Structure and Reducibility of CeO2 Doped with Trivalent Cations

Article pubs.acs.org/JPCC

Structure and Reducibility of CeO2 Doped with Trivalent Cations Aoife K. Lucid,* Patrick R. L. Keating, Jeremy P. Allen, and Graeme W. Watson* School of Chemistry and CRANN, Trinity College Dublin, Dublin 2, Ireland ABSTRACT: The doping of CeO2 with trivalent cations is a common technique for enhancing ionic conductivity in electrolytes for solid oxide fuel cell applications. However, the local defect structure in these materials is yet to be fully explored. Furthermore, many studies have overlooked the effect of the dopants on the reducibility of CeO2, which is important as electronic conductivity can short-circuit the fuel cell. Density functional theory (DFT)+U calculations have been performed on a series of CeO2 systems doped with trivalent cations. The most stable configuration and the relative attraction between dopant cations and oxygen vacancies were determined, and it was found that the defect structure is principally dependent on the ionic radius of the dopant cations. The reduction energy was found to be dependent on the structure around the dopants but did not vary significantly between dopants of similar ionic radii. From these results, it is possible to suggest which trivalent cations would be most suitable to enhance ionic conductivity without increasing electronic conductivity in solid oxide fuel cell electrolytes.

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INTRODUCTION In this environmentally conscious era a significant amount of research is now devoted to the study of environmentally friendly technologies. Solid oxide fuel cells (SOFCs) have emerged as a promising candidate for the future of energy production due to their high efficiency, fuel flexibility, and low pollutant output.1−5 However, one of the main challenges has been finding electrolyte materials with high ionic conductivities in the intermediate temperature range (∼773−1073 K).6 CeO2, also known as ceria, is one of the most widely studied potential materials for SOFC electrolytes due to its high thermal stability and ionic conductivity.7−10 While pure CeO2 displays ionic conductivity, due to intrinsic O vacancies,11 it is very low at ∼3.13 × 10−3 S cm−1. The introduction of additional O vacancies through aliovalent doping has been shown to significantly increase ionic conductivity. In Kröger−Vink notation, the doping of CeO2 with a trivalent cation is given by x 2CeCe + OOx + M 2O3 → 2M′Ce + V •• O + 2CeO2

defect in CeO2 due to a low defect formation (reduction) energy24 and can be highly detrimental to the operation of a SOFC electrolyte. In Kröger−Vink notation the formation of an intrinsic oxygen vacancy is given by x OOx + 2CeCe → V •• O + 2Ce′Ce +

(2)

The formation of the oxygen vacancy leads to the reduction of two Ce ions from Ce(IV) to Ce(III) (Ce′Ce). These excess electrons can lead to electronic conductivity, thus shortcircuiting the operation of the fuel cell.1−3 When choosing dopants to increase the ionic conductivity, it has been found that the greatest rise in ionic conductivity is observed for dopants that cause the least distortion to the host lattice.25 A study by Kim described the critical ionic radius (rc = 1.038 Å for ceria) as the ionic radius of a dopant which will cause neither expansion nor contraction of the host lattice.26 Some of the highest reported conductivities for doped CeO2 have been with gadolinium,12,15,16,19,21,22,27−30 which has been linked to the ionic radius of the Gd(III) ion (1.05 Å) being very close to rc of CeO2.31 The effect of dopants on the CeO2 lattice has also been investigated computationally32−34 with two important factors identified as to how trivalent cations affect lattice distortions: first, the formation of the O vacancy, and second, the difference between the ionic radii of the host cation, Ce(IV), and the dopant cations. The former causes a contraction in the lattice due to electrostatic interactions, whereas the latter leads to lattice expansion through steric effects. Marrocchelli et al.33 determined an ionic radius of a

(1)

where CexCe is a Ce4+ ion on a Ce lattice site (with x representing the neutral charge of the site), OxO is an O2− ion at an O lattice site, MCe ′ is the trivalent dopant at a Ce lattice site with an effective charge of −1 (represented by the prime), and V•• O is a vacancy at an O lattice site with an effective charge of +2 (represented by two dots). X-ray diffraction results from several experimental studies have confirmed that such dopants are readily taken into bulk CeO2.12−23 As seen in eq 1, an O vacancy is formed to compensate the charge created when two Ce(IV) atoms are replaced with trivalent cations. These vacancies, hereafter referred to as charge compensating vacancies (CCVs), act as pathways for the diffusion of O ions and hence increase ionic conductivity. Beyond the CCVs caused by aliovalent dopants, intrinsic vacancies are a common © XXXX American Chemical Society

1 O2 (g) 2

Received: August 11, 2016 Revised: September 21, 2016

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DOI: 10.1021/acs.jpcc.6b08118 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

association energies they calculated are only between a vacancy and a single dopant. Second, ionic movement in doped CeO2 was only calculated for diffusion next to the dopants, and hence there is the possibility that the larger dopants would in fact trap CCVs at next-nearest-neighbor sites, similar to that which was observed by Andersson et al.25 The advantage of a CCV in doped CeO2 is that it introduces a pathway for ionic diffusion without creating Ce(III) ions which can act as carriers for electronic conductivity. Since it is important to avoid electronic conductivity, the dopants chosen should not increase the reducibility of CeO2, meaning the dopants should not make it easier to form intrinsic O vacancies that will reduce Ce(IV) ions to Ce(III). Experimental studies have investigated the reducibility of trivalently doped CeO2, but there are discrepancies between the results. Zaja̧c and Molenda, using thermogravimetric techniques, studied the reducibility of CeO2 doped with Y, Nd, Sm, Gd, and Dy.46 They determined that the concentration of O vacancies did not vary between different dopants, but only as a function of the concentration of dopant ions. However, Yahiro et al. investigated the electronic conductivity of CeO2 doped with Sm, Gd, Yb, and La as a function of partial O pressure.47 They too carried out a thermogravimetric analysis, but in contrast to the work of Zaja̧c and Molenda, they found that the concentration of O vacancies present, and therefore the reducibility of doped CeO2, varied between dopants at the same level of concentration, with Smdoped CeO2 displaying the most resistance to reduction. In this study, PBE+U calculations are used to determine the lowest energy structure for a variety of trivalent dopants (in order of increasing ionic radius: Al, Ga, Sc, Sb, In, Lu, Tl, Yb, Tm, Er, Ho, Y, Dy, Tb, Gd, Eu, Sm, Nd, Pr, Bi, and La) in CeO2, taking particular note of the association between dopant ions and oxygen vacancies. The effect of these dopants on the reducibility of CeO2 is also explored to determine whether it is the dopant radius, or alternate factors, that most affects the formation of O vacancies. This information will shed light on which dopants are most effective for SOFC electrolyte materials.

