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I used IBRION = 8 in vasp 5.2 to calculate the piezoelectric constant. The OUTCAR provides the following information:
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PIEZOELECTRIC TENSOR for field in x, y, z (e Angst)
XX YY ZZ XY YZ ZX
--------------------------------------------------------------------------------
x 0.00175 -0.00425 -0.00376 0.00000 0.00000 -0.46312
y -0.00326 -0.00050 0.00142 0.00000 -0.46769 0.00000
z -1.26333 -1.26333 2.24289 0.00000 0.00000 0.00000

PIEZOELECTRIC TENSOR for field in x, y, z (C/m^2)
XX YY ZZ XY YZ ZX
--------------------------------------------------------------------------------
x 0.00000 0.00000 0.00000 0.00000 0.00000 -0.11850
y 0.00000 0.00000 0.00000 0.00000 -0.11850 0.00000
z -0.31991 -0.31991 0.56796 0.00000 0.00000 0.00000

PIEZOELECTRIC TENSOR IONIC CONTR for field in x, y, z (C/m^2)
XX YY ZZ XY YZ ZX
--------------------------------------------------------------------------------
x 0.00050 0.00050 0.00046 0.00000 0.00000 -1.98755
y 0.00025 0.00025 0.00136 0.00000 -2.39180 0.00000
z -1.18988 -1.18988 -5.21482 0.00000 0.00000 0.00000
=========================================================
When I add ionic contribution to electronic contribution, I got:
e33=-4.65C/m^2, e31=-1.51C/m^2, e15=-2.11C/m^2
The reference value is:
[a] e33= 4.41C/m^2, e31= 2.06C/m^2, e15= 6.63C/m^2
e33= 3.23C/m^2, e31= -0.93C/m^2, e15= 3.15C/m^2
[a]:PRL, 95, 037601(2005), Zhigang Wu and Ronald E.Cohen
:PRL, 80, 4321(1998), Gotthard Saghi-Szabo and Ronald E. Cohen

I have calculated the elastic constant using strain-stress curve, it is almost same with the ref [a]'s value. I think my POSCAR is fully optimized and is OK.

I also calculated the Born effective charge and polarization, they fit very well with all the reference values.

The different is that first the sign of my piezoelectric constant is negative. Secondly, the absolute value of my e33 is very close to ref. [a], while e31 and e15 are far away from the reference value of both ref. [a] and ref. .

Do you have any idea about this difference?
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My INCAR:

SYSTEM = PbTiO3
ISMEAR = -5
LASPH = T
PREC = Accurate
ADDGRID = .TRUE.
LREAL = F
EDIFF = 1E-9
IBRION = 8
LEPSILON = .TRUE.

My KPOINTS:

Monkhorst-Pack
0
Monkhorst-Pack
6 6 6
0 0 0
<span class='smallblacktext'>[ Edited ]</span>

anyone can help?

I have the same problem. who can help?

I have a question about how you add the stress to your system,Do you set the stress by the PSTRRESS or others ?

Waiting for your reply .

Actually, I use another method rather than PSTRESS. This can control any strain in any direction.

Any reply?

ISMEAR = -5 should use G-center in the POSCAR not Monkhorst-Pack .
Second : should improve ENCUT MUCH HIGHER than default value

Can you tell me how you solved your problem?
Thanks!

the same question. any reply?

The sign is matter of definition. You can keep the sign of all components of the piezoelectric tensor or change all of them.
The calculation of the tetragonal PbTiO3 gives this:
[a] e33=4.49C/m3, e31=1.92C/m2, e15=6.17C/m2
e33=4.39C/m2, e31=1.91C/m2, e15=6.74C/m2
in good agreement with
[c] e33=4.41C/m2, e31=2.06C/m2, e15=6.63C/m2
All parameters chosen as in [c]=PRL 95(2005)037601
[a]= 111 unit cell (666 KP), = 222 supercell (333KP)

Dear Admin,
I want to known the INCAR you used for the calculations of piezoelectric tensor of PbTiO3.

Thanks.