Abstract
The band structures, lattice parameters, densities of states and bond characteristics of two different Li7La3Zr2O12 (LLZO) solid electrolyte materials in tetragonal and cubic phases were calculated by the first-principles method based on density functional theory (DFT). The reason why the ionic conductivity of the tetrahedral phase is lower than that of cubic phase was explained by the electronic structural characteristics based on the theoretical calculation results. Two kinds of crystalline structure LLZO materials were designed based on first principles calculation of LLZO and prepared by the high temperature solid phase method, and the properties of LLZO pellets with different sintering time were analysed. The effect of the synthesis process parameters on the properties of Li7La3Zr2O12 was explored. Results show that the average lattice size of cubic Li7La3Zr2O12 (C-LLZO) is a=b=c= 1.302 246 nm, while that of tetragonal Li7La3Zr2O12 (T-LLZO) is a=b=1.313 064 nm, c=1.266 024 nm. The C-LLZO sintered at 1000 ℃ for 12 h has a pure cubic phase and a maximum ionic conductivity of 9.8×10-5 S·cm-1 is realized at room temperature (25 ℃). The ionic conductivity of T-LLZO at room temperature (25 ℃) is 5.96×10-8 S·cm-1, which has a pure tetragonal phase structure after sintering at 800 ℃ for 6 h, basically in agreement with the calculation results.
Lithium-ion batteries have the potential to be the candidate for the next generation of batteries because of their high energy density, high working voltage, remarkable cycling performance, and lack of pollution to the environment[1]. In the past few years, lithium-ion batteries have been widely used in electric vehicles, mobile phones, laptops, medical equipment and other fields. Many explosion accidents associated with traditional liquid lithium-ion batteries have attracted attention for all-solid-state lithium-ion batteries[2]. The most prominent advantage of all-solid-state lithium-ion batteries is high safety because the electrolyte of all-solid-state batteries is replaced by solid-state electrolytes (SSEs), which can hinder the formation of lithium dendrites[3]. However, one challenge regarding solid-state electrolyte materials is their electrochemical stability with increased energy density and fast charging and discharging processes. Another SSE material challenge is the low Li ionic conductivity of solid electrolytes compared with that of the currently used organic carbonate liquid solutions. To solve these problems, different types of solid-state electrolyte (SSE) materials have become a popular research topic, including polymers, oxides and sulfide electro-lytes[4].
The ion conductivity of polymer electrolytes is lower than that of inorganic solid electrolytes at room temperature (10-5~10-6 S·cm-1), and the mechanical strength is particularly worse than that of inorganic solid electrolytes, which leads to the fact that when lithium metal is used as a negative electrode, polymer solid electrolytes have difficulty in effectively pre-venting the growth of lithium dendrites[3,4]. Sulfide solid electrolytes are unstable against lithium metal and sensitive to moisture. In the range of superionic conducting oxide electrolytes, Li1.5Al0.5Ti1.5(PO4)3 (LATP) and Li0.33La0.55TiO3 (LLTO) are unstable against lithium metal[5]. Garnet-type Li7La3Zr2O12 (LLZO) is the only candidate material that shows a unique combination of high ionic conductivity (10-4~ 10-3 S·cm-1), wide electrochemical potential window, high electrochemical stability and stability against Li metal[6]. LLZO has attracted increasing attention and has good application prospects regarding the safety problems that traditional organic electrolytes have shown over the last few years. In fact, there are two different crystalline phases, i.e., tetragonal and cubic phases. The ordering of the lithium ions in the tetragonal phase (T-LLZO) allows this phase to remain stable at room temperature, and the disorder in the lithium ions in the cubic phase (C-LLZO) causes the ionic conductivity of this phase to be two orders of magnitude higher than that of the tetragonal phase[7,8]. To obtain stable cubic phase LLZO, a long sintering time and a higher sintering temperature are required[9]. Obtaining a deep understanding of the ion diffusion mechanism and optimizing the stability of the bulk structure are major challenges of LLZO large-scale applications. First principles calculation based on density functional theory (DFT) is a good tool that can assist experimental design and material synthesis[10,11].
In this study, the crystalline structures of T-LLZO and C-LLZO were established by VASP, and the intrinsic electronic structure, energy band, bond population and bond length were calculated by first principles method. A comparative discussion can provide insight that aids understanding of the origin of the considerable difference between the ionic conductivities of the two phases. Two kinds of crystalline structure LLZO materials were designed based on first principles calculation of LLZO and prepared by the high temperature solid phase method, and the properties of LLZO pellets with different sintering time were analysed. LLZO powders were observed by X-ray diffraction (XRD) and scanning electron microscopy (SEM). The Nyquist diagram of the LLZO pellets was measured by an electrochemical workstation.
