Kinetics of all-solid-state sulfur cathodes

Journal Pre-proof Kinetics of All-Solid-State Sulfur Cathodes Yuxing Wang, Tongjie Liu, Luis Estevez, Jitendra Kumar PII:

S2405-8297(20)30045-3

DOI:

https://doi.org/10.1016/j.ensm.2020.02.006

Reference:

ENSM 1088

To appear in:

Energy Storage Materials

Received Date: 25 November 2019 Revised Date:

19 January 2020

Accepted Date: 5 February 2020

Please cite this article as: Y. Wang, T. Liu, L. Estevez, J. Kumar, Kinetics of All-Solid-State Sulfur Cathodes, Energy Storage Materials, https://doi.org/10.1016/j.ensm.2020.02.006. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier B.V.

Author Contribution Statement Yuxing Wang: Conceptualization, Methodology, Software, Validation, Formal Analysis, Investigation, Resources, Writing – Original Draft, Writing – Review & Editing, Visualization, Supervision, Project administration Tongjie Liu: Investigation, Resources Luis Estevez: Resources Jitendra Kumar: Supervision, Project administration, Funding acquisition

Kinetics of All-Solid-State Sulfur Cathodes Yuxing Wanga,*, Tongjie Liub, Luis Esteveza, Jitendra Kumara,b,* a University of Dayton Research Institute, 300 College Park, Dayton, OH, 45469-7531, USA b University of Dayton, 300 College Park, Dayton, OH, 45469-7531, USA Corresponding author * Dr. Yuxing Wang: [email protected], * Dr. Jitendra Kumar: [email protected] ORCID Yuxing Wang: 0000-0002-7828-9399

Acknowledgments This was sponsored by the Federal Aviation Administration under the Contract No. of DTFACT16-C-00045. The authors are grateful to Prof. Wei Lai at Michigan State University for helpful suggestions. We thank Dr. Badri Shyam for his help with XRD characterization.

Conflicts of interest The authors declare no competing financial interest.

Kinetics of All-Solid-State Sulfur Cathodes Abstract All-solid-state lithium sulfur batteries (ASLSB) have many advantages over liquid electrolytebased lithium sulfur batteries such as high sulfur utilization, low electrolyte-to-sulfur ratio and low self-discharge. However, the kinetics of all-solid-state sulfur cathodes is not well understood, which is critical to achieve their full potential. In this work, we determine the contributions of different processes to the overall kinetics of sulfur electrodes using Electrochemical Impedance Spectroscopy (EIS) and Gravimetric Intermittent Titration Technique (GITT). We show that the impedance of sulfur electrodes can be well described by the Transmission Line Model (TLM). It is found that the kinetics of the sulfur electrode is determined primarily by ionic migration at the electrode level and diffusion within the sulfur active materials. Cell performances with different electrode compositions are compared. Based on this understanding, we compared kinetics of sulfur electrodes with different solid electrolytes and mixing methods. Electrodes using amorphous sulfide solid electrolyte and impregnated S/C composites display the best kinetics. ASLSB possess high capacities at moderate rates at room temperature, and can operate even at 120 °C. Combined with the negligible self-discharge over a year, we believe that ASLSB is a promising candidate for as high-energy primary batteries.

Keywords: solid state battery; sulfur electrode; transmission line model; lithium primary battery

1. Introduction Lithium sulfur (Li-S) batteries have higher theoretical energy densities than state-of-the-art lithium ion batteries. The majority of the Li-S battery research employs ether-based liquid electrolytes. Despite three decades of research, commercialization of liquid electrolyte-based LiS batteries still faces great fundamental challenges such as short cycle life, low coulombic efficiencies, poor safety and high self-discharge, etc..[1,2] More importantly, sulfur conversion relies on the dissolution of intermediate products, lithium polysulfides. As a result, the electrolyte quantity relative to sulfur (E/S ratio in mL/g) needs to be high due to the limited solubility of polysulfides, which lowers the overall energy densities.[3] All-solid-state lithium sulfur batteries (ASLSB) have been gaining popularity recently. In ASLSB, sulfur is directly converted to Li2S in the solid state. Such mechanism does not rely on the quantity of the electrolyte, so an E/S ratio of less than 1 (in g/g) can be easily achieved which translates into much higher practical specific energies and energy densities. Furthermore, polysulfide dissolution and shuttling effects are eliminated, so the self-discharge rate is much lower. Since sulfur is a poor ionic and electronic conductor, sulfur, conductive carbon and sulfide-based solid electrolytes (SE) are intimately mixed at the nanoscale.[4] This is normally achieved by planetary milling. In liquid Li-S battery research, it is common to prepare sulfur/carbon (S/C) composites by impregnating sulfur into porous carbon hosts.[5] This method has recently been successfully applied to ASLSB.[6] Sulfide-based SE are ideal for sulfur chemistry from the compatibility and interfacial contact point of view. Li3PS4 is the most common composition although other compositions have also been employed.[6–8] Most of the ASLSB research is targeted for rechargeable battery applications. Cycling of Li metal anode in the solid state generally faces great challenges such as dendrite penetration and delamination due to electrochemical stripping.[9,10] Although sulfide-based SE allow Li metal cycling at certain current densities and capacities,[10,11] cycling at the capacities required to match ASLSB cathodes of practical loadings is still beyond reach. Moreover, sulfur electrodes experience large volume expansion upon discharge, leading to severe mechanical issues. This is why a majority of the reports employ low cathode loadings and Li-In anodes, which is clearly not practical for high energy batteries.[6][12][13] Therefore, we believe that practical rechargeable ASLSB are still fundamentally challenged. In this work, we investigate ASLSB as promising candidates for primary lithium batteries. Prominent Li primary battery chemistries include Li/MnO2, Li/SOCl2 and Li/CFx; among which, the Li/CFx system provides the highest specific energy (400 – 600 Wh/kg). Although CFx cathodes have a higher operating voltage of 2.5 V vs. 1.8 V for all-solid-state sulfur cathodes, sulfur delivers twice the specific capacity of CFx (x=1). Therefore, sulfur cathodes have a higher theoretical energy density than CFx cathodes. In this work, we will frame our discussions in the context of primary ASLSB. Nevertheless, findings and methodologies presented are completely applicable to rechargeable ASLSB. Wang, et al. recently reported that the low-temperature phase Li7P2S8Br0.5I0.5 (LPSBI) possesses an excellent ionic conductivity of 5 mS cm-1 at room temperature (r.t.).[10] In addition, LPSBI forms stable and low-impedance interface of 5 Ω·cm2 at r.t. with Li metal anodes. Here, we apply the novel SE to ASLSB. Electrochemical characterization of ASLSB in literature is mostly limited to basic methods and qualitative analysis. For example, Nagata, et al. determined the capacities of their ASLSB at different rate with electrode loading from 1.3 mg cm-2 to 9.6 mg cm-2, but no impedance analysis or explanation for the observed rate performance was given.[14] No studies have attempted to apply rigorous analysis on impedance data or to apply advanced