dopant for which the electrostatic and steric effects would cancel each other, 1.03 Å, which is consistent with the experimental value of rc determined by Kim.26 When the ionic radius of the dopant is below this value, the electrostatic effects dominate and the lattice contracts while for ionic radii larger than 1.03 Å the steric effects dominate and the lattice expands. Another method for increasing ionic conductivity in CeO2 is codoping. The theory is that by selecting one dopant with a radius less than rc and one whose radius is greater, the expansion and contraction of the CeO2 lattice are balanced out and high conductivities can be achieved. Examples of such codopant systems include lutetium (0.98 Å) and neodymium (1.11 Å),35 lanthanum (1.17 Å) and yttrium (1.02 Å),20 and gadolinium (1.05 Å) and yttrium (1.02 Å).21 However, comparable increases in ionic conductivities have also been observed for codoped materials such as gadolinium (1.05 Å) and bismuth (1.16 Å),12 samarium (1.08 Å) and neodymium (1.11 Å),36,37 and gadolinium (1.05 Å) and praseodymium (1.13 Å).38 These examples, in which all the radii are greater than rc, would suggest the increased ionic conductivity arising from codoping is not just due to the counteracting expansive and contractive forces. The local structure around the dopants in CeO2 could have a strong influence on the movement of ions in CeO2 and therefore the ionic conductivity, and hence it is vital to obtain a detailed knowledge of the structure of doped CeO2. For example, extended X-ray absorption fine structure (EXAFS) studies have observed the charge compensating vacancy and the dopant ions forming clusters,39 implying that there is a strong binding energy between the vacancy and the dopants which is likely to hinder ionic conductivity by “trapping” the vacancies next to the dopants. Force-field-based molecular dynamics studies have shown that while diffusion of the O anions does take place in doped CeO2, the O vacancies are preferentially attracted to the dopant ions, e.g., Y(III),40,41 Gd(III),42 and La(III).43 However, these studies disagree over the degree of association between vacancies and dopants. Cheng et al.40 stated that for Y-doped CeO2 CCVs would preferentially lie at a next-nearest-neighbor (NNN) position with respect to the Y(III) cations. This result was also observed by Burbano et al.,41 but only a slight preference for this arrangement was measured. In contrast, Inaba et al.42 and Hayashi et al.43 determined that for Gd-, La-, and Y-doped CeO2 dopant− vacancy−dopant clusters would form. The structure of doped CeO2 has also been investigated using density functional theory (DFT) calculations. For example, Andersson et al.25 used PW91-DFT44 to determine the association energies for a series of trivalent dopants in CeO2. For the rare-earth dopants, they determined that the lowest association energies were for ions with ionic radii between Sm(III) (1.08 Å) and Pm(III) (1.09 Å), which is significantly higher than the value of ∼1.03 Å obtained by Marrocchelli33 and Kim.26 A PBE+U study by Nakayama and Martin45 also investigated the relationship between ionic radius and ionic conductivity for trivalent rare-earth dopants. They found that dopants with smaller radii (e.g., Sc) had a tendency to trap vacancies next to them, while larger dopants (e.g., La) repelled CCVs but hindered the movement of O ions past them. Hence, they reasoned, dopants with intermediate ionic radii, such as Y(III) (1.02 Å), would be most suitable for fuel cell applications.25 There were two areas that the study by Nakayama and Martin failed to cover. First, the dopants may form neutral dopant−vacancy−dopant clusters, but the

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METHODS All calculations were performed with the Vienna ab initio simulation package (VASP),48−50 using a plane wave basis set (500 eV cutoff) with the Projector Augmented Wave (PAW)51 method (Sc [Ne], Y [Ar,3d10], Al [Ne], Ga [Ar,3d10], In [Kr, 4d10], Tl [Xe,4f145d10], Sb [Kr, 4d10], Bi [Xe,4f145d10], O [He], and La−Lu [Kr, 4d10]). These calculations were carried out with the generalized gradient approximation exchange correlation functional developed by Perdew, Burke, and Ernzerhof.52 Previous studies have shown that standard DFT functionals are incapable of correctly modeling localized electronic states due to the inherent self-interaction error (SIE).53−56 This study will investigate reduced CeO2, i.e., CeO2 that contains intrinsic O vacancies, which are well-known to lead to localized electrons on Ce ions neighboring the vacancy. To counteract the SIE associated with these defects, a U correction is applied to the Ce 4f states.57 There are several suggested U values in the literature for the Ce 4f states, e.g., 4.5 eV58 and 5.5 eV.59 The variance in reported U values is because the results are not overly sensitive to the value of U and will vary depending on the functional used and the method of determining the orbital occupations. Furthermore, U values are often chosen to fit experimental properties and therefore are dependent on the properties and criteria chosen. In this study, B


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Figure 1. Starting configurations for doped CeO2 with a CCV placed (a) nearest neighbor to the dopants, (b) next-nearest neighbor to the dopants, (c) nearest neighbor to one of the dopants, and (d) far away from the dopants. Ce, O, and dopant ions are shown in white, red, and brown, respectively. The position of the CCV is denoted by the yellow sphere.

UCe = 5.0 eV, which was derived by fitting to XPS data, was applied to the Ce 4f states60−64 and in addition UO = 5.5 eV, which was determined from a Koopmans’ like fitting process, was applied to the O 2p states;24,65,66 the presence of the UO value corrects for the SIE associated with the O 2p states. This UO value was used to be consistent with our previous studies.24,66,67 Some of the dopants studied (Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, and Yb) also have unpaired 4f electrons, which requires either treating these electrons as part of the core25 or applying a U value to these states. In this study, U = 5 eV was also applied to the 4f states of these dopants; although this value may not be the most suitable choice for all the dopants, it should provide sufficient electron localization to model the correct electronic structure, allowing for a comparison of the doped systems. The pure sesquioxides for materials with unpaired 4f electrons were investigated in both a ferromagnetic (FM) and antiferromagnetic (AFM) configuration; for Sm, Tb, Dy, Ho, and Tm it was found that the AFM configuration was more energetically favorable, while all others were FM. Occupation matrix control was used to control orbital occupation in the DFT+U calculations where required.68 All structures were converged to 0.01 eV Å−1. Optimization of bulk CeO2 was performed on a 12 atom unit cell using a 4 × 4 × 4 Monkhorst−Pack k-point mesh.69 A series of calculations were performed with varying lattice constants, under the constraint of a constant volume. The resulting energy−volume data were then fitted to the Murnaghan equation of state70 to give the equilibrium lattice constant, a process which minimizes the associated problem of Pulay stress.71 The equilibrium lattice constant was calculated to be 5.48 Å, in good agreement with the experimental lattice constant of 5.41 Å.72 The bulk modulus (B0) of CeO2 was

calculated to be 185 GPa, compared to the experimental B0 of 236 GPa.72 All defect calculations were carried out in a 2 × 2 × 2 expansion of the optimized 12 atom unit cell (96 atoms) and employed a 2 × 2 × 2 k-point mesh. To create the doped cells, two Ce ions were replaced with two trivalent dopant ions (Al, Ga, Sc, Sb, In, Lu, Tl, Yb, Tm, Er, Ho, Y, Dy, Tb, Gd, Eu, Sm, Nd, Pr, Bi, or La), giving a dopant concentration of 6.25 mol %, and a CCV was created to conserve the charge. The position of the CCV was varied to determine the lowest energy structure for the doped cells. The doping energy, Edop, was calculated according to the equation Edop = E[Ce30M 2O63] + 2E[CeO2 ] − (E[Ce32O64 ] + E[M 2O3]) (3)

where M is the dopant cation. The doping energy indicates how easily a dopant would be accepted into the host lattice. The energy difference between the structure where the CCV is in the nearest-neighbor (NN) position and the next-nearestneighbor position with respect to the dopants (ΔE = ENN − ENNN) was calculated. From ΔE it can be determined how easily oxygen vacancies can move from a NN to NNN position, which is likely to be the dominant conduction pathway in systems with realistic dopant concentrations (e.g., 10−20%) or in regions of uniform dopant concentration. The association energy (Eass) between the dopants and the CCV is calculated by finding the difference between the structure where the CCV is far away from the dopants (Figure 1d) and the lowest energy structure. This is an indicator of whether oxygen vacancies would be trapped by dopants in regions of nonuniform dopant concentration in a system. To model reduced CeO2, an additional O ion was removed from the system to assess if dopants are likely to cause unwanted electrical conductivity. C


