Investigation of the Potential Energy Landscape for Vacancy

Feb 12, 2014 - The activation energies for (1) vacancy dissociation from Sc7sites or (2) for the ... (15) This energy is unusually large compared to t...
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Investigation of the Potential Energy Landscape for Vacancy Dynamics in Sc-Doped CeO2 Sabyasachi Sen,* Trenton Edwards, Seong K. Kim, and Sangtae Kim* Department of Chemical Engineering and Materials Science, University of California, Davis, California 95616, United States ABSTRACT: Here, we provide a comprehensive picture of the potential energy landscape (PEL) for oxygen-vacancy migration in Sc-doped ceria (SDC) based on the results from a combined application of 45Sc and 17O nuclear magnetic resonance (NMR) and electrochemical impedance spectroscopy (EIS). The oxygen vacancies in SDC perform rapid symmetry-related jumps in the nearest-neighbor coordination shell of Sc traps as well as hopping from one Sc trap to another over length scales of a few nanometers. The activation energies for these two processes are determined to be 0.4 and 1.2 eV, respectively. The depths of these potential wells are modulated via high-frequency elastic deformation of the lattice, with a characteristic activation energy of ∼0.2 eV. The hopping of vacancies between Sc traps control the ionic conduction process in SDC, and the corresponding time scale is identical to the conductivity relaxation time scale. denoted as Sc7 and Sc8, respectively).11 The characteristic time scale for this hop is dominated by the time a vacancy spends being trapped in the nearest-neighbor coordination shell of a Sc atom, and its activation energy of ∼1.2 eV includes the energy needed to dissociate the vacancy from the neighboring Sc7 site. However, the length scale of this effective hop between a Sc7 and Sc8 pair is determined by their distance of separation in the CeO2 host lattice, which, for typical Sc concentrations of a few cation percent, is more than 1 nm. Therefore, the actual hopping process involves several intermediate steps where the vacancy has to hop in the Sc-free regions of the CeO2 lattice, between the coordination shells of Ce4+ ions. The activation energies for (1) vacancy dissociation from Sc7sites or (2) for the hopping in the Sc-free regions of the CeO2 lattice are not known a priori. These energies and the corresponding time scales are intimately related to the underlying PEL for vacancy hopping. Besides these two dominant components of the PEL for vacancy hopping, recent low-temperature 45Sc NMR spectroscopic studies of SDC by Subbi and co-workers have also indicated a rapid hopping motion of the vacancy within the coordination shell of a single Sc7 site.14 Although no direct NMR line-shape analysis was carried out in these studies to determine the time scales and activation energy associated with this localized hopping process, a tentative and indirect assignment of an activation energy of ∼0.37 eV was made on the basis of 45Sc NMR spin−lattice relaxation results for the Sc7 site.15 This energy is unusually large compared to the typical vacancy-dissociation energies in doped CeO2 and ZrO2 lattices that are on the order of ∼0.6 eV.16 Moreover, the relative degree of coupling between all of these dynamical processes

1. INTRODUCTION Ionic transport plays a key role in controlling a wide range of properties and processes important for applications such as catalysis, batteries, fuel cells, environmental sensors, and resistive random-access memory devices.1−8 For most of these applications, an outstanding need exists for ionically conducting materials with enhanced transport of charge carriers and consequently high conductivities at lower temperatures. The two most important factors that control the hopping transport of charge carriers are their concentration and mobility in the host structure. The effect of charge-carrier concentration on electrical conductivity has been investigated extensively over the last several decades in relation to transport in the bulk as well as near interfaces, and it is well-understood within the framework of microscopic and mesoscopic models of ionic conduction.9,10 In contrast, a fundamental understanding of the controlling factors for charge-carrier mobility in ionic conductors remains rudimentary at best, and it necessitates a detailed knowledge of the interactions between the mobile charge carriers and the potential energy landscape (PEL) provided by the immobile host lattice. Combined applications of high-temperature dopant cation (e.g., 45Sc and 89Y) nuclear magnetic resonance (NMR) spectroscopy and electrochemical impedance spectroscopy (EIS) have recently allowed direct observation of long-range transport of oxygen vacancies in the fluorite-structured lattices of Sc-doped CeO2 and Y-doped ZrO2.11−13 Sc-doped CeO2 (SDC) serves as a model oxide-ion conductor where the vacancies are found to be strongly bound to Sc3+ ions in deep traps (i.e., potential wells). The vacancy-hopping frequencies obtained from NMR and EIS measurements in these studies indicated that the fundamental step for long-range ionic conduction in SDC is an effective hop of an oxygen vacancy between a seven-coordinate Sc site with one oxygen vacancy and an eight-coordinate Sc site with zero vacancy (henceforth © 2014 American Chemical Society

