From Micro- to Nanostructured Fast Ionic Conductor Li0.30La0.56

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From Micro- to Nanostructured Fast Ionic Conductor Li0.30La0.5600.13TiO3: Size Effects on NMR Properties Anthony Boulant, Jo€el Emery,* Alain Jouanneaux, Jean-Yves Buzare, and Jean-Franc) ois Bardeau Laboratoire de Physique de l0 Etat Condense (UMR CNRS 6087), Institut de Recherche en Ingenierie Moleculaire et Materiaux Fonctionnels (FR CNRS 2575), Universite du Maine, Avenue O. Messiaen, 72085 Le Mans Cedex 9, France

bS Supporting Information ABSTRACT: This paper is devoted to the study of the changes in the NMR properties in the ionic superconductor Li0.3La0.5600.13TiO3 due to confinement. Stuctural studies were performed on micro- and nanostructured materials with grain sizes from 1.2 μm to 14 nm using complementary techniques such as Powder X-ray Diffraction (PXRD) analysis, the BrunauerEmettTeller method (BET), Transmission Electronic Microscopy (TEM), and Scanning Electron Microscopy (SEM) techniques. Thermogravimetric Analysis (TGA) linked to mass spectroscopy (TGA-MS) was used to evidence surface reactivity and quantify the mass loss, and Fourier transform Infrared (FT-IR) measurements revealed the presence of carbonate. When the size decreases toward the nanometric scale, the strong surface reactivity leads to an Li+/H+ exchange which was observed on the 1H NMR spectrum. This spectrum is similar to the one of the exchanged compound (named HLTO) with an additional contribution due to the protons attached on the surface. These surrounding modifications and the confinement bring new boundary conditions leading also to the modification of the 7Li static and dynamical properties. Below 1 mm an additional line appears in the nanometric systems, and the Zeeman relaxation measured by T1 becomes more complex. Cross relaxation effects are highlighted in the saturation recovery magnetization of the proton and the lithium.

I. INTRODUCTION The idea that the physical properties could be modified in systems with nanometric sizes has been developed in the past two decades:1 in nanostructured systems, the interfaces are so closely spaced that their influence on the overall property becomes significant if not prevailing. For several years, the size effect has been studied in semiconductors, where it leads to important changes of the physical properties based on the quantum mechanical confinement effect.25 At the same time, it has been suggested614 that ionic transport properties at the interfaces may become preponderant and influence the ionic transport in the bulk. So, it appears interesting to study confinement effects on the titanium-based perovskite phase (Li3xLa2/3x01/32x)TiO31518 (hereafter referred to as LLTO) which is one of the highest crystalline lithium-ion conductors reported in the literature with a bulk lithium conductivity as high as 103 S cm1 at room temperature for x = 0.10. An exhaustive review of all the papers that appeared in the literature about these titanate compounds can be found in ref 19. Until now, LLTO was synthesized by a Solid State Reaction (SSR) leading to microstructured samples. The structural studies17,18 were mainly performed by Powder X-ray Diffraction (PXRD) analysis with the Rietveld method.20 In its microstructured state, the LLTO structural model consists of a tetragonal distortion of the cubic ABO3 perovskite structure with a = aperov ≈ 3.87 Å and c ≈ 2aperov. For x = 0.10, the LLTO PXRD pattern r 2011 American Chemical Society

involves two sets of reflections: one set is formed of (hkl) Bragg peaks with l = 2n related to the cubic perovskite structure, and the other set consists of a broader superstructure (hkl) reflections with l = 2n + 1, which appears because of an unequal distribution of La3+ ions along the c axis. The local properties of the Li+ ions in this microstructured system were studied by 7Li and 6Li Nuclear Magnetic Resonance (NMR).2125 The lithium NMR spectra exhibit two lines, and the lithium dynamics is characterized by only one T1. The existence of a single T1 remains unexplained until now. This paper is devoted to the study of confinement effects on local properties as observed by 7Li NMR. As the maximum of conductivity in the micrometric size systems was measured for x = 0.10, we focus the present study on samples with this composition. As shown in ref 26, LLTO exhibits a strong surface reactivity. Interaction with atmospheric H2O and CO2 leads to Li2CO3 formation and H+/Li+ exchange. Therefore, an increase of these effects in nanometric systems can be expected, and the proton NMR experiments were also performed. The first part of the present study focuses on the accurate structural characterization of the samples and the surface reactivity of the nanostructured LLTO. The second and main part of Received: December 26, 2010 Revised: July 1, 2011 Published: July 01, 2011 15575

dx.doi.org/10.1021/jp2048794 | J. Phys. Chem. C 2011, 115, 15575–15585

The Journal of Physical Chemistry C

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the paper is devoted to the study of size effects on local properties using 1H and 7Li Magic Angle Spinning Nuclear Magnetic Resonance (MAS NMR).

