Liquid-like Ionic Diffusion in Solid Bismuth Oxide Revealed by

Article pubs.acs.org/cm

Liquid-like Ionic Diffusion in Solid Bismuth Oxide Revealed by Coherent Quasielastic Neutron Scattering Julia Wind,† Richard A. Mole,‡ Dehong Yu,‡ and Chris D. Ling*,† †

School of Chemistry, The University of Sydney, Sydney 2006, Australia Australian Centre for Neutron Scattering, ANSTO, New Illawarra Road, Lucas Heights 2234, Australia

‡

ABSTRACT: The exceptional oxide ionic conductivity of the high-temperature phase of bismuth oxide gives rise to a characteristic “quasielastic” broadening of its neutron scattering spectrum. We show that the oscillating form of this broadening can be fit using a modified version of a jumpdiffusion model previously reserved for liquid ionic conductors. Fit parameters include a quantitative jump distance and a semiquantitative diffusion coefficient. In the case presented here, the results show that diffusion is isotropic (liquid-like) even though some directions present shorter oxygen−vacancy distances, an insight corroborated by computational dynamics simulations. More broadly, the results show for the first time that quasielastic neutron scattering can be directly analyzed to yield quantitative insights into the atomic-scale mechanisms of solid-state ionic conduction, even when the diffusing species is a coherent neutron scatterer such as oxygen. This shows its power as a tool for studying functional solid-state materials, notably for solid-oxide fuel cells and, potentially, lithium-ion batteries.

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INTRODUCTION

However, QENS analysis is far more complex when the diffusing atoms have significant coherent neutron scattering cross sections. Oxygen and lithium (and, in fact, most isotopes of most elements) fall into this category. Many INS studies of oxygen (an almost purely coherent scatterer) SSICs have noted the appearance of QENS in the ionic conduction temperature regime but have been unable to model it. Instead, they use the experimental GDOS to validate computer simulations;22−24 i.e., the key insights into diffusion come indirectly from simulations rather than directly by fitting data. Similarly, INS studies of lithium SSICs have modeled the incoherent contribution to the QENS signal, but not the equally significant coherent contribution, resulting in imperfect fits and incomplete results.25−27 A quantitative empirical model for coherent QENS in solids would be a powerful tool for studying solid-oxide fuel cell and lithium-ion battery materials. Some attempts have been made to do this by applying the so-called Sköld modification28 to the Chudley−Elliot jump-diffusion model for incoherent neutron scatterers,29 notably, the work of Ross et al.30 (oxygen), Hutchings et al.31 (chlorine and fluorine), and Cook et al.32 (deuterium). However, none have successfully extracted quantitative information about ionic motion, largely because of the weakness of the signal and consequent uncertainty in the fits.

The search for new and improved solid-state ionic conductors (SSICs) is one of the most active and important fields in materials chemistry, driven by the key role they play in solidstate battery1−3 and fuel cell technologies.4−6 The paradoxical chemical and structural requirements of SSICs are challenging: long-range order to provide a mechanically stable framework together with short-range disorder so that selected atoms can migrate through it. Rational design and optimization of SSICs depend on a detailed understanding of the atomic-scale mechanisms by which this paradox is resolved. One of the most powerful probes of atomic-scale structure and dynamics is nuclear magnetic resonance (NMR),7 which has shed light on diffusion in proton,8−10 oxide,11,12 and lithium13 SSICs. Further insights are gained in combination with Raman spectroscopy, which is sensitive to the underlying lattice dynamics that can help activate diffusion.14,15 Inelastic neutron scattering (INS) is arguably even more powerful, as the only experimental technique that simultaneously measures diffusion processes [as quasielastic neutron scattering (QENS)] and lattice dynamics [as a generalized density of states (GDOS)].16 In SSICs where the diffusing atoms have predominantly incoherent neutron scattering cross sections, key parameters describing diffusion can be extracted directly by modeling the form of the QENS. The archetypal case is hydrogen, an almost purely incoherent scatterer. QENS analysis has been successfully applied to hydrogen dynamics in solidoxide fuel cell materials,17 organic−inorganic perovskite solar cells,18 porous organic cages,19 and even biological systems.20,21 © 2017 American Chemical Society

