Fe-doped effects on phase transition and electronic structure of CeO2 under compressed conditions from ab initio calculations

Ab initio study of high-pressure phase transition and electronic structure of Fe-doped CeO2 with Fe concentrations of 3.125, 6.25, and 12.5 at% has been reported. At a constant-pressure consideration, the lattice constants and the volume of the supercell were decreased with an increasing concentration of Fe. The average bond length of Fe–O is lower than that of Ce–O. As a result, Fe doping induces the reduced volume of the cell, which is in good agreement with previous experiments. At high pressure (~ 30 GPa), it was found that the transition pressure from the fluorite to the cotunnite orthorhombic phase decreases at a higher concentration of Fe, indicating that the formation energy of the compound is induced by Fe-doping. Furthermore, compression leads to interesting electronic properties too. Under higher pressures, the bandgap increases in the cubic structure under compression and then suddenly plummets after the transition to the orthorhombic phase. The 3d states of Fe mainly induced the impurity states in the bandgap. In both the undoped and Fe-doped systems, the bandgap increased in the cubic phase at high pressure, while the gap and p-d hybridization decrease in the orthorhombic phase.


Introduction
Cerium oxide (CeO 2 ) is an attractive material with various applications, mainly for automobile catalytic converters to decrease pollutants, as well as solid oxide fuel-cell technologies and optical equipment [1][2][3][4][5][6][7][8][9][10]. Due to the importance of the CeO 2 properties, such as a high dielectric constant as well as a good epitaxial layer on Si, it is also viewed as a prospective material for future microelectronic applications. Hence, CeO 2 has been proposed to be a possible gate dielectric material in metal-oxide-semiconductor devices of the next generation [25]. Several experiments, such as highpressure Raman spectroscopy, reported that the pressureinduced transition of CeO 2 from cubic fluorite structure to orthorhombic PbCl 2 structure occurs at around 31 GPa [12]. These results are very close to that investigated by energydispersive X-Ray diffraction with phase transition pressure of 31.5 GPa [13]. Later, the properties of CeO 2 have been developed by doping transition metals and searching the candidate material, which has great potential for applications in spintronic and multifunctional electronic devices [14][15][16][17][18][19]. The structural and physical properties of the CeO 2 doped with Fe have been investigated by previous studies [20][21][22][23][24].
For the crystal structure of Ce 1-x Fe x O 2 , which was synthesized by various methods, it was shown that Fe-doped CeO 2 exhibited only fluorite structure with a small percentage of dopant. This fluorite phase was the only structure without the appearance of another phase of ceria and secondary impurity phase of Fe 2 O 3 until the Fe concentration was increased to 25% [25,26]. For electronic and optical properties, many previous studies have been obviously revealed the optical bandgap of Fe-doped CeO 2 decreases with an increase of Fe concentration [27,28]. However, there is a lack of clear explanation on, especially, electronic and optical properties of Fe-doped CeO 2 . A deeper understanding of those will be useful for further applications. In addition, high-pressure phase transformation has also been lacking both experiment and theory. Therefore, the aim of this study is to investigate the effects of Fe-doped CeO 2 at concentrations of 3.12%, 6.25%, and 12.50%. The details of structural phase transition and electronic structure of Fe-doped CeO 2 based on density functional theory study are discussed.
In this work, the structural relaxation of undoped CeO 2 has been carried out using first-principles calculations based on the Kohn-Sham equations to investigate the phase stability as a function of pressure. Further Fe-doped CeO 2 has been studied up to 50 GPa. This is because the fluorite phase transforms into the cotunnite phase at a pressure of 29.94 GPa, which is in good agreement with the experimental observations [12,13]. As a result of this, the structural phase transition of undoped CeO 2 is, in a way, similar to that of the Fe-doped case. At this point, it is interesting to note that the percentage of Fe is a key factor for the changing transition pressure. With respect to the dopant, the results demonstrate that the transition pressure depends on the percentage of Fe with respect to the undoped CeO 2 . Fe-doped CeO 2 further reveals that the relative bulk moduli of both the fluorite and cotunnite phases play important roles in the nature of the chemical bonding, hinting at easier compression. Regarding its potential for electronic properties, the concentration of Fe is shown to possibly have an effect on the energy gap. Finally, these findings provide crucial details for fundamentally understanding the structural phase transformation, the changing transition pressure, and the electronic properties of the Fe-doped CeO 2 under compressed conditions.

