Bauxite Extraction
The first step in extracting aluminium is to remove it from the Earth in mining. This is relatively simple given the abundance of the material. However aluminium is never found isolated in the Earth (due to its reactivity) but instead it is found bound to other elements in compounds. This means that aluminium alone in can never be dug up, but compounds of it, often containing oxygen and silicon, are.

Bayer process on industrial scale (click image for enlargement)
The bauxite then has to be purified using the Bayer process, whose development changed the course of aluminium's history. The process occurs in two main steps. Firstly the aluminium ore is mixed with the sodium hydroxide in which the oxides of aluminium and silicon will dissolve, but other impurities will not. These impurities can then be removed by filtration. Carbon dioxide gas is then bubbled through the remaining solution, which forms weak carbonic acid neutralising the solution and causing the aluminium oxide to precipitate, but leaving the silicon impurities in solution. After filtration, and boiling to remove water, purified aluminium oxide can be obtained.

The Hall Heroult Process (click image for enlargement)
Once purified aluminium oxide has been manufactured aluminium can be removed from it by the Hall-Heroult Method. In this the aluminium oxide is mixed with cryolite (made of sodium fluoride and aluminium fluoride) and then heated to about 980 C to melt the solids. This is much lower than the temperature required to melt pure aluminium oxide so much energy is saved. The molten mixture is then electrolysed with a very large current and the aluminium ions are reduced to form aluminium metal (at the cathode) and oxygen gas is formed at the anode, where it reacts with the carbon the anode is made from to give carbon dioxide gas.

As the process is so long and requires so much energy (in electricity) the aluminium metal obtained is quite expensive, but still it is competitively priced in relation to other metals unlike earlier in its history.

Summary: Aluminium is extracted from the ground in compounds, it is the purified to alumina (aluminium oxide) in the bayer process, and the metal is finally obtained after electrolysis in a cryolite solution. The full process needs a lot of energy and is quite expensive.

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