electrochemical technique such as GITT. Therefore, factors that govern the kinetics of sulfur cathodes especially at high loadings required for primary batteries are not well understood. In this work, we first investigate the kinetics of all-solid-state sulfur cathodes using EIS and GITT. The insight is then applied to understand the practical aspect of sulfur electrodes of various compositions.

2. Material and Methods 2.1. Materials preparation 2.1.1 Solid electrolytes LPSBI SE were prepared by planetary ball milling following the procedure in literature[10]. Crystalline LPSBI (c-LPSBI) was obtained by heating the amorphous LPSBI (a-LPSBI) powder at 160 °C for 1 h. Amorphous Li3PS4 (a-LPS) was prepared the same way as a-LPSBI except for different stoichiometry. 2.1.2. Sulfur/carbon composites Impregnated S/C composites were prepared by heating sulfur (Sigma-Aldrich) and BP2000 porous carbon (Cabot Corporation) in a sealed argon-filled container at 155 °C for 16 h. Alternatively, S/C composites were prepared by planetary-milling sulfur and BP2000 carbon for 2 h (denoted as PM-S/C) without any liquid solvents. The S/C weight ratio was 70:30. 2.1.3. All-solid-state sulfur cathodes All-solid-state sulfur cathodes were prepared by dry planetary-milling S/C composites and SE for 2 h. Table 1 shows the compositions of four cathodes studied. All cathodes have an S/C composites to SE weight ratio of 60:40, with a final composition (by weight) of S/C/SE of 42/18/40. 2.2. Materials Characterization A Rigaku Ultima III x-ray diffractometer was used for structural characterization. The radiation source was Cu Kα. All samples were in the powder form. The scan rate was 2° min-1 for a 2-theta range of 10° to 70°. Samples containing SE were covered with a piece of 8-µm thick Kapton film to prevent exposure to air. Raman spectra were measured with a Renishaw InVia Raman microscope with a 514 nm laser excitation. All samples were in the powder form and covered by a piece of 150-µm thick cover glass during the test. 2.3. Preparation of ASLSB and electrochemical testing ASLSB batteries were prepared and tested in a polyether ether ketone pressing die with a diameter of 10 mm. A c-LPSBI SE layer was first pressed at 60 MPa. A predetermined amount of cathode powder was then spread onto one side of the SE layer and pressed at 360 MPa. Finally, a piece of Li metal was pressed on the other side at 120 MPa. Penta-layer cells for direct ion resistivity measurement of electrodes were made by sequentially pressing a layer of SE, the electrode, another layer of SE and two pieces of Li foils at 120 MPa. All electrochemical data were collected with a Solartron 1260/1287 potentiostat. EIS were collected from 10 kHz to 0.01 Hz with 6 data points per decade and a voltage modulation of 5 mV. C-rate calculation was based on a theoretical capacity of 1600 mAh/g. High temperature testing was carried out in an environmental chamber. Impedance fitting was performed using Matlab.

3. Results and discussion 3.1. XRD and Raman characterization As seen from the XRD patterns (Figure 1), sulfur impregnation reduced sulfur into the amorphous state. The LPSBI SE after milling was indeed purely amorphous. With annealing, a-

LPSBI was converted to partially crystalline state (c-LPSBI). All the peaks matched well with the low-temperature phase of LPSBI. However, the sulfur electrode with c-LPSBI and S/C composites was largely amorphous, suggesting that the planetary milling process destroyed the crystalline structure of the SE. Raman spectra provide the local bond information. Peaks in the Raman spectrum of a-LPSBI corresponds to different modes of PS43-. The Raman spectrum of impregnated S/C composites was magnified by 50 times due to the weak signal. The spectrum corresponds well with sulfur. The Raman spectra of sulfur cathodes with c-LPSBI and a-LPSBI are nearly identical to that of sulfur, indicating that the milling process greatly modified the local structure of the SE, which is consistent with the XRD data. It has been reported that Li3PS4 can react with sulfur to form Li3PS4+n.[15] We believe that the high-energy planetary milling strongly promoted interaction between the SE and sulfur and completely changed the long-range and short-range structure of the SE. 3.2. General characteristics of the TLM Figure 2 shows the equivalent circuit of a classic transmission line model of battery electrodes. and represent the resistance associated with Li ion and electron transport through the electrode. The element represents impedance associated with active sites which can be further broken down into more fundamental elements. According to the classical model for a mixed-phase electrode[16,17] of thickness , the overall impedance 2 + (1) = + + coth ( ⁄ ) + sinh ( ⁄ ) + where =(

)/ + and are resistivity in the unit of Ω cm. is in the unit of cm. Case I: is purely capacitive as in a non-faradaic process, = 1/ -3 where is capacitance in the unit of F cm . At high frequencies, → 0, / → ∞, + ( → ∞) = + (1 − ) ( + + )$⁄ (2 ) ⁄ ≫ , Under the condition where (

