Dear experts,
I am trying to match the spontaneous polarization value of BaTiO3 using PBE functional from the following paper - https://journals.aps.org/prb/abstract/10.1103/PhysRevB.96.035143.
I am using the LCALCPOL = .true. for both the polar and nonpolar structure of BaTiO3. For polar structure, I am getting in OUTCAR -
Ionic dipole moment: p[ion]=( 0.00000 0.00000 2.21711 ) electrons Angst Total electronic dipole moment: p[elc]=( 3.99793 -3.99793 -0.24222 ) electrons Angst
For non-polar structure -
Ionic dipole moment: p[ion]=( 0.00000 0.00000 0.00000 ) electrons Angst Total electronic dipole moment: p[elc]=( 4.03311 4.03311 4.03311 ) electrons Angst
Could anyone please help me how to get the spontaneous polarization of BaTiO3 from the above information? I have attached the relaxed polar and non-polar structure of BaTiO3.
Hello Bikash,
You are on the right track, since the polarization of the polar structure can only be defined relative to the non-polar structure. However, polarization values can include arbitrary multiples of the "polarization quantum" added or subtracted. To obtain the correct polarization, you also need to calculate several intermediate images interpolated between the two endpoints, find the polarization quantum, and then add or subtract it from the data as necessary to make all the polarization data points lie on the same sloped line.
This paper is a very helpful guide https://arxiv.org/pdf/1202.1831.pdf I use ISODISTORT to generate intermediate images; once you upload the non-polar structure, it will give you several options, the fourth option is the one you need. You can use this to export a "cif movie" which has CIFs of the intermediate images, and you can control the number of images with the options at the bottom of that screen.
Steven is absolutely right. I just want add some useful technics that you can use.
On you POSCAR:
1. People usually use same lattice constant for both polar and non-polar structures. (not a necessity tho)
2. I see you have shifted the order of elements in your POSCAR, please check your POTCAR uses the same order.
On your results:
1. Note that in your result, the polarization along x and y axis equal exactly to their lattice constants. This means we can safely deem them to be zero. ( polarization quantum = Integer * Lattice_constant )
2. DIPOLE tag is very important if you want to use VASP's ionic polarization result. Based on your result, I can say with confidence that you did not specify this tag... However, we can always perform this manually: Dipole_{ion}=Sigma(Z_{ion}*Position_{ion}).
Rationalize your result:
Since we can clearly see the polarization along x and y axis equals to zero, we now only need to worry about z axis.
Here, since you've allowed lattice constants to be different, we have to choose a dipole moment that doesn't equals to zero (so that the effect of lattice constant change can take effect). I choose fractional coordinate 0.3 as the dipole origin (DIPOL) to calculate the ionic polarization.
This yields:
Polarization_{ion(nonpolar)} = 0.00000 elect*Ang
Polarization_{ion(polar)} = 1.85000 elect*Ang
since we already have the electronic part of the polarization, the final polarization can be easily calculated.
Dear Steven and Chengcheng ,
Thank you for your help.
You are right that I did'n use DIPOLE tag in my calculation. Thanks for pointing out
that one.
Does anybody know how to take the reference centrosymmetric structure
for spontaneous polarization calculation following the Berry phase approach
for the materials except BaTiO3/PbTiO3 reported in the following paper -
Article Comparative first-principles studies of prototypical ferroel...
I generally use PSEUDO to search for higher-symmetry structures with the minimum atomic displacement relative to the polar phase. The default parameters are usually fine, but it's worth reading the tutorial and background info just for understanding. You might have to go through several intermediate high-symmetry structures before you reach one with inversion symmetry, if the starting symmetry is very low. https://www.cryst.ehu.es/cryst/pseudosymmetry.html
Steven Hartman Dear Steven, You mentioned about polarisation quantum https://arxiv.org/pdf/1202.1831.pdf in this paper. Can you help me how to choose a unit cell such that polarisation lattice values 3/2,5/2 values are generated? (page -4 )
In the paper only -1/2 and +1/2 polarisation lattice values are mentioned.
Subhajit Sau I don't know of any way to guarantee that certain polarization lattice values will be generated, although it might be possible. It shouldn't matter which ones you get as long as you have enough data points to fit the line correctly.
Steven Hartman actually Nicola Spladin has also uploaded some tutorial videos on this topic. There also she mentioned we can choose an appropriate unit cell such that those polarisation lattice values will be generated, we don't need to fit any data point.
The attached pdf has all the steps you can use to obtain polarization branches and spontaneous polarization for BaTiO3 using Berry phase method.
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