Diffuse Reflexions of X-Rays by Crystals
Proceedings of the Royal Society A
In 1937 Dr H. Wilman and I (Finch and Wilman 1937) first drew atte n tion to a new effect consisting in the occurrence of broad bands or areas of blackening in electron diffraction transmission patterns obtained from crystals of organic compounds such as long-chain hydrocarbons and poly cyclic aromatic compounds. We found th a t the position of these diffuse areas corresponded to the arrangement and separation of the carbon atoms in the molecules. Subsequently, in collaboration with Dr A.
... sby (1939), we were able to show th a t this diffuse-area pattern appeared to be due to molecules which, though orientated with respect to the beam in accordance with the crystal orientation, nevertheless bore no definite phase relationship to each other, and this pattern thus resembled th a t of a gaseous stream of orientated molecules. We found th a t this lack of phase relationship could be explained on the assumption that, due to therm al agitation, the individual molecules were displaced from their mean position in a random fashion, there being no connexion between the displacement of adjacent molecules. The expres sion for the diffracted beam intensity can be w ritten where A 2 -\-B2 is the structure factor for the complete unit cell, whereas A 2 + Bp is the structure factor for each independently moving group or molecule. < j> is the phase angle introduced by the motion of each molecule from its mean position and hence depends on the direction of the emergent and incident beams, as well as on the amplitude of motion. The factor (cos (f))2 is a thermal factor, decreasing the spot intensity a t increasing dis tances from the central spot. On the other hand, 1 -cos2 (f> increases with the distance. The pattern thus consists of a spot pattern modified by a thermal factor, and also of a diffuse area pattern corresponding to the orientation of the individual molecules in the crystal, the latter p art of the pattern being such th at the intensity near the central spot is very small, bu t increases to a finite limit on receding away from the central spot.