Fracture Dynamics in Silicon Anode Solid-State Batteries
AUTHORS
D. Lars Nelson1, Stephanie E. Sandoval1, Jaechan Pyo2, Donald Bistri2, Talia A. Thomas3, Kelsey
Anne Cavallaro1, John A. Lewis1, Abhinav S. Iyer3, Pavel Shevchenko4, Claudio V. Di Leo*2, and
Matthew T. McDowell*1,3
AFFILIATIONS
1. School of Materials Science and Engineering, Georgia Institute of Technology, Atlanta,
GA, 30332, USA
2. Daniel Guggenheim School of Aerospace Engineering, Georgia Institute of Technology,
Atlanta, GA, 30332, USA
3. George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology,
Atlanta, GA, 30332, USA
4. Advanced Photon Source, Argonne National Laboratory, Lemont, IL, USA
*Corresponding author:
mattmcdowell@gatech.edu
cvdileo@gatech.edu
Keywords: Batteries, energy storage, X-ray tomography, chemo-mechanics
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ABSTRACT
Solid-state batteries (SSBs) with silicon anodes could enable improved safety and energy density
compared to lithium-ion batteries.1,2 However, degradation arising from the massive volumetric
changes of silicon anodes during cycling are not well understood in solid-state systems. Here, we
use operando X-ray computed microtomography to reveal micro-to-macro-scale chemomechanical degradation processes of silicon anodes in SSBs. Mud-type channel cracks driven
by biaxial tensile stress form across the electrode during delithiation. We also find detrimental
cracks at the silicon/solid electrolyte interface that form due to local reaction competition between
neighboring domains of different sizes. Continuum phase-field damage modeling quantifies
stress-driven channel cracking and shows that the lithiated silicon stress state is critical for
determining the extent of interfacial fracture. This work reveals novel mechanisms that govern
SSBs compared to conventional lithium-ion batteries and provides guidelines for engineering
chemo-mechanically resilient electrodes for high-energy batteries.
2
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INTRODUCTION
Silicon shows great promise as a lithium battery anode material due to its high specific capacity
(3579 mAh g-1),3 natural abundance,4 low cost,4 environmental friendliness,2 and ease of
manufacturing.1,5 However, its use in conventional lithium-ion batteries has been limited because
of massive volumetric changes during cycling (>300%).3,6 Expansion and contraction during
lithiation/delithiation cause continuous growth of the solid-electrolyte interphase (SEI) as the liquid
electrolyte reacts with newly exposed surface each cycle.6–9 In SSBs, this continuous SEI growth
and associated capacity fade are largely mitigated since the electrolyte does not flow into
cracks.1,2,10–12 Due to limited SEI growth, micron-scale silicon particles can be used within SSB
anodes,2,10 whereas nano-sized silicon with complex engineered structure is needed to minimize
SEI growth in liquid-electrolyte systems.7,9,13 Recent studies have achieved stable cycling of
silicon-based SSBs at relatively high stack pressure, highlighting the potential of silicon as a SSB
anode.10,14–17
Despite recent promising performance, the fundamental understanding of and control over the
dynamic evolution of silicon anodes in SSBs has yet to be realized.1,2 The nanoscale reaction
mechanisms of silicon with lithium have previously been investigated with a variety of in situ
experiments, including X-ray diffraction,18,19 transmission electron microscopy,20–22 and nuclear
magnetic resonance,23,24 and the behavior of silicon electrodes in lithium-ion batteries is fairly well
understood.25–27 However, SSBs present a completely different electro-chemo-mechanical
environment with different expected behavior. Morphology evolution and chemo-mechanical
damage of silicon electrodes in SSBs have been observed ex situ with scanning electron
microscopy (SEM) and focused-ion beam (FIB) SEM.5,10,15–17,28 Thick silicon electrodes operated
under stack pressure in SSBs have been shown to exhibit a vertically-oriented network of “mudcracks” after delithiation,5,10,17,28 similar to silicon electrodes in liquid-electrolyte systems.6,8,29,30
While these observations provide a glimpse into the behavior of silicon electrodes, they fail to
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capture dynamic evolution and they can only provide a limited view of the silicon/solid-state
electrolyte (SSE) interface (<100 µm). Additionally, ex situ characterization is destructive and is
performed after removal of the stack pressure present during testing, which likely alters the
interface from its true state. Thus, operando characterization is needed to relate structural
evolution to electrochemical performance.
X-ray computed tomography (XCT) is a powerful technique for revealing the morphological
evolution of materials and buried interfaces due to its broad field of view and non-destructive
nature. XCT imaging has proven invaluable for observing the evolution of battery materials,31–34
and efforts have focused on understanding the behavior of lithium metal anodes.35–38 XCT has
also been used to characterize silicon electrodes for lithium-ion batteries.39–41 Recent
investigations of composite silicon anodes in SSBs have investigated electrode additives and
examined composite electrode evolution,42,43 but comprehensive investigation of degradation at
the SSE/silicon interface is needed.