Received: December 20, 2013 Revised: February 11, 2014 Published: February 12, 2014 1918

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data collection. A saturation-recovery pulse sequence was used with a saturation comb of 16 π/2 rf pulses (2 μs), and 16−32 FIDs were averaged and Fourier-transformed to obtain the 17O NMR spectra at different relaxation delays. The 17O magnetization recovery was found to be single exponential at all temperatures, and the characteristic SLR time, T1, was determined by fitting the time dependence of the recovered magnetization, M(t), to the relation M(t) = M∞(1 − exp(−t/T1)), where M∞ represents the fully recovered magnetization. The 17O NMR chemical shifts were externally referenced to tap water (δiso = 0 ppm). EIS measurements were carried out on dense pellets of 0.5 cation % Sc-doped SDC. Detailed sample-preparation procedures can be found in ref 1. Two parallel faces of a pellet were polished and painted with Pt paste (5349 Heraeous, USA). To ensure good contact of the electrodes (Pt) with the sample, the pellet was annealed at 1000 °C for 5 h with heating and cooling rates of 5 °C/min under air. The EIS measurements of the SDC pellet were carried out under air in the temperature range of 250−700 °C using a Novocontrol Alpha AN modulus analyzer in the frequency range of 10−1 to 107 Hz. The fittings of the measured impedance spectra with an appropriate equivalent circuit model were performed using the software Z-View. The frequency-dependent ac conductivity, σ(ω), of SDC is computed over a wide range of frequency, ω, using the values of the real and imaginary parts of the impedance, Z′(ω) and Z″(ω), respectively, as determined from EIS measurements and using the relation

associated with vacancy motion remains unknown to date. Clearly, at the high-temperature limit, the time scales of all atomic/vacancy dynamics should converge with the phonon frequency. However, to the best of our knowledge, establishment of a time scale versus temperature map for these dynamical processes has never been attempted in the literature. Here, we report the results of a study of temperaturedependent vacancy dynamics in SDC as a function of Sc (and hence of vacancy) concentration using a combination of 45 Sc and 17O NMR and EIS to examine the effects of the PEL on vacancy transport.

