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Local structure and oxygen ion dynamics in La doped ceria: 17O NMR study
Solid State Ionics 181 (2010) 1309–1315
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Solid State Ionics j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / s s i
Local structure and oxygen ion dynamics in La doped ceria:
17
O NMR study
Ivo Heinmaa ⁎, Tanel Joon, Helgi Kooskora, Jüri Pahapill, Juhan Subbi National Institute of Chemical Physics and Biophysics, 23 Akadeemia tee, Tallinn 12618, Estonia
a r t i c l e
i n f o
Article history: Received 3 March 2009 Received in revised form 19 July 2010 Accepted 22 July 2010 Keywords: Doped CeO2 17 O MAS NMR Spin-lattice relaxation Oxygen diffusion
a b s t r a c t The local order and oxygen dynamics in La doped ceria (LDC) has been studied by 17O NMR techniques. High resolution 17O MAS NMR spectra show several oxygen resonances which are assigned to the lattice sites with 0, 1 and 2 nearest neighbor (nn) La3+ ions. The site with 1 nn La contributes two different lines depending on the presence or absence of oxygen vacancy. The sites with 2 nn La ions are represented by one single line, which indicates that two neighboring La3+ ions always bind one vacancy. Spin-lattice relaxation (T1) measurements on static samples were carried out between 293 K and 1073 K. The temperature dependence of T1 has been interpreted assuming two independent relaxation paths. The relaxation below 600 K is assigned to the oxygen dynamics in the lattice without involving vacancy diffusion. The relaxation at a higher temperature is interpreted to be caused by the oxygen hopping between vacant and occupied sites. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Oxygen ion conductors have many important technological applications. They can be used in devices like solid oxide fuel cells (SOFC), oxygen pumps, sensors, etc. [1–4]. Ceria (CeO2), when doped with cations of lower valence than the host cation, is one of the best solid electrolytes [5–7]. Due to relatively simple fluorite-type crystal structure (see Fig. 1) it is an attractive model compound for theoretical calculation of the electronic structure, the vacancy migration parameters and ionic conductivity [8–10]. Systematic studies of the ionic conductivity of rare earth doped ceria MxCe1 − xO2 − x/2 [11–13] show that the conductivity depends on the concentration and on the size of the doped M3+ ion. The highest conductivity is obtained for Sm3+ and Gd3+ doped ceria at x around 0.2 [12]. Fuda et al. [14,15] demonstrated that oxygen 17O nuclear magnetic resonance (NMR) spin-lattice relaxation (T1) measurements reveal activation energy (Ea) and the correlation time (τc) of the local oxygen motion in Y doped ceria (YDC). 17O is a spin-5/2 quadrupolar nucleus and its most effective relaxation mechanism is caused by fluctuations of the local electric field gradient (efg) at the nucleus. Since ionic hopping in solids always results in the efg fluctuations, the T1 measurements provide unique experimental data about the ionic hopping rates. For YDC the authors reported interesting T−1 vs. 1 temperature (T) curves with two maxima. Usually a maximum in such a curve occurs at a temperature where characteristic temperature activated fluctuation rate 1/τc reaches the nuclear resonance (Larmor) frequency ω0. Two maxima in the curve would mean two different
⁎ Corresponding author. E-mail address: ivo@kbfi.ee (I. Heinmaa). 0167-2738/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.ssi.2010.07.027
fluctuation processes. Fuda et al. assigned the relaxation maximum at T = 600 K to the mechanism of oxygen jumps via vacancies. The activation energy of the process was determined Ea = 0.49 eV and, surprisingly, the hopping rate 1/τc was found to be independent of dopant concentration. The relaxation process above T = 600 K was ascribed to the motion of thermally activated Frenkel type point defects. Later Adler et al. [16] calculated 17O T1 values for YDC using the dynamic Monte Carlo method. Their numerical simulations suggested that the two relaxation maxima could be ascribed to a single motion of oxygen vacancies. The main idea in their model was that at a low temperature the efg fluctuations at an oxygen nucleus in the YDC lattice are mainly caused by the hopping of the neighboring vacancies, while the hopping of the oxygen ion itself is too slow. At a higher temperature the efg fluctuations due to the hopping of vacancies are too rapid compared to the Larmor frequency and the effective relaxation is caused by the hopping of the oxygen ions. The two characteristic frequencies were assigned to the vacancy jump rate, 1/τvac, and to the oxygen jump rate 1/τox. In the case of ion diffusion via vacancies the oxygen hopping rate is N/n times slower than the vacancy hopping rate, where n is the number of vacancies and N is the number of oxygen ions per unit volume. Although the Monte Carlo calculations [16] gave qualitative agreement with experimental data, the authors found that the two relaxation maxima do not correspond to the actual oxygen/vacancy ratio. In order to get better agreement with the experimental data, they had to introduce the relatively large Sternheimer antishielding factor γ∞ = −185. The number (1 − γ∞) shows how many times the actual efg value at the nucleus is larger than that calculated from the distribution of ionic charges in the lattice. A table value for 17O is γ∞ = −13.8 [17]. A well known issue in the studies of oxygen dynamics in doped ceria is that the NMR relaxation gives much smaller activation energy value than the number obtained from conductivity measurements.
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enrichment to the ~5% level was carried out by heating the samples at 800 °C, 10 h, in 17O enriched oxygen atmosphere. 17 O MAS NMR spectra were recorded on AVANCE-II-600 at 14.1 T magnetic field (17O resonance frequency 81.4 MHz) using home built MAS probe and 4 mm zirconia rotors. The spectra were referenced to H2O resonance frequency. Simple one pulse acquisition sequence was used, with a 1.4 μs excitation pulse (1/3 of the 90 degree pulse for H2O). Temperature dependencies of 17O spin-lattice relaxation of the static LDC samples were measured at two magnetic fields 8.5 T (17O resonance frequency 48.8 MHz) and 4.7 T (27.1 MHz) using saturation recovery pulse sequence. The measurements were carried out on Bruker AMX 360 spectrometer using a home built high temperature probe. To avoid possible changes in the samples at high temperatures the powder samples were sealed into 5 mm od. quartz tubes. 3. Results and discussion Fig. 1. Fluorite type crystal structure of CeO2. Every Ce ion is surrounded by eight oxygen ions; every oxygen ion is surrounded by four nearest neighbor cerium ions.
For YDC at a low doping level, x = 0.1%, the conductivity measurements give Ea = 0.88 eV [11], much higher than the NMR number Ea = 0.49 eV [14] noted above. For yttria-stabilized zirconia (YSZ) the difference between the activation energy from conductivity measurements and from the NMR relaxation is even larger. Reported activation energy values for YSZ from conductivity measurements are between 1.17 eV and 1.33 eV [18], about three times higher than the value ~0.3 eV from NMR relaxation [19]. Much closer value of the activation energy (0.7 eV) was obtained from the NMR line shape analysis [20]. It is argued that the activation energy from NMR is much lower, because NMR relaxation is sensitive to local single ion hops, whereas the conductivity probes the long range transport where the highest barrier may determine the conductivity. Indeed, in most of the ionic conductors the NMR data yield much smaller activation energy than the conductivity measurement (see review [21]), except in some cases e.g. doped BaF2 (fluorite structure) where the NMR relaxation and conductivity data are shown to be in good agreement [22]. In this paper we present 17O NMR data of La doped ceria (LDC) LaxCe1 − xO2 − x/2. The main aim of the study was to determine the doping induced changes in the local structure of ceria by high resolution magic angle spinning (MAS) NMR spectra and the activation energy for the vacancy jump by recording of the temperature dependence of T1. The activation energy for vacancy jump in weakly doped LDC is not well established and quite different values between Ea = 0.77 eV (x = 0.003) [11] and 1.03 eV (x = 0.05) [23] can be found. At higher doping, x = 0.2 [13], YDC has considerably lower activation energy than LDC (0.73 eV and 0.92 eV, respectively). Different vacancy migration parameters have been explained by different local distortion of the lattice [8]: a smaller Y3+ ion which substitutes Ce4+ ion in the CeO2 lattice causes local shrinking of the lattice whereas a larger La3+ ion causes local expansion of the lattice. Thus, with comparison of T1 curves of LDC to that of YDC we expect to see differences in the oxygen dynamics.