→ ∞) =

( (1 − ) 2 at high frequencies is a 45° line starting from

Therefore, the Nyquist plot for axis. At low frequencies, / → 0, (

→ 0) = =

Under the condition where (

≫

→ 0) =

+ * 3

+ , +

+'

+ * 3

+ 3

+

=

+ +

+ + +

++ ++ 3

+

1 1

(2)

(3) (4)

(5) at the real

(6)

(7)

Therefore, the Nyquist plot of transitions from the 45° line to a 90° line at a real value of ⁄3 + at low frequencies. The crossover angular frequency , is defined by setting | ⁄ | = 1, (8) + ). . . , =( Case II: In a faradaic process, is modeled by an RC circuit of charge transfer resistance and interfacial capacitance, (9) = 1/(1⁄ / + ) 3 Note the unit of / is Ω cm . The high-frequency behavior of is similar to case I, since 0 ≫ 1/ / . At low frequencies, the Nyquist plot of shows a semicircle typical of an RC circuit, offset by the same amount as in Case I. the slope of the initial part of semicircle is + ). At extremely large / , the model approaches Case I. Smaller determined by / / ( means more electrical leakage through the faradaic process, and the slope is smaller. The / crossover frequency is / 1 1 (10) + − , =* 1 ( + ) / If / ≪ ( + ), it has minimal influence on the crossover frequency. 3.3. Analysis of kinetics of ASLSB cathodes Figure 3 shows the impedance spectra of ASLSB before discharge using a-LPSBI as SE and impregnated S/C composites. The weight of the cathode powder was 2.5 mg and 10 mg, corresponding to an areal loading of 3.2 mg/cm2 and 12.7 mg/cm2, respectively. The cells were constrained by a screw-tightened clamp setup with an estimated pressure of 120 MPa. The spectra can be divided into two regions of straight lines with different slopes. The slope at high frequencies is about 45° which is a typical Warburg behavior. The slope at low frequencies is greater than 45°. The Warburg behavior in batteries generally arises from two types of processes, diffusion inside the active materials and macroscopic charge transport with frequencydependent leakage, as described by the TLM. Han et al. attributed the Warburg behavior in their sulfur cathodes to the solid diffusion of Li+ into the bulk of sulfur particles.[6] We show here that the Warburg behavior at high frequencies is in fact due to the second process. 3.3.1. Impedance fitting using an RC model for 34 The slopes of the low-frequency lines are both substantially smaller than 90° in the cells with thin and thick electrodes, indicating appreciable faradaic leakage so the RC model is appropriate. A constant phase element was used instead of a capacitor to account for the distributed nature of the capacitance due to inhomogeneity. The overall cell impedance also includes the resistance of the SE layer and the impedance at the Li-SE interface in addition to from the sulfur cathode. As shown in Wang et al.’s report[10], the interfacial impedance of Li-SE can be modeled by a finite-length Warburg element, and has a small value of 5 Ω cm2. Here, we ignore the imaginary part of the interfacial impedance and combine the real part with the SE layer resistance into one resistive element, 5 . The experimental data were fitted to an equivalent circuit - 5 - where stands for stray capacitance. Estimated values of 0.002 and 0.008 were fixed for the 2.5-mg and 10-mg electrode, respectively. A fixed 5 value of 15 Ω was used. The fitted results are summarized in Table 2. A superscript ‘F’ is added to differentiate the fitted values and parameters defined in the TLM. Parameters in the TLM are not geometry-specific whereas the fitted values are specific to a fixed area of 7 which is 0.785 cm2 in the current case. Dimensionless parameters such as 89-8 are naturally independent of geometry. The relationships between the two sets of parameters are

(11)* = 7 : ; and = ; /7 * and 8<-< are used interchangeably. x can be ‘ion’, ‘e’, or ‘ct’. ; Note that and ; are not differentiable from the model. We assume that the resistive ; element with a larger value is . This is because the ion transport is far more resistive than electron transport for the high carbon-content (18 wt%) electrodes. We confirmed the attribution later by direct ion transport measurement of the electrodes. ; ; ≪ so the condition is met for Equation 5 and 7. The Firstly, it can be seen that intercept on the real axis at high frequencies is ; + 5 , where 5 is fixed at 15 Ω. As 5 may vary from cell to cell and there is no way to know the exact value of 5 for each cell, we slightly underestimated the 5 value so convergence can be achieved for all cells. Unfortunately, any estimation error of 5 will be introduced into ; . As 5 is likely underestimated, ; is likely ; overestimated which strengthens the condition that ; ≪ . ; /3 values are 160 Ω and 250 Ω for the 2.5-mg and 10-mg electrodes, respectively, which corresponds well with the projection of the 45° line on the real axis in the Nyquist plots. However, the resistivity value calculated from the 2.5-mg electrode is about 250% that of the 10mg electrode. This is clearly an anomaly as the resistivity should not depend on the electrode thickness. We have conducted the same experiment several times with good reproducibility and consistent observation of the anomaly. Therefore, the anomaly appears to be systemic. We speculate that the anomaly was due to poor spread of the sulfur cathode powder in the 2.5-mg electrode. It is difficult to spread a small amount of powder uniformly over the entire area, more so at lower loadings. When pressed at high pressures, the powder has the tendency to flow and minimize the inhomogeneity, but such effect becomes less pronounced at lower loadings. Poor spread will result in a larger effective electrode thickness and a smaller effective electrode area than the nominal values. Consider the effective electrode thickness == to be > (> > 1), then the effective electrode area 7 == is 7⁄>, or @/(> ), where @ is the volume of the electrode which is a constant for a cell. :

7

==

==

=

;

(12)