2. EXPERIMENTAL DETAILS Two SDC samples with 5 and 0.5 cation % Sc were synthesized via a precipitation method using NH4OH(aq) as the precipitating agent and nitrates of the cations as precursors. Details of the synthesis can be found elsewhere.17 The powders were calcined at 700 °C for 2 h under air prior to consolidation into cylindrical pellets via a cold isostatic press at 276 MPa. The green pellets were sintered at 1400 °C for 5 h with heating and cooling rates of 5 °C/min under air. The density of the pellets was determined by Archimedes’ method and was found to be 95% of the theoretical density of ceria. For 17O NMR measurements, a part of the 5 cation % Sc-doped sample was heated in a sealed silica glass tube in 50% 17O-enriched oxygen gas at 1000 K for 12 h. For NMR measurements, sintered pellets were ground in an agate mortar. The desired fluorite cubic crystal structure and phase purity of the obtained powder were verified with powder X-ray diffraction (Scintag XDS-2000), and the Sc contents of the samples were verified using energy-dispersive X-ray spectroscopy in an SEM (FEI XL30SFEG microscope operated at 10 kV of accelerating voltage). 45Sc NMR spectra were collected at a Larmor frequency of 121.49 MHz (11.7 T) using a Bruker wide-bore magnet and a Bruker Avance-500 solid-state NMR spectrometer. High-resolution 45Sc magic-anglespinning (MAS) NMR spectra of similar samples can be found in the literature.11,14 Here, we focus on the temperature dependence of the nonspinning (static) 45Sc NMR line shape of SDC samples. The corresponding variable-temperature static 45Sc NMR spectra of the SDC samples were collected over a temperature range of 160 to 280 K using Bruker 4 and 7 mm triple-resonance probes. The crushed samples were packed into ZrO2 rotors with a Macor cap. Static 45Sc NMR spectra were collected using a 0.4 μs rf pulse (π/10 tip angle) and a recycle delay of 0.1 s. Approximately 4000−16 000 freeinduction decays (FID) were averaged and Fourier-transformed to obtain each spectrum. The 45Sc NMR chemical shifts were externally referenced to an aqueous solution of ScCl3. Sample temperature was controlled by flowing N2 gas that was passed through a heat-exchanger coil submerged in a dewar of liquid N2. Temperatures were calibrated externally using the previously reported temperature dependence of the 1H NMR chemical-shift separation between the OH and CH3 resonances for methanol (CH3OH).18 The high-resolution 17O MAS NMR spectrum of the 17O-isotopeenriched 5 cation % Sc-doped SDC sample was collected using a Bruker 4 mm triple-resonance probe. The crushed sample was packed into a ZrO2 rotor with Kel-F cap and spun at 30 kHz. Single-pulse NMR spectrum was collected using a solids π/10 rf pulse (0.23 μs) and a recycle delay of 0.25 s; 2056 FIDs were averaged and Fouriertransformed to obtain the 17O NMR spectrum. The high-temperature (up to 823 K) 17O NMR spin−lattice relaxation (SLR) data were collected on this sample using a high-temperature MAS probe (Doty Inc.). The powdered sample was loaded into a boron nitride capsule that was inserted into a 7 mm Si3N4 rotor and spun at spinning rates of between 2 and 3 kHz. N2 gas boil off from a high-pressure liquid N2 dewar was used for spin and temperature control of the sample. The temperature of the probe was calibrated externally using the temperature dependence of the 63Cu chemical shift of CuBr.19 The sample temperature was increased from 298 to 873 K stepwise and was allowed to reach equilibrium at each temperature for 10 min before

σ(ω) =

⎛L⎞ Z′(ω)2 + Z″(ω)2 ⎜ ⎟ ⎝ A⎠

where L and A denote the sample thickness and the electrode area, respectively. The σ(ω) of SDC presents two distinctive regions over the frequency range of interest, as seen in Figure 2, that can be described by the Almond−West expression20

σ(ω) = σdc{1 + (ω /ω h)n } where σdc and ωh denote the bulk dc conductivity and the average hopping frequency of oxygen vacancies, respectively, and n is a fitting parameter. This expression implies that σ(ω) = σdc when ω ≪ ωh, whereas σ(ω) = σdc(ω/ωh)n if ω ≫ ωh. The σ(ω) data at various temperatures have been fitted to this expression to determine the temperature dependence of σdc and ωh in SDC.

3. RESULTS AND DISCUSSION Figure 1 shows the 45Sc static NMR spectrum of the 0.5 cation % Sc-doped SDC collected at 160 K. At such low temperature, the 45Sc static NMR line shape of the Sc8 site is a symmetric Gaussian centered at an isotropic shift δiso = −43 ppm with negligible quadrupolar broadening, consistent with the cubic symmetry of such sites in the fluorite structure of CeO2 lattice. In contrast, the 45Sc static NMR line shape of the Sc7 site is controlled by chemical-shift-anisotropy (CSA)-related broadening that displays a nearly uniaxial symmetry for the CSA tensor (Figure 1). This line shape for the 0.5 cation % Sc-doped SDC sample can be simulated well with the three principal components of the chemical-shift tensor: δ11 = 29, δ22 = 27, and δ33 = 2 ppm (δiso = 19.3 ppm). The nearly uniaxial symmetry of the CSA tensor implies that the unique axis of symmetry of this tensor is most likely oriented along the line joining the central Sc atom with the vacancy in the nearest-neighbor shell. Integration of these line shapes yields relative fractions of ∼55% Sc7 and 45% Sc8 in these SDC samples, which are consistent with all of the oxygen vacancies in the lattice being associated with Sc atoms as nearest neighbors. These results are in excellent agreement with those reported in a recent study by Subbi and co-workers.14 A comparison of the 45Sc static line shapes of the Sc7 site in the two SDC samples (Figure 1, inset) indicates that although the line shape for the SDC sample with 1919

