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NMR studies on lithium ion migration in sulfide-based conductors, amorphous and crystalline Li3PS4
SOSI-13701; No of Pages 8 Solid State Ionics xxx (2015) xxx–xxx
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NMR studies on lithium ion migration in sulfide-based conductors, amorphous and crystalline Li3PS4 Kikuko Hayamizu a, Yuichi Aihara b, Taku Watanabe b, Takanobu Yamada b, Seitairo Ito b, Nobuya Machida c a b c
Institute of Applied Physics, University of Tsukuba, Tsukuba 305-8573, Japan Samsung R&D Institute Japan, Senba-nishi, Minoshi, Osaka 562-0036, Japan Department of Chemistry, Konan University, Higashinada-ku, Kobe 658-8501, Japan
a r t i c l e
i n f o
Article history: Received 23 January 2015 Received in revised form 9 June 2015 Accepted 12 June 2015 Available online xxxx Keywords: Sulfide-based lithium ion conductors Pulsed-gradient spin-echo (PGSE) NMR Parameter-dependent diffusion 7 Li NMR
a b s t r a c t 7 Li spectra were observed for amorphous and crystalline Li3PS4 to study the structure of lithium ions. Lithium migration was studied using pulsed-gradient spin-echo 7Li NMR between 30 °C and 120 °C. The lithium diffusion behavior depended on the observation time and the pulsed-field gradient strength, and was quite different from the lithium diffusion in liquid electrolytes. Amorphous Li3PS4 showed higher ionic conductivity than crystalline Li3PS4, and similarly, the lithium diffusion rate was faster in amorphous samples. The lithium diffusion behavior in both conductors was not uniform and was distributed widely in time and space. © 2015 Elsevier B.V. All rights reserved.
1. Introduction Inorganic solid ion conductors have attracted much attention because of their potential application in all solid-state batteries, as summarized in a recent review article [1]. In addition to many types of oxide electrolyte systems, sulfide-based electrolytes are important candidates for lithium batteries. Li2S-P2S5 solid electrolytes are known to have high ionic conductivity, and their applications in all-solid-state batteries have been attempted [2,3]. These conductors are usually synthesized from proper mixtures of Li2S and P2S5 and their conductivity is influenced significantly by the preparation methods used. It is known that mechanical ball-milling affords high conductivity and further heat treatment increases the ionic conductivity [4,5]. Recently, a liquid-phase synthesis of Li3PS4 was performed to produce materials for all-solid-state lithium batteries [6]. The addition of lithium halides was attempted to improve the conductivity of 0.7Li2S-0.3P2S5 [7]. Samples that have not been subjected to heat treatment are called amorphous solids or glasses, and those that have been subjected to heat treatment are denoted as crystalline solids or glass ceramics. The characterization of these materials has been performed mainly via their ionic conductivity (σ), X-ray diffraction (XRD) pattern and scanning electron microscopy (SEM) micrographs. To understand their high conductivity, visualization of the conduction pathways in Li2S-P2S5 conductors was performed using computational modeling methods based on data from synchrotron X-ray and time-of-flight neutron diffraction measurements. It was shown that lithium ions E-mail address: [email protected] (K. Hayamizu).
were located in stable and metastable regions, in which complicated pathways occurred in the range of 10 nm [8]. The local motion of lithium ions could be observed from 7Li and 6Li relaxation times on the Å (~10−10 m) order local space, because the NMR relaxation times originate from a single or multiple flips of the lithium ions (~ 10−9 s). The longer range diffusion of lithium ions can be measured using pulsedgradient spin-echo (PGSE) NMR, which affords lithium diffusion over longer distances in the 10−6 m scale during time intervals of around 10−2 to 1 s. Importantly, over longer distances, uniform and homogeneous migration cannot be assumed. On the other hand, the ionic conductivity measured by the AC method always affords a definite value at a given temperature. The ionic conductivity is defined as the mobility (normalized by distance) multiplied by the number of charge-carrier ions in a unit volume, and does not explicitly include the distance. However, the proper thickness is required to measure the ionic conductivity of compressed solid samples (pellets). High conductivity is induced by lithium ion migration because standing anions do not contribute to the ionic conductivity. We have observed lithium migration in crystalline 0.7Li2S-0.3P2S5 [9,10] using PGSE NMR, and found that lithium migration was heterogeneous and depended on the measuring parameters such as observation time and pulsed-field gradient (PFG) strength. Recently, we observed similar phenomena in a polycrystalline garnet-type solid conductor [11]. The translational movement of the lithium ions observed using PGSE NMR is very complicated. Within short periods, the lithium ions move quickly, collide and are diffracted. Lithium migration observed over longer observation times were slowed by averaging processes, accompanied by subsequent collision and diffraction. Experimentally, the observation
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Please cite this article as: K. Hayamizu, et al., NMR studies on lithium ion migration in sulfide-based conductors, amorphous and crystalline Li3PS4, Solid State Ionics (2015), http://dx.doi.org/10.1016/j.ssi.2015.06.016
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time (Δ) is the time traveled by a marked species from its initial position to its final position for detection. The precise processes occurring during Δ are unknown. Even if a system has favorable NMR relaxation times (T1 and T2), Δ is usually limited from 10 ms to 2 s over 10−5 – 10−6 m order diffusing space. The PGSE NMR method allows an explicit time interval to measure lithium diffusion and the length of continuous migration space. In the present study, owing to the extremely short 7Li T2 (b5 ms) and short 7Li T1 (b1 s) of the lithium ions in the conductors, we had strict limitations of the possible Δ values obtained at a reasonable sensitivity, in which we could observe the Δ-dependent lithium diffusion. Among the sulfide-based lithium conductors, 0.75Li2S-0.25P2S5 (7525) has a stoichiometric composition of Li3PS4, and the anion structure is assumed to be uniform. The 7Li NMR spectral pattern at ambient temperature consists of narrow and broad components and changes as temperature increase. The temperature-dependent 7Li spectrum was analyzed for crystalline 7525 (7525C) and compared with those of amorphous 7525 (7525A). 2. Experimental 2.1. Sample preparation Amorphous 7525A (stoichiometric Li3PS4) powder was prepared by high-energy ball-milling of Li2S (Alfa Aesar, purity 99.9%) and P2S5 (Aldrich Chemicals, purity 99%) (in a molar ratio of 75:25) at 380 rpm for 35 h in a zirconium pot with 10 and 3 mm diameter ZrO2 milling media (7 and 10 balls, respectively) and a grinding bowl fastener, P-7 (Fritsch, Germany) under an Ar atmosphere. To prepare the crystalline 0.75Li2S-0.25P2S5, the pellets were heated at 250 °C for 5 h. The entire procedure was performed in an Ar gas–filled glove box. The solid electrolyte powder (400 mg) was placed into a 13 mm diameter die, and a load of 4 tons was applied at 25 °C for 30 s using a hydraulic press. The average thickness of the electrolyte pellets produced was 630 and 185 μm for 7525A and 7525C, respectively. The sample density was estimated from the weight and volume of the pellets, and was 1.65 and 1.63 g cm−3 for 7525A and 7525C, respectively. To measure ionic conductivity, indium-foil blocking electrodes were used. A sample pellet was placed between two indium foils with the same diameter (13 mm) and placed in a Teflon cell with two stainless steel electrodes. For the NMR measurements, a sample was broken into smaller pieces (N 1 mm3 blocks) and placed into a micro-NMR glass tube with a diameter of 5 mm; BMS-005 J, which was made especially for flame sealing (Shigemi, Tokyo, Japan), has a height of 10 mm, in which a linear PFG is guaranteed. The sample tubes were then flamesealed. 2.2. Powder X-ray diffraction Powder X-ray diffraction (XRD) was measured using an Empyrean XRD system (PANalytical, CuKα, 45 kV, 40 mA) for both the original amorphous powder and the heat-treated samples at room temperature. An Ar gas–filled sample holder was used to prevent degradation from moisture.
