Density Functional Theory Evaluation of Ceramics Suitable for Hybrid

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C: Surfaces, Interfaces, Porous Materials, and Catalysis

Density Functional Theory Evaluation of Ceramics Suitable for Hybrid Advanced Oxidation Processes: A Case Study for Ce Doped BaZrO 4+

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Syed Muhammad Alay-e-Abbas, Farrukh Javed, Ghulam Abbas, Nasir Amin, and Amel Laref J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b12221 • Publication Date (Web): 20 Feb 2019 Downloaded from http://pubs.acs.org on February 21, 2019

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The Journal of Physical Chemistry

Density Functional Theory Evaluation of Ceramics Suitable for Hybrid Advanced Oxidation Processes: A Case Study for Ce4+ Doped BaZrO3 Syed Muhammad Alay-e-Abbas *, 1, Farrukh Javed 1, Ghulam Abbas 2, Nasir Amin 1 and Amel Laref 1

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Computational Materials Modeling Laboratory, Department of Physics, Government

College University Faisalabad, 38040 Faisalabad, Pakistan 2

Hefei National Laboratory for Physical Sciences at the Microscale, University of Science

and Technology of China, Hefei 230026, China 3

Department of Physics and Astronomy, College of Science, King Saud University, Riyadh,

11451 Saudi Arabia * Corresponding author Email: [email protected]; Tel: +92-41-9201372

Abstract Ceramic photocatalysts have become a focus of large amount of research in the sonochemsitry community owing to their potential for enhancing the degradation of organic pollutants during sonocatalytsis or sonophotocatalysis. Although various ceramic materials have been developed and employed in hybrid advanced oxidation processes over the past decades, the physics and chemistry governing the photocatalytic performance of these materials at the atomistic-level is usually derived from assumptions based on experimental observations. In the present study we employ computationally economical density functional 1

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theory (DFT) based ab-initio calculations for evaluating the physical properties of undoped and doped modifications of large band gap ceramics. Motivated by a recent experimental work we have studied the thermodynamic and opto-electronic properties of pristine and Ce4+ doped BaZrO3 compounds for selected concentrations of cerium dopant (x = 0, 0.037 and 0.125). Our results provide clear insight into the relationship between dopant concentration x and the improved optical properties of BaZr1-xCexO3 compounds which is directly related with enchantment in their photocatalytic activity. The physical properties of Ce4+ doped BaZrO3 ceramics obtained using DFT calculations are not only found to be in good agreement with experiment, they are also able to provide a deeper understanding of their tunable opto-electronic properties which can be tailored to attain functionalities required for particle applications. Based on our results, we conclude that modern DFT can serve as an efficient tool for predicting ceramic photocatalsyts suitable for advancing hybrid advanced oxidation processes of sonochemsitry.

1. Introduction The use of semiconductor photocatalysts in hybrid advanced oxidation process (HAOP) is an active area of research owing to pressing needs for developing efficient and economical water treatment technologies for the removal of organic pollutants1-3. Among the two HAOPs that combine sonolysis with photocatalysis, namely sonophotocatalysis and sonocatalysis, the former does not require an external UV radiation source for deriving photocatalytic activity in a semiconductor4-6. This is due to the fact that sonoluminesence in an aqueous medium produced during sonolysis can be utilized by a photocatalyst present in the same medium. This results in the production of reactive oxide species which consequently enhance the

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degradation of organic pollutants3. In order to make the HAOPs more efficient, it is usually required to tune the optical properties of a semiconductor; enabling the photocatalyst to strongly absorb radiations produced during sonoluminesence6. This has lead to numerous studies over the past decades where the main focus has generally been directed at increasing the photocatalytic activities of traditional binary semicondcutors like TiO2 and ZnO7-9. On the contrary, relatively little attention has been paid to large band gap ceramics for their applications in HAOPs. Since the discovery of photocatalytic activity in titanium dioxide, numerous non-toxic and photosensitive binary metal oxide semiconductors constituting the first-generation of photocatalysts were studied for their usefulness in assisting decomposition of organic and inorganic compounds10-12. However, the need for tailoring the absorption thresholds of these materials to visible and near-UV radiations saw the rise of second-generation photocatalysts based on doped modifications of binary metal oxide semiconductors like TiO2, ZnO, WO3 and Fe2O312, 13. In spite of that, commercial application of binary metal oxide semiconductors as photocatalysts has been marred by their low quantum yields and chemical instability12. In this context, large band gap ternary complex oxides have emerged as potential thirdgeneration photocatalysts14. In particular, inorganic perovskite oxide ceramics having general chemical formula ABO3 have recently become a focus of increasing research work due to the fact that the presence of two cations A and B allow for a wide range of variation in the electronic and optical properties of these compounds12. Moreover, the ability to control thermal and chemical stability, band edge positions and charge carriers in the doped modifications of inorganic perovskite oxide

15, 16

offer unambiguous advantages over binary

oxides. In retrospect, it is clear that tailoring opto-electronic properties of large band gap perovskite oxide ceramics by either repositioning their conduction and valence band edges or 3



by creating mid-gap states can provide great opportunities for designing new photocatalysts12, 17.

