Journal of The Electrochemical Society, 160 (1) A77-A81 (2013)
0013-4651/2013/160(1)/A77/5/$28.00 © The Electrochemical Society

A77

Effect of Compressive Stress on Electrochemical Performanceof Silicon Anodes
Daniela Molina Piper, Thomas A. Yersak, and Se-Hee Leez
Department of Mechanical Engineering, University of Colorado at Boulder, Boulder, Colorado 80309, USA
In this study, we report on the effect that an externally applied compressive stress has on the electrochemical performance of Si
anodes. Using the compression of an all-solid-state cell as a convenient format for simulating volume confinement, the electrochemical
performance of Si anodes as a function of externally applied compressive stress has been systematically investigated. We verify thatthe extent of Si lithiation is limited by confining the free volume expansion of nano-Si particles. Volume confinement of Si particles
is manifested as an overpotential and results in a stable anode for lithium-ion batteries. These results are foundational and lead to thebest understanding to date of the complex electrochemomechanics of a Si-based anode.
© 2012 The Electrochemical Society. [DOI: 10.1149/2.064301jes] All rights reserved.
Manuscript submitted September 12, 2012; revised manuscript received October 22, 2012. Published November 7, 2012.

Si is one of the most promising anode materials for next generation
Li-ion batteries because of its natural abundance and its specific capacity in excess of 3500 mAh g−1 .1 To achieve such a massive capacity,
it is well known that Si undergoes a volume expansion of roughly
300% accommodating 3.75 mole Li per mole of Si to form Li15 Si4at room temperature.2–4 During volume expansion and contraction,
Si particles crack and pulverized fragments can become detachedand electrically isolated. The utilization of nano-Si has largely addressed the active material pulverization issue because nanoparticles
can better accommodate the large strains associated with lithiation.5,6
However, expansion of nano-Si particles can also pulverize the composite electrode structure such that electrical contact is lost between
active material and conductive additives.7–11
The development of a scheme to limit the extent of Si lithiation
would improve the cycleability of Si electrodes while only moderately reducing maximum specific capacity. Mechanical confinement
provided by an electrochemically inactive matrix or coating to limit
the volume expansion of Si may be such a scheme.12–16 Along theselines, J. Saint et al. observed improved cycleability when nano-Si wascoated with a dense carbon matrix.13 The authors speculated that themechanical confinement of the nano-Si particles by the carbon matrix
enabled the electrode particles to maintain good electrical contact andlimited the pulverization of the electrode during cycling. S.-B. Son
et al. described a similar outcome as a consequence of the mechanical confinement of nano-Si particles in a Lix Ti4 Ni4 Si7 matrix.12 The
authors observed that the discharge plateau of their Si-Ti-Ni alloy electrode occurred at a lower potential than that of a Si control electrode.
S.-B. Son et al. believe that the overpotential is a manifestation of theinternally generated pressure provided by the Lix Ti4 Ni4 Si7 matrix.12
Neither work was capable of characterizing the internally generated stress needed to limit lithiation of Si. Our prior work investigatedthe performance of nano-Si and μm-Si in a bulk-type all-solid-state
cell configuration.17,18 In order to simulate a condition of volume confinement, we utilize a similar all-solid-state construction and apply auniaxial external pressure in order to characterize the electrochemomechanics of Si. To the best of our knowledge, no other work has
characterized bulk Si electrodes in such a way. Using the cold compression of an all-solid-state cell as a convenient format for simulating
volume confinement, we verify that mechanical confinement limits theextent of Si lithiation and is manifested as an overpotential.
Experimental
All processes including synthesis of material, assembly of test
cells, and testing of cells were carried out in a dry Argon environment.
The 77.5Li2 S-22.5P2 S5 glass solid-state electrolyte (SSE) used as thebasis for our all-solid-state construction is prepared by milling anappropriate ratio of Li2 S (Aldrich, 99.999%, reagent grade) and P2 S5z