using the cell constant and bulk resistance. The bulk resistance was determined from the x-axis intercept value (linear regression) over the high-frequency linear region. 2.4. NMR measurements All of the NMR spectra were measured on a Tecmag Apollo spectrometer (Houston, USA) equipped with a 4.7 T wide-bore magnet using a fully tunable PFG probe (JEOL) and controlled by a JEOL console. The 7Li spectra were measured at 78.4 MHz. 7Li T1 and T2 observations were performed for the narrow central peak using the usual inversion recovery (180°-τ-90°-Acq.) and Hahn echo (90°-τ-180°-τ-Acq.) sequences, respectively. The 7Li spectral pattern observations and the 7 Li T1 and T2 measurements were performed in the temperature range 30 °C to 120 °C. 7 Li diffusion phenomena were observed at 30 °C, 50 °C, 80 °C and 120 °C using the stimulated-echo (STE) PGSE NMR pulse sequence, as shown in Fig. 1. The echo attenuation, E, is related to the experimental variables, and in homogenous space the diffusion coefficient D can be obtained by use of the Stejskal and Tanner equation [12,13]. Sðg; δ; ΔÞ ¼
E ¼ exp −γ 2 δ2 g 2 DðΔ−δ=3Þ ¼ expð−bDÞ; E0
ð1Þ
where γ is the 7Li gyromagnetic ratio (1.03977 × 108 s−1 T−1), g is the strength of the PFG with duration δ, and Δ defining the time scales of the diffusion measurement. In homogeneous systems, D is independent of g and Δ. A single-exponential diffusion plot following Eq. (1) indicates free diffusion for a single diffusion species. When the diffraction patterns were observed, the echo attenuation was plotted in the commonly named q-space, where q = γδg/2π m−1 [14]. In this study, g was set between 4.8 and 15 Tm−1. With a fixed g, δ was varied from 0.1 to 3.0 ms with τ2 = 3.4 ms and the observation time Δ was set at 10, 20, 30, 50 and 70 ms. The echo signals were averaged from 64 to 240 times, depending on the measurement conditions. 3. Results and discussion 3.1. XRD The XRD patterns of the synthesized powders of amorphous 7525A and crystalline 7525C are shown in Fig. 2. Since the 7525A was milled, the XRD pattern did not show crystalline peaks, confirming its amorphous state. In contrast, a number of well-defined peaks were observed in the 7525C sample. There were no peaks corresponding to the starting materials (Li2S and P2S5) in the 7525C sample. It is known that 7525C has three crystal phases, namely, α, β and γ phases [16]. We assigned the major component of the 7525C sample as β-Li3PS4 phase. However, extra peaks were observed around 2θ = 20° and 40°. It is certain that the 7525C has multiphases, with other (minor) crystalline and amorphous phases in addition to the major β-Li3PS4 phase. The broad linewidth also indicated a low-degree of crystallinity. In the Raman
τ2
τ1
τ2
2.3. Ionic conductivity determination The ionic conductivity was determined using the AC impedance method (electrochemical impedance spectroscopy, EIS) employing a Solartron SI 1260 impedance analyzer equipped with a Solartron 1470E cell test system controlled by a personal computer in the frequency range of 1 MHz to 0.1 Hz with a ±10 mV perturbation versus open-circuit potential. A temperature chamber, ESPEC SU241, was used to maintain the measurement temperature conditions. The EIS measurements were conducted by decreasing the temperature from 50 °C to − 10 °C in 5 °C steps. The ionic conductivity was calculated
Fig. 1. The STE echo sequence of the PGSE NMR used in this study. Two PFGs with strength g and duration δ were applied at a time interval Δ.
Please cite this article as: K. Hayamizu, et al., NMR studies on lithium ion migration in sulfide-based conductors, amorphous and crystalline Li3PS4, Solid State Ionics (2015), http://dx.doi.org/10.1016/j.ssi.2015.06.016
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broad components were 5.1 and 11.4 kHz for 7525A and 7525C, respectively. The heat treatment of the sample from 7525A to 7525C induced the 7Li linewidth to be broader. At 110 °C, clear differences were obtained in the 7Li spectral patterns between the two samples; 7525A exhibited a single line with a linewidth of 1.1 kHz, while the 7Li spectrum of 7525C was composed of two Lorentz curves with linewidths of 1.5 and 5.7 kHz. The 7Li pattern of the 7525C showed slight temperature dependence, while 7525A exhibited clear narrowing of the linewidth, and collapsed into a narrow component at 80 °C, in which the ratio of the narrow component increased significantly in the high-temperature range. The heat treatment afforded the crystalline structure (see XRD data in Fig. 2), lower ionic conductivity (Fig. 3), and a slightly broader linewidth in the 7Li resonance (Fig. 4). Since the 7Li spectral pattern of 7525C was almost unchanged at higher temperatures, the lithium structure was stabilized by the heat treatment. 3.4. T1 and T2 of the 7Li resonance
Fig. 2. XRD patterns for (a) 7525C and (b) 7525A. The asterisks indicate β-Li3PS4 peaks identified in previous work [15].
spectroscopy data, similar to our previous work, a small shoulder peak, assigned to the P2S4− anion was observed at 386 cm−1 for the 7525C 6 sample [17]. 3.2. Ionic conductivity Arrhenius plots of the ionic conductivity (σ) are shown in Fig. 3 for 7525A and 7525C. The σ values were 1.24 × 10− 4 and 5.66 × 10− 5 Scm−1 at 25 °C for 7525A and 7525C, respectively. Clearly, the amorphous sample showed a larger value of σ. The corresponding activation enegy was 39.4 and 39.3 kJ mol−1 for 7525A and 7525C, respectively, and the difference between them was small. For the amorphous sample, the ionic conductivity was reproduced well at 25 °C in different synthesized samples [17], and in the same sample, a compatible value of the activation energy was obtained in a narrow temperature range. 3.3. 7Li spectra The 7Li NMR spectra of 7525A and 7525C were observed between 20 °C and 120 °C, and spectra obtained at 30 °C and 110 °C are shown in Fig. 4, in which 7525A clearly had a smaller linewidth versus 7525C. At 30 °C, both spectra were composed of narrow and broad components and were fitted by an overlap of two Lorentz curves. The linewidths of the narrow components were 0.30 and 1.6 kHz, and those of the
Fig. 3. Arrhenius plot of the ionic conductivity of 7525A (squares) and 7525C (circles).