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RESULTS Structure of Doped Ceria. The most stable structure of doped CeO2 was first determined. A range of different locations was tested for the CCV to determine where it would preferentially lie with respect to the dopants: first, with the CCV nearest neighbor to the dopants (Figure 1a); second, with the CCV next-nearest neighbor to the dopants (Figure 1b); third, with the CCV nearest neighbor to a single dopant (Figure 1c); and finally, with the CCV far away from the dopants (Figure 1d). For each CCV position, the doping energy was calculated, and the location with the lowest doping energy was deemed the most stable structure. These doping energies are shown in Table 1 in order of increasing ionic radii. Table 1. Summary of the Ionic Radii,31 Preferred Dopant Sites, Doping Energies, Difference in Energy between NextNearest-Neighbor and Nearest-Neighbor Charge Compensating Vacancy Positions (ΔE = ENN − ENNN), Reduction Energies, and Association Energies for the Trivalent Dopants Examined in This Studya dopant

ionic radius

position

Edop

Al Ga Sc Sb In Lu Tl Yb Tm Er Ho Y Dy Tb Gd Eu Sm Nd Pr Bi La

0.39 0.47 0.86 0.87 0.92 0.98 0.98 0.99 0.99 1.00 1.01 1.02 1.03 1.04 1.05 1.07 1.08 1.11 1.13 1.16 1.17

alternative alternative NN NN NN NN NN NN NN NN NN NN NN NN NN NN NN NNN NNN NN NNN

4.56 4.26 2.19 2.19 0.99 1.32 2.40 1.15 1.06 0.86 1.09 0.76 0.83 0.72 0.70 0.65 0.71 0.49 0.35 1.25 0.52

ΔE

Eass

Ered

−1.13 −0.83 −0.95 −0.54 −0.62 −0.53 −0.51 −0.15 −0.48 −0.41 −0.28 −0.11 −0.11 0.07 0.07 −0.47 0.15

3.93 2.81 1.01 1.30 1.17 0.69 1.11 0.51 0.55 0.51 0.62 0.85 0.46 0.47 0.37 0.25 0.30 0.27 0.29 1.24 0.78

−0.77 −0.71 −0.09 −0.22 −0.01 −0.03 0.00 +0.06 −0.02 -0.02 −0.21 0.00 +0.30 +0.11 0.00 −1.84 +0.53 +0.65 +0.69 −0.04 +0.66

Figure 2. Lowest energy structure for Al-doped CeO2. The dopant cations are represented by the light blue spheres. The structure for Gadoped CeO2 is similar.

Figure 3. Lowest energy structure for Sb, Sc, In, Tl, Y, and Bi-doped CeO2. The dopant cations are represented by the purple spheres.

lies in the next-nearest-neighbor position with respect to both the dopants (Figure 4). These dopants also display the three lowest doping energies of 0.49, 0.35, and 0.52 eV. Al and Ga have the smallest ionic radii of the dopants studied, and hence there is more space for distortion of the lattice, similar to small divalent dopants in CeO2.73,74 The Al and Ga ions that are nearest neighbor to the CCV move 0.91 and 0.80 Å, respectively, from the original Ce(IV) lattice position, while the other Al and Ga ions move 0.75 and 0.56 Å, respectively. The local structures around the Al and Ga dopants have similar bond lengths and bond angles to those observed in their native oxides. As the ionic radii of the dopants increase, they are more constrained to lattice positions, and hence the defect structure around the dopants bears less relation to the structure of the cations in their native oxides. For Sc, Sb, In, Lu, Tl, Yb, Tm, Er, Ho, Y, Dy, Tb, Gd, Eu, and Sm the CCV is most stable when nearest neighbor to the two dopants (Figure 3). These dopants encompass a wide range of ionic radii (0.86−1.08 Å) that are either less, or not significantly larger, than ∼1.03 Å, the critical ionic radius identified by Kim and Marrocchelli.26,33 There is minimal distortion of the lattice, with the M(III)−O bond lengths similar to the Ce(IV)−O bond length of 2.37 Å.24

a

The ionic radii are given in Å, and energies are given in eV. The reduction energies are given relative to the reduction energy of pure CeO2, 2.23 eV. Values shown in bold correspond to those which are within the criteria set out in the text for suitable dopants for SOFC applications.

The analysis of the lowest energy structures revealed that the defect structures could be grouped according to the ionic radius of the dopant ions. For Al- and Ga-doped CeO2, the CCV preferentially forms in the nearest-neighbor position to one of the dopants, and ∼5.47 Å from the other, as seen in Figure 2. Al- and Ga-doped CeO2 also display the largest doping energies of 4.56 and 4.26 eV respectively. When doped with Sc, Sb, In, Lu, Tl, Yb, Tm, Er, Ho, Y, Dy, Tb, Gd, Eu, Sm, or Bi, the doped cells adopt the structure seen in Figure 3, where the CCV is nearest neighbor to both the dopant cations. Sc and Sb both have a doping energy of 2.19 eV, and Tl has a doping energy of 2.40 eV. All other dopants with nearest-neighbor oxygen vacancy positions have doping energies in the range of 1.32− 0.65 eV. For the remaining dopants, Nd, Pr, and La, the CCV D


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Figure 4. Lowest energy structure for Nd, Pr, and La-doped CeO2. The dopant cations are represented by the blue spheres.

Figure 5. Charge density around the (a) Y and (b) Bi cations and CCV in doped CeO2. The charge density plot ranges from 0 (blue) to 0.4 e/Å3 (red).

Furthermore, as the CCV can be considered an area of effective positive charge and the trivalent dopants are less positively charged than the host Ce(IV) cations, it is more favorable to have the CCV nearest neighbor to the dopants than to four Ce(IV) ions. The M(III)−M(III) distances for these dopants range from 3.99 to 4.23 Å. This is similar to the Ce(III)− Ce(III) distance in reduced CeO2 (4.07 Å) when the O vacancy neighbors the Ce(III) ions. As the ionic radius increases there is a threshold around 1.09 Å, beyond which steric effects of the dopants on their surroundings overcome the electrostatic effects of the CCV. This is the case for Nd, Pr, and La, where it becomes energetically favorable for the CCV to be in the next-nearestneighbor position to both dopants (Figure 4). The M(III)−O bond lengths increase to an average of 2.45 Å (Nd and Pr) and 2.46 Å (La) compared to the Ce(IV)−O bond length of 2.37 Å.24 The exception to this is the O anion that bridges the two dopant cations and also neighbors the CCV. This O ion moves toward the CCV, which is an area of effective positive charge, increasing the M(III)−O bond length to 2.59 Å (Nd), 2.60 Å (Pr), and 2.63 Å (La). The M(III)−M(III) distances are 3.85 Å (Nd), 3.86 Å (Pr), and 3.89 Å (La), which closely match the Ce(IV)−Ce(IV) distance of 3.87 Å seen in bulk CeO2. An exception to the relationship between ionic radius and defect structure was found for the case of Bi-doped CeO2. The ionic radius of Bi (1.16 Å) is similar to La (1.17 Å). However, the CCV was found to preferentially form in the nearestneighbor position. Previous studies have shown that the highly asymmetric structure of α-Bi2O3 is due to the formation of lone pairs on the Bi ions.75,76 The valence charge density around the CCV and the dopants is displayed for Y- and Bi-doped CeO2 in Figures 5a and 5b, respectively. It should be noted that the charge density observed for Y-doped CeO2 matches that which is observed for the other dopants studied. It can be seen that the electron density around the Y ions is symmetric whereas around the Bi ions there is an asymmetric electron density that is oriented toward the CCV, which is caused by lone pairs. The only other exception is Sb, which also displays lone pairs in CeO2. However, the ionic radius of Sb is in the range where it would be expected that the CCV would be in the nearestneighbor position, regardless of the presence of lone pairs. Further evidence that the asymmetric electron density is due to the formation of lone pairs is found by studying the partial

electronic density of states (PEDOS). In the calculated PEDOS (Figure 6) there are two important interactions in the

Figure 6. Electronic density of states for Bi-doped CeO2. The blue lines represent Bi 6s states, the orange lines Bi 6p states, the green line Ce 4f states, and the red lines O 2p states. The heights of the Bi states have been magnified ×80 for clarity. The top of the valence band has been is aligned to 0 eV.

