In-situ visualization of the space-charge-layer effect on interfacial lithium-ion transport in all-solid-state batteries

The space charge layer (SCL) is generally considered one of the origins of the sluggish interfacial lithium-ion transport in all-solid-state lithium-ion batteries (ASSLIBs). However, in-situ visualization of the SCL effect on the interfacial lithium-ion transport in sulfide-based ASSLIBs is still a great challenge. Here, we directly observe the electrode/electrolyte interface lithium-ion accumulation resulting from the SCL by investigating the net-charge-density distribution across the high-voltage LiCoO2/argyrodite Li6PS5Cl interface using the in-situ differential phase contrast scanning transmission electron microscopy (DPC-STEM) technique. Moreover, we further demonstrate a built-in electric field and chemical potential coupling strategy to reduce the SCL formation and boost lithium-ion transport across the electrode/electrolyte interface by the in-situ DPC-STEM technique and finite element method simulations. Our findings will strikingly advance the fundamental scientific understanding of the SCL mechanism in ASSLIBs and shed light on rational electrode/electrolyte interface design for high-rate performance ASSLIBs.

The authors reported in-situ study of SCL formed at LCO/LPSCl interface by DPC STEM. This is indeed interesting new challenge and should give very important information if obtained data were properly interpreted. However, the authors interpretation of DPC STEM results appears to be still missing some points. To visualize SCL at heterointerfaces, it is essential to differentiate the pure SCL contribution from the positive and negative charge layers resulted from the mean-inner-potential difference across the two different phases forming the heterointerfaces.
However, the authors do not discuss the mean-inner-potential effect. Indeed, the mean-inner-potential effect can also accounts for the negative and positive charge visualized in Fig. 1d. The LCO/LPSCI/BTO triple-phase interface is more complex structure, so the mean-inner-potential effect in the DPC image should be discussed and differentiated from the pure SCL effect. Furthermore, polarities of the BTO nanoparticles may also affect the DPC images, but not considered here. Therefore, I cannot recommend this paper for Nature Communications.
Response: Thank you very much for your kind comments and helpful suggestions. We have revised the manuscript according to your kind suggestions. The revisions are highlighted with yellow in the manuscript and supplementary information.
(1) To visualize SCL at heterointerfaces, it is essential to differentiate the pure SCL contribution from the positive and negative charge layers resulted from the mean-inner-potential difference across the two different phases forming the heterointerfaces. However, the authors do not discuss the mean-inner-potential effect. Indeed, the mean-inner-potential effect can also accounts for the negative and positive charge visualized in Fig. 1d. The LCO/LPSCI/BTO triple-phase interface is more complex structure, so the mean-inner-potential effect in the DPC image should be discussed and differentiated from the pure SCL effect.
Response: Thank you very much for your useful suggestions. We fully agree that it is essential to differentiate the pure SCL contribution from the positive and negative charge layers resulted from the mean-inner-potential (MIP) difference across the two different phases forming the heterointerfaces. In the initial manuscript, we only focused on differentiating the pure SCL contribution from the effect of the MIP and possible dynamical diffraction at bias voltage by subtracting the corresponding electric-field result at 0 V before the partial differential treatment, [1][2][3] but neglected the relevant discussions without bias voltage. Following your suggestions, we have added the corresponding discussions on page 4 and 8 in the manuscript, and page 7, 10−12 in the supplementary information .
