Effect of Cation Ordering on Oxygen Vacancy Diffusion Pathways in

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Effect of cation ordering on oxygen vacancy diffusion pathways in double perovskites Blas Pedro Uberuaga, and Ghanshyam Pilania Chem. Mater., Just Accepted Manuscript • DOI: 10.1021/acs.chemmater.5b01474 • Publication Date (Web): 29 Jun 2015 Downloaded from http://pubs.acs.org on July 4, 2015

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Chemistry of Materials

Effect of cation ordering on oxygen vacancy diffusion pathways in double perovskites Blas Pedro Uberuaga∗ and Ghanshyam Pilania Materials Science and Technology Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States E-mail: [email protected]

Abstract Perovskite structured oxides (ABO3 ) are attractive for a number of technological applications, including as superionics because of the high oxygen conductivities they exhibit. Double perovskites (AA’BB’O6 ) provide even more flexibility for tailoring properties. Using accelerated molecular dynamics, we examine the role of cation ordering on oxygen vacancy mobility in one model double perovskite SrLaTiAlO6 . We find that the mobility of the vacancy is very sensitive to the cation ordering, with a migration energy that varies from 0.6 eV to 2.7 eV. In the extreme cases, the mobility is both higher and lower than either of the two end member single perovskites. Further, the nature of oxygen vacancy diffusion, whether one-dimensional, two-dimensional, or three-dimensional, also varies with cation ordering. We correlate the dependence of oxygen mobility on cation structure to the distribution of Ti4+ cations, which provide unfavorable environments for the positively charged oxygen vacancy. Our results demonstrate the potential of using tailored double perovskite structures to precisely control the behavior of oxygen vacancies in these materials.

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Introduction Complex oxides, defined here as oxides with more than one cation sublattice, are important for a number of technological applications. In many of these applications, the fast transport of oxygen is a critical enabling feature. Such applications of these superionic 1 compounds include solid oxide fuel cells, 2,3 supercapacitors, 4,5 and chemical sensors. 6 In particular, perovskites, with general formula ABO3 , have been studied extensively for potential use in these applications. 1,2,7 Through aliovalent doping, the concentrations of oxygen vacancies, the carriers for ionic conductivity in these materials, can be dramatically increased. Perovskites are particularly amenable to doping as they can accommodate a wide range of chemistries, as evident from the large number of chemically distinct perovskites that have been synthesized. 8 One important consequence of this chemical flexibility is that, by partial substitution on either the A or B cation sublattices, so-called double perovskites can be formed, which have received great attention in their own right because of their diverse set of properties and potential applications. 9–12 Depending on the nature of the cations, different types of cation ordering can consequently arise in these compounds. 13–15 For half substitution of A’ on the A sublattice and B’ on the B sublattice, there are three common ways in which each of the two sublattice can order, leading to a total of nine different ordered arrangements of the four cation species. Specifically, each of the cation sublattices can order in a columnar (1D), layered (2D) or rocksalt (3D) arrangement. That the cations can order into very specific arrangements leads to interesting possibilities regarding tailored functionality. 16–21 Inspired by the fact that studies of disordered compounds have shown significant dependencies of mass transport on cation ordering 22–24 and that oxygen transport in perovskites is of great practical interest, here we consider the influence that cation order in double perovskites has on oxygen vacancy mobility, using the compound SrLaTiAlO6 as a model for double perovskites more generally. This compound was chosen as its constiutents – SrTiO3 (STO) and LaAlO3 (LAO)– exhibit significantly different mobilities for the oxygen vacancy. 25 Further, because of the range of valences rep2


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resented by the cations in these two single perovskites, we expect significant consequences on the mobility of oxygen vacancies. Finally, solid solutions of this compound have been experimentally realized with varying amounts of STO and LAO, 26–29 though none of these experiments has produced an ordered double perovskite structure. However, given the stability of abrupt STO/LAO interfaces 30 and the results presented below, we expect that such an ordered phase does indeed exist and with further treatment can be synthesized. We find that the mobility of oxygen vacancies is very sensitive to the cation ordering in the double perovskite. In particular, oxygen vacancies avoid, if possible, sites coordinated with Ti4+ ions. This is not always possible depending on the cation ordering. Thus, there is a wide range in the predicted migration energies of oxygen vacancies depending on the cation ordering, from nearly 3 eV in the slowest case to 0.6 eV in the fastest.

