Effect of solid-electrolyte pellet density on failure of solid-state batteries

Despite the potentially higher energy density and improved safety of solid-state batteries (SSBs) relative to Li-ion batteries, failure due to Li-filament penetration of the solid electrolyte and subsequent short circuit remains a critical issue. Herein, we show that Li-filament growth is suppressed in solid-electrolyte pellets with a relative density beyond ~95%. Below this threshold value, however, the battery shorts more easily as the density increases due to faster Li-filament growth within the percolating pores in the pellet. The microstructural properties (e.g., pore size, connectivity, porosity, and tortuosity) of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$75\%{{{{{\rm{L}}}}}}{{{{{{\rm{i}}}}}}}_{2}{{{{{\rm{S}}}}}}-25\%{{{{{{\rm{P}}}}}}}_{2}{{{{{{\rm{S}}}}}}}_{5}$$\end{document}75%Li2S−25%P2S5 with various relative densities are quantified using focused ion beam–scanning electron microscopy tomography and permeability tests. Furthermore, modeling results provide details on the Li-filament growth inside pores ranging from 0.2 to 2 μm in size. Our findings improve the understanding of the failure modes of SSBs and provide guidelines for the design of dendrite-free SSBs.


Introduction
Among alternatives to conventional Li-ion batteries, solid-state batteries (SSBs) show potential for higher energy density and improved safety because they may enable the use of Li-metal anodes and replacement of flammable liquid electrolytes with solid electrolytes (SEs). [1,2]Computational [3,4] and experimental efforts have led to the discovery of SE materials including Li7La3Zr2O12 (LLZO) [5] ,  2  −  2  5 (LPS) [6] , and  6  5  [7] with high ionic conductivities comparable to those of liquid electrolytes (~10 −3 /).However, further improvement of the processability and scalability of these materials is critical for their commercialization. [8]The processing conditions of SEs, such as the fabrication pressure and processing temperature, significantly affect the measured ionic conductivity [9] , likely leading to the large discrepancies in reported values. [10]e ionic conductivity of LLZO increases from 10 −6 to 10 −4 / upon increasing the sintering temperature from 1000 ℃ to 1150 ℃, with a corresponding decrease in the porosity from 6.59% to 4.52%. [11]Likewise, the conductivity of LPS increases from 3 × 10 −4 to 1.1 × 10 −3 / when increasing the fabrication pressure during hot pressing ( 200 ℃ ) from 47  [12] to 270  [13] , with a corresponding increase in the relative density from 85% to 98%.
Intuitively, optimizing the relative density should not only increase the ionic conductivity of the SE but also suppress Li-dendrite growth.However, extensive studies have demonstrated Lifilament penetration of LPS [14] and LLZO [15] regardless of their density or crystallinity. [16,17]ny studies have indicated that the penetration may be related to low ionic conductivity at grain boundaries [18] , inhomogeneous plating at the Li metal/SE interfaces [19] , electronic conductivity in the SE [20,21] , low relative density of the SE [22] , and pre-existing microstructural defects (such as cracks and pores) on the surface of and in bulk SEs [23] ; however, consensus on the mechanism in various SEs has not yet been reached.As most of these factors are influenced by the fabrication conditions, it is important to quantify the effect of processing parameters such as the densification pressure on the micro-and macrostructural properties (e.g., porosity, tortuosity, pore networks) of the SE and on the failure of SSBs due to Li-filament growth.
In this work, we provide insight on the failure mechanism of SSBs due to Li-filament growth by investigating the effect of the fabrication pressure on the micro-and macrostructure of LPS,.
We first show that fully dense LPS SE (relative density >99%) is produced at fabrication pressures above 600 .The ionic conductivity increases linearly during densification of the LPS pellet, as reported in similar studies. [12,13]However, the failure behavior of SSB cells as a function of densification is found to be more complicated: a symmetric cell (Li|LPS|Li) fails much faster as the density of the LPS pellet increases, before reaching a critical relative density (~95% for a fabrication pressure of 500 ) beyond which cell failure does not occur.To explain this highly non-linear failure behavior the micro-and macrostructure (pore size and connectivity, porosity, tortuosity) of LPS pellets are quantified using surface scanning electron microscopy (SEM), focused ion beam (FIB)-SEM tomography, and pellet-permeability tests, revealing that the pore networks formed during processing play a key role in the failure of SSBs.Our modeling results confirm the much higher Li-filament growth rate (and therefore faster cell failure) in denser pellets because of the much smaller pore sizes.

