J. Phys. Chem. C 2008, 112, 9291–9300
9291
Tuning the Li Diffusivity of Poor Ionic Conductors by Mechanical Treatment: High Li Conductivity of Strongly Defective LiTaO3 Nanoparticles M. Wilkening,* V. Epp, A. Feldhoff, and P. Heitjans† Institute of Physical Chemistry and Electrochemistry, and Center for Solid State Chemistry and New Materials, Gottfried Wilhelm Leibniz UniVersity HannoVer, Callinstr. 3a, D-30167 HannoVer, Germany ReceiVed: February 19, 2008; ReVised Manuscript ReceiVed: April 7, 2008
Lithium tantalum oxide, LiTaO3, with an average particle size in the µm range is known as a very poor Li ion conductor. It is shown here that its Li conductivity can be drastically increased by ball milling. The so-obtained nanostructured powder with an average particle size of about 20 nm shows a dc conductivity, σdc, of about 3 × 10-6 S cm-1 at T ) 450 K (σdcT ) 1.4 × 10-3 S cm-1 K) which is about 5 orders of magnitude larger than that of the corresponding microcrystalline powder at the same temperature. The activation energy EA is reduced by about one-third, i.e., it decreased from EA ) 0.90(1) eV to about EA ) 0.63(1) eV. The effect of different milling times on the ionic conductivity is studied. Furthermore, the thermal stability of the nanocrystalline materials against grain growth has been examined by in situ impedance spectroscopy. Interestingly, the Li conductivity of a sample milled for 16 h does not change much even when the material is exposed to about 700 K for several hours. Moreover, the Li self-diffusion in the nanostructured as well as the coarse grained materials has been investigated by various solid-state 7Li NMR techniques. 1. Introduction Fast solid ion conductors are characterized by a large number of vacancies or other defects as well as by pathways that enable the ions to move over long distances. In order to be mobile, an ion should be small and have a low charge. Besides hydrogen, Li+ is the smallest and thus one of the fastest cations. Actually, much effort is spent on further enhancing the Li conductivity of a number of materials representing promising candidates useful as, e.g., electrodes in secondary ion batteries.1,2 One possibility is to reduce the crystallite size in order to benefit from nanosize effects.3,4 In nanocrystalline materials, a large volume fraction of interfacial regions and grain boundaries are present.5 In many nanocrystalline ceramics, these regions provide pathways for fast cation migration.6 However, there are also examples known where either no significant enhancement is found or the ionic mobility is even decreased.6–10 The microstructure of these pathways is still not known in detail. Recently, we have used lithium niobate, LiNbO3, as a model substance to study the effects of nanostructure on the Li diffusivity.11–13 In its single-crystalline and microcrystalline form (average particle size in the µm-range) it is a very poor Li conductor.14 Ball milling of LiNbO315 and other oxides16 for several hours yields a heterogeneous material consisting of highly disordered interfacial regions and nanocrystalline grains.6,13,17–19 Remarkably, ball-milled nanocrystalline LiNbO3 exhibits an increase of the overall room temperature Li conductivity by 6 orders of magnitude when compared with the conductivity of the coarse grained source material.14 Glass et al.20 reported on a similar effect when pure glassy LiNbO3, obtained after laborious preparation by twin roller-quenching, is compared with its coarse grained form. The same holds for similarly structured LiTaO3.20 However, it is interesting to know * To whom correspondence should be addressed. E-mail: wilkening@ pci.uni-hannover.de. Fax: +49 511 762 19121. Tel: +49 511 762 3273. † E-mail:
[email protected]. Web: www.heitjans.pci. uni-hannover.de.
whether this drastic enhancement can be simply achieved also by mechanical treatment of LiTaO3. Note that ball milling does not necessarily lead to an increase of the ionic conductivity; to this extent, it has so far been observed only for LiNbO3. Here, we report about Li diffusion in high-energy ball-milled LiTaO3 which is studied by both impedance spectroscopy and 7Li nuclear magnetic resonance (NMR) spectroscopy. The latter includes line shape analyses and measurements of 7Li NMR spin-lattice relaxation rates. LiTaO3 crystallizes in the same space group as LiNbO3, i.e., R3c. The lattice constants of the two compounds (LiTaO3: a ) 0.515 nm, c ) 1.378 nm; LiNbO3: a ) 0.515 nm, c ) 1.386 nm) as well as the radii of Ta5+ (64 pm) and Nb5+ (69 pm), when octahedrally coordinated by oxygen anions, are very similar. The results from impedance and 7Li NMR spectroscopy of the present study show that also in the case of LiTaO3 the ionic conductivity is drastically increased after high-energy ball milling the source material for several hours at room temperature. We will show that by the combination of milling and subsequent annealing the Li conductivity of LiTaO3 can be easily tailored over a range of 6 orders of magnitude. Interestingly, even at very short milling times, a drastic increase of the Li diffusivity is observed in LiTaO3. Therefore, the present paper aims also at contributing to answer the question what happens during mechanical treatment of LiTaO3. First studies on the thermal stability of the milled samples against grain growth and grain boundary relaxation have been useful to get (indirect) information about the degree of disorder introduced, which is also qualitatively seen in the corresponding 7Li NMR spectra of ball-milled LiTaO3. 2. Experimental Section Pure lithium tantalum oxide (99.9%) was obtained from Alfa Aesar. The average particle size of the source material lies in the µm range. The white powder showed the typical XRD pattern of LiTaO3 (Figure 1) Nanocrystalline LiTaO3 was
10.1021/jp801537s CCC: $40.75 2008 American Chemical Society Published on Web 05/30/2008
9292 J. Phys. Chem. C, Vol. 112, No. 25, 2008
Figure 1. XRD patterns of micro- and nanocrystalline LiTaO3 obtained after different milling times ranging between 0 and 16 h as indicated. With increasing milling times the XRD lines are increasingly broadened. When the samples milled for 16 h and 30 min were annealed at 700 and 1000 K, respectively, the lines narrowed again (upper two patterns).
