@Kevin5275 - As far as I know Tiberium dust does not duplicate, however it does grow into nice tall (valuable) spires after being placed on the bare ground. While growing you should hear a little pinging sound every-so-often letting you know that it is growing. I'm not certain if the sound stops once maturity has been reached or not.
Because Tiberium is so rare to find, there are ways to maximize the gem once you do have one. If you have 'University Life' and a scientific sim just have your sim analyze the uncut gem to obtain a mineral sample (do this as many times as you want). With a high enough science skill, your sim can turn the analyzed samples back into the gem, which can be cut again.