Comparaciones Del Modelo Con Trabajos Anteriores

The mechanical properties of an organic crystal can determine many aspects of their commercial production [42], Experimentally, it is very difficult to measure such data because of the relative softness of intermolecular interactions. Therefore there is a need of a computational approach to predict elastic constants of these crystals. Elastic properties are mainly determined by the second derivative of the potential [41]. Hence, the choice of the intermolecular potential is important for these types of calculations. It is possible to calculate the mechanical properties in the latest version of DMAREL [226]. This would be particularly useful, not just for judging the model potential, but it could eliminate weaker structures found in the crystal structure search. The mechanical properties can provide information not just for the single crystal, but also for crystalline aggregates. The latter is especially important for the pharmaceutical industry, where depending on the mechanical properties; the crystallites can undergo plastic deformation, brittle fracture, or elastic deformation on compression to form tablets. An example where the mechanical properties are important is the production of paracetamol [227-229]. The most stable form of paracetamol (Form 1) is the crystal form currently used in production. However, this form has poor tabletting properties due to its rigid elastic structure. Form 2 can be tabletted directly, but it is not easy to produce. Beyer et al. have performed studies on the prediction, morphology and mechanical properties of the polymorphs of paracetamol [43]. In this case, some low energy hypothetical structures, although formally mechanically stable, were only just so, and so seemed unlikely to be observed.

9.6.2 Simulated powder diffraction pattern

Different polymorphs have different crystal symmetry and/or unit cell parameters, which directly influence the reflection characteristics of powders. Therefore X-ray powder diffraction can be used to identify different polymorphs or a mixture of polymorphs in a reproducible and reliable way. Powder diffraction patterns are much easier to obtain than single crystal X-ray diffraction patterns of a metastable polymorph. In advantageous cases, it may be possible to characterise a crystal structure from the powder pattern [36]. However, predicted powder patterns may be useful in characterising a solid when an experimental powder pattern cannot be indexed. Hence, to help identify possible polymorphs, powder diffraction patterns could be calculated using Cerius^ software [230].

9.6.3 Morphology

The shape of a crystal is determined by the relative rates of depositions of materials on various crystal faces [231]. In general, the slower a face of the crystal grows the larger its size on the crystal. A face's growth rate is directly proportional to the interaction energy between the molecules in a growth layer and those in the underlying bulk of the crystal (the attachment energy of the face) [45]. This New Models for Intermolecular Repulsion and their Application to van der W aals Helen H.Y. Tsui

9 Crystal Structures of Chlorothalonil_________________________________________________ 165 information could provide evidence on whether certain types of crystal structures are easy to grow, and we can eliminate the structures that has a poor growth rate as less likely to exist experimentally. It is possible to perform morphology calculations by calculating the attachment energies for the predicted crystal structure. This method has been quite successful for the predictions of paracetamol [43], where the morphology calculations have eliminated some of the hypothetical structures that are unlikely to be observed. Therefore, this reduced the number of predicted structures to undergo further observations and investigations. The models we used for calculating the morphology in Cerius^ software [232] are as follow.

The morphological importance of a face (its relative area on the crystal) is proportional to the inter-planar spacing of its corresponding lattice plane. (Proposed by Bravais [233] in 1866 and validated by extensive observations by Friedel [234] in 1907). Donnay and Harker [44] (1937) extended this approach to take into account reductions in inter-planar spacing due to space group symmetry, and hence, it is often termed the BFDH model.

Hartman and Perdok's method [45] for calculating the relative growth rates of faces, the attachment energy model, is very widely applied. This technique determines relative growth rates from the magnitude of the intermolecular interactions with crystals. For organics, these interactions are the relatively weak, non-covalent cohesive forces between molecules, including highly directional hydrogen bonds. The total intermolecular energy per mol in a crystal is termed the lattice energy E^ , , which is approximately equal to the negative enthalpy of sublimation. Hartman-Perdok theory partitions the lattice energy into two contributions: the interaction within a slice of thickness and the interaction between the molecules in the slice and molecules in the rest of the crystal. The energy per mol within a slice E^, is effectively the energy of formation of a slice from the gas phase. The energy per molecule between the slice and the bulk is effectively twice the energy per molecule of attaching the slice to the underlying crystal face (hkl). The energy between slice and bulk is termed the attachment energy E^„ . For any face (hkl), the sum of the slice energy and the attachment energy is a constant E,^„.

(9.11) Hartman and Perdok suggested a relationship between attachment energy and the rate at which material attaches to a face. Therefore the growth rate of a face must increase with increasing magnitude of the attachment energy.

(9.12) where Rhki is the rate of growth of face (hkl) in the direction of its normal. The relative rates of growth can be used in conjunction with a Wulff construction [46] to draw the shape. The model implies that faces with larger grow faster and are less prominent on a crystal. Since energy is in general a function of intermolecular distance, it is consistent with the Law of Bravais: faces with small inter- planar distances have large This is illustrated by observation that any easy to cleave faces dominate the morphology. Faces that are easiest to cleave have strong cohesive forces between

New Mcxjels for Intermolecular Repulsion and their Application to van der W aals Helen H.Y. Tsui

9 Crystal Structures of Chlorothalonil_________________________________________________ 166