Mauguin limit

Deformed cholesteric. Assume that Eq, (8) describes le initial structure of the director, but that the cell is filled ith a cholesteric liquid crystal with equilibrium pitch = lir/q. For p = we have an ordinary Grandjean struc-ire. Voxp q elastic stresses are present which in principle [lould be revealed when the cholesteric interacts with light, n the Mauguin limit, the equations describing this interac-on are given by (11) except that 2K -K 2K ... 

Figure 2 shows the plot of T u) as a function of M, the so-called Gooch and Tarry curve. For large values of u, the transmitted intensity T(u) drops to zero and the Mauguin limit is fulfilled. Additional intensity... 

The periodicity of a lattice limits the number of compatible rotation operations to onefold, twofold, threefold, fourfold, and sixfold. This, in turn, limits the number of point groups to thirty-two. Point groups are used to describe individual molecules. Table 14.1 shows the thirty-two point groups in both the Hermann-Mauguin notation and the Schoenflies notation divided into seven crystal systems triclinic, monoclinic, orthorhombic, tetragonal, trigonal, hexagonal, and cubic. 

A rotoinversion l about an axis is a rotation by the angle (f> followed by an inversion through a point on the axis. This is also a combined operation of the second type which is neither a pure rotation nor a pure inversion. It is easily seen that each rotoinversion is equivalent to a rotoreflection ) = S n(j>), S() = n + ). Thus, operations of the second type may be represented by either rotoreflections or by rotoinversions. We could limit ourselves to one or other of these two representations. However, the two most commonly used systems of nomenclature applied to geometrical symmetry do not use the same convention. The Schoenfiies system is based on rotoreflections, whereas the Hermann-Mauguin (or international) system is based on rotoinversions. In crystallography we prefer to use the Hermann- Mauguin system. The correspondence between l and S is shown in Table 2.1. 

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