The MIP is a volumetric average of the electrostatic potential in a material with respect to a distant vacuum reference region at 0 V. 4,5 The MIP is an intrinsic material property, which depends on its structure, elemental composition, and electronic configuration. The MIP originates from the opposing electric field contributions of the positive atomic nuclei in the material, and partial screening by dispersed electron clouds. Therefore, the MIP is always a net positive potential, and equal in the same material 4,6 . Thus, the electric field caused by MIP is a constant in our DPC-STEM specimens with uniform thickness. The charge density we offered is obtained by partially differentiating the electric-field. The partial differential result of the equal electric field is zero. As a result, the effect of MIP on the charge distribution can be eliminated in the same material. Although the dynamical diffraction can affect the electric field of the sample with different crystal orientations, [7][8][9] similarly, the effect of the dynamic diffraction can also be eliminated by the partial differential treatment. However, the partial differential treatment unavoidably brings about a sudden change at the interface (also called "edge effect"), which will influence the charge distribution at the interface to some extent. To explain more clearly, the electric field caused by MIP of LCO and LPSCl is assumed to be 50 V/nm and 80 V/nm, respectively ( Supplementary Fig. 10a). After the same partial differential treatment as before, it can be found that the effect of MIP has been be eliminated except obvious "edge effect" (Supplementary Fig. 10b). As for the LCO/LPSCl interface without bias voltage, much more charges are accumulated at the interface, which can neutralize some effect of false image from "edge effect". Therefore, the DPC-STEM result of LCO/LPSCl interface can still appear the charge distribution with positive and negative charge separation. By comparison, much less charges are accumulated at the interface after BTO modification. Accordingly, the effect of false image from "edge effect" is particularly obvious. Thereupon, the DPC-STEM result of LCO/LPSCl interface does not appear the obvious charge distribution with positive and negative charge separation, but appears a false image of only the positive charge layer. Since there is some inaccuracy in the DPC-STEM results without bias voltage, we have moved these results to the supplementary information just for reference because it can still explain the charge distribution of BTO-LCO/LPSCl interface from the side. The corresponding discussions have been supplemented on page 4 and 8 in the manuscript, and page 7, 10−12 in the supplementary information . Figure 10. Schematic illustration the "edge effect" on the DPC result of the charge distribution at the interface without bias voltage. a, The assumed electric-field results caused by MIP of LCO (e.g. 50 V/nm) and LPSCl (e.g. 80 V/nm). b, The partial differential results of Supplementary Fig. 10a. (2) Furthermore, polarities of the BTO nanoparticles may also affect the DPC images, but not considered here.

Supplementary
Response: Thank you very much for your kind suggestion. The electric field from the SCL or the polarity of the BTO nanoparticles does deflect electron beam slightly and thus affect the DPC images, but this deflection effect is exactly the basis of our DPC imaging. [10][11][12] However, the DPC technique really can't differentiate the individual effect from the polarity of the BTO nanoparticles on the DPC images, because the obtained DPC image is the integrated result of the SCL and polarity of the BTO nanoparticles after modification. Nevertheless, there is no doubt that the polarity of the BTO nanoparticles does affect the distribution of SCL. What we are concerned about in this manuscript is the evolution of SCL at bias voltage after BTO modification. And the obtained DPC results do indicate that much less charges are accumulated at the interface after BTO modification, which is the effect from the polarity of the BTO nanoparticles. Moreover, the effect from the polarity of the BTO nanoparticles on the SCL has also been confirmed by FEM simulation results, which is consistent with the in-situ DPC results.
On the other hand, actually, the quantitative measurement of the evolution of the SCL layer and the polarity of the BTO nanoparticles during the charge and discharge process is an attractive but challenging project. In this regard, in-situ HADDF-STEM and ABF-STEM characterization can be more effective, because there has been reported that the polarity of BaTiO 3 can be calculated by measuring the average Ti displacement using HADDF-STEM combined with ABF-STEM. [13][14][15] Therefore, we will give more in-situ HADDF-STEM and ABF-STEM results with quantitative information in our next work.

Minor comments:
On Lines 178-187, the description of the phenomena is not very clear. The authors should explain more clearly and concretely how lithium ions migrate and the charge distribution varies.
Response: Thank you very much for your useful suggestion. To better understand how lithium ions migrate and the charge distribution varies, we have given a schematic illustration in Fig. 5c.
It is recommended that you can refer to this schematic illustration when read this description of the phenomena. Moreover, according to your kind suggestion, we have also revised the description of the phenomena to explain more clearly and concretely as far as possible.
