Contribution of intermediate submicrometer structures to physical properties nearTcin Pb(Zn1/3Nb2/3)O3-9%PbTiO3

Abstract

Complementary use of coherent x-ray diffraction (CXD), x-ray diffuse scattering, conventional x-ray diffraction techniques, and dielectric measurements has enabled us to investigate Pb(Zn${}_{1/3}$Nb${}_{2/3}$)-9%PbTiO${}_{3}$ with a multiple-length-scale approach from the macroscale (lattice constants, bulk averaged) and microscale to the nanoscale [polar nanoregions (PNRs)] and discuss the contribution of each scale to the dielectric permittivity. We estimate that diffuse scattering mainly originates from intra-PNR dynamics, which contributes to ``ionic'' polarization and results in high-frequency permittivity. Meanwhile, the appearance of intermediate submicrometer (sub-$\ensuremath{\mu}$m) structures observed by CXD is consistent with the appearance of low-frequency dielectric relaxation. The sub-$\ensuremath{\mu}$m structures exhibit large fluctuations at ${T}_{\mathrm{c}}$. This is also consistent with previously reported results obtained by x-ray intensity fluctuation spectroscopy and should give a lower limit for the low-frequency dielectric dispersion. We have suggested that the fluctuation is due to the competition between the growth of sub-$\ensuremath{\mu}$m structures and the appearance of the macroscopic tetragonal-ferroelectric phase. Since the present CXD mainly detected the strain field spreading throughout the crystal, we here demonstrate that the sub-$\ensuremath{\mu}$m structures are due to networks among PNRs connected by the strain field.