prepared by high-energy ball milling using a SPEX 8000 shaker mill. We have used an alumina vial set with a single ball made from Al2O3 for milling. The weight of the ball was about 4 g. The ball-to-powder weight ratio chosen was 4:1. We milled the LiTaO3 in air as well as in Ar atmosphere. For the milling in inert gas atmosphere, the vial set was placed in an airtight container made of steel. The container was filled in an Ar glovebox with less than 5 ppm water vapor inside. The crystallite diameter was estimated using the Scherrer equation via the broadening of the XRD lines (see next section). XRD patterns were recorded by means of a Phillips PW 1800 diffractometer (Bragg-Brentano geometry) using Cu KR radiation. Prior to the determination of the line broadening, the KR1 and KR2 contributions were separated from each other using the correction procedure introduced by Rachinger.21 For transmission electron microscope (TEM) investigations, a powder specimen was dispersed in ethanol, and a drop of 10 µL of suspension was dried on a copper-supported holey carbon film. (Scanning) transmission electron microscopy (S)TEM was made at 200 kV on a field-emission instrument of the type JEOL JEM-2100F-UHR in bright-field, dark-field, and phase contrast. Most of the samples for impedance measurements were prepared by room temperature pressing of the corresponding powder under uniaxial pressure of 1 GPa in air. One sample which was milled for 16 h in Ar was pressed also in Ar atmosphere and placed afterward into the impedance cell which was put into the Ar glovebox. The cell was closed in the Ar box and connected to a stream of dry nitrogen for the impedance measurements outside the glovebox. In all cases, platinum powder (Merck, 99.9%) was used as electrode material. The duration of pressing ranged from about 30 min to several hours depending on the sample. The powders milled for 30 min and more could be pressed very easily. A suitable pellet from the
Wilkening et al. microcrystalline source material was only obtained via hotpressing at about 500 K in air. Room-temperature pressing, even for about 10 h, led to fragile pellets which broke easily while handling. After successfully pressing the material and the electrodes, pellets were obtained 8 mm in diameter and about 1 mm thickness in a sandwich configuration with the two platinum electrodes. Impedance spectra were recorded with an HP 4192 A impedance analyzer. An alternating voltage of100 mV amplitude was applied to the sample over a frequency range from 5 Hz to 1 MHz. Spectra were recorded between room temperature and 1000 K under nitrogen atmosphere. For the NMR measurements, the material was dried in vacuum at 373 K for several hours and sealed in quartz tubes of 5 mm diameter and 3 cm in length. Solid state 7Li NMR measurements were performed using a modified Bruker MSL 100 spectrometer connected to a variable field Oxford cryomagnet and a Kalmus 400 W amplifier. A standard broadband probe from Bruker equipped with a coil of 8 mm diameter was used to record 7Li NMR spectra and spin-lattice relaxation rates (1/T1) in the laboratory frame. The resonance frequency was 77.72 MHz. The temperature in the sample chamber was controlled by means of an Oxford ITC with an accuracy of about ( 1 K. We have used a Ni-Cr-Ni thermocouple, placed next to the sample, to measure the temperature. 1/T1 rates were measured by means of the classical saturation recovery pulse sequence. The π/2 pulse length was 5 µs. We have used a series of 10 π/2 pulses to destroy the longitudinal magnetization. Its subsequent recovery was recorded after variable delay times t. To this end, the areas under the corresponding free induction decays were plotted as a function of t. 7Li NMR spectra were measured using the solid-echo pulse sequence, π/2 - te - 64° - acq. A 64° detection pulse, see ref 22 for details, was used in order to record the correct ratio between the central and satellite intensities. The interpulse delay te was chosen to lie between 10 and 20 µs. Echoes were Fourier transformed beginning always from the top of the echo. 3. Results and Discussion 3.1. XRD and TEM Analysis. Nanostructured LiTaO3 was prepared by high-energy ball milling of the coarse grained microcrystalline material (µm-sized particles) using a SPEX 8000 shaker mill. By varying the duration of milling, tmill, powders with different mean particle sizes were easily obtainable. Figure 1 shows the XRD patterns which were used for the analysis. The mean crystallite size of the samples was roughly estimated using the Scherrer equation23
L0 )
Kλ β cos θ
(1)
where K is a constant of the order of unity depending on the particle shape (0.89 for spherical particles), λ is the X-ray wavelength, θ is the diffraction angle, and β is the width of the peak after correction for instrumental broadening. We have used the most intense XRD lines between 2θ ) 20° and 40° to estimate L0 (hkl ) 012, 104 and 110). The peaks have Lorentzian shape. Thus, β was calculated according to
β ) Bm - Bstandard
(2)
where Bm is the measured line width and Bstandard is the width of a reference determining the instrumental broadening. We have used the microcrystalline source material to obtain Bstandard. As an example the broadening of the (012) XRD line at 2θ ) 23.72° is shown in Figure 2. The corresponding L0 values are presented in Figure 3. It should be noted that a possible influence of stress
Li Diffusivity of LiTaO3 Nanoparticles
Figure 2. Broadening of the (012) XRD line of LiTaO3 due to different milling times. β is the relative broadening of the line after correction concerning instrumental broadening. Sharp XRD lines were reobtained after annealing the sample at higher temperatures.
