Non-centrosymmetric phases

The structure of FeRu2(CO)i2 " has proved more interesting than expected. The cluster also undergoes a phase transition, from a centrosymmetric disordered phase at temperatures above 228 K, to a non-centrosymmetric phase below this temperature. The non-centrosymmetric phase is disordered in the metal atom positions immediately below the phase-transition temperature, but becomes perfectly ordered at 173 K. As discussed above, the cluster has approximate C2 symmetry, but the overall geometry is that of the Dt, type structure with some small distortions. 

If the liquid crystal is composed of chiral molecules, then one linear term is allowed in the free energy. This is the term that changes sign when the axes are inverted, which is allowed in a chiral (non-centrosymmetric) phase. Thus for chiral liquid crystals, the proper free energy expression is... 

However, recent theoretical studies [90] indicate that systems exhibiting attractive interactions of the A and D blocks generally should favour an -ABCDABCD- sequence leading to a non-centrosymmetric lamellar phase. As the theoretical phase diagram (Fig. 28) predicts that the annealing process goes through a mixed centrosymmetric phase (MCS BC) before the fully separated centrosymetric one (CS) is reached, the prediction may not be at... 

Fig. 28 Mean-field phase diagram for ABCD tetrablock quaterpolymer melts with 0=1/4. Flory-Huggins parameters are xab = X except /Ad- Phases abbreviations MCS BC mixed centrosymmetric NCS non-centrosymmetric CS centrosymmetric. From [90]. Copyright 2004 American Chemical Society...

Diphenyl-l,3,4-oxadiazole crystallization revealed two polymorphic forms (centrosymmetric and non-centrosymmetric) of the substance. Raman spectra of both phases recorded between 15 and 1700 cm-1 showed well-resolved internal modes and the external lattice vibrations below 200 cm-1, offering a fast tool for discrimination between different polymorphs. The internal modes were dominated by two groups, one around 1000 cm-1 and the second one between ca. 1500 and 1600 cm-1 <2003JST219>. 

Karle, J. and Hauptman, H. (1956). A theory of phase determination for the four types of non-centrosymmetric space groups 1P222, 2P22, 3Pj2, 3P22. Acta Crystallogr. 9, 635-651. 

Due to termination of the series, however, p(r) is severely affected by ripples. In addition, especially in the case of non-centrosymmetric crystals, the phase of vector F(S) is not known with precision and this affects a correct reconstruction of the density. Therefore, Fourier summation cannot be used for precise and accurate mapping of electron density. On the other hand, a model is necessary to overcome these limitations and to produce a function that is sufficiently close to the real, quantum mechanical />(r) in all regions of the crystal. 

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. 

Fig. 21S. Determination of the absolute configuration of a non-centrosymmetric structure by using anomalous scattering. Left—Scattering by anomalously scattering atom JP and by the rest of the molecule, E. Centre—Representation of amplitudes and phases ot waves. Right—Corresponding vector representation (scale of amplitudes doubled).

Special problems arise when two different heavy atom derivatives, with the heavy atoms in different sites, are used for the purpose of determining phase angles in non-centrosymmetric crystals (see p. 387) it is essential to know the relative positions of the two heavy atoms. Perutz (1956) found that a sort of combination difference Patterson synthesis —a Fourier synthesis in which the coefficients are... 

The transform concept has been illuminating in many ways. One more example will be mentioned. In the transform of a centrosymmetric group of atoms, the phase angle is necessarily either 0 or n, and regions of opposite sign are separated by nodal lines of zero intensity in the transform of a non-centrosymmetric group there is no such limitation of phase angles, so that the intensity does not have to go... 

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