crystal polymorphism

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."{{Cite journal |title=Polymorphic transition |url=https://goldbook.iupac.org/terms/view/P04748 |access-date=January 28, 2024 |website=IUPAC Gold Book |date=2019 |doi=10.1351/goldbook |editor-last1=Gold |editor-first1=Victor |doi-access=free }} 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."{{Cite book |last=McCrone |first=W. C. |title=Physics and Chemistry of the Organic Solid State |date=1965 |publisher=Wiley-Interscience |editor-last=Fox |editor-first=D. |volume=2 |pages=726–767 |chapter=Polymorphism |author-link=Walter McCrone |editor2-last=Labes |editor2-first=M. |editor3-last=Weissberger |editor3-first=A.}}{{Cite journal |last1=Dunitz |first1=Jack D. |last2=Bernstein |first2=Joel |date=1995-04-01 |title=Disappearing Polymorphs |url=https://pubs.acs.org/doi/abs/10.1021/ar00052a005 |journal=Accounts of Chemical Research |language=en |volume=28 |issue=4 |pages=193–200 |doi=10.1021/ar00052a005 |issn=0001-4842}} 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. 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. 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.{{Cite web |title=Definition of trimorphism - mindat.org glossary |url=http://www.mindat.org/glossary/trimorphism |access-date=2016-10-23 |website=www.mindat.org}}

Polymorphism is of practical relevance to pharmaceuticals, agrochemicals, pigments, dyestuffs, foods, and explosives.

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.{{Cite book |last=Bernstein |first=Joel |title=Polymorphism in Molecular Crystals |publisher=Oxford University Press |year=2002 |isbn=0198506058 |location=New York, USA |pages=94–149}} The measurement of crystal density was also used by Wilhelm Ostwald and expressed in Ostwald's Ratio.{{Cite journal |last=Cardew |first=Peter T. |year=2023 |title=Ostwald Rule of Stages - Myth or Reality? |url=https://pubs.acs.org/crystal |journal=Crystal Growth & Design |volume=23 |issue=6 |pages=3958−3969 |doi=10.1021/acs.cgd.2c00141|doi-access=free |bibcode=2023CrGrD..23.3958C }}

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 (DSC), 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 (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.

Computational chemistry may be used in combination with vibrational spectroscopy techniques to understand the origins of vibrations within crystals.{{Cite journal |last1=Parrott |first1=Edward P.J. |last2=Zeitler |first2=J. Axel |year=2015 |title=Terahertz Time-Domain and Low-Frequency Raman Spectroscopy of Organic Materials |journal=Applied Spectroscopy |volume=69 |issue=1 |pages=1–25 |doi=10.1366/14-07707|pmid=25506684 |bibcode=2015ApSpe..69....1P |s2cid=7699996 }} 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.{{Cite journal |last1=Bowskill |first1=David H. |last2=Sugden |first2=Isaac J. |last3=Konstantinopoulos |first3=Stefanos |last4=Adjiman |first4=Claire S. |last5=Pantelides |first5=Constantinos C. |year=2021 |title=Crystal Structure Prediction Methods for Organic Molecules: State of the Art |journal=Annu. Rev. Chem. Biomol. Eng. |volume=12 |pages=593–623 |doi=10.1146/annurev-chembioeng-060718-030256|pmid=33770462 |s2cid=232377397 }}

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."Pharmaceutical Stress Testing: Predicting Drug Degradation, Second Edition Steven W. Baertschi, Karen M. Alsante, Robert A. Reed 2011 CRC Press

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.{{cite journal| last1 = Wöhler | first1 = F. | last2 = Liebig | first2 = J. | last3 = Ann | title=Untersuchungen über das Radikal der Benzoesäure | journal=Annalen der Pharmacie | publisher=Wiley | volume=3 | issue=3 | year=1832 | issn=0365-5490 | doi=10.1002/jlac.18320030302 | pages=249–282 | language=de| hdl = 2027/hvd.hxdg3f | hdl-access = free }} Present-day analysis{{cite journal | doi = 10.1002/anie.200701383 | volume=46 | title=Polymorphism in Benzamide: Solving a 175-Year-Old Riddle | year=2007 | journal=Angewandte Chemie International Edition | pages=6729–6731 | last1 = Thun | first1 = Jürgen| issue=35 | pmid=17665385 }} 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.