Figure 3. Average XRD peak width (0, left ordinate) with increasing milling time. (fwhm: full width at half-maximum). The line width shown here is not corrected concerning instrumental broadening. For comparison, the estimated crystallite sizes (O, right ordinate) are shown vs milling time, too.
introduced by ball milling is not taken into account by the Scherrer equation. Thus the following results should be regarded as a rough estimation. For example, milling for 8 and 16 h yields mean crystallite sizes of about 37 and 27 nm, respectively. Larger milling times than 16 h should result in a sample with a crystallite size of about 20 nm which is usually the limit reachable by high-energy ball milling using a SPEX 8000 M shaker mill.6,16 A milling time of 5 min does not reduce the particle size significantly; the 5 min sample can be still regarded as a material with µm-sized particles. The sample milled for 30 min exhibits still a rather large crystallite size of about 280 nm. For milling times equal and larger than 8 h we have observed abrasion of the Al2O3 vial set used. The corresponding XRD lines are marked in Figure 1 by triangles. The admixing of (nanocrystalline) insulator particles to the conducting phase can significantly influence the overall Li diffusivity.24–27 However, in the present case, no differences in Li conductivity between the samples milled for 16 and 2 h only (see next
J. Phys. Chem. C, Vol. 112, No. 25, 2008 9293 section) are observed. For the 2 h sample, abrasion of Al2O3 is virtually not detectable by XRD. Furthermore, as compared to the influence of ball milling on Li conductivity, the effect of such a small admixture of an insulator seems to be negligible. For comparison, in the case of LiNbO3 we intentionally added nanocrystalline Al2O3, prepared also by ball milling. The nanocrystalline composite (1 - x)LiNbO3:xAl2O3 at, e.g., x ) 0.05, showed an increase of the conductivity by a factor of only 1.3 over the value for x ) 0, see ref 28. This is completely negligible as compared to the increase of the conductivity by about 105 when going from the microcrystalline to nanocrystalline LiNbO3. As is illustrated in Figures 2 and 3, annealing of the sample, milled for 16 h, for about 95 h at 700 K leads to significant narrowing of the XRD peaks. In the case of nanocrystalline LiNbO3 prepared by high-energy ball milling (tmill ) 16 h), DSC measurements showed an exothermic peak at around 700 K, see ref 13, which is absent for the microcrystalline source material. Thus, this observation can be attributed to grain growth and to grain boundary relaxation. The annealed LiTaO3 sample (16 h ball milled) shows a mean crystallite size which is comparable to that of the sample milled for 8 h (see arrows in Figure 3). LiTaO3 which was only milled for 30 min was annealed for 4 days at 1000 K [as well as for 16 h at 1170 K (only the (012) XRD line is shown in Figure 2)]. Coincidentally, the different annealing conditions gave very similar XRD patterns. The average crystallite size increased from 280 nm to about 0.5 µm (see arrows in Figure 3). In Figure 4, scanning transmission electron microscopy (STEM) images of the microcrystalline source material as well as of the samples which were ball-milled for 30 min and 16 h, respectively, are presented. The so-called microcrystalline material shows a particle size of a several hundred nm. The 30 min sample exhibits a rather large distribution of particle sizes. Besides larger crystallites, smaller particles with diameters between 20 and 100 nm are visible. This characteristic is also noticeable in the TEM bright field micrograph of Figure 5. A mean crystallite size of about 280 nm which was determined from the corresponding XRD pattern is in good agreement with this result from TEM. The sample mechanically treated for 16 h looks rather homogeneous (Figure 4). The mean particle size is much less than 100 nm. Due to the compaction during the milling process, the individual nanoparticles are inclined to build larger agglomerates. The high-resolution (HR) TEM micrographs of Figure 5 clearly show that these agglomerates consist of differently oriented crystallites with diameters between about 10 and 30 nm. This is in good agreement with the results estimated by means of the XRD patterns of Figure 1 (see above). There might be a thin amorphous layer covering the nanocrystalline particles. However, in the case of LiNbO3, such amorphous regions were visible in a much clearer way by HRTEM and had a thickness of about 2 nm.13 Recent EXAFS (extended X-ray absorption fine structure) investigations by Chadwick and co-workers19,29 and by our group13 confirmed the presence of amorphous regions in ball-milled LiNbO3. 3.2. Impedance Spectroscopy. In Figure 6 a set of typical conductivity spectra of nanocrystalline LiTaO3, high-energy ball milled for 16 h, is shown for a range of temperatures T between 352 and 510 K as an example. Similar results were obtained for the other samples investigated, however, shifted to higher or lower conductivities. The frequency dependent conductivity real part) can be approximated by a power law30
9294 J. Phys. Chem. C, Vol. 112, No. 25, 2008
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Figure 4. STEM dark-field micrographs of so-called microcrystalline LiTaO3 as well as of LiTaO3 which was high-energy ball-milled for 30 min and 16 h, respectively. With increasing milling time the mean particle size is reduced leading to a homogeneous nanocrystalline material after 16 h mechanical treatment. For further explanations, see the text.
Figure 6. Conductivity spectra of nanocrystalline LiTaO3 in the temperature range from 352 to 510 K showing the dc plateau and the dispersive region at higher frequencies f ) ω/2π. Nanocrystalline LiTaO3 was prepared by high-energy ball milling for 16 h. Its average particle size is about 20 nm.
Figure 5. TEM micrographs of lithium niobate mechanically treated for 30 min and 16 h, respectively. The image placed on the right bottom corner represents an enlarged section of the micrograph above which exhibits LiTaO3 crystallites with an average diameter of about 20 nm.
