The last element in the lanthanide series, lutetium is also considered to be the rarest element, second only to thulium; moreover it is also the smallest of the rare earths. It is also the element with the highest density and hardness. Rarity also implies high cost: lutetium is expensive, which is partly why it is not used in many applications.
- Used as a catalyst in cracking, hydrogenation, and polymerization
- Positron emission tomography detectors