Electronic Band Structure Variations in the Ceria Doped Zirconia: A First Principles Study

Abstract

Using first principle calculations, the effect of Ce with different doping concentrations in the network of Zirconium dioxide (ZrO₂) is studied. The ZrO₂ cell volume linearly increases with the increasing Ce doping concentration. The intrinsic band gap of ZrO₂ of 5.70 eV reduces to 4.67 eV with the 2.08% Ce doping. In 4.16% cerium doped ZrO₂, the valence band maximum and conduction band minimum come closer to each other, about 1.1 eV, compared to ZrO₂. The maximum band gap reduction of ZrO₂ is observed at 6.25% Ce doping concentration, having the value of 4.38 eV. No considerable shift in the band structure is found with further increase in the doping level. The photo-response of the ZrO₂ is modulated with Ce insertion, and two distinct modifications are observed in the absorption coefficient: an imaginary part of the dielectric function and conductivity. A 2.08% Ce-doped ZrO₂ modeled system reduces the intensities of peaks in the optical spectra while keeping the peaks of intrinsic ZrO₂. However, the intrinsic peaks related to ZrO₂ completely vanish in 4.16%, 6.25%, 8.33%, and 12.5% Ce doped ZrO₂, and a new absorption hump is created.

1. Introduction

Recently, zirconia (ZrO₂) based ceramic materials got increasing attention from researchers due their wide range of applications, including thermal barrier coatings (TBC), solid oxide fuel cells, catalysis, and energy conversion [1,2,3]. In thermal barrier coatings, zirconia in its pure form faces two main problems. The first one is its phase transformation from tetragonal to monoclinic, leading to volume expansion, cracking, and failure. Secondly, its thermal conductivity is not sufficiently low, and it could be lowered by mixing it with other oxides, including CeO₂, Sc₂O₃, and In₂O₃. Moreover, the mixing of ZrO₂ with aforementioned oxides stabilizes ZrO₂ at high temperature [4,5].

Ceria (CeO₂) is widely used in the modern catalytic industry, automotive exhaust catalysis, solid oxide fuel cells, and water-gas shift (WGS) reactions [6,7]. For an oxygen storage material, it is used as a component in automotive three-way catalysts. The oxygen storage capabilities of CeO₂ are found to degrade at high temperature, which strongly limits its applications. It is reported that the thermal stability of CeO₂ can be improved by mixing it with zirconium oxide [8,9,10].

Charge compensation is essential in the case of substitutional doping. Ce⁴⁺ and Zr⁴⁺ both are tetravalent ions, and the substitution of Zr⁴⁺ by Ce⁴⁺ would not lead to any charge imbalance. Thus, the cerium insertion in the network of ZrO₂ would reduce the thermal conductivity while creating minimum structure distortion. Experimentally, it is proven that Ce mixing with ZrO₂ can lead to improved thermal stability at higher temperature, along with lowering thermal conductivity [11]. On the other hand, the addition of Zr into the bulk of CeO₂ can improve the oxygen storage capacity of a ceria-zirconia solid solution, and it can broaden the application spectrum of CeO₂. Zr doping in the structure of CeO₂ is widely studied. Andersson et al. [10] used ab-initio calculations to calculate the redox thermodynamics and kinetics of CeO₂ mixed with ZrO₂. It was found that Zr⁴⁺ doping decreased the vacancy formation energy and the migration barrier in CeO₂ [10]. Yang [6] and his co-workers studied the effect of Zr doping on the redox properties of CeO₂. Zr doping substantially lowered the formation energy of an O vacancy when the vacancy was created next to the Zr dopant [6].

With the Ce doping concentration Ce_1−xZr_xO₂ (x = 0.25, 0.5, 0.75, 1), Tian et al. [12] reported the replacement of Ce by Zr, leading to the formation of a pseudo-cubic fluorite-type structure. Moreover, increasing the Zr doping concentration linearly decreased the lattice parameters and cell volume of CeO₂ [12]. Because it is considered a solid solution, it would be important to increase the doping concentration of Ce in the cubic ZrO₂ and investigate its effect on the structure and properties. Moreover, Ce doping in the structure of cubic ZrO₂ should be studied in detail.