Under the built-in electric field of BTO, the lithium ions will redistribute on the LCO/LPSCl/BTO triple-phase interface (TPI). Driven by the Coulomb interaction, both lithium ions in LPSCl initially located behind the BTO (near the side of positive poles of BTO) and lithium ions in LCO originally located across from the BTO (near the side of negative poles of BTO) will migrate toward the vicinities of the LCO/LPSCl/BTO TPI in order to maintain local charge neutralities. Owing to the limited action scope of Coulomb interaction, the amount of lithium ions that migrate to the interface decreases as they move away from the LCO/LPSCl/BTO TPI. Therefore, overall, the lithium-ion-deficient negative charge region on the LPSCl side and the lithium-ion-enriched positive charge region on the LCO side should be significantly restrained.
Unfortunately, the result of corresponding charge distribution at 0 V was not obtained by DPC-STEM due to the greater impact from the "edge effect". As for the LCO/LPSCl interface without bias voltage, much more charges are accumulated at the interface, which can neutralize some effect of false image from "edge effect". Therefore, the DPC-STEM result of LCO/LPSCl interface can still appear the charge distribution with positive and negative charge separation. By comparison, much less charges are accumulated at the interface after BTO modification.
Accordingly, the effect of false image from "edge effect" is particularly obvious. Thereupon, the DPC-STEM result of LCO/LPSCl interface does not appear the obvious charge distribution with positive and negative charge separation, but appears a false image of only the positive charge layer.
Since there is some inaccuracy in the DPC-STEM results without bias voltage, we have moved these results to the supplementary information just for reference because it can still explain the charge distribution of BTO-LCO/LPSCl interface from the side. The corresponding discussions have been revised on page 8 in the manuscript. Response: Thank you very much for the good question. As the answers above, the partial differential treatment unavoidably bring about a sudden change at the interface (also called "edge effect"), which will influence the charge distribution at the interface to some extent. As for the LCO/LPSCl interface without bias voltage, much more charges are accumulated at the interface, which can neutralize some effect of false image from "edge effect". Therefore, the DPC-STEM result of LCO/LPSCl interface can still appear the charge distribution with positive and negative charge separation. By comparison, much less charges are accumulated at the interface after BTO modification. Accordingly, the effect of false image from "edge effect" is particularly obvious. More details of FEM simulations should be described. What chemical potentials of lithium ion were assumed?
Response: Thank you very much for your nice suggestion. According to your suggestion, the more details of FEM simulations have been described on page 15 in the manuscript. Our FEM simulations are based on the semiconductor analogy via the commercial software COMSOL Multiphysics. In this software, the parameters to be assumed include the relative dielectric constant, the band gap, the electron affinity, the state effective density (valence band and conduction band), electron mobility and hole (lithium-ion) mobility. Therefore, the chemical potential of lithium ions was not directly assumed in our FEM simulations. The chemical potential of lithium ions in this work is related to the inherent properties of semiconductor materials. The chemical potential of lithium ions in LCO and LPSCl reported in previous literature 16,17 is about −4.02 eV and −2 eV, respectively.
In Fig. 6b the total potential difference looks smaller than Fig. 6a. The lithium diffusion may stop when the chemical potential and electrostatic potential is balanced. Why does the lithium diffusion stop in the case of Fig. 6b?
Response: Thank you very much for this question. Takada et al. 18 reported that solid electrolytes will suffer from anodic polarization at the interface when contacting high-voltage cathodes. Since the electrochemical potential of lithium ions (μL i + = μ Li + + eϕ, where μL i + and μ Li + are the electrochemical and chemical potential of lithium ions, respectively, and e and ϕ are the elementary charge and the local electrostatic potential, respectively) should be constant across the interface, the anodic polarization increases the electrostatic energy (eϕ) and thus decreases μ Li + on the electrolyte side 19 . Additionally, lithium ions are weakly bonded to the anionic framework in sulfide electrolytes, indicating relatively high μ Li + in the bulk. Therefore, the lithium-ion concentration on the LPSCl side of the interface will decrease, while the lithium-ion concentration on the LCO side of the interface will increase. And as you pointed out, the lithium diffusion may be stopped when the chemical potential and electrostatic potential is balanced. This is also the origin of the internal electrical field from SCL. After introducing a reverse electric field from the polarity of the BTO nanoparticles, the interface lithium ions will be redistributed, which leads to the restrained SCL effect similar to the result of the suppressed lithium diffusion from LPSCl to LCO. Therefore, in Fig. 6b the total potential difference looks smaller than Fig. 6a. When the chemical potential and electrostatic potential is balanced in the BTO-LCO/LPSCl interface, the lithium diffusion will be also stopped in the case of Fig. 6b.