; (13) = 7/> (2.5CD) = Since (10CD), assuming that the 10-mg electrode is uniform (effective values are the same with nominal values), we estimated > to be 1.63; in other words, the powder was effectively spread over only 60% of the area. It is important to recognize that such inhomogeneity does not affect the determination of / ; and , the differential elements are in series along the and 89-< ; . This is because for direction of , whereas they are in parallel for / and 89-<. ; ; 7 (14) / = / == 7 == = / ; ; Indeed, the / and 89-< values are very similar for the two cells, despite the inhomogeneity of the 2.5-mg electrode. From a practical standpoint, the determination of is far more accurate with thick electrodes, under the condition that the measured spectrum captures the crossover region and the lowfrequency region. When the condition is not met, and cannot be determined because they are coupled at the high-frequency region (Equation 5). On the other hand, the determination of is more accurate with thin electrodes, because the crossover frequency , increases / and

with decreasing (Equation 10), and more of the spectrum in the low-frequency region can be captured within the same frequency range, to which / and are most sensitive. ; From the value of the 10-mg electrode, is determined to be 7.5 x 104 Ω cm. The Li ion conductivity of the electrode is 1.3 x 10-5 S cm-1. This value is about two orders of magnitude lower than the amorphous LPSBI. This is expected as the volume fraction of the SE in the electrode is only about 40% and milling with S/C composites significantly modified the longrange and the short-range structure of the SE as seen from the XRD and Raman results. To estimate the area-specific charge transfer resistance, the active surface area per unit volume is needed. The sulfur weight fraction of 70% in the S/C composite was selected so that sulfur fills all the inner pores of BP2000. BP2000 is a porous carbon with particle sizes ranging from 20 nm to 50 nm. The structure of BP2000 can be inferred from the nitrogen absorption measurement. According to literature[6], BP2000 has a total specific surface area of 1739 m2 g-1 with 1124 m2 g-1 for micropores (defined as < 2 nm pores) and 559 m2 g-1 for mesopores (defined as 2 - 50 nm pores). The pore volumes are dominated by mesopores. The pore size distribution shows pores ranges from small micropores (<1 nm) to large mesopores (> 20 nm). Sulfur impregnation fills the micropores and the mesopores so the surface area decreases and corresponds to the outer surface of the S/C spheres (EFG, ), which is estimated to be 170 m2 g-1 by assuming the carbon spheres have an average diameter of 30 nm. We assume that by mixing the SE and the S/C, the SE phase encloses each S/C particle individually and the active areas is the opening of BP2000 outer pores filled by sulfur. The area-specific charge transfer resistance HIJ (15) = / ; 7KLM N EFG, N / -3 where KLM is the gravimetric density of the electrode with an estimated value of 2 g cm , N is the weight fraction of BP2000 in the electrode which is 0.18, N is the fraction of carbon outer surface area that is pore opening with an estimated value of 0.2. Using the / ; value from the 2.5-mg electrode, / HIJ is about 1200 kΩ cm2. This is a very large value compared to other systems. We will show later that this value is in fact inaccurate because of the limitation of the model. The capacitance arises from charge accumulation at the carbon/SE interface. We assume that the capacitance associated with the S/C interface is negligible as there is no mobile species in sulfur before discharge. The area-specific capacitance is HIJ (16) = ; [7KLM N EFG, (1 − N )]. -2 ; HIJ Using the 89-< value from the 2.5-mg electrode, is 15 µF cm , which is typical of a SE/electronic conductor interface. 3.3.2. Effect of testing pressure The impedance of the cell was dependent on the pressure on the cell (Figure 4). When a lower pressure was used, the overall impedance increased for both thin and thick electrodes. The intercept at the real axis shifted to a higher value especially in the case of thin electrode. The ; fitted parameters are summarized in Table 2. Recall that the absolute value of is not important, but the relative change reveals the evolution of electron transport. Comparing the parameters for the 2.5-mg electrode, ; increases significantly with a lower pressure. This is ; reasonable as contact resistance is highly sensitive to pressure. also nearly doubles suggesting the change of the compactness in the electrode is significant enough to affect Li ion transport. The increase of / ; is likely due to a partial loss of active area (S/SE interface) and the decrease of 89-< ; is likely due to a partial loss of contact between carbon and SE. The lower 89-8; values indicate that the distributed nature of the capacitance is exaggerated.

