One of the best ways to determine what a material is is to look at it under a high powered microscope. Different impurities and alloying additions often have a large effect on the microstructure, and combined with a hardness test, you can usually get pretty conclusive results.
Alternatively you could run EDX analysis in an electron microscope (SEM or TEM), though this would only tell you if it were "roughly" pure due to the low mass sensitivity of this technique.
SIMS analysis has the highest mass sensitivity, though you need to know what you're looking for to be able to calibrate the machine.
Finally, for complete overkill, you could run it through the 3D position sensitive time of flight atom probe. This will give you the location and type of each atom within a small sample.
However, I fear most of these techniques would be taking it a little over the top.
8-ball
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