Enhancement of Ionic Transport in Complex Oxides through Soft

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Enhancement of ionic transport in complex oxides through soft lattice modes and epitaxial strain Xinyu Li, and Nicole A. Benedek Chem. Mater., Just Accepted Manuscript • DOI: 10.1021/acs.chemmater.5b00445 • Publication Date (Web): 24 Mar 2015 Downloaded from http://pubs.acs.org on March 25, 2015

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Chemistry of Materials

Enhancement of ionic transport in complex oxides through soft lattice modes and epitaxial strain Xinyu Li and Nicole A. Benedek∗ Materials Science and Engineering Program, The University of Texas at Austin, 1 University Station, Austin, Texas 78712 USA E-mail: [email protected]

Abstract Lattice dynamics is increasingly acknowledged as playing an important role in the ionic transport mechanisms of many oxide ion conductors. In particular, specific structural distortions – so-called octahedral rotations – have been suggested as the origin of the enhanced mobility observed in Ln2 NiO4+δ Ruddlesden-Popper phases (Ln = La, Pr, Nd), where oxide interstitial diffusion occurs through an interstitialcy mechanism. In this work, we use theory and first-principles calculations to unravel and quantify the microscopic link between soft lattice modes and migration barriers in the Ln2 NiO4+δ family of materials. We show that the magnitude of the migration barriers can be correlated with the tendency of each material to undergo an octahedral rotation distortion: as the tendency of a material to undergo such a distortion increases, the migration barrier decreases. We then use this insight to formulate simple design guidelines for further decreasing migration barriers through epitaxial strain, and that connect trends in the ionic transport properties of the Ruddlesden-Popper phases with the structures of the parent ANiO3 perovskites. ∗

To whom correspondence should be addressed

1

ACS Paragon Plus Environment


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Introduction One of the most distinctive and technologically important features of ABO3 perovskites is the strong coupling between their functional properties and particular structural distortions. The tolerance factor, t, is a commonly used empirical measure that relates the chemical composition of a particular perovskite to its tendency to undergo a structural distortion and is defined as, RA−O t= √ , 2RB−O

(1)

where RA−O and RB−O are the ideal A-O and B-O bond lengths for a given pair of ions in the undistorted cubic perovskite structure. Materials with t < 1 have under-coordinated A-sites and generally undergo octahedral rotation distortions, which are associated with unstable zone-boundary phonons of the cubic structure and generally have a significant effect on the properties of perovskites. In the rare earth nickelates 1,2 and manganites 3,4 for example, octahedral rotation distortions drive both metal-insulator and magnetic ordering transitions, the temperature of which increases as t decreases. Although the detailed microscopic physics of the properties of perovskites is often complicated, understanding the link between lattice dynamics, properties and crystal structure and bonding has made it possible in many cases to identify simple design guidelines that not only capture the behavior and properties of known materials and phases, but can also predict new or enhanced properties in as-yet hypothetical materials. Octahedral rotation distortions appear to promote fast ionic transport in the perovskiterelated phases La2 NiO4+δ , 5,6 Pr2 NiO4+δ , 7 La2 CoO4+δ 8 and La2 CuO4+δ . 9 Room temperature oxide-ion transport in SrFeO2.5 10 and Nd2 NiO4+δ 11 was attributed to the existence of soft, low energy phonon modes and a “phonon-assisted" diffusion mechanism. Lattice relaxation is also assumed to enable fast oxide-ion transport in other families of oxides, 12 such as the melilites. 13 Although soft lattice modes are generally acknowledged as promoting fast ionic transport in layered perovskites, 14 so far the link between lattice dynamics and ionic

