HCP miller indices in Orthogonal coordinate system

[anurag]

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 am not sure what you mean with "orientation". Could it be that you have been given the coordinates of the atoms in fractional coordinates
http://en.wikipedia.org/wiki/Fractional_coordinates
and want to convert to Cartesian ones?

 

[anurag]

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.

 

[DrDu]

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

 

[anurag]

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.