This 2D cross-section drives the same solid-state-diffusion sintering kinetics as the 3D kiln scene: a pressed bed of powder grains (green body) densifies as atoms migrate to the necks between touching particles, grain boundaries advance and the pore network shrinks — no melting involved. Densification and grain growth share the same Arrhenius rate, which is exactly why firing hotter always densifies faster but also coarsens grains faster.
k(T) = exp[ -Q/R (1/T - 1/Tref) ] Arrhenius rate, Q ≈ 380 kJ/mol
(x/a)^5 = C · k(T) · t / a^3 two-sphere neck-growth model
ρ(t) = ρ0 + (ρf-ρ0)[1 - exp(-5(x/a)^2)] densification from neck ratio
d^3 = d0^3 + Kg · k(T) · t cubic grain-growth law
σf = σ0 · exp(-b·P) · sqrt(d0/d) Ryshkewitch porosity term × Hall-Petch grain term
- Sintering temperature — sets k(T). The Arrhenius term is exponential, so a few hundred degrees changes both densification and grain-coarsening rates by an order of magnitude or more.
- Initial particle size — neck growth scales as 1/a³, so finer powders sinter dramatically faster at the same temperature.
- Furnace time speed — how fast simulated kiln time (hours) advances; watch density climb while grains keep coarsening even after most porosity is gone.
- Predicted strength — combines the Ryshkewitch porosity law σf = σ0·exp(-b·P) with Hall-Petch-type grain-size strengthening, so strength can fall if you fire well past the density plateau.