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Comparative Study on Sulfide and Oxide Electrolyte Interfaces with Cathodes in All-Solid-State Battery via First-Principles Calculations

  • Yukihiro Okuno*
    Yukihiro Okuno
    Research and Development Management Headquarters, FUJIFILM Corporation, 210 Nakanuma, Minamiashigara, Kanagawa 250-0193, Japan
    *Email: [email protected] (Y.O.).
  • Jun Haruyama
    Jun Haruyama
    Institute for Solid State Physics, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8581, Japan
    More by Jun Haruyama
  • , and 
  • Yoshitaka Tateyama*
    Yoshitaka Tateyama
    Center for Green Research on Energy and Environmental Materials (GREEN) and International Center for Materials Nanoarchitectonics (MANA), National Institute for Materials Science (NIMS), 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan
    Elements Strategy Initiative for Catalysts & Batteries, Kyoto University, 1-30 Goryo-Ohara, Nishikyo-ku, Kyoto 615-8245, Japan
    *Email: [email protected] (Y.T.).
Cite this: ACS Appl. Energy Mater. 2020, 3, 11, 11061–11072
Publication Date (Web):October 28, 2020
https://doi.org/10.1021/acsaem.0c02033

Copyright © 2022 American Chemical Society. This publication is licensed under these Terms of Use.

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Abstract

The interfacial resistance between the solid electrolyte (SE) and the cathode of all-solid-state battery can crucially affect its performance. However, the microscopic mechanisms due to which this resistance occurs depend on the SE type and are still debatable. In this study, we performed a comparative analysis of the characteristics of sulfide electrolyte (Li3PS4) and oxide electrolyte (Li3PO4 and Li7La3Zr2O12) interfaces with a typical oxide cathode (LiCoO2). We considered the Li vacancy formation associated with the Li chemical potential and the cation exchange related to the reaction layer formation, and used the density functional theory based on first-principles calculations. Compared to the case of sulfide SE interfaces, the oxide SE interfaces have fewer Li sites that have lower vacancy formation energy and are stable against the mutual cation exchange with the oxide cathode. These results indicate that the oxide electrolytes show less dynamical Li+ depletion upon initial charging and less formation of the reaction layer compared to those of sulfide electrolytes, which can be associated with the relatively low interfacial resistance observed experimentally. In addition to the material dependence, we also investigated the effect of the orientations of the SE and cathode at the interface. We demonstrated that the orientations strongly affect the ease of Li vacancy formation and mutual cation exchange. Interfaces of the buffer layer material of Li4Ti5O12 with a Li3PS4 SE and the LiCoO2 cathode were also evaluated. The results show that such oxide buffer layers suppress the Li vacancy formation, leading to less Li+ depletion. The present comparative analysis provides electronic and Li+ tendencies around the interfaces between the SE and the cathode, which will be useful for interface design in the future.

1. Introduction

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There has been a rapid growth in the portable power source market owing to lithium-ion batteries (LIBs), which are presently attracting considerable attention for use in larger power sources such as electric vehicles and energy storage systems because of their high energy densities. (1−4) However, serious safety concerns exist around such future use because of their use of flammable organic solvent electrolytes. All-solid-state batteries (ASSBs), in which the organic liquid electrolyte is replaced with an inorganic solid electrolyte (SE), have many advantages such as safety, high energy density, and a long cycle life. (5,6) The development of Li-ion solid electrolytes has proceeded rapidly in recent years, and the conductivities of some systems have reached 25 mS cm–1, approaching ∼100 mS cm–1 of the typical liquid electrolyte. For example, new sulfide SEs such as Li10GeP2S12 (7) and Li9.54Si1.74P1.44S11.7Cl0.3 (8) show ion conductivities of σ > 10 mS cm–1 at room temperature, and oxide SEs such as Li7La3Zr2O12 (9) (LLZO) and La2/3–xLixTiO3 (10) also typically show room-temperature ion conductivity of the order of 0.1 and 1 mS cm–1, respectively.
Although various SE materials have already been synthesized, Li-ion ASSBs fabricated with these materials do not always show the expected performance because there are problems associated with the grain boundaries within the SE and the interface between the SE and the cathode. (11) For the latter, the interfacial resistance at the sulfide SE interfaces and the proposed solution by the interposition of an oxide buffer layer (e.g., Li4Ti5O12 (LTO), (12) LiNbO3, (13) and Li2SiO3 (14)) are well-known. (11) Several mechanisms were suggested as the origin of the interfacial resistance: (15) formation of a space-charge layer (SCL) of Li ions, (16,17) a structural disorder induced by interfacial chemical reactions involving mutual exchange of ions, (18−20) and the formation of secondary phases by the SE decomposition. (18−20) Although a buffer layer was introduced, the mutual ion exchange was still observed, and secondary phases were formed. In this respect, the SCL mechanism is still a reasonable candidate. (21−24) Compared to the sulfide SEs, the well-constructed oxide SEs showed low interfacial resistances for the cathode interfaces. Haruta et al. recently reported very low interfacial resistance for Li migration in a damage-less LiCoO2 (LCO) cathode and Li3PO4–xNx (LiPON) oxide electrolyte interface. (25) A low interface resistance of 7.6 Ω cm2 was also reported for a system of LiNi0.5Mn1.5O4 cathode and LiPON electrolyte (26) and for the interface of the LLZO electrolyte (27) and a Li metal anode. These results suggested the intrinsic absence of interfacial resistance for oxide SEs and that the structural disorder seems to be the more dominant origin of the interfacial resistance.
Thermodynamic calculations (28−33) and direct-interface calculations (21−24,34−36) within the density functional theory (DFT) framework were already performed computationally for the SE–cathode interfaces. The former studies showed a tendency for the sulfide SEs to have narrower electrochemical windows than those of oxide SEs, suggesting that interfacial reactions involving the appearance of secondary phases can occur thermodynamically more easily in the sulfide cases. The direct interface calculations demonstrated that at the sulfide SE–cathode interfaces specific mutual ion exchanges and the dynamical Li+ depletion with interfacial electron transfer can occur during operation. (21−24) Note that this dynamical Li+ depletion is different than the conventional static SCL formation mechanism. This suggests that in the initial stage of charging the Li+ depletion layer is dynamically generated from the Li sites that have a lower Li vacancy-formation energy near the interface along with electronic oxidation. (21,23,24) These findings can be related to the microscopic origin of the increase in interfacial resistance. In the direct approach, the buffer layer effect was also explained along with the above context. However, the comparison between the sulfide and oxide SEs and the investigation of interface orientation dependence are still lacking. In particular, the latter cannot be examined by the thermodynamic approach, but the surface/interface reactivity can be affected by the orientation.
We addressed this gap in existing research. In this study, we performed a comparative investigation between the sulfide Li3PS4 (LPS) and the oxide (Li3PO4 (LPO) and LLZO) SE interfaces with the LCO cathode materials in the framework of DFT direct-interface calculations. Using the interfacial structure search, we determined the probable interface structures and calculated the site-dependent Li vacancy-formation energy (Ef(VLi_j) for the jth Li site), corresponding to the negative Li chemical potential (μLi_j), to discuss the possibility of dynamical Li+ depletion. We also calculated the mutual cation exchange energy at the interface of the SE and the cathode and examined cation diffusion across the interface. Following that, we investigated the interface orientation dependence of those quantities by calculating the Li vacancy-formation energy and the mutual cation exchange energy at LCO(110) and LCO(104) interfaces with LPS and LPO SEs. We constructed several slab models for each pair of cathode–SE interface and examined the physical quantities of the probable metastable structures because several metastable SE–cathode interfaces can appear under the actual battery operation. Furthermore, the buffer layer effect was investigated with LTO. We have already analyzed the buffer layer effect of LiNbO3 (LNO) in our previous study (21) and suggested that electronic insulator oxide with d0 state of the transition metal is effective. To explore this effect, we selected LTO that has different crystal structure from LNO in this study. Taking all the results into account, together with the experimental observations, we evaluated the hypotheses proposed for the origin of interfacial resistance thus far and show differences in the interface properties between the sulfide and oxide SEs.

