Phase relation, structure and ionic conductivity of Li_7−x−3yAl_yLa₃Zr_2−xTa_xO₁₂

Abstract

The phase relation, structure and ionic conductivity of garnet-like Li_7−x−3yAl_yLa₃Zr_2−xTa_xO₁₂ were investigated. The improved sample dissolution process in the ICP measurements enabled the exclusion of the ambiguity of the atomic composition in the samples. The tetragonal phase formed at x = 0–0.375 and the cubic phase appeared with x = 0.4–2.0 in the Li_7−xLa₃Zr_2−xTa_xO₁₂ system. In the Al-doped system of Li_7−x−3yAl_yLa₃Zr_2−xTa_xO₁₂, the tetragonal phase was formed at x + 3y < 0.4. The border between the tetragonal and the cubic phases exists at Li_6.6−z/2Al_z/2□_0.4La₃Zr_1.6+zTa_0.4−zO₁₂. The tetragonal/cubic structure change corresponds to the order/disorder of lithium ions and is dependent on the cation content at the lithium sites. The ionic conductivity of the cubic compounds has a positive tendency with respect to the lithium content, whereas that of the tetragonal compounds is opposite. A high total ionic conductivity exceeding 5.0 × 10⁻⁴ S cm⁻¹ at 25 °C was observed for Al-doped Li_6.6−z/2Al_z/2La₃Zr_1.6+zTa_0.4−zO₁₂. The highest total conductivity of 1.03 × 10⁻³ S cm⁻¹ at 25 °C with an activation energy of 0.35 eV was obtained at z = 0.275. Nuclear magnetic resonance spectroscopy revealed that Al³⁺ substitution decreases the diffusion of lithium ions in the structure. The high total conductivity of Al-doped Li_6.6−z/2Al_z/2La₃Zr_1.6+zTa_0.4−zO₁₂ may be due to the enhancement of lithium diffusion at the grain boundaries.

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Introduction

Fast lithium-ion conductors are key materials for the development of next generation energy storage devices such as all-solid-state lithium secondary batteries and rechargeable lithium–air batteries.^1–3 Many oxide lithium-ion conductors such as perovskite-type La_2/3−xLi_3xTiO₃,⁴ NASICON-type Li_1.4Ti_1.6Al_0.4(PO₄)₃,⁵ LISICON-type Li₁₄Zn(GeO₄)₄ (ref. 6) and their derivatives have been investigated; however, most of these are electrochemically unstable in contact with lithium metal. Among the fast lithium-ion conductors reported, garnet-like oxides are one of the most promising materials because of their excellent chemical and electrochemical stability with lithium metal.^2,7,8

The garnet-like Li₅La₃M₂O₁₂ (M = Nb and Ta) compounds were discovered by Hyooma and Hayashi during investigation of the La₂O₃–Li₂O–M₂O₅ ternary systems.⁹ Thangadurai and co-workers firstly reported these compounds as lithium-ion conductors.⁷ Although the ionic conductivity of these compounds was low, there have been extensive efforts to improve the ionic conductivity because Li₅La₃Ta₂O₁₂ is stable in contact with lithium metal.⁷ The ideal garnet has a general chemical formula of A₃B₂C₃O₁₂, where A, B and C are eight, six and four oxygen-coordinated cation sites, which is a cubic structure. The garnet-like compounds mentioned previously contain excess lithium ions that occupy the tetrahedral C-sites; the interstitial sites in the ideal garnet structure.^10,11 The ionic conductivity of garnet-like compounds has a strong correlation with the lithium content and generally increases with an increase of excess lithium in the structure.^12,13

Garnet-like Li₇La₃Zr₂O₁₂ (LLZ), which exhibits a high bulk conductivity above 3 × 10⁻⁴ S cm⁻¹ at 25 °C and has excellent chemical and electrochemical stability with lithium metal was reported by Murugan et al.⁸ However, it was difficult to synthesize pure LLZ due to compositional changes during the sintering process. This caused a misunderstanding of the phase relations in LLZ. Three stable phases were reported as LLZ: a high temperature (H.T.) cubic phase,^8,14 a tetragonal phase with ordered lithium arrangement,¹⁵ and a low temperature (L.T.) cubic phase.^16,17 Among these phases, only the H.T.-cubic phase exhibits high ionic conductivity. Recent studies of the phase relations in stoichiometric Li₇La₃Zr₂O₁₂ suggest that the tetragonal phase is stable at room temperature, and a reversible phase transition between the tetragonal and H.T.-cubic phases occurs at 640 °C, which corresponds to the ordering/disordering of lithium-ions.¹⁸ The high ionic conductivity cubic phase is stabilized at room temperature by doping with Al³⁺.^18–20 The stability between the cubic and tetragonal phases is dependent on the Li⁺ and Al³⁺ contents. On the other hand, it has become apparent that the L.T.-cubic phase is formed by a Li⁺/H⁺ exchange reaction with moisture in air below 400 °C.¹⁶