formation of lone pairs: between the Bi 6s and O 2p states and between the Bi 6s, Bi 6p, and O 2p states. An interaction between the Bi 6s states and the O 2p states is seen at ∼−9 eV, and there is also an interaction at the top of the valence band (−0.5 to 0 eV) between the O 2p, Bi 6s, and Bi 6p states. This is in agreement with the findings of Walsh et al., where it was shown that in the α-Bi2O3 PEDOS there are two major interactions between the Bi 6s and O 2p states and between the Bi 6p and O 2p states.75 The region between −12 and −8 eV was identified as a bonding interaction between the Bi 6s and O 2p states while the second region between −5 eV and the valence band maximum can be further split into two parts. Between −5 and −1.5 eV the Bi 6p and the O 2p states interact, and from the −1.5 eV to the valence band maximum E


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Effect of Dopants on the Reducibility of CeO2. The operation of a SOFC requires that the electrolyte is purely an ionic conductor; any electronic conductivity can serve to shortcircuit the cell. Since the formation of additional O vacancies which reduce Ce(IV) to Ce(III) can cause electronic conductivity in CeO2, the dopant should not increase the concentration of such defects; i.e., it should not make the material more reducible. Therefore, an additional O vacancy was introduced to the doped systems to determine the effect of the dopant ions on the reducibility of CeO2. For most dopants, one position was tested, an O vacancy near to the dopants (Figure 7a). For Al- and Ga-doped CeO2 an extra position for

there is also a contribution from the Bi 6s states. This interaction of Bi 6s and O 2p is a filled antibonding interaction that is stabilized through coupling to the filled Bi 6p states, thus creating the distinctive lone pairs observed in α-Bi2O3.75 The peaks seen here for Bi-doped CeO2 correspond with the previously identified bonding and antibonding interactions between Bi 6s and O 2p states, along with some mixing of Bi 6p states with the latter, confirming the presence of lone pairs in Bi-doped CeO2. In Bi2O3, as well as other materials containing Bi(III), Pb(II), and Sn(II), the formation of lone pairs due to an asymmetric coordination environment has been shown to greatly reduce the energy in the system.75−80 Therefore, it is more stable to have the CCV nearest neighbor to the Bi ions, creating an asymmetric environment and forming lone pairs, despite the size of the Bi ions. In Table 1 the energy difference between the structure where the dopants are nearest neighbor to the CCV and the structure where the dopants are next-nearest neighbor to the CCV (ΔE) are displayed as a function of ionic radius, along with the calculated association energy (Eass) between the dopants and the CCV and the reduction energy (Ered). The magnitude of ΔE should be as low as possible as it is an indication of the energy which would be required for the CCV to move from a nearest-neighbor site to a next-nearest-neighbor site. The sign associated with this value simply indicates whether the most stable site is nearest neighbor or next-nearest neighbor. This value is particularly relevant for realistic doping levels where the maximum ionic conductivity has been found for concentrations of between 15 and 20 mol %.15,27,81,82 In such systems few sites would exist for CCVs which are neither nearest neighbor nor next-nearest neighbor to a dopant. This value is not calculated for Al- or Ga-doped CeO2 as the most stable structure is not a nearest-neighbor or a next-nearest-neighbor site. It is also not calculated for Sb- or Sc-doped CeO2 because the next-nearestneighbor structure optimizes to the nearest-neighbor structure as the next-nearest-neighbor structure is not stable which indicates that vacancies are very strongly bound to the dopant in the nearest-neighbor structure. For the remaining dopants the magnitude of ΔE generally decreases with increasing ionic radius, although some exceptions to this are Y-, Bi-, and Ladoped CeO2 which have a ΔE of −0.15 eV, −0.47, and 0.15 eV, respectively. Y-doped CeO2 has a ΔE smaller than those with similar ionic radii, while both La- and Bi-doped CeO2 have ΔE values larger than those with similar ionic radii. The highest values of ΔE are seen for In-, Lu-, and Tl-doped CeO2: −1.13, −0.83, and −0.95 eV, respectively. The lowest values are found for Y, Gd, Eu, Sm, Nd, Pr, and La, meaning that O vacancies should be particularly mobile in these systems. For SOFC applications, the association energy should also be as small as possible, as larger values would trap the CCV at the dopant ions and thus hinder ionic conductivity in systems with regions of low dopant concentration. Al- and Ga-doped CeO2 have the largest values of association energy, 3.93 and 2.81 eV, respectively. Sb- and Bi-doped CeO2 have the next highest association energy at 1.30 and 1.24 eV, respectively. The comparatively higher values found for these dopants are likely due to the extra stability associated with the lone pairs on the cations. All of the rare-earth dopants (and Y) have low association energies, with Eu, Sm, Nd, and Pr having particularly low values. Therefore, O vacancies in these doped materials (at low dopant concentrations) should be comparatively free to move and hence should display good ionic conductivity.

Figure 7. Two positions tested for an intrinsic oxygen vacancy in doped CeO2: (a) near to the dopants and (b) alternate position (Aland Ga-doped CeO2 only). The position of the intrinsic vacancy is represented by the green sphere. The isosurfaces show the spin density of the Ce(III) ions. They are shown in blue and are set to 0.05 e/Å3.

the reduction was also carried out (Figure 7b). This O ion was chosen because it is undercoordinated compared to other bulk O ions due to the coordination of Al and Ga, and previous work on divalently doped CeO2 has shown that it is easier to remove undercoordinated O ions from CeO2.73,74 The reduction energies and their relation to pure CeO2 (2.23 eV74) are displayed in Figure 8. The smaller dopants, Al and Ga (shown in the inset), do not significantly affect the reduction energy for a nearby, fully coordinated O ion, but for undercoordinated O ions, the energy is far lower. When the CCV is nearest neighbor to the dopant ions (Sc, Sb, In, Tl, Yb, Tm, Er, Ho, Y, Dy, Tb, Gd, Sm, and Bi), the reduction energy F


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to be an exception to this, as despite having a larger ionic radius than La, the lowest energy structure was found for a CCV neighboring the dopants. It was determined when the CCV is nearest neighbor to the dopants, lone pairs form on the Bi and Sb ions, stabilizing the local asymmetric structure of the NN site. The results on the reduction energy of doped CeO2 would suggest that the largest effect on the reducibility is how the dopants change the structure of the lattice. The increased distortion created by the Al and Ga dopant ions lead to undercoordinated O ions which are far easier to remove from the lattice than fully coordinated ions. For Sm, Nd, Pr, and Ladoped CeO2 it becomes much harder to remove oxygens ions close to the dopants, most likely due to steric strain between the dopants and Ce(III) ions. For the remaining dopants, which cause the least distortion to the lattice, we find that the reduction energy is mostly unchanged from pure CeO2. To help summarize the results, some of the values in Table 1 are shown in bold according to the following criteria: doping energy less than 1.0 eV; the magnitude of the energy difference between the structure where the CCV is in the nearestneighbor position and the next-nearest-neighbor position (ΔE = ENN − ENNN) less than 0.30 eV; association energies less than 0.40 eV; and does not decrease the reduction energy significantly (less than 0.05 eV). These criteria were selected to provide a good framework for comparing the dopants and determining which are best suited for SOFC applications. The doping energy indicates how easily a dopant is taken into the host lattice and so is a very important criterion, as if the doping energy is too high then the dopant will not be suited to the host system. The ΔE value is a measure of how mobile O vacancies are in systems with realistic dopant concentrations and in regions of uniform dopant concentration, so the magnitude of this energy should be as low as possible. The association energy is a similar measure but is more applicable to regions of low or nonuniform dopant concentrations. Finally, the reduction energy is a measure of how easily Ce(IV) is reduced to Ce(III), which is vital information for the operation of the SOFC; if the reduction energy is decreased by the presence of a particular dopant, this suggests that excess electrons may be present in the cell which would result in short-circuiting of the device. It is apparent that neither Al nor Ga would be suitable dopants for SOFC applications: they have high doping energies and a high association energy, and they decrease the reduction energy of CeO2, increasing the amount of intrinsic O vacancies and hence the amount of Ce(III). This is perhaps not surprising, as Al- and Ga-doped CeO2 have been linked to enhanced oxygen storage capacity.83,84 From the remaining dopants, Sc, Sb, In, Lu, Tl, and Bi are poor choices for fuel cell applications. Sb and Bi have very high association energies, a result of the stabilizing effect of lone pairs on the dopant ions which suggests strong trapping of the O vacancies. They both also decrease the reduction energy in CeO2. In the case of Sc, In, Lu, and Tl, their moderate ΔE and association energies, coupled with the high doping energies of Sc and Tl, make them less desirable compared to other dopants studied. A study by Omar et al.85 found that Lu-doped CeO2 had the highest activation energy out of the rare-earth dopants studied (Lu, Yb, Er, Y, Dy, Gd, Sm, Nd), which agrees with the calculated ΔE and association energies calculated here. There has not been much focus on doped CeO2 featuring In and Tl ions in the literature, as their smaller ionic radius would perhaps be better

