Crystals symmetry analysis

For crystal symmetry analysis, inorganics can be divided into two compounds of ternary and higher oxides and compounds containing halides and noble gases are classed as inorganics, and the remainder are classed as intermetallics. One of Laves principles states that structures aim at the highest symmetry. Figure 2 shows the distribution of compounds by crystal system. ... 

The ability to record diffraction intensities over a range of incident-beam angles makes CBED readily accessible for quantitative comparison with simulations. In the past 15 years, CBED has evolved from a tool primarily for crystal symmetry analysis to the most accurate technique... 

However, the crystal, as an infinite network, can not be reduced to the imit cell. Moreover, the crystal symmetries analysis was previously considered only by the symmetry elements and operations associated to the reflection plan, to the rotation axis and to the inversion center. 

The most characteristic feature of any crystal is its symmetry. It not only serves to describe important aspects of a structure, but is also related to essential properties of a solid. For example, quartz crystals could not exhibit the piezoelectric effect if quartz did not have the appropriate symmetry this effect is the basis for the application of quartz in watches and electronic devices. Knowledge of the crystal symmetry is also of fundamental importance in crystal stmcture analysis. 

An asymmetric photosynthesis may be performed inside a crystal of -cinnamide grown in the presence of E-cinnamic acid and considered in terms of the analysis presented before on the reduction of crystal symmetry (Section IV-J). We envisage the reaction as follows The amide molecules are interlinked by NH O hydrogen bonds along the b axis to form a ribbon motif. Ribbons that are related to one another across a center of inversion are enantiomeric and are labeled / and d (or / and d ) (Figure 39). Molecules of -cinnamic acid will be occluded into the d ribbon preferentially from the +b side of the crystal and into the / ribbon from the — b side. It is well documented that E-cinnamide photodimerizes in the solid state to yield the centrosymmetric dimer tnixillamide. Such a reaction takes place between close-packed amide molecules of two enantiomeric ribbons, d and lord and / (95). It has also been established that solid solutions yield the mixed dimers (Ila) and (lib) (Figure 39) (96). Therefore, we expect preferential formation of the chiral dimer 11a at the + b end of the crystal and of the enantiomeric dimer lib at the —b end of the crystal. Preliminary experimental results are in accordance with this model (97). 

Powder X-ray diffraction has verified that the isomerization occurs via a crys-tal-to-crystal reaction process, and that the diffraction profiles of the crystals after photoirradiation consist of overlapped patterns of diffraction due to the crystals of 10 and 11. This indicates that the crystal domains of each isomer exist simultaneously in the crystals accompanied by crystal phase separation during the photoisomerization. Single crystal structure analysis has disclosed that the crystals of 11 as the photoproduct have a symmetry different from that of the starting crystals of 10 (Fig. 14). 

A single crystal structure analysis of 56a revealed the molecule as a symmetric mesoionic betaine having a plane of symmetry (6 2w) with all delocalized C-N bonds being approximately the same length (1.34 A). In this respect, the molecule can be considered as a cyanine chromophore <2004CC1860>. 

A crystal structural analysis of the complex [NEtO[CclL3] (HL = benzothiazole-2(3if)-thione) (120) has been reported the anion possesses strict C3 symmetry with the ligand acting as a bidentate N,S donor (Cd—S, 2.667 A Cd—N, 2.47 A).840... 

If the symmetry analysis for the unit cell is compared with that for the single chain (section III. A. 1.), several interesting features of the vibrational spectrum are seen to emerge. First, infrared active modes of the single chain having a polarization should be split in the crystal, with... 

On the basis of x-ray and infrared studies we may now accept the syndiotactic chain configuration for crystalline PVC. If, in addition, we accept the proposed crystal structure [Natta and Corradini (154)), it is possible to base the symmetry analysis of the spectrum on the unit cell instead of just on a single chain, as was done in the earlier work [Krimm and Liang (101)). The results of this analysis are given here. The unit cell, shown in Fig. 10, has the following symmetiy elements E, Cs2(a), 6(b). C (c), [Pg.123]

Trihalosulfonium Ions. Of the parent trihalosulfonium ions, X3S+ (X = F, Cl, Br), F3S+ and C13S+ were reported first. The reaction product of SF4 and BF3 was described by Bartlett as the SF4BF3 adduct,199 but it was subsequently proved by structural studies (NMR, Raman, IR)200 201 to be the F3S 1 BF4 salt. According to crystal structure analysis,202 the ion F3S+ is of C3v symmetry and has very short S—F bonds (1.495 and 1.499 A) indicative of a substantial positive charge on sulfur. Other F3S+MF6 (M = As, P, Sb) salts were studied by Gillespie and co-workers.200... 

