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The Miller indices can be used to specify directions and planes in a crystal
[Ashcroft76,Kittel96]. The Miller indices of a plane are defined in the
following way: First, three lattice vectors have to be defined. For cubic
crystal systems, the lattice vectors are chosen along the edges of the
crystallographic unit cell (unit cube). Any crystal plane intercepts the axes
in certain points. The Miller indices are the ratios of these points and are
given as a triplet of integer values . A Miller index 0 means that
the plane is parallel to the respective axis. Negative indices are indicated
with a bar written over the number.
In the notation of [Ashcroft76], with square brackets instead of round
brackets, denotes a direction in the basis of the lattice vectors. The notation
denotes all planes that are equivalent to
by the
symmetry of the crystal. Similarly, the notation
denotes all directions that are equivalent to
by symmetry.
In cubic crystal systems the Miller indices of a plane are the same as those of the direction perpendicular to the plane.
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Previous: 3.3 Stress-Strain Relations Up: 3.3 Stress-Strain Relations Next: 3.3.2 Strain Resulting from Uniaxial Stress |