The T1 and T2 data are required to set the PGSE NMR measuring conditions. Arrhenius plots of the 7Li T1 and T2 data of the narrow component of 7525A and 7525C are shown in Fig. 5. The T1 values were between 0.1 and 0.6 s and the activation energy was 12.6 ± 0.2 and 8.7 ± 0.1 kJ mol−1 for 7525A and 7525C, respectively. Since the 7Li T1 is related to either one or several jumps of the migrating lithium ions in the local environment, much smaller activation energies (about one-third or less) were observed compared with the ionic conductivity, suggesting that local motion is not directly connected to the long-range ion conduction. Since the value of T2 of 7525C was shorter than that of 7525A, the longer accumulation time for 7525C was necessary in the lithium diffusion measurements. In Fig. 5(b), the temperature dependence of T2 for 7525A showed a maximum value at 60 °C in which the broader component became small and diminished above 90 °C as shown in Fig. 4(e). The T2 maximum was probably due to the change of two components in the spectrum. 3.5. Diffusion measurements using the PGSE-NMR method We observed that lithium migration was highly heterogeneous, and the diffusion phenomena observed by the PGSE-NMR method varied significantly depending on the measuring conditions, such as the observation time Δ and the PFG strength g shown in Fig. 1. Δ-dependent diffusion phenomena are known for particles diffusing in media having inner structures, such as polymer electrolytes, zeolites and membranes. In addition, lithium diffusion in the solid conductors, the Δ-dependent diffusion phenomena, are often observed as shown previously [9–11]. Lithium diffusion plots of 7525C following Eq. (1) measured at various Δ values from 10 to 70 ms are shown in Fig. 6, which were observed using a fixed g = 9.8 Tm−1 at 30 °C. As shown in Fig. 6, the dependence of the lithium diffusion on the observation time was large. When we estimated the apparent diffusion constant, Dapparent from the initial decay of the echo attenuation, for Δ = 10, 20, 30, 50 and 70 ms, the value of Dapparent of 7525A was 40, 14, 6.0, 1.4 and 0.65 × 10−12 m2s−1 and that of 7525C changed as 52, 13, 4.9, 0.75 and 0.13 × 10−12 m2s−1 at 30 °C, respectively. This variation depending on Δ was extremely large and is the order of 60 times from 70 to 10 ms. When Δ = 10 to 30 ms, the minima were observed in the plots (diffusive diffraction). It should be noted that without diffraction, the lithium echo signals were always in the in-phase mode in the real-mode plots. When diffraction was observed, the lithium echo signals passed through the out-of-phase mode and returned to the in-phase mode, probably owing to Coulombic interactions with anions. All the plots were made in the magnitude-mode echo signals without any phase information. When the value of Δ increased, the value of Dapparent decreased and the degree of the Δ-dependence became smaller, as shown at Δ = 50 and 70 ms. When the lithium ions migrated quickly in the short time period, the collision with anions
Please cite this article as: K. Hayamizu, et al., NMR studies on lithium ion migration in sulfide-based conductors, amorphous and crystalline Li3PS4, Solid State Ionics (2015), http://dx.doi.org/10.1016/j.ssi.2015.06.016
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Fig. 4. 7Li spectral patterns of (a) and (c) 7525A and (b) and (d) 7525C observed at 30 °C and 110 °C, respectively.
induced a diffractive pattern. When the lithium ions traveled for longer time periods, averaging processes reduced the Dapparent values from multiple collisions and diffractions. It is surprising that the Dapparent changed markedly over the time scale of ms order. The pathways of the lithium migration are probably strongly related to the distance of the moving lithium ions on the ms scale. The lithium diffusion of 7525A at 30 °C is approximately comparable to that of 7525C at 80 °C. When the Δ was short, the echo attenuation profiles were insensitive to temperature. For example, plots of the echo attenuation versus b for 7525A with Δ = 20 ms at g = 9.8 Tm− 1 measured at 30 °C, 80 °C and 120 °C are shown in Fig. 7. The echo attenuation profiles versus b for Δ = 20 ms were not much different at the three temperatures, except for the shape of the diffraction patterns, which were gradually distorted as the temperature increased. In addition, the position of the minima was slightly changed at 80 °C among the three plots. Only a slight temperature dependence of the echo attenuation profiles was obtained, probably owing to trivial effects of the thermal activation on the diffusive diffraction phenomena. A similar effect on the lithium ion diffusion for short Δ was observed for 7525C, as has been observed in a garnet-type solid conductor in our recent observation [11]. Temperature dependence measurements were performed and the diffusion plots at four temperatures 30 °C, 50 °C, 80 °C and 120 °C are shown for 7525C in Fig. 8. As shown in Fig. 8(a), the temperature dependence was trivial for Δ = 30 ms, and the plots almost overlapped at the four temperatures. The value of Dapparent was about 4.7 × 10− 12 m2s− 1. From Fig. 8(b), when Δ became longer as 70 ms, the diffusion plots indicated clear temperature dependence and the value of Dapparent was 0.9 and 1.7 × 10−12 m2s−1 for 80 °C and 120 °C, respectively. The initial decay was not clearly calculated from the plots at 30 °C and 50 °C, because in this temperature range, the plots were not linear and contained slower components.
It can be seen that the lithium migration at 30 ms between 30 °C and 120 °C was faster than that on 70 ms at 120 °C. This is characteristic of lithium ion migration in solid conductors. As described in our previous papers, lithium migration in sulfidebased conductors [9,10] and a garnet-type ionic conductor [11] depends on the PFG strength, g. This experimental fact is very curious, and is not observed in liquid lithium electrolytes. In general, the fast lithium diffusion is observed by small g and slowly diffusing lithium ions require a large g to be observed enough echo decay. Suitable g values must be chosen to obtain a reasonable diffusion constant (D). In the solid conductors, we noticed a faster Dapparent was observed with smaller g, and by setting a larger g, Dapparent decreased. The g-dependent effect reduced as Δ increased and, in this work, we observed g-dependent migration in 7525A and 7525C, as shown in Fig. 9. As shown in Fig. 9, a smaller g gave a larger echo decay in the diffusion plots for both 7525A and 7525C, even if the temperatures were different. The Dapparent value of 7525A at 30 °C was 7.2, 4.8, 1.9 and 1.4 × 10−12 m2s− 1 for g = 2.3, 4.8, 7.3 and 9.8 Tm−1, respectively, and decreased depending on the value of g. The value of Dapparent for 7525C was observed as 1.8 × 10−12 m2s−1 for g = 4.8 Tm−1 and with an increase in g, the echo decay decreased. The value of Dapparent = 9.0 × 10−13 m2s−1 for g = 9.8 Tm−1 and about 5.2 × 10−13 m2s−1 for g = 12.4 and 14.9 Tm−1 were observed. If all the lithium ions migrate homogeneously at the same speed, then a g-dependent behavior would not be observed. The lithium ions in 7525A and 7525C migrate at various speeds, and the slower lithium ions can be detected using a larger g. For longer Δ, the system approaches homogeneous diffusion and the value Dapparent tends to approach a small finite value. In our experience, g values above 15 Tm− 1 did not produce linear plots in Eq. (1) for sulfide-based conductors. In addition, the adequate echo decay observed in liquid electrolytes (examples of which are given in our
Please cite this article as: K. Hayamizu, et al., NMR studies on lithium ion migration in sulfide-based conductors, amorphous and crystalline Li3PS4, Solid State Ionics (2015), http://dx.doi.org/10.1016/j.ssi.2015.06.016
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Fig. 7. Plot of the echo attenuation of 7525A versus b for g = 9.8 Tm−1 and Δ = 20 ms at three temperatures: 30 °C (downward-triangles), 80 °C (upward-triangles) and 120 °C (circles).