II. EXPERIMENTAL SECTION Proceeding experimentally in an identical way for all the samples is required owing to the instability of these compounds against the air/water:26 after synthesis, samples were kept exposed to air at room temperature for about 5 h before measurements (after 1 h this reactivity in air is stabilized). Preparation and Characterization of the Powdered Samples. Nanostructured LLTO is obtained by using low-tempera-

ture procedures: the polymerizable precursor27 method was applied in the present study. The synthesis procedure used for preparing nanostructured materials was described in detail elsewhere.2729 A fine white powder of pure LLTO with crystallites of nanometric size was obtained after annealing the amorphous organic precursor powder for 2 h at 700 C. Moreover, changes in the crystallite size can be ensured by annealing the precursor at a given temperature in the range 700 1150 C. In the following, the samples will be named according to their annealing temperature. For instance, LLTO_700 refers to the sample annealed at 700 C. Only four samples will be considered: LLTO_700, LLTO_900, LLTO_1000, and LLTO_1150. To synthesize the samples at either 1000 or 1150 C, a pellet of LLTO_900 powder was made to avoid the loss in Li2O at high temperature and then sintered at the appropriate temperature in air for 2 h. After sintering, the pellet was ground in an agate mortar to obtain the powder studied in this work. Details of the characterization are reported in the Supporting Information (SI) file. PXRD Rietveld19 analysis was used (i) to follow up the crystallite size of the four samples and (ii) also to control the LLTO mean structure. The BrunauerEmett Teller30 method (BET), Transmission Electronic Microscopy (TEM), and Scanning Electron Microscopy (SEM) techniques were also used to provide more information and/or to confirm the previous results about grain sizes. Thermogravimetric Analysis (TGA) and TGA coupled with mass spectroscopy (TGAMS) measurements enabled us to identify and quantify the mass loss. Fourier Transform Infrared spectroscopy (IR) is used to specify the surface reactivity. NMR Experiments. NMR spectra were recorded with a Bruker Avance 300 spectrometer working at frequency ν0 = 116.64 MHz for 7Li and ν0 = 300.13 MHz for 1H. The experiments were performed on powdered samples spun at the magic angle with a standard 4 mm MAS probe. All the spectra were reported to the mass of LLTO powder in the rotor and will be named “mass normalized spectra”. The DMFIT software31 was used to reconstruct the spectra and obtain the line widths, the peak positions (in Hz or ppm), and the relative intensity of each contribution. Cross-Polarization Magic Angle Spinning (CP-MAS), CP-MAS modified by a Hahn echo on the 1H channel, and {1H7Li} HETero CORrelation (HETCOR) experiments were also carried out to obtain information about lithium-proton environments (see SI). Since the Bloembergen, Purcell, and Pound (BPP) pioneering works32 on the relation between the relaxation and the motion, it is usual to start dynamical studies by the measurement of spinlattice

Figure 1. PXRD patterns of LLTO_700, LLTO_900, and LLTO_1000 samples in the selected angular range [6280] 2θ, showing the increase of the Bragg peak width when the synthesis temperature decreases.

Table 1. Apparent Crystallite Size V and Strain Parameter ε Obtained from Rietveld Refinements for Phase 1 (Cubic Peaks with l = 2n) and Phase 2 (Superstructure Peaks with l = 2n + 1)a l=2n V sample

(nm)

(nm)

LLTO_700 LLTO_900

14 55

5 26

LLTO_1000

215

LLTO_1150

ÆDæmicroscopy average

l=2n+1 V

26 15

4

ε(*10 ) 39 16 6.9

(nm) 14 ( 1 89 ( 15 810 ( 120 1200 ( 400

a

For LLTO_1150, only the crystallite size of phase 2 could be evaluated. ÆDæmicroscopy is the average value obtained by using Lince software in average TEM and BEM experiments.

relaxation time T1. T1 measurements were performed on 7Li and 1 H at room temperature by using a saturation-recovery pulse sequence. In a first step, the experimental data were processed in the logarithm scale. The use of this scale makes easier the evidence and the determination of the different T1. Then in a second step, these values are checked in the linear scale results. In this work, the total magnetizations were recorded together with the individual ones (site per site). In this last case, the evolution of the magnetization M(τ) was determined for each site of the 7Li nuclei by using the DMFIT software.31

III. RESULTS Structural Investigation and Determination of the Crystallite Size. PXRD patterns of LLTO_700, LLTO_900, and

LLTO_1000 samples in the selected angular range [6280] 2θ are displayed in Figure 1. A significant line broadening is observed when the annealing temperature decreases, indicating changes in the crystallite size and/or strain effects. The quantitative study of PXRD patterns was performed using the Rietveld method20 which enabled us to demonstrate that no change occurs in the LLTO mean structure whatever the annealing temperature is, the mean structure being identical to that of the compounds synthesized by SSR (see SI). Applying the Langford method33 for microstructural characterization on PXRD patterns allowed us to extract the values of apparent crystallite sizes of the cubic “phase” and 15576

dx.doi.org/10.1021/jp2048794 |J. Phys. Chem. C 2011, 115, 15575–15585


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Figure 2. Comparison of the average crystallite sizes (squares) obtained from the coherent diffraction length (full squares, ; and open squares, ) (a) with strain parameters (full circle) versus the annealing temperature and (b) with the specific surface area (SSA, full triangle) versus the annealing temperature.