In this paper, Ce doping in ZrO₂ has been studied with the Ce doping concentration of 2.08%, 4.16%, 6.25%, 8.33%, and 12.5%, corresponding to the Ce/Zr ratio of 6.25%, 12.5%, 18.75%, 25%, and 37.5%, respectively. Furthermore, the effect of Ce doping on the geometrical structure, electronic band structure, and optical properties is elucidated.

2. Methodology

The Kohn-Sham density functional theory (DFT) calculations were performed with Materials Studio 8.0 [13]. The valence electronic states were expanded in a basis of plane waves, and the oscillating wave function of core electrons were represented by a projected augmented wave approach. Moreover, the special Perdew-Burke-Ernzerhof functional for solids (PBEsol) [14,15] was used as an exchange correlation functional with ultrasoft pseudopotential [16]. For the plane–wave set, a cut-off energy of 400 eV and 3 × 3 × 3 k-points mesh was utilized. Simulated models were optimized with respect to cell parameters and atomic positions using the Broyden, Fletcher, Goldfarb, Shanno (BFGS) minimization scheme under the maximum force of 0.01 eV/Å. Furthermore, the stress tensor on the cell was less than 0.02 GPa [17,18].

A conventional 12 atoms cubic unit cell of zirconia (space group Fm-3m), extended to 2 × 2 × 1 repetition forming a 48 atom supercell, was utilized. Cerium (Ce) doped zirconia models were introduced by replacing a regular lattice Zr atom with a Ce atom. The cerium doping concentration can be increased by increasing the number of Ce atoms substituting the Zr sites. The Ce doped zirconia modeled systems and their corresponding Ce doping concentration and Ce/Zr ratio are summarized in

Table 1. The Ce doping concentration and Ce/Zr ratio of simulated models.

S. No.	Model	Representation	Ce Doping Concentration (%)	Ce/Zr Ratio (%)
1	Zr16O32	Zr-0	0	100
2	CeZr15O32	CeZr-1	2.08	6.25
3	Ce2Zr14O32	CeZr-2	4.16	12.5
4	Ce3Zr13O32	CeZr-3	6.25	18.75
5	Ce4Zr12O32	CeZr-4	8.33	25.0
6	Ce6Zr10O32	CeZr-6	12.5	37.5

. The CeZr-1 and CeZr-6 models are visualized in Figure 1.

3. Results and Discussion

3.1. The Effect of Ce Inclusion on the ZrO₂ Structure

The optimized lattice parameters and cell volumes of the zirconia structure are summarized in

Table 2. Lattice parameters and unit cell volumes of Ce doped zirconia modeled systems.

Model	a (Å)	b (Å)	c (Å)	Cell Volume (Å3)
Zr-0	5.0790	5.0790	5.0796	131.0392
Zr-0 (calculations [12])	5.0654	5.0654	5.0654	129.974
Zr-0 (experiments [20])	-	-	5.090	-
CeZr-1	5.0959	5.0945	5.0925	132.8176
CeZr-2	5.1179	5.1179	5.1132	133.9314
CeZr-3	5.1489	5.1520	5.1482	136.5704
CeZr-4	5.1582	5.1582	5.1604	137.3086
CeZr-6	5.1886	5.1886	5.1733	139.2799

. The pure ZrO₂ system has a = 10.158 Å, b = 10.158 Å (double values because of 2 × 2 × 1 supercell), and c = 5.0796 Å. The optimized lattice parameters are in close agreement with the available calculated data [12,19] and experimental values [20]. Substituting Ce at Zr sites induces slight change in the lattice parameters in the form of elongation. Table 2 depicts that as the content of Ce increases, the elongation in the lattice parameters increases. The higher ionic radii of Ce⁴⁺ = 0.97 Å in comparison to Zr⁴⁺ = 0.84 Å is responsible for this change [6]. Furthermore, the cell volume of zirconia gradually increased with the increasing Ce concentration.

The behavior of the cell volume with the Ce doping concentration is displayed in Figure 2. A linear increase in the unit cell volume is found with the increasing Ce doping concentration. Cerium (0.97 Å) insertion at Zr (0.84 Å) sites is responsible for the increase in cell volume.

The average bond lengths of the optimized Ce doped ZrO₂ modeled systems are summarized in

Table 3. Bond lengths (averaged) of the simulated systems.

