Amethyst is a type of quartz that is mostly found in geodes and hollow agates. It is composed of silicon dioxide, and scores a 7 on the Mohs hardness scale. From different angles, amethyst occurs in primary hues from a light pinkish violet to a deep purple.
Jade is an ornamental rock. The term jade is applied to two different metamorphic rocks that are composed of different silicate minerals: nephrite and jadeite. Nephrite and jadeite were used from prehistoric periods for hardstone carving. Jadeite has about the same hardness as quartz. Nephrite is slightly softer, but is tougher (more resistant to breakage) than jadeite.