To achieve further improvement of the ionic conductivity, the solid solution between Li₅La₃M₂O₁₂ (M = Nb and Ta) and Li₇La₃Zr₂O₁₂ has been investigated. Ohta et al. reported the cubic phase exhibited high total conductivity of 8.0 × 10⁻⁴ S cm⁻¹ at 25 °C for Li_6.75La₃Zr_1.75Nb_0.25O₁₂,²¹ and Wang and Lai reported Li_6.7La₃Zr_1.7Ta_0.3O₁₂ with bulk conductivity of 9.6 × 10⁻⁴ S cm⁻¹ at 25 °C.²² Ishiguro et al. reported Al contamination from an Al₂O₃ crucible in the Li_7−xLa₃Zr_2−xTa_xO₁₂ system and a bulk conductivity of 6.5 × 10⁻⁴ S cm⁻¹ at 25 °C was obtained for Li_6.75La₃Zr_1.75Ta_0.25O₁₂.² Inada et al. reported that the cubic Al-free Li_7−xLa₃Zr_2−xTa_xO₁₂ system with x = 0.5 exhibited conductivity of 6.1 × 10⁻⁴ S cm⁻¹ at 25 °C.²³ These reports indicate that the substitution of Ta⁵⁺/Nb⁵⁺ in LLZ results in the highest ionic conductivities among the garnet-like compounds. However, the difficulty in the determination of the Li⁺ and Al³⁺ contents has impeded understanding of the conduction properties of these compounds.

Difficulty of the determination of the atomic compositions by inductivity coupled plasma-optical emission spectroscopy (ICP-OES) comes from the problem of dissolubility of in these compounds containing Zr⁴⁺ and Ta⁵⁺ ions. Therefore, we tried to improve the dissolution method of these compounds. In the present study, we have investigated the phase relation, structure and ionic conductivity in the Li_7−x−3yAl_yLa₃Zr_2−xTa_xO₁₂ system based on the exact atomic composition. We began by investigation of the phase relations in the pseudo-binary Li₅La₃Ta₂O₁₂–Li₇La₃Zr₂O₁₂ system, and then extended the investigation to the Al-doped system. Al-free Li_7−xLa₃Zr_2−xTa_xO₁₂ pellets were fired in a magnesia crucible to avoid contamination with Al. To prevent the formation of the L.T.-cubic phase, which is easily formed by the Li⁺/H⁺ exchange reaction with moisture in air below 400 °C, the samples obtained were annealed in an inert atmosphere prior to measurements. The structure and conduction properties of these compounds were then investigated using neutron diffraction, and AC impedance and nuclear magnetic resonance (NMR) spectroscopies. The relationship between the structure and ionic conductivity is discussed based on the results obtained.

Experimental

Polycrystalline Li_7−x−3yAl_yLa₃Zr_2−xTa_xO₁₂ (x = 0–2.0, y = 0–0.14) was synthesized by solid-state reaction. Appropriate amounts of Li₂CO₃ (Nacalai Tesque, 99%), La(OH)₃ (Aldrich, 99.9%), ZrO₂ (Tosoh), Ta₂O₅ (Rare Metallic, 99.9%), and Al₂O₃ (Alfa Aesar, 99.997%) were mixed with hexane and ball-milled. When the samples were sintered at 1200 °C, an excess 5–10 mol% of lithium was added to prevent lithium evaporation. The mixed powder was pressed into a pellet and then calcined in air at 950 °C for 5 h on a gold sheet in an Al₂O₃ crucible. The pellet was powdered by further ball-milling in hexane, pelletized by cold isostatic pressing, covered with the mother powder, and then sintered in air at 1200 °C for 8 h. Al-free Li_7−xLa₃Zr_2−xTa_xO₁₂ pellets were fired in a magnesia crucible.

To investigate the phase relations of the Al-doped Li_7−x−3yAl_yLa₃Zr_2−xTa_xO₁₂ system, the samples were synthesized in air at 950 °C for 10 h covered with the mother powder on a gold sheet in an Al₂O₃ crucible and characterized using X-ray diffraction (XRD) measurements. For AC impedance spectroscopy measurements, well-sintered pellets of Al-doped Li_7−x−3yAl_yLa₃Zr_2−xTa_xO₁₂ were prepared by sintering in air at 1200 °C for 8 h covered with the mother powder in an Al₂O₃ crucible. The sintered pellets were quenched from above 400 °C to prevent reaction with CO₂ and H₂O in the air. The pellets were annealed again in an inert atmosphere at 800 °C prior to the measurements.

Phase identification was conducted using XRD (Rigaku RINT 2500 and Bulker D8) with Cu Kα radiation. Diffraction data were collected at each 0.02° step width in the 2θ range from 10 to 80°. Neutron diffraction data were corrected using time-of-flight (TOF) diffractometers: iMATERIA (BL20)^24,25 at the Material and Life science Facility (MLF) of the Japan Proton Accelerator Research Complex (JPARC). A 6 mm diameter vanadium cell was used and samples were sealed with an indium ring under an Ar atmosphere. Structural parameters were refined using the Rietveld refinement programs Z-Rietveld²⁶ and Topas Ver. 4 (ref. 27) for neutron diffraction and XRD data, respectively. The Li, La, Zr, Ta, Mg and Al compositions were analyzed using ICP-OES (Agilent Technologies ICP-OES 710).

