Position and electric field dependent local lattice strain detected by nanobeam x-ray diffraction on a relaxor ferroelectric single crystal

Under a static electric field, we present the scanning nanobeam x-ray diffraction of a relaxor ferroelectric single crystal. The x-ray intensity distributions of a Bragg peak in reciprocal space diffracted from local volumes on the surface of a $0.7\mathrm{Pb}\left({\mathrm{Mg}}_{1/3}{\mathrm{Nb}}_{2/3}\right){\mathrm{O}}_3-0.3\mathrm{PbTi}{\mathrm{O}}_3$ (PMN-30PT) single crystal show position and electric field dependence. While the spatially averaged intensity distribution has a single peak corresponding to the average crystal structure, intensity distributions from each local volume have several strong sharp peaks and a weak broad peak, and show strong position dependence as the translation symmetry is broken in nano- to microscale. A static local lattice strain with spatially valuable lattice constants and nanodomains is responsible for peak splitting and heterogeneous crystal structure. The locally strained lattice exhibits a significant tensile lattice strain caused by an electric field, which is compatible with its large piezoelectric constant of approximately $2\times {10}^3\mathrm{pC}/\mathrm{N}$. When the electric field surpasses the coercive field of 3 kV/cm, polarization switching causes a substantial shear lattice strain with intensity redistribution. Position dependence can also be seen in the piezoelectric constants and coercive fields calculated from x-ray diffraction data for each local location. The standard deviation of the local lattice strain distribution is $3\times {10}^{-3}$ regardless of the electric field, which is greater than the piezoelectric lattice strain of $1\times {10}^{-3}$ caused by an electric field of 8 kV/cm. The enormous electric field induced lattice strain and fatigue-free polarization switching are enabled and facilitated by the nano- to microscale heterogeneous crystal structure with widely and continuously distributed local lattice strain.

Figure 1

Experimental layout of the scanning nanobeam XRD of PMN-30PT under a static electric field. The position and electric field dependence of the 002 Bragg intensity distribution from each local volume were measured.

Figure 2

X-ray intensity distributions of (a) unsplit and (b) split Bragg peaks of a whole crystal of PMN-30PT measured using unfocused x rays and a cylindrical imaging plate. Vertical and horizontal axes are parallel to the cylindrical and 2θ axes, respectively. One pixel size is 0.03° in 2θ which corresponds to about $0.01{\AA }^{-1}$ in $Q=4\pi sin\left(\theta \right)/\lambda$. (c) The average rhombohedral crystal structure model of PMN-30PT with atomic displacement ellipsoids at 50% probability level. The atom labeled $B$ is chemically disordered Mg, Nb, and Ti.

Figure 3

Position ($z$) dependence of x-ray intensity distributions of 002 Bragg peak of PMN-30PT in the $Q_{\mathrm{h}}{Q}_{\mathrm{v}}$ reciprocal space under static electric fields of (a) $E=-8$ and (b) 0 kV/cm. The average intensity distributions obtained by averaging the 21 intensity distributions through $z=0-10\mu \mathrm{m}$ are also shown at the bottom.

Figure 4

Position ($z$) dependence of (a) $Q_{\mathrm{h}}$ and (b) $Q_{\mathrm{v}}$ one-dimensional 002 Bragg profiles of PMN-30PT at $E=0\mathrm{kV}/\mathrm{cm}$ through the intensity maximum points. The average intensity profiles obtained by averaging the 21 intensity distributions through $z=0-10\mu \mathrm{m}$ are also shown at the bottom.

Figure 5

Position ($z$) dependence of (a) shear local lattice strain $s_{\mathrm{h}}\left(z,E\right)$ and (b) tensile local lattice strain $s_{\mathrm{v}}\left(z,E\right)$ of the (002) lattice plane of PMN-30PT at $E=-8$, −4, and 0 kV/cm.

Figure 6

Position ($z$) dependence of (a), (c) $Q_{\mathrm{h}}$ and (b), (d) $Q_{\mathrm{v}}$ one-dimensional 004 Bragg profiles through the intensity maximum points measured for another PMN-30PT before (a), (b) and after (c), (d) coating with Au electrodes using the shorter wavelength x ray to reduce surface effects.

Figure 7

Electric field ($E$) dependence of x-ray intensity distributions of 002 Bragg peak of PMN-30PT in the $Q_{\mathrm{h}}{Q}_{\mathrm{v}}$ reciprocal space at (a) $z=0$ and (b) 2.5 μm.

Figure 8

Electric field ($E$) dependences of (a) $Q_{\mathrm{h}}$ and (b) $Q_{\mathrm{v}}$ one-dimensional 002 Bragg profiles of PMN-30PT at $z=0\mu \mathrm{m}$ through the intensity maximum points.

Figure 9

Schematic drawing of (a) the average structure of the rhombohedral lattice and (b) the heterogeneous structure of the polar nanodomains when the electric field $E$ along [001] is smaller (left) and larger (right) than the coercive field $E_{\mathrm{c}}(>0)$. E and P vectors show electric field and polarization, respectively. The rhombohedral lattice viewed along [100] is drawn by solid lines in (a), deformed to a monoclinic lattice under the electric field. Pb(1) and Pb(2) atoms in the rhombohedral structure are drawn by solid and open circles in (a), respectively. Polar nanodomains drawn by circles in (b) have polarizations slightly different in magnitude and orientation with each other.

Figure 10

Electric field ($E$) dependences of (a) shear local lattice strain $s_{\mathrm{h}}\left(z,E\right)$ and (b) tensile local lattice strain $s_{\mathrm{v}}\left(z,E\right)$ of the (002) lattice plane of PMN-30PT at $z=0$, 5.0, and 10 μm. The black and gray arrows indicate directions of the forward and backward processes, respectively.