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Atomically engineered interfaces yield extraordinary electrostriction


Electrostriction is a property of dielectric materials whereby an applied electric field induces a mechanical deformation proportional to the square of that field. The magnitude of the effect is usually minuscule (<10–19 m2 V–2 for simple oxides). However, symmetry-breaking phenomena at the interfaces can offer an efficient strategy for the design of new properties1,2. Here we report an engineered electrostrictive effect via the epitaxial deposition of alternating layers of Gd2O3-doped CeO2 and Er2O3-stabilized δ-Bi2O3 with atomically controlled interfaces on NdGaO3 substrates. The value of the electrostriction coefficient achieved is 2.38 × 10–14 m2 V–2, exceeding the best known relaxor ferroelectrics by three orders of magnitude. Our theoretical calculations indicate that this greatly enhanced electrostriction arises from coherent strain imparted by interfacial lattice discontinuity. These artificial heterostructures open a new avenue for the design and manipulation of electrostrictive materials and devices for nano/micro actuation and cutting-edge sensors.

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Fig. 1: Multilayer structure and electrostrictive property of NGO/CGO/[ESB/CGO]n.
Fig. 2: Structural analysis of NGO/CGO/[ESB/CGO]n.
Fig. 3: Mechanism of interlayer interaction.
Fig. 4: Mechanism of enhanced electrostriction.

Data availability

The data supporting this study’s findings are available from the corresponding authors on reasonable request.

Code availability

The code used for the creation of the physical and atomic-scale models is available from the corresponding authors on reasonable request.


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This research was supported by the BioWings project, funded by the European Union’s Horizon 2020, Future and Emerging Technologies programme (grant no. 801267), and by the Danish Council for Independent Research Technology and Production Sciences for the DFF—Research Project 2 (grant no. 48293). N.P. and D.V.C. acknowledge funding from Villum Fonden for the NEED project (no. 00027993) and from the Danish Council for Independent Research Technology and Production Sciences for the DFF—Research Project 3 (grant no. 00069 B). V.E. acknowledges funding from Villum Fonden for the IRIDE project (no. 00022862). N.G. and J.V. acknowledge funding from the GOA project ('Solarpaint') of the University of Antwerp. The microscope used in this work was partly funded by the Hercules Fund from the Flemish Government. D.J. acknowledges funding from the FWO Project (no. G093417N) from the Flemish Fund for Scientific Research. D.C. acknowledges TOP/BOF funding from the University of Antwerp. This project has received funding from the European Union’s Horizon 2020 Research Infrastructure—Integrating Activities for Advanced Communities—under grant agreement no. 823717-ESTEEM3. We thank T. D. Pomar and A. J. Bergne for English proofreading.

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Authors and Affiliations



H.Z., N.P. and V.E. conceived the idea and designed the project. H.Z. and S.S. prepared samples and characterized their electromechanical properties. N.G. performed STEM measurements and analysed STEM–EELS results. D.J. assisted with processing of HAADF–STEM data analysis. D.C. performed statistical analysis of the EDX results under the supervision of N.G. and J.V. D.-S.P., P.M., D.D. and D.A.R. performed XRD and RSM characterization. H.Z., I.L. and I.E.C. performed atomic-scale simulations and analysis. D.V.C. performed finite-element simulations. A.R.I., I.L. and P.M. developed the analytical model. H.Z., V.E. and N.P. wrote the manuscript with input from all authors. All authors have read and agreed to the published version of the manuscript.

Corresponding authors

Correspondence to Haiwu Zhang, Nini Pryds or Vincenzo Esposito.

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The authors declare no competing interests.

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Extended data figures and tables

Extended Data Fig. 1 STEM analysis of the heterostructures.

a. HAADF-STEM images for NGO/CGO[ESB/CGO]10 viewed along the [110] and [001] directions of the substrate from left to right, respectively. b. STEM-EELS compositional maps. For each sample, the leftmost image is the HAADF signal acquired simultaneously with the EELS measurement, followed by cerium M4,5 in red, erbium M4,5 in yellow, and neodymium M4,5 in green (colour code: Ce: red; Er: yellow, Nd: green). c. STEM-EDX compositional maps.

Extended Data Fig. 2 Electrostriction Measurements.

a. Electrostrictive response of NGO/CGO/[ESB/CGO]7 under an alternating electric field. The strain developed at the second harmonic of the applied electric field. b. Field-induced stress as a function of the electrical field for NGO/CGO/[ESB/CGO]N measured at 1 Hz. The field-induced stress increases linearly with an increase in the squared electric field. No saturation was observed within the measured electric field range, regardless of the modulation length. The dash-dotted lines represent linear fittings of the measured results.

