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Polymorphism (material science)
In materials science, polymorphism describes the phenomenon where a compound or element can crystallize into more than one crystal structure. The preceding definition has evolved over many years and is still under discussion today. [Ref: Bernstein, Fromm] Discussion of the defining characteristics of polymorphism involves distinguishing among types of transitions and structural changes occurring in polymorphism versus those in other phenomena.

It is also useful to note that materials with two polymorphic phases can be called dimorphic, those with three polymorphic phases, trimorphic, etc.[4]

Example:

Overview
Phase transitions (phase changes) that help describe polymorphism include polymorphic transitions as well as melting and vaporization transitions. According to IUPAC, a polymorphic transition is "A reversible transition of a solid crystalline phase at a certain temperature and pressure (the inversion point) to another phase of the same chemical composition with a different crystal structure."[1]

Additionally, Walter McCrone described the phases in polymorphic matter as "different in crystal structure but identical in the liquid or vapor states." McCrone also defines a polymorph as “a crystalline phase of a given compound resulting from the possibility of at least two different arrangements of the molecules of that compound in the solid state.”[2][3] These defining facts imply that polymorphism involves changes in physical properties but cannot include chemical change. Some early definitions do not make this distinction.

Eliminating chemical change from those changes permissible during a polymorphic transition delineates polymorphism. For example, isomerization can often lead to polymorphic transitions. However, tautomerism (dynamic isomerization) leads to chemical change, not polymorphism. (Bernstein) As well, allotropy of elements and polymorphism have been linked historically. However, allotropes of an element are not always polymorphs. A common example is the allotropes of carbon, which include graphite, diamond, and londsdaleite. While all three forms are allotropes, graphite is not a polymorph of diamond and londsdaleite. The reason is that graphite is chemically distinct, having sp2 hybridized bonding, while diamond, and londsdaleite are chemically identical, both having sp3 hybridized bonding. Diamond and londsdaleite differ in their crystal structures but do not differ chemically. (Brogg) Isomerization and allotropy are only two of the phenomena linked to polymorphism. For additional information about identifying polymorphism and distinguishing it from other phenomena, see the review by Brogg et. al. [ref]

Experimental Methods
Early records of the discovery of polymorphism credit Eilhard Mitscerlich and Jöns Jacob Berzelius for their studies of phosphates and arsenates in the early 1800s. The studies involved measuring the interfacial angles of the crystals to show that chemically identical salts could have two different forms. Mitscerlich originally called this discovery isomorphism. [Bernstein] The measurement of crystal density was also used by Wilhelm Ostwald and expressed in Ostwald's Ratio. [Cardew]

The development of the microscope enhanced observations of polymorphism and aided Moritz Ludwig Frankenheim’s studies in the 1830s. He was able to demonstrate methods to induce crystal phase changes and formally summarized his findings on the nature of polymorphism. Soon after, the more sophisticated polarized light microscope  came into use, and it provided better visualization of crystalline phases allowing crystallographers to distinguish between different polymorphs. The hot stage was invented and fitted to a polarized light microscope by Otto Lehmann in about 1877. This invention helped crystallographers determine melting points and observe polymorphic transitions. [Bernstein]

While the use of hot stage microscopes continued throughout the 1900s, thermal methods also became commonly used to observe the heat flow that occurs during phase changes such as melting and polymorphic transitions. One such technique, differential scanning calorimetry  (DSC), continues to be used for determining the enthalpy of polymorphic transitions. [Bernstein]

In the 20th century, X-ray crystallography  became commonly used for studying the crystal structure of polymorphs. Both single crystal x-ray diffraction and powder x-ray diffraction techniques are used to obtain measurements of the crystal unit cell. Each polymorph of a compound has a unique crystal structure. As a result, different polymorphs will produce different x-ray diffraction patterns. [Bernstein]

Vibrational spectroscopic methods came into use for investigating polymorphism in the second half of the twentieth century and have become more commonly used as optical, computer, and semiconductor technologies improved. These techniques include infrared (IR) spectroscopy,  terahertz spectroscopy  and  Raman spectroscopy. Mid-frequency IR and Raman spectroscopies are sensitive to changes in hydrogen bonding patterns. Such changes can subsequently be related to structural differences. Additionally, terahertz and low frequency Raman spectroscopies reveal vibrational modes resulting from intermolecular interactions in crystalline solids. Again, these vibrational modes are related to crystal structure and can be used to uncover differences in 3-dimensional structure among polymorphs. [Zeitler]

Computational methods
Computational chemistry may be used in combination with vibrational spectroscopy techniques to understand the origins of vibrations within crystals. [Axel] The combination of techniques provides detailed information about crystal structures, similar to what can be achieved with x-ray crystallography. In addition to using computational methods for enhancing the understanding of spectroscopic data, the latest development in identifying polymorphism in crystals is the field of crystal structure prediction. This technique uses computational chemistry to model the formation of crystals and predict the existence of specific polymorphs of a compound before they have been observed experimentally by scientists. [ Bowskill]

Other inorganic materials[edit]
Elements:

Allotropy is the term used when describing elements having different forms and is used commonly in the field of metallurgy. Some (but not all) allotropes are also polymorphs. For example iron has three allotropes that are also polymorphs. Alpha-iron, which exists at room temperature, has a bcc form. Above 910 degrees gamma-iron exists, which has a fcc form. Above 1390 degrees delta-iron exists with a bcc form. (p1074; Chemistry of the Elements second ed., NN Greenwood and A. Earnshaw, Butterworth-Heinemann, Oxford, 1997 ISBN 0 7506 3365 4) Another example is tin, which has two allotropes that are also polymorphs. At room temperature, beta-tin exists as a white tetragonal form. When cooled below 13.2 degrees, alpha-tin forms which is gray in color and has a cubic diamond form. (p.371-2, Chem of the Elements)

Minerals:

A classical example of polymorphism is the pair of minerals calcite, which is rhombohedral, and aragonite, which is orthorhombic. Both are forms of calcium carbonate.(p109, Chem of the Elements) A third form of calcium carbonate is vaterite.

β-HgS precipitates as a black solid when Hg(II) salts are treated with H2S. With gentle heating of the slurry, the black polymorph converts to the red form.


 * 1) REDIRECT Armand G. Winfield