Long-range Li diffusion parameters of amorphous LiNbO3 are probed by
7Li two-time spin-alignment echo NMR spectroscopy which is sensitive to slow Li dynamics. The jump rates which were extracted from the spin-alignment echo decay curves exhibit Arrhenius behaviour between 293 K and 413 K. The activation energy (0.41(1)eV) is in good agreement with that of the high-temperature flank of the 7Li NMR spinlattice relaxation rate peak. The latter was predicted to be about 0.4 eV when taking into account the frequency dependence of the corresponding spin-lattice relaxation rates on the low-T flank (see Wilkening et al., Phys. Chem. Chem. Phys. 4 (2002) 3246). Previous measurements of the spin-lattice relaxation rate had to be restricted to temperatures below 450 K in order to avoid crystallization of the material. Thus, only the low-temperature flank of the diffusion induced spin-lattice relaxation rate peak had been accessible yielding information about short-range Li diffusion

Heitjans, Paul

Masoud, Muayad

Wilkening, Martin

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diffusion-fundamentals   The Open-Access Journal for the Basic Principles of Diffusion Theory, Experiment and Application www.diffusion-fundamentals.org, ISSN 1862-4138; © 2005-2008    Diffusion Fundamentals 8 (2008) 5.1 – 5.8  © 2008, M. Wilkening Li Dynamics in Amorphous LiNbO3 as Probed by Solid State NMR on Different Length Scales Martin Wilkening,*  Muayad Masoud, Paul Heitjans Leibniz Universität Hannover, Institut für Physikalische Chemie und Elektrochemie, and  Zentrum für Festkörperchemie und Neue Materialien, Callinstr. 3a, 30167 Hannover, Germany  E-Mail: wilkening@pci.uni-hannover.de   Presented on the Bunsen Colloquium: Diffusion and Reactions in Advanced Materials September 27th − 28th, 2007, Clausthal-Zellerfeld, Germany Keywords: lithium niobate, Li diffusion, solid state NMR, stimulated echoes, amorphous ceramics    Abstract. Long-range Li diffusion parameters of amorphous LiNbO3 are probed by 7Li two-time spin-alignment echo NMR spectroscopy which is sensitive to slow Li dy-namics. The jump rates which were extracted from the spin-alignment echo decay curves exhibit Arrhenius behaviour between 293 K and 413 K. The activation energy (0.41(1) eV) is in good agreement with that of the high-temperature flank of the 7Li NMR spin-lattice relaxation rate peak. The latter was predicted to be about 0.4 eV when taking into account the frequency dependence of the corresponding spin-lattice relaxation rates on the low-T flank (see Wilkening et al., Phys. Chem. Chem. Phys. 4 (2002) 3246). Previous measurements of the spin-lattice relaxation rate had to be restricted to temperatures below 450 K in order to avoid crystallization of the material. Thus, only the low-temperature flank of the diffusion induced spin-lattice relaxation rate peak had been accessible yield-ing information about short-range Li diffusion.  1  Introduction Lithium niobate (LiNbO3) is currently one of the most intensively studied ferroelectric mate-rials. Due to its excellent electro-optic, acousto-optic as well as its non-linear optic properties it is used in many important applications, e.g., as photorefractive material for optical wave-guides in telecommunication. In many of these applications various diffusion processes are important. In general Li diffusion plays an important role in developing new electrode mate-rials for secondary ion batteries. Recent investigations by impedance and 7Li NMR spectros-copy revealed that the room temperature Li conductivity in amorphous LiNbO3 is by about a factor of 106 higher than that in the corresponding poly- as well as single-crystalline material [1]. It is an ideal model system to show that the introduction of disorder can lead to a dramatic increase of ionic mobility. The Li hopping process in amorphous LiNbO3 was investigated previously by temperature and frequency dependent measurements of the 7Li NMR spin-lattice relaxation (SLR) rate Wilkening