3.1.
17
O high resolution MAS NMR spectra
17 O MAS NMR spectra of low doping level samples are given in Fig. 2. Due to high symmetry of the CeO2 crystal structure the electric field gradient (efg) tensor in the undoped crystal is zero. Therefore the main resonance line at 876.5(1) ppm of LDC at low doping levels is extremely narrow (FWHH = 0.5 ppm). Careful inspection of the two spectra allows detecting of additional three small lines at 878.0, 875.7 and 874.5 ppm at the noise level (denoted by arrows in Fig. 2). The intensities of the small resonances have a tendency to grow with higher doping level. Although the relative intensities of the lines are depending on the base line correction the computer fit gives the small peak total contribution as 2.3 and 5.5% in the spectra of 0.2%LDC and 0.5%LDC samples respectively. We believe that these small peaks are caused by La3+ ions in the next-nearest neighborhood of the oxygen. In fluorite structure (see Fig. 1) every oxygen site in the LDC
2. Experimental Four samples of LaxCe1 − xO2 − x/2 with doping level x = 0.002, 0.005, 0.052 and 0.116 (in the following we use notation 0.2%LDC, 0.5%LDC, 5.2%LDC and 11.6%LDC) were synthesized as described in Ref. [24]. Appropriate amounts of La and Ce nitrate solutions were added to neutralized oxalic acid solution. After precipitation the product was washed, dried and subsequently sintered at 1200 °C (15 h). Lanthanum content of the LDC powders was determined by inductively coupled plasma (ICP) mass spectrometry. Oxygen 17O
Fig. 2. 17O MAS NMR spectra of LaxCe1 − xO2 − x/2 samples at given low doping levels. The spectra are recorded at 14.1 T field with the sample spinning speed of 10 kHz. The arrows refer to the small peaks at the noise level.
I. Heinmaa et al. / Solid State Ionics 181 (2010) 1309–1315
Fig. 3. 17O MAS NMR spectra of LaxCe1 − xO2 − x/2 samples with x = 0.052 (top), and x = 0.116 (bottom). Different components of the spectrum are noted as A, B, C, and D. Thin lines denote corresponding Lorentzian component from the computer fit. Asterisks mark spinning sidebands.
lattice has 4 nearest (nn) Ce4+ ions at 2.34 Å distance. The next neighborhood contains 12 Ce ions (nnn) at 4.48 Å. At given low doping levels the probability to find an nn La3+ ion is very small: 0.008 and 0.020 for 0.2%LDC and 0.5%LDC, respectively. Besides, we see below that nn La3+ ions induce considerable shift and broadening of the line; therefore these peaks cannot be associated with oxygen whose nearest neighbor is La3+. The probability to find a La3+ ion as nnn is 0.024 and 0.058, in 0.2%LDC and 0.5%LDC respectively. Thus, the tiny peaks could belong to the oxygen sites having La3+ ion as the next-nearest neighbor. However, we wanted to notify that the La3+ ion in the next-nearest neighborhood causes the change in the peak position at most 2 ppm, which is more than an order of magnitude smaller (see below) local field distortion than that caused by La3+ ion in the nearest neighborhood. The resonance lines in 17O MAS NMR spectra of higher La content samples are much broader (see Fig. 3) and additional peaks denoted B, C and D appear at a lower chemical shift. Since 17O is a spin-5/2 nucleus, the NMR line of the powder sample can show additional singularities due to the second order quadrupolar interaction (see references in [17]). In this case the line width and the position of the singularities are strongly field-dependent. We did record the spectrum of 11.6%LDC at 8.5 T field and found that the peak positions and relative intensities of the components in the spectrum did not depend on the
Table 1 Peak positions and relative intensities in
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magnetic field. Consequently, different peaks in the spectrum correspond to different sites in the lattice. The peak positions and relative intensities of the components are given in Table 1. Recently Kim and Stebbins [25] published the first high resolution 17 O MAS NMR spectra of YDC. They found almost similar lines in the spectrum, which they assigned to local arrangements around oxygen with 0, 1, 2 or 3 Y3+ ions substituting Ce4+ ions in the nearest neighborhood. Here we follow a similar approach, although the NMR intensity of a quadrupolar nucleus is not a good parameter since it usually depends on the excitation pulse length and quadrupolar coupling strength. Assuming that La3+ ions substitute Ce4+ ions randomly, one has 5 different oxygen local configurations with 0, 1, 2, 3 or 4 La3+ ions as the nearest neighbors. We labeled these sites as Ce4La0, Ce3La1,…, Ce0La4, respectively, and in Table 2 relative populations of the configurations in present LDC samples are given. The numbers in Table 2 show that the 5.2%LDC sample has only two configurations (Ce3La1 and Ce2La2) with a probability higher than 10−3, besides the configuration Ce4La0. Accordingly, line A belongs to the site Ce4La0 and the lines B and C to the sites Ce3La1. The intensity of the site Ce2La2 is below the detection level. The two sites B and C, in analogy to the YDC case [25], can be explained by the presence of a vacancy. One of the lines (presumably the broader line B) belongs to the oxygen site where the neighboring La3+ ion is accompanied by oxygen vacancy, we notify it as [Ce3La1]+, because the net charge of the complex is positive relative to the undisturbed lattice. The other resonance line (line C) belongs to the configuration [Ce3La1]−, where the La3+ ion is not accompanied by the vacancy. We admit that the probabilities of the sites and relative intensities of the lines do not perfectly agree. The intensity ratio favors line A. Quite obvious reason for the mismatch is caused by different quadrupolar coupling at these sites. In the case of large quadrupolar coupling (compared to the sample spinning rate) mostly central (−1/2 ↔ + 1/2) transition of I = 5/2 nucleus contributes to the spectrum, whereas in the case of small quadrupolar coupling, all transitions add to the same line. In the present case we are somewhere between these extremes. Remarkable spinning sidebands of the line A (see Fig. 3) indicate nonzero quadrupolar coupling for this site, but it should be much smaller than the coupling at site B or C where the symmetry of the local charge configuration is definitely not cubic. Assignment of the lines in the spectrum of the sample 11.6%LDC is done in a similar manner. Line A belongs to the configuration Ce4La0, lines B and C to the site [Ce3La1]+/− and line D we attribute to the configuration Ce2La2. Concerning vacancy distribution we note that the resonance D is a single broad line, which means that two adjacent La3+ ions are always accompanied by the vacancy. Comparing our spectra with that of YDC [25] we see two major differences. At first, the average chemical shift change caused by one nn La3+ ion is about ΔσCeLa = −34 ppm, whereas the average change caused by one nn Y3+ is about ΔσCeY = −60 ppm. The ratio of these numbers roughly corresponds to the ratio of 17O chemical shift differences in CeO2 and four-coordinated oxygen sites in corresponding oxides, i.e. ΔσCeLa / ΔσCeY = (σCeO2 − σLa2O3) / (σCeO2 − σY2O3), where the chemical shift of four-coordinated oxygen in La2O3 is taken σLa2O3 = 584 ppm [26] and the average value in Y2O3 is σY2O3 = 369 ppm [27]. The second major difference in the spectra of YDC and LDC is that the oxygen site Ce2La2 with two nearest La3+ ions shows only one line, whereas the corresponding site in YDC, with two nearest Y3+
17
O MAS NMR spectra of 5.2% and 11.6%LDC samples.
