Features of the incommensurate phase in (formula presented)

The features of the incommensurate phase in (formula presented) which has a simple perovskite structure, have been investigated in the whole incommensurate region of the phase diagram by transmission electron microscopy. The incommensurate phase basically exists in the Ti-content range of (formula presented) though the coherence length of the incommensurate modulation in samples with (formula presented) is very short. In view of its modulated structure, the normal phase of the commensurate phase is not the high-temperature paraelectric phase and its crystal structure involves both the (formula presented) antiferroelectric and ferroelectric displacements. The phase transition from the normal phase to the incommensurate phase then takes place by the introduction of the (formula presented) rotational displacement of the oxygen octahedra. That is, the incommensurate modulation can be identified as the modulation of the rotational angle of the oxygen octahedron, which results in an alternating array of two (formula presented) microdomains, as was proposed in our previous paper [S. Watanabe and Y. Koyama, Phys. Rev. B 63, 134103 (2001)]. The antiphase boundaries of the (formula presented) displacement present in the normal phase may also play the role of a discommensuration with a phase slip of π in the incommensurate phase. In addition to these features as a modulated structure, the slight increase in the periodicity of the incommensurate modulation and the growth of the one-variant region on heating were observed in the incommensurate phase with a long coherence length of about 1 µm. Of these two phenomena, the former increase can be explained as being due to the increase in the size of the (formula presented) microdomain, which would be produced by the decrease in the rotational angle via the spontaneous strain coupled to the angle. Based on this, the size of every incommensurate-variant region should be enlarged as a total. However, only the one-variant region was observed to grow on heating. This suggests that the growth of the one-variant region was due to a thin-film effect; that is, the surface effect. As for the short coherence length of the incommensurate modulation in samples with (formula presented) we discuss its origin in terms of the impurity effect of the substituted Ti ion.