materials science Materials science is an interdisciplinary field of researching and discovering materials. Materials engineering is an engineering field of finding uses for materials in other fields and industries. The intellectual origins of materials sci ...

, Ostwald's rule or Ostwald's step rule, conceived by

Wilhelm Ostwald Wilhelm Friedrich Ostwald (; – 4 April 1932) was a Latvian chemist and philosopher. Ostwald is credited with being one of the founders of the field of physical chemistry, with Jacobus Henricus van 't Hoff, Walther Nernst and Svante Arrhenius. ...

, describes the formation of polymorphs. The rule states that usually the less

stable A stable is a building in which working animals are kept, especially horses or oxen. The building is usually divided into stalls, and may include storage for equipment and feed. Styles There are many different types of stables in use tod ...

polymorph crystallizes first. Ostwald's rule is not a universal law but a common tendency observed in nature. This can be explained on the basis of irreversible thermodynamics, structural relationships, or a combined consideration of

statistical thermodynamics In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. Sometimes called statistical physics or statistical thermodynamics, its applicatio ...

and structural variation with temperature. Unstable polymorphs more closely resemble the state in solution, and thus are kinetically advantaged. For example, out of hot water,

metastable In chemistry and physics, metastability is an intermediate energetic state within a dynamical system other than the system's state of least energy. A ball resting in a hollow on a slope is a simple example of metastability. If the ball is onl ...

, fibrous crystals of

benzamide Benzamide is an organic compound with the chemical formula of C7H7NO. It is the simplest amide derivative of benzoic acid. In powdered form, it appears as a white solid, while in crystalline form, it appears as colourless crystals. It is slightly ...

appear first, only later to spontaneously convert to the more stable rhombic polymorph. A dramatic example is

phosphorus Phosphorus is a chemical element; it has Chemical symbol, symbol P and atomic number 15. All elemental forms of phosphorus are highly Reactivity (chemistry), reactive and are therefore never found in nature. They can nevertheless be prepared ar ...

, which upon sublimation first forms the less stable white phosphorus, which only slowly

polymerizes In polymer chemistry, polymerization (American English), or polymerisation (British English), is a process of reacting monomer molecules together in a chemical reaction to form polymer chains or three-dimensional networks. There are many form ...

to the red

allotrope Allotropy or allotropism () is the property of some chemical elements to exist in two or more different forms, in the same physical state, known as allotropes of the elements. Allotropes are different structural modifications of an element: the ...

. This is notably the case for the

anatase Anatase is a metastable mineral form of titanium dioxide (TiO2) with a Tetragonal crystal system, tetragonal crystal structure. Although colorless or white when pure, anatase in nature is usually a black solid due to impurities. Three other Pol ...

polymorph of

titanium dioxide Titanium dioxide, also known as titanium(IV) oxide or titania , is the inorganic compound derived from titanium with the chemical formula . When used as a pigment, it is called titanium white, Pigment White 6 (PW6), or Colour Index Internationa ...

, which having a lower

surface energy In surface science, surface energy (also interfacial free energy or surface free energy) quantifies the disruption of intermolecular bonds that occurs when a surface is created. In solid-state physics, surfaces must be intrinsically less energe ...

is commonly the first phase to form by crystallisation from amorphous precursors or solutions despite being metastable, with

rutile Rutile is an oxide mineral composed of titanium dioxide (TiO2), the most common natural form of TiO2. Rarer polymorphs of TiO2 are known, including anatase, akaogiite, and brookite. Rutile has one of the highest refractive indices at vis ...

being the equilibrium phase at all temperatures and pressures.

References

Mineralogy Gemology Crystallography {{mineralogy-stub

See also

References