"Diffraction by helical structures"

Date:
1956-1957
Reference:
PP/CRI/H/2/17
Catalogue details

Licence: In copyright

Credit: "Diffraction by helical structures". Source: Wellcome Collection.

    12/98
    therefore plot the Cf and z co-ordinates of each atom on a plane with rectangular co-ordinates V» z, This plot is identical (apart from a scale factor) with that which we should obtain by projecting A-t all the atoms radially on to a cylindrical surface^ some mean radins r 0 and then unrolling the surface in the manner described above. We shall thus call this kind of a plot a cySdtMrîesl projection» The value of the cyliMri-e-al projection is that it enables us to compare, at least qualitatively, the magnitudes of the G n? £ (B) terms for all pairs n and € at the same time. For, as we have shown in the last section ? in this case the may be generally be reduced to structure factors T n> £ for a two-dimensional crystal, with n and L playing the role of Miller indices» To each reciprocal lattice point (n, ) f there will correspond in real space a sat of parallel lines which we may denote by the same pair of integers (n, -L ), If we think of these lines as marking the zero-angle lines of a set of cosine and sine waves, we can easily estimate the ■tfct contribution of each atom to •© concerned» This is illustrated in Fig» (la) where we have drawn dotted lines corresponding to (3» -1)» from which we can read off the contributions of the atoms to the term $3^1, Just as one uses Bragg-Lipson charts for two-dimensional structure factors» Note that the set of lines (n, 4L ) make n interception the horizontal axis and ■€ intercepts on the z axis» Furthermore we see that we can thin£ of the set (hn, h-t ), where h is an integer, as the h tix order of the set (n, )• In 3 dissnsions the set of lines (n, L ) representa set of continuous helices underlying