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Quartz is a form of silicon dioxide (this particular compound has lots of polymorphs, including glass). The silicon and oxygen ions are arranged to make an ionic tetrahedral structure (the silicon is in the centre, surrounded by four oxygen). This basic structure is very versatile and is the basis of all the silicates, including families of minerals like mica and pyroxene. In the case of quartz, all of the silicate tetrahedra share an oxygen with another tetrahedron, leading to a strong interconnected framework structure. Sometimes the ion in the centre of an ionic compound can be replaced with a cation with a similar ionic radius (regardless of charge -- size is more important). The most common replacements for silicon are iron and aluminium. In Amethyst, some of the silicon has been replaced with iron. If the amethyst has been exposed to natural gamma radiation over a period of time, the iron ion can change oxidation state. This change in oxidation state leads to purple colour centres. Hence amethyst's famous hue. This process also make amethyst very vulnerable to UV, don't place it in direct sunlight as it will fade.