Crystal faces, hemihedral

The formation of hemihedral crystal faces in a chiral crystal as induced by solvent. 

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. 

FIGURE 9.1 Crystals of sodium ammonium tartrate, obtained under conditions yielding the hemihedral facets (darkened crystal faces) distinctive of the chiral crystalline forms. Also shown is the crystal morphology of racemic sodium ammonium tartrate. 

Compounds that are optically active often form crystals with hemihedral faces. 

III. Relationship between Macroscopic and Microscopic Structures as Illustrated by Quartz and its Nonsuperimposable Hemihedral Crystal Faces... 

In 1822, the British astronomer Sir John Herschel observed that there was a correlation between hemihedralism and optical rotation. He found that all quartz crystals having the odd faces inclined in one direction rotated the plane of polarized light in one direction, while the enantiomorphous crystals rotate the polarized light in the opposite direction. 

Some of the difficulties encountered in establishing the effect of solvent on crystal growth may be circumvented by focusing on polar crystals. This is because the difference in the rates of growth of opposite faces (hid) and (hkl) along a polar direction must arise primarily from differences in their solvent-surface interactions. Thus, one generally does not have to be concerned with faces other than the hemihedral ones in question. We illustrate below an approach to understanding solvent-surface interactions in the polar crystals of resorcinol (102). 

An equimolar mixture of two enantiomers is called a racemate. The separation of two enantiomers that constitute a racemate is called optical resolution or resolution. Their crystalline forms best characterize types of racemates. A racemic mixture is a crystal where two enantiomers are present in equal amounts. A conglomerate is a case where each enantiomer has its own crystalline form. Sometimes their crystals have so-called hemihedral faces, which differentiate left and right crystals. For over a hundred years, crystallization processes have been used for the separation and purification of isomers and optical resolution, both in the laboratory and on an industrial scale. 

In 1848, the French scientist Louis Pasteur prepared the sodium ammonium salt of racemic tartaric acid and allowed it to crystallize in large crystals which are visually distinctive from hemihedral forms.4 By discriminating the asymmetric faces of the crystals, he picked out the two kinds of crystals mechanically with a pair of tweezers and a loupe. Finally he obtained two piles of crystals, one of (+) and one of (-)-sodium ammonium tartrate. This was the first separation of optically active compounds from their racemate. 

In general, however, the occurence of spontaneous resolution of racemate is rare. Moreover cases in which the crystals of the enantiomers have visually distinct hemihedral face are extremely rare. 

G. B. Kauffman and I. Bernal, Alfred Werner s awareness of spontaneous resolutions and the meaning of hemihedral faces in optically active crystals , Structural Chem., 1993, 4 (2), 131-138. 

The first method of enantiomeric separation by direct crystallization is the mechanical technique use by Pasteur, where he separated the enan-tiomorphic crystals that were simultaneously formed while the residual mother liquor remained racemic. Enantiomer separation by this particular method can be extremely time consuming, and not possible to perform unless the crystals form with recognizable chiral features (such as well-defined hemihedral faces). Nevertheless, this procedure can be a useful means to obtain the first seed crystals required for a scale-up of a direct crystallization resolution process. When a particular system has been shown to be a conglomerate, and the crystals are not sufficiently distinct so as to be separated, polarimetry or circular dichroism spectroscopy can often be used to establish the chirality of the enantiomeric solids. 

Curie, J., and Curie, P. Developpement, par pression, de I electricite polaire dans les cristaux hemihedres a faces inclinees. [Development of polar electricity in hemihedral crystals with inclined faces.] Comptes Rendus, Acad. Sci. (Parts) 91, 294-295 (1880). 

FIGURE 14.14. (a) Hemihedral faces (shaded) of sodium ammonium tartrate compared (b) with the holohedral faces (shaded) of the racemate. The hemihedral faces in (a) were used by Peisteur to separate left-handed and right-handed crystals. 