The ionic conductivity was measured by the AC impedance method using a frequency response analyzer (Solartron 1260) in the frequency range of 0.1 Hz to 1 MHz and in the temperature range from −20 to 100 °C in an inert gas atmosphere. A Au/Li_7−x−3yAl_yLa₃Zr_2−xTa_xO₁₂/Au symmetric cell was prepared using well-sintered pellets with relative densities of 95% in an inert atmosphere. The pellets used were annealed in an inert atmosphere prior to measurement to prevent the adsorption of CO₂ and H₂O. Lithium diffusion in the bulk was determined from pulsed-gradient spin-echo (PGSE) NMR measurements. A powder sample was prepared from a pellet in a glove box and placed in a 5 mm diameter NMR sample tube with a length of approximately 8 mm. The sample tube was flame sealed under vacuum. The samples were stable and provided reproducible data throughout the NMR measurements. ⁷Li NMR spectra were observed at 78.4 MHz using a Tecmag Apollo spectrometer (Houston, USA) equipped with a 4.7 T wide-bore superconducting magnet (SCM). A pulsed-field gradient (PFG) probe with an amplifier (50A, Jeol, Tokyo) provided good rectangular PFG shapes from 0.1 to 10 ms up to g = 22 T m⁻¹.

The temperature was increased up to 400 K. The lithium diffusion constant is dependent on the PFG strength (g) and the observation time (Δ); therefore, the measurement parameters such as Δ = 100 ms and g = 9.8 T m⁻¹ were fixed based on previous experiments.²⁸

Results and discussion

Chemical composition

The chemical compositions of the obtained samples were analyzed using ICP-OES and the results are summarized in Table 1, where the ratios are normalized with respect to the La content fixed to 3. In many reports on the garnet-like lithium ion conductors, the accuracy of the composition determined using ICP-OES has always been a problem because of difficulties in the preparation of completely dissolved solutions. A higher La content than the nominal composition has been typically reported,^2,29 which is probably due to imperfect dissolution of oxides containing Zr⁴⁺ and Ta⁵⁺ ions, even in aqua regia solution. However, the H₂SO₄ acidic solution dissolved Zr⁴⁺ and Ta⁵⁺ oxides, so that the Li⁺ content was measured as lower than that compared with other acids. This may be due to the low solubility of Li₂SO₄ in water. After many trials, analytical results with good reproducibility and reasonable La : Zr : Ta ratios were obtained when the solution was prepared by dissolving the samples in a mixed solution of H₂SO₄ and HCl at 100 °C for 12 h in an enclosed autoclave. The measured Li : La : Ta : Zr atomic ratio is in good agreement with the nominal composition of Al-free Li_7−xLa₃Zr_2−xTa_xO₁₂. No impurity elements, such as Mg and Al, were detected in the Li_7−xLa₃Zr_2−xTa_xO₁₂ samples. For the Al-doped Li_7−x−3yAl_yLa₃Zr_2−xTa_xO₁₂ samples synthesized at 950 °C on Au sheet, the cation ratio was in good agreement with the nominal composition. On the other hand, slightly higher amounts of Li⁺ and Al³⁺ than the composition expected from the nominal La : Zr : Ta ratios were observed for the samples synthesized at 1200 °C using an Al₂O₃ crucible. The small amount of Al contamination from the crucible may form the amorphous Li–Al–O phase at grain boundaries with excess lithium.^2,30 The exact atomic composition has been obtained by ICP measurement due to improvements in the sample dissolution process. The compositional dependence of the phase relation, structure and ionic conductivity will be discussed more preciously using the exact composition data.

Table 1 Molar ratio of element for Li_7−x−3yAl_yLa₃Zr_2−xTa_xO₁₂. The ratios are normalized with respect to the La content fixed to 3

Sample	Synthesis conditions	Crucible	Li	La	Zr	Ta	Al
Li7La3Zr2O12	1200 °C, 8 h	MgO	6.93	3	2.00	0.02	—
Li6.75La3Zr1.75Ta0.25O12	1200 °C, 8 h	MgO	6.73	3	1.74	0.24	—
Li6.6La3Zr1.6Ta0.4O12	1200 °C, 8 h	MgO	6.53	3	1.63	0.42	—
Li6.5La3Zr1.5Ta0.5O12	1200 °C, 8 h	MgO	6.46	3	1.53	0.53	—
Li6.25La3Zr1.25Ta0.75O12	1200 °C, 8 h	MgO	6.18	3	1.26	0.77	—
Li6La3ZrTaO12	1200 °C, 8 h	MgO	6.03	3	1.01	1.02	—
Li5La3Ta2O12	1200 °C, 8 h	MgO	5.08	3	0.00	2.00	—
Li6.58Al0.015La3Zr1.625Ta0.375O12	950 °C, 10 h	Au	6.50	3	1.62	0.38	0.00
Li6.52Al0.08La3Zr1.75Ta0.25O12	950 °C, 10 h	Au	6.47	3	1.73	0.26	0.08
Li6.45Al0.14La3Zr1.875Ta0.125O12	950 °C, 10 h	Au	6.50	3	1.87	0.17	0.14
Li6.58Al0.015La3Zr1.625Ta0.375O12	1200 °C, 8 h	Al2O3	6.45	3	1.65	0.39	0.06
Li6.52Al0.08La3Zr1.75Ta0.25O12	1200 °C, 8 h	Al2O3	6.69	3	1.74	0.24	0.10
Li6.45Al0.14La3Zr1.875Ta0.125O12	1200 °C, 8 h	Al2O3	6.86	3	1.88	0.14	0.20

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Phase relation

Fig. 1 shows XRD patterns for (a) Al-free Li_7−xLa₃Zr_2−xTa_xO₁₂ sintered in air at 1200 °C for 8 h and (b) expanded patterns in the 2θ range of 52–54°. All diffraction peaks of the sample with x = 0 could be indexed as the tetragonal garnet structure with space group I4₁/acd.¹⁵ The (642) and (624) peaks observed at 52.2° and 52.7° in the tetragonal phase shifted to higher angle and the (426) peak observed at 53.4° shifted to lower angle with increasing x. These peaks merged into a broad peak at x = 0.25.

