Question 4 of 7: Pyrometallurgical Processes / Refining (20 marks)

Question 4 — Pyrometallurgical Processes / 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 (typically a reactive or refractory material such as silicon, germanium, titanium or gallium, where no aqueous or fluxing route to high purity exists) by passing a narrow molten zone slowly along its length, repeatedly, using a travelling induction or resistance heater. The physics that makes this work is the equilibrium distribution (segregation) coefficient of the solute between solid and liquid at the moving solid/liquid interface, $$k=\frac{C_s}{C_l}$$ the ratio of solute concentration in the freshly frozen solid to that in the adjacent liquid at equilibrium. For most impurities of interest $k<1$: the solid rejects solute preferentially into the liquid as it freezes.

Because $k<1$ everywhere on the diagram, the first solid to freeze from a uniform melt of concentration $C_0$ is purer, $C_s=kC_0$, and the rejected solute raises the concentration of the remaining liquid zone as the interface advances. Pfann's normal-freezing analysis gives the solid composition as a function of distance $x$ along a bar of zone length $l$ after one pass, $$C_s(x)=C_0\left[1-(1-k)\,e^{-kx/l}\right]$$ which starts near $kC_0$ at the leading end and rises toward the trailing end, where the last liquid zone freezes in one lump carrying essentially all the impurity it swept up. Repeating the pass, typically many times in the same direction, drives the bulk of the bar's impurity content down further with each pass while concentrating it into an ever-smaller region at the tail, which is cut off and discarded. The technique needs no crucible, flux or chemical reagent at all — only a controlled heat source and a very pure starting charge — which is why it is the method of choice for the ultra-high-purity ($\text{parts-per-billion}$) semiconductor-grade silicon and germanium that no aqueous or slag-based refining route can reach.

(b) Vacuum refining. Vacuum refining purifies a liquid metal by holding it under sub-atmospheric pressure, which shifts the equilibrium of any refining reaction that produces a gaseous product, and separately raises the vapour pressure advantage of any dissolved metallic impurity relative to the base metal. Two distinct mechanisms are both called "vacuum refining":

Gas-forming reactions (degassing). In steelmaking, dissolved carbon and oxygen react to form CO gas, $$\mathrm{\underline{C} + \underline{O} \longrightarrow CO(g)}$$ with equilibrium constant $K=P_{CO}/(a_C\,a_O)$. At fixed activities of dissolved C and O, lowering the CO partial pressure $P_{CO}$ (i.e. pulling vacuum) drives the reaction toward products by Le Chatelier's principle, so a lower equilibrium carbon content can be reached at a given oxygen activity than is possible at atmospheric pressure — this is the basis of vacuum oxygen decarburisation (VOD) and RH degassing for ultra-low-carbon and clean steels, and the same pressure lever removes dissolved hydrogen ($2\underline{H}\rightarrow H_2(g)$) and nitrogen.

Vacuum distillation of volatile impurities. Where the impurity itself is the volatile species (zinc, lead, bismuth, magnesium dissolved in copper or in another less-volatile base metal), reducing total pressure increases the impurity's evaporation rate relative to the base metal roughly in proportion to the ratio of their vapour pressures, since the maximum (Langmuir) evaporation flux $J=p_i\sqrt{M_i/(2\pi RT)}$ scales directly with the species' own vapour pressure $p_i$ at that temperature. Because the base metal's own vapour pressure is far lower, holding the melt under vacuum at a temperature where the impurity is volatile but the base metal is not lets the impurity be pumped off and condensed separately, with essentially no loss of the base metal — the industrial route for de-zincing and de-leading copper, and for producing high-purity magnesium.