Intermediate ferroelectric orthorhombic and monoclinic $M_B$ phases in [110] electric-field-cooled $\mathrm{Pb}\left({\mathrm{Mg}}_{1∕3}{\mathrm{Nb}}_{2∕3}\right){\mathrm{O}}_3$–30%$\mathrm{Pb}\mathrm{Ti}{\mathrm{O}}_3$ crystals

Structural phase transformations of [110] electric-field-cooled $\mathrm{Pb}\left({\mathrm{Mg}}_{1∕3}{\mathrm{Nb}}_{2∕3}\right){\mathrm{O}}_3$-30%$\mathrm{Pb}\mathrm{Ti}{\mathrm{O}}_3$ (PMN-30%PT) crystals have been performed by x-ray diffraction. A phase sequence of cubic $\left(C\right)\to$ tetragonal $\left(T\right)\to$ orthorhombic $\left(O\right)\to$ monoclinic $\left(M_{\mathit{B}}\right)$ was found on field cooling (FC); and a rhombohedral $\left(R\right)\to M_B\to O$ sequence was observed with increasing field, beginning from the zero-field-cooled condition at room temperature. The application of the [110] electric field induced a dramatic change in the phase sequence in the FC condition, compared to the corresponding data for PMN-30%PT crystals in a [001] field, which shows that the phase sequence in the FC condition is altered by the crystallographic direction along which a modest electric field $\left(E\right)$ is applied. Only when $E$ is applied along [110] are intermediate $O$ and $M_B$ phases observed.

Figure 1

$E\text{−}T$ phase diagram. Top panel (a) is PMN-30%PT in the FC condition by Bai (Ref. 15) with $E$ along [001]; bottom panel (b) is PMN-30%PT in the FC condition with $E$ along [110]. Arrows indicate the sequence of phase transition in the FC condition. Dotted lines indicate the ZFC condition, and solid lines indicate the FC condition.

Figure 2

(Color online) Mesh scans of (002), (200), (2$\overline{2}$0), and (220) of PMN-30%PT with $E=1\mathrm{kV}∕\mathrm{cm}$ applied along [110] at 375 K in the FC condition.

Figure 3

(Color online) Mesh scans of (002), (200), (2$\overline{2}$0), and (220) of PMN-30%PT with $E=1\mathrm{kV}∕\mathrm{cm}$ applied along [110] at 325 K in the FC condition.

Figure 4

(Color online) Mesh scans of (002), (200),(2$\overline{2}$0), and (220) of PMN-30%PT with $E=1\mathrm{kV}∕\mathrm{cm}$ applied along [110] at 298 K in the FC condition.

Figure 5

Temperature dependence of (a) lattice constants for PMN-30%PT with $E=1\mathrm{kV}∕\mathrm{cm}$ along [110], in which the lattice parameters $a_{\mathrm{O}}∕\sqrt{2},b_{\mathrm{O}}∕\sqrt{2}$, and $c_{\mathrm{O}}$ and $c_{M_B},a_{M_B}∕\sqrt{2}$, and $b_{M_B}∕\sqrt{2}$ are plotted, and (b) dielectric behavior under various levels of electric field at $f=1\mathrm{kHz}$ in the FC condition.

Figure 6

Schematic of tetragonal, orthorhombic, and monoclinic $M_C$ phases in PMN-30% PT with $E$ along [110]. Arrows indicate the polar vector. Panel (a) is twin domains developed in the tetragonal phase; only two polarizations are constrained within the (001) plane. Panel (b) shows the single domain developed in the orthorhombic phase. Panel (c) indicates the domains developed in the $M_B∕M_A$ phase, in which the polarization vectors are constrained with the (110) plane.

Figure 7

(Color online) (002) mesh scans at 298 K with increasing fields of (a) $0\mathrm{kV}∕\mathrm{cm}$, (b) $2\mathrm{kV}∕\mathrm{cm}$, (c) $10\mathrm{kV}∕\mathrm{cm}$, and (d) after removal of field in the poled condition.

Figure 8

Electric-field dependence of the lattice parameters at 298 K beginning from the ZFC condition, where lattice parameters $a_{\left(220\right)}∕\sqrt{2},b_{\left(2\overline{2}0\right)}∕\sqrt{2}$, and $c_{\left(002\right)}$ are plotted. Solid lines represent data obtained on field increasing; dotted lines represent data obtained on field decreasing. At $E=0\mathrm{kV}∕\mathrm{cm},c_{\left(002\right)}=a_R$, and once $E$ is applied, $a_{\left(220\right)}∕\sqrt{2},b_{\left(2\overline{2}0\right)}∕\sqrt{2}$, and $c_{\left(002\right)}$ correspond to $a_{M_B}∕\sqrt{2},b_{M_B}∕\sqrt{2}$, and $c_{M_B}$ in the $M_B$ phase and to $a_{\mathrm{O}}∕\sqrt{2},b_{\mathrm{O}}∕\sqrt{2}$, and $c_{\mathrm{O}}$ in the $O$ phase, respectively.