Role of Oxide Ions in Thermally Activated Lithium Diffusion of Li[Li1

Apr 24, 2015 - Raman spectroscopy, “big data”, and local heterogeneity of solid state synthesized lithium titanate. Dmitry V. Pelegov , Boris N. S...
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Role of Oxide Ions in Thermally Activated Lithium Diffusion of Li[Li1/3Ti5/3]O4: X‑ray Diffraction Measurements and Raman Spectroscopy Kazuhiko Mukai* and Yuichi Kato Toyota Central Research and Development Laboratories, Inc., 41-1 Yokomichi, Nagakute, Aichi 480-1192, Japan S Supporting Information *

ABSTRACT: Although Li[Li1/3Ti5/3]O4 (LTO) has been considered as an ideal electrode material for lithium-ion batteries (LIBs) because of its “zero-strain” character, initial LTO exhibits high Li conductivity (σLi) at high temperatures (T). In this paper, to clarify the inter-relation between LTO’s Li-diffusive nature and structural environment, we performed a systematic structural study on LTO using X-ray diffraction (XRD) measurements and Raman spectroscopy. The average and static information obtained by XRD measurements suggested that the bottleneck radius for Li conduction is limited to ∼0.41 even at 873 K, which is too small to explain the high σLi values in LTO. However, Raman spectroscopy demonstrated the dynamic structural changes of the LiO6 octahedron with T; the bond interaction between Li and O atoms decreases with T because of its anharmonic potential energy. Because the Raman-active modes in LTO correspond to changes in oxide ion position, oxide ions are determined to play a crucial role in obtaining high σLi values.

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INTRODUCTION The increasing demands for safer and more stable lithium-ion batteries (LIBs) require the volume changes during charging and discharging reactions (δv) in both positive and negative electrodes to be minimized. Lithium titanium oxide Li[Li1/3Ti5/3]O4 (LTO) satisfies this requirement owing to its “zero-strain” character, i.e., δv = ∼0%.1,2 Figure 1a schematically depicts the LTO unit cell, in which Li+ ions occupy both tetrahedral 8a and octahedral 16d sites, Ti4+ ions occupy only the octahedral 16d site, and O2− ions occupy only the tetrahedral 32e site in the space group of Fd3̅m. Here, Li+ and Ti4+ ions are randomly distributed in the 16d site. LTO exhibits the following electrochemical reaction (Li)8a [Li1/3Ti5/3]16d O4 + Li+ + e− ↔ (Li 2)16c [Li1/3Ti5/3]16d O4

Figure 1. Schematic of the crystal structure of Li[Li1/3Ti5/3]O4 (LTO): (a) unit cell of LTO, (b) zigzag conduction pathway of Li+ ions in the 8a → 16c → 8a direction, (c) tetrahedral bottleneck radius (rtet) of the LiO4 tetrahedron, and (d) octahedral bottleneck radii (roct1 and roct2) of the LiO6 octahedron. In the crystal lattice of LTO, Li+ ions occupy both the 8a and 16d sites, while Ti4+ ions only occupy the 16d site of the Fd3̅m space group. ltet is the length of the side of the equilateral triangles forming the surface of the LiO4 tetrahedron. loct1 and loct2 are the length of the long and narrow sides, respectively, of the isosceles triangles forming the surface of the LiO6 octahedron.

(1)

where the 16c site is initially vacant. Thus, as shown in Figure 1b, the Li+ ions travel a zigzag conduction pathway in the 8a → 16c → 8a direction. Before the discovery of the zero-strain character, an initial LTO, viz., LTO as-synthesized, was known to function as a solid electrolyte at high temperatures (T).3−13 Kanno et al.3 reported that its electrical conductivity (σele) was 5.6 × 10−4 S· cm−1 at 673 K, though all Ti ions were in an electronic insulator state with d0. Because neutron radiography indicates that the transport number of Li+ ions reaches ∼0.99 at 1173 K,4,5 the high σele values of the initial LTO are attributed to the diffusion of Li+ ions in the LTO lattice.4−13 © XXXX American Chemical Society

Received: March 5, 2015 Revised: April 21, 2015

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DOI: 10.1021/acs.jpcc.5b02179 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C Table 1. Structural Parameters at 298 K for the Li[Li1/3Ti5/3]O4 Sample and Its Γ-Point Phonon Modes atom Li1 Li2 Ti O a

Wyckoff position

site symmetry

8a 16d 16d 32e ΓIR = 4F1u, ΓRaman

occupancy g

x

y

z

Γ-point phonon modes

Bisoa

Td 1.0 0.125 0.125 0.125 0.7(2) D3d 0.166 0.5 0.5 0.5 1.1(1) D3d 0.834 0.5 0.5 0.5 1.1(1) C3v 1.0 0.263(1) 0.263(1) 0.263(1) 1.2(1) = A1g + Eg + 3F2g, Γacoustic = F1u, and Γsilent = 2A2u + 2Eu + F1g + 2F2u

F1u + F2g A2u + Eu + 2F1u + F2u A2u + Eu+ 2F1u + F2u A1g + A2u + Eg + Eu + F1g + 2F1u + 2F2g + F2u

Constraint: Biso(Li2) = Biso(Ti).

