[Wien] Primitive Brillouin zone of Monoclinic base-centered structure

[Marcelo Barbosa]

Thank you very much for you suggestion!

I calculated the primitive reciprocal vectors by hand considering the same coordinate system as XCrySDen uses for the primitive cell and found out that in fact it gets the right reciprocal vectors for this space group. Only the primitive Brillouin zone that is drawn for the band path selection is wrong.
Therefore, by manually introducing the k-points coordinates of the desired points in the table that shows up for the band structure script, I was able to create the correct xcrysden.klist file to be used by WIEN2k.

Since the high-symmetry points were known for the C2/m representation of the space group, I just used the transformation matrix as described in “Part 5. Transformations in crystallography” of Volume A from the “International Tables for Crystallography” (as suggested in the email) to get the high symmetry points coordinates in the B2/m representation.

Once again, thank you very much for your help.

Best regards,
Marcelo


> On 5 Oct 2017, at 21:25, Gavin Abo <gsabo at crimson.ua.edu> wrote:
> 
> I don't know if it helps or not:
> 
> I could be wrong, but I believe XCrySDen has a bug for the b-centered monoclinic:
> 
> https://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.at/msg06205.html <https://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.at/msg06205.html>
> https://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.at/msg12479.html <https://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.at/msg12479.html>
> 
> However, I haven't looked into it further.
> 
> The "International Tables for Crystallography" [ http://dx.doi.org/10.1107/97809553602060000001 <http://dx.doi.org/10.1107/97809553602060000001> ] likely contains a transformation (rotation matrix) that you could use, but I don't know what volume or page it would be on.  Maybe it is in "Part 5. Transformations in crystallography" of Volume A [ http://it.iucr.org/Ab/contents/ <http://it.iucr.org/Ab/contents/> ].
> 
> On 10/5/2017 5:01 AM, Marcelo Barbosa wrote:
>> Dear Sirs,
>> 
>> I tried the following solution to my problem but it seems that changing the space group to P1 makes the Primitive Brillouin Zone to be equal to the Conventional Brillouin zone.
>> However, for a base-centered monoclinic structure, they are not equal and to get the right band structure one must use the Primitive Brillouin zone high symmetry points (as have been shown in https://doi.org/10.1016/j.commatsci.2010.05.010 <https://doi.org/10.1016/j.commatsci.2010.05.010>).
>> 
>> In that article, they have a table with all the symmetry points for a base-centered monoclinic structure.
>> Unfortunately, they consider the lattice vectors with alpha < 90º instead of the gamma != 90º required by WIEN2k.
>> How can I transform those points from one representation to another?
>> And if I can calculate those points, can I manually choose them in XCrysden to generate the klist file instead of choosing them from the 3D image (since the image is wrong)?
>> 
>> Best regards,
>> Marcelo
>> 
>>> On 22 Sep 2017, at 19:09, Yundi Quan <yquan at ucdavis.edu <mailto:yquan at ucdavis.edu>> wrote:
>>> 
>>> It happens sometimes. One possible workaround is to set the space group to P1 and use the same a, b, c, alpha, beta and gamma. That way you can select k-points and use the for C2/m structure.
>>> 
>>> On Fri, Sep 22, 2017 at 4:00 AM, Marcelo Barbosa <marcelo.b.barbosa at gmail.com <mailto:marcelo.b.barbosa at gmail.com>> wrote:
>>> Dear Sirs,
>>> 
>>> I’m trying to get the Brillouin zone and high-symmetry points of Ga2O3, which has a monoclinic base-centered lattice.
>>> However, after plotting it using XCrysDen, one of the vectors (b*) doesn’t go through the center of any plane in the Brillouin zone (see figure in attachment).
>>> Since the Brillouin zone is defined has the Wigner-Seitz cell of the reciprocal lattice, shouldn’t all the reciprocal vectors go through the center of the planes by definition?
>>> 
>>> To generate the structure, I used the following .cif file (CIF <http://www.crystallography.net/cod/2004987.cif>) but since the parameters in the file are in the C 2/m representation, I started by running "x sgroup” to get the structure with the parameters in the B 2/m representation (as WIEN2k requires).
>>> 
>>> Thank you for your help.
>>> 
>>> Best regards,
>>> Marcelo
>>> 
>>> <Brillouin zone.png>
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