Dissertation in Draft: Chapter IV

Date:
1953
Reference:
PP/CRI/F/1/4
Catalogue details

Licence: In copyright

Credit: Dissertation in Draft: Chapter IV. Source: Wellcome Collection.

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    S. CHAPTER IV ADDITIONAL THEORETICAL CONSI DERATIONS mil Iii I m. IL I- fi■ ■ Il -- -m* nr9» M . mm • i ■> iHu»^ , . > wmmiß -»«»■'' « »■> ■ ■ » «. ■ ■■ i f ■ n i if«i iA».| mi» iwbiii^I i na 1. INTRODUCTION In this chapter a number of variations on the simple helical- theory are set out for reference. Most of these have arisen because the solution was required in some actual application of the theory, but one or two have suggested themselves on general grounds. The cases considered are the effect on the X-ray pattern of slight changes in the screw axis; the effect of multiple chains, arranged in various ways; the significance of the reflexions from a single layer line; and a simple relationship which holds when all the atoms are at the same radius. 2. VARIATION OF THE SCREW AXIS M I Ml. ~j.i-.wi ■■lailllUI 1 I ■' «'■ ' *1 ' ■' ,r - 1 ■ Imagine that we are considering a helical structure whose co-ordinates are precisely defined. What is the general effect on the diffraction pattern of a slight change in the values of F and p ? ■ For example, suppose the ©¿ -helix, instead of having 3.60 residues per turn, had about 3.58, so that the structure repeated exactly after ' 17 turns containing 61 residues. We can most easily see what happens by fixing attention on a given Bessel function, whose position is defined ■ • by n and m. ——^ Now since „ \ r, r + 12 S( ' ') £ - ■ £ •-) < ' P p' and if S(l/P) and £(l/p) are small, the Bessel function under consideration will move only a small distance in reciprocal space, especially if n and m are also small. As the true unit cell becomes larger, and the layer lines more closely spaced together, Bessel