2. Calculation

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2.1. Interface Construction

In this study, we performed first-principles calculation analyses of five solid–solid interfaces: LCO/LPS, LCO/LPO, LCO/LLZO, LTO/LPS, and LCO/LTO. As model surface orientations for the interfaces, we selected LCO(104), LCO(110), LPS(010), LPO(010), LPO(001), LLZO(001), and LTO(111) because these are energetically probable. To prepare stable surface structures first, we chose the surface termination so as not to break the polyhedrons constructed by the transitional metal and anion atoms as much as possible within the stoichiometric surface slab. These slabs were approximately dipole-free as well. Next, we utilized a simpler version of the interface structure search scheme with the pristine surfaces in this study, although a comprehensive structure search technique for heterogeneous solid–solid interfaces was developed in a recent study. (24) In the construction of the supercell, the surface slab of LCO or LTO was set first, and the second material (SE) slab was put on it. To determine energetically stable structures, we explored several rigid lateral shifts of the second slab followed by local structure optimization. There was vacuum in the region surrounding the slabs (up to 1.5 nm) so that we can focus on the selected interface. We constructed several interface structures by randomly moving one side of the slab model in lateral directions for each solid–solid interface structure and calculated statistics of physical quantities such as Li vacancy-formation energies and cation exchange energies. Calculating the statistics of the physical properties is important to obtain reliable results. We believe that the various solid–solid interface structures obtained here will be realized in real ASSBs. The interface slab models were sampled, and the energy difference between each calculated structure and the most stable structure was evaluated; the structure with the energy difference of 1 order of magnitude higher than the others was excluded from further investigation.
The choices of the orientations were made with the following considerations. The (110) and (104) surfaces were chosen for LCO. Although the larger stability of the (104)-oriented LCO surface was suggested, (37) the (110) surface still exists in the LCO particles and is one of the theoretically well-studied LCO surfaces. (38−40) As a sulfide SE example, we adopted β-Li3PS4 (LPS) that shows high Li-ion conductivity (1.64 × 10–4 S cm–1 at room temperature). (41) The LPS (010) surface was selected because the Li+ conduction path in LPS is in the b direction. (42) γ-Li3PO4 (LPO) was selected as a model oxide electrolyte. Crystalline γ-Li3PO4 has an orthorhombic Pnma (43) structure, and in particular, LiPON (44,45) electrolyte materials are developed based on LPO. The (010)- and (001)-oriented LPO surfaces were selected in this work because b and c directions are Li+ conduction paths in LPO. (46,47) Considering the rather low elastic modulus of LPS, the LPS lattice constants are adjusted to that of LCO for the lattice mismatch at the LCO/LPS interface in the construction of the interface slab models. On the LPO surface, to keep the structure of the PO4 tetrahedron at the interface, the outermost interface layer is composed of Li ions.
We also investigated LLZO as another oxide SE. LLZO has a garnet-type crystal structure with a relatively higher Li+ conductivity than the other oxide electrolytes. (9,48) In the cubic phase of the Ia3d space group with Li ions partially occupying 24 d tetrahedral and 48 g/96 h octahedral sites, LLZO shows a high Li-ion conductivity (43) of the order of 10 × 10–4 S/cm2. We selected the (001)-oriented surface of the cubic LLZO phase for the interfaces. On the Li sites of the Ia3d cubic phase, 7/9 of 24 d and 96 h sites of Li in the LLZO crystal are occupied. According to the previous calculations, (48) we introduced the vacancy in 50% and 40% of the 96 h and 24 d sites, respectively. (49,50) On the outermost surface of the LLZO slab, few LaO8 dodecahedrons were broken, while the ZnO6 octahedron structures were maintained.
For the oxide buffer layer, we selected Li4Ti5O12 (LTO) (12) in this study. The LTO compound has a spinel structure with space group Fd3m (51) in which the 8 a positions are occupied by Li ions and 16 d positions are shared between Li and Ti in a ratio of 1:5. We treated the LTO (111)-oriented surface, where the Li ions can migrate through. (52) To maintain the TiO6 octahedron structures, the outermost surfaces were composed of Li ions (8 a sites) on the TiO layers. The Li-terminated surface has the sequence of the (111) atomic-layer stacking similar to the bulk, implying that the Li-terminated (111)-oriented surface is stable for LTO. For the lattice constants parallel to the interface, the average of the two lattices is considered for the slab models with LCO and the oxide materials.
The thickness of all slab models is around 1–2 nm, which is sufficiently thick to show the bulk character in the central region of each slab. We also introduced a vacuum region with about 1–1.5 nm width in the outside of the interface slab. Note that a supercell without a vacuum usually involves two interfaces, which are atomically different in most cases.
The selected surface structures are shown in Figure 1, where the VESTA package (53) is used for visualization. The optimized lattice constants of bulk crystals are provided in Table S1 of the Supporting Information. The detailed structures of the slab models are also provided in the Supporting Information.

Figure 1

Figure 1. Surfaces of (a) LiCoO2 (LCO)-(104), (b) LCO-(110), (c) β-Li3PS4 (LPS)-(010), (d) γ-L3PO4 (LPO)-(001), (e) Li7La3Zr2O12 (LLZO)-(001), and (f) Li4Ti5O12(LTO)-(111), examined in this work. Li, O, P, S, Co, La, Zr, and Ti are depicted as light green, red, purple, yellow, blue, brown, blue, and light blue spheres, respectively. CoO6, PS4, PO4, ZrO6, LaO8, and TiO6 complexes are represented by blue, green, gray, light green, brown, and light blue polyhedrons, respectively.