Figure 1: Columnar, layered and rocksalt orderings on the B-site cation sublattice in the double perovskite structure. Only B-site cation octahedra are shown for clarity. Similar orderings occur on the A sublattice. The directions of the cartesian axes assumed in this work are also indicated.

Methodology The migration properties of oxygen vacancies were examined in a model double perovskite – STO+LAO – to understand how the cation ordering within the structure influences the mobility of the vacancy. Nine different ordered structures were considered in which the ordering on the A-site and B-site cation sublattices were varied. In particular, on each sublattice, the corresponding cations were ordered in either a columnar (C), layered (L), or rocksalt (R) arrangement (cf. Fig. 1). This leads to a natural notation to refer to each 3



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ordered compound: AC/BL, for example, refers to that compound with a columnar ordering of the A cations and a layered ordering of the B cations. The interactions between the ions were described using Buckingham potentials, which has the form Vij = Aij exp(−rij /ρij ) − Cij /rij6 where Vij is the energy between ions i and j, rij is the distance between the two ions, and Aij , ρij and Cij are parameters typically fit to experimental observables. The first term is meant to capture the repulsive exchange energy while the second term accounts for the dispersion energy. 31 These potentials have been shown to produce physically relevant trends for the properties of perovskites, including the mobility of oxygen vacancies. The parameters were taken from Grimes et al. 32–35 and are summarized in Table 1 for reference. The Buckingham interaction is supplemented with long-range Coulomb interactions, which were summed using the Ewald method. Table 1: Potential parameters used in this study. The parameters originally appeared in Refs. 32–34 and Ref. 35 Full formal charges are used: +2 for Sr, +4 for Ti, +3 for La and Al, -2 for O. Interaction

A (eV)

ρ (˚ A)

C (eV·˚ A6 )

Sr-O

682.172

0.39450

0

Ti-O

2179.122

0.30384

8.986

La-O

2088.79

0.3460

23.25

Al-O

1725.20

0.28971

0.0

O-O

9547.96

0.21916

32.0

We do not expect these potentials to provide quantative accuracy as compared to experiment or higher quality calculations such as density functional theory. However, they do reproduce physical trends. In the case of the single perovskites that comprise the double perovskite studied here, these potentials predict oxygen vacancy migration energies of 1.2 4


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eV and 0.7 eV in STO and LAO, respectively. 25 The migration energy of oxygen vacancies in STO has been recently estimated by various experimental techniques, with values ranging from 0.6 eV (measured by isotope diffusion 36 ) to 0.84 eV (measured by dielectric relaxation 37 ) to 0.98 eV as measured by anelasic relaxation. 38 In LAO, on the other hand, migration energies range from 0.74 eV (measured by the DC four point probe method 39 to 0.82 eV (using AC impedence techniques 40 ). While several of these authors point out challenges in measuring these values – including vacancy clustering, association between vacancies and dopants, and the need to know the defect chemistry and boundary conditions of the experiment – these results suggest that migration of oxygen vacancies in LAO might be just slightly faster than in STO, in accordance with the predictions from the potentials. That said, we are not after quantitative accuracy, but rather the physical trends of how oxygen vacancy migration might be influenced by the cation ordering in double perovskites. For reference, using this set of parameters, the lattice constants of the perovskite with each ordering were minimized. The relative volume and the relative formation energy per formula unit (f.u.) for each ordered structure were determined using simulation cells containing 960 atoms, or 96 formula units. These are presented in Figs. 2a and 2b, respectively. There is no obvious relationship between the cation ordering and the volume of the compound. The ordering with the smallest volume is AR/BR while that with the largest volume is AC/BL. However, unlike relative volume, the relative formation energy shows a clear trend with respect to the orderings at A- and B-site sublattices. For a given B-site order, layered ordering at the A-site is always favored, followed by columnar and rocksalt orderings. For the B-site sublattice the most favored ordering is again the layered configuration, followed by rocksalt and columnar orderings (irrespective of the A-site order). Hence, the ordering with the lowest energy is AL/BL while that with the highest energy is AR/BC. To determine the pathway for the oxygen vacancy through each of the nine structures, we used temperature accelerated dynamics (TAD), 41 an accelerated molecular dynamics method 42 that allows for the long-time simulation of a system with full fidelity of the under-

