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Time–temperature transformation diagram or quenching diagram of steel. M s corresponds to the starting point of martensite formation and M f to the end of the formation. Pearlite: a -Fe + C + Fe 3 C and bainite: a different 

Time–temperature transformation diagram or quenching diagram of steel. M s corresponds to the starting point of martensite formation and M f to the end of the formation. Pearlite: a -Fe + C + Fe 3 C and bainite: a different 

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This review on polymorphism is a personal, non-comprehensive view on the field of polymorphism – a term which is often misused. Indeed, the discussion about polymorphism and related terms is still ongoing in the area of crystal engineering. This is why we felt it timely to look into the historical development of its definition and to delimit it. A...

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... (68%). 58 In terms of polymorphism, related to atom connectivity, it would thus be reasonable to consider a transition between FCC and HCP as polymorphic transition, while the one between BCC and FCC or HCP is not. For example, in the case of the iron, the transition between the e -ferrite and the c -austenite is a polymorphic transition but the transition between c -austenite and a -ferrite is not (Fig. 12). These different crystal structures have a direct impact on the metal properties. For example, lead (Pb) and gold (Au), which belong to the FCC lattice, are plastic metals because of the presence of a lot of planes along which rows of atoms can slide: the slip planes. In comparison, metals like titanium or cobalt, which possess an HCP structure with less slip planes, are harder to deform. 61 This property of deformation of metals under stress is called the plasticity (ductility: tensile stress and malleability: compressive stress). The metal crystal structure can however change depending on the conditions, namely pressure and temperature. Iron (Maiden): let’s play metal.... A good example of such metal phase transitions is iron (Fe). The iron manufacturing and processing is an ancient knowledge that was passed on through the centuries. Nowadays the production of iron and its derivatives is well understood and controlled, using tools such as the phase diagram and the transition temperature point. It is a very good case study for the allotropism of metals and alloys and is also very important for the industry. Iron adopts two different packing types upon heating: BCC ( a -ferrite) at low temperature then FCC ( c -ferrite) upon heating, and back to a BCC system ( d -ferrite) at even higher temperature (Fig. 12). This BCC system of d -ferrite has a larger distance between the iron atoms than the one of a -ferrite. Since the connectivity of the atoms in these two phases is the same, they are considered as polymorphs. Several important modifications of properties arise from these allotropic/polymorphic transformations. For example, the cell volume decreases, but the density, the number of bonds between atoms and the solubility towards carbon increase from BCC to FCC. The carbon solubility is very low in the case of the BCC a -ferrite, however in the FCC c -austenite, it is higher due to the larger distance between the Fe atoms. Thus, the carbon can be more easily inserted into the host structure of the FCC lattice. 62 By a rapid quenching of the FCC structure, doped with carbon, the BCT (body centered tetragonal) forms ( a 9 -martensite) can be obtained. The connectivity between atoms change between the FCC and BCT lattice, thus, this transformation is allotropic. The BCT, body centered tetragonal, lattice can be seen as a deformed BCC lattice. This deformed BCC lattice of iron and carbon is commonly called steel or martensite (Fig. 13). This leads us to the subject of alloy formation, solid solutions and, in particular, steel and its processing, into which we will now make a short excursion. Alloys/solid solutions – hard as rock: the steel!. The steel and iron industry is one of the pillars of the industrial development and has a huge economic impact on our society since the Middle Ages and even before. Its manufacturing process and development are strongly correlated with the allotropic properties of the iron and its capability to solvate carbon and many other metals and additives. One of the most important examples of the use of the properties of the iron-carbon alloy is the tempering. This ancient method is employed in forging to improve and fine- tune mechanical properties (hardness, toughness, ductility, ...) out of a mix of iron with low carbon content by rapid cooling (quenching) from high temperature. By using this type of technique, carbon-containing austenite ( c -Fe + C) can be transformed into the metastable phase of carbon-containing martensite ( a 9 -Fe + C) which yields a very hard steel (Fig. 13 and 14). 