et al., Li Diffusion in Amorphous LiNbO3   diffusion-fundamentals    www.diffusion-online.org  Diffusion Fundamentals 8 (2008) 5.1 – 5.7  © 2008, M. Wilkening  (1/T1) in the laboratory frame [2]. Due to the thermal sensitivity of amorphous LiNbO3 to crystallization these investigations had to be restricted to temperatures below 450 K. Up to this temperature only the low-temperature flank of the diffusion induced relaxation rate peak could be partly observed. This means that only short-range diffusion parameters were accessi-ble by 7Li NMR relaxation. The corresponding high-temperature flank, however, yields in-formation about long-range parameters [3]. The frequency dependence of the low-T rate 1/T1 was used to predict the long-range activation energy EA of SLR-NMR. According to this pre-diction  EA should be around 0.4 eV, see ref. [2].  Analogous measurements in the rotating frame probing diffusion on a longer length scale would shift the position of the corresponding relaxation rate peak to lower temperatures. However, these measurements failed in the present case because of a drastic increase of the so-called non-diffusive background relaxation rate covering any diffusively induced contribu-tion to the corresponding rate in the rotating frame, 1/T1ρ. In the present paper 7Li stimulated echo NMR, see e.g., refs. [4-7] for details of the me-thod, is used to study Li dynamics in amorphous LiNbO3. The method is capable of probing Li dynamics on a longer length scale at moderate temperatures [8,9], i. e., below 450 K in the present case. Results from 7Li stimulated echo NMR are compared with activation energies obtained by 7Li SLR-NMR spectroscopy (in the laboratory frame) and dc-conductivity mea-surements taken from the literature. As the methods probe Li dynamics on different length scales they do not necessarily give the same results. Especially in an amorphous solid with a non-homogenous behaviour concerning Li diffusion, time-scale dependent activation energies are expected. 2   Experimental  Amorphous LiNbO3 was prepared following a sol-gel routine from LiNb(OEt)6 dissolved in ethanol. The same sample was used previously for a spin-lattice relaxation NMR study, see ref. [2]. Cf. also ref. [2] for details of sample preparation. It cannot be excluded that the sam-ple still contains a small amount of organic residuals. The sample is X-ray amorphous and consists of particles with diameters of 1 to 20 mm. A sample heated at 720 K shows the typi-cal diffraction pattern of pure phase LiNbO3 [10].   7Li stimulated echoes (spin-alignment echoes, SAE) were measured using the three-pulse sequence introduced by Jeener and Broekaert [11]: 90° – tp – 45 ° – tm – 45°. The first two pulses, separated by the preparation time tp (10 µs … 100 ms), are used to generate spin-alignment order which decays during the subsequent period whose duration is determined by the mixing time tm (10 µs … 100 s). The last pulse converts spin-alignment order into an ob-servable transverse magnetization. The spin-alignment echo is detected at t = tp directly after the 45° reading pulse. The echo amplitude S2 is recorded at fixed tp and for variable tm as a function of temperature. We have used a Bruker MSL 100 and an MSL 400 solid state spec-trometer for the measurements. The spectrometers are connected to a field-variable Oxford cryomagnet (MSL 100) for measurements at ν = 39 MHz and 78 MHz, and to a shimmed Ox-ford cryomagnet at fixed field (MSL 400) corresponding to a 7Li resonance frequency ν of 155 MHz, respectively. The 90° pulse length was about 5 µs in both cases. Up to 64 scans were accumulated for each spin-alignment echo. The recycle delay was at least 5 T1. The spin-lattice relaxation rates 1/T1 were measured using the well-known saturation pulse sequence [12]. The sample was sealed in a quartz tube under vacuum. The temperature near the sample was controlled (± 2 K) via an Oxford ITC using a Ni-CrNi thermocouple.   