Defect Clustering in Rare-Earth-Doped BaTiO3 and SrTiO3 and Its

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Defect Clustering in Rare-Earth-Doped BaTiO and SrTiO and Its Influence on Dopant Incorporation 3

Yohandys A. Zulueta, Teik-Cheng Lim, and James A. Dawson J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b08500 • Publication Date (Web): 04 Oct 2017 Downloaded from http://pubs.acs.org on October 5, 2017

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The Journal of Physical Chemistry

Defect Clustering in Rare-Earth-Doped BaTiO3 and SrTiO3 and its Influence on Dopant Incorporation Y. A. Zulueta1,2, T.C. Lim3 and J. A. Dawson*4 1

Departamento de Física, Facultad de Ciencias Naturales, Universidad de Oriente, CP- 90500, Santiago de Cuba, Cuba

2

Department of Chemistry, KU Leuven, B-3001 Leuven, Belgium

3

School of Science and Technology, Singapore University of Social Sciences, Singapore

4

Department of Chemistry, University of Bath, Bath BA2 7AX, United Kingdom

1 Environment ACS Paragon Plus


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*Corresponding author. E-mail: [email protected]

ABSTRACT Rare-earth (RE) doping of BaTiO3 and SrTiO3 has received tremendous research attention in recent decades. Although RE doping has been a particularly popular topic, little or no attention has been given to the contribution from different defect arrangements. In this study, we use a proven interatomic potential model to calculate the binding energies of different RE donor defect (Ba/Sr-site doping) configurations in BaTiO3 and SrTiO3. We consider two standard donor defect mechanisms, namely, charge compensation from cation vacancies. Consistently stronger negative binding energies are calculated for SrTiO3 compared to BaTiO3. We also show that SrTiO3 can accept a larger range of RE ion sizes at the divalent cation site than BaTiO3. This is highlighted by the simple trend of increasing binding energy with decreasing RE ion size found for the defect configurations with a Ti vacancy in SrTiO3. Conversely, defect clustering in BaTiO3 can cause significant strain on the lattice, resulting in positive binding energies. Our results show that one standard defect arrangement per incorporation mechanism cannot be applied to all dopants. We clearly show that the lowest energy defect configuration is dependent on both the dopant and host material. The consequences of these findings for the overall defect incorporation energetics in BaTiO3 and SrTiO3 are also presented.


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1. Introduction The ABO3 perovskite structure endows BaTiO3 and SrTiO3 with a wide selection of useful electrical and structural properties. These powerful properties have promoted the use of BaTiO3 and SrTiO3 ceramics in a range of technological applications, including multilayer ceramic capacitors1,2, random access memories3,4, positive temperature coefficient of resistance thermistors5,6, thermoelectrics7,8 and microwave devices9,10. These two materials are generally considered as cornerstones of the electroceramics industry. The incorporation of dopant ions, in a wide range of concentrations, into the ABO3 perovskite structure is essential for refining the properties and applications of these materials. In particular, trivalent rare-earth (RE) ions have received prodigious attention because of their ability to tailor the electrical properties of BaTiO311–13 and the thermoelectric properties of SrTiO37,8,14. However, RE elements are expensive and potential methods to reduce their usage or use them more efficiently are therefore highly desired. There are a variety of RE incorporation mechanisms that can occur in these materials, depending on the RE3+ ion size and the A-/B-site ratio. For large RE ions, like La, doping is known to occur at the A-sites of the perovskite structure with charge compensation in oxidizing conditions coming from Sr or Ti vacancies for SrTiO3 and BaTiO3, respectively, or from reduction of Ti4+ to Ti3+ in reducing conditions. This has been confirmed both experimentally12,15–17 and computationally18–25. Mid-sized ions, such as Eu, Gd and Dy, whose ionic radii lie in-between the radii of the A-site and Ti ions, are reported to dope at the A-sites, Ti-sites or both sites



