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Dear Vasp-Users,

I would like to know whether the "relaxed-ion piezoelectric tensor" PIEZOELECTRIC TENSOR for field in x, y, z in the OUTCAR) as specified in [1] is the _proper_ piezoelectric tensor ( e$_{\alpha \beta \gamma}$ /e$_{\alpha j}$?

Thank you very much for your help

[1] http://cms.mpi.univie.ac.at/vasp/vasp/V ... ensor.html

Hi phenyl

9 years later, I am here asking the same question...

Have you found the answer?

Best wishes
Jacek

This page of the manual explains what exactly is calculated by Vasp.

Hi Martin

Thanks for your reply. Can I clarify with you the following?

According to the manual entry on IBRION=6 , inversion of ionic Hessian matrix and its multiplication with the internal strain tensor are calculated as described in ref 4 (i.e. PhysRevB.72.035105) and the pieozelectric tensor can be calculated using the LEPSILON = TRUE .

However, PhysRevB.72.035105 notes that "there is some subtlety in the definition of the piezoelectric tensors related to the specification of the
energy functional when both fields and strains are present, leading to a distinction between “proper” and “improper” piezoelectric constants."

In LEPSILON tag's manual entry you attached, it is not mentioned how the piezoelectric tensor is calculated; however in theory, as the internal strain tensor is involved in the relaxed-ion piezoelectric tensor, I suppose VASP is using the approach presented in PhysRevB.72.035105. Can I verify with you if this is correct?
Also, as it is not mentioned explicitly that VASP is calculating the "proper" tensors as presented by PhysRevB.72.035105, can I also verify with you that VASP is indeed calculating the "proper" terms instead of the "improper" terms?

Thanks
Yaze

In this reference, the implementation in Vasp is documented in more detail. Unfortunately, you need to confirm for yourself, whether that is equivalent to the reference that you mention.

Thanks Martin!