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. The bottom panel plots this equilibrium curve live alongside the terminal voltage under load:
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 (watch the gap between the two curves in the bottom panel widen).
- Temperature — warmer electrolyte lowers ionic resistance, shrinking η so the terminal voltage tracks the true equilibrium curve more closely.
- Graphene sheets — how many sheets (and therefore galleries) the stack view renders; the occupied-gallery pattern for each stage always keeps the same fraction (¼, ⅓, ½, all) no matter how many galleries there are.
- Drag the stack view — rotate the cross-section left/right and tilt it up/down to see the gallery spacing and ion ordering from any angle; scroll to zoom.
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.