unit cell transformation

[Anna Kuznetsova]

Dear Developers and users,

I need to transform the traditional  F43m (cubic) unit cell of 3C-SiC to unit cell with lower P3 symmetry, which is obtained when I view the cubic structure along its body diagonal. This allows to see ABC layers better. How can I do such unit cell transformation by rotation? Is there any procedure in VESTA that can define a new unit cell if a different symmetry group (usually of lower symmetry) is specified for the same structure ?

Thank you!

Anna 

[Philip Howie]

Dear Anna,

You can use the following steps to convert the atom positions from one coordinate system to another:

1. Write the new basis vectors in terms of the old:
    a' = a1 a + a2 b + a3 c

    b' = b1 a + b2 b + b3 c

    c' = c1 a + c2 b + c3 c

2. Construct the transformation matrix T and calculate its inverse, T-1:

           (a1 b1 c1)

    T  = (a2 b2 c2)

           (a3 b3 c3)

3. Write the coordinates of the new origin in the old basis set, if required:

           (o1)

     o = (o2)

           (o3)

4. Transform the old coordinates (u) to the new (u') using

     u' = T-1 . (u - o)

I don't know any way of doing this automatically within VESTA, but you should be able to combine it with the procedural generation of input files you mention in your other question fairly straightforwardly.

Hope that helps,

Phil