Fragile phase stability in $(1-x)\mathrm{Pb}\left({\mathrm{Mg}}_{1∕3}{\mathrm{Nb}}_{2∕3}{\mathrm{O}}_3\right)\text{−}x\mathrm{Pb}\mathrm{Ti}{\mathrm{O}}_3$ crystals: A comparison of [001] and [110] field-cooled phase diagrams

Phase diagrams of [001] and [110] field-cooled (FC) $(1-x)\mathrm{Pb}\left({\mathrm{Mg}}_{1∕3}{\mathrm{Nb}}_{2∕3}{\mathrm{O}}_3\right)\text{−}x\mathrm{Pb}\mathrm{Ti}{\mathrm{O}}_3$ or PMN-$x\mathrm{PT}$ $(0.15⩽x⩽0.38)$ crystals have been constructed, based on high-resolution x-ray diffraction data. Comparisons reveal several interesting findings. First, a region of abnormal thermal expansion $(c\ne a)$ above the dielectric maximum was found, whose stability range extended to higher temperatures on application of electric field $\left(E\right)$. Second, the rhombohedral $\left(R\right)$ phase of the zero-field-cooled (ZFC) state was replaced by monoclinic $M_A$ in the [001] FC diagram, but with monoclinic $M_B$ in the [110] FC. Third, the monoclinic $M_C$ phase in the ZFC and [001] FC diagram was replaced by an orthorhombic $\left(O\right)$ phase in the [110] FC diagram. Finally, in the [001] FC diagram, the phase boundary between tetragonal $\left(T\right)$ and $M_A$ phases was extended to lower PT content $(x=0.25)$; whereas in the [110] FC diagram, this extended region was entirely replaced by the $O$ phase. These results clearly demonstrate that the phase stability of PMN-$x\mathrm{PT}$ crystals is quite fragile—depending not only on modest changes in $E$, but also on the direction along which $E$ is applied.

Figure 1

(a) Rotation of polarization vectors in monoclinic perovskite unit cells. The thick lines represent the paths followed by the end of the polarization vector in the $M_A$ phase where the polarization rotates in a plane between rhombohedral $\left(R\right)$ and tetragonal $\left(T\right)$, in the $M_B$ phase where the polarization rotates between $R$ and orthorhombic $\left(O\right)$ phases, and in the $M_C$ phase where the polarization rotates between $O$ and $T$ phases. The $M_A$, $M_B$, and $M_C$ notation is adopted following Vanderbilt and Cohen (Ref. 18). (b) Polarization vectors of the rhombohedral $\left(R\right)$ and monoclinic $M_A$ $\left(Cm\right)$ phases, represented with the same monoclinic angle $\beta$ in the $\mathit{HHL}$ zone of reciprocal space. The $R$ unit cell can be expressed in terms of a monoclinic one by $a_m=2a_r\cos (\alpha ∕2)$, $b_m=2a_r\sin (\alpha ∕2)$, $a_m=a_r$, $\cos \left(\beta \right)=[1-2{\sin }^2(\alpha ∕2)]∕\cos (\alpha ∕2)$, where $a_r$ and $\alpha$ are the $R3m$ cell parameters.

Figure 2

Modified phase diagrams of (a) [001] and (b) [110] electric-field-cooled PMN-$x\mathrm{PT}$ crystals. The dotted lines and open square signs were based on prior studies by Noheda et al. (Ref. 14). The bracketed italic $R$ and $M_C$ represent the rhombohedral and monoclinic phases of the zero-field-cooled condition. The solid squares represent the temperature of the dielectric maximum $\left(T_M\right)$. The solid circles represent the temperature of the phase transition in the FC condition. The $C^{\prime }$ phase below the upper dashed curve was determined by a region of abnormal thermal expansion. Solid curves drawn through these data point are only to guide the eyes.

Figure 3

(Color online) Lattice parameters as a function of temperature for [001] field-cooled PMN-$x\mathrm{PT}$ crystals: (a) PMN-0.15PT, $E=0.5\mathrm{kV}∕\mathrm{cm}$; (b) PMN-0.24PT, $E=0.5\mathrm{kV}∕\mathrm{cm}$; (c) PMN-0.27PT, $E=0.5\mathrm{kV}∕\mathrm{cm}$; and (d) PMN-0.28PT under $E=0.25\mathrm{kV}∕\mathrm{cm}$.

Figure 4

(Color online) Mesh scans taken about the pseudocubic (002), (220), and (200) reflections for [001] field-cooled PMN-$x\mathrm{PT}$ crystals: (a) PMN-0.15PT, $E=0.5\mathrm{kV}∕\mathrm{cm}$ at $270\mathrm{K}$; (b) PMN-0.35PT, $E=2\mathrm{kV}∕\mathrm{cm}$ at $300\mathrm{K}$; and (c) PMN-0.38PT, $E=3\mathrm{kV}∕\mathrm{cm}$ at $243\mathrm{K}$.

Figure 5

(Color online) Lattice parameters as a function of temperature for [110] field-cooled PMN-$x\mathrm{PT}$ crystals: (a) PMN-0.15PT, $E=0.5\mathrm{kV}∕\mathrm{cm}$; (b) PMN-0.22PT, $E=2\mathrm{kV}∕\mathrm{cm}$; and (c) PMN-0.28PT, $E=0.25\mathrm{kV}∕\mathrm{cm}$.

Figure 6

(Color online) Mesh scans taken about the pseudocubic (002), (220), and (200) reflections for [110] field-cooled PMN-$x\mathrm{PT}$ crystals: (a) PMN-0.15PT, $E=0.5\mathrm{kV}∕\mathrm{cm}$ at $253\mathrm{K}$; (b) PMN-0.35PT, $E=2\mathrm{kV}∕\mathrm{cm}$ at $300\mathrm{K}$; and (c) PMN-0.38PT, $E=3\mathrm{kV}∕\mathrm{cm}$ at $243\mathrm{K}$.

Figure 7

(Color online) Lattice parameter as a function of temperature derived from the (002) reflection of PMN-0.28PT under different electric field levels applied along (a) $E\Vert \left[001\right]$, and (b) $E\Vert \left[110\right]$.