207Pb NMR Studies on Ion Dynamics in Tetragonal

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F/119Sn/207Pb NMR Studies on Ion Dynamics in Tetragonal PbSnF4: Spectroscopic Evidence for Defect-Driven Conductivity

Miwa Murakami,*,† Yoshiyuki Morita,† and Motohiro Mizuno‡ †

Office of Society-Academia Collaboration for Innovation, Kyoto University, Uji, Kyoto 611-0011, Japan Department of Chemistry, Graduate School of Natural Science and Technology, Kanazawa University, Kanazawa 920-1192, Japan

‡

S Supporting Information *

ABSTRACT: Ion dynamics in tetragonal PbSnF4, which shows high conductivity ∼10−3 S cm−1 at room temperature, was examined by using 19 119 F/ Sn/207Pb solid-state NMR at 7 and 14 T. While the observed temperature dependence of 19F spin−lattice relaxation time (T1) decreases monotonously with increasing temperature at the temperature range studied (ca. 230−360 K), 119Sn and 207Pb T1 bear T1 minima. From the short 119Sn T1 minimum value at 14 T (ca. 0.85 ms) and its dependence on the strength of the static magnetic field, it was concluded that the relaxation mechanism of 119Sn is fluctuation of the chemical-shift anisotropy (CSA). The activation parameters for the motion responsible for the CSA relaxation were found to be τ0 = (8.8 ± 3.1) × 10−15 s and Ea = 26.9 ± 0.1 kJ/mol. We showed that mutual exchange of two F− ions does not affect the size and orientation of the CSA tensor and thus cannot be the CSA-relaxation mechanism. As a mechanism to affect the CSA tensor, we invoked exchange between a F− ion and a defect (the defect-diffusion motion). As the activation energy of the defect-diffusion motion is consistent with that obtained from temperature-dependent conductivity (∼28 kJ/mol), we concluded the defect-diffusion motion is the motion responsible for ion conduction. characterization of this β-PbSnF4 sample, we adopted various spectroscopic means and found in the course of examination of high-resolution solid-state NMR that the spin−lattice relaxation time (T1) of 119Sn at 14 T is unexpectedly short (107 Hz (b) and with the apex angle of 38° and the rate >107 Hz (c). Apodization by an exponential broadening function was applied to the calculated FID data before Fourier transformation: 9 kHz broadening for the static data at −40 and 25 °C, and 4 kHz for 90 °C.

three temperatures. At −40 °C (Figure 4(a)), which is the lowest temperature achievable, the line shape becomes nonaxially symmetric, and at the highest temperature (90 °C; Figure 4(c)), it becomes axially symmetric. Apparently there is a motion affecting the CSA interaction. From the 119Sn T1 experiment, the fluctuation of the CSA interaction of 119Sn was also indicated. However, the calculated correlation time of the motion responsible for the 119Sn T1 minimum is 10−8∼10−10 s for the temperature range studied and is much shorter than the inverse of the size of the CSA interaction (∼10−6 s). Therefore, temperature dependence of the 119Sn line shape shown in Figure 4 is not ascribable to this motion. In other words, a part

(10)