Results
Effect of pellet density on cell conductivity.Figure 1a confirms that the relative density of the LPS pellet was well controlled by the fabrication pressure, with an almost fully dense LPS pellet (99.9%) obtained at a fabrication pressure of 700 , consistent with previous results. [13]Figure 1b presents Nyquist plots from sequential electrochemical impedance spectroscopy (EIS) measurements of the LPS pellet with a density of 95.3% (LPS-95.3%).The resistance increases for the initial 2 ℎ, before leveling off for the remaining 10 ℎ, behavior rates consistent with chemical reaction between LPS and Li metal [24] and early passivation of the solid-electrolyte interphase (SEI). [15,25]Figure 1c clearly shows the strong effect of the pellet density on the bulk resistance and its temporal evolution as well as passivation of all the cells during the initial 2 h.As depicted in Figure 1d, the ionic conductivity linearly increases with increasing LPS density, and the initial overpotential decreases. [12]The increase in conductivity is likely related to the increase in contact area between the LPS particles at higher density.Effect of pellet density on cell shorting.The effect of the LPS pellet density on Li-filament growth was investigated through electrochemical (EC) measurements.A total of 35 cells (5 cells per LPS density) were charged with a current density of 0.2 / 2 until failure of the cell or depletion of the counter electrode.Failure occurred when the voltage dropped to zero and depletion occurred when the voltage rapidly increased to the cutoff value (1 ). Figure 2a presents the voltage curves of four representative cells with different LPS pellet densities.Cell shorting took longer for LPS-81.8%(18 ℎ) than for LPS-89.2%(16 ℎ) and LPS-95.3%(8 ℎ), whereas depletion was observed in the LPS-99.9%cell after charging for more than 40 ℎ. Figure 2c presents a schematic of our hypothesis explaining the non-monotonic relation between the cell-shorting time and the LPS pellet density.At lower density, the LPS pellet is more porous with larger and interconnected pores, whereas the pores become smaller and more isolated at higher density. [11].As a result, a pore network connecting two electrodes may exist in low-density LPS pellets, indicated as the "pore-percolating zone" (orange area in Figure 2c), whereas in high-density pellets, the pores become non-percolating (green area in Figure 2c).These microstructural features are responsible for the shorting behavior of the symmetric cells observed in Figure 2b: (1) Li filaments propagate easily in the percolating pores until shorting occurs when the LPS density is low (pore-percolating regime); however, propagation is suppressed by the nonpercolating pores when the LPS density is in the non-percolating zone.( 2  Tomography and permeability tests of LPS pellets at various densities.To validate the aforementioned hypothesis, quantitative analyses of the pore microstructure and connectivity were performed using FIB-SEM tomography and permeability tests.The pore structures in the (50 ) 3 volume from different pellets (LPS-89.2%,LPS-95.3%,LPS-99.9%) are shown in Figure 3a-c, respectively, with the different colors representing different interconnected pore networks.The pores are large and well connected in the LPS-89.2%cube, as exemplified by the largest pore network shown in red occupying most of the total pore volume.In contrast, the pores in the LPS-95.3%cube are small and connected, whereas the pores in the LPS-99.9%cube are small and isolated.The pore size, porosity, and connectivity (defined as the ratio between the largest pore volume and the total pore volume) of the three cubes were calculated statistically and are summarized in Table 1, with details provided in Figure SI-6 and SI-8.   