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J. Phys. Chem. C 2008, 112, 5672-5678
Conductivity and Fluoride Ion Dynamics in r-PbSnF4; Diffraction Studies
19F
Field-Cycling NMR and
Eoin Murray,† Dermot F. Brougham,*,†,‡ Jovan Stankovic,§ and Isaac Abrahams§ School of Chemical Sciences, Dublin City UniVersity, GlasneVin, Dublin 9, Ireland, National Institute for Cellular Biotechnology, School of Chemical Sciences, Dublin City UniVersity, GlasneVin, Dublin 9, Ireland, and Centre for Materials Research, School of Biological and Chemical Sciences, Queen Mary, UniVersity of London, Mile End Road, London, E1 4NS, United Kingdom ReceiVed: NoVember 14, 2007; In Final Form: January 31, 2008
Fast-field cycling 19F NMR relaxometry has been applied to investigate fluoride ion dynamics in the layered anionic conductor PbSnF4. Two dynamic processes, on different timescales, were shown to drive the 19F relaxation. By considering the temperature dependencies of the NMR, conductivity, and diffraction data, a complete mechanism for fluoride transport can for the first time be proposed. The slower process is due to anion exchange between equivalent sites (F(2)) in the conducting fluoride plane, which lie between Sn and Pb layers. This is a diffusive process related directly to the mechanism of electrical conduction. The activation barriers for this motion agree closely with those determined from the temperature dependence of the DC conductivity. The faster process is due to non-diffusive exchange between the occupied sites (F(2)) and nominally vacant sites (F(1)), which lie between Sn planes. While this process does not directly limit conductivity, it generates vacancies on the F(2) sites and partial occupancy of the F(1) sites. Above 340 K, the fast process shows an increase in activation energy, as increased occupancy of F(1) sites necessitates the formation of a Frenkel defect on a significant proportion of the F(1) sites prior to an F(2)-F(1) jump. In this temperature range, the slow process shows a decrease in the activation energy, also observed in the conductivity data, due to increased numbers of vacancies in the F(2) sites which provide additional diffusive pathways through the conducting fluoride plane. The results demonstrate that R-PbSnF4 is essentially a two-dimensional (anisotropic) conductor, in which nondiffusive fluoride exchange into sites normal to the conducting plane provides a high population of vacancies within the conducting plane, resulting in unusually high conductivity.
Introduction PbSnF4, is a member of the MSnF4 family (M ) Pb, Ba, and Sr) of layered anionic conducting solids. The conduction mechanisms across this family are of interest because of their high conductivities. PbSnF4 has the highest ambient temperature anionic conductivity, 10-3 S cm-1, of any known material and has been studied using a range of techniques focusing on structural, thermal, electrical and dynamic properties.1-3 Technologically, PbSnF4 is a viable electrolyte in solid-state oxygen sensors, as the alternative oxides have low room-temperature conductivity, which limits the sensor response time.4 R-PbSnF4 was first reported by Donaldson and Senior.1 More recently, Ahmad and co-workers5 observed a discontinuity in the temperature dependence of the conductivity at around 340 K and reported barriers to conductivity of 22 kJ mol-1 (0.23 eV) in the low-temperature range and 30 kJ mol-1 (0.31 eV) in the high-temperature range. Several authors have reported phase transitions, or other anomalous behavior, between 340 and 350 K in PbSnF4. Reau et al.6 had earlier suggested a transition from a monoclinic (R) to a tetragonal (β) phase, while Denes et al.7 suggested that there are no symmetry changes or phase transitions at this temperature. In a recent neutron diffraction study, Castiglione and coworkers8 demonstrated that pure PbSnF4 is tetragonal, in the * Corresponding author. E-mail:
[email protected]. † School of Chemical Sciences, Dublin City University. ‡ National Institute for Cellular Biotechnology. § University of London.
