Electrostriction is a second order electromechanical response present in all solid dielectrics. According to the scaling law derived more than two decades ago by Prof. R. Newnham (Penn State), the hydrostatic electrostriction polarization coefficient (Q_h) for a wide range of classical electrostrictors scales with the ratio of the elastic compliance to the dielectric permittivity.

Since 2012, a number of ion 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). These include such well-studied oxygen ion conductors as trivalent rare-earth doped ceria, (Nb,Y)-stabilized cubic Bi₂O₃ and proton conducting, acceptor-doped BaZr_1-xX_xO_3-x/2+δH_2δ ceramics, where X= Ga, Sc, In, Y or Eu, and 0.05 ≤x≤0.2. For these materials, the longitudinal electrostriction strain coefficient |M₃₃| is >10^-17 to 10^-16 m²/V², i.e., 20-1000 times larger than expected and has been shown to originate in elastic dipolar strain induced by point defects. According to EXAFS measurements and DFT modeling, polarizable elastic dipoles originate from local lattice distortion around oxygen vacancies involving both the first and second coordination shells. The resulting strain field has a characteristic interaction length ≤ two - three unit cells (1.4nm).

Under ambient conditions, |M₃₃| for oxygen ion conductors decays by more than two orders of magnitude at frequencies above ~1 Hz, and, as has been found for intermediate temperature ionic conductivity, reaches a maximum for approx. 10 mol% Gd- and Sm- doped ceria. This correlation suggests that ionic conductivity and NCES electrostriction may have similar underlying physical origins, which impart mobility to oxygen vacancies in an electric field while allowing elastic dipoles to reorient. Unexpectedly, oxygen ion conductors contract parallel to the electric field with fully recoverable saturation strain < -15 ppm. However, application of DC bias ~7.5 kV/cm to 5-10 mol% Sm- or Gd- doped ceria pellets for > 14 hours produces positive strain at the ceramic surface layer of ~ 600 ppm; strain falls with higher dopant content, paralleling the decrease in |M₃₃|. Following bias removal, strain persists at room temperature for at least 24 hrs. Upon heating to 140 °C for 5 hours, the unstrained state is recovered. This cycle of field-induced expansion and annealing can be repeated multiple times, providing evidence for some type of order-disorder transition of the vacancy-induced elastic dipoles. According to our current understanding, reorientation of elastic dipoles under an electric field may be related to either dielectric and/or elastic compliance anisotropy, as vacancy-induced elastic dipoles do not have a permanent electric dipole moment.

For anhydrous, acceptor-doped BaZr_1-xX_xO_3-x/2+δH_2δ, |M₃₃|= (1-7) ·10^-16m²/V² below, and ≈10^-18-10^-17m²/V² above, the Debye-type relaxation frequency. Hydration by ~60% does not significantly affect the magnitude of |M₃₃|, but does increase the relaxation frequency by a factor of 10 to 100, suggesting that, in the presence of interstitial protons, NCES can respond more rapidly than those based solely on oxygen vacancies.

Such a combination of large longitudinal electrostriction strain coefficient, low dielectric permittivity and large elastic modulus, as observed in NCES, emerges due to elastic and dielectric properties which are largely defined by the host lattice, while electrostrictive strain is controlled by the strength and polarizability of the elastic dipoles. We suggest that NCES may be a common feature for polycrystalline, solid dielectrics containing mobile point defects. NCES may also emerge in materials with isovalent doping, e.g., Zr-doped ceria, if the difference in ionic radius of the host and dopant cations is sufficiently large that local instability results, leading to dynamic elastic dipole formation.