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 (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: 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.{{cite journal

|author1=Graeme M. Day |author2=Andrew V. Trask |author3=W. D. Samuel Motherwell |author4=William Jones | title = Investigating the Latent Polymorphism of Maleic Acid

| journal = Chemical Communications

| year = 2006

| volume = 1

| issue = 1

| pages = 54–56

| doi = 10.1039/b513442k

| pmid= 16353090 }}

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.{{cite journal

|vauthors=Thallapally PK, Jetti RK, Katz AK | title = Polymorphism of 1,3,5-trinitrobenzene Induced by a Trisindane Additive

| journal = Angewandte Chemie International Edition

| year = 2004

| volume = 43

| issue = 9

| pages = 1149–1155

| doi =10.1002/anie.200352253

| pmid= 14983460 }}

Acridine has been obtained as eight polymorphs{{cite journal |doi=10.1021/acs.cgd.9b00557 |title=The (Current) Acridine Solid Form Landscape: Eight Polymorphs and a Hydrate |year=2019 |last1=Schur |first1=Einat |last2=Bernstein |first2=Joel |last3=Price |first3=Louise S. |last4=Guo |first4=Rui |last5=Price |first5=Sarah L. |last6=Lapidus |first6=Saul H. |last7=Stephens |first7=Peter W. |journal=Crystal Growth & Design |volume=19 |issue=8 |pages=4884–4893 |bibcode=2019CrGrD..19.4884S |s2cid=198349955 |url=https://discovery.ucl.ac.uk/id/eprint/10080967/1/Price%20AAM%20Acridine_Review_CGD_Rev.pdf }} and aripiprazole has nine.{{cite journal |doi=10.1021/acs.cgd.9b01645 |title=Application of the Method of Molecular Voronoi–Dirichlet Polyhedra for Analysis of Noncovalent Interactions in Aripiprazole Polymorphs |year=2020 |last1=Serezhkin |first1=Viktor N. |last2=Savchenkov |first2=Anton V. |journal=Crystal Growth & Design |volume=20 |issue=3 |pages=1997–2003 |bibcode=2020CrGrD..20.1997S |s2cid=213824513 }} The record for the largest number of well-characterised polymorphs is held by a compound known as ROY.{{cite web|url=https://www.chemistryworld.com/news/red-orange-yellow-reclaims-polymorph-record-with-help-from-molecular-cousin/4012160.article|title=Red–orange–yellow reclaims polymorph record with help from molecular cousin|date=2020-07-29|last=Krämer|first=Katrina |website=chemistryworld.com|access-date=2021-05-07}}{{cite journal |doi=10.1016/j.chempr.2020.04.009 |title=Encapsulated Nanodroplet Crystallization of Organic-Soluble Small Molecules |year=2020 |last1=Tyler |first1=Andrew R. |last2=Ragbirsingh |first2=Ronnie |last3=McMonagle |first3=Charles J. |last4=Waddell |first4=Paul G. |last5=Heaps |first5=Sarah E. |last6=Steed |first6=Jonathan W. |last7=Thaw |first7=Paul |last8=Hall |first8=Michael J. |last9=Probert |first9=Michael R. |journal=Chem |volume=6 |issue=7 |pages=1755–1765 |pmid=32685768 |pmc=7357602 |bibcode=2020Chem....6.1755T }} Glycine crystallizes as both monoclinic and hexagonal crystals. Polymorphism in organic compounds is often the result of conformational polymorphism.{{cite journal |doi=10.1021/cr400249d|title=Conformational Polymorphism|year=2014|last1=Cruz-Cabeza|first1=Aurora J.|last2=Bernstein|first2=Joel|journal=Chemical Reviews|volume=114|issue=4|pages=2170–2191|pmid=24350653}}

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 (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.{{Cite book |last1=Greenwood |first1=N. N. |title=Chemistry of the Elements |last2=Earnshaw |first2=A. |publisher=Butterworth-Heinemann |year=1997 |isbn=0-7506-3365-4 |edition=Second |location=Oxford}}

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 londsdaleite. 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 (alpha) form and a rhombohedral (beta) form.

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.{{Cite web|url=http://www.mindat.org/glossary/polymorphism|title=Definition of polymorphism - mindat.org glossary|website=www.mindat.org|access-date=2016-10-23}}

"Polymorphism in nanocrystalline binary metal oxides", S. Sood, P.Gouma, Nanomaterials and Energy, 2(NME2), 1-15(2013).