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occupying the adjacent corners of the octahedron (cube). Such special arrangements of oxygen atoms may result from relaxation of the coordination polyhedron of Sc upon introduction of a vacancy and can account for the lack of quadrupolar broadening associated with the Sc7 site. The temperature dependence of the 45Sc static NMR line shapes for the Sc7 sites in the two SDC samples are shown in Figure 2. Increasing the temperature from 160 to 280 K results

Figure 1. 45Sc static NMR spectrum (bottom) of a 0.5 cation % Scdoped sample at 160 K. Corresponding Sc7 and Sc8 environments for the two resonances are shown schematically, where Sc and O atoms are shown in purple and yellow, respectively, and the open circle with dashed outline on Sc7 represents an oxygen vacancy. The uniaxial CSA tensor for the Sc7 line shape is shown to the left of the spectrum where the unique axis of symmetry is along the line joining the central Sc with the vacancy (see text for details). Inset (top left) shows an expanded view comparing of the Sc7 resonance line shape between the 0.5 and 5 cation % Sc-doped samples.

Figure 2. Temperature dependence of the 45Sc static NMR line shape for the Sc7 site in 0.5 (left) and 5 (right) cation % Sc-doped samples. The arrow indicates accentuated intensity near the isotropic shift in the Sc7 line shape of the 0.5 cation % Sc-doped sample at 200 K. This increased intensity is indicative of symmetry-related jumps of highsymmetry molecules.

0.5 cation % Sc can be simulated well with a single CSA tensor the line shape for the sample with 5% Sc requires consideration of a distribution of CSA parameters. This result is suggestive of increasing site disorder and appearance of a distribution of site symmetry for the Sc7 sites in SDC as the concentration of Sc (and that of oxygen vacancies) increases in the SDC lattice. This site disorder is possibly a result of a nonlocal distortion of the CeO2 lattice because of the incorporation of a substantial concentration of Sc−V•• O pairs. It is rather interesting to note that the emergence of a CSA powder pattern for the Sc7 site, typical for spin-1/2 nuclides, is unusual for a quadrupolar nuclide such as 45Sc (I = 7/2) where quadrupolar broadening typically dominates the line shape. This lack of quadrupolar broadening is only possible if the trace of the electric-field gradient (EFG) tensor at the Sc7 site is practically zero. The EFG is manifest from both the electronic charge-density distribution around the nucleus and the arrangement of neighboring ions, or point charges. The negligible EFG at the Sc8 sites is thus consistent with the fact that these Sc atoms replace Ce at sites of cubic symmetry in the CeO2 lattice and is surrounded by a fully occupied oxygen nearest-neighbor shell. However, it is intuitively expected that by incorporating a vacancy in the nearest-neighbor shell of Sc atoms to create a Sc7 site would destroy the cubic site symmetry and thus introduce a nonzero EFG. However, it has been shown that certain unique noncubic nearest-neighbor configurations may also yield zero EFG at the site of the central atom.21 One such scenario is a 4 + 3 configuration of the seven oxygen atoms in the nearest-neighbor shell of the Sc7 site where the nearest-neighbor coordination polyhedron can be decomposed into a cube and an octahedron with 4 (3) oxygen atoms

in motional narrowing of the CSA powder pattern for the Sc7 site because of a dynamical averaging of the CSA interaction (Figure 2). The corresponding static 45Sc NMR powder pattern for this site collapses to a Lorentzian peak centered at the isotropic chemical shift for Sc7 at higher temperatures. This dynamical averaging of the CSA can be related to a vacancyhopping process within the coordination shell of the Sc7 sites that results in rapid time-dependent reorientation of the CSA tensor. These dynamical changes in the 45Sc line shapes are found to be completely reversible upon cooling and reheating of the sample. The temperature-dependent 45Sc static NMR line shapes of the Sc7 site in the 0.5 cation % Sc-doped SDC sample were simulated (Figure 3) using a model of isotropic reorientation of the 45Sc CSA tensor, resulting in a random exchange among N different orientations under the rigid-lattice (T = 160 K) powder pattern. The analytic expression for the resulting line shape is given by the real part of g(ω),22 where 1 L g (ω) = N 1 − (L /τjump) and L=

∑

[i(ω − ωj) + 1/T2j + N /τjump]−1

j = 1, N

In these expressions, ωj is the frequency, T2j is the reciprocal of the intrinsic line width corresponding to orientation j, and 1/ 1920

