Direct Observation of Defect Dynamics in Nanocrystalline CaF2

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Direct Observation of Defect Dynamics in Nanocrystalline CaF2: Results from 19F MAS NMR Spectroscopy Pragati Jain,† Sangtae Kim,† Randall E. Youngman,‡ and Sabyasachi Sen*,† †

Dept. of Chemical Engineering and Materials Science, University of California, Davis, California 95616, and Corning Incorporated, Corning, New York 14831

‡

ABSTRACT The structure and F--ion dynamics in nanocrystalline CaF2 is studied using 19F fast magic angle spinning nuclear magnetic resonance (MAS NMR) spectroscopy in the temperature range 22 °C e T e 240 °C. The 19F MAS NMR spectra of nanocrystalline CaF2 (diameter ∼ 25 nm) shows the presence of ∼0.55% of the F- ions in interstitial sites that are found to be highly mobile at elevated temperatures and undergo rapid site exchange with regular fluorine sites in the lattice via hopping. It is shown that an increased concentration of these defects formed in nanocrystalline CaF2 may result in an enhancement in ionic conductivity by nearly 3 orders of magnitude compared to that of bulk CaF2. SECTION Nanoparticles and Nanostructures

T

he high anionic conductivity of crystalline ionic fluorides at elevated temperatures has attracted significant attention over the past several decades, and these materials have been extensively studied as model systems to understand defect mobility, diffusion, and sublattice melting in ionic solids.1-4 In the high-temperature regime (T g 600 °C) the electrical conductivity of the solid electrolyte CaF2 is known to be “intrinsic” and thus controlled by thermally activated hopping of F- as well as by the formation of fluorine vacancies/interstitial F- ions (i.e., defects) in the lattice.5-7 On the other hand, at lower temperatures, the conductivity is considered to be “extrinsic”, being controlled exclusively by the motion of the defects. Such a change in the mechanism of ionic transport results in a corresponding change in the activation energy of ionic conductivity of CaF2 from a value of ∼2.0 eV in the “intrinsic” regime to ∼0.9 eV in the “extrinsic” regime.5,6 However, whether the conductivity is controlled by the motion of the fluorine vacancies or the interstitials, i.e., vacancy versus interstitialcy mechanism, remains unknown. A recent study has shown that the ionic conductivity of nanocrystalline CaF2 can be orders of magnitude higher than its microcrystalline counterpart.8 It has been suggested that such a difference in ionic conductivity may arise from the presence of a large fraction of grain boundaries in the nanocrystalline sample. While there are numerous reports on the enhancement of ionic conductivity in nanocrystalline materials, the exact mechanism of conduction, their defect chemistry, and the nature of the disorder is still relatively unknown.9-13 NMR spectroscopy is a useful tool to study ionic dynamics and has been applied to study diffusion in solid electrolytes in the past.6,7,14-19 These studies have been primarily concerned with measurements of NMR spin-lattice relaxation (SLR) times T1 and spin-spin relaxation times T2 as well as line widths of static spectra that were used to obtain information