Despite extensive studies such as Raman9 and FT-IR14 spectroscopy, Li NMR measurements,10−12 and neutron diffraction (ND) measurements,15 the Li-diffusive nature of the initial LTO remains unclear. Raman spectroscopy9 and Li NMR10−12 measurements indicated a conduction pathway in the 8a → 16c → 8a direction, which is identical to that of the electrochemical reaction described by eq 1. However, the ND measurements15 suggested that the 32e site near the 16c site, rather than the 16c site, is the stable configuration for Li+ ions. Moreover, two successive phase transitions of (Li) 8a [Li 1/3 Ti 5/3 ] 16d O 4 → [Li□] 16c [Li 1/3 Ti 5/3 ] 16d O 4 → [Li4/3□2/3]16c[□1/3Ti5/3]16dO4 above 800 K were determined using Raman spectroscopy9 and Li NMR measurements,12 whereas such structural phase transitions were not observed by the ND measurements up to 973 K.15 Therefore, these inconsistencies prompted us to perform a systematic study of LTO concerning the relation between the diffusion of Li+ ions and the crystal structure at high T. An in-depth understanding of thermally activated Li diffusion in the initial LTO would provide crucial information not only for elucidating the zerostrain reaction scheme of LTO but also for developing advanced solid electrolytes for all-solid-state LIBs. The present paper focuses on the role of O2− ions in LTO because O2− ions are important for thermally activated Li diffusion (see Figures 1c and 1d). We first performed X-ray diffraction (XRD) measurements to clarify the existence/ absence of structural phase transitions at high T and then examined the T dependence of “bottleneck” radii at the 8a and 16c sites. These results offer static and average information regarding the crystal structure of LTO. Second, we performed Raman spectroscopy at a wide T range of 23−873 K to obtain dynamic and local structural information for the O2− ions. Raman spectroscopy has previously been applied to the characterization of LTO.9,16−20 For instance, recently, using ex situ Raman spectroscopy during the charge and discharge reactions, we demonstrated that the zero-strain reaction scheme is achieved by local structural changes in the LiO6 and TiO6 octahedra.20 The present Raman study focuses on lattice dynamics with respect to T, i.e., anharmonic vibrations between Li (Ti) and O atoms, which significantly affect structural stability, thermal expansion, and transport properties. Broadening of the Raman band with T was examined using a fourphonon (quartic anharmonicity) process model.21 Note that to the best of our knowledge, a comprehensive explanation for changes in the Raman spectra with T has not demonstrated for LIB materials, including LTO. As a result, we confirmed that no structural phase transitions occurred up to 873 K and thereby revealed that the bond interaction between Li and O atoms plays an important role in fast diffusion of the Li+ ions in LTO.

three O2− ions on the LiO4 surface. The radius of the gap, which is known as the bottleneck radius at the tetrahedral site (rtet), is given by rtet =

ltet − rO2 − 3

(2)

where ltet =

2 (1/4 + |Δu|)ac

(3)

Here, ltet is the length of the side of the equilateral triangle forming the LiO4 surface; rO2− is the ionic radius of the O2− ions; Δu is the difference between ideal oxygen parameter u(0.25) and actual u; and ac is the cubic lattice parameter of LTO. Because the O2− ions are coordinated with one Li+ ion at the 8a site and three Li+/Ti4+ ions at the 16d site, rO2− = 1.38 Å.22 In contrast to rtet, two different values of the bottleneck radius are observed at the octahedral 16c site: roct1 and roct2 (Figure 1d). This is because the LiO6 polyhedron is not a regular octahedron but a distorted octahedron because of the deviations of u from the ideal position (0.25). Eight panels of the octahedron contain four equilateral triangles with all sides as loct1 and four isosceles triangles with one side as loct1 and two sides as loct2. The four equilateral triangles are shared with four panels of the LiO4 tetrahedron, while the four isosceles triangles are shared with the other four panels of the LiO4 tetrahedron, in which the Li+ ions occupy the 48f site. Thus, roct1 is given by roct1 =

loct1 − rO2 − 3

(4)

where loct1 =

2 (1/4 + |Δu|)ac

(5)

As can be clearly understood by eqs 3 and 5, loct1 = ltet, resulting in roct1 = rtet. For roct2, an accurate value cannot be determined; however, the range can be defined as loct2 l − rO2 − ≤ roct2 < oct1 − rO2 − 3 3

(6)

where loct2 =

2 ac 4

(7)

When Δu = 0, roct2 is equal to rtet (roct1); however, when Δu ≠ 0, roct2 is smaller than rtet (roct1). The difference between roct2 and rtet (roct1) increases with increasing u. Thus, the proposed conduction pathway of 8a → 16c → 48f → 16d10 is less probable. Full occupation at the 16d site also disturbs Li conduction from 48f to 16d sites. Irreversible Representation. Raman spectroscopy is based on inelastic scattering of phonons. In one-phonon emission, i.e., a first-order Raman process, Raman active modes