Received: June 8, 2017 Revised: August 3, 2017 Published: August 7, 2017 7408

DOI: 10.1021/acs.chemmater.7b02374 Chem. Mater. 2017, 29, 7408−7415

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Chemistry of Materials

Figure 1. Inelastic neutron scattering data. (a) Dynamic scattering function S(Q,ω) for δ-Bi2O3 at 730 °C measured at a λ of 6 Å showing a very clear and strong QENS broadening as well as a pronounced structure along the elastic line (ω = 0). (b) Fits of two Gaussian peaks to the purely elastic (width of resolution function) structure factor S(Q,ω=0), showing two maxima at Q values of 0.7 and 1.3 Å−1 corresponding to lattice spacings of 9.1 and 4.8 Å, respectively (error bars are smaller than symbols). (c) Fit of one Lorentzian peak and one δ function convoluted with the resolution function (measured using vanadium) against a selected constant Q = 1.3 Å−1 slice of S(Q,ω) space (error bars are smaller than symbols). scattered by the sample and detected using the 1 m high detector bank that spans 125°. The sample rod (8 g, 7 mm × 35 mm) was placed inside a platinum can and hung into the vacuum furnace using a platinum wire. A pressed sample rod was used to minimize the contact area and thus to avoid reactions between the sample and the platinum can at high temperatures. The sample was heated at a rate of 10 °C/ min to 700 °C. The temperature was then increased in 5 °C increments, allowing equilibration times of 10 min until the phase transition from the α to δ phase (recognized by the disappearance of Bragg peaks in the measured Q range) was observed at a temperature of 730 °C. A short data collection at 3 Å confirmed the presence of the δ phase (three Bragg peaks). Data were collected between 730 and 790 °C in 10 °C steps with a 10 h collection time at each temperature at λ = 6 Å. Additional short (2 h) data collections at a wavelength of 3 Å were made between 730 and 790 °C in 20 °C steps to monitor and confirm the presence of the δ phase. Two more data sets (4 h collections) on the supercooled δ phase were collected at 700 and 680 °C. Finally, data on the β phase were collected at 600 °C for 10 h (λ = 6 Å). A vanadium standard was measured for detector normalization and to determine the resolution function for the quasielastic neutron scattering (QENS) analysis. The background was corrected by subtracting an empty sample can. The corrected time-of-flight spectra were then converted to S(Q,ω). All data manipulations were performed using the Large Array Manipulation Program (LAMP).44 For QENS analysis, detectors containing Bragg reflections were removed from the data prior to further data processing (necessary for

Here, we set out to develop and test such a model by starting with the ideal case: an SSIC in which the diffusing atom is an almost purely coherent scatterer (oxygen), the structure is simple, and the QENS signal is strong. This is the hightemperature cubic form of bismuth oxide, δ-Bi2O3, which has the highest known solid-state oxide ionic conductivity (1−2 S cm−1)33,34 over its narrow stability range of 729−817 °C. Although it was recently shown that δ-Bi2O3 can be stabilized in thin films,35 low-temperature transitions in bulk δ-Bi2O3 make it impractical for real-world applications. Nevertheless, it is an ideal model system in which to consider the dynamics of solidstate oxide conduction and has been extensively studied as such.36−41

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EXPERIMENTAL METHODS

Data Collection and Analysis. A polycrystalline rod of α-Bi2O3 (Sigma-Aldrich, 99.999%) was pressed at 40 MPa in a hydrostatic press and sintered in air at 600 °C for 6 h. Inelastic neutron scattering (INS) experiments were performed on this rod using the cold neutron time-of-flight spectrometer PELICAN at the Australian Centre for Neutron Scattering, ANSTO.42,43 The instrument was optimized for 6 Å incident neutrons, affording an energy resolution of 65 μeV at the elastic line. Data were also collected at 3 Å by rephasing the choppers to allow only λ/2, giving a resolution of 0.52 meV. The neutrons were 7409


