Crystalline Pyro-, Piezo- and Ferroelectrics

The discussion of ferroelectricity in liquid crystalline phase is based on the concepts developed for the sohd crystals. Therefore, we have to start from a brief survey of the elementary physics of ferroelectricity in crystals [1,2], 

In Section 7.2.1 we discussed polarization of molecular isotropic liquids. We introduced the equations for dielectric permittivity s and dielectric susceptibility X and wrote the microscopic definition of the polarization vector P as a sum of dipole moments in the unit volume = pNJM (p is density, Np is Avogadro number, M is molecular mass)  

Here Pe is the electric dipole induced by the electric field in a molecule having mean molecular polarizability y. Then we used the Lorentz approximation for the local field acting on a molecule and found corresponding field induced polarization. From that we have obtained the electric susceptibility of the dielectric (Eq. 7.18)  

This formula is very important for the further discussion because it predicts the polarization catastrophe . For small molecular polarizability y, susceptibility x depends linearly on y. However, when y 3/Annv, the denominator of (13.2) tends to zero and diverges. 

Its physical sense is well seen from the equations (7.17) for P and Eioc- For a fixed concentration of molecules and given local field, the polarization should be linear function of y. However, with increasing P, Eioc itself begins to grow and this results in the non-linear, avalanche-like increase of susceptibility. Finally, for small, densely packed molecules n is large) with high polarizability y, would tend to infinity. It means that an infinitesimally low field, even a small fluctuation of a local field, may create a finite polarization. In other words, polarization may appear spontaneously, without any applied field. The appearance of the spontaneous polarization is a necessary (but not sufficient) condition for phenomenon called ferroelectricity. 

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