Its Gibbs free energy is very less (very much stable oxide). Few commercially available oxides are stable than it, also their elemental forms are costlier than Al. Hence if we try to extract Al by reducing Al2O3 in any pyrometallurgical method, first it will need very high energy input, secondly it will not be commercially viable.

One possible reason is the high melting point of alumina that would make the extraction difficult and costly.

Thank you ?

Its Gibbs free energy is very less (very much stable oxide). Few commercially available oxides are stable than it, also their elemental forms are costlier than Al. Hence if we try to extract Al by reducing Al2O3 in any pyrometallurgical method, first it will need very high energy input, secondly it will not be commercially viable.

Aluminum usually encases himself with a layer of oxide thickness to prevent formation of high thickness, but if you add some chemicals like acids or bases to help increase the oxide layer. Alumina with high melting point of up to 2000 degrees Celsius. That's where the stable phase in this material is the alpha alumina, and can be production of this material by converting alumina phases (gamma and Beta) of chemical preparations to prepare stable phase (Alpha Alumina) by exposing it to high temperatures.

Not only alumina is extremely stable and protects aluminium very well against further oxidation, but aluminium is also extremely reducing. Therefore, for reducing alumina, an even better reducer than aluminium is required. Such materials exist but are not protected by their oxides as aluminium is. As a consequence, they (alkaline metals, for example) ignite spontaneoulsy in air, and their handling is hazardous. In summary, aluminium is an excellent reducer for pyrometallurgy, but has not equivalent for reducing its own oxide in a similar way.

Alain

You can better understand the answer by looking at Ellingham diagrams representing the Gibbs Free Energy vs Temperature. Please take a look at it while reading this answer.

In a typical pyrometallurgical operation you use carbon as reducing agent, at high temperature, to reduce a metal oxide. However in the case of aluminum, the Gibbs Free Energy associated to the oxidation of carbon is always higher than that one associated to the reduction of aluminum (the line describing the free energy for aluminum reduction is always under the line describing the free energy for the oxidation of carbon). Thus the reduction does not occur...not even at high temperatures.

The same situation happens for all those oxides under the line describing the oxidation of carbon (the one with inverse slope since it is an oxidation). To reduce them you cannot use a pyrometallurgical operation but you need electrolysis from molten salt.

In other words you can use a pyrometallurgical operation only for those oxides whose Gibbs Free Energy of reduction is higher than Gibbs Free Energy related to the oxidation of carbon. For example, take a look at the Mn-MnO2 line. It crosses the C-CO2 line at 1400°C, which means that by mixing MnO2 with carbon and by heating above 1400 °C you could reduce manganese oxide to manganese metal.

Aluminum never crosses the carbon line!

Thermodynamically, carbothermic reduction of alumina occurs around 2100 0C. At this temperature more that 30% Aluminium gets vaporized and the remaining form carbides. Consequently the recovery is extremely poor. The reduction temperature although can be lowered by using other metals but  the process will be expensive.