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lying potential but for times much longer than possible with conventional molecular dynamics (MD). The basic idea of TAD is to use an MD trajectory at a temperature Thigh much higher than the temperature of interest to explore the current energy basin of the 3N dimensional system. As the trajectory leaves the basin, it is interrupted and the corresponding event is characterized using the nudged elastic band (NEB) method to obtain the saddle energy of the process. 43,44 This allows for the extrapolation of the time of the event from the high temperature to the low temperature Tlow of interest, which is exact if harmonic transition state theory (HTST) holds for the system. The trajectory is then placed back in the original basin. The trajectory is continued until a stopping criterion, based on an assumed minimum rate prefactor νmin and uncertainty factor δ, is met, at which point the event with the shortest time at the low temperature is accepted, the trajectory placed in the corresponding basin, and the process repeated for the new state. In this way, exact (within HTST) state-to-state dynamics can be generated with no assumptions of possible events. See Ref. 41 for details. In these simulations, we typically used Thigh = 1000 K and Tlow = 500 K, though in some cases the barriers for migration were quite large and necessistated raising these temperatures to Thigh = 2000 − 4000 K and Tlow = 1000 − 2000 K. In all simulations we used νmin = 1012 /s and δ = 0.05. The computational boost over conventional MD typically ranged from a rather modest 1.5 times to as much as 940 times. These longer time scales also come with the identification and characterization of every event that occured during the evolution of the trajectory, providing a very rich database of information regarding the properties of the material in question. We note that these are very high temperatures for these compounds, and the HTST assumption could break down at such high temperatures, with anharmonicities creeping in. However, as we will only report static values of migration energies as determined from the NEB calculations, which are not influenced by any anharmonicities, and not any properties that are a direct function of the dynamical nature of the trajectory itself, the high temperatures will not impact any values we report here.

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Results

Figure 2: (a) Relative relaxed volumes, (b) relative energies and (c) relative oxygen vacancy formation energies of different orderings in SrTiLaAlO6 double perovskite. The relative volumes and energies are reported as per formula unit (f.u.). The reference structure in each panel is indicated by an arrow.

We begin by consdering the relative formation energy of an oxygen vacancy within each of the nine ordered structures. These are provided in Fig. 2c. The oxygen vacancy is easiest to form in the AL/BC compound while it is hardest to form in the AR/BR compound. There is a general trend that the stability of the vacancy is much more sensitive to the ordering of the B cations than the A cations. By changing the A ordering, the vacancy formation energy changes by at most 0.5 eV, but changes by more than 2.3 eV when the B cation ordering is modified. These relative formation energies would provide some insight into the relative thermal concentrations of vacancies within each compound (assuming a common 7



