"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.

    10/98
    Since for all the atoms r=r Q , let us write *i - 9: T o a. ¿H* where a=2nr 0 . The rectangular co-ordinates of the 3th atoa in this frame will be <xj, zj), and we can imagine the two-dimensional pattern repeated indefinitely, the repeat in the x direction being a » 2fTr 0 , a{ « ?(\tc*A cto-tL cr( tkiy tz^LaX /xL-ea-À^ aüucriUA and the z repeat being c.^.The diffraction pattern of this arrangement of atoms is clearly« F((,()- $(¡^£«(<^♦<5.)] f») in the usual notation, and we see that there is considerable similarity between this expression and equation (!)• To bring this out more clearly, write Then since is independent of j, f IM,k) - 2 Í a («, y ) 2 f, (~3 *43J -- 2. MM) T^e (Mr) where T. lt . (5) is a complex number independent of both R and • Thus the whole diffraction pattern can be characterised by a set of complex numbers which we can plot as in Figure (lb) at the points of a two-dimen sional lattice with rectangular co-ordinates n and -£ (strictly n/a and X/e), Identifying n and h in equations (?) and (3), we see that the T a ¿ array is nothing but the weighted reciprocal lattice of the two-dimensional pattern of atoms. To show the geometrical relationships alone, consider the