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regarding the activation energy and time scale of ionic motion.6,7,14,15 However, information about atomic-scale mechanisms of ionic motion are rather difficult to obtain from these results. On the other hand, high-resolution NMR spectroscopy at high temperature combined with line shape analysis has recently been shown by us and others to be quite useful in obtaining detailed mechanistic information regarding ionic transport in solid oxide electrolytes.16-19 In this contribution, we report the results of a comparative study of the structure and F--ion dynamics in bulk (microcrystalline) and nanocrystalline CaF2 using high-resolution and high-temperature 19F magic angle spinning nuclear magnetic resonance (MAS NMR) spectroscopy. Figure 1 shows the 19F MAS NMR spectra of bulk and two nanocrystalline CaF2 samples with crystallite diameters of ∼25 and 50 nm. These spectra were collected at a 19F Larmor frequency of 470.24 MHz (11.7 T) using a sample spinning rate of 33 kHz. The 19F MAS NMR spectrum of the bulk sample is characterized by a single peak centered at -108.5 ppm with a full width at half-maximum (fwhm) of 865 Hz, a result that is consistent with the findings reported in previous studies.20 This peak is also present at the same position in the 19F MAS NMR spectrum of the two nanocrystalline samples. However, the fwhm of this peak is somewhat larger compared to that characteristic of the bulk and is found to increase from ∼1200 to 1700 Hz as the crystallite size decreases from 50 to 25 nm. The larger fwhm of this peak in the nanocrystalline sample is likely to be indicative of increasing fluorine site disorder due to increasing surface area-to-volume ratio compared to the bulk sample. On the other hand, besides this main peak at Received Date: February 3, 2010 Accepted Date: March 4, 2010 Published on Web Date: March 16, 2010

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DOI: 10.1021/jz100152j |J. Phys. Chem. Lett. 2010, 1, 1126–1129

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-108.5 ppm, the 19F MAS NMR spectra of the nanocrystalline samples are characterized by an additional peak centered around -131.6 ppm that constitutes about 0.55% of the total 19 F NMR signal for the 25 nm crystallites and decreases to ∼0.27% as the crystallite size increases to 50 nm (Figure 1). It may be noted that this additional signal was observed in the 19F MAS NMR spectra of multiple samples of nanocrystalline CaF2 prepared from different batches of starting materials. The chemical shift of this peak is within 0.4 ppm of the 19F NMR chemical shift of KF (-132 ppm). If this peak results from KF impurities, then it would require the presence of about ∼0.8 wt % KF in the 25 nm nanocrystalline sample. However, electron probe microanalysis of this sample showed the absence of KF or any other impurities within the limit of detection of ∼0.1 wt %. Therefore, this peak must correspond

to fluorine atoms located within the nanocrystalline CaF2 lattice at a relatively well-defined “defect” site such as the cuboctahedral interstitial site in the unit cell (see Figure S2 in the Supporting Information).21 This hypothesis is supported by the fact that this “defect” peak in the 19F NMR spectrum becomes weaker upon coarsening of the crystallite size from ∼25 nm to ∼50 nm in diameter and is completely absent in the 19F MAS NMR spectrum of the bulk CaF2 sample (Figure 1). These results strongly suggest that such defects are most likely introduced into the structure of CaF2 in significant concentration in response to the grain size reduction and the consequent increase in the surface area in the nanocrystalline sample. Although it cannot be ascertained from the data at hand, it is possible that these defects would be largely concentrated near the surface of the nanocrystallites due to their lower formation enthalpy in this region compared to that in the bulk.22 It should be noted that the formation of an interstitial F- (F0i ) is expected to be accompanied by the creation of a fluorine vacancy (V•F) in the CaF2 • 0 lattice, resulting in a Frenkel defect pair (cf. F F þ Vi f Fi þ VF in the Kroger-Vink notation, where FF and Vi denote a lattice “F” and an interstitial site “i”, respectively). The temperature-dependent evolution of 19F MAS NMR spectra of the nanocrystalline CaF2 sample with crystallite size of 25 nm in the temperature range of 100 °C e T e 240 °C are shown in Figure 2. These spectra were collected at a 19 F Larmor frequency of 188.9 MHz (4.7 T) using a sample spinning rate of 23 kHz. The 19F signal at -108.5 ppm does not change significantly in this temperature range for the nanocrystalline sample, implying that the average mobility of the lattice F F sites is very low in this temperature range. A similar result was also obtained for the bulk CaF2 crystal, although it is not particularly surprising as the F F diffusivity in the bulk sample is expected to be rather low in this temperature range.5 However, and more interestingly, with increasing temperature, the intensity of the defect peak at -131.6 ppm in the

Figure 1. From bottom to top: 19F MAS NMR spectra of bulk and nanocrystalline CaF2 with crystallite sizes of ∼50 and 25 nm, respectively. Inset shows the region between -140 ppm and -120 ppm for these samples, magnified by 20.