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simultaneously (self-compensation mechanism) in BaTiO3 and SrTiO3, depending on the thermodynamic conditions7,18–21,23,26–30. In BaTiO3, smaller RE ions, like Yb and Lu, dope exclusively at the Ti-site with oxygen vacancy charge compensation11,21,31–33. For SrTiO3, there are very few reports on Yb and Lu doping. One experimental study suggests that Sr-site incorporation is possible for Yb-doping34. Computationally, self-compensation is shown to be energetically preferred23,29,35. Similar to the mid-sized RE ions, it is highly likely that the smaller RE ions can dope at both the Sr- and Ti-sites, as well via selfcompensation, in SrTiO3. When calculating the energetics of dopant incorporation or defect formation for a material, it is essential to consider any potential cohesion or repulsion between the dopants and any resulting charge compensating defects. This is true regardless of whether the defect energetics are calculated by potential-based methods or density functional theory (DFT). Various computational studies have shown the importance of these binding interactions in a variety of perovskite materials.21–25,36–41 The magnitudes of the binding energies in BaTiO3 and SrTiO3 have been shown to be large and have a drastic effect on the overall lowest energy incorporation mechanism predicted21,23. This means that it is simply not enough to only consider isolated dopants in such calculations. However, this is often the approach used in the literature for most materials. Furthermore, when binding interactions are calculated, one low energy defect configuration is usually applied to all dopant ions, with little or no consideration of the binding between other potential configurations. This is unlikely to be an issue for simple defect pairs, such as the binding between one RE ion at an


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A-site and one RE at a neighboring Ti-site (self-compensation), but for complex defect clusters, the binding energy will vary significantly for different configurations. In this study, we investigate the magnitude and variation of defect binding energies in numerous defect arrangements for two fundamental RE dopant incorporation mechanisms, namely, the donor-doping of RE ions into cubic BaTiO3 and SrTiO3 with charge compensation from either Ti or Ba/Sr vacancies:

• //// 2 RE2O3 + 4 BaBa / SrSr + TiTi → 4 REBa / Sr + VTi + 3BaO / SrO + BaTiO3 / SrTiO3

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Scheme 1: Incorporation of RE3+ at Ba/Sr2+ with Ti4+ vacancy compensation.

• // RE2O3 + 3BaBa / SrSr → 2 REBa / Sr + VBa / Sr + 3BaO / SrO

Scheme 2: Incorporation of RE3+ at Ba/Sr2+ with Ba/Sr2+ vacancy compensation.

In scheme 1, four RE3+ ions dope at the A-sites, which creates a net charge of 4+ that is compensated for by one Ti vacancy. In scheme 2, two RE3+ ions dope at the A-sites and the total 2+ charge is compensated for by a single A-site vacancy. As discussed, schemes 1 and 2 are the dominant dopant incorporation mechanisms for large RE ions in BaTiO3 and SrTiO3, respectively. While we have only considered the two donor doping mechanisms in this study because of the wide range of complex defect clusters available for these mechanisms, the methods used and results found are certainly applicable to acceptor doping and self-compensation mechanisms.

2. Methodology The interatomic potential-based simulations performed in this work have been extensively used to calculate the defect properties and energetics of perovskite 5 Environment ACS Paragon Plus

