SOL 102 › Lab
Lab 102-D — Segregation Analogue: Impurity Rejection During Freezing
Goes with: Unit 6. Time: 1 h setup, overnight freezing, 1 h measurement. Cost: about \(20–\)40 (estimate).
Goal
Freeze salt water slowly from one side, cut the ice into layers, and measure the salt content of each melted layer. The first ice to form is much purer than the starting solution, and salt piles up in the last liquid to freeze — the same physics (segregation, Scheil) by which crystal growth purifies silicon and concentrates impurities in ingot tails.
Shopping list
| Item | Spec / example | Qty | Approx. cost (estimate) | Where |
|---|---|---|---|---|
| TDS/EC meter | range ≥ 0–9990 ppm or EC in µS/cm (e.g., HM Digital TDS-3 or COM-100 class) | 1 | $15–40 | Amazon |
| Table salt (non-iodised preferred), food dye | — | — | $3 | grocery |
| Insulated containers | thick foam cup or small foam cooler; a plastic cup that fits inside | 2–3 | $5 | grocery |
| Kitchen scale (0.1 g ideal) | — | 1 | $15 | Amazon |
| Measuring jug, distilled water | distilled water gives a clean baseline | 2 L | $2 | grocery |
| Serrated knife or ice pick, small cups, labels | — | — | — | household |
Safety
No significant hazards. Take care cutting ice (gloves, stable board).
Procedure
- Make 1 L of 5 g/L salt solution (0.5 %) in distilled water; add a few drops of food dye (a visual tracer that also tends to be rejected). Measure its TDS/EC: this is \(C_0\). (Stay within the meter's range — dilute samples if needed and record the dilution.)
- Pour ~300 mL into a thin plastic cup nested inside a thick foam cup, open at the top only, so freezing proceeds from the top surface downward (directional solidification). Put it in the freezer.
- Check every 1–2 h. Stop when roughly 60–80 % has frozen (an ice layer on top, liquid below) — note the time.
- Pour off and keep the remaining liquid (the "tail"). Lift out the ice disc; slice it into 3–5 horizontal layers (top = first frozen). Rinse each slice quickly with a splash of ice-cold distilled water to remove clinging brine (note: rinsing also removes a little ice).
- Melt each slice in a labelled cup; weigh it (mass → fraction solidified) and measure TDS/EC at room temperature.
- Optional: repeat with a fast freeze (thin dish, no insulation) and compare.
Analysis
- Compute the cumulative fraction solidified \(f_s\) at the middle of each slice from the masses.
- Plot \(C_\text{slice}/C_0\) vs \(f_s\), plus the liquid tail's concentration.
- Fit the Scheil equation \(C_S/C_0 = k(1 - f_s)^{k-1}\) to find an effective segregation coefficient \(k_\text{eff}\) (spreadsheet Solver or
scipy.optimize.curve_fit). - Mass balance check: \(\sum m_i C_i + m_\text{tail} C_\text{tail} \approx m_0 C_0\).
Expected results
- Top (first) slices noticeably clearer and with far lower conductivity than \(C_0\); salt and dye concentrated in lower slices and especially in the remaining liquid.
- Effective \(k\) well below 1 — perhaps 0.05–0.3 for slow freezing and higher for fast freezing (estimate; brine trapped between ice crystals raises \(k_\text{eff}\)).
- Slow freezing purifies better than fast freezing.
How to interpret
| Lab observation | Silicon analogue |
|---|---|
| first ice is purer | the seed end of a Cz ingot is purer than the melt (k ≪ 1 for metals) |
| salt accumulates in the remaining liquid | impurities and excess dopant accumulate in the melt and ingot tail |
| fast freezing traps brine (k_eff closer to 1) | fast growth or poor melt mixing reduces purification (effective vs equilibrium k) |
| conductivity used to infer salt | resistivity (four-point probe) used to infer dopant concentration along an ingot |
Sources
- Scheil equation: Unit 6 references.
- TDS meters convert conductivity to "ppm" with a calibration factor (often ~0.5 for NaCl-type scales; check your meter's manual).