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reference state), but would not be relevant if the vacancy population is controlled via, for example, doping. However, if the spatial ordering of the A and B sublattices is not uniform, these energetics would dictate in which regions of the double perovskite the vacancies would concentrate. The pathways for oxygen vacancy migration, as well as the associated migration energies, have been extracted from the TAD simulations and these are summarized in Fig. 3 and Table 2. As is clear from Table 2, the overall migration energy of the oxygen vacancy is very sensitive to the ordering of the cations. Oxygen vacancy migration is fastest in the AR/BL compound and slowest in the AL/BC compound. The difference in the migration energies within these two orderings is over 2 eV. Thus, we find that in some orderings, oxygen vacancies can migrate very quickly – a 0.6 eV barrier corresponds to a hopping timescale of about 1 ms at 300 K assuming a prefactor of 1013 /s – while in others, the vacancy is essentially immobile (at 300 K, the time scale for vacancy hops in the AL/BC compound is 1032 seconds). In contrast to the vacancy formation energies, there is not as much sensitivity on the migration energies with B cation ordering. Migration is clearly slowest in those compounds with BC ordering, irrespective of the ordering of the A cations. However, the values of the migration energy for BL and BR ordering are similar. Further, for BL ordering, there is a strong dependence of the migration energy on the A cation ordering. Overall, however, there are no clear trends between ordering and migration energies, as there was for the formation energies. Perhaps more surprising, the dimensional nature of the migration is also sensitive to the ordering. In the majority of cation orderings, the lowest energy oxygen migration pathway is two-dimensional in nature, confined either to an x − y or an x − z plane (cf. Fig. 1 for the definition of axes). However, in a few cases, one-dimensional migration dominates and in one case three-dimensional diffusion is preferred. To illuminate these differences, Fig. 3 presents the pathway for the oxygen vacancy to migrate through each of the ordered compounds.

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Table 2: Migration energies and coordination of lowest energy oxygen vacancy site as a function of cation ordering. Migration energies for oxygen vacancy diffusion (eV) Cation Ordering (B↓,A→)

Sr/La columnar

Sr/La layered

Sr/La rocksalt

Ti/Al columnar

2D (xz): 2.1

2D (xy): 2.7

1D (z): 2.2 3D: 2.5

Ti/Al layered

1D (y): 1.3

2D (xy): 0.8

2D (xy): 0.6

Ti/Al rocksalt

1D (y): 1.0

2D (xy): 1.3

3D: 1.3

Coordination environment of lowest energy oxygen vacancy site Cation Ordering (B↓,A→)

Sr/La columnar

Sr/La layered

Sr/La rocksalt

Ti/Al columnar

2 Sr, 2 La, 2 Al

4 La, 2 Al

2 Sr, 2 La, 2 Al

Ti/Al layered

2 Sr, 2 La, 2 Al

2 Sr, 2 La, 2 Al

2 Sr, 2 La, 2 Al

Ti/Al rocksalt

2 Sr, 2 La, 1 Ti, 1 Al 2 Sr, 2 La, 1 Ti, 1 Al 2 Sr, 2 La, 1 Ti, 1 Al

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Figure 3: Pathways for oxygen vacancy migration as a function of cation ordering in various double perovskite structures. The pathways represent net center-of-mass translation of the oxygen vacancy to an equivalent but translated position within the lattice. The dashed line connects sites that describe a complete center-of-mass pathway in the crystal. Green spheres/octahedra represent Sr/Ti, respectively, while black spheres/grey octahedra represent La/Al. Oxygen, not shown for clarity, reside at the vertices of each octahedra.

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In each panel of Fig. 3, the migration path of the oxygen vacancy is highlighted by the blue spheres connected by the dashed lines. Thus, the terminal sites of each path represent the vacancy at the lowest energy site within the compound and the pathway is one which takes it from one lowest energy position to another equivalent but translated position. Thus, in panels in which only two blue spheres are highlighted, there is only one type of site that is necessary for net migration through the crystal. However, in the other panels, there is more than one type of site and migration occurs through higher energy metastable sites. We first comment on the environment of the lowest energy position of the oxygen vacancy within each cation ordering, which is summarized in Table 2. For the most part, the oxygen vacancy minimizes coordination with Ti. Except in those orderings containing rocksalt ordering at the B-site, within which there are no oxygen environments that are not coordinated with Ti, the oxygen vacancy in its most preferred location does not coordinate with Ti. This makes physical sense as the positively charged vacancy minimizes interaction with the Ti cation which has the greatest positive charge of all of the cations in the system. However, simple arguments based on charge do not explain all of the results. For example, in the AL/BC structure, the vacancy resides in a plane of La ions, which have a higher charge (+3) than the corresponding plane of Sr ions (+2). If charge were the only factor, one might imagine that the vacancy would prefer the Sr environment. This counterintuitive behavior is discussed below. Preference for particular coordinations also explains the trends in vacancy formation energy presented in Fig. 2c. In the BR structures, the vacancy is always coordinated to Ti and this explains why it is higher in energy in those structures. However, it does not explain the difference in formation energies for the BC versus BL structures, as those have similar coordination but differ in energy by about 1 eV. The desire of the oxygen vacancy to minimize its interaction with Ti also qualitatively explains the trends in migration energies observed in Table 2. Migration is most difficult in the BC compounds and this is because, for migration, the oxygen vacancy has to pass from a site that is uncoordinated with Ti through a metastable site (for AC and AR) or a