2.2. Computational Details

DFT calculations were performed by using Quantum Espresso code. (54) The Hubbard U (DFT+U) (55) method was utilized d-orbitals of transition metal and ultrasoft pseudopotentials (56) were used for the treatment of the core electrons of atoms. The PBE (57) exchange correlation functional was used, and for the +U augmented treatment of Co 3d orbitals, we set the Hubbard U values as 4.9 eV. (58) The cutoff energies of wave function and charge density were set as 40 and 320 Ry, respectively. With regard to the K-point mesh, we set 2 × 1 × 1 for LCO(110)/LPS(010) and LCO(110)/LPO(001), and for other interface models, we set only the Γ-point. We set the system to be neutral, and the occupation number was determined by the Gaussian smearing technique with a smearing parameter of 0.001 Ry. With regard to the spin polarization of Co on the LCO surface, the spin-polarized state is stable because of the missing Co–O bonds. (59) However, we have investigated the Li passivation of the LCO(110) with and without spin polarization and found that energy difference among the low-, intermediate-, and high-spin states are within 0.2 eV per Co atom. Thus, we limit the present discussion to the spin-unpolarized case. The calculation conditions for the LLZO and LTO interfaces are the same as those for LCO(110)/LPS(010) and LCO(110)/LPO(001). Spin nonpolarization is assumed for these interfaces. For Ti, Zr, and La, no U values were applied.
The Li vacancy-formation energy at the jth Li site, Ef(VLi_j), is defined as (21)
(1)
where Etot(VLi_j) and Etot are the total energies of the relaxed interface obtained by DFT+U calculations with and without Li vacancy at the jth site, respectively. ELi is the chemical potential of the bcc Li metal. To compare the stabilities of many Li sites in several interface systems, we adopted ELi of Li metal as a common reference energy in this study. Ef(VLi_j) indicates the energy required for the reaction LinX → Lin–1X + Li(s) (n = integer and X = the rest moiety after Li vacancy formation at the jth site), which corresponds to the voltage with respect to the reference redox couple of Li/Li+. This is the negative chemical potential of Li with respect to Li metal, μLi_j. A lower Ef(VLi_j) (a higher μLi_j) indicates that the Li+ at this site can be removed more easily. This scheme is valid when the electron can be extracted simultaneously; this means that the preceding chemical reaction can be divided into two electrochemical reactions: LinX → Lin-1X + Li+(sol) + e and Li+(sol) + e → Li(s).
As a part of the reaction layer formation between the SE and cathode, we focused on the mutual cation exchange across the interface. The mutual ion exchange energy is defined as (22)
(2)
Here, Etot is the total energy of the unexchanged pristine interface, and Etot(Aj ↔ Bk) represents the total energy of a relaxed interface in which the jth A ion and kth B ion are mutually exchanged from the pristine interface. The negative exchange energy indicates that the mutual exchange is energetically favored. Note that the full evaluation of the exchange probability requires a consideration of the reaction kinetics.

3. Results and Discussion

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3.1. LCO/LPS Interface

First, we investigated the interface between the LCO cathode and a sulfide SE, LPS. Following the screening for the energy values, we sampled three and eight different structures for the LCO(104)/LPS(010) and LCO(110)/LPS(010) interfaces, respectively. The difference in energy per interface area between the most stable state and that with the highest energy among the selected states is 0.0053 and 0.0054 eV/Å2, respectively, which is sufficiently low. In Figure 2, we show typical stable structures of LCO(104)/LPS(010) and LCO(110)/LPS(010) interfaces. For the LCO(104)/LPS(010) interface, almost half of the outermost Co cations in the LCO side attract S anions to form CoO5S octahedrons, and the remaining outermost Co, not in close proximity to S anions, form CoO5 quadrangular cones. Li ions in the LPS side are electrostatically attracted to O atoms in the LCO side and are located on the top position of O atoms. The estimated adhesion energy of the LCO(104)/LPS(010) interface is 0.025 eV/Å2, where the definition of adhesion energy (60) of solid–solid interface is given in the Supporting Information. On the boundary of the LCO(110)/LPS(010), CoO4 pseudotetrahedrals appear instead of typical CoO6 octahedrons, and CoO4S pentahedrons are also partly formed by attracting a S anion to a Co cation in the boundary region, as reported in a previous study. (21) Li ions in the LPS side of the interface interact with O atom in the LCO side and are located at the bridge positions with the O atoms. In summary, although the interface consists of the same substances as the cathode and electrolyte, the atomic structures formed at the interface are different if the crystal orientations are different.

Figure 2

Figure 2. Calculated interface structures with the lowest energies of (a) LCO(104)/LPS(010) and (b) LCO(110)/LPS(010). The insets show the detailed atomic structures at the interface. CoO6 and PS4 complexes are represented by blue and green polyhedrons.

Figure 3 shows the calculated partial density of states (PDOS) of the LCO(104)/LPS(010) interface. This PDOS is obtained from the most stable interface structures, whereas the PDOS features are common to the eight sampled structures. The result denotes that the valence band maximum (VBM) and the conduction band minimum (CBM) are composed of the orbitals originating from the LCO. In particular, the CBM is observed to be an in-gap state, consisting of the Co3d orbitals of CoO5 quadrangular cones at the interface. The detailed PDOS of the first layer of LCO facing the LPS is shown in Figure S2.

Figure 3

Figure 3. PDOS of the calculated lowest energy interface of LCO(104)/LPS(010). Red line: total DOS; green line: LCO atoms; blue line: LPS atoms; brown line: LCO atoms facing the vacuum; light blue line: the first LCO layer facing the LPS slab. We set zero reference energy as the center of the band gap. LCO vac and LCO 1st correspond to the LCO layer facing the vacuum and the interface with LPS, respectively.

Next, we estimated the Li vacancy-formation energies at the LCO/LPS interface. Figure 4 shows the distribution of Li vacancy-formation energies. The Li sites were selected from each interfacial Li layer in the perpendicular direction of the cathode–SE interface. In Figure S3 and Table S3, we summarize Ef(VLi_j) of the most stable and the highest energy structures of LCO(110)/LPS(010) interfaces we calculated.