Parameter changes of the 10-mg electrode with a lower pressure shows similar tendencies but to a smaller extent, which may be because of better homogeneity than the 2.5-mg electrode. 3.3.3. Impedance at different depth of discharge (DOD) The 2.5-mg and 10-mg cells were discharged at a C/5 rate. After each hour, the cells were rested for 10 min before the impedance was measured. Figure 5a shows the discharge profiles without displaying the rest periods. The specific capacity of the thick electrode was 1560 mAh/g; for the thin electrode, the voltage did not reach the cutoff of 1 V even after a capacity of 1920 mAh/g. It is not uncommon that the discharge capacity of all-solid-state sulfur cathodes exceeds the theoretical capacity, because the SE also contributes to the capacity. Also, the thin electrode is more prone to errors during the weight measurement. Note that each current step after the rest period is in fact a GITT test from which kinetic information about the transient, non-equilibrium state can be extracted. First, we discuss the kinetics around the equilibrium as inferred from the impedance measurement. Figure 6 shows the impedance spectra after each rest period. Because the spectra heavily overlap, we slightly shifted each spectrum for clear presentation. The same equivalent circuit where is modeled by an RC circuit was applied and the fitted parameters for the 2.5-mg electrode are tabulated. We assume that the cell reached 100% DOD. As shown in Figure 7, ; is largely ; independent of DOD whereas decreases gradually till 50% DOD and then stabilizes. Such decrease in the resistivity of the SE may be due to the replenishment of Li ions as the milling process may induce partial oxidation of the SE by sulfur. / ; decreases sharply during the first hour of discharge. / ; is largely stable after the initial drop, and increases slightly as the electrode reaches the end of discharge. 89-< ; increases gradually with discharge. This is because as sulfur is lithiated, the S/C interface starts to contribute additional capacitance. The crossover frequency 0, decreases initially and then stabilizes, so a smaller portion of the ; ; low-frequency region can be seen with discharge. + ; R shows a similar / / Q ; decreasing trend as / , so the slope at the low-frequency region becomes smaller. The combined effect is that the crossover region becomes obscure in the Nyquist plots. At the end of ; discharge, / ; / Q + ; R increases so the low-frequency region becomes visible again. In the case of the 10-mg electrode, 0, is smaller before discharge due to a larger . Upon discharge, 0, moves out of the measured frequency range so the determination of / ; was not ; possible. In addition, independent determination of 89-< ; and was not possible either because they are coupled at the high-frequency region (Equation 5). 3.3.4. GITT analysis So far, our equivalent model assumes that the kinetics of sulfur active materials is chargetransfer-controlled. This may not be true as the electronic and ionic resistivities of lithiated sulfur species (LixS, x<2) may be very high. Despite the short diffusion length, we cannot rule out the possibility that sulfur conversion is diffusion-controlled. In addition, it is an open question whether the diffusion limitation is due to the electron transport or the ion transport. Sulfur and Li2S have electronic conductivities of 10-17 S/cm and 10-14 S/cm, respectively.[18] By extrapolating conductivity values of a Li2S single crystal at high temperatures[19], we estimated that the Li diffusion coefficient of Li2S at room temperature is on the order of 10-15 cm2 s-1. Simulation studies of the transport in Li2S also resulted in Li diffusion coefficient in the vicinity of this value.[20] The estimated ionic conductivity is on the order of 10-11 S/cm, which is much higher than the electronic conductivity. It is tempting to conclude that sulfur conversion is limited by electron transport. However, sulfur contains a trace amount of metal elements, and

many metal sulfides are good electronic conductors.[21] For instance, TiS2 is considered a semiconductor.[22] Arguably, the electronic conductivities of sulfur and lithiated sulfur species are determined by extrinsic impurities. We hypothesize that the impurities have a larger effect on the electronic conductivity than the ionic conductivity of lithiated sulfur species. It has been reported that Li2S-LiI solid solutions have higher ionic conductivities and better rate performance than Li2S,[12] which supports the ion-diffusion-limited hypothesis. Therefore, we assume that Li ion diffusion is the limiting transport mechanism in the work. The classic transient voltage-current response of a diffusion-controlled solid-state system[23] predicts that S9 S9 (17) ∝ W ' ( YZ [ . ⁄ (U ≪ \ ⁄YZ [ ) SX S √U where W is applied current, 9 is voltage response. S9 ⁄SX is the change of equilibrium voltage with stoichiometry, which is the slope in a steady-state voltage measurement. \ is diffusion length. Assuming a diffusion length of 10 nm as the characteristic pore length of BP2000, we estimated that the time required to reach steady state is about 1000 s, corresponding to 0.001 Hz. Recall that the crossover frequency for the 2.5-mg electrode is about 0.1 – 0.01 Hz. There should be a time window between 10-100 s and 1000 s that the diffusion limitation dictates the voltage drop. Note that there are two Li ion transport processes in the electrode, ion transport within the SE phase at the electrode level and ion transport within the sulfur particles at the microscopic level. The first transport is ion migration driven by electric fields since the SE is a single ion conductor; the second transport is ion diffusion driven by concentration gradients. Figure 7b shows the 9 vs U / curve of the 2.5-mg electrode for the first 1000 s after each rest period. All curves are manually shifted to have the same starting voltage for comparison. For the first discharge, clearly there are two linear regions with a clear transition at about 10 s, which corresponds to the crossover frequency as measured by impedance spectroscopy. The linearity indicates that both regions are governed by diffusion or diffusion-equivalent processes. For simplicity, we assume that the electrode was thin enough that all sulfur particles were discharged at the same rate. The short-time region corresponds to the high-frequency region in the Nyquist plot. By performing Fourier transform on equation 5 and converting 9 to the time domain, one can see that 9 is indeed proportional to U / , and the slope at short time (E ) is proportional to ( / ) / (Equation 18). The slope changes correspond well with change of ( / )/ values as determined by EIS fitting. The transition time into the second linear region increases with DOD, in consistency with the decreasing trend of the crossover frequencies with DOD. (18) E ∝ W( / )/ Li diffusion coefficients can be determined from the slopes of the second region using Equation 36 from reference[23]. By estimating S9 ⁄SX from Figure 5a and the slopes of the second linear region at different DOD, we estimated that the diffusion coefficient at 17% DOD is about 20% that at 0% DOD. It decreases further slightly at larger DOD. In other words, Li ion diffusion becomes slower upon discharge, which is consistent with Islam’s calculation[20]. The estimated YZ [ for 17% DOD is about 5 × 10-15 cm2 s-1. It should be noted that S9 ⁄SX values are ideally extracted from a coulometric titration curve. The C/5 rate is a relatively slow rate for the 2.5-mg electrode, but hardly a steady-state condition, so the estimation of the S9 ⁄SX values is subject to large errors especially at 0% DOD. More detailed investigation is in progress.