Figure 2. Figure on the left shows experimental (solid line) and simulated (dashed line) 19F MAS NMR spectra of nanocrystalline (∼25 nm) CaF2 at temperatures ranging between ambient and 240 °C. The experimental and simulated line shapes are slightly offset for visual clarity. Temperatures and corresponding exchange frequencies are given alongside each spectrum. The region between -140 ppm and -120 ppm of these spectra is magnified in the figure on the right.


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F MAS NMR spectra of the nanocrystalline sample is found to progressively decrease, and the peak appears to merge with the main peak at -108.5 ppm (Figure 2). These temperature-dependent changes are found to be reversible upon cooling (see Figure S3 in the Supporting Information). This observation indicates that increasing temperature results in rapid exchange between the F F and the F0i via hopping in the nanocrystalline CaF2 lattice. At the highest temperature (240 °C), the two peaks are completely merged, implying that the corresponding hopping or exchange frequency between the two fluorine sites has to be comparable to the separation (∼4 kHz) between the two peaks in the NMR spectrum. Such diffusive exchange between the two fluorine sites provides additional evidence that the peak at -131.6 ppm in the 19F MAS NMR spectrum of the nanocrystalline sample corresponds to fluorine sites that are intrinsic to the CaF2 lattice and not to any extrinsic impurities. The high-temperature 19F MAS NMR line shapes of the nanocrystalline sample can indeed be simulated well using a two-site random cross-exchange model in order to obtain the exchange frequency between the F F site at -108.5 ppm and the F0i site at -131.6 ppm in the lattice as a function of temperature (Figure 2). The general expression for the equation of motion of magnetization Mj(t) for any individual site j with resonance frequency ωj that exchanges with sites k can be written as23 X dMj ðtÞ ¼ iωj Mj ðtÞ -½Mj ðtÞ=T2j þ Πjk Mk ðtÞ ð1Þ dt k

Figure 3. Arrhenius plot of conductivity determined from τNMR values from simulation of 19F NMR spectra of nanocrystalline CaF2 (solid circles) compared with experimentally measured conductivities of bulk (solid line) and nanocrystalline (dashed line) CaF2 reported in the literature.8

γ is approximated to be ∼1 for uncorrelated hopping, an assumption that is justified for the small concentration of mobile F0i atoms in the lattice, and d is taken to be on the order of a few angstroms. It may be noted here that γ = 1, 0.65, and 0.74 for uncorrelated interstitial hopping, a vacancy mechanism, and an interstitialcy mechanism, repectively.5 The dc conductivity values thus obtained from these calculations are compared with the previously reported experimental results for bulk and nanocrystalline CaF2 in Figure 3. The calculated dc conductivities of the nanocrystalline CaF2 sample studied here are nearly 3 orders of magnitude higher than those previously reported for bulk CaF2 and are characterized by a significantly lower activation energy (∼0.25 eV) compared to that reported for bulk CaF2 (∼0.9 eV). A recent study of ionic conductivity of nanocrystalline CaF2 with comparable crystallite size (∼9 nm in diameter) by Puin et al. has indeed shown an enhancement in conductivity by nearly 3 orders of magnitude compared to the bulk, although the activation energy remains similar (Figure 3).8 Such enhancement in conductivity was attributed by these authors to the overlap of space charge zones and hence to the pronounced space charge effect, i.e. enhancement in charge carrier concentration, in nanocrystalline CaF2. However, our results directly demonstrate that the population of F- sites present as interstitial defects in nanocrystalline CaF2 is highly mobile and must play an important role in ionic transport and electrical conductivity. The relatively low activation energy of 0.25 eV of the fundamental fluorine hopping frequency is consistent with the activation energies of the temperature dependence of 19F NMR line width and of SLR times T1 (0.26 to 0.36 eV), reported for bulk CaF2 in previous studies.6,7 This similarity in the activation energies implies that in the low temperature “extrinsic” regime the ionic conductivity in bulk and nanocrystalline CaF2 is dominated by the motion of interstitial F- ions. In this scenario, the significant enhancement in conductivity in nanocrystalline CaF2 can be attributed to the higher concentration of the interstitial F- sites in these materials compared to their microcrystalline counterpart. The discrepancies between the NMR activation energies and those of the experimentally determined electrical