space group P4/nmm, over the temperature range 298-591 K, and adopts an ordered fluorite-type structure. The structure may be described as being based on an ordered cubic close packed (ccp) array of cations (Sn2+ and Pb2+), resulting in a layered tetragonal structure, Figure 1. In the ideal fluorite structure, fluoride ions fully occupy all of the available tetrahedral interstices in the ccp lattice, with octahedral interstices remaining vacant. In R-PbSnF4, the room-temperature distribution of fluoride ions was found8 to deviate from the ideal fluorite structure with three-quarters of the fluoride ions located in two crystallographic sites F(2) (4f) and F(3) (2b) corresponding to those in the ideal fluorite structure and the remaining fluoride ions located in an essentially octahedral site F(4) (2c) between the Sn and Pb layers. Ions located in the F(4) site were found to be preferentially coordinated to the Sn atoms. The remaining tetrahedral site, F(1) between adjacent Sn layers, shows no measurable occupancy at 298 K. The structure remains tetragonal above 340 K, but there is increased fluoride disorder, with greater anion density linking the F(2) and F(4) sites. While critical in determining the structure of the fluoride sublattice, diffraction studies can only provide spatially and temporally averaged atomic positions. Furthermore, refinement of the diffraction data is difficult because of large anisotropic thermal parameters and partial site occupancies. 19F NMR spectroscopy is sensitive to fluoride motion and has been used to study the mechanism of conductivity in some members of the MSnF4 group. In a recent report,9 spin-lattice relaxation time measurements and 19F and 119Sn MAS NMR spectra were
10.1021/jp7108708 CCC: $40.75 © 2008 American Chemical Society Published on Web 03/14/2008
Conductivity and Fluoride Ion Dynamics
J. Phys. Chem. C, Vol. 112, No. 14, 2008 5673 tysonite structure.14 Slow and fast fluoride motions were observed, neither of which conformed to the BPP formalism. Thus, it is well-established that NMR relaxation time analysis, and in particular field-cycling relaxometry, can provide atomicscale measurements of the timescales of ionic motions (τc) and that these can often be related to the time-averaged macroscopic ion flow or conductivity. In this paper, we report the first field-cycling 19F NMR relaxometry study on a layered fluoride ion conductor. From the analysis of these data, we propose a mechanism for anion motion that gives insights, not obtainable from other techniques, into the role and nature of vacancies in determining the high conductivity of this material. The mechanism is supported by the excellent agreement of the dynamic and structural parameters with the independent conductivity measurements and diffraction analysis. Experimental Methods
Figure 1. Structure of R-PbSnF4 showing the cation layers and the four fluoride sites; the nominally vacant F(1) sites; the mobile F(2) and F(4) sites between Sn and Pb layers; and the static F(3) sites between two Pb layers.
used to demonstrate that conductivity in BaSnF4 is due to twodimensional fluoride motion between the Ba and the Sn layers, with exchange between the static and the mobile sub-lattices occurring on a much slower (millisecond) time scale. These sublattices are identifiable in the 19F spectrum. Previous NMR studies of PbSnF4 have shown that, unlike BaSnF4, rapid fluoride motion makes identification of the mobile and rigid sub-lattices difficult, even at room temperature. Second, moment analysis5 of data from the temperature range 160 to 295 K yielded a barrier for the process responsible for line-narrowing of 18.5 kJ mol-1 (0.193 eV). This is somewhat less than what is obtained from conductivity indicating that non-diffusive modes contribute to the line narrowing. Yamada and co-workers have also published10 a conductivity, impedance spectroscopy, and 19F, 119Sn, and 87Rb NMR study on RbSn F , conclusively 2 5 demonstrating that this material exhibits two-dimensional fluoride conduction. A discontinuity in the temperature dependence of the conductivity was observed at 368 K. By using field-cycling NMR techniques, the magnetic field dependence of the spin-lattice relaxation time, T1(ω), can be measured. The field (and hence frequency) dependence of the relaxation rate R1(ω) ) 1/T1(ω), commonly referred to as the relaxation profile, maps out the spectral density for the motional 