Figure 4

Figure 4. Distributions of Li sites classified with the Li vacancy-formation energies at the (a) LCO(104)/LPS(010) and (b) both LCO/LPS interfaces, respectively. The vacancy-formation energies of 65 Li sites in 8 different interface structures (23 sites in three different interface structures) are calculated for LCO(104)/LPS(010) and (LCO(110)/LPS(010)). The distributions are normalized by the total number of calculated Li sites. The blue bars denote the distribution of all the calculated Li sites in the LCO/LPS and the red bars denote those of calculated Li sites located in the LPS region.

The distributions of Li sites classified by their vacancy-formation energies (Figure 4) show that sites with lower Ef(VLi_j) (<2.0 eV) appear in both LCO(104)/LPS(010) and LCO(110)/LPS(010) interfaces. The sites with such low Ef(VLi_j) are concentrated in the LPS side of the interfaces. In particular, we found that mobile Li sites in the original β-Li3PS4 crystal have a tendency to have low Ef(VLi_j). The Li ions at these sites can be removed, together with oxidation of the materials, at the undervoltage condition upon the initial charging and lead to dynamical Li+ depletion in the interfacial LPS side. Such sites appear more frequently in the less stable LCO(110)/LPS(010) interfaces than in LCO(104)/LPS(010) interfaces, thereby reflecting the interface stability. As the dynamical Li+ depletion can be a major origin of the interfacial resistance, the LCO(110) interfaces have a higher resistance than that of the LCO(104). The details of the structure dependence of the Li vacancy-formation energies in LCO/LPS interfaces are discussed in Figure S3 and Table S3.
We also discuss the mutual cation exchange energies between the LCO(104)/LPS(010) and LCO(110)/LPS(010) interfaces. We previously calculated these energies in LCO(110)/LPS(010), (22) where the exchange between Co and P in the LCO/LPS interface was highly exothermic and energetically preferable to the unmixing pristine case. In Figure 5, we show the typical structure with the site assignments around the LCO(104)/LPS(010) interface and their corresponding cation exchange energies. We selected the Co and P atoms in the first and second layers from the LCO/LPS boundary. Co1, Co2, and Co3 form CoO5S octahedrons, CoO5 quadrangular cone, and CoO6 octahedrons, respectively.

Figure 5

Figure 5. (a) Representative LCO(104)/LPS(010) interface structure with the site labels and the mutual cation exchange energies for (b) Co ↔ P and (c) Co ↔ Li.

As in the case of LCO(110)/LPS(010), the LCO(104)/LPS(010) interfaces show that the Co ↔ P exchange reaction is exothermic for the Co ↔ P1 (P cations in the first layer from the LCO/LPS boundary) case. However, the mixing reaction energies are around −0.7 to −1.2 eV, which are smaller than the energy of the LCO(110)/LPS(010) case (around −2 eV). (22) For the second-layer P cations, the exchange energies are almost endothermic, except for Co2 ↔ P2 in the LCO(104)/LPS(010) case. The results are in contrast to the LCO(110)/LPS(010) case. These results suggest that mutual cation exchange reactions are less likely to occur at the LCO(104) interface compared to the LCO(110). The reduced preference of Co ↔ P at the LCO(104)/LPS(010) interfaces is also confirmed in a recent study with an efficient sampling technique for the interface structures. (24) With regard to the Co ↔ Li exchange energies, the mixing reactions are about 2–3 eV endothermic even for the first layer of Li ions from the LCO/LPS boundary. Consequently, the Co cations cannot migrate to the neighboring Li sites. In this way, it was found that the mutual cation exchange energy depends on the interface orientation as in the Li vacancy-formation energy near the LCO/LPS boundary. In Figure S4, we also show the structure dependence of the mutual Co ↔ P exchange energy. The Co ↔ P exchange reaction is more likely to occur in structures with higher energy than in the most stable ones.
The mutual cation exchange can facilitate the generation of sites with low Ef(VLi_j). In Table S4, we show the Li vacancy-formation energies for the LCO(104)/LPS(010) interface where we set Co ↔ P mixing in the first layer at the LCO/LPS interface as shown in Figure S5. The Co ↔ P mixing around the LCO/LPS boundary induces the generation of sites with lower Ef(VLi_j), which may be related to the in-gap states appearing on the LCO interface as shown in PDOS (Figure S6). The Co ↔ P mixing increases the in-gap states composed of Co d-orbitals around the Fermi level, which lowers the electron transfer energy from LPS to LCO accompanied by the generation of a Li vacancy in the LPS side, and consequently, Ef(VLi_j) in the LPS side decreases. As a result, the cation mixing introduces the Li+ depletion phase and becomes the origin of the high-resistance phase at the LCO/LPS interface. Note that in the high-energy interface the mutual Co ↔ P exchange is more likely to occur than in the stable interface state. Therefore, if the many interface structures between the cathode and SE are high-energy metastable states, the mutual cation exchange will proceed further. Note that the thermodynamic calculations (30) suggest LPS decomposition to P2S7, Co(PO3)2, Co2S, and so on, in contact with LCO. Here we emphasize that the mutual cation exchange examined here is regarded as the initial stages of such chemical reactions toward the thermodynamically stable phases at the interface.

3.2. LCO/LPO Interface

We also investigated the characteristics of the oxide SE case to compare with the sulfide SE by focusing on γ-Li3PO4. For the LCO (104) surface, we prepared (010)- and (001)-oriented LPO surfaces, considering probable Li+ transport pathways. We considered five and four different interface structure models for the LCO(104)/LPO(010) and LCO(104)/LPO(001) structures, respectively. The energy difference per interface area between the most stable and the highest energy states among the calculated slab models are within 0.023 and 0.104 eV/Å2 for the LCO(104)/LPO(010) and LCO(104)/LPO(001) interfaces, respectively.
In Figure 6, we show the optimized structures of the most stable LCO/LPO interfaces. The ion positions near the boundary of the LCO/LPO interfaces are not so deviated compared to the LCO/LPS case. For both interfaces, more than half of the outermost Co atoms at the LCO surface formed CoO6 octahedrons by sharing the O atoms in the PO4 tetrahedrons in the LPO region. These newly formed CoO6 octahedrons may be related to the rather smooth arrangement at the LCO/LPO interfaces. The adhesion energy of the LCO(104)/LPO(010) and LCO(104)/LPO(001) interfaces are 0.028 and 0.021 eV/Å2, respectively.

Figure 6

Figure 6. Optimized interface structures of (a) LCO(104)/LPO(010) and (b) LCO(104)/LPO(001). The insets show the detailed atomic structures at the interface. CoO6 and PO4 complexes are represented by blue and gray polyhedrons.

We show the calculated PDOS of the representative LCO(104)/LPO(001) interface in Figure 7. As in the case of the sulfide SE, the VBM is composed of LCO orbitals, and the contribution of LPO to the valence band lies ∼1 eV lower than the VBM. The CBM consists of LCO components, and the in-gap state around 0.7 eV originated from Co’s d-orbital at the interfacial LCO.

