eli5 – how does the process of purifying metals goes?
It’s different for every metal, and again different depending on which impurity you want to remove. Smelting iron ore (= iron oxide) into iron metal is for example done by adding coal, and letting the coal react with the oxide to produce carbon dioxide and metallic iron. Aluminum is vastly different, since aluminum oxide is way harder to break apart it has to be done by electrolysis. Titanium is even more complex, requiring multiple steps to arrive at the metal (that’s the main reason titanium metal is expensive; the titanium ore is dirt cheap).
Purifying metals that are already mostly metal, but contaminated with other stuff can e.g. be done by using an acid that dissolves the metal, but not the impurities, or vice versa. Or my favorite “wacky method”, react the metal into some compound that’s a liquid (e.g. nickel carbonyl or silicon tetrachloride), then distilling the liquid, then reacting the compound back into pure metal.
I described zone melting, electrolysis and chemical purification in your other post. Smelting is the most common and crudest method, and relies on the fact that bulk contaminants are often both lighter than, and insoluble in, the molten metal. They form a crust on top of the melt which can be skimmed off.
Isotope separation on the other hand is an especially accurate method, which can separate atoms of the same metal which differ slightly in weight. This is important for nuclear power plants and nuclear weapons, where the exact composition of the atomic nucleus makes a major difference in how they react.
There are several methods for this, but the most common is using a bunch of centrifuges and a gaseous compound of the metal. the heavier isotope is slightly more concentrated near the outer edge of the centrifuge, but lots and lots of centrifuge stages are needed in order to make a meaningful difference.
A method used in the US for the WWII atomic bombs was to accelerate the desired atoms in a particle accelerator, and bend the resulting beam using a big magnet. The heavier atoms bent less than the lighter ones, so the beams could be separated and captured. They borrowed 14700 tons of silver from the US treasury in order to build the magnetic coils for this, because copper (which is commonly used for this) was in short supply as it was needed for the war effort.
My answer to your other post should expand on the methods already mentioned here:
Depends a lot on the metal and the impurities, as well as the level of perfection you want. General methods non-exhaustively include: different melting points, leaching/dissolving of parts or all by acid (including chemical separation and recovery), electrolysis (in solution as a salt or as molten metal), (re-)crystallization (from solutions, molten state or even vapor), chromatography, and a bunch of really exotic methods.
One of the most common impurities in gold are silver and copper. They all melt around 1000°C and mix/alloy pretty well, so separation by heat is not an option. Nitric acid dissolves the latter two, but not gold. Yet that only works of the acid can reach all of them, but if the alloy is relatively pure (say above 80% gold) to begin with, a lot of the impurities are enclosed by gold, never to be reached by acid. This is resolved by first adding even more silver/copper (melt it, throw silver in), so that now the gold is a minority and left over as fine dust by the acid.
The result of that is, say 99.9% pure (not actual numbers). To get even better, you could dissolve the gold with cyanide (acidic potassium cyanide solution) or as chloride (with aqua regia or HCl+H2O2). Then you put gold electrodes (i.e. just sticks) into that solution and apply some electricity (say 5 volts); this will make gold atoms move to the minus one (“cathode”), creating a rather pure layer. Note that the center part you started with may have lesser purity, but should at least by reasonably pure (say 99%).
Oh, and if you want to separate the silver from copper as well, you can again use nitric acid (you already dissolved them in the first step anyway). the created silver and copper nitrate are both soluble in water. Now add table salt (sodium chloride): silver chloride is insoluble, while copper chloride is soluble. Hence every silver chloride created will immediately fall out, partially to the bottom and partially as a white milky suspension. Just add enough salt, and all silver will be in that form. Then filter the solid stuff off, and do one of many options to get the silver chloride back into silver (just enough heat should already do the trick). You can also recover the copper, but that usually is not worth it.
It depends on the metal you can use electrolysis or working with molten metals and skimming off the floating lighter impurities.