ABSTRACT
This chapter introduces and defines the theoretical bases and terms which are fundamental to descriptions of GB geometry. The term ‘GB structure’ is concerned with atomic positions in the GB region and requires more sophisticated methods for its investigation. The starting point for a geometrical description of a GB is a definition of its degrees of freedom. A GB in a bicrystal has eight degrees of freedom in total; five of these are known as macroscopic, and the other three microscopic. An alternative interpretation of the GB degrees of freedom start from the standpoint of the relative rotation between the orientations of the two neighbouring lattices. The angle/axis defines only the relationship between the two neighbouring lattices and not the position of the GB itself. The angle/axis pair is one way in which the misorientation geometry of a GB may be described mathematically.
