Miller-Bravais Notation

A bcc structure showing two distinct (111) planes with their intercepts (left) and as seen from along the [110] direction (right). The center atom lies between the two (111) planes indicated by heavy dashed lines. 

The designation of planes is more straightforward and proceeds as before. Plane A intersects the a-axis at -1/2 and axes b and c at 1. If it is perpendicular to the basal plane, it would be designated as (2110). If it also intersected the z-axis at one unit, it would be (2111). Plane B intercepts the b-axis at 1, the a-axis at —1, and the c-axis not at all. It would thus be denoted (ilOO). Again note that the sum of the first three Miller-Bravais indices is always zero in this notation. 

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Fig. 8. (a) Schematic picture of how a unit strength dislocation in a close-packed hexagonal structure may dissociate to yield two partials with Burgers vectors bx and ba. (b) Unit vectors in the Miller-Bravais notation [h k = —i). 

FIGURE 5.6 Indices of planes (using Miller-Bravais notation) and directions (using three-index Miller notation) in the hexagonal unit cell. 

The two notations are related and it is straightforward to convert between them. The Miller-Bravais system is widely used in ceramics because alumina (sapphire) often behaves as if it were hexagonal, although it is actually trigonal. 

Miller-Bravais indices Pearson classification point groups reducing cell method Schoenflies notation space groups stereographic projection symmetry perturbations Weiss zone law Wulff map... 

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