In the past two decades barium zirconate, BaZrO3, has become an attractive material for a large proportion of the materials science community owing to its potential applications in both electronic and energy devices18-22. However, the large band gap of BaZrO3 and small quantum yield in the UV region of electromagnetic spectrum has kept it of lesser interest for application in optical devices. This is the main reason why this thermally stable simple cubic ternary oxide has not earned much consideration for its use in HAOPs. Knowing that the large band gap of BaZrO3 can be tuned to tailor its applications in UV and visible region of elelctromagentic spectra23, doping with isovalent rare-earth atoms having ionic radii comparable to Ba or Zr in BaZrO3 provides unique opportunities for improving photocatalytic performance of barium zirconate24. In this context, the similar charge state and minor difference between ionic radii of Zr4+ (0.72 Å) ion and Ce4+ (0.87 Å) ion reveals that cerium would be easily accommodated at a Zr site of BaZrO3 lattice25. Importantly, the unique property of Ce4+ ion to become Ce3+ by absorbing a photogenerated electron can be highly beneficial for increasing its photocatalytic performance. Hence, tuning the optical properties of large band gap BaZrO3 by doping Ce4+ ion at the Zr site can satisfy the requisites of a photocatalyst suitable for both sonophotocatalysis and sonocatalysis processes26. In a recent work, Zhang et al. showed that the photocatalytic activity of Ce4+ doped BaZrO3 powders significantly increases the sonocatalytic degradation of norfloxacin in aqueous solution27. Using various characterization techniques for structural and optical properties it was shown that the lattice volume of cubic BaZrO3 increases whereas the band gap decreases with increasing concentration of Ce dopant from x = 0 to x = 0.064; resulting in

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bathchormic shift in the UV absorption spectrum of cerium doped barium zirconate. Similar reports on the shift of optical absorption from high energy to low UV or even visible region of electromagnetic spectrum upon cerium doping in transition metal oxides are available in literature28, 29. A striking aspect of the above-mentioned experimental study by Zhang et al. is that the degradation ratio of norfloxacin is increased from ~ 45% to ~75% when the concentration of Ce4+ ion doped in to BaZrO3 lattice is increased from x = 0.032 to x = 0.064 27.

Although the reduction of band gap and the ability of cerium ion to restrict the

recombination of photogenerated electron by changing its charge state from 4+ to 3+ are important factors in increasing the photocatalytic activity of Ce4+ doped BaZrO327, the impact of cerium dopant concentration on electronic structure of BaZrO3 and the resulting enhancement in the absorption of electromagentic radiations produced by sonoluminesence require a deeper atomistic-level explanation. Moreover, since cerium atoms are also likely to form other substitutional and interstitial point defects in ABO3 perovskites30, 31, it is equally important to examine the chemical environment which allows successful incorporation of Ce4+ ion at a Zr site of BaZrO3. In order to address these issues, we employ density functional theory (DFT) based first-principles calculations for exploring the impact of substitutional cerium doping on the electronic and optical properties of bulk barium zirconate. Our results agree well with experimental findings where increasing concentration of cerium dopant allows stronger absorption of UV radiations. At the same time, a quantum chemical insight into the thermodynamics and opto-electronic properties of doped materials is provided that can serve as a guideline for designing materials based on large band gap perovskite oxides for application in HAOPs.

2. Methodology

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All the first-principles calculations reported in this study are carried out using the WIEN2k code which employs the all-electron full potential linear augmented planewave (FP-LAPW) method within the framework of density functional theory32. For computing the thermodynamic and structural properties we employ the Perdew-Burke-Ernzerhof revised for solids (PBEsol) generalized gradient approximation (GGA) functional33, while the electronic and optical properties are computed using the modified Becke-Johnson local density approximation (mBJ-LDA) exchange-correlation potential34. In the FP-LAPW method a muffin-tin model for partitioning core and valence states is implemented in such a way that there is no shape approximation applied while expanding the potentials. The core states are treated fully relativestically inside the muffin-tin spheres, while the valence states are treated scalar relativestically in the interstitial region32. For the present calculations we use muffintin radii of 2.3 bohr, 1.85 bohr, 1.87 bohr and 1.6 bohr for Ba, Zr, Ce and O atoms, respectively, while an energy cut-off of -9.0 Ry is used for separating the core states from the semi-core and valence states. The planewave cut-off (R0Kmax), maximum value of angular momentum (lmax) and maximum G value for Fourier expansion of charge density are set to 8.0, 10 and 18 bohr-1, respectively. We have constructed the Pm3m unit cell of BaZrO3 by positioning the Ba, Zr and O atoms at the (0, 0, 0), (0.5, 0.5, 0.5) and (0.5 ,0.5 ,0) sites of the cubic lattice using experimental lattice parameter 4.190 Å35. For the cubic Pm3m unit cell, the self-consistent FP-LAPW calculations are performed using a 12 × 12 × 12 k-mesh which corresponds to 72 k-points in the irreducible wedge of first Brillouin zone. The two doped modification of Cedoped BaZrO3 have been realized by constructing 135-atom 3 × 3 × 3 and 40-atom 2 × 2 × 2 supercells of pristine BaZrO3. The chemical compositions of cerium doped barium zirconate in 3 × 3 × 3 and 2 × 2 × 2 supercells can be represented by general chemical formula BaZr16


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xCexO3

where replacing one Zr atom for Ce atom corresponds to x = 0.037 and x = 0.125

doping concentrations, respectively. It is worth pointing out here that the BaZr0.963Ce0.037O3 composition using a 3 × 3 × 3 is in accordance with the experimentally reported BaZr0.968Ce0.032O3, while our choice of using 2 × 2 × 2 for obtaining BaZr0.875Ce0.125O3 composition is necessitated by the need to eliminate the influence of low symmetry structures on the calculated results36. In case of both BaZr0.963Ce0.037O3 and BaZr0.875Ce0.125O3 compounds the supercell structures retain the Pm3m cubic symmetry of the pristine barium zirconate for which the total energy calculations are performed using 4 × 4 × 4 and 6 × 6 × 6 k-meshes, respectively. All the self-consistent calculations are iteratively repeated until the total energy difference in two successive iterations is less than 10-6 Ry. In addition, the atomic positions inside the supercells of both BaZr0.963Ce0.037O3 and BaZr0.875Ce0.125O3 compounds are allowed to relax within cubic symmetry until the forces on each atom is below 1 mRy/a.u..

