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## Axes used in dielectric tensor [SOLVED]

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jerkov
Posts: 28
Joined: Tue Nov 26, 2019 6:02 pm

### Axes used in dielectric tensor

Hi all,

I am confused about what axes are used in the output dielectric, electro-optic, and piezoelectric (d tensor) tensors.

I did not align my the optic axis along the z axis, and my axes are non-orthogonal. I understand that most of the well-known formulas from [Veithen2005] use the principal axes. But how do interpret if I didn't work in this system?

For example, say my three primitive lattice vectors are a,b,c, and they are written in terms of the cartesian x,y,z. Then for the dielectric tensor epsilon_ij, do the i and j refer to the cartesian x,y,z or to the direction of my lattice vecotrs a,b,c? The same question goes for the EO r_ijgamma and piezoelectric tensor d_gamma_mu_nu.

Also, I'm trying to apply strain to this system. To get the diagonals of the infinitesimal strain tensor, for example eta_11, must I dilate all three components of a by the same value or just the first a_x? For the off-diagonal components, like eta_2,3, how do I rotate my lattice vectors? At the moment, my approach is to find the axis of rotation, which would be cross(b,c), and then rotate b or c along this axis. Or should I just rotate around the x-axis to obtain eta_23?

Thanks so much,
J

ebousquet
Posts: 469
Joined: Tue Apr 19, 2011 11:13 am
Location: University of Liege, Belgium

### Re: Axes used in dielectric tensor  [SOLVED]

Dear jerkov,

The properties are outputed in Cartesian axis.

To find the way how to pass from a,b,c to Cartesian and the other way around, you have to use the corresponding transformation matrix.
rprim should give you a hint on that, see in the doc https://docs.abinit.org/variables/basic/#rprim.

In some unusual axes orientations, it can be non-trivial...

Best wishes,
Eric

jerkov
Posts: 28
Joined: Tue Nov 26, 2019 6:02 pm

### Re: Axes used in dielectric tensor

Hi Eric,

That makes sense, thanks a bunch!

J