Here, we use operando XCT to investigate the structural evolution of 99.0% microparticle silicon
anodes in SSBs with Li6PS5Cl (LPSC) solid-state electrolyte. Vertical mud-type channel cracks
grow through the thickness of the silicon during delithiation, as driven by shrinkage-induced biaxial
tensile stress. These cracks are observed to close near the SSE interface during partial relithiation. XCT analysis reveals newly observed interfacial fracture processes at the silicon/LPSC
interface, in which interfacial cracks can form during both delithiation and relithiation. The
formation of interfacial cracks is caused by the local morphological dynamics of neighboring
silicon domains, indicating that electrode inhomogeneities can lead to interfacial contact loss and
reduction of active electrode area. To quantify the links between stress and damage, a diffusiondeformation-damage continuum phase-field framework is developed44,45 which captures the
dynamic formation of the observed mud-type channel cracks and demonstrates that crack spacing
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depends on electrode thickness/material properties. The formation of interfacial cracks is modeled
in the presence of film imperfections, revealing the importance of initial stress state within the
silicon in determining interfacial fracture. Together, these results provide new insight and
strategies for engineering the chemo-mechanical properties of silicon electrodes, and they shed
light on key mechanistic differences between emerging solid-state and conventional liquidelectrolyte battery systems.
RESULTS AND DISCUSSION
Visualizing Fracture Dynamics
We carried out operando synchrotron XCT with half cells in a custom cell housing with 2 mm
internal diameter to enable transmission of X-rays (Fig. 1a).35,36,38 The working electrode consisted
of 99.0 wt% silicon microparticles slurry-cast on copper foil with an areal loading of 2.0 mg Si cm2
(7.15 mAh cm-2), and the counter electrode was lithium metal. The cylindrical cell was rotated
during galvanostatic testing under X-ray illumination to collect projection images, which were then
reconstructed into three-dimensional datasets of the cell stack with voxel size of 1.4 mm (Fig. 1a).
An experiment with voltage curves shown in Fig. 1b involved first collecting a 3D dataset of the
pristine cell, then lithiating the silicon electrode and collecting another 3D dataset. Operando
scans were then performed during further delithiation and relithiation of this cell, with 30 operando
datasets collected during delithiation and 12 during lithiation at 15-min intervals. The slight divots
in the operando voltage curves in Figure 1b occurred during X-ray exposure, as has been reported
in prior work.35 While this small-scale XCT cell showed similar electrochemical behavior to 1-cm
diameter anvil cells during the first cycle (Fig. S1),10,15,16 the cutoff voltage during the operando
relithiation portion was reached prematurely compared to anvil cells, resulting in lower capacity.
This also resulted in accelerated capacity decay in the tomography cells with further cycling (Fig.
S1). The reasons for this are discussed subsequently.
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Figure 1: Experimental design and selected images from operando XCT. (a) Schematic
representation of the operando XCT cell design, imaging, and image reconstruction procedure.
(b) Galvanostatic voltage profile of a silicon half cell cycled during the operando XCT experiment
at 0.5 mA cm-2 current density, 10 MPa stack pressure, and 25 °C. XCT images were collected
before and after the first lithiation, and then every 15 min during delithiation and relithiation. (c)
Reconstructed 3D rendering of the cell stack from XCT data, with different 2D slices highlighted.
(d) Vertical cross-section images showing the silicon/LPSC interface in the (i) pristine, (ii) lithiated,
(iii) delithiated, and (iv) relithiated states, with false-color overlay highlighting silicon and LPSC in
(i). (e-g) Planar images from the midpoint of the silicon electrode in the (e) lithiated, (f) delithiated,
and (g) relithiated states.
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Figure 1c shows the reconstructed 3D volume obtained from the operando XCT experiment with
two different 2D sections highlighted. One shows the silicon/LPSC interface, with 2D crosssectional image slices at different times shown in Fig. 1d. The other is oriented within the silicon
electrode plane, and its 2D image slices are shown in Fig. 1e-g. As seen in the cross-sectional
images, the ~10 mm thick pristine silicon electrode (Fig. 1d(i)) increases in thickness after
lithiation and exhibits slightly darker absorption contrast due to uptake of lithium (Fig. 1d(ii)).
Individual particulates in the pristine film are less distinct after lithiation, and the electrode is more
continuous due to the volume expansion and merging into larger LixSi particles. The merging of
silicon particles to form continuous films during lithiation has been observed in previous
studies10,16,28 and is qualitatively evident from the change in visual texture from rough and
particulate in the pristine state (Fig. 1d(i)) to smooth and conjoined in the lithiated state (Fig.
1d(ii)). However, the resolution of these experiments (1.4 µm voxel size) does not allow for
detailed analysis of particle merging or visibility of the binder material (PVDF). Some thin cracks
are also visible in select locations of the lithiated electrode, but these are very few.
