Landau expansion parameters and the O-T phase transition of a 0.64Pb(Mg1/3Nb2/3)O3−0.36PbTiO3 single crystal

Landau free-energy expansion parameters for $0.64\mathrm{Pb}(\mathrm{M}{\mathrm{g}}_1/3\mathrm{N}{\mathrm{b}}_2/3){\mathrm{O}}₃\ensuremath{-}0.36\mathrm{PbTi}{\mathrm{O}}₃$ single crystal were determined from the temperature-dependent polarization-electric field ($P\ensuremath{-}E$) hysteresis loops along ${[001]}_C$, the temperature-dependent dielectric constant ${\ensuremath{\varepsilon}}₁₁$, and the electric-field-induced tetragonal-rhombohedral phase-transition temperature. Using these obtained parameters, the phase-transition behavior, polarization, dielectric, and piezoelectric constants can all be calculated, which showed good agreement with experimental results. An orthorhombic-to-tetragonal phase transition was predicted to be around $\ensuremath{-}15{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{\circ}}\mathrm{C}$, near which coexisting orthorhombic phase and tetragonal phase were confirmed by experiments. Based on our calculations, we concluded that the commonly observed monoclinic phase around the orthorhombic-to-tetragonal phase-transition temperature was an adaptive structure due to the coexistence of tetragonal and orthorhombic phases. Additionally, large shear piezoelectric responses exist near room temperature due to the instability caused by the competition between the coexisting tetragonal and orthorhombic phases.