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For example, for ordinary fluids, we have polar and apolar ones. The "rule of thumb" is that polar fluids mix with each other, and also apolar fluids mix with each other, but polar fluids don't mix with apolars.

Of course, it is not a very exact rule. For example, bensene mixes in water - but it does it badly. While the also polar ethanol mixes water very well.

What is the case with liquid metals? Does some analogous - possibly more complex - category structure exist?

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    $\begingroup$ Most liquid metals mix with each other. Cases of non-miscibility are rare. $\endgroup$ – Ivan Neretin Aug 11 '20 at 10:47
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    $\begingroup$ @IvanNeretin Thanks! But, for example, molten uranium does not mix with molten iron. Iron does not mix with gold. And so on. $\endgroup$ – peterh Aug 11 '20 at 11:18
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    $\begingroup$ @IvanNeretin - rare, perhaps, but common enough once you've seen enough phase diagrams. Lead in particular is prone to miscibility gaps. Then you get some weird things like Ag-Cu has a eutectic, Cu-Ni is mainly completely soluble (with a solid miscibility gap at low temperatures), but Ag-Ni has a huge liquid miscibility gap that only disappears around 3000K. And all are fcc metals. So, no, there is no 'rule of thumb' that works. $\endgroup$ – Jon Custer Aug 11 '20 at 14:00
  • $\begingroup$ @NilayGhosh Amalgams are a specific form of mixtures, i.e. when one of the parts is mercury. It is a sub-set of the question, i.e. if we would only see the miscibility of only the water with other liquids. The "rule of thumb" I described, would work: polar liquids mostly mix with water, apolar ones don't. $\endgroup$ – peterh Aug 12 '20 at 7:56
  • $\begingroup$ chemistry.stackexchange.com/questions/35014/… chemistry.stackexchange.com/questions/42248/… $\endgroup$ – Mithoron Aug 13 '20 at 22:49
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Bottom line: there are no simple rules of thumb.

To demonstrate this, I will show a round robin of phase diagrams for fcc metals ($\ce{Ag}$, $\ce{Cu}$, $\ce{Au}$, $\ce{Ni}$) with no intermetallic compounds - just fcc solid and liquid.

  1. $\ce{Ag}$-$\ce{Au}$, full mutual solubility, liquid and solid enthalpies of mixing pretty close:

Ag-Au phase diagram

  1. $\ce{Ag}$-$\ce{Cu}$, with limited mutual solid solubility and a eutectic:

Ag-Cu$ phase diagram

  1. $\ce{Ag}$-$\ce{Ni}$, no solid solubility, a huge liquid miscibility gap:

Ag-Ni phase diagram

  1. $\ce{Au}$-$\ce{Cu}$, complete mutual solid solubility plus a eutectic:

Au-Cu phase diagram

  1. $\ce{Au}$-$\ce{Ni}$, solid miscibility gap at lower temperatures, but complete solid miscibility above that, a slightly irregular liquidus:

Au-Ni phase diagram

  1. $\ce{Cu}$-$\ce{Ni}$, solid miscibility gap at lower temperatures, pretty ideal liquidus:

Cu-Ni phase diagram

Bottom line: even for nominally 'simple' combinations of near-ideal fcc metals coming up with a workable rule of thumb just doesn't work.

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  • $\begingroup$ After visualising a simplified version of your answer, I found this line: $\ce{Ag-Au-Cu-Ni}$. Metals on this line mix well with their neighbors. Maybe some real number parameter, like an $x$, could be ordered to them, and then we could say, they mix well if their $x$-parameters are close? $\endgroup$ – peterh Aug 12 '20 at 11:01
  • $\begingroup$ ...we could even append iron to the end of the list. Nickel mixes well with iron, but not with the others. $\endgroup$ – peterh Aug 12 '20 at 11:38
  • $\begingroup$ @peterh-ReinstateMonica - Indeed, Fe-Cu has limited solubility and a bit of an odd liquidus (nearly a small miscibility gap), Fe-Ag has a huge liquid solubility gap, and Fe-Au has a small eutectic and almost a range of complete solubility in the fcc phase across the composition range. Fe-Ni has complete fcc solubility, and even an ordered fcc low temperature phase. $\endgroup$ – Jon Custer Aug 12 '20 at 14:25
  • $\begingroup$ There are about 75 experimentally observable metals in the periodic table. That means 2775 miscibility disagrams. Is it somewhere available? I think, some AI could find the most relevant and most simple ruleset quite easily. $\endgroup$ – peterh Aug 12 '20 at 14:31
  • $\begingroup$ ...it would not need even AI, simple gradient walking would be enough. $\endgroup$ – peterh Aug 12 '20 at 14:35

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