Hexagonal crystals and Miller-Bravais indices

In reality this third index is not needed. However, it does help to bring out the relationship between the planes. Using four indices, the planes are A, (1 120) B, (1210) and C, (21 10). Because it is a redundant index, the value of i is sometimes replaced by a dot, to give indices (hk.l). This nomenclature emphasises that the hexagonal system is under discussion without actually including a value for i. 

The response of a crystal to an external stimulus, such as a tensile stress, electric field and so on, is usually dependent on the direction of the applied stimulus. It is therefore important to be able to specify directions in crystals in an unambiguous 

As with MiUer indices, it is sometimes convenient to group together all directions that are identical by virtue of the symmetry of the structure. These are represented by the notation (uvw). In a cubic crystal, (100) represents the six directions [100], [100], [010], [OlO], [001], [001]. 

A zone is a set of planes, all of which are parallel to a single direction, called the zone axis. The 

It is sometimes important to specify a vector with a definite length perhaps to indicate the displacement of one part of a crystal with respect to another part, as in an antiphase boimdary or crystallographic shear plane. In such a case, the direction of the vector is written as above, and a prefix is added to give the length. The prefix is usually expressed in terms of the unit cell dimensions. For example, in a cubic crystal, a displacement of two unit cell lengths parallel to the b axis would be written 2ao[0 1 0]- 

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