I think this will help batteries become more affordable. I think this is good for all things that are battery powered.

One such suggestion from the scientists is that a sufficiently large battery might be used to temporarily store an entire year's output from a nuclear power station, for instance. ??? Waow may it be true !!! Seams so incredible !

How do we dig minerals and build those batteries after Peak Oil?

@ Freyr Gunnar
Peak Oil does not mean that we have run out of oil. It means that we have reached a peak in the amount we can extract per day (or per whatever). That means that there will come a time when demand exceeds supply and unless we can reduce that demand, we will not be able to do all the things we used to do before we hit Peak Oil's limit to supply.
Then, of course, there is Fracking to consider, but perhaps on another day, when all the Fracking hype has died down and we can face up to reality.
For homework, surf the web for Peak Prosperity's 'The Crash Course' or Gail Tverberg's 'Our Finite World.'

Magnesium is inflammable, so what are the chances of battery using it catching fire?

So give us some number. Nominal voltage? Voltage under a 1C load? Resistance? Capacity will surely improve, but voltage and resistance are more or less fixed.

"unfortunately many of those materials are rapidly diminishing.." What could that possibly mean? We are sending them into outer space so they no longer exist on earth?
"a kilogram of Magnesium is some 15 times cheaper.." How can something be 15 times cheaper? Presumably one times cheaper would be zero or free. .

More hype and lies from grant seekers. There are plenty of low cost materials to make batteries from that perform better than this one. And how will well mine the materials to make them with oil, simple, clean electricity as many mines already use. Most metals too are now made, refined with electricity.

Colin, great article.... I think the main take-away for all is:
"...researchers believe that the inexpensive and scalable nature of the new device is such that it could be used to construct enormous storage cells for power stations.... In essence, if a big enough battery is constructed, it could potentially store many terawatt-hours of energy."
Commercial take-aways -feel free to connect more dots...
1. Home energy usage - replacing emergency generators and enabling battery backup of entire neighborhoods.
2. Military hardware - instant long-term FOB power
3. Somewhere in Texas, someone will take this to where this needs to go. "Texas?", you say? Yes. Texas has an electrical grid that is independent from the rest of the U.S. This is not by accident. This is potentially a way of utilizing the over-abundance of energy they are producing by utilizing the battery storage almost as a huge capacitor, keeping it separate but allowing massive amounts of energy to be sold to the rest of the U.S. grid.
thoughts...?

Promising, yes, but 40 charge/discharge cycles is nothing. Even 400 is weak; call back when it's 4000.
To tob, "15 times cheaper" is, indeed, nonsense. In context, it has to mean the ratio of cost is 15 and magnesium is the cheaper.
To Nik, magnesium may be flammable, but so is lithium. We can deal with it.
To author: a whole year's nuclear energy in storage is possible already; it's just prohibitively expensive ... and useless.