related to superstructure Bragg peaks and of upper limit of strain ε (see SI). These values are gathered in Table 1. In Figure 2 are reported, for a larger sample set studied in the temperature range 700900 C, the values of apparent crystallite sizes and , of the strain parameter ε, and of the Specific Surface Area (SSA) obtained by the BET method. The behavior of the SSA is consistent with the crystallite sizes evolution. The grain morphology was studied by TEM for LLTO_700 and LLTO_900 nanometric systems and by SEM for LLTO_1000 and LLTO_1150 micrometric ones (see SI). In obtained by using Table 1, the average grain sizes ÆDæmicroscopy average the Lince software are compared with the apparent crystallite size of the coherent diffracting domains determined by PXRD. The values are consistent for the nanometric systems, but they become very different in the micrometric ones. In LLTO_1000, the comparison of the grain size determined by SEM with the crystallite/coherent diffracting domain V clearly highlights that the grain is built from antiphase domains as already observed in LLTO_1150 prepared by SSR.18 This conclusion can be extended to the larger sample set studied in the temperature range 700900 C. Surface Reactivity Investigation. DTA_GTA and GTA coupled to a mass spectrometer (GTA-MS) show that, during heating, LLTO_700 loses H2O and CO2 molecules between 100 and 200 C. Above this temperature, CO2 only seems to be lost. In LLTO_900, the losses are due to H2O and carbon monoxide (CO). For the other samples LLTO_1000 and LLTO_1150, the mass loss is only due to water desorption (see SI). These results are confirmed by IR spectroscopy which is sensitive to (H2O) and (CO3) vibrations (see SI). NMR Results. 1H Results. The 1H synchronized MAS spectra (spinning frequency νR = 10 k Hz) are reported in Figure 3(a) for the different samples. These mass normalized spectra show that the proton amount increases strongly when the average grain size decreases, indicating that protons are present on the oxide surface. 1H being a I = 1/2 nucleus, the line position, in a MAS spectrum, is defined by its isotropic chemical shift. The line width is due to dipolar couplings and/or to disorder. Table 2 gives the 1 H spectrum parameters of the samples. Figures 3(b) and 3(c) which display nonsynchronized MAS spectra recorded at different spinning frequencies show that the 1H anisotropy interactions (both dipolar and chemical shift) are weak as the spinning side bands are very weak even at low spinning frequency. In Figure 4(a) the LLTO_700 Hahn echo spectra were recorded

Figure 3. 1H NMR LLTO powder spectra recorded 5 h after synthesis annealing. (a) MAS (10 kHz) synchronized Hahn Echo spectra. Spectra are mass normalized. (b) and (c): Nonsynchronized spectra for LLTO_700 and LLTO_900 showing the spinning side band (*).

with a variable delay between the echoes (T2 filter). Two components under the broad band are clearly evidenced from this 15577



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experiment. Figure 4(b) gives the T2 curves for these two components. Such an experiment was also performed in LLTO_900, and the results are reported in Figures 4(df). It leads to the same conclusions, and Figures 4(c) and 4(f) give the 1H reconstructed spectra with the parameters given in Table 2. Five contributions (1H, 2H, 3H, 4H, 5H) characterize these spectra. The contribution 5H is very weak and randomly present in the Table 2. Parameters Used in the Reconstruction of the Proton Spectra (MAS νr = 10 kHz)a LLT0_700 δ

LLT0_900

Δ

δ

LLT0_1000

Δ

δ

Δ

(ppm) (ppm) % (ppm) (ppm) % (ppm) (ppm) % Raie 1H

4.04

1.28

4

3.92

1.20

13

3.92

1.23

16

Raie 2H Raie 3H

5.08 6.31

2.48 2.58

85 7

4.99 5.70

3.63 2.29

69 13

4.99 5.70

3.20 1.62

76 4

Raie 4H

9.22

5.08

4

9.22

1.96

2

9.22

1.96

2

1.12

1.12

3

1.12

1.52

2

Raie 5H

Precision: position δ ( 0.05, linewidth Δ ( 0.02, contribution % ( 1. 1 ppm = 300.13 Hz. a

different synthesis: so we will not take this line into account in the following. Owing to the weak 1H amount in LLTO_1000 and LLTO_1150, it was not possible to perform this T2 filter experiment for these samples. Nevertheless the LLTO_1000 spectrum was reconstructed with the line positions obtained in LLTO_900. Among the four contributions 1H, 2H, 3H, and 4H, three of them, 1H, 3H, and 4H, correspond to those observed in the Li+/H+ exchanged samples. So the 2H contribution has to be assigned to the proton at the surface (see Figure 10 in ref 32). The T2 values are reported in Table 3. Two transverse relaxation times T2 characterize these systems with nearly one decade between them: fast T2 around 0.4 ms and the slow one around 3 ms. Furthermore, the two T2 are very similar in the two compounds. The short contribution increases as the size is decreasing. Furthermore, in both LLTO_700 and LLTO_900, the contribution of the long T2 is very close to that of the 2H contribution to the spectrum, while the fast one corresponds to 1H, 3H, and 4H contributions together. The saturation-recovery magnetizations during the T1 experiments are reported in Figure 5(a) for LLTO_700 and LLTO_900. The values are reported in Table 3. Two T1 are clearly evidenced in LLTO_900. Nearly three decades separate these two values: the first T1 (87 ms) and the second one (13 s) correspond to