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STRUCTURAL CONSIDERATION Bottleneck Radius. As seen in Figure 1c, the Li+ ion at the 8a site passes through a gap in an equilateral triangle forming B

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The Journal of Physical Chemistry C can be predicted by factor group analysis23 because Raman active phonons are limited to those at the center of the Brillouin zone (Γ-point). As listed in Table 1, the site symmetries of the 8a, 16d, and 32e sites are Td, D3d, and C3v, respectively. Because the 16d site is randomly occupied by both Li+ and Ti4+ ions, factor group analysis of LTO provides a total of 17 Γ-point phonon modes of Ag + 2A2u + Eg + 2E2u + Fg + 5F1u + 3F2g + 2F2u, where one F1u mode is an acoustic mode and seven A2u + 2E2u + F1g + 2F2u modes are silent modes. Considering the selection rules, the four IR active modes of 4F1u and five Raman active modes of A1g + Eg + 3F2g are provided for LTO. Note that in all Ramanactive modes Li+/Ti4+ ions at the 16d site are motionless, while only O2− ions change their positions.20 Therefore, T dependence of the Raman spectrum of LTO offers local structural changes of the O2− ions.

laser (HR320, HORIBA Jobin Yvon S. A. S.) was 514.5 nm, and the intensity of the laser beam was 100 mW.

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RESULTS AND DISCUSSION Characterization. The synthetic procedure for the present LTO sample is essentially the same as that for a recently reported LTO compound.20 However, we first briefly describe its electrochemical properties before describing the results of the XRD measurements and Raman spectroscopy. We can evaluate the composition, homogeneity, and crystallinity of the sample from its electrochemical properties, such as operating voltage and rechargeable capacity (Qrecha). Figure 2 shows the

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EXPERIMENTAL SECTION Preparation and Characterization. A polycrystalline sample of LTO was synthesized by a previously reported solid-state reaction technique.20 The reaction mixture of LiOH· H2O (Wako Pure Chemical Industries, Ltd.) and TiO2 anatase (Wako Pure Chemical Industries, Ltd.) was mixed with a mortar and pestle and pressed into a pellet with a 23 mm diameter and ∼5 mm thickness. The pellet was heated at 1023 K in air for 12 h, followed by preheating at 673 K in air for 12 h. The obtained LTO powder was characterized by XRD measurements using iron Kα radiation at room temperature (D8 ADVANCE, Bruker AXS, Inc.), as well as electrochemical charge and discharge cycle tests. Details of the electrochemical tests are described elsewhere.20 HT-XRD Measurements. High-temperature (HT)-XRD measurements were performed using copper Kα radiation (RINT-TTR, Rigaku Co. Ltd.) at a T range of 298−873 K under air flow. The T of the sample was controlled by a programmable temperature controller (PTC-30, Rigaku Co. Ltd.). Approximately 0.5 g of LTO powder was packed in a Pt holder and placed in the sample stage of the RINT-TTR diffractometer. The measurements were conducted at 298, 323, 373, 473, 573, 673, 773, and 873 K. A holding time of at least 10 min was used to stabilize the T of the sample after reaching every T setting. After all measurements were completed, we again performed an XRD measurement at 298 K to determine possible changes over the course of the HT-XRD measurements. The values of ac, u, and isotropic atomic displacement factors (Biso) were determined by Rietveld analysis with RIETAN2000 software.24 The crystal structure of LTO was illustrated with the crystallographic software, VESTA.25 Raman Spectroscopy. Raman spectroscopy was performed using a 532 nm excitation wavelength supplied by a diode-pumped solid-state (DPSS) laser (NRS-3300, Jasco Co. Ltd.) at a T range of 83−773 K. For measurements below room temperature, a cooling probe stage (LTS-E350, Linkam Scientific Instruments) equipped with liquid N2 was used. For measurements above room temperature, a heating probe stage (10016, Linkam Scientific Instruments) was used. The intensity of the laser beam was 0.1 mW, and the acquisition time for one Raman spectrum was 10−90 s. After cooling or heating measurements, we again performed a measurement at 298 K to clarify any possible changes over the course of cooling or heating. We also conducted Raman spectroscopy at 22 K using liquid He. The excitation wavelength supplied by an Ar

Figure 2. Charging and discharging curves of the Li/Li[Li1/3Ti5/3]O4 cell operated at a current density of 0.15 mA·cm−2 and 298 K.

charging and discharging curves of the Li/LTO cell operated at a voltage range of 1.0−3.0 V, a current density of 0.15 mA· cm−2, and a temperature of 298 K. The cell shows a nearly constant operating voltage, approximately 1.6 V, suggesting a topotactic two-phase reaction. The Qrecha value reaches approximately 164 mAh·g−1, which corresponds to ∼94% of the theoretical capacity (175 mAh·g−1) on the basis of eq 1. The electrochemical properties of the present LTO sample are consistent with previous results for LTO,1,2,20 suggesting that the sample has a single-phase spinel structure. XRD Measurements. Figure 3 shows the results of the Rietveld analyses for the LTO sample at (a) 298 K, (b) 573 K,