3. Results and Discussions 3.1. Thermodynamics Stability Diagram of Pristine BaZrO3 Since the stable formation of a pristine compound and the introduction of point defects in solids is governed by thermodynamic reservoirs of the atomic species involved in chemical reaction37-40, we first calculate the stability diagram of BaZrO3 by assuming that the atomic 𝑠𝑜𝑙𝑖𝑑 𝑔𝑎𝑠 chemical potentials of Ba (𝜇𝐵𝑎 = 𝜇𝑠𝑜𝑙𝑖𝑑 𝐵𝑎 + 𝛥𝜇𝐵𝑎) Zr (𝜇𝑍𝑟𝑎 = 𝜇𝑍𝑟 + 𝛥𝜇𝑍𝑟) and O (𝜇𝑂 = 𝜇𝑂

+ 𝛥𝜇𝑂) atoms can be referenced to the chemical potentials of their respective solid and gaseous phases. This means that the values of 𝛥𝜇𝐵𝑎,𝛥𝜇𝑍𝑟 and 𝛥𝜇𝑂 should always be < 0, such that BaZrO3 can be synthesized stably with respect to its competing binary phases BaO and

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ZrO2. In other word, only those values of atomic chemical potentials are valid which satisfy the following equations 3 … (1) 𝛥𝜇𝐵𝑎 + 𝛥𝜇𝑍𝑟 + 3𝛥𝜇𝑂 = 𝛥𝐻𝐵𝑎𝑍𝑟𝑂 𝑓

𝛥𝜇𝐵𝑎 + 𝛥𝜇𝑂 ≤ 𝛥𝐻𝐵𝑎𝑂 𝑓 … (2) 2 … (3). 𝛥𝜇𝑍𝑟 + 2𝛥𝜇𝑂 ≤ 𝛥𝐻𝑍𝑟𝑂 𝑓

3 2 In Eqs. (1) to (3), 𝛥𝐻𝐵𝑎𝑍𝑟𝑂 , 𝛥𝐻𝐵𝑎𝑂 and 𝛥𝐻𝑍𝑟𝑂 are the enthalpies of formation of barium 𝑓 𝑓 𝑓

ziconate, barium oxide and zirconia, respectively, which are obtained from the total energies 3 of PBEsol GGA optimized unit cells of Pm3m BaZrO3 (𝐸𝐵𝑎𝑍𝑟𝑂 ), Fm3m BaO (𝐸𝐵𝑎𝑂 𝑡 ), P21/c 𝑡 2 𝑏𝑐𝑐 ℎ𝑐𝑝 ZrO2 (𝐸𝑍𝑟𝑂 ), Im3m Ba 𝐸𝐵𝑎 and P63/mmc Zr (𝐸𝑍𝑟 ) using 𝑡 𝑡 𝑡

3

3 3 𝑏𝑐𝑐 ℎ𝑐𝑝 𝛥𝐻𝐵𝑎𝑍𝑟𝑂 = 𝐸𝐵𝑎𝑍𝑟𝑂 −𝐸𝐵𝑎 −𝐸𝑍𝑟 −2𝐸𝑂𝑡 2… (4) 𝑓 𝑡 𝑡 𝑡

1

𝐵𝑎𝑏𝑐𝑐 𝛥𝐻𝐵𝑎𝑂 = 𝐸𝐵𝑎𝑂 −2𝐸𝑂𝑡 2… (5) 𝑓 𝑡 −𝐸𝑡

2 2 ℎ𝑐𝑝 𝛥𝐻𝑍𝑟𝑂 = 𝐸𝑍𝑟𝑂 −𝐸𝑍𝑟 −𝐸𝑂𝑡 2… (6) 𝑓 𝑡 𝑡

In all cases 𝐸𝑂𝑡 2 is the total energy of an oxygen molecule which has been corrected with reference to experimental cohesive energy of oxygen to overcome the overestimation caused by PBEsol functional41, 42.

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Table 1. The calculated lattice parameters, enthalpies of formation and cohesive energies of stable solid phases of BaZrO3, BaO, ZrO2, Ba and Zr. Experimental and PBE GGA data reported in earlier studies are also presented for comparison with PBEsol GGA results computed in this work. Solid

This Work

PBE GGA

Experiment

BaZrO3 (Pm3m) a0 (Å) Hf (eV/f.u.)

4.184 -19.208

4.244 43 -16.620 43

4.190 35 -18.270 44

BaO (Fm3m) a0 (Å) Hf (eV/f.u.)

5.493 -5.967

5.579 45 -5.330 43

5.539 46 -5.680 47

ZrO2 (P21/c) a0 (Å) b0 (Å) c0 (Å) β Hf (eV/f.u.)