Figure 7

Figure 7. PDOS of the optimized interfaces of LCO(104)/LPO(001). Red line: total DOS; green line: PDOS from LCO atoms; blue line: PDOS from LPO atoms; brown line: PDOS from LCO atoms facing the vacuum; light blue line: PDOS from first LCO layer facing the LPO slab. We set zero reference energy as the band gap center.

We then evaluated the Li site distribution classified by the vacancy-formation energy around the LCO/LPO interfaces (Figure 8). The energy range is between 1.6 and 3.6 eV, which is more than 1 eV smaller than that in the bulk region of LPO (about 5.0 eV). Ef(VLi_j) in the LPO side is about 3.6 eV at the maximum, and it reflects the band offset between the LCO and LPO interfaces. In bulk LPO, the electron extracted with the Li vacancy formation is located at the VBM of LPO, while in the LCO/LPO interface, the electron is extracted from the LCO band as shown in Figure 7. Figure 8 shows that the percentage of sites with low Ef(VLi_j) is low for the LCO/LPO interface compared to the LCO/LPS interface. Notably in the LCO(104)/LPO(010) interface (Figure 8a), even in the highest energy state in our sampling models, there is no Li site with low Ef(VLi_j) less than 2.0 eV. With regard to the structural dependence of Ef(VLi_j) for LCO(104)/LPO(001) (Figure 8b), we found that sites with low Ef(VLi_j) are observed in high-energy interface structures. This may be related to the fact that the low interfacial resistance of the LCO/LPO interface requires a damage-less LCO cathode and a Li3PO4–xNx (LiPON) oxide electrolyte interface. (25) Detailed analyses of Ef(VLi_j) are provided in Figure S9 and Table S6.

Figure 8

Figure 8. Distributions of Li sites divided by their Li vacancy-formation energies at the (a) LCO(104)/LPO(010) and (b) LCO(104))/LPO(001) interfaces. The vacancy-formation energies of 28 Li sites in four different interface structures and 36 sites in five different interface structures are calculated for LCO(104)/LPO(010) and LCO(104)/LPO(001), respectively. The distributions are normalized by the total number of calculated Li sites. The blue bar graphs denote the distribution of all the calculated Li sites in LCO/LPO, and the red bar graphs denote those of the calculated Li sites located in the LPO region.

In Figure 9a, we show a schematic picture of the LCO(104)/LPO(001) interface with the Li and cation sites where mutual cation exchange energies were calculated. With regard to the cation sites where the mutual ion exchanges were evaluated, Co1 and Co3 are the outermost surface-Co ions on the LCO surface, and Co2 is a second-layer Co ion from the LCO/LPO boundary. We selected the Li and P atoms in the first and second layers of LPO from the LCO/LPO boundary.

Figure 9

Figure 9. (a) Schematic picture of the optimized LCO(104)/LPO(001) interface with the sites where we calculated mutual cation exchange energy. (b) Co ↔ P and (c) Co ↔ Li cation exchange energies corresponding to sites denoted in (a).

From Figure 9b,c, we see that the reaction energies of cation exchange between LCO and LPO are highly endothermic. Unlike the sulfide LPS case, the exchange energies of Co ↔ P and Co ↔ Li are over 3 eV, and the LPO surface is inert to reactions with the LCO surface. This result suggests that unlike in case of LPS, Co diffusion is less likely to occur on the LPO phase. Here, we point out that the thermodynamics consideration can also show the inertness of interface reactivity between LCO and LPO. In Figure S10, we also show the vacancy-formation energies of Li sites in the LCO(110)/LPO(010) interface. Compared with the LCO(104)/LCO(010) case, the percentage of sites with low Ef(VLi_j) increases, and it may be related to the strong chemical activity of the LCO(110) surface compared to that of LCO(104). However, when compared to the sulfide SE, we can conclude that the number of occurrences of Li sites with low Ef(VLi_j) decreases at LCO/LPO. This result suggests the absence of a high-resistance phase at the LCO/LPO interface is related to the LCO/LiPON interface, in which the high-resistance phase is absent, as demonstrated by Haruta et al. (25) LPO has a larger bandgap and a lower valence-band maximum than that of LPS. The large band offset of the valence band between the cathode and SE is an obstacle for electron transfer from SE to the cathode when Li+ ions are removed from the SE side, leading to the suppression of dynamical Li+ depletion layer generation, which can be associated with the suppression of interfacial resistance. (21,23)

3.3. LCO/LLZO Interface

We investigated the interface with another oxide electrolyte, LLZO, which is unique in that it is a fast Li-ion conductor among the oxide electrolytes. For the surface of LLZO with the LCO (104), we chose the (001) surface maintaining the structure of the ZrO6 octahedron in LLZO. We considered four different interface structure models for the LCO(104)/LLZO(001) interface. The energy difference per interface area between the most stable and the highest energy states in the calculated models is 0.038 eV/Å2 for the LCO(104)/LLZO(001) interface.
In Figure 10, we show typical stable structures of LCO(104)/LLZO(001). At the LCO–LLZO boundary, more than half of the outermost Co atoms form CoO6 octahedrons by sharing O atoms in the ZrO6 tetrahedrons in the LLZO region, as shown in the insets of Figure 10.

Figure 10

Figure 10. Optimized interface structures of LCO(104)/LLZO(001). The insets show the detailed atomic structures at the interface. CoO6, ZrO6, and LaO8 complexes are represented by dark blue, light green, and brown polyhedrons.

Figure 11 shows the calculated PDOS of the LCO(104)/LLZO(001) interface. Both the VBM and CBM are composed of LCO orbitals as in the case of the LCO/LPO interface. The CBM is an in-gap state which consists of Co 3d orbitals of CoO5 quadrangular cones at the interface, and it is one of the common properties of LCO(104) and the oxide SE interfaces that we investigated. The contribution of LLZO orbitals to the conduction band is at least 1 eV above the CBM, and the band offset of LCO/LLZO on the conduction band is considerably large. The top of the valence band is also composed of LCO orbitals, and the contribution of LLZO to the valence band appears just around 0.2 eV lower than the VBM, leading to a smaller band offset. We also show the PDOS of LCO(104)/LLZO(001), divided to show each ion contribution in Figure S14. The VBM of the LLZO side mainly consists of O orbitals and hybridization between the O orbital and that of Zr (or La) in the LLZO slab and is not as strong as in the case of the oxygen and Co in the LCO slab.

Figure 11

Figure 11. PDOS of the optimized interfaces of LCO(104)/LLZO(001). Red line: total DOS; green line: LCO atoms; blue line: LLZO atoms; violet line: LCO atoms facing the vacuum; light blue line: the first LCO layer facing the LLZO slab. We set zero reference energy as the center of the band gap.

