Crystals faces polarities

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. 

In the orthorhombic point group mm2 there is an ambiguity in the sense of the polar axis c. Conventional X-ray diffraction does not allow one to differentiate, with respect to a chosen coordinate system, between the mm2 structures of Schemes 15a and b (these two structures are, in fact, related by a rotation of 180° about the a or c axis) and therefore to fix the orientation and chirality of the enantiomers with respect to the crystal faces. Nevertheless, by determining which polar end of a given crystal (e.g., face hkl or hkl) is affected by an appropriate additive, it is possible to fix the absolute sense of the polar c axis and so the absolute structure with respect to this axis. Subsequently, the absolute configuration of a chiral resolved additive may be assigned depending on which faces of the enantiotopic pair [e.g., (hkl) and (hkl) or (hkl) and (hkl)] are affected. 

Fig.3i. Sdmnatic representation of the angular distribution ejected atoms from the (001) crystal face of a face-centered cubic metal The polar angle is 0 and the azimuthal angle = 4S° corresponds to the close-packed row of surface atoms. (From Rrf. 1.)...

When ionic or polar forces play an important part in binding atoms or molecules together in a crystal, matters are more complex, since the rates of growth of crystal faces appear to be influenced by the distribution of electric charges as well as the reticular density (Kossel, 1927). The subject has not so far received much attention, and it is unwise to attempt to formulate generalizations. 

Srebrodolski and Yushkin tested 14 brimstone crystals for hardness anisotropy and plotted from the data (Table 7.1) hardness rosettes for four crystal faces (Fig. 7.3). Apart from finding the normal anisotropy of 2nd order from the hardness ratio determined on two faces, they also determined the polar anisotropy of 1st order on each of the faces under test. 

There are several methods of measuring the thickness of thin oxide films. Interference colors may be used as an approximate measure in the range of 200 to 2500 A. Oxide films from less than 10 to about 1000 A. in thickness can be measured by the change in the ellipticity of reflected polarized light, and with this method it was found that the rates of oxidation varied greatly with the crystal face exposed at the surface (25). For example, after 50 min. at 178°, the thickness of oxide on the (100) face was 1000 A., while that on the (311) face was about 60 A. Rhodin (26) has also studied the oxidation of copper crystals with a microbalance. 

Fig. 4.2. Diagrammatic representation of the experimental crystal and beam geometries for p-polarized radiation incident upon the (111) crystal face as viewed (a) from the side and (b) from the top including the second atomic plane ( ). The crystal coordinates are labeled x, y, z with the Z direction along the [211] crystal direction. The beam coordinates are labeled s, k, z. From Ref. 122.

The effect of active spots on the polarization of adsorbed molecules by a dielectric absorbent (Sec. V,6) is very great. The nature of the active spots is the same as of those which affect the attraction of ions or dipoles. Edges or corners of crystals, other crystallographic faces, and especially those places where the growth of individual crystal faces stopped, as well as lattice disturbances in the surface, will be active. 

V-UV Application Specular Reflection by Crystal Faces. If one focuses the incoming beam 70 onto a single crystal face, the specular UV-vis reflectivity (and its polarization) can be measured. The crystal is mounted on a goniometer head the orientation of the crystal axes relative to the instrumental axes must be predetermined separately on an X-ray diffractometer. 

Figure 14 Polarized reflectance of MTPP(TCNQ)2 for different crystal faces. The electric vector is parallel to the TCNQ stacks direction in the case of faces rf(100) and /(Oil) (a) and is parallel to the TCNQ long axis for /(010) (b). (From Ref. 69.)...

Utilized selective anisotropic solvent adsorption on specific crystal faces to favour the growth of morphologically polar crystals. Some additional reports of the study of crystal modification and nonlinear optical activity include those on anhydrous and hydrated sodium / -nitrophenolate (Brahadeeswaran et al. 1999), derivatives of 2-benzylideneindan-l,3-dione (Matsushima et al. 1992), straight-chain carbamyl compounds (Francis and Tiers 1992), benzophenone derivatives (Terao et al. 1990), a 1,3-dithiole derivative (Nakatsu et al. 1990), o -[(4 -methoxyphenyl)methylene]-4-nitro-benzene-acetonitrile (Oliver et al. 1990) and so-called lambda shaped molecules (Yamamoto et al. 1992). Hall et al. (1988) followed the thermal conversion of the centrosymmetric P2 /c) form of 2,3-dichloroquinazirin to the non-centrosymmetric Pc form by monitoring the development of an SHG signal. Consistent with the earlier observation, the centrosymmetric form was obtained under equilibrium conditions, while the non-centrosymmetric one could be obtained under more kinetic conditions. 

Fig. 6.23 Normal incidence polarized reflection spectra of the two forms molecule 6-XVII (R = Et, R = OH). For each crystal modiflcation there are two spectra measured with the light polarized along each of the two directions (the so-called principal directions), as indicated in the upper right hand corner, which also shows the projection of the molecule(s) onto the crystal face studied, (a) Triclinic polymorph, (100) face (b) monoclinic polymorph, (100) face. (From Tristani-Kendra and Eckhardt 1984, with permission.)...

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