Triclinic cell

Figure C2.3.3. Molecular packing of SDS monohydrate viewed as projected on the ac plane. This polymoriDh crystallizes in a triclinic cell with unit cell constants a, b and c of 10.423 A, 5.662 A and 28.913 A, respectively, and with a = 86.70°, (3 = 93.44°, y = 89.55°. There are four molecules per unit cell. Adapted from figure 2 of [18].

Many semicrystalline polymers are polymorphic and exist in different crystal forms. When PBT fiber is uniaxially stretched [75], the contracted gauche-trans-gauche a-crystal chain is extended to a fully trans conformation of a y-crystal. Above 20% strain, the crystal form is 100% y-crystal with a longer c-axis triclinic cell dimension. Thus, it is reasonable to ask whether the... 

Triclinic crystals. None of the angles of a triclinic cell are right angles in consequence, none of the axes of the reciprocal lattice are... 

For monoclime and triclinic cells, the formulae for the spacings are very unwieldy. Graphical methods based on the conception of the reciprocal lattice are recommended (Chapter VI). 

The unit cell of Ph5As has been reported by Wheatley and Wittig (187). From these data it has been concluded that the molecule adopts the expected trigonal-bipyramidal conformation, very similar to that found for pentaphenylphosphorane (189). It is interesting to mention here that the unsolvated Ph5Sb crystallizes with square-pyramidal geometry (15,188) in a triclinic cell rather than in the monoclinic Cc... 

Construction of reciprocal lattice vectors a, b, c in a general triclinic cell of sides a, b, c. 

The only possible cells in two dimensions are oblique (p only), rectangular (p and c) and hexagonal (p). For each of the seven three-dimensional crystal systems primitive and centred cells can be chosen, but centring is not advantageous in all cases. In the case of triclinic cells no centred cell can have higher symmetry than the primitive and is therefore avoided. In all there are 14 different lattice types, known as the Bravais lattices Triclinic (P), Monoclinic (P,C), Orthorhombic (P,C,I,F), Trigonal (R), Tetragonal (P,I), and Cubic (P,I,F). 

The solid state structure of a homologous series of mesogenic aromatic-aliphatic azomethine ether polymers (AZMEP-n), with n (=1-16) methylene spacers in the main chain, has been studied by X-ray fiber diffraction techniques. Unit cell parameters determined from the fiber patterns of heat-treated single filaments have been used to classify the polymers into distinct groups having different chain conformations and crystal systems. The even members of the. series, where n = 2 4, have C-centered monoclinic unit cells while the unit cells for polymers with n = 6 8 are I-centered monoclinic. When n is even and 10 the unit cells are (primitive) triclinic. The fiber repeat, in the triclinic cells correspond to one chemical moiety while in the monoclinic cells the fiber repeat corresponds to two chemical residues. In addition, the fiber repeat distances are consistent with the methylene spacers adopting an all-trans conformation for all even AZMEP-n polymers. 

When n is odd and 5, the unit cells are orthorhombic and contain either two (n = 1 5) of four (n = 3) chains. The fiber repeat consists of two chemical moieties and the methylene spacers are extended. When n = 7 9, the unit cells are I-centered monoclinic and similar to the those observed for n = 6 8. In the series where n is large and odd (AZMEP-n, n = 11, 13 15), the unit cells are triclinic and closely resemble the triclinic cells found for the high even polymers (n = 10). However, the observed fiber repeats in polymers where n is odd and 7 necessitate the presence of non-trans conformers in the aliphatic portions of the chains. The thermal and mechanical properties of the homologous series of polymers are discussed in light of the observed solid state structures. 

The Debye-Scherrer powder X-ray diffraction data for dilithiomethane, reported by the same authors unfortunately consist of 12 lines only, several of which overlap and except for one, all peaks are of low intensity. The low-symmetry crystal system and the limited number of lines made solving the crystal structure impossible. In an attempt to analyse the 12-line diffraction pattern a triclinic cell was obtained, which, however, cannot be considered as definitive. 

For thicker films (-750 A) of 2, the (110) peak was observed in thin-fihn XRD spectra, which supports this hypothesis. The fact that a fraction of the molecules are lying down is likely to have a detrimental effect on the electronic transport properties of films of 2, since the preferred transport direction occurs within the ab plane. With a full set of and data, the complete thin-film unit cell can be determined. Both films have triclinic cells. The r/oorspacing calculated from these unit cells was 31.83 A for 1 and 27.03 A for 2, which is in good agreement with the values from wide-angle XRD (31.83 and 26.97 A, respectively). 

The non-equal signs for the unit cell parameters mean no necessity to be equal i.e. logically a triclinic cell with a = b = c (within experimental error) is possible. 

The unit cells given for DHDK 0.4 CHCI3 and DHDK 0.5 C2H5OH are both the Dirichlet and Delaunay reduced triclinic cells. 

This form has been characterized by Chatani et al. from WAXD data from fibers originally in the planar zigzag polymorph and then exposed to benzene, toluene, or p-xylene vapours below 50°C for several days. A triclinic cell was determined containing six monomer units and with a crystallographic density of 0.939 g/cm. The chain conformation is —TTgG2T2G2)— which may be considered as intermediate between the original —(IT)— conformation and the hehcal conformation... 

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