Aluminum metal is a widely-used material. It costs ~$2.5/kg. A significant fraction of its production cost is electricity.
Currently, Na metal is produced by Downs cell electrolysis of NaCl. Making sodium metal with electrolysis requires much less energy per mass of sodium than making aluminum. The raw material used (NaCl) is very cheap. Why, then, is sodium several times as expensive as aluminum? There's not a clear market price for it, but it's typically considered to be ~$10/kg on a large scale.
Partly, that's because:
But the process is also inherently more expensive. Why?
The cells used for Al electrolysis are open to the atmosphere. Oxygen and CO2 comes out of them. Electrolysis of NaCl produces Cl2, which is too hazardous to just release. So, it has to be collected. NaCl has a boiling point of 1413 C, so some salt evaporates, which causes problems in the chlorine handling system.
Na metal has a relatively high solubility in NaCl, so it continuously reacts with the generated chlorine, reducing efficiency.
There's a recent paper (open access) describing a new method for producing Na metal. The idea is:
Add Na carbonate so that electrolysis produces O2 instead of Cl2.
Normally, adding carbonate leads to carbon buildup on the electrode, because the voltage for that is basically the same as Na production. So, they use a liquid tin electrode, which reduces the voltage for Na electrolysis.
That of course means that some energy is needed to separate the Na from the tin. They do that separation with vacuum distillation. This isn't unprecedented for metal production: most Mg metal production uses the Pidgeon process which involves separating Mg metal by distillation. In this case, the effective boiling point of the Na might be increased by ~400 K.
The professor involved in that paper also previously did a similar thing with potassium.
Of course, most Na carbonate is made from NaCl, and the chlorine has to go somewhere. Combining the above electrolysis with the Solvay Process, the net reaction would be:
2 NaCl + CaCO3 -> 2 Na + CaCl2 + CO2 + 1/2 O2
How do I find things like this? Well, in this case, I noticed that paper because I searched Google Scholar for papers doing this exact thing because I was curious if anyone tried it.
The big question is the cost of the electrolysis process. It's similar to the electrolysis part of aluminum production plus the vacuum distillation of magnesium in the Pidgeon process, so we can do a rough extrapolation from those, but there are some major differences, including:
For aluminum production, ~60% of the cost is raw materials and electricity. Then there's replacement of electrodes and sealing paste.
Anyway, ~$1800/ton seems plausible for the process and capital costs - much of that being for the vacuum distillation. That more than doubles the cost, but a net price of $2.85/kg is still a lot less than current prices.
The authors of that paper focused on a particular application for that Na production: using it to produce Mg from MgCl2.
As for Mg metal production, note that making 1 kg of Mg would require 1.9 kg of Na. It seems like it'd be ~$3500/ton to make Mg that way, which is...similar to current prices, but if you look at a graph of historical Mg prices there's a lot of variation. Anyway, if the process was scaled up, it might be approximately competitive with current Mg production.
While the authors were focused on Mg production, there's another use for cheaper Na metal that comes to mind: thermal energy storage.
Some previous "power tower" solar-thermal plants have used molten salts that are basically a mix of nitrates. ("Solar salt" and "HITEC salt" are some relevant terms.) Sodium and potassium nitrates are now ~$600/ton; let's say $700/ton for a solar salt.
Yes, at ~$3/kg, sodium metal would still be a lot more expensive than molten salts, but it has some big advantages:
On the other hand, sodium metal is flammable, but it's been used industrially and hasn't been that big a problem.
Is the higher cost a good tradeoff for those advantages? That depends on peak_power / stored_energy. Sodium metal makes the power conversion cheaper but the storage more expensive. There's a wide range where sodium is better than molten salt - but for short-term energy storage you also have to compare it to batteries.
Supposing you have a solar-thermal plant with 33% efficiency, molten sodium and tanks might cost $45/kWh. Considering that you also need turbines and heat exchangers, that might not sound very good if lithium-ion batteries are supposedly close to $100/kWh, but I can tell you that the big battery installations in eg California actually cost a lot more than that. Also, unlike Li-ion batteries, the sodium metal would never degrade.
However, thermal energy storage was supposed to be the big advantage of solar-thermal over solar panels, and it's not clear that it has enough advantages over batteries to ever justify solar-thermal on that basis. The cost of 2-axis mirrors for solar-thermal plants seems to have come down a lot (to ~$100/m2) from better designs, but clouds remain a big problem for any kind of concentrated solar power, which limits the practical locations a lot.
Yes, solar-thermal can have ~2x the efficiency of silicon solar panels, but at least in the US there's not a shortage of places to put solar panels. It still doesn't make economic sense (without subsidies) to put them on roofs, but solar panels over sheep pastures works fine, and there's a lot of land used for pastures.
If you instead have a compressed air energy storage system, the stored heat becomes electricity at high efficiency, but you also have to store compressed air, and you don't already have turbines from a power generation system. Then there's solar-thermal with integrated CAES, but that's beyond the scope of this post.