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HCP miller indices in Orthogonal coordinate system

by anurag
Tags: coordinate, indices, miller, orthogonal
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anurag
#1
Jul2-14, 12:54 PM
P: 5
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
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DrDu
#2
Jul3-14, 02:45 AM
Sci Advisor
P: 3,560
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
#3
Jul3-14, 03:15 AM
P: 5
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
#4
Jul4-14, 12:50 AM
Sci Advisor
P: 3,560
HCP miller indices in Orthogonal coordinate system

Ok, I see. Maybe you can show us your attempt to calculate the vectors and we can help you where you got stuck.
anurag
#5
Jul4-14, 04:35 AM
P: 5
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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