Figure 8. Reduction energies for doped CeO2. The blue points represent vacancies formed close to the dopant cations. Because the radii of Al and Ga are significantly smaller than the other dopants studied, the results for these two dopants are shown in an inset on the graph, with additional results for removing an undercoordinated O ion (light blue). The green line represents the reduction energy of pure CeO2, and the black dashed line indicates the ionic radius of Ce(IV).

is largely unaffected, although Dy and Sm are seen to increase the reduction energy by 0.30 and 0.53 eV, respectively. As the ionic radii of the NN dopants are closer to that of Ce(IV) than the NNN dopants, the CeO2 lattice is not greatly distorted by their presence, and hence only minor changes to reduction energy are observed. An exception to this is Eu-doped CeO2 which shows a drastic decrease in reduction energy when the vacancy forms near the dopants. The reason for this becomes apparent upon studying the electronic structure. It was found that excess electrons associated with the formation of the neutral O vacancy preferentially localized on the Eu(III) ions, reducing them to Eu(II). It should be noted that in Figure 8 Eu is plotted at the ionic radius of Eu(III) (1.07 Å) rather than that of Eu(II) (1.25 Å). This result is to be expected as Eu(II) is relatively stable, confirmed by the fact that Eu(II) forms despite its large ionic radius compared to Ce(IV). It was expected that a similar result would be seen for Yb(III) due to the theoretically stable electronic configuration of Yb(II), but the electronic structure for calculations with Yb(II) failed to converge. For Sm, Nd, Pr, and La the energy to form an O vacancy near the dopants is significantly higher than for pure CeO2, indicating that Ce(IV) would be unlikely to be reduced to Ce(III) in the presence of these dopants.

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DISCUSSION The results demonstrate that the structure of doped CeO2 is dependent on the ionic radius of the dopants. When the dopants are much smaller than the host cations, e.g., Al and Ga, the dopant ions are comparatively free to move off the lattice site, leading to distortion in the CeO2 lattice. As the ionic radius of the dopant cations increases, the dopant cations are more constrained and less deformation of the lattice occurs. For ionic radii up to 1.08 Å, it was observed that the lowest energy structure occurs when the CCV neighbors the dopants. This is due to the CCV experiencing less electrostatic repulsion from the dopant cations than from the Ce(IV) ions. As the ionic radius increases beyond 1.08 Å, the steric effects of the dopants begin to dominate, and eventually the CCV is forced away from the dopants to the next-nearest-neighbor position. Bi was found G


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lower than for Gd and Sm, which corresponds with our calculated values of ΔE and association energy. Anjaneya et al.92 found Sm to have the lowest activation energy and the highest ionic conductivity, although it should be noted that Gd, Sm, and Nd were all seen to have activation energies within 0.03 eV of each other. Gd does not lower the reduction energy and Sm, Nd, and Pr actually increase it, as seen in Table 1, helping to prevent any unwanted electronic conductivity in CeO2. The resistance to reduction in the presence of Sm is in agreement with the findings of Yahiro et al.47 These results demonstrate that a combination of doping energy, ΔE, association energy, and reduction energy provides a good basis for assessing the suitability of dopants for fuel cell applications.

suited for materials such as zirconia, where there would be less mismatch between the dopants and the host cation (Zr(IV) = 0.84 Å).86,87 This is clear from the high ΔE and association energies for In and Tl which suggest that trapping of the CCV would occur, thus hindering ionic conductivity. For Eu, the reduction energy has been significantly lowered due to the reduction of Eu(III) to Eu(II). This would suggest that Eu will act as a divalent dopant in CeO2. Eu(II) may still be suitable for SOFC applications; Eu-doped CeO2 has been experimentally observed to be a good ionic conductor,22 which suggests the facile formation of the second vacancy without the formation of Ce(III) is beneficial for ionic conductivity. Eu-doped CeO2 also displays the lowest association energy (0.25 eV) at an ionic radius of 1.07 Å. This is in line with the critical ionic radius calculated by Andersson et al.25 The data show Y and La could be potential dopants for SOFC electrolytes. They exhibit low doping energies and low ΔE, and while their association energies are not as low as other dopants, neither are they excessively high. The low ΔE values indicate that at a realistic level of doping Y and La would perform quite well as ionic conductors. However, their association energies of 0.85 and 0.78 eV indicate that in regions of low dopant concentration, dopant−vacancy clusters will be more likely to form as has been observed in experiment.88 Experimental studies have calculated the activation energies of Y- and La-doped CeO2 to be 0.78 eV85 and 0.75 eV,22 respectively, which closely match the association energies of 0.85 and 0.78 eV. Additionally, the presence of La in CeO2 is shown to increase the reduction energy, which would help to avoid short-circuiting the operation of an SOFC by preventing the formation of intrinsic O vacancies. Of the remaining dopants investigated in this study, Yb, Tm, Er, Ho, Dy, and Tb are reasonable candidates for SOFC applications. They all have low doping energies and relatively low ΔE and exhibit relatively low association energies with the CCV. Furthermore, none of these dopants significantly lower the reduction energy of CeO2 and thus do not increase unwanted electronic conductivity. In fact, Dy and Tb increase the reduction energy of CeO2. Tm, Ho, and Tb have not received much attention experimentally, most likely because all three are very rare, even among the rare-earth elements. Yb, Er, and Dy are far more abundant and have been observed to be good ionic conductors at low temperatures when used as dopants in ceria.85,89 Of these three, Dy is seen to have the highest ionic conductivity in experiment85 which is in line with the low association energy (0.46 eV) and low ΔE (0.48 eV) calculated here. Dy has also been shown to be an effective codopant for CeO2 (with Sm),90 as well as in singly doped systems, where it displays high ionic conductivities at low temperatures23 that are even comparable to Gd, which is often cited as showing the highest conductivity of the doped cerias.15 Out of all the dopants studied, Gd, Sm, Nd, and Pr are seen to be the most promising candidates for SOFC applications. As seen in Table 1, they are the only dopants that fall under the desired criteria in all cases. Their low doping energies ensure that they are readily incorporated into CeO2 while their low ΔE and low association energies indicate that the CCV is unlikely to be trapped by the dopant cations, thus aiding ionic conductivity. Gd- and Sm-doped CeO2 have been widely studied, and their effectiveness for SOFC applications is wellknown.16,19,81,91 A study by Pikalova et al.89 measured the activation energy and conductivity for a series of rare-earth dopants and found the activation energy for Nd was slightly

