develop freely without attachment, for instance, within gypsum. α-quartz crystallizes in the trigonal crystal system, space group P3121 or P3221 (space group 152 or 154 resp.) depending on the chirality. Above , α-quartz in P3121 becomes the more symmetric hexagonal P6422 (space group 181), and α-quartz in P3221 goes to space group P6222 (no. 180). These space groups are truly chiral (they each belong to the 11 enantiomorphous pairs). Both α-quartz and β-quartz are examples of chiral crystal structures composed of achiral building blocks (SiO4 tetrahedra in the present case). The transformation between α- and β-quartz only involves a comparatively minor rotation of the tetrahedra with respect to one another, without a change in the way they are linked. However, there is a significant change in volume during this transition, and this can result in significant microfracturing in ceramics and in rocks of the Earth's crust. Varieties (according to microstructure) Although many of the varietal names historically arose from the color of the mineral, current scientific naming schemes refer primarily to the microstructure of the mineral. Color is a secondary identifier for the cryptocrystalline minerals, although it is a primary identifier for the macrocrystalline varieties. Varieties (according to color) Pure quartz, traditionally called rock crystal or clear quartz, is colorless and transparent or translucent, and has often been used for hardstone carvings, such as the Lothair Crystal. Common colored varieties include citrine, rose quartz, amethyst, smoky quartz, milky quartz, and others. These color differentiations arise from the presence of impurities which change the molecular orbitals, causing some electronic transitions to take place in the visible spectrum causing colors. The most important distinction between types of quartz is that of macrocrystalline (individual crystals visible to the unaided eye) and the microcrystalline or cryptocrystalline varieties (aggregates of crystals visible only under high magnification). The cryptocrystalline varieties are either translucent or mostly opaque, while the transparent varieties tend to be macrocrystalline. Chalcedony is a cryptocrystalline form of silica consisting of fine intergrowths of both quartz, and its monoclinic polymorph moganite. Other opaque gemstone varieties of quartz, or mixed rocks including quartz, often including contrasting bands or patterns of color, are agate, carnelian or sard, onyx, heliotrope, and jasper. Amethyst Amethyst is a form of quartz that ranges from a bright vivid violet to a dark or dull lavender shade. The world's largest deposits of amethysts can be found in Brazil, Mexico, Uruguay, Russia,