Figure 3. Results of Rietveld analyses for the Li[Li1/3Ti5/3]O4 (LTO) sample at (a) 298 K, (b) 573 K, and (c) 873 K. The diffraction line indicated by * is due to TiO2 anatase, which was used as a starting material for synthesizing LTO. The 220 diffraction line shown in the inset is evidence that Li+ ions occupy the tetrahedral 8a site. C

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remains nearly constant up to 873 K. According to previous ND measurements,15 u was reported to increase slightly from 0.26246(3) at 288 K to 0.26348(5) at 973 K. This is surprising because the accuracy of u for LTO is generally limited to three decimal places.2,7,9,26−28 Although u increases with T, its change is less than 0.4% over the wide T (∼700 K) range. This implies that macroscopically the bond interaction between Li+/Ti4+ and O2− ions does not change drastically with T. An atomic displacement parameter corresponds to deviation (σ) from an equilibrium position caused by thermal vibrations. When we assume harmonic vibration with normal (Gaussian) distribution, Biso is equal to 8π2σ2. As seen in Figure 4c, all Biso values, Biso(8a), Biso(16d), and Biso(32e), increase with T, suggesting that the σ values for Li+, Ti4+, and O2− ions increase with T. Here, we determined the Biso(16d) value using the constraint Biso(Li+) = Biso(Ti4+) because the Li+ and Ti4+ ions are randomly distributed in the 16d site. Notably, the T dependence of Biso(8a) differs from those of the other two. Both Biso(16d) and Biso(32e) increase monotonically with T, in which the slope of dBiso(16d)/dT is similar to that of dBiso(32e)/dT. Conversely, Biso(8a) remains nearly constant (∼0.6 Å2) up to 373 K and then increases linearly with further increasing T. The slope of dBiso(8a)/dT is greater than those of dBiso(16d)/dT and dBiso(32e)/dT, suggesting that Li+ ions at the 8a site are especially mobile at high T, as compared with Li+/Ti4+/O2− ions at the 16d and 32e sites. Large Biso values resulting from mobile Li+ ions were also observed in the delithiated LixCoO2 compounds with x = ∼0.5.28 Figure 5a shows the T dependence of bottleneck radii ri, where i = tet and oct1, which were calculated by eq 2 and 4,

and (c) 873 K. All XRD patterns between 298 and 873 K are shown in Figure S1 of the Supporting Information. The XRD pattern at 298 K strongly resembles the single-phase spinel structure with the Fd3m ̅ space group. The small XRD peak indicated by * is the 101 diffraction line of TiO2 anatase, which was used as a starting material. The reliability indices of the Rweighted pattern factor (Rwp) and goodness-of-fit indicator (S) were 6.78% and 1.52, respectively. Note that the 220 diffraction line, which comes from a diamond glide plane of the Fd3̅m space group, clearly appears around 2θ = 30° (see Figure 3a, inset). This confirms the presence of Li+ ions at the tetrahedral 8a site, as was seen with previous XRD measurements at room temperature.2 The XRD patterns at both 573 and 873 K are also assigned as the single-phase spinel structure with Fd3̅m space group. The 220 diffraction line is observed around 2θ = 30° at both temperatures, as seen in the insets of Figures 3b and 3c. Hence, the two successive phase transitions (Li) 8a [Li 1/3 Ti 5/3 ] 16d O 4 → [Li□] 16c [Li 1/3 Ti 5/3 ] 16d O 4 → [Li4/3□2/3]16c[□1/3Ti5/3]16dO4, which were proposed by previous Raman spectroscopy9 and Li NMR measurements,12 do not occur in the present LTO sample. This is consistent with the results of recent ND measurements of LTO.15 Figure 4 shows the T dependence of the structural parameters (a) ac, (b) u, and (c) Biso for the LTO sample.

Figure 4. Temperature dependence of the structural parameters of the Li[Li1/3Ti5/3]O4 sample: (a) cubic lattice parameter (ac), (b) oxygen position parameter (u), and (c) isotropic atomic displacement factors of the 8a [Biso(8a)], 16d [Biso(16d)], and 32e [Biso(32e)] sites. These structural parameters were determined through Rietveld analyses. The constraint of Biso(Li+) = Biso(Ti4+) was used at the 16d site. Figure 5. Temperature dependence of (a) tetrahedral and octahedral bottleneck radii, rtet and roct1, and (b) its ratio to the ionic radius of the Li+ ion (rLi+). Two different rLi+ values were used depending on the coordination number (C. N.); rLi+ = 0.59 Å when C. N. = 4 and rLi+ = 0.76 Å when C. N. = 6.