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CONCLUSIONS PBE+U calculations have been applied to a series of trivalent dopants in CeO2. They demonstrate that the structure of doped CeO2 is dependent on the ionic radius of the dopants within a given range of radii: smaller dopants will adopt a structure similar to that of their native oxide; intermediate sized dopants will occupy Ce lattice sites and form a charge compensating vacancy (CCV) that neighbors them; larger dopants will also occupy Ce lattice sites and the CCV will be positioned at a next-nearest-neighbor site. The effect of the dopants on the reducibility of CeO2 was also tested. The results indicate that the defect structure affects the reducibility of CeO2. In doped CeO2, dopants that share similar defect structures also had similar reduction energies regardless of the differences between ionic radii. This study thus provides an atomic description of the properties important in understanding the suitability of dopants for enhanced ionic conductivity. From the range of dopants considered in this study, Gd, Sm, Nd, and Pr are the most promising for SOFC applications. First, they all exhibit low doping energies, meaning that they will easily form solid solutions with CeO2. Second, the energy difference between the structure with the vacancy at the nearest-neighbor and next-nearest-neighbor site and the level of association between the dopant cations and the CCV are all exceptionally low. This ensures the CCV will not become trapped by the dopant cations, promoting good ionic conductivity. Finally, these dopants either do not affect the reduction energy of CeO2 (Gd) or raise it (Sm, Nd, and Pr) which serves to limit unwanted electronic conductivity in CeO2.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail [email protected]; phone +353 1 896 1357 (A.K.L.). *E-mail [email protected]; phone +353 1 896 1357 (G.W.W.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was supported by Science Foundation Ireland (SFI) through the Principal Investigator Programme (Grant 12/IA/1414). All calculations were performed using the Kelvin (funded through grants from the Higher Education Authority, through its PRTLI program), Lonsdale (funded through grants from SFI), and Pople (funded by SFI- 12/IA/1414) supercomputers, maintained by the Trinity Centre for High Performance Computing (TCHPC), and the Stokes and Fionn supercomputers, maintained by ICHEC. H


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(23) Acharya, S. A. The Effect of Processing Route on Sinterability and Electrical Properties of Nano−Sized Dysprosium−Doped Ceria. J. Power Sources 2012, 198, 105−111. (24) Keating, P. R. L.; Scanlon, D. O.; Morgan, B. J.; Galea, N. M.; Watson, G. W. Analysis of Intrinsic Defects in CeO2 using a Koopmans-Like GGA+U Approach. J. Phys. Chem. C 2012, 116, 2443−2452. (25) Andersson, D. A.; Simak, S. I.; Skorodumova, N. V.; Abrikosov, I. A.; Johansson, B. Optimization of Ionic Conductivity in Doped Ceria. Proc. Natl. Acad. Sci. U. S. A. 2006, 103, 3518−3521. (26) Kim, D. J. Lattice Parameters, Ionic Conductivities, and Solubility Limits in Fluorite-Structure MO2 Oxide [M = Hf4+, Zr4+, Ce4+, Th4+, U4+] Solid Solutions. J. Am. Ceram. Soc. 1989, 72, 1415− 1421. (27) Avila-Paredes, H. J.; Choi, K.; Chen, C.-T.; Kim, S. DopantConcentration Dependence of Grain-Boundary Conductivity in Ceria: A Space-Charge Analysis. J. Mater. Chem. 2009, 19, 4837−4842. (28) Cheng, J.; Zha, S.; Fang, X.; Liu, X.; Meng, G. On the Green Density, Sintering Behavior and Electrical Property of Tape Cast Ce0.9Gd0.1O1.95 Electrolyte Films. Mater. Res. Bull. 2002, 37, 2437− 2446. (29) Kumar, V. P.; Reddy, Y. S.; Kistaiah, P.; Prasad, G.; Reddy, C. V. Thermal and Electrical Properties of Rare-Earth Co-Doped Ceria Ceramics. Mater. Chem. Phys. 2008, 112, 711−718. (30) Fu, Y. P.; Chen, S. H. Preparation and Characterization of Neodymium-Doped Ceria Electrolyte Materials for Solid Oxide Fuel Cells. Ceram. Int. 2010, 36, 483−490. (31) Shannon, R. D. Revised Effective Ionic Radii and Systematic Studies of Interatomic Distances in Halides and Chalcogenides. Acta Crystallogr., Sect. A: Cryst. Phys., Diffr., Theor. Gen. Crystallogr. 1976, 32, 751−767. (32) Bishop, S. R.; Marrocchelli, D.; Fang, W.; Amezawa, K.; Yashiro, K.; Watson, G. W. Reducing the Chemical Expansion Coefficient in Ceria by Addition of Zirconia. Energy Environ. Sci. 2013, 6, 1142− 1146. (33) Marrocchelli, D.; Bishop, S. R.; Tuller, H. L.; Yildiz, B. Understanding Chemical Expansion in Non-Stoichiometric Oxides: Ceria and Zirconia Case Studies. Adv. Funct. Mater. 2012, 22, 1958− 1965. (34) Marrocchelli, D.; Bishop, S. R.; Tuller, H. L.; Watson, G. W. Charge Localization Increases Chemical Expansion in Cerium−Based Oxides. Phys. Chem. Chem. Phys. 2012, 14, 12070−12074. (35) Omar, S.; Wachsman, E. D.; Nino, J. C. A Co−doping Approach Towards Enhanced Ionic Conductivity in Fluorite−Based Electrolytes. Solid State Ionics 2006, 177, 3199−3203. (36) Omar, S.; Wachsman, E. D.; Nino, J. C. Higher Ionic Conductive Ceria-Based Electrolytes for Solid Oxide Fuel Cells. Appl. Phys. Lett. 2007, 91, 144106. (37) Burbano, M.; Nadin, S.; Marrocchelli, D.; Salanne, M.; Watson, G. W. Ceria Co-Doping: Synergistic or Average Effect? Phys. Chem. Chem. Phys. 2014, 16, 8320−8331. (38) Baral, A. K.; Sankaranarayanan, V. Dielectric Relaxation Properties of Nanostructured Ce0.8Gd0.1Pr0.1O2−δ Material at Intermediate Temperatures. Appl. Phys. Lett. 2009, 94, 074101. (39) Kossoy, A.; Frenkel, A. I.; Wang, Q.; Wachtel, E.; Lubomirsky, I. Local Structure and Strain-Induced Distortion in Ce0.8Gd0.2O1.9. Adv. Mater. 2009, 22, 1659−1662. (40) Cheng, C. H.; Lee, S. F.; Hong, C. W. Ionic Dynamics of an Intermediate-Temperature Yttria-Doped-Ceria Electrolyte. J. Electrochem. Soc. 2007, 154, 158−163. (41) Burbano, M.; Norberg, S. T.; Hull, S.; Eriksson, S. G.; Marrocchelli, D.; Madden, P. A.; Watson, G. W. Oxygen Vacancy Ordering and the Conductivity Maximum in Y2O3-Doped CeO2. Chem. Mater. 2012, 24, 222−229. (42) Inaba, H.; Sagawa, R.; Hayashi, H.; Kawamura, K. Molecular Dynamics Simulation of Gadolinia−Doped Ceria. Solid State Ionics 1999, 122, 95−103.