5.133 5.212 5.301 99.60 -12.109

5.219 48 5.271 48 5.411 48 99.40 48 -10.662 48

5.151 49 5.203 49 5.316 49 99.20 49 -11.410 50

Ba (Im3m) a0 (Å) Ec (eV/atom)

4.887 -2.052

5.030 51 -1.886 52

5.002 53 -1.900 54

Zr (P63/mmc) a0 (Å) b0 (Å) Ec (eV/atom)

3.178 5.126 -6.925

3.233 55 5.173 55 -6.260 52

3.230 56 5.149 56 -6.250 54

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Figure 1. The stability diagram of BaZrO3 computed using the PBEsol GGA functional. Points A, B, C and D enclose the stability region of pristine BaZrO3, while point E represents chemical environment for stable incorporation of Ce4+ ion at a Zr-site in the BaZrO3 lattice. Table 1 presents the PBEsol GGA calculated lattice parameters, enthalpies of formation and cohesive energies of the solids involved in determining the stability diagram of BaZrO3 which is shown in Figure 1. The mean absolute percentage error (MAPE) for lattice parameters of BaZrO3, BaO, ZrO2, Ba and Zr computed using PBEsol functional (0.018 %) is clearly an order of magnitude better when compared with the MAPE for PBE GGA functional (0.161 %). On the other hand, the MAPE for the calculated enthalpies of formation and cohesive energies of all the solids listed in Table 1 are found to be 1.027 % and 1.806 % 10


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for PBEsol and PBE GGA functionals, respectively. These results clearly demonstrate better performance of PBEsol GGA in predicting structural and energetic properties of solids. Figure 1 shows the calculated stability diagram for BaZrO3 where the atomic chemical potentials laying in triangular region between the line A-D and 𝛥𝜇𝑍𝑟 axis would result in the formation of BaO. Similarly ZrO2 is formed for the atomic chemical potentials laying in the triangular region between the line B-C and 𝛥𝜇𝐵𝑎 axis. Figure 1 also shows that the stoichiometric formation of BaZrO3 can only be achieved within the stability region enclosed by the points A, B, C and D. Within this stability region, the atomic chemical potential of oxygen can be varied between 0.000 eV and -6.055 eV to obtain a large range of atomic chemical potentials for Ba and Zr that satisfy Eqs. (1) to (3).

3.2. Structural Properties For examining the structural properties of BaZr1-xCexO3 for x = 0.037 and 0.125, we compare the calculated lattice parameters, bond lengths and bulk modulus with structural properties of bulk unit cell of pristine BaZrO3. The structural models and the volume optimization curves for BaZr0.963Ce0.037O3 and BaZr0.875Ce0.125O3 obtained by fitting equation of state to the PBEsol GGA’s total energy vs volume data are presented in Figure 2 and the corresponding structural properties are listed in Table 2. Clearly, the calculated lattice parameter and bulk modulus of pristine BaZrO3 is in agreement with experimental data35, 57. It can be seen from Figure 2 that the volume of the barium zirconate perovskite lattice increases with increasing Ce concentration which is in accordance with the larger experiential lattice parameter of pseudocubic BaCeO3 perovskite structure (4.390 Å to 4.431 Å58, 59) as compared to barium zirconate (4.190 Å35). From the bond lengths obtained after minimizing the internal forces, we note that the Ba-O bond length increases almost linearly with increasing Ce concentration.

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On the other hand, the Zr-O bond length is found to decrease by 0.048 Å with respect to pristine BaZrO3 for the Ce concentration x = 0.037. The Zr-O bond length is further decreased by 0.005 Å on going from BaZr0.963Ce0.037O3 to BaZr0.875Ce0.125O3. Contrary to the decrease in Zr-O bond lengths, the Ce-O bond length is found to increase on going from x = 0.037 to x = 0.125. These results indicate that upon doping with Ce the maximum contribution to the increasing volume of barium zirconate perovskite lattice originates from the increasing Ba-O bond length. Contrary to the increasing trends in lattice parameters, the bulk modulus are found to decrease with increase in the concentration of Ce dopant in the BaZrO3 lattice. This is understandable given the fact that the zirconate of barium in cubic perovskite structure is much harder materials as compared to barium cerate57, 60.

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Figure 2. The total energy vs volume curves for Ce-doped BaZrO3 for Ce concentration (a) x = 0.037 and (b) x = 0.125. The 135-atom 3 × 3 × 3 and 40-atom 2 × 2 × 2 supercells of Ce4+ doped BaZrO3 used for computing the data are shown as insets. Table 2. Calculated lattice parameters, the cation-O bond lengths, bulk modulus and the defect formation energies of BaZr1-xCexO3 for x = 0, 0.037 and 0.125. Bond lengths (Å) Ce

Bulk modulus (GPa)

𝐸𝑓[𝐶𝑒𝑍𝑟](eV/defect)

160.477

-

159.142

0.814

concentration a0 (Å) Ba-O Zr-O Ce-O x 0 0.037

4.184 2.958 2.092

-

4.197 2.982 2.044 2.179 13



0.125

4.220 3.009 2.039 2.181

157.185

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0.943

3.3. Thermodynamics of Ce4+ doping in BaZrO3 The stability region enclosed by the points A, B, C and D in Figure 1 give us the limits of atomic chemical potentials for oxygen which are only applicable for stable synthesis of pristine barium zirconate. In order to evaluate the substitutional doping of Ce4+ at a Zr site in BaZrO3 lattice (i.e. BaZr0.963Ce0.037O3 and BaZr0.875Ce0.125O3 compounds), it is also necessary that the atomic chemical potentials of oxygen should restrict the precipitation of CeO2. Therefore, we apply additional constraint on the valid limits of atomic chemical potentials of oxygen and cerium by requiring that 2 … (7) . 𝛥𝜇𝐶𝑒 + 2𝛥𝜇𝑂 ≤ 𝛥𝐻𝐶𝑒𝑂 𝑓

