Defect Complexion Induced Electrostriction in Doped Ceria—Origin and Implications

Electrostriction is a second-order electromechanical response present in all solid dielectrics. With a simple ion-pair potential, Uchino related the electrostriction polarization coefficient (Q) with the ratio of the anharmonic and harmonic factors in the atomistic interactions. A macroscopic scaling law for a wide range of classical electrostrictors was derived by Newnham to correlate the hydrostatic Q scales linearly with the ratio of the elastic compliance to the dielectric permittivity. Thus, both the atomistic and macroscopic origins for classical electrostriction have been discussed as a bulk effect considering all the ions in the lattice.

Since 2012, a number of ionic conducting ceramics and thin films have been reported to exhibit longitudinal electrostriction strain coefficients (M₃₃) much larger than that predicted by the classical scaling law, i.e., non-classical electrostriction (NCES). A representative example is ceria, including trivalent and isovalent doped ceria, calling for new theories for the origin of non-classical electrostriction.

The introduction of defects into a material, such as ceria, affects the local bonding environments thus producing short-range bond distortions and long-range elastic fields. Consequently, the interaction between the defect and the applied macroscopic stress can be analogous to the interaction of an electric dipole with an applied electric field. Such defect property is called elastic dipole and is characterized by a second-rank tensor. The elastic dipole tensor can be calculated directly from defect-containing structures via density functional theory (DFT) calculations, bridging both the local environment around point defects and the macroscopic strain. Further combining DFT with molecular dynamics (MD) simulations can illustrate how the elastic dipoles re-orientate under applied electric or stress fields, leading to the quantification of the electrostrictive coefficient.

Using the newly developed computational approach, electrostriction originated from various defects was illustrated:
In reduced CeO₂, the elastic dipole in the vicinity of an oxygen vacancy (Vo) is anisotropic, as the Vo is surrounded by two Ce³⁺ and two Ce⁴⁺. The elastic dipoles can be reorientated quickly by electron rearrangement under an electric field. However, due to the low concentration of intrinsic Vo in CeO₂, the electrostriction (proportional to the defect concentration) is not significant.
In Gd-doped CeO₂, Gd and Vo form extended defects and cause anisotropic elastic dipole. The elastic dipole is sensitive to the distance between Gd and Vo. Under an electric field or strain field, local Vo hopping leads to elastic dipole reorientation, giving rise to a net strain change (giant electrostriction) that only exists under low frequency.
A more promising case is Zr-doped CeO₂. Zr-doped CeO₂, Zr_xCe_1-xO₂ (x<0.2), displays electromechanical properties rivaling those of the best-performing electrostrictors, in addition to its low relative permittivity, high modulus, non-toxic, and fully compatibility with Si-based microfabrication processes. In Zr-doped CeO₂, the smaller Zr ions vibrate anharmonic inside the oxygen cage. Although there is no permanent elastic dipole on average, the [ZrO₈] can be easily deformed by an electric field, giving rise to “dynamic” elastic dipoles, i.e., elastic dipoles that are formed only under an external field due to anharmonicity. Moreover, with increasing Zr dopant concentration, Zr and Zr pairs display enhanced anharmonicity, which can be pinned by oxygen vacancies.
These modeling results collectively agreed well with the local bonding probed by X-ray absorption spectroscopy (XAS) and the measured macroscopic electrostriction in a variety of doped ceria, providing guidance to explore other defects containing non-classical electrostrictors.