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materials and are presented in detail elsewhere42,43. In these calculations, the total energy of a system is made up of contributions from the long-range and short-range interactions with respect to the atomic positions in the lattice. The long-range forces are accounted for by Coulombic interactions and the short-range forces are represented by interatomic potentials that include electron repulsion and van der Waals interactions. In this work, we use the well-established potential model of Freeman et al.21 and Dawson et al.23, which have proven to be effective in modelling a wide variety of defect phenomena in perovskites14,29,30,44. The potential model was originally fitted for BaTiO321 using DFT calculations and was later extended to SrTiO3 and CaTiO323. A full description of the potential fitting procedure is available in Ref. 21. This model replicates both the experimental cell parameters and lattice energies of BaTiO3, SrTiO3 and their respective end-member oxides with precision. It is crucial that the perfect bulk structures are accurately reproduced before attempting to calculate the defect properties. A cutoff of 12 Å was used for all the interatomic potentials. The RE potentials were taken from Ref. 25. The ionic polarization in our simulations is accounted for by the shell model of Dick and Overhauser45. This model divides atoms into negatively charged massless shells and positively charged cores. The electrostatic interactions between the cores and shells are replaced by a harmonic term that is determined by the spring constant, k. The defect simulations were completed using the Mott-Littleton method46, whereby the crystal lattice is partitioned into two regions, an inner region and an outer region. Interactions are calculated explicitly in the inner region and are approximated using a dielectric continuum method in the outer region. All calculations were carried out using the general utility lattice program (GULP)47.


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The binding energy (Ebind) between oppositely charged defects is defined as the difference between the total energy of the isolated defects and the energy when the same defects are simulated together in a cluster: Ebind = E(X) + E(Y) – E(XY)

(3)

where a negative value implies a stable cluster and binding behavior.

We note that DFT could also be used to calculate the binding energies of defect clusters in these materials. However, given the significantly high number of calculations involved in this work, as a result of the large number of RE ions and defect configurations considered, the computational expense would be a limiting factor. Therefore, a computationally more efficient approach is necessary.

3. Results and discussion 3.1. Perovskite structure and defect configurations In the conventional ABX3 perovskite structure (see Figure 1(a)), the A and B sites are occupied by cations and the X site is an anion. In BaTiO3 and SrTiO3, the B-site Ti4+ ion is octahedrally coordinated to six O2- ions, while the A-site Ba2+ or Sr2+ ion is cubo-octahedrally coordinated to twelve O2- ions. The calculated lattice parameters for cubic BaTiO3 and SrTiO3 are 4.01 and 3.96 Å, respectively, in excellent agreement with X-ray diffraction values of 4.0048 and 3.91 Å49, respectively. We consider six defect configurations for scheme 1 and five for scheme 2, as illustrated in Figures 2 and 3, respectively. These configurations account for all possible defect arrangements of schemes 1 and 2 on the basis of a single perovskite unit cell. Only a single perovskite cell is considered since the interactions between oppositely charged neighboring defects will clearly be stronger than those between



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defects with larger interatomic separations. This is in addition to the fact that the number of defect arrangements grows exponentially with increasing unit cells, thereby making the number of calculations impractical. A more detailed description of the six scheme 1 arrangements is given by Gröting et al.50, who used them to probe the chemical order and local structure in Na0.5Bi0.5TiO3. For scheme 2, the defects are always in a particular plane to produce layered structures. For configurations 1 and 2, the defects are ordered in the (001) plane. In configurations 3 and 4, there is defect ordering in the (110) plane, while in configuration 5, (111) defect ordering is present.

Fig. 1. (a) Cubic perovskite structure for BaTiO3 and SrTiO3. Blue spheres represent Ba/Sr ions, the TiO6 octahedra are given in grey and red spheres are oxygen ions.


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1

2

3

aaaaaaaaa 4

5

6

Fig. 2. (a) Binding energy defect configurations considered for scheme 1. Purple spheres represent RE dopants and the Ti vacancy is indicated by the white sphere at the center of the unit cells.



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1

2

4

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3

5

Fig. 3. Binding energy defect configurations considered for scheme 2. The Ba/Sr vacancy is indicated by the white sphere at the corner of the unit cells.

3.2. Binding energies

The calculated binding energies for scheme 1 in BaTiO3 and SrTiO3 are presented using heat maps in Figure 4. The first result to note is that the majority of binding energies are strongly negative. In the case of SrTiO3, all values are negative and in excess of -2 eV, thereby highlighting the significantly favorable defect interactions in these clusters. For BaTiO3, all of the calculated binding energies are weaker than the respective values for SrTiO3. This can be explained by simple Coulombic arguments, since the SrTiO3 lattice parameter of 3.96 Å is smaller than that for BaTiO3 (4.01 Å), resulting in a stronger electrostatic attraction between the positively charged RE ions


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and the negatively charged vacancy. Similar findings have been reported previously21,23, with even more substantial energies reported for CaTiO3. (a)

(b)

Fig. 4. Binding energies (eV) for each scheme 1 defect configuration in (a) BaTiO3 and SrTiO3.

