Unstable point domains in ferroelectrics

It is shown by employing statistical-mechanical considerations that unstable point domains can nucleate in ferroelectrics under the influence of low electric fields under certain conditions. A fixed number of domains are in equilibrium in the given field, but evaporate as soon as the field is removed. The theory predicts a peculiar variation of the dielectric constant under the given conditions. KNbO₃, PbNb₂{O}₆$, and (${NH}₂CH₂COOH)₃{·}H₂SO ₄ (TGS) are used as test cases. It is possible to calculate the critical volume, the critical energy of nucleation, and the wall energy. The wall-energy calculations show that these nucleations are different in character from the thermally stable point domains that nucleate at the sites of the dislocations. Further, it is found that these unstable domains nucleate at the sites of the excess vacancies in ferroelectric crystals. Since such low fields as are required for nucleation exist in crystals even in the absence of the externally applied field on account of the space charges, it follows that some point domains of this type should normally exist in crystals, as has already been found experimentally. Thus, the theory can distinguish between stable point domains and unstable ones, clearing the existing confusion in this respect, and providing the rationale for the existence of both types of point domains.