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transport has not been quantified, and no attempt has been made to exploit this link to create design principles. 15,16 In this work, we use theory and first-principles calculations to demonstrate that the migration barriers for oxide-ion transport in a series of Ln2 NiO4+δ Ruddlesden-Popper phases (Ln = rare earth) are correlated with the tendency of each material to undergo an octahedral rotation distortion: as the tendency of a material to undergo such a distortion increases (as quantified through the force constant of the relevant mode), the migration barrier decreases. We exploit the connection between octahedral rotations in perovskites and epitaxial strain to show that tensile strain softens the octahedral rotation mode and further decreases the barrier for oxide-ion migration. Finally, we demonstrate that the lattice dynamics of the parent ANiO3 phases can be used as a rule of thumb to predict trends in the migration barriers of the corresponding Ruddlesden-Popper materials. Our work has thus identified a specific structural distortion – octahedral rotations – as the key structural feature that correlates with the magnitude of the migration barriers in this family of materials. This insight then allows us to formulate simple design guidelines for fast ionic transport in excessoxygen Ruddlesden-Popper phases. We consider the series of Ruddlesden-Popper phases Ln2 NiO4+δ with Ln = La, Pr, Nd, Eu, Sm and Gd. The La, Pr and Nd members have been extensively investigated for their potential applications as Solid Oxide Fuel Cell (SOFC) cathodes because they exhibit a wide range of oxygen stoichiometry, excess oxygen is accommodated as interstitials and these interstitials are highly mobile over a wide temperature range. 17–21 In addition, molecular dynamics simulations 6 suggest that octahedral rotations are involved in the migration mechanism of interstitial oxide ions in this family of materials. La2 NiO4 is tetragonal in space group I4/mmm above 700 K and undergoes two successive phase transitions at lower temperatures, first to an orthorhombic space group Bmab then to a tetragonal phase with P 42 /ncm symmetry. 22 Both transitions are driven by the same phonon, transforming like the irreducible representation (irrep) X3+ , and involve octahedral rotations about different 3



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crystallographic axes. The transition temperatures increase as the size of the Ln cation decreases, so both Pr2 NiO4 and Nd2 NiO4 are already distorted at room temperature. 23,24 Sm2 NiO4+δ has been prepared and characterized as a doped specimen 25 but it is unclear whether the Eu and Gd members actually form in the Ruddlesden-Popper structure; we include them here in order to better understand trends across a series of materials.

Structures and Methods Crystallography of Ln2 NiO4+δ Phases Structural phase transitions in the oxygen hyperstoichiometric materials depend sensitively on the oxygen content, δ. Whereas the transition to the undistorted I4/mmm phase occurs above the melting point of both stoichiometric Nd2 NiO4 and Pr2 NiO4 , the uptake of excess oxygen significantly decreases the transition temperature to 790 K and 690 K, respectively; 26 La2 NiO4+δ remains tetragonal down to room temperature. The octahedral rotation pattern in Nd2 NiO4+δ and Pr2 NiO4+δ corresponds to that of the Bmab space group, whereas we find that the octahedral rotation pattern of our fully relaxed materials with δ > 0 corresponds to that of the P 42 /ncm phase, which is the lowest temperature phase experimentally. This is as expected, given our calculations are performed at zero Kelvin. Given the complexity of the phase transition behavior of these materials, for the sake of consistency across the series and to make our calculations tractable we correlate our calculated migration barriers with the force constants of the octahedral rotation mode of the stoichiometric I4/mmm phase; hence, we are using the force constant of the rotation distortion in the I4/mmm structure as a proxy for the softness or stiffness of the same distortion in the excess-oxygen phases. Although the lattice dynamics of any given material will change with temperature and the value of δ, 11 previous experimental studies 22–24,26,27 suggest that the trends in their lattice dynamical properties as a function of Ln cation are roughly constant under a given set of experimental conditions. 4


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Computational Methodology First-principles calculations were performed using (spin-polarized) density functional theory with projector augmented wave (PAW) potentials 28,29 and the PBEsol+U functional, as implemented in VASP. 30–33 We used U = 4.5 eV and JH = 0.7 eV for the Ni-ion on-site Coulomb and exchange parameters 34 respectively (there is no qualitative change in our results for reasonable changes of U ; see Supplementary Information Table S1) and a Gaussian smearing of 0.1 eV. We used PAW potentials for Ni and O with the electronic configurations 3s2 3p6 3d8 4s2 and 2s2 2p4 respectively. For Pr – Gd we used potentials with the f-electrons frozen in the core. Force constants were calculated using both the method of frozen phonons and density functional perturbation theory on a 6×6×4 Monkhorst-Pack mesh and 600 eV plane wave cutoff. Migration barriers were calculated using the Climbing Image-Nudged Elastic Bands (CI-NEB) technique 35 on a 4×4×2 Monkhorst-Pack mesh for an oxygen interstitial concentration of δ = 0.125, which corresponds to a 2×2×1 supercell supercell of the undistorted I4/mmm phase with 56 atoms (δ ranges from ∼0.10 to ∼0.24 in experiments 36 ). We allowed the ions to fully relax along each image of the migration path. The symmetry of the excess-oxygen phases is thus lower than I4/mmm (the addition of the interstitial breaks all symmetries) and we do see octahedral rotation distortions in these structures, corresponding to that of the P 42 /ncm phase, as mentioned above. Hence, the effect of octahedral rotations on the migration barriers is taken into account. We also performed calculations with lower interstitial concentrations and larger supercells and those results can be found in the Supplementary Information (Tables S3 and S4). We used three images for all our CI-NEB calculations, the sufficiency of which we tested with calculations on up to nine images. The materials we considered are not magnetically ordered at the temperatures of interest for practical applications (the stoichiometric phases are G-type antiferromagnets below their respective Néel temperatures). We therefore follow standard practice 37 and enforce ferromagnetic spin ordering for all calculations; we checked that both the lattice dynamical properties and migration barriers are not qualitatively sensitive to the spin order. A force 5