Figure 4. (a,b,c) LLTO_700 superimposition of 1H NMR MAS (10 kHz) Hahn echo for several echo delays. (b) 1H T2 magnetization decrease. Experiments (a) and (b) allow us to evidence lines 1H and 3H masked by 2H contribution. (c) Reconstruction of 1H NMR MAS (10 kHz). The echo delays are from 400 μs for the lower spectrum to 10 μs for the higher one. (d,e,f) the same for LLTO_900. 15578



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Table 3. SpinLattice Relaxation Time T1 and Transverse Relaxation Time T2 of the 1H Nucleus Measured in a MAS Experiment (νr = 10 kHz)a Tfast 1 (ms)

%

Tslow (s) 1

%

Tfast 2 (ms) 0.42 (0.02)

91 (8)

2(0.1)

9(7)

87(7)

65 (5)

12(2)

35(3)

0.36 (0.02)

67 (6)

4.4(0.3)

33 (3)

LLTO_700 LLTO_900 a

%

Tslow (ms) 2

%

For LLTO_700, the spinlattice relaxation (T1) was analyzed in the cross relaxation process.

Figure 5. (a) 1H NMR MAS (10 kHz) total magnetization recovery during the T1 experiment for samples LLTO_700 (square) and LLTO_900 (circle). Inset is a zoom of the [07] s range. Lines are only a guide for the eye. (b) Particular behavior of the magnetization recovery in LLTO_700. The line corresponds to the curve calculated using the cross-relaxation model with the parameters given in the text.

contributions of 65% and 35%, respectively. The peculiar behavior in LLTO_700 is sketched in Figure 7(b): the magnetization rapidly grows in a short time around 90 ms and very weakly decreases to its equilibrium value in a very long time (several hundreds of seconds). 7 Li Results. The line position depends upon the chemical shift and the quadrupolar parameter. The central transition position is not affected at first order of perturbation, and as the quadrupolar parameter is weak, its position depends only on the chemical shift. The isotropic line positions will be only dependent on the chemical shift, and the spinning side band accounts for the anisotropy effects on the satellite transition. 7 Li single pulse acquisition spectra recorded in the non synchronized mode are sketched in Figure 6. Inset (a) is a zoom of spinning side band #2, and inset (b) gives the mass normalized spectra recorded in synchronized mode (νR = 10 kHz). From these results, we can deduce that the lithium amounts are nearly the same in the four samples and that no paramagnetic defects are present (otherwise the associated line of the observed lithium should be drastically modified either by high chemical shift or/ and by rapid spinlattice relaxation). Spinning side bands in Figures 6(a,b) allow us to highlight drastic anisotropy effects in the LLTO_700 and LLT0_900 spectra. In Figures 7(a,b), we compare the 1H/7Li cross-polarization spectra for LLTO_700 and LLTO_900 together with the single pulse 7Li synchronized spectra. Their reconstructions are reported in Figures 7(cf). For LLTO_1000 and LLTO_1150, the very weak 1H amounts do not allow us to obtain a significant CP signal. In the CP experiment, the signal intensity depends upon the distance between the two nuclei through the dipolar interaction, and the spectrum gives information about the most sensitive proton neighboring lithium. For LLTO_700 and LLTO_900, CP experiments (Figures 7(a,b)) enable us to separate one component in the spectra. LLTO_700 and LLTO_900 7Li spectra are reconstructed with three components (Li1, Li2, Li3), while only two lines (Li1, Li2) are enough for LLTO_1000 and LLTO_1150, the parameters of which are given in Table 4. Li3

revealed by the CP experiment is very sensitive to the grain size. Li1 and Li2 correspond to those observed in samples synthesized by SSR.27,28 So, Li3 is a specificity of nanometric systems. In LLTO_1000 and LLTO_1150 spectra (Figures 6), the spinning side band amplitudes are very weak as previously observed for LLTO synthesized by SSR27,28 and are assigned to dipolar anisotropy. In LLTO_700 and LLTO_900, the spinning side bands spread over a larger frequency range and are assigned to quadrupolar anisotropy. We need two contributions to account for the spinning side band #2 as shown in the inset (a) in Figure 6. These spinning side bands are the ones of isotropic lines Li2 and Li3. 2D HETCOR maps are reported in Figures 8(a,b). These 2D maps give evidence of a correlation between the 7Li sites corresponding to Li3 and the 2H proton sites. So, we can deduce that the 2H protons are those which are implied in the CP transfer. This conclusion is supported by the comparison of the T2 decrease of the 1H magnetization with the 7Li CP signal amplitude obtained with a modified CP sequence as reported in Figures 8(c,d). In this sequence, the CP signal was recorded after a Hahn echo sequence with a variable delay. Only the five first points have to be considered because for an echo delay above 0.8 ms the signal is too weak and noisy to be validly processed. These figures reveal that the CP signal amplitude follows the T2 decrease of the 1H magnetization for the delays below 1 ms. This value corresponds also to the delay above which line 2H in Figures 4(a) and 4(d) becomes negligible. Several attempts to analyze the 7Li nucleus magnetization by using the KohlrauschWilliamWatt (KWW) stretched exponential function were inefficient. Furthermore, this function cannot account for the specific behavior of the 1H magnetization in LLTO-700. So, the results of 7Li recovered magnetization during the T1 experiments were processed by using several relaxation times. In Figure 9(a), we report the recovery of the 7Li total magnetization recorded during the T1 experiments. The lines correspond to reconstructions with several exponential functions, 15579