REFERENCES

(1) Badwal, S. P. S.; Foger, K. Solid Oxide Electrolyte Fuel Cell Review. Ceram. Int. 1996, 22, 257−265. (2) Blum, L.; Meulenberg, W. A.; Nabielek, H.; Steinberger-Wilckens, R. Worldwide SOFC Technology Overview and Benchmark. Int. J. Appl. Ceram. Technol. 2005, 2, 482−492. (3) Brett, D. J. L.; Atkinson, A.; Brandon, N. P.; Skinner, S. J. Intermediate Temperature Solid Oxide Fuel Cells. Chem. Soc. Rev. 2008, 37, 1568−1578. (4) Goodenough, J. B. Oxide-Ion Electrolytes. Annu. Rev. Mater. Res. 2003, 33, 91−128. (5) Mahato, N.; Banerjee, A.; Gupta, A.; Omar, S.; Balani, K. Progress in Material Selection for Solid Oxide Fuel Cell Technology: A Review. Prog. Mater. Sci. 2015, 72, 141−337. (6) Jacobson, A. J. Materials for Solid Oxide Fuel Cells. Chem. Mater. 2010, 22, 660−674. (7) Krok, F.; Abrahams, I.; Wrobel, W.; Kozanecka-Szmigiel, A.; Dygas, J. R. Oxide−Ion Conductors for Fuel Cells. Mater. Sci. Polym. 2006, 24, 13−22. (8) Thangadurai, V.; Weppner, W. Recent Progress in Solid Oxide and Lithium Ion Conducting Electrolytes Research. Ionics 2006, 12, 81−92. (9) Tietz, F.; Buchkremer, H. P.; Stover, D. 10 Years of Materials Research for Solid Oxide Fuel Cells at Forschungszentrum Julich. J. Electroceram. 2006, 17, 701−707. (10) Yano, M.; Tomita, A.; Sano, M.; Hibino, T. Recent Advances in Single-Chamber Solid Oxide Fuel Cells: A Review. Solid State Ionics 2007, 177, 3351−3359. (11) Basu, S.; Sujatha, D.; Maiti, H. S. Synthesis and Properties of Nanocrystalline Ceria Powders. J. Mater. Res. 2004, 19, 3162−3171. (12) Fu, Y. P.; Tseng, C. W.; Peng, P. C. Effect of Bismuth Addition on the Electrical Conductivity of Gadolinium-Doped Ceria Ceramics. J. Eur. Ceram. Soc. 2008, 28, 85−90. (13) Fu, Y.-P.; Chen, S.-H.; Huang, J.-J. Preparation and Characterization of Ce0.8M0.2O2−δ (M = Y, Gd, Sm, Nd, La) Solid Electrolyte Materials for Solid Oxide Fuel Cells. Int. J. Hydrogen Energy 2010, 35, 745−752. (14) Esposito, V.; Zunic, M.; Traversa, E. Improved Total Conductivity of Nanometric Samaria-Doped Ceria Powders Sintered with Molten LiNO3 Additive. Solid State Ionics 2009, 180, 1069−1075. (15) Kuharuangrong, S. Ionic Conductivity of Sm, Gd, Dy and ErDoped Ceria. J. Power Sources 2007, 171, 506−510. (16) Rambabu, B.; Ghosh, S.; Hrudananda, J. Novel Wet−Chemical Synthesis and Characterization of Nanocrystalline CeO2 and Ce0.8Gd0.2O1.9 as Solid Electrolyte for Intermediate Temperature Solid Oxide Fuel Cell (IT-SOFC) Applications. J. Mater. Sci. 2006, 41, 7530−7536. (17) Sen, S.; Avila-Paredes, H. J.; Kim, S. Direct Spectroscopic Observation of Size-Dependent Vacancy Distribution in Y−Doped CeO2. J. Mater. Chem. 2008, 18, 3915−3917. (18) Zhu, B.; Liu, X.; Zhu, Z.; Ljungberg, R. Solid Oxide Fuel Cells (SOFCs) using Industrial Grade Mixed Rare-Earth Oxide Electrolytes. Int. J. Hydrogen Energy 2008, 33, 3385−3392. (19) Zha, S.; Xia, C.; Meng, G. Effect of Gd (Sm) Doping on Properties of Ceria Electrolyte for Solid Oxide Fuel Cells. J. Power Sources 2002, 115, 44−48. (20) Sha, X.; Lu, Z.; Huang, X.; Miao, J.; Ding, Z.; Xin, X.; Su, W. Study on La and Y Co−Doped Ceria−Based Electrolyte Materials. J. Alloys Compd. 2007, 428, 59−64. (21) Guan, X.; Zhou, H.; Liu, Z.; Wang, Y.; Zhang, J. High Performance Gd3+ and Y3+ Co−Doped Ceria−Based Electrolytes for Intermediate Temperature Solid Oxide Fuel Cells. Mater. Res. Bull. 2008, 43, 1046−1054. (22) Balaguer, M.; Solis, C.; Serra, J. M. Structural−Transport Properties Relationships on Ce1−xLnxO2−δ System (Ln = Gd, La, Tb, Pr, Eu, Er, Yb, Nd) and Effect of Cobalt Addition. J. Phys. Chem. C 2012, 116, 7975−7982. I


Article


Reduction and the Adsorption of CO and NO2. J. Phys. Chem. C 2009, 113, 11095−11103. (65) Morgan, B. J.; Watson, G. W. Polaronic Trapping of Electrons and Holes by Native Defects in Anatase TiO2. Phys. Rev. B: Condens. Matter Mater. Phys. 2009, 80, 233102. (66) Keating, P. R. L.; Scanlon, D. O.; Watson, G. W. Computational Testing of Trivalent Dopants in CeO2 for Improved High−κ Dielectric Behaviour. J. Mater. Chem. C 2013, 1, 1093−1098. (67) Keating, P. R. L.; Scanlon, D. O.; Watson, G. W. The Nature of Oxygen States on the Surfaces of CeO2 and La−Doped CeO2. Chem. Phys. Lett. 2014, 608, 239−243. (68) Allen, J. P.; Watson, G. W. Occupation Matrix Control of d- and f-electron Localisations using DFT + U. Phys. Chem. Chem. Phys. 2014, 16, 21016−21031. (69) Monkhorst, H. J.; Pack, J. D. Special Points for Brillouin−Zone Integrations. Phys. Rev. B 1976, 13, 5188−5192. (70) Murnaghan, F. D. The Compressibility of Media Under Extreme Pressures. Proc. Natl. Acad. Sci. U. S. A. 1944, 30, 244−247. (71) Allen, J. P.; Scanlon, D. O.; Parker, S. C.; Watson, G. W. Tin Monoxide: Structural Prediction from First Principles Calculations with van der Waals Corrections. J. Phys. Chem. C 2011, 115, 19916− 19924. (72) Gerward, L.; Olsen, J. S. Powder Diffraction Analysis of Cerium Dioxide at High Pressure. Powder Diffr. 1993, 8, 127. (73) Scanlon, D. O.; Morgan, B. J.; Watson, G. W. The Origin of the Enhanced Oxygen Storage Capacity of Ce1−xPd/PtxO2. Phys. Chem. Chem. Phys. 2011, 13, 4279−4282. (74) Kehoe, A. B.; Scanlon, D. O.; Watson, G. W. Role of Lattice Distortions in the Oxygen Storage Capacity of Divalently Doped CeO2. Chem. Mater. 2011, 23, 4464−4468. (75) Walsh, A.; Watson, G. W.; Payne, D. J.; Edgell, R. G.; Guo, J.; Glans, P.-A.; Learmonth, T.; Smith, K. E. Electronic Structure of the α and δ Phases of Bi2O3: A Combined Ab−initio and X−ray Spectroscopy Study. Phys. Rev. B: Condens. Matter Mater. Phys. 2006, 73, 235104. (76) Walsh, A.; Payne, D. J.; Egdell, R. G.; Watson, G. W. Stereochemistry of Post-Transition Metal Oxides: Revision of the Classical Lone Pair Model. Chem. Soc. Rev. 2011, 40, 4455−4463. (77) Watson, G. W. The Origin of the Electron Distribution in SnO. J. Chem. Phys. 2001, 114, 758−763. (78) Watson, G. W.; Parker, S. C.; Kresse, G. Ab initio Calculation of the Origin of the Distortion of α-PbO. Phys. Rev. B: Condens. Matter Mater. Phys. 1999, 59, 8481−8486. (79) Watson, G. W.; Parker, S. C. Origin of the Lone Pair of α-PbO from Density Functional Theory Calculations. J. Phys. Chem. B 1999, 103, 1258−1262. (80) Walsh, A.; Watson, G. W. The Origin of the Stereochemically Active Pb(II) Lone Pair: DFT Calculations on PbO and PbS. J. Solid State Chem. 2005, 178, 1422−1428. (81) Inaba, H.; Tagawa, H. Ceria−Based Solid Electrolytes. Solid State Ionics 1996, 83, 1−16. (82) Huang, H.; Gur, T. M.; Saito, Y.; Prinz, F. High Ionic Conductivity in Ultrathin Nanocrystalline Gadolinia-Doped Ceria Films. Appl. Phys. Lett. 2006, 89, 143107. (83) Dong, Q.; Yin, S.; Guo, C.; Sato, T. Aluminium−Doped Ceria− Zirconia Solid Solutions with Enhanced Thermal Stability and High Oxygen Storage Capacity. Nanoscale Res. Lett. 2012, 7, 542. (84) Collins, S.; Finos, G.; Alcántara, R.; del Rio, E.; Bernal, S.; Bonivardi, A. Effect of Gallia Doping on the Acid-base and Redox Properties of Ceria. Appl. Catal., A 2010, 388, 202−210. (85) Omar, S.; Wachsman, E. D.; Jones, J. L.; Nino, J. C. Crystal Structure-Ionic Conductivity Relationships in Doped Ceria Systems. J. Am. Ceram. Soc. 2009, 92, 2674−2681. (86) Irvine, J. T. S.; Dobson, J. W. L.; Politova, T.; Garcia, S.; Martin, J. C.; Shenouda, A. Co−Doping of Scandia-Zirconia Electrolytes for SOFCs. Faraday Discuss. 2007, 134, 41−49. (87) Parvulescu, V.; Coman, S.; Parvulescu, V. I.; Grange, P.; Poncelet, G. Reaction of Hexane, Cyclohexane, and Methylcyclopen-

