Polymorphism (materials science)
Polymorphism in materials science 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 elemental solids. Together with polymorphism the complete morphology of a material is described by 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 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. 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; α-quartz, β-quartz, tridymite, cristobalite, coesite, and stishovite.
In terms of thermodynamics, there are two types of polymorphism. 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 will be irreversible. For an enantiotropic system, a plot of the free energy against temperature shows a crossing point before the various melting points, and it may be possible to convert reversibly between the two polymorphs on heating and cooling.
The first observation of this property is attributed to Friedrich Wöhler and Justus von Liebig when in 1832 they  examined a boiling solution of benzamide: on cooling the benzamide initially crystallised as silky needles but on 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 monoclinic form II. This type is followed by the centrosymmetric form III (observed by Wöhler/Liebig) in which aromatic stacking is the dominant feature. The most stable form is monoclinic form I which is optimized for hydrogen bonding.
Despite the potential implications, polymorphism is not always well understood. In 2006 a new crystal form was discovered of maleic acid 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 caffeine - maleic acid co-crystal (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 has been known in the space group Pbca. In 2004, a second polymorph was obtained in the space group Pca21 when the compound was crystallized in the presence of an additive, trisindane. This experiment shows that additives can induce the appearance of polymorphic forms. 
Ostwald's rule or Ostwald's step rule   conceived by Wilhelm Ostwald states that in general it is not the most stable but the least stable polymorph 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.
Ostwald suggested that the solid first formed on crystallization 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. The Ostwald's rule is not a universal law but is only a possible preferred tendency in the nature.
Polymorphism in pharmaceuticals
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.
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 Fuijsawa 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 criticized by in one review  because these techniques at the most suggest a different crystal structure but are unable to specify one. These techniques also tend to overlook chemical impurities or even co-components. Abbott researchers realized 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 elusive 2nd polymorph 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. The form II is stable only at 100 K and reverts back to form I at ambient temperature. In the (unambiguous) form I, two salicylic molecules form centrosymmetric dimers through the acetyl groups with the (acidic) methyl proton to carbonyl hydrogen bonds, and, in the newly-claimed form II, each salicylic molecule forms the same hydrogen bonds, but then with two neighboring molecules instead of one. With respect to the hydrogen bonds formed by the carboxylic acid groups, both polymorphs form identical dimer structures.
Walter McCrone 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.
Crystal Polymorphs can disappear. There have been cases of individual laboratories growing one crystal form. They then grow a different crystal form, and are unable to make the first form again. Also, they find that they can make the first form again, but it now converts to the second form over time. The drug Paroxetine was subject to a law suit that hinged on such a pair of polymorphs (A link to a discussion of cases in Canada and the US has been given below). An example is known when a so-called 'disappeared' polymorph re-appeared after 40 years. These so-called 'disappearing' polymorphs are probably metastable kinetic forms.
- F. Wöhler, J. Liebig, Ann. Pharm. 1832, 249 – 282.
- Polymorphism in Benzamide: Solving a 175-Year-Old Riddle Jorgen Thun, Lena Seyfarth, Jorgen Senker, Robert E. Dinnebier, and Josef Breu Angew. Chem. Int. Ed. 2007, 46, 6729 –6731 doi:10.1002/anie.200701383
- Graeme M. Day, Andrew V. Trask, W. D. Samuel Motherwell and William Jones (2006). "Investigating the latent polymorphism of maleic acid". Chemical Communications. 1: 54–56. doi:10.1039/b513442k.
- Thallapally PK, Jetti RKR, Katz AK (2004). "Polymorphism of 1,3,5-trinitrobenzene induced by a trisindane additive". Angewandte Chemie International Edition. 43 (9): 1149–1155.
- Ostwald, W. (1897). "Studies upon the forming and changing solid bodies". Zeitschrift fur Physikalische Chemie. 22: 289–330.
- Threlfall, T. (2003). "Structural and thermodynamic explanations of Ostwald's Rule". Organic Process Research and Development. 7 (6): 1017–1027. ISSN 1083-6160. Retrieved 2007-10-30.
- Polymorphisms and Patent, Market, and Legal Battles: Cefdinir Case Study Walter Cabri, Paolo Ghetti, Giovanni Pozzi, and Marco Alpegiani Org. Process Res. Dev.; 2007; 11(1) pp 64 - 72; (Review) doi:10.1021/op0601060
- Peddy Vishweshwar, Jennifer A. McMahon, Mark Oliveira, Matthew L. Peterson, and Michael J. Zaworotko (2005). "The Predictably Elusive Form II of Aspirin". J. Am. Chem. Soc. 127 (48): 16802–16803. doi:10.1021/ja056455b.
- Andrew D. Bond, Roland Boese, Gautam R. Desiraju (2007). "On the Polymorphism of Aspirin: Crystalline Aspirin as Intergrowths of Two "Polymorphic" Domains". Angewandte Chemie International Edition. 46 (4): 618–622. doi:10.1002/anie.200603373.