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Figure 6. 7Li MAS NMR spectra recorded at different spinning frequencies in the nonsynchronized mode for the different samples. Spinning side bands (symbol *) spread over a larger band in nanomatric systems (LLTO_700 and LLTO_900) than in the micrometric ones (LLTO_1000 and LLTO_1150). The inset (a) is a zoom of the spinning side bands #2 in LLTO_700 (experimental: dashed line) with its reconstruction; the inset (b) corresponds to the spectra recorded in the synchronized mode.

the parameters of which are reported in Table 5. It is worth noting that to account for the magnetization recovery in LLTO_1150 we need only one T1 with the same value (10 ms) as the one obtained in the compound synthesized by SSR with a micrometric size. Two T1 characterize the magnetization recovery in LLTO_1000. The more important contribution = 10 ms, and a small (97%) is related to the short T(1) 1 contribution (3%) is due to a long T(2) 1 = 3 s. Three relaxation times account for the total magnetization behavior in LLTO_700 and LLTO_900. In LLTO_700, these relaxation times are longer than in LLTO_900. When the size decreases, the results reported in Table 5 show that the contribution of: (2) - the slowest T(3) 1 and the medium T1 relaxation times increase, (1) - the fastest relaxation time T1 decreases. In each sample, the relaxation time contributions do not correspond to the contributions of lines Li1, Li2, and Li3 in the spectrum, indicating that the different lithium ions 1, 2, or 3 do not independently relax. Figures 9(b,c) give the magnetization recovery for the individual contributions Li1, Li2, and Li3 of the 7Li spectra in the two nanometric systems LLTO_700 and LLT0_900. For each sample, the data were processed with the three T1 values obtained for the total magnetization, and we report the different contributions

in Table 6. The contributions obtained for the three lines are also consistent with the ones obtained with the total magnetization. In LLTO_700, all sites exhibit nearly the same behavior, whereas in LLTO_900 all the contributions behave differently.

IV. DISCUSSION Structural properties of our samples have been carefully characterized by several techniques: PXRD Rietveld analysis shows that the mean structure is identical to that of the compounds synthesized by SSR. The evolution of the grain sizes was followed up by PXRD line-broadening analysis, BET, TEM, and SEM measurements. As shown in Table 1, the reduction of the annealing temperature from 1150 to 700 C allows obtaining powdered samples with an apparent domain size decreasing from micrometer at high temperature to 14 nm at 700 C. For LLTO_1000, the material is microstructured with a domain size which has strongly increased up to 215 nm. Consequently, using the method of polymerizable complexes enabled us to synthesize the lithium lanthanum titanate (Li0.3La0.5600.13)TiO3 with grain sizes going from the micrometer to the nanometer. The complementary DTA_GTA, GTA_MS, and FT-IR measurements confirm the strong surface reactivity of the material: H+/Li+ exchange appears at the surface as well as Li2CO3 formation as explained in ref 26. 15580



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Figure 7. (a,b) 7Li LLTO _700 and LLTO_900 single pulse (dashed line) and CP (full line) spectra: comparison of the line positions. (c,d,e,f) 7Li different sample spectra recorded in synchronized mode. Experimental and reconstructed spectra (full line) are exactly superimposed. The different contributions are in dotted lines. For the micrometric systems (LLTO_1000 and LLTP_1150), two contributions (1,2) are unambiguously observed. The third line (3) is characteristic of the LLTO_700 and LLTO_900 nanometric systems.

Table 4. Parameters Used in the Reconstruction of the 7Li Spectra (MAS νr = 10 kH)a LLTO_700 line Li 1 Li 2 Li 3 a

δ 1.76 0.2 0.24

Δ

LLTO_900 %

δ

1.25

6

1.88

9.7

69

1.16

1.68

25

0.39

Δ 1.57 11.3 2.27

LLTO_1000 δ

% 28

1.51

62

1.4

Δ 2.83 17.0

LLTO_1150 %

δ

51

1.51

49

1.4

Δ 2.67 14.9

% 44 56

10

Precision: for lines 1 and 3, δ((0.05), Δ((0.02), %((0.5) and δ((0.5), Δ((0.5), %((1) for line 2. 1 ppm = 116.64 Hz.

The 1H/7Li exchange and the strong surface reactivity were also observed by studying the proton NMR spectra. Four types of proton were evidenced: three of them (1H, 3H, 4H) are identified as the ones observed in HLTO obtained after H+/Li+ exchange,32 and the fourth site 2H, which is characteristic of the nanometric size, was assigned to protons at the surface. The proton amount decreases when the size increases. The lithium 7Li NMR spectra enabled us to highlight three sites in the nanometric compounds when only two sites are observed in the micrometric compounds. The cross-polarization, HETCOR, and T2 experiments showed that the third lithium site Li3, only observed in the nanometric compounds, is strongly connected to the protons of the surface (2H). So, we deduce that lithium 3 is near the surface, and this signal is characteristic of the nanometric compounds. Lines Li1 and Li2, specific of the micrometric systems, are common to the four compounds and