These structural parameters at 298 and 323 K ≤ T ≤ 873 K are summarized in Table 1 and Table S1 of the Supporting Information, respectively. The ac value monotonically increases from 8.3568(1) Å at 298 K to 8.4278(1) Å at 873 K with a linear thermal expansion coefficient (αL) of 1.5 × 10−5. This αL is in agreement with the value (∼1.6 × 10−5) calculated by ND measurements at a T range of 288−973 K.15 Moreover, the present αL value is approximately two times larger than that of Li[LixMn2−x]O4 with x > 0 (∼7.0 × 10−6);26 however, it is comparable to that of LiCoO2 (∼1.1 × 10−5).27,28 As seen in Table 1 and Figure 4b, u = 0.263(1) at 298 K, suggesting that the LiO6/TiO6 octahedron is distorted from the regular octahedron because of Coulombic interactions between Li+/ Ti4+ and O2− ions. As T increases from 298 K, the u value

respectively. Both ri values monotonically increased with increasing T, specifically ri = 0.391(1) Å at 298 K and ri = 0.409(1) Å at 873 K. As shown in Figure 4b, Δu remains nearly constant with T. Thus, the increase in ri with T can be attributed to the increase in ac, i.e., the thermal expansion of LTO (see eqs 3 and 5). We discarded the roct2 values from Figure 5a because as described in Section 2 the conduction pathway of 16c → 48f → 16d is unavailable unless we assume vacancies at the 16d site. If we calculate the minimum roct2 D

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and F2g modes, respectively.20 Additionally, the A1g, Eg, and F2g modes correspond to a symmetric stretching vibration (νsym) between Ti and O atoms, an asymmetric stretching vibration (νasym) between Li and O atoms, and a bending vibration (δ) between Ti and O atoms, respectively, according to a previous Raman study of LTO.20 Three Raman bands at 513, 403, and 143 cm−1 are due to TiO2 anatase, which was also seen as an impurity in the XRD patterns of LTO (Figure 3). Origins of the last three Raman bands at 747, 345, and 273 cm−1 are currently unclear. However, these Raman bands can be explained by introducing a difference in bond length between Li−O and Ti− O atoms. The Raman bands at 747, 345, and 273 cm−1 are consequently assigned as νsym between Li and O atoms, νasym between Ti and O atoms, and δ between Li and O atoms, respectively. The number of Raman bands is associated with the crystal symmetry of the material.23 A new Raman band or splitting of degenerate vibration modes should be observed when the crystal symmetry transforms into a lower direction. As shown in Figure 6b−f, the number of Raman bands does not change upon decreasing T. Also, the Raman spectrum at 22 K, which is shown in Figure S2 of the Supporting Information, is similar to that at 298 K. Hence, the spinel structure with the Fd3̅m space group is maintained down to 22 K. As shown by the red guide lines in Figures 6a−f, the T dependencies of the A1g, Eg, and F2g modes differ. The frequencies of the A1g (672 cm−1) and F2g (232 cm−1) modes remain nearly constant down to 83 K, whereas the frequency of the Eg mode (429 cm−1) increases with decreasing T. This indicates that the local structure around the TiO6 octahedron does not change with T but that around the LiO6 octahedron changes drastically with T. This differs from the results of the XRD measurements because as evidenced by the T dependence of u no obvious change was seen in the structural environment of the LiO 6 /TiO 6 octahedron. Figure 7 shows the T dependence of Raman spectra for LTO at (a) 773 K, (b) 753 K, (c) 713 K, (d) 673 K, (e) 633 K, (f) 593 K, (g) 553 K, (h) 513 K, (i) 373 K, and (k) 298 K. The measurements were performed with heating. As in the case for

values using eq 6, roct2 = 0.306(1) Å at 298 K and roct2 = 0.320(1) Å at 873 K. The previous structural study of LTO indicated that the ratio of ri to the ionic radius of the Li+ ion (rLi+), ri/rLi+, corresponds to the activation energy (Ea) for Li diffusion.6 When ri/rLi+ approaches 1, Ea becomes smaller; however, when ri/rLi+ is much less than 1, Ea becomes larger. This implies that ri/rLi+ can be regarded as an indicator for evaluating the mobility of Li+ ions. Figure 5b shows the T dependence of ri/rLi+, where i = tet and oct1. Because the ionic radius generally depends on coordination number (C. N.), we calculated ri/rLi+ using two different values; i.e., rLi+ = 0.59 Å when C. N. = 4 and rLi+ = 0.76 Å when C. N. = 6.22 Thus, roct1/rLi+ at 298 K is 0.515(1), which is ∼77% of rtet/rLi+. This suggests that the Ea for the 16c → 8a pathway is greater than that for the 8a → 16c pathway. As T increases from 298 K, both rtet/rLi+ and roct1/rLi+ monotonically increase. However, rtet/rLi+ is limited to 0.693(1) even at the highest T (873 K), where the conductivity of the Li+ ions (σLi) in LTO reaches 10−2−10−3 S·cm−1.6,8,9,13 This is surprising because solid electrolytes with high σLi typically have large ri/ r L i + values; e.g., that of a series of perovskite Li3xLa2/3‑x□1/3−2xTiO3 (LLTO) compounds was ∼1.4.29 As described above, the present XRD measurements of LTO confirmed that Li+ ions occupy the tetrahedral 8a site up to 873 K, although previous Raman9 and NMR12 studies indicated migration to the octahedral 16c site. Furthermore, the ri/rLi+ values are too small to explain the high σLi values in LTO. Because XRD measurements provide static and average information, we now proceed to dynamic and local structural viewpoints of LTO, which are obtained by Raman spectroscopy. Raman Spectra. Figure 6 shows the T dependence of Raman spectra for LTO at (a) 298 K, (b) 273 K, (c) 223 K, (d)