Figure 4(b) shows a strong trend of increasing binding energy with decreasing RE ion size for all configurations in SrTiO3, as discussed previously23, with relatively little variation between the different defect configurations. However, this is not the case for BaTiO3. Although configurations 1 and 3 show a clear trend with ionic radii, the other configurations do not. For example, while the energies for La in the six configurations are similar, the variation for smaller RE ions is much greater, with many positive binding energies produced. This can perhaps be expected given that such mid- and small-sized RE ions cannot dope solely at the Ba-site in BaTiO3. These results suggest that SrTiO3 is capable of accommodating a greater range of RE ion sizes at the Sr site than BaTiO3 can for the Ba site. Our findings also indicate that the extent to which different defect configurations influence the binding energy, and



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therefore the overall defect incorporation energetics, is dependent on both the host material and the dopant ion. Previous calculations have reported that configuration 1 is the lowest in energy for scheme 1 in both BaTiO321 and SrTiO323 as a result of the large dipole formed from the four RE ions being in the same plane. This is in agreement with our results for all dopants in BaTiO3 with the exception of La and Pr, where configurations 2 and 5 are the lowest in energy, respectively. Conversely, for SrTiO3, while configuration 1 is the most favorable for La doping, other configurations are preferred for smaller RE ions, particularly configuration 5. This highlights the importance of considering different binding configurations for different dopants as they can have a significant effect on the overall dopant formation energies. The binding energies of scheme 2 in BaTiO3 and SrTiO3 are displayed in Figure 5. Unlike scheme 1, every calculated binding energy is negative, suggesting that the interaction between two RE dopants and Ba or Sr vacancy is favorable regardless of the dopant, host material or configuration. The binding is SrTiO3 is again stronger than in BaTiO3 as a result of the reduced distance between the oppositely charged defects. As expected, the interactions between these defect clusters are generally weaker given the lower number of defects and reduced charges involved. Similar general trends have been reported previously21,23.


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(a)

(b)

Fig. 5. Binding energies (eV) for each scheme 2 defect configuration in (a) BaTiO3 and (b) SrTiO3.

By comparing Figures 4 and 5, it is clear that there is no trend between RE ion size and binding energy for the scheme 2 defect clusters. This is particularly true for BaTiO3, where it can be seen from Figure 5(a) that the variation in energy with RE ion is small, with only one color dominating each defect configuration. The large separation between the A sites, which results in the lack of a strong network to link the sites is likely to be the reason for the absence of this trend21. Although there is little binding energy variation between different RE ions, there is significant variation between the different configurations, especially for smaller RE ions, such as Yb and Lu. For example, there is a difference of ~0.6 eV between the most (configuration 1) and least (configuration 2) favorable configurations in BaTiO3. A similar difference also exists between configurations 2 and 4 in SrTiO3. It is perhaps surprising that such variation can exist in a relatively simple defect cluster made up of only three defects ordered in five possible ways. These findings again illustrate the importance of testing different defect clusters.



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3.3. Influence on dopant incorporation

Binding energies are often combined with defect solution or formation energies to produce a more accurate prediction of the total energy required for dopant incorporation. To illustrate the variation in binding energies reported here and how they influence the overall energetics of dopant incorporation, we combine our results with previously calculated solution energies for La-, Nd-, Eu-, Gd-, Ho-, Yb- and Ludoping in BaTiO321 and SrTiO323. The solution energy represents the energy required for a particular dopant to substitute into a host lattice by taking into account any charge compensating defects that may be required. More details are on how these solution energies are calculated are available in Refs. 21 and 23. The solution and total energies for schemes 1 and 2 in BaTiO3 and SrTiO3 are plotted as a function of RE ionic radius in Figure 6. The minimum and maximum total energies represent the solution energies combined with the strongest and weakest binding energies, respectively, obtained for each RE ion. The binding energy applied to the solution energy is divided by the number of dopants involved in the cluster, i.e., the binding energy per dopant.


