[QE-users] Polarization calculation using nscf

[Lucian D. Filip]

The number outside of the bracket is the polarization value on one of 
the polarization branches. That value by itself can rarely be used as it 
is. In my experience, for BTO unit-cell the value you obtained initially 
is the one that corresponds to the real polarization which is obtained 
from experimental measurements. This is a coincidence. You can test this 
by doing a number of scf followed by nscf with Berry phase calculations 
for a sequence of distortions of the BTO atoms. You start with the 
centrosimmetric state where polarization will be zero (again, this is 
not always the case!) then you introduce a distortion along the z axis 
by moving the atoms towards their equilibrium position in the state with 
polarization P. By doing successice calculations like this and plotting 
the obtained polarization vs distortion, for BTO you will get a straight 
line from 0 to the value you obtained correspondint to the stable 
ferroelectric state.

I have not checked for BTO but I suspect that using a super-cell what 
happens is you end up on a different polarization branch. In the modern 
polarization theory, the polarization value is defined until a 
polarization quantum. To get the actual physical value that one obtaines 
from measurements one has to take the difference between the 
polarization obtained for the ferroelectric state and the 
centrosimmetric state. But here is the catch: both are obtained modulo a 
polarization quantum! So here is what happens:

The polarization for the centrosimmetric state is: Pcentrosimmetric = Pc 
+ n * Pq. Pcentrossimetric are the possible values that can be obtained 
starting from the calculated value Pc (the one given in the output) and 
the polarization quantum Pq and n is an integer. So if Pc = 0 initially, 
Pcentrossimetric can take the following vallues: ...., -2 Pq, -Pq, 0, 
Pq, 2Pq , ...etc.

For the ferroelectric state something similar happens only: 
Pferroelectric= Pf + m*Pq. Pf is the value you obtain from the output 
and m is another integer! There is no guarantee that n=m!

The value you are after is deltaP=Pferroelectric-Pcentrosimmetric as the 
theory states. But if n != m this difference will still be defined up to 
an integer times Pq! The catch is to make sure that both 
Pcentrosimemtric and Pferroelectric reside on the same branch defined by 
the same integer.

Now it is easy to tell if by luck both values are initially on the same 
branch then the difference makes sense physically. If they aren't then 
successibe calculations are needed. How many? that dependes on the 
complexity of the super cell and the material! I am not sure of the 
rules on this forum but I have proposed a way to obtain the polarization 
by doing only three calculations: one for the centrosimmetric state, one 
for the ferroelectric state and one for an intermediary state very close 
to the centrossimetric one. If you are interested I can send the paper 
over, maybe it will help!


All the best,


Lucian




On 22/06/2022 15:46, Amar Singh via users wrote:
> What I understood up to now is that the bracketed number (mode 0.5099 
> C/m2) is, what the reference calls the "quantum of polarization", and 
> it depends upon the size and choice of the unit-cell selected. On the 
> other hand, the number outside bracket is the "change in 
> polarization", which is typically known as saturation polarization (Ps).
>
> Now, when I did some experiment with my unit-cell choice, the quantum 
> of polarization 0.5 C/m2 for 2X2X2 supercell changed to 2 C/m2 
> (exactly four times) for 1X1X1 cell, whereas Ps changed from -0.16 
> C/m2 to 0.34 C/m2.
>
> I was expecting the quantum of polarization to either scale with the 
> size of supercell or remain invariant, but here, on reducing the 
> supercell volume to 1/8th, its value is quadrupled. On the other hand, 
> change in polarization, which I was expecting to be independent of the 
> choice of supercell size, has changed its magnitude as well as direction.
>
> I will really appreciate your help in understanding these numbers.
> Thanks
>
>
> _______________________________________________
> The Quantum ESPRESSO community stands by the Ukrainian
> people and expresses its concerns about the devastating
> effects that the Russian military offensive has on their
> country and on the free and peaceful scientific, cultural,
> and economic cooperation amongst peoples
> _______________________________________________
> Quantum ESPRESSO is supported by MaX (www.max-centre.eu)
> users mailing listusers at lists.quantum-espresso.org
> https://lists.quantum-espresso.org/mailman/listinfo/users
-- 
*Dr. Lucian Dragos Filip*
National Institute of Materials Physics
Atomistilor str. 405A, PO Box MG. 7
Magurele, 077125
Bucharest, Romania
E-mail: lucian.filip at infim.ro
Website: https://lucianfilip.wordpress.com/
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.quantum-espresso.org/pipermail/users/attachments/20220623/a60cb653/attachment.html>