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convergence tolerance of 2.5 meV/Å was used for structural relaxations, which was increased to 0.01 eV for the CI-NEB calculations. Table 1: Force constant of the X3+ octahedral rotation mode of the oxygen-stoichiometric I4/mmm phase at the equilibrium volume and under 1.5% tensile and compressive strain. Material La2 NiO4 Pr2 NiO4 Nd2 NiO4 Sm2 NiO4 Eu2 NiO4 Gd2 NiO4

Force constant [eV/Å2 ] Equilibrium Tensile Compressive -0.32 -0.83 0.31 -1.08 -1.56 -0.42 -1.44 -1.90 -0.76 -2.09 -2.56 -1.46 -2.43 -2.89 -1.74 -2.77 -3.16 -2.17

Results and Discussion Quantifying the relationship between octahedral rotations and ionic transport Our hypothesis is that materials with softer octahedral rotation modes will have lower migration barriers for oxide-ion interstitial diffusion. To test this hypothesis, we first calculated the force constant of the X3+ octahedral rotation mode for each of our materials in the undistorted I4/mmm space group. Recall that a mode transforming like the irrep X3+ drives both sets of octahedral rotation phase transitions in this family of materials. Table 1 shows that the force constant becomes larger and more negative as the size of the Ln cation decreases (the force constants are negative because at 0 K the ground-state structure is not I4/mmm, but one with octahedral rotations). That is, as the Ln cation size decreases, the tendency to undergo an octahedral rotation distortion increases and the force constant becomes ‘softer’. This tendency is reflected in and entirely consistent with the trends in the transition temperatures of the La – Pr members: as the Ln cation size decreases the temperature of the transition from the Bmab phase to the undistorted I4/mmm one increases (TC = 700 K for 6


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La2 NiO4 , 22 the extrapolated temperatures for Pr2 NiO4 24 and Nd2 NiO4 23 are ∼1500 K and ∼1900 K, respectively). Now that we have established a link between lattice dynamics and crystal chemistry, we can make the connection to migration barriers. We used the CI-NEB method to calculate the migration barrier for oxide-ion diffusion for the interstitialcy mechanism identified as the lowest energy migration pathway in Ref.; 6 see Figure 1a. Figure 1b shows that as the force constant of the octahedral rotation mode becomes more negative, the migration barrier also decreases, in apparent agreement with our hypothesis. We emphasize again that although we are correlating the migration barriers with the force constant of the undistorted I4/mmm phase, the ions are allowed to fully relax in the excess-oxygen phases and the effect of octahedral rotations on the barriers is taken into account. Note that two variables are changing as we move from La – Gd: the octahedral rotation mode becomes softer and the unit cell volume decreases. It is well known that ionic transport properties (migration barriers and diffusion coefficients) are sensitive to volume. 38,39 Typically, expanding the space available to the migrating ion or defect tends to decrease migration barriers, whereas restricting the space available tends to increase migration barriers. In our case, Gd2 NiO4 has both the smallest unit cell volume and the lowest migration barrier, which lends support to our hypothesis that it is the octahedral rotation modes (as opposed to volume changes) that play a dominant role in the ionic transport mechanism in this family of materials. Next, we analyzed the structures of all our materials along the CI-NEB migration path and found that the path becomes increasingly curved as the Ln cation size decreases. The initial fractional coordinates of the migrating interstitial are x = 0.5 and y = 0.25, with a final position of x = 0.5, y = 0.75. As the Ln cation size decreases, the x coordinate deviates increasingly from 0.5 (to ∼0.54 for Gd2 NiO4 ). Although this feature has been associated with enhanced mobility in several previous studies of oxide-ion transport in perovskites, 43,44 it is not clear how a curved path may lead to lower migration barriers for the materials