63,64 The allotropic transformations that occur inside the iron– carbon alloy are related to the transition that we described for the iron case. In addition, in the case of theses alloys, two or more phases can coexist, for example ferrite can coexist with Fe 3 C (cementite), and are dependent on the total carbon content (Fig. 14). The transformations can happen following two different ways: (i) Slow transformation, which is accom- panied by diffusion of atoms and the redistribution of carbon between the phases, which leads to the formation of several distinct phases. The thermodynamically more stable phases are formed (slow heating/cooling). (ii) Rapid transformation, achieved by quick shear or thermal stress mechanisms, which implies a collective movement of atoms without redistribution of atoms between phases, which is called displacive transformation (supercooling). The metastable, kinetic phases can be obtained in this way. This is in essence the principle of the quenching/tempering (Fig. 15). For the Fe–C solid solution/alloy, it has been shown that allotropic transitions have a strong impact on the final physical properties of the material: several very important properties of steel depend directly on these phenomena: solubility difference of carbon in the different phases of iron, crystal shape, the morphology and composition of grain and the physical properties, for examples plasticity, toughness or hardness depend on it. 67 The ‘Devil’s’ metal: the tin (Sn). It has been shown that the iron–carbon allotropism allows to obtain a stronger material, the steel, with tunable physical properties. In this paragraph now, the ‘‘negative’’ effects of allotropism on the properties of a metal will be presented on behalf of tin. Tin has a historically interesting allotropism. It is known from the antiquity and was mainly used in bronze alloys (mix of Cu and Sn). It possesses several phases and undergoes allotropic transitions. The so- called tin pest is an allotropic transformation of white (BCT) b -Sn to grey (FCC) a -Sn. 68 The physical properties and the aspect of the white and grey tin are totally different. The white tin is ductile, metallic with a silvery shine, while grey tin is brittle, nonmetallic, darker, less smooth, and it tends to form a powder (Fig. 16). This transition from white to grey tin occurs below 13.2 u C. The kinetic of the transition is relatively slow but once nuclei of grey a -Sn are already formed and contaminate the white b -Sn, the kinetic of conversion becomes fast, as an auto- catalytic process (within several hours up to days for a total conversion depending on the temperature). Even bronze (an alloy of Cu and Sn) can undergo a similar process if prolonged storage at low temperature occurs. 69,71 This transition affects mainly the tin by increasing its unit cell volume and decreasing its electronic conductivity (Fig. 17). Some well-known stories relate the effect of this tin pest on the human activities: 72,73 In 1812, the tin buttons on the clothes of Napoleon’s soldiers were attacked by tin disease and crumbled in the harsh Russian winter of 1812. Napoleon was thus unprepared for the Russian winter ‘‘right down to the buttons’’. In 1850, Organ pipes made of tin in the old castle church at Reitz crumbled into gray powder during the winter, one of many such occurrences in cold northern European Cathedrals. Before the chemical explanation was available, this was sometimes attributed to the work of the devil. In 1912, Captain Robert Scott and his entire expedition to the South Pole perished. This tragedy has been attributed to an attack of tin disease. The kerosene for the return journey was stored in cans soldered with tin. The fuel escaped out of the cans resulting in the loss of all the lives to the Antarctic cold. Even today, tin is still widely used, mainly for solder purposes. In order to fix the allotropic transition problem, some lead, bismuth and other heavy metals are now added to form stable alloys. 74 From this example, we can conclude that an allotropic transition can cause important changes in properties like ductility or conductivity of materials, e.g. changing a conduct- ing metal into an insulator. The transition in itself is in principle reversible but the structural/mechanical damages on the material are not, and integrity is completely lost as in the case of tin. A video showing the decomposition of a tin block: After having discussed two cases of allotropy for metals, let us now turn towards binary compounds, for which also some examples are chosen. Zirconia-based materials are used as a simulant of gems and diamond, 75 as electroceramic, 76 and also for dental implants because of its biocompatibility and high fracture toughness. 77 Pure zirconia, ZrO 2 , however, undergoes a process of unit cell expansion during its manufacturing process (sintering/heat- ing). The ZrO 2 crystal system changes from a monoclinic crystal system at low temperature to a tetragonal one upon heating and finally ends in a cubic system at high temperature (Fig. 18). 79 This volume expansion causes internal stress during the cooling process leading to cracks, fractures, and thus inhomogeneity in the material, which is therefore prone to major failure. One solution found to prevent this was to add some yttria (yttrium oxide) and/or other oxides to the zirconia in order to fill the voids in the structure and stabilize the tetragonal metastable form or even the cubic form with a high content of dopant (electroceramics) (Fig. 19). By doing this, a polymorphic transformation can be turned into a useful process. Thus, when cracks form in the metastable tetragonal material via an external source, the induced local stress delivers energy to the system and will trigger the polymorphic transition from the tetragonal to the monoclinic system, causing a decrease of the unit cell volume and an overall contraction of the material in the concerned stress zone. Thus, the crack, ...

