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

Abstract

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 $0.7\mathrm{Pb}({\mathrm{Mg}}_{1/3}{\mathrm{Nb}}_{2/3}){\mathrm{O}}_{3}\ensuremath{-}0.3\mathrm{PbTi}{\mathrm{O}}_{3}$ (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 $2\ifmmode\times\else\texttimes\fi{}{10}^{3}\phantom{\rule{0.16em}{0ex}}\mathrm{pC}/\mathrm{N}$. 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 $3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ regardless of the electric field, which is greater than the piezoelectric lattice strain of $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ 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.