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9,10] The third group of ferroelectrics consists of ionic crystals with crystal structures closely related to the perovskite structure. Examples are BaTi0 3 , SrTi03, KNb03 and PbTi03. The perovskite structure is one of the simpler structures to exhibit ferroelectricity. 5 shows the structure of BaTi0 3. In the unpolarized state the crystal is cubic with Ba 2+ ions at the cube corners, 0 2 - ions at the centers of the cube faces, and Ti 4 + ions at the cube centers. Below the Curie temperature of 393 K the structure is first deformed to a tetragonal structure, the positive ions being displaced relative to the negative ones along a [100] direction, thereby developing a polarization in this direction.
2b]. 1 A physical meaningful dielectric constant is also measured in the paraelectric state as T--+To or on single domain crystals. 3]. First there is Rochelle salt, NaK(C4H406) ·4H 20, and related isomorphous salts. Rochelle salt is a complicated crystal; for a summary of properties see Mueller and Mason [304]. The second group of ferroelectric crystals is the KDP group, where KDP stands for KD 2P0 4. From an analysis of the structure of KH 2P0 4 it appears that the P0 4 groups form tetrahedrons with the four oxygens at the corners and the phosphorus at the center.
U (~), v (~) are the displacements of ion cores and shells, respectively, zeo is the charge of the cation; xeo and yeO are the charges of the core and shell of the anion, and (x + y)eo = -zeo is the charge of the anion. S, S' and T, T' are effective core-shell and corecore force constants, and k is the isotropic core-shell force constant of the anion. By using the method of long waves and the procedure described in [Ref. 6, Sect. 1 J, calculate the piezoelectric constant e and the effective charge z ..