For Eq. (7) the enthalpy of formation for CeO2 has been computed using 2 2 𝑓𝑐𝑐 𝛥𝐻𝐶𝑒𝑂 = 𝐸𝐶𝑒𝑂 −𝐸𝐶𝑒 −𝐸𝑂𝑡 2… (8) 𝑓 𝑡 𝑡

2 𝑓𝑐𝑐 where 𝐸𝐶𝑒𝑂 and 𝐸𝐶𝑒 are the minimum total energies of cubic CeO2 and fcc Ce computed 𝑡 𝑡

using their respective unit cells optimized with PBEsol GGA functional. Since our calculated values of enthalpy of formation for CeO2 is -12.071 eV/f.u., it is evident that only the oxygen chemical potential between 0 eV > 𝛥𝜇𝑂 > -6.036 eV would correspond to chemical environments that allow substitutional doping of Ce4+ ion for a Zr4+ ion in BaZrO3. Considering that stable synthesis of Ce4+ doped BaZrO3 is allowed under the same conditions as that of the pristine BaZrO327, we set 𝛥𝜇𝑂 = -3.018 eV, which corresponds to 𝛥𝜇𝐵𝑎 = -3.515 eV, 𝛥𝜇𝑍𝑟 = -6.662 and 𝛥𝜇𝐶𝑒 = -6.035 eV; giving us point E in the stability diagram (Figure 1) which is located near the center of mass of quadrangle ABCD. 14


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Using the atomic chemical potentials of Zr and Ce defined by point E we have computed the defect formation energies of Ce4+ doped BaZrO3 using the relation61, 62 3 𝐸𝑓[𝐶𝑒𝑍𝑟] = 𝐸𝑡[𝐶𝑒𝑍𝑟]−𝐸𝐵𝑎𝑍𝑟𝑂 + ∑𝑛𝜇𝑥… (9) 𝑡

3 where 𝐸𝑡[𝐶𝑒𝑍𝑟] and 𝐸𝐵𝑎𝑍𝑟𝑂 are the minimum total energies of a Ce4+ doped BaZrO3 supercell 𝑡

and an equally sized pristine supercell of BaZrO3, respectively. The quantity n in Eq. (9) represents the species X added (-1) or removed (+1) from the supercell, while 𝜇𝑋 are the atomic chemical potentials given by points E (Figure 1). The calculated defect formation energies of 0.814 eV and 0.943 eV for BaZr0.963Ce0.037O3 and BaZr0.875Ce0.125O3, respectively, demonstrate that the Ce4+ ion can be easily substituted for a Zr4+ ion in BaZrO3. This result is also supported by the calculated enthalpies of formation of BaZr0.963Ce0.037O3 (-19.156 eV/f.u.) and BaZr0.875Ce0.125O3 (-19.015 eV/f.u.) which are no more than 0.193 eV/f.u. larger 3 than 𝛥𝐻𝐵𝑎𝑍𝑟𝑂 . 𝑓

3.4. Electronic Properties The calculated thermodynamic properties of cerium doping in BaZrO3 are in accordance with experimental observations where Ce4+ ion was found to substitute a Zr4+ ion and an increase in dopant concentration causing sonoluminesence driven photocatalytic activity to enhance27. In order to accurately study the effect of cerium concentration on opto-electronic response of BaZrO3 we have employed mBJ-LDA exchange-correlation potential functional in the present work using the parameters suggested by Koller et al.63. Figure 3 shows the electronic band structure diagrams computed using PBEsol GGA and mBJ-LDA functionals, where better performance of the later in determining electronic properties of large band gap materials is evident. In case of both the exchange-correlation parameteriztion schemes used 15



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for computing the band structures of BaZrO3, an indirect fundamental energy band gap (Eg) is found between the valence band minimum (VBM) and conduction band maximum (CBM) located at R and Γ symmetry points, respectively. The indirect Eg computed using PBEsol GGA and mBJ-LDA are 3.186 eV and 4.626 eV, respectively. Compared to an earlier value of indirect (R-Γ) Eg = 4.670 eV and direct (Γ-Γ) Eg = 4.99 eV computed using HSE functional64, 65, it can be seen that the mBJ-LDA calculated indirect (Eg = 4.626 eV) and direct (Eg = 4.940 eV) band gaps are in excellent agreement with experimental data66,

27.

Since the electronic band structures computed using mBJ-LDA are obtained at a significantly lower computational cost as compared to hybrid DFT calculations, the use of mBJ-LDA functional in the present work for exploring opto-electronic properties of pristine and cerium doped barium zrcoante is justified. For understanding the improved performance of mBJ-LDA over the PBEsol GGA, total (TDOS) and partial density of states (PDOS) plots for pristine BaZrO3 computed using both the exchange-correlation parameterization schemes are displayed in Figure 4. One can clearly see that the valence band maximum (VBM) computed using these exchangecorrelation approximations are dominated by the contribution of O-2p states, however a close comparison of the PDOS obtained using PBEsol GGA and mBJ-LDA shows that the density of O-2p states near the VBM is considerably increased upon employment of the later functional. On the other hand, the conduction band minimum (CBM) is found to be predominantly made up of Zr-4d states, where the contribution of Zr-4d state’s in the CBM is shifted upward in energy when mBJ-LDA is used; giving electronic transition energies in better agreement with experimental data27, 66. All in all, Figure 3 & 4 testify that mBJ-LDA provides a clearer picture of the electronic properties of large band gap BaZrO3 and is,

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therefore, used for computing the electronic properties of Ce4+ doped BaZrO3 reported hereafter.

