Tellurite Nanocrystal Ostwald Ripening

Heat Treatment

Temperature T 620 K

Time speed 1.0×

Initial nanocrystal count 160

Coarsening State

Surviving

160

Mean r

2.0 nm

Elapsed

0 min

Critical radius r_c

2.0 nm

Largest crystal

2.0 nm

How it works

Tellurite (TeO₂-based) glass, heat-treated near its crystallisation temperature, precipitates a population of Te-rich nanocrystals inside the amorphous matrix. Once nucleation is done, the population evolves by Ostwald ripening: Te and O atoms diffuse through the glass from small crystals — whose curvature raises their surface chemical potential (the Gibbs–Thomson effect) — toward larger ones, so small crystals shrink and dissolve while large ones grow, even though the total precipitated volume barely changes.

Gibbs–Thomson: μ(r) ∝ 1/r   (a smaller sphere has a higher solubility)

Mean-field growth (LSW-style):
  dr/dt = (k(T) / r²) · (1/r_c − 1/r)

  r_c = current mean radius of surviving crystals (self-consistently
        keeps total solute flux ≈ 0: crystals with r > r_c grow,
        r < r_c shrink, r = r_c is momentarily stationary)

  k(T) = k0 · exp(−Ea / (kB·T))   — diffusion-limited rate constant,
        Arrhenius-activated by temperature

Temperature — sets k(T); hotter glass diffuses Te/O faster, so ripening and dissolution run 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 with a small random spread of starting radii.
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.

Growing (r > r_c) Shrinking (r < r_c)

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