Hi, I had the same doubt once. Think that the cation displaced along the c-axis sits in an energy minimum and stays happily there. Therefore its linear response to AC field is relatively small (at the contrary of the large non-linear ferroelectric response) when the field is along the c-axis. On the opposite, the non centrosymmetric cell has no hysteresis for field on the a-axis but it is easy to distort (polarize), determining a larger dielectric constant.

Marco Asa

Thank you for kinds reply clearly !

You mean that if the AC-field is applied for BaTiO3 along the c-axis, the polarization can't respond to AC-field well because the cation stays in the energy minimum site so can not move fast along the c-axis AC field.

As I asked, I expected that the polarization can move like flipping well along the polarization direction if there is the AC field applied for the same direction.

But, it can not happen well..

If the DC-field is applied for BaTiO3 along the c-axis, the hysteresis occurs due to the polarization, but the a-axis can not has the hysteresis because there is little polarization..but, it is easy to distort resulting in a larger dielectric constant if the AC field applied !!

Wow,,,I almost got it..understand the concept..

So, the polarization of the c-axis is stronger, the dielectric constant of the a-axis is also bigger in the applied AC field?

Could I get some references saying about the contents what we discuss if you are available?

Thank you for again

Also is related to the stability of the phase (tetragonal), the non centrocimetry occurs by the movement of the central atom (Ti+4), the polarization occurs in the c-axis because the cell have more "empty" space in that direction. I recomend you some papers:

1. Tazaki, R., Fu, D., Itoh, M., Daimon, M. & Koshihara, S. Y. Lattice distortion under an electric field in BaTiO3 piezoelectric single crystal. J. Phys. Condens. Matter 21, (2009).

2. Liu, Q.-J., Zhang, N.-C., Liu, F.-S., Wang, H.-Y. & Liu, Z.-T. BaTiO3: Energy, geometrical and electronic structure, relationship between optical constant and density from first-principles calculations. Opt. Mater. (Amst). 35, 2629-2637 (2013).

3. Acosta, M. et al. BaTiO 3 -based piezoelectrics: Fundamentals, current status, and perspectives. Appl. Phys. Rev. 4, 041305 (2017).

Williams Marcel Caceres Ferreira

Thank you for great reply !

I should check those papers to understand the relation between the polarization and dielectric constant.

I find more other materials with ferroelectricity also have the higher dielectric constant not along the polarization direction.

Thank you, sir.