3.6. Comparison of crystalline 7525C and amorphous 7525A
Fig. 5. Arrhenius plots of (a) 7Li T1 and (b) 7Li T2 of the narrow component in 7525A (up-triangles) and 7525C (down-triangles).
previous paper [10]) cannot be obtained for longer Δ. The Dapparent value may tend to a constant value, but such experiments have not yet been achieved for sulfide-based conductors because of the short 7Li T2 and T1. The experimental limitation on Δ is induced by the short relaxation times. A larger g did not give linear diffusion plots with enough decay, which are observed in usual liquid electrolytes. Therefore, it was difficult to obtain reliable values of the very slow diffusion coefficient as a unique value in our samples.
To compare the lithium migration in amorphous 7525A and crystalline 7525C, it was necessary to fix the measuring conditions and the echo attenuations were plotted on the same charts. In Fig. 10, diffusion plots of 7525C and 7525A are shown at 30 °C and 120 °C. The value of g was fixed at 9.8 Tm−1 and δ was changed from 0.1 to 3 ms (20 points). The value Δ was changed between 10 and 70 ms. The echo attenuation decay was faster in 7525A than 7525C for each measuring condition, which suggests that lithium migration was faster in 7525A compared with 7525C, for the same measuring conditions. When the diffraction patterns appeared in the diffusion plots, it was convenient to plot the echo attenuation in the q-space, where q = γgδ/ 2π in units of m−1 [14]. From the analogy of restricted diffusion for a particle confined in a sphere, the inverse of q at the first diffraction minimum was defined as Rdiffraction. The simultaneous display of echo attenuations in 7525C and 7525A in the q-space plots are shown for Δ = 10, 20 and 30 ms at 30 °C in Fig. 11. The value of the Rdiffraction is denoted in Fig. 11. For Δ N 40 ms, no collision and no diffraction pattern was observed. Sample 7525A showed higher values of Rdiffraction compared with 7525C. The value of Rdiffraction increased when Δ decreased. Also,
Fig. 6. Lithium diffusion plots of (a) 7525A (δ was changed from 0.1 to 4 ms) and (b) 7525C (δ was changed from 0.1 to 3 ms) at 30 °C. For a fixed g = 9.8 Tm−1, Δ was varied from 10 to 70 ms.
Please cite this article as: K. Hayamizu, et al., NMR studies on lithium ion migration in sulfide-based conductors, amorphous and crystalline Li3PS4, Solid State Ionics (2015), http://dx.doi.org/10.1016/j.ssi.2015.06.016
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Fig. 8. Lithium diffusion plots of 7525C at four temperatures: 30 °C (squares), 50 °C (circles), 80 °C (up-triangles) and 120 °C (down-triangles) for g = 9.8 Tm−1 and (a) Δ = 30 and (b) 70 ms.
the lithium ions exhibited clearer diffraction patterns in the amorphous sample. This suggests that the lithium ions in the amorphous sample collided and were diffracted more, and that the collision and diffraction behaviors must be related to the inner inhomogeneous structure of the lithium pathways. The crystalline sample provided slightly smoother transport routes. The collision and diffraction process of the migrating lithium ions must be related deeply structures and shapes of diffusing pathways related to grain boundaries. Precise studies are required to clarify the diffusive diffraction and grain boundaries. 3.7. Relationship between the ionic conductivity and the diffusion coefficient of 7525A Using the conductivity data, we can estimate the lithium diffusion coefficient for 7525A by assuming a value of carrier density. Sulfidebased ion electrolytes are single ion conductors without any anion
migration. Since anions do not contribute to the ionic conductivity, the Nernst–Einstein relationship can be simplified to [18], DðT Þ ¼
kT σ ðT Þ; Ne2
ð2Þ
where N is the total number of Li ions in a specific volume, e is the electron charge, and k is the Boltzmann constant. At 30 °C, the lithium diffusion coefficient (DLi) was estimated to be 2.5 × 10− 13 m2s−1 from σ = 2.4 × 10−4 Scm−1 and the sample density, if all of the lithium ions contribute to conduction. From Fig. 4, the existence of a broad component in the 7Li spectrum suggests that not all of the Li ions contribute to ion conduction. If one-third of the lithium ions contributed to the ionic conductivity, the estimated D was 7.6 × 10−13 m2s−1. The value of Dapparent (6.5 × 10− 13 m2s− 1) measured for g = 9.8 Tm− 1 and Δ = 70 ms was close to this value. At 80 °C, σ = 1.7 × 10− 3
Fig. 9. The lithium migration of (a) 7525A observed for Δ = 50 ms at 30 °C and (b) 7525C for Δ = 70 ms at 80 °C for various g values. The value of δ was changed from 0.1 to 3 ms (20 points).
Please cite this article as: K. Hayamizu, et al., NMR studies on lithium ion migration in sulfide-based conductors, amorphous and crystalline Li3PS4, Solid State Ionics (2015), http://dx.doi.org/10.1016/j.ssi.2015.06.016
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Fig. 10. Simultaneous diffusion plots of 7525C (down-triangles) and 7525A (up-triangles) at 30 °C (left-hand side) and 120 °C (right-hand side) for a fixed g = 9.8 Tm−1 and δ varying 0.1 to 3 ms.
Scm−1, and the estimated value was DLi = 1.97 × 10−12 m2s−1 (100% Li+ migration) and 5.9 × 10−12 m2s−1 (33%). The observed Dapparent afforded two values 1.6 and 3.4 × 10−12 m2s− 1 for g = 9.8 Tm− 1 at Δ = 70 ms. The ion conductivity measurements provided a unique value at each temperature, despite the scattered values of Dapparent from the NMR diffusion measurements. However, these empirical results indicate that the value of Dapparent obtained in the NMR measurements is in the reasonable range and is not an unrealistic value.
4. Conclusion
Fig. 11. q-Space plots of the echo attenuation for 7525C (down-triangles) and 7525A (up-triangles) for g = 9.8 Tm−1 at 30 °C for Δ = (a) 10, (b) 20, and (c) 30 ms.
The 7Li NMR spectra of 7525A and 7525C are composed of narrow and broad components. The migrating lithium ions enter into the narrow component, whose ratio is related to the number of charge carriers. The ratio of the narrow component was insensitive to temperature in 7525C, and changed slightly from 0.30 to 0.35 on increasing temperature from 30 °C to 120 °C. This trend is different from behavior in 7525A, in which the ratio of the narrow component increased from 0.5 at 30 °C to 1.0 at 90 °C. Heat treatment stabilized some of the moving lithium ions in the conductor. From the changes in 7525A to 7525C, the ratio of the migrating lithium ions decreased, especially at higher temperatures. The lithium diffusion measured using PGSE-NMR showed very complicated behaviors in both 7525A and 7525C. It was found that the lithium ions migrate in a widely spread manner in time and space. For shorter observation time, the lithium ions moved more quickly. For Δ b 30 ms, the lithium ion migration was accompanied by collisions and diffraction, and a small thermal activation was observed. As the observation time increased, lithium diffusion became slower without any collisions and diffraction profiles in the echo attenuation. The lithium ions in 7525A collided more frequently than in 7525C. The long-range lithium pathways must be narrow and tortuous instead of wide and straight in space. At present, we cannot discuss the collision in a short time period connecting to grain boundaries. For longer observation times, the lithium migration in 7525C became slower than 7525A, which is related to the higher ionic conductivity of 7525A compared with that of 7525C.
