Lesson 2, Topic 12
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Directions in Crystal

Abdulaziz July 26, 2020
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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