Incidentally, Al and Ni form an intermetallic (brittle phase), and rather aggressively at that: the reaction is exothermic (you could think of it as forming the salt "nickel aluminide"), which has even been used to kind of instant-weld some materials together. So, I wouldn't recommend welding a Ni-plated Al alloy.
If it doesn't need strength, very pure aluminum would seem to be promising. It is fairly corrosion resistant; mostly, impurities cause it to corrode faster. Still, all Al alloys are prone to corrosion at non-neutral pH.
If the density can be no more than that, or even up to say twice that, that basically includes beryllium, magnesium, titanium, and not much else on the Periodic Table. And of those, magnesium is less corrosion resistant, and titanium is much higher resistance (not to mention needs special equipment to weld). Beryllium, the less said of it the better (working it, produces dust, that causes berylliosis).
Density does not vary appreciably with alloying, and is never much less than the constituents; and resistivity is always higher than the pure constituents, so this pretty much covers everything. At least, everything you'd even slightly want to use -- maybe, like, lightly-alloyed scandium would do better, but it's rarer than hen's teeth so you can't exactly go out and buy a spool of it!
Does it need to be welded? Can it be soldered? (Anything can be soldered, the question is with what flux -- for Al, Ti, etc. a quite nasty fluoride blend is needed.) Crimped or bolted?
Note that platings may help in the latter case; you can get a reliable connection on bare aluminum with crimping, or clean bolted faces, either way greased with a bit of NOALOX; dry connections can be plated and bolted, at least I would think. (But do check standards for this -- aluminum is notoriously tricky to use reliably. For example, if that plating should ever flake or wear off, that connection is ruined. It may be that some platings aren't actually good enough in practice; I don't know.)
And yep, as above -- if you need strength in the conductor itself, you WILL pay a price in conductivity. The reason phosphor bronze and beryllium copper* exist, is not because they're as conductive as copper -- they're rather awful in fact -- but because they give a better strength to conductivity ratio than copper. So you need to use more material for the same ampacity, but not as much as would be needed to handle the mechanical load in pure copper.
*Less nasty than straight Be -- the amount is small and fairly well mixed in with the copper. Still, clean up, wear a mask, basic precautions like that.
Mind that conductivity even varies with material condition -- work hardening serves a similar role as alloying elements do, and so, full-hard has higher resistivity than annealed copper, for example. Likewise, plated metal tends to retain internal stresses, so for example PCB traces are worse than annealed, too. (For platings on bulk metal, this is basically N/A, as the layer is so thin. It can matter to RF applications, where a nice silver layer might be used -- skin effect forces the current flow to the surface, so that the bulk actually doesn't participate at all, and so going for the best (silver) is a nice option.)
Neat thing about aluminum and alloys, I guess; the amount is usually pretty small (many are essentially still >95% pure aluminum), so while they're far from the resistivity of pure Al (~28nΩm), they're not terrible (6061: ~40nΩm), and you get similar numbers for most alloys, so take your pick from them, basically.
(Whereas among many brasses/bronzes, Cu might be <80%, and so the conductivity is even worse; C360 brass for example ~66nΩm; compare to pure Zn ~59. Looks like BeCu gets up to 100 or more (despite being ~98% Cu!), but also it is one of the strongest among all copper alloys -- challenging even many steel alloys -- so yeah, its resistivity is well worth its strength!)
Tim
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