Coercive field in ferroelectrics perovskites

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An expression of coercive field
Hi community, I am trying to find an expression of coercive field in lithium niobate crystals on the context of interaction energy, we know that the coercive field in ferroelectrics is the reverse electric field necessary to bring the polarization to zero, in other words and in the case of Lithium niobate which the orientation of the spontaneous polarization Ps is determined by the position of Li+ and Nb5+ ions along the z-axis with respect to the oxygen layers, the coercive field, Ec represents the minimum electric field required to displace Li+ and Nb5+ ions from the configuration of fig. 4.6a, to that of fig. 4.6b.
Screenshot 2024-04-13 011808.png

If we considered that the Nb ion with charge q1 is displaced from its centrosymmetric position by (a/2) - R10 while the Li ion with charge q2 is displaced from its centrosymmetric position by a distance R20 and taking in account that the interaction energy between crystal planes in LiNbO3 is given by the following equation ( a is the distance between two oxygen planes and b is the lattice constant )

Screenshot 2024-05-10 000748.png

Is the following expression of Ec that I obtained logical and acceptable ? (n=1)
Screenshot 2024-05-10 001909.png

such that I followed the following steps to get the result

Screenshot 2024-05-10 004526.png


  • Screenshot 2024-05-10 001909.png
    Screenshot 2024-05-10 001909.png
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