By far, the most common method of making metal alloys is to melt all the required metal elements together and mix them in the liquid state. If the finished parts are made by a casting process, then you go straight to casting the part. If the finished parts are forged or some other method… then you still cast a billet (big slug of material) and then get to work on rolling it out and forming it and cutting it and forming it some more, until the final shape is achieved. But even a part that is “forged” started out it’s life with the alloy mixed in the liquid state and cast into a billet.
There are other methods adding elements after a metal is solidified (such as carburizing or nitriding of steel) but these methods are not how alloys are made. They are ways of fine-tuning the amount of certain elements on the surface of a part.
Another method (more specialized) would be to take fine powders of two elements and mix the powders, press the blended powder into a shape, then fire it in a furnace (similar to making a fired clay pot). This can allow the two elements to diffuse together and form an alloy without ever actually melting any of the powder. — Powder Metallurgy
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