Figure 3d depicts the relation between the outlet Ar gas flowrate  and the pressure gradient (∆ =  0 −   ) across LPS pellets with varying densities, showing that a higher Ar gas flux was measured for LPS-81.8% and LPS-89.2%,whereas little to no Ar gas flux was measured for LPS-95.3% and LPS-99.9%.These results confirm the presence of percolated pores in the lowdensity pellets and non-percolated pores in the high-density pellets.A more quantitative permeability analysis based on the modified Darcy's law [26,27] in the SI (The permeability tests and analysis) shows that their respective permeability values are  82% = 1.50 × 10 −3  2 ,  89% = 3.86 × 10 −4  2 ,  95% = 1.82 × 10 −5  2 , and  99% ≈ 0.  Simulation of Li-filament growth in the pore.Electro-chemo-mechanical modeling was employed was employed to quantify the Li propagation rate within pores in SE pellets . [21,28]Liions conduction in the SE is described by Ohm's relation, the Li electrodeposition on SE/anode interface is described by the Butler-Volmer relation, and the Li deformation in the SE pore is described by elastoplastic mechanics.More details are provided in the Method section.Figure 4a presents a simplified model to describe the growth of Li (gray area) within a pore (white area) present in the LPS pellet (yellow area) near the Li-metal anode.Li ions are stripped from the counter electrode at the bottom, conducted through the SE, and deposited at the interface between the LPS and the top Li-metal electrode (line AB and CD) and the surface of the pore (line BE and CF).Li initially deposits at the three-phase corner B and C, where both Li+ ions (from LPS) and electrons (from the Li metal) electrode are available.The four dashed lines represent the Li boundary at four charging times (0.5, 1.0, 1.5, 1.9 ℎ) under a current density of 0.2 / 2 .The metallic Li grows both radially and longitudinally toward the counter electrode.For example, it takes 1.9 ℎ to close a 2--diameter pore while growing to a depth of 2.5  in the LPS pellet.
Figure 4b shows the deposition current along the interface (line A-B) and the pore surface (line B-E) at the four charging times.The current reaches a maximum at the advancing tip of the Li filament (location E) due to the lower resistance to reach this point.This maximum current density increases as the Li filament grows towards the counter electrode, from 0.5 / 2 at  = 0.5 ℎ to 1.0 / 2 at  = 1.9 ℎ.It should be noted that this local current density is five times the nominal current.
When the Li width ( =  1 +  2 ) reaches the pore size (  ) the radially deposited Li will start to extrude longitudinally.For example, when  > 1.9 ℎ in Figure 4a, the newly deposited Li extrudes longitudinally, which accelerates the Li-filament propagation.Figure 4c shows the starting time of Li extrusion for three different pore diameters: 0.5  (green line), 1  (blue line), and 2  (red line), which takes 0.63, 1.0, and 1.9 ℎ, respectively.Figure 4d presents the propagation length of the Li filaments perpendicular to the electrodes within these pores.These results confirm the important fact that Li filaments indeed grow much faster towards the opposite electrode for smaller pore sizes.But the growth appears bilinear, rather than linear in time due to the changing mechanism as the pore is filled.Notably, the Li extrusion starts at t = 1.9 ℎ in the 2- pore but accelerates at t = 2.9 ℎ (Figure 4d).This is because the extruded Li needs to first fill in the void space (such as the area in B-C-F-E in Figure 4a), which takes 1 h for the 2- pore.
The stable Li growth rate   after the acceleration can be obtained from Figure 4d, with the maximum (20.7 /ℎ) observed for the smallest pore (0.5 ), followed by 10.3 and 5.1 /ℎ for the 1- and 2- pores, respectively.This Li growth rate from the simulation can be directly compared with the cell-shorting time presented in Figure 2b.