Wilkening et al., Li Diffusion in Amorphous LiNbO3   diffusion-fundamentals    www.diffusion-online.org  Diffusion Fundamentals 8 (2008) 5.1 – 5.7  © 2008, M. Wilkening  3  Results and Discussion  The decay of spin-alignment echo NMR correlation functions S2 is either caused by quadrupo-lar spin-lattice relaxation or due to slow Li jumps between electrically inequivalent Li sites. Inequivalence means that the sites involved in the hopping process are labelled by different quadrupole frequencies ωq. The quadrupole frequency ωq results from the interaction of the quadrupole moment of the 7Li nucleus (spin-3/2 probe) with a non-vanishing electric field gradient produced by the electric charge distribution of the neighbouring ions at the Li site. The mobile Li+ ions experience site-specific electrical interactions and thus, from the point of view of a jumping ion, ωq becomes a function of tm leading therewith to a damping of the echo amplitude S2. The temperature dependence of the decay constant (1/τSAE) of the corre-sponding correlation function S2(tm), which usually can be described by a stretched exponen-tial, can be used directly to probe slow Li hopping processes. By using 7Li SAE-NMR the upper limit of accessible decay constants is given by the spin-spin relaxation rate which is typically of the order of 104 s−1. The lower limit is given by the (quadrupolar) spin-lattice re-laxation rate which is usually of the order of a few seconds. Using a short preparation time is a necessary pre-condition to ensure that mainly spin-alignment order is created after the first two rf-pulses of the Jeener-Broekaert pulse sequence [13]. Only in this case a (two-time) single particle correlation function S2 is obtained. 7Li spin-alignment echoes at 373 K and fixed tm but for variable preparation times are shown in Fig. 1. Whereas at short tp mainly quadrupolar order is created (fast decaying part of the echo), at larger preparation time, see e.g. the echo at tp = 60 µs, dipolar contributions increasingly be-come important (slowly decaying part of the echo). If not stated otherwise, tp = 10 µs was used for all experiments. Fourier transformation (Fig. 2) of the stimulated echoes is helpful to clarify the impact of homonuclear dipole-dipole interactions on the echo formation at various preparation times. Although the spin-alignment spectrum recorded at tp = 10 µs is dominated by a broad Gaussian shaped quadrupole part, central components are visible even at very short tp = 10 µs. However the latter take only 13 % of the total area. In order to study the evolution of dipolar contributions, we have read out the spin-alignment echo intensity either at t = tp and at t′ = tp + 70 µs. Due to the fast decay of the spin-alignment echo intensity the signal inten-sity determined at t′ only reflects dipolar contributions. The result for T = 389 K and 373 K is shown in Fig. 3. A similar behaviour was found previously for other Li conductors [14]. Whereas at short tp the spin-alignment echo intensity is already maximal, the weaker dipolar contribution reaches its maximum at around 100 µs at 373 K. At 400 µs the echo and its Fou-rier transform is exclusively composed of a sharp resonance resulting from homonuclear dipo-                          Fig. 1: 7Li NMR echoes recorded with the Jeener-Broekaert pulse sequence at fixed mixing time tm = 10 µs but for variable preparation times tp as indicated. The results were obtained at 373 K and 155 MHz.  Wilkening et al., Li Diffusion in Amorphous LiNbO3   diffusion-fundamentals    www.diffusion-online.org  Diffusion Fundamentals 8 (2008) 5.1 – 5.7  © 2008, M. Wilkening  lar interactions. The decay constant of the quadrupole part is roughly obtained when the data points at t′ are subtracted form those determined at t = tp. The resulting decay curve S2(tp) p 2,SAEexp( / )t T∝ −  yields 2,SAE 55 s.