Soft-mode spectroscopy has been long applied to probe lattice dynamic instability of the second order ferroelectric phase transition, but it has some practical limitations. The limitations of soft-mode spectroscopy can be mostly resolved by hard-mode spectroscopy. Hard-mode spectroscopy is sensitive for detection of phonon frequency shift corresponding to phase transition. Phase transition is characterized by the relation between the frequency shift of the hard-mode phonon and the order parameter of phase transition.
To find out a relation between macroscopic dielectric response and the hard-mode phonon shift, Slater\'s approach is adopted for lattice dynamics. As a result of simpler calculations, the inverse dielectric susceptibility is rederived to be proportional to the frequency shift of a hard-mode nondegenerate lattice vibration. The dimensional argument reveals that the proportionality constant may be equivalent to the moment of inertia of dipole moment induced by a negligible change in binding energy of ions. This relation of hard-mode frequency shift can be extended to non Curie-Weiss type phase transition.
The lead ytterbium niobate(PYN) based solid solution doped with lead titanate(PT), in which the diffuse first order antiferroelectric phase transition occurs, is analyzed by the hard-mode spectroscopy of a nondegerate $A_{1g}$ mode and degenerate $F_{2g}$ mode. The octahedral ordering energy and the superstructural ordering energy are determined, as corresponding to $T_{HS}$ and $T_{RM}$., by nondegenrate and degenerated modes. The maximum peak temperature $T_M$, at which dielectric constant reaches maximum values, is observed between $T_{HS}$ and $T_{RM}$.. The diffusiveness of phase transition may result from the variations of local stabilization energies and structural frustrations with this energy level. The phase transition of PYN doped with 6% PT is well analyzed to the hard-mode relation. The proportionality constant of 0.94PYN-0.06PT is determined to be $1.6×10^{-7}cm^{-1}$ by Raman spectroscopic and dielectric measurements.
The 0.80PYN-0.20PT system shows the dielectric response with a broad frequency dispersion, corresponding to relaxor ferroelectrics. From the data by Vogel-Fulcher relation, we could determine the paramenter value as $T_G = 302.4K$, $E_a = 20.2meV$ and $f_0 = 1.9GHz$. The $A_{1g}$ mode of relaxor PYN-PT shows a strong asymmetry possibly due to otcahedral phase coexistence. The asymmetric band shape is analyzed in terms of a paraelectric matrix and a polar order region(POR). The volume fraction of POR is estimated to be about 55-65% in the 0.8PYN-0.2PT system and does not vary with applied electric field and temperature. Raman Optical Activitiy of the $A_1g$ mode is observed to change with temperature above $T_G$, and it may be ascribed to the orientational ordering of these polar clusters in the relaxor ferroelectrics.