After delithiation, the entire electrode shows mud-type channel cracking, with vertical cracks
forming between distinct domains of silicon (Fig. 1d(iii) and Fig. 1f). The average diameter of
these domains is 29.5 μm ± 5.4 μm. Channel cracking has been observed in previous studies
using thin film or dense silicon electrodes in liquid electrolytes, and it arises due to biaxial tension
in the delithiated region under constraint from the remainder of the film.6,29,30 The average silicon
domain size after one cycle is much larger than the initial average silicon particle size of 3.31 μm
± 1.92 μm (Fig. S2), which further indicates that the LixSi particles merge to become a continuous
LixSi film during lithiation. A few delamination-type interfacial cracks separating silicon domains
from the LPSC are also visible in the cross section after delithiation (Fig. 1d(iii)). After relithiation
and volume expansion (Fig. 1d(iv)), most interfacial cracks are closed, but one is visible in the
cross-sectional image, isolating a silicon domain and leaving it unreacted. The planar view of the
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relithiated state (Fig. 1g) shows a significant reduction in the number of channel cracks due to
swelling of the silicon electrode. Since relithiation was only partial, not all cracks were completely
closed, with some remaining open near the current collector interface (Fig. 1d(iv)).
Quantifying Fracture Processes
To observe the evolution of the crack network, we used image segmentation procedures to
classify and sort fractured voxels from other phases based on intensity after applying an edgepreserving Gaussian blur filter (see Methods and SI Section S2). Figure 2a-c show renderings of
the 3D crack network in the lithiated, delithiated, and partially relithiated states. Figure 2d shows
a tilted view of the 3D crack network in the delithiated state, highlighting the channel cracks
extending through the thickness of the silicon electrode. Figure 2e shows the same tilted view
after partial relithiation. Interfacial cracks at the silicon/LPSC interface are also visible in both the
delithiated and partially relithiated states; they appear as dark regions in Figure 2b-c that span
single silicon domains within channel crack boundaries. There are more interfacial cracks after
delithiation than relithiation, and very few cracks of either type are present in the lithiated state
(Fig. 2a).
The images in Fig. 2a-e provide a top-down view of the segmented crack network as it evolves
during delithiation and relithiation. Resolvable channel cracks begin forming across the entire
electrode after ~1-h of delithiation. As these cracks widen, additional channel cracks linking them
begin to form, uniformly increasing the crack density across the electrode as delithiation
progresses. Interfacial cracks form sporadically later in the delithiation process in some regions
enclosed by channel cracks. This suggests that local chemo-mechanical interactions between
neighboring LixSi domains, rather than bulk stress evolution across the entire electrode, contribute
to interfacial fracture during delithiation. During relithiation, almost all the interfacial cracks vanish,
and this occurs before the channel cracks surrounding them disappear. As the electrode is further
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relithiated, many channel cracks are closed, but some persist because the relithiation was only
partial (Fig. 1b).
The limited relithiation capacity arose because the cutoff voltage was reached prematurely
compared to larger-diameter anvil cells (Fig. S1). The smaller diameter of the tomography cell (2
mm) as compared to typical laboratory anvil cells (~10 mm) results in a greater fraction of the
SSE and electrode that are influenced by interactions with the cells walls. We quantified the
porosity within the SSE pellet via image segmentation and found greater porosity near the cell
edges (Fig. S3), which would increase impedance near the cell edges. Such edge effects are
expected to play a greater role in cells with smaller areas. We thus believe that the lower
reversibility of the tomography cell was largely due to cell edge effects, but that this does not
affect the local and global fracture mechanisms we identify and investigate herein.
The dynamics of fracture described above were quantified by tracking the segmented crack
volume and the “unimpeded area ratio” with time (Fig. 2f). The unimpeded area ratio is defined
as the fractional electrode area through which there is a continuous visible pathway through
electrode material (i.e., there is no void voxel in each column of voxels between the current
collector and the SSE). The total crack volume and unimpeded area ratio follow inverse S-shaped
trends (Fig. 2f). There is a ~1-h period at the beginning of delithiation before the channel cracks
appear. The total crack volume then starts increasing rapidly as the channel crack network opens,
resulting in a decrease in unimpeded area. This increase in crack volume continues as interfacial
cracks start forming, but the rate of crack volume growth slows in the second half of delithiation
as the existing cracks widen without forming any new cracks. The opposite trend is observed
during relithiation, as the lithiation of silicon first near the LPSC interface causes the cracks to
close near this interface. Some crack volume remains after relithiation (Fig. 2c) due the partial
reaction of the electrode, as discussed above. Figure 2c shows that some of the remaining crack
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volume is in the form of channel cracks, especially near the edges of the electrode, again
suggesting spatially variable lithiation due to edge effects.
Figure 2: Quantifying fracture processes with image segmentation. (a-c) Renderings of the
segmented 3D crack network for the (a) lithiated, (b) delithiated, and (c) relithiated states of the
operando XCT experiment viewed from the current collector interface. (d) Tilted views of the 3D
crack network in the (d) delithiated and (e) relithiated states with the silicon volume overlaid in
gray. (f) Plots of total crack volume (top), unimpeded area ratio (middle), and galvanostatic voltage
curves (bottom) with time during delithiation and relithiation.