Fig. 1 XRD patterns for (a) Al-free Li_7−xLa₃Zr_2−xTa_xO₁₂ synthesized in air at 1200 °C for 8 h and (b) expanded patterns in the 2θ range of 52–54°. Diffraction patterns for the tetragonal phase¹⁵ and the cubic phase¹⁴ are also shown.

These broadened peaks gradually became sharpened from x = 0.25 to 0.4. At x = 0.4, the peak intensity became almost twice as high as that for x = 0–0.375. The (422) and (224) peaks in the tetragonal phase merged completely into one peak. As discussed later, no difference between the a and c lattice parameters was observed. All diffraction peaks for the samples from x = 0.40 to 2.0 could be assigned to the cubic structure with the space group Ia3̄d.^8,14 No impurity phases were observed in any of the measured samples. Fig. 2 shows the change in the lattice parameters with x in Li_7−xLa₃Zr_2−xTa_xO₁₂. Linear decrease and increase of the a and c parameters, respectively, were observed from x = 0 to 0.375. The lattice parameter of the cubic phase decreased linearly from x = 0.4 to 2.0. The decrease of the tetragonality from x = 0 to 0.375 may correspond to a decrease of the electrostatic repulsion energy between adjacent lithium-ions in the structure. The linear change of the lattice parameter from x = 0.4 to 2.0 could be explained by the difference in the ionic radii of Zr⁴⁺: r(Zr⁴⁺) = 0.72 Å (6 coordination) and Ta⁵⁺: r(Ta⁵⁺) = 0.64 Å (6 coordination). The linear change of the lattice parameters is in good agreement with the systematic compositional change Li_7−xLa₃Zr_2−xTa_xO₁₂.

Fig. 2 Lattice parameters as a function of x in Li_7−xLa₃Zr_2−xTa_xO₁₂.

Ishiguro et al. suggested the composition of Li_7−xLa₃Zr_2−xTa_xO₁₂ was changed by Al³⁺ contamination from the Al₂O₃ crucible during high temperature sintering.² To confirm the effect of Al³⁺ contamination on the structure, the phase relation was investigated by controlling the Li⁺ and Al³⁺ contents in the composition range of 0 ≤ x ≤ 0.4 and 0 ≤ y ≤ 0.14 in Li_7−x−3yAl_yLa₃Zr_2−xTa_xO₁₂. Fig. 3 shows XRD patterns for the solid solution between x = 0.4 in Li_7−xLa₃Zr_2−xTa_xO₁₂ (i.e. Li_6.6La₃Zr_1.6Ta_0.4O₁₂) and y = 0.2 in Li_7−3yAl_y□_2yLa₃Zr₂O₁₂ (i.e. Li_6.4Al_0.2La₃Zr₂O₁₂) synthesized on Au sheet at 1200 °C for 8 h, which is rewritten as Li_6.6−z/2Al_z/2□_0.4La₃Zr_1.6+zTa_0.4−zO₁₂ (x = 0.4 − z, y = z/2 in Li_7−x−3yAl_yLa₃Zr_2−xTa_xO₁₂) to focus on the lithium vacancy concentration. All diffraction peaks of z = 0–0.275 in Li_6.6−z/2Al_z/2□_0.4La₃Zr_1.6+zTa_0.4−zO₁₂ could be indexed as the cubic structure with the space group Ia3̄d.^8,14 No impurity phases were observed.

Fig. 3 XRD patterns for Li_6.6−z/2Al_z/2La₃Zr_1.6+zTa_0.4−zO₁₂ synthesized at 1200 °C for 8 h.

Fig. 4 shows the phases that appeared in the Li_7−x−3yAl_yLa₃Zr_2−xTa_xO₁₂ system at room temperature. The tetragonal and cubic phases are plotted as solid triangles and circles, respectively. The data for Li_7−3yAl_y□_2yLa₃Zr₂O₁₂ (x = 0 in Li_7−x−3z/2Al_z/2□_x+zLa₃Zr_2−xTa_xO₁₂) was taken from previous reports.^19,20 The chemical formula of Li_7−3yAl_y□_2yLa₃Zr₂O₁₂ is also represented as Li_7−3y′/2Al_y′/2□_y′La₃Zr₂O₁₂ (y′ = 2y in Li_7−3yAl_y□_2yLa₃Zr₂O₁₂). The tetragonal phase appears in the range 0 ≤ y′ < 0.4 and the cubic phase becomes stable at y′ > 0.4 in Li_7−3y′/2Al_y′/2□_y′La₃Zr₂O₁₂.^19,20 The stable phase changed from the tetragonal phase to the cubic phase at x = 0.4 in the Al³⁺-free system of Li_7−x□_xLa₃Zr_2−xTa_xO₁₂. For the Al³⁺ and Ta⁵⁺ doped Li₇La₃Zr₂O₁₂ system, the cubic phase stabilized in the composition range of Li_6.6−z/2Al_z/2La₃Zr_1.6+zTa_0.4−zO₁₂ (z = 0–0.275). These results suggest that the stable phase between the tetragonal/cubic phases is dependent on the cation contents at the lithium sites in the garnet-like structure.