As seen from the 9 vs U / curve, the portion of the voltage drop attributed to ion migration through the SE is larger than that of the diffusion region, suggesting that the electrode is largely ion-migration-controlled. We will not attempt to apply similar analysis to the 10-mg electrode because: 1) the crossover frequencies are lower but the diffusion length is the same, so the transient region is more obscure. 2) State of charge varies more along the direction of due to a larger ion migration effect, so the potential is more mixed. 3.3.5. Impedance fitting using a Warburg model for 34 So far, the impedance spectra have been fitted using an RC model for . This is not correct under conditions where diffusion contribution cannot be neglected, which is the case according to our GITT analysis. Therefore, we added a finite-length Warburg element to the RC circuit ( is | / -^_ ). (^_ -<)]5.c d /[ (^_ -<)]5.c (19) `a = (^_ - ) cothb[ Again, a constant phase element was used. The result of the fitting for the 2.5-mg/0-h data is summarized in Table 3. The goodness of fit e using the Warburg model was 3.98 (for 37 data points) compared to 14.3 for the RC model, so the fitting was greatly improved by adding the Warburg element. Most of the fitted parameters are very similar except that / ; decreases from 12.1 to 0.613. The impedance of the / -^F branch is compensated by the Warburg impedance. | `f | is about 7 times the value of / ; at 0.01 Hz so sulfur conversion is indeed diffusionlimited. YZ [ can be calculated from ^_ -< (20) YZ [ = \ /(^_ -<) -15 2 ; Again, assuming that \ is 10 nm, YZ [ is ~ 10 cm /s. Using the updated / value, / HIJ is calculated to be 57 kΩ cm2, which makes more physical sense than the value predicted using the RC model. It is still much higher than most common electrode systems. For instance, LiCoO2 in organic liquid electrolytes has an area-specific charge transfer resistance of < 1 kΩ cm2. LiCoO2 interfaced with lithium garnet oxides has an area-specific charge transfer resistance of around 4 kΩ cm2. It was assumed in Equation 15 that the active area is all the contact area between sulfur and SE. However, due to the small electronic conductivities of sulfur and SE, the effective active area may only be at the triple boundaries. Also, S/C particles may not be perfectly dispersed. Therefore, / HIJ may be overestimated. To further evaluate if the improvement in the fitting was real or merely the effect two additional variables, we fixed 89-< ; at values around the optimized value of 231.6 and fitted other parameters. As seen from Figure 8a, there was a local minimum of the obtained e around the optimized 89-< ; value, but the sensitivity was not very good. The test confirms that the diffusion process represented by the Warburg element is significant and should not be neglected, which is consistent with the observation of a clear second linear region in the 9 vs U / curve. When the model was applied to the 2.5-mg/1-h data, e was only marginally improved and an unphysical value for 89-< ; was obtained. The model also failed the sensitivity test, as e was insensitive to varying 89-< ; . We believe this is because the crossover frequency decreases so the data become increasingly unfit for fitting the low-frequency region. When the model was applied to the 10-mg/0-h data, e was only slightly improved. The model also failed the sensitivity test probably due to the same reason. Although the RC model has limitations, the results should not be dismissed as erroneous entirely. The addition of the Warburg element has large effects only on / ; . Other parameters such as ; and 89-< ; should be considered properly fitted. For majority of the DOD, e was in fact

quite small using the RC model (Figure 8b). Nevertheless, the improvement of e with increasing DOD should not be interpreted such that sulfur conversion becomes more chargetransfer controlled, but merely because that the data have less of the diffusion contribution due to the decreasing crossover frequency. 3.3.6. Direct Li ion resistivity measurement of the electrode The solid-state sulfur cathode is a mixed electron/ion conductor. Resistivity associated with the ion transport can be determined using a penta-layer structure shown in Figure 9a. A sulfurelectrode layer is sandwiched by two SE layers, which interface with Li metal electrodes. When a constant current W was applied, the cell voltage eventually reach a steady-state value of 9FF . Because the SE layers are electron-blocking, only the ion transport through the sulfur-electrode layer contributes to the DC current. Neglecting the impedance of the SE layers and the Li/SE interfaces, the resistance of the sulfur electrode is then 9FF /W. A typical 9 vs. U curve is shown in Figure 9b. The current was 0.1 mA and the weight of the electrode was 10 mg. After 500 s, the cell can be considered in a quasi-steady state. The simple explanation in the previous paragraph cannot explain the slow voltage increase before reaching steady state. As shown in Figure 9a, there are actually two processes that contribute to the overall current before the cell reaches steady state. The first pathway is ion transport through the sulfurelectrode layer, represented by Z . The second pathway involves faradaic reactions within the sulfur-electrode layer, represented by ; . , Sulfur is reduced as Li ions enter the sulfur electrode from one side. On the other side, the SE in the sulfur electrode is oxidized since sulfur is already in the oxidized state. The latter faradaic reaction feeds electrons to the former reaction. The reaction changes the chemical potential of the opposite parts of the electrode in opposite directions. Steady state is reached when the chemical potential gradient is offset by the electrical potential gradient at any point within the electrode, and electron transfer and faradaic reactions cease. It can be shown that 9 (U) (21) W; (U) = [1 − ]W 9 (U → ∞) where W; is the current contributed by faradic reactions of the sulfur electrode. Therefore, the relative contributions of the two processes to the overall charge can be visualized by the relative area in the 9 vs. U curve. We calculated that the total charge of the faradaic reactions was around 0.001 mAh, which was very small compared to the total capacity of the electrode (about 7 mAh). Therefore, the effect of the faradaic reactions on the ion resistivity can be neglected. Using this method, the resistivity is determined to be 8.8 x 104 Ω cm, which is fairly close to the value determined from impedance spectroscopy. Note that the electrode in the penta-layer cell was compressed at a lower pressure than the ASLSB, which explains the slightly higher resistivity. 3.4. Rate capability of ASLSB with different electrode compositions Figure 10a shows the DC polarization result of penta-layer cells with different electrode compositions. Among electrodes with the same impregnated S/C composite but different SE, the electrode with amorphous LPSBI shows the lowest resistivity. Intriguingly, although crystalline LPSBI has better ionic conductivity than amorphous LPSBI, the resistivity of the electrode using c-LPSBI is higher. The XRD data shows that the crystalline structure was completely altered after mixing. Nevertheless, it is still unclear why the resulting electrode had a higher resistivity. The electrode with a-LPS as the SE shows a much higher resistivity. It has been reported that the addition of lithium halides is beneficial to ion conductivities of lithium thiophosphate

