under normal conditions is hexagonal β- (the mineral calcite). Other forms can be prepared, the denser (2.83 g/cm3) orthorhombic λ- (the mineral aragonite) and hexagonal μ-, occurring as the mineral vaterite. The aragonite form can be prepared by precipitation at temperatures above 85 °C; the vaterite form can be prepared by precipitation at 60 °C. Calcite contains calcium atoms coordinated by six oxygen atoms; in aragonite they are coordinated by nine oxygen atoms. The vaterite structure is not fully understood. Magnesium carbonate () has the calcite structure, whereas strontium carbonate () and barium carbonate () adopt the aragonite structure, reflecting their larger ionic radii. Polymorphs Calcium carbonate crystallizes in three anhydrous polymorphs, of which calcite is the thermodynamically most stable at room temperature, aragonite is only slightly less so, and vaterite is the least stable. Crystal Structure The calcite crystal structure is trigonal, with space group (No. 167 in the International Tables for Crystallography), and Pearson symbol . Aragonite is orthorhombic, with space group (No 62), and Pearson Symbol . Vaterite is composed of at least two different coexisting crystallographic structures. The major structure exhibits hexagonal symmetry in space group , the minor structure is still unknown. Crystallization All three polymorphs crystallize simultaneously from aqueous solutions under ambient conditions. In additive-free aqueous solutions, calcite forms easily as the major product, while aragonite appears only as a minor product. At high saturation, vaterite is typically the first phase precipitated, which is followed by a transformation of the vaterite to calcite. This behavior seems to follow Ostwald's rule, in which the least stable polymorph crystallizes first, followed by the crystallization of different polymorphs via a sequence of increasingly stable phases. However, aragonite, whose stability lies between those of vaterite and calcite, seems to be the exception to this rule, as aragonite does not form as a precursor to calcite under ambient conditions. Aragonite occurs in majority when the reaction conditions inhibit the formation of calcite and/or promote the nucleation of aragonite. For example, the formation of aragonite is promoted by the presence of magnesium ions, or by using proteins and peptides derived from biological calcium carbonate. Some polyamines such as cadaverine and Poly(ethylene imine) have been shown to facilitate the formation of aragonite over calcite. Selection by organisms Organisms, such as molluscs and arthropods, have shown the ability to grow all three crystal polymorphs of calcium carbonate, mainly as protection (shells) and