Fig. 4 Phase relations of Li_7−x−3yAl_yLa₃Zr_2−xTa_xO₁₂ at room temperature. The data for Li_7−3y′/2Al_y′/2□_y′La₃Zr₂O₁₂ was taken from previous reports.^19,20 The tetragonal and cubic phases are plotted as solid triangles and circles, respectively.

Crystal structure

The structure of Li_7−x−3yAl_yLa₃Zr_2−xTa_xO₁₂ was determined by neutron diffraction. The powder neutron diffraction data for Li₇La₃Zr₂O₁₂ (x = y = 0 in Li_7−x−3yAl_yLa₃Zr_2−xTa_xO₁₂) was refined using a structure model with the space group I4₁/acd.^15,25 The data for Li_6.6La₃Zr_1.6Ta_0.4O₁₂ (x = 0.4 in Li_7−xLa₃Zr_2−xTa_xO₁₂) and Li_6.52Al_0.08La₃Zr_1.75Ta_0.25O₁₂ (z = 0.15 in Li_6.6−z/2Al_z/2La₃Zr_1.6+zTa_0.4−zO₁₂) were refined based on a garnet-like structure with the space group Ia3̄d.^10,11,15 For the two samples with the cubic space group, no change of the occupancy values was observed for Zr⁴⁺ and Ta⁵⁺ at 16a (0, 0, 0) sites. Therefore, these values were fixed to the nominal composition during the refinement. For Li_6.52Al_0.08La₃Zr_1.75Ta_0.25O₁₂, the distribution of Al³⁺ was considered during the refinement procedure based on the following structural models: (1) occupation at the tetrahedral 24d (3/8, 0, 1/4) site, (2) occupation at the octahedral 96h (x, y, z) site, and (3) both occupation at 24d and 96h sites. Only the first model satisfies the charge neutrality; therefore, the refinement was continued using structure model (1). Fig. 5 shows the final refined pattern for Li_6.52Al_0.08La₃Zr_1.75Ta_0.25O₁₂ as representative data. The atomic coordinates are listed in Table 2. Rietveld analysis results for x = 0 and x = 0.4 in Li_7−xLa₃Zr_2−xTa_xO₁₂ are shown in Fig. S2 and S3,† respectively, and the refined structural parameters are summarized in Tables S1 and S2.† For Li₇La₃Zr₂O₁₂, the profile fittings provided good agreement factors of R_wp = 6.69%, R_p = 5.28%, R_B = 4.16%, R_F = 4.00%, and χ² = 5.16. For Li_6.6La₃Zr_1.6Ta_0.4O₁₂, the profile fitting provided good agreement factors of R_wp = 8.92%, R_p = 7.90%, R_B = 3.52%, R_F = 3.39%, and χ² = 3.82. For Li_6.52Al_0.08La₃Zr_1.75Ta_0.25O₁₂, the profile fitting also provided good agreement factors of R_wp = 7.46%, R_p = 6.97%, R_B = 3.86%, R_F = 5.78%, and χ² = 1.95.

Fig. 5 Observed, calculated and difference plots for the Rietveld analysis of Li_6.52Al_0.08La₃Zr_1.75Ta_0.25O₁₂.

Table 2 Atomic coordinates of Li_6.52Al_0.08La₃Zr_1.75Ta_0.25O₁₂^a

Atom	Site	g	x	y	z	B/Å^2
a Space group: Ia3̄d (230) a = 12.94962(8) Å, Rwp = 7.46%, Rp = 6.97%, RB = 3.86%, RF = 5.78%, χ^2 = 1.95.
Li(1)	24d	0.353(2)	3/8	0	1/4	2.68(9)
Al	24d	0.025(14)	3/8	0	1/4	=B(Li(1))
Li(2)	96h	0.449(4)	0.0966(2)	0.6879(2)	0.5780(2)	1.87(7)
La	24c	1	1/8	0	1/4	0.569(6)
Zr	16a	0.875	0	0	0	0.451(6)
Ta	16a	0.125	0	0	0	=B(Zr)
O	96h	1	0.9685(2)	0.6879(2)	0.5781(2)	0.879(6)

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The coordinates and lattice parameters of Li₇La₃Zr₂O₁₂ are in good agreement with the previous reports.^15,31 Fig. 6(a) shows the lithium sites configuration of the tetragonal Li₇La₃Zr₂O₁₂. Lithium ions fully occupy a tetrahedral 8a, octahedral 16f and 32g sites, and a tetrahedral 16e site is empty. Fig. 6(b) and (c) show the local structure of octahedral 16f site and that of octahedral 32g, respectively. The octahedral 32g site is connected by face sharing with tetrahedral 16e and tetrahedral 8a sites, whereas the octahedral 16f site is connected with two empty 16e sites. The repulsion from the short distance between lithium ions results in the formation of an ordered arrangement. The position of lithium ion at 32g site shifts to the empty tetrahedral site to relieve the electrostatic repulsion energy with the lithium ion at the adjacent tetrahedral 8a site. As a result, the Li(3)O₆ octahedron distorts from an ideal octahedron. The ordering of polyhedra with different sizes may distort the structure to the tetragonal symmetry.

Fig. 6 The lithium configuration in the garnet-like structure. (a) Lithium distribution in the tetragonal Li₇La₃Zr₂O₁₂. Li1 (8a), Li2 (16f) and Li3 (32g) sites are colored in light yellow, green and light blue respectively. (b) Local structure of octahedral 16f (green) site, and adjacent 16e (sky blue) sites in the tetragonal Li₇La₃Zr₂O₁₂. (c) Local structure of octahedral 32g (light blue) site, and adjacent tetrahedral 8a (light yellow) and 16e (sky blue) sites in the tetragonal Li₇La₃Zr₂O₁₂. (d) Lithium distribution in the cubic Li_6.6La₃Zr_1.6Ta_0.4O₁₂. Li1 (24d) and Li2 (96h) sites are colored in light yellow and light blue respectively.