Please cite this article as: K. Hayamizu, et al., NMR studies on lithium ion migration in sulfide-based conductors, amorphous and crystalline Li3PS4, Solid State Ionics (2015), http://dx.doi.org/10.1016/j.ssi.2015.06.016
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NMR studies on lithium ion migration in sulfide-based conductors, amorphous and crystalline Li3PS4 Kikuko Hayamizu a, Yuichi Aihara b, Taku Watanabe b, Takanobu Yamada b, Seitairo Ito b, Nobuya Machida c a b c
Institute of Applied Physics, University of Tsukuba, Tsukuba 305-8573, Japan Samsung R&D Institute Japan, Senba-nishi, Minoshi, Osaka 562-0036, Japan Department of Chemistry, Konan University, Higashinada-ku, Kobe 658-8501, Japan
a r t i c l e
i n f o
Article history: Received 23 January 2015 Received in revised form 9 June 2015 Accepted 12 June 2015 Available online xxxx Keywords: Sulfide-based lithium ion conductors Pulsed-gradient spin-echo (PGSE) NMR Parameter-dependent diffusion 7 Li NMR
a b s t r a c t 7 Li spectra were observed for amorphous and crystalline Li3PS4 to study the structure of lithium ions. Lithium migration was studied using pulsed-gradient spin-echo 7Li NMR between 30 °C and 120 °C. The lithium diffusion behavior depended on the observation time and the pulsed-field gradient strength, and was quite different from the lithium diffusion in liquid electrolytes. Amorphous Li3PS4 showed higher ionic conductivity than crystalline Li3PS4, and similarly, the lithium diffusion rate was faster in amorphous samples. The lithium diffusion behavior in both conductors was not uniform and was distributed widely in time and space. © 2015 Elsevier B.V. All rights reserved.
1. Introduction Inorganic solid ion conductors have attracted much attention because of their potential application in all solid-state batteries, as summarized in a recent review article [1]. In addition to many types of oxide electrolyte systems, sulfide-based electrolytes are important candidates for lithium batteries. Li2S-P2S5 solid electrolytes are known to have high ionic conductivity, and their applications in all-solid-state batteries have been attempted [2,3]. These conductors are usually synthesized from proper mixtures of Li2S and P2S5 and their conductivity is influenced significantly by the preparation methods used. It is known that mechanical ball-milling affords high conductivity and further heat treatment increases the ionic conductivity [4,5]. Recently, a liquid-phase synthesis of Li3PS4 was performed to produce materials for all-solid-state lithium batteries [6]. The addition of lithium halides was attempted to improve the conductivity of 0.7Li2S-0.3P2S5 [7]. Samples that have not been subjected to heat treatment are called amorphous solids or glasses, and those that have been subjected to heat treatment are denoted as crystalline solids or glass ceramics. The characterization of these materials has been performed mainly via their ionic conductivity (σ), X-ray diffraction (XRD) pattern and scanning electron microscopy (SEM) micrographs. To understand their high conductivity, visualization of the conduction pathways in Li2S-P2S5 conductors was performed using computational modeling methods based on data from synchrotron X-ray and time-of-flight neutron diffraction measurements. It was shown that lithium ions E-mail address: [email protected] (K. Hayamizu).
were located in stable and metastable regions, in which complicated pathways occurred in the range of 10 nm [8]. The local motion of lithium ions could be observed from 7Li and 6Li relaxation times on the Å (~10−10 m) order local space, because the NMR relaxation times originate from a single or multiple flips of the lithium ions (~ 10−9 s). The longer range diffusion of lithium ions can be measured using pulsedgradient spin-echo (PGSE) NMR, which affords lithium diffusion over longer distances in the 10−6 m scale during time intervals of around 10−2 to 1 s. Importantly, over longer distances, uniform and homogeneous migration cannot be assumed. On the other hand, the ionic conductivity measured by the AC method always affords a definite value at a given temperature. The ionic conductivity is defined as the mobility (normalized by distance) multiplied by the number of charge-carrier ions in a unit volume, and does not explicitly include the distance. However, the proper thickness is required to measure the ionic conductivity of compressed solid samples (pellets). High conductivity is induced by lithium ion migration because standing anions do not contribute to the ionic conductivity. We have observed lithium migration in crystalline 0.7Li2S-0.3P2S5 [9,10] using PGSE NMR, and found that lithium migration was heterogeneous and depended on the measuring parameters such as observation time and pulsed-field gradient (PFG) strength. Recently, we observed similar phenomena in a polycrystalline garnet-type solid conductor [11]. The translational movement of the lithium ions observed using PGSE NMR is very complicated. Within short periods, the lithium ions move quickly, collide and are diffracted. Lithium migration observed over longer observation times were slowed by averaging processes, accompanied by subsequent collision and diffraction. Experimentally, the observation
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Please cite this article as: K. Hayamizu, et al., NMR studies on lithium ion migration in sulfide-based conductors, amorphous and crystalline Li3PS4, Solid State Ionics (2015), http://dx.doi.org/10.1016/j.ssi.2015.06.016
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time (Δ) is the time traveled by a marked species from its initial position to its final position for detection. The precise processes occurring during Δ are unknown. Even if a system has favorable NMR relaxation times (T1 and T2), Δ is usually limited from 10 ms to 2 s over 10−5 – 10−6 m order diffusing space. The PGSE NMR method allows an explicit time interval to measure lithium diffusion and the length of continuous migration space. In the present study, owing to the extremely short 7Li T2 (b5 ms) and short 7Li T1 (b1 s) of the lithium ions in the conductors, we had strict limitations of the possible Δ values obtained at a reasonable sensitivity, in which we could observe the Δ-dependent lithium diffusion. Among the sulfide-based lithium conductors, 0.75Li2S-0.25P2S5 (7525) has a stoichiometric composition of Li3PS4, and the anion structure is assumed to be uniform. The 7Li NMR spectral pattern at ambient temperature consists of narrow and broad components and changes as temperature increase. The temperature-dependent 7Li spectrum was analyzed for crystalline 7525 (7525C) and compared with those of amorphous 7525 (7525A). 2. Experimental 2.1. Sample preparation Amorphous 7525A (stoichiometric Li3PS4) powder was prepared by high-energy ball-milling of Li2S (Alfa Aesar, purity 99.9%) and P2S5 (Aldrich Chemicals, purity 99%) (in a molar ratio of 75:25) at 380 rpm for 35 h in a zirconium pot with 10 and 3 mm diameter ZrO2 milling media (7 and 10 balls, respectively) and a grinding bowl fastener, P-7 (Fritsch, Germany) under an Ar atmosphere. To prepare the crystalline 0.75Li2S-0.25P2S5, the pellets were heated at 250 °C for 5 h. The entire procedure was performed in an Ar gas–filled glove box. The solid electrolyte powder (400 mg) was placed into a 13 mm diameter die, and a load of 4 tons was applied at 25 °C for 30 s using a hydraulic press. The average thickness of the electrolyte pellets produced was 630 and 185 μm for 7525A and 7525C, respectively. The sample density was estimated from the weight and volume of the pellets, and was 1.65 and 1.63 g cm−3 for 7525A and 7525C, respectively. To measure ionic conductivity, indium-foil blocking electrodes were used. A sample pellet was placed between two indium foils with the same diameter (13 mm) and placed in a Teflon cell with two stainless steel electrodes. For the NMR measurements, a sample was broken into smaller pieces (N 1 mm3 blocks) and placed into a micro-NMR glass tube with a diameter of 5 mm; BMS-005 J, which was made especially for flame sealing (Shigemi, Tokyo, Japan), has a height of 10 mm, in which a linear PFG is guaranteed. The sample tubes were then flamesealed. 2.2. Powder X-ray diffraction Powder X-ray diffraction (XRD) was measured using an Empyrean XRD system (PANalytical, CuKα, 45 kV, 40 mA) for both the original amorphous powder and the heat-treated samples at room temperature. An Ar gas–filled sample holder was used to prevent degradation from moisture.
