Physics-based modeling of cyclic and calendar aging of LIBs with Si-Gr composite anodes

This paper presents a physics-based model that disentangles and analyzes the distinct degradation mechanisms of silicon-graphite composite anodes in lithium-ion batteries, specifically addressing the interplay between SEI growth, particle cracking, and active material loss under various cycling, storage, and check-up conditions to inform future battery optimization.

The Gist

Imagine a lithium-ion battery as a bustling city where tiny workers (lithium ions) travel back and forth between two districts: the "Graphite City" and the "Silicon Village." The goal is to keep this city running smoothly for as long as possible.

This paper is about a new digital simulation (a physics-based model) created by researchers to understand why batteries, specifically those with a "Silicon Village," eventually wear out. They wanted to figure out exactly what breaks the city down and how to predict it.

Here is the breakdown of their findings using simple analogies:

1. The Problem: The "Breathing" Silicon

The researchers are studying batteries that use a mix of Graphite and a little bit of Silicon (about 1.4%) in their negative electrode.

• The Analogy: Think of the Graphite as a sturdy brick house that stays the same size. The Silicon, however, is like a giant, inflatable balloon. When the battery charges, the balloon swells up (expands); when it discharges, it shrinks back down.
• The Issue: Because the balloon inflates and deflates so much, it puts a lot of stress on the walls. Eventually, the walls crack. In the battery, this means the silicon particles crack, lose contact with the electrical grid, and stop working.

2. The Two Main Villains of Aging

The model identifies two main ways the battery gets damaged:

A. The "Rust" (SEI Growth)

• What it is: When the battery is active, a thin protective layer called the Solid-Electrolyte Interphase (SEI) forms on the surface. It's like a layer of rust or paint that protects the metal but also eats up some of the battery's fuel (lithium) to stay thick.
• The Finding: In normal driving (cycling), this "rust" grows slowly and steadily over time. The researchers found that a specific type of "electron diffusion" (electrons moving through the rust) is the main driver of this growth.

B. The "Earthquake" (Particle Cracking)

• What it is: When the silicon balloon expands and shrinks too violently (especially when the battery is drained very low), the silicon particles crack.
• The Consequence:
  1. Loss of Land: Pieces of the silicon break off and become "islands" that are cut off from the power grid (Loss of Active Material).
  2. Fresh Rust: When a crack happens, it exposes fresh, unprotected silicon to the battery fluid. This causes a sudden, massive burst of "rust" (SEI) to form instantly to cover the new wound. This is a huge drain on the battery's life.

3. The "Check-Up" Surprise

The researchers tested batteries that sat on a shelf (storage) but were taken out periodically for a "Check-Up" (CU). A Check-Up involves fully charging and discharging the battery to measure its health.

• The Discovery: They found that the Check-Ups themselves were doing more damage than the sitting on the shelf.
• The Analogy: Imagine a patient recovering from a broken leg. The doctor says, "Don't walk, just rest." But every week, the doctor forces the patient to run a marathon to test their leg. The patient gets worse not because of the resting, but because of the weekly marathons.
• The Result: The frequent "Check-Ups" caused the silicon balloons to crack repeatedly, leading to rapid aging. The model showed that most of the damage during storage was actually caused by these testing cycles, not the storage itself.

4. How to Drive Safely (Operating Conditions)

The model acts like a traffic guide for battery usage:

• Low SoC (Low State of Charge) is Dangerous: When the battery is drained very low (below 20-30%), the silicon balloon is forced to work the hardest and expands the most. This is where the "earthquakes" (cracks) happen.
• The Sweet Spot: If you keep the battery in the "middle" range (not too full, not too empty), the silicon doesn't stretch as much. The model showed that batteries cycled in this middle range last much longer, even if you charge them fast.
• Temperature Matters: The model works well at normal temperatures (20°C and 35°C). However, at very high temperatures (50°C), the model started to guess wrong. This suggests that at high heat, other invisible forces (like the battery fluid drying out or the silicon changing its internal structure) start to break the battery in ways the current model doesn't see yet.

Summary

The researchers built a computer model that successfully predicts how silicon-graphite batteries age. They proved that:

1. Silicon cracking is the biggest enemy when batteries are drained deeply.
2. Frequent testing (Check-Ups) can accidentally kill a battery by forcing it to crack repeatedly.
3. Keeping the battery in a middle range (avoiding deep drains) is the best way to protect the fragile silicon "balloons."

The model is a powerful tool for understanding why batteries fail, but the researchers admit that at very high temperatures or extreme speeds, the "city" gets too chaotic for their current map to handle perfectly.

Technical Summary

1. Problem Statement

Lithium-ion batteries (LIBs) require higher energy densities and longer lifetimes to meet the demands of electric vehicles (EVs). Silicon (Si) is a promising anode material due to its high specific capacity, but it suffers from massive volume expansion (~300%) during lithiation/delithiation. This leads to:

• Particle Cracking: Mechanical stress causes silicon particles to fracture.
• Loss of Active Material (LAM): Cracks lead to electrical isolation of silicon fragments.
• Accelerated Degradation: Freshly exposed silicon surfaces react with the electrolyte, causing rapid Solid-Electrolyte Interphase (SEI) growth and consumption of Lithium Inventory (LLI).

Existing models often struggle to disentangle these coupled mechanisms (SEI growth vs. cracking vs. LAM) or rely on empirical fitting without physical consistency. Furthermore, the impact of Check-Up (CU) procedures (periodic testing cycles during storage) on observed calendar aging has not been fully understood, particularly regarding how CUs themselves induce degradation.

2. Methodology

The authors developed a physics-based degradation model integrated into the Single Particle Model with electrolyte effects (SPMe) using the PyBaMM framework. The model focuses on a commercial Sony Murata US18650VTC5A cell with a Silicon-Graphite (Si-Gr, 1.4% wt Si) composite anode and an NCA cathode.

Core Degradation Mechanisms Modeled:

The model isolates two primary mechanisms to avoid overfitting:

1. Continuous SEI Growth: Modeled via electron diffusion through the SEI layer. The current density driving SEI formation depends on the SEI overpotential and electron diffusion coefficients ($D_{e^-}$).
2. Silicon Particle Cracking:
   • Stress-Driven Evolution: Cracking is driven by tangential tensile stress ($\sigma_{t,surf}$) arising from lithium concentration gradients during cycling. The crack length evolution follows a fatigue law ($\partial_t l_{cr} \propto \sigma^m$).
   • Consequences of Cracking:
     • LAMSi: Loss of active silicon volume due to particle isolation.
     • Surface Modification: Cracks create new surface areas.
       • Instantaneous SEI: Fresh surfaces exposed to electrolyte immediately form a thin SEI layer ($d_{SEI}$), consuming Li-ions instantly.
       • Continuous SEI: The newly created "additional active area" contributes to ongoing continuous SEI growth.

Experimental Validation:

The model was validated against extensive experimental data from Wildfeuer et al. [24], covering:

• Storage: 96 weeks at various SoCs (10–100%) and temperatures (20°C, 35°C, 50°C) with varying CU frequencies (every 6, 12, or 96 weeks).
• Cycling: Various protocols including different C-rates, Depth of Discharge (DoD), and mean SoC.
• Check-Up Cell: A dedicated cell (C389) subjected only to repeated CUs to isolate CU-induced degradation.

3. Key Contributions

• Unified Physics-Based Framework: The model successfully integrates SEI growth (electron diffusion) and mechanical fatigue (cracking) into a single consistent SPMe framework without empirical fitting for every condition.
• Disentanglement of Mechanisms: It quantitatively separates the contributions of LAMSi, continuous SEI growth, and instantaneous SEI growth to total Capacity Loss (CL).
• Quantification of Check-Up Impact: The study reveals that CUs are not merely diagnostic; they are a primary source of degradation in Si-anodes due to the induction of cracking and subsequent instantaneous SEI formation.
• Operational Window Definition: The model identifies specific operating regimes (SoC, DoD, Temperature) where silicon degradation dominates versus where standard graphite degradation (SEI growth) dominates.

4. Key Results

A. Degradation during Check-Ups (CU)

• Dominance of Instantaneous SEI: For a cell subjected to 54 consecutive CUs, ~73% of the capacity loss was attributed to instantaneous SEI growth on freshly cracked surfaces.
• Self-Mitigating Effect: As cracking progresses, the total active surface area increases. This distributes the current density, reducing local stress and slowing down further crack propagation (a self-mitigating effect observed in the SoHSi profile).
• Non-Linearity: Doubling the CU frequency does not linearly double degradation because the rate of new crack formation slows as the particle surface area increases.

B. Cyclic Aging (Cycling Protocols)

• Low SoC / High DoD: When cycling extends into low SoC regions (where silicon is actively utilized), particle cracking becomes the dominant degradation driver, leading to significant LAMSi and instantaneous SEI loss.
• Intermediate SoC: In moderate SoC ranges (where silicon usage is minimal), continuous SEI growth is the dominant mechanism. The model confirms that electron diffusion accurately describes this growth across various C-rates.
• Temperature Effects:
  • At 35°C, the model (calibrated at 20°C) transfers well to both storage and cycling.
  • At 50°C, the model underestimates Capacity Loss and LAMSi, suggesting additional thermal degradation mechanisms (e.g., crystalline Si phase transitions or electrolyte dry-out) not captured by the current physics.

C. Storage Aging

• CU Frequency: Higher CU frequencies lead to higher total degradation, primarily because the CUs themselves induce cracking and instantaneous SEI growth.
• SoC Dependence: Higher SoC storage leads to higher degradation. However, at 100% SoC, the model underestimates LAMSi, suggesting structural reorganization of silicon (crystallization) occurs during long-term storage at high potentials.

5. Significance and Limitations

• Significance:
  • Provides a tool to optimize battery usage protocols (e.g., avoiding low SoC cutoffs to prevent cracking).
  • Demonstrates that "storage aging" in Si-anodes is heavily influenced by the frequency of testing/cycling, challenging the assumption that storage is purely chemical.
  • Validates electron diffusion as the correct physical mechanism for SEI growth in cycling conditions.
• Limitations:
  • High Temperatures (>50°C): The model fails to capture rapid degradation, likely due to unmodeled thermal effects or changes in SEI composition.
  • High C-Rates: The SPMe model struggles at very high currents (≥4C), leading to overestimated stress and cracking.
  • Parameter Uncertainty: Lack of precise cell-specific characterization (e.g., exact OCV alignment, thermal dependencies) introduces some deviation in predictions.

Conclusion

The paper presents a robust physics-based model that successfully decouples the complex degradation mechanisms of Silicon-Graphite anodes. It highlights that silicon cracking and the resulting instantaneous SEI growth are the primary drivers of degradation when silicon is actively cycled (low SoC/high DoD) or subjected to frequent check-ups. Conversely, in moderate operating windows, continuous SEI growth dominates. The work underscores the necessity of accounting for mechanical fatigue and instantaneous surface reactions to accurately predict the lifetime of next-generation high-energy batteries.