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Chemistry of Materials only 3 Å data). The obtained Q slices were then fit using the QENS_fit program within LAMP. All the data could be adequately described by a δ function and one Lorentzian peak convoluted with the measured resolution function (vanadium standard) and a linear sloping background. Ab Initio Calculations. Ab initio molecular dynamics (AIMD) calculations were performed using density functional theory-based methods as implemented in the Vienna ab initio Simulation Package (VASP).45,46 Calculations used projector-augmented wave (PAW) pseudopotentials47 with a plane wave cutoff of 400 eV within the generalized gradient approximation (GGA) and the PBE (Perdew− Burke−Ernzerhof)48 exchange-correlation functional. Sampling of the electronic structure in reciprocal space was performed at the Γ point only. Following the approach of previous AIMD studies,39,40 our initial model for δ-Bi2O3 used an adaptation of the array of oxygen/vacancy ordering as present in β-Bi2O3 and a lattice parameter a of 5.66 Å.49 For simulations, we used a 2 × 2 × 2 supercell of the cubic fluorite structure (a = 11.32 Å) consisting of 80 atoms. A fixed time step of 2 fs was used in all our simulations. A simulation of 55000 steps corresponding to 110 ps of simulation time was performed at a temperature of 1100 K, very close to the melting point, using the canonical (NVT) ensemble. The first 5000 steps (10 ps) were removed from the trajectory prior to analysis to allow the system to equilibrate. To investigate the temperature dependence of the diffusion behavior, two additional shorter simulations (a 40 ps simulation with a 10 ps equilibration) at 1000 and 1060 K, corresponding to our lowest and highest experimental temperatures, respectively, were performed. To investigate the influence of the cell size, another short simulation was performed using a 3 × 3 × 3 cell (a = 16.98 Å) containing 270 atoms. The MD trajectories were analyzed using nMoldyn.50 Note that because of practical computational limits on simulation length (i.e., energy resolution) and, more restrictively, the simulation cell size (required to obtain a suitable Q resolution especially at low Q values), it is not feasible to simulate Scoh(Q,ω) from AIMD simulations. It might be possible using classic MD simulations on a large cell (>8 × 8 × 8) with thoroughly tested and optimized potentials (including the polarizability of Bi), but this is beyond the scope of the work presented here.

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RESULTS AND DISCUSSION Inelastic Neutron Scattering from δ-Bi2O3. The measured quantity in an INS experiment is dynamic structure factor S, which has incoherent and coherent components: S(Q , ω) = Sinc(Q , ω) + Scoh(Q , ω)

(1)

Figure 2. Temperature dependence of the λ = 6 Å neutron data. (a) Elastic structure factor S(Q,0) and (c) total Q, illustrating the decrease in elastic intensity with an increase in temperature. Note the significant decrease in the extent of diffuse scattering and the appearance of three sharp Bragg peaks below the transition to the β phase at 600 °C. (b) Lorentzian peak broadening as a function of Q and (d) integrated over all Q (using ΔQ = 0.1 Å−1) shows an increase in the level of quasielastic broadening with an increase in temperature. No such QENS broadening, and thus no oxygen diffusion on the accessible time scale, is observed for the β phase.

where Q is neutron momentum transfer (i.e., diffraction space) and ω is neutron energy transfer. Figure 1a shows this dynamic neutron scattering function S(Q,ω) for Bi2O3 measured using an incident neutron wavelength (λ) of 6 Å at 730 °C, within the stability range of the cubic δ phase. A strong QENS broadening of the elastic line is observed over the measured Q range, which contains no Bragg peaks. The clear streak into the inelastic region at the highest Q is a phonon emerging from the ⟨111⟩ Bragg reflection at Q = 1.9 Å−1, just outside the accessible Q range on the elastic line. Some very weak but clear structure along the elastic line due to diffuse coherent scattering was also observed. The extracted elastic intensity, S(Q,0) (Figure 1b), shows two pronounced broad peaks centered at Q values of 0.7 and 1.3 Å−1 corresponding to lattice spacings (d) of 9.1 and 4.8 Å, respectively. Integrating S(Q,ω) over the full range of measured energies yields the total static structure factor, S(Q), which shows the same broad diffuse features as the purely elastic structure factor, which are slightly less pronounced (Figure 2a). Such features are commonly observed in melts or glasses51 and suggest weak intermediate-range ordering in the oxygen sublattice. Their

positions do not change significantly over the measured temperature range. Below the transition to the metastable β phase at 600 °C, they disappear and are replaced by two sharp Bragg reflections due to β-type ordering of the oxygen sublattice (Figure 2a). The pronounced QENS broadening of the elastic line over the whole accessible Q range is an unambiguous sign of translational diffusion in the sample. For all Q values, the intensity of S(ω) decreases (Figure 2c) as the broadening increases (cf. Figure 2b and the normalized data in Figure 2d), confirming that the rate of diffusion increases with temperature. After transformation to the relatively non7410