LDC sample
Peak A ppm
I
Peak B ppm
I
Peak C ppm
I
Peak D ppm
I
5.2% 11.6%
878.3(2) 880.4(2)
0.922(2) 0.673(4)
855.4(1) 856.8(3)
0.045(2) 0.15(2)
832.9(1) 836.3(2)
0.033(2) 0.10(2)
– 807.8(8)
– 0.077(6)
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Table 2 Probabilities for oxygen sites having 0, 1…or 4 nearest neighbor La3+ ions. Sample
PCe4La0
PCe3La1
PCe2La2
PCe1La3
PCe0La4
5.2%LDC 11.6%LDC
0.808 0.611
0.177 0.320
0.015 0.063
0.000 0.006
0.000 0.000
ions, gives two lines into the spectrum [25]. This may indicate that in LDC two neighboring La ions always bind one oxygen vacancy, whereas in YDC the two Y ions may or may not have a vacancy in the nearest neighborhood. 3.2. Motional narrowing Existence of different peaks in the room temperature MAS NMR spectrum provides an estimate to the minimum residual time of a vacancy, τvac, in a particular site. If line B (see Fig. 3) is the site [Ce3La1]+, with one nn La3+ plus a vacancy, then after vacancy jump the site becomes [Ce3La1]−, that is nn La3+ without vacancy, represented by line C. According to the general understanding of motional narrowing [28], transfer of the case of infrequent jumping to the case of rapid jumping occurs when τΔω≈ 1, where Δω is the separation of the resonance lines in the absence of exchange motion. The splitting between lines B and C is about Δω/2π = 1000 Hz in 8.5 T magnetic field. Since the lines are clearly separated, the residual time of a vacancy at room temperature is at least τvac N 1.6 × 10−4 s. −1 The hopping frequency of oxygen ions τox can be obtained from the temperature dependence of the line width. The NMR line width of solid powder samples at low temperatures is typically a broad line because the nuclei are located at sites with different local fields. At a higher temperature the ions start to move through the solid causing averaging of the local fields experienced by the nucleus and motional narrowing of the resonance line. The narrowing takes place if the hopping rate of the ions τ − 1 becomes much faster than the rigid lattice line width. Temperature dependence of the NMR line width of the static 0.2%LDC sample is given in Fig. 4. The room temperature line width (half width at half height, HWHH) wA = 300 Hz narrows to the value wB = 105 Hz above T N 700 K. An estimate to the hopping rate can be obtained using a formula given by Gutowsky and Pake [29]: −1
τ
#
! π w2 −w2B = αw tan ; 2 w2A −w2B
ð1Þ
where w is the HWHH of the resonance line, wA is the width of the rigid lattice line, wB is that of the motionally narrowed line and α is a constant of the order of unity. Taking α = 1, it follows from Eq. (1) that the hopping rate becomes equal to the line width at a temperature where −1
τ
1 = w = pffiffiffi 2
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi w2A + w2B :
ð2Þ
Using wA and wB values as given above we get the estimate: −1 τox = w = 225 s−1 at temperature T = 425 K (see Fig. 4.). 3.3. Temperature dependence of the in LDC
17
O spin-lattice relaxation rate
A key experiment for understanding the oxygen dynamics in doped ceria is recording of the spin-lattice relaxation rate vs. the temperature curve. In a classical BPP theory [30] the relaxation rate can be expressed in a form: " −1
T1
=C
# τc 4τc + ; 1 + ω2L τ2c 1 + 4ω2L τ2c
ð3Þ
Fig. 4. Temperature dependence of 17O NMR line width of the static 0.2%LDC sample in 8.5 T magnetic field. Dashed lines are guiding the eye to estimate the oxygen jump rate from the line width at 425 K, see text.
where C is a constant which characterizes the amplitude of the fluctuations of the quadrupolar interaction, ωL is the Larmor frequency and the correlation time, τc, of the fluctuations follows exponential temperature dependence τc = τ0 exp
Ea ; kB T
ð4Þ
where Ea is the activation energy of the process, T is the temperature, and the pre-exponential factor τ0 is the inverse of a trial frequency. If τc is given by Eq. (4), it is straightforward to determine activation energy from the slope in the Arrhenius plot ln(T−1 1 ) vs. 1/T. Furthermore, in the case of a maximum in this plot, one has a unique possibility to determine the absolute value of the correlation time τc almost model free. In Fig. 5 we have plotted the T−1 1 data for LDC samples measured in 8.5 T magnetic field. All T1 values were determined from a single exponential fit to the magnetization recovery. Exponential magnetization recovery was observed in all experiments, in the entire temperature range and it usually means that the relaxation is homogeneous i.e. every observed nucleus in the lattice is influenced by the same fluctuation spectrum, or the spin diffusion in the spin system is fast enough to equalize the inhomogeneous relaxation. The role of spin diffusion can be suppressed by measuring the relaxation in the MAS experiment. We found that the relaxation of lightly doped LDC samples at room temperature at MAS did not change noticeably. The relaxation at MAS of the samples 5.2%LDC and 11.6%LDC was different for different resonance lines. In addition, the magnetization recovery in these samples at MAS could not be described by a single exponential. Thus the relaxation at room temperature of lightly doped ceria is homogeneous, whereas that of heavily doped samples is intrinsically inhomogeneous depending on the local environment of the nucleus. In measurements of static samples the latter inhomogeneity is averaged by spin diffusion.
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(3) eV for process A is close to the value 0.49 eV of the low temperature relaxation process in YDC [14]. The activation energy EBa = 0.96(5) eV for oxygen hopping via vacancy, process B, is probably a good estimate to the activation barrier in lightly doped LDC, well in the range of the numbers from conductivity measurements, Ea = 0.77 eV (x= 0.3%) [11] and 1.03 eV (x= 5%) [23]. Similar to the case of YDC [15], in samples of a higher doping level, the relaxation due to the oxygen hopping through the vacancies (process B) cannot be described by a single activation energy Ea. Following the approach by Fuda et al. [15] we have simulated the curves using a distribution of activation energies ρ(E). The relaxation rate has been calculated as an average rate: −1
T1
= C∫ρðEÞdE
τc 4τc + ; 1 + ðωL τc Þ2 1 + ð2ωL τc Þ2
ð5Þ
where τc(E) was calculated by Eq. (4) and the dependence of the preexponential factor τ0 on E was neglected. Due to the motion of oxygen the magnetization recovery should be still exponential, despite of the distribution of energy barriers. For ρ(E) we have used uniform energy distribution:
ρðEÞ =
Fig. 5. 17O spin-lattice relaxation rate T−1 of LDC samples at 8.5 T magnetic field as a 1 function of inverse temperature. Solid lines are computer simulations with the parameters given in Table 3 (see text).
