Interfacial Chemistry in Solid-state Batteries: Formation of

Supporting Information Interfacial Chemistry in Solid-state Batteries: Formation of Interphase and Its Consequences Shaofei Wang, Henghui Xu, Wangda Li, Andrei Dolocan and Arumugam Manthiram* Materials Science and Engineering Program & Texas Materials Institute The University of Texas at Austin, Austin, TX 78712, USA AUTHOR INFORMATION Corresponding Author *E-mail: manth@austin.utexas.edu (A. Manthiram) CONTENT: Section Ⅰ Thermodynamic Analysis of Interphase Formation and Consequences for Electrochemical Behaviors Section Ⅱ Supporting Figures and Tables Section Ⅲ Supplementary Videos S1

Section I: Thermodynamic Analysis of Interphase Formation and Consequences for Electrochemical Behaviors The formation of interphase is not only a simple result of a direct chemical reaction but also is affected by the electrochemical processes during battery cycling. To understand the formation and evolution of the interphase, first, the thermodynamic analysis of the electrochemical and chemical processes is given. Then, the consequences of the interphase formation with different properties are elaborated. Finally, the influence on the electrochemical window of the solid electrolyte is discussed as well. Figure S1. Schematic diagram of the symmetric cell Li-LYZP-Li. The schematic diagram of the cell structure and electrochemical reaction process are shown in Fig. S1. Regarding the anode side, the electrochemical reaction is the lithium stripping process: Li e - = Li +. Regarding the cathode side, two possible reactions could occur; one is the electrochemical reduction of the Zr: Zr + + xe - = Zr (4-x)+, and the other one is the lithium plating reaction: Li + + e - = Li. The chemical process should be determined by the Gibbs energy of the S2

electrochemical reaction processes. The Gibbs energy for these two reactions are given as follows: G Li Li =µ Li/Li ++η Li/Li ++ IR i INT + IR i INT /SE + IR i SE + IR i INT /SE + IR i INT +η Li + /Li +µ Li + /Li G Li Zr =µ Li/Li ++η Li/Li ++ IR i INT + IR i INT /SE + IR i SE + IR e INT + 1 x η + 1 Zr 4+ /Zr ( 4 x )+ x µ Zr 4+ ( 4 x )+ /Zr where µ Li/Li+ is the theoretical electrochemical potential for the oxidation of Li, µ Li+/Li is the theoretical electrochemical potential for the reduction of Li +, µ Zr4+/Zr(4- x)+ is the theoretical electrochemical potential for the reduction of Zr 4+, x is the number of electrons transferred in the reduction reaction, and η Li/Li+, η Li+/Li and η Zr4+/Zr(4-x)+ are the polarizations of the electrochemical reactions at the interface. I is the current density, R i-int is the Li + transport resistance in the interphase layer, R i-se is the Li + transport resistance in the solid electrolyte, R i-int/se is the Li + transport resistance at the interface between interphase and solid electrolyte, and R e-int is the electronic-transport resistance in the interphase layer. The electrochemical reaction during current flow depends on which process has a lower Gibbs energy. In order to compare the Gibbs energy of the two reactions, the same components in the two equations are removed and shown as follows: G Li Li IR i INT /SE + IR i INT +η Li + /Li +µ Li + /Li G Li Zr IR e INT + 1 x η + 1 Zr 4+ /Zr ( 4 x )+ x µ Zr 4+ ( 4 x )+ /Zr Therefore, the Gibbs energy of the electrochemical reaction is not only determined by the theoretical electrochemical potential (µ Li/Li+, η Li+/Li,and µ Zr4+/Zr(4- S3

