Unexpected Negative Value of d33 Under Biaxial Strain in Wurtzite Structure

Running Abinit Response calculations
1

Dear ABINIT Community,

I am studying the piezoelectric properties of a wurtzite structure. When applying biaxial strain, I observed that the piezoelectric constant d33​ increases with tensile strain up to +4%. However, beyond this point (for strains greater than +4%), d33​ unexpectedly becomes negative.

I have thoroughly checked my calculations:

  • Convergence parameters are well tested.
  • The structures are fully relaxed, with stresses and forces converged to satisfactory levels.
  • Phonon frequencies are verified to ensure no imaginary modes.
  • I also tested with different values of dilatmx (1.01 and 1.05) to ensure robustness in the structural relaxation.
  • I am using the GGA exchange-correlation functional along with norm-conserving pseudopotentials.

Given these considerations, is it normal for d33​ to exhibit such behavior under biaxial tensile strain in a wurtzite structure? Could this result from the physics of the system, or might I be overlooking some numerical or physical aspect?

Any insights or similar experiences would be greatly appreciated.

Thank you in advance!

Best regards,

2

Hello,

Strange indeed. d33 is given as the derivative of the electrical displacement vector, which could be pointing the other way. I imagine you relax each strained structure separately. Is the wurzite distortion inverted somehow for 4%?

You could do calculations for the inverted structure to see if this convention affects the d33.

You could also perform calculations of the Berry phase polarization to get P(strain) and see how it evolves. If it maxes out at 4% then the dfpt is correct, even if the direction of D is still the same.

4% is a lot of strain, so it’s a bit academic, but could be interesting anyway. I imagine you have looked through the literature for other cases of non monotonous dxx?

Keep us posted

Matthieu