are attributed to the lithium in the bulk. The Li3 contribution increases as the grain size decreases, while the line Li1 contribution drastically decreases. In the same time, site 2 acquires quadrupolar interaction. Following the results of ref 32, we can attribute this line to Li2CO3 formed at the surface. This behavior indicates that the boundary conditions (“Li2CO3” + HLTO on one hand and confinement on another hand) will play a more and more important role when the size decreases. Hereafter, we will name “crust” as the (HLTO + Li2CO3) entity and “boundary condition” effects or “size” effects as the confinement and the crust effects. So, the nanometric size is characterized by (i) a fourth line (2H) in the proton spectrum, (ii) a third line (Li3) with an anisotropic quadrupolar interaction for the 7Li nucleus with a strong correlation with 2H sites, and (iii) a change in the site 2 properties which acquires an anisotropic quadrupolar interaction as observed in Li2 contribution to the spectrum. 15581



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Figure 8. (a,b) 2D HETCOR maps showing the correlations of sites Li3 and 2H. The vertical axis is the 1H dimension. (c,d) Comparison of the intensity of the cross-polarization signal (CP sequence preceded by an Hahn echo) with the T2 decrease of the 2H site proton signal for LLTO_700 (c) and LLTO_900 (d). These signals become null before the millisecond as that of the line 2H. Lines are guides for the eye. 1

H magnetization recovery exhibits a particular behavior in LLTO_700 when the 7Li one depends on several T1. To explain the peculiar behavior of the 1H magnetization observed during the saturation-recovery in LLTO_700 (Figure 6(b)), we can use two 1H reservoirs between which spin diffusion and crossrelaxation take place. It is worth noting that the overlap of the different contributions to the spectrum makes easier the transfer of magnetization between the different 1H sites. Our analysis is based on the method described in ref 35. The T1 results obtained in LLTO_900 suggest that a strong difference between the relaxation times also exists in LLTO_700 for the two species a = 2H and b = (1H + 3H + 4H). So, such a difference leads to the appearance of a magnetization gradient. This gradient arises through the T1 magnetization selection: during the magnetization recovery, the magnetization of species “a” grows very rapidly, whereas that of species “b” grows very slowly. This magnetization gradient modifies the intrinsic relaxation mechanism of site “b”. To account for this mechanism, the relaxation Bloch equations are modified with some supplementary terms associated with the cross relaxation process.34,35 The relaxation matrix is 1 0 1 1 R aa ¼ a R ab¼ B ≈ T1 T ab C C B C R ¼B 1 1 A @ R ba ¼ R bb ¼ b T ba T1 whose diagonal matrix elements Raa are the inverse of the intrinsic spinlattice relaxation time Ta1 of the “a” spins, while the off diagonal Rab parameters account for the cross relaxation between the two “a” and “b” spin species.

The calculated curve reproduces the experimental data, as can be observed in Figure 7(b) with the parameters (in s1) Raa = 11.1, Rab = 3.3 103, Rba = 5, and Rbb = 3.3 103 and M0a = 0.5 and M0b = 0.08. The M0a and M0b values are in the ratio of the 2H and (1H + 3H + 4H) contributions obtained from the spectrum. The inverse of the Raa and Rbb parameters is in the range of T1 (Ta1 = 90 ms, Tb1 = 200 s, Tba = 0.2 s, Tab = 300 s) measured in LLT0_900. As it was expected, the site relaxation time Ta1 is strongly shorter than the Tb1 one. This last one cannot influence the relaxation of the a species. Nevertheless, this twospin system leads to nonequal off-diagonal element Rab 6¼ Rba. The strong difference between these two parameters can originate from several causes. For example, we can quote the number of spins for each species and their own spin temperatures,36 the differences in the couplings, and the presence of an extraneous nucleus (such as 7Li). The off-diagonal relaxation rates Rab and Rba depend on the ratio between the correlation time τc, the number of spins in each species on one hand, and the distance rab between spins on another hand. When the grain size increases, rab increases, and the off-diagonal matrix elements decrease. Hence, the atypical behavior disappears. Conversely, when the grain size decreases, the correlation time and the number of spins decrease, and again the off-diagonal matrix elements decrease to zero leading to the normal behavior. So, we expect that the atypical behavior in the relaxation time can exist only in a limited range as observed in our results. Spin diffusion can also establish a spin temperature leading to a single T1. Finally, the three coupled proton mechanisms should also account for our results. Such a mechanism arises from the MAS rotation in which the first-order dipolar spin 15582



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Table 6. 7Li Relaxation Parameters Used to Reconstruct the Individual Magnetization Recovery in Figure 9(a) for LLTO_700 and 9(b) for LLTO_900 T(1) 1 line

(ms)

Li1 LLTO_900

Li2 Li1 Li2 Li3

Figure 9. (a) Recovery of the total 7Li magnetization during the T1 experiments for the different samples. These results clearly show the T1 to be increasing when going from micro to nanosystems due to a long time component which increases when size grain decreases. (b,c) T1 magnetization recovery (non-normalized) behaviors of the 7Li individual magnetizations (lines 13) for the nanometric systems (LLTO_700 and LLTO_900). (b) In LLTO_700, the three contributions exhibit a nearly similar behavior. (c) In LLTO_900, the three contributions exhibit different behaviors. Full line in the inset corresponds to the calculated curves with parameters given in Table 5. Dashed line (blue) corresponds to the total magnetization.

