In materials science, polymorphism is the ability of a solid material to exist in more than one form or crystal structure. Polymorphism can potentially be found in any crystalline material including polymers, minerals, and metals, and is related to allotropy, which refers to chemical elements. The complete morphology of a material is described by polymorphism and other variables such as crystal habit, amorphous fraction or crystallographic defects. Polymorphism is relevant to the fields of pharmaceuticals, agrochemicals, pigments, dyestuffs, foods, and explosives.
When polymorphism exists as a result of a difference in crystal packing, it is called packing polymorphism. Polymorphism can also result from the existence of different conformers of the same molecule in conformational polymorphism. In pseudopolymorphism the different crystal types are the result of hydration or solvation. This is more correctly referred to as solvomorphism as different solvates have different chemical formulae. An example of an organic polymorph is glycine, which is able to form monoclinic and hexagonal crystals. Silica is known to form many polymorphs, the most important of which are; ?-quartz, ?-quartz, tridymite, cristobalite, moganite, coesite, and stishovite. A classical example is the pair of minerals, calcite and aragonite, both forms of calcium carbonate.
In terms of thermodynamics, there are two types of polymorphic behaviour. For a monotropic system, a plot of the free energy of the various polymorphs against temperature do not cross before all polymorphs melt—in other words, any transition from one polymorph to another below melting point will be irreversible. For an enantiotropic system, a plot of the free energy against temperature shows a crossing point threshold before the various melting points. It may also be possible to revert interchangeably between the two polymorphs by heating or cooling, or through physical contact with a lower energy polymorph.
The first observation of polymorphism in organic materials is attributed to Friedrich Wöhler and Justus von Liebig when in 1832 they examined a boiling solution of benzamide: upon cooling, the benzamide initially crystallised as silky needles, but when standing these were slowly replaced by 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 (observed by Wöhler/Liebig). 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.
Polymorphs have different stabilities and may spontaneously convert from a metastable form (unstable form) to the stable form at a particular temperature. Most polymorphs of organic molecules only differ by a few kJ/mol in lattice energy. Approximately 50% of known polymorph pairs differ by less than 2 kJ/mol and stability differences of more than 10 kJ/mol are rare. They also exhibit different melting points, solubilities (which affect the dissolution rate of drug and consequently its bioavailability in the body), X-ray crystal and diffraction patterns.
Various conditions in the crystallisation process is the main reason responsible for the development of different polymorphic forms. These conditions include:
Despite the potential implications, polymorphism is not always well understood. In 2006 a new crystal form of maleic acid was discovered 124 years after the first crystal form was studied. Maleic acid is a chemical manufactured on a very large scale in the chemical industry and is a salt forming component in medicine. The new crystal type is produced when a co-crystal of caffeine and maleic acid (2:1) 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; but, in form I, the sheets alternate with respect of the net dipole moment, whereas, in form II, the sheets are oriented in the same direction.
1,3,5-Trinitrobenzene is more than 125 years old and was used as an explosive before the arrival of the safer 2,4,6-trinitrotoluene. Only one crystal form of 1,3,5-trinitrobenzene was known in the space group Pbca. 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.
Walter McCrone has stated 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." 
Ostwald's rule or Ostwald's step rule, conceived by Wilhelm Ostwald, states that in general it is not the most stable with the least amount of free energy but the least stable polymorph closest in energy to the original state that crystallizes first. See for examples the aforementioned benzamide, dolomite or phosphorus, which on sublimation first forms the less stable white and then the more stable red allotrope. This is notably the case for the anatase polymorph of titanium dioxide, which having a lower surface energy is commonly the first phase to form in crystallisation from amorphous precursors or solutions despite being metastable, with rutile being the equilibrium phase at all temperatures and pressures .
Ostwald suggested that the solid first formed on crystallisation of a solution or a melt would be the least stable polymorph. This can be explained on the basis of irreversible thermodynamics, structural relationships, or a combined consideration of statistical thermodynamics and structural variation with temperature. Ostwald's rule is not a universal law but is only a possible tendency in nature.