Computational details
Ab initio study based on density functional theory (DFT) within the CASTEP code [29] was employed to investigate high-pressure phase transition and electronic structure of Fedoped and undoped CeO 2 . Generalized gradient approximation (GGA) functional [30] based on Perdew-Burke-Ernzerhof (PBE) [31] exchange-correlation functional was performed. The results of the high-pressure structural phase transition and electronic properties of CeO 2 are in good agreement with experimental results by previous studies [12,13]. The ultrasoft pseudopotential was used with electronic configurations of Fe: 3d 6 4s 2 , Ce: 4d 1 5s 2 5p 6 5d 1 6s 2 and O: 2s 2 2p 4 . The plane wave basis was set as E cut = 500 eV, and the k-point was sampled using a mesh size of 0.04 2 /Å −1 . For all the structures, the total energy convergence has been tested within a tolerance level of 0.005 meV/atom. The unit cell parameters and atomic positions were optimized using the BFGS algorithm [32] with the convergence tolerance as 0.01 eV/Å, within the pressure range that corresponds to experiments [12,13]. For the Fe-doped CeO 2 , the supercells that have been constructed for 3.125, 6.25, and 12.50% doping of Fe are 2 × 2 × 2, 2 × 2 × 1, and 2 × 1 × 1 of both phases, respectively. Fe atom was replaced on a Ce site at the center of the supercell. The Birch-Murnaghan equation of state [33] was used to calculate the pressure values. Since the DFT method performs at absolute zero temperature, minimum Gibbs free energy of the state leads to its enthalpy. The stable phase at each pressure was compared by considering the minimum enthalpy. For band structure calculation, the k-point mesh that has been used is 0.03 2 /Å −1 for all structures. Spin setup in GGA-PBE was added for splitting spin types up and down on electronic band and density of states (DOS) calculations. It was performed to clarify the effect of Fe atom on the bandgap reduction, which has been reported by previous studies [27,28].

