*5.2.3. Why the soft mode is not the slater mode ?*

The reason why *P* <sup>→</sup> is not along the cubic axes (as expected from the softening of the Slater mode) but along the tetragonal axes would be closely related to the existence of the rhombo‐ hedral (parallel to [111]c) nano-scale clusters in STO18 ,which were found in the NMR experi‐ ment by Blinc et al. [40]. They revealed that below 70 K rhombohedral polar clusters are formed in the tetragonal matrix. These clusters subsequently grow in concentration, freeze out, and percolate, leading to an inhomogeneous ferroelectric state below *Tc*. This shows that the elusive ferroelectric transition in STO-18 is indeed connected with local symmetry lowering and implies the existence of an order–disorder component in addition to the displacive soft mode one.

Referring to this result we have shown in a recent paper [37] that the dipole interaction between the rhombohedral polar clusters is the very probable reason for the formation of *P* <sup>→</sup> // <sup>110</sup> *<sup>c</sup>*. The calculation shows that a pair of dipoles located in the same X-Y plane gives the strongest attractive interaction than any other possible pair interaction. The unification of such a pair of rhombohedral polar clusters generates *P* <sup>→</sup> parallel *not* to the cubic axes but to the tetragonal axes. Spontaneous polarization *P* <sup>→</sup> generated by this process would percolate and grow to the macroscopic ferroelectric domains.

Thus, the dipole interaction model is consistent with various peculiarities observed in the Raman spectra [36], such as the inhomogeneity, the imperfect softening, and the appearance of the relaxational mode near *Tc*. The origin of the relaxational mode observed near *Tc* would be the increase of the orientational fluctuations of *P* <sup>→</sup> in the X-Y plane. Its coupling with the soft mode propagating along the Z axis would suppress the perfect softening.

Finally, we admit that the question "why the isotope substitution of O16 by O18 makes the ferroelectric transition possible in SrTiO3" has not yet been fully solved.