19F spin system at that temperature. The accessible frequency range of 10 kHz to about 20 MHz11 provides sensitivity to dynamic processes with correlation times, τc, ranging from 10-5 to 10-9 s. For complex dynamic systems, this approach has advantages over conventional fixed-field NMR relaxometry. The number and shape of the spectral density contributions are readily apparent from the relaxation profile, which can be fitted using the appropriate spectral density function. Thus, a single random dynamic process is appropriately modeled using a Lorentzian (BPP)12 spectral density function, but more complex processes may require multiple Lorentzians or other approaches. Furthermore, the correlation time, τc, for the motion at the measurement temperature is obtained directly from the fit. Thus, the nature of the thermal activation, be it Arrhenius or otherwise, can be tested13 by recording profiles at a number of temperatures. A field-cycling 19F NMR study has been reported for the high-temperature fluoride conductor, LaF3, which adopts the
Preparation. Samples of PbSnF4 were prepared by conventional solid-state methods. Stoichiometric amounts of SnF2 (Aldrich, 99%) and PbF2 (BDH, 99%) were ground as a slurry in methylated spirits using an agate mortar and pestle. After drying, the mixture was sealed in an evacuated Pyrex tube and heated in a tube furnace at 523 K for approximately 18 h. After cooling, the sample was reground as a slurry in methylated spirits and dried at 353 K for 3 h. The dry sample was then resealed in a Pyrex glass tube and heated for a further 18 h at 523 K, before being cooled to room temperature. X-ray powder diffraction was used to assess phase purity with data collected at room temperature on an automated Philips PW1050/30 X-ray diffractometer, using Ni filtered Cu KR radiation (λ ) 1.5418 Å), in flat plate θ/2θ geometry. Neutron Diffraction. Neutron diffraction data were collected on the Polaris diffractometer at the ISIS facility, Rutherford Appleton Laboratory, United Kingdom. A 200 µA data set collected on the back-scattering detectors over the time-of-flight range from 1.0 to 20 ms was used in subsequent refinement. The sample was contained in a cylindrical 11 mm diameter vanadium can located in front of the back-scattering detectors. The structure of PbSnF4 was refined by the Rietveld method using the GSAS suite of programs.15 The structure described by Castiglione et al.8 was used a starting model for the structure of PbSnF4. Minor contributions from the unreacted starting materials, R-SnF216 and β-PbF2,17 were included in the final refinement. Anisotropic parameters were refined for all atoms in the primary phase. Crystal and refinement parameters are included in the Supporting Information as Table S1 along with the fitted diffraction profile, Figure S1. Field-Cycling NMR Relaxometry. 19F spin-lattice relaxation data were recorded in the range from 10 kHz to 18 MHz on a Stelar FFC200018 operating at a 19F measuring frequency of 9.81 MHz. A field slew rate of 20 MHz ms-1 was used in all cases, with a switching time of 1 ms to allow the electromagnet to settle. A digitization rate of 1 MHz was used, while the dead time of the spectrometer was about 24 µs. The FID was sampled with 512 points in the time range 25-540 µs after the front edge of the 90° pulse, which was of 7 µs duration. The relaxation rates, R1, were determined from the magnetization recovery curves by least-squares fitting. The R1 values were not sensitive to the time over which the FID was sampled. In a typical experiment, 1 g of polycrystalline PbSnF4 was used. The sample temperature was controlled using a thermostatted flow of dried air that ensured temperature precision within 1 K over
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TABLE 1: Refined Structural Parameters for r-PbSnF4 with Estimated Standard Deviations Given in Parentheses atom
site
Pb Sn F(2) F(3) F(4)
2c 2c 4f 2b 2c
a ) 4.2219(2) Å, c ) 11.3960(7) Å x y z 0.25 0.25 0.75 0.75 0.25
0.3771(3) 0.8687(4) 0.2213(12) 0.5 0.6864(6)
Anisotropic Thermal Parameters U22 U33
atom
U11
Pb Sn F(2) F(3) F(4)
0.0184(9) 0.036(1) 0.34(2) 0.016(1) 0.26(1)
a
0.25 0.25 0.25 0.25 0.25
0.0184(9) 0.036(1) 0.057(5) 0.016(1) 0.26(1)
0.040(2) 0.005(2) 0.32(2) 0.033(2) 0.046(5)
Ueqva (Å2) 0.026(4) 0.026(4) 0.24(5) 0.022(4) 0.19(3) U12
U13
0.0 0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.0
Ueqv ) (U11 + U22 + U33)/3.