Discussion
Our experimental observations in Figure 2b demonstrate the non-monotonous behavior of shorting time with pellet density.This finding implies that two different density regimes exist: In the percolating-pore regime a higher degree of densification actually leads to more rapid shorting as the volume of pores that needs to be filled decreases.Beyond a critical density where pores no longer percolate, simple growth of Li filaments through the conductor pellet is no longer possible and other mechanisms need to become active to shorten the cell.Indeed, while we find no shorting at low current density for the densest pellet, shorting of the cell can still be achieved at high current density, implying that in the non-percolating regime current-dependent mechanisms, such as stress build up [29] or internal Li deposition due to electron leakage [21,30] may contribute to failure.
Our modeling results, incorporating both transport and mechanics confirm the hypothesis built from the experiments: Pore walls are observed to fill with lithium in a droplet-like geometry grows counter to the Li+ flow, along a distance that is multiple times the pore diameter.For example, the 0.5m pore fills over a length of 20m even after only 1.5 hours charging at 0.2mA/cm 2 .It is challenging to make a quantitative comparison between our simulations and experiments as in reality percolating pore networks are tortuous, have varying radius along the path, and may join and branch, as shown schematically in Fig. 5 and for a real pellet in Figure SI-10.Although this paper emphasizes the importance of pellet density on SSB failure due to Lifilament propagation through percolating pores, it should be noted that this is not the only mechanism but simply an easier path for Li-filament growth compared with SE fracture [31] , electrochemical reaction [32] , and SE electronic conductivity. [30]The four different mechanisms that have been identified as being responsible for Li-filament growth within the solid-state cell are illustrated in Figure 5: 1) propagation through a percolating pore network, 2) growth of the SEI due to chemical reaction of SE and Li, 3) isolated Li deposition due to electronic conductivity of the SE, and 4) Li penetration and SE fracture at higher current density.Mechanism 1 (percolating pores) discussed in this paper is the most prevalent cause of SSB failure because most SE pellets used in the literature never reach the required threshold density (>95%), as discussed in Figure 2.
Lithium filaments prefer to propagate inside the percolating pores first because very low overpotential is needed for the growth.Mechanism 2 (chemical reaction) is present when the SE material is chemically unstable against Li metal, as is the case for all sulfides and some oxides.It has been reported that SSB failure can occur via this mechanism if an unstable SEI layer is formed. [32]Our results in Figure 1c indicate that the chemical reaction between the Li metal and LPS pellet occurs in the first 2 h but stops after a stable SEI layer is formed.Therefore, this mechanism has limited effect in our study.Mechanism 3 (electronic conductivity) enables Li-metal deposition in the isolated pores in the SE, which eventually become interconnected and short the SSB once the percolating point is reached. [21,30]Given the non-negligible electronic conductivity (~10 −4 mS/ cm) of LPS we performed a control experiment using a buffer layer of Li3N+LiF [24] to limit the possible transfer of electrons into the SE.The results shown Figure SI-11 produced similar observations as those in Figure 2 indicating that electron conductivity plays a minor role when the pellet is in the percolating pore regime.Mechanism 4 (SE fracture) can be observed when the SE material has low fracture toughness, and a high current density is applied. [42]As a large overpotential (or mechanical stress) is needed to trigger this mechanism, SE fracture is not likely to occur when a percolating pore network pre-exists in the LPS pellet but may become important for pellets in the "non-percolating regime" at escalated external current.Our control experiment in Figure SI-12, confirms that a short circuit can still occur in dense pellets without percolating pores (LPS-99.2% and LPS-99.9%)under higher applied current densities (3.2 and 6.4 / 2 , respectively), further pointing at a current-dependent failure mechanism in this regime.
While these four mechanisms are usually entangled, it is worth noting that Mechanism 2 (chemical reaction), Mechanism 3 (electronic conductivity) and Mechanism 4 (SE fracture) are related to the material properties of the selected SE, whereas Mechanism 1 (percolating pores) is dependent on the microstructure of the SE pellet.Therefore, the detailed observations highlighted in the Results section are not exclusive to sulfide battery systems.The threshold relative density (~95% for the LPS used in this work) for closing the percolating pore network is a general requirement for the SE pellets made from other SE materials.This discovery explains the puzzling results reported in many works that Li dendrites still propagate into SEs even when the SE pellets are very dense.For example, it was reported that LLZO, even with a density close to that of a single crystal, can still have Li filaments propagating through. [33]straightforward solution to prevent percolating pores in SE pellets is to prepare a sufficiently dense pellet using various fabrication methods (cold pressing, hot pressing, high-temperature sintering, etc.).However, it can be challenging to densify certain SE materials, such as oxide materials.Unlike sulfides, which are soft enough for cold pressing, oxide SEs require high sintering temperature to achieve good densification.Several solutions for the densification of ceramics have been investigated with no breakthroughs yet, making the path to densification difficult. [21,34]Therefore, alternative methods should be explored.For example, the use of an interlayer or additives in the SE to reduce Li deposition in pores, or engineering on the pore connectivity in the SE to prevent the percolating network, etc.
The understanding of the mechanisms by which the current affects the propagation of Li within the SE is still puzzling.It is recognized that the growth of Li dendrites within the SE alters the distribution of local current, leading to an intensified current at the tip of the dendrite.
Consequently, this results in a shift of the plating potential (the voltage at which plating, or deposition of Li occurs) inside the SE, deviating the 0V potential. [28,35,36]However, the specific length scale at which this current focusing occurs in the lateral direction of the SE relative to the dendrite tip remains uncertain.Further investigation is necessary to determine the spatial extent over which the intensified current is concentrated around the dendrite tip.