E-mail: sehee.lee@colorado.edu(Aldrich, 99%) with a planetary ball mill (Across International PQN2). 2 g net weight of material is milled in a 500 mL stainless steel vial
(Across International) with two 16 mm diameter and twenty 10 mmdiameter stainless steel balls at 400 rpm for 20 hours. The composite
electrode is a 1:1:5 weight ratio of crystalline Si powder (50 nm, Alfa
Aesar, 98%), copper powder (20–40 nm, Alfa Aesar, 99.9%) and glass
SSE, respectively. The composite anode is a vortex mixed 1:4 weightratio mixture of stabilized lithium metal powder (SLMP, Lectro Max
Powder 100, FMC Lithium corp.) and SSE, respectively. A tri-layerpellet, 1.3273 cm−2 in diameter, is made by first pressing 200 mg of
SSE in the Titanium/Polyetheretherketone (PEEK) die at 1 metric ton.
2 mg of composite electrode and 20 mg of composite anode are thenattached to opposite sides of the SSE pellet by pressing at 5 metrictons. Each cell is then uniaxially compressed to a different pressure(3, 150, 230 MPa) that was held constant throughout cell testing. 3
MPa is the typical external pressure applied to cold-compacted allsolid-state test cells to ensure good performance. To apply pressures of
150 and 230 MPa during cycling, we used reinforced cell die clamps,
which are similar in design to those used in previous studies (Fig. 1).
Electrochemical measurements were carried out using an Arbin 2000
battery test station using a constant current testing scheme to cycle
the cells. These electrochemical half-cells were discharged (alloying,lithiation) and charged (de-alloying, delithiation) at 50 μA with avoltage range of 0.01–1.0 V (vs. Li/Li+ ).
Results and Discussion
Figure 2a presents the cycling capacities of the three cells uniaxially compressed to 3 (blue circles), 150 (red diamonds) or 230(black squares) MPa. The 3 MPa cell only survives 8 cycles of operation before failure due to an unstable Lithium counter electrode.19,20
Each cell was cycled at a rate of C/20 to ensure full lithiation of ournano-Si particles. Despite such a slow rate, we find that the initial discharge capacity decreases with an increasing applied pressure. Initialdischarge capacities of each cell are circled in yellow. The trend of
decreasing initial discharge capacity with increasing applied pressure
is highlighted by arrows. The 3 MPa cell achieves a nearly theoretical capacity of 3.7 mole Li per mole of Si while the 150 MPa cellachieves 3 mole Li and the 230 MPa cell achieves only 1.6 mole Li.
However, a fraction of the initial capacity must be attributed to theirreversible formation of a solid electrolyte interphase (SEI). A fraction of the nano-Si in the electrode is likely electrochemically inactive
because nano-Si particles have a tendency to agglomerate during electrode mixing. With this in mind, the 3 MPa solid-state cell does notachieve a theoretical lithiation despite having an initial capacity of 3.7
mole Li.
The first cycle Coulombic efficiency (CE) for the cell under only
3 MPa of pressure was 55%, while both cells under higher pressure had
a first cycle CE of only 40%. Like liquid cells, initial capacity loss in abulk-type solid-state cell can also be attributed to SEI layer formation.
In our case, the SEI will form at the interface between the Si particle

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Journal of The Electrochemical Society, 160 (1) A77-A81 (2013)

Figure 1. To apply a large uniaxial external compressive stress, this experiment utilized reinforced Ti/PEEK cell dies. The bulk-type all-solid-state Li
battery design is based upon the Li2 S-P2 S5 glass solid-state electrolyte.

and the glass electrolyte. While the composition of the SEI will bedifferent in a solid-state electrode than in a conventional electrode,the effect of first cycle capacity loss is still the same. S.-B. Son et al.
have previously identified the SEI of solid-state Si electrodes.18 To
explain the low first cycle CE of the nano-Si electrodes, we must
consider the total area of the solid-solid interface between the SSE
and Si particles. The Si-SSE interfacial area will be much larger for

Figure 2. (a) Electrochemical performance and CE of solid-state nano-Si
composite anodes cycled at a rate of C/20 under compressive pressures of
3 (blue), 150 (red) and 230 (black) MPa. (b) Specific charge (delithiation)
capacity retention as a percentage of initial specific capacity.