TABLE 2: Significant Contact Distances (Å) in r-PbSnF4, at 298 K Pb-F(2) Sn-F(2) F(1)..F(2) F(2)..F(3) a
2.758(10) 2.347(7) 2.522a 3.176(14)
Pb-F(3) Sn-F(4) F(2)..F(2) F(2)..F(4)
2.533(2) 2.078(10) 2.985(1) 2.359(7)
F(1) vacant in refinement, assumed to be at 0.75, 0.25, 0.0.
the full temperature range, 228-423 K. Temperatures were calibrated externally using a Cu-Al thermocouple in a 10 mm NMR tube.
Figure 2. Thermal ellipsoid plots (30% probability) showing cation coordination environments in R-PbSnF4: (a) tin and (b) lead.
Results Crystallography. The refined structural parameters derived from the Rietveld analysis of the neutron data are presented in Table 1 with significant contact distances in Table 2. The structure is found not to deviate significantly from that presented by Castiglione et al.8 Both Sn and Pb are in their subvalent state and exhibit asymmetric coordination environments as a result of stereochemical distortion from the lone pairs of electrons on these atoms. As is often seen, the degree of stereochemical distortion is more pronounced in Sn, which may essentially be described as five coordinate with one short and four longer bonds, constituting a capped square pyramidal coordination environment (Figure 2a). Pb shows distorted cubic coordination with four short and four longer bonds to fluoride ions (Figure 2b). NMR Relaxometry. Field-cycling NMR profiles were recorded for PbSnF4 samples at various temperatures in the range from 228 to 423 K. The magnetization recovery curves were monoexponential at all fields and at all temperatures. Data at selected temperatures are presented in Figure 3. There is strong dependence of the spin-lattice relaxation on temperature across the 19F frequency range 0.014-16 MHz. Visual inspection of the data indicates the presence of a broad dispersion, which moves to higher frequencies with increasing temperature. At temperatures above 273 K, a second spectral density contribution becomes apparent at the lower end of the accessible frequency range. This feature is also observed to move to higher frequency with increasing temperature. It is possible to measure R1 values above 1000 s-1 by fieldcycling techniques. However, given the magnetic field slew rate used, 20 MHz ms-1, the conservative approach of removing all R1 values in excess of this value (T1 < 1 ms) was adopted, to avoid possible systematic errors.
Figure 3. 19F NMR data for PbSnF4, showing the change in relaxation at (a) reduced temperature (green square 228 K, light blue circle 248 K, torquoise triangle 263 K, * 273 K, 1 283 K), and (b) elevated temperatures (0 298 K, red open circle 323 K, orange open triangle 373 K, and olive upside down open triangle 423 K).