Figure 3. Electronic band structure diagram of pristine BaZrO3 computed using PBEsol GGA (black lines) and mBJ-LDA (red lines) functional along high symmetry points of the cubic Pm3m crystal structure.

17



Figure 4. The total density of states (TDOS) and partial density of states (PDOS) plots of pristine BaZrO3 computed using PBEsol GGA (black lines) and mBJ-LDA (red lines) functionals. The Fermi level EF is set to 0 eV which is represented by a dashed vertical line. The PDOS of Ba-6s, Zr-4d and O-2p orbitals are shown. In Figure 5 the mBJ-LDA calculated TDOS and PDOS plots of BaZr0.963Ce0.037O3 and BaZr0.875Ce0.125O3 are compared with pristine BaZrO3. From the TDOS plots it is evident that the occupied states of pristine as well as Ce4+ doped BaZrO3 compounds below the Fermi level are spread over similar energy ranges (0 eV and -4 eV) showing some differences in the 18


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overall details. Importantly, sudden decreases in the TDOS for BaZr0.963Ce0.037O3 near the VBM (around ~ -0.213 eV) and the bottom of the valence band (around ~ -3.044 eV) can be seen which are also reflected in the decreasing contribution of O-2p states in the PDOS plots for this composition. Comparison of the PDOS plots for BaZr0.963Ce0.037O3 shown in Figure 5 also reveal the presence of O-2p states above the Fermi level which are hybridized with the narrowly distributed Ce-4f states. This peculiar presence of O-2p states above the Fermi level is caused by the mixing of Ce-4f states with the anti-bonding region of O-2p states which are also observed in experimental as well as hybrid DFT studies of cerium dioxide67, 68. Contrary to the case of BaZr0.963Ce0.037O3, the PDOS plots for BaZr0.963Ce0.037O3 show that the distribution of O-2p states above and below the Fermi level are identical to those of pristine BaZrO3. The difference in the contribution of O-2p states in the valence bands of BaZr0.963Ce0.037O3 and BaZr0.875Ce0.125O3 can be attributed to intricate covalent and ionic nature of Ce-O bond for which the nature of on bonding and occupation of cerium 4f orbitals have remained a subject of longstanding debate among the materials research community 69.

67-

Since Ce4+ should have a formal 4f0 configuration for ionic nature of bonding with

neighbouring oxygen atoms, it is clear that the decreased contribution of O-2p states in the valance band and the resulting hybridization of O-2p states with Ce-4f states above the Fermi level arises due to a slightly more covalent nature of Ce-O bond in case of BaZr0.963Ce0.037O3. On the other hand, the larger values of lattice parameter and Ce-O bond length in case of BaZr0.875Ce0.125O3 (Table 2) causes a reduction in the covalent nature of Ce-O bonding. Hence, the slightly increased covalent nature of Ce-O bond in BaZr0.963Ce0.037O3 as compared to BaZr0.875Ce0.125O3 is responsible for the decreased contributions of O-2p states in the valence band which are also supported by bonding properties of Ce4+ doped BaZrO3 compounds discussed later.

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Figure 5. TDOS and PDOS plots for BaZr0.963Ce0.037O3 (left panel) and BaZr0.875Ce0.125O3 (right panel) computed using mBJ-LDA. For the sake of comparison, TDOS and PDOS of BaZrO3 computed using mBJ-LDA are also shown (black dashed lines). Figure 5 also shows that the introduction of Ce dopant in BaZrO3 does not significantly alter the contribution of Zr-4d states in the conduction band located above 4.620 eV. Moreover, for both BaZr0.963Ce0.037O3 and BaZr0.875Ce0.125O3 compounds the contribution of Ce-5d states is only significant above ~ 6.5 eV. Interestingly, increasing the Ce concentration in BaZrO3 from x = 0.037 to x = 0.125 shows that Ce-5d states are shifted upwards towards more positive energy, hinting at increased repulsion coming from O-2p states in the valence band. For both the BaZr0.963Ce0.037O3 and BaZr0.875Ce0.125O3 compounds the unoccupied states appearing in between occupied O-2p and unoccupied Zr-4d states are

20


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mainly composed of Ce-4f contribution. In case of BaZr0.963Ce0.037O3, a single unoccupied narrow distribution of Ce-4f states centered around 3.655 eV is produced which reduces the band gap to 3.542 eV for this compound. This behaviour is similar to the electronic properties observed for CeO2 and BaCeO3 where the unoccupied Ce-4f states appear as narrow bands6770.

The hybridization of the unoccupied O-2p states with Ce-4f states suggests that a

photogenerated electron in the conduction band of BaZr0.963Ce0.037O3 would easily recombine with the hole in the valence band, decreasing the probability of utilizing a photogenerated electron in photocatalysis for this concentration of Ce-doped BaZrO3. On the other hand, the density of states for BaZr0.875Ce0.125O3 (Figure 5) shows an increased distribution of the Ce-4f states between 3 eV and 4 eV as well as significantly reduced mixing of Ce-4f states with the anti-bonding region of O-2p states. The decreased hybridization of O-2p states in the defect band also restores the contribution of occupied O-2p states in the valence band of BaZr0.875Ce0.125O3. Moreover, the Ce-4f defect states are split into two contributions centered around 3.277 eV and 3.658 eV, respectively, which further reduce the band gap to 3.168 eV in case of BaZr0.875Ce0.125O3.

