Miller-Bravais coordinate system

For a crystal having a hexagonal symmetry, a set of four numbers, [uvtw], named the Miller-Bravais coordinate system (see Figure 1.5), is used to describe the crystallographic directions, where the first three numbers, that is, u, v, t, are projections along the axes at, a2, and a3, describing the basal plane of the hexagonal structure, and w is the projection in the z-direction [2,3],... 

MILLER-BRAVAIS INDICES FOR HEXAGONAL COORDINATE SYSTEMS... 

Fig. B.2. Coordinate system used for Miller-Bravais indices...

In hexagonal crystals, where the base plane exhibits a 120° symmetry, the Miller-Bravais system is used to specify planes and directions, using a coordinate system with four axes Three of these, with angles of 120° between them, lie in the base plane and are equivalent, the fourth is perpendicular to the base plane [hkil] (figure B.2). In this way, the symmetry of the crystal is reflected in the indices. The first three indices obey the additional constraint... 

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