1 First Principles Calculation of LLZO
1.1 Computational methodology
Density functional theory (DFT) that uses the Perdew-Burke-Enzerhof (PBE) exchange correlation function was used throughout. All the computations were carried out within the Vienna Ab Initio Simulation Package (VASP) with cell size according to the formula Li7La3Zr2O12. The structure of LLZO was A7B3C2O12, containing a B3C2O12 framework substructure with B cations in the 8-coordination sites and C cations in the octahedral sites[12]. The electronic wave functions were represented by a plane wave basis with a cut-off energy of 430 eV.
The exchange and correlation interactions were incorpo-rated through the GGA and PBE. A Monkhorst-Pack 2×2×2 k-point mesh was used for the geometry optimization calculations, whereas a 4×4×4 k-point mesh was used for the density of state (DOS) calculations. The energy and forces were converged up to 10-5 eV and 0.3 eV/nm, respectively.
1.2 Discussion of calculation result
Fig.1a shows the basic unit cell of cubic LLZO (), in which Li atom partially occupies the 24d and 48g sites[13] with cell dimensions of a=1.298 27 nm, b=1.298 27 nm, and c=1.298 27 nm. In contrast, in the tetragonal LLZO, it belongs to space group No.142 () with lattice parameter of a=1.3134 nm, b=1.3134 nm, and c=1.2663 nm, and all available Li1 (8a), Li2 (16f), and Li3 (32g) sites are filled with Li ions (Fig.1b). The resulting dimension values of different lattice parameters are proposed by Meier et al[14] and Eiichi et al[15].
Fig.1 Atomic structures of C-LLZO (a) and T-LLZO (b)
Fig.2 shows the band structure, DOS and partial densities of states (PDOSs) of C-LLZO. The electronic configuration of La, Li, O and Zr are 5d16s2, 1s22s1, 2s22p4 and 4d25s2, respectively. The energy band structure is mainly divided into the following parts: part 1 of -50~-48 eV is mainly the s-orbit with low energy level of Li and Zr; part 2 in the range of -35~ -34 eV and -28~-27 eV is mainly p-orbits of La and s-orbits of Zr, respectively; the s, p and d-orbits of La, Zr, Li and O in the ranges of -22~-16 eV, 8~-5 eV and -1~1 eV partially coincide, indicating that the metal atoms form tetrahedrons and octahedrons with oxygen at these energy levels; the top layer of the valence band (0~-1 eV) below the Fermi surface is mainly the p-orbit of O and the d-orbit of Zr, and the bottom layer of the conduction band (0~1.5 eV) above the Fermi surface is mainly the d-orbit of Zr, indicating that the key electrochemical properties of LLZO solid electrolyte materials are affected by Zr atoms. According to the calculation of the energy band structure, the band gap △E of C-LLZO is 0.039 eV.
Fig.2 Band structure (a), DOS (b) and PDOS (c~f) of C-LLZO: (c) La, (d) Li, (e) O, and (f) Zr
Fig.3 shows the band structure, DOS and PDOSs of T-LLZO, which reveal that the band structure of T-LLZO is similar to that of C-LLZO. The difference is that the partial densities of states of different orbits of Li, La, Zr and O atoms are at different energy levels. According to the calculation, the band gap ΔE of T-LLZO is 4.11 eV, while the ΔE of C-LLZO is 0.039 eV. The smaller band gap is conducive to increasing the efficiency of the conductivity because the energy required for electrons to jump from the valance band to the conduction band decreases. In LLZO lithium ion conductors, the electronic conduction is positively correlated with the ion conduction, which has been confirmed by the data in Table 5 and Table 6 below. This shows that the C-LLZO structure has better conductivity than T-LLZO.