S. No.	Model	O-Zr (Å)	O-O (Å)	O-Ce (Å)
1	Zr-0	2.1993	2.5395	-
2	CeZr-1	2.2004	2.5430	2.2885
3	CeZr-2	2.2049	2.5507	2.2919
4	CeZr-3	2.2127	2.5643	2.2992
5	CeZr-4	2.2144	2.5650	2.2944
6	CeZr-6	2.2199	2.5813	2.3006

. The zirconia system is optimized with the O-Zr and O-O bond lengths of 2.1993 Å and 2.5395 Å, respectively. The calculated data is in good agreement with the theoretical [12] and experimental [21] findings. Substituting Ce at Zr sites elongates the O-Zr and O-O bond lengths. Table 3 depicts that the O-Zr and O-O bond lengths linearly increase with an increasing Ce doping concentration. The increasing trend of the O-Zr and O-O bond lengths is ascribed to the difference in the ionic radii of Ce⁴⁺ and Zr⁴⁺. It is interesting to note that the O-Ce bond length initially showed an increasing trend, which became nearly constant for CeZr-2, CeZr-3, CeZr-4, and CeZr-6.

3.2. The Effect of Ce Inclusion on the Electronic Band Structure of Zirconia

The band structures of Ce doped ZrO₂ modeled systems are shown in Figure 3. Generalized gradient approximation (GGA) calculations underestimate the band gap due to the well-known shortcoming of density functional theory (DFT) [22]. For cubic ZrO₂, the calculated band gap is 3.307 eV, which is underestimated compared to the experimental value of 5.70 eV. A constant scissor operator is applied for all investigated structures for making the band structure comparable to the experimental value [23]. Intrinsic insulating behavior is clarified from Figure 3a, displaying the Fermi level at the top of the valence band. No isolated states appear in the forbidden region due to Ce doping. Cerium inclusion in the ZrO₂ network modified the band structure of ZrO₂. No specific trend is observed in the band gap of ZrO₂ with an increasing Ce doping concentration. The band gap of CeZr-1 is reduced to 4.67 eV, compared to the 5.70 eV for Zr-0. The valence band and conduction band come closer to each other, giving a gap of 4.60 eV in the case of CeZr-2. A minimum band gap has been observed for the CeZr-3 model, although CeZr-4 and CeZr-6 possess higher Ce doping concentrations compared to CeZr-3. With the Fermi level at valence band maximum, the distance between the top of the valence and bottom of the conduction band at the gamma point in CeZr-4 and CeZr-6 systems are 4.56 eV and 4.39 eV, respectively.

Ce doping modified the intrinsic band structure of ZrO₂, and the modifications in the band gap of Ce doped ZrO₂ modeled systems are depicted in Figure 4. One should note that Ce doping reduced the band gap of ZrO₂; however, the different doping systems have different reduction values. The 6.25% Ce doped ZrO₂ results in a maximum reduction of 1.32 eV in the ZrO₂ band gap. No linear modification in the band gap is found with the increasing Ce doping concentration. The maximum Ce doping concentration reported in this paper of 12.5% reduced the band gap around 1.31 eV, compared to pure zirconia.

The density of states is calculated for elaborating the electronic structure of the modeled systems in detail. As verified from Figure 5, the recent calculations show no gap states between the valence and conduction band. The only modification that Ce doping performed is the shifting of the valence band edge and conduction band closer to each other. The band gap is modified due to Ce insertion in the ZrO₂ network, and all Ce doped ZrO₂ modeled systems depict a reduced band gap. The density of states findings are consistent with the reported data [12].

3.3. The Effect of Ce Inclusion on the Photo-Response of Zirconia

The photo-response of zirconia originates from the interactions of photons with the electrons in ZrO₂, leading to the transition of electrons between the occupied and unoccupied states. CASTEP calculates the real and imaginary part of the dielectric function, which are further used to calculate the other optical properties like absorption, reflectivity, and conductivity [24,25]. The imaginary part of the dielectric function given in Equation (1) is used to calculate the optical absorption (Equation (2)).

$${\epsilon }_2(\hslash \omega )=\frac{2\pi e^2}{\mathsf{\Omega }{\epsilon }_o}{{\displaystyle \sum _{c,v}{\displaystyle \sum _k\left|\langle {\psi }_k^c|\widehat{u}.r|{\psi }_k^v\rangle \right|}}}^2\delta (E_k^c-E_k^v-\hslash \omega )$$

(1)

$$\alpha (\omega )=\sqrt{2}\omega {\left[\sqrt{{\epsilon }_1^2(\omega )+{\epsilon }_2^2(\omega )}{\epsilon }_1(\omega )\right]}^{\frac{1}{2}}$$

(2)

The Ω, v, c, ω, and k in Equation (1) represent the volume of the elementary cell, valence band, conduction band, frequency, and the vector defining the polarization direction of the electric field. Absorption coefficient (Equation (2)) is represented by $\alpha (\omega )$.