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(a)

(b)

Fig. 6. Solution and total energies plotted as a function of RE ionic radius for schemes 1 and 2 in (a) BaTiO3 and (b) SrTiO3. The solution energies for BaTiO3 and SrTiO3 are taken from Refs. 21 and 23, respectively. The minimum and maximum total energies represent the solution energies combined with the strongest and weakest binding energies, respectively, obtained for each RE ion.



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The most important finding from Figure 6 is that the lowest energy scheme can vary depending on the choice of binding energy/defect cluster used. It is well known that large RE ions, like La, dope at the Ba site of BaTiO3 with Ti vacancy charge compensation (scheme 1)12,21,51,52. This is confirmed by our calculations regardless of the defect complex considered (Figure 6(a)). However, for other RE ions, the maximum scheme 1 and minimum scheme 2 energies are very similar, meaning that is not now clear what scheme will dominate. This problem is even clearer for SrTiO3 (Figure 6(b)), where it is known that donor doping of large RE ions occurs at the Sr sites with Sr vacancy charge compensation (scheme 2)16,17,23,53. Our calculations also predict this, but only when the strongest binding energies are added to the solution energy. When this is not the case, La is predicted to incorporate via scheme 1. Essentially, our results show that not determining the lowest energy defect cluster for each dopant ion can lead to incorrect predictions of its incorporation scheme. It is important to bear in mind that we have only considered two donor doping schemes in this work. In reality, the prediction of a dopant incorporation scheme in these materials is more complex as it also involves acceptor doping and self-compensation mechanisms. This means that the potential for incorrectly predicting the doping site as well as the compensating defects becomes higher. Many works have shown the importance of binding energies in the calculation of defect formation energies. In this study, we have shown the importance of calculating the lowest possible binding energies from numerous defect cluster configurations. These findings have been presented using interatomic potential-based calculations of perovskites, but they could potentially apply to any defect cluster in any material, regardless of the calculation methods.


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4. Conclusions Using interatomic potential-based defect calculations, we have explored defect binding in RE-donor-doped BaTiO3 and SrTiO3, and analyzed its overall impact on the energetics of dopant incorporation in these materials. The key findings of this study are as follows: -

Binding between the RE dopants and their charge compensating defects is shown to be generally favorable, particularly for SrTiO3.

-

Our results suggest that SrTiO3 can accept a larger range of RE ion sizes at its A site than BaTiO3.

-

Defect clustering in BaTiO3 can cause significant strain on the lattice, resulting in positive binding energies.

-

One standard defect arrangement per incorporation mechanism cannot be applied to all dopants as the lowest energy defect configuration is dependent on both the dopant and host material.

-

Not considering defect clustering or considering the wrong defect cluster can result in incorrect predictions of the dominant dopant incorporation scheme.

The atomic-scale insights presented in this study have fully illustrated the importance of defect clustering in oxide perovskite materials and how the binding behavior of these clusters can vary dramatically. In addition, the findings presented here are certainly not limited to only these two materials, or indeed only potential-based calculations. We hope that this work will encourage more in-depth studies of the interactions between clustered defects in a wide variety of materials.

ACKNOWLEDGEMENTS



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The authors thank the Japan Society for the Promotion of Science (JSPS) for funding through a JSPS fellowship (Grant No. 2503370). JAD is grateful to Dr. Pedro “Pete” Canepa for insightful discussions regarding data presentation.

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Defect Clustering in Rare-Earth-Doped BaTiO3 and SrTiO3 and Its

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