Fig. 5 shows that at low doping levels the relaxation rate curve has two maxima: at around 600 K and at 1000 K. At higher doping levels the relaxation curve has a similar slope at a low temperature, indicating similar activation energy, whereas at higher temperatures instead of the second maximum we see a broad flat region. The temperature and doping dependence of the relaxation rate are similar to that reported for YDC [14,15]. In comparison with the YDC data the main difference is that in LDC the two maxima are much better resolved. According to the interpretation below, this indicates higher activation barrier for oxygen hopping in LDC. We describe the relaxation data of LDC in assumption of two independent relaxation paths. The one at a low temperature (process A) and the other one at a high temperature (process B). For process A, we note only that it is caused by the local efg fluctuations, the correlation time of which follows the Arrhenius law and it is only weakly depending on dopant concentration. Process B is caused by the efg fluctuations due to oxygen hopping through the vacant sites. The hopping frequency obviously depends on the dopant concentration as can be seen from the change of the high temperature maximum in the relaxation curve. The relaxation of the 0.2%LDC sample is well described by these two independent processes with Eqs. (3) and (4). The computer fit gives two sets of parameters as given in Table 3. The activation energy EAa = 0.45
Table 3 Simulation parameters for the two relaxation paths: activation energies Ea, E1 and E2, the average 〈Ea 〉, pre-exponential term τ0, and fluctuation amplitude parameter of the quadrupolar coupling C. LDC Process A Process B sample Ea τ0 C E1 E2 [eV] [10−13 s] [106 s−2] [eV] [eV]
〈Ea 〉 [eV]
τ0 C [10−13 s] [106 s−2]
– 0.65 0.48 0.45
0.96 0.81 0.68 0.64
1.1(5) 3.2 4.0 5.6
0.2% 0.5% 5.2% 11.6%
0.45(3) 0.43 0.38 0.34
2.5(5) 4.0 13 24
78(2) 180 750 750
0.96(5) 0.96 0.88 0.82
190(20) 580 2500 5000
8 > < > :
1 ; for E1 ≤ E ≤ E2 E2 −E1 0
ð6Þ
otherwise:
Frequency/field dependence of the relaxation rate gives additional dimension for evaluating the relaxation mechanism. According to Eq. (3) one expects T1− 1 ∝ 1/ ω2L dependence at low temperatures, whereas at a high temperature T1− 1 ∝ τc, independent of frequency. Our relaxation measurements at two magnetic fields (the Larmor frequencies ωL/2π = 48.8 MHz and 27.1 MHz) show (see Fig. 6) that the agreement between experimental and simulated curves is remarkably good. The simulation parameters are given in Table 3. The case of uniform distribution of activation energy ρ(E) in diffusion process has been calculated in effective medium approximation [31]. According to this calculation, in the case of not too wide energy distributions, the high temperature value of the diffusion coefficient has Arrhenius type temperature dependence with activation energy equal to the mean value of the barrier 〈Ea 〉. Thus, the average activation energies 〈Ea 〉 for process B in Table 3 give relatively good estimates to the effective values of activation energies for ionic conductivity in LDC samples. 3.4. Two relaxation paths Although the concept of two independent relaxation paths in LDC gives good description of the experimental data, we need to ask about the origin of process A. Which motion in the lattice of ceria is responsible for process A? To clarify the issue we have drawn the temperature dependence of the fluctuation rates of the two processes in 0.2%LDC (Fig. 7) together with the estimates from the other experiments. The oxygen hopping rate from the line-width analysis (see Section 3.2), and from several conductivity measurements clearly indicates that process B can be attributed to the process of oxygen hopping in the lattice. Can we assign process A to the lattice fluctuations caused by the hopping of the distant vacancies as proposed for YDC by Adler et al. [16]? We estimated above the vacancy hopping rate at room temperature for 5.2%LDC to be less than 6000 s−1. This is about an order of magnitude slower than the fluctuation rate of process A. Kim and Stebbins [25] demonstrated that a noticeable change in the MAS NMR spectrum of YDC takes place at temperatures above 380 K. Most probably this change in the spectrum indicates the temperature where the vacancy hopping in YDC exceeds 104 s−1. This estimate is more than two orders of magnitude slower than the fluctuation rate of process A. In addition, above we saw that
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Fig. 6. Computer simulation of the experimental T1 rate data of the LDC sample measured in magnetic fields 48.8 MHz (circles) and 27.1 MHz (squares). The 11.6%LDC sample has been measured only at the 48.8 MHz field. Simulation parameters are given in Table 3.
the high resolution 17O MAS NMR spectrum shows very little changes due to distant vacancies, meaning that small amplitude modulation of the quadrupolar coupling due to hopping of distant vacancies cannot cause effective and homogeneous relaxation. Therefore, assignment of process A to the vacancy migration is not very likely. There are no good candidates for this low temperature fluctuation process. As we saw, this process has a thermally activated nature, every oxygen ion is equally influenced by this process, and it is not migration of the vacant sites. A couple of resonant motions in doped ceria have been detected in electrical relaxation studies [32,33]. Unfortunately, the frequency scale of these motions is very different from that of process A. Recently Yashima et al. [34–36] have carefully analyzed the neutron diffraction patterns of pure and doped ceria. Using the maximumentropy method they discovered structural disorder of oxygen positions even for a pure ceria. They found that in the fluorite-type structure of ceria the regular oxygen site O1 (Wyckoff index 8c) is not completely occupied while some oxygen ions occupy the other site O2 (32f ). Each O1 site is tetrahedrally surrounded by four O2 sites at 1.03 Å distance. At room temperature the neutron diffraction data reveal that 0.012 of O2
sites are occupied [34]. This would mean that about 5% of oxygen ions were not in regular sites. The local symmetry of the site O2 implies nonzero quadrupolar coupling which would show up in the high resolution NMR spectrum as distinct line and broadening due to disorder. Above we demonstrated an extremely narrow MAS NMR line for 0.2%LDC. In the sample of a slightly higher La content the line is noticeably broader. Thus, 17O MAS NMR spectra clearly show that there is not that much disorder even in 0.2%LDC, unless the disorder seen by neutron diffraction was dynamic. In the latter case the O2 sites are occupied for a short time only, short enough to cause motional narrowing of the NMR line (see above) and the disorder detected by neutron diffraction snapshot will not show up in the NMR spectrum. At the same time such hopping between the O1 and O2 sites would be an effective cause for nuclear T1 relaxation. In addition, the relaxation would be equal for every oxygen ion in the lattice and its characteristic temperature dependence would be nearly independent of the doping level in lightly doped samples. Therefore we wanted to attribute the relaxation process A to the back and forth hopping of oxygen ion in b111N direction from the stable O1 site to one of the (metastable) O2 positions. Such interpretation of the NMR relaxation strongly supports
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hopping between occupied and vacant sites through the nearest O2 sites. At low doping level (0.2%LDC) this process is characterized by activation energy Ea = 0.96(5) eV. At higher doping levels the data were described assuming uniform distribution of the activation energy in the range between 0.45 and 0.96 eV.
Acknowledgements This study has been supported by the Estonian Science Foundation grant 8198, by grant SF0690034s09 from the Estonian Ministry of Education and Research and by AS Elcotec.
References
Fig. 7. Temperature dependence of the fluctuation rate of process A (dashed line), that of process B (full line) from the T1 analysis of 0.2%LDC together with the estimates from other experiments: empty triangle — upper limit to the vacancy hopping rate from the MAS NMR spectrum; cross — estimate to the oxygen hopping rate from the temperature dependence of the static line width; oxygen hopping rates calculated from conductivity data: stars — 5%LDC [23]; open pentagrams — 0.3%LDC [11]; full pentagram — 20%LDC [13].