σ ′ ) σdc + Aωs
(3)
where σdc is the frequency independent dc conductivity and s is a temperature dependent exponent which lies between 0 and 1. Here, 0.54 < s < 0.68 is found in the T range from 352 to 510 K. This is in agreement with the results previously found for nanocrystalline LiNbO3 prepared by ball milling, too. At low frequencies all spectra show a characteristic plateau representing σdc whereas at higher frequencies the spectra exhibit a dispersive regime. Both regions can best be differentiated at low temperatures. The deviation from the dc plateau at higher temperatures (above 450 K) and for f ) ω/2π < 100 Hz is due to blocking electrode effects. In Figure 7 the product σdcT is shown in an Arrhenius plot. For comparison, the results of the sample ball milled for only 30 min and of the source material are also shown. For all three samples σdcT(1/T) obeys Arrhenius behavior according to
( )
σdcT ∝ exp -
EA kBT
(4)
kB is Boltzmann’s constant. Expectedly, the lowest conductivity and the highest activation energy EA (≈ 0.9 eV) are found for
Figure 7. Temperature dependence of σdc for microcrystalline (0 h) and nanocrystalline LiTaO3 produced by high-energy ball milling for 30 min and 16 h, respectively, of the microcrystalline material. The dotted lines represent the temperature behaviour of micro- (taken from refs 13 and 14) and nanocrystalline LiNbO3 ball-milled also for 16 h in the same shaker mill.
the starting material. A similar result was previously obtained for micro- and nanocrystalline LiNbO3 and is shown by the dotted lines in Figure 7, for comparison. As can be seen from Figure 7, ball milling largely influences ionic conductivity. The 16 h sample exhibits an activation energy of about 0.63 eV. The lower limit of σdc being detectable with the impedance spectrometer used is about 10-9 S cm-1. Reducing the milling time to 8 h does not change the absolute values of σdcT as well
Li Diffusivity of LiTaO3 Nanoparticles
Figure 8. Temperature dependence of the dc conductivity of the LiTaO3 samples milled for 0.5, 2, 8, and 16 h. The first data point of the 2 h ball-milled sample reflects the influence of surface water (see text). The influence of annealing on the conductivity of the samples milled for 16 h and 30 min is also shown. For clarity reasons the data points of the 16 h sample are shifted by a factor of 10 towards higher values because the data of the samples milled for 2, 8, and 16 h coincide. Further explanations see text.
as that of EA. Even when the microcrystalline material is ballmilled for only 2 h a significant decrease of the Li conductivity is not observed (see Figure 8 where the samples milled for 2, 8, and 16 h are shown). Therefore, the corresponding conductivity parameters seem to represent an upper limit which is already reached after mechanical treatment for 2 h, although the corresponding XRD line width is still increasing (see Figure 3). Note that in Figure 8 for clarity reasons the data points of the 16 h sample are shifted by a factor of 10 toward higher values. A sample which was milled for 30 min yields an Li conductivity which is about 1 order of magnitude smaller (Figure 8) than the other nanosamples. Interestingly, EA of this sample is identical to that found for the samples produced by milling for several hours. The possible influence of water on the measurements should be mentioned. As an example, we focus on the conductivity values of the 2 h ball-milled sample which are shown in Figure 8. The first data point represents the influence of surface water on Li conductivity. This sample was always handled in air and showed a much higher conductivity than expected at room temperature. However, water can be removed from the sample when it is heated above 373 K in a stream of dry nitrogen for about one hour. Even if the temperature is decreased afterward, the conductivity values do not deviate from the linear behavior found above 373 K. A sample which was prepared by ball milling for 16 h in Ar atmosphere (as mentioned above) gave identical results compared with a sample exposed to air and dried above 373 K in a stream of dry nitrogen. Furthermore, the annealing of the 16 h ball-milled sample up to 700 K (see below) exhibits no deviation from the Arrhenius behavior shown in Figure 8 which would be interpretable as an effect due to residual water. The activation energy of nanocrystalline LiTaO3 found here is very similar to that found for LiNbO3 (0.61 eV) which was prepared by ball milling for 16 h in the same shaker mill. Its dc conductivity is only slightly shifted to higher values (cf. Figure 7). The difference is less than 1 order of magnitude. We have recently shown that LiNbO3 milled for 16 h contains a significant amount of amorphous regions.13 Furthermore, the Li diffusion properties of pure amorphous LiNbO3 are very similar to those of a sample high-energy ball-milled for several
J. Phys. Chem. C, Vol. 112, No. 25, 2008 9295 hours.12 One might thus conclude that also in the case of similarly structured LiTaO3 the observed increase of ionic conductivity is, to a certain degree, due to amorphous regions introduced by mechanical treatment for many hours. Pure glassy LiTaO3, prepared by roller quenching, exhibits an Li conductivity being very similar to that found for LiTaO3 milled for 16 h, see ref 20. In this context it should be noted that LiTaO3 is somewhat harder (5.5 on Mohs’ scale) than LiNbO3 (5.0). Interestingly, in the case of LiTaO3 even when ball milled for 30 min only, a drastic enhancement of σdc accompanied by a reduction of the activation energy by one-third is observed in comparison with the starting material. As the mean particle size is only partly reduced (Figures 3 to 5) after such a relatively short milling time (see above), one may suppose that partial amorphization of that sample does not play the only role in explaining the observed conductivity enhancement. This is corroborated by the fact that the samples milled for 2, 8, and 16 h show no differences in conductivity although the process of particle reduction is not completed for the sample milled for 2 h. After compaction, the 30 min sample can be regarded as a dense-packed material of differentially oriented particles with unequal sizes where the highly defective grain boundaries build a network of fast Li pathways. Moreover, one may suppose that in addition to grain