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The direction of the crystal plane is represented by the normal vector to the plane (enclosed in square brackets)
Example: Crystal Directions
Note that a plane & the direction normal have precisely the same indices —just change the bracket.
Crystal-direction vector
- For a cubic crystal, the angle θ between directions
the above equation is established by forming the dot product between the two direction vectors
r1 = h1a + k1b + l1c and r2 = h2a + k2b + l2c
Summary on the Notation of crystallographic planes and directions
- A particular crystal plane, e.g. (001) round bracket
- A family of equivalent planes: e.g. curly bracket {001}
- A particular crystal direction, e.g. [001] square bracket
- A family of directions: e.g. <001> angle bracket