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Chemistry of Materials conducting β phase52 below 600 °C, the QENS signal disappears (i.e., overlays the vanadium resolution function). Careful inspection of the Q dependence of the QENS broadening (Figure 2b) shows that it narrows when the elastic structure factor (Figure 2a) reaches its maximum. This socalled de Gennes narrowing16,53 is commonly observed in coherent QENS from liquids. A maximum in S(Q,0) corresponds to short-range order; i.e., a certain local structural configuration is energetically favored over other configurations. It takes more energy to break up these favored configurations, making them longer-lived,54 resulting in an increased correlation time (slower diffusion) at the same Q values. Modeling Coherent Quasielastic Neutron Scattering from a Solid-State Ionic Conductor. The incoherent part of dynamic structure factor Sinc(Q,ω) (eq 1) is the double-Fourier transform of the time-dependent self-correlation function, Gs(r,t), the probability of finding a particle at a location r (relative to its original position) at time t. This describes the dynamics of individual particles and is thus directly related to diffusion. In the simple limiting case of long times and displacements (unrestricted diffusion),16 this assumes the hydrodynamic form described by Fick’s law: Gs(r , t ) =

⎛ 1 r2 ⎞ − exp ⎜ ⎟ ⎝ 4Ds|t | ⎠ (4πDs|t |)3/2

tributions) peak, convoluted with the experimental resolution function (Figure 1c). All fits were done over an energy range of −1 ≤ ω ≤ 1, chosen to be symmetric around ω = 0 without interference from phonons on the negative side. Extending the fitting range on the positive side (where no phonons are observed in that Q range) did not affect the results or the χ2 values. A simple linear background was included in the fit, the constant of which did not vary with Q beyond the order of the error for the Lorentzian intensity (∼2 × 10−5). Variations in the slope were even smaller (5 × 10−6) over the entire Q range. Thus, we are confident that our fits are the best that can be reasonably obtained without overparameterizing. The Lorentzian HWHM shows an oscillatory Q dependence, which is characteristic of a jump-diffusion process.29 Fitting the iCE model to the data yields a jump length of approximately half a unit cell length, as reported by Mamontov.41 However, the fit (dashed black line in Figure 3) is clearly unsatisfactory, especially for Q values of 1 Å−1. Thus, coherency effects, i.e., the structure factor, must be included in the analysis. This has been done successfully for liquids (notably, liquid argon56) using the so-called Sköld modification28 to the Chudley−Elliot model, in which Q is replaced by Q / S(Q ) . This requires knowledge of structure factor S(Q) in absolute units, which in liquids can be reliably obtained as it approaches 1 at high Q values. In solids, the presence of Bragg peaks and the limited accessible Q range of INS instruments make this more difficult. In the case presented here, we assume it approaches 1 at the highest measured Q value, just below the first Bragg peak. We then obtain a modified, coherent Chudley−Elliot (cCE) model: Δω(Q ) =

sin(Qd) ⎤ 1 ⎡ ⎥ ⎢1 − Qd ⎦ τS(Q ) ⎣

(4)

We can use this model to reliably determine the geometry (jump length) of the diffusion process. However, it should be noted that we can estimate residence time τ only because of its direct relationship to the normalization of S(Q), which could itself only be estimated. Including the structure factor to 7411


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Figure 4. (a) Locally relaxed average crystal structure of δ-Bi2O3.49 Bi atoms (4a site) are shown as large purple spheres. Red tetrahedra represent disordered O positions: a central O on the 8c site (25% occupancy) surrounded by four 32f sites (12.5% occupancy). Black arrows indicate possible oxygen jumps in ⟨100⟩, ⟨110⟩, and ⟨111⟩ directions. (b) Possible jumps between tetrahedral cavities. (c) Fit to the cCE model using the weighted average jump length (). Colored lines are the fits for individual jumps matching the colors in panel b, along the ⟨100⟩ (dashed), ⟨110⟩ (dashed− dotted), and ⟨111⟩ (dotted) directions.

