I'm assuming they need constant torsion or flexing to produce electricity but what sort of amounts are we talking about and how big do they need to be to light up an LED? Would a small crystal be enough to light an LED if subject to centripetal force for example?
I had a feeling it was the flex that created an instantaneous voltage, so if you bend a crystal, and keep it bent, it only does something on the first bend.
Rocks don't conduct electricity, so whilst you can get a decent voltage out of them, the current available is very low. You'd need a lot of crystal and continuous flexing to get an LED lit.