In Fig. 4e-i, it is not clear if the charge density at 0 V is subtracted similarly in Fig. 1.
Response: Thank you very much for your question. In Fig.4e−i, the charge density at 0 V is subtracted similarly in Fig. 1. The corresponding description has been supplemented on page 8 in the manuscript.

Replies to Reviewer #2:
High interface impedance is one of the bottle neck in the solid state battery technology, and the so-called space charge layers (SCL, also called electrical double layer) might be one of the culprit.
Direct microscopy imaging of the SCL effect has hitherto not possible. By using the latest imaging technology called differential phase contrast -scanning transmission electron microscopy technique and shown that the thickness of the SCL was 10 nm. Moreover, they also concluded that the maximum potential height of the SCL was 1.3 V. Although it is an important advancement for the quantitative measurement of the SCL, it may not actually reflect the true state of the SCL because they did not consider the effects of the MIP and possible dynamical diffraction as the first reviewer pointed out. From our DPC results ( Fig. 1 and Fig. R1) of LCO/LPSCl interface, it can be found that the plausible width of the SCL is about 10−20 nm at the lower bias voltage (e.g. 1.0,

V).
With the increasing of the bias voltage, the width and electric-field seem to get larger.
Specially, width expansion to the cathode side may be more pronounced than expansion to the electrolyte side. Nevertheless, based on the existing DPC imaging technique, it is still difficult to accurately identify the width and electric-field of the SCL evolving with the bias voltage.
Therefore, the key point of our manuscript has been put on the interfacial charge distribution and accumulation resulting from SCL. Anyway, we will keep an eye on your good questions and try to make new progress in future.

Reviewers' Comments:
Reviewer #1: Remarks to the Author: After reading the response letter, I still confused about the authors' explanation. In DPC STEM, what we initially obtain should be the electric field map, that is the differential of the electrostatic potential. This is different from electron holography. Electron holography visualizes electrostatic potential. So, what the color contrast in Fig1? I thought it should be related to in-plane electric field vector but there is no such color wheel. If this is the total charge density map obtained by differentiating the electric field vector map obtained by DPC STEM, it should be well documented.
The MIP difference at the heterointerface causes built-in electric field. Because of this, further differentiation of DPC images also causes contrast at the interface due to the MIP difference. Therefore, when we observe the charge density map of the heterointerface by differentiating DPC, the image should be the superposition of the charges due to the built-in electric field (MIP difference) and the charges due to the redistribution of ions and electrons at the interface. The authors obviously would like to visualize the latter, but the former is always there. Therefore, we should extract the latter from the images somehow. This is what I said the effect of MIP. The authors say in the response, "The partial differential result of the equal electric field is zero. As a result, the effect of MIP on the charge distribution can be eliminated in the same material." If there is no MIP differences, the differentiation will eliminate the electric field effect. BUT, at the interface, there must be the MIP difference and the resultant built-in electric field. Supplementary Fig10 is very confusing. MIP does not cause the electric field in the constant thickness, but MIP gradient causes the electric field. So what the authors called "edge effect" is the built-in electric field due to the difference in MIP. This electric field component due to the MIP differences should be removed from the DPC images in order to discuss the true SCL structures. Therefore, this point must be cleared.
Reviewer #2: Remarks to the Author: All my questions have been clearly addressed by the authors. I recommend publication in its present form.

