Presets
Playback
Temperature program
The beaker starts at the start temperature and cools (or heats) toward the target at the chosen rate.
Solution and seeds
More dissolved salt means a higher saturation temperature; seeds are crystals already in the beaker.
Crystal and nucleation
Interfacial energy sets the nucleation barrier; G0 the growth speed; habit the length-to-width ratio.
Camera
Layers
Quality
Model checks
The science
What this bench shows
A hot salt solution is cooled in a beaker. Crystals form in two stages: a rare nucleation event, then growth as molecules attach. Everything on this page, from the thermometer to the graphs, comes from one small model that conserves the dissolved salt.
1. Solubility and supersaturation
The solubility of the salt rises steeply with temperature, ceq(T) = c20 exp[k (T - 20 °C)] with c20 = 5.9 g per 100 g water and k = 0.053 per °C (roughly potassium alum; the numbers are illustrative). The driving force is the supersaturation S = c / ceq(T), with σ = S - 1. S < 1: crystals dissolve. S > 1: they grow.
2. Why a metastable zone exists
A nucleus of radius r has free energy ΔG(r) = -(4πr³/3v) kT ln S + 4πr²γ. Its maximum is at r* = 2γv/(kT ln S) with barrier ΔG* = 16πγ³v²/[3(kT ln S)²]. The rate is J = J0 exp(-ΔG*/kT), which is negligible until S reaches a threshold: between S = 1 and that limit (dashed red curve) the solution is metastable: existing crystals grow, but no new ones appear. Past it (labile zone) new crystals appear in showers.
3. Growth: BCF spirals and the boundary layer
Molecules attach at steps spiralling around screw dislocations (Burton-Cabrera-Frank): G = G0 (σ²/σ1) tanh(σ1/σ). This is quadratic in σ for small σ and linear for large σ. Stirring thins the diffusion boundary layer, which acts as a second resistance in series: 1/Geff = 1/G + 1/(kdσ). The habit slider multiplies the c-axis rate and divides the side rate by √(ratio), changing a stubby crystal into a needle.
4. Mass balance
Dissolved salt = total salt - crystal mass. Crystal volume is a hexagonal prism plus a truncated hexagonal pyramid of density 1.75 g/cm³. Because every step takes exactly what the crystals gain from the solution, slow cooling to 20 °C ends with the equilibrium yield given by the lever rule (Model check 1).
5. What to try
Run Slow cooling and Crash cooling from the presets: the same recipe gives a few large crystals or dozens of small ones, depending only on whether the solution path crosses the dashed metastable limit. Raise the interfacial energy to push that limit away. Click a crystal to read its size and mass.
Honest simplifications
One uniform solution (no concentration gradients except through the boundary-layer resistance), no secondary nucleation by contact or attrition, crystals do not interact, sizes are capped at the beaker (9 mm radius, 46 mm length) and at most 14 crystals are tracked, so a real shower of millions of nuclei is represented by the first 14, a single hexagonal habit, J0 = 1030 m-3s-1, constant density and solution volume. The numbers show the physics, not a particular product.