Mode

Nucleation + growth
Anneal grain-growth

Stats

Grains—
Mean grain Ø—
Anneal step / time—
Hall–Petch σy—
Polycrystals are built of grains — crystallites that meet at dark grain boundaries. Seeds nucleate with random orientation, then grow. During annealing, boundaries migrate to cut their curvature, so small grains vanish and the mean size D rises as D ∝ tn. Finer grains are stronger: Hall–Petch σy = σ0 + k·D−1/2.