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Figure 4. Temperature dependence of τh (red circles) and τjump (black squares) for the 0.5 cation % Sc-doped sample. Straight lines through the data points are linear least-squares fits. Green circle represents the correlation time for 45Sc NMR SLR of the Sc7 site in a sample of similar composition reported by Subbi et al.23

Figure 3. Experimental 45Sc static NMR line shape for the Sc7 site in a 0.5 cation % Sc-doped sample at the temperatures indicated (left) and corresponding simulated spectra (right). The frequencies of isotropic rotational reorientation used to simulate these line shapes are given alongside of each simulated spectrum. See text for details of the simulation procedure.

of the t1 minimum reported in this study where ωτNMR ∼ 1 (ω being the resonance frequency of the nuclide under observation), shows excellent agreement with the τ jump predicted at this temperature upon extrapolation of the experimental data presented in Figure 4. Therefore, the SLR of the Sc7 site is most likely controlled by the symmetry-related jumps of a bound vacancy in the coordination shell of the Sc atom. The temperature dependence of the average time scale of hopping of oxygen vacancies between Sc traps, τh = (ωh)−1, for the 0.5 cation % Sc-doped SDC sample, as obtained from the EIS results, is shown in Figure 5. The corresponding activation energy is ∼1.2 eV and was found to be the same as that of σdc. A similar activation energy was also obtained for 5 cation % Scdoped SDC sample in a previous study.11 This agreement is consistent with the expectation that hopping between Sc3+ trap sites controls the ionic conduction process in these materials and the conductivity relaxation time scale is identical with the time scale of vacancy hopping between Sc traps. Further support of this hypothesis comes from the excellent agreement between τh determined in this study with the virtual exchange frequency between Sc7 and Sc8 sites that can be obtained from the high-temperature 45Sc NMR line shape reported by Subbi et al.19 on a sample of similar composition where the Sc7 and Sc8 NMR signals show the onset of coalescence (Figure 5). Assuming a random distribution of Sc dopants in the CeO2 lattice, the average separation, d, between such traps is expected to be ∼14 and 25 Å, respectively, for the 5.0 and 0.5 cation % Sc-doped SDC samples. If the effective diffusivity of vacancy motion in ceria lattice remains unchanged for Sc doping levels of up to 5 cation %, then the effective vacancy-hopping time scale, τh, between Sc traps should scale as the square of the intertrap distance (i.e., τh ∼ d2). Hence, the vacancy-hopping time scale for the 0.5 cation % Sc-doped SDC sample is expected to be 3 times longer than that for the 5.0 cation % Scdoped SDC sample. A comparison of the vacancy-hopping time scales, τh, for these two samples, as obtained from the EIS data, shows this to be indeed the case (Figure 5). A comparison of the temperature dependence of the time scales for τh and τjump, as shown in Figure 4, indicates that extrapolation of both of these time scales to infinite temperature under the assumption

τjump is the frequency of the reorientational exchange of the CSA tensor. In this analysis, the frequencies, ωj, corresponding to 400 orientations (N) were generated by taking that many angular steps through the expression for the uniaxial powder pattern. The value of T2j was kept constant at 0.9 ms for all orientations in all of the simulations. A single-average temperature-dependent tumbling frequency, τjump−1, was used to simulate all line shapes (Figure 3). It should be noted that although the agreement between the experimental and the simulated line shapes is generally good at all temperatures, some discrepancies exist at intermediate temperatures near 200 K where the experimental line shape shows an accentuated intensity near the isotropic shift. This increased intensity near the isotropic shift is the hallmark of symmetry-related jumps typically observed in high-symmetry molecules.23,24 This is a natural consequence of the fact that as the nearest-neighbor vacancy exchanges position with the oxygen atoms in the coordination polyhedra of Sc7 sites, it results in jumps of the unique axis of the CSA tensor between symmetry-related positions in the crystal lattice. Although such a jump model cannot be used without prior knowledge of the symmetry of the Sc7 coordination polyhedra, including oxygen and vacancy positions, it has been shown in the literature that fairly accurate jump frequencies can be obtained from lineshape simulation on the basis of a liquid-like model of isotropic reorientation of the CSA tensor.23,24 This is particularly true for jumps between sites related by cubic symmetry in the fluorite lattice. The temperature dependence of the time scale, τjump, for this vacancy jump process is shown in Figure 4 as an Arrhenius plot. The corresponding activation energy was found to be ∼0.42 eV. This activation energy is in good agreement with that reported by Gerhardt et al. for dielectric and anelastic relaxation process in SDC that was ascribed to jumps of bound vacancy around Sc sites.25 A similar activation energy (∼0.37 eV) was also reported by Subbi and co-workers15 for NMR SLR of the Sc7 site in SDC at T ≥ 250 K. In fact, the correlation time for the 45Sc NMR SLR for this site, as obtained from the location 1921