Fig. 6(d) shows the lithium sites configuration in the cubic Li_6.6La₃Zr_1.6Ta_0.4O₁₂. For Li_6.6La₃Zr_1.6Ta_0.4O₁₂, lithium ions partially occupy the tetrahedral 24d and distorted octahedral 96h sites. The occupancy values of lithium ions at 24d and 96h sites are 0.367 and 0.456, respectively. The composition calculated from the refinement results is in good agreement with the nominal composition. The 24d tetrahedra and 96h octahedra are connected with each other by face sharing. These sites form a three-dimensional conduction pathway in the structure. The Li⁺–Li⁺ distance between these respective sites are 1.604 and 2.372 Å, where only the latter is acceptable for the simultaneous occupation of lithium ions. The short distance between the adjacent lithium ions means that the lithium ion at the interstitial octahedra requires at least one vacant tetrahedral site adjacent to maintain the distance between them. The introduction of lithium vacancies to Li₇La₃Zr₂O₁₂ changes the lithium distribution from the ordered arrangement to a disordered arrangement. The occupancy value of lithium ion at the tetrahedral sites increases from 1/3 to 0.367 and the occupancy value at the octahedral sites decreases from 1 to 0.91.

For Li_6.52Al_0.08La₃Zr_1.75Ta_0.25O₁₂, the occupancy values of lithium ions at 24d and 96h sites are 0.370 and 0.448, respectively, and that of Al³⁺ at 24d sites is 0.029. The composition calculated from the refinement results is in good agreement with the nominal composition. The small increase in the occupancy value of cations at the tetrahedral site and the small decrease of the occupancy value at the octahedral site are explained using a comparison with those of Li_6.6La₃Zr_1.6Ta_0.4O₁₂, as follows. The substitution of a trivalent cation to the tetrahedral lithium site may require the existence of vacancies at adjacent octahedra to maintain the charge neutrality in the local environment. As a result, a lithium ion is pushed off to the tetrahedral site and the occupancy value at the octahedral site may decrease slightly. The Li⁺–Li⁺ distance between adjacent tetrahedral/octahedral sites are 1.607 and 2.373 Å, respectively. These values are slightly longer than those for Li_6.6La₃Zr_1.6Ta_0.4O₁₂, which reflects the larger lattice size of Li_6.52Al_0.08La₃Zr_1.75Ta_0.25O₁₂. No significant difference was observed between the Li_6.6La₃Zr_1.6Ta_0.4O₁₂ and Li_6.52Al_0.08La₃Zr_1.75Ta_0.25O₁₂ structures. The structure of garnet-like compounds is thus mainly determined by the cation content at the lithium sites.

The variation of the lithium distribution with the cation content at lithium sites is in good agreement with the previous reports.^12,13 The tetrahedral sites are fully occupied by lithium ions and the interstitial octahedral sites are empty in Li₃Nd₃Te₂O₁₂ with the general formula of garnet compounds.³² Therefore, the introduction of excess lithium ion causes occupation at the interstitial octahedral sites. Lithium ions at interstitial octahedra require at least one vacant tetrahedron adjacent to maintain the distance from the nearest lithium ion. As a result, the content of lithium ions in the garnet-like structure decreases linearly at the tetrahedral sites and increases at octahedral sites.^12,13,31

Although it was difficult to determine which octahedral site, 48g or 96h, in the cubic structure is occupied by the lithium ions, the short distance between the tetrahedral and the octahedral lithium sites suggests that occupation is more likely at the 48g octahedral site, of which the position is at the center of the octahedron and is permitted when both adjacent tetrahedral sites are empty. If simultaneous occupation at the adjacent tetrahedral 24d and 48g sites is possible, then the simultaneous occupation of three adjacent 24d–48g–24d sites is permitted. However, in such a case, lithium ions at the tetrahedral sites are not required to decrease with the increase of the lithium content in the garnet-like structure. For Li₇La₃Zr₂O₁₂, lithium ions form an ordered arrangement with vacancies rather than simultaneous occupation of an adjacent octahedron and two tetrahedra. The octahedral 32g site is connected by face sharing with tetrahedral 16e and tetrahedral 8a sites. The octahedral 16f site is connected with two empty 16e sites. The lithium ion at the 32g site shifts to the empty tetrahedral site. These observations suggest that occupation at the center of the octahedral sites is difficult when lithium ions are present at the adjacent tetrahedral sites.

The increase in the tetragonality for lithium contents of x < 0.4 indicates that the introduction of excess lithium ions enhances the ordering of lithium ions to maintain the distance between adjacent lithium ions. The short distance between adjacent lithium sites causes a large electrostatic repulsion energy between lithium ions that predominantly determines the structure of the garnet-like compounds.

