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hmdan

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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.

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 )

Is the following expression of Ec that I obtained logical and acceptable ? (n=1)

such that I followed the following steps to get the result

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 )

Is the following expression of Ec that I obtained logical and acceptable ? (n=1)

such that I followed the following steps to get the result