(Invited) Large Electromechanical Coupling in Zr-Doped Ceria
Authors: Varenik Maxim , Xu Boyuan , Pechersky-Savich Tali , Li Junying , Wachtel Ellen , Ehre David , Routh Prahlad Kumar , Khodorov Sergey , Lubomirsky Igor , Frenkel Anatoly I. , Qi Yue 
Published: August 2024

The catalytic, ion-transport and chemo-mechanical properties of Zr-doped ceria have been the subjects of broad ranging investigation by the materials research community. Yet, until recently, electromechanical coupling in ZrxCe1-xO2-δ has not been studied: ZrxCe1-xO2-δ ceramics were not expected to be electromechanically active. We have investigated the electrostriction (ES) effect, a second order electromechanical response, i.e., strain,
u
, is proportional to M·E
2, where E is the applied electric field and M is the longitudinal electrostriction strain coefficient. Large electrostriction in ceria has generally been associated with oxygen vacancies (Vo) which provide charge compensation for aliovalent dopants or for cerium reduction (Ce3+). The electrostriction effect induced by oxygen vacancies is restricted to frequency <1 Hz and is characterized by low saturation strain (|usat| <15 ppm).
By contrast, isovalent doping with Zr (unexpectedly) results in a large electrostriction strain coefficient, reaching |M|=10-16 m2/V2 for x=0.1. This effect persists to frequency ≥3 kHz with |u| ≥220 ppm, making Zr0.1Ce0.9O2 competitive with the best commercial electrostrictor (PMN-PT15), but with ~100 times lower dielectric constant and three-fold higher elastic modulus. XAS data, DFT modelling and ab initio molecular dynamics (AIMD) calculations demonstrate that, unlike the permanent, but orientationally labile, elastic dipoles (i.e. local distortions with symmetry lower than that of the host lattice) formed by oxygen vacancies, 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, however, displacement of Zr by an anisotropic 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. In fact, a relatively small, isovalent dopant cation, such as Zr, along with nearest neighbor anions, vibrating anharmonically in a relatively large cage (compared to that of the host cation) may in fact facilitate electromechanical coupling.
|M| 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 at 100Hz, 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.
When the concentration of Ce3+ is ≥ 100 ppm in ZrxCe1-xO2-δ, ( i.e., the material has not been completely re-oxidized), accompanied by the formation of oxygen vacancies (VO) for charge compensation, electrical conductivity is increased and electrostriction is suppressed. In addition, by co-doping Zr0.1Ce0.9O2 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 ZrCe:VO is 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-VO] 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.