oxygen diffusion schemes in doped ceria through the nearest O2 sites along, b100N, b010N and b001N as proposed in the analysis of neutron diffraction data [35]. 4. Conclusions Different local environments of oxygen ions in the LDC structure were detected by high resolution 17O MAS NMR spectra at room temperature depending on the number of nn La3+ ions. We found that La3+ distribution in the lattice is almost random. At low La concentrations about half of the La3+ ions are not directly bound to the vacancy. At a higher concentration two La3+ ions in adjacent lattice sites always bind one vacancy. Oxygen dynamics in La doped ceria was studied by temperature and frequency dependence of 17O spin-lattice relaxation in the temperature range from 293 K to 1073 K. The analysis of the 17O data was performed assuming two different dynamic processes: A and B. It is found that the low temperature process A is characterized by homogeneous activation energy Ea = 0.45(3) eV, and it is not directly related to the ion diffusion in the lattice. This process is assigned to thermally activated efg fluctuations due to oxygen hopping in the CeO2 lattice between the regular site O1 (site 8c) and metastable site O2 (site 32f ). At a higher temperature the relaxation is dominated by process B. The latter is caused by efg fluctuations due to oxygen
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J.A. Kilner, Solid State Ionics 129 (2000) 13. S.J. Skinner, J.A. Kilner, Mater. Today 6 (3) (2003) 30. N.P. Brandon, S. Skinner, B.C.H. Steele, Annu. Rev. Mater. Res. 33 (2003) 183. J.B. Goodenough, Annu. Rev. Mater. Res. 33 (2003) 91. H. Inaba, H. Tagawa, Solid State Ionics 83 (1996) 1. M. Mogensen, N.M. Sames, G.A. Topsett, Solid State Ionics 129 (2000) 65. J.W. Fergus, J. Power Sources 162 (2006) 30. H. Hayashi, R. Sagawa, H. Inaba, K. Kawamura, Solid State Ionics 131 (2000) 281. H. Yoshida, T. Inagaki, K. Miura, H. Inaba, Z. Ogumi, Solid State Ionics 160 (2003) 109. D.A. Anderson, S.I. Simak, N.V. Skorodumova, I.A. Abrikosov, B. Johansson, Proc. Natl Acad. Sci. USA 103 (2006) 3518. J. Faber, G.C. Roux, A. Sylvestre, P. Abélard, Appl. Phys. A 49 (1989) 225. K. Eguchi, T. Setoguchi, T. Inoue, H. Arai, Solid State Ionics 52 (1992) 165. H. Yoshida, H. Deguchi, K. Miura, M. Horiuchi, T. Inagaki, Solid State Ionics 140 (2001) 191. K. Fuda, K. Kishio, S. Yamauchi, K. Fueki, J. Phys. Chem. Solids 45 (1984) 1253. K. Fuda, K. Kishio, S. Yamauchi, K. Fueki, J. Phys. Chem. Solids 46 (1985) 1141. S.B. Adler, J.W. Smith, J.A. Reimer, J. Chem. Phys. 98 (1993) 7613. K.J.D. MacKenzie, M.E. Smith, Multinuclear Solid State NMR in Inorganic Materials, Pergamon, Amsterdam, 2002. P. Abelard, J.F. Baumard, Phys. Rev. B 26 (1982) 1005. T. Viefhaus, T. Bolse, K. Müller, Solid State Ionics 177 (2006) 3063. N. Kim, C.-H. Hsieh, H. Huang, F.B. Prinz, J. Stebbins, Solid State Ionics 178 (2007) 1499. P. Heitjans, S. Indris, J. Phys. Condens. Matter 15 (2003) R1257. D.R. Figueroa, A.V. Chadvick, J.H. Strange, J. Phys. C: Solid State Phys. 11 (1978) 55. S. Dikmen, P. Shuk, M. Greenblatt, Solid State Ionics 126 (1999) 89. J.V. Herle, T. Horita, T. Kawada, N. Sakai, H. Yokokawa, M. Dokiya, J. Am. Ceramic Soc. 80 (1997) 933. N. Kim, J. Stebbins, Chem. Mater. 19 (2007) 5742. T.J. Bastow, S.N. Stuart, Chem. Phys. 143 (1990) 459. P. Florian, D. Massiot, G. Humbert, J.P. Coutures, Compt. Rend. Acad. Sci. Paris. Série II 320 (1995) 99. C.P. Slichter, Principles of Magnetic Resonance, Third ed., Springer-Verlag, Berlin– Heidelberg, New-York, 1990, p. 596. H.S. Gutowsky, G.E. Pake, J. Chem. Phys. 18 (1950) 162. N. Bloembergen, E.M. Purcell, R.V. Pound, Phys. Rev. 73 (1948) 679. P. Argyrakis, A. Milchev, V. Pereyra, K.W. Kehr, Phys. Rev. E 52 (1995) 3623. A.S. Nowick, B.S. Lim, Phys. Rev. B 63 (2000) 184115. H. Yamamura, S. Takeda, K. Kakinuma, Solid State Ionics 178 (2007) 889. M. Yashima, S. Kobayashi, T. Yasui, Solid State Ionics 177 (2006) 211. M. Yashima, S. Kobayashi, T. Yasui, Faraday Discuss. 134 (2006) 369. M. Yashima, Solid State Ionics 179 (2008) 797.
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Local structure and oxygen ion dynamics in La doped ceria:
17
O NMR study
Ivo Heinmaa ⁎, Tanel Joon, Helgi Kooskora, Jüri Pahapill, Juhan Subbi National Institute of Chemical Physics and Biophysics, 23 Akadeemia tee, Tallinn 12618, Estonia
a r t i c l e
i n f o
Article history: Received 3 March 2009 Received in revised form 19 July 2010 Accepted 22 July 2010 Keywords: Doped CeO2 17 O MAS NMR Spin-lattice relaxation Oxygen diffusion
a b s t r a c t The local order and oxygen dynamics in La doped ceria (LDC) has been studied by 17O NMR techniques. High resolution 17O MAS NMR spectra show several oxygen resonances which are assigned to the lattice sites with 0, 1 and 2 nearest neighbor (nn) La3+ ions. The site with 1 nn La contributes two different lines depending on the presence or absence of oxygen vacancy. The sites with 2 nn La ions are represented by one single line, which indicates that two neighboring La3+ ions always bind one vacancy. Spin-lattice relaxation (T1) measurements on static samples were carried out between 293 K and 1073 K. The temperature dependence of T1 has been interpreted assuming two independent relaxation paths. The relaxation below 600 K is assigned to the oxygen dynamics in the lattice without involving vacancy diffusion. The relaxation at a higher temperature is interpreted to be caused by the oxygen hopping between vacant and occupied sites. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Oxygen ion conductors have many important technological applications. They can be used in devices like solid oxide fuel cells (SOFC), oxygen pumps, sensors, etc. [1–4]. Ceria (CeO2), when doped with cations of lower valence than the host cation, is one of the best solid electrolytes [5–7]. Due to relatively simple fluorite-type crystal structure (see Fig. 1) it is an attractive model compound for theoretical calculation of the electronic structure, the vacancy migration parameters and ionic conductivity [8–10]. Systematic studies of the ionic conductivity of rare earth doped ceria MxCe1 − xO2 − x/2 [11–13] show that the conductivity depends on the concentration and on the size of the doped M3+ ion. The highest conductivity is obtained for Sm3+ and Gd3+ doped ceria at x around 0.2 [12]. Fuda et al. [14,15] demonstrated that oxygen 17O nuclear magnetic resonance (NMR) spin-lattice relaxation (T1) measurements reveal activation energy (Ea) and the correlation time (τc) of the local oxygen motion in Y doped ceria (YDC). 17O is a spin-5/2 quadrupolar nucleus and its most effective relaxation mechanism is caused by fluctuations of the local electric field gradient (efg) at the nucleus. Since ionic hopping in solids always results in the efg fluctuations, the T1 measurements provide unique experimental data about the ionic hopping rates. For YDC the authors reported interesting T−1 vs. 1 temperature (T) curves with two maxima. Usually a maximum in such a curve occurs at a temperature where characteristic temperature activated fluctuation rate 1/τc reaches the nuclear resonance (Larmor) frequency ω0. Two maxima in the curve would mean two different
⁎ Corresponding author. E-mail address: ivo@kbfi.ee (I. Heinmaa). 0167-2738/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.ssi.2010.07.027
fluctuation processes. Fuda et al. assigned the relaxation maximum at T = 600 K to the mechanism of oxygen jumps via vacancies. The activation energy of the process was determined Ea = 0.49 eV and, surprisingly, the hopping rate 1/τc was found to be independent of dopant concentration. The relaxation process above T = 600 K was ascribed to the motion of thermally activated Frenkel type point defects. Later Adler et al. [16] calculated 17O T1 values for YDC using the dynamic Monte Carlo method. Their numerical simulations suggested that the two relaxation maxima could be ascribed to a single motion of oxygen vacancies. The main idea in their model was that at a low temperature the efg fluctuations at an oxygen nucleus in the YDC lattice are mainly caused by the hopping of the neighboring vacancies, while the hopping of the oxygen ion itself is too slow. At a higher temperature the efg fluctuations due to the hopping of vacancies are too rapid compared to the Larmor frequency and the effective relaxation is caused by the hopping of the oxygen ions. The two characteristic frequencies were assigned to the vacancy jump rate, 1/τvac, and to the oxygen jump rate 1/τox. In the case of ion diffusion via vacancies the oxygen hopping rate is N/n times slower than the vacancy hopping rate, where n is the number of vacancies and N is the number of oxygen ions per unit volume. Although the Monte Carlo calculations [16] gave qualitative agreement with experimental data, the authors found that the two relaxation maxima do not correspond to the actual oxygen/vacancy ratio. In order to get better agreement with the experimental data, they had to introduce the relatively large Sternheimer antishielding factor γ∞ = −185. The number (1 − γ∞) shows how many times the actual efg value at the nucleus is larger than that calculated from the distribution of ionic charges in the lattice. A table value for 17O is γ∞ = −13.8 [17]. A well known issue in the studies of oxygen dynamics in doped ceria is that the NMR relaxation gives much smaller activation energy value than the number obtained from conductivity measurements.