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. A third form of calcium carbonate is vaterite, which is hexagonal and relatively unstable.{{Cite journal |last1=Perić |first1=J. |last2=Vučak |first2=M. |last3=Krstulović |first3=R. |last4=Brečević |first4=Lj. |last5=Kralj |first5=D. |title=Phase Transformation of Calcium Carbonate Polymorphs |url=https://www.sciencedirect.com/science/article/abs/pii/0040603195027483 |journal=Thermochimica Acta |date=1996 |volume=277 |issue=1 May 1996 |pages=175–86 |doi=10.1016/0040-6031(95)02748-3 |bibcode=1996TcAc..277..175P |via=Science Direct}}

{{Multiple image|total_width = 400

|image1=Calcite jaune.jpg

|image2=Aragonite 2 Enguidanos.jpg

|footer=Calcite (on left) and Aragonite (on right), two forms of calcium carbonate. Note: the colors are from impurities.}}

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.{{cite book |doi=10.1002/9780470132326.ch7|chapter=Red Mercuric Sulfide|year=1939|last1=Newell|first1=Lyman C.|last2=Maxson|first2=R. N.|last3=Filson|first3=M. H.|title=Inorganic Syntheses|pages=19–20|volume=1|isbn=9780470132326}}

According to Ostwald's rule, usually less stable polymorphs crystallize before the stable form. The concept hinges on the idea that unstable polymorphs more closely resemble the state in solution, and thus are kinetically advantaged. The founding case of fibrous vs rhombic benzamide illustrates the case. Another example is provided by two polymorphs of titanium dioxide.[https://link.springer.com/article/10.1007/s10853-010-5113-0 Anatase to Rutile Transformation](ART) summarized in the Journal of Materials Science 2011 Nevertheless, there are known systems, such as metacetamol, where only narrow cooling rate favors obtaining metastable form II.{{Cite journal |last1=Drebushchak |first1=V. A. |last2=McGregor |first2=L. |last3=Rychkov |first3=D. A. |date=February 2017 |title=Cooling rate "window" in the crystallization of metacetamol form II |url=http://link.springer.com/10.1007/s10973-016-5954-0 |journal=Journal of Thermal Analysis and Calorimetry |language=en |volume=127 |issue=2 |pages=1807–1814 |doi=10.1007/s10973-016-5954-0 |s2cid=99391719 |issn=1388-6150}}