contribute unique information to our understanding of SSICs with this structure type. Validating Computer Simulations against Experimental Data. Computational studies, including classical36,37 and ab initio molecular dynamics (AIMD)38−40 simulations, have previously been used to model the local atomic-scale structure and diffusion dynamics in δ-Bi2O3. While practical computational limits (especially ab initio) on the length (energy resolution) and size (Q resolution) of these simulations mean that the Q dependence of the QENS cannot be obtained, it is possible to extract a generalized density of states (GDOS). Having shown that we can model coherent QENS in an oxide SSIC for the first time, we can now harness the full power of the INS experiment to simultaneously probe ionic diffusion and lattice dynamics. Comparing our experimental GDOS to calculated versions from dynamics simulations will benchmark the accuracy of the simulations and validate any insights concerning diffusion mechanisms that are obtained from them. The GDOS is obtained from S(Q,ω) using the equation

account for coherency effects in the sample greatly improved the fit to our data (red line in Figure 3; an iCE model using the same d and τ is shown as a solid black line). Interestingly, while a jump length d of 2.83 Å (the distance between average oxygen sites, as obtained by Mamontov41 using the iCE model) gives a reasonable fit, the optimized fit shown in Figure 3 yields a d of 3.33 Å. This does not correspond to any discrete distance between oxygen sites in δBi2O3. To reconcile this, we considered all possible oxygen− oxygen jump distances in the widely accepted model of δ-Bi2O3 that allows local structural relaxation of oxygen from its average (8c) fluorite-type site to one of a tetrahedrally distributed set of possible (32f) interstitial sites49 (Figure 4a). Jumps between neighboring sites in this model can start and end in average or interstitial sites (Figure 4b) and vary from 1.87 Å (the shortest distance between corners of neighboring tetrahedra along the ⟨100⟩ directions), through jumps along the ⟨110⟩ face diagonal, to 4.90 Å (the longest possible jump along the ⟨111⟩ body diagonal). The solid black line in Figure 4c shows the weighted average of all the possible jumps within a unit cell, fit to our QENS data in the cCE model, while colored lines show how this fit would look for individual jumps. The best fit to the cCE model using the average jump length suggests that oxide ionic diffusion in δ-Bi2O3 is essentially isotropic, not dominated by jumps along ⟨100⟩ as suggested by the fit to the iCE model. An isotropic (liquid-like) diffusion mechanism for δ-Bi2O3 is consistent with the liquid-like structure factor observed at the elastic line (Figure 2a). This invites comparison to superionic conduction in thermoelectric compound Cu2−xSe, which has essentially the same structure as δ-Bi2O3: an antifluorite-type lattice in which the Cu sites are distributed over a tetrahedron of partially occupied sites. Cu2−xSe was recently shown to exhibit liquid-like ionic diffusion, using high-resolution in situ transmission electron microscopy.57 Such an experiment would not be possible with δ-Bi2O3 because of its volatility in the ionic conducting temperature regime. Our QENS results thus

g (Q , ω) =

⎡ ⎛ ω ⎞⎤ ω S(Q , ω)⎢1 − exp⎜ − ⎟⎥ 2 ⎢⎣ Q ⎝ kBT ⎠⎥⎦

(5)

followed by integration over Q. Figure 5a shows the experimental GDOS measured at 730 °C using an incident neutron wavelength λ of 6 Å. These data can be compared to the simulated GDOS extracted from our MD trajectories, by taking the appropriate slice of the experimentally accessible (Q,ω) space. The partials are weighted by their neutron scattering cross sections and the number of atoms per formula unit. At low-energy transfers, the simulated GDOS is dominated by bismuth, while at higher-energy transfers, it is dominated by oxygen. The largely featureless shape of the GDOS is explained by the high degree of disorder and mobility of the oxygen atoms, which creates a large range of O−O distances in the structure and therefore a continuous distribution of vibrational states. 7412


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ficient DO of 1.7 × 10−5 cm2/s at a simulation temperature of 1100 K. This is consistent with the value of 1.0 × 10−5 cm2/s previously obtained from similar calculations at a lower simulation temperature of 1033 K,40 and others at 1100 K.39 Comparing oxygen MSDs in the ⟨100⟩, ⟨110⟩, and ⟨111⟩ directions (Figure 5b) shows the isotropic nature of the diffusion, consistent with the mean jump length obtained from the cCE fit to QENS data (Figure 4). Finally, the temperature dependence of the self-diffusion coefficient as obtained from the MSD slopes (Figure 5c) yields an activation energy of 0.40 eV, in perfect agreement with the experimental value reported by Harwig and Gerards.34