Here we simply assumed that the activation energy for the motion responsible for

() 1 T1

is that obtained from the analysis

D

of 19F T1, that is, 7.7 kJ/mol. Then the remaining parameters to 2631

DOI: 10.1021/acs.jpcc.6b13053 J. Phys. Chem. C 2017, 121, 2627−2634

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The Journal of Physical Chemistry C of the CSA interaction has been averaged out by this motion, and what we observed at −40 °C (Figure 4(a)) is described by the “left-over” of the CSA interaction, which is further modulated by other motions. We therefore assumed the line shape obtained at −40 °C as the “static” pattern and leastsquares fitted to the calculated static pattern. The best-fit CSA values were (σ11, σ22, σ33) = (−534 ppm, −633 ppm, −1412 ppm), and the calculated spectrum is plotted in red (Figure 4(a)). Note that the span Ω = |σ33 − σ11| = 878 ppm and the skew χ = 3(σ22 − σiso)/Ω = 0.78 are comparable to those of BaSnF4 (Ω = 890 ppm and χ = 1.0),21 whose conductivity is 1− 2 orders of magnitude smaller than that of β-PbSnF4. With the fluctuation of the CSA interaction indicated by T1 and the local structure of Sn shown in Figure 2(b), we adopted the wobbling motion where the σ33 axis is hopping around the Sb−F(2c) direction. We further assumed four-site hopping motion, in which the σ33 axis is reoriented among the ridges of the regular quadrangular pyramid with its vertex placed at the Sn atom as schematically illustrated in Figure 2(b). The parameters for fitting are the apex angle and the correlation time, and we found that the observed powder patterns at 25 and 90 °C were consistent with those calculated with the apex angle of 34° and 38°, respectively. The line shape is not sensitive to the correlation time, which was estimated roughly to be 10−7 ∼ 10−8 s. The correlation time thus obtained is consistent with that for the fast motion detected by the relaxometry study.18 Hence, we concluded that the 119Sn CSA is first averaged by the motion responsible for the T1 minimum and further modulated by the fast motion detected by the relaxometry study. Since our simulation program for MAS spectra does not allow us to include the Hahn echo, the calculated line shape with the above parameters at 25 °C is deviated from the observed one appreciably (Figure S4 in Supporting Information). As it is difficult to incorporate the Hahn-echo process into the MAS simulation program, we have not tried to analyze the MAS spectrum extensively. Here let us examine how F− motion can affect the CSA interaction of 119Sn. From the above T1 analysis and also from the line shape analysis, it is envisaged that the direction and the size of the σzz = σ33 axis of the CSA tensor are modulated by F− motion. Figure 5 schematically illustrates effects of motion of F− ions on the direction of the σ33 axis of the 119Sn CSA tensor. It is notable that mutual exchange of F− ions by local hopping motion (Figure 5(a)) does not affect the size and the orientation of the σ33 axis. To affect the σ33 axis, change in the local structure is necessary. As large amplitude motion of the Sn atom is unlikely, we postulate that exchange between a F− ion and a defect/vacancy (Figure 5(b)) is responsible for the change of the local structure. The σ33 axis of the CSA tensor of a 119Sn spin with a defect in its neighboring site (the 4f site for example in Figure 5(b)) should be deviated from the 2c site as schematically illustrated. The entry of a F− ion to the defect site reorients the σ33 axis to point to the 2c site as its local symmetry is recovered. In other words, the motion does also reorient the σ33 axis of the 119Sn spin, into whose neighboring occupied site the defect moves. The defect motion is thus effective as a relaxation mechanism by modulating the CSA interactions of immobile 119Sn spins. As this defect-diffusion motion with its activation energy (26.9 ± 0.1 kJ/mol) is consistent with that for ion conduction (ca. 28 kJ/mol), we conclude that the motion detected by 119Sn T1 in the

Figure 5. Schematic illustration of effects of motion of F− ions (green and yellow) on the direction of the σ33 axis of the 119Sn (blue) CSA tensor for the case of (a) mutual exchange by local hopping motion and (b) exchange between a F− ion and a defect designated by a dotted green circle.

temperature range studied is responsible for ion conduction. Hereafter, we shall refer to this motion as the defect motion. In Figure 6, we plotted the three correlation times calculated by using the Arrhenius equation (eq 1) for the fast and the slow

Figure 6. Plot of the calculated correlation times of the slow (red) motion and the fast (green) motion reported in ref 18 and that of the defect motion (blue) obtained from the analysis of 119Sn T1 in the present work. The horizontal dotted lines are drawn at the inverse of the Larmor frequencies of 19F (green), 119Sn (blue), and 207Pb (red) at 14 T.

motions found by the fast-field cycling 19F NMR relaxometry18 and the defect motion found in the present work. Note that the reported distribution of the correlation time for the fast motion is ignored in the plot. In Figure 6, we also indicated the inverse of the Larmor frequencies of 19F, 119Sn, and 207Pb at 14 T and by the horizontal dotted lines. A motion becomes most 2632

DOI: 10.1021/acs.jpcc.6b13053 J. Phys. Chem. C 2017, 121, 2627−2634

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The Journal of Physical Chemistry C

homonuclear dipolar interactions between N − 2 pairs are modulated, while for a (N − 1)-spin system with one defect, (N − 2)/2 pairs are affected by exchange between a spin and a defect. Hence, the defect motion is less effective for modulation of the homonuclear dipolar interaction. Currently we are engaging further refinement of the structure by combined analysis of the neutron and the synchrotron X-ray diffraction data to determine the occupancy ratio of F atoms, which will be published elsewhere together with the results for the other forms of PbSnF4. To summarize, the present analysis of 119Sn T1 data shows that 119Sn T1 at 14 T in the temperature range studies is governed by a motion with a single correlation time, and from consideration of its relaxation mechanism being fluctuation of CSA, the defect motion was invoked. The remaining problem may be the nature of the defect. Is it the Frenkel defect or the Schottky defect? So far, effects of defect formation on the preexponential factor τ0 have been invoked and examined.22 One example may be found in the 19F T1 study of one of the starting materials. Boyce et al.23 examined 19F T1 of β-PbF2 and showed that 19F T1 below 250 K can be fit by using a single correlation time, which is in agreement with the ion jump time calculated from the conductivity, with τ0 = 1.1 × 10−15 s and Ea = 71.4 kJ/ mol. The τ0 value is much shorter than the inverse of the optical phonon frequency ∼10−13 s, and they ascribed this to formation of the Frenkel defect. Murray et al. attributed the long τ0 values (∼10−10 s) for the fast and the slow motion below 340 K to anion motion into a pre-existing vacancy.18 Further, the defect formation with increased F-ion population in the Sn−Sn layers at higher temperature (∼700 K) was suggested by MD simulation.18,24 For the defect motion in the present work, τ0 is ∼10−14 s, which is not so short to invoke the Frenkel defect. At present, we consider that the defect is most likely a pre-existing one produced during its synthetic process.

