Phase coexistence and Landau expansion parameters for a 0.70Pb(Mg1/3Nb2/3)O3−0.30PbTiO3 single crystal

Multidomain relaxor-based ferroelectric single crystals $(1\text{\ensuremath{-}}x)\mathrm{Pb}(\mathrm{M}{\mathrm{g}}_{1/3}\mathrm{N}{\mathrm{b}}_{2/3}){\mathrm{O}}_{3}\text{\ensuremath{-}}x\mathrm{PbTi}{\mathrm{O}}_{3}$ (PMN-PT) have extraordinarily large electromechanical properties, but the origin of their giant piezoelectric properties is still not well understood. The Landau-like phenomenological theory is a feasible tool to study domain structures and their correlation with piezoelectric effects, but so far no expansion coefficients have been measured due to the phase mixture complication involved. In this work, the Landau free-energy expansion parameters for $0.70\mathrm{Pb}(\mathrm{M}{\mathrm{g}}_{1/3}\mathrm{N}{\mathrm{b}}_{2/3}){\mathrm{O}}_{3}\text{\ensuremath{-}}0.30\mathrm{PbTi}{\mathrm{O}}_{3}$ (PMN-0.30PT) single crystal were determined from the temperature-dependent polarization-electric field $(P\text{\ensuremath{-}}E)$ hysteresis loops along ${[001]}_{\mathrm{C}}$ and ${[011]}_{\mathrm{C}}$ directions, and the rhombohedral $(R)$ to tetragonal $(T)$ phase-transition temperature. Using the obtained parameters, ferroelectric and dielectric properties were quantitatively calculated and compared with experiments. Good agreement was achieved in the temperature regions of $T$ and $R$ phases, but deviations were found in the cubic-phase temperature region since the contribution of polar nanoregions was not considered. In the phase-coexistence region from 73 to $93{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{\circ}}\mathrm{C}$, the polarization and dielectric constant can be quantitatively explained with the volume fractions of the coexisting $R$ and $T$ phases predicted by the canonical distribution. These obtained parameters can help theoretical studies and simulations of these relaxor-based ferroelectric single crystals to reveal the correlation between domain microstructures and the origin of giant electromechanical properties of multidomain PMN-PT single crystals.