Ionic conductivity

Fig. 7 shows typical impedance plots for (a) Li_7−xLa₃Zr_2−xTa_xO₁₂ at 25 °C and (b) Li_6.45Al_0.14La₃Zr_1.875Ta_0.125O₁₂ at various temperatures. The impedance plot for each x = 0.5 and 0.75 were composed of a part semicircle, a small semicircle, and a spike in the low-frequency range, which correspond to the bulk, grain boundary, and electrode contribution, respectively. In contrast, only part of a semicircle was observed for the samples with x = 0.4 in the high frequency range and a spike in the low-frequency range. The bulk and grain boundary contributions could not be separated clearly from the impedance data. The sum of the bulk and grain boundary resistivity was obtained from the intercepts of the semicircle with the real axis. For Li_6.45Al_0.14La₃Zr_1.875Ta_0.125O₁₂, a partial semicircle was observed in the high-frequency range with a spike in the low-frequency range, which is due to the electrode contribution. The small resistivity of the grain boundary meant that the bulk and grain boundary contributions could not be separated clearly.

Fig. 7 Typical impedance plots for (a) Li_7−xLa₃Zr_2−xTa_xO₁₂ at 25 °C and (b) Li_6.45Al_0.14La₃Zr_1.875Ta_0.125O₁₂ at various temperatures.

The semicircle is attributed to the sum of the bulk and grain boundary components and the total resistivity was obtained from the intercepts of the semicircle with the real axis. The ICP measurement for this system showed higher Li⁺ and Al³⁺ contents than the nominal composition, which suggests the residual lithium reacted with contaminated Al³⁺ to form amorphous Li–Al–O phase at the grain boundaries, which would decrease the grain boundary resistance of the samples containing Al³⁺.³⁰ The total resistance decreased with increasing temperature.

Fig. 8 shows the temperature dependence of the total conductivity for (a) Li_7−xLa₃Zr_2−xTa_xO₁₂ and (b) Li_6.6−z/2Al_z/2La₃Zr_1.6+zTa_0.4−zO₁₂. All measured samples showed a linear increase of conductivity against the temperature. The activation energy was calculated from the slope in the temperature range of −20 to 100 °C. The ionic conductivity at 25 °C, the activation energy and the density of the measured pellets are summarized in Table 3. Fig. 9 shows the variation of the ionic conductivity at 25 °C and activation energy changes with the lithium vacancy concentration in Li_7−x−3yAl_y□_x+2yLa₃Zr_2−xTa_xO₁₂. The ionic conductivity of Li_7−x□_xLa₃Zr_2−xTa_xO₁₂ increased and the activation energy decreased from x = 0 to 0.4, whereas for x > 0.4, the ionic conductivity decreased and the activation energy increased with x. The sample with x = 0.4 had a conductivity of 4.7 × 10⁻⁴ S cm⁻¹ with the lowest activation energy of 0.38 eV. The ionic conductivity of Li_6.6−z/2Al_z/2La₃Zr_1.6+zTa_0.4−zO₁₂ increased from z = 0 to 0.275. The highest total conductivity of 1.03 × 10⁻³ S cm⁻¹ at 25 °C and an activation energy of 0.36 eV were observed for z = 0.275, which is comparable to the highest ionic conductivity among the garnet compounds.^2,21–23

Fig. 8 Temperature dependence of the conductivity for (a) Li_7−xLa₃Zr_2−xTa_xO₁₂ and (b) Li_6.6−z/2Al_z/2La₃Zr_1.6+zTa_0.4−zO₁₂.

Table 3 Ionic conductivity at 25 °C, the activation energy and the density of the measured pellets

Sample	Relative density (%)	σbulk/S cm^−1	σtotal/S cm^−1	Ea/eV
Li7La3Zr2O12	90.4	2.8 × 10^−7	1.4 × 10^−7	0.58
Li6.75La3Zr1.75Ta0.25O12	94.7		2.2 × 10^−5	0.43
Li6.625La3Zr1.675Ta0.375O12	94.6		1.2 × 10^−4	0.42
Li6.6La3Zr1.6Ta0.4O12	95.5		4.7 × 10^−4	0.38
Li6.5La3Zr1.5Ta0.5O12	95.5	3.2 × 10^−4	2.6 × 10^−4	0.38
Li6.25La3Zr1.25Ta0.75O12	96.2	1.9 × 10^−4	1.5 × 10^−4	0.44
Li5La3Ta2O12	96.4		3.4 × 10^−5	0.52
Li6.58Al0.02La3Zr1.625Ta0.375O12	94.6		6.6 × 10^−4	0.38
Li6.52Al0.08La3Zr1.75Ta0.25O12	93.7		7.7 × 10^−4	0.36
Li6.45Al0.14La3Zr1.875Ta0.125O12	91.3		1.03 × 10^−4	0.36

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Fig. 9 Ionic conductivity at 25 °C and activation energy changes as a function of the lithium vacancy concentration in Li_7−x−3yAl_yLa₃Zr_2−xTa_xO₁₂.

The introduction of lithium vacancies to Li₇La₃Zr₂O₁₂ increases the ionic conductivity and decreases the activation energy in the composition range of x + 2y < 0.4 where the phase of the tetragonal structure is stable. In contrast, the ionic conductivity and activation energy show the opposite tendency in the cubic phase region. The different tendency of the conductivity corresponds to the difference in the lithium arrangements between the tetragonal and cubic structures. The introduction of lithium vacancies to the tetragonal structure enhances the ionic conductivity because it relieves the electrostatic repulsion energy between adjacent lithium-ions and disarrays the ordered arrangement of the lithium ions. On the other hand, the ionic conductivity of the cubic phase shows a positive tendency with the lithium content, which is in good agreement with the conductivity observed for garnet-like compounds.^12,13 The highest ionic conductivity was obtained at x + 2y = 0.4, which is the upper limit of the Li⁺ and Al³⁺ composition where the cubic structure is formed. In Li_6.6−z/2Al_z/2La₃Zr_1.6+zTa_0.4−zO₁₂, the total ionic conductivity increased with the Al³⁺ content. However, it is not obvious whether this is simply an increase of the conductivity in the garnet structure, or enhancement by formation of highly conductive amorphous Li–Al–O compounds at the grain boundaries.

