Thermodynamic theory of the lead zirconate-titanate solid solution system, part IV: Tilting of the oxygen octahedra

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Abstract
Values of coefficients related to the tilting of the oxygen octahedra in the low-temperature rhombohedral phase of the lead zirconate-titanate (PZT) solid solution system are needed in the development of a thermodynamic theory of the PZT system. In this paper these coefficients will be determined from experimental spontaneous strain and oxygen octahedral tilt angle data. Values of the tilt angle related coefficients β1,β11, and φ are assumed to be independent of temperature, and are then related to P L, θL, and T R, where P L and θL are the spontaneous polarization and tilt angle of the low-temperature rhombohedral phase at the transition temperature T R between tilted and untilted structures. P L and θL are derived from experimental data for the PZT 90/10 composition, and used together with spontaneous strain values at this composition to determine electrostrictive (Q 44) and rotostrictive (R 44) constants. These constants are then in turn used to derive P L and θL values for other PZT compositions from spontaneous strain vs temperature at each composition, and in the final paper in this sequence to derive the β1, β11, and φ values for these compositions

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