Phase diagrams and physical properties of single-domain epitaxialPb(Zr1−xTix)O3thin films

The equilibrium polarization states and physical properties of single-domain $\mathrm{Pb}({\mathrm{Zr}}_{1\ensuremath{-}x}{\mathrm{Ti}}_{x}){\mathrm{O}}_{3}$ (PZT) thin films epitaxially grown on dissimilar cubic substrates have been examined by a nonlinear thermodynamic theory. In contrast to the former theoretical studies of PZT films, the two-dimensional straining and clamping of a film by a thick substrate is correctly taken into account in the reported calculations. The ``misfit strain-temperature'' phase diagrams are developed for PZT films of several different compositions $(x=0.9,$ 0.8, 0.7, 0.6, 0.5, and 0.4). The characteristic feature of these diagrams is the presence of a ``monoclinic gap'' separating the stability ranges of the tetragonal out-of-plane and the orthorhombic in-plane polarization states. It is found that this gap widens with the increase of Zr content, and its center shifts from positive values of the misfit strain towards zero. The dependences of the polarization components on the misfit strain and composition at the room temperature are calculated and compared with the available experimental data. The small-signal dielectric and piezoelectric responses of single-domain PZT films are also determined, and their misfit-strain dependence is discussed.