Inconsistency between Elastic Moduli Tensor Obtained from Theory and from VASP (IBRION=6)

[Nishat Tasnim Hiramony]

Dear users and developers,

I obtained the elastic tensor for a material using IBRION=6. The obtained total elastic moduli (kBar) is as follows:

TOTAL ELASTIC MODULI (kBar)
Direction XX YY ZZ XY YZ ZX
--------------------------------------------------------------------------------
XX 228.6477 83.8015 0.1557 0.0060 1.6150 -0.0357
YY 83.8015 228.5368 0.1111 -0.0005 -1.5993 0.0633
ZZ 0.1557 0.1111 -0.2190 0.0280 -0.0101 -0.0598
XY 0.0060 -0.0005 0.0280 72.1719 -0.0181 1.7111
YZ 1.6150 -1.5993 -0.0101 -0.0181 -4.7055 0.1320
ZX -0.0357 0.0633 -0.0598 1.7111 0.1320 -4.6553

My material is a hexagonal crystal and hence, C66 should be equal to ((C11-C12)/2) but that does not seem to be the case. Any suggestions as to why this inconsistency exists? I have calculated the elastic moduli for other 2D materials as well and the C66 obtained from (C11-C12)/2 seems to make more sense to me than the one obtained via IBRION=6. I would like to mention that my material is 2D and hence there is a vacuum length of around 20 Å along the z-axis.

[pedro_melo]

Dear Nishat Tasnim Hiramony,

Would it be possible for you to upload here the input files and an OUTCAR for the job which is giving these results?

Kind regards,
Pedro Melo

[Nishat Tasnim Hiramony]

Dear Pedro,

Unfortunately, I can't do that. However, I noted from two different papers that (C11-C12)/2 calculated by me using VASP (IBRION=6) agrees very well with the reported C66. But the C66 obtained by me using VASP doesn't agree at all with the reported C66.

I also calculated C_ij using another open-source code and the C66 obtained from there also agrees very well with (C11-C12)/2 obtained from IBRION=6 in VASP. I would've used that open-source code for my novel material as well but for some reason, I can't get it to converge there. Therefore, I've decided to trust (C11-C12)/2 from VASP as the actual C66 for my hexagonal lattice monolayer.

Thanks and regards.

[juergen.furthmueller]

Dear Nishat Tasnim Hiramony,

It seems there is no real problem: The only problem is just the way the elastic tensor is printed in OUTCAR!
The 66 component is the "XYXY" component printed in ROW 4 / COLUMN 4 (with a value of 72.1719 which is
not so far away from (228.6477-83.8015)/2=72.4231 ; the remaining error is numerical noise in the stresses)!
The wrong output order is something that needed to be fixed; 4 = YZ , 5 = ZX , 6 = XY in correct notation, so
the somewhat weired and unusual/wrong output order of the matrix components is currently:

C11 C12 C13 C16 C14 C15
C12 C22 C23 C26 C24 C25
C13 C23 C33 C36 C34 C35
C16 C26 C36 C66 C46 C56
C14 C24 C34 C46 C44 C45
C15 C25 C35 C56 C45 C55

Best regards.
Jürgen Furthmüller