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Which crystal structure the fluid will form depends on the chemistry of the fluid, the conditions under which it is being solidified, and also on the ambient pressure. The process of forming a crystalline structure is often referred to as crystallization.

While the cooling process usually results in the generation of a crystalline material, under certain conditions, the fluid may be frozen in a noncrystalline state. In most cases, this involves cooling the fluid so rapidly that atoms cannot travel to their lattice sites before they lose mobility. A noncrystalline material, which has no long-range order, is called an amorphous, vitreous, or glassy material. It is also often referred to as an amorphous solid, although there are distinct differences between solids and glasses: most notably, the process of forming a glass does not release the latent heat of fusion. For this thermodynamic reason, many scientists consider glassy materials to be viscous liquids rather than solids, although this is a controversial topic; see the entry on glass for more details.

Crystalline structures occur in all classes of materials, with all types of chemical bonds. Almost all metal exists in a polycrystalline state; amorphous or single-crystal metals must be produced synthetically, often with great difficulty. Ionically bonded crystals can form upon solidification of salts, either from a molten fluid or when it condenses from a solution. Covalently bonded crystals are also very common, notable examples being diamond, silica, and graphite. Polymer materials generally will form crystalline regions, but the lengths of the molecules usually prevents complete crystallization. Weak Van der Waals forces can also play a role in a crystal structure; for example, this type of bonding loosely holds together the hexagonal-patterned sheets in graphite.

Most crystalline materials have a variety of crystallographic defects. The types and structures of these defects can have a profound effect on the properties of the materials.