Lithium Metal Deformation Behavior

• Lithium metal deformation behavior is defined by its power-law creep and extreme shear-thinning, which govern stress response and battery efficiency.
• Modeling based on the Herschel–Bulkley flow law quantifies yield stress and strain rate, elucidating mechanisms behind SEI defect-induced lithium extrusion.
• Coupling SEI fracture-healing dynamics with morphological control strategies provides actionable guidelines for optimizing battery performance and mitigating safety risks.

Lithium metal exhibits highly non-linear deformation behavior resulting from its distinctive power-law creep and sensitivity to interfacial phenomena. This deformation is central to both the utility and the challenges of lithium metal batteries, which rely on direct lithium plating for high energy density but are susceptible to disruptive microstructural evolution such as whisker formation. In lithium metal batteries, deposition-induced stresses beneath the solid-electrolyte interphase (SEI) can cause extrusion of lithium, leading to the formation of one-dimensional whiskers. The mechanisms governing this behavior, rooted in both the rheology of lithium and the dynamics of SEI fracture and healing, are crucial for understanding and controlling battery performance, safety, and Coulombic efficiency (Werres et al., 27 Mar 2025).

1. Constitutive Laws Governing Lithium Deformation

Lithium’s response to stress during electrochemical cycling is well described by the Herschel–Bulkley flow law,

$\tau = \tau_0 + K\,\dot{\gamma}^n,$

where $\tau$ is shear stress, $\tau_0$ the yield stress, $K$ the consistency index, $\dot{\gamma}$ the shear rate, and $n$ the flow index. For lithium at near-ambient temperatures, the experimentally observed flow index is $n \approx 6.6$, indicating extreme shear-thinning and power-law creep. The yield stress $\tau_0$ for bulk lithium is in the range of 0.4–1.3 MPa, though for modeling microscale extrusion, a higher value ($\tau_0 = 10$ MPa) is adopted to account for size-dependent strengthening effects.

Werres et al. employ a regularized viscosity form,

$$\mu_{\mathrm{eff}}(\dot{\gamma}) = C \, (\dot{\gamma})^{n-1} + \tau_0 \frac{1 - \exp(-m\,\dot{\gamma})}{\dot{\gamma}},$$

where $C = K$ for high shear rates and $m$ is a small regularization constant to avoid singularity as $\dot{\gamma} \to 0$. Parameters are established via uniaxial or torsional creep tests, followed by fitting strain rate–stress relationships in the power-law form and extrapolating to appropriate boundary conditions representative of the lithium-SEI interface (Werres et al., 27 Mar 2025).

2. Stress-Induced Extrusion through SEI Defects

Under operational conditions, lithium plating causes stress accumulation beneath the SEI. When SEI membrane strain surpasses approximately 10%, local fractures develop, resulting in cracks typically of radius $\sim 0.1\,r_{\mathrm{nucleus}}$. Lithium then extrudes through these cracks, modeled as laminar, steady Herschel–Bulkley flow within a narrow planar slit:

$$\frac{\partial p}{\partial x} = \frac{\partial}{\partial y}[\tau(y)],$$

with $$\tau(y) = \mu_{\mathrm{eff}}(\dot{\gamma})\,\partial v/\partial y$$, subject to no-slip at the SEI walls and prescribed pressure drop from the nucleus interior ($p_0$) to the electrolyte (zero). The simulation imposes constant plating influx at the SEI interface and free outflow at the crack exit. This model captures the fundamental mechanistic coupling between lithium rheology and local SEI defect evolution (Werres et al., 27 Mar 2025).