μ≈T   7Li SAE-NMR amplitudes, S2(tp = 10 µs, tm), vs. tm · T recorded at 155.5 MHz and at vari-ous temperatures are shown in a semi-logarithmic plot in  Fig. 4. The solid lines in Fig. 4 rep-resent fits with stretched exponentials, S2(tp = 10 µs, tm) SAEexp( ( / ) )mtγτ∝ − . The stretching               Fig. 2: 7Li stimulated echo spectra (373 K, 155MHz) recorded at tm = 10 µs and variable tp asindicated. With increasing preparation time thebroad quadrupole contribution disappears and thespectra are increasingly governed by homonuc-lear dipole-dipole interactions (sharp line).                     Fig. 3: Stimulated echo intensity as a function of tp read out at  t = tp (+) and at t′ = tp + 70 µs (×), respectively for two temperatures. The latter one represents the dipolar contributions to the echo. Only at short tp a sufficiently good separation of both parts is possible.   Wilkening et al., Li Diffusion in Amorphous LiNbO3   diffusion-fundamentals    www.diffusion-online.org  Diffusion Fundamentals 8 (2008) 5.1 – 5.7  © 2008, M. Wilkening  exponent γ  ranges from 0.6 to 0.25 between T = 150 K and 450 K. γ is constant up to T = 200 K and decreases then linearly with decreasing1/T. Strongly stretched hopping correlation functions might be due to the presence of a distribution of jump rates in amorphous LiNbO3. The corresponding decay rates, partly measured at different resonance frequencies (39, 78 and 155 MHz), are shown in Fig. 5.  Below about 200 K (γ = const., see above) the S2 decay is dominated by spin-lattice relaxa-tion effects because of two reasons: i) 1/τSAE, although much larger than 1/T1, shows the same weak temperature dependence as the corresponding SLR rates and ii) 1/τSAE depends on fre-quency as is also found for 1/T1, which reflects the non-diffusive background rates in this temperature range [2]. Between 200 K and 300 K a crossover regime is found leading to the temperature range where 1/τSAE finally follows Arrhenius behaviour with EA = 0.41(1) eV, cf. ref. [15]. In this T-range the S2-decay is induced by slow Li jumps in amorphous LiNbO3. Taking into account the background effects, i. e., extrapolating the low-T values of 1/τSAE to higher T and subtracting the extrapolated rates from the measured ones, the activation energy increases to 0.46(2) eV. As expected for a correlation rate, above 300 K the S2 decay constant   Fig. 5: Two-time correlation functions (S2(tp = 10 µs, tm) vs. tm · T) of amorphous LiNbO3 measured at 155 MHz and for various temperatures. The inset shows the shape of the correlation functions at smaller values tm · T.         Fig. 6: 7Li SAE-NMR decay rates 1/τSAE vs. 1/T. Between room temperature and 400 K the data points were recorded at three dif-ferent resonance frequencies as indicated. For comparison, diffusion induced SLRrates 1/T1 diff vs. 1/T (measured in the labo-ratory frame for ν = 23 MHz and 78 MHz) are shown, too. The solid lines represent linear fits and lead to the activation energies shown. Wilkening et al., Li Diffusion in Amorphous LiNbO3   diffusion-fundamentals    www.diffusion-online.org  Diffusion Fundamentals 8 (2008) 5.1 – 5.7  © 2008, M. Wilkening  is independent of the resonance frequency ν. This is in contrast to 1/T1 diff which generally depends on frequency (cf. ref. [2]). In the present case 1/T1 diff = ν−α with α = 1.7(2) was found [2]. Ideal Bloembergen-Purcell-Pound (BPP) behaviour [16], implying random iso-tropic diffusion, would lead to α = 2. Values of α in the range 1 ≤ α < 2 indicate that the hop-ping process is influenced by structural disorder and/or Coulomb interactions between the hopping ions which is assumed by several models [17-19]. Below 500 K only the low-temperature flank of the 1/T1 diff(1/T) peak is accessible reflecting short-range Li motions. The activation energy of the low-temperature flank at 23 MHz is lTA 0.29(1) eV=E (Fig. 6). The corresponding value of the high-T flank, hTAE , which is sensitive to long-range Li diffusion, is linked with lTAE via the expression lT hTA A( 1)α= −E E , see e.g. [20]. Thus, from the low-T fre-quency dependence of 1/T1 diff an activation energy hTAE = 0.41(7) eV is roughly predicted. This is in good agreement with the measured value using 7Li stimulated echo NMR between 300 K and 400 K. Activation energies of amorphous LiNbO3 from dc-conductivity measure-ments range between 0.4 and 0.6 eV depending on the preparation route, see e.g., Refs. [1,21,22]. Table 1 summarizes the results obtained from various methods probing Li diffusion on different length scales. It points out the heterogeneous nature of Li transport in a disor-dered material and corroborates our previous result that SAE-NMR provides a microscopic access to the long-range activation energy [9].  