Discussion 19F
NMR Relaxation Data Analysis. The observation of monoexponential relaxation at all frequencies and temperatures strongly suggests that the measured relaxation rates are repre-
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J. Phys. Chem. C, Vol. 112, No. 14, 2008 5675
sentative of the bulk material and that all motional fluoride ions are at a common spin temperature because of fast spin diffusion. In analyzing the data, it was assumed that the relaxation is driven by modulation of the homonuclear dipolar 19F-19F interactions arising from anion dynamics. Calculations based on the crystallographic data show that, given the isotopic abundance and significantly lower gyromagnetic ratios of these nuclei, the heteronuclear dipolar 19F-117Sn, 19F-119Sn, and 19F-207Pb interactions are too weak to contribute significantly to the observed fast 19F relaxation. The theory of dipolar relaxation in polycrystalline solids can therefore be applied, and at a given temperature, the frequency dependent spin-lattice relaxation rate, R1(ω), is given by
R1(ω) )
( )
1 9 µ0 2 4 2 1 γF p [J1(ω) + J2(2ω)] ) T1(ω) 8 4π rFF6
(1)
where, µ0 is the vacuum permeability, γF is the gyromagnetic ratio for the 19F nucleus, rFF is the fluoride ion jump distance, and J(ω) is the spectral density at frequency ω, at the temperature in question. For temperatures above 263 K, it is only possible to fit the relaxation profiles by assuming a superposition of two motional processes. It is also apparent (Figure 3) that the faster motion, which lies within the frequency window at all temperatures, does not have a Lorentzian form. There are several spectral density functions19 that can be used to fit such data, including the Cole-Davidson and log-normal distributions of barrier heights. The absence of a low-frequency plateau in the R1 data suggests that the best fit is obtained by using the Cole-Cole equation20 as the spectral density for this motion. This phenomenological approach was developed for dielectric spectroscopy and has been previously used to interpret NMR relaxation data.21 It is effectively a stretched-Lorentzian with a parameter, δ, which is interpreted as relating to the extent of correlation of the motional process, or to the width of the distribution of correlation times.
JCC(ω,τc,δ) )
( )[
]
(ωτc)δ δπ 2 sin (2) ω 2 1 + ($τ )2δ + {2 cos(δπ/2)}(ωτ )δ c c where τc is the characteristic time for the dynamic fluoride process at a given temperature; it is usually interpreted as the mean time between jumps. For δ ) 1, the Cole-Cole equation reduces to a simple Lorentzian function, while δ ) 0 corresponds to the highest degree of correlation possible. For the faster motion in PbSnF4, we found that the δ value was weakly temperature dependent below 340 K. The data from this temperature range can be fitted by fixing the δ value to the average value, 0.68, without altering the extracted rates, although in the analysis presented, the δ value was a free parameter. Above 340 K, the δ value decreases significantly with temperature, to 0.32 at 400 K, and it is not possible to fit the data assuming a constant δ value. This can be interpreted as an increase in the extent of correlation in the motional process or of the width of the distribution of barriers. Having modeled the faster process in this way, the slower process, which is only observed above 263 K, can be successfully modeled with a simple Lorentizan spectral density contribution. This corresponds to uncorrelated motion of the fluoride anions over a single barrier. Typical fits to the data are shown in Figure 4. It should be noted that is possible to produce comparably good fits to the relaxation profiles using the “multi-Lorentzian”
Figure 4. 19F NMR profiles recorded; (a) at 297 K (9), the solid line is a fit using a Cole-Cole/Lorentzian spectral density function, the dashed lines are the individual contributions from the Cole-Cole and the Lorentzian components which are added to generate the solid line; (b) at 238 K (0) fitted with a Cole-Cole spectral density function only.