Structural changes occur due to polymorphic transitions in binary metal oxides and these lead to different polymorphs in binary metal oxides. Table below gives the polymorphic forms of key functional binary metal oxides, such as: CrO2, Cr2O3, Fe2O3, Al2O3, Bi2O3, TiO2, SnO2, ZrO2, MoO3, WO3, In2O3.
|Metal oxides||Phase||Conditions of P and T||Structure/Space Group|
|CrO2||?-phase||Ambient conditions||Rutile-type Tetragonal (P42/mnm)|
|?-phase||RT and 14 GPa||CaCl2-type Orthorhombic|
|RT and 12±3 GPa|
|Cr2O3||Corundum phase||Ambient conditions||Corundum-type Rhombohedral (R3c)|
|High pressure phase||RT and 35 GPa||Rh2O3-II type,|
|Fe2O3||?-phase||Ambient conditions||Corundum-type Rhombohedral (R3c)|
|?-phase||Below 773 K||Body centered cubic (Ia3)|
|?-phase||Up to 933 K||Cubic, spinel structure (Fd3m)|
|Bi2O3||?-phase||Ambient conditions||Monoclinic (P21/c)|
|?-phase||603-923 K and 1 atm||Tetragonal|
|?-phase||773-912 K or RT and 1 atm||Body centered cubic|
|?-phase||912-1097 K and 1 atm||FCC (Fm-3m)|
|In2O3||Bixbyite-type phase||Ambient conditions||Cubic (Ia3)|
|Corundum-type||15-25 GPa at 1273 K||Corundum-type Hexagonal (R3c)|
|Rh2O3(II)-type||100 GPa and 1000 K||Orthorhombic|
|Al2O3||?-phase||Ambient conditions||Corundum-type Trigonal, (R3c)|
|?-phase||773 K and 1 atm||Cubic (Fd-3m)|
|SnO2||?-phase||Ambient conditions||Rutile-type Tetragonal (P42/mnm)|
|CaCl2-type phase||15 KBar at 1073 K||Orthorhombic, CaCl2-type (Pnnm)|
|?-PbO2-type||Above 18 KBar||?-PbO2-type (Pbcn)|
|TiO2||Rutile||Equilibrium phase||Rutile-type Tetragonal|
|Anatase||Metastable phase (Not stable)||Tetragonal (I41/amd)|
|Brookite||Metastable phase (Not stable)||Orthorhombic (Pcab)|
|ZrO2||Monoclinic phase||Ambient conditions||Monoclinic (P21/c)|
|Tetragonal phase||Above 1443 K||Tetragonal (P42/nmc)|
|Fluorite-type phase||Above 2643 K||Fluorite-type (Fm3m) cubic structure|
|MoO3||?-phase||553-673 K & 1 atm||Orthorhombic (Pbnm)|
|?-phase||553-673 K & 1 atm||Monoclinic|
|h-phase||High pressure and high temperature phase||Hexagonal (P6a/m or P6a)|
|MoO3-II||60 kbar and 973 K||Monoclinic|
|WO3||?-phase||Up to 220 K||Monoclinic (Pc)|
|?-phase||220-300 K||Triclinic (P1)|
|?-phase||300-623 K||Monoclinic (P21/n)|
|?-phase||623-900 K||Orthorhombic (Pnma)|
|?-phase||Above 900 K||Tetragonal (P4/ncc)|
Polymorphism is important in the development of pharmaceutical ingredients. Many drugs receive regulatory approval for only a single crystal form or polymorph. In a classic patent case the pharmaceutical company GlaxoSmithKline defended its patent for the polymorph type II of the active ingredient in Zantac against competitors while that of the polymorph type I had already expired. Polymorphism in drugs can also have direct medical implications. Medicine is often administered orally as a crystalline solid and dissolution rates depend on the exact crystal form of a polymorph. Polymorphic purity of drug samples can be checked using techniques such as powder X-ray diffraction, IR/Raman spectroscopy, and utilizing the differences in their optical properties in some cases.