Table 1: Activation energies EA of the Li diffusivity in amorphous LiNbO3 as probed by different methods Method SLR-NMR 7Li NMR line shapes SAE-NMR dc-conductivity EA (eV) 0.27 … 0.29(1); [2] ≈ 0.35; [2] 0.41(1); [15] 0.46(2); see text  0.4 … 0.6; [1,21,22] 4  Conclusion  The present comparison of experimental results about Li diffusion in a disordered model sub-stance like amorphous LiNbO3 shows that 7Li stimulated echo NMR technique is highly ca-pable to complement frequency dependent relaxation NMR methods to study Li dynamics in solid ionic conductors. As it probes slow Li motions, SAE-NMR usually does not require high temperatures so that diffusion parameters on a longer length-scale are accessible via a micro-scopic NMR technique at moderate temperatures. The technique is applicable to a large num-ber of Li conductors. In the present case, the SAE-NMR activation energy is in fair agreement with that which was roughly predicted by the frequency dependence of the diffusion induced spin-lattice relaxation rate of the low-T flank. Interestingly, although the two methods probe different correlation functions, consistent results are obtained. References  [1]  P. Heitjans, M. Masoud, A. Feldhoff, M. Wilkening, Faraday Discuss. 134 (2007) 67. [2]  M. Wilkening, D. Bork, S. Indris, P. Heitjans, Phys. Chem. Chem. Phys. 4 (2002) 3246. [3]  P. Heitjans, S. Indris, M. Wilkening, Diffusion Fundamentals 2 (2005) 45. [4]  M. Wilkening, W. Küchler, P. Heitjans, Phys. Rev. Lett. 97 (2006) 065901. [5]  M. Wilkening, P. Heitjans, J. Phys.: Condens. Matter 18 (2006) 9849  [6]  F. Qi, G. Diezemann, H. Böhm, J. Lambert, R. Böhmer, J. Magn. Res. 169 (2004) 225. [7]  R. Böhmer, J. Magn. Res. 147 (2000) 78. [8]  M. Wilkening, R. Amade, W. Iwaniak, P. Heitjans, Phys. Chem. Chem. Phys. 9 (2007) 1239. [9]  M. Wilkening, C. Mühle, M. Jansen, P. Heitjans, J. Phys. Chem. B 111 (2007) 8691. [10]  M. Wilkening, Ph.D. thesis, Universität Hannover, 2005. [11]  J. Jeener, P. Broekaert, Phys. Rev. 157 (1967) 232. [12]  E. Fukushima, S. B. W. Roeder, Experimental Pulse NMR, Addison-Wesley, Reading, 1981. [13]  X.-P. Tang, Y. Wu, J. Magn. Res. 133 (1988) 155. Wilkening et al., Li Diffusion in Amorphous LiNbO3   diffusion-fundamentals    www.diffusion-online.org  Diffusion Fundamentals 8 (2008) 5.1 – 5.7  © 2008, M. Wilkening  [14]  F. Qi, T. Jörg, R. Böhmer, Solid State Nucl. Magn. Res. 22 (2002) 484. [15]  M. Wilkening, P. Heitjans, Solid State Ionics 177 (2006) 3031. [16]  N. Bloembergen, E. M. Purcell, R. V. Pound, Phys. Rev. 73 (1948) 679. [17]  K. L. Ngai, O. Kanert, Solid State Ionics 53 (1992) 963. [18]  K. Funke, Prog. Solid State Chem. 22 (1993) 11. [19]  A. Bunde, P. Maass, M. Meyer, in: P. Heitjans and J. Kärger (Eds.), Diffusion in Condensed Matter - Methods, Materials, Models, Springer, Berlin, 2005. [20]  P. Heitjans, A. Schirmer, S. Indris, in: P. Heitjans and J. Kärger (Eds.), Diffusion in Condensed Matter - Methods, Materials, Models, Springer, Berlin, 2005. [21]  A. Glass, K. Nassau, T. Negran, J. Appl. Phys. 49 (1978) 4808. [22]  S. Ono, H. Mochizuki, S. Hirano, J. Ceram. Soc. Japan 104 (1996) 574. 

Li dynamics in amorphous LiNbO 3 as probed by solid state NMR on different length scales

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Li dynamics in amorphous LiNbO 3 as probed by solid state NMR on different length scales

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