Table 5. T1 Values of the 7Li Total Magnetization Measured during the Saturation Recovery T1 Sequence Synchronized MAS Experiment (νr = 10 kHz) T(1) 1 (ms)

%

T(2) 1 (s)

%

T(3) 1 (s)

%

LLTO_700

20.(3)

12(3)

0.2(0.02)

37(3)

3.(0.3)

51(2)

LLTO_900 LLTO_1000

11.(2) 10.(1)

64(2) 97(1)

0.13(0.02) 1.4(0.2)

25(2) 3(1)

3.(0.3)

9(2)

coupling is averaged and the dipolar order arises from the second-order perturbation which couples three spins.37 This was suggested by varying the spin rotation which modifies the spinlattice relaxation times.38

%

(ms)

55(3) 11.(3)

Li3 LLTO_700

T(2) 1 (1)

90(5) 35(2) 2(2) 12(3)

%

(s)

17(3) 130(20)

50(5) 20.(3)

T(3) 1 (2)

7(2)

28(2) 2.9(0.3)

23(3) 200(20)

24(2) 19(2) 41(2)

%(3)

3(2) 27(3)

2.9(0.3)

41(2) 79(2) 47(2)

For 7Li, the total magnetization and the individual ones depend upon the same relaxation times. The relaxation times of the three lithium sites (1, 2, 3) are sensitive to sample size. These results show that the relaxations of the three sites are not independent and are monitored by a complex mechanism which evolves when size effects become important: at the beginning of the grain size decrease, the 7Li ions of the bulk monitor the relaxation process. Then, as the boundary conditions become more and more important, these are the lithium nuclei in the “crust” which monitor the relaxation of the lithium nuclei in the bulk. At first, these mechanism effects are to render complex the relaxation in sites Li1 and Li2 by breaking the T1 uniformity which existed in the micrometric compounds. This complexity does not result from electronic paramagnetic defects which would have shortened T1, which is not observed. At least two reasons make us push aside the assumption that these different contributions are due to the I = 3/2 spin value (refs S29S33 in SI). First, the contributions change with the sizes while they should remain constant. Second, we have to keep in mind that a single relaxation time is observed in the micrometric system LLTO_1150 and in samples synthesized by SSR. Then, to understand the origin of this single relaxation time in the micrometric systems, we have to call upon a mechanism which uniformizes the relaxation on sites Li1 and Li2 with a single high-spin temperature.36 This mechanism, which can only be the spin diffusion, leads us to conclude that in the case of nanostructured systems this diffusion is switched off and each site belongs to a specific Zeeman reservoir that we call R1, R2, and R3 (which are the ones observed in a T1 experiment). This hypothesis is supported by the proton results in LLTO_700. Furthermore, the common three relaxation times indicate that these reservoirs are connected. In the spirit of the model used for the proton, the dynamics of the three magnetizations is described by some (3,3) relaxation matrix. This matrix we have to consider will have three eigenvalues, and at the equilibrium the magnetization on each site will depend on these three eigenvalues which are the T1 values used to account for the magnetization behavior. The spin diffusion switch off which originates from the boundary conditions is due to the breaking of the flip-flop mechanism. The quadrupolar interaction on site Li3 and the appearance of quadrupolar interaction in lithium site Li2 make some flip-flop impossible between the different lithium sites because there is no Zeeman energy conservation. At first order, this energy conservation is only possible for +1/2 and 1/2 levels. On one hand, the MAS switches off the Bloembergen spin diffusion (without motion) by averaging to zero the dipolar interaction spatial parameter at first order in ωr/ωl (with ωr being the 15583


The Journal of Physical Chemistry C angular rotation frequency and ωl being the amplitude of the local dipolar field) but gives rise to three spin couplings at second order.37 On the other hand, in micrometric systems having a single T1, the self-diffusion (diffusion induced by the motion) is not averaged by the MAS rotation and can be at the origin of this single T1. So it seems reasonable that the appearance of several relaxation times is due to the spin diffusion switch off. This could originate from some speeding up of the local motion accompanied by some breaking of its correlation length. On one hand, the speeding up hypothesis is supported by the line width decrease on the three sites when going from LLTO_900 to LLTO_700. On the other hand, the breaking of the self-spin diffusion correlation length is supported by the appearance of three relaxation times. So, the presence of several relaxation times for individual magnetization would certainly be due to a more complex process of relaxation due to the confinement. The distribution of the grain sizes as observed by electronic microscopy was ruled out because it cannot account for the specific behavior of the 1H magnetization recovery. The relaxation times of the three lithium sites as well as their contributions are grain size sensitive as previously highlighted. Nevertheless, the most surprising fact is the increase of the fast T1 when the size decreases because the reverse is generally accepted. An analytical study of the confinement effects on the relaxation was already presented in ref 39. The authors consider that the dynamic of the bulk magnetization is monitored by the T1 process and by the spin diffusion process. This diffusion results from the on-surface magnetization which diffuses in the material by modifying the intrinsic relaxation time of the bulk. They also supposed that the magnetization on the surface relaxed very quickly because of a higher number of degrees of freedom. In our case, lithiums on the surface are the ones locked in “crust” and thus present a very slow relaxation due to a weak mobility compared with that of the LLTO. So, it is the bulk which imposes the relaxation of the magnetization of the surface when this latter is too small. Under a critical grain size, it is the surface which monitors the bulk relaxation, and its effects increases when the grain size decreases. This relaxation time is not any more the one of pure Li2CO3 which is of the order of hundreds of seconds but falls in the field of second.