Figure 6. Temperature (T) dependence of the Raman spectra of the Li[Li1/3Ti5/3]O4 sample at (a) 298 K, (b) 273 K, (c) 223 K, (d) 173 K, (e) 123 K, and (f) 83 K. The measurements were performed with cooling. Three dashed red lines at 672, 429, and 232 cm−1 are used as guides to highlight the frequency shifts with decreasing T. The solid blue line is the Raman spectrum at 298 K following the cooling measurements. Figure 7. Temperature dependence of the Raman spectra of the Li[Li1/3Ti5/3]O4 sample at (a) 773 K, (b) 753 K, (c) 713 K, (d) 673 K, (e) 633 K, (f) 593 K, (g) 553 K, (h) 513 K, (i) 473 K, (j) 373 K, and (k) 298 K. The measurements were performed with heating. Three red lines are used as guides to highlight the frequency shifts with increasing T. The solid blue line is the Raman spectrum at 298 K following the heating measurements.

173 K, (e) 123 K, and (f) 83 K. The five Raman bands of A1g + Eg + 3F2g are predicted by factor group analysis of LTO.23 However, at least nine Raman bands at 747, 672, 513, 429, 403, 345, 273, 232, and 143 cm−1 are seen at 298 K. Three of these Raman bands, 672, 429, and 232 cm−1, are assigned as A1g, Eg, E

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A decrease in frequency with T is generally understood by a decrease in the force constant (k) due to thermal expansion. Here, k is represented by

Raman spectra at low T, the number of Raman bands does not change upon increasing T, suggesting no structural phase transition takes place up to 773 K. Each Raman band appears to broaden with increasing T. Note that the background of the Raman spectrum increases, particularly above 700 K, because of blackbody radiation of the sample. Also, because of a difference in signals of the blackbody radiation between LTO and TiO2 anatase, the intensity of the Raman band at ∼140 cm−1 increases with increasing T. The frequencies of the A1g (672 cm−1) and F2g(232 cm−1) modes show no obvious change with increasing T. Conversely, the frequency of the Eg (429 cm−1) mode decreases with increasing T, suggesting a local structural change around the LiO6 octahedron. Force Constant and Anharmonic Vibration. The Raman spectrum of LTO indicated several changes with respect to T regarding the frequency and width of the Raman bands. Through measurement at 298 K following cooling or heating measurements, we confirmed that such changes are reversible (see the Raman spectra indicated by the solid blue lines in Figures 6 and 7). To examine these changes, the Raman spectrum of LTO was fitted with nine components by a Voigt function, i.e., a convolution with Gaussian and Lorentzian functions. The fitting result at 298 K is shown in Figure S3 in the Supporting Information as an example. Figure 8 shows the T dependence of frequencies of the (a) A1g, (b) Eg, and (c) F2g modes, which correspond to the νsym

k = (2πcν)2 μ

(8)

where c is the speed of light, ν the frequency, and μ the reduced mass between Li (or Ti) and O atoms. Figure 9 shows the T

Figure 9. Temperature dependence of the force constant (k) for the A1g, Eg, and F2g modes, which correspond to the νsym between Ti and O atoms, νasym between Li and O atoms, and δ between Ti and O atoms, respectively. The squares represent the k values calculated using eq 9.

dependence of the A1g, Eg, and F2g modes, which correspond to the νsym between Ti and O atoms, νasym between Li and O atoms, and δ between Ti and O atoms, respectively. For the A1g mode, k remains nearly constant [∼3.2(1) mdyn·Å−1] up to 773 K. This value is slightly larger than that (2.6 mdyn·Å−1) of the A1g mode in TiO2 rutile, which is also assigned as νsym between Ti and O atoms.30 The T dependence of the F2g mode is similar to that of the A1g mode. For the Eg mode, k decreases from 0.56(1) mdyn·Å−1 at 83 K to 0.46(1) mdyn·Å−1 at 673 K, indicating that the bond interaction between Li and O atoms weakens with increasing T. The k value of the Li−O bond for Li-containing compounds is empirically given by31 Figure 8. Temperature dependence of frequencies of the (a) A1g, (b) Eg, and (c) F2g modes, which correspond to the νsym between Ti and O atoms, νasym between Li and O atoms, and δ between Ti and O atoms, respectively.

k(dLi − O) = k 0 exp( −dLi − O/ρ)