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saddle (AL) that is coordinated with Ti. The migration energies in these compounds are over 2 eV, which correlates with the relative formation energy of the oxygen vacancy in those compounds in which the vacancy is forced to have Ti coordination. That is, the 2 eV migration energy is a direct measure of the roughly 2 eV cost of putting the vacancy in a site that is coordinated with Ti. On the other hand, in the BL and BR compounds, the coordination of the vacancy is constant. In the BL compounds, it is always coordinated with Al, never with Ti, as the layered arrangement of the B cations allows for a pathway that keeps it within the Al plane. In the BR compounds, the vacancy always has mixed Al/Ti coordination and thus there is no great penalty for moving into a Ti-coordinated site. That is, for the BL compounds, there is a higher energy Ti-coordinated site, but the vacancy can avoid it (for 1D and 2D migration) while for the BR compounds, the sites are all mixed coordination and their energy differences are not so great. In fact, for the AR/BR ordering, the sites are all equivalent and diffusion in this structure is three dimensional. Said another way, in the BL compounds, the oxygen vacancy can migrate between low energy sites via a relatively small barrier without ever encountering at Ti-coordinated site. In the BR compounds, all sites are coordinated by Ti and thus all have relatively high energy, so the vacancy can hop between them with a relatively small barrier. In contrast, in the BC compounds, however, the vacancy hops between low (no Ti coordination) and high (Ti coordinated) sites and that change in site energy drives the overall higher migration energy in this set of compounds. Finally, the ordering of the cations provides insight into the nature of the pathway for oxygen vacancy migration. For example, for the AC/BC structure, the vacancy avoids sites with full Ti coordination – the sites where the vertices of two Ti (green) octahedra touch. Further, once in the metastable state where the vertices of the Ti (green) and Al (grey) octahedra meet, the vacancy perfers to maximize interaction with La (maintain “bonds” with La) over Sr and so it can only move along one edge of the Ti octahedra. These limits result in 2D diffusion in the x − z plane. Similar constraints are observed in the other

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orderings. Further, in some cases a two-step processes is necessary for net migration while in others a single event describes diffusion. These tend to be cases in which the desire to minimize coordination with Ti is possible for all sites along the pathways, primarily for those compounds with BL ordering. For AC/BR and AL/BR orderings, there is a very fast process that keeps the vacancy coordinated to a central Ti ion and a larger barrier that moves it along the edge of an Al octahedron to a translated but equivalent state. This second barrier is key for net migration, but the first barrier provides access to other pathways that enhance the mobility of vacancy, similar to the effects described in Ref. 45

Discussion Figure 4 compares the migration energies found for the single perovskites 25 and those found in the various orderings of the double perovskite. Clearly, there is no monotonic relationship between the migration energies and the composition of the compound. In fact, based on the results above, the mobility is directly tied to the connectivity of Ti octahedra. If there are regions in which the Al octahedra are arranged in a way that the edges never intersect vertices of Ti octahedra, there will be fast diffusion pathways. Further, if all vertices are mixed, shared between Al and Ti octahedra, migration will be still be reasonably fast. However, if the pathways take the oxygen vacancy from vertices that belong only to Al octahedra through vertices that are mixed, as is true for the BC compounds, diffusion will be slow. This offers the opportunity for fine control of the transport in these materials. Given that, with today’s thin film growth techniques, 46 layer-by-layer growth of complex perovskite structures is possible, one can imagine constructing morphologies with regions of BL ordering for fast ion transport separated by regions of BC ordering that act as diffusion barriers. Further, the diffusion of oxygen in solid solutions of (1 − x)STO(x)LAO will likely be non-monotonic with x, primarily due to varying concentrations of and thus trapping by Ti.

