A Ni-YSZ anode works because fuel, electrons and oxygen ions can all meet at triple-phase-boundary (TPB) lines — the contact between a nickel particle, the YSZ ceramic backbone and the pore gas. Over thousands of hours at 650–850 °C, nickel migrates by surface diffusion and sinters: small particles shrink, large ones grow, exactly as predicted by Lifshitz–Slyozov–Wagner (LSW) coarsening. Fewer, bigger particles mean less Ni surface area per unit volume, so TPB length density falls and cell resistance climbs.
Mean radius: r̄(t)³ = r̄₀³ + K·t
Rate constant: K = K₀ · exp(−Eₐ / R·T) (Eₐ ≈ 200 kJ/mol)
TPB density: TPB(t) ∝ 1 / r̄(t) (surface/volume of fixed Ni fraction)
Cell voltage: V(t) = OCV − j · ASR(t), ASR(t) = ASR₀ · r̄(t)/r̄₀
- Temperature — sets the Arrhenius rate constant K; every +50 °C roughly doubles the coarsening rate, the classic lifetime-vs-operating-temperature trade-off of real SOFC stacks.
- Current density — besides setting the ohmic voltage drop j·ASR, it also adds a current-induced migration term (electromigration of Ni under polarization is documented in SOFC literature) that mildly accelerates coarsening — an illustrative, simplified coupling, not a fitted value from one specific study.
- Time acceleration — real degradation unfolds over 10,000–40,000 h; this slider compresses that into a watchable animation.
- Individual particle radii are a simplified visualization of ensemble broadening (small particles shrink and vanish, large ones grow); the reported mean radius, TPB density and voltage follow the closed-form LSW/Arrhenius equations above, not the per-particle noise.
Real-world relevance: Ni coarsening is one of the two or three dominant long-term degradation mechanisms in planar SOFC stacks (alongside Cr poisoning and interconnect oxidation), and is a major reason stack designers trade peak efficiency (higher T, higher j) against a 40,000+ hour lifetime target.