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Crystal plane perpendicularity to direction

  1. Sep 6, 2012 #1
    1. The problem statement, all variables and given/known data
    Show that the direction [hkl] is perpendicular to the plane (hkl) in a cubic system.

    2. Relevant equations
    None, maybe cross product


    3. The attempt at a solution
    I've tried to define the crystal translation vectors(cubic means a=b=c):
    [itex] \vec{a}_1 = a\hat{x}\\
    \vec{a}_2 = a\hat{y}\\
    \vec{a}_3 = a\hat{z}
    [/itex]
    I just can't imagine how to obtain the vector normal to the plane. I cannot use the reciprocal space as we haven't gone over that yet. Please help me, it is not to be handed in i just need to understand it.

    My question is: What is the connection between Miller Indicies of a plane and the plane's normal vector.
     
  2. jcsd
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