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It is particularly interesting to note that in the fastest case (AR/BL) in which the migration barrier of the oxygen vacancy is 0.6 eV, the migration of oxygen vacancies is faster than it is in either of the two single perovskites (1.2 and 0.7 eV in STO and LAO with these potentials, respectively). While this is only a modest decrease compared to LAO, it shows that, from a fast ion conduction perspective, the mobility of oxygen vacancies can be higher than in either constituent compound. It is possible that, with different choices of A and B cations, this gain can be increased even further via changes in either the chemistry or strain of the compound. Further, the slowest case, AL/BC, exhibits vacancy mobilities much slower than either end member, highlighting the sensitivity and the possibilities for precise control of oxygen vacancy migration in these structures.

Figure 4: Comparison of migration pathways in STO, STO+LAO, and LAO. Different colors (shapes) of the markers are used to distinguish between different A-site (B-site) cation orderings of STO+LAO. Three different ordered compounds exhibiting a migration energy of 1.3 eV, have been shown with an additional offset of 0.05 on the composition axis for clarity. The two different vacancy diffusion modes (i.e., 1D(z) and 3D) exhibited by the AR/BC ordered structure are indicated. The experiments described in the Introduction typically report admixtures of (1−x)STO(x)LAO as solid solutions, with no long-range ordering of the cations. Our results suggest that there should indeed be thermodynamic driving forces for ordering, at least for x=0.5, favoring 14


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layered orderings in both the A and B cation sublattices. Our predictions are further supported by the fact that an abrupt STO(001)[001]/LAO(001)[001] heterointerface is indeed stable. 30 That the ordered bulk structures are not observed experimentally suggests that the experiments are performed at high enough temperatures that entropy dominates, leading to disorder. If these compounds were annealed for sufficiently long times at lower temperatures, we anticipate ordered structures to form. However, as pointed out by previous researchers, 47–49 many potential double perovskite combinations may not thermodynamically mix to form a true double perovskite, and might rather decompose into other phases. As mentioned before, in the AL/BC structure, for example, the vacancy prefers to have La rather than Sr coordination. The energy difference of placing the vacancy at the Lacoordinated site is 0.3 eV lower than in the Sr-coordinated site. This is counterintuitive as Sr has a smaller charge than La, so the the positively charged oxygen vacancy, if electrostatics were the only consideration, should prefer the Sr environment. Indeed, the electrostatic potential, calculated using the GULP code, 50,51 is (slightly) higher at the La-coordinated oxygen site than the Sr-coordinated site by 0.02 V, suggesting it should prefer the Sr environment. However, it does not. Further, the relaxation volume of the oxygen vacancy is ˚3 ), so it should prefer oxygen sites with greater volumes associated with positive (∼ 33 A them. The Voronoi volume (calculated using the voro++ code 52 ) of the Sr-coordinated site, ˚3 , respectively), so this also however, is larger than the La-coordinated site (12.6 vs 11.8 A does not explain the preference for La coordination. In fact, the only feature we have been able to identify that might explain the preference for La is the fact that the short-range chemical interaction of the La-O potential is more repulsive than the Sr-O potential, suggesting that there might be some benefit for removing oxygen that is La-coordinated. However, this also demonstrates that there are many subtle and competing effects that dictate the final stability of the vacancy. Table 2 further reveals that the nature of the migration pathways is nicely correlated with the ordering of the cations. If one of the two sublattices is rocksalt ordered, such that