Results and discussion
The atomic structures of 3.125% Fe-doped CeO 2 in cubic (Fm-3 m) and orthorhombic (Pnma) phases are presented as shown in Fig. 1. In Table 1, it is shown that the undoped CeO 2 lattice constant is 5.4634 Å which agrees within 1-2% with the experiment results of 5.411 Å [34] and 5.406 Å [13]. The effect of the Fe atom obviously influences the crystal volume because of the different atomic sizes between Ce and Fe. The decrement of a 0 with the increment of Fe is due to the smaller size of Fe atoms. Values of electron affinity and electronegativity in the periodic table of Fe are higher than that of Ce. This also corresponds to the experimental results [20,21,28]. At high-pressure consideration, a phase transition from fluorite phase to cotunnite phase is calculated at 28.0 GPa with a volume reduction of 6.45% for undoped CeO 2 . The relationship between enthalpy versus pressure of four compositions (pristine and three doped cases) is presented in Fig. 2. The decrement of the transition pressure trend depends on the percentage of Fe. This is because the free energy of CeO 2 systems is decreased at a high concentration of Fe-doping. Therefore, Fe-doping reduces free energy in the high-pressure phase more than the ambient pressure phase.  Following the remarkable result, as shown in Table 2, it is worthy to note that the transition pressure depends on the percentage of Fe, resulting in the dramatic decrease in the transition pressure with the percentage of Fe. This implies that the computational results might be considered to be consistent with the increase of Fe concentrations. Besides, it is interesting to note the bulk moduli because the percentage of Fe plays a critical role in the mechanical properties. The result of the relative bulk moduli, therefore, has been carefully investigated by comparing to Fe-doped CeO 2 of both fluorite and cotunnite phases. Subsequently, the relative bulk modulus of fluorite is smaller than that of cotunnite with the increasing percentage of Fe, supporting the transition pressure behavior. A possible cause for this could be the nature of the chemical bonding that is the Fe-O being the weaker bonds, and thus, it is easier to compress.
For Fe-doped CeO 2 , it has two naturally occurring energy bandgaps. The first one, the optical bandgap, is the gap between the maximum of the valence band, situated under the Fermi level, which are mainly O-2p states, and the narrow upper bands mainly contributing by Ce-4f states. The electronic bandgap is due to the unoccupied conduction bands formed by Ce-5d states hybridizing with O-2p states. The two energy bandgaps of undoped fluorite CeO 2 and Fedoped CeO 2 at ambient pressure are shown in Fig. 3b. The   [36]. At 3.125% of Fe, the optical and electronic gaps dramatically decrease to 1.06 and 4.76 eV, respectively. They further slightly reduce when the concentration of Fe increases to 6.25% and 12.50%. To further understand the electronic property of Fe-doped CeO 2 , energy dispersion of Ce 0.9688 Fe 0.0312 O 2 along with the high symmetry directions in the Brillouin zone, the total density of states (DOS) and partial density of states (PDOS) are shown in Fig. 4. The finding obviously discloses the effect of Fe-doped CeO 2 . There are two pieces of evidence consisting of: (1) states of Fe-3d that are situated around the Fermi level. These consist of two energy bands and are represented by the solid line in PDOS. The first one, exhibiting Fig. 2 The relationship between relative enthalpy versus pressure of 0.00%, 3.125%, 6.25% and 12.50% of Fe concentration for a, b, c, and d, respectively    Fig. 5. It was first verified for pure CeO 2 and found that spin-up gave a lower energy level compared with spin down, which relates to basic idea in quantum chemistry. The edge of the conduction band minimum is due to the spin-up state of the f-state in Ce atom. Under high pressure in the cubic phase up to 25 GPa, it was found that the bandgap of pure CeO 2 increased. The CBM gets pushed to a higher energy level with pressure. This supports the idea that the decreasing bond length and cell volume are mainly influenced by the electronic states of the nearly free electrons in CeO 2 . After phase transition to the orthorhombic phase, the electronic DOS was calculated at 35 GPa. The gap between CBM and VBM is decreased in the orthorhombic phase. Reconstruction of the new stable phase increases the average bond length of Fe-O, although cell volume reduces under compression. The new stable phase (Pnma) results in the reduction of the bandgap and energy states of CBM in pure CeO 2 , as shown in Fig. 5a. The same trend is seen for the Fe-doped system between 0 and 35 GPa, and the DOS of 3.125%Fe is depicted in Fig. 5b. Fe atom gave contribute to impurity states between VBM and CBM. Figures 5c and d shows that for 3.125 and 6.25% of Fe, the DOS is not significantly different. Figure 5e presents the DOS in the orthorhombic phase and shows that the p-d hybridization decreases when compared with the cubic phase.
In addition, the two bandgaps slowly decrease for Fe concentrations at 6.25% and 12.50%. This can be clearly explained because of the saturation of Fe electronic states, which cannot be much more extensive over the edge of the bands at high Fe concentrations. The decrease of volume at high concentrations of Fe affects the decrease in bond length of Ce-O, and it directly leads to the increasing bandgaps as well. However, these results are useful to clarify the background phenomena of doping Fe in CeO 2 ; on the other hands, these also need evidence from the further experiment, which is still lacking. Furthermore, effects of Fe concentrations that are investigated in this study would be beneficial to material engineering for designing modern electronic devices.

Conclusions
CeO 2 doped with Fe has been investigated using first-principles computational techniques. The effect of Fe doping with concentrations of 3.12, 6.25, and 12.5% has been considered. The GGA-PBE functional was employed to calculate the stability of electronic-crystal structures under high pressure based on the fluorite to cotunnite phase transition, as well as the change of the optical and electronic bandgaps. The calculated lattice constant and density of the cubic fluorite structure at ambient pressure decrease with increasing concentration of Fe dopants because the substituting Fe atom is smaller and lighter than the Ce atom. The two bandgaps dramatically decrease at 3.12% of doping of Fe, and they further sluggishly reduce at two higher Fe concentrations and 6.25% and 12.50%. The 3d states of Fe atom are the main cause of impurity states within the intrinsic bandgap. In both the undoped and Fe-doped systems, the bandgap increases for the cubic phase under pressure, while the gap and p-d hybridization suddenly decrease after the phase transition. We believe that these results of the effects of Fe will be beneficial to bandgap engineering in materials for designing modern electronic devices.