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Figure 6. 17O MAS NMR spectrum of the 5 cation % Sc-doped SDC sample. Inset: magnified view showing the presence of a weak second resonance near ∼824 ppm in addition to the main peak at ∼877 ppm.

Figure 5. Bode plot displaying frequency dependence of σ(ω) of the 0.5 cation % Sc-doped sample at different temperatures. Crosses denote average oxygen-vacancy hopping frequency, ωh, at different temperatures. Inset: temperature dependence of the oxygen-vacancy hopping time scale, τh =(ωh)−1, for the 0.5 cation % Sc-doped sample measured in this study (red circles). The blue square represents the oxygen-vacancy hopping frequency estimated from the high-temperature 45Sc NMR line shape of a sample of similar composition reported by Subbi et al.22 The solid line through the data points is a linear leastsquares fit. The solid line immediately below represents temperature dependence of τh for the 5 cation % Sc-doped SDC sample determined in a previous study.

Figure 7. Temperature dependence of 17O T1 of the 5 cation % Scdoped SDC sample. Dashed curve is 17O T1 calculated using τh as the correlation time for EFG fluctuation and the BPP model. The temperature dependence of τh is taken from data in Figure 5. Solid curve is 17O T1 calculated using the same model but with an activation energy of 0.2 eV for the correlation time τNMR for EFG fluctuation and constraining the location of the T1 minimum at 770 K where ωτNMR ∼ 1 (see text for details).

of a temperature-independent activation energy yields a time scale of ∼1014 s, which corresponds closely to phonon frequencies. This result suggests that the attempt frequencies for both the local vacancy jump and long-distance hopping processes are practically identical and correspond to the atomic vibrations in the lattice. The 17O MAS NMR spectrum of the 5 cation % Sc-doped SDC sample is shown in Figure 6. This spectrum is characterized by a strong symmetric resonance centered at ∼877 ppm, corresponding to oxygen atoms with 4 Ce nearest neighbors, O(Ce4),26 and a significantly weaker peak centered at ∼824 ppm that presumably corresponds to oxygen sites with 3 Ce and 1 Sc nearest neighbors, O(Ce3Sc1). Integration of the corresponding peak areas indicate that the O(Ce3Sc1) environment constitutes ∼6% of the total oxygen sites, consistent with that expected from such low-doping levels where pairing of Sc atoms and formation of O(Ce2Sc2) environments would be unlikely in the lattice. The temperature dependence of the 17O NMR SLR time T1 for the O(Ce4) site is shown in Figure 7. The 17O T1 decreases monotonically and shows a local plateau near 770 K, beyond which it decreases again with further increase in temperature to 873 K. This result implies the presence of two dynamically distinct processes that control the 17 O SLR in SDC in the high- and low-temperature regimes, consistent with results reported in previous studies of 17O NMR SLR in doped ceria.26,27 The 17O SLR in doped ceria results from dynamical processes that give rise to fluctuation of

the EFG at the site of the oxygen nuclides. It is believed that in the high-temperature regime the 17O SLR is controlled by EFG fluctuations resulting from long-distance vacancy hopping associated with ionic conduction because the activation energy for the SLR in this regime is similar to that of dc conductivity.26 However, in the low-temperature regime, the EFG fluctuation responsible for 17O SLR results from a dynamical process that is faster and has lower activation energy compared to those characteristic of the long-distance vacancy hopping or conductivity relaxation. The exact nature of this dynamical process, however, has remained unclear. Unfortunately, because of experimental limitations, we did not observe the hightemperature relaxation regime for the 5 cation % Sc-doped SDC sample in Figure 7. However, the 17O T1 in this regime can be simulated using the classical BPP model and τNMR = τh as the correlation time for EFG fluctuation using the expression28 ⎡ ⎤ 4τNMR τNMR 1 ⎥ = C⎢ + 2 2 2 2 T1 1 + 4ω τNMR ⎦ ⎣ 1 + ω τNMR 1922

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Article •• dissociation of a Sc−V•• O pair and a Ce−VO pair, the time scale for the latter process will be orders of magnitude faster than that for the former process. There is a finite probability that the vacancy may return to its original site, which could presumably be facilitated via rapid elastic deformation of the lattice that can modulate the depths of these wells by as much as ∼0.2 eV.