Interfacial Fracture
To shed light on the localized dynamics of channel-type and interfacial fracture, Figure 3 shows
time series of different cross-sectional image slices during delithiation and relithiation. Figure 3a
shows a local region that features channel cracking without substantial interfacial cracking. Some
small voids were observed in the lithiated state before delithiation (top image of Fig. 3a), though
these are mostly unresolvable with image segmentation due to their small size compared to the
larger cracks after delithiation. As delithiation progresses, the vertical channel cracks initially
appear extended through the full electrode thickness and grow laterally as the LixSi shrinks,
becoming the widest at the end of delithiation. The vast majority of vertical channel cracks across
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the electrode become visible around the same time. Although the vertical cracks are already
extended through the electrode thickness once they become resolvable, they must initiate and
propagate through the electrode over timescales faster than the experimental temporal resolution
(15 min). The LPSC interface also moves upward to accommodate the shrinking LixSi as the
opposing lithium counter electrode expands. During relithiation, the vertical cracks close near the
LPSC interface as lithiation causes swelling near this interface.
Figure 3b shows how delithiation-driven interfacial fracture typically occurs. In this region, there
is a thicker LixSi domain in the center of the image that extends ~20 µm deeper into the LPSC
than the neighboring LixSi. As the LixSi electrode is delithiated, this large domain shrinks
preferentially, exhibiting a greater linear dimensional change because of its larger size (see SI
Section S3). This results in severe interfacial delamination at the interface between the large
domain and the LPSC as the domain shrinks, but less interfacial fracture for the surrounding
thinner LixSi domains. During relithiation, the crack closes within the first two image frames due
to lithiation and swelling, indicating that this domain still retains sufficient contact to the interface
or with neighboring domains to be electrochemically or chemically lithiated. Thus, the capacity
associated with this material was not lost. Interfacial cracks were found to cover 1.5% of the total
electrode area after delithiation (calculated from Fig. 2b). Other ex situ SEM imaging studies have
reported interfacial fracture across wide areas of silicon electrodes,28 which may artificially arise
from delamination during sample preparation due to the need to remove the materials from the
stack pressure in the cell. In contrast, our operando results show that delithiation-driven interfacial
fracture occurs only under thicker silicon domains (Fig. S4 shows other examples), indicating that
divergent dimensional changes among neighboring domains of different thickness can intrinsically
drive interfacial contact loss, a phenomenon unique to SSBs. This finding indicates that silicon
electrodes with uniform thickness will likely provide enhanced interfacial contact retention and
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better performance, and future investigations of sputtered Si films with uniform thickness, as well
as methods to improve the thickness uniformity of slurry-cast electrodes, would be beneficial.
Figure 3c shows the process by which a Si domain undergoes interfacial fracture upon relithiation.
This region of the interface features a relatively large LixSi domain as in Figure 3b, and there is
evidence of minor fracture and contact loss at the LPSC interface upon delithiation as before. Due
to a lack of transport pathways at the beginning of relithiation, this domain cannot swell as quickly
as the surrounding silicon regions. The neighboring silicon expands and causes the LPSC
interface to move downward before the larger domain can expand appreciably, resulting in growth
of the interfacial crack and full separation of the large domain from the LPSC during relithiation.
The large silicon domain is thus prevented from participating in electrochemical cycling due to
delamination and represents “dead silicon.” This effect was observed for several other LixSi
domains and, similarly to the local dynamics in Fig. 3b, the lithiation-driven interfacial fracture in
Fig. 3c only occurred at locally thicker silicon domains (Fig. S5). Very few examples of this
mechanism were observed, comprising only 0.85% of the total electrode area (calculated from
Fig. 2c). These findings indicate that relithiation-driven interfacial fracture occurs due to reaction
competition from neighboring LixSi domains and highlights the importance of understanding
dynamic relationships between evolving domains at solid-solid electrochemical interfaces.
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Figure 3: Time-series cross-sectional XCT image slices from different locations at the
silicon/LPSC interface showing the delithiation and relithiation processes. (a) Images
showing the formation and partial closure of the vertical channel-crack network. (b) Images
showing delithiation-driven interfacial fracture caused by neighboring particle interactions. (c)
Images showing relithiation-driven interfacial fracture again caused by neighboring particle
interactions. The false-color overlays in the top row highlight the LixSi and LPSC regions.
The data in Figs. 1-3 are from a half cell, and to verify that these observed fracture mechanisms
are not strongly affected by the choice of counter electrode with different volume change
characteristics, we performed ex situ XCT imaging on a silicon-anode full cell with an NMC622/LPSC composite cathode (Fig. S6). Vertical channel cracking is readily apparent in the
delithiated state, creating individual delithiated silicon domains as in the half cell. The average
diameter of the delithiated silicon domains after delithiation in the full cell is 50.6 ± 7.6 μm, which
is larger than the average diameter of the domains in the half cell in Fig. 1-3 (29.5 ± 5.4 μm). This
size difference can may be influenced by the different Coulombic efficiencies of these experiments
(60.7% for the half cell compared to 45.8% for the full cell) resulting in different degrees of
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delithiation and shrinkage of the LixSi domains. Still, several delithiation-driven interfacial cracks
are observed under larger silicon domains in the full cell (Fig. S6), similar to the half cell. In both
the half and full cell datasets, we stress that the formation of smaller interfacial cracks that are
not resolvable by XCT is possible, but the interfacial cracks resolved herein in both cells appear
to form via similar mechanisms. Overall, these data provide firm evidence that the evolution of
interfacial contact in silicon anodes depends strongly on local inhomogeneities, thickness
variation, and competition among neighboring domains rather than being influenced by the
counter electrode.