(9)

where dLi−O is the bond length between Li and O atoms and k0 (950 mdyn·Å−1) and ρ (0.265 Å) are the constant values for Licontaining compounds.31 According to the Rietveld analyses of LTO, the dLi−O value decreases from 1.989(1) Å at 298 K to 2.004(1) Å at 873 K. These dLi−O values provide a linear decrease in k with T; k = 0.52(1) mdyn·Å−1 at 298 K and k = 0.49(1) mdyn·Å−1 at 873 K. As seen in Figure 9, the calculated k values are almost consistent with the experimental k values, although differences are observed, especially above 450 K. Anharmonic vibrations of crystal lead to spontaneous decay of an optical phonon into two or three acoustical phonons. The relaxation time of such a decay determines the line width in Raman scattering, IR spectroscopy, and neutron scattering.21,32 We employed a four-phonon decay model, i.e., the model of one optical phonon into three acoustical phonons, because such a model can explain the increase in line width of silicon, especially above 300 K.21 Thus, the T dependence of full width at half-maximum (fwhm, Γ) is expressed by21

between Ti and O atoms, νasym between Li and O atoms, and δ between Ti and O atoms, respectively. The frequency of the A1g mode decreases slightly from 674(1) cm−1 at 83 K to 668(1) cm−1 at 773 K. Lower T dependence is also observed in the F2g mode (Figure 8c). However, the frequency of the Eg mode decreases drastically from 441(1) cm−1 at 83 K to 409(1) cm−1 at 633 K and then levels off to a constant value (∼410 cm−1) with further increasing T (Figure 8b). We obtained similar T dependence in the Raman bands for the νsym between Li and O atoms and the νasym between Ti and O atoms (see Figure S4 in the Supporting Information). The frequency of the former significantly decreases with T, while the frequency of the latter remains nearly constant. The T dependence of these frequencies confirms the local structural change around the LiO6 octahedron. F

DOI: 10.1021/acs.jpcc.5b02179 J. Phys. Chem. C XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry C ⎞ ⎛ ⎛ 2 ⎞⎟ 3 3 Γ(T ) = A⎜1 + x + B ⎜1 + y + y ⎟ 2 ⎝ e − 1⎠ e −1 (e − 1) ⎠ ⎝ + Γ0

(10)

where x=

ℏω0 2kBT

(11)

ℏω0 3kBT

(12)

and y=

Figure 11. (a) Schematic of the local structural environment of Li[Li1/3Ti5/3]O4 when the Li+ ion at the 8a (or 16c) site migrates to the 16c (or 8a) site. The decrease in bond interaction and the asymmetric stretching vibration between Li and O atoms facilitate the migration. One vibration is shown for the Eg mode. (b) The potential energy between Li and O atoms (U) as a function of the average distance between Li and O atoms (dLi−O). In eq 13, when the f term is dominant compared to the g term, the U curve shifts from the black line to the red line. The dLi−O value increases from d0 to d1 to d2, associated with the increase in energy level from E0 to E1 to E2.

Here, ℏ is the reduced Planck constant; ω0 is the frequency of the optical phonon; kB is the Boltzmann constant; and Γ0 is the T-independent term. In addition, A and B are the parameters at T = 0 K, which correspond to a three-phonon decay (cubic anharmonicity) process and four-phonon process, respectively. Figure 10 shows the T dependence of fwhm for the Eg mode, which is assigned as the νasym between Li and O atoms. The

forming on the LiO4 surface, the strong bond interaction between Li and O atoms disturbs the Li diffusion. However, because of the decrease in bond interaction with T, the Li+ ion easily migrates to the 16c site at high T, even though the rtet/rLi+ value is considerably low compared with that for LLTO.29 As seen in Figure 11a, the asymmetrical vibration of the Eg mode also helps with Li diffusion because it has the advantage of increasing the rtet/rLi+ value. Here, although the Eg mode is a doubly degenerate vibration mode, one vibration mode is illustrated for clarity. The same consequence is found for the other Eg mode.20 Migration of Li+ ions, i.e., local compositional inhomogeneity, produces local stress in a crystal lattice. This is known as diffusion-induced stress (DIS),34−37 which should be minimized to obtain LIBs with high rate capability and long cycle life. The decrease in bond interaction between Li and O atoms with T unambiguously changes the nature of the Li−O bond to be more flexible. Thus, the flexible Li−O bond reduces the DIS produced when Li+ ions at the 8a site migrate to the 16c site. This is consistent with our recent results for Li[LixMn2−x]O4 (LMO),37 which is isostructural to LTO. The LMO compound with x = 0.1 possesses the maximum Li-diffusion coefficient over the entire range of x due to the most flexible nature.37 The decrease in bond interaction between Li and O atoms originated from the anharmonicity of the potential energy (U). Figure 11b shows U as a function of dLi−O. Although U is generally described as a summation of repulsive and attractive interactions, such as the Lennard−Jones potential, it is approximately represented by38

Figure 10. Temperature dependence of fwhm for the Eg mode, which is assigned as the νasym between Li and O atoms. The solid line represents the fitting result using eq 10.

