Geometrical considerations about intermetallic crystal structures

5 Geometrical considerations about intermetallic crystal structures. When discussing the factors which control the structures of the metallic elements, Laves (1956) proposed three interrelated principles that are mainly geometric in character and also related to the atomic dimensional characteristics  

These principles may be considered to be valid to a certain extent for the intermetallic phase structures and not only for the metallic elements. 

1 The principle of highest symmetry (symmetry principle). According to Laves, a tendency to build configurations with high symmetry is evident. This tendency is particularly clear in metallic structures, especially in the simple ones. 

However, according to Hyde and Andersson (1989), for instance, the validity extension of this principle is difficult to evaluate. As time passes, crystallographers are able to solve more and more complex crystal structures, and these tend to have low symmetry. The symmetry principle could be restated by observing that a crystal structure has the highest symmetry compatible with the efficient use of space and the specific requirements of chemical bonding between nearest neighbours. 

For a discussion on the symmetry principle , its alternative formulations and the history of its development, papers by Brunner (1977) and by Baminghausen (1980) may be consulted. In these papers a number of statements are reported which may be considered equivalent. When considering close sphere packings, the following statements are especially worthy of mention. 

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