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the sublattice is isotropic in the structure, then the fastest migration pathway has the same nature as the ordering of the other sublattice. That is, if the B sublattice is rocksalt, then the diffusion is one-dimensional for AC ordering (which consists of ordered one-dimensional columns of A cations), two-dimensional for AL (two-dimensional layers of A cations), and three-dimensional for AR (again, isotropic three-dimensional ordering of A cations). Similar trends are observed as a function of the B sublattice ordering when the A cation sublattice has the rocksalt ordering. For other cases, the competing effects of A versus B ordering lead to less obvious patterns of migration. Real double perovskites will exhibit more complex arrangements of cations, though the orderings considered here are observed in experiments. 12 Our results indicate that in disordered double perovskites oxygen vacancy migration will be dictated by the distribution of cations with the largest charge states. Given that, in any random distribution of cations, there will be islands relatively void of such highly charged cations separated by regions of high concentrations of those cations, migration will tend to be sluggish. The oxygen vacancy will be effectively trapped in the regions with few Ti ions with long waiting times to move through regions of high Ti concentration to another island of low Ti concentration. The dynamics will thus be dictated by these long jumps between Ti-sparse islands. More generally, in solid solutions of these compounds with varying concentrations of Ti, the mobility of oxygen vacancies will depend on the interconnectedness of Al-rich regions and whether percolation paths exist between them or if they are isolated, which will depend on the global Ti concentration. Other factors will certainly play a role in determining the migration properties of oxygen defects in double perovskites. Recently, Li and Benedek showed that the softness of the octahedral tilt modes in A2 BO4+δ Ruddlesden-Popper phases, which depend on the chemistry of the material, directly correlates with oxygen interstitial mobility. 53 More generically, isolated Ruddlesden-Popper faults can trap oxygen defects and enhance the mobility of oxygen vacancies but retard the mobility of oxygen interstitials. 54 Further, the charge state of the

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defect can also be a factor. Here, as constrained by the potentials used, the oxygen vacancy always has a charge of 2+. Depending on the doping and Fermi level of the material, the preferred charge state could vary and this will impact how the vacancy migrates through the material. In fact, the charge state can change during the course of the migration event, as described by Mastrikov et al., 55 where they found that the difference in oxygen vacancy migration in Ba and La containing perovskites was due to different magnitudes of charge transfer at the saddle point. All of these factors can complicate the behavior of the oxygen vacancy. Finally, we expect the basic physical trends observed here to apply to other double perovskites, particularly those with cations with larger valences. The primary factor determining the mobility and pathways for oxygen vacancies is the connectedness of the B cation octahedra with the largest valence state. As long as the valence state is constant versus cation disorder, the vacancy will tend to reside in sites that minimize interaction with those cations with large valences and find pathways that avoid those cations, if they exist. Migration will be fast if all sites are connected to these cations or if there are pathways in which no sites are connected to them. If there is a mixture of sites such that pathways must pass from sites unconnected to high valence cations through sites that are connected to such cations, migration will be most sluggish. We expect that these effects will be less dramatic in double perovskites in which the charges on all cations are the same (all 3+ for example) and greatest in those compounds in which the disparity in valence is greatest, such as those in which one cation has a 5+ charge state.

Conclusions To conclude, atomistic simulations using accelerated molecular dynamics reveal that the kinetic behavior of oxygen vacancies in double perovskites is very sensitive to the cation ordering. By simply changing the ordering of the cations, the migration energy of oxygen

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vacancies can change from 0.6 to 2.7 eV while the nature of the migration path can change from one- to two- to three-dimensional. The migration in the fastest and slowest cases is faster and slower than in either of the constitutent single perovskites. While these results were obtained using a specific double perovskite chemistry, we expect them to apply to double perovskites more generally as they can be related to fundamental interactions between the cations in the structure. These results demonstrate the ability to control oxygen vacancy migration, and hence ionic conductivity, in these materials and provide new opportunities for tailoring double perovskites for advanced applications.

Acknowledgement This work was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division. Los Alamos National Laboratory, an affirmative action equal opportunity employer, is operated by Los Alamos National Security, LLC, for the National Nuclear Security Administration of the U.S. DOE under contract DE-AC52-06NA25396. GP acknowledges support from the LANL LDRD program.

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Effect of Cation Ordering on Oxygen Vacancy Diffusion Pathways in

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