In this expression, T2j is the inverse of the line width of site j without any exchange, and Πjk is the exchange matrix. For N sites exchanging at a rate of 1/τNMR, the exchange matrix Πjk = 1/τNMR (1 - Nδjk). Since the probability for exchange of one site with any one of the other N - 1 sites is 1/τNMR, the offdiagonal elements of this exchange matrix (δjk = 0) are 1, and the diagonal elements are -(N - 1) such that ΣjkΠjk = 0. The final expression for the line shape g(ω) resulting from crossexchange between N distinct sites is given by g(ω) = 1 3 A(ω)-1 3 W, where 1 is the unit matrix, A(ω) = i(ω1 - ω) - Π, ω includes the T2 term, and W is the initial probability vector, i.e., populations or relative fractions of the N sites. In the present case, N is equal to 2, and 1/τNMR is the exchange frequency between the two F sites. The value of T2j of 0.6 ms was obtained from simulation of the room-temperature spectrum with an exchange frequency (1/τNMR) of 0 and has been treated as a constant for both F sites in all of the simulations at higher temperatures. The τNMR values obtained from these simulations exhibit an Arrhenius temperature dependence in the temperature range of 100 °C e T e 240 °C with an activation energy of ∼0.25 eV. These τNMR values can be used to calculate direct current (dc) conductivity σ that results from this dynamic of interstitial fluorine sites in nanocrystalline CaF2 using the Nernst-Einstein relation: σ = [z2e2cγd2(τ-1 NMR)]/6kT, with z, e, k, T, γ, c, and d being the charge number, elementary charge, Boltzmann constant, absolute temperature, correlation factor, concentration of the F0i sites, and the average hopping distance of the mobile fluorine atoms, respectively. As γ and d are not known a priori,


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conductivity in bulk and nanocrystalline CaF2 (Figure 3) is reminiscent of similar observations recently made by Stebbins and co-workers in their 17O NMR studies of oxygen hopping in solid oxide electrolytes.16 These authors suggested that such discrepancy may arise from several sources. For example, the NMR line shapes and relaxation may be sensitive to backward-forward correlated jumps of mobile ions that do not contribute to long-range diffusion and dc conductivity. Moreover, the activation energy of mobile ion hopping as measured via NMR line shape and T1 modeling may be related to the migration energy while that of electrical conductivity includes the effects of both association and migration energies. In spite of such inherent difficulties in making quantitative comparison between NMR and electrical conductivity results, the 19F NMR results presented here provide clear evidence for the formation of a measurable fraction of F0i sites in CaF2 upon reduction of crystallite size into the nanometer regime. Moreover, F0i sites are shown to be significantly more mobile than those in regular lattice sites and may enhance the intrinsic ionic conductivity of nanocrystalline CaF2 by several orders of magnitude compared to their microcrystalline counterpart.

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SUPPORTING INFORMATION AVAILABLE Experimental

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details of synthesis and characterization. This material is available free of charge via the Internet at http://pubs.acs.org. (19)

AUTHOR INFORMATION (20)

Corresponding Author: *To whom correspondence should be addressed.

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ACKNOWLEDGMENT This work was supported by the National Science Foundation Grant DMR 0906070 to S.S.

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REFERENCES

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Direct Observation of Defect Dynamics in Nanocrystalline CaF2

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