nano-Si based electrodes than for μm-Si based electrodes. More SEI
will initially form in a nano-Si electrode than in a μm-Si electrode.
S.-B. Son measured an initial CE of 75% for μm-Si electrodes18 while
our 3 MPa nano-Si electrode has an initial CE of only 55%. The lower
CE is due to a larger interfacial area. However, the pressurized 150
and 230 MPa cells have an even lower initial cycle CE of 40%. We can
explain the lower CE by considering that the interfacial contact area
between Si particles and the SSE particles is further increased underpressure. In order to fully validate this theory more characterization
data would be needed; nevertheless, the CEs of the two pressurizedcells improve rapidly to match that of the 3 MPa cell.
Figure 2b presents specific charge (delithiation) capacity retention
as a percentage of initial specific capacity. The 3 MPa control cell’s
specific charge capacity (blue) rapidly fades and is only 76.1% reversible by its 8th cycle. However, the 150 (red) and 230 (black) MPa
cells quickly stabilize and are 87.3% and 99% reversible by the 21stcycle, respectively. While the application of an external load limits
achievable capacity, it also stabilizes the capacity of the cells. Thus, alower initial capacity is countered by a stable cycling behavior which
is an attribute favored for battery materials.
When the voltage profiles of these three cells are studied, we noticethat a lower initial discharge capacity is associated not only with anincreased externally applied pressure but also with an overpotential(Fig. 3a and 3c). The overpotential observed in Fig. 3 is emphasizedwith arrows. We expect that the application of pressure will result inbetter interparticle contact and therefore a decrease in interparticle
resistance. However, an increase of bulk and interfacial conductivities
would lead to a drop in overpotential, which is not what we observed in
our pressurized cells. Therefore, the overpotential observed is dominated by the free volume confinement of Si expansion and not bymechanical contact issues.
The same result is presented as the differential capacity (dQ/dV)of each cells’ 1st and 3rd cycle in Fig. 3b and 3d, respectively. Arrows highlight the shift of cathodic (alloying) dQ/dV peaks to lower
potentials with the application of a larger external pressure. During
the first lithiation (discharge), we observe a voltage plateau at approximately 0.1 V and a corresponding sharp dQ/dV peak. This sharp
peak is attributed to the reaction of Li with crystalline Si (c-Si) toform amorphous Lix Si (a-Lix Si). Upon subsequent cycles, we do not
observe a voltage plateau nor do we observe a sharp dQ/dV peak.
Instead, we observe sloping voltage profiles and two broad dQ/dV
peaks in both anodic (de-alloying) and cathodic (alloying) regimes.
A sloping voltage profile and two broad dQ/dV peaks are consistent
with the solid solution reaction of Li with a-Lix Si.10 The absence of acathodic c-Si dQ/dV peak on subsequent cycles indicates the uniform
lithiation of electrochemically active nano-Si in our composite electrodes. The absence of an anodic Li15 Si4 dQ/dV peak indicates thatthe crystalline Li15 Si4 phase was not nucleated at full discharge. The
small diameter of our nano-Si (≤50 nm) particles may have made it
thermodynamically unfavorable to nucleate the crystalline phase.10
We have shown that the overpotential, or discharge polarization,is related to the mechanical confinement of Si’s expansion. During afree volume expansion, Si is allowed to expand unrestricted and no energy is expended for the expansion. The 3 MPa cell approximates thiscondition because void spaces in the all-solid-state electrode accommodate Si’s volume change (Fig. 4a). Our all-solid-state electrodes
are formed by cold-compaction without a sintering or densification
step so we expect that voids exist between Li2 S-P2 S5 SSE particles.21
However, these voids are mechanically closed when the all-solidstate electrodes are subjected to large external pressures of 150 and
230 MPa. With the application of a large external pressure, the allsolid-state electrode behaves more like an ideal volume confining elastic matrix.18 The assumption that the Li2 S-P2 S5 SSE behaves as anelastic matrix is a good one because the electrochemical data presents areversible system. If the Li2 S-P2 S5 SSE underwent substantial plastic
deformation during Si lithiation, then the loss of interparticle contact
upon Si delithiation would result in rapid capacity fade. Under a condition of volume confinement, energy is expended to counteract thevolumetric strains generated by Si’s expansion (Fig. 4b). This energy

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Journal of The Electrochemical Society, 160 (1) A77-A81 (2013)

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Figure 3. (a) 1st cycle voltage profiles, (b) 1st cycled differential capacity, (c) 3rd cycle voltage profiles and (d) 3rd cycle differential capacity.