Next, we examined the distribution of Ef(VLi_j) around the LCO(104)/LLZO(001) interface, which is shown in Figure 12. In the sampling of LCO(104)/LLZO(001) interfaces, we excluded the interface structures that became metallic due to the in-gap state originated from the LLZO surface. The metallic interface structures had energies per interface area that were 2 orders of magnitude larger with respect to the most stable structure than those of the other insulating interface structures. The percentage of Li sites with low Ef(VLi_j) decreases for the LCO(104)/LLZO(001) interface compared to the LCO/LPS interface. However, the number of Li sites with low Ef(VLi_j) increases compared to that of the LCO/LPO case. This property is related to the small offset in the valence band of the LCO(104)/LLZO(001) case, where the electron transfer from SE to the cathode easily occurs compared to the LCO/LPO interface. The sites with low Ef(VLi_j) appear in the interface structures with rather high energies. In the LCO(104)/LLZO(001) interface, some LaO8 complexes in LLZO are broken at the interface and deform the atomic structure. As a result, a high-energy interface structure is formed, which can be an origin of Li+ transport resistance. The details of Ef(VLi_j) are provided in Figure S15 and Table S9.

Figure 12

Figure 12. Distributions of the Li sites classified by their Li vacancy-formation energies at the LCO(104)/LLZO(001) interface. The vacancy-formation energies of 36 Li sites in four different interface structures are calculated. The distributions are normalized by the total number of calculated Li sites. The blue bar graphs denote the distribution of all the calculated Li sites in LCO/LLZO, and the red bar graphs denote those of the calculated Li sites located in the LLZO region.

The reactivity of the LCO(104)/LLZO(001) surface was examined by estimating mutual cation exchange energies among Co atoms in the LCO phase and those of Zr, La, and Li atoms in the LPO phase. In Figure 13, we show the mutual cation exchange energies of Co ↔ Zr and Co ↔ La. The mutual exchange energy of Co ↔ Li is provided in Figure S16, and we only briefly describe the results. As shown in Figure 13, both cation exchange energies are endothermic. The Co ↔ La exchange energy is endothermic by over 1 eV, and in particular, the exchange of the Co atom in the second layer from the boundary of LCO/LLZO is endothermic by more than 3.0 eV and is less likely to occur. The endothermic reaction energies of the Co ↔ Zr exchange are 0.7–1 eV and are smaller than that of Co ↔ La. This suggests that the ion radii and oxygen ligand environment of Co atoms are more similar to those of Zr atoms than those of La atom. The Co ↔ Li exchange energies are 2–3 eV, and Li sites are present in the first and second layers from the LCO/LLZO boundary. Overall, the cation exchange of the LCO/LLZO interface is unlikely to occur. However, if we compare the LCO/LPO surface, where all the cation exchange reaction energies are endothermic by over 3 eV, the reaction layer formation related to the cation exchange at the LCO/LLZO interface seems easier than at the LCO/LPO interface.

Figure 13

Figure 13. (a) Structure of the LCO(104)/LLZO(001) interface (upper panel) and its corresponding (b) Co ↔ Zr and (c) Co ↔ La mutual cation exchange reaction energies (lower panel). The positive values of exchange energies indicate endothermic reactions.

3.4. Interface of Oxide Buffer Layer LTO

Finally, we analyzed the interface properties of the oxide buffer layer, which is often introduced between the oxide cathode and sulfide SE to reduce the interfacial resistance. We have previously investigated the effect of the oxide buffer layer LiNbO3 between LCO and LPS and found that the introduction suppresses the appearance of sites with low Ef(VLi_j) in the LPS side and the interfacial electron transfer leading to the LPS oxidation. In this study, to understand the common features of the buffer later, we examined Li4Ti5O12 (LTO), a representative oxide used as a buffer layer.
We first discuss a low-energy structure of the LTO(111)/LPS(010) interface (Figure 14), where no TiO6 octahedron is broken at the boundary to LPS, and the interface bond with S atoms of LPS is not formed, unlike in the case of LCO/LPS. Thus, the interface preserves the atomic structure of the bulk crystal. It is also found at the LTO/LPS interface that the Li atoms of LPS closest to the LTO surface are located on the bridge position between the O atoms of the LTO surface. The PDOS of the LTO/LPS interface is shown in Figure 15. In contrast to the LCO/LPS interface, there is no gap state around the interface. The CBM is composed of LTO and the LPS states are located 1 eV higher than the CBM, while the VBM consists of the LPS state and the states of LTO are lower than −1.5 eV with respect to the VBM. The adhesion energy between LTO and LPS is 0.019 eV/Å2 and is smaller than those of the LCO/LPS interfaces.

Figure 14

Figure 14. Optimized interface structures of LTO(111)/LPS(010). The insets show the detailed atomic structures at the interface. TiO6 and PS4 complexes are represented by light blue and green polyhedrons.

Figure 15

Figure 15. PDOS of the optimized interfaces of LTO(111)/LPS(010). Red line: total DOS; gray line: LTO atoms; blue line: LPS atoms. We set zero reference energy as the center of the band gap.

We then examined the distribution of the Li vacancy-formation energies around the LTO(111)/LPS(010) interface, as shown in Figure 16. The values of Ef(VLi_j) in the LTO phase are in the range of 3.0–4.0 eV, and these values are ∼1 eV smaller than the calculated value for the LTO bulk of around 5.0 eV. It reflects the valence band offset between the LTO and LPS. In the bulk LTO, the electron extracted with Li vacancy formation is located at the valence band top of LTO, while in the LTO/LPS interface, the electron is extracted from the LPS-originated band. With regard to the Li vacancy-formation energies in the LPS side, although the sites with Ef(VLi_j) = 2.0–2.5 eV are generated, the distribution of the sites with Ef(VLi_j) above 2.5 eV is widened compared to the that of LCO/LPS. In our sampling of Ef(VLi_j), no site with Ef(VLi_j) less than 2.0 eV was found. The electronic states and the vacancy-formation energies indicate that the dynamical Li+ depletion is suppressed by the LTO buffer later, which may lead to lower interfacial resistance.

Figure 16

Figure 16. Distributions of Li sites divided by their Li vacancy-formation energies at the LTO(111)/LPS(010) interface. The vacancy-formation energies of 31 Li sites in four different interface structures are calculated. The distributions are normalized by the total number of calculated Li sites. The blue bar graphs denote the distribution of all the calculated Li sites in LTO/LPS, and the red bar graphs denote those of calculated Li sites located in the LPS region.

