[Wien] Transformation from rhombohedral to hexagonal coordinates - swapping of x and y components

[Juergen Spitaler]

Dear Prof. Blaha,
it is true that hex2rho and rho2hex are compatible,
since both of them use the same hexagonal Bravais matrix
with the swapped two lines.
Writing the hexagonal lattice vectors in rows, they both use
    H1 = (0         1     0)
    H2 = (0.866  -0.5     0)
    H3 = (0         0     1)
    (I will call this rhomb2hex setting)
instead of
    H1 = (0.866  -0.5     0)
    H2 = (0         1     0)
    H3 = (0         0     1)
  (I will call this usersguide setting) 

There are 4 points about this lattice choice:
- The change of the Bravais matrix cannot be
  a matter of row/column vectors. That would
  leave, eg., the H(1,1) component unchanged
- The coordinate system defined in the rhomb2hex
  setting is left-handed, and not right-handed anymore.
  Apart from that, the order of H1 and H2 should
  not change the "physics".
- In both cases, "nn" yields exactly the same nearest
 neighbor distances, as one could expect, and in both
 cases it is found that all 12 Al atoms are  equivalent,
 and all 18 O atoms equivalent.
- "symmetry" finds 12 symmetries in the rhomb2hex setting,
  but no symmetry at all for the usersguide setting.

In this context it would also be interesting why even in
the rhomb2hex setting only 12 symmetry operations are found,
instead of 36; this problem was already described
Swati Chaudhury in Aug 2007, but to my understanding it has
not been answered so far.

Best wishes,
Juergen



 
 

> I cannot answer this in general.
> All I see from simple tests is that hex2rho and rho2hex are converting coordinates
> into each other properly.
> WIEN takes sometimes row, sometimes column vectors ....
>
> We would need to look into a specific example where you have some structural
> data and need to set them into WIEN2k-format. Then check eg. the nn-distances,
> symmetry,....
>
> Juergen Spitaler schrieb:
>   
>> Dear Prof. Blaha!
>> Recently I have been dealing with the conversion from rhombohedral to
>> hexagonal coordinates. I was surprised that the x and y  values I
>> obtained for the hexagonal coordinates were just swapped with
>> respect to the ones "expected" by sgroup/symmetry
>> and the ones obtained by rhomb2hex.
>> When I looked into the source of rhomb2hex I found that
>> the first and second line of the Bravais matrix for the hexagonal
>> lattice are swapped with respect to the lattice vectors given in
>> the usersguide. Now my questions are:
>> - How can this swapping be explained?
>> - Are the coordinates I obtain using the "swapped" hexagonal Bravais matrix
>>   compatible with all other parts of the Wien-code?
>>
>> Best regards,
>> Juergen Spitaler
>>
>>     
>
>   


-- 
Dr. Jürgen Spitaler
Material Center Leoben and
Chair of Atomistic Modelling and Design of Materials, Leoben University
Franz-Josef-Straße 18    
8700 Leoben
Tel.: ++43 (0)3842 402 4404
E-Mail: juergen.spitaler at unileoben.ac.at


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