Polymorphs have disparate stabilities. Some convert rapidly at room (or any) 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.{{cite journal|last1=Nyman|first1=Jonas|last2=Day|first2=Graeme M.|title=Static and lattice vibrational energy differences between polymorphs|journal=CrystEngComm|volume=17|issue=28|pages=5154–5165|date=2015|doi=10.1039/C5CE00045A|doi-access=free}} Polymorph stability may change upon temperature{{Cite journal |last1=Dubok |first1=Aleksandr S. |last2=Rychkov |first2=Denis A. |date=2023-04-04 |title=Relative Stability of Pyrazinamide Polymorphs Revisited: A Computational Study of Bending and Brittle Forms Phase Transitions in a Broad Temperature Range |journal=Crystals |language=en |volume=13 |issue=4 |pages=617 |doi=10.3390/cryst13040617 |issn=2073-4352 |doi-access=free |bibcode=2023Cryst..13..617D }}{{Cite journal |last1=Borba |first1=Ana |last2=Albrecht |first2=Merwe |last3=Gómez-Zavaglia |first3=Andrea |last4=Suhm |first4=Martin A. |last5=Fausto |first5=Rui |date=2010-01-14 |title=Low Temperature Infrared Spectroscopy Study of Pyrazinamide: From the Isolated Monomer to the Stable Low Temperature Crystalline Phase |url=https://pubs.acs.org/doi/10.1021/jp907466h |journal=The Journal of Physical Chemistry A |language=en |volume=114 |issue=1 |pages=151–161 |doi=10.1021/jp907466h |pmid=20055514 |bibcode=2010JPCA..114..151B |hdl=11336/131247 |issn=1089-5639|hdl-access=free }}{{Cite journal |last1=Hoser |first1=Anna Agnieszka |last2=Rekis |first2=Toms |last3=Madsen |first3=Anders Østergaard |date=2022-06-01 |title=Dynamics and disorder: on the stability of pyrazinamide polymorphs |url=https://scripts.iucr.org/cgi-bin/paper?S2052520622004577 |journal=Acta Crystallographica Section B Structural Science, Crystal Engineering and Materials |volume=78 |issue=3 |pages=416–424 |doi=10.1107/S2052520622004577 |issn=2052-5206 |pmc=9254588 |pmid=35695115|bibcode=2022AcCrB..78..416H }} or pressure.{{cite journal |last1=Smirnova |first1=Valeriya Yu. |last2=Iurchenkova |first2=Anna A. |last3=Rychkov |first3=Denis A. |date=2022-08-17 |title=Computational Investigation of the Stability of Di-p-Tolyl Disulfide "Hidden" and "Conventional" Polymorphs at High Pressures |journal=Crystals |language=en |volume=12 |issue=8 |pages=1157 |doi=10.3390/cryst12081157 |issn=2073-4352 |doi-access=free |bibcode=2022Cryst..12.1157S }}{{Cite journal |last1=Rychkov |first1=Denis A. |last2=Stare |first2=Jernej |last3=Boldyreva |first3=Elena V. |date=2017 |title=Pressure-driven phase transition mechanisms revealed by quantum chemistry: l -serine polymorphs |journal=Physical Chemistry Chemical Physics |language=en |volume=19 |issue=9 |pages=6671–6676 |doi=10.1039/C6CP07721H |pmid=28210731 |issn=1463-9076|doi-access=free |bibcode=2017PCCP...19.6671R }} Importantly, structural and thermodynamic stability are different. Thermodynamic stability may be studied using experimental or computational methods.{{Cite journal |last=Rychkov |first=Denis A. |date=2020-01-31 |title=A Short Review of Current Computational Concepts for High-Pressure Phase Transition Studies in Molecular Crystals |journal=Crystals |language=en |volume=10 |issue=2 |pages=81 |doi=10.3390/cryst10020081 |issn=2073-4352 |doi-access=free |bibcode=2020Cryst..10...81R }}{{Cite journal |last1=Fedorov |first1=A. Yu. |last2=Rychkov |first2=D. A. |title=Comparison of Different Computational Approaches for Unveiling the High-Pressure Behavior of Organic Crystals at a Molecular Level. Case Study of Tolazamide Polymorphs |date=September 2020 |url=https://link.springer.com/10.1134/S0022476620090024 |journal=Journal of Structural Chemistry |language=en |volume=61 |issue=9 |pages=1356–1366 |doi=10.1134/S0022476620090024 |bibcode=2020JStCh..61.1356F |s2cid=222299340 |issn=0022-4766}}

Polymorphism is affected by the details of crystallisation. The solvent in all respects affects the nature of the polymorph, including concentration, other components of the solvent, i.e., species that inhibiting or promote certain growth patterns.{{Cite journal |last1=Rychkov |first1=Denis A. |last2=Arkhipov |first2=Sergey G. |last3=Boldyreva |first3=Elena V. |date=2014-08-01 |title=Simple and efficient modifications of well known techniques for reliable growth of high-quality crystals of small bioorganic molecules |url=https://scripts.iucr.org/cgi-bin/paper?S1600576714011273 |journal=Journal of Applied Crystallography |volume=47 |issue=4 |pages=1435–1442 |doi=10.1107/S1600576714011273 |issn=1600-5767|doi-access=free }} A decisive factor is often the temperature of the solvent from which crystallisation is carried out.{{Cite book |last=Buckley |first=Harold Eugene |url=https://books.google.com/books?id=OzZRAAAAMAAJ |title=Crystal Growth |date=1951 |publisher=Wiley |language=en}}

