Roles of ferroelectricity, antiferroelectricity, and rotational displacement in the ferroelectric incommensurate phase of Pb(Zr_1−xTi_x)O₃

Crystallographic features of the ferroelectric incommensurate phase in Pb(Zr_1−xTi_x)O₃ have been investigated by transmission electron microscopy, mainly using x = 0.05 samples obtained by cooling from a high-temperature paraelectric phase under an electric field of 500 V/cm. The present experimental data clearly indicate that the incommensurate and ferroelectric domains coexist independently, and that the incommensurate structure is characterized by not only a periodic-microdomain structure consisting of two M₃ variants, but also a periodic array of antiphase boundaries for the M′₅ antiferroelectric displacement. These observations suggest that the normal structure of the incommensurate structure should be ferroelectric and that the rotational angle of the M₃ rotational displacement can be identified as a modulation mode. In addition, the antiphase boundary of the M′₅ antiferroelectric displacement may play the role of discommensuration with a phase slip of Π.