Custom has to some extent restricted its use to inorganic chemistry; the corresponding property of organic compounds being generally termed isomerism.
Some classic examples of solids showing allotropy are phosphorus (in "red" and "white" forms) and carbon (in the form of graphite, diamond, or fullerenes). The term may also be used to refer to the molecular form of an element (such as diatomic gas), even if there is only one such form.
Allotropy specifically refers to the chemical bond structure between atoms and should not be confused with the existence of multiple physical states, such as with water, which can exist as a gas (steam), a liquid (water), or a solid (ice). These phases of water are not allotropes, since they are caused by changes in the physical bonding between water molecules, rather than changes in the chemical bonding of the water molecules themselves.
The word allotropy is usually restricted to the case of pure elements and is a special case of Polymorphism.
As can be seen with the example of carbon allotropes, certain physical properties can vary dramatically from allotrope to allotrope. Allotropy can be attributed to differences in how the atoms of the bulk form of the element are connected. In diamond, carbon atoms are connected each to four other carbon atoms in a tetrahedral lattice structure, whereas in graphite, each carbon atom is firmly bonded to just three other carbon atoms in hexagonal sheets. These hexagonal sheets are then less loosely coupled to one another in stacks. The structure of fullerenes (a carbon allotrope found in soot) resembles that of graphite, except that instead of hexagons of carbon atoms, smaller polygons are formed, such as a mix of hexagons and pentagons, such that the sheet can fold back onto itself into closed spheroids, as with the seams of a soccer ball.
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