Large Electromechanical Coupling in Zr-Doped Ceria

We have investigated the electrostriction (ES) effect in Zr-doped ceria (Zr_xCe_1-xO_2-δ) ceramics. ES is a second order electromechanical response, <i>i.e.,</i> strain, <b><i>u</i></b>, is proportional to <b>M*</b><b>E</b>², where <b>E</b> is the applied electric field and <b>M</b> is the longitudinal electrostriction strain coefficient. Large ES in ceria has generally been associated with oxygen vacancies (V_o) which provide charge compensation for aliovalent dopants or for cerium reduction (Ce³⁺). The ES induced by V_o is restricted to frequency &lt;1 Hz and low saturation strain (|u_sat| &lt;15 ppm).<br/>Doping CeO₂ with Zr results in a large ES strain coefficient, reaching |M|=10^-16 m²/V² for x=0.1. This effect persists to frequency ≥3 kHz with |u| ≥220 ppm, making Zr_0.1Ce_0.9O₂ competitive with the best commercial electrostrictor (PMN-PT15), but with ~100 times lower dielectric permittivity and three-fold higher elastic modulus. XAS data, DFT modelling and <i>ab initio </i>molecular dynamics (AIMD) calculations demonstrate that elastic dipoles formed by Zr-doping are dynamic. In the absence of an E-field, [ZrO₈]-local bonding units remain, on average, centered with respect to the second (cation) coordination shell. Due to bond anharmonicity displacement of Zr by an E-field requires less energy than displacement of the host cations, resulting in a large dynamic elastic dipole. This polarizable elastic dipole gives rise to large electrostrictive strain and constitutes the first example of non-classical electrostrictors (NCES) relying solely on substitutional point defects.<br/>|<b>M</b>| of Zr-doped ceria increases exponentially with Zr content for x=0-0.1, suggesting that the contribution of Zr-ions to electrostrictive strain may not be simply additive. Zr-doping also increases the relative dielectric permittivity, from ~26 (x=0), to ~220 (x=0.1) and lowers the elastic modulus from 227GPa (x=0) to 214GPa (x=0.1), even though the number of chemical bonds remains unchanged. AIMD calculations report that stiffness for moving [CeO₈]-local bonding units is essentially isotropic and is 2-2.4 times higher than for [ZrO₈]. Stiffness for moving [CeO₈] first nearest neighbor to Zr, is only slightly decreased from that in the bulk. These results can provide the theoretical basis for the reduction of the Young’s modulus and increase in the dielectric permittivity with Zr doping.<br/>When the concentration of Ce³⁺ is ≥ 100 ppm in Zr_xCe_1-xO_2-δ, accompanied by the formation of oxygen vacancies (V_O) for charge compensation, ES is suppressed. In addition, by co-doping Zr_0.1Ce_0.9O₂ with 0.5mol% of aliovalent cations - Ca, Sc, Yb or La - we observed that the aliovalent dopant reduces the electrostriction strain coefficient by more than an order of magnitude and restores the values of Young’s modulus and dielectric permittivity to values close to those of undoped ceria. Since all these co-dopants, irrespective of valence and ionic radius, lead to a similar result, we concluded that the species responsible for the suppression of electrostriction in Zr doped ceria must be the oxygen vacancies. This finding is supported by XAS measurements and AIMD calculations. Fourier transform of Zr K-edge EXAFS spectra reveal that, even though the molar ratio Zr_Ce:V_Ois 40:1 in the co-doped compounds, oxygen vacancies nevertheless succeed in introducing enhanced disorder into the second coordination shell (cation) of Zr. DFT modelling predicts that a [ZrO₇-V_O] local bonding unit is stiff and asymmetrically distorts adjacent unit cells, leading to an elastic interaction length in the lattice between Zr-ions ≥ two-and-a-half-unit cells, which, in the absence of oxygen vacancies, can allow limited collective motion. However, such collective motion does not lead to a phase transition even at 123 K, implying that interaction between Zr-ions is neither sufficiently strong nor sufficiently long-range to produce freezing of the displacement, an effect that has been observed for perovskite relaxors.