Standard orientation for non cubic unit cells

[Mike Chapman]

I am working on experimentally verifying a model that predicts microstructures through a specific martensitic phase transformation.

Your software has been a big help, and you may be able to answer one big question I have had with the EBSD systems.

I am working with monoclinic and triclinic unit cells, and I can't figure out how the unit cell sits at a (0,0,0) rotation.  For a cubic cell it is simple, the 100, 010, and 001 axes align with the x, y, and z axes.  But with the non-orthogonal cells this isn't true.  

Specifically I am working on the Oxford hkl system (I don't know if it varies between the different companies)

Thanks!

Mike

[Ralf Hielscher]

Hi Mike,

you are absolutely right that when working with monoclinic one has to be very careful about how to set up orthogonal coordinate system x,y,z into the non Euclidean crystal coordinate system a, b, c.In MTEX this can be specified by options when defining crystal symmetry and unit cell.

E.g. if you want to have z parallel to c and x parallel to a* (the dual coordinate system) you have to use the command

cs = symmetry('m',[aa bb cc],[alpha beta gamma],'z||c','x||a*')

where aa, bb, cc are placeholder for the length of the edges of the unit cell and alpha, beta, gamma are placeholders for the angles of the unit cell. Accordingly, you can also set x parallel to c and y parallel to b* by

cs = symmetry('m',[aa bb cc],[alpha beta gamma],'x||c','y||a*')

I hope this helps,

Ralf.