using the cell constant and bulk resistance. The bulk resistance was determined from the x-axis intercept value (linear regression) over the high-frequency linear region. 2.4. NMR measurements All of the NMR spectra were measured on a Tecmag Apollo spectrometer (Houston, USA) equipped with a 4.7 T wide-bore magnet using a fully tunable PFG probe (JEOL) and controlled by a JEOL console. The 7Li spectra were measured at 78.4 MHz. 7Li T1 and T2 observations were performed for the narrow central peak using the usual inversion recovery (180°-τ-90°-Acq.) and Hahn echo (90°-τ-180°-τ-Acq.) sequences, respectively. The 7Li spectral pattern observations and the 7 Li T1 and T2 measurements were performed in the temperature range 30 °C to 120 °C. 7 Li diffusion phenomena were observed at 30 °C, 50 °C, 80 °C and 120 °C using the stimulated-echo (STE) PGSE NMR pulse sequence, as shown in Fig. 1. The echo attenuation, E, is related to the experimental variables, and in homogenous space the diffusion coefficient D can be obtained by use of the Stejskal and Tanner equation [12,13]. Sðg; δ; ΔÞ ¼
E ¼ exp −γ 2 δ2 g 2 DðΔ−δ=3Þ ¼ expð−bDÞ; E0
ð1Þ
where γ is the 7Li gyromagnetic ratio (1.03977 × 108 s−1 T−1), g is the strength of the PFG with duration δ, and Δ defining the time scales of the diffusion measurement. In homogeneous systems, D is independent of g and Δ. A single-exponential diffusion plot following Eq. (1) indicates free diffusion for a single diffusion species. When the diffraction patterns were observed, the echo attenuation was plotted in the commonly named q-space, where q = γδg/2π m−1 [14]. In this study, g was set between 4.8 and 15 Tm−1. With a fixed g, δ was varied from 0.1 to 3.0 ms with τ2 = 3.4 ms and the observation time Δ was set at 10, 20, 30, 50 and 70 ms. The echo signals were averaged from 64 to 240 times, depending on the measurement conditions. 3. Results and discussion 3.1. XRD The XRD patterns of the synthesized powders of amorphous 7525A and crystalline 7525C are shown in Fig. 2. Since the 7525A was milled, the XRD pattern did not show crystalline peaks, confirming its amorphous state. In contrast, a number of well-defined peaks were observed in the 7525C sample. There were no peaks corresponding to the starting materials (Li2S and P2S5) in the 7525C sample. It is known that 7525C has three crystal phases, namely, α, β and γ phases [16]. We assigned the major component of the 7525C sample as β-Li3PS4 phase. However, extra peaks were observed around 2θ = 20° and 40°. It is certain that the 7525C has multiphases, with other (minor) crystalline and amorphous phases in addition to the major β-Li3PS4 phase. The broad linewidth also indicated a low-degree of crystallinity. In the Raman
τ2
τ1
τ2
2.3. Ionic conductivity determination The ionic conductivity was determined using the AC impedance method (electrochemical impedance spectroscopy, EIS) employing a Solartron SI 1260 impedance analyzer equipped with a Solartron 1470E cell test system controlled by a personal computer in the frequency range of 1 MHz to 0.1 Hz with a ±10 mV perturbation versus open-circuit potential. A temperature chamber, ESPEC SU241, was used to maintain the measurement temperature conditions. The EIS measurements were conducted by decreasing the temperature from 50 °C to − 10 °C in 5 °C steps. The ionic conductivity was calculated
Fig. 1. The STE echo sequence of the PGSE NMR used in this study. Two PFGs with strength g and duration δ were applied at a time interval Δ.
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broad components were 5.1 and 11.4 kHz for 7525A and 7525C, respectively. The heat treatment of the sample from 7525A to 7525C induced the 7Li linewidth to be broader. At 110 °C, clear differences were obtained in the 7Li spectral patterns between the two samples; 7525A exhibited a single line with a linewidth of 1.1 kHz, while the 7Li spectrum of 7525C was composed of two Lorentz curves with linewidths of 1.5 and 5.7 kHz. The 7Li pattern of the 7525C showed slight temperature dependence, while 7525A exhibited clear narrowing of the linewidth, and collapsed into a narrow component at 80 °C, in which the ratio of the narrow component increased significantly in the high-temperature range. The heat treatment afforded the crystalline structure (see XRD data in Fig. 2), lower ionic conductivity (Fig. 3), and a slightly broader linewidth in the 7Li resonance (Fig. 4). Since the 7Li spectral pattern of 7525C was almost unchanged at higher temperatures, the lithium structure was stabilized by the heat treatment. 3.4. T1 and T2 of the 7Li resonance
Fig. 2. XRD patterns for (a) 7525C and (b) 7525A. The asterisks indicate β-Li3PS4 peaks identified in previous work [15].
spectroscopy data, similar to our previous work, a small shoulder peak, assigned to the P2S4− anion was observed at 386 cm−1 for the 7525C 6 sample [17]. 3.2. Ionic conductivity Arrhenius plots of the ionic conductivity (σ) are shown in Fig. 3 for 7525A and 7525C. The σ values were 1.24 × 10− 4 and 5.66 × 10− 5 Scm−1 at 25 °C for 7525A and 7525C, respectively. Clearly, the amorphous sample showed a larger value of σ. The corresponding activation enegy was 39.4 and 39.3 kJ mol−1 for 7525A and 7525C, respectively, and the difference between them was small. For the amorphous sample, the ionic conductivity was reproduced well at 25 °C in different synthesized samples [17], and in the same sample, a compatible value of the activation energy was obtained in a narrow temperature range. 3.3. 7Li spectra The 7Li NMR spectra of 7525A and 7525C were observed between 20 °C and 120 °C, and spectra obtained at 30 °C and 110 °C are shown in Fig. 4, in which 7525A clearly had a smaller linewidth versus 7525C. At 30 °C, both spectra were composed of narrow and broad components and were fitted by an overlap of two Lorentz curves. The linewidths of the narrow components were 0.30 and 1.6 kHz, and those of the
Fig. 3. Arrhenius plot of the ionic conductivity of 7525A (squares) and 7525C (circles).
