Polymorphism (materials science)
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; α-quartz, β-quartz, tridymite, cristobalite, moganite, coesite, and stishovite. A classical example is the pair of minerals, calcite and aragonite, both forms of calcium carbonate.
An analogous phenomenon for amorphous materials is polyamorphism, when a substance can take on several different amorphous modifications.
Background
In terms of thermodynamics, there are two types of polymorphic behaviour. For a monotropic system, plots of the free energies 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. 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 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, 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:
- Solvent effects
- Certain impurities inhibiting growth pattern and favour the growth of a metastable polymorphs
- The level of supersaturation from which material is crystallised
- Temperature at which crystallisation is carried out
- Geometry of covalent bonds
- Change in stirring conditions
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
Ostwald's rule or Ostwald's step rule,conceived by Wilhelm Ostwald, states that in general it is not the most stable with the lowest 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 by 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 is 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 a common tendency observed in Nature.
In binary metal oxides
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 | α phase | Ambient conditions | Rutile-type Tetragonal |
| CrO2 | β phase | RT and 14 GPa | CaCl2-type Orthorhombic |
| CrO2 | β phase | RT and 12±3 GPa | CaCl2-type Orthorhombic |
| Cr2O3 | Corundum phase | Ambient conditions | Corundum-type Rhombohedral |
| Cr2O3 | High pressure phase | RT and 35 GPa | Rh2O3-II type |
| Fe2O3 | α phase | Ambient conditions | Corundum-type Rhombohedral |
| Fe2O3 | β phase | Below 773 K | Body-centered cubic |
| Fe2O3 | γ phase | Up to 933 K | Cubic spinel structure |
| Fe2O3 | ε phase | -- | Rhombic |
| Bi2O3 | α phase | Ambient conditions | Monoclinic |
| Bi2O3 | β phase | 603-923 K and 1 atm | Tetragonal |
| Bi2O3 | γ phase | 773-912 K or RT and 1 atm | Body-centered cubic |
| Bi2O3 | δ phase | 912-1097 K and 1 atm | FCC |
| In2O3 | Bixbyite-type phase | Ambient conditions | Cubic |
| In2O3 | Corundum-type | 15-25 GPa at 1273 K | Corundum-type Hexagonal |
| In2O3 | Rh2O3-type | 100 GPa and 1000 K | Orthorhombic |
| Al2O3 | α phase | Ambient conditions | Corundum-type Trigonal |
| Al2O3 | γ phase | 773 K and 1 atm | Cubic |
| SnO2 | α phase | Ambient conditions | Rutile-type Tetragonal |
| SnO2 | CaCl2-type phase | 15 KBar at 1073 K | Orthorhombic, CaCl2-type |
| SnO2 | α-PbO2-type | Above 18 KBar | α-PbO2-type |
| TiO2 | Rutile | Equilibrium phase | Rutile-type Tetragonal |
| TiO2 | Anatase | Metastable phase | Tetragonal |
| TiO2 | Brookite | Metastable phase | Orthorhombic |
| ZrO2 | Monoclinic phase | Ambient conditions | Monoclinic |
| ZrO2 | Tetragonal phase | Above 1443 K | Tetragonal |
| ZrO2 | Fluorite-type phase | Above 2643 K | Cubic |
| MoO3 | α phase | 553-673 K & 1 atm | Orthorhombic |
| MoO3 | β phase | 553-673 K & 1 atm | Monoclinic |
| MoO3 | h phase | High-pressure and high-temperature phase | Hexagonal |
| MoO3 | MoO3-II | 60 kbar and 973 K | Monoclinic |
| WO3 | ε phase | Up to 220 K | Monoclinic |
| WO3 | δ phase | 220-300 K | Triclinic |
| WO3 | γ phase | 300-623 K | Monoclinic |
| WO3 | β phase | 623-900 K | Orthorhombic |
| WO3 | α phase | Above 900 K | Tetragonal |
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. Polymorphic purity of drug samples can be checked using techniques such as powder X-ray diffraction, IR/Ramanspectroscopy, 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 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 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.
- Paracetamol powder has poor compression properties; this poses difficulty in making tablets, so a new polymorph of paracetamol was found which is more compressible.
- Due to differences in solubility of polymorphs, one polymorph may be more active therapeutically than another polymorph of same drug.
- Cortisone acetate exists in at least five different polymorphs, four of which are unstable in water and change to a stable form.
- Carbamazepine beta-polymorph developed from solvent of high dielectric constant ex aliphatic alcohol, whereas alpha polymorph crystallized from solvents of low dielectric constant such as carbon tetrachloride.
- Estrogen and chloramphenicol also show polymorphism.
Disappearing polymorphs
Polytypism
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 has more than 170 known polytypes, although most are rare. All the polytypes of SiC have virtually the same density and Gibbs free energy. Themost common SiC polytypes are shown in Table 1.
Table 1: Some polytypes of SiC.
| Phase | Structure | Ramsdell Notation | Stacking Sequence | Comment |
| α-SiC | hexagonal | 2H | AB | Wurtzite form |
| α-SiC | hexagonal | 4H | ABCB | |
| α-SiC | hexagonal | 6H | ABCACB | The most stable and common form |
| α-SiC | rhombohedral | 15R | ABCACBCABACABCB | |
| β-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. 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.