3.5. Bonding Properties In order to understand the differences seen in the characteristics of Ce-4f defect states in BaZr0.963Ce0.037O3 and BaZr0.875Ce0.125O3 compounds we have computed 3D density isosurfaces (shown in Figure 6) for the relevant energy ranges of the PDOS corresponding to lowest unoccupied states above Fermi level. It can be seen from Figure 6 that for pristine BaZrO3 the empty Zr-4d orbitals are localized at the Zr4+ ions. In case of BaZr0.963Ce0.037O3 the Ce-4f states are composed of a combination of general (𝑓3𝑧 ) and cubic (𝑓3𝑥and𝑓3𝑦) orbitals which are localized at the dopant site71. These atomic-like Ce-4f orbitals are also slightly

21



extended to the nearest-neighbour O atoms which is in accordance with the hybridization of anti-bonding O-2p states with Ce-4f states seen in the PDOS plots of BaZr0.963Ce0.037O3 (Figure 5). Contrary to this, the 3D density isosurfaces computed for the lowest unoccupied Ce-4f states in case of BaZr0.875Ce0.125O3 are composed of cubic𝑓𝑥(𝑧2−𝑦2)and𝑓𝑦(𝑧2−𝑥2)orbitals which are highly localized at the Ce4+ ion71. On the other hand, the high laying Ce-4f states of BaZr0.875Ce0.125O3 centered around 3.658 eV are still composed of𝑓3𝑧 ,𝑓3𝑥and𝑓3𝑦orbitals (not shown here) with a slightly increased extension to the oxygen sites.

Figure 6. The mBJ-LDA calculated 3D density isosurfaces of BaZrO3 (left panel) projected in the 4.5 eV to 4.8 eV energy range, BaZr0.963Ce0.037O3 (middle panel) projected in the 3.5 eV to 3.8 eV energy range and BaZr0.875Ce0.125O3 (right panel) projected in the 3.1 eV to 3.4 eV energy range of their respective PDOS plots shown in Figure 5. The charge densities associated with Zr-4d and Ce-4f orbitals are represented by gray and green colours, respectively, and an isosurface charge density value of 0.05 Å-3 is used. Based on above findings we can contemplate that the competition in the bond lengths of Zr-O and Ce-O bonds for low (x = 0.037) and high (x = 0.125) concentrations of Ce dopant and the resulting bond character dictates the behaviour of lowest unoccupied Ce-4f defect states in BaZr1-xCexO3 compounds. This is supported by the Zr-O and Ce-O bond lengths 22


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listed in Table 2 where increase in Ce concentration from x = 0.037 to x = 0.125 causes the Zr-O bond length to decrease as compared to its bulk limits. On the other hand, the Ce-O bond length increases on going from BaZr0.963Ce0.037O3 to BaZr0.875Ce0.125O3. The above trends are an indication of the partially ionic bonding nature of O atom with its surrounding cation within the complex ionic-covalent bonding in BaZrO3 perovskite lattice72, 73, which increases for the high concentration of Ce considers in this work (i.e. x = 0.125). A direct quantitative evidence of this increased ionic bonding of O atom with its surrounding cation is confirmed by computing the effective Bader charges74 which are found to be -1.493e, -1.414e and -1.499e for an oxygen atoms nearest-neighbour to dopant site in case of BaZrO3, BaZr0.963Ce0.037O3 and BaZr0.875Ce0.125O3, respectively. The larger effective Bader charge of oxygen atom in case of and BaZr0.875Ce0.125O3 shows an increase in the ionic nature of bonding which reduces 2p-4f hybridization causing Ce-4f states to split into two distinct contributions. The empty Ce-4f orbitals localized to the Ce4+ ion not only reduces the band gap to 3.168 eV, they are also able to restrict recombination of photogenerated electrons; confirming experimental observed increased photocatalytic activity in cerium doped BaZrO3 with increasing dopant concentration27.

3.6. Optical Properties The calculated optical properties of BaZrO3, BaZr0.963Ce0.037O3 and BaZr0.875Ce0.125O3 are presented in Figure 7 in terms of real and imaginary parts of the complex dielectric function ε(ω) = ε1(ω) + i ε2(ω)75, 76. From Figure 7 it can be readily seen that the overall behaviour of real and imaginary parts of complex dielectric function over the large energy range of incident photon’s energy (0 – 30 eV) does not differ much for these materials. This can be attributed to the major contribution of Zr-4d and O-2p states in the conduction and valence

