Thermodynamic theory of PbZrO₃

A thermodynamic theory is presented to model the phase transitions and properties of lead zirconate. The free energy ΔG is expressed as a power series in terms of the ferroelectric polarization (P_i=P _ai+P_bi) and antiferroelectric polarization (p _i=P_ai-P_bi) including all possible terms up to the sixth power, but only first-order cross coupling terms and couplings to elastic stress. Under the assumption that only the lowest-order coefficients of P_i and p_i are linearly temperature dependent (Curie-Weiss behavior) and all other constants are temperature independent, experimental data are used to define the constants and permit calculation of ferroelectric and antiferroelectric free energies as a function of temperature. Use of the function to define the averaged dielectric permittivity at room temperature in the antiferroelectric phase gives a value of ε_R=120 in good agreement with recent microwave measurements. A simplified technique for modifying the function to explore solid solution with lead titanate is examined, and shown to lead to excellent agreement with the known phase diagram.