effective as a T1 relaxation mechanism at temperature where its correlation time is close to the inverse of the Larmor frequency (ω0τc ∼ 1). Apparently, the slow motion is too slow and thus is less effective than for the relaxation mechanism for 19F, 119Sn, and 207Pb at 14 T. It appears that the correlation time of the fast motion is also long, and it cannot be an efficient T1 mechanism. However, in the distribution of the correlation time, a correlation time close to the inverse of the 19F Larmor frequency should exist, which governs 19F T1 at 7 T and 14 T. The correlation time of the defect motion equals the inverse of the Larmor frequencies of 19F, 119Sn, and 207Pb at 1000/T ∼ 3.2, 3.5, and 3.7, respectively. Indeed, we observed the T1 minimum for 119Sn and 207Pb at these temperatures. However, effects of this motion to 19F T1, which becomes most prominent at 1000/T ∼ 3.2, are not discernible. This indicates that the defect motion is less effective as a relaxation mechanism for 19F. The inefficiency of the defect motion as the 19F T1 mechanism can be attributable to the small number of the defects. Note here that only a few defects in one unit cell are enough for all 119Sn spins to relax by the CSA mechanism. Furthermore, even if there are an appreciable number of defects, the defect motion is still less effective as for the 19F T1 mechanism because the number of 19F−19F dipolar pairs reduces appreciably by the presence of the defects. To appreciate this, let us consider a four-spin system (Figure 7(a)) and a system with three spins and one defect (Figure

4. CONCLUDING REMARKS Solid-state NMR studies on dynamics in ionic conductors have mostly been done by observing NMR lineshapes and relaxation times (T1, T1ρ, and T2) of conducting nuclear spins, such as 7Li, 23 Na, and 19F.22 In this work, we showed that the observation of 19 F NMR line shape and T1 did not provide information directly relatable to the ion-conduction mechanism. This is understandable as dynamics of ion conduction is not always simple, and the lineshapes as well as its relaxation times of conducting ions are affected by various motional modes. To unravel the complex effects on the NMR observables of a conducting ion and study motion corresponding to bulk ion conduction, one may have to examine the NMR observables over a wide temperature range under various strengths of the static field. One good example is the relaxometry study.18 In this work, we showed that motion corresponding to bulk ion conduction can also be investigated by examination of relaxation of immobile nuclear spins forming a conduction pathway. This is because the spin relaxation of immobile nuclear spins at the “wall” of the conduction pathway is affected solely by motion of conducting ions. In particular, we showed that participation of a defect in ion conduction can unequivocally be proven by showing that the relaxation mechanism is the fluctuation of the CSA interaction. As the size of the CSA interaction is proportional to the strength of the static field, this mechanism becomes more prominent at higher fields. Hence, to appreciate the CSA relaxation of a low-γ

Figure 7. Schematic illustration to appreciate fluctuation of the dipolar interaction among the spins: (a) mutual exchange between spin-#2 and spin-#4 and (b) exchange between spin-#2 and a defect at the site#4.

7(b)). The mutual exchange of the spins at #2 and #4 in Figure 7(a) reorients the homonuclear dipolar interactions between the following four pairs (1−2, 1−4, 3−2, and 3−4), while only two dipolar interactions among 1−2 and 2−3 are modulated by exchange between spin-#2 and the defect at #4. For a N-spin system with one pair of spins undergoing exchange, the 2633

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The Journal of Physical Chemistry C nuclear spin, such as 207Pb in this case, use of a higher magnetic field is desirable. Lastly, we would like to point out that the quadrupolar interaction can also be fluctuated by the defect motion; hence, the relaxation measurement of a quadrupolar spin (I > 1/2) should also be useful for examination of the role of a defect in ion conduction.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.6b13053. Crystal and refinement parameters (Tables S1−S3) and fitted neutron diffraction profile (Figures S1), thermal ellipsoid plots (Figure S2), and temperature dependence of 207Pb T1 together with calculated curves (Figure S3). Experimental and calculated 119Sn MAS spectra are given in Figure S4 with some details about simulation algorism (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected]. Tel.: +81-774-384967. Fax: +81-774-38-4996. ORCID

Miwa Murakami: 0000-0001-6209-4450 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by R&D Initiative for Scientific Innovation on New Generation Batteries II (RISING II) Project administrated by New Energy and Industrial Technology Development Organization (NEDO). The authors thank Prof. K. Takegoshi for the use of the 7 T magnet and Prof. M. Yonemura for the neutron diffraction experiments, which were conducted as part of the S-type project of the High Energy Accelerator Research Organization (KEK) (Proposal 2014S10). The authors thank Mr. Takashi Moroishi and Mr. Takahiro Terada for their experimental support. The packing structure in Figure 2, and Figure S2 in the Supporting Information was prepared using VESTA.25

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REFERENCES

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