(43) Hayashi, H.; Sagawa, R.; Inaba, R.; Kawamura, K. Molecular Dynamics Calculations on Ceria-Based Solid Electrolytes with Different Radius Dopants. Solid State Ionics 2000, 131, 281−290. (44) Perdew, J. P.; Wang, Y. Accurate and Simple Analytic Representation of the Electron-Gas Correlation Energy. Phys. Rev. B: Condens. Matter Mater. Phys. 1992, 45, 13244−13249. (45) Nakayama, M.; Martin, M. First−Principles Study on Defect Chemistry and Migration of Oxide Ions in Ceria Doped with Rare− Earth Cations. Phys. Chem. Chem. Phys. 2009, 11, 3241−3249. (46) Zaja̧c, W.; Molenda, J. Properties of Doped Ceria Solid Electrolytes in Reducing Atmospheres. Solid State Ionics 2011, 192, 163−167. (47) Yahiro, H.; Eguchi, K.; Arai, H. Electrical Properties and Reducibilities of Ceria Rare Earth Oxide Systems and Their Applications to Solid Oxide Fuel Cell. Solid State Ionics 1989, 36, 71−75. (48) Kresse, G.; Hafner, J. Ab−initio Molecular-Dynamics Simulation of the Liquid-Metal Amorphous-Semiconductor Transition in Germanium. Phys. Rev. B: Condens. Matter Mater. Phys. 1994, 49, 14251−14269. (49) Kresse, G.; Furthmüller, J. Efficient Iterative Schemes for Ab− initio Total-Energy Calculations using a Plane-Wave Basis Set. Phys. Rev. B: Condens. Matter Mater. Phys. 1996, 54, 11169−11186. (50) Kresse, G.; Furthmüller, J. Efficiency of Ab−initio Total Energy Calculations for Metals and Semiconductors using a Plane-Wave Basis Set. Comput. Mater. Sci. 1996, 6, 15−50. (51) Blöchl, P. E. Projector Augmented−Wave Method. Phys. Rev. B: Condens. Matter Mater. Phys. 1994, 50, 17953−17979. (52) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865−3868. (53) Scanlon, D. O.; Walsh, A.; Morgan, B. J.; Watson, G. W. An Ab−initio Study of Reduction of V2O5 through the Formation of Oxygen Vacancies and Li Intercalation. J. Phys. Chem. C 2008, 112, 9903−9911. (54) Scanlon, D. O.; Walsh, A.; Morgan, B. J.; Nolan, M.; Fearon, J.; Watson, G. W. Surface Sensitivity in Lithium−Doping of MgO: A Density Functional Theory Study with Correction for On−site Coulomb Interactions. J. Phys. Chem. C 2007, 111, 7971−7979. (55) Morgan, B. J.; Scanlon, D. O.; Watson, G. Small Polarons in Nb− and Ta−Doped Rutile and Anatase TiO2. J. Mater. Chem. 2009, 19, 5175−5178. (56) Nolan, M.; Watson, G. W. The Electronic Structure of Alkali Doped Alkaline Earth Metal Oxides: Li Doping of MgO Studied with DFT−GGA and GGA+U. Surf. Sci. 2005, 586, 25−37. (57) Dudarev, S. L.; Botton, G. A.; Savrasov, S. Y.; Humphreys, C. J.; Sutton, A. P. Electron−Energy−Loss Spectra and the Structural Stability of Nickel Oxide: An LSDA+U Study. Phys. Rev. B: Condens. Matter Mater. Phys. 1998, 57, 1505−1509. (58) Fabris, S.; Vicario, G.; Balducci, G.; de Gironcoli, S.; Baroni, S. Electronic and Atomistic Structures of Clean and Reduced Ceria Surfaces. J. Phys. Chem. B 2005, 109, 22860−22867. (59) Castleton, C. W. M.; Kullgren, J.; Hermansson, K. Tuning LDA +U for Electron Localization and Structure at Oxygen Vacancies in Ceria. J. Chem. Phys. 2007, 127, 244704. (60) Nolan, M.; Parker, S. C.; Watson, G. W. The Electornic Structure of Oxygen Vacancy Defects at the Low Index Surfaces of Ceria. Surf. Sci. 2005, 595, 223−232. (61) Nolan, M.; Parker, S. C.; Watson, G. W. CeO2 Catalysed Conversion of CO, NO2 and NO from First Principles Energetics. Phys. Chem. Chem. Phys. 2006, 8, 216−218. (62) Galea, N. M.; Scanlon, D. O.; Morgan, B. J.; Watson, G. W. A GGA + U Study of the Reduction of Ceria Surfaces and their Partial Reoxidation through NO2 Adsorption. (63) Keating, P. R. L.; Scanlon, D. O.; Watson, G. W. Intrinsic Ferromagnetism in CeO2: Dispelling The Myth of Vacancy Site Localization Mediated Superexchange. J. Phys.: Condens. Matter 2009, 21, 405502. (64) Scanlon, D. O.; Galea, N. M.; Morgan, B. J.; Watson, G. W. Reactivity on the (110) Surface of Ceria: A GGA + U Study of Surface J


Article

The Journal of Physical Chemistry C tane over Gallium−, Indium−, and Thallium−Promoted Sulfated Zirconia Catalysts. J. Catal. 1998, 180, 66−84. (88) Deguchi, H.; Yoshida, H.; Inagaki, T.; Horiuchi, M. EXAFS Study of Doped Ceria using Multiple Data Set Fit. Solid State Ionics 2005, 176, 1817−1825. (89) Pikalova, E. Y.; Murashkina, a. A.; Maragou, V. I.; Demin, a. K.; Strekalovsky, V. N.; Tsiakaras, P. E. CeO2 Based Materials Doped with Lanthanides for Applications in Intermediate Temperature Electrochemical Devices. Int. J. Hydrogen Energy 2011, 36, 6175−6183. (90) Zheng, Y.; Zhou, M.; Ge, L.; Li, S.; Chen, H.; Guo, L. Effect of Dy on the Properties of Sm−Doped Ceria Electrolyte for IT−SOFCs. J. Alloys Compd. 2011, 509, 1244−1248. (91) Pikalova, E. Y.; Bamburov, V. G.; Murashkina, A. A.; Neuimin, A. D.; Demin, A. K.; Plaksin, S. V. Solid Electrolyte Based on CeO2 for Medium−Temperature Electrochemical Devices. Russ. J. Electrochem. 2011, 47, 690−696. (92) Anjaneya, K.; Nayaka, G.; Manjanna, J.; Govindaraj, G.; Ganesha, K. Studies on Structural, Morphological and Electrical Properties of Ce0.8Ln0.2O2−δ (Ln = Y3+, Gd3+, Sm3+, Nd3+ and La3+) Solid Solutions prepared by Citrate Complexation Method. J. Alloys Compd. 2014, 585, 594−601.

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