To further quantify the factors governing interfacial fracture, the differences in thickness between
LixSi domains and their surroundings were averaged for all domains that underwent delithiationdriven interfacial fracture. In the operando half cell experiment, the average initial thickness
difference between the 10 LixSi domains that underwent delithiation-induced interfacial fracture
and surrounding domains was 24.2 μm ± 8.6 μm, with 13.3 μm being the smallest observed
thickness difference leading to fracture. After delithiation, the average thickness difference
decreased to 20.7 μm ± 6.4 μm. In the ex situ full cell experiment, the average thickness difference
measured for the six observed fractured domains after delithiation was 22.6 μm ± 14.8 μm (Fig.
S6), which agrees with the half cell data. Importantly, in both cells, all domains with this range of
thickness variation showed interfacial fracture behavior. These quantified values suggest that
variations in thickness between neighboring silicon domains that are on the order of 15-25 μm will
result in severe degradation of the LixSi/SSE interface. This also suggests that the maximum
silicon particle size in slurry-cast electrodes must be kept below these values to prevent protrusion
of individual silicon particles.
Impedance Evolution During Cycling
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To consider the chemo-mechanical evolution of silicon electrodes in SSBs in the context of
electrochemical cycling, in situ potentiostatic electrochemical impedance spectroscopy (EIS) was
performed on a 1-cm-diameter anvil-type silicon half cell with Li6PS5Cl (LPSC) SSE and a lithium
counter electrode. The working electrode consisted of 99.0 wt% silicon microparticles slurry-cast
on copper foil with an areal loading of 1.75 mg Si cm-2 (6.25 mAh cm-2). Figure 4a shows the
voltage profile of the cell during the first two cycles; the voltage relaxations at intervals of 0.4 mAh
cm-2 correspond to rest periods when EIS was performed. The cell shows increased reversibility
compared to the smaller tomography cells due to a reduced influence of edge effects, as already
described.
Figure 4b-c displays the impedance spectra collected during the first two cycles of this cell. Note
that control experiments on Li/Li symmetric cells with similar areal capacities showed only very
minor shifts of the spectra with no change of the spectral shape, indicating that the Li counter
electrode did not significantly contribute to impedance evolution under these conditions (Fig. S7).
The Nyquist plot in Figure 4b reveals a small drop of impedance during the first lithiation when
the silicon electrode expands. The spectral shape during the first lithiation consists of a partial
semicircle at high frequencies and a short tail at lower frequencies, with an approximate semicircle
width of ~32 Ω cm2 (Fig. 4b). There is then a continuous increase of impedance during the first
delithiation (Fig. 4b), with the inflection point at ~2 kHz in the spectra increasing almost tenfold
from 30 Ω cm2 initially to 321 Ω cm2 after delithiation. The first-cycle Coulombic efficiency was
84.6%.
The ex situ SEM images in Figure 4e-f show pristine, lithiated, and delithiated silicon electrodes
cycled in half cells. The initially particulate material (Fig. S2) became pulverized and densified
after lithiation (Fig. 4e), followed by extensive fracture after delithiation with cracks aligned
perpendicularly to the SSE interface (Fig. 4f).10 The average diameter of the silicon domains in
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Figure 4f found by measuring in two perpendicular directions is 30.8 µm ± 5.3 µm, which is similar
to that measured in the operando XCT cell (29.5 μm ± 5.4 μm). To further verify that the choice of
counter electrode does not affect the observed microstructural evolution, ex situ SEM images of
silicon anodes cycled in full cells vs LiNi0.6Co0.2Mn0.2O2 (NMC622) were also collected (Fig. S8),46–
48
and both sets of data show similar microstructures.
The second cycle (Fig. 4c) shows a similar EIS trend as the first cycle, with a decrease of
impedance during lithiation and an increase during delithiation. However, the widths of the spectra
remain larger throughout the second cycle (Fig. S9 shows demagnified spectra). Ex situ SEM
images after the second cycle are provided in Fig. S10. The spectra for the second cycle also
feature a slightly different shape of the high frequency region compared to the first cycle, with an
additional large semicircular feature between 200 kHz and 2 kHz.
Recent studies have shown that evolving interfacial contact complicates the analysis of EIS data
in SSBs, potentially making linear equivalent circuit models inaccurate.49–51 To analyze the EIS
spectra, we nevertheless use a simple equivalent circuit to extract the total resistance
corresponding to the width of all semicircular features (Fig. 4d; see Fig. S11 for the equivalent
circuits). Figure 4d shows that the overall resistance of the cells increases significantly near the
end of delithiation, which is likely due to both interfacial and bulk electrode evolution leading to
contact loss and current constriction, as detailed previously. Moreover, the resistance during the
second delithiation cycle is higher than the first.
