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Homework Help: Find angle between planes (011) and (001)

  1. Jan 27, 2012 #1
    Please help me!
    Find angle between planes (011) and (001)?
  2. jcsd
  3. Jan 28, 2012 #2

    Simon Bridge

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  4. Jan 28, 2012 #3
    Thanks spo much!
    So according to that
    to find the angle btw planes (011) and (001) in a cubic crystal (they are perpendicular) I need to normalize vectors.

    Normalizing vectors:
    ll v ll = sqrt( 0^2 +1^2+1^2)= sqrt(2)

    llwll = sqrt (0^2 + 0^2 +1^2)= 1

    v vector normalized:
    x/1.41= 0/1.41= 0
    y/1.41= 0.71
    z/1.41= 0.71
    v = 0.71j +0.71 k

    w vector normalized:
    x/1=0/1= 0
    y/1=0/1= 0
    w = k

    v dot w= 0.71+0.71= 1.41

    then, the angle theta between planes (011) and (001)
    theta= v dot w/( llvll * llwll)
    theta= inverse of cosine ( 1.41/( sqrt (2)) (sqrt(1))= 1.41/ sqrt (2) (1))
    theta= inverse cosine (0.997)
    theta= 4.4

    DOes this make sense???
    if I do inverse cosine of 0.997 I get theta= 4.4
    but I do inverse cosine of 1 I get angle is 0

    not sure what I'm doing wrong =( please some help!!
  5. Jan 28, 2012 #4

    Simon Bridge

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    ... how do you figure that?
    ...don't think so. How did you get this result?

    Note: It helps to explicitly keep √2 like that instead of converting to a decimal.
    ... yes - though ||v||=||w||=1 because you just normalized them didn't you?

    To understand this approach:
    The strategy is to find a vector perpendicular to each plane - related to the Miller indices how?
    The angle between the planes is the angle between these two vectors.

    I don't think you need to normalize them - just turns the dot product into the cosine of the angle.
    The problem wants you to understand what the Miller notation is telling you.
    Last edited: Jan 28, 2012
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