Centrosymmetric space group

An irreversible extinction of the SHG signal at 150-200°C is observed for a number of other fluoride and oxyfluoride compounds of tantalum and niobium that crystallize in centrosymmetric space groups. This phenomenon is especially typical for the compounds prepared by precipitation from solutions [206]. The appearance of the weak SHG signal for such compounds is related to imperfections in their crystal structure and the creation of dipoles. Nevertheless, appropriate thermal treatment improves the structure and leads to the disappearance of dipoles and to the irreversible disappearance of the corresponding SHG signal. 

Fig. 100. Irreversible extinction of SHG signal during heating of compounds that crystallize in centrosymmetric space groups. SHG signal is normalized by signal of alpha-quartz (a-SiO/f.

In contrast to sulfurous acid, H2S03, which is not known as pure substance, the respective selenium compound can be obtained in crystalline form. H2Se03 crystallizes with the non-centrosymmetric space group P2 2,2] and contains pyramidal H2Se03 molecules.54 Within the molecules the bond lengths Se-O and SeOH differ by about 10 pm and the molecules are connected to puckered layers by strong hydrogen bonds. 

In centrosymmetric space groups all the phases are centric with phases... 

Karle, J. Hauptman, H.A. (1956). A theory for the four types of non-centrosymmetric space groups 1P222, 2P22, 3Pi2, 3P22- Acta Cryst. 9, 635-651. 

In a second step d5mamical effects must be taken into account. For dynamical refinement we used a multi-slice least squares (MSLS) procedure [21], where the centre of laue circle, crystal thickness and scaling factor were refined for each zone separately with fixed atom positions. In the case of non-centrosymmetric space groups the enantiomorph used for refinement can be chosen for each zone, additionally. After the basic parameters have been derived satisfactorily, the atom positions can be refined. The R-values (see Eq. 2) refined by MSLS usually dropped down to 6-13%. 

The compound N,N -diphenylguanidinium 5-nitrouracilate dihydrate cristallizes in a centrosymmetric space group with one anion, one cation and two water molecules per asymmetric unit cell (Figure. 3). The inversion centre that relates the ions in the unit cell obliterates the non-linear optical response of this compound. Other 5-nitrouracil compoimds permit efficient blue-light generation from a pulsed laser source [14]. 

In the 25 analyzed dpg/dpg+ eompounds 10 crystallize in non-centrosymmetric space groups (5 are chiral). In HOFDAH the chiralization is forced by introducing a chiral negative ion in the structure (L-tartrate, Figure. 5). In other cases, chiralization is spontaneous and it can be achieved either by... 

However, FriedeFs law no longer holds if a compound containing an anomalous scatterer, besides other elements, crystallizes in a non-centrosymmetric space group then the following inequalities between Friedel pairs apply ... 

As discussed in detail in Ref. 36, for use in optoelectronics only systems crystallizing in non-centrosymmetric crystal lattices are of interest if the use of expensive enantiomers of chiral molecules is to be avoided. This considerably limits the available crystal lattices since most organic achiral molecules crystallize into centrosymmetric space groups. An interesting example of enantioselective inclusion complexation was reported by Gdaniec and coworkers [37]. 

The prototypical organic material with high P (all values of P quoted here are for 1.06 1 light unless noted) is p-nitroaniline (PNA). In electrostatic units (esu), P for PNA is 34.5 x 10 30 esu. (37) It has a dipole moment of 6.8 D. Extension of the chromophore by insertion of a single double bond to produce 4-amino-4 -nitrostilbene increases P dramatically 248 x 10"30 esu. (38) However, both crystalline materials are centrosymmetric, and so no SHG is possible. Most achiral molecules crystallize in centrosymmetric space groups, but some do not. Several materials have been discovered during the last few years which have combinations of hyperpolarizability, crystal growth and habit, and linear spectral properties which make them candiates for useful NLO materials. As will be obvious from the comparison, considerable compromise must be made to yield a practical material. 

An X-ray crystallographic analysis of DAD single crystals shows a triclinic system with the non-centrosymmetric space group P1 and that the direction of polarization of DAD in the molecular crystal is perfectly aligned in one dimension. 

Molecular and crystal structure of DAD are shown in Figure 3 and 4. DAD crystallize in a triclinic system with the non-centrosymmetric space group P1. The direction of polarization of DAD in the molecular crystal is perfectly aligned in one dimension as shown in Figure 4. X-ray crystal analysis of DAD also shows the existence of two hydrogen bonds between adjacent molecules, 0 1--H... 

In regard to the observation of SHG activity, all crystals without a centrosymmetric space group have the possibility of SHG, whereas the ability is dependent on the packing and the electronic condition of the molecules. Then, the crystals with, Pna21 and Cc, which are achiral, in Table 2 also show SHG. We can not perfectly select out the chiral crystals from these methods however, we can easily increase the probability to find the chiral crystals without X-ray structural analysis. 

All cations are located within the equatorial plane of the 02--octahedra in the paraelectric high-temperature phase [15], In this case the crystal belongs to the centrosymmetric space group P4/mbm. In the low-temperature phase the metal atoms are displaced out of this plane. As a result the crystal structure is transferred into the polar space group P4bm and the polar... 

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