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I've recently learned more about Indium and Gallium, and I find them quite interesting, especially how an alloy can be manually made simply by rubbing them together. I'm curious though, is there a convenient way to get them back apart?

Also, say for example I had them in a test tube after mixing them together (or even after separating them), how could the metal be removed from the container cleanly? I know they both dissolve in acids, but how would I then precipitate them back out of the acid?

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The Gallium-Indium binary system is assessed by Bridget C. Rugg and Tim G. Chart in Calphad 14(2) 115-123 (1990). It is a very simple system, exhibiting essentially no solubility of In in Ga, and limited (< 5at.%) solubility of Ga in In. There are no intermediate phases, and a shallow eutectic about 15K below the Ga melting point at about 14 at.% In.

The diagram (comparing their Calphad calculations with experimental data) is:

enter image description here

So, how to separate (at least roughly) the constituents? One answer is using zone melt refining, although there will be limits to what you can do. I will presume starting with a ~50/50 atomic ratio. You will need something to melt the material in (repeatedly), while maintaining a temperature gradient.

So, at the 50/50 point, it should be molten at 350K. as you lower that temperature, you hit the liquidus line and the solid that forms is indium with a few atomic percent of Ga. Say you arrange the temperature gradient so that forms on the bottom of you test tube. Keep lowering the temperature, causing more indium to solidify, and the remaining melt to get progressively more gallium rich. Eventually you will hit the eutectic point, and the last bit to solidify will be at 289K and 14 at.% In in Ga.

Cut that last bit off - that is as pure of Ga you can get with this technique (sadly).You can now reprocess the In-rich portion to refine more of the Ga out, but given the fairly low solubility of Ga in the In to begin with, there might not be much point to that.

Not perfect, but it pretty much works.

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