Conclusions
A systematic investigation of the effect of LPS-pellet fabrication pressure (or relative density) on the failure mechanism of SSBs was performed.We showed that SSBs with denser SE fail more easily before a critical relative density is reached; after which failure is prevented.The most prevalent failure mechanism is the Li-filament growth in percolating pores within the SE, which is suppressed when the pores become isolated and small in high density pellets above the critical relative density (>95%).While different processing conditions (such as hot, warm, or cold pressing) may be required to obtain dense SE pellets, the critical relative density requirement for closing the percolating pore networks appears to be independent of the choice of SE material.Our study provides a quantitative guide for relative density optimization of SE pellet to prevent one of the most prevalent failure modes for Li-filament growth.

Preparation of Li|LPS|Li Cell
Glassy LPS material was synthesized following the procedure developed in our previous work [37] using  2  (99.9% metal basis, Alfa Aesar) and  2  5 (99.9% metal basis, Alfa Aesar).The Li|LPS|Li cell was prepared in the following sequence.Symmetric lithium electrodes were prepared by rolling Li-metal chunks (99.9% metal basis, Alfa Aesar) onto copper foil.The cells were assembled using an in-house-designed cell-making toolkit (as illustrated in Figure SI-1).A constant stack pressure of 5  was applied to the cell to maintain the conformal Li-SE interfacial contact.Notably, the symmetric cell was assembled inside a small PEEK tube, which may be subjected to non-negligible deformation when very high pressing pressure is applied.This deformation changes the diameter of the cells accordingly; therefore, the final cell diameter should be calculated, with detailed simulated in Figure SI-2.

Electrochemical Cycling and Electrochemical Impedance Spectroscopy
Each cell was tested following two sequential stages: 1) Initial rest stage: the cells were rested for 12 ℎ after assembly under the stack pressure.EIS measurement was conducted every 1.3 ℎ to monitor the temporal evolution of both the bulk and interfacial resistances.2) Electrochemical (EC) cycle stage.The charge, cycling, and EIS measurements were performed using a potentiostat (VMP-300, BioLogic).The EC and EIS measurements were conducted in a temperature chamber to ensure a constant cycling temperature.The EC measurements were performed using a current  = 15.84 , with an electrode diameter  = 3.175  to maintain the current density at  =

Permeability tests
The permeability tests were performed by pumping Ar gas through a custom-made piping and hose system, as shown in

Modeling of Li deposition in pores
An in-house-developed code based on the finite element method and the MOOSE framework [39] was implemented to solve all the coupled PDEs numerically.The default values of the parameters used in this work were obtained from experimental measurements of LPS-type SE and are listed in the last column of Table 1.