compounds.[24,25] The electrode with planetary milled S/C composites shows a slightly higher resistivity than the electrode with impregnated S/C composites. The rate capability were tested with 10-mg electrodes at room temperature (Figure 10b) All cells were discharged in a sequence of constant currents at C/20, C/10, C/5, C/2, C/20 for 15 min each and then at C/5 to the cutoff voltage. The rate capabilities follow the order of electrode conductivities, which is consistent with the conclusion that the electrode resistivity is the limiting factor of sulfur cathodes at high loadings. Despite having a fair rate capability, the electrode with planetary milled S/C composites shows a lower specific capacity, indicating that some of the sulfur particles were not utilized probably due to insufficient mixing. Therefore, the impregnation method is advantageous in terms of S/C mixing. The method is also more scalable. 3.5. Performance of ASLSB with the optimal composition Clearly, sulfur electrodes with impregnated S/C composites and amorphous LPSBI as the SE show the best overall performance. As shown in Figure 11a, at a relatively low current rate of C/20, the 10-mg electrode cell delivered a capacity of 1870 mAh/g. At a high rate of C/2, the cell still delivered a capacity of 1250 mAh/g, but the discharge voltage was much lower. When the electrode loading was doubled, the cells delivered a capacity of 1300 mAh/g at C/20 and 1590 mAh/g at C/40. When a 10-mg cell was tested at 120 °C, it showed a much higher discharge voltage and a capacity of 1750 mAh/g. The cell impedance before discharge was relatively stable at 120 °C for at least 24 h (Figure 11b), suggesting that side reactions were minimal. Note that the temperature was higher than the melting point of sulfur. The ASLSB also showed negligible self-discharge at ambient conditions as the OCV was stable for almost a year upon storage (Figure 11c). This is in stark contrast to liquid-base Li-S cells, where the self-discharge issue is very severe due to polysulfide shuttling. Based on the data of the 20-mg cell, a large-format 4 Ah pouch-type ASLSB cell will have a projected specific energy of 660 Wh/kg at C/40. Note that the specific energy can be achieved only at a relatively low rate of C/40 due to a very high loading of 25.5 mg/cm2. All other parameters such as current collector thicknesses are comparable to commonly used values. In comparison, Rayavoc developmental D size Li/CFx batteries are claimed to have a specific energy of 592 Wh/kg at a discharge rate of C/76.[26] We believe that the ASLSB chemistry is potentially superior to the Li/CFx chemistry, especially for low-power and extreme-environment applications. ASLSB have potential to reach much higher specific energies through fundamental improvement and engineering optimizations such as enhancing electrode kinetics, reducing current collector thicknesses and switching to a bipolar design.

4. Conclusions The kinetics of all-solid-state sulfur cathodes is determined by four major processes in series, 1) electron transport at the electrode level, 2) ion migration at the electrode level, 3) charge transfer reaction, 4) ion diffusion within sulfur particles. We show that the impedance of all-solid-state sulfur cathodes can be well described by the Transmission Line Model. Impedance and GITT analysis on thin and thick electrodes suggest that 1) Electronic resistivity can be ignored 2) Ionic migration at the electrode level is rate limiting for electrodes with appreciable loadings. 3) Sulfur conversion is diffusion-limited. Diffusion coefficients of Li within sulfur particles decrease upon discharge. 4) High testing pressures improve electrode kinetics

The Li ion resistivity of the electrode determined using an electron-blocking cell structure is consistent with the result from impedance spectroscopy. Electrodes using amorphous LPSBI display better rate capabilities than those using crystalline LPSBI and amorphous Li3PS4. S/C composites prepared via the impregnation method show higher sulfur utilization than planetary milled S/C composites. ASLSB possess high capacities and moderate rate capabilities. In addition, they can be operated at 120 °C and show negligible self-discharge for a year when stored under ambient conditions. We believe that ASLSB is a promising system for high-energy primary batteries.

Appendix. List of Symbols 7

7

==

HIJ ;

89-< ; 89-8 YZ [ X 9 N N W W; \

==

>

5

/

/ HIJ /

;

;

; ; Z

KLM E EFG, U @ ^_ ^_ -< ^_ e `f

Nominal geometric area of electrode (cm2) Effective geometric area of electrode (cm2) Interfacial capacitance per unit volume (F cm-3) Area-specific interfacial capacitance (µF cm-2) Parameter for impedance fitting analogous to (F cm-1) Capacitance of constant phase element for impedance fitting (F cm-1) Parameter of constant phase element (unitless) Li diffusion coefficient (cm2 s-1) Stoichiometry as in LiδS (unitless) Voltage (V) Weight fraction of carbon in an electrode (unitless) Fraction of carbon outer surface area that is pore opening (unitless) Current (A) Current contributed by faradic reactions in a penta-layer structure (A) Imaginary number (unitless) Diffusion length inside sulfur particles (nm) Nominal thickness of electrode (cm) Stray inductance (H) Effective thickness of electrode (cm) Parameter defined by Equation 2 (cm) Equal to == / (unitless) Combined resistance from SE layer and Li/SE interface (Ω) Charge transfer resistance per unit volume (Ω cm3) Area-specific charge transfer resistance (Ω cm2) Parameter for impedance fitting analogous to / ; (Ω cm) Electron resistivity in the TLM model (Ω cm) Parameter for impedance fitting analogous to (Ω cm-1) Effective resistance associated with Faradaic reactions in a penta-layer structure (Ω) Ion resistivity in the TLM model (Ω cm) Parameter for impedance fitting analogous to (Ω cm-1) Li ion resistance of a sulfur electrode in a penta-layer structure (Ω) Gravimetric density of electrode (g cm-3) Slope of the first linear region in an 9 vs U / curve (V s-0.5) Total surface area of sulfur/carbon composites (cm2 g-1) Time (s) Volume of electrode (cm3) Warburg element for Li diffusion inside sulfur particles Parameter of ^_ in Equation 19 (s) Parameter of ^_ in Equation 19 (Ω cm) Goodness of fit (unitless) Overall impedance of the circuit shown in Figure 2 (Ω cm2) Defined in the TLM in Figure 2 (Ω cm3) Impedance of ^_ (Ω cm)

