Definition of the spontaneous polarization is not always straightforward. It is determined with respect to a reference structure. The choice of the reference structure is a tricky part and depends on how the polarization manifests itself in an experimental
situation. I would suggest checking those two tutorials to begin with:
Calculation of the response to strain (a piezoelectric coefficient) requires relaxation of atomic positions to be realistic. It also becomes not a trivial analysis, since the polarization changes due to two effects: the volume change as well as atomic
displacements. It seems that the "raw" Berry phase is more suitable for this purpose. Please check the section "Calculation of piezoelectric coefficients" in http://olegrubel.mcmaster.ca/publications/2017/Rubel_SR_2017.pdf
I hope this will help
Oleg
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Oleg Rubel (PhD, PEng) Department of Materials Science and Engineering McMaster University JHE 359, 1280 Main Street West, Hamilton, Ontario L8S 4L8, Canada Email: rub...@mcmaster.ca Tel: +1-905-525-9140, ext. 24094 Web: http://olegrubel.mcmaster.ca
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