Crystal stability and the theory of ferroelectricity part II. Piezoelectric crystals

In Part I the dielectric properties of cubic crystals with atoms in special positions were discussed, with particular reference to crystals which become unstable against a transverse optic mode of vibration of long wavelength. These considerations are now extended to crystals of general symmetry, and it is shown that the anomalous temperature dependence of certain dielectric, piezoelectric, and elastic constants in the paraelectric phase of ferroelectric crystals can be described and correlated in a very natural way in terms of crystal stability. A formula relating the dispersion frequency of the anomalous dielectric constant to the spontaneous polarization and the displacements of the atoms in a ferroelectric transition, previously derived for barium titanate, is generalized. The transitions in KH₂PO₄ and in NH₄H₂PO₄, and the ordering of the hydrogen atoms in these crystals, are discussed qualitatively in terms of the stability of normal modes of vibration.