At the LTO/LPS interface, we did not observe the stabilization of the interface structure by mutual cation exchange as observed in the LCO/LPS case, and both the Ti ↔ P and Ti ↔ Li cation exchange energies are over 1 eV endothermic. (The details are shown in Figures S19 and S20.) This result suggests that the effect of the LTO buffer layer is inert to the LPS surface. Therefore, the LTO buffer layer is effective from two viewpoints, suppressing the generation of Li sites with low Ef(VLi_j) and suppressing the cation diffusion into the sulfide electrolyte.
Here, we comment on the other oxide buffer layer. We previously evaluated the values of Ef(VLi_j) around the interface region between LiNbO3 (LNO) and LPS and demonstrated that the vacancy formations energies have an average of around 3.0 eV and a minimum of 2.4 eV. (21) These are larger than those of the present LTO/LPS interfaces, implying that the LNO buffer layer is superior to LTO for decreasing the interfacial resistance.
To conclude, we briefly describe the calculation results of the LCO(104)/LTO(111) interface. The details of the calculation are shown in section S7 of the Supporting Information. The probability of appearance of sites with low Ef(VLi_j) is very low at this interface. Sites with Ef(VLi_j) below 2.5 eV did not appear. Therefore, the coating of LTO on the LCO surface do not produce the interfacial resistive phase between these two phases.

4. Summary

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We investigated the LCO/LPS, LCO/LPO, LCO/LLZO, and LCO/LTO/LPS interfaces by using first-principles calculations. Statistics of physical quantities such as Li vacancy-formation energies (Ef(VLi_j)) and mutual cation exchange energies were evaluated for several solid–solid interfaces with reasonable stabilities. Subsequently, the interfacial reactivities and ionic resistances were discussed based on the calculated quantities.
Compared to the sulfide SE, oxide SEs such as LPO and LLZO clearly show fewer sites with low Ef(VLi_j) and are less reactive to the LCO surface. In the oxide SE, the large valence band offset at the cathode–SE interface suppresses the electron transfer from the electrolyte to the cathode; this causes a decrease in the number of sites with low Ef(VLi_j). These results indicate that the appearance of interfacial disorder is suppressed in oxide SEs; this is consistent with the recent experimental results (25) of interfaces between LCO and LiPON. Although LiPON is amorphous, we believe that our calculated models of LCO/LPO capture the characteristics of actual LCO/LiPON, such as band offsets and atomic structure at the interface. Furthermore, when considering the LPO and LLZO oxide SEs, there is a difference in the tendency of the generation of sites with low Ef(VLi_j). The observation can be mainly attributed to the difference in valence band offsets at the cathode and electrolyte. A smaller band offset in VBM in the LCO/LLZO interface compared to the LCO/LPO interface will allow easier electron transfer from the electrolyte; this results in SE oxidation and generates sites with low Ef(VLi_j). Furthermore, the LLZO interface tends to become a high-energy structure because of the atomic disorder caused by broken complexes such as LaO8 in LLZO. Therefore, a high-energy metastable state is likely to occur, which may induce dynamical Li+ depletion.
Different surface orientations of crystals at the boundary of the cathode and electrolyte were compared. Compared to the LCO(104) surface, the LCO(110) surface is more reactive to LPS and generates more sites with low Ef(VLi_j) at the boundary with LPS. It suggests that the Li conductive resistivity at the cathode-SE interface depends on the crystal orientation of the surface and that the LCO(110) surface has a higher interface resistance than that of LCO(104). This tendency is also observed at the boundary of the LCO/LPO interface. Other than the orientation dependence of the LCO cathode material, the orientation of LPO to the LCO interface also affects the generation of sites with low Ef(VLi_j). In addition, we show that high-energy interface structures show a tendency of increased number of sites with low Ef(VLi_j).
On the buffer coating layer, we calculated LTO/LPS and LTO/LCO interface models. The LTO surface suppressed the low Ef(VLi_j) of the sites and was inert to the LPS surface. The calculated results are consistent with the fact that LTO is an effective buffer layer oxide for sulfide SE. (12) The reason for the effectiveness of the buffer layer could be attributed to several factors, but in particular, the large valence band offset of the LTO/LPS interface could play an important role.
In this study, we limit the interfacial structures we dealt with to clean interfaces that are free from defects and reaction phase. For more realistic interface structure, a more efficient structure search method for interface region is needed. (23,24) Such a method will enable to examine more complicated interfaces such as Li6PS5Cl/Li2S (61) and Li3+xP1–xSixO4/LiFePO4 interfaces (62) with large resistances recently investigated.
The results on the atomic scale of the interfaces between the cathode and electrolyte and the comparison between oxide and sulfide SE interfaces provide useful guidelines for designing stable cathode–electrolyte and buffer oxide–electrolyte interfaces, which is a crucial bottleneck in the development of ASSBs.

Supporting Information

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The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsaem.0c02033.

  • Calculated bulk structures and vacancy formation energies of LCO, LPS, LPO, and LLZO; structure models, projected density of states, representative sampled structures, site-dependent vacancy formation energies, cation mixing energies, obtained in the calculations of the LCO(104)/LPS(010), LCO(110)/LPS(010), LCO(104)/LPO(001), LCO(104)/LPO(010), LCO(110)/LPO(010), LCO(104)/LLZO(001), LTO(111)/LPS(010), and LCO(104)/LTO(111) interfaces (PDF)

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Most electronic Supporting Information files are available without a subscription to ACS Web Editions. Such files may be downloaded by article for research use (if there is a public use license linked to the relevant article, that license may permit other uses). Permission may be obtained from ACS for other uses through requests via the RightsLink permission system: http://pubs.acs.org/page/copyright/permissions.html.

Author Information

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  • Corresponding Authors
    • Yukihiro Okuno - Research and Development Management Headquarters, FUJIFILM Corporation, 210 Nakanuma, Minamiashigara, Kanagawa 250-0193, Japan Email: [email protected]
    • Yoshitaka Tateyama - Center for Green Research on Energy and Environmental Materials (GREEN) and International Center for Materials Nanoarchitectonics (MANA), National Institute for Materials Science (NIMS), 1-1 Namiki, Tsukuba, Ibaraki 305-0044, JapanElements Strategy Initiative for Catalysts & Batteries, Kyoto University, 1-30 Goryo-Ohara, Nishikyo-ku, Kyoto 615-8245, JapanOrcidhttp://orcid.org/0000-0002-5532-6134 Email: [email protected]
  • Author
  • Notes
    The authors declare no competing financial interest.