Metastable polymorphs are not always reproducibly obtained, leading to cases of "disappearing polymorphs", with usually negative implications on law and business.Crystal Engineering: The Design and Application of Functional Solids, Volume 539, Kenneth Richard Seddon, Michael Zaworotk 1999{{cite journal | last1 = Bučar | first1 = D.-K. | last2 = Lancaster | first2 = R. W. | last3 = Bernstein | first3 = J. | year = 2015 | title = Disappearing Polymorphs Revisited | journal = Angewandte Chemie International Edition | volume = 54 | issue = 24| pages = 6972–6993 | doi = 10.1002/anie.201410356 | pmid = 26031248 | pmc = 4479028 }}{{cite journal | last1 = Surov | first1 = Artem O. | last2 = Vasilev | first2 = Nikita A. | last3 = Churakov | first3 = Andrei V. | last4 = Stroh | first4 = Julia | last5 = Emmerling | first5 = Franziska | last6 = Perlovich | first6 = German L. | year = 2019| title = Solid Forms of Ciprofloxacin Salicylate: Polymorphism, Formation Pathways and Thermodynamic Stability | journal = Crystal Growth & Design | volume = 19| issue = 5| pages = 2979–2990| doi = 10.1021/acs.cgd.9b00185 | bibcode = 2019CrGrD..19.2979S | s2cid = 132854494 }}

Approximately 37% or more of organic compounds exist as more than one polymorph.{{cite journal |doi=10.1021/acs.chemrev.3c00384 |title=Ionic Liquids: New Forms of Active Pharmaceutical Ingredients with Unique, Tunable Properties |date=2023 |last1=Shamshina |first1=Julia L. |last2=Rogers |first2=Robin D. |journal=Chemical Reviews |volume=123 |issue=20 |pages=11894–11953 |pmid=37797342 }} The existence of polymorphs has legal implications as drugs receive regulatory approval and are granted patents for only a single polymorph. In a classic patent dispute, the GlaxoSmithKline defended its patent for the Type II polymorph of the active ingredient in Zantac against competitors while that of the Type I polymorph had already expired.{{Cite web|url=http://www.rsc.org/images/Shape%20shifters_tcm18-83943.pdf|title = Accredited Degree Programmes}} Polymorphism in drugs can also have direct medical implications since dissolution rates depend on the polymorph. The known cases up to 2015 are discussed in a review article by Bučar, Lancaster, and Bernstein.

Clozapine exists in 4 forms compared to 60 forms for olanzapine. .{{Citation |last=Bhardwaj |first=Rajni M. |title=Exploring the Physical Form Landscape of Clozapine, Amoxapine and Loxapine |date=2016 |url=http://link.springer.com/10.1007/978-3-319-27555-0_7 |work=Control and Prediction of Solid-State of Pharmaceuticals |series=Springer Theses |pages=153–193 |access-date=2023-12-20 |place=Cham |publisher=Springer International Publishing |doi=10.1007/978-3-319-27555-0_7 |isbn=978-3-319-27554-3}}

The original formulations licensed as Noxafil were formulated utilising form I of posaconazole. The discovery of polymorphs of posaconazole increased rapidly and resulted in much research in crystallography of posaconazole. A methanol solvate and a 1,4-dioxane co-crystal were added to the Cambridge Structural Database (CSD).{{Cite journal |last1=McQuiston |first1=Dylan K. |last2=Mucalo |first2=Michael R. |last3=Saunders |first3=Graham C. |date=2019-03-05 |title=The structure of posaconazole and its solvates with methanol, and dioxane and water: Difluorophenyl as a hydrogen bond donor |url=https://www.sciencedirect.com/science/article/pii/S0022286018313413 |journal=Journal of Molecular Structure |volume=1179 |pages=477–486 |doi=10.1016/j.molstruc.2018.11.031 |bibcode=2019JMoSt1179..477M |s2cid=105578644 |issn=0022-2860}}

The antiviral drug ritonavir exists as two polymorphs, which differ greatly in efficacy. Such issues were solved by reformulating the medicine into gelcaps and tablets, rather than the original capsules.{{cite journal|vauthors=Bauer J, etal |title=Ritonavir: An Extraordinary Example of Conformational Polymorphism|journal=Pharmaceutical Research|volume=18|pages=859–866|year=2004|doi=10.1023/A:1011052932607|pmid=11474792|issue=6|s2cid=20923508}}

One polymorph ("Form I") of aspirin is common. "Form II" was reported in 2005,{{cite journal

|author1=Peddy Vishweshwar |author2=Jennifer A. McMahon |author3=Mark Oliveira |author4=Matthew L. Peterson |author5=Michael J. Zaworotko |name-list-style=amp | title = The Predictably Elusive Form II of Aspirin

| journal = J. Am. Chem. Soc.