x)+) and interfacial polarization of the electrochemical reaction (η Li/Li+, η Li+/Li, and η Zr4+/Zr(4-x)+ ), but also affected by the ionic and electronic transport through the interphase layers (R i-int and R e-int ) and across different interfaces (R i-int/se ). When the interphase has a very high ionic conductivity, but low electronic conductivity, R i-int and R i-int/se would keep relatively a small value as the thickness is increased, while the R e-int will significantly increase as the thickness is increased. Therefore, G Li-Li is mainly determined by µ Li+/Li and η Li+/Li, while G Li- Zr would be significantly increased when the thickness of the interphase is increased. The G Li-Zr would become larger than G Li-Li when the interphase grew beyond a certain thickness, resulting in the lithium plating reaction only. When the interphase has a very low ionic conductivity, but high electronic conductivity, R e- INT would keep a relatively small value, while the R i-int and R i-int/se will significantly increase when the thickness is increased. Therefore, G Li-Zr is mainly determined by µ Zr4+/Zr(4-x)+ and η Zr4+/Zr(4-x)+, while G Li-Li would significantly increase when the thickness of the interphase is increased. The G Li-Li value would become larger than G Li-Zr when the interphase grows beyond a certain thickness, resulting in an electrochemical reduction of Zr 4+. When both the electronic conductivity and ionic conductivity are very high or very low, no general conclusions could be simply deduced. The electrochemical process would be determined by the Gibbs energies of the two electrochemical reactions, which depend on the specific value of the factors. During the electrochemical process, the chemical reaction between lithium metal and solid electrolyte also occurs, where a very thin interphase layer can be S4

formed. The chemical reaction is to occur via two elementary steps: (1) the diffusion of reacting species through the interphase layer and (2) the reaction at the interface. Since the small lithium atom has a much faster diffusion rate than other chemical species, a reasonable assumption can be made that the direct chemical reaction would mainly rely on the diffusion of lithium atoms across the interphase and their reactions with the solid electrolyte. As the transport of lithium atoms requires simultaneous diffusion of electrons and lithium ions, the chemical reaction process would be affected by the electronic conductivity and ionic conductivity of the interphase. Only when the interphase has high ionic conductivity and electronic conductivity at the same time, can the chemical reaction can continuously occur between the solid electrolyte and lithium metal, resulting in an increase in the interphase thickness. If either electronic conductivity or ionic conductivity is very low, only a very thin interphase layer forms upon direct chemical reaction due to the limited diffusion rate of lithium. In summary, both the electrochemical and chemical reactions occur at the same time, resulting in an interphase formation. The ionic and electronic conductivities of the interphase in turn affect the electrochemical and chemical processes. If both the electronic and ionic conductivity are very high, an interphase would be easily formed upon the contact between the solid electrolyte and the metal anode. Regardless of which electrochemical reaction occurs during cycling, the electrolyte would be continuously consumed during cycling because of the direct chemical reaction upon contact. If the interphase has a very high electronic conductivity while very low ionic conductivity, only a very thin interphase could be formed by S5

direct chemical reaction. Electrochemical reaction would result in a continuous growth of the interphase because of the lower Gibbs energy of the electrochemical reaction of the solid electrolyte. If the interphase has a lower electronic conductivity while a high ionic conductivity, the direct chemical reaction could only result in a very thin interphase. The electrochemical reaction may result in an increase of the thickness of the interphase at the start of cycling. When the interphase grows beyond a certain thickness, the electrochemical reduction of the solid electrolyte would be stopped, a stable interphase would be formed, and only the lithium stripping/plating process could happen. If both the electronic and ionic conductivities were very low, the direct chemical reaction would result in a very thin interphase layer. Regardless of which electrochemical reaction happened during cycling, the formation of interphase layer would lead to a very large interfacial resistance. Therefore, only the interphase with low electronic conductivity and high ionic conductivity enables a stable electrochemical lithium plating and striping reaction. These results are summarized in Table 1 in the main text. After the formation of interphase with a certain thickness, the electrochemical reduction of solid electrolyte at cathode side would be stopped, only the electrochemical lithium plating and stripping could occur because of the lower Gibbs energy, resulting in a high coulombic efficiency of charge and discharge. During cycling, the proper thickness of the interphase layer could be retained dynamically on the top of the lithium anode during cycling because of the chemical reduction and electrochemical reduction, which could effectively prevent fast growth of dendrite tips and enable a uniform plating of lithium during cycling. S6

