Effect of Ba2+ substitution on the stability of the antiferroelectric and ferroelectric phases in (Pb1−xBax)ZrO3: Phenomenological theory considerations

The relative stability of the ferroelectric rhombohedral ${(F}_{R})$ and antiferroelectric orthorhombic ${(A}_{O})$ phases of $({\mathrm{Pb}}_{1\ensuremath{-}x}{\mathrm{Ba}}_{x}){\mathrm{ZrO}}_{3}$ has been investigated as a function of ${\mathrm{Ba}}^{2+}$ concentration (x) using phenomenological theory considerations. It is shown that all the unknown parameters in the free-energy expressions for the ${F}_{R}$ and ${A}_{O}$ phases can be evaluated using the dielectric and x-ray-diffraction data as a function of temperature. We show that the differences in the energies of antiferroelectric and ferroelectric phases decrease with increasing ${\mathrm{Ba}}^{2+}$ concentration, indicating the gradual destabilization of the antiferroelectric phase. The theoretically predicted critical composition $x=0.17\ifmmode\pm\else\textpm\fi{}0.0025,$ above which no antiferroelectric phase can exist, is found to be in excellent agreement with the experimental observations.