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enrichment to the ~5% level was carried out by heating the samples at 800 °C, 10 h, in 17O enriched oxygen atmosphere. 17 O MAS NMR spectra were recorded on AVANCE-II-600 at 14.1 T magnetic field (17O resonance frequency 81.4 MHz) using home built MAS probe and 4 mm zirconia rotors. The spectra were referenced to H2O resonance frequency. Simple one pulse acquisition sequence was used, with a 1.4 μs excitation pulse (1/3 of the 90 degree pulse for H2O). Temperature dependencies of 17O spin-lattice relaxation of the static LDC samples were measured at two magnetic fields 8.5 T (17O resonance frequency 48.8 MHz) and 4.7 T (27.1 MHz) using saturation recovery pulse sequence. The measurements were carried out on Bruker AMX 360 spectrometer using a home built high temperature probe. To avoid possible changes in the samples at high temperatures the powder samples were sealed into 5 mm od. quartz tubes. 3. Results and discussion Fig. 1. Fluorite type crystal structure of CeO2. Every Ce ion is surrounded by eight oxygen ions; every oxygen ion is surrounded by four nearest neighbor cerium ions.
For YDC at a low doping level, x = 0.1%, the conductivity measurements give Ea = 0.88 eV [11], much higher than the NMR number Ea = 0.49 eV [14] noted above. For yttria-stabilized zirconia (YSZ) the difference between the activation energy from conductivity measurements and from the NMR relaxation is even larger. Reported activation energy values for YSZ from conductivity measurements are between 1.17 eV and 1.33 eV [18], about three times higher than the value ~0.3 eV from NMR relaxation [19]. Much closer value of the activation energy (0.7 eV) was obtained from the NMR line shape analysis [20]. It is argued that the activation energy from NMR is much lower, because NMR relaxation is sensitive to local single ion hops, whereas the conductivity probes the long range transport where the highest barrier may determine the conductivity. Indeed, in most of the ionic conductors the NMR data yield much smaller activation energy than the conductivity measurement (see review [21]), except in some cases e.g. doped BaF2 (fluorite structure) where the NMR relaxation and conductivity data are shown to be in good agreement [22]. In this paper we present 17O NMR data of La doped ceria (LDC) LaxCe1 − xO2 − x/2. The main aim of the study was to determine the doping induced changes in the local structure of ceria by high resolution magic angle spinning (MAS) NMR spectra and the activation energy for the vacancy jump by recording of the temperature dependence of T1. The activation energy for vacancy jump in weakly doped LDC is not well established and quite different values between Ea = 0.77 eV (x = 0.003) [11] and 1.03 eV (x = 0.05) [23] can be found. At higher doping, x = 0.2 [13], YDC has considerably lower activation energy than LDC (0.73 eV and 0.92 eV, respectively). Different vacancy migration parameters have been explained by different local distortion of the lattice [8]: a smaller Y3+ ion which substitutes Ce4+ ion in the CeO2 lattice causes local shrinking of the lattice whereas a larger La3+ ion causes local expansion of the lattice. Thus, with comparison of T1 curves of LDC to that of YDC we expect to see differences in the oxygen dynamics.
3.1.
17
O high resolution MAS NMR spectra
17 O MAS NMR spectra of low doping level samples are given in Fig. 2. Due to high symmetry of the CeO2 crystal structure the electric field gradient (efg) tensor in the undoped crystal is zero. Therefore the main resonance line at 876.5(1) ppm of LDC at low doping levels is extremely narrow (FWHH = 0.5 ppm). Careful inspection of the two spectra allows detecting of additional three small lines at 878.0, 875.7 and 874.5 ppm at the noise level (denoted by arrows in Fig. 2). The intensities of the small resonances have a tendency to grow with higher doping level. Although the relative intensities of the lines are depending on the base line correction the computer fit gives the small peak total contribution as 2.3 and 5.5% in the spectra of 0.2%LDC and 0.5%LDC samples respectively. We believe that these small peaks are caused by La3+ ions in the next-nearest neighborhood of the oxygen. In fluorite structure (see Fig. 1) every oxygen site in the LDC
2. Experimental Four samples of LaxCe1 − xO2 − x/2 with doping level x = 0.002, 0.005, 0.052 and 0.116 (in the following we use notation 0.2%LDC, 0.5%LDC, 5.2%LDC and 11.6%LDC) were synthesized as described in Ref. [24]. Appropriate amounts of La and Ce nitrate solutions were added to neutralized oxalic acid solution. After precipitation the product was washed, dried and subsequently sintered at 1200 °C (15 h). Lanthanum content of the LDC powders was determined by inductively coupled plasma (ICP) mass spectrometry. Oxygen 17O
Fig. 2. 17O MAS NMR spectra of LaxCe1 − xO2 − x/2 samples at given low doping levels. The spectra are recorded at 14.1 T field with the sample spinning speed of 10 kHz. The arrows refer to the small peaks at the noise level.
I. Heinmaa et al. / Solid State Ionics 181 (2010) 1309–1315
Fig. 3. 17O MAS NMR spectra of LaxCe1 − xO2 − x/2 samples with x = 0.052 (top), and x = 0.116 (bottom). Different components of the spectrum are noted as A, B, C, and D. Thin lines denote corresponding Lorentzian component from the computer fit. Asterisks mark spinning sidebands.
lattice has 4 nearest (nn) Ce4+ ions at 2.34 Å distance. The next neighborhood contains 12 Ce ions (nnn) at 4.48 Å. At given low doping levels the probability to find an nn La3+ ion is very small: 0.008 and 0.020 for 0.2%LDC and 0.5%LDC, respectively. Besides, we see below that nn La3+ ions induce considerable shift and broadening of the line; therefore these peaks cannot be associated with oxygen whose nearest neighbor is La3+. The probability to find a La3+ ion as nnn is 0.024 and 0.058, in 0.2%LDC and 0.5%LDC respectively. Thus, the tiny peaks could belong to the oxygen sites having La3+ ion as the next-nearest neighbor. However, we wanted to notify that the La3+ ion in the next-nearest neighborhood causes the change in the peak position at most 2 ppm, which is more than an order of magnitude smaller (see below) local field distortion than that caused by La3+ ion in the nearest neighborhood. The resonance lines in 17O MAS NMR spectra of higher La content samples are much broader (see Fig. 3) and additional peaks denoted B, C and D appear at a lower chemical shift. Since 17O is a spin-5/2 nucleus, the NMR line of the powder sample can show additional singularities due to the second order quadrupolar interaction (see references in [17]). In this case the line width and the position of the singularities are strongly field-dependent. We did record the spectrum of 11.6%LDC at 8.5 T field and found that the peak positions and relative intensities of the components in the spectrum did not depend on the
Table 1 Peak positions and relative intensities in
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magnetic field. Consequently, different peaks in the spectrum correspond to different sites in the lattice. The peak positions and relative intensities of the components are given in Table 1. Recently Kim and Stebbins [25] published the first high resolution 17 O MAS NMR spectra of YDC. They found almost similar lines in the spectrum, which they assigned to local arrangements around oxygen with 0, 1, 2 or 3 Y3+ ions substituting Ce4+ ions in the nearest neighborhood. Here we follow a similar approach, although the NMR intensity of a quadrupolar nucleus is not a good parameter since it usually depends on the excitation pulse length and quadrupolar coupling strength. Assuming that La3+ ions substitute Ce4+ ions randomly, one has 5 different oxygen local configurations with 0, 1, 2, 3 or 4 La3+ ions as the nearest neighbors. We labeled these sites as Ce4La0, Ce3La1,…, Ce0La4, respectively, and in Table 2 relative populations of the configurations in present LDC samples are given. The numbers in Table 2 show that the 5.2%LDC sample has only two configurations (Ce3La1 and Ce2La2) with a probability higher than 10−3, besides the configuration Ce4La0. Accordingly, line A belongs to the site Ce4La0 and the lines B and C to the sites Ce3La1. The intensity of the site Ce2La2 is below the detection level. The two sites B and C, in analogy to the YDC case [25], can be explained by the presence of a vacancy. One of the lines (presumably the broader line B) belongs to the oxygen site where the neighboring La3+ ion is accompanied by oxygen vacancy, we notify it as [Ce3La1]+, because the net charge of the complex is positive relative to the undisturbed lattice. The other resonance line (line C) belongs to the configuration [Ce3La1]−, where the La3+ ion is not accompanied by the vacancy. We admit that the probabilities of the sites and relative intensities of the lines do not perfectly agree. The intensity ratio favors line A. Quite obvious reason for the mismatch is caused by different quadrupolar coupling at these sites. In the case of large quadrupolar coupling (compared to the sample spinning rate) mostly central (−1/2 ↔ + 1/2) transition of I = 5/2 nucleus contributes to the spectrum, whereas in the case of small quadrupolar coupling, all transitions add to the same line. In the present case we are somewhere between these extremes. Remarkable spinning sidebands of the line A (see Fig. 3) indicate nonzero quadrupolar coupling for this site, but it should be much smaller than the coupling at site B or C where the symmetry of the local charge configuration is definitely not cubic. Assignment of the lines in the spectrum of the sample 11.6%LDC is done in a similar manner. Line A belongs to the configuration Ce4La0, lines B and C to the site [Ce3La1]+/− and line D we attribute to the configuration Ce2La2. Concerning vacancy distribution we note that the resonance D is a single broad line, which means that two adjacent La3+ ions are always accompanied by the vacancy. Comparing our spectra with that of YDC [25] we see two major differences. At first, the average chemical shift change caused by one nn La3+ ion is about ΔσCeLa = −34 ppm, whereas the average change caused by one nn Y3+ is about ΔσCeY = −60 ppm. The ratio of these numbers roughly corresponds to the ratio of 17O chemical shift differences in CeO2 and four-coordinated oxygen sites in corresponding oxides, i.e. ΔσCeLa / ΔσCeY = (σCeO2 − σLa2O3) / (σCeO2 − σY2O3), where the chemical shift of four-coordinated oxygen in La2O3 is taken σLa2O3 = 584 ppm [26] and the average value in Y2O3 is σY2O3 = 369 ppm [27]. The second major difference in the spectra of YDC and LDC is that the oxygen site Ce2La2 with two nearest La3+ ions shows only one line, whereas the corresponding site in YDC, with two nearest Y3+
17
O MAS NMR spectra of 5.2% and 11.6%LDC samples.