expenditure reduces the spontaneity of the reaction and reduces thepotential of the initial alloying of c-Si (c-Si → a-Lix Si). At 20% of theinitial discharge, the 150 MPa cell exhibits an overpotential of 36 mV
and the 230 MPa cell exhibits an overpotential of 50 mV with respect
to the 3 MPa cell. After the initial cycle, the solid solution reactionof Li with a-Si (a-Si → a-Lix Si) exhibits a typical sloping profile
between 0.3 and 0.01 V. The same overpotential effect is observedin these subsequent cycles as well because the SSE in the composite
electrode accommodates Si’s volumetric strain elastically.
Under an appropriately large external pressure, our all-solid-stateelectrode approximates the physics of the previously reported densecarbon coating13 and Ti4 Ni4 Si7 matrix.12 To better understand the behavior of nano-Si expansion in an elastic matrix, we desire to define
how the volumetric strain energy increases as a function of Li concen-

Figure 4. Alloying of a nano-Si particle under a condition of (a) free volume
expansion results in full lithiation, while alloying nano-Si under a conditionof (b) volumetric confinement in an isotropic elastic matrix results in limited
lithiation.

tration in Lix Si. We chose to focus our attention on the case of a solid
solution reaction between a-Si and a-Lix Si. The results are presented
in Fig. 5. Unlike the lithiation of c-Si, the lithiation of a-Si does not
result in large structural changes. For this reason, we can apply several
simplifications to our analysis: 1) The activity coefficient, γ, of Li in
a-Lix Si remains constant with respect to Li concentration, [Li]. 2) The

Figure 5. Free energy diagram of the amorphous Si/amorphous Lix Si solid
solution under conditions of free volume expansion (solid green), and confinedvolumetric expansion (dashed blue).

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Journal of The Electrochemical Society, 160 (1) A77-A81 (2013)

volume of a-Lix Si particle changes linearly with a change in [Li]. The
Gibb’s free energy of a solid solution reaction follows Eq. 1 where theactivity of Li, aLi , alloyed in Si is proportional to [Li]. G 0 accounts
for the standard Gibb’s free energy and the activity coefficient of thereaction (G 0 + RT lnγ). Under a condition of free volume expansion,
the alloying of a-Si will proceed to the room temperature theoreticalvalue of 3.75 mole Li per mole of Si (green solid line). Because our
3 MPa nano-Si electrode achieves a very high capacity and because
volume energy will decrease according to r3 while surface energy will
only increase according to r2 , we will neglect the impact that surface
energy has on the free energy of nano-Si lithiation.10
G = G 0 + RT ln [Li][1]

We assume that amorphous nano-Si particles expand isotropicallyand that the Li2 S-P2 S5 glass SSE is an isotropic linear elastic solid.
As previously mentioned, the sloping voltage profile of our electrodes
indicates the solid solution reaction of Li with a-Lix Si. Amorphousmaterials have no long-range order and therefore no preferential Litransport direction that would cause anisotropic expansion. In thiscase, the problem simplifies to a state of hydrostatic stress and we
consider the bulk modulus of the matrix, K, as a function of volumetricstress, σ, and strain, εν , of the Si particle, Eq. 2. Rearranging Eq. 2 wesolve for Si volumetric stress as a function of matrix bulk modulus
and Si volumetric strain, δV/V, Eq. 3.
σ
K =−
[2]
εν
δV
[3]
V
In this analysis we do not consider stresses generated inside theSi nano-particle. Here, we are concerned only with the external stressthat the expanding Si particle exerts on the matrix, and the equal but
opposite stress of the matrix on Si. After substituting the appropriate
expressions for volumetric strain, volumetric stress is expressed as afunction of unstrained particle radius, r0 , and alloyed radius, r, Eq. 4.
The integration term in Eq. 4 is strictly a substitution of the δV term in
Eq. 3. To ensure a linear elastic treatment of the matrix deformation,
it is required that the change in radius is small.
 3

 r
r
K
2
4πr dr = −K
− 1 , r − r0  r0[4]
σ=−4 3r03
πr0 r03
σ = −K

Finally, volumetric strain energy, U, is given as a function of volumetric stress, Eq. 5.
1
1 σ2= Stress × Strain[5]
2K
2With these results it is shown that Li concentration is proportional
to volumetric stress according to Eq. 6, 7, and 8.
U=[Li] ∝ V ∝ r 3[6]

