I started by looking for dirt with lots of clay, very little organic matter, and no carbonate minerals. (If it bubbles with hydrochloric acid, find something else)
My dirt had a lot of rocks, so the first thing I did was to separate the clay:
I stirred in some water it, and and poured the silty water into a separate container. After letting the silt settle out, I drained off the water and transferred 150 mL of the clay to a beaker:
Industrially, the aluminium is extracted using hot sodium hydroxide, but this won't work for my silica-rich dirt due to the formation of insoluble sodium aluminosilicates.
Instead, I added 150 ml of hydrochloric acid, which slowly converts the aluminium oxides into aluminium chloride, but leaves silicon untouched:
I covered the beaker and and kept the mixture warm (80 °C) for two days, with occasional stirring. Once it was done reacting, I let the dirt settle for a few hours and poured off the solution:
Looks like the acid dissolved a lot of iron. To remove it, I added sodium hydroxide to neutralize all the acid:
This cause both the iron and aluminium to precipitate as hydroxides. Because aluminium hydroxide can't decide if it's a base or an acid, it redissolves once excess sodium hydroxide is added:
After filtering out the iron precipitate, I was left with a mildly yellow alkaline aluminium solution:
To get it out, I slowly poured in hydrochloric acid while monitoring the pH with phenolphthalein:
In strongly basic solutions, phenolphthalein is colorless, but it turns pink when the solution approaches neutral. I stopped once all the pink disappeared for a second time, indicating that the solution was slightly acidic and that all the aluminium had re-precipitated.
After filtering, I washed the precipitate a few times with water and was left with a off-white paste:
I dried the paste at 800 °C, which decomposed the aluminium hydroxide decomposes into aluminium oxide:
Aluminium metal is very reactive, and just like with alkali metals, the best way to make it is molten salt electrolysis:
However, pure aluminium oxide melts at 2,072 °C, which is way hotter then any of my furnaces can get up to. Instead, I dissolved the alumina in cryolite (sodium hexafluoroaluminate) which melts around 1,000 °C.
Cryolite can be produced from sodium aluminate and HF, but because it's just a solvent and isn't consumed in the process, just bought some. (I also didn't want to work with hydrofluoric acid, which is very nasty)
After mixing 500 mg of my aluminium oxide with 12g (~4%) of cryolite, I loaded it into a graphite crucible, which would become the negative electrode:
I placed the crucible into an electric furnace and heated it put to 1000 °C. Once it melted, I stuck in a preheated graphite electrode and ran the cell with a 22 amp, 18 volt power supply:
After running it for 10 minutes, I dumped out the flux and... nothing.
I was expecting this because the power supply was only able to push around 0.8 amps of current though the cell. Over the course of 10 minutes, this would have at most produced 44mg of metal – a quantity small enough to go unnoticed in the large volume of flux.
This high resistance was caused by the "Anode Effect" where — above a certain current density — a layer of gas forms around the positive electrode. Once it forms, the gas layer reduces the available electrode surface, increasing the current density...
Once this cycle starts, it drastically increases the cell resistance, and it only gets worse the harder you try and shove current though it.
For the next run, I used a larger electrode, and set up a rig to hold it in place so I could focus on controlling the current:
The critical current density depends on alumina concentration. For the second run, I bumped it up to 15% by adding more alumina from a few more batches of dirt.
This time, the cell drew 22 amps at just under 5 volts, just like the real ones in industry.
After 20 minutes, I turned off the current and kept it at 1000 °C for 5 minutes let the metal consolidate. After dumping out the crucible, one piece of flux had an exposed metal bead:
... after breaking away the flux:
Here's what I collected after smashing apart the rest of the flux:
It's not quite enough (0.29 g) to make an airplane, but still quite neat.
The math:
The electrolysis was the only step that used reasonably pure starting materials, so it's what I'll focus on.
Twenty two amps for 20 minutes should have produced around 2 grams of metal, so my faradic yield was 13%. The cell was running at ~4.7 volts, so the energy efficiency was around 7.2% (excluding the heat used at startup).
Chemically, I had 1.5 grams of alumina in the melt for a 37% yield. Industrially, the cells are run continuously so this yield doesn't really matter.
Geology notes:
I couldn't find any aluminium in the waste water, so I'd guess the main reason for the small yield of Al2O3 was that the acid just didn't leach that much aluminium from the dirt.
Most dirt only has a few percent aluminium, and most minerals contain both silicon and aluminium oxides. With these minerals, the reaction will be limited by the formation of a layer of pure silicates on the surface.
The best solution would be to source better ore, but the formation of Bauxite requires very long periods of chemical weathering. Something really can't happen at at my place — with constant erosion and glaciers coming though every hundred thousand years or so.
... but if you live somewhere flat, wet and warm, you might have better luck.