Ferroelectric domain structures near the morphotorpic phase boundary in the piezoelectric material Pb(Zr$_{1-x}$Ti$_{x})$O$_{3}$

In the simple perovskite oxide Pb(Zr$_{1-x}$Ti$_{x})$O$_{3}$, an\textbf{ }excellent piezoelectric response was obtained in the vicinity of a morphotropic phase boundary (MPB) between the ferroelectric monoclinic (F$_{M})$ and rhombohedral (F$_{R})$ phases. To understand the origin of the excellent response, we have investigated the detailed features of ferroelectric domain structures near the MPB in PZT by transmission electron microscopy. In the F$_{M}$ side of the MPB, as a result, there were two types of domain structures at room temperature. On the other hand, a usual domain structure having the 109\r{ } and 180\r{ } boundaries existed at room temperature in the F$_{R}$ side. The notable feature is that each domain in the F$_{M}$ and F$_{R}$ domain structures near MPB can be identified as an aggregation of nanometer-sized domains with an average size of about 10 nm. Based on this feature, we propose a new concept of an aggregation-type domain structure for ferroelectric domain structures near the MPB.