Presets
Playback
Cooling
Start and final temperature, cooling rate and seed batches (applied on restart).
Nucleation and habit
Surface energy, wetting angle of the vessel wall and impurity blocking the end faces.
View
Clock speed and crystal magnification.
Layers
Model checks
The science
What happens
A saturated salt solution is cooled. Solubility falls with temperature, so the solution becomes supersaturated. Nothing happens at first (the metastable zone) because a tiny crystal nucleus has to pay a surface-energy price before it can grow. Once supersaturation is high enough, nuclei appear in a burst, grow, and pull the concentration back to the solubility curve.
Equations
Supersaturation ratio S = C / C_s(T), with van t Hoff solubility C_s = C_0 exp[-(dH/R)(1/T - 1/T_0)]. Classical nucleation theory: the free energy of a spherical nucleus is dG(r) = 4 pi r^2 gamma - (4/3) pi r^3 kT ln(S) / v, with maximum at the critical radius r* = 2 gamma v / (kT ln S) and barrier dG* = 16 pi gamma^3 v^2 / [3 (kT ln S)^2]. The nucleation rate is J = J0 exp[-f(theta) dG* / kT], where the wetting factor f(theta) = (2 + cos theta)(1 - cos theta)^2 / 4 lowers the barrier on a vessel wall or dust (theta = 180 degrees is homogeneous nucleation).
Growth is driven by the supersaturation corrected by the Gibbs-Thomson term S exp(-2 gamma v / (kT a)); side faces and end faces have different kinetic laws, and an impurity that blocks the end faces turns needles into plates. After full equilibration the lever rule gives the crystal mass m_total - C_s V.
Honest simplifications
The salt is a generic nitrate-type salt with textbook-scale solubility numbers; the nucleation pre-factor and kinetic constants are illustrative, not fitted to one real system. Crystals are idealised hexagonal prisms with pyramid caps, nucleation is a Poisson process and growth is bulk-limited only (no stirring or heat-transfer limits). The 2D page uses the same model module as the 3D page.
Checks in the page
Check 1 compares the numerical maximum of dG(r) with the closed forms r* and dG*. Check 2 runs a seeded no-nucleation experiment and compares the final crystal mass with the lever rule. Check 3 checks mass conservation after a full cooling run and the solubility anchors.
What to try
- Run Slow cooling and then Crash cooling: fast cooling drives supersaturation high, so many tiny crystals nucleate instead of a few big ones.
- Choose Seeded growth: the seeds soak up the supersaturation before the nucleation limit is reached.
- Choose Impurity blocks end faces: the habit gallery flattens from needles to plates.
- Choose Dirty vessel: a wetting angle of 50 degrees lowers the barrier and nucleation starts at a much smaller supersaturation.