Extended Data Fig. 3 Electrostriction measurements for heterostructures with different stacking sequences.

Comparison of electrostriction coefficients for thick CGO films and bulk materials Multilayer* denotes NGO(100)/ESB/CGO/…/CGO, where ESB was deposited as the first layer.

Extended Data Fig. 4 Fatigue measurements.

Electromechanical response of NGO/CGO/[ESB/CGO]7 as a function of time. a. Electric field. b. Electromechanical stress in response to an electric field at 1 Hz c. Electromechanical stress as a function of the measured cycles at 1, 50, and 200 Hz. All measurements were performed by applying a sinusoidal electric field with a constant amplitude of 17.4 kV/cm.

Extended Data Fig. 5 Calculated field-induced strains in different directions.

a. CGO20; b. ESB20; c. heterostructure (Λ = 2.33 nm). An electrical field was applied along the (100)-crystallographic direction. All lattice parameters were allowed to relax during the application of the electrical field. εxx, εxy, and εxz denote the strain developed along the X-, Y-, and Z-axis, respectively when the electric field is applied along with the X-axis. The Cartesian axes X, Y, and Z correspond to the (100), (01-1) and (011) crystallographic directions, respectively. Note that the lattices of CGO20, ESB20, and the heterostructure exhibit similar deformation in response to an electric field, that is, contract along the (100)-crystallographic direction and expand along with the (011) and (01-1)-crystallographic directions.

Extended Data Fig 6 Electrostriction as a function modulation length for heterostructures with different crystal structures.

a. fluorite: CGO20/YSZ8; b. perovskite: SFTO10/BYZO10; c. garnet: GGMO10/LSFO10; d. spinel: MGMO10/ZAZO10. The chemical formula for YSZ8, SFTO10, BYZO10, GGMO10, LSFO10, MGMO10 and ZAZO10 are \(({{\rm{Zr}}}_{0.92}^{4+}{{\rm{Y}}}_{0.08}^{3+}{){\rm{O}}}_{1.96}^{2-}\), \({{\rm{Sr}}}_{1.0}^{2+}{({\rm{Fe}}}_{0.1}^{3+}{{{\rm{Ti}}}_{0.9}^{4+}){\rm{O}}}_{2.95}^{2-}\), \({{\rm{Ba}}}_{1.0}^{2+}{({\rm{Y}}}_{0.1}^{3+}{{{\rm{Zr}}}_{0.9}^{4+}){\rm{O}}}_{2.95}^{2-}\), \({{\rm{Gd}}}_{3.0}^{3+}({{\rm{Ga}}}_{4.5}^{3+}{{{\rm{Mg}}}_{0.5}^{2+}){\rm{O}}}_{11.75}^{2-}\), \({({\rm{La}}}_{2.5}^{3+}{{\rm{Sr}}}_{0.5}^{2+}){{{\rm{Fe}}}_{5.0}^{3+}{\rm{O}}}_{11.75}^{2-}\), \({{\rm{Mg}}}_{1.0}^{2+}({{\rm{Ga}}}_{1.8}^{3+}{{{\rm{Mg}}}_{0.2}^{2+}){\rm{O}}}_{3.90}^{2-}\), \({{\rm{Zn}}}_{1.0}^{2+}({{\rm{Al}}}_{1.8}^{3+}{{{\rm{Zn}}}_{0.2}^{2+}){\rm{O}}}_{3.90}^{2-}\), respectively. The defects are generated at random within the heterostructures. The insets schematically show the unit cell of the ideal structure. All the lattice parameters are allowed to relax during the application of the electrical field. Note that the optimal modulation length yielding maximized electrostriction coefficient (Mxx) is material dependent.

Extended Data Fig. 7 Ion distribution within the heterostructures.

Radial distribution function of heterostructures as a function of modulation length (Λ). The first, second, and third peaks correspond to the cation–anion, anion–anion, and cation–cation distances, respectively. No electric field was applied.

Extended Data Fig. 8 Mechanism of elastic dipole and electric dipole formation.

a. An ideal tetrahedron with cations having equivalent distances and three C2 symmetry axes present. Schematic illustration of the elastic dipole formation resulting from tetrahedral deformation along the b. (100), c. (010), and d. (001) directions. The off-site displacements of the cations result in local-symmetry breaking. Note that replacing one of the ions with Gd will result in a structure with three variants that are equivalent to the distortion of Ceria without Gd.

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Zhang, H., Pryds, N., Park, DS. et al. Atomically engineered interfaces yield extraordinary electrostriction. Nature 609, 695–700 (2022).

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