iG FUNDAMENTALS OF SUBMI C RO S COPI C MORPHOLOGY I 



movement and the maintenance of non-equilibria. As soon, however, 

 as chemical substances are withdrawn from the metabolic processes, 

 the ordering forces can intervene and form periodic structures, as, 

 for instance, with the skeleton substances cellulose, chitin, collagen, 

 keratin, etc. Therefore, to study the structure of protoplasm, other 

 methods should be applied which, however, are partly based on the 

 results of the investigations on crystal structure. For this reason this 

 important branch of morphology must be briefly touched upon. 



a. Crystal Structure 



Lattice. The essential nature of lattices is determined by the fact that 

 certain locations of points, which in the more simple cases are identical with 

 the centre of gravity of the atoms, periodically repeat themselves in three 

 given directions in space. These directions coincide with the axes of the 

 crystallographic system. The distance from one point to the next identical 

 one is designated as the identity period or spacing. Depending on the 

 crystallographic system, the spacings are the same in either three (cubic) or 

 only two directions (tetragonal, hexagonal, rhombohedral), or they are 

 different in all three dimensions (rhombic, monoclinic, triclinic). The reg- 

 ularly repeated points form an array of points. Displacing such a row by 

 constant amounts in a direction either perpendicular or obliquely to its own 

 direction, we obtain the lattice plane, while finally the crystal lattice results 

 from displacing such a plane. If a point in the lattice is moved in the three 

 principal directions, each time covering the identity period involved, and if 

 the three vectors obtained are completed to a three-dimensional parallel- 

 epiped, we obtain the so-called elementary or unit cell of the crystal lattice. In 

 analogy to a gas molecule, which represents the smallest unit with all the 

 chemical properties of the gaseous phase, the unit cell is the smallest unit 

 which still shows all physical and symmetry properties of the crystal. It may 

 contain one or several molecules (and in the case of high polymers even 

 parts of molecules). We are, therefore, dealing with a geometrical concept 

 and by no means with a chemical one. If the unit cell is decomposed into its 

 elements, the crystalline properties are lost. As the base cell possesses all the 

 properties of the crystal, and this crystal can be obtained by displacing the 

 elementary unit in the principal directions, structure analysis aims at de- 

 termining the dimensions and the symmetry of the base. Its shape is de- 

 termined by three identity periods a:b:c in Angstrom units, to which in 

 monoclinic and triclinic systems one must add the angle ^, or the angles 

 a, /3, y formed by the edges of the unit cell. The macroscopically determined 

 proportions between the axes of the crystals agree with the proportions 

 between the dimensions of the unit cell, provided analogous planes are 

 considered. 



X-ray analysis measures the distances between the lattice planes. In the 



