[QE-users] Polarization calculation using nscf

[Lucian D. Filip]

Dear Amar,

I am glad you found the paper useful. regarding the polarization quanta you need to look at the definition. for materials like BTO the polarization direction is along the c side (or z axis if you will) and for these materials the Pq = q * c / V. but this simplifies to q/ a^2 for this particular case. It is easy to see that if the supercell becomes 2x2x2 then Pq is exactly 4 times less than for the 1x1x1 case.

You are correct that Pq is invariant of the branch, but it is dependent of the geometry like you said in an earlier message. In the paper that was mentioned before by Paolo, there is the more general definition of Pq which applies to cases where the polarization is not along one of the crystal axes as is the case for BTO.

For an more interesting case check out the polarization of BiFeO3!

Regards,

Lucian

On 23 June 2022 14:37:16 EEST, Amar Singh via users <users at lists.quantum-espresso.org> wrote:
>Dear Lucian,
>I managed to find your paper and its clears most of my doubts. However, I am still not able to understand the reason why the quantum of polarization (which you call Pq), is reducing to one fourth on a supercell of size eight times. Unlike P_FS or P_CS, Pq is independent of the "branch" picked up by the system and should remain invariant.
>thanks
>
>From: "Amar Singh"<amarsingh122014 at rediffmail.com>
>Sent: Wed, 22 Jun 2022 18:16:26
>To: "users"<users at lists.quantum-espresso.org>
>Subject: Re: Polarization calculation using nscf
>
>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
> 
-- 
Sent from my Android device with K-9 Mail. Please excuse my brevity.
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