Crystal external shapes

Crystals composed of the R and S enantiomers of the same racemic mixture must be related by mirror symmetry in terms of both their internal structure and external shape. Enantiomorphous crystals may be sorted visually only if the crystals develop recognizable hemihedral faces. [Opposite (hid) and (hkl) crystal faces are hemihedral if their surface structures are not related to each other by symmetry other than translation, in which case the crystal structure is polar along a vector joining the two faces. Under such circumstances the hemihedral (hkl) and (hkl) faces may not be morphologically equivalent.] It is well known that Pasteur s discovery of enantiomorphism through die asymmetric shape of die crystals of racemic sodium ammonium tartrate was due in part to a confluence of favorable circumstances. In the cold climate of Paris, Pasteur obtained crystals in the form of conglomerates. These crystals were large and exhibited easily seen hemihedral faces. In contrast, at temperatures above 27°C sodium ammonium tartrate forms a racemic compound. 

All the crystal forces that we treat in this section can be considered in terms of the recognition between a given, reference molecule and the cavity it is to occupy in the crystal. In chiral systems the cavity is clearly of different shape in the d and / crystals, and this generally results in differential incorporation of R and S molecules. However, in molecules containing the sec-butyl group, discrimination is often ineffective. This is because the two enantiomers can assume different conformations with very similar external shapes, and they can then interchangeably enter the same cavity in the crystal. This effect was recognized some time ago (55), and recently its consequences have been studied in detail (56). In the case where two enantiomers may readily replace one another in the crystal, it follows that there is a tendency to conformational disorder (see biphenyl, above), and in many cases, the resolved enantiomers and the racemates are isostructural. 

In the second class of systems the reaction is such that it involves little or no change of the molecular geometry in the vicinity of the reacting sites, nor of the external shape of the crystal. The concept of the reaction cavity is useful in this context (184). This cavity is the space in the crystal containing the reactive molecule(s), and its surface defines the area of contact between this molecule and its immediate surroundings. Only if the shape of this cavity is little altered as reaction proceeds will the activation energy for the process be reasonably small and the rate of reaction nonzero. 

Observations of crystals between crossed polarizers are particularly valuable in the case of some of those twin combinations which in their external shape simulate a single crystal having a symmetry higher than that of one of the individuals. The observation of different extinction directions in different regions demonstrates at once that the crystal is... 

CRYSTAL HABIT. The external shape of a crystal, which depends on the relative development of the different faces, as well as upon the interfacial angles characteristic of ihe crystal. 

Crystal growth is governed by both internal and external factors. Internal factors such as the three-dimensional (3-D) crystal structure and crystal defects will determine the nature and strength of the intermole-cular interactions between the crystal surface and the solution whereas external factors such as temperature, supersaturation, solvent, and the presence of impurities will affect the type of interactions at the solid-liquid interface. The external shape or morphology of a crystal is a consequence of the relative growth rates of the... 

The external shape of the crystal can be described in terms of its habit, which is affected by the rate of crystallisation and by the presence of impurities, particularly surfactants. The habit of a crystal is of pharmaceutical importance, since it affects the compression characteristics and flow properties of the dmg during tableting and also the ease with which the suspensions of insoluble dmgs will pass through syringe needles. 

In 1962 Mackay introduced some amazing structures built with hard spheres as possible models for atomic clusters. Their external shape was that of a regular IC, and their size could be extended from the atomic scale to infinity. Despite the perfect fivefold symmetry of these structures, their internal local order was nearly that of a crystal. 

Without a doubt, crystals such as diamonds, emeralds and rubies, whose beauty has been exposed by jewelry-makers for centuries, are enjoyable for everybody through their perfect shapes and astonishing range of colors. Far fewer people take pleasure in the internal harmony - atomic structure -which defines shape and other properties of crystals but remains invisible to the naked eye. Ordered atomic structures are present in a variety of common materials, e.g. metals, sand, rocks or ice, in addition to the easily recognizable precious stones. The former usually consist of many tiny crystals and therefore, are called polycrystals, for example metals and ice, or powders, such as sand and snow. Besides external shapes and internal structures, the beauty of crystals can be appreciated from an infinite number of distinct diffraction patterns they form upon interaction with certain types of waves, e.g. x-rays. Similarly, the beauty of the sea is largely defined by a continuously changing but distinctive patterns formed by waves on the water s surface. 

Perhaps the most obvious connection of polyhedra with practical chemistry and crystallography is that crystals normally grow as convex polyhedra. The shapes of single crystals are subject to certain restrictions arising from the fact that only a limited number of types of axial symmetry are permissible in crystals, as explained in Chapter 2. We shall not be concerned here with the external shapes of crystals but with polyhedra which are of interest in relation to their internal structures and more generally to the structures of molecules and complex ions. 

The regular external shape of a crystal is the result of regular internal arrangements of atoms, molecules, or ions. Crystals of the ionic solid sodium chloride, NaCl, from a kitchen saltshaker have the same shape as the large crystal shown here. 

Nevertheless, the shape of crystals is really a secondary characteristic, since it depends on, and is a consequence of, the interior arrangement of atoms. Sometimes the external shape of a crystal is rather obviously related to its smallest building block, the unit cell, as in the httle cubical grains of ordinary table salt (NaCl has a cubic lattice) or the six-sided prisms of natural quartz crystals (hexagonal lattice). In many other cases, however, the crystal and its unit cell have quite different shapes gold, for example, has a cubic lattice, but natural gold crystals are octahedral in form, i.e., bounded by eight planes of the form 111. ... 

By making a comparison of the rates of dehydration of sec-butanol over Linde lOX and 5A zeolites at relatively high temperature and low conversion, Weisz (7) also found that the rate constant per unit volume of 5A was between two and three orders of magnitude smaller than that of lOX. These relative magnitudes were consistent with the ratio of available surface areas (0.6-3.5 m /gm for the external area of l-5/i sized crystals of shape-selective 5A and 500-700 m /gm for lOX, where the internal surface was accessible to the sorbate. 

However, a positive proof for hula-twist could not be obtained by X-ray diffraction, as the product phase became amorphous. The external shape of the crystal did not change at the microscopic level, but AFM indicated some loss of acetone on (100) by efflorescence, forming a protective cover which can be correlated with the crystal packing. Further molecular migrations on other faces were not detected with the molecular sensitivity of AFM [6], The crystal stayed clear transparent, but a topotactic conversion is excluded if a crystalline phase becomes an amorphous product phase. 

The external shape of a crystal is termed the habit, and a variety of shapes have been defined in Table 3.5. The habit of a crystal arises due to the way in which the solutes orientate themselves when growing therefore, the general shape of a crystal is the result of the way individual faces grow. During growth, the fastest growing faces are usually eliminated. 

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