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<p>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. <br>
</p>
<p>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:</p>
<p>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.</p>
<p>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!</p>
<p>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. <br>
</p>
<p>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!</p>
<p><br>
</p>
<p>All the best,</p>
<p><br>
</p>
<p>Lucian<br>
</p>
<p><br>
</p>
<p><br>
</p>
<p><br>
</p>
<div class="moz-cite-prefix">On 22/06/2022 15:46, Amar Singh via
users wrote:<br>
</div>
<blockquote type="cite"
cite="mid:1655795224.S.1468.13178.f5mail-224-158.rediffmail.com.1655901986.11077@webmail.rediffmail.com">
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<span style="color: rgb(0, 0, 0); font-family: Helvetica,
sans-serif, arial; font-size: 12px;">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).</span><br style="text-size-adjust: 100%;
color: rgb(0, 0, 0); font-family: Helvetica, sans-serif, arial;
font-size: 12px;">
<br style="text-size-adjust: 100%; color: rgb(0, 0, 0);
font-family: Helvetica, sans-serif, arial; font-size: 12px;">
<span style="color: rgb(0, 0, 0); font-family: Helvetica,
sans-serif, arial; font-size: 12px;">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.</span><br style="text-size-adjust: 100%; color:
rgb(0, 0, 0); font-family: Helvetica, sans-serif, arial;
font-size: 12px;">
<br style="text-size-adjust: 100%; color: rgb(0, 0, 0);
font-family: Helvetica, sans-serif, arial; font-size: 12px;">
<font face="Helvetica, sans-serif, arial" color="#000000"><span
style="font-size: 12px;">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.</span></font><br style="text-size-adjust:
100%; color: rgb(0, 0, 0); font-family: Helvetica, sans-serif,
arial; font-size: 12px;">
<br style="text-size-adjust: 100%; color: rgb(0, 0, 0);
font-family: Helvetica, sans-serif, arial; font-size: 12px;">
<span style="color: rgb(0, 0, 0); font-family: Helvetica,
sans-serif, arial; font-size: 12px;">I will really appreciate
your help in understanding these numbers.</span><br>
Thanks<br>
<br>
<br>
<fieldset class="moz-mime-attachment-header"></fieldset>
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<div class="moz-signature">-- <br>
<b>Dr. Lucian Dragos Filip</b><br>
National Institute of Materials Physics<br>
Atomistilor str. 405A, PO Box MG. 7<br>
Magurele, 077125<br>
Bucharest, Romania<br>
E-mail: <url><a class="moz-txt-link-abbreviated" href="mailto:lucian.filip@infim.ro">lucian.filip@infim.ro</a></url><br>
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