The optical properties of Ce doped ZrO₂ modeled systems are displayed in Figure 6. Due to the intrinsic wide band gap (5.70 eV for ZrO₂), pure ZrO₂ is found to absorb high energy photons. As clarified from Figure 6a, pure zirconia has a strong absorption peak, around 38.6 nm and 54.9 nm. Moreover, a wide absorption band is observed starting from 101 nm and ending at 224.1 nm. These peaks might originate from the transitions of electrons between O 2p and Zr 3d states. Ce doping modified the optical response of ZrO₂. Increasing Ce doping concentration created substantial change in the absorption curves of ZrO₂. The CeZr-1 depicted an absorption peak at 39.4 and 54.0 nm, with less intensity compared to pure zirconia. The broad absorption band in case of CeZr-1 is shifted to longer wavelengths ending at 274.8 nm. The changes induced in the optical absorption spectra of CeZr-1 are attributed to the insertion of Ce 4f states in the band structure. It is interesting to note that the models CeZr-2, CeZr-3, CeZr-4, and CeZr-6 exhibit different behavior to upcoming photons. The peaks around 39 nm and 54 nm completely disappeared. Moreover, the broad peak is shifted to longer wavelengths starting at 122.7 nm and ending at 290.2 nm. One should note from Figure 6a that there is very small difference between the absorption spectra of CeZr-2, CeZr-3, CeZr-4, and CeZr-6. The shifting of the absorption peaks and the creation/disappearance of new/existing peaks are ascribed to the states introduced due to Ce doping. The imaginary of dielectric function is shown in Figure 6b. Peaks for Zr-0 and relatively smaller peaks for CeZr-1 are found at 38.6 nm, 54.0 nm, and 176.1 nm attributed to the excitations of electrons from O 2p to Zr 3d states. The optical absorption drastically changed in CeZr-2, CeZr-3, CeZr-4, and CeZr-6 modeled systems. The peaks around 38.6 nm and 54 nm disappeared, and the absorption hump is found centering at around 225 nm. Electronic transitions are responsible for the optical spectra. One should note that the band structure of the doped systems changed due to the creation of Ce 4f states, leading to modification in the optical spectra. The peak hump around 225 nm is attributed to excitations of electrons between O 2p to Ce 4f and Zr 3d states. The absorption spectra and the imaginary part of the dielectric function verify the band structure findings. Figure 6c summarizes the conductivity of the simulated models. Computational results of the conductivity of Zr-0, as seen from Figure 6c, show peaks at 38.6 nm and 54 nm. Following the peaks, a broad absorption is found starting at 99.2 nm and ending at 227.7 nm. The 2.08% Ce doped ZrO₂ displays peaks with less intensity compared to Zr-0 at 38.6 nm and 54 nm. Moreover, the broad absorption hump is also found with reduced intensity. It is interesting to note that the hump starting at 101 nm for CeZr-1 is shifted to higher wavelengths ending at 275.7 nm. CeZr-2, CeZr-3, CeZr-4, and CeZr-6 demonstrate a single absorption band starting at 124.5 nm and ending at around 300 nm.

4. Conclusions

Ce doping significantly modified the electronic band structure and photo-response of ZrO₂. The cell volume of the basic unit cell of ZrO₂ exhibited linear variations with the Ce doping concentration. The electronic band gap of ZrO₂ was reduced considerably by doping ZrO₂ with Ce. A maximum reduction of about 1.32 eV was found for the CeZr-3 model, with a Ce doping concentration of 6.25%. The optical properties investigation revealed that the intrinsic peaks of ZrO₂ were maintained at low doping levels, and these peaks completely vanished at high doping levels, leading to the creation of a new absorption band. The Ce inclusion in ZrO₂ is expected to reduce the thermal conductivity, which would widen the utilization of Ce doped ZrO₂ in thermal barrier coating applications.