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The term polymorphism (Greek for ‘‘many forms’’) is, depending on the communities, associated with different meanings. For example, in Biology, it can apply to species with different phenotypes, designating even sexual dimorphism, lipid polymorphism, nuclear dimorphism and frond dimorphism. In Computer Science, it refers to a programming language feature which allows to handle data of different types with the same interface, and in Medicine, the term polymorphism relates to a signal series seen in an electrocardiogram. In Chemistry, and this is what we will focus on, the term means that a solid compound can adopt different forms and/ or crystal structures. The formation of a solid generally includes a crystallization step, based on nucleation and growth. Nucleation is a kinetically controlled process during which atoms, ions and/or molecules aggregate into small clusters, first in a reversible way before forming stable nuclei. The latter are then able to grow into crystallites and crystals. It is thus easy to understand that in p rinciple, this first nucleation process can lead the way to different arrangements of atoms, ions and/or molecules in the solid state, depending on how the building blocks of the solid meet. Probably all scientists dealing with solid state compounds and crystals have experienced that the more one looks for new structures of a compound, the more one can find. Indeed, while interactions between ions are usually strong, the interactions between organic molecules can be numerous, and are often weak and non-directional, allowing thus for many options to combine with each other into a stable structure. It is therefore a challenge to predict the solid state structure of a compound, and many theoretical approaches have been tested to find more and more successful predictions. For example: 1–7 Indeed, the Cambridge Crystallographic Data Centre (CCDC) hosts since 1999 approximately every two to three years the Crystal Structure Prediction Blind Test, a defeat in principle for every chemist. 5,8–11 The results are very encouraging, yet, Nature holds still enough surprises for us with unexpected new forms that are found in the solid state. Polymorphism is not only interesting in the context of basic science, understanding the concepts of intermolecular interactions, but the industry dealing with materials as well as with pharmaceuticals, has also a huge stake in this area. For materials, control over the solid state is crucial for their physical properties, e.g. conductivity or tensile strength, while for pharmaceutically active compounds, the form of the solid state structure can determine its activity or even toxicity. In March 2013, the Web of Science counts more than 66 000 papers on polymorphism in the areas restricted to chemistry, pharmacology/pharmacy and materials science. 12 The number of publications on polymorphism has increased dramatically from 393 in 1992 to more than 5400 in 2012, showing the interest in this research area, but also the widespread of use of the term ‘‘polymorphism’’ – not always with the same meaning. This is why this Review starts with a chapter on the historical development of the term, as well as the current definitions which can be found in the literature. It will then give some chosen examples out of each class of compounds, inorganic/metallic, organic and coordination compounds, in order to give the scientists first of all an idea about the types of polymorphisms which may exist, and second, a handful of tools to decide whether they have or not themselves cases of polymorphism among their own compounds. This Review is non-comprehensive. Since the definition of polymorphism has varied greatly over time and space, let us start by unrolling the story of polymorphism and finding a definition for ourselves. We will also highlight different types of polymorphism discussed in the literature in order to include or exclude them from our personal comprehension of polymorphism. Historically, it is Klaporoth in 1788 who identified and described a first case of a compound adopting several crystal forms, namely three forms of calcium carbonate: calcite, vaterite and aragonite. 13 In 1832, the first case of polymorphism in an organic compound, benzamide, is discovered by W ̈hler & Liebig, 14 but it isn’t until 1938 when Robertson & Ubbelohde find the first X-ray diffraction structure of polymorphs with resorcinol, and this is, to the best of our knowledge, the first crystal structure determination of polymorphism. 15 To this apparently simple question, the literature provides numerous different definitions, which are all based on the one given by McCrone in 1965: ‘‘A polymorph is a solid 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.’’ 16 In 1969, Rosenstein & Lamy propose an alternative definition: ‘‘When a substance can exist in more than one crystalline state it is said to exhibit polymorphism.’’, 17 which allows an interpretation including a lot of different forms, for example also solvates. Continuing the overview of the different definitions found in the literature, the one given by Burger in 1983 is noticeable: ‘‘If these (solids composed of only one component) can exist in different crystal lattices, then we speak of polymorphism.’’ 18 but as pointed out by Bernstein, this last definition seems to be unclear about the terms crystal lattice and crystal structure 19 and the possibility of polymorphism in co-crystals, solvates or salts is excluded. The more complete definitions are probably given by (i) Sharma in 1987: ‘‘Polymorphs means the different crystal forms, belonging to the same or different crystal systems, in which the identical units of the same element or the identical units of the same compound, or the identical ionic formulas or identical repeating units are packed differently’’, 20 or (ii) more recently by Gavezzotti in 2007 with a definition in three points: ‘‘Polymorphs are a set of crystals (a) with identical chemical composition; (b) made of molecules with same molecular connectivity, but allowing for different conformations by rotation about single bonds, (c) with distinctly different three-dimensional translationally periodic symmetry opera- tions’’, 21 or iii) also by Purojit & Venugoplan in 2009: ‘‘thus it is defined as the ability of a substance to exist as two or more crystalline phases that have different arrangements or conformations of the molecules in the crystal lattice.’’ 22 In its recommendation of 1994, IUPAC defines the polymorphic transition as ‘‘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.’’. 23 Based on all these definitions, we have now a good idea of what polymorphism is, but now, it must be defined how to limit and use the term ‘‘same substance’’ or ‘‘compound’’. IUPAC, the term ‘‘chemical substance’’ is used for ‘‘a matter of constant composition, best characterized by the entities (molecules, formula units, atoms) it is composed of. The physical properties such as density, refractive index, electric conductivity, melting point etc. characterize the chemical substance.’’ 23 This definition contains a first contradiction with polymorphs, as, indeed one of the characteristics of polymorphs is that they can have different physical properties, like for example the melting point, solubility or refractive index. For this reason, we prefer to use the term compound with the meaning of ‘‘identical chemical composition’’ in this Review. As a consequence, ‘‘identical chemical composition’’ excludes thus the phenomenon often called pseudopolymorphism – a confusing term to define solvates – from the list of possible types of polymorphism. Indeed, already in 1965, McCrone referred to pseudopolymorphism as a term ‘‘..., which is convenient to use here but which should never be allowed to come into general use, is meant a variety of phenomena sometimes confused with polymorphism.’’. 16 We should however point out the fact that the U.S. Food and Drugs Administration (FDA) uses a wider definition for the ‘‘classification of polymorphs’’. ‘‘Different crystalline forms of the same substance. This may include solvation or hydration products (also known as pseudopolymorphs) and amorphous forms.’’ 24 For the pharmaceutical industry, pseudopolymorphism is a case of polymorphism, and, more surprisingly, amorphous forms are also a case of polymorphism. This broad definition allows to cover 72 different forms for axitinib, out of which five are anhydrate forms, and among the remaining 67 solvates, some co-crystals (definition see later in the chapter) are found. 25 Excluding the pseudopolymorphism allowed by the FDA definition, there remain two cases of polymorphism to be considered: The first one is due to the possible rotation about single bonds in a molecule leading to several possible conformations, thus called conformational polymorphism