Acknowledgments

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Y.O acknowledges the support of Mrs. M. Suzuki at FujiFilm Corporation. This work was supported in part by MEXT as “Program for Promoting Researches on the Supercomputer Fugaku (Fugaku Battery & Fuel Cell Project), Grant JPMXP1020200301, Elements Strategy Initiative, Grant JPMXP0112101003, and the Materials Processing Science project (“Materealize”), Grant JPMXP0219207397. The work was also supported by JSPS KAKENHI Grant JP19H05815. The calculations were performed on the K computer at the RIKEN AICS through the HPCI System Research Projects (project IDs: hp160081, hp170292, and hp190039).

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  • Abstract

    Figure 1

    Figure 1. Surfaces of (a) LiCoO2 (LCO)-(104), (b) LCO-(110), (c) β-Li3PS4 (LPS)-(010), (d) γ-L3PO4 (LPO)-(001), (e) Li7La3Zr2O12 (LLZO)-(001), and (f) Li4Ti5O12(LTO)-(111), examined in this work. Li, O, P, S, Co, La, Zr, and Ti are depicted as light green, red, purple, yellow, blue, brown, blue, and light blue spheres, respectively. CoO6, PS4, PO4, ZrO6, LaO8, and TiO6 complexes are represented by blue, green, gray, light green, brown, and light blue polyhedrons, respectively.

    Figure 2

    Figure 2. Calculated interface structures with the lowest energies of (a) LCO(104)/LPS(010) and (b) LCO(110)/LPS(010). The insets show the detailed atomic structures at the interface. CoO6 and PS4 complexes are represented by blue and green polyhedrons.

    Figure 3

    Figure 3. PDOS of the calculated lowest energy interface of LCO(104)/LPS(010). Red line: total DOS; green line: LCO atoms; blue line: LPS atoms; brown line: LCO atoms facing the vacuum; light blue line: the first LCO layer facing the LPS slab. We set zero reference energy as the center of the band gap. LCO vac and LCO 1st correspond to the LCO layer facing the vacuum and the interface with LPS, respectively.

    Figure 4

    Figure 4. Distributions of Li sites classified with the Li vacancy-formation energies at the (a) LCO(104)/LPS(010) and (b) both LCO/LPS interfaces, respectively. The vacancy-formation energies of 65 Li sites in 8 different interface structures (23 sites in three different interface structures) are calculated for LCO(104)/LPS(010) and (LCO(110)/LPS(010)). The distributions are normalized by the total number of calculated Li sites. The blue bars denote the distribution of all the calculated Li sites in the LCO/LPS and the red bars denote those of calculated Li sites located in the LPS region.

    Figure 5

    Figure 5. (a) Representative LCO(104)/LPS(010) interface structure with the site labels and the mutual cation exchange energies for (b) Co ↔ P and (c) Co ↔ Li.

    Figure 6

    Figure 6. Optimized interface structures of (a) LCO(104)/LPO(010) and (b) LCO(104)/LPO(001). The insets show the detailed atomic structures at the interface. CoO6 and PO4 complexes are represented by blue and gray polyhedrons.

    Figure 7

    Figure 7. PDOS of the optimized interfaces of LCO(104)/LPO(001). Red line: total DOS; green line: PDOS from LCO atoms; blue line: PDOS from LPO atoms; brown line: PDOS from LCO atoms facing the vacuum; light blue line: PDOS from first LCO layer facing the LPO slab. We set zero reference energy as the band gap center.

    Figure 8

    Figure 8. Distributions of Li sites divided by their Li vacancy-formation energies at the (a) LCO(104)/LPO(010) and (b) LCO(104))/LPO(001) interfaces. The vacancy-formation energies of 28 Li sites in four different interface structures and 36 sites in five different interface structures are calculated for LCO(104)/LPO(010) and LCO(104)/LPO(001), respectively. The distributions are normalized by the total number of calculated Li sites. The blue bar graphs denote the distribution of all the calculated Li sites in LCO/LPO, and the red bar graphs denote those of the calculated Li sites located in the LPO region.

    Figure 9

    Figure 9. (a) Schematic picture of the optimized LCO(104)/LPO(001) interface with the sites where we calculated mutual cation exchange energy. (b) Co ↔ P and (c) Co ↔ Li cation exchange energies corresponding to sites denoted in (a).

    Figure 10

    Figure 10. Optimized interface structures of LCO(104)/LLZO(001). The insets show the detailed atomic structures at the interface. CoO6, ZrO6, and LaO8 complexes are represented by dark blue, light green, and brown polyhedrons.

    Figure 11

    Figure 11. PDOS of the optimized interfaces of LCO(104)/LLZO(001). Red line: total DOS; green line: LCO atoms; blue line: LLZO atoms; violet line: LCO atoms facing the vacuum; light blue line: the first LCO layer facing the LLZO slab. We set zero reference energy as the center of the band gap.

    Figure 12

    Figure 12. Distributions of the Li sites classified by their Li vacancy-formation energies at the LCO(104)/LLZO(001) interface. The vacancy-formation energies of 36 Li sites in four different interface structures are calculated. The distributions are normalized by the total number of calculated Li sites. The blue bar graphs denote the distribution of all the calculated Li sites in LCO/LLZO, and the red bar graphs denote those of the calculated Li sites located in the LLZO region.

    Figure 13

    Figure 13. (a) Structure of the LCO(104)/LLZO(001) interface (upper panel) and its corresponding (b) Co ↔ Zr and (c) Co ↔ La mutual cation exchange reaction energies (lower panel). The positive values of exchange energies indicate endothermic reactions.

    Figure 14

    Figure 14. Optimized interface structures of LTO(111)/LPS(010). The insets show the detailed atomic structures at the interface. TiO6 and PS4 complexes are represented by light blue and green polyhedrons.

    Figure 15

    Figure 15. PDOS of the optimized interfaces of LTO(111)/LPS(010). Red line: total DOS; gray line: LTO atoms; blue line: LPS atoms. We set zero reference energy as the center of the band gap.

    Figure 16

    Figure 16. Distributions of Li sites divided by their Li vacancy-formation energies at the LTO(111)/LPS(010) interface. The vacancy-formation energies of 31 Li sites in four different interface structures are calculated. The distributions are normalized by the total number of calculated Li sites. The blue bar graphs denote the distribution of all the calculated Li sites in LTO/LPS, and the red bar graphs denote those of calculated Li sites located in the LPS region.

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    • Calculated bulk structures and vacancy formation energies of LCO, LPS, LPO, and LLZO; structure models, projected density of states, representative sampled structures, site-dependent vacancy formation energies, cation mixing energies, obtained in the calculations of the LCO(104)/LPS(010), LCO(110)/LPS(010), LCO(104)/LPO(001), LCO(104)/LPO(010), LCO(110)/LPO(010), LCO(104)/LLZO(001), LTO(111)/LPS(010), and LCO(104)/LTO(111) interfaces (PDF)


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