23



bands of BaZr0.963Ce0.037O3 and BaZr0.875Ce0.125O3, which is similar to the case of pristine BaZrO3. The zero frequency limits of the real part of complex dielectric function, ε1(0), shown in Figure 7 gives us the static dielectric constants for the materials under investigation. In case of pristine BaZrO3 ε1(0) = 3.685 is in good agreement with experimental value of 4.0 which gives this material high capacitance densities suited for its use as gate dielectric material in dynamic random access memories (DRAM)77. When a Ce dopant concentration of x = 0.037 is introduced into barium zirconate the static dielectric constant reduces to ε1(0) = 3.382. This reduction can be understood from the PDOS plots of defect band for BaZr0.963Ce0.037O3 shown in Figure 5 where the decreased contribution of O-2p states in the valence band and their hybridization with Ce-4f states decreases its dielectric nature. On the other hand, increasing the Ce concentration to x = 0.125 reduces the hybridization of O-2p states with Ce-4f states which somewhat rosters the static dielectric constant of the host perovskite to ε1(0) = 3.657. As the imaginary part of the complex dielectric function, ε2(ω), is closely related with the band structure of a material, the thresholds for imaginary part of the complex dielectric function are found to be at located at 4.626 eV, 3.542 eV and 3.168 eV for BaZrO3, BaZr0.963Ce0.037O3 and BaZr0.875Ce0.125O3, respectively. It can be seen from Figure 7 that for BaZr0.963Ce0.037O3 the increase in ε2(ω) beyond 3.542 eV is not as abrupt as compared to the increase of ε2(ω) in case of both pristine and heavily cerium doped modifications of BaZrO3. This is due to the nature of the defect states discussed earlier where the hybridization of O-2p states with the Ce-4f states restrain the absorption of electromagnetic radiations. For both the Ce-doped modifications of BaZrO3 the large values of ε2(ω) between 5 eV and 12 eV are conserved, however noticeable decrease in the peaks located at 7.333 eV, 8.830 eV and 9.891

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eV are also evident which can be attributed to the differences in the contribution of Ce-5d states in the conduction bands of these two doped compounds (see Figure 5).

Figure 7. Comparison of the the calculated optical properties of BaZrO3 (black line), BaZr0.973Ce0.037O3 (red line) and BaZr0.875Ce0.125O3 (blue line). The real (top left) and imaginary (top right) parts of complex dielectric function as a function of incident photon’s energy are shown along with the optical absorption (bottom) of pristine and Ce4+ doped BaZrO3 as a function of wavelength of electromagnetic radiations. From the optical absorption plots of BaZrO3 shown in Figure 7, it is clear that pristine barium zirconate absorbs well in the far UV region of electromagnetic radiations for wavelengths < 250 nm. The overall profile of the optical absorption of BaZr0.963Ce0.037O3 is

25



similar to BaZrO3 with only slight increase in the absorption of electromagnetic radiation with wavelengths between 350 nm < λ < 250 nm. On the other hand, the optical absorption plots of BaZr0.875Ce0.125O3 show considerable increase in the 390 nm > λ > 225 nm wavelength range, indicating that this concentration of Ce4+ doped BaZrO3 can efficiently absorb the near UV radiations as compared to BaZr0.963Ce0.037O3. Although, the doping concentration (x = 0.125) of Ce4+ considered in the present study is slightly larger than the doping concentration reported in experiment (x = 0.064), comparison of our calculated optical properties of the two cerium doping concentrations in this work clearly show that increasing Ce concentration beyond x = 0.037 considerably improves the optical absorption of barium zirconate up to λ = 390 nm27.

4. Conclusions In conclusion, the effect of Ce4+ doping on thermodynamic, structural, electronic and optical properties of BaZrO3 have been studied for selected doping concentrations (x = 0.037 and x = 0.125). The thermodynamic and structural properties are computed using PBEsol GGA functional which is found to perform better than the PBE GGA functional. Increasing cerium doping concentration has been found to expand the volume of cubic perovksite lattice, which is mainly caused by the increase in Ba-O and Ce-O bond lengths. The thermodynamic stability diagram of of barium zirconate computed using PBEsol GGA allowed us to determine chemical environment favouring stable incorporation of Ce4+ ion at a Zr site of BaZrO3. Within the stability region of pristine BaZrO3 we find that the oxygen chemical potential 𝛥𝜇𝑂 > -3.018 eV yields low defect formation energies (𝐸𝑓[𝐶𝑒𝑍𝑟] = 0.814 eV and 𝐸𝑓

[𝐶𝑒𝑍𝑟] = 0.943 eV for BaZr0.963Ce0.037O3 and BaZr0.875Ce0.125O3, respectively) confirming that BaZr1-xCexO3 compounds with cerium concentration x = 0.037 and x = 0.125 can be easily 26


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fabricated. For the case of BaZr0.963Ce0.037O3 the atomic-like Ce-4f states are found to be hybridized with unoccupied O-2p states. On the other hand, the Ce-4f defect states in case of BaZr0.875Ce0.125O3 are split into two distinct contributions such that the hybridization with O2p states is considerably reduced for the low laying Ce-4f states. We conclude that the increasing Ba-O/Ce-O bond lengths and ionic nature of bonding between oxygen and its nearest-neighboring cations are responsible for repositioning unoccupied Ce-4f states to lower energies which are localized to the Ce atom. Consequently, the optical absorption of BaZr0.875Ce0.125O3 in the UV region is improved as compared to the low cerium doping modification; BaZr0.963Ce0.037O3. Our findings are in excellent agreement with experiential observations where increasing cerium doping in barium zirconate has been shown to reduce the recombination of photongenerated electrons and holes which enhance the photocatalytic activity of these ceramics. These results clearly demonstrate that DFT can serve as an efficient tool for predicting materials for utilization in sonocatalytic degradation of pollutants.

Acknowledgments The authors are grateful to the Higher Education Commission of Pakistan for the Startup Research Grant Project No. 21-1599/SRGP/R&D/HEC/2017. This research project was supported by a grant from the “Research Centre of Female Scientific and Medical Colleges”, Deanship of Scientific Research, King Saud University. The calculations were performed using computational resources supported by Computational Materials Modeling Laboratory, Department of Physics, Government College University Faisalabad.

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Density Functional Theory Evaluation of Ceramics Suitable for Hybrid

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