When the absolute structure has been determined, the result must be correlated with some physical property of the crystal, otherwise the result has no use to the chemist. The obvious correlation is with the direction of rotation of the plane of plane-polarized light, that is, whether the compound or crystal is dextrorotatory or levorotatory. Another correlation can be made with crystal appearance this was shown for zinc blende with its matte and shiny faces, and for silica and sodium ammonium tartrate crystals for the disposition of their hemihedral faces. If such data are not available, it may be necessary to list physical properties of diastereomers made with chiral complexing agents. Then, whenever this same compound is encountered by a chemist, its absolute structure is well known. 

It crystallizes in anhydrous tables belonging to the monoclinic system, with hemihedral faces. The shape of... 

Even in the case of crystalline substances, where the differences between the various forms are greater, it is not always easy to discriminate between the /-mixture and the racemic compound. The occurrence of hemihedral faces was considered by Pasteur to be a sufficient criterion for an optically active substance. It has, however, been found that hemihedry in crystals, although a frequent accompaniment of optical activity, is by no means a necessary or constant expression of this property. Other rules, also, which were given, although in some cases reliable, were in other cases insufficient and all were in so far unsatisfactory that they lacked a theoretical basis. 

It sometimes happens in the formation of a derivative form that alternate faces are excessively developed, producing at length entire obliteration of the others, as shown in Fig. 12. Such crystals are said to be hemihedral. They can be developed only in a system having a principal axis. 

It was the observation of the hemihedral crystals of sodium ammonium tartrate tetrahydrate that enabled Pasteur (1822-1895) to make a decisive step forward in stereochemistry. The problem he encountered was the contamination of the potassium salt of tartaric acid with that of another acid (which Gay-Lussac (1778-1850) called the racemic acid) that made it unsuitable for commercial use. The two acids had the same chemical composition, and Biot showed that whereas tartaric acid and its salts could rotate the plane of polarized light, the racemic acid itself was inactive. In 1848, Pastern-found the solution to this problem.He noticed that crystals of tartaric acid, like its salts, have hemihedral faces, but that the racemic sodium ammonium tartrate exists as two distinct crystals in which the hemihedral faces are mirror images of each other. One of these crystalline forms is identical to the optically active tartrate. In solution, it rotates the plane of polarized light in a dextrorotatory manner, while the other form (a mirror image of the first) is levorotatory, that is in solution it rotates the plane of polarization towards the left (Figure 2.5). 

Each crystal system contains several classes that exhibit only a partial symmetry for instance, only one-half or one-quarter of the maximum number of faces permitted by the symmetry may have been developed. The holohedral class is that which has the maximum number of similar faces, i.e. possesses the highest degree of symmetry. In the hemihedral class only half this number of faces have been developed, and in the tetrahedral class only one-quarter have been developed. For example, the regular tetrahedron (4 faces) is the hemihedral form of the holohedral octahedron (8 faces) and the wedge-shaped sphenoid is the hemihedral form of the tetragonal bipyramid Figure 1.9). 

Pasteur was convinced that there must be some molecular difference between the two salts, and he made the problem the subject of his first major piece of research. He prepared several salts of tartaric acid and found that in all cases the crystals were asymmetric (Pasteur used the term dissymmetric), and displayed hemihedral faces. Pasteur was tempted to speculate that such asymmetric crystals were typical of optically active materials, and were the manifestation of asymmetry of the molecules. He then found that crystals of the optically inactive sodium ammonium paratartrate also displayed hemihedral faces, but on careful examination he saw that two types of crystal were present, one the mirror image of the other (Figure 10.13). He carefully sorted some of the crystals by hand. Those with right-handed hemihedry gave a solution which was dextrorotatory and identical with a solution of sodium ammonium tartrate. A solution of equal concentration of the crystals with left-handed hemihedry rotated polarised light to an equal extent in the opposite direction. A solution of equal concentrations of each crystalline form was optically inactive. Pasteur thereby demonstrated that paratartaric acid was... 

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