The high ionic conductivity and proper thickness will give rise to a low resistance of the interphase layer, enabling the battery operation at a low inner resistance. Therefore, the ideal interphase for metal anode solid-state battery should exhibit low electronic conductivity, high ionic conductivity, proper thickness, uniform coverage, and long-term stability. Figure S2. Schematic graph of the electrochemical window of a solid electrolyte with interphase layers. Besides the effects on lithium plating, an interphase with a high ionic conductivity and low electronic conductivity could also widen the electrochemical window of the solid electrolyte materials (Fig. S2). According to previous thermodynamic analysis, the formation of interphase would give rise to an increase in the Gibbs energy of the electrochemical reduction of the electrolyte. If the Gibbs energy of the electrochemical reduction of the electrolyte is higher than the Gibbs energy of the cathode electrochemical reaction, the reduction of the electrolyte would be stopped. Similar to the cathode side, the interphase formed on the anode side could also increase the Gibbs S7

energy of electrochemical oxidation of the solid electrolyte. If the Gibbs energy of electrochemical oxidation of the electrolyte is larger than the anode electrochemical reaction, the electrochemical oxidation of the solid electrolyte would stop, only the effective electrochemical reaction takes place afterwards. Therefore, the formation of interphases with low electronic conductivity could widen the electrochemical stability window. At the same time, high ionic conductivity is required to reduce the total resistance of the modified solid electrolyte. Finally, a thermodynamically unstable but kinetically stable solid electrolyte could be obtained by the formation of an interphase with low electronic conductivity and high ionic conductivity. S8

Section Ⅱ Supporting Figures and Tables Figure S3. Impedance of the solid electrolytes with ionic blocking electrode and reversible electrodes: (a) Nyquist and (b) bode plots of Au-LYZP-Au and Li-LYZP-Li cells. (c) Nyquist plots and (d) bode plots of Au-NZSP-Au and Na-NZSP-Na cells. The conductivities of LYZP and NZSP are, respectively, 3 10-5 s cm -1 and 5 10-4 s cm -1. S9

Table S1. Parameters for the impedance fitting of the symmetric cells Li-LYZP-Li and Na-NZSP-Na Li-LYZP-Li Na-NZSP-Na Component Value Component Value R 1 1689 Ω R 1 497.5 Ω R 2 13678 Ω R 2 434.7 Ω Q 1 3.8 10-9 S/s n Q 1 8.3 10-9 S/s n n 1 0.78 n 1 0.91 C 1 6.3 10-8 F C 1 2.9 10-8 F R 3 24382 Ω R 3 2403 Ω Q 2 2.4 10-8 S/s n Q 2 6.4 10-7 S/s n n 2 0.79 n 2 0.64 C 2 1.7 10-7 F C 2 2.4 10-7 F R 4 2650 Ω R 4 3845 Ω Q 3 3.0 10-4 S/s n Q 3 4.5 10-5 S/s n n 3 0.38 n 3 0.43 C 3 4.2 10-4 F C 3 4.5 10-4 F Figure S4. SEM images of the pristine ceramic solid electrolytes and after contacting with lithium or sodium metal at 75 o C for 10 min: (a) pristine LYZP, (b) LYZP-Li, (c) LYZP-Na, (d) pristine NZSP, (e) NZSP-Li, and (f) NZSP-Na. The corresponding photo of each sample is inserted. S10

Figure S5. (a) XPS survey spectra of the interphase formed between LYZP and Li metal with different sputtering time of 10, 20, and 65 s. High-resolution XPS spectra of Zr 3d (b and f), P 2p (c and g), Y 3d (d and h), O 1s (e and i) collected from LYZP before (upper row) and after (bottom row) contacting with Li metal. S11

