Applicability of the small anharmonicity approximation to electrostriction in Zr-doped ceria

We have analyzed the compatibility of the Uchino-Cross small anharmonicity model for chemical bonds with recent observations of giant electrostriction in 10 mol% Zr-doped ceria (ZCO10), which exhibits a large negative longitudinal electrostriction strain coefficient M₃₃ ∼ -10^-16 m² V^-2; a negative saturation strain exceeding 250 ppm; and a zero-stress dielectric permittivity . While the small anharmonicity approximation is applicable to strong classical electrostrictors such as PMN-PT15 and to non-classical electrostrictors such as Gd-doped ceria, electrostriction data for ZCO10 cannot be understood within this framework. For ZCO10, the permittivity change (Δε₃) associated with the converse electrostriction effect exceeds the zero-stress value , i.e., . Such behavior is incompatible with weak anharmonicity, suggesting that for ZCO10 the anharmonic contribution to the bond-deformation energy is not negligible relative to the harmonic term. This finding agrees with the previously suggested microscopic model based on EXAFS measurements and density functional theory (DFT)-based simulation, which posits that the Zr ion has freedom to move within a certain "free volume". We have also observed that, despite the very large and negative longitudinal response, M₃₃, the transverse coefficient, M₃₁, is found by both direct and converse measurement techniques to be approximately one to two orders of magnitude smaller. Indeed, small M₃₁ is necessary in order to avoid driving the transverse dielectric permittivity negative. These results identify Zr-doped ceria as a material whose electromechanical response requires extending the existing theoretical framework and which opens a pathway for designing electrostrictors that operate beyond the small anharmonicity limit.