Fig.3 Band structure (a), DOS (b) and PDOS (c~f) of T-LLZO: (c) La, (d) Li, (e) O, and (f) Zr
Table 5 Ionic conductivity of T-LLZO samples with different sintering time
| Sintering time/h | 6 | 12 |
|---|
|
Ionic conductivity/×10-8 S·cm-1 |
5.96 |
4.46×10-8 |
Table 6 Ionic conductivity of C-LLZO pellets with different sintering time
| Sintering time/h | 1 | 6 | 12 | 18 |
|---|
|
Ionic conductivity/×10-5 S·cm-1 |
7.77 |
8.48 |
9.8 |
3.42 |
The computed population and bond length of C-LLZO are listed in Table 1. The inter-atomic populations and bond lengths of C-LLZO (Table 1) show that compared to the O-La overlap population (0.19) and bond length, the overlap population of the O-Zr bonds (0.6) is higher, and the bond length is shorter (0.210 315 nm), demonstrating that the O-Zr bond has the strongest covalent properties. With this bond as its skeleton, C-LLZO has good electrochemical stability, which can be confirmed by the PDOSs of C-LLZO (Fig.2). This result shows that C-LLZO has a long cycle life during Li ion migration. Although the bond length between Li-O (0.202 934 nm) is shorter than that of O-La (0.296 621 nm), the overlap population of Li-O (0.04) is smaller, indicating that the covalency between Li-O is weaker, so the Li ions have the strongest migration performance.
Table 1 Population and bond length of C-LLZO
| Bond in C-LLZO | Population | Bond length/×10-1 nm |
|---|
|
Li-O |
0.04 |
2.029 34 |
|
Li-Li |
-0.03 |
2.804 59 |
|
O-Zr |
0.6 |
2.103 15 |
|
Li-Zr |
-0.91 |
2.676 28 |
|
Li-La |
-2.3 |
2.767 82 |
|
O-O |
-0.03 |
2.939 32 |
|
O-La |
0.19 |
2.966 21 |
The computed overlap populations and bond lengths of T-LLZO are listed in Table 2. Analysis shows that the population and bond length data of T-LLZO in Table 2 lead to roughly the same conclusions as those of C-LLZO in Table 1. Comparing Table 1 and Table 2, on the one hand, the O-Zr overlap population (0.6) of C-LLZO is larger than that of T-LLZO (0.53), and the C-LLZO bond length (0.210 315 nm) is shorter than that of T-LLZO (0.213 142 nm). The short bond length of the O-Zr in C-LLZO indicates that the covalent nature of this bond is stronger. Therefore, C-LLZO has a more stable structure and a longer cycle life during the Li-ion deintercalation and intercalation process; on the other hand, under the same electron cloud overlap population (0.04), the Li-O bond length (0.202 934 nm) of C-LLZO is longer than that of T-LLZO. This shows that C-LLZO Li-ions more easily deintercalate and intercalate and have better Li-ion migration performance, and it can be inferred that the C-LLZO ionic conductivity is better.
Table 2 Populations and bond lengths of T-LLZO
| Bond in T-LLZO | Population | Bond length/×10-1 nm |
|---|
|
Li-O |
0.04 |
1.943 22 |
|
Li-Li |
0.01 |
2.593 64 |
|
O-Zr |
0.53 |
2.131 42 |
|
Li-Zr |
-0.02 |
2.924 45 |
|
O-O |
-0.03 |
2.927 64 |
|
O-La |
0.28 |
2.496 26 |
2.1 Preparation of LLZO powders
The high-temperature solid phase method was employed for the preparation of LLZO, in which the Li, La and Zr sources come from high-purity LiOH·H2O (0.001% trace metals, Tianjin Kermel Chemical Reagent Co., Ltd, 90%), La2O3 (Sigma-Aldrich, 99.99%) and ZrO2 (Sigma-Aldrich, 99.5%), respectively. In particular, an excess of 15wt% LiOH·H2O was added to compensate for the loss of lithium during high-temperature calcination. 2.887wt% Al2O3 (Xilong Chemical Co., Ltd) was added to stabilize the cubic phase. La2O3 was heat treated at 1000 ℃ for 10 h to remove CO2 and H2O absorbed from the air, and ZrO2 was dried in a blast drying box at 100 ℃ to maintain the chemical stoichiometric ratio[16]. Typically, the raw materials were weighed according to the chemical stoichiometric ratio and mixed by ball milling with isopropyl alcohol for 10 h. Then, the slurries were dried at 70 °C. After drying, the mixture was poured into a covered crucible, compacted by vibration and calcined at 800 ℃ for 10 h at a heating rate of 5 ℃/min. The LLZO primary powder was obtained by sieving with a 160 mesh sieve[17,18].