The T1 and T2 data are required to set the PGSE NMR measuring conditions. Arrhenius plots of the 7Li T1 and T2 data of the narrow component of 7525A and 7525C are shown in Fig. 5. The T1 values were between 0.1 and 0.6 s and the activation energy was 12.6 ± 0.2 and 8.7 ± 0.1 kJ mol−1 for 7525A and 7525C, respectively. Since the 7Li T1 is related to either one or several jumps of the migrating lithium ions in the local environment, much smaller activation energies (about one-third or less) were observed compared with the ionic conductivity, suggesting that local motion is not directly connected to the long-range ion conduction. Since the value of T2 of 7525C was shorter than that of 7525A, the longer accumulation time for 7525C was necessary in the lithium diffusion measurements. In Fig. 5(b), the temperature dependence of T2 for 7525A showed a maximum value at 60 °C in which the broader component became small and diminished above 90 °C as shown in Fig. 4(e). The T2 maximum was probably due to the change of two components in the spectrum. 3.5. Diffusion measurements using the PGSE-NMR method We observed that lithium migration was highly heterogeneous, and the diffusion phenomena observed by the PGSE-NMR method varied significantly depending on the measuring conditions, such as the observation time Δ and the PFG strength g shown in Fig. 1. Δ-dependent diffusion phenomena are known for particles diffusing in media having inner structures, such as polymer electrolytes, zeolites and membranes. In addition, lithium diffusion in the solid conductors, the Δ-dependent diffusion phenomena, are often observed as shown previously [9–11]. Lithium diffusion plots of 7525C following Eq. (1) measured at various Δ values from 10 to 70 ms are shown in Fig. 6, which were observed using a fixed g = 9.8 Tm−1 at 30 °C. As shown in Fig. 6, the dependence of the lithium diffusion on the observation time was large. When we estimated the apparent diffusion constant, Dapparent from the initial decay of the echo attenuation, for Δ = 10, 20, 30, 50 and 70 ms, the value of Dapparent of 7525A was 40, 14, 6.0, 1.4 and 0.65 × 10−12 m2s−1 and that of 7525C changed as 52, 13, 4.9, 0.75 and 0.13 × 10−12 m2s−1 at 30 °C, respectively. This variation depending on Δ was extremely large and is the order of 60 times from 70 to 10 ms. When Δ = 10 to 30 ms, the minima were observed in the plots (diffusive diffraction). It should be noted that without diffraction, the lithium echo signals were always in the in-phase mode in the real-mode plots. When diffraction was observed, the lithium echo signals passed through the out-of-phase mode and returned to the in-phase mode, probably owing to Coulombic interactions with anions. All the plots were made in the magnitude-mode echo signals without any phase information. When the value of Δ increased, the value of Dapparent decreased and the degree of the Δ-dependence became smaller, as shown at Δ = 50 and 70 ms. When the lithium ions migrated quickly in the short time period, the collision with anions
Please cite this article as: K. Hayamizu, et al., NMR studies on lithium ion migration in sulfide-based conductors, amorphous and crystalline Li3PS4, Solid State Ionics (2015), http://dx.doi.org/10.1016/j.ssi.2015.06.016
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Fig. 4. 7Li spectral patterns of (a) and (c) 7525A and (b) and (d) 7525C observed at 30 °C and 110 °C, respectively.
induced a diffractive pattern. When the lithium ions traveled for longer time periods, averaging processes reduced the Dapparent values from multiple collisions and diffractions. It is surprising that the Dapparent changed markedly over the time scale of ms order. The pathways of the lithium migration are probably strongly related to the distance of the moving lithium ions on the ms scale. The lithium diffusion of 7525A at 30 °C is approximately comparable to that of 7525C at 80 °C. When the Δ was short, the echo attenuation profiles were insensitive to temperature. For example, plots of the echo attenuation versus b for 7525A with Δ = 20 ms at g = 9.8 Tm− 1 measured at 30 °C, 80 °C and 120 °C are shown in Fig. 7. The echo attenuation profiles versus b for Δ = 20 ms were not much different at the three temperatures, except for the shape of the diffraction patterns, which were gradually distorted as the temperature increased. In addition, the position of the minima was slightly changed at 80 °C among the three plots. Only a slight temperature dependence of the echo attenuation profiles was obtained, probably owing to trivial effects of the thermal activation on the diffusive diffraction phenomena. A similar effect on the lithium ion diffusion for short Δ was observed for 7525C, as has been observed in a garnet-type solid conductor in our recent observation [11]. Temperature dependence measurements were performed and the diffusion plots at four temperatures 30 °C, 50 °C, 80 °C and 120 °C are shown for 7525C in Fig. 8. As shown in Fig. 8(a), the temperature dependence was trivial for Δ = 30 ms, and the plots almost overlapped at the four temperatures. The value of Dapparent was about 4.7 × 10− 12 m2s− 1. From Fig. 8(b), when Δ became longer as 70 ms, the diffusion plots indicated clear temperature dependence and the value of Dapparent was 0.9 and 1.7 × 10−12 m2s−1 for 80 °C and 120 °C, respectively. The initial decay was not clearly calculated from the plots at 30 °C and 50 °C, because in this temperature range, the plots were not linear and contained slower components.
It can be seen that the lithium migration at 30 ms between 30 °C and 120 °C was faster than that on 70 ms at 120 °C. This is characteristic of lithium ion migration in solid conductors. As described in our previous papers, lithium migration in sulfidebased conductors [9,10] and a garnet-type ionic conductor [11] depends on the PFG strength, g. This experimental fact is very curious, and is not observed in liquid lithium electrolytes. In general, the fast lithium diffusion is observed by small g and slowly diffusing lithium ions require a large g to be observed enough echo decay. Suitable g values must be chosen to obtain a reasonable diffusion constant (D). In the solid conductors, we noticed a faster Dapparent was observed with smaller g, and by setting a larger g, Dapparent decreased. The g-dependent effect reduced as Δ increased and, in this work, we observed g-dependent migration in 7525A and 7525C, as shown in Fig. 9. As shown in Fig. 9, a smaller g gave a larger echo decay in the diffusion plots for both 7525A and 7525C, even if the temperatures were different. The Dapparent value of 7525A at 30 °C was 7.2, 4.8, 1.9 and 1.4 × 10−12 m2s− 1 for g = 2.3, 4.8, 7.3 and 9.8 Tm−1, respectively, and decreased depending on the value of g. The value of Dapparent for 7525C was observed as 1.8 × 10−12 m2s−1 for g = 4.8 Tm−1 and with an increase in g, the echo decay decreased. The value of Dapparent = 9.0 × 10−13 m2s−1 for g = 9.8 Tm−1 and about 5.2 × 10−13 m2s−1 for g = 12.4 and 14.9 Tm−1 were observed. If all the lithium ions migrate homogeneously at the same speed, then a g-dependent behavior would not be observed. The lithium ions in 7525A and 7525C migrate at various speeds, and the slower lithium ions can be detected using a larger g. For longer Δ, the system approaches homogeneous diffusion and the value Dapparent tends to approach a small finite value. In our experience, g values above 15 Tm− 1 did not produce linear plots in Eq. (1) for sulfide-based conductors. In addition, the adequate echo decay observed in liquid electrolytes (examples of which are given in our
Please cite this article as: K. Hayamizu, et al., NMR studies on lithium ion migration in sulfide-based conductors, amorphous and crystalline Li3PS4, Solid State Ionics (2015), http://dx.doi.org/10.1016/j.ssi.2015.06.016
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Fig. 7. Plot of the echo attenuation of 7525A versus b for g = 9.8 Tm−1 and Δ = 20 ms at three temperatures: 30 °C (downward-triangles), 80 °C (upward-triangles) and 120 °C (circles).
