Question 4 of 7: Refining (20 marks)

Question 4 — Refining (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

(a) Zone refining. Zone refining purifies a solid bar without ever melting it completely: a narrow molten zone is passed slowly along the bar (by moving a heater or the bar itself), and as it advances, solid freezes behind it while fresh solid melts ahead of it. The mechanism that makes this purify the bar, rather than just melt and re-freeze it unchanged, is the equilibrium distribution (segregation) coefficient

defined at the solid–liquid interface from the phase diagram: $C_s$ and $C_l$ are the solute concentrations in the solid and liquid that are in equilibrium with each other at that interface, read directly off the solidus and liquidus curves at the interface temperature. For almost all impurities of practical interest in a metal host, $k<1$ — the liquidus and solidus both slope down away from the pure-metal melting point, and the solidus lies to the left of the liquidus at any given temperature below it, so the freezing solid is always purer than the melt it is freezing from.

Because $k<1$, every increment of solid that freezes behind the zone is purer than the liquid it came from, and the rejected solute is swept forward into the melt, which carries it further down the bar as the zone advances. Repeating the pass (multi-pass zone refining) drives an ever-larger fraction of the total impurity toward the final-to-freeze end, which is cut off and discarded, leaving the bulk of the bar progressively purer. Pfann's equation describes the concentration left behind a single pass of a zone of length $l$ starting from a uniform bar of concentration $C_0$:

which shows the purified region asymptotically approaching $kC_0$ (a large, permanent improvement when $k\ll1$) everywhere except in the final transient near the end of the bar, where the rejected solute concentrates sharply. The technique is the basis of ultra-high-purity semiconductor-grade silicon and germanium production, where impurity levels below 1 part per billion are required.

(b) Vacuum refining. Vacuum refining removes dissolved gases and volatile impurities from a molten metal by holding the melt under a chamber pumped to a pressure well below atmospheric, driving the equilibrium of every gas-forming dissolution reaction toward the gas phase.

For a diatomic gas dissolving atomically in the melt, e.g. hydrogen,

so the equilibrium dissolved concentration is proportional to $\sqrt{p_{H_2}}$. Reducing the chamber pressure lowers $p_{H_2}$ (and equally $p_{N_2}$, $p_{O_2}$), which by Le Châtelier's principle drives the reaction to the left — dissolved hydrogen and nitrogen recombine and evolve as gas, $\mathrm{2[H]\rightarrow H_2(g)}$ and $\mathrm{2[N]\rightarrow N_2(g)}$, until a new, much lower equilibrium concentration is reached. Dissolved carbon and oxygen behave differently because their reaction product is not simply a re-combined diatomic gas but carbon monoxide,

whose equilibrium constant $K=p_{CO}/([\%C][\%O])$ means that lowering the ambient pressure (and hence $p_{CO}$) again pulls the reaction to the right, decarburising and deoxidising the melt simultaneously — the basis of vacuum-oxygen decarburisation (VOD) in stainless-steel refining, where it reaches low carbon without over-oxidising the chromium. Vacuum treatment is also used to separate metals of differing volatility directly, since a metal's vapour pressure rises steeply with temperature; distilling a volatile impurity (e.g. zinc from a copper-base alloy, or magnesium from a lead bullion in the Pidgeon-type dephlegmation step) out of a less-volatile bath is thermodynamically the same statement — reduced total pressure lowers the boiling point of the volatile component below the process temperature, so it leaves as vapour while the higher-boiling host stays liquid.