2.2 Preparation of LLZO electrolyte pellets
The LLZO primary powders were pressed into several circular pellets with a diameter of 15 mm and a thickness of 2.5 mm by a stainless-steel die. LLZO electrolyte pellets that were covered with primary powders to reduce possible Li loss were placed in an alumina crucible[19,20]. Thereafter, sintering at 800 ℃ for 6 and 12 h was used to prepare tetragonal LLZO. Then, sintering at 1000 ℃ for 1, 6, 12, and 18 h was used to prepare cubic LLZO. The surfaces of some LLZO electrolyte pellets were polished. The relative density of LLZO electrolyte was measured to be about 97.3%. Conductive silver paint was applied on both sides of the polished LLZO electrolyte pellets, and a stainless-steel plate was added to assemble the blocking batteries (SS/Ag/LLZO/Ag/SS). The thickness of the polished LLZO electrolyte pellets was approximately 1.6 mm. Other LLZO electrolyte pellets were milled for 10 h at 400 r/min. The calcined pellets were pulverized into powders by a second ball milling and sieved through a 160-mesh sieve to characterize the powders.
The crystal structure of the LLZO was analysed by an X-ray diffractometer (XRD, Bruker D8 Advance, 40 kV, 30 mA) with Cu Kα radiation in the 2θ range of 10°~90°. To under-stand the microstructure of LLZO, the surface morphology of LLZO was observed by a field-emission scanning electron microscope (SEM, ∑IGMA). The ionic conductivity of LLZO was measured in a blocking battery (SS/Ag/LLZO/Ag/SS) by AC impedance. Impedance spectra were collected from an electrochemical workstation (CHI660E) in the frequency region from 1 MHz to 0.01 Hz.
2.4 Discussion of experimental results
The XRD patterns of T-LLZO samples with different sintering time are shown in Fig.4. The peaks in Fig.4 indicate that the structure of T-LLZO is purely tetragonal phase, and all of the peaks fit well to the tetragonal structure[21]. The lattice parameters of the T-LLZO samples are obtained by the X-ray diffraction refinement method, as shown in Table 3.
Fig.4 XRD patterns of T-LLZO powders sintered at 800 ℃ for different time
Table 3 shows that the 6 h and 12 h prepared T-LLZO samples belong to space group No.142 () and have a tetragonal structure. As the sintering time increases, the lattice size of the sample increases, and its average lattice size is a=b=1.313 064 nm, c=1.266 024 nm, which is in good agreement with the calculated lattice parameters of T-LLZO.
Table 3 Lattice parameters of T-LLZO samples with different sintering time
Sintering time/h | Phase structure | Space group | a/nm | b/nm | c/nm |
|---|
|
6 |
Tetragonal |
|
1.312871 |
1.312871 |
1.265792 |
|
12 |
Tetragonal |
|
1.313257 |
1.313257 |
1.266256 |
The XRD patterns of the C-LLZO samples with different sintering time are shown in Fig.5. The peak of 12 h indicates that the structure of LLZO is purely cubic phase, and all of the peaks fit well to the garnet structure (JCPDS NO. 45-0109), whereas 1 h and 6 h prepared samples reveal a mixture of lanthanum aluminium compounds (LaAlO3). The Al in the lanthanum aluminium compound phase comes from an aluminium-containing corundum crucible[22]. Literature stu-dies[23] have shown that the main role of adding Al2O3 in the synthesis process is to promote the formation of a stable cubic LLZO (C-LLZO) structure, rather than to improve its electrical conductivity. Conversely, it may reduce the conduc-tivity[24]. La2Zr2O7 second phases are observed in 18 h prepared powder with increasing the sintering time. LLZO is trans-formed into pyrochlore La2Zr2O7 due to the volatilization of lithium at high temperature[9]. All the LLZO powders exhibit strong diffraction peaks and well-developed crystallinity. The major sharp diffraction peaks at 16.66°, 25.60°, 27.40°, 30.68°, 33.69°, and 37.81° can be indexed to the (211), (321), (400), (420), (422), and (521) crystal faces, respectively. The lattice parameters of the T-LLZO samples can be obtained by the X-ray diffraction refinement method, as shown in Table 4.
Fig.5 XRD patterns of C-LLZO powders sintered at 1000 ℃ for different time
Table 4 Lattice parameters of C-LLZO samples with different sintering time
Sintering time/h | Phase structure | Space group | a/nm | b/nm | c/nm |
|---|
|
1 |
Cubic |
|
1.303177 |
1.303177 |
1.303177 |
|
6 |
Cubic |
|
1.303514 |
1.303514 |
1.303514 |
|
12 |
Cubic |
|
1.303544 |
1.303544 |
1.303544 |
|
18 |
Cubic |
|
1.298747 |
1.298747 |
1.298747 |
All the C-LLZO samples belong to space group and have a cubic structure. Similar to the T-LLZO samples, the lattice size of the sample (except sample for 18 h) becomes larger as the sintering time increases, and its average lattice size is a=b=c=1.302 246 nm, which is in good agreement with the calculated lattice parameters of C-LLZO.