LDC sample
Peak A ppm
I
Peak B ppm
I
Peak C ppm
I
Peak D ppm
I
5.2% 11.6%
878.3(2) 880.4(2)
0.922(2) 0.673(4)
855.4(1) 856.8(3)
0.045(2) 0.15(2)
832.9(1) 836.3(2)
0.033(2) 0.10(2)
– 807.8(8)
– 0.077(6)
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Table 2 Probabilities for oxygen sites having 0, 1…or 4 nearest neighbor La3+ ions. Sample
PCe4La0
PCe3La1
PCe2La2
PCe1La3
PCe0La4
5.2%LDC 11.6%LDC
0.808 0.611
0.177 0.320
0.015 0.063
0.000 0.006
0.000 0.000
ions, gives two lines into the spectrum [25]. This may indicate that in LDC two neighboring La ions always bind one oxygen vacancy, whereas in YDC the two Y ions may or may not have a vacancy in the nearest neighborhood. 3.2. Motional narrowing Existence of different peaks in the room temperature MAS NMR spectrum provides an estimate to the minimum residual time of a vacancy, τvac, in a particular site. If line B (see Fig. 3) is the site [Ce3La1]+, with one nn La3+ plus a vacancy, then after vacancy jump the site becomes [Ce3La1]−, that is nn La3+ without vacancy, represented by line C. According to the general understanding of motional narrowing [28], transfer of the case of infrequent jumping to the case of rapid jumping occurs when τΔω≈ 1, where Δω is the separation of the resonance lines in the absence of exchange motion. The splitting between lines B and C is about Δω/2π = 1000 Hz in 8.5 T magnetic field. Since the lines are clearly separated, the residual time of a vacancy at room temperature is at least τvac N 1.6 × 10−4 s. −1 The hopping frequency of oxygen ions τox can be obtained from the temperature dependence of the line width. The NMR line width of solid powder samples at low temperatures is typically a broad line because the nuclei are located at sites with different local fields. At a higher temperature the ions start to move through the solid causing averaging of the local fields experienced by the nucleus and motional narrowing of the resonance line. The narrowing takes place if the hopping rate of the ions τ − 1 becomes much faster than the rigid lattice line width. Temperature dependence of the NMR line width of the static 0.2%LDC sample is given in Fig. 4. The room temperature line width (half width at half height, HWHH) wA = 300 Hz narrows to the value wB = 105 Hz above T N 700 K. An estimate to the hopping rate can be obtained using a formula given by Gutowsky and Pake [29]: −1
τ
#
! π w2 −w2B = αw tan ; 2 w2A −w2B
ð1Þ
where w is the HWHH of the resonance line, wA is the width of the rigid lattice line, wB is that of the motionally narrowed line and α is a constant of the order of unity. Taking α = 1, it follows from Eq. (1) that the hopping rate becomes equal to the line width at a temperature where −1
τ
1 = w = pffiffiffi 2
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi w2A + w2B :
ð2Þ
Using wA and wB values as given above we get the estimate: −1 τox = w = 225 s−1 at temperature T = 425 K (see Fig. 4.). 3.3. Temperature dependence of the in LDC
17
O spin-lattice relaxation rate
A key experiment for understanding the oxygen dynamics in doped ceria is recording of the spin-lattice relaxation rate vs. the temperature curve. In a classical BPP theory [30] the relaxation rate can be expressed in a form: " −1
T1
=C
# τc 4τc + ; 1 + ω2L τ2c 1 + 4ω2L τ2c
ð3Þ
Fig. 4. Temperature dependence of 17O NMR line width of the static 0.2%LDC sample in 8.5 T magnetic field. Dashed lines are guiding the eye to estimate the oxygen jump rate from the line width at 425 K, see text.
where C is a constant which characterizes the amplitude of the fluctuations of the quadrupolar interaction, ωL is the Larmor frequency and the correlation time, τc, of the fluctuations follows exponential temperature dependence τc = τ0 exp
Ea ; kB T
ð4Þ
where Ea is the activation energy of the process, T is the temperature, and the pre-exponential factor τ0 is the inverse of a trial frequency. If τc is given by Eq. (4), it is straightforward to determine activation energy from the slope in the Arrhenius plot ln(T−1 1 ) vs. 1/T. Furthermore, in the case of a maximum in this plot, one has a unique possibility to determine the absolute value of the correlation time τc almost model free. In Fig. 5 we have plotted the T−1 1 data for LDC samples measured in 8.5 T magnetic field. All T1 values were determined from a single exponential fit to the magnetization recovery. Exponential magnetization recovery was observed in all experiments, in the entire temperature range and it usually means that the relaxation is homogeneous i.e. every observed nucleus in the lattice is influenced by the same fluctuation spectrum, or the spin diffusion in the spin system is fast enough to equalize the inhomogeneous relaxation. The role of spin diffusion can be suppressed by measuring the relaxation in the MAS experiment. We found that the relaxation of lightly doped LDC samples at room temperature at MAS did not change noticeably. The relaxation at MAS of the samples 5.2%LDC and 11.6%LDC was different for different resonance lines. In addition, the magnetization recovery in these samples at MAS could not be described by a single exponential. Thus the relaxation at room temperature of lightly doped ceria is homogeneous, whereas that of heavily doped samples is intrinsically inhomogeneous depending on the local environment of the nucleus. In measurements of static samples the latter inhomogeneity is averaged by spin diffusion.
I. Heinmaa et al. / Solid State Ionics 181 (2010) 1309–1315
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(3) eV for process A is close to the value 0.49 eV of the low temperature relaxation process in YDC [14]. The activation energy EBa = 0.96(5) eV for oxygen hopping via vacancy, process B, is probably a good estimate to the activation barrier in lightly doped LDC, well in the range of the numbers from conductivity measurements, Ea = 0.77 eV (x= 0.3%) [11] and 1.03 eV (x= 5%) [23]. Similar to the case of YDC [15], in samples of a higher doping level, the relaxation due to the oxygen hopping through the vacancies (process B) cannot be described by a single activation energy Ea. Following the approach by Fuda et al. [15] we have simulated the curves using a distribution of activation energies ρ(E). The relaxation rate has been calculated as an average rate: −1
T1
= C∫ρðEÞdE
τc 4τc + ; 1 + ðωL τc Þ2 1 + ð2ωL τc Þ2
ð5Þ
where τc(E) was calculated by Eq. (4) and the dependence of the preexponential factor τ0 on E was neglected. Due to the motion of oxygen the magnetization recovery should be still exponential, despite of the distribution of energy barriers. For ρ(E) we have used uniform energy distribution:
ρðEÞ =
Fig. 5. 17O spin-lattice relaxation rate T−1 of LDC samples at 8.5 T magnetic field as a 1 function of inverse temperature. Solid lines are computer simulations with the parameters given in Table 3 (see text).
