Amethyst is by far and away one of the most popular crystals that people have today, many people around the world have a piece of Amethyst as a specimen, jewellery, thumb-stone, tumbled stone etc. Amethyst is a Silicon Dioxide with traces of Iron. In other words and rather prosaically amethyst is a purple quartz.
Diopside is a Calcium Magnesium Silicate that belongs to the pyroxene group of minerals. Diopside is an important rock forming mineral in igneous rocks, it also can be found in meteorites. Diopside has several varieties, including a chromium-rich gem variety called chrome diopside. Violan is a rare blue variety found in some localities in Italy. There is a green "cat's eye" variety that contains minute inclusions, probably of rutile.