HCP miller indices in Orthogonal coordinate system

  1. Hi everyone,
    I am doing MD simulation for zirconium (hcp). I have to input some orientation for crystal in simulation. But i have orientation in 4-index bravais miller indices. and i have to convert (plane and direction) it from 4-index to 3-index orthogonal coordinate system. Please help me.
    Thanks a lot
  2. jcsd
  3. DrDu

    DrDu 4,639
    Science Advisor

    I am not sure what you mean with "orientation". Could it be that you have been given the coordinates of the atoms in fractional coordinates
    and want to convert to Cartesian ones?
  4. Thanks for your help DrDu,
    I have some plane in hcp ( in 4-index Bravais miller indices). I have to find out it's (plane's perpendicular direction) normal indices in orthogonal coordinate system.
  5. DrDu

    DrDu 4,639
    Science Advisor

    Ok, I see. Maybe you can show us your attempt to calculate the vectors and we can help you where you got stuck.
  6. As you know, miller Indices of normal of plane is same as plane indices in cubic system. So, I assumed the same for hcp system. I got transformation matrix to change from 4-index to 3-index orthogonal system. Matrix is given below:
    For a plane with the indices (h k i l):
    tr([u v w])=[1 0 0 0; 0 1/sqrt(3) -1/sqrt(3) 0; 0 0 0 (a/c)]*tr([h k i l])
    For a direction with indices (p q r s):
    tr([a b c])=[3/2 0 0 0; 0 sqrt(3)/2 -sqrt(3)/2 0; 0 0 0 (c/a)]*tr([p q r s])

    If i have a plane with indices (4 -3 -1 9), then i am not getting the same indices for plane and normal in orthogonal-system. I think matrix is wrong.
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