The electrochemical effects of crack formation are apparent in the context of these in situ EIS
data in Fig. 4b-d, although these measurements were on different cells and thus cannot be directly
correlated. The vertical channel crack network and the interfacial cracks are likely the major
contributors to the increasing impedance observed during delithiation. While most silicon domains
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within enclosed channel cracks can still participate as active material during delithiation, current
constriction occurs at the edges of these regions of lost contact. Current constriction is known to
exacerbate impedance increases because of locally high current densities.49,50 The relithiation
process involves rapid crack closure near the LPSC interface, which likely reduces current
constriction effects and correlates to the fast decrease in interfacial impedance visible in Fig. 1c
during second cycle lithiation.
Figure 4: In situ EIS of a silicon anode solid-state battery half cell with corresponding ex
situ SEM images. (a) Voltage curves from an anvil-type silicon half cell under galvanostatic
testing during which EIS spectra were collected at intervals of 0.4 mAh cm-2. The cell was cycled
twice at 25 °C under 10 MPa stack pressure and a current density of 0.2 mA cm-2. (b-c) Nyquist
plots from the two cycles shown in panel (a) during (b) the first and (c) the second cycles. (d)
Extracted total area-specific resistance plotted against time for each half cycle of the in situ EIS
experiment. (e, f) Ex situ SEM images of (e) lithiated and (f) delithiated silicon electrodes removed
from cells viewed from the interface that formerly contacted the current collector.
Modeling of Stress and Damage
To further investigate the links between fracture and electrochemical cycling, we developed a
diffusion-deformation-damage continuum model which is solved using finite elements. A diffusion-
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deformation model44 is augmented to capture crack formation via a phase-field damage
framework52–54 (see SI and Figs. S15-S16 for model derivation). The framework captures the
coupled species diffusion and concurrent elastic-plastic deformation and fracture of the silicon
anode due to the large volumetric changes.45,54–56 The phase-field damage approach has the
unique benefit that crack paths are not pre-defined and can evolve based on local stress state.
Inherent microstructural heterogeneities are numerically modeled by prescribing a spatially
varying uniform distribution of the silicon fracture toughness.
Figure 5a shows a representative two-dimensional plane-strain LixSi/LPSC model in which the
LixSi is of uniform thickness. The LixSi simulation domain (blue region in Fig. 5a) is 150 μm by 10
μm and is attached to a 300 μm thick LPSC simulation domain (grey region in Fig. 5a). The LixSi
domain is modeled through the coupled deformation-diffusion-damage continuum theory, while
the LPSC electrolyte is treated as a purely linear-elastic material (see SI for details). The
simulation thus mimics the experimental results shown in Fig. 3a. Figure 5a illustrates the
evolution of damage contours (i.e., fracture) across this LixSi film during the first delithiation halfcycle. Note that damage 𝑑 is defined to range from zero to one with 𝑑 = 0 denoting the pristine
undegraded material and 𝑑 = 1 denoting the fully fractured solid (SI Section S4). Before the
delithiation step, the initial lithiation step was also simulated, resulting in no observed damage
since the film remains under compression. During delithiation, significant tensile stresses develop,
leading to the formation and growth of multiple vertical channel cracks in qualitative agreement
with the experiments. Consistent with the experimental observations, the simulated cracks
propagate across the depth of the silicon film with an average spacing of ~30 μm (see SI Section
S5 and Fig. S17). Figure S18 includes the corresponding contours of normalized state of
concentration (𝑐̅) and horizontal stress, (𝑇!! ). This agreement between simulation and experiment
demonstrates that the modeling framework can be used to quantify aspects of stress and damage
evolution.
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Figure 5b shows another simulation with the LixSi of nonuniform thickness, as experimentally
observed in Fig. 3b. During delithiation, vertical cracks form and subsequently grow underneath
the thicker region at the LixSi/LPSC interface. The simulated results are in qualitative agreement
with the observed crack patterns shown in Fig. 3b, including both the delamination of the interface
and the concentration of vertical cracks away from the imperfection. The interfacial delamination
is driven by the exacerbated vertical shrinkage of the thicker portion of the silicon electrode,
leading to the presence of tensile stresses under the imperfection.
Further simulations showed that the initial stress state within the thick LixSi domain influences the
extent of interfacial fracture. Delamination during delithiation is concentrated beneath the
imperfection when there is little stress built up during lithiation (Fig. S19). In contrast, if
compressive residual stresses are present in the LixSi region after lithiation, interfacial fracture is
expected away from the imperfection. This finding suggests that much of the stress associated
with lithiation in the experiments is accommodated through the merging of the silicon particles
and associated plastic deformation, resulting in little or no accumulation of stresses in the film at
the end of the first lithiation cycle.
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Figure 5: Phase-field modeling of the delithiation of LixSi electrodes in contact with LPSC
SSE. Contours of damage evolution in a LixSi/LPSC simulation domain with LixSi electrodes of
(a) uniform thickness, with the initial LixSi simulation domain being 150 μm by 10 μm and attached
to a 300 μm thick LPSC domain, and b) non-uniform thickness. The LPSC electrolyte is treated
as a purely linear-elastic material (see SI).