or model free approach for the spectral density.22 In this approach, merit function analysis is used to determine the number of Lorentzian spectral density components required to fit the data. For our data, 3 Lorentzians are required in the temperature range 273-348 K and 2 are required above and below this range. As a result, there are steps in temperature dependence of the dynamic (τc) and structural (rFF) parameters obtained, which are not related to any physical changes but rather reflect the instability of this model for these data. The Cole-Cole/Lorentzian model is preferred as it requires fewer fitting parameters (a maximum of five; two τc values, two rFF values, and one frequency independent offset); it produces quantitative agreement between the extracted dynamic and structural parameters with those obtained from independent crystallographic and conductivity measurements, and the fits are stable over the full temperature range explored. Fluoride Ion Dynamics. The τc values extracted using the Cole-Cole/Lorentzian model indicate that there are two fluoride motions on distinctly different timescales. For the slow motion τc ranges from 2 × 10-5 s to 5 × 10-7 s over the temperature range, while for the fast motion, τc ranges from 1 × 10-7 s to 9 × 10-8 s. Arrhenius behavior is observed for both processes, Figure 5, with a discontinuity evident at around 340 K. This is very close
5676 J. Phys. Chem. C, Vol. 112, No. 14, 2008
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Figure 5. Thermal dependence of anion dynamics in PbSnF4. The rates were extracted using the Cole-Cole/Lorentzian model analysis of the NMR data. Open and filled symbols are associated with the slower and faster processes, respectively. Solid lines are straight-line fits to the data. The dashed line indicates the approximate temperature at which the conductivity changes.
TABLE 3: Dynamic Data for PbSnF4, from an Arrhenius Analysis of the Rate Data Obtained Using the Cole-Cole/ Lorentzian Model with Estimated Standard Deviations Given in Parentheses process fast slow
temperature range
Eact (kJ mol-1)
Eact (eV)
τ0-1 (s-1)
high low high low
59(3) 13(1) 20(2) 30(3)
0.62(3) 0.14(1) 0.21(2) 0.32(3)
5.29(3) × 1016 1.15(1) × 1010 4.69(6) × 108 4.46(2) × 1010
to the temperature where the change in the activation energy for conductivity was reported.5 The activation energies and prefactors obtained from straight-line fits to the NMR data, from above and below the critical temperature, are given in Table 3. It is very interesting to note that the reported activation energy for DC conductivity in PbSnF4 is 30 kJ mol-1 and 22 kJ mol-1, below and above 340 K, respectively.5 The numerical agreement with the values from the NMR analysis, of 30 ( 3 and 20 ( 2 kJ mol-1, and the observation of the same transition temperature strongly suggest that the slower motion, which is observed on a microscopic level by NMR is directly related to the mechanism of bulk conductivity. This assignment also means that the faster motion, observed by NMR, is not a translational motion of anions through the lattice; instead, it must be a local exchange process. The Arrhenius pre-factor, derived from the NMR analysis, for the slower (Lorentzian) motion in the low-temperature range is τ0-1 ) 4.46 × 1010 s-1, which is slightly lower than expected, given that the vibrational time scale of an ion trapped in a normal lattice site is of the order of picoseconds. However, low prefactors are often observed in superionic solids.23 More significantly, the pre-factor is far smaller, by more than 3 orders of magnitude, than that expected for the generation of a Frenkel defect.23 This strongly suggests that even below 340 K, where the fluoride lattice is relatively ordered, there are large numbers of vacancies available. This situation is consistent with the presence of a faster independent process which generates the required vacancies. Above 340 K, the pre-factor for the slower process is lower at τ0-1 ) 4.69 × 108 s-1, and the barrier to the motion is lower. These changes may be due to additional
Figure 6. Comparison of the NMR jump distances (rFF) for PbSnF4 from the Cole-Cole (0) and the Lorentzian (red open circle) spectral density components, with the crystallographic fluorine-fluorine contact distances F(2)-F(2) (red filled triangle), F(2)-F(4) (blue filled upside down triangle) and F(2)-F(1) (9).8 The solid lines are guides to the eye.