The morphologies of C-LLZO powders with different sintering time was studied by SEM. As shown in Fig.6, the LLZO consists of crystals with average diameters of 10~15 μm. Fig.6c shows that the particles of LLZO are distinct and uniform, and the dispersibility between the particles is good after 12 h of sintering. In Fig.6d, with increasing the sintering time, the crystal structure of LLZO is destroyed by excessive volatilization of lithium at high temperature.
Fig.6 SEM morphologies of C-LLZO powders sintered at 1000 ℃ for different time: (a) 1 h, (b) 6 h, (c) 12 h, and (d) 18 h
Nyquist diagrams of LLZO samples with different sintering time in air are presented in Fig.7. For all the samples, the Nyquist plots consist of a high-frequency semicircle and a low-frequency oblique line. The high frequency semicircle represents the intracrystal conductivity of the battery, and the low frequency tilt line is related to lithium ion diffusion[17]. Fig.7 shows the equivalent circuit, where Rb represents the volume resistance of the battery, Rgb stands for the grain boundary resistance, and Rel represents the resistance of the electrode reaction between Li and Ag. The low frequency intercept of the semicircle on the real axis is the total resistance (Rtotal=Rb+Rgb)[5]. The total ion conductivity (σ) is calculated by Rtotal and the material size:
Fig.7 Nyquist diagrams of T-LLZO samples (a) and C-LLZO samples (b) with different sintering time
where L, S and R denote the thickness of the electrolyte membrane, the cross-sectional area of the electrode, and the ionic resistance of the electrolyte, respectively. The ion conductivity values of the LLZO samples at room temperature were obtained from the Nyquist plots, as shown in Table 5 and Table 6. It can be seen from Table 5 and Table 6 that the ion conductivity of the T-LLZO materials (5.96×10-8 S·cm-1) sintered for 6 h is the highest, while the ion conductivity of
the C-LLZO materials (9.8×10-5 S·cm-1) sintered for 12 h is the highest, which is 3 orders of magnitude larger than that of T-LLZO. This is consistent with the previous conclusions obtained through theoretical calculations. The comparison of ionic conductivity of sintered samples that made in this study and other researchers are listed in Table 7. Compared with other researches[25,26], C-LLZO prepared in this work has higher ionic conductivity, and ionic conductivity of T-LLZO is also higher than that reported in Ref.[27]. However, whether it is the C-type or T-type synthesized in this study, they are in the same order of magnitude as Ref.[25-27]. The synthesis method needs to be improved in the future to enhance the ionic conductivity of LLZO.
Table 7 Comparison of C-LLZO and T-LLZO conductivity
| Phase structure | Final sintering temperature/°C -time/h | Ionic conductivity/S·cm-1 | Ref. |
|---|
|
Cubic |
1000-6 |
8.48×10-5 |
This work |
|
Cubic |
1000-7 |
≈10-5 |
[25] |
|
Cubic |
1000-12 |
9.8×10-5 |
This work |
|
Cubic |
1000-12 |
0.28×10-5 |
[26] |
|
Tetragonal |
800/12 |
4.46×10-8 |
This work |
|
Tetragonal |
800-10~15 |
1.6×10-8 |
[27] |
1) The C-LLZO sintered at 1000 °C for 12 h shows a pure cubic phase and realizes a maximum ionic conductivity of 9.8×10-5 S·cm-1; T-LLZO sintered at 800 ℃ for 6 h has a pure tetragonal phase structure and an ionic conductivity of 5.96×10-8 S·cm-1 is obtained, in reasonable agreement with the calculation results.
2) The Li-ion conductivity of two different Li7La3Zr2O12 (LLZO) solid electrolyte materials with tetragonal and cubic phases is governed by two main factors. (1) The band gap of cubic Li7La3Zr2O12 (0.039 eV) is smaller than that of tetrahedral Li7La3Zr2O12 (4.11 eV), and a smaller band gap is conducive to improving the conductivity efficiency. (2) Under the same overlap population (0.04), the Li-O bond length (0.202 934 nm) of C-LLZO is longer than that of T-LLZO. This shows that C-LLZO has better Li-ion migration performance, and it can be inferred that the C-LLZO ionic conductivity is better.
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