Replies to Reviewer #1:
After reading the response letter, I still confused about the authors' explanation. In DPC STEM, what we initially obtain should be the electric field map, that is the differential of the electrostatic potential. This is different from electron holography. Electron holography visualizes electrostatic potential. So, what the color contrast in Fig. 1? I thought it should be related to in-plane electric field vector but there is no such color wheel. If this is the total charge density map obtained by differentiating the electric field vector map obtained by DPC STEM, it should be well documented.
Response: Thank you very much for your question. As you mentioned above, in DPC-STEM measurements, what we initially obtain is exactly the electric field map. In the following we will detail what the color contrast in Fig. 1. In Fig. 1 can be removed from the DPC electric field images at different bias voltages by subtracting the corresponding electric-field result at 0 V before the partial differential treatment (described in detail on page 15, 16 of manuscript). [1][2][3] So, in order to study the true SCL effect on interfacial lithium-ion transport, we investigate the interface net electric field, in which the electric field component due to the MIP difference has been removed from the DPC electric field images at different bias voltages. Supplementary Fig. 6 shows the corresponding net electric field map of According to the Gauss's law, the charge density map can be obtained by calculating the differential of the electric field map measured by DPC-STEM. [4][5][6][7][8][9] Therefore, the color contrast in The MIP difference at the heterointerface causes built-in electric field. Because of this, further differentiation of DPC images also causes contrast at the interface due to the MIP difference.
Therefore, when we observe the charge density map of the heterointerface by differentiating DPC, the image should be the superposition of the charges due to the built-in electric field (MIP difference) and the charges due to the redistribution of ions and electrons at the interface. The authors obviously would like to visualize the latter, but the former is always there. Therefore, we should extract the latter from the images somehow. This is what I said the effect of MIP. The authors say in the response, "The partial differential result of the equal electric field is zero. As a result, the effect of MIP on the charge distribution can be eliminated in the same material." If there is no MIP differences, the differentiation will eliminate the electric field effect. BUT, at the interface, there must be the MIP difference and the resultant built-in electric field. Supplementary   Fig. 10  removed from the DPC electric field images at different bias voltages by subtracting the corresponding electric-field result at 0 V before the partial differential treatment. 1-3 Therefore, the net charge density distribution results in the DPC images at different bias voltages exactly reflect the effect of the true SCL, which is enough to support our conclusion.
Of course, in order to better understand the pristine charge density distribution from the true SCL, this electric field component due to the MIP difference should be best removed from the DPC electric field images at 0 V before the partial differential treatment. However, although we can obtain the pristine electric field of cathode and electrolyte respectively before their contact, the electric field component due to the MIP difference at 0 V can't be removed accurately by subtracting because the electric field due to the MIP difference at the interface has changed after cathode/electrolyte contact, accompanied by the electric field generated by the migration of Li ions (i.e. SCL). Therefore, in Supplementary Fig. 10 (last submitted supplementary information), the schematic illustration of the "edge effect" on the DPC result of the charge density distribution at the interface without bias voltage is really not accurate, because the electric field caused by MIP of LCO and LPSCl were assumed as a constant respectively without considering the change of interface electric field after cathode/electrolyte contact. As a result, we have deleted this figure in the supplementary information. However, there is no doubt that the built-in electric field due to the MIP difference does interfere the DPC-STEM result (only from the SCL) at 0 V to some extent.
Unfortunately, to the best of our knowledge, so far there have been no any feasible methods to remove the electric field component due to the MIP difference from the DPC images at 0 V. As a result, this is also why the previous studies with in-situ EH-TEM or DPC-STEM didn't show the result at 0 V. [1][2][3]16 The Li element mapping obtained by EELS can reflect the migration of Li ions after cathode/electrolyte contact, 17-19 so we further analyze the Li and Co elemental profiles from the EELS line scan (Supplementary Fig. 8) at 0 V on the interface. On the cathode side, it can be found that interfacial lithium ions are more than bulk lithium ions before BTO coating ( Supplementary Fig. 8a,c). This indicates that there appears obvious lithium-ion enrichment on the LCO side at the interface due to the lithium-ion diffusion from electrolyte to cathode. However, this lithium-ion enrichment on the LCO side is clearly suppressed after BTO coating ( Supplementary Fig. 8b,d).