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... 5 Polymorphs and solvates often display significant differences in physicochemical properties, introducing an extra level of complexity to drug design and manufacturing. 6 A number of well-documented cases highlighting the impact of polymorphism on the pharmaceutical industry have made this an important contemporary research area. 7,8 In 1998, the capsule form of the HIV drug Ritonavir had to be temporarily removed from the market because the original Form I converted to a more stable and less soluble form, Form II, in the final formulation. ...
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Understanding and controlling polymorphism in molecular solids is a major unsolved problem in crystal engineering. While the ability to calculate accurate lattice energies with atomistic modelling provides valuable insight into the associated energy scales, existing methods cannot connect energy differences to the delicate balances of intra- and intermolecular forces that ultimately determine polymorph stability ordering. We report herein a protocol for applying Quantum Chemical Topology (QCT) to study the key intra- and intermolecular interactions in molecular solids, which we use to compare the three known polymorphs of succinic acid including the recently-discovered γ form. QCT provides a rigorous partitioning of the total energy into contributions associated with topological atoms, and a quantitative and chemically intuitive description of the intra- and intermolecular interactions. The newly-proposed Relative Energy Gradient (REG) method ranks atomistic energy terms (steric, electrostatic and exchange) by their importance in constructing the total energy profile for a chemical process. We find that the conformation of the succinic acid molecule is governed by a balance of large and opposing electrostatic interactions, while the H-bond dimerisation is governed by a combination of electrostatics and sterics. In the solids, an atomistic energy balance emerges that governs the contraction, towards the equilibrium geometry, of a molecular cluster representing the bulk crystal. The protocol we put forward is as general as the capabilities of the underlying quantum-mechanical model and it can provide novel perspectives on polymorphism in a wide range of chemical systems.
... Polymorphism of a new drug substance describes existence of crystalline forms which differ in their physical properties. In a regulatory environment, the term also covers solvation or hydration (pseudopolymorphs), as well as amorphous forms of a new moiety (1,20,21). The appropriate solid state of an API should be specified when there is evidence of potential differences in performance, bioavailability, or stability of the drug product. ...
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... 2021, 5, x FOR PEER REVIEW 2 of 10 change that has invited the application of the theory of martensite crystallography to transformation. Reinforcement mechanisms for zirconium-based materials as ZrO2toughened ceramics (ZTC) is possible thanks to this martensitic transformation [7,8]. ...
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... Both imply changes in intermolecular interactions, such as π-π interactions, van der Waals forces and hydrogen bonds. As changing the crystalline form of the solid results in a new unit cell with different interactions between the atoms, the physical and chemical properties of each polymorph will be different from each other [1][2][3][4][5]. ...
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... This rank order is consistent with IDR data and confirms the employment of IDR test to have a better understanding of relationships between dissolution rate and the solid crystalline form. Depending on the excipient and the type of processing (with or without co-milling), high pressure compaction might be able to generate destabilization, rearrangement and fragilization of IBU intermolecular interactions and trigger new IBU/excipientinteractions, leading to changes in the arrangements between the molecules, i.e. packing polymorphism where the molecules possess quasi the same conformation (Brog et al., 2013). ...
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