To understand the effect of the Al³⁺ substitution for the lithium diffusion in the bulk, PGSE NMR measurements were performed for Li_6.6−z/2Al_z/2La₃Zr_1.6+zTa_0.4−zO₁₂ with z = 0 and 0.150. The lithium diffusion constant is dependent on g and Δ; therefore, the measurement parameters we fixed as Δ = 100 ms and g = 9.8 T m⁻¹ based on previous experiments,²⁸ and the apparent diffusion constant (D_apparent) was determined for Li_6.6La₃Zr_1.6Ta_0.4O₁₂ and Li_6.52Al_0.08La₃Zr_1.75Ta_0.25O₁₂. Fig. 10 shows the temperature dependence of the apparent diffusion constant (D_apparent) for Li_6.6La₃Zr_1.6Ta_0.4O₁₂ and Li_6.52Al_0.08La₃Zr_1.75Ta_0.25O₁₂, where D_apparent increased with the temperature. The activation energies for these compounds were almost comparable to those obtained by electrochemical measurement. The D_apparent values for Li_6.6La₃Zr_1.6Ta_0.4O₁₂ were larger than those for Li_6.52Al_0.08La₃Zr_1.75Ta_0.25O₁₂, which indicates that the partial substitution of Al³⁺ at the lithium sites does not enhance lithium diffusion in the cubic structure. The neutron refinement results revealed a decrease in the lithium content by Al³⁺ substitution in the structure. The precise number of carrier ions cannot be determined from these experiments; therefore, the reason for the discrepancy between the conductivity and NMR data is not yet known. However, the improvement of the total ionic conductivity of Al-doped Li_6.6−z/2Al_z/2La₃Zr_1.6+zTa_0.4−zO₁₂ was due to the enhancement of lithium diffusion at the grain boundary by the formation of Li–Al–O compounds with an excess lithium source.

Fig. 10 Temperature dependence of the apparent diffusion constant (D_apparent) of Li_7−x−3yAl_yLa₃Zr_2−xTa_xO₁₂ measured at fixed d = 9.8 T m⁻¹ and Δ = 100 ms.

Conclusions

The phase relation, and the relationship between the structure and the ionic conductivity of garnet-like Li_7−x−3yAl_yLa₃Zr_2−xTa_xO₁₂ were investigated by careful control of the cation content during synthesis. The tetragonal phase was formed in the range of x = 0–0.375 for the Li_7−xLa₃Zr_2−xTa_xO₁₂ system, while the cubic phase appeared in the range of x = 0.4–2.0. In the Al-doped system of Li_7−x−3yAl_yLa₃Zr_2−xTa_xO₁₂, the tetragonal phase was formed at x + 3y < 0.4. The border between the tetragonal and cubic phases exists at Li_6.6−z/2Al_z/2□_0.4La₃Zr_1.6+zTa_0.4−zO₁₂. The stable phase, whether tetragonal or cubic, is dependent on the cation content at the lithium sites. The introduction of lithium vacancies disarrays the ordered lithium arrangement in the tetragonal structure and stabilizes the cubic structure with a disordered lithium arrangement.

The ionic conductivity of the cubic compounds had a positive tendency with the lithium content, whereas the opposite tendency was observed for the tetragonal compounds. High ionic conductivity was obtained at x + 2y = 0.4, which is the upper limit of the Li⁺ and Al³⁺ composition that forms the cubic structure. High ionic conductivity exceeding 5.0 × 10⁻⁴ S cm⁻¹ at 25 °C was observed for Al-doped Li_6.6−z/2Al_z/2La₃Zr_1.6+zTa_0.4−zO₁₂. The highest total conductivity was obtained for z = 0.275 at 1.03 × 10⁻³ S cm⁻¹ (25 °C) with an activation energy of 0.35 eV. NMR measurement revealed that Al³⁺ substitution decreases the lithium diffusion in the cubic structure. Chemical analysis of Al doped Li_7−x−3yAl_yLa₃Zr_2−xTa_xO₁₂ suggests that the Al reacts with excess lithium to form Li–Al–O compounds at the grain boundaries. Although the presence of Al³⁺ decreased the lithium diffusion in the cubic structure, lithium diffusion at the grain boundaries may be enhanced. The improvement of such fast ionic conducting oxides is expected to promote the development of next-generation energy storage devices such as all-solid-state lithium secondary batteries and rechargeable lithium–air batteries.

Acknowledgements

This work was partly supported by the Japan Science and Technology Agency (JST) under the project “Advanced Low Carbon Technology Research and Development Program, Specially Promoted Research for Innovative Next Generation Batteries (ALCA Spring)”. The neutron scattering experiment was performed at the iMATERIA (BL20) at the Material and Life science Facility (MLF) of the Japan Proton Accelerator Research Complex (JPARC). (IPTS Proposal No. 2015PM0002) The authors are greatly thankful to the iMATERIA group of Ibaraki University for experimental assistance at J-PARC.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c6ra13317g

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