size reduction the introduction of a large number of point defects, dislocations and/or internal interfaces during mechanical treatment might be responsible for the observed high Li conductivity for the sample milled for 30 min. Such defects might be of long-range order and represent fast through-going pathways for Li diffusion. These paths can be regarded as the necessary early stages to enable the larger sized crystallites to break into smaller particles while milling. In order to study the possible structural differences of the two samples (30 min and 16 h) we have exposed them stepwise to higher temperatures as is shown in Figure 8. Interestingly, heating the 16 h sample slowly up to 700 K leads to no change of the corresponding Arrhenius behavior. Thus, the influence of grain growth in this T range on the conductivity is much smaller than expected. Usually it takes about 20 min until temperature stability ((5 K) is reached. The times shown in Figure 8 indicate the time interval between the measurements. Annealing the 16 h sample for 95 h at 700 K in the impedance cell leads to a decrease of the conductivity by less than a factor of 10 (see Figure 8). Subsequent cooling of the material shows that the annealing process had no influence on the activation energy. However, when the 30 min sample is exposed to temperatures higher than 650 K, this has a much larger effect on σdc. Annealing the sample for only 20 min at 650 K reduces the conductivity already by a factor of about five indicating its less good temperature stability. The same effect, but much more pronounced, was obtained for a sample milled for 5 min only (not shown). The Li conductivity of that sample lies in between that of the 30 min sample on the one hand and microcrystalline LiTaO3 on the other hand. Obviously, the defects introduced after short milling times can be healed much easier by annealing than it is the case when the material is mechanically treated for 16 h. In other words, the process of grain growth of a 16 h milled sample needs much higher temperatures than healing defects in a more coarse grained crystalline material as it is obviously the case for the samples milled for 30 min and less. Further annealing of the 30 min sample for 4 days at 1000 K leads to the σdcT values shown in Figure 8. The same result is found for a sample which was milled for 30 min and exposed to 1170 K for 16 h. This is consistent with the fact that the two samples show the same XRD pattern (see above). The so
9296 J. Phys. Chem. C, Vol. 112, No. 25, 2008 obtained materials exhibit activation energies of about 0.90 eV which is identical to the value found for the source material. It should be noted that the conductivity of the starting material is still 1 order of magnitude smaller. However, annealing a sample milled for only 5 min at 700 K for 1 h yields conductivities which coincide with those of the source material. Interestingly, although the XRD peak widths of the 16 h sample annealed at 700 K and of the sample milled for 8 h are similar, both samples give different results concerning Li conductivity. Thus, in the case of LiTaO3, the particle size is clearly not the only relevant parameter which defines the transport properties. In fact, the microstructure of the (nano)material, which is determined, e.g., by the preparation route and the thermal history, i.e., the annealing process chosen, has to be taken into account, too. In conclusion, the combination of milling and subsequent annealing offers the possibility to produce LiTaO3 powder samples with desired transport parameters. Following this way the Li conductivity of LiTaO3 can be set in a range of many orders of magnitude. Thus, this may be regarded as one of the first steps of the ubiquitous attempt in materials science to design materials with tailored transport properties. 3.3. Solid State NMR. Besides dc conductivity measurements by which macroscopic transport properties are probed, Li diffusion parameters can be studied alternatively by nuclear magnetic resonance (NMR) spectroscopy, however, from a microscopic point of view.31,32 In order to get further insight into the parameters which determine the Li diffusivity of the milled LiTaO3 samples, we have recorded 7Li solid-echo NMR spectra (of nonrotating samples) as well as 7Li NMR spin-lattice relaxation rates 1/T1 between about 100 and 500 K. 7Li NMR spectra and spin-lattice relaxation NMR measurements are used to elucidate short-range Li dynamics. Additionally, 7Li NMR spectra are used to characterize the local electronic structure to which the Li ions are exposed. 3.3.1. 7Li NMR Line Width Analysis (Motional Narrowing). Recording 7Li NMR line widths as a function of temperature provides one of the easiest methods to probe Li diffusivity by NMR. The line width of the central transition of a 7Li NMR spectrum depends on the Li diffusivity which is present at a given temperature. At low T where the mean Li jump rate is much smaller than the line width, Li diffusion does not exert any influence on the spectrum. This range is called the rigidlattice regime. However, with increasing temperature the Li jump rate increases, and consequently, dipolar interactions between the spins are increasingly averaged so that the initially dipolarly broadened NMR line starts to narrow continuously (motional narrowing, MN). At sufficiently high temperatures the narrowing process is completed and the final line width is determined only by the inhomogeneity of the static magnetic field used (extreme narrowing regime). In Figure 9, the 7Li NMR line width (fwhm ) full width at half-maximum) of the central transition (see next section and, e.g., Figure 10) is plotted as a function of temperature T. Data were recorded at a resonance frequency of 77.72 MHz. In the case of the sample which was milled for 16 h all three regimes can be well recorded between 150 and 550 K. Nearly the same MN behavior was observed for LiNbO3 ball milled for 16 h, see refs 11–13 and 17. The central 7Li NMR line starts to narrow already below room temperature indicating the fast Li diffusivity of 16 h ball milled LiTaO3. Incipient MN means that the corresponding jump rate is larger than about 103 s-1. At about 370 K, where the dc conductivity takes a value of about 10-7 S cm-1, the inflection point of the MN curve is observed. Here, the inflection point is
Wilkening et al.
