Directions in Lattice Systems of Crystals
- Practical Electron Microscopy and Database -
- An Online Book -

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There are several important, related notations:
        i) Plane(s):
           i.a) The notation (hkl) represents a plane.
           i.b) The notation {hkl} denotes the family of all the planes that are equivalent to (hkl) by the symmetry of the lattice.
        ii) Direction(s):
           ii.a) The notation [hkl] represents a direction that denotes the direction in the basis of the direct lattice vectors instead of the reciprocal lattice.
           ii.b) The notation <hkl> represents a family of the directions that are equivalent to [hkl] by symmetry.

As an example, Figure 2504 shows a method to evaluate the crystal direction in a cubic lattice if the direction intercepts on a plane.

Evaluation of the crystal direction in a cubic lattice

Figure 2504. Evaluation of the crystal direction in a cubic lattice.

 

 

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