Figure 1 .
Figure 1.Effect of pellet density on cell resistance.a) Relative density of LPS pellet for various fabrication pressures (theoretical LPS density of 1.88 / 3 ).b) Nyquist plots from

Figure
Figure 2b summarizes the effect of the LPS pellet density on the cell survivability.Each data ) Within the porepercolating regime, Li filaments propagate faster with decreasing pore size, causing faster cell shorting because of the reduction in the fillable volume.

Figure 2 .
Figure 2. Effect of pellet density on Li-filament growth.a) Charging voltage of cells with different LPS pellet densities.b) Cell-shorting time ("cell-shorting regime") as a function of fabrication pressure and LPS relative density and threshold where the cell voltage increases rapidly ("no-short regime").c) Schematic of Li deposition within pores of LPS pellets with different pellet densities.Symmetric cells in the "percolating regime" have pore networks

Figure 3 .
Figure 3. Characterizations of micro-and macrostructure of LPS.3D structure of pores within the LPS pellets at densities of a) 89.2%, b) 95.3%, and c) 99.9%.d) Flowrate of Ar gas flowing out of LPS pellet as a function of Ar pressure gradient across the pellet.

Figure 4 .
Figure 4. Simulation of Li deposition in SE pores.(a) Boundaries (dashed lines) of Li filament (gray area) at different charging times (in h) within a pore of 2- diameter.The Li metal on the top is the anode during charging.The maximum Li width at a specific time is the summation of the Li width on each side ( =  1 +  2 ).(b) Deposition current density along line A-B-E at different charging times.The labels "A", "B", and "E" along the x-axis correspond to locations A, B, and E in 4a.Note that location E changes at different time steps.(c) Maximum Li width in the pore when   = 10  (dashed black line),   = 2  (red line),   = 1  (blue line), and   = 0.5  (green line).(d) Length of Li filament in the pore when   = 2  (red line),   = 1  (blue line), and   = 0.5  (green line).

Figure 5 .
Figure 5. Schematics of Li-filament (Gray) growth in the solid electrolyte (Orange) at different conditions.a) Li (gray) deposit within the tortuous pore network at low current density with multiple branches and varying thickness.The yellow line represents the SEI layer formed due to the chemical reaction between LPS and the Li filament.b) Li (Gray) deposit within the tortuous pore network and isolated pores at high current density.c) Li deposit in isolated pores at low current density.d) Li deposits in isolated pores and causes fracture at high current density.Four identified mechanisms in the symmetric SSB: percolating pores (Mechanism 1), chemical reaction (Mechanism 2), electronic conductivity (Mechanism 3), and SE fracture (Mechanism 4).Li metal, the SEI layer, and voids are colored gray, yellow, and white, respectively.The dashed lines for Mechanism 3 represent electron conduction due to electronic conductivity of the SE.The red FigureSI-9.The inlet flow of Ar gas was measured and compared with the outlet Ar gas flow, which was used to determine the permeability of the tested sample.The LPS pellet was sealed inside two cylindrical tubes, with Ar gas flowing into the pellet from the bottom tube and flowing out to the top tube.The pneumatic pressure (  ) of the inlet Ar gas in the bottom tube was controlled by the valve on the Ar tank.The flow rate () of the outlet Ar gas in the top tube was measured using a highly sensitive flow meter (sensitivity of 0.01 /).The pneumatic pressure (  ) of the outlet Ar was measured very close to the atmospheric pressure (  =   ).

Table 1 .
Key parameters used in this work.