Gradient stress induced coexistence of tetragonal and rhombohedral phases in Pb(Zr,Ti)O3 films

Thermodynamic theory has been used to explain quantitatively the coexistence of tetragonal and rhombohedral phases in Zr-rich Pb(Zr, Ti)O3 (PZT) films grown on a compressive substrate. The key is to consider a set of gradient thermal stresses imposed on the films. The 'stress-temperature' phase diagrams were developed for PZT films of several different compositions (Ti/Zr=20/80, 30/70, 40/60, 50/50). The characteristic feature of the phase diagrams for Zr-rich PZT films is the coexistence of tetragonal and rhombohedral phases in the compressive stress region. The volume fractions of the rhombohedral phase were calculated for the Zr-rich PZT films grown on MgO substrate. The result agrees with the experiment.