Strahle and co-workers971 were the first to report the synthesis of the dichloroni-tronium ion [Eq. (4.226)]. According to X-ray crystal structure analysis of the hexachloroantimonate salt, which shows a remarkable stability up to 145°C, the cation is almost planar (maximum deviation from the plane is 0.038 A) and has Cs symmetry. The N—O bond distance is 1.31 A, that is, lies between the length of a NO single bond (1.151 A) and a NO double bond (1.47 A). This is indicative of a decreased Tt-bond contribution, which is also reflected in the IR spectrum (stretching vibration at 1650 cm 1 as compared to 1827 cm-1 of phosgene). 

The unstable bright yellow crystals of 577-benzo /]-l,2,3,4-tetrathiepine-l-oxide 26 (Section 13.17.5.3) were characterized by an X-ray diffraction study <1996ZN1511>. The X-ray crystal structural analysis of bis-tetrathiepinyliden 6 (Figure 11) showed that it possesses C, symmetry with a central exocyclic CC double bond similar to tetrathiaful-valences <1995CB561>. 

The crystal structure of pentathiepino [6,7- indole has been determined <1994TL5279>. X-Ray crystal structure analysis revealed that 4,5-ethylenedithio-4,5-pentathiotetrathiofulvalene <1999AM758> moiety has a bent structure resembling the molecular structure of neutral bis(ethylenedithio)tetrathiafulvalene and that the pentathio group adopts a chair-formed conformation. The intradimer interplane distance is 3.35 A, which is much shorter than the interdimer one (4.45 A). In a molecule, there are many intermolecular S-S contacts shorter than the sum of the van der Waals radii (3.7 A), and a two-dimensional network of sulfur atoms was developed between the pentathio groups and tetrathiafulvalene moieties. Furthermore, chlorobenzene molecules are beside the anion and occupy the void space as the interstitial solvent. They are also located on the mirror plane and are disordered at two positions with inversion symmetry because of the cavity structure of the void space. 

The crystal structure analysis (by two-dimensional Fourier methods) was facilitated by the fact that the crystal space group requires the molecule to have symmetry 222, the asymmetric crystal unit consisting of one-quarter of the chemical molecule. If there were no distortions from a regular planar model with a trigonal arrangement of bonds... 

Preliminary X-ray investigations of crystals of 9,10-dihydro-anthracene (66) (Iball, 1938) showed that the most likely space group was P2X which, with two molecules in the unit cell, gave no indication of the molecular symmetry. A non-planar conformation for 9,10-dihydroanthracene has been established by Ferrier and Iball (1954). Their crystal structure analysis, using two-dimensional Fourier methods, shows clearly that the molecule is not planar but is bent about the line joining the carbon atoms 9 and 10. Each half of the molecule appears to be planar, the two halves being inclined to each other at approximately 145°. 

In contrast to 9,10-dihydroanthracene, 9,10-dihydro-l,2-5,6-dibenzanthracene (67) approximates closely to a planar conformation. Preliminary X-ray analysis (Iball, 1938) established that the molecule possesses a centre of symmetry and therefore that the naphthalenic portions of the molecule must be parallel. A more detailed crystal structure analysis, using two-dimensional Fourier methods, has been completed by Iball and Young (1958), who concluded that the molecule was essentially planar (the r.m.s. deviation of the carbon atoms from the mean molecular plane is 0-039 A, the maximum displacement, 0-081 A). This planar conformation has been explained by Herbstein (1959) as arising from the need to minimize the repulsion between the... 

Lochhead and Bray (1995) studied Eu3+ doped sodium disilicate glass with a high-pressure fluorescence line-narrowing technique. This technique was used to characterize the local structure of the Eu3+ ions up to a pressure of 21 GPa. For the crystal-field analysis they assumed a C2v site symmetry which allowed for a complete splitting of the crystal-field components. The crystal-field strength was determined according to eq. (11). The effect of pressure... 

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