Polymer Spherulite Growth & Avrami Crystallization

When a semicrystalline polymer melt cools below its melting point, crystals nucleate at scattered points and grow outward as roughly spherical "spherulites" until they run into their neighbors. This simulator reproduces that process in 3D: nuclei appear either continuously (sporadic nucleation) or all at once (instantaneous nucleation), each seeding a spherulite that expands at a constant radial growth rate G. A Monte-Carlo sampler measures the true crystallized volume fraction every frame and plots it live against the analytic Johnson–Mehl–Avrami–Kolmogorov curve X(t) = 1 − exp(−K tⁿ), letting you see directly how nucleation rate, growth rate and nucleation mode (n = 3 vs n = 4) shape the S-shaped crystallization kinetics that govern real injection-molding and fiber-spinning cooling schedules.