q8 fundamentals of submicroscopic morphology I 



lines as a result of cellulose chains which do not belong to the crystal 

 lattice (Sauter, 1937). 



2. From the density of interferences the number of atoms in the net- 

 planes can be derived, since the lattice planes reflect the X-rays more 

 intensely in proportion as they contain more atoms. The density of 

 interferences can be estimated, or measured photometrically. In Fig. 



67 two black spots can be seen on 

 the equator, with a mutual distance 

 of 261/4 i^rn. Their great density is 

 caused by the family of net-planes 

 which contain the glucose rings of 

 the cellulose chains and, as both 

 points correspond to the front plane 

 of Fig. 68, the ring of the glucose 

 units must lie in this plane. In this 

 way it is possible from the intensity 

 of the interferences to determine 

 the orientation of the molecular 

 models (obtained on structural 

 chemical grounds) in the unit cell 

 (derived from X-ray analysis). 



3. From the breadth of the interferences one can calculate the width of 

 the undisturbed lattice regions, using a method developed by 

 Scherrer (1920) for metals, i.e., substances absorbing X-rays, and 

 worked out by Laue (1926) for non-absorbing substances. To do this 

 the density must be measured photometrically. The breadth at half- 

 maximum of the density peaks in the photometer curve (Fig. 70, p. 102) 

 is a measure of the dimension of the crystalline regions perpendicular 

 to the set of net-planes causing the interference. The broader the X- 

 ray interference in the diagram is, the smaller is this dimension. In 

 Fig. 67 the interference spots on the equator are clearly broader than 

 those near the poles of the diagram. It follows from this that, in the 

 fibre, the dimensions of the lattice regions are considerably smaller in 

 directions perpendicular to the fibre axis than in directions parallel 

 to this axis. They must, therefore, be rod-shaped, in conformity with 

 the conclusion drawn from the character of their form birefringence. 

 Hengstenberg and Mark (1928) find 50-60 A for the thickness of 

 these rodlets. Their length cannot be measured accurately, the for- 



Fig 



68. Crystal lattice of cellulose (from 

 Meyer and Misch, 1937). 