Effect of Defects and Geometry
The simulation results further show that microstructural defects, introduced here though spatial
variation of fracture toughness, do not govern the global crack pattern. Rather, as has been
discussed in relation to fragmentation of silicon films, the spacing of the vertical cracks is primarily
dictated by geometry (e.g., film thickness) and material properties (e.g., yield stress and
toughness).6,57,58 To illustrate this, we performed simulations on flat LixSi/LPSC interfaces with two
distinct distributions of fracture toughness. Figure S17 illustrates the spatial distributions of
fracture roughness and the corresponding simulated crack patterns. Irrespective of the variations
in microstructural heterogeneity, vertical cracks at similar average spacing consistently propagate
across the three silicon films. Additional simulations show that the crack spacing depends on film
thickness,57,58 with simulations of thinner 6 μm thick films forming cracks with smaller spacing (20
μm) compared to the 10 μm films. Additionally, we performed sensitivity studies on lithium
diffusivity, yield strength, and fracture toughness (Figs. S20-S22).
CONCLUSION
Our operando experiments have revealed the formation of cracks governed by three mechanisms
in silicon-anode SSBs: (1) vertical mud-type channel cracks that grow through the thickness of
the silicon, (2) delithiation-driven interfacial fracture, and (3) relithiation-driven interfacial fracture,
where (2) and (3) occur under relatively thick silicon domains. In situ EIS revealed that the
increase of impedance during delithiation of silicon anode SSBs is likely correlated to the
development of the large crack network throughout the silicon electrode. Modeling of the
silicon/SSE system showed that interfacial fracture occurs due to magnified tensile stress under
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thicker domains, rather than global electro-chemo-mechanical phenomena. Likewise, regions of
the silicon electrode that are relatively uniform in thickness are unlikely to experience interfacial
fracture and will thus retain lower interfacial impedance, suggesting that methods for producing
highly uniform electrodes (such as sputtered films) over large areas will enhance performance.
While imaging of successive cycles was not possible during this experiment due to synchrotron
time constraints, future operando XCT experiments exploring different applied stack pressures
over multiple cycles would enhance our understanding of these mechanisms as they apply to
silicon SSBs operating under commercially relevant conditions. Furthermore, investigation of the
effects of adhesion between silicon and various SSEs on interfacial fracture is needed. Our work
demonstrates that operando visualization of dynamics in emerging battery systems is critical for
understanding new mechanisms that govern behavior, and it provides a step forward in the
understanding and control of high-capacity alloy electrodes for SSBs.
METHODS
Silicon electrode preparation: Silicon electrodes were prepared with crystalline silicon powder
(Sigma-Aldrich, 325 mesh), n-methyl-2-pyrrolidone (NMP) solvent (Sigma-Aldrich), and
polyvinylidene fluoride (PVDF) binder (Sigma-Aldrich) using 1.0% PVDF and 99.0% silicon by
mass. Slurry casting was performed with a tape caster (MTI) and doctor blade. Slurries were dried
overnight in air at 50 °C. The areal loadings were 1.75 mg Si cm-2 (6.25 mAh cm-2) for the in situ
EIS experiment and 2.0 mg Si cm-2 (7.15 mAh cm-2) for the operando XCT experiment. Electrodes
were punched out with a 3/8-in diameter hole punch for anvil cell assembly and a 2 mm diameter
hammer punch for tomography cell assembly.
LNTO-coated NMC-622 composite cathode: Inside an argon-filled glovebox, 20 mg lithium
acetate (Sigma-Aldrich) was combined with 4 mL anhydrous ethanol (Sigma-Aldrich), 36 µL
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niobium ethoxide (Sigma-Aldrich), and 60 µL tantalum butoxide (Sigma-Aldrich) and stirred at 250
RPM for 6 h or until all lithium acetate was dissolved. Single-crystal NMC-622 (MSE Supplies)
was combined with the solution in a ratio of 2 g NMC / 1 mL solution and then sonicated for 1 h.
Outside of the glovebox, the mixture was placed in a vacuum oven overnight at 70 °C until all
solvent was evaporated. In a steel-lined crucible, the dried powder was heated to 300 °C over 30
min and held at this temperature for 10 h, and it was then heated to 450 °C over 15 min and held
at this temperature for 1 min before cooling to room temperature. In an argon-filled glovebox, the
LNTO-coated NMC-622 powder was combined with LPSC and carbon nanofibers (CNF) in a
mass ratio of 70% NMC-622 / 27.5% LPSC / 2.5% CNFs and then ball milled three times for 15
min at 150 RPM with 5 min of rest between each cycle.
Solid-state anvil cell assembly: Solid-state anvil cells were assembled inside an argon-filled
glovebox (MBraun, <4 ppm O2) with silicon electrodes, commercial LPSC (MSE Supplies, ultrafine
particle size (~1 micron)), and either 70% LNTO-coated NMC-622 composite cathode (full cells)
or lithium foil (MSE Supplies, half cells) in custom-made cell housings consisting of a PEEK
cylinder with a 10 mm inner diameter and two titanium rods (just under 10 mm diameter) contained
by two steel plates and 4 screws with hex nuts.15 LPSC was first pressed in the PEEK cylinder at
100 MPa to keep the LPSC pellet in place. The silicon electrode was then added, and the stack
was pressed at 325 MPa for 5 min, followed by a release period of 1 min. For full cells, enough
70% LNTO-coated NMC-622 composite cathode was added to the opposite side of the LPSC to
achieve an N:P ratio of 1.2 before pressing to 325 MPa for 5 min. For half cells, 3/8-in diameter
lithium foil was added to the opposite side of the LPSC after the 325 MPa pressing step, and then
the stack was pressed to 25 MPa for 5 min. A stack pressure of 10 MPa was applied to the battery
during testing. Cells were cycled inside the argon-filled glovebox.