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a) La Ni O Oi

c

a b

b)

Decreasing A-site radius Decreasing unit cell volume

1.15 1.1

Migration barrier [eV]

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La2NiO4

1.05 1 0.95

Pr2NiO4

0.9

Nd2NiO4

0.85 0.8 0.75 0.7

Eu2NiO4

Sm2NiO4

Gd2NiO4

−2.5

−2

−1.5

−1

−0.5 −2

Force constant [eV Å ]

Figure 1: a) Snapshot from a CI-NEB calculation of interstitial oxide ion migration via an interstitialcy mechanism in La2 NiO4+δ , δ = 0.125 (see also Figure 3 of Ref. 6 ). The migrating oxide ion Oi is depicted as a purple sphere and the arrows show the direction of travel. The migrating oxide ion will displace the apical oxygen of the NiO6 octahedron, which will move into the interstitial site denoted by the purple square. Note the tilting of the octahedra away from the interstitial. Previous theoretical 6 and experimental 40–42 work has shown that oxideion transport in this family of Ruddlesden-Popper phases is highly anisotropic, being orders of magnitude faster along the ab plane b) Migration barrier for the interstitialcy pathway shown in a) as a function of the force constant of the X3+ octahedral rotation mode.

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studied here because the relevant bond lengths (between the migrating interstitial and the surrounding oxygens and Ln cations, for example) still decrease on going from La2 NiO4 to Gd2 NiO4 . We also noticed that as the interstitial moves along the migration path, it passes through two triangles formed by the Ln cations, 45 as shown in Figure 2. Whereas the first triangle is fairly regular (in terms of Ln-Ln bond lengths) across the series of materials, the second triangle becomes more and more distorted as the Ln cation size decreases. The area of the second triangle does increase slightly from La (1.32 Å2 ) – Gd (1.36 Å2 ), relative to the size of the Ln cation, although probably not by enough to account for the drop in migration barrier across the series. We strongly suspect that the microscopic origin of the decreased barriers involves a complex interplay between the crystal structure and electronic structure of the Ni ion. Indeed, the strong coupling between crystal structure and electronic/magnetic structure is one of the defining features of perovskites, and the nickelates are no exception. 1,2 Hence, the usual rationalization of the ionic transport properties in terms of purely geometric criteria, such as bond lengths, will not be adequate; Mastrikov and co-workers found this to be the case in their study of vacancy migration in doped cobaltites. 46 We are continuing our investigations into the role of geometric and electronic effects on the microscopic origin of the transport mechanism in this family of materials.

Epitaxial strain effects on ionic transport Having correlated the magnitude of the migration barriers with the softness of the octahedral rotation modes in these Ruddlesden-Popper phases, we can now take advantage of the wealth of previously established design rules for perovskites. For example, octahedral rotations in perovskites are known to be sensitive to pressure and epitaxial strain. 47–49 Can we exploit this sensitivity to further lower migration barriers to oxide interstitial diffusion in this family of materials? We recalculated the force constant of the X3+ mode under 1.5% tensile and compressive biaxial strain in the ab plane and the results are shown in Table 1. Tensile strain further softens the octahedral rotation mode whereas compressive strain stiffens it. 9



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Oi Oa

Figure 2: Part of the structure of La2 NiO4+δ showing the two Ln cation triangles through which pass the interstitial oxygen Oi and apical oxygen Oa . The interstitial Oi passes through the first triangle to displace the apical oxygen Oa of a NiO6 octahedron. Oa then passes through the second triangle to move into the interstitial place between the Ln-O layers. We then recalculated the migration barriers for both sets of strained materials and found that while tensile strain acts to lower the barriers, compressive strain increases them, as shown in Figure 3. In fact, Figure 3 shows that there is a remarkable, essentially linear relationship between force constant and migration barrier. As mentioned above, expanding (decreasing) the volume available for the diffusing defect also tends to lower (increase) migration barriers, so it is not so straightforward to disentangle the effects of the octahedral rotation modes and the volume increase/decrease due to the strain on the migration barriers. However, given that all of the migration barriers fall on the same line as a function of force constant, it is not unreasonable to assume that it is the softness of the octahedral rotation mode that has the more significant effect on the migration barrier.

