International
Tables for
Crystallography
Volume B
Reciprocal space
Edited by U. Shmueli

International Tables for Crystallography (2006). Vol. B, ch. 4.4, pp. 462-463   | 1 | 2 |

Section 4.4.4.4.1. Crystal-E

P. S. Pershana*

aDivision of Engineering and Applied Science and The Physics Department, Harvard University, Cambridge, MA 02138, USA
Correspondence e-mail: pershan@deas.harvard.edu

4.4.4.4.1. Crystal-E

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Fig. 4.4.4.7[link] illustrates the intralayer molecular packing proposed for the crystalline-E phase (Levelut, 1976[link]; Doucet, 1979[link]; Levelut et al., 1974[link]; Doucet et al., 1975[link]; Leadbetter et al., 1976[link]; Richardson et al., 1978[link]; Leadbetter, Frost, Gaughan & Mazid, 1979[link]; Leadbetter, Frost & Mazid, 1979[link]). The molecules are, on average, normal to the layers; however, from the optical birefringence it is apparent that the site symmetry is not uniaxial. X-ray diffraction studies on single crystals by Doucet and co-workers demonstrated that the biaxiality was not attributable to molecular tilt and subsequent work by a number of others resulted in the arrangement shown in Fig. 4.4.4.7(a)[link]. The most important distinguishing reciprocal-space feature associated with the intralayer `herringbone' packing is the appearance of Bragg peaks at [\sin(\theta)] equal to [\sqrt{7}/2] times the value for the lowest-order in-plane Bragg peak for the triangular lattice (Pindak et al., 1981[link]). These are illustrated by the open circles in Fig. 4.4.4.7(b)[link]. The shaded circles correspond to peaks that are missing because of the glide plane that relates the two molecules in the rectangular cell.

[Figure 4.4.4.7]

Figure 4.4.4.7 | top | pdf |

(a) The `herringbone' stacking suggested for the crystalline-E phase in which molecular rotation is partially restricted. The primitive rectangular unit cell containing two molecules is illustrated by the shaded region. The lattice has rectangular symmetry and [a \neq b]. (b) The position of the Bragg peaks in the plane in reciprocal space that is parallel to the layers. The dark circles indicate the principal Bragg peaks that would be the only ones present if all molecules were equivalent. The open circles indicate additional peaks that are observed for the model illustrated in (a). The cross-hatched circles indicate peaks that are missing because of the glide plane in (a).

Leadbetter, Mazid & Malik (1980[link]) carried out detailed studies on both the crystalline-E phase of isobutyl 4-(4-phenylbenzylideneamino)cinnamate (IBPBAC) and the crystalline phase immediately below the crystalline-E phase. Partially ordered samples of the crystalline-E phase were obtained by melting the lower-temperature crystalline phase. Although the data for the crystalline-E phase left some ambiguity, they argued that the phase they were studying might well have had molecular tilts of the order of 5 or 6°. This is an important distinction, since the crystalline-H and crystalline-J phases are essentially tilted versions of the crystalline-E. Thus, one important symmetry difference that might distinguish the crystalline-E from the others is the presence of a mirror plane parallel to the layers. In view of the low symmetry of the individual molecules, the existence of such a mirror plane would imply residual molecular motions. In fact, using neutron diffraction Leadbetter et al. (1976[link]) demonstrated for a different liquid crystal that, even though the site symmetry is not axially symmetric, there is considerable residual rotational motion in the crystalline-E phase about the long axis of the molecules. Since the in-plane spacing is too small for neighbouring molecules to be rotating independently of each other, they proposed what might be interpreted as large partially hindered rotations.

References

Doucet, J. (1979). In Molecular physics of liquid crystals, edited by G. W. Gray & G. R. Luckhurst, pp. 317–341. London/New York: Academic Press.
Doucet, J., Levelut, A. M., Lambert, M., Lievert, L. & Strzelecki, L. (1975). Nature de la phase smectique. J. Phys. (Paris) Colloq. 36, C1–13–C1–19.
Leadbetter, A. J., Frost, J. C., Gaughan, J. P. & Mazid, M. A. (1979). The structure of the crystal, smectic E and smectic B forms of IBPAC. J. Phys. (Paris) Colloq. 40, C3–185–C3–192.
Leadbetter, A. J., Frost, J. C. & Mazid, M. A. (1979). Interlayer correlations in smectic B phases. J. Phys. (Paris) Lett. 40, L325–L329.
Leadbetter, A. J., Mazid, M. A. & Malik, K. M. A. (1980). The crystal and molecular structure of isobutyl 4-(4′-phenylbenzylideneamino) cinnamate (IBPBAC) – and the crystal smectic E transition. Mol. Cryst. Liq. Cryst. 61, 39–60.
Leadbetter, A. J., Richardson, R. M. & Carlile, C. J. (1976). The nature of the smectic E phase. J. Phys. (Paris) Colloq. 37, C3–65–C3–68.
Levelut, A. M. (1976). Etude de l'ordre local lié à la rotation des molécules dans la phase smectique B. J. Phys. (Paris) Colloq. 37, C3–51–C3–54.
Levelut, A. M., Doucet, J. & Lambert, M. (1974). Etude par diffusion de rayons X de la nature des phases smectiques B et de la transition de phase solide–smectique B. J. Phys. (Paris), 35, 773–779.
Pindak, R., Moncton, D. E., Davey, S. C. & Goodby, J. W. (1981). X-ray observation of a stacked hexatic liquid-crystal B phase. Phys. Rev. Lett. 46, 1135–1138.
Richardson, R. M., Leadbetter, A. J. & Frost, J. C. (1978). The structure and dynamics of the smectic B phase. Ann. Phys. 3, 177–186.








































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