In the case of the antiviral drug ritonavir, not only was one polymorph virtually inactive compared to the alternative crystal form, but the inactive polymorph was subsequently found to convert the active polymorph into the inactive form on contact, due to its lower energy and greater stability making spontaneous interconversion energetically favourable. Even a speck of the lower energy polymorph could convert large stockpiles of ritonavir into the medically useless inactive polymorph, and this caused major issues with production which ultimately were only solved by reformulating the medicine into gelcaps and tablets, rather than the original capsules.
Cefdinir is a drug appearing in 11 patents from 5 pharmaceutical companies in which a total of 5 different polymorphs are described. The original inventor Fujisawa now Astellas (with US partner Abbott) extended the original patent covering a suspension with a new anhydrous formulation. Competitors in turn patented hydrates of the drug with varying water content, which were described with only basic techniques such as infrared spectroscopy and XRPD, a practice criticised in one review because these techniques at the most suggest a different crystal structure but are unable to specify one; however, given the recent advances in XRPD, it is perfectly feasible to obtain the structure of a polymorph of a drug, even if there is no single crystal available for that polymorphic form. These techniques also tend to overlook chemical impurities or even co-components. Abbott researchers realised this the hard way when, in one patent application, it was ignored that their new cefdinir crystal form was, in fact, that of a pyridinium salt. The review also questioned whether the polymorphs offered any advantages to the existing drug: something clearly demanded in a new patent.
Acetylsalicylic acid has an elusive second polymorph that was first discovered by Vishweshwar et al.; fine structural details were given by Bond et al. A new crystal type was found after attempted co-crystallization of aspirin and levetiracetam from hot acetonitrile. In form I, two aspirin molecules form centrosymmetric dimers through the acetyl groups with the (acidic) methyl proton to carbonyl hydrogen bonds, and, in form II, each aspirin molecule forms the same hydrogen bonds, but then with two neighbouring molecules instead of one. With respect to the hydrogen bonds formed by the carboxylic acid groups, both polymorphs form identical dimer structures. The aspirin polymorphs contain identical 2-dimensional sections and are therefore more precisely described as polytypes.
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Crystal polymorphs can disappear. There have been cases of laboratories growing crystals of a particular structure and when they try to recreate this, the original crystal structure isn't created but a new crystal structure is. Also, findings of one crystal structure intermittently polymorphing over time into another have been recorded. The drug paroxetine was subject to a lawsuit that hinged on such a pair of polymorphs. An example is known when a so-called "disappeared" polymorph re-appeared after 40 years. These so-called "disappearing" polymorphs are most likely metastable kinetic forms.
Polytypes are a special case of polymorphs, where multiple close-packed crystal structures differ in one dimension only. Polytypes have identical close-packed planes, but differ in the stacking sequence in the third dimension perpendicular to these planes. Silicon carbide (SiC) has more than 170 known polytypes, although most are rare. All the polytypes of SiC have virtually the same density and Gibbs free energy. The most common SiC polytypes are shown in Table 1.
Table 1: Some polytypes of SiC.
|Phase||Structure||Ramsdell Notation||Stacking Sequence||Comment|
|?-SiC||hexagonal||6H||ABCACB||The most stable and common form|
|?-SiC||face-centered cubic||3C||ABC||Sphalerite or zinc blende form|
A second group of materials with different polytypes are the transition metal dichalcogenides, layered materials such as molybdenum disulfide (MoS2). For these materials the polytypes have more distinct effects on material properties, e.g. for MoS2, the 1T polytype is metallic in character, while the 2H form is more semiconducting. Another example is Tantalum disulfide, where the common 1T as well as 2H polytypes occur, but also more complex 'mixed coordination' types such as 4Hb and 6R, where the trigonal prismatic and the octahedral geometry layers are mixed. Here, the 1T polytype exhibits a charge density wave, with distinct influence on the conductivity as a function of temperature, while the 2H polytype exhibits superconductivity.
ZnS and CdI2 are also polytypical. It has been suggested that this type of polymorphism is due to kinetics where screw dislocations rapidly reproduce partly disordered sequences in a periodic fashion.