Cell Breathing Lab — voltage and lattice response on one clock

Slide the state of charge of a schematic graphite half-cell. The voltage walks its curve; the interlayer spacing dilates as lithium fills the galleries.

Model honesty: both curves are smooth illustrative teaching constructions for a graphite half-cell versus lithium. The voltage follows V(s) = 1.4·exp(−3s) + 0.11 + 0.06·(1 − s) — a monotonic decay with a soft low-voltage plateau region — standing in for graphite’s genuinely staged, stepped plateau structure, which this widget deliberately smooths. The plotted spacing follows s → 3.35 + 0.35·(0.15s + 0.85s²) Å, a smooth teaching coordinate representing gallery expansion from the graphite value toward the fully lithiated spacing — it is not a crystallographic indexing model for every graphite staging compound; the real evolution proceeds through discrete staged compounds resolved by operando diffraction. The lithiation labels (low/mid/high) are teaching bins, not stage assignments. All quantities are illustrative; no real electrode’s curve should be read off this widget.