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Prove all vectors lie on a cone (Laue Cone)

  1. Apr 11, 2012 #1
    1. The problem statement, all variables and given/known data

    Consider a family of planes that belong to a zone axis. In the Laue experiment, the incident beam has a direction s0, which is fixed. Each plane in the zone diffracts a particular X-ray wavelength into a direction s,which is different for each plane. You are told that all the diffracted directions s lie on a cone around the zone axis.
    Prove the above statement, that all outgoing vectors s lie on a cone. Hint: consider the meaning of the vector difference s - s0

    2. Relevant equations

    a(cos αn − cos α0) = a · (s − s0) = nxλ.
    b(cos βn − cos β0) = b · (s − s0) = nyλ
    c(cos γn − cos γ0) = c · (s − s0) = nzλ,

    3. The attempt at a solution
    Hold nx fixed (order of reflection), then the path length stays the same but angle changes? I don't know how to do this mathematically.
     
  2. jcsd
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