3.6. Comparison of crystalline 7525C and amorphous 7525A
Fig. 5. Arrhenius plots of (a) 7Li T1 and (b) 7Li T2 of the narrow component in 7525A (up-triangles) and 7525C (down-triangles).
previous paper [10]) cannot be obtained for longer Δ. The Dapparent value may tend to a constant value, but such experiments have not yet been achieved for sulfide-based conductors because of the short 7Li T2 and T1. The experimental limitation on Δ is induced by the short relaxation times. A larger g did not give linear diffusion plots with enough decay, which are observed in usual liquid electrolytes. Therefore, it was difficult to obtain reliable values of the very slow diffusion coefficient as a unique value in our samples.
To compare the lithium migration in amorphous 7525A and crystalline 7525C, it was necessary to fix the measuring conditions and the echo attenuations were plotted on the same charts. In Fig. 10, diffusion plots of 7525C and 7525A are shown at 30 °C and 120 °C. The value of g was fixed at 9.8 Tm−1 and δ was changed from 0.1 to 3 ms (20 points). The value Δ was changed between 10 and 70 ms. The echo attenuation decay was faster in 7525A than 7525C for each measuring condition, which suggests that lithium migration was faster in 7525A compared with 7525C, for the same measuring conditions. When the diffraction patterns appeared in the diffusion plots, it was convenient to plot the echo attenuation in the q-space, where q = γgδ/ 2π in units of m−1 [14]. From the analogy of restricted diffusion for a particle confined in a sphere, the inverse of q at the first diffraction minimum was defined as Rdiffraction. The simultaneous display of echo attenuations in 7525C and 7525A in the q-space plots are shown for Δ = 10, 20 and 30 ms at 30 °C in Fig. 11. The value of the Rdiffraction is denoted in Fig. 11. For Δ N 40 ms, no collision and no diffraction pattern was observed. Sample 7525A showed higher values of Rdiffraction compared with 7525C. The value of Rdiffraction increased when Δ decreased. Also,
Fig. 6. Lithium diffusion plots of (a) 7525A (δ was changed from 0.1 to 4 ms) and (b) 7525C (δ was changed from 0.1 to 3 ms) at 30 °C. For a fixed g = 9.8 Tm−1, Δ was varied from 10 to 70 ms.
Please cite this article as: K. Hayamizu, et al., NMR studies on lithium ion migration in sulfide-based conductors, amorphous and crystalline Li3PS4, Solid State Ionics (2015), http://dx.doi.org/10.1016/j.ssi.2015.06.016
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Fig. 8. Lithium diffusion plots of 7525C at four temperatures: 30 °C (squares), 50 °C (circles), 80 °C (up-triangles) and 120 °C (down-triangles) for g = 9.8 Tm−1 and (a) Δ = 30 and (b) 70 ms.
the lithium ions exhibited clearer diffraction patterns in the amorphous sample. This suggests that the lithium ions in the amorphous sample collided and were diffracted more, and that the collision and diffraction behaviors must be related to the inner inhomogeneous structure of the lithium pathways. The crystalline sample provided slightly smoother transport routes. The collision and diffraction process of the migrating lithium ions must be related deeply structures and shapes of diffusing pathways related to grain boundaries. Precise studies are required to clarify the diffusive diffraction and grain boundaries. 3.7. Relationship between the ionic conductivity and the diffusion coefficient of 7525A Using the conductivity data, we can estimate the lithium diffusion coefficient for 7525A by assuming a value of carrier density. Sulfidebased ion electrolytes are single ion conductors without any anion
migration. Since anions do not contribute to the ionic conductivity, the Nernst–Einstein relationship can be simplified to [18], DðT Þ ¼
kT σ ðT Þ; Ne2
ð2Þ
where N is the total number of Li ions in a specific volume, e is the electron charge, and k is the Boltzmann constant. At 30 °C, the lithium diffusion coefficient (DLi) was estimated to be 2.5 × 10− 13 m2s−1 from σ = 2.4 × 10−4 Scm−1 and the sample density, if all of the lithium ions contribute to conduction. From Fig. 4, the existence of a broad component in the 7Li spectrum suggests that not all of the Li ions contribute to ion conduction. If one-third of the lithium ions contributed to the ionic conductivity, the estimated D was 7.6 × 10−13 m2s−1. The value of Dapparent (6.5 × 10− 13 m2s− 1) measured for g = 9.8 Tm− 1 and Δ = 70 ms was close to this value. At 80 °C, σ = 1.7 × 10− 3
Fig. 9. The lithium migration of (a) 7525A observed for Δ = 50 ms at 30 °C and (b) 7525C for Δ = 70 ms at 80 °C for various g values. The value of δ was changed from 0.1 to 3 ms (20 points).
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Fig. 10. Simultaneous diffusion plots of 7525C (down-triangles) and 7525A (up-triangles) at 30 °C (left-hand side) and 120 °C (right-hand side) for a fixed g = 9.8 Tm−1 and δ varying 0.1 to 3 ms.
Scm−1, and the estimated value was DLi = 1.97 × 10−12 m2s−1 (100% Li+ migration) and 5.9 × 10−12 m2s−1 (33%). The observed Dapparent afforded two values 1.6 and 3.4 × 10−12 m2s− 1 for g = 9.8 Tm− 1 at Δ = 70 ms. The ion conductivity measurements provided a unique value at each temperature, despite the scattered values of Dapparent from the NMR diffusion measurements. However, these empirical results indicate that the value of Dapparent obtained in the NMR measurements is in the reasonable range and is not an unrealistic value.
4. Conclusion
Fig. 11. q-Space plots of the echo attenuation for 7525C (down-triangles) and 7525A (up-triangles) for g = 9.8 Tm−1 at 30 °C for Δ = (a) 10, (b) 20, and (c) 30 ms.
The 7Li NMR spectra of 7525A and 7525C are composed of narrow and broad components. The migrating lithium ions enter into the narrow component, whose ratio is related to the number of charge carriers. The ratio of the narrow component was insensitive to temperature in 7525C, and changed slightly from 0.30 to 0.35 on increasing temperature from 30 °C to 120 °C. This trend is different from behavior in 7525A, in which the ratio of the narrow component increased from 0.5 at 30 °C to 1.0 at 90 °C. Heat treatment stabilized some of the moving lithium ions in the conductor. From the changes in 7525A to 7525C, the ratio of the migrating lithium ions decreased, especially at higher temperatures. The lithium diffusion measured using PGSE-NMR showed very complicated behaviors in both 7525A and 7525C. It was found that the lithium ions migrate in a widely spread manner in time and space. For shorter observation time, the lithium ions moved more quickly. For Δ b 30 ms, the lithium ion migration was accompanied by collisions and diffraction, and a small thermal activation was observed. As the observation time increased, lithium diffusion became slower without any collisions and diffraction profiles in the echo attenuation. The lithium ions in 7525A collided more frequently than in 7525C. The long-range lithium pathways must be narrow and tortuous instead of wide and straight in space. At present, we cannot discuss the collision in a short time period connecting to grain boundaries. For longer observation times, the lithium migration in 7525C became slower than 7525A, which is related to the higher ionic conductivity of 7525A compared with that of 7525C.
Please cite this article as: K. Hayamizu, et al., NMR studies on lithium ion migration in sulfide-based conductors, amorphous and crystalline Li3PS4, Solid State Ionics (2015), http://dx.doi.org/10.1016/j.ssi.2015.06.016
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Please cite this article as: K. Hayamizu, et al., NMR studies on lithium ion migration in sulfide-based conductors, amorphous and crystalline Li3PS4, Solid State Ionics (2015), http://dx.doi.org/10.1016/j.ssi.2015.06.016