σ ∝ r3[7][Li] ∝ σ[8]

Using Eq. 5, it follows that volumetric strain energy is proportional
to the square of Li concentration, Eq. 9 and 10.
U ∝ σ2[9]U ∝ [Li]2[10][Li] – Lithium concentration in Lix Si
G – Gibb’s free energy
G0 – Standard Gibb’s free energyG0 = G0 + RTlnγ
aLi – Lithium activity in Lix Si
K – Elastic bulk modulus

U – volumetric strain energy
σ – volumetric stressεν – volumetric strainr0 – initial radius of nano-Si particler – radius of nano-Lix Si particle
When the solid solution free energy curve is combined with theparabolic volumetric strain energy curve we obtain a convex curvethat achieves equilibrium at a much lower [Li] (Fig. 5, blue dashedline). The coefficient, a, of the parabolic profile is influenced by thebulk modulus K; if K increases so will a. With this result, we cometo the understanding that each incremental increase in [Li] requires a
rapidly increasing energy expenditure to elastically deform the matrix
in order to accommodate the coincident increase in volume. In thisway, the bulk modulus of the matrix can be tailored to achieve a certain
degree of Si lithiation. It is important to understand that the experimental trend of decreasing capacity among the 3, 150 and 230 MPa
all-solid-state cells is not related to a change in the Li2 S-P2 S5 SSE’s
bulk modulus. Instead, this effect is a result of mechanically closing
void spaces with the application of external pressure to more accurately simulate complete volume confinement.
The analysis presented here closely approximates any example
where Si is embedded in a linear elastic isotropic matrix (i.e. ourall-solid-state nano-Si electrodes under large external pressure andSi-Ti-Ni alloys12 ). The physics of thin elastic coatings are much more
complex and will require a more detailed approach, though the general
conclusions presented here are still relevant. For matrices and thicker
coatings, there is opportunity to greatly improve the theoretical analysis by treating the assumptions made in this paper more rigorously.
For example, our analysis assumes the linear elastic deformation of
the matrix such that the volumetric strain of Si particles is small (i.e.
r – r0  r0 ). For large volumetric strains, a more rigorous non-linear
approach should be taken. Yet, a confined particle may only expand
volumetrically by 50% or less such that r is only 14% larger than r0
and our simplified analysis is still valid. An improved analysis may
also consider the effects that a compressive stress has on Li+ transportkinetics in Si. Our theoretical analysis only considers the thermodynamic equilibrium of the system. This restricts a direct correlation of
our experiments to the theoretical work because the experimental data
inevitably includes kinetic polarizations.
Conclusions
S.-B. Son et al. previously reported that their Si-Ti-Ni alloy exhibited an overpotential with respect to a bulk-Si control cell.12 We
observe an increasing discharge polarization with increasing appliedexternal pressure and confirm the hypothesis of S.-B. Son et al.’s
study. An all-solid-state electrode under a sufficiently large externalpressure confines the volume expansion of nano-Si particles and limits the extent of lithiation. Reducing the extent of nano-Si electrodevolume expansion is important if the mechanical pulverization of acomposite electrode structure is to be prevented. The application of apressure, either internally or externally generated, results in a much
more stable and long-lasting anode for lithium-ion batteries. Such astable anode is achieved by sacrificing a fraction of overall capacity.
However, total cell specific capacity is not limited by the anode if
the anode can achieve a capacity of at least 1000–1200 mAh g−1 .
Improvements beyond this number result in diminishing returns as
far as overall cell specific capacity is concerned.1 The design of mechanically confining matrixes is therefore an exciting avenue for thedevelopment of stable nano-Si anodes.
Acknowledgments
This work was supported by a grant from the National Science
Foundation (NSF, DMR-1206462) and by the National Science Foundation Graduate Research Fellowship Program (NSF-GRFP). Authors
Daniela Molina Piper and Thomas A. Yersak contributed equally tothis work.

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Journal of The Electrochemical Society, 160 (1) A77-A81 (2013)
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