| year = 2005

| volume = 127

| issue = 48

| pages = 16802–16803

| doi = 10.1021/ja056455b

| pmid= 16316223 |bibcode=2005JAChS.12716802V }}{{cite journal

|author1=Andrew D. Bond |author2=Roland Boese |author3=Gautam R. Desiraju | title = On the Polymorphism of Aspirin: Crystalline Aspirin as Intergrowths of Two "Polymorphic" Domains

| journal = Angewandte Chemie International Edition

| year = 2007

| volume = 46

| issue = 4

| pages = 618–622

| doi = 10.1002/anie.200603373

| pmid= 17139692 }} found after attempted co-crystallization of aspirin and levetiracetam from hot acetonitrile.

In form I, pairs of aspirin molecules form centrosymmetric dimers through the acetyl groups with the (acidic) methyl proton to carbonyl hydrogen bonds. In form II, each aspirin molecule forms the same hydrogen bonds, but 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.{{cite web|url=http://reference.iucr.org/dictionary/Polytypism|title=Polytypism - Online Dictionary of Crystallography|website=reference.iucr.org}}

Pure Form II aspirin could be prepared by seeding the batch with aspirin anhydrate in 15% weight.

Paracetamol powder has poor compression properties, which poses difficulty in making tablets. A second polymorph was found with more suitable compressive properties.{{cite journal |last1=Wang |first1=In-Chun |last2=Lee |first2=Min-Jeong |last3=Seo |first3=Da-Young |last4=Lee |first4=Hea-Eun |last5=Choi |first5=Yongsun |last6=Kim |first6=Woo-Sik |last7=Kim |first7=Chang-Sam |last8=Jeong |first8=Myung-Yung |last9=Choi |first9=Guang Jin |title=Polymorph Transformation in Paracetamol Monitored by In-line NIR Spectroscopy During a Cooling Crystallization Process |journal=AAPS PharmSciTech |date=14 June 2011 |volume=12 |issue=2 |pages=764–770 |doi=10.1208/s12249-011-9642-x |pmid=21671200 |pmc=3134639 }}

Cortisone acetate exists in at least five different polymorphs, four of which are unstable in water and change to a stable form.

Carbamazepine, estrogen, paroxetine,{{cite web|url=http://www.blakes.com/english/view_disc.asp?ID=249|archive-url=https://archive.today/20120720200824/http://www.blakes.com/english/view_disc.asp?ID=249|url-status=dead|title=Disappearing Polymorphs and Gastrointestinal Infringement|date=20 July 2012|archive-date=20 July 2012|website=blakes.com}} and chloramphenicol also show polymorphism.

Pyrazinamide has at least 4 polymorphs.{{Cite journal |last1=Castro |first1=Ricardo A. E. |last2=Maria |first2=Teresa M. R. |last3=Évora |first3=António O. L. |last4=Feiteira |first4=Joana C. |last5=Silva |first5=M. Ramos |last6=Beja |first6=A. Matos |last7=Canotilho |first7=João |last8=Eusébio |first8=M. Ermelinda S. |date=2010-01-06 |title=A New Insight into Pyrazinamide Polymorphic Forms and their Thermodynamic Relationships |url=https://pubs.acs.org/doi/10.1021/cg900890n |journal=Crystal Growth & Design |language=en |volume=10 |issue=1 |pages=274–282 |doi=10.1021/cg900890n |bibcode=2010CrGrD..10..274C |issn=1528-7483}} All of them transforms to stable α form at room temperature upon storage or mechanical treatment.{{Cite journal |last1=Cherukuvada |first1=Suryanarayan |last2=Thakuria |first2=Ranjit |last3=Nangia |first3=Ashwini |date=2010-09-01 |title=Pyrazinamide Polymorphs: Relative Stability and Vibrational Spectroscopy |url=https://pubs.acs.org/doi/10.1021/cg1004424 |journal=Crystal Growth & Design |language=en |volume=10 |issue=9 |pages=3931–3941 |doi=10.1021/cg1004424 |bibcode=2010CrGrD..10.3931C |issn=1528-7483}} Recent studies prove that α form is thermodynamically stable at room temperature.

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."The basics of crystallography and diffraction", Christopher Hammond, Second edition, Oxford science publishers, IUCr, page 28 {{ISBN|0 19 8505531}}.