Solid-state tomography cell assembly: Solid-state tomography cells were assembled inside an
argon-filled glovebox with silicon electrodes, commercial LPSC, and either 70% LNTO-coated
NMC-622 composite cathode (full cells) or lithium foil (half cells) in custom-made cell housings
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consisting of a PEEK housing with a 2 mm inner diameter and two titanium rods contained by two
hex-head screws with O-rings between the head of the screw and the edges of the PEEK
housing.35,36 LPSC was first pressed in the PEEK housing to keep the LPSC pellet in place by
applying moderate pressure by hand with a titanium rod. The silicon electrode was then added,
and the stack was pressed to >300 MPa for 5 min, followed by a release period of 5 min. For full
cells, enough 70% LNTO-coated NMC-622 composite cathode was added to achieve an N:P ratio
of 1.2 to the opposite side of the LPSC before pressing to >300 MPa for 5 min. For half cells, 2
mm diameter lithium foil was added to the opposite side of the LPSC after the >300 MPa pressing
step. A stack pressure of 10 MPa was applied to the battery during testing with the two hex-head
screws. Cells were sealed using the O-rings between the screws and the PEEK and were cycled
outside of the argon-filled glovebox for XCT imaging.
Electrochemical characterization: All electrochemical measurements and tests were performed
using a Bio-Logic SP-200 potentiostat. Potentiostatic EIS scans were collected over a frequency
range of 2 MHz to 2 Hz with 10 steps per decade. Lab-scale anvil cells were cycled at a current
density of 0.2 mA/cm2 in an argon glove box, while tomography cells were cycled at 0.5 mA/cm2.
Half cells had a lower voltage cutoff of 0.0 V and an upper voltage cutoff of 1.5 V for lab-scale
cells and 1.0 V for the tomography cells. Full cells were cycled between 2.5 V and 4.0 V.
Scanning electron microscopy: SEM was performed on a Zeiss Ultra60 FE-SEM using an
accelerating voltage of 8 kV and scanning speed of 6 during imaging.
X-ray computed microtomography: XCT was performed at Argonne National Laboratory’s
Advanced Photon Source (APS) on Beamline 2-BM. Monochromatic X-rays with an energy of
25.5 keV were used to image cells with a voxel size of 1.4 µm. 1500 projections, each with an
exposure time of 400 ms, were collected over an angle of 180° with an Oryx 5.0 MP Mono 10GigE
detector and a 2x magnification lens. 2 mm diameter tomography cells were made in a custom
solid-state cell housing (Figure 2a) that allowed for stack pressure to be maintained throughout
cycling while keeping the battery materials sealed in argon.
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Digital image processing: Image reconstruction was performed at APS with the TomoPy toolbox
for Python using the Gridrec method.59 Image segmentation was performed in MATLAB 2023a by
first converting all scans to 16-bit depth through a normalized scale and then applying a bilateral
filter (Gaussian smoothing with edge preservation) to each image using a standard deviation of
3.0 (detailed in the SI and Figs. S12-S14). Intensity-based thresholding was applied to each
image to isolate the crack network. The segmentation code is included in the supplementary
materials. 3D reconstructions of the images and segmented volumes were created in ORS
Dragonfly (non-commercial license version).
Phase-field modeling: The supplementary information contains comprehensive information on
the phase-field modeling framework.
ACKNOWLEDGMENTS
Support is acknowledged from NASA Grant Number 80NSSC21M0101. This work was performed
in part at the Georgia Tech Institute for Matter and Systems, a member of the National
Nanotechnology Coordinated Infrastructure (NNCI), which is supported by the National Science
Foundation (ECCS-2025462). This research used resources of the Advanced Photon Source, a
U.S. Department of Energy (DOE) Office of Science user facility operated for the DOE Office of
Science by Argonne National Laboratory under Contract No. DE-AC02-06CH11357.
AUTHOR CONTRIBUTIONS
D.L.N. and M.T.M. conceived the ideas for the study. D.L.N., S.E.S., T.A.T., K.A.C., and P.S.
performed the synchrotron X-ray computed tomography. D.L.N., T.A.T., and J.A.L. designed and
fabricated the tomography-scale battery housings. D.L.N., S.E.S., and A.S.I. developed the
segmentation procedures and framework. J.P., D.B., and C.V.D.L. developed the continuum
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phase-field model and performed the simulations. D.L.N., J.P., D.B., C.V.D.L., and M.T.M. wrote
the manuscript. All authors discussed the results and commented on the manuscript.
COMPETING INTERESTS
The authors declare no competing interests.
ADDITIONAL INFORMATION
Supplementary Information is available for this paper.
Correspondence and requests for materials should be addressed to Matthew McDowell.
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