broadening of the potential well for anion dynamics, associated with an increase in fluoride disorder. The pre-factor for the faster (Cole-Cole) motion in the lowtemperature range, τ0-1 ) 1.15 × 1010 s-1, is also close to the time scale expected for anion motion into a pre-existing vacancy. However, above 340 K, the pre-factor for this motion is much larger τ0-1 ) 5.29 × 1016 s-1, and the activation energy is higher. This strongly suggests that, for the non-translational fluoride exchange process, the onset of fluoride disorder is associated with the requirement for defect generation. Assignment of the Motions. The 19F dipolar coupling constants are proportional to the inverse sixth power of the fluorine-fluorine jump distance, rFF, eq 1. So NMR relaxometry provides a direct and sensitive measure of the physical separation of the fluoride ion minima. In crystallographic analysis, on the other hand, a model for all of the atomic positions is refined against the measured diffraction pattern. For PbSnF4, large anisotropic thermal parameters are required to fit the diffraction data reflecting a high degree of positional/thermal disorder. Therefore, the reasonable agreement between the structural information from the NMR and the diffraction analyses, presented in Figure 6, is encouraging and confirms our assumption that the 19F spin-lattice relaxation in PbSnF4 is due to homonuclear 19F-19F dipolar interactions only. It should be noted that the crystallographic F(2)-F(1) distances are open to interpretation. Below 700 K, there is no measurable occupancy of the F(1) site; in both the present study and that of Castiglione et al.,8 for the calculation of inter-site separations, this site has been assumed to lie at the ideal fluorite position. It should also be noted that the variation in the rFF values with temperature is far greater than can be accounted for by thermal expansion of the lattice over this temperature range. By comparing the crystallographic and NMR distances at 298 K, the slow (Lorentzian) motion can be assigned to F(2)-F(2) in-plane anion jumps. As the temperature is increased, the jump distance for this process decreases to a value between the F(2)F(2) and the F(2)-F(4) crystallographic distances. We interpret this as reflecting the onset of F(2)-F(4) exchange which mixes with the translational F(2)-F(2) motion. While the onset of F(2)/ F(4) disorder above 340 K had been suggested in the diffraction study,8 the reduction in both the activation barrier and the pre-
Conductivity and Fluoride Ion Dynamics
Figure 7. Detail of conduction mechanism, above 340 K, in R-PbSnF4 showing F(2)-F(2) and F(2)-F(4) translational motions and F(2)F(1) local jumps. Below 340 K, the F(2)-F(4) motion is quenched.
factor for the process measured by NMR relaxometry confirm this interpretation. As might be expected, the faster motion corresponds to a shorter anion jump-distance (rFF ) 2.4 ( 0.2 Å) at all temperatures. From the rFF values at 298 K, this motion could correspond to either F(2)-F(4) in-plane or F(2)-F(1) out-ofplane jumps. We assign it to F(2)-F(1), in the low-temperature range, as F(2)-F(4) motion would require the generation of a defect, which is precluded on the basis of the measured prefactor, τ0-1 ) 1.15 × 1010 s-1. This assignment is also consistent with the diffraction analysis,8 which showed that the thermal ellipsoids on F(2) extend toward the vacant F(1) site and that the F(1) partial occupancy is very low below 700 K. Low occupancy is expected, as the F(1) residence time must be very short, since the barrier to reverse F(1)-F(2) jumps must be significantly lower than that for F(2)-F(1) jumps. The good agreement between the extracted fluoride jump distances and the crystallographic data, confirms that the fluoride atoms in the F(3) sites are not part of the dynamic fluoride lattice and that our experiments are not sensitive to their relaxation. Apparently, T2 of this rigid sub-lattice is very short, and its 19F magnetization contribution dephases completely during the short switching time required for field stabilization at the NMR detection field. In BaSnF4, the time scale for exchange between the mobile and the static lattices was shown by NMR9 to be milliseconds. Processes on this ultra-slow time scale fall outside the dynamic range of the field-cycling experiment. Mechanism for Fluoride Ion Dynamics. A consistent picture of the fluoride dynamics emerges