Crystal polymorphism
In crystallography, polymorphism is 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. Discussion of the defining characteristics of polymorphism involves distinguishing among types of transitions and structural changes occurring in polymorphism versus those in other phenomena.
Overview
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 to another phase of the same chemical composition with a different crystal structure." 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." 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 leads to chemical change, not polymorphism. 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 lonsdaleite. While all three forms are allotropes, graphite is not a polymorph of diamond and lonsdaleite. 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 Brog et al.
It is also useful to note that materials with two polymorphic phases can be called dimorphic, those with three polymorphic phases, trimorphic, etc.
Polymorphism is of practical relevance to pharmaceuticals, agrochemicals, pigments, dyestuffs, foods, and explosives.
Detection
Experimental methods
Early records of the discovery of polymorphism credit Eilhard Mitscherlich 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. Mitscherlich originally called this discovery isomorphism. The measurement of crystal density was also used by Wilhelm Ostwald and expressed in Ostwald's Ratio.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.
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, continues to be used for determining the enthalpy of polymorphic transitions.
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.
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 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.
Computational methods
may be used in combination with vibrational spectroscopy techniques to understand the origins of vibrations within crystals. 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.Beyond the experimental possibilities, computational methods have been employed to study atomistic changes in crystal structures at varying temperatures and under different atmospheres. In the case of porous materials, the presence of guest molecules can induce guest-specific structural phases.
Examples
Many compounds exhibit polymorphism. It has been claimed that "every compound has different polymorphic forms, and that, in general, the number of forms known for a given compound is proportional to the time and money spent in research on that compound."Organic compounds
Benzamide
The phenomenon was discovered in 1832 by Friedrich Wöhler and Justus von Liebig. They observed that the silky needles of freshly crystallized benzamide slowly converted to rhombic crystals. Present-day analysis identifies three polymorphs for benzamide: the least stable one, formed by flash cooling, is the orthorhombic form II. This type is followed by the monoclinic form III. The most stable form is monoclinic form I. The hydrogen bonding mechanisms are the same for all three phases; however, they differ strongly in their pi-pi interactions.Maleic acid
In 2006 a new polymorph of maleic acid was discovered, 124 years after the first crystal form was studied. Maleic acid is manufactured on an industrial scale in the chemical industry. It forms salt found in medicine. The new crystal type is produced when a co-crystal of caffeine and maleic acid is dissolved in chloroform and when the solvent is allowed to evaporate slowly. Whereas form I has monoclinic space group P21/c, the new form has space group Pc. Both polymorphs consist of sheets of molecules connected through hydrogen bonding of the carboxylic acid groups: in form I, the sheets alternate with respect of the net dipole moment, while in form II, the sheets are oriented in the same direction.1,3,5-Trinitrobenzene
After 125 years of study, 1,3,5-trinitrobenzene yielded a second polymorph. The usual form has the space group Pbca, but in 2004, a second polymorph was obtained in the space group Pca21 when the compound was crystallised in the presence of an additive, trisindane. This experiment shows that additives can induce the appearance of polymorphic forms.Other organic compounds
has been obtained as eight polymorphs and aripiprazole has nine. The record for the largest number of well-characterised polymorphs is held by a compound known as ROY. Glycine crystallizes as both monoclinic and hexagonal crystals. Polymorphism in organic compounds is often the result of conformational polymorphism.Inorganic matter
Elements
Elements including metals may exhibit polymorphism. Allotropy is the term used when describing elements having different forms and is used commonly in the field of metallurgy. Some 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.Another metallic 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.
A classic example of a nonmetal that exhibits polymorphism is carbon. Carbon has many allotropes, including graphite, diamond, and lonsdaleite. However, these are not all polymorphs of each other. Graphite is not a polymorph of diamond and londsdaleite, since it is chemically distinct, having sp2 hybridized bonding. Diamond and londsdaleite are chemically identical, both having sp3 hybridized bonding, and they differ only in their crystal structures, making them polymorphs. Additionally, graphite has two polymorphs, a hexagonal form and a rhombohedral form.
Binary metal oxides
Polymorphism in binary metal oxides has attracted much attention because these materials are of significant economic value. One set of famous examples have the composition SiO2, which form many polymorphs. Important ones include: α-quartz, β-quartz, tridymite, cristobalite, moganite, coesite, and stishovite.| Metal oxides | Phase | Conditions of P and T | Structure/Space Group |
| α phase | Ambient conditions | Cl2-type Orthorhombic | |
| RT and 12±3 GPa | - | - | |
| Corundum phase | Ambient conditions | Corundum-type Rhombohedral | |
| High pressure phase | RT and 35 GPa | Rh2O3-II type | |
| α phase | Ambient conditions | Corundum-type Rhombohedral | |
| β phase | Below 773 K | Body-centered cubic | |
| γ phase | Up to 933 K | Cubic spinel structure | |
| ε phase | -- | Rhombic | |
| α phase | Ambient conditions | Monoclinic | |
| β phase | 603-923 K and 1 atm | Tetragonal | |
| γ phase | 773-912 K or RT and 1 atm | Body-centered cubic | |
| δ phase | 912-1097 K and 1 atm | FCC | |
| Bixbyite-type phase | Ambient conditions | Cubic | |
| Corundum-type | 15-25 GPa at 1273 K | Corundum-type Hexagonal | |
| Rh2O3-type | 100 GPa and 1000 K | Orthorhombic | |
| α phase | Ambient conditions | Corundum-type Trigonal | |
| γ phase | 773 K and 1 atm | Cubic | |
| α phase | Ambient conditions | Rutile-type Tetragonal | |
| CaCl2-type phase | 15 KBar at 1073 K | Orthorhombic, CaCl2-type | |
| α-PbO2-type | Above 18 KBar | α-PbO2-type | |
| Rutile | Equilibrium phase | Rutile-type Tetragonal | |
| Anatase | Metastable phase | Tetragonal | |
| Brookite | Metastable phase | Orthorhombic | |
| Monoclinic phase | Ambient conditions | Monoclinic | |
| Tetragonal phase | Above 1443 K | Tetragonal | |
| Fluorite-type phase | Above 2643 K | Cubic | |
| α phase | 553-673 K & 1 atm | Orthorhombic | |
| β phase | 553-673 K & 1 atm | Monoclinic | |
| h phase | High-pressure and high-temperature phase | Hexagonal | |
| MoO3-II | 60 kbar and 973 K | Monoclinic | |
| ε phase | Up to 220 K | Monoclinic | |
| δ phase | 220-300 K | Triclinic | |
| γ phase | 300-623 K | Monoclinic | |
| β phase | 623-900 K | Orthorhombic | |
| α phase | Above 900 K | Tetragonal |