Once you finish the main questline, you'll get a quest from Cayde in which you have to place beacons all over the Dreadnaught ([i]The Vanguard's Hand[/i]).
After completing this, you'll get a quest called [i]A Broken Will[/i] from Shaxx.
For this, you need to find 25 Hadium flakes scattered throughout the Dreadnaught. You also need 10 motes of light. Once you get these, talk to Shaxx again and he'll give you the refined Hadium, which you can use to pick one of the three swords.
[b]How to get Hadium quickly:[/b]
Each chest has a flake, so there's not really any RNG involved. Look inside rooms in the walls. Sort of like where you'd expect enemies to spawn. Just use the main spawn area and look around. Once you can't find anymore in that area, go back to orbit and start again.
The reason why I say to stay in the main area is because there aren't that many locations on the rest of the Dreadnaught where they're right out in the open. The spawn area is your best bet.
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The mausoleum is the best spot there are quite a few rooms that can have chest spawn in them