An enormous centuries-long effort has been devoted to the art and science of separating metals. One thing becomes clear: very pure metals are very difficult to make. Most of the successful methods involve a combination of chemical reactions and crystallization plus filtration.
For space-based industry, any process that requires a chemical reagent is expensive; there are always leaks and no recovery method is perfect, so each kg of final product requires consuming some amount of another chemical. In most cases that other chemical is not available locally and has to be shipped from Earth. For some processes this is still mass-effective; if 1kg of reagent can help produce 10t of product then it is probably worth the cost. Still, this is an additional level of complication and expense. Also, filtration may seem like a simple thing to do but try it in space using automated equipment and a recoverable filter while removing sub-millimeter crystals from a vat of molten metal. Possible but not easy.
The ideal separation processes would require only heat, pressure, electricity or gravity since we can provide any or all of those without consumables. It seems reasonable to think that if one metal has a low melting point and another metal has a high melting point, that a mix of the two would be easy to separate just by heating it enough to melt metal A but not enough to melt metal B. Here nature has a wonderful surprise: eutectic alloys.
Let's take aluminum and silicon as examples: aluminum melts at 660 °C and silicon melts at 1414 °C. However, something special happens as the silicon concentration rises from 0% to about 12%: the melting point of the mixture decreases to 577 °C! (12.2% atomic, 12.6% mass). What this means is if you slowly cool a molten mixture of aluminum and silicon that has more than 12.6% silicon, pure silicon crystals will form until the remaining melt reaches the eutectic ratio. At that point an alloy phase of aluminum-silicon crystallizes. On the other hand, if the silicon concentration is less than 12.6% then the first crystals that form will be pure aluminum. The same sequence of steps occurs: aluminum crystallizes out until the liquid reaches the eutectic mixture, then an alloy forms.
The same thing occurs with plenty of liquids (though usually called azeotropes rather than eutectics); water and ethanol are a prime example. You cannot distill pure ethanol from a mixture of the two; you can only get to 95.6% ethanol (191-proof alcohol) in the vapor phase. The liquid phase can reach pure water, so this is not exactly the same end result as eutectic metal alloys.
This is not the end of the world, fortunately. Very pure aluminum is extremely soft and very easy to deform; even if we could easily get perfectly pure metal we would still need to add an alloying element to make it stronger. For aluminum, the most effective elements are atoms that are smaller than aluminum atoms: silicon, copper and iron are common choices. The eutectic alloy of 12% silicon is roughly equivalent to A413 aluminum alloy, with a yield strength of 131 MPa. Stronger alloys are possible but require the addition of carefully-controlled amounts of copper and iron, plus other trace elements like phosphorus and strontium which may not necessarily be available or could already be present at levels much higher than required.
We can filter out the crystals of relatively pure metal for later alloying, but this is not a simple process to automate and would be most effectively handled by actual humans on-site. Most of the effective interventions that might be made to improve material properties are going to be simplest and most effective when a human metallurgist is available to perform the work. Stockpiling the primary crystals would be an option for early robotic operations and would provide a profitable target for human operations down the road. By separating specific minerals before producing metals from them, mixes that are rich in aluminum, iron, silicon or titanium should be possible to make; that would mean that fairly pure samples of each of those metals could be obtained by filtration and careful cooling. For early missions, however, it pays to consider what can be done with the eutectic mixtures,
Let's take the example a step further and make something useful out of the alloy. A liquid oxygen tank on Earth is typically rated to operate at 250 PSI or a bit under 1.8 MPa. Pressure vessels normally use a safety factor of 4; I normally reduce that to 2 for aerospace parts but in this case we're not dealing with a high-tech material so 4 is still a good number. Our vessel needs to handle 1000 PSI or 6.9 MPa, and our material's maximum stress is 131 MPa.
If we make a cylinder out of our alloy then the main limiting factor is the hoop stress. Hoop or cylinder stress is approximately the pressure times radius divided by wall thickness, so we need to choose either the tank radius or the wall thickness. Suppose we are making relatively small tanks with thin walls of 6mm; the maximum radius we can use is then max stress times thickness (in meters) divided by pressure, or 0.1139 meters.
If our cylinder is 1 meter in total length with round endcaps then the cylinder section is 1 - 2r or 0.772m. The internal volume of the tank is the cylinder section, 0.772m x pi x 0.1079m² (the radius minus thickness, squared) = 0.028m³ plus the two hemisphere endcaps 4/3 * pi * 0.1079m³ (radius minus thickness, cubed) = 0.005m³, a total of 0.033m³ or 33 liters. Liquid oxygen has a density of 1.141 g/cc (g/cc is also kg/l and t/m³) so our tank can hold 37.65 kg of liquid oxygen.
The mass of metal used is handled the same way: take the volume of each section using the outer radius minus the volume of each section using the inner radius; this gives the volume of the walls. Multiply that by the material density to get the mass. Outer volume is 0.03765m³ and inner volume is 0.03350 m³, requiring 0.00415 m³ of wall. The alloy's density is 2.66g/cc and we have 4150 cc, so that's 11.039 kg. Adding a valve and a safety ring on top will cost about another 0.4 kg, so the whole tank is just under 11.5 kg empty and 49.2 kg full. Our tankage fraction is 11.5/49.2 or 23.4%, not very good. This fraction will be the same for cylinders in this same shape made out of the same material.
Consider a much larger tank, spherical, with about 1 m³ capacity. This tank will have a radius of 0.62 m more or less. Spherical tanks use a different formula, max stress = (pressure * radius) / (2 * thickness), so our thickness is (pressure * radius) / (2 * max stress) or 0.01633 m. The inner radius is now 0.6037 m, volume is 0.9216 m³ and payload is 1,052 kg liquid oxygen. The tank wall is 0.0767 m³ or 204 kg (plus maybe another kg for valve, etc.); filled mass is 1,257 kg so our tankage fraction is 16.3%. That's not exactly cutting edge but it's not terrible either. We can't improve on this without improving the yield stress of the metal, probably by adding trace amounts of iron or copper and including work hardening and annealing.