Crystal Nucleation & Growth

Simulating solidification: nuclei form stochastically, then grow outward with preferred crystallographic orientations. Competing grains form grain boundaries.

Grains: 0 Crystallized: 0% Step: 0
Nucleation rate: 0.003
Growth rate: 1.0
Anisotropy: 0.5
Temperature: 0.5

Classical Nucleation Theory

Nucleation rate J ∝ exp(−ΔG*/kT) where ΔG* is the free-energy barrier for a critical nucleus. Above the barrier, growth is thermodynamically favorable. Each grain has a random crystallographic orientation (angle), causing anisotropic growth: fastest along preferred lattice directions. Where expanding grains meet, grain boundaries form — regions of mismatch causing mechanical weakness and chemical reactivity. The Avrami equation describes fraction crystallized: X(t) = 1 − exp(−Kᵐtⁿ).