Angular frequency (s-1) Crossover angular frequency (s-1)

,

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List of Tables Table 1. Composition of the ASLSB electrodes. Table 2. Results of fitting of ASLSB impedance using an RC model for h Table 3. Result of fitting of ASLSB impedance of 2.5-mg electrode at 0% DOD using a Warburg model for h

List of Figures Figure 1. XRD patterns and Raman spectra of various S/C composites, solid electrolytes and sulfur electrodes. Figure 2. Schematics of a solid-state sulfur battery. Kinetics of a sulfur electrode can be represented by a transmission line model. Figure 3. The entire range (left) and the high-frequency regions (right) of the impedance spectra of ASLSB with a-LPSBI and impregnated S/C composites at low and high loadings. Figure 4. Impedance spectra of ASLSB with a-LPSBI and impregnated S/C composites under low and high testing pressures. Figure 5. (a) Discharge voltage profiles of ASLSB with a-LPSBI and impregnated S/C composites at low and high loadings. (b) 9 vs U / curve of the 2.5-mg cell for the first 1000 s after applying current. Figure 6. Impedance spectra of ASLSB with a-LPSBI and impregnated S/C composites at various DOD with (a) the 2.5-mg electrode and (b) the 10-mg electrode. The spectra are shifted manually for clear presentation. Figure 7. Various fitted and derived parameters as a function of DOD for the 2.5-mg electrode. Figure 8. (a) Sensitivity test results for ^_ -<. (b) Goodness-of-fit as a function of DOD using an RC model for h . ‘F’ refers to parameters that were used or obtained from the fitting with ^_ -< fixed. ‘O’ refers to parameters that were obtained with ^_ -< relaxed (and hence optimized). Figure 9. (a) Schematics of processes within a penta-layer cell upon application of a DC current. (b) The voltage response of a penta-layer cell to a charging current of 0.1 mA. The electrode consisted of a-LPSBI as SE and impregnated S/C composites. Figure 10. (a) Direct Li ion resistivity measurement and (b) rate capability test of various 10-mg electrodes. Figure 11. (a) Discharge performance of ASLSB electrodes with a-LPSBI as SE and impregnated S/C composites at various loadings, C rates and temperatures. (b) Impedance evolution of an ASLSB at 120 °C within 24 h. (c) Open circuit voltage of an ASLSB stored under ambient conditions.

Table 1. Composition of the ASLSB electrodes. Electrode a-LPSBI c-LPSBI a-LPS a-LPSBI c-LPSBI a-LPS Solid electrolyte Impregnated S/C Impregnated S/C Impregnated S/C S/C composite

PM-S/C a-LPSBI PM-S/C

Table 2. Results of fitting of ASLSB impedance using an RC model for h ; ; ; Electrode 89-< ; / 2.5 mg, high pressure 251800 5104 12.1 5.89 10 mg, high pressure 95020 612 10.1 5.40 2.5 mg, low pressure 453500 28400 18.5 4.64 10 mg, low pressure 101700 2390 12.7 4.47 2.5 mg after 1h 191900 5412 1.35 18.6 2.5 mg after 2h 170260 5392 1 29.3 2.5 mg after 3h 134600 5235 0.98 30.7 2.5 mg after 4h 137900 5169 1.05 32.6 2.5 mg after 5h 141200 5239 1.27 34.7 2.5 mg after 6h 133600 5253 2.19 37.3

89-8 0.920 0.995 0.86 0.94 1 1.01 0.97 0.96 0.95 0.96

Table 3. Result of fitting of ASLSB impedance of 2.5-mg electrode at 0% DOD using a Warburg model for h ; ; ; 89-8 ^_ -< ^_ 89-< ; / 277730 7621 0.614 6.17 1.05 231.6 16.6

Figure 1. XRD patterns and Raman spectra of various S/C composites, solid electrolytes and sulfur electrodes.

Figure 2. Schematics of a solid-state sulfur battery. Kinetics of a sulfur electrode can be represented by a transmission line model.

Figure 3. The entire range (left) and the high-frequency regions (right) of the impedance spectra of ASLSB with a-LPSBI and impregnated S/C composites at low and high loadings.

Figure 4. Impedance spectra of ASLSB with a-LPSBI and impregnated S/C composites under low and high testing pressures.

Figure 5. (a) Discharge voltage profiles of ASLSB with a-LPSBI and impregnated S/C composites at low and high loadings. (b) 9 vs U / curve of the 2.5-mg cell for the first 1000 s after applying current.

Figure 6. Impedance spectra of ASLSB with a-LPSBI and impregnated S/C composites at various DOD with (a) the 2.5-mg electrode and (b) the 10-mg electrode. The spectra are shifted manually for clear presentation.

Figure 7. Various fitted and derived parameters as a function of DOD for the 2.5-mg electrode.

Figure 8. (a) Sensitivity test results for ^_ -< . (b) Goodness-of-fit as a function of DOD using an RC model for h . ‘F’ refers to parameters that were used or obtained from the fitting with ^_ -< fixed. ‘O’ refers to parameters that were obtained with ^_ -< relaxed (and hence optimized).

Figure 9. (a) Schematics of processes within a penta-layer cell upon application of a DC current. (b) The voltage response of a penta-layer cell to a charging current of 0.1 mA. The electrode consisted of a-LPSBI as SE and impregnated S/C composites.

Figure 10. (a) Direct Li ion resistivity measurement and (b) rate capability test of various 10-mg electrodes.

Figure 11. (a) Discharge performance of ASLSB electrodes with a-LPSBI as SE and impregnated S/C composites at various loadings, C rates and temperatures. (b) Impedance evolution of an ASLSB at 120 °C within 24 h. (c) Open circuit voltage of an ASLSB stored under ambient conditions.

Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: