A graphite anode is a stack of parallel graphene sheets. During charging, Li+ ions leaving the cathode intercalate into the galleries between sheets, forming LixC6 (0 ≤ x ≤ 1). Because Li–Li repulsion favors ions gathering in as few galleries as possible, they don't fill randomly — they order into stages: the fraction of occupied galleries increases in discrete jumps as x grows (the Daumas–Herold staging model):
Stage IV (dilute): x < 0.23 → ~1 in 4 galleries occupied
Stage III: 0.23-0.50 → ~1 in 3 galleries occupied
Stage II (LiC12): 0.50-0.75 → every other gallery occupied
Stage I (LiC6): 0.75-1.00 → every gallery occupied
Each stage transition is a distinct phase change, so the anode's open-circuit voltage vs Li/Li+ traces a real staircase, not a smooth slope — flat plateaus where two stages coexist, separated by short steps:
V(x) ≈ piecewise plateaus, 0.22 V (x≈0) down to ~0.005 V (x≈1)
Terminal V = V(x) + η, η = ±C-rate · R(T) (charge/discharge overpotential)
R(T) falls as temperature rises (faster Li+ diffusion, lower cell resistance)
As galleries fill, they also expand — interlayer spacing grows from the empty-graphite value of 3.35 Å toward ≈3.70 Å in fully-lithiated LiC6, which is the literal source of the ~10% anode swelling every Li-ion cell has to accommodate.
- Charge / Discharge — pick lithiation or delithiation direction; Play drives x toward 1 or 0 at the rate set by the C-rate slider.
- C-rate — higher current moves the stage front faster but also raises the kinetic overpotential η, pushing the terminal voltage away from the equilibrium staircase.
- Temperature — warmer electrolyte lowers ionic resistance, shrinking η so the terminal voltage tracks the true equilibrium curve more closely.
Real-world relevance: this staging behavior is exactly why a Li-ion cell's discharge curve has that distinctive multi-plateau shoulder near the end of discharge, and why fast charging past the stage-I threshold risks metallic lithium plating instead of intercalation.