3. Coupling of SEI Fracture and Healing Dynamics

The emergence of lithium whiskers is controlled by the dynamic balance between SEI thinning, caused by continued lithium growth, and SEI self-healing. SEI thickness and substrate radius evolve as

$$\frac{dr_{\mathrm{nuc}}}{dt} = \frac{I\,V_m^{\mathrm{Li}}}{2\pi r_{\mathrm{nuc}}^2 F},$$

$$\frac{dL_{\mathrm{SEI}}}{dt} = \frac{V_m^{\mathrm{SEI}} D_{e^-} c_{e^-}}{L_{\mathrm{SEI}}} - \frac{2 L_{\mathrm{SEI}}}{r_{\mathrm{nuc}}} \frac{dr_{\mathrm{nuc}}}{dt},$$

where $I$ is current per nucleus, $V_m^{\mathrm{Li}}$ and $V_m^{\mathrm{SEI}}$ are molar volumes, $D_{e^-}$ and $c_{e^-}$ are electron diffusivity and concentration in the SEI. If the stretch-to-fracture time $$(\tau_{\mathrm{strain}} \sim r_{\mathrm{nuc}}/\dot{r}_{\mathrm{nuc}})$$ is shorter than the healing time $$(\tau_{\mathrm{heal}} \sim L_{\mathrm{SEI}}^2/(D_{e^-} c_{e^-} V_m^{\mathrm{SEI}}))$$, cracks form, allowing lithium extrusion and whisker nucleation. Otherwise, rapid self-healing prevents crack formation, promoting smoother lithium deposition.

Fracture is governed by the hoop strain criterion $$\epsilon_\theta \sim \Delta r_{\mathrm{nuc}}/r_{\mathrm{nuc}} \geq \epsilon_c \approx 0.1$$, with corresponding local critical stress $\sigma_c \approx E_{\mathrm{SEI}} \epsilon_c$ (1–10 GPa), reflecting the high stiffness of typical SEI phases (Werres et al., 27 Mar 2025).

4. Morphology and Growth Kinetics of Lithium Whiskers

Lithium extruded into the electrolyte adopts a one-dimensional, plug-like geometry determined by the crack through which it flows. In this regime, the strong shear-thinning of lithium’s rheology ($\mu_{\mathrm{eff}}$ large at low $\dot{\gamma}$) results in plug flow, with continuity requiring

$$A_{\mathrm{SEI}} v_{\mathrm{in}} \approx A_{\mathrm{whisker}} v_{\mathrm{extrus}}.$$

Given that $v_{\mathrm{extrus}} \gg v_{\mathrm{in}}$, the whisker cross-sectional area is much smaller than that of the crack, so the radius remains essentially that of the originating crack. Simulations indicate, for $v_{\mathrm{in}} \approx 10$ nm s⁻¹ (corresponding to $\sim 7.4$ mA cm⁻²), the whisker radius remains $100$–$1000$ nm for $t \lesssim 1$ s, while whisker length grows linearly with time at $v_{\mathrm{extrus}}$, two orders of magnitude higher than $v_{\mathrm{in}}$. The analytic prediction $r_{\mathrm{whisker}} = r_c$ (crack radius) remains valid until the crack geometry changes significantly (Werres et al., 27 Mar 2025).

5. Principles for Morphological Control and Safety

A key design rule emerges: “Either operate at currents low enough that SEI self-healing outpaces SEI thinning ($j \lesssim$ mA cm⁻² in good-SEI electrolytes), or at ultra-high currents where SEI simply fails everywhere and Wulff-shaped particles form.” Robust SEI design—favoring high electronic conductivity, rapid SEI growth, high modulus, and fracture toughness—inhibits crack formation and thus suppresses stress-driven whisker growth.

Repeated lithium deposition and stripping cycles promote interface stress accumulation, raising the risk of local SEI failure and thus “mossy” or “dead” lithium formation compacted beneath or away from the electronically active interface. The mechanical integrity of the SEI and the anode–separator interface is critical to Coulombic efficiency, safety, and the avoidance of short-circuit events.

Understanding and controlling lithium’s power-law creep and SEI fracture–healing mechanisms supports targeted approaches in electrolyte engineering, interfacial coatings, and cell design for high-performance lithium metal battery systems (Werres et al., 27 Mar 2025).