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1.2 Migration barrier [eV]

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Compressive Equilibrium Tensile

1.1 1 0.9 0.8 0.7 −3.5 −3 −2.5 −2 −1.5 −1 −0.5 0 0.5 −2

Force constant [eV Å ]

Figure 3: Migration barriers for strained and equilibrium structures as a function of the force constant of the X3+ mode. The data for this figure can be found in table form (Table S2) in the Supplementary Information.

Linking ionic transport in the Ruddlesden-Popper phases to structural properties of the parent perovskites We now consider whether it may be possible to link the ionic transport properties of the Ruddlesden-Popper phases to the structures and lattice dynamics of their parent LnNiO3 perovskites. A design principle for new polar or ferroelectric materials was recently demonstrated 50–52 whereby two different ABO3 perovskites with the P bnm structure are layered to create a (polar) AA′ B2 O6 double perovskite 53–56 or Ruddlesden-Popper phase. 57,58 The criteria governing selection of the materials for the layered systems originate in the structures and lattice dynamics of the parent ABO3 (and A′ BO3 ) perovskites, i.e., the parent perovskites are used as ‘building blocks’ in the design of new polar materials. Can such an approach be extended to the ionic transport properties of the Ruddlesden-Popper phases studied here? LnNiO3 perovskites (Ln = Pr – Gd) have an orthorhombic structure in space group P bnm (see inset of Figure 4) over a wide temperature range and undergo a structural phase transition to a monoclinic phase at low temperatures; the transition temperature increases as t decreases. LaNiO3 is rhombohedral R¯3c.

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Figure 4 shows that the migration barrier decreases as the tolerance factor of the parent ANiO3 perovskite decreases (see also Ref. 43 ). Hence, as t decreases the tendency towards an octahedral rotation increases and the rotation distortions themselves become larger in magnitude (in the P bnm structure), as quantified by the Ni-O-Ni tilting angles 1 shown in Figure 4. The tendency of the corresponding Ruddlesden-Popper phases towards an octahedral rotation distortion is thus inherited from the parent perovskites, as one would expect. Our results suggest that the tolerance factor – easily calculated by hand – can be used as a simple proxy (in place of the force constant) for the softness of the octahedral rotation mode. More generally, our results suggest that the lattice dynamical properties of the parent perovskites may be able to be used as a rule of thumb to predict trends in the migration barriers of their respective Ruddlesden-Popper phases, opening the door to the kinds of ‘building block’ design approaches that have been used so successfully in other contexts. Although much further work will be necessary to really establish whether this kind of approach can be used to design fast oxide ion conductors, our results – preliminary as they may be – are encouraging. 1.15 1.1 Migration barrier [eV]

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La2NiO4 165.2°

1.05 1 0.95 0.9 Sm2NiO4 153.4°

0.85 0.8

Gd2NiO4 143.1°

0.75 0.93

Pr2NiO4 158.7° Nd2NiO4 157.1°

Eu2NiO4 147.9°

0.94

0.95

0.96

0.97

0.98

Tolerance factor

Figure 4: Migration barrier for the unstrained materials as a function of the tolerance factor of the parent ANiO3 perovskites. The P bnm structure adopted by most bulk nickelates (except LaNiO3 ) is shown in the inset and the angles 1 underneath the label for each material refer to the Ni-O-Ni tilting angle (in P bnm) discussed in the text.

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Connecting theory to experiments Finally, we discuss the connection between our results and the experimental literature on ionic transport in Ln2 NiO4+δ , Ln = La, Pr, Nd. The measured activation energies for La2 NiO4+δ range from 0.19 eV in thin-films 41 to ∼0.9 eV for single crystals 40 and ceramics. 59 For Pr2 NiO4+δ and Nd2 NiO4+δ the most recent measurements 60 on single crystals yielded activation energies of ∼0.7 eV and ∼1.4 eV, respectively. Our calculated migration barriers thus appear to over-estimate the experimental values in the case of Ln = La and Pr and to underestimate the experimental values in the case of Ln = Nd. Diffusion coefficients and activation energies are generally sensitive to the concentration of the diffusing species and the materials studied here are no exception. 36 Table S3 in the Supporting Information shows that our calculated migration barriers for δ = 0.0625 are lower and in better agreement with experiment for Ln = La and Pr. We also note that, depending on the experimental conditions under which measurements are performed, migration barriers can sometimes be higher than activation energies. For example, Stratton and Tuller 61 showed for UO2+x (another excess-oxygen material in which the diffusing defect is oxygen interstitials) that oxygen diffusion measurements under high oxygen partial pressures are characterized by the migration enthalpy of the interstitials alone, i.e. in this regime one measures only the migration enthalpy and the defect reaction enthalpy is negative, which results in a value for the activation energy that is lower than the migration barrier. The transport properties of the Nd phase are somewhat curious. Previous experiments show that activation energies are lower and and diffusion is faster in Pr2 NiO4+δ than La2 NiO4+δ and our calculated migration barriers for these materials are consistent with this. However, as mentioned above, the experimentally measured activation energy for Nd2 NiO4+δ is higher than the other two materials, despite the fact that at high temperatures (700◦ C) diffusion in Nd2 NiO4+δ is comparable to Pr2 NiO4+δ whereas at lower temperatures (500◦ C) it is an order of magnitude slower. One explanation 60 is that a reduction of the c lattice parameter from La-Nd may suppress the low energy phonon modes that are responsible for enabling 13



