Some easy nondestructive at-home indicators:
Density. Weigh it, submerge it in water, and find how dense it is. Compare this to an online density chart to narrow down your options.
Tap it on glass. This should make a noise, which with some experience can indicate a material.
Feel how much it bends – do not bend it too far as to permanently deform it, but enough that you get a sense of how flexible it is. Again, this can further narrow down your options.
Magnetism. See if it interacts with magnetism.
Nondestructive lab tests:
X-ray spectrometry. Blast it with x-rays, and measure the x-rays that return.
Conductivity. Measure how well it conducts electricity.
Thermal inertia/specific heat. Measure how much heat it takes to warm the object up, and compare that to a chart.
Destructive tests:
See how it reacts to heat. Color changes, sparks, flames, melting, and so on. Different metals have these properties.
Hardness. See what its hardness is by scratching it with different things.
Chemistry. See what can dissolve it, and what colors its solutions have.
Optical emission spectrometry. Put it in a glass tube and blast the hell out of it with electricity. See what colors it glows, and compare to known spectra.
Latest Answers