In other words, it is concluded that the incorporation of the doped Ce 3+ ion into Y 2 O 3 host crystal results in an insulator to semiconductor transition.
To achieve foundational understanding of the bonding character and distribution of electrons of Y 2 O 3 :Ce crystal, we have carried out a calculation on the electron localization functions based on the ground state structure. The visually ELF of the structure and (100) plane are presented together in Figure 6. Obviously, the electrons near the cationic atoms are greatly localized with ELF values at ∼0.9 while the ELF values FIGURE 3 | The simulated XRD patterns for ground state Y 2 O 3 :Ce and isomers (a-d), compared with measured spectra.
in the crystal lattice are nearly zero. This result indicates that the electrons localization on Ce and Y atoms broadens toward O atoms, forming a complete charge delocalization in the vicinity of O atoms. The strong ionic bonds are identified between Ce-O and Y-O. Furthermore, our calculations also show that the value of ELF at Ce atom is relatively larger than the ELF of Y atoms. This phenomenon can be explained as the remaining 4f (Masanori et al., 2020)

CONCLUSION
To summarize, we have systematically reported the structural evolutions, doping site locations and electronic properties of Y 2 O 3 crystal doped with Ce 3+ ions. By using the CALYPSO method in conjunction with first-principles calculations, a novel stable phase with R-3 space group is identified for the first time. For the ground state structure, the doped Ce 3+ can naturally occupy the central Y 3+ site in the crystal lattice of Y 2 O 3 , forming a standard cage-like structure. The cationic site symmetry of Ce 3+ is calculated to be C 3i with six equal Ce-O bonds. The first four candidate isomers present different doping sites for Ce 3+ , which is helpful to investigate the structural evolution of Y 2 O 3 :Ce. By comparing the simulated XRD patterns with experimental data, we demonstrate the validity of the lowest energy structure. The dynamically stability of Y 2 O 3 :Ce crystal is carefully examined through the calculation of phonon dispersions. Our results of electronic band structures reveal that both of the conduction band minimum and valence band maximum are located at Γ site, leading to a band gap value of 4.20 eV. This band gap suggests a semiconductor character of Y 2 O 3 :Ce system. Interestingly, an extremely narrow valence band near Fermi level is observed in the band structure and the contribution of this band is assigned to f orbital. In addition, the calculated results of visually ELF show that the charge localizations between O-O atoms are dramatically strong, suggesting the covalent bond character of O atoms in the Y 2 O 3 :Ce crystal. These findings could provide important information of the microstructures of rare-earth doped laser materials.

DATA AVAILABILITY STATEMENT
All datasets generated for this study are included in the article/supplementary material.

AUTHOR CONTRIBUTIONS
MJ, JW, and CZ conceived the idea. MJ, JH, YJ, YC, WS, and SL performed the calculations. MJ, JH, and WS wrote the manuscript. All authors reviewed the manuscript.