In this expression, ω is the angular Larmor frequency of the 17O nuclide, and the value of C was constrained to 109 s−2, typical for doped ceria with similar dopant concentrations. The result shown in Figure 7 demonstrates that the 17O T1 in the lowtemperature regime has negligible contribution from the hightemperature dynamical process. The activation energy of the low-temperature 17O T1 is ∼0.2 eV (Figure 7). This is lower than the value of ∼0.38 eV observed for 17O SLR in 5 cation % La-doped ceria by Heinmaa et al.,26 but it is similar to that (0.19 to 0.23 eV) observed by Gerhardt et al.25 in 2 cation % Sc-doped SDC for the dynamical process responsible for dielectric and anelastic relaxation. Moreover, considering the location of the low-temperature T1 minimum in Figure 7 to be ∼770 K where ωτNMR ∼ 1 (Figure 7), an extrapolation of the corresponding correlation time to near ∼130 K using an activation energy of 0.2 eV yields a correlation time for this process of ∼10−3 s, consistent with the dielectric relaxation results. The low-temperature dielectric relaxation results of Gerhardt et al.25 suggest that the associated dynamical process involves less than a full atomic jump. From the comparison between the time scales of the various dynamical processes in Figure 4, it is tempting to hypothesize that τNMR in the lowtemperature regime is associated with EFG fluctuation resulting from elastic deformations of the lattice that happens at a much faster rate compared to the vacancy-jumping and -hopping processes and may serve as a precursor to the latter processes. When taken together, the results presented in this work yield a comprehensive perspective of the PEL governing oxygenvacancy transport and dynamics at relatively low-doping levels (≤5 cation %) in SDC where vacancy and dopant clustering are negligible. This energy landscape is shown in Figure 8. The

4. CONCLUSIONS Results from a combined application of NMR and EIS provide an important mechanistic understanding of ionic transport in SDC. The oxygen vacancies perform hierarchical dynamics in a complex PEL that involves symmetry-related jumps of a bound vacancy, intertrap long-distance hopping, and modulation of the potential wells via elastic deformation of the lattice. The activation energies for these processes are 0.4, 1.2, and 0.2 eV, respectively. The event of intertrap hopping is responsible for dc conductivity, and its time scale can be obtained from dc-toac crossover frequency in impedance spectra that coincides with the exchange frequency between Sc7 and Sc8 sites in the 45Sc NMR line shape. The characteristic length scale for successful hopping responsible for dc conductivity is determined by the intertrap distance, whereas the characteristic time scale is controlled by the time that an oxygen vacancy remains trapped near a Sc7 site in between successful hops.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (S.S.). *E-mail: [email protected] (S.K.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS S.S. was supported by a grant from the National Science Foundation (NSF GOALI 1104869). S.K. is grateful for the support by the U.S.−Israel Binational Science Foundation (BSF 2012237).

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REFERENCES

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Figure 8. Schematic representation of the potential energy landscape for hopping transport of oxygen vacancies in Sc-doped ceria (see text for details).

oxygen vacancy is strongly bound to the Sc traps and performs rapid symmetry-related jumps between the eight nearestneighbor sites with an activation energy of ∼0.4 eV. Every once in a while, the vacancy breaks free of the dopant trap and performs random walk through a Sc-free region of the ceria lattice until it finds another Sc trap. In the Sc-free region of the ceria lattice, the potential wells are expected to be significantly shallower (∼0.6 eV) for the vacancy compared to the deep potential well for a Sc−V•• O pair (∼ 1.2 eV), primarily because of the nominal lack of Coulombic interaction between the Ce− V•• O pair. Therefore, considering the same attempt frequency for 1923

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Chemistry of Materials

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dx.doi.org/10.1021/cm4041852 | Chem. Mater. 2014, 26, 1918−1924