# HCP miller indices in Orthogonal coordinate system

## Main Question or Discussion Point

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

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.

DrDu
Ok, I see. Maybe you can show us your attempt to calculate the vectors and we can help you where you got stuck.

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.