Figure 9. 7Li NMR line widths (fwhm) of micro- (0 h) and nanocrystalline LiTaO3 ball milled for 16 h. For comparison the line widths of the sample milled for 30 min and of that milled for 30 min and heated for four days at 1000 K (triangles) are shown, too. The line widths were obtained from the central transition of the 7Li NMR spectra recorded at 77.72 MHz. The lines are guides for the eye.
just taken as a reference point for comparison. The averaging process is nearly complete at approximately 470 K. For comparison, the line width of the LiTaO3 microcrystalline source material does not show any change in this T range. Up to 525 K only the rigid-lattice regime is detected demonstrating its extremely low Li diffusivity and ionic conductivity. The latter is estimated to be smaller than 4 × 10-10 S cm-1 at 525 K, see the extrapolated dashed line in Figure 7. The material which was milled for only 30 min shows already a significant reduction of the line width with increasing T. Motional narrowing starts at a temperature which is similar to that found for the 16 h ball-milled sample. However, the narrowing process extends on a much larger temperature range. Interestingly, at the inflection point of the MN curve (≈440 K) the dc conductivity is about 10-7 S cm-1 once again. Heating the sample up to 1000 K and annealing it for several days leads back to the result which is obtained for the source material. The same result is obtained when the sample milled for 30 min is annealed for 16 h at T ) 1170 K in air. 7Li NMR motional narrowing of the annealed samples as well as of the source material is expected to start at temperatures higher than 570 K. For comparison, σdc of the microcrystalline material reaches 10-7 S cm-1 at 800 K (σdcT ≈ 10-4 S cm-1 K-1, see Figure 7). Thus, one may expect the inflection point of the corresponding MN curve around this temperature. 3.3.2. 7Li Solid-Echo NMR Spectra. Besides recording NMR line widths we have used solid echo NMR spectroscopy to study the local structure of the different samples. In particular, we focused on the samples milled for 16 h and 30 min and compared the results with the data obtained for the source material. In Figure 10, 7Li solid-echo NMR spectra of micro- and nanocrystalline LiTaO3 (16 h) recorded at a radio frequency of 77.72 MHz are shown for comparison. The NMR spectrum of the coarse grained source material is composed of a central line and a well-defined quadrupole powder pattern consisting of a pair of “inner satellites” with their outer wings. This is typical of 7Li nuclei (spin-quantum number of 3/2) residing in a well ordered crystalline material where only one crystallographic site is occupied by the Li cations. All nuclei are exposed to the same electric field gradient (EFG) which is produced by the electric charge distribution of the oxygen anions in the
Li Diffusivity of LiTaO3 Nanoparticles
Figure 10. Solid-echo 7Li NMR spectra of micro- and nanocrystalline LiTaO3 (milled for 16 h) recorded at 283 K and a radio frequency of 77.72 MHz. The insets show magnifications of the quadrupole part of the two spectra.
neighborhood.33–36 The interaction of the EFG with the quadrupole moment of the 7Li nucleus alters the Zeeman levels and leads to the spectrum shown in Figure 10 taking into account the different orientations of the crystallites with respect to the external magnetic field. The quadrupole splitting ∆νq, i.e., the frequency difference of the inner satellite peaks, is about 36.5(5) kHz. This results in a quadrupole coupling constant of 73(1) kHz which is twice ∆νq when an axially symmetric field gradient is assumed. The simulation of the measured spectrum using WSolids software37 taking into account the whole shape of the quadrupole pattern leads to 78.6(5) kHz and ηq ) 0 being the anisotropy parameter of the electric quadrupole interaction. This result is in agreement with literature values for 7Li ranging between 76.4(3) and 78.3(8) kHz38–40 and consistent with the value 60.2(3) kHz for 8Li measured by beta-NMR on a LiTaO3 single crystal.41 Milling has a drastic effect on the shape of the NMR satellite intensities. Whereas the shape of the central line is unaffected the quadrupole powder pattern is “smeared out” (Figure 10). It looks distorted and the intensity of the inner satellite peaks is largely decreased. This is apparently due to a distribution of Li sites with slightly different EFGs caused by distortions of the site symmetry. Although the former quadrupole structure is still visible, its shape resembles that of a structurally disordered material. In fact, as mentioned above in the case of ball-milled LiNbO3, a significant amount of amorphous regions is introduced by high-energy ball milling. This was verified in the case of LiNbO3 recently by means of HRTEM and EXAFS measurements and was supported as well by results from X-ray diffraction and Raman spectroscopy.13 In Figure 11, the 7Li NMR spectra of the 30 min sample before and after annealing are shown. As in the case of Figure 10, the spectra are recorded at 283 K and at a resonance frequency of 77.72 MHz. In contrast to the sample milled for 16 h, the spectrum of the 30 min sample before annealing reveals a quadrupole shape which is indeed distorted but still comparable to that found for the source material. This resemblance seems to indicate that the 30 min material consists of larger, well-crystalline regions. Expectedly, the powder pattern of the source material reappears after annealing the sample for 4 days at 1000 K. The quadrupole coupling constants are similar to those found for the microcrystalline and 16 h ball-milled samples.
J. Phys. Chem. C, Vol. 112, No. 25, 2008 9297
Figure 11. Solid-echo 7Li NMR spectra of LiTaO3 milled for 30 min (bottom) and annealed for 4 days at 1000 K (top). The NMR spectra were recorded at 283 K and a radio frequency of 77.72 MHz. The insets show the magnifications of the quadrupole part of the two spectra (see Figure 10, for comparison).