V. CONCLUSION LLTO powders with grain sizes ranging from 14 nm up to several micrometers were obtained using a polymerizable precursor method. PXRD analysis shows that no change occurs in the LLTO mean structure when going from the micro- to nanometric scale. Evidence of modifications of the grain boundary and formation of Li2CO3 were revealed by IR. Li+/H+ exchange (HLTO formation) is revealed by DTA, TGA_MS, and NMR. These results allowed us to identify accurately 1H and 7Li NMR signals, which are sensitive to the confinement. In compounds of size of the order of 14 nm (LLTO_700), cross relaxation effects are evidenced between HLTO protons and the ones of the surface. The boundary conditions strongly modify the 7Li spin properties. In the nanometric system, one site in the bulk acquires quadrupolar anisotropy, and a spinlattice relaxation time multiplicity is observed. To explain this multiplicity in the nanometric systems, we introduced the presence of three 7Li reservoirs with spin diffusion and cross-relaxation between them. These dynamical properties need more theoretical investigations about quasi invariants of the system.40,41 The present work shows

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the effects of the size on the relaxation and demonstrates that the spin diffusion is the origin of the single T1 in micrometric systems. Finally, the drastic modifications in the local dynamics of the lithium ion should have consequences on the conduction properties. Investigations on pellets obtained by flash sintering are in progress.

’ ASSOCIATED CONTENT

bS

Supporting Information. Additional experimental details. This information is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*Tel.: (33)-2-43-83-32-90. Fax: (33)-2-43-83-35-18. E-mail: joel. [email protected].

’ ACKNOWLEDGMENT The authors are grateful to Stephanie Kodjikian for her help in the studies by electronic microscopy, to M. Pechon for his help in the determination of the specific surface area by the BET method, and to M. Grolleau for his help during GTA-MS experiments (Institut Jean Rouxel-Nantes-France). ’ REFERENCES (1) Maier, J. Nat. Mater. 2005, 4, 805–815. (2) Brus, L. E. J. Chem. Phys. 1984, 80, 4403–4409. (3) Reed, M.; Kirle, W.P. Nano structure physics and fabrication; Academic: New York, 1989. (4) Ploog, K. Semi conductor interface; Lay, Derrien, J., Boccara, N., Eds.; Springer Proceedings in Physics 22, Springer: Berlin, 1987; 1042. (5) Haug et, R. J.; Von Kiltzing, K. FED J. 1995, 6, 4. (6) Despotuli, A.; Nikolaichik, V. I. Solid State Ionics 1993, 60, 275–278. (7) Maier, J. Sol. State Ionics 2002, 154, 291–301. (8) Maier, J. Sol. State Ionics 2003, 157, 327–334. (9) Maier, J. Sol. State Ionics 2002, 148, 367–374. (10) Maier, J. Phys. Z. Chem. 2003, 217, 415–436. (11) Maier, J. Solid State Ionics 2004, 175, 7–12. (12) Tuller, H. L. Solid. State Ionics 2000, 131, 143–157. (13) Schoonman, J. Sol. State Ionics 2005, 157, 319–326. (14) Jamnik, J.; Maier, J. Phys. Chem. Chem. Phys. 2003, 5, 5215–5220. (15) Belous, A. G.; Novitskaya, G. N.; Polyanetskaya, S. V.; Gornikov, Y. I. Izv. Akad. Nauk SSSR 1987, 23, 412–415. (16) Inaguma, Y.; Chen, L.; Itoh, M.; Nakamura, T.; Uchida, T.; Ikuta, H.; Wakihara, M. Solid State Commun. 1993, 86 (10), 689–693. (17) Roberston, A. D.; West, A. R.; Ritchie, A. G. Solid State Ionics 1997, 104, 1–11. (18) Fourquet, J.-L.; Duroy, H.; Crosnier-Lopez, M. P. J. Solid State Chem. 1996, 127, 282–294. (19) O. Bohnke, Emery, J.; Fourquet, J.-L.; Badot, J.C. “Li+ ion dynamics in the defective perovskite Li3xLa2/3-xTiO3”. Recent Developments in Solid State Ion; Pandalai, S.G., Ed.;Transworld Research Network Publishers: Kerala, India, 2003; Vol. 1 and references therein. (20) Rietveld, H. M. J. Appl. Crystallogr. 1969, 2, 65–71. (21) Emery, J.; Buzare, J. Y.; Bohnke, O.; Fourquet, J.-L. Solid State Ionics 1997, 99, 41–51. (22) Bohnke, O.; Emery, J.; Veron, A.; Fourquet, J.-L.; Buzare, J.-Y.; Florian, P.; Massiot, D. Solid State Ionics 1998, 109, 25–34. (23) Emery, J.; Bohnke, O.; Fourquet, J.-L.; Buzare, J. Y.; Florian, P.; Massiot, D. J. Phys.: Condens. Matter 1999, 11, 10401–10417. 15584



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