Here’s an attempt :)

# caveats

This is just my feeling. I looked only at the binary phase diagrams, in reality there could be ternary or quaternary compounds. The article mentions that the alloy is an Al-rich matrix with the other elements in small crystals within it, with different structures and compositions. So the picture is quite complicated. To get a definitive answer, someone would need to do a proper study. I am not saying that it is impossible, just that it sounds very hard. That said, there could very well be other ways that escape me at the moment. I am happy to investigate further for a fee :)

# Fe-Al, looking at the phase diagram here [1]

There is a tiny temperature range (between around 650 and 660 °C) in which solid Al coexists with liquid Fe-Al. So in theory the mixture could be heated until it is all molten, then cooled slightly to precipitate Al, which could then be taken out, leaving Fe-enriched liquid. It seems feasible but impractical (temperature control would need to be absolutely spot on, and other elements would probably change the picture a bit).

# Ti-Al, phase diagram here [2]

There is a temperature range in which Al-rich liquid coexists with solid TiAl3. That solid could be removed, leaving a liquid that is mostly Al but still has significant Ti impurities.

# Co-Al, phase diagram here [3]

This one is similar to Ti-Al, except that Co is more soluble in liquid Al than Ti is, so there would be more Co impurities after taking out the Co2Al9 solid. The temperature range is also much narrower (650°C-700°C, eyeballing the diagram).

# Ni-Al, phase diagram here [4]

It’s worse than the others, because Ni is soluble even in solid Al. Also, melting is almost congruent, meaning that all the solid would melt at the same time, there is no coexistence of a liquid and a solid phase. This prevents from trapping the impurities in a solid to purify the liquid or the other way around. I don’t really see a way with this one.

# magnetism

Using magnetism was mentioned in the thread. I don’t think it would help. At high temperature, all these elements are paramagnetic. Some of them (Fe, Ni and Co) have a larger magnetic moment and would be more strongly attracted in a magnetic field than Al and Ti, but I don’t think it would be sufficient to really separate them (all of them are in minority compared to Al). And Al and Ti are not that different from a magnetic point of view and i don’t see them being separated by a magnetic field.

# oxidation

It is not inconceivable to inject oxygen to try to trap some elements in oxides that have typically much higher melting points than the metals, which would help with the narrow temperature ranges. These metals can form spinel compounds, at least TiFe2O4, NiFe2O4, and many more. One problem is that Al2O3 is also very stable (which is why it is very costly to get aluminium metal from aluminium ore. There are also aluminate compounds such as FeAl2O4. Figuring out which one is more stable and whether it could be feasible is quite a bit of work in itself.

[1] https://www.researchgate.net/profile/Qingyou-Han/publication...

[2] https://www.researchgate.net/publication/325471220/figure/fi...

[3] https://www.mdpi.com/materials/materials-13-03152/article_de...

[4] https://www.researchgate.net/profile/Matthew-Weeks-3/publica...