Terbium (Tb)
Terbium
                    (https://en.wikipedia.org/wiki/Terbium#/media/File:Terbium-2.jpg)

Properties
Terbium is extremely rare and very expensive. Little is known about this REE.

Applications
Terbium has a wide range of applications in today's world. It speeds up the X-ray process when you brake a bone and don't want to be irradiated for too long. It is used in a special alloy called Tefenol-D, a type of metal that expands or contracts depending on the strength of a magnetic field. Interestingly, terbium allows fuel cells to operate at an elevated temperature. How does it do all of these things? I honestly do not know. Perhaps the protection of intellectual property has something to do with the total lack of information I could find. At any rate, Terbium is extremely scarce on the Earth's surface and its uses seem to be shrouded by trade secrets.