2D companion to the 3D scene: the same Lifshitz–Slyozov–Wagner (LSW) mean-field ripening model for Te-rich nanocrystals precipitated in heat-treated tellurite (TeO2) glass, drawn as a flat crystal map plus a live size-distribution histogram instead of rendered spheres. Small crystals have a higher surface chemical potential (Gibbs–Thomson effect), so Te/O diffuses from small crystals to large ones until the small ones dissolve.
Gibbs–Thomson: μ(r) ∝ 1/r (a smaller sphere has a higher solubility)
Diffusion-limited LSW growth law:
dr/dt = (k(T) / r²) · (1/r_c − 1/r)
r_c = mean radius of surviving crystals (self-consistently
keeps total solute flux ≈ 0: r > r_c grows, r < r_c shrinks)
k(T) = k0 · exp(−Ea / (kB·T)) — Arrhenius-activated diffusion rate
- Temperature — sets k(T); hotter glass diffuses Te/O faster, so ripening runs visibly faster.
- Time speed — scales simulated minutes per real second; the physics (r_c, dr/dt) is unaffected.
- Initial nanocrystal count — how many crystals are seeded at t = 0.
- Initial size spread — how widely the starting radii scatter around 2.0 nm; a wider spread hands ripening a head start (some crystals already sit far from r_c).
- Reseed matrix — draws a fresh population and resets the clock.
Real-world relevance: controlling the nanocrystal size distribution this way is exactly how tellurite glass-ceramics are engineered for nonlinear/IR photonics — the crystal size sets scattering loss and the local field enhancement that gives tellurite hosts their unusually strong optical nonlinearity.