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facile diffusion in this family of materials. However, our results show that the tendency of Nd2 NiO4 to undergo an octahedral tilting distortion is larger than the other two materials, i.e., the phonon mode that assists diffusion is more favorable in Nd2 NiO4 than La2 NiO4 and Pr2 NiO4 . In addition, the recent experiments of Perrichon, et al., 11 clearly demonstrate that low energy phonons play an important role in the ionic transport properties of Nd2 NiO4 . Hence, a more likely explanation is that the reduction in the c lattice parameter reduces the space available to accommodate interstitials in the rocksalt layers, thereby raising the energy of formation for this defect. In fact, Tsvetkov and co-workers 62 recently showed that Nd2 NiO4+δ thin-films with tensile strain applied along the c-axis had expanded rocksalt layers (more space to accommodate interstitials) and faster oxygen exchange kinetics than unstrained films and films that had been compressively strained along the c-axis. It is thus possible that although the migration barrier may be lower in the Nd-containing material, the interstitial formation energy is much higher (in contrast to the La and Pr phases), resulting in a higher activation energy (recall that the activation energy is the sum of the migration and defect formation energies). It may be that in Pr2 NiO4+δ the relevant lattice modes are soft enough to assist diffusion, but the lattice parameter is large enough such that the formation of oxide interstitials is not significantly hindered. We are now calculating defect formation energies for each material considered here to more fully understand their differences in transport properties.

Summary and Conclusions We have used first-principles calculations to unravel and quantify the microscopic link between octahedral rotation modes in Ln2 NiO4+δ Ruddlesden-Popper materials and their migration barriers to oxide interstitial diffusion. Not only have we shown that rotations play a key role in the transport mechanism in this family of materials, but we have demonstrated how changes in mode softness due to crystal chemistry and epitaxial strain may be har-

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nessed to design materials with low barriers to oxide ion migration. We have also identified the tolerance factor of the parent perovskite as a simple, easily calculated descriptor that can predict trends in the ionic transport properties of the corresponding Ruddlesden-Popper phases. However, we note that ionic transport is of course a complex physical process and many factors may influence activation energies and diffusion coefficients. In our case, it may be that while migration barriers decrease as the tolerance factor (Ln cation radius) decreases, interstitial formation energies may increase, leading to larger activation energies. The trends we have identified are specific to the migration mechanism in this particular family of nickelate Ruddlesden-Popper phases and further work is required to determine the extent to which these trends apply to other families of materials. However, recent work in other systems has demonstrated that soft lattice modes play an important role in facilitating fast, low-temperature diffusion in a number of materials families. Hence, there is no reason in principle why our approach could not be applied to systematically and quantitatively understand the interplay between lattice dynamics and ionic transport in other families of oxides, and we hope that our work spurs further studies in this direction.

Supporting Information Available Results of convergence tests, force constants and migration barriers in table form and the effects of different excess oxygen concentrations on the migration barriers. This material is available free of charge via the Internet at http://pubs.acs.org/.

Acknowledgement This work was supported by a Ralph E. Powe Junior Faculty Enhancement Award (to NAB) from Oak Ridge Associated Universities. All calculations were performed using the highperformance compute facilities of the Texas Advanced Computing Center (TACC). The authors gratefully acknowledge Penghao Xiao and Graeme Henkelman for their assistance with the CI-NEB calculations. We also thank Bilge Yildiz, Blas Uberuaga, Dane Morgan 15



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and Harry Tuller for helpful discussions.

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Enhancement of Ionic Transport in Complex Oxides through Soft

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