Crystal centrosymmetry

The use of chiral diamines in Schiff bases complexes allowed exploration of the powder SHG efficiency of crystalline materials based on this class of NLO chromophores, otherwise inactive because of the almost always crystal centrosymmetry. Relatively high powder SHG efficiency (up to 13 times that of urea) has been achieved in the case of the (l/ ,2/ )-(+)-l,2-diphenylethylenediamine Ni derivative [108]. Analogous Zn complexes using the chiral (R)-(-l-)-l-phenylethylamine have given appreciable powder SHG efficiencies [109]. This strategy has been extended using a series of chiral amino alcohols [110] and amino acids [111] to obtain noncentrosymmetric crystals based on Sn derivatives, with an attempt to correlate their SHG efficiencies with the molecular chirality. 

Table 8.3 Classification of the 32 crystallographic point groups with respect to crystal centrosymmetry and polarity (Uchino, 1994). 

The crystal structure of 2-bromo-l,4-phenylenediyl bis(tran5-4-n-prop-ylcyclohexanoate) was determined by Hartung and Winter [114]. The molecules exhibit pseudo-centrosymmetry in consequence of a special kind of disorder within the crystal lattice. The peculiarity of the crystal structure is the disorder of the molecules with respect to the position of their bromine atoms which occupy the 2- or 5-position of the phenyl ring in a statistical manner. 

For the diolefin crystals, including unsymmetrical diolefin crystals, each packing of the a- and j8-types is further classified into translation- and centrosymmetry-type packings. Of the photoproducts derived from unsymmetrical diolefins, the cyclobutane ring which has the same substituent on a ring is called a homo-adduct, and that which has different substituents is called a hetero-adduct. Corresponding to the molecular arrangements of these diolefin crystals, four types of photoproducts (a- and jS-types, and homo- and hetero-adducts) are expected to be formed based on the topochemical principle, as shown in Scheme 2. 

In the crystal of 7 OEt, two molecules form a molecular pair as is the case in the crystal of 7 OMe. Considering the intermolecular distances between the ethylenic double bonds (3.714 and 3.833 A within the pair, and 4.734 and 4.797 A between the pairs), each molecule can react only with its partner in the molecular pair and not with any molecule of another pair. Since paired molecules are related by centrosymmetry, two pairs of facing ethylenic double bonds should be equal in photoreactivity, affording two... 

In the case of MAP, the concept of chirality was used so as to prevent centrosymmetry a chiral molecule cannot be superimposed on its image by a mirror or center of symmetry so that a crystal made only of left or right-handed molecules can accomodate neither of these symmetry elements. This use of the chirality concept ensures exclusion of a centrosymmetric structure. However as we shall see in the following, the departure of the actual structure from centrosymmetry may be only weak, resulting in limited nonlinear efficiencies. A prerequisite to the introduction of a chiral substituent in a molecule is that its location should avoid interfering with the charge-transfer process. 

The Laue symmetry of the diffraction pattern is now reduced to the symmetry of the non-centrosymmetric point group to which the crystal belongs (see Table 2 a listing of symmetry-equivalent reflections in the non-centrosymmetric point groups is available26). Under these circumstances, it is possible to determine different manifestations of non-centrosymmetry in a crystal, such as ... 

Fig. 146. Anomalous scattering in a non-centrosymmetrie crystal. Effect on -f and — reflections. Left representation of amplitudes and phases of waves. Right corresponding vector diagrams (scale of amplitudes doubled), a and b 002 and 002 reflections of structure of Fig. 145, when scattering is normal for both atoms, c and d the same reflections when scattering is anomalous for atom giving wave E.

The anomalous phase-displacement method detects essentially a polar axis this means that it can detect lack of centrosymmetry in general, for all non-centrosymmetric crystals have polar directions. For instance, although crystal class 4 is not usually referred to as a polar class (for its fourfold axis is not polar), nevertheless, except for the fourfold axis and all directions normal to it, all other directions are polar (see International Tables, 1952, p. 43), and the corresponding regions of the reciprocal lattice will therefore show the intensity differences which have been described. 

The only positively identified magnetic dipole transition at room temperature so far is the 7Fo Di transition in Eu3+ at 5250 A. The abscence of centrosymmetry in crystal allows the changes in J and L upto seven units due to admixture of states (through sixth order terms) giving rise to weak electric dipole transition. The weak intensities of the intra f—f transition can be accounted for by the Laporte selection rule. 

The EO effect is a second-order nonlinear optical (NLO) effect. Only non-centrosymmetrical materials exhibit second-order NLO effects. This non-centrosymmetry is a condition, both at the macroscopic level of the bulk arrangement of the material and at the microscopic level of the individual molecule. All electro-optic modulators that are presently used by telecom operators are ferro-electric inorganic crystals. The optical nonlinearity in these materials is to a large fraction caused by the nuclear displacement in the applied electric field, and to a smaller fraction by the movement of the electrons. This limits the bandwidth of the modulator. The nonlinear response of organic materials is purely electronic and, therefore, inherently faster. 

The oxygen atom was found to be disordered at the crystallographic inversion center and therefore refined with half occupation factors on each side of the B-B bond (model A, Space Group C2/c, No. 15). This disorder is connected with the centrosymmetry in the crystal lattice, which is also strictly valid for the C(SiMe3)3 substituents. In spite of the disorder of the oxygen atom in the crystal, the bond length of the B-B bond could be determined with satisfactory precision [1.601 (7)... 

Since the first nonlinear susceptibility is a third-rank tensor, it is only non-zero in non-centrosymmetric media. To break the centrosymmetry of the macroscopic media, poling techniques using optical and electric fields have been developed, or use was made of the inherent polar ordering in Langmuir-Blodgett films and crystals with non-centrosymmetric point groups. 

FIGURE 8.5. (a) The probability P E) of iJ having certain values depends on whether the structure is centrosymmetric (solid line) or noncentrosymmetric (broken line). Thus, if values are known, a plot of the number with different ranges of I E I will indicate the centrosymmetry (or lack of it) in the crystal structure, (b) The cumulative distribution curves for centrosymmetric and noncentrosymmetric crystals N Z) is the fraction of Bragg reflections with intensities (or E p values) less than or equal to Z times the mean intensity. 

The requirement of non-centrosymmetry is not restricted to the molecular level, but also applies to the macroscopic nonlinear susceptibility, which means that the NLO molecules have to be organized in a non-centrosymmetric alignment. The first measurements of the macroscopic second-order susceptibility, have been performed on crystals without centrosymmetry [5]. However, many organic molecules crystallize in a centrosymmetric way. Other condensed oriented phases such as Langmuir-Blodgett (LB) films and poled polymers therefore seem to be the most promising bulk systems for NLO applications. 

XH.2O 51), equally good agreement between the calculated and observed structure amplitudes was obtained in all three space groups. It is not therefore possible to decide whether the distribution of the oxygen atoms, and thus the whole crystal structure, is centrosymmetric or non-centrosymmetric. It can be concluded, however, that if the latter is the case, the deviation from centrosymmetry has to be small. 

Substituting this result back into the expansion for the total energy, it is noted that for crystals with centrosymmetry, this term will vanish because every term involving XRj y will have a compensating partner —XR y. 

Raman and infrared measurements see fundamental (i.e., single phonon excitations) vibrational modes only at qf = 0. In crystals having centrosymmetrie structures, a given mode is not both Raman and infrared active. 

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