3.3.3. 7Li NMR Spin-Lattice Relaxation. In addition to the NMR line shape analysis 7Li NMR spin-lattice relaxation rates were studied at a resonance frequency ω/2π ) 77.72 MHz between 140 and 500 K. In the case of the microcrystalline source material, the corresponding magnetization transients M(t), which were recorded via the saturation recovery method, can be fitted with a slightly stretched exponential
M(t) ) M0 - M0exp(-(t/T1)γ)
(5)
M0 denotes the equilibrium magnetization at t f ∞. The stretching factor γ was about 0.85 in the investigated temperature range. In general, the relaxation rate 1/T1 is the sum of a diffusion induced 1/T1diff and a nondiffusive background contribution (1/T1bgr):
1/T1 ) 1/T1diff + 1/T1bgr
(6)
Whereas 1/T1bgr shows usually a weak temperature dependence, 1/T1diff vs T exhibits a diffusion induced rate maximum. The maximum shows up when the mean jump rate reaches a value of the order of the Larmor frequency used to measure the spin-lattice relaxation rates; that is, it is characterized by ωτ ≈ 1. The corresponding rates of the high- and low-temperature side of this rate peak vary rapidly with temperature. For ωτ . 1, i.e., in the low-temperature regime which was investigated here, the jump rate 1/τ is much smaller than the Larmor frequency ω/2π. Therefore, local or short-range Li diffusion parameters are sampled in this T region. The T dependence of 1/T1diff in this region is described by the Arrhenius relation
(
1/T1 ∝ exp -
EA,SLR kBT
)
(7)
EA,SLR denotes the activation energy for local hopping. In Figure 12 the rates 1/T1 are plotted vs 1/T for microcrystalline LiTaO3. Up to room temperature, only the relaxation background is detected. Above 300 K the rates slightly increase, thus, 1/T1 starts to be additionally affected by Li diffusion. However, Li diffusion is extremely slow and, therefore, the slight increase only suggests the beginning of the low temperature flank of the corresponding relaxation rate peak 1/T1,diff(1/T). It cannot be excluded that this increase is still due to the temperature dependence of 1/T1bgr. The situation changes when the material
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Wilkening et al.
Figure 12. 7Li NMR spin-lattice relaxation rates of microcrystalline LiTaO3 recorded at a Larmor frequency of 77.72 MHz in comparison with those obtained from the samples milled for 30 min and 16 h, respectively. The solid line represents a fit to the rates above 350 K. Above this temperature the overall rate 1/T1 is dominated by 1/T1diff.
Figure 13. Temperature dependence of the 7Li NMR spin-lattice relaxation rates of LiTaO3 milled for 30 min (left-hand scale) together with that of the stretching factors of the corresponding magnetization transients (right-hand scale). Below 300 K, γ ) 0.85 is found. Increasing Li diffusivity leads to a significant reduction of γ. Similar results were obtained for the sample milled for 16 h.
is milled for about 30 min. First, an increase of the background rates by a factor of about 1.5 is found. Second, as expected from dc conductivity measurements, due to the enhanced Li diffusivity compared to that of the source material the low-T flank of the rate peak becomes partly visible above ambient temperature. A further important characteristic is the following: Below 300 K the transients M(t) can be fitted with eq 5 using γ ) 0.85 (see above). However, for T > 300 K when 1/T1diff becomes larger than 1/T1bgr the stretching exponent decreases continuously reaching a value of about 0.5 at T ) 500 K. The γ values are shown together with the corresponding spin-lattice relaxation rates vs 1/T in Figure 13. When going to the 16 h ball-milled sample a further change of the 1/T1(1/T) behavior is observed (Figure 12). The background rates increased once more and exhibit a slightly stronger temperature dependence between 150 and 250 K. Contrary to the 30 min sample, the diffusion induced low-T flank of the corresponding relaxation rate peak is now clearly visible above 330 K. In this T range, the relaxation rate is strongly affected by relatively fast Li diffusion. Altogether, the trend of Li diffusivity for the three samples shown in Figure 12 is fully consistent with that shown in Figure 9. As in the case of the sample milled for 30 min, the magnetization transients of the material which was mechanically
Figure 14. 7Li NMR magnetization transients M(t), normalised to the equilibrium magnetization M0, of LiTaO3 milled for 16 h, 30 min, and 0 h (source material). The transients were recorded at 393 K and a resonance frequency of 77.72 MHz.
treated for 16 h show large deviations from a single exponential function. An example is shown in Figure 14 where the magnetization transients recorded at 393 K of the three samples are presented for comparison. Whereas the dashed lines in Figure 14 represent fits using a single exponential function, the solid lines show fits according to eq 5. Similarly to the 30 min sample, the stretching factors start to decrease with temperature above 300 K (cf. Figure 13). The slight deviation of the transients from single exponential functions in the case of microcrystalline LiTaO3 and below 300 K for the other two samples is presumably due to the fact that 7Li is a spin-3/2 quadrupole nucleus. In such a case the transients are expected to show twoexponential behavior.42 However, this time dependence is often masked by the influence of dipolar interactions of the nuclei. The influence of quadrupolar relaxation becomes significant when the quadrupole coupling constant is much larger than the line width of the central transition of the spin-3/2 nucleus. In the present case, fitting the transients below 300 K with a twoexponential function leads to two different relaxation rates, T1a-1 and T1b-1 which are, for all samples, related by T1a-1 ) 0.29(2) T1b-1. This ratio is in fair agreement with the theoretical value of 0.25, see ref 42, which is obtained when the nuclei are excited with a 90° pulse.
Li Diffusivity of LiTaO3 Nanoparticles
J. Phys. Chem. C, Vol. 112, No. 25, 2008 9299 4. Conclusions
Figure 15. Temperature dependence of the ac-conductivity of nanocrystalline LiTaO3 which was prepared by ball milling of the coarse grained source material for 16 h. Data were recorded at a frequency of 1 MHz. For comparison, the corresponding dc conductivities and the 7 Li NMR spin-lattice relaxation rates recorded at 77.72 MHz are also shown. The activation energy from relaxation NMR is the same as obtained from impedance measurements at 1 MHz.