from the NMR study. At temperatures below 340 K, there is an in-plane exchange process associated with tetrahedral (F(2)) sites that can lead to translational fluoride motion, which is directly related to the mechanism of bulk ionic conduction. At temperatures above 340 K, the process involves both tetrahedral (F(2)) and octahedral (F(4)) sites. The activation energy barrier, for anion dynamics and conductivity, is lower as an alternative pathway is accessible, Figure 7. The low pre-factors and Lorentzian spectral densities, observed for this process at all temperatures, show that the motion must be into a pre-existing vacancy on the F(2) sites. These are generated by a faster local fluoride exchange process. At temperatures below 340 K, the faster dynamic process can be assigned to F(2)-F(1) exchange, on the basis of the anion jump distance and the pre-factor. At all temperatures, the fast
J. Phys. Chem. C, Vol. 112, No. 14, 2008 5677 process has a non-Lorentzian spectral density. This is probably because the Sn lone pairs extend into the nominally vacant F(1) plane and so are strongly affected by transient F(1) occupancy, altering the barrier to fluoride jumps onto nearby F(1) sites and perhaps altering the position of the minimum for such sites. This situation would be expected to give rise to non-stochastic dynamics. At temperatures above 340 K, the barrier and the pre-factor for the fast process both increase, and the value of δ decreases, which indicates an increase in the extent of correlation. These observations are consistent with increased disruption of the lone pairs as the rate of fluoride exchange into the F(1) sites continues to rise with temperature. This may also explain the high dielectric constant reported for PbSnF4,6 which was ascribed to space-charge polarization. It is also interesting to note that the NMR data suggest that the F(2)-F(1) jump distance decreases with temperature, to about 2.2 ( 0.1 Å by 400 K. One could speculate that this is due to the formation of anion interstitials as part of the Frenkel F(2)-F(1) process, which are closer to the F(2)-F(2) plane than the formal F(1) fluorite site location. Conclusion From the NMR analysis, we can propose a detailed mechanism for conduction that is consistent with both the diffraction and the conductivity measurements. The conductivity is twodimensional at all temperatures. The decrease in the barrier to conductivity above 340 K can be attributed to a mixing of translational anion motions across the F(2) and F(4) sites, which arises because of increased numbers of vacancies on the F(2) sites, driven by rapid F(2)-F(1) out-of-plane exchange. On reducing the temperature below 340 K, the absence of the translational motions across the F(2) and F(4) sites results in a room-temperature conductivity almost an order of magnitude lower than would otherwise be observed. Acknowledgment. E.M. gratefully acknowledges the financial support of the Irish Research Council for Science, Engineering and Technology Embark scholarship funded by the National Development Plan. D.B. acknowledges Enterprise Ireland (Basic Research Grant SC/2002/336) and the Higher Education Authority of the Republic of Ireland for support in equipment purchase. J.S. is grateful to the Royal Society of Chemistry for financial support. We also gratefully acknowledge the ISIS Facility, Rutherford Appleton Laboratory for neutron beam time and Dr S. Hull for helpful discussions. Supporting Information Available: Crystal and refinement parameters and fitted neutron diffraction profile. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Donaldson, J. D.; Senior, B. J. J. Chem. Soc. A 1967, 1822118225. (2) Collin, A.; Denes, G.; Le Roux, D.; Madamba, M. C.; Parris, J. M.; Salaun, A. Int. J. Inorg. Mater. 1999, 1, 289. (3) Denes, G.; Yu, Y. H.; Tyliszczak, T.; Hitchcock, A. P. J. Solid State Chem. 1993, 104, 239-252. (4) Eguchi, T.; Suda, S.; Amasaki, H.; Kuwano, J.; Saito, Y. Solid State Ionics 1999, 121, 235-243. (5) Ahmad, M. M.; Yamada, K.; Okuda, T. J. Phys.: Condens. Matter 2002, 14, 7233-7244. (6) Reau, J.-M.; Lucat, C.; Portier, J.; Hagenmuller, P. Mater. Res. Bull. 1978, 13, 877-882. (7) Denes, G.; Yu, Y. H.; Tyliszczak, T.; Hitchcock, A. P. J. Solid State Chem. 1993, 104, 239-252. (8) Castiglione, M.; Madden, P. A.; Berastegui, P.; Hull, S. J. Phys.: Condens. Matter 2005, 17, 845-861.
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