**6.3. Raman spectra of stretching modes in Ice-XI**

Interpretation of Raman and infrared spectra of ice in the OH stretch region above 2800 cm-1 has been also a topic of long-standing discussion. The lowest Raman peak and the central IR peak were assigned to in-phase symmetric (*ν*1) and antisymmetric stretch (*ν*3) vibrations of the two O-H bonds in a single water molecule, respectively (See Fig.18(c)). Whalley summar‐ ized the spectral features in ice-Ih and assigned the four stretching bands in terms of LO/TO splitting of *ν*3 vibrations as follows [49]:

band 1 3083 cm−1 = *ν*1 (in-phase)

band 2 3209 cm−1 = *ν*3 (TO)

geometries and polarizations, no frequency shift is observed. This means that the shift of the

axis. In other words, the modes at 237 cm−1 should be assigned as the LO modes while the mode at 231 cm−1, of which displacements are perpendicular to *b* is the corresponding TO mode. When the effect of the local depolarization electric field is larger than the crystal anisotropy, the LO/TO character dominates the symmetry of modes. Therefore, it is more appropriate to assign the peak at 237 cm−1 as the LO mode with mixed symmetry of A1/B2 and the peak at 231 cm−1 as the TO mode with mixed symmetry of A2/B1. Contribution of B2 component to LO was

→

*p* has a component parallel to the *b*-

. (a)

→ *<sup>p</sup>*//*c* .

*<sup>p</sup>*//*b* and (b) *K*

7

peak from 231 cm−1 to 237 cm−1 takes place only when *K*

26 Ferroelectric Materials – Synthesis and Characterization

confirmed in the a(b,c)c spectra shown in Fig.7 of ref.[46].

Fig.17 Dependence of the Raman spectra on the phonon propagation direction *K <sup>p</sup>*

Very strong peak at 237 cm-1 is observed only in (cc) spectrum in (a) corresponding to the A1 component of LO.

The present result is the first experimental confirmation of the LO/TO splitting in ice. The 6±0.5 cm-1 of the LO/TO splitting agrees with 4cm−1 obtained in the IR reflection spectra of ice-Ih by Klug et al*.* [47] and also close to 10 cm−1 of the calculation by Marchi et al*.* [48]. Another feature of the LO (A1/B2) mode at 237 cm−1 is the fact that its intensity is strong only in the spectra with polarization (cc). From the selection rule, the A1 mode is active

**Figure 17.** Dependence of the Raman spectra on the phonon propagation direction *K*

**Very strong peak at 237 cm-1 is observed only in (cc) spectrum in (a)** 

→

*<sup>p</sup>* . (a) *K* →

Fig.17

*K* // *b p*

and (b) *<sup>K</sup>* // *<sup>c</sup> <sup>p</sup>*

**corresponding to the A1 component of LO.**

band 3 3323 cm−1 = *ν*3 (LO)

band 4 3420 cm−1 = *ν*1 (out-of-phase)

Figure 18 shows the polarized Raman spectra in the range 2900–3600 cm−1 of single crystal of ice-Ih and ice-XI at about 60 K. Spectra are composed of four bands and look similar for both phases except for the significant intensity increase in the depolarized spectra of the band 1 such as a(b, c)b [50].

In order to see whether Whalley's assignments are valid in ice-XI or not, spectra for different propagation vectors *K* → *<sup>p</sup>* were measured. Observed spectra for *K* → *<sup>p</sup>*//*c* and //b are, however, almost identical to the spectra for *K* → *<sup>p</sup>* ⊥*c* shown in Fig. 18(b). The frequency of the band 3 (3327 cm−1) does not vary in c(, )*c*¯ or in b(, )*b* ¯. Furthermore, as shown in Fig.13 of ref. [50], the polarized Raman spectra (aa) and (bb) have the same intensity as that of (cc). This means that, in contrast to the translational mode case, Raman intensity of the stretching modes is not affected by the long-range electric field produced by the transformation to ice-XI. Thus, from the present work we could not find any direct evidence of band 3 being the *ν*3 (LO) mode. We assign the band 2 and 3 simply as the in-phase and out-of-phase of *ν*<sup>3</sup> mode. Although the lowest frequency band 1 is no doubt the in-phase symmetric stretching mode *ν*1, the origin of the highest frequency weak band *ν*4 near 3400 cm−1 is still not certain. Present results show that for the Fig.18 (New)

8

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

stretching vibrations in ice I (Ih and XI), the effect of the short-range intermolecular coupling is dominant than the long-range interaction produced by the proton ordering [50]. 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** 

### **7. Summary and conclusions in ice-XI.**

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 polar modes were described mainly based on our experimental results. 

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

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 various propagation directions (*K*¯ *<sup>p</sup>*), it was shown that the spontaneous polarization *P* <sup>→</sup> is not a result of the freezing of the Slater mode. Therefore, the ferroelectric phase transition of STO18 is *not* an ideal soft mode type quantum phase transition.

In section 6, the first clear evidence of the LO/TO splitting in the Raman spectra of the translational mode in the proton-ordered (ferroelectric) ice-XI was given.

To conclude, the following points must be taken into account for the correct interpretation of Raman spectra in ferroelectric crystals:

