**Acknowledgements**

stretching vibrations in ice I (Ih and XI), the effect of the short-range intermolecular coupling

**Figure 18.** Polarization dependence of Raman spectra at about 60 K in the stretching mode range. (a) Ice-Ih and (b) ice-XI. Scattering geometries are a( , )b. (c) Displacement pattern of stretching mode corresponding to band 1,2 and 3. Only

Fig.18 Polarization dependence of Raman spectra at about 60 K in the stretching mode range. (a) ice Ih and (b) ice XI. Scattering geometr**y is** a( , )b. **(c) Displacement pattern of stretching mode corresponding to band 1,2 and 3. Only the depolarized spectra of band 1 significantly increase** 

Lattice vibrations that carry an electric dipole moment (polar phonons) have radically different long-wavelength properties from nonpolar vibrations. Soft modes in ferroelectric crystals are the typical polar modes. In this chapter, characteristics of soft modes and Raman spectra of

In section 2, general properties of polar modes are given. In section 3, the physical meaning of the susceptibility *χ<sup>Q</sup>* (*ω*) such as the damped-harmonic-oscillator (DHO) and the Debye-type relaxation, which are often used in the analysis of the overdamped soft mode Raman spectra,

In section 4, the difficulty in discriminating between the displacive-type and the order– disorder-type phase transition is shown in the case of KDP. Particularly, the analysis of the overdamped soft mode spectra using an arbitrary susceptibility could be very ambiguous.

In section 5, the peculiar nature of the Raman spectra related to the ferroelectric transition of the isotope exchanged ferroelectric SrTiO3 (STO18) was discussed. From the spectra with

a result of the freezing of the Slater mode. Therefore, the ferroelectric phase transition of STO18

*<sup>p</sup>*), it was shown that the spontaneous polarization *P*

<sup>→</sup> is not

8

was discussed in terms of the proposed generalized form of susceptibility (GVWF).

is dominant than the long-range interaction produced by the proton ordering [50].

polar modes were described mainly based on our experimental results.

**7. Summary and conclusions**

the depolarized spectra of band 1 significantly increase in ice-XI.

**in ice-XI.**

Fig.18 (New)

28 Ferroelectric Materials – Synthesis and Characterization

various propagation directions (*K*¯

is *not* an ideal soft mode type quantum phase transition.

The author thanks Yasunari Takagi for the collaboration during the analysis of the Raman spectra of KDP and the generalization of the susceptibility. He also thanks Kohji Abe for his long-term collaboration and valuable discussions during the studies on STO18 and ice-XI. We wish to thank Prof. Mitsuru Ito of Tokyo Institute of Technology for providing the high-quality sample of STO18. The experiments were supported by the enthusiastic collaboration of a number of graduate students in UEC.