Fig. 5 shows that at low doping levels the relaxation rate curve has two maxima: at around 600 K and at 1000 K. At higher doping levels the relaxation curve has a similar slope at a low temperature, indicating similar activation energy, whereas at higher temperatures instead of the second maximum we see a broad flat region. The temperature and doping dependence of the relaxation rate are similar to that reported for YDC [14,15]. In comparison with the YDC data the main difference is that in LDC the two maxima are much better resolved. According to the interpretation below, this indicates higher activation barrier for oxygen hopping in LDC. We describe the relaxation data of LDC in assumption of two independent relaxation paths. The one at a low temperature (process A) and the other one at a high temperature (process B). For process A, we note only that it is caused by the local efg fluctuations, the correlation time of which follows the Arrhenius law and it is only weakly depending on dopant concentration. Process B is caused by the efg fluctuations due to oxygen hopping through the vacant sites. The hopping frequency obviously depends on the dopant concentration as can be seen from the change of the high temperature maximum in the relaxation curve. The relaxation of the 0.2%LDC sample is well described by these two independent processes with Eqs. (3) and (4). The computer fit gives two sets of parameters as given in Table 3. The activation energy EAa = 0.45
Table 3 Simulation parameters for the two relaxation paths: activation energies Ea, E1 and E2, the average 〈Ea 〉, pre-exponential term τ0, and fluctuation amplitude parameter of the quadrupolar coupling C. LDC Process A Process B sample Ea τ0 C E1 E2 [eV] [10−13 s] [106 s−2] [eV] [eV]
〈Ea 〉 [eV]
τ0 C [10−13 s] [106 s−2]
– 0.65 0.48 0.45
0.96 0.81 0.68 0.64
1.1(5) 3.2 4.0 5.6
0.2% 0.5% 5.2% 11.6%
0.45(3) 0.43 0.38 0.34
2.5(5) 4.0 13 24
78(2) 180 750 750
0.96(5) 0.96 0.88 0.82
190(20) 580 2500 5000
8 > < > :
1 ; for E1 ≤ E ≤ E2 E2 −E1 0
ð6Þ
otherwise:
Frequency/field dependence of the relaxation rate gives additional dimension for evaluating the relaxation mechanism. According to Eq. (3) one expects T1− 1 ∝ 1/ ω2L dependence at low temperatures, whereas at a high temperature T1− 1 ∝ τc, independent of frequency. Our relaxation measurements at two magnetic fields (the Larmor frequencies ωL/2π = 48.8 MHz and 27.1 MHz) show (see Fig. 6) that the agreement between experimental and simulated curves is remarkably good. The simulation parameters are given in Table 3. The case of uniform distribution of activation energy ρ(E) in diffusion process has been calculated in effective medium approximation [31]. According to this calculation, in the case of not too wide energy distributions, the high temperature value of the diffusion coefficient has Arrhenius type temperature dependence with activation energy equal to the mean value of the barrier 〈Ea 〉. Thus, the average activation energies 〈Ea 〉 for process B in Table 3 give relatively good estimates to the effective values of activation energies for ionic conductivity in LDC samples. 3.4. Two relaxation paths Although the concept of two independent relaxation paths in LDC gives good description of the experimental data, we need to ask about the origin of process A. Which motion in the lattice of ceria is responsible for process A? To clarify the issue we have drawn the temperature dependence of the fluctuation rates of the two processes in 0.2%LDC (Fig. 7) together with the estimates from the other experiments. The oxygen hopping rate from the line-width analysis (see Section 3.2), and from several conductivity measurements clearly indicates that process B can be attributed to the process of oxygen hopping in the lattice. Can we assign process A to the lattice fluctuations caused by the hopping of the distant vacancies as proposed for YDC by Adler et al. [16]? We estimated above the vacancy hopping rate at room temperature for 5.2%LDC to be less than 6000 s−1. This is about an order of magnitude slower than the fluctuation rate of process A. Kim and Stebbins [25] demonstrated that a noticeable change in the MAS NMR spectrum of YDC takes place at temperatures above 380 K. Most probably this change in the spectrum indicates the temperature where the vacancy hopping in YDC exceeds 104 s−1. This estimate is more than two orders of magnitude slower than the fluctuation rate of process A. In addition, above we saw that
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Fig. 6. Computer simulation of the experimental T1 rate data of the LDC sample measured in magnetic fields 48.8 MHz (circles) and 27.1 MHz (squares). The 11.6%LDC sample has been measured only at the 48.8 MHz field. Simulation parameters are given in Table 3.
the high resolution 17O MAS NMR spectrum shows very little changes due to distant vacancies, meaning that small amplitude modulation of the quadrupolar coupling due to hopping of distant vacancies cannot cause effective and homogeneous relaxation. Therefore, assignment of process A to the vacancy migration is not very likely. There are no good candidates for this low temperature fluctuation process. As we saw, this process has a thermally activated nature, every oxygen ion is equally influenced by this process, and it is not migration of the vacant sites. A couple of resonant motions in doped ceria have been detected in electrical relaxation studies [32,33]. Unfortunately, the frequency scale of these motions is very different from that of process A. Recently Yashima et al. [34–36] have carefully analyzed the neutron diffraction patterns of pure and doped ceria. Using the maximumentropy method they discovered structural disorder of oxygen positions even for a pure ceria. They found that in the fluorite-type structure of ceria the regular oxygen site O1 (Wyckoff index 8c) is not completely occupied while some oxygen ions occupy the other site O2 (32f ). Each O1 site is tetrahedrally surrounded by four O2 sites at 1.03 Å distance. At room temperature the neutron diffraction data reveal that 0.012 of O2
sites are occupied [34]. This would mean that about 5% of oxygen ions were not in regular sites. The local symmetry of the site O2 implies nonzero quadrupolar coupling which would show up in the high resolution NMR spectrum as distinct line and broadening due to disorder. Above we demonstrated an extremely narrow MAS NMR line for 0.2%LDC. In the sample of a slightly higher La content the line is noticeably broader. Thus, 17O MAS NMR spectra clearly show that there is not that much disorder even in 0.2%LDC, unless the disorder seen by neutron diffraction was dynamic. In the latter case the O2 sites are occupied for a short time only, short enough to cause motional narrowing of the NMR line (see above) and the disorder detected by neutron diffraction snapshot will not show up in the NMR spectrum. At the same time such hopping between the O1 and O2 sites would be an effective cause for nuclear T1 relaxation. In addition, the relaxation would be equal for every oxygen ion in the lattice and its characteristic temperature dependence would be nearly independent of the doping level in lightly doped samples. Therefore we wanted to attribute the relaxation process A to the back and forth hopping of oxygen ion in b111N direction from the stable O1 site to one of the (metastable) O2 positions. Such interpretation of the NMR relaxation strongly supports
I. Heinmaa et al. / Solid State Ionics 181 (2010) 1309–1315
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hopping between occupied and vacant sites through the nearest O2 sites. At low doping level (0.2%LDC) this process is characterized by activation energy Ea = 0.96(5) eV. At higher doping levels the data were described assuming uniform distribution of the activation energy in the range between 0.45 and 0.96 eV.
Acknowledgements This study has been supported by the Estonian Science Foundation grant 8198, by grant SF0690034s09 from the Estonian Ministry of Education and Research and by AS Elcotec.
References
Fig. 7. Temperature dependence of the fluctuation rate of process A (dashed line), that of process B (full line) from the T1 analysis of 0.2%LDC together with the estimates from other experiments: empty triangle — upper limit to the vacancy hopping rate from the MAS NMR spectrum; cross — estimate to the oxygen hopping rate from the temperature dependence of the static line width; oxygen hopping rates calculated from conductivity data: stars — 5%LDC [23]; open pentagrams — 0.3%LDC [11]; full pentagram — 20%LDC [13].
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