observed fwhm at the lowest T is 40 cm−1. As T increases, fwhm gradually increases with changing slope, reaching a constant value (∼72 cm−1) above 600 K. Upon fitting the fwhm data below 600 K with eq 10, A and B were determined to be 0.17(4) and 3.2(2) cm−1, respectively. This indicates that the four-phonon process is dominant for the local structural change in the LiO6 octahedron. The four-phonon process is also dominant in the E mode for LiNH2.33 Role of Oxide Ions in Li Diffusion. Although macroscopic XRD measurements of LTO indicated no significant structural change with T, Raman spectroscopy clarified changes of the LiO6 octahedron: (i) the bond interaction between Li and O atoms weakens with T and (ii) the anharmonic vibration between Li and O atoms is mainly explained by the fourphonon process. These local structural changes correspond to variations in the oxide ions of the LiO6 octahedron. In this section, we discuss the role of oxide ions in Li diffusion of LTO. Figure 11a shows the schematic of the local structural environment of LTO when the Li+ ion at the 8a site migrates to the 16c site. The LiO4 tetrahedron and Li/TiO6 octahedron connect with edge sharing, where the Li/Ti ions occupy the 16d site. Thus, one corner of the O2− ion in LiO4 is shared with three corners of the O2− ions of three different Li/TiO6 octahedra. This means that the local structural changes described in (i) and (ii) are closely related with those of LiO4. When the Li+ ion at the 8a site passes through the gap

U (dLi − O) = adLi2 − O − gdLi3 − O − fdLi4 − O

(13)

where a is the parameter for harmonic contribution and g and f are the parameters for anharmonic contribution, which steepens the dU/ddLi−O slope on the left side and flattens the bottom of the U curve, respectively. Note that as g increases the repulsive interaction between Li and O atoms increases, whereas as f increases, the bond interaction between Li and O atoms decreases. Thus, as seen in Figure 11b, the U curve indicated by the black line shifts to that indicated by the red line when g is greater than f. G

DOI: 10.1021/acs.jpcc.5b02179 J. Phys. Chem. C XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry C

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ACKNOWLEDGMENTS We wish to thank Dr. N. Nunotani of TCRDL for fruitful discussions on the Li-conduction pathway in LTO. K.M. was supported in part by a Grant-in-Aid for Scientific Research (C), 25410207, from the Ministry of Education, Culture, Sports, Science, and Technology, Japan.

For the Li−O bond, as T increases from 0 K, the energy level of the vibration increases from E0 to E1 to E2. Thus, the average dLi−O value increases from d0 to d1 to d2. The f term for the Li− O bond should be dominant as compared with the g term because as seen in Figure 9 kLi−O decreases with increasing T. This seems to be consistent with the fitting results of the fwhm of the Raman band; as shown by A = 0.17(4) and B = 3.2(4) cm−1, the four-phonon process is dominant as compared with the three-phonon process. The recent Raman study of LiNH2 clarified that the g and f terms correspond to the A and B terms, respectively.33 As described above, the O2− ions connected with the Li+ ions rather than the structural phase transitions play an essential role on the Li conduction in LTO. This is similar to the origin of the zero-strain character, in which the bond length between Li and O atoms decreases with Li insertion to maintain the spinel framework.20 Since the occupancy of the Li+ ions at the 16d site is 0.1666, the random distribution of the Li+ ions is also important for high σLi values in LTO.

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CONCLUSION Systematic structural analyses were performed for the initial Li[Li1/3Ti5/3]O4 (LTO), which exhibits high Li conductivity (σLi) at high temperatures. XRD measurements confirmed no significant structural change upon heating; i.e., the Li+ ions still occupy the tetrahedral 8a site up to 873 K. This is inconsistent with previous reports on LTO, where two successive phase transitions of (Li)8a[Li1/3Ti5/3]16dO4 → [Li□]16c[Li1/3Ti5/3]16dO4 → [Li4/3□2/3]16c[□1/3Ti5/3]16dO4 were proposed as the reason for high σLi values. XRD measurements also confirmed that the bottleneck radius for Li conduction is too small as compared with other Li-ion conductors. However, Raman spectroscopy, which provides dynamic and local structural information, demonstrated the obvious structural change in the LiO6 octahedron. The bond interaction between Li and O atoms decreases with increasing T because of its anharmonic potential energy. Because such dynamic and local structural changes are related to those of oxide ions, they play an essential role in determining σLi. This indicates that we must pay more attention to the anions present in materials for developing solid electrolytes with high σLi. ASSOCIATED CONTENT

S Supporting Information *

XRD patterns for the LTO sample at a T range of 298−873 K, structural parameters for a T range of 323−873 K, Raman spectrum at 22 K, fitting result of the Raman spectrum at 298 K, and T dependence of frequencies, which are assigned as the νsym between Li and O atoms, νasym between Ti and O atoms, and δ between Li and O atoms, respectively. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.5b02179.

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AUTHOR INFORMATION

Corresponding Author

*Phone: +81-561-71-7698. Fax: +81-561-63-6948. E-mail: [email protected]. Notes

The authors declare no competing financial interest. H

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