HCP miller indices in Orthogonal coordinate system

  • Thread starter anurag
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  • #1
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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
 

Answers and Replies

  • #2
DrDu
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  • #3
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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.
 
  • #4
DrDu
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Ok, I see. Maybe you can show us your attempt to calculate the vectors and we can help you where you got stuck.
 
  • #5
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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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