The additional deviation from single exponential time behavior of M(t) observed above 300 K is likely due to the disorder introduced via high-energy ball milling. This assumption is supported by the fact that the degree of deviation increases with increasing milling time. A similar effect was found for the dispersed ionic conductors Li2O:X2O3 with X ) B, Al.26,27 The magnetization transients of microcrystalline Li2O are singleexponential even at low T due to the cubic site symmetry. Therefore, the deviation observed for the nanocrystalline composites was used to differentiate between the fast ions located in the grain boundaries and the slower ones in the grains. Such a procedure is difficult to carry out in the present case because of the noncubic site symmetry of Li in LiTaO3. From the fit shown in Figure 12, an activation energy of 0.37(1) eV is obtained for the sample milled for 16 h. As expected, this value is much smaller than that which is obtained from the dc conductivity measurements (0.63 eV) in the same temperature range. Whereas the latter value reflects the longrange Li transport in nanocrystalline LiTaO3, the first one characterizes the short-range Li hopping process which is accessible by spin-lattice relaxation NMR here. Li dynamics on shorter length and thus time scales can be probed by recording ac conductivities at higher frequencies. In Figure 15, the ac conductivities σac read out at a frequency of 1 MHz (cf. Figure 6) for the 16 h sample are shown, multiplied by the temperature, together with the corresponding σdcT values taken from Figure 7 as well as the spin-lattice relaxation rates 1/T1 measured at 77.72 MHz (cf. Figure 12). The activation energy obtained from the ac conductivities (0.38 eV) is as expected smaller than that from dc conductivity measurements (0.64 eV). It is in close agreement with that deduced from 7Li spin-lattice relaxation NMR measurements (0.37 eV) carried out at 77.72 MHz. The result of Figure 15 represents another example of the fact that different methods when applied in comparable time windows can yield the same diffusion parameter values.6,43,44 Furthermore, it points out the heterogeneous nature of Li diffusion in nanostructured LiTaO3 with fast Li ions in grain boundaries and/or grain junctions and slower cations in the crystalline interior of the grains.
Besides LiNbO3, lithium tantalate is a new example where the Li conductivity can be dramatically enhanced when the material is mechanically treated in a high-energy ball mill. A sample mechanically treated for 16 h exhibits an amorphouslike behavior concerning Li diffusion which is remarkably similar to pure glassy LiTaO3 studied in ref 20. However, even at short milling times the Li diffusivity is enhanced by several orders of magnitude as probed by impedance measurements and supported by 7Li NMR spectroscopy. The latter technique, in comparison with the results from impedance spectroscopy, exhibits the heterogeneous Li dynamics of the materials. The structural changes which occur during the milling process seem to be rather complex. Obviously, the results cannot be explained simply by the fact that the particles are reduced in size. In fact, the microstructure of the pathways which the Li ions use for fast migration has to be taken into account. For example, the results which were obtained on a sample milled for 30 min lead to the assumption that in addition to the effect of reducing the crystallite size, a high defect concentration in the interior and/or on the surface of the grains is generated, which seems to contribute also to the large increase of Li conductivity of LiTaO3. Although the grain size is not drastically reduced after 30 min of milling, mechanical treatment has a large effect on the transport parameters. TEM analysis has proved that the microstructure of the 30 min sample takes an intermediate position between the source and the material which was milled for many hours. However, the dynamic properties are more comparable with the latter rather than to the source material. The fact that the samples milled for 30 min and 16 h are structurally different is also expressed in their different behavior when exposed to higher temperatures as well as supported by 7Li solid echo NMR spectroscopy. Whereas the 16 h sample is remarkably stable at 700 K, the Li conductivity of the sample, which was milled for only 30 min, is greatly affected by the annealing process. The latter observation is presumably due to healing of defects as well as to grain boundary relaxation rather than due to grain growth. Finally, the desired conductivity can obviously be adjusted when the following two procedures are controlled: milling and subsequent annealing of the ceramics. Acknowledgment. We thank the Deutsche Forschungsgemeinschaft (DFG) for financial support and P. Bottke for his help with some of the NMR measurements during his chemistry studies. References and Notes (1) Whittingham, M. S. Chem. ReV. 2004, 104, 4271. (2) Winter, M.; Besenhard, J. O.; Spahr, M. E.; Nova´k, P. AdV. Mater. 1998, 10, 725. (3) Maier, J. Solid State Ion. 2000, 131, 13. (4) Balaya, P.; Bhattacharyya, A. J.; Jamnik, J.; Zhukovskii, Yu. F.; Kotomin, E. A.; Maier, J. J. Power Source 2006, 159, 171. (5) Gleiter, H. Acta. Mater. 2000, 48, 1. (6) Heitjans, P.; Indris, S. J. Phys.: Condens. Matter 2003, 15, R1257. (7) Mondal, P.; Klein, A.; Jaegermann, W.; Hahn, H. Solid State Ion. 1999, 118, 331. (8) Kavan, L.; Procha´zka, J.; Spitler, T. M.; Kalba´cˇ, M.; Zukalova´, M.; Drezen, T.; Gra¨tzel, M. J. Electrochem. Soc. 2003, 150, 1000. (9) Brossmann, U.; Kno¨ner, G.; Schaefer, H.-E.; Wu¨rschum, R. ReV. AdV. Mater. Sci. 2004, 6, 7. (10) Wagemaker, M.; Borghols, W. J. H.; van Eck, E. R. H.; Kentgens, A. P. M.; Kearly, G. J.; Mulder, F. M. Chem. Eur. J. 2007, 13, 2023. (11) Bork, D.; Heitjans, P. J. Phys. Chem. B 2001, 105, 9162. (12) Wilkening, M.; Bork, D.; Indris, S.; Heitjans, P. Phys. Chem. Chem. Phys. 2002, 4, 3246.
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