Centrosymmetric crystal structure

Figure 6. Successive changes of the phase value of a Fourier wave with index h = 2 moves the region with high potential (black areas) from the origin at X = 0 in the top map towards X = 1/4 in the map at the bottom. This shows that the value of the phase (f) determines the positions with high potential within the unit cell, whereas the amplitude A just affects the intensity. Note, that the maps with a phase shift of (j) = 0° and (f) = 180° have a centre of symmetry at the origin of the unit cell, whereas the other maps have no symmetry centre. From this we can draw another important conclusion if we put the origin of the unit cell on a centre of symmetry we have only two choices for the phase value, = 0° or (j)= 180°. As we will see later, this feature is of great importance for solving centrosymmetric crystal structures.

Several methods have been known so far to prevent centrosymmetric crystal structures. 

In this paper, I propose a promising new electron acceptor of cyclobutenedione for nonlinear optical materials to prevent centrosymmetric crystal structures by the introduction of chirality and hydrogen bonding property into the acceptor itself. Compared with electron donative groups, electron acceptor is not yet well studied for nonlinear optical materials. The most commonly used electron acceptor is nitro (NO2) group. Therefore, we evaluated the possibility of cyclobutenedione as a new electron acceptor for nonlinear optical materials. One of the most simple cyclobutenediones is squaric acid. Squaric acid is known to be soluble in water and show very strong acidityQ2), as squarylium anion formed in water has a stable 2n delocalized electron system as shown below. 

Even in such molecules with large ground state dipole moment, we observed the production of non-centrosymmetric crystal structures exhibiting SHG by introduction of asymmetric amino acid derivatives into the cyclobutenedione. (-)4-(4,-dimethylaminophenyl)-3-(2l-hydroxypropylamino) cyclobutene-1,2-dione (DAD) (3), (+)4-(4 -di-... 

The basis functions, in both cases, are complex. This is a known complicating factor in the analysis of non-centrosymmetric crystal structures. In computational chemistry the problem is circumvented by using only real basis functions. The definition and limitation of such functions are discussed in section 2.6.3, but there is a more important mathematical factor that militates against this procedure ... 

Threefold donor-acceptor-substituted benzene derivatives like [109] (Ledoux et al., 1990) or [110] (Verbiest et al., 1994 Wolff et al., 1996b Wortmann et al., 1997 Wolff and Wortmann, 1998) show better performance for [109], only powder data and computational results are available. Both are of the hexasubstituted type, but strong intra- and inter-molecular hydrogen bonds provide for planarity. The discrepancy (Bredas et al., 1992) between the observation of a moderate powder SHG efficiency of [109] and the published (Cady and Larson, 1965) centrosymmetric crystal structure (PT) has been resolved. The powder consists of two polymorphs, with the second one adopting the close to optimal space group P3i (Voigt-Martin et al., 1996,1997). 

Most TL studies are centered on enolate compounds, in particular, rare-earth / -dike-tonates. Present evidence points to morpholinium tetrakis(dibenzoyhnethanato)europate (in) and triethylammonium tetrakis(dibenzoyhnethanato)europate(in) as the first and second most efficient triboluminescent compounds, respectively. In these cases the coexistence of disorder in the chelating ring and the non-centrosymmetric crystal structures may contribute to major charge separation upon cleavage and, consequently, to higher luminescence intensity. 

The principal structural requirement for second order nonlinear effects in assemblies of molecules is the lack of a centre of symmetry, and considerable efforts have been expended in trying to induce potentially useful molecular entities to crystallize in non-centrosymmetric or polar crystals (Curtin and Paul 1981 Liter et al. 1991). As demonstrated below, this is a necessary, but not sufficient condition for obtaining nonlinear effects. True to form, the variety of crystallization experiments has led to a number of polymorphic structures, and to information about the relationship between the properties of these materials and their structures, as well as useful guidelines for attempting to obtain the desired non-centrosymmetric crystal structures. 

New molecular design approach for non-centrosymmetric crystal structures - A-shaped molecules for frequency doubling. Appl Phys. Lett., 60, 935-7. [213]... 

The centrosymmetric crystal structure of [Me2NC2H4N(Me)MgMe]2 (34) has some analogy with the cryptand cleavage product 21, but has... 

If two centrosymmetric crystal structures are isomorphous, the arrangement of atoms is the same in both and only one atom (sometimes more than one) has a different atomic number in the two structures. The differences in the intensities for the Bragg reflections, therefore, result only from the differences in the scattering powers of the two atoms, M, and M2, that can replace each other. The contribution to the structure factors made by the rest of the structure, F/j, is the same for both crystal structures. If the structure amplitudes are F and F2 for a given Bragg reflection in the two structures, then the calculated difference is illustrated by the use of vectors as ... 

Centrosymmetric crystal structure A crystal structure whose space group, and therefore arrangement of atoms, contains a center of symmetry. When the origin of the unit cell is at a center of symmetry, the relative phase angle for each Bragg reflection is either 0° or 180° in the absence of X-ray anomalous dispersion. 

Han, F-S., and Chang, S-L. Determination of a centrosymmetric crystal structure using experimentally determined phases with the direct method. Acta Crg-t A39, 98-101 (1983). 

Figure 9-5. A fragment of a centrosymmetric crystal structure with the molecules (represented as arrows parallel to their molecular dipoles) NH+—N hydrogen-bonded into antiparallel chains along [y] (the anions are neglected for clarity). The ideal crystal structure with antiparallel molecules in neighbouring chains is marked in green (full arrowheads). Due to defects in the fourth and seventh chains, in which 5 and 6 molecules have reversed orientation, respectively, two polar nanoregions are formed. The red and blue colours and open arrowheads mark these nanoregions, the polarisation of which is indicated with large grey arrows...

Figure 1. Destruction method of centrosymmetric crystal structure.

Urea is usually used as a standard material. Although the S.H.G. intensity ratio of dimethyl-CD and p-NA is below 0.1 and 0 respectively, the dimethyl -CD complex with p-NA has a ratio of i l compared to urea. This indicates that the formation of dimethyl -CD complex destroys the centrosymmetric crystal structure. 

A new method of destroying the centrosymmetric crystal structure which forbids second harmonic generation was demonstrated based on formation of inclusion complexes. 

However, these most commonly used Ewald transformation formulas are correct for centrosymmetric crystal structures but give results [98 101] that... 

Most theoretical discussions for molecules concentrate on calculations of second-order nonlinear optical properties. These results can be used equally well for the design of either molecules or molecular fragments. The latter are intended for inclusion in polymers as either a solid solution or side-chains. These are discussed in detail in section 4.3, together with systems in which a crystalline phase is dispersed in a polymer matrix. In molecularly dispersed systems the incorporation and orientation of an active species in a polymer obviates the need for a non-centrosymmetric crystal structure but does require the imposition of a polar state on the polymer (e.g. with an applied electric field). Thus molecular species that as crystals are not useful as second-order nlo materials (because they adopt a centrosymmetric structure) may be applicable in a polymeric system. Though it has received less attention in the past, considerable effort has recently been devoted to theoretical studies of... 

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