Figure S6. TOF-SIMS depth profiles and corresponding 3D view of the sputtered volumes of (a) LYZP (Zr + in green), (b) LYZP Na (Zr + in green and Na + in red), (c) LYZP Li (Zr + in green and Li + in red), (d) NZSP (Zr + in green), (e) NZSP Na (Zr + in green and Na + in red), and (f) NZSP Li (Zr + in green and Li + in red). The depth profiles were acquired in high current mode over 100 x 100 µm 2 areas using a Bi + analysis ion beam at 30 kev ion energy and a O + 2 sputtering ion beam S12

at 2 kev ion energy used to ablate the surface over an area of 300 x 300 µm 2 centered around the acquisition area. The sputtered depth is relative, therefore presented as O + 2 sputtering time; however, a sputtering rate of 1 nm/s could be estimated in this case. Figure S7. Cycled NZSP ceramic collected from a symmetric cell using sodium anode. (a) Optical image and TOF-SIMS element mapping of (b) Na +, (c) Zr +, (d) Si +, (e) P +, and (f) O +. S13

Section Ⅲ Supplementary Videos The supplementary videos were obtained from the TOF-SIMS depth profiles shown in Figure S6 in the Supporting Information. A TOF-SIMS 5 spectrometer (ION-TOF GmbH 2010) was used for the TOF-SIMS studies. The analysis chamber was maintained at a base pressure of 10-9 mbar. All detected secondary ions of interest had a mass resolution of > 5,000 and possessed positive polarity. A pulsed 30 kev Bi + (20 ns) analysis ion beam set in either the High Current mode or Burst Alignment mode (with seven bursts) was applied for depth profiling or high lateral resolution mapping (resolution: 200 nm) analysis, respectively. The depth profiles were acquired in a non-interlaced mode (sequential analysis and sputtering), while raster scanning the Bi + analysis ion beam (~ 3 pa measured sample current) over an area of 100 100 µm 2 and O + 2 sputtering with an ion beam at 2 kev ion energy (~ 620 na measured sample current) over an area of 300 300 µm 2 centered around the acquisition area. The sputtered depth is relative, therefore, presented as O + 2 sputtering time; however, a sputtering rate of 1 nm/s could be estimated in this case. At each step along the depth profile, the analysis beam yields intensity distribution maps for various masses of interest. By plotting the total number of counts in such maps for a given species of interest as a function of O + 2 sputtering time, the depth profile of that particular species was obtained. The videos pass sequentially through these maps at different depths/o + 2 sputtering times. Based on the elemental spatial distribution, 3D structures of interphases and dendrites could be reconstructed. Supplementary Video 1: LYZP Ceramic, Zr (green) spatial distributions in LYZP ceramic. S14

Supplementary Video 2: LYZP-Na Interphase, Zr (green) and Na (red) spatial distributions in LYZP-Na interphase. Supplementary Video 3: LYZP-Li Interphase, Zr (green) and Li (red) spatial distributions in LYZP-Li interphase. Supplementary Video 4: NZSP Ceramic, Zr (green) spatial distributions in NZSP ceramic. Supplementary Video 5: NZSP-Na Interphase, Zr (green) and Na (red) spatial distributions in NZSP-Na interphase. Supplementary Video 6: NZSP-Li Interphase, Zr (green) and Li (red) spatial distributions in NZSP-Li interphase. Supplementary Video 7: Li-LYZP-Li Cycled Interphase, Zr (green) and Li (red) spatial distributions in interphase of Li-LYZP-Li cell. Supplementary Video 8: Na-NZSP-Na Cycled Interphase, Zr (green) and Na (red) spatial distributions in Na-NZSP-Na cell Supplementary Video 9: Na-NZSP-Na Dendrite, Na dendrite (blue) spatial distributions in Na-NZSP-Na cell. S15