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CONCLUSIONS We have shown that it is possible to extract quantitative physical parameters concerning the atomistic nature of diffusion in a solid-state ionic conductor from quasielastic neutron scattering data, even when the diffusing species has a significant coherent neutron scattering cross section. Our test case of δBi2O3 has yielded the first direct evidence of liquid-like oxideion diffusion in a solid. The result is consistent with ab initio computational dynamics simulations, the validity of which was supported by comparing the simulated lattice dynamics to data obtained in the same inelastic neutron scattering experiment. We should emphasize that our solution is not unique; rather, it is the best and most reasonable solution that adequately fits our experimental and computational results. In principle, the different jumps that contribute to this weighted average should have different energetics and activation energies. The two most common methods for introducing this would be to fit the data to more than one Lorentzian, with each Lorentzian representing a different process, or to transform it to I(Q,t) and fit it to a stretched exponential, where the stretching parameter gives information about the range of motions. However, both of these options would result in overparameterization of the data, given that it is already adequately fit by one Lorentzian. Additionally, if the latter option were used, transformation to I(Q,t) would result in a reduction in the quality of the data due to the inevitable ringing from the fast Fourier transform. Coherent QENS analysis can now be applied to more complex solid-state oxide ionic conductors of direct practical interest for solid-oxide fuel cells, to inform the rational design of new and improved materials. It should nevertheless be noted that δ-Bi2O3 is the best-case scenario for coherent QENS analysis, because of its exceptionally high conductivity (and therefore strong QENS signal) from a purely coherent scatterer (O) in a very small unit cell (fluorite-type). The next logical steps will be to systematically move to larger unit cells with high conductivity (doped variations of δ-Bi2O3) and lowerconductivity materials with small unit cells (yttria- and ceriastabilized zirconia). The limiting factors will be instrumental: the sensitivity and resolution of the detectors, the experimentally accessible temperature range, and the accessible time window, which must match the scale of diffusion. Ultimately, we hope to apply this approach to mixed coherent−incoherent scatterers. This will be challenging because of the need to separate the components using polarization analysis, further weakening the signal. The case of lithium is the most promising, because its lighter mass as a mobile ion will bring more dynamics into the accessible S(Q,ω) window of INS instruments, and the lower operating temperatures of lithium-ion batteries open a wider range of

Figure 5. Computational results. (a) Experimental vs simulated GDOS, including partial contributions from Bi and O. (b) Meansquare displacements (MSDs) of Bi and O atoms (directional average) as well as directional MSD for O atoms as a function of simulated time interval t. Note that the directional MSDs are so similar that the dashed lines appear to be superimposed. (c) Temperature dependence of oxygen MSDs.

As expected, for the δ phase, neither the experimental nor the simulated GDOS shows any significant temperature dependence (the Bose population factor accounts for the temperature). For the non-ionically conducting β phase, the GDOS shows significantly more features (gray curve in Figure 5a), consistent with its relatively well-ordered oxygen sublattice and consequently better defined vibrational modes compared to those of the disordered δ phase. The excellent agreement between our experimental and simulated GDOS gives us the confidence to look more closely at the details of those simulations and compare them to previous dedicated computational studies. One key parameter frequently reported in the literature is the diffusion coefficient. Per the Einstein relation, diffusivity D is given by

D = lim

t →∞

r2 2dt

(6)

2

where r denotes the mean-square displacement (MSD) of the respective atom, d = 1−3 is the dimensionality of the diffusion process, and t is the simulation time. Figure 5b shows the MSDs extracted from our simulations. As expected, and as previously reported,39,40 the MSD for Bi atom saturates at very low values, corresponding to thermal vibrations around an equilibrium position. In contrast, the linear increase in the MSD of oxygen over the course of the simulation corresponds to spatially unrestricted diffusion, with the slope of the corresponding MSD line yielding an oxygen-diffusion coef7413


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material design possibilities by which to capitalize on the insights gained.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Chris D. Ling: 0000-0003-2205-3106 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank Prof. Gordon Kearley for useful discussions. This work was supported by the Australian Research Council (Grant DP150102863) and the Australian Institute for Nuclear Science and Engineering (Postgraduate Research Award to J.W.).

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Liquid-like Ionic Diffusion in Solid Bismuth Oxide Revealed by

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