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.{{Cite journal|last1=Li|first1=Xiao|last2=Zhu|first2=Hongwei|date=2015-03-01|title=Two-dimensional MoS2: Properties, preparation, and applications|journal=Journal of Materiomics|volume=1|issue=1|pages=33–44|doi=10.1016/j.jmat.2015.03.003|doi-access=free}}

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.{{cite journal |last1=Wilson |first1=J.A. |last2=Di Salvo |first2=F. J. |last3=Mahajan |first3=S. |date=October 1974 |title=Charge-density waves and superlattices in the metallic layered transition metal dichalcogenides |journal=Advances in Physics |volume=50 |issue=8 |pages=1171–1248 |doi=10.1080/00018730110102718 |s2cid=218647397 }} 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.C.E. Ryan, R.C. Marshall, J.J. Hawley, I. Berman & D.P. Considine, "The Conversion of Cubic to Hexagonal Silicon Carbide as a Function of Temperature and Pressure," U.S. Air Force, Physical Sciences Research Papers, #336, Aug 1967, p 1-26. 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.

File:Energy-Temperature diagrams of a system exhibiting two polymorphic forms with enantiotropic behaviour (left) and monotropic behaviour (right)..jpg]In terms of thermodynamics, two types of polymorphic behaviour are recognized. For a monotropic system, plots of the free energies of the various polymorphs against temperature do not cross before all polymorphs melt. As a result, any transition from one polymorph to another below the melting point will be irreversible. For an enantiotropic system, a plot of the free energy against temperature shows a crossing point before the various melting points.{{cite journal | doi = 10.1021/acs.cgd.5b00237 | volume=15 | title=Solid-State Investigation of Polymorphism and Tautomerism of Phenylthiazole-thione: A Combined Crystallographic, Calorimetric, and Theoretical Survey | year=2015 | journal=Crystal Growth & Design | pages=2461–2473 | last1 = Carletta | first1 = Andrea| issue=5 | bibcode=2015CrGrD..15.2461C }} It may also be possible to convert interchangeably between the two polymorphs by heating or cooling, or through physical contact with a lower energy polymorph.

A simple model of polymorphism is to model the Gibbs free energy of a ball-shaped crystal as $G\; =\; a\; r^2\; -\; b\; r^3$. Here, the first term $ar^2$ is the surface energy, and the second term $-br^3$ is the volume energy. Both parameters $a,\; b\; >\; 0$. The function $G(r)$ rises to a maximum before dropping, crossing zero at $r\_\{crit\}$. In order to crystallize, a ball of crystal much overcome the energetic barrier to the $r\; >\; r\_\{crit\}$ part of the energy landscape.{{Cite journal |last=Ward |first=Michael D. |date=February 2017 |title=Perils of Polymorphism: Size Matters |url=https://onlinelibrary.wiley.com/doi/10.1002/ijch.201600071 |journal=Israel Journal of Chemistry |language=en |volume=57 |issue=1–2 |pages=82–92 |doi=10.1002/ijch.201600071 |issn=0021-2148}}

File:Polymorphism Gibbs free energy.png

Now, suppose there are two kinds of crystals, with different energies $G\_1\; =\; a\_1\; r^2\; -\; b\_1\; r^3$ and $G\_2\; =\; a\_2\; r^2\; -\; b\_2\; r^3$, and if they have the same shape as in Figure 2, then the two curves intersect at some $r\text{'}\_\{crit\}\; >\; r\_\{crit,\; 1\}$. Then the system has three phases:

• . Crystals tend to dissolve. Amorphous phase.
• . Crystals tend to grow as form 1.
• $r\; >\; r\text{'}\_\{crit\}$. Crystals tend to grow as form 2.

If the crystal is grown slowly, it could be kinetically stuck in form 1.

{{Commons category|Polymorphism}}

• Allotropy
• Isomorphism (crystallography)
• Dimorphism (Wiktionary)
• Polyamorphism
• Disappearing polymorphs

{{Reflist|30em}}

• [https://web.archive.org/web/20160303181456/http://acaschool.iit.edu/lectures04/JLiangXtal